Chemo- And Stereospecific Solid-State Thermal Dimerization of Sodium trans-2-Butenoate and γ-Ray-Induced Single-Crystal-to-Single-Crystal Dimerization of Hexaaquamagnesium trans-2-Butenoate Dihydrate: Both Give rel-(3 S,4 R)-1-Hexene-3,4-dicarboxylate but by Different Mechanisms. Stereospecific γ-Ray-Induced Trimerization of Sodium trans-2-Butenoate

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Chemo- and Stereospeciﬁc Solid-State Thermal Dimerization of

Sodium trans-2-Butenoate and γ‑Ray-Induced Single-Crystal-to-

Single-Crystal Dimerization of Hexaaquamagnesium trans-2-

Butenoate Dihydrate: Both Give rel-(3S,4R)‑1-Hexene-3,4-

dicarboxylate but by Diﬀerent Mechanisms. Stereospeciﬁc γ‑Ray-

Induced Trimerization of Sodium trans-2-Butenoate

Wen Shang, Roxana F. Schlam, Magali B. Hickey, Jingye Zhou, Kraig A. Wheeler,

Graciela C. Diaz de Delgado, Chun-Hsing Chen, Barry B. Snider,* and Bruce M. Foxman*

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ABSTRACT: γ-Irradiation of crystalline hexaaquamagnesium trans-

2-butenoate dihydrate aﬀords rel-(3S,4R)-1-hexene-3,4-dicarboxy-

late by a single-crystal-to-single-crystal reaction. The reaction

proceeds by a radical chain mechanism with anti addition to the

butenoate double bond, as established by deuterium labeling. The

product structure is that expected from the orientation of trans-2-

butenoates in the pristine crystal. The same dicarboxylate is formed

by heating crystalline sodium trans-2-butenoate at 300 °C, but the

thermal ene reaction was shown by deuterium labeling to proceed by syn addition to the butenoate double bond as expected for a

concerted ene reaction. γ-Irradiation of sodium trans-2-butenoate forms a single trimer chemo-, regio-, and stereospeciﬁcally. The

structure of sodium trans-2-butenoate was determined, and the crystal packing is consistent with both the observed ene dimerization

and γ-ray-induced trimerization.

polymeric products were mostly amorphous and atactic, with a

unique stereoregular example.²⁴

INTRODUCTION

■

The design and discovery of new classes of materials that

undergo solid-state transformations to give products unavailable

from solution chemistry and the elucidation of the principles

that govern their reactivity remain important challenges in the

ﬁeld.¹⁻⁴The use of ionizing radiation as an excitation source

provides new synthetic opportunities distinct from thermal or

photochemical stimuli. ⁶⁰Co γ-rays can initiate radical chain

reactions in crystals that lead to products from alkenes very

diﬀerent from those obtained photochemically, such as the

cyclobutane derivatives obtained by solid-state [2 + 2]

photocycloadditions of cinnamates and other highly conjugated

alkenes.⁵⁻¹⁴Nonetheless, the distance criterion of the top-

ochemical postulate (C···C contacts ≤4.2 Å), ﬁrst established by

Schmidt and co-workers,^5,6appears to hold well for radical chain

reactions in the solid state.¹⁻⁴⁶⁰Co γ-ray initiated radical chain

solid-state polymerization of solid metal acrylates was ﬁrst

discovered nearly 60 years ago.^15,16Ionizing radiation also

eﬀectively initiates single-crystal-to-single-crystal solid-state

polymerization of a wide range of diacetylenes and muconate

esters.¹⁷⁻²²Although ⁶⁰Co γ-ray irradiation of solid metal

complexes of acrylates, methacrylates, propynoates, and other

unsaturated carboxylates showed widespread reactivity,^15,23the

Naruchi and co-workers found that heating crystalline sodium

trans-2-butenoate (1) at 300−320 °C stereo- and chemo-

selectively provides the dimer disodium rel-(3S,4R)-1-hexene-

3,4-dicarboxylate (2a) in 84% yield, probably by a thermal ene

reaction (see Scheme 1).^25,26This facile process suggests that

crystalline 1 contains short C···C contacts and a favorable

Scheme 1. Thermal Dimerization of 1 to Give 2a and γ-Ray-

Induced Trimerization of 1 to Give 3a

Received: October 26, 2020

Revised: December 1, 2020

Published: December 14, 2020

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orientation of adjacent molecules that lead to the eﬃcient

thermal formation of 2a. We therefore suspected that 1 might

show sensitivity to ionizing radiation and were pleased to ﬁnd

that irradiation of 1 with ⁶⁰Co γ-rays (156 kGy) initiates a radical

chain reaction that aﬀords one of eight possible diastereomers of

trisodium 2,4-dimethyl-6-heptene-1,3,5-tricarboxylate (3a) in

68% yield.¹The eﬃcient conversion of 1 to 3a suggested that

further exploration of the γ-ray-induced radical chain chemistry

of crystalline trans-2-butenoates would be productive.

Scheme 2. Formation of cis,trans-Nepetate 5-d₂and

trans,trans-Nepetate 7-d₂by γ-Irradiation of 4-d and 6-d,

Respectively

Thus, our approach to discovering and elucidating reactive

phases was guided by ﬁve ideas and/or observations. First, the

elegant suggestion by Herbert Morawetz that changing the

metal counterion of a reactive unsaturated carboxylate will

change the crystal structure, and therefore, the reactivity,

provides an eﬃcient way to generate novel crystal structures that

may react diﬀerently.¹⁵Second, metal salts and complexes with

relatively short radii and coordination numbers of six or less have

structural features that might allow short intermolecular

contacts and thus would be reactive in the solid state. Third, a

survey of the Cambridge Structural Database in 2000 showed

that bilayer structures are dominant (92%) for salts and

complexes of ≥4-carbon aliphatic acids.^27,28Such bilayer

structures promote close-packing of the organic side chains,

often leading to solid-state reactivity between adjacent groups.

Depending upon the structure of a given material and the

observed short contacts, reactivity may occur either solely

between molecules within one section (i.e., one-half) of a

bilayer^3,23or between molecules in the two sections of a bilayer.⁴

Fourth, with a view to exploring solid-state reactivity of the trans-

2-butenoate moiety, we found 147 structures of metal salts and

complexes in the current version of the Cambridge Structural

Database containing the trans-2-butenoate anion, including our

own contributions.²⁹We have surveyed many of these, and most

do not contain arrangements suitable for γ-ray-induced

reactivity. The lack of reactivity is obvious for some, e.g., the

high-coordination number complexes of large rare-earth metals

in which bulkiness disfavors close approach of unsaturated

groups,^30,31and complexes containing large ligands that prevent

close approach of the butenoates³²for alignment of the

unsaturated groups. Finally, we note that ammonium trans-2-

butenoate has a bilayer structure and favorable contacts for

reaction but is insensitive to γ-rays, suggesting that the presence

of a metal is important for trans-butenoate reactivity.³³We thus

began our study with trans-2-butenoate salts and complexes of

metals with small radii, possible bilayer structures, and no

additional ligands other than water.

To our delight, irradiation of bis(trans-2-butenoato)calcium

(4) with ⁶⁰Co γ-rays initiates a radical chain reaction that

proceeds stereospeciﬁcally to give calcium cis,trans-nepetate (5)

as only one of four possible stereoisomers in high yield, but at

low conversion (see Scheme 2).^2,3The disordered crystal

structure of 4 indicates that only 4.8% of the trans-2-butenoates

have the appropriate orientation for the production of cis,trans-

nepetate 5. Heating the sample to 60 °C for 24 h between two

irradiations of 7 kGy likely induces a “pedal” rotation^34,35and

increases the yield of 5 to 7.5%. We thought that a group IIA

metal with a shorter radius might also form a trans-2-butenoate

salt with the correct orientation to form a cyclodimer, hopefully

the diastereomeric trans,trans-nepetate 7. The crystal structure

of triaquabis(trans-2-butenoato)magnesium (6) is indeed

correctly oriented with short C···C contact distances, and

⁶⁰Co γ-irradiation of 6 aﬀords trans,trans-nepetate (7) in high

yield at low conversion.³

In attempting to prepare lithium trans-2-butenoate, we

isolated anhydrous lithium trans-2-butenoate (8) and a solvate,

lithium trans-2-butenoate·formamide (10), that both aﬀord the

same dimer, dilithium trans-5-methyl-2-heptenedioate, upon

⁶⁰Co γ-irradiation (see Scheme 3).⁴However, stereochemical

Scheme 3. Formation of Dilithium trans-5-Methyl-2-

heptenedioates 9-d₂and 11-d₂by γ-Irradiation of 8-d and 10-

d, Respectively

analysis of products 9-d₂and 11-d₂from the analogous crystals

of 8-d and 10-d established that both C−C and C−H bond

formation occur stereospeciﬁcally by syn-addition to the double

bond with 8-d leading to 9-d₂and by anti-addition to the double

bond with 10-d leading to 11-d₂.⁴

The formation of 3, 5, 7, 9, and 11 probably proceeds by a

radical chain reaction initiated by a γ-ray-induced abstraction of

a hydrogen atom from the methyl group to give an allylic radical

that then adds to a second molecule of trans-2-butenoate with an

orientation and regiochemistry determined by crystal packing.

The crystal lattice controls the two or three propagation steps

that produce the observed product and regenerate the allylic

radical. Using deuterium-labeled substrates, we established that,

in the ﬁnal propagation step, hydrogen atom transfer is also

stereospeciﬁc. Although all of these steps individually are

precedented in solution, their occurrence to give the observed

products selectively is clearly a result of a favorable orientation of

the trans-2-butenoate species in the crystal. The formation of

both carbon−carbon bonds and hydrogen atom transfer is

unequivocally topochemical, stereospecific, and not the result of a

random process.^3,4As indicated above, γ-ray-initiated solid-state

polymerization reactions have been extensively studied.¹⁵⁻²⁴On

the other hand, there are very few examples of reactions of

radical chain solid-state reactions that lead cleanly to

monomeric, dimeric, or trimeric compounds. In addition to

the formation of 3, 5, 7, 9, and 11, the only examples we are

aware of are the isomerizations of α-lactose monohydrate,^36,37

D-fructose,^36,38−40and 2-deoxy-β-D-erythro-pentoypyra-

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nose^36,41and the dimerization of a bis alkyne.⁴²In all of the

highly stereospeciﬁc reactions we studied, the single crystals

become amorphous as the reaction proceeds. While there are

many examples of single-crystal-to-single-crystal transforma-

tions that arise from thermal and/or photochemical pro-

cesses,^43,44we are unaware of examples of γ-ray-induced

transformations that proceed to monomeric, dimeric, or trimeric

compounds with retention of single-crystal quality.

conversion of 12 to 2b over time: 2 d (0%), 4 d (1.8%), 8 d

(7.4%), 16 d (23.1%), 32 d (45.5%), 64 d (65.6%), and 128 d

(80.3%). The ¹H NMR spectrum of 2b was identical to that of

authentic 2a prepared by heating 1 at 300 °C as reported by

Naruchi.²⁵The NMR spectrum of a mixture of sodium salt 2a

and magnesium salt 2b showed that only a single organic moiety

was present. Thus, the dimerization of 12 to form 2b is a sixth

mode of γ-ray-initiated radical chain chemistry of trans-2-

butenoate that once again occurs under topochemical

control.¹⁻⁴

The formation of 2 by both the pyrolysis of 1 and the γ-ray-

initiated radical chain reaction of 12 was surprising. The

conversion of 1 to 2a most likely occurs by a thermal ene

reaction as shown in Scheme 5. Like the better-known Diels−

The γ-ray-induced radical chain solid-state dimerization

reactions of trans-2-butenoic acid are orthogonal to the better-

known solid-state [2 + 2] photocycloadditions of cinnamates

and other highly conjugated alkenes.⁵⁻¹⁴Cinnamates lack the

allylic hydrogen atom needed for initiation of the radical chain

upon γ-irradiation. Even with the heavy atom, crystalline (E)-4-

bromocinnamic acid aﬀords the cyclobutane dimer β-truxinic

acid in only 24% yield after exposure to a very large 1160 kGy γ-

ray dose.⁴⁵Similarly, γ-irradiation (30−5000 kGy) of crystalline

trans,trans-2,4-hexadiendioic acid, its methyl ester, or trans,-

trans-2,4-hexadienoic acid provides only ∼2% dimer and no

oligomer, whereas ultraviolet irradiation produces the cyclo-

butane dimers in 60% yield.^46,47It was proposed that

photochemical dimerization involves direct reaction between

an excited double bond and an adjacent double bond in the

ground state, while γ-irradiation produces highly excited states

that break down without giving the particular state necessary for

dimerization.⁴⁶Conversely, the allylic hydrogen atoms, which

are needed for γ-ray-induced free-radical chain dimerizations

and trimerizations of trans-2-butenoates, prevent [2 + 2]

photocycloaddition on UV irradiation. trans-2-Butenoic acid

isomerizes to cis-2-butenoic acid, which then undergoes

photoenolization by 1,5-sigmatropic hydrogen shift and

protonation to give 3-butenoic acid.^48,49

Scheme 5. Thermal Concerted Ene Reaction of 1 to Give 2a

Alder reaction, the ene reaction is a concerted reaction

proceeding through transition state 13 that typically occurs on

heating. However, an ene reaction of 12 to give 2b cannot occur

at room temperature by γ-irradiation. Dimer 2b must be formed

by a diﬀerent mechanism.

As we have previously reported,^3,4deuterium labeling

provides important stereochemical information about the

mechanism of formation of 5, 7, 9, and 11, and we thought it

would also be helpful in understanding the mechanism of

formation of 2a and 2b. trans-2-Butenoic-3-d acid was prepared

as we have previously described³and converted to crystalline

sodium trans-2-butenoate-3-d (14) and crystalline hexaaqua-

magnesium trans-2-butenoate-3-d dihydrate (16) analogously

to the preparation of 1 and 12 (see Scheme 6).

RESULTS AND DISCUSSION

■

Solid-State Chemistry of 12. Slow evaporation of aqueous

solutions of magnesium trans-2-butenoate over 1−2 weeks gave

two diﬀerent types of crystals, prismatic hexaaquamagnesium

trans-2-butenoate dihydrate (12) and plate-like triaquabis-

(trans-2-butenoato)magnesium (6), which could be separated

manually (see Scheme 4). Alternatively, a diﬀusion technique

A sample of 14 sealed under vacuum was heated for 4 h at 300

°C to give 55% of disodium rel-(3S,4R,5S)-1-hexene-3,4-

dicarboxylate-2,5-d₂(15) and 45% of unreacted 14. A sample

of 16 sealed under vacuum was γ-irradiated to give a mixture of

unreacted 16 and magnesium rel-(3S,4R,5R)-1-hexene-3,4-

dicarboxylate-2,5-d₂(17). The conversion was about 3% after

12 d, 28% after 30 d, and 53% after 90 d. Most signiﬁcantly, the

geminal coupling constant between H₄and H₅of 15 is 3.6 Hz,

whereas that of 17 is 11 Hz. This unambiguously establishes that

the addition to the double bond is syn for 15 and anti for 17, as

discussed below.

Scheme 4. Conversion of 12 to rel-(3S,4R)-1-Hexene-3,4-

dicarboxylate (2b) by γ-Irradiation

Conformational analysis⁵⁰⁻⁵⁶suggests that the C₄−C₅bond

preferentially adopts the conformation shown with the methyl

group on C₅anti to the large CH₂=CH(CO₂H)CH substituent

on C₄as shown in the top structures in Scheme 6. This allows the

assignment of structure 15 to the product from 14 because the

dihedral angle between H₄and H₅is 60°, resulting in a small 3.6

Hz coupling constant and assignment of structure 17 to the

product from 16 because the dihedral angle between H₄and H₅

is 180°, resulting in a large 11.0 Hz coupling constant.

Examination of the red bonds in the lower structures of Scheme

6 indicates that the addition to the double bond of 14 is syn as

expected for the thermal ene reaction shown in Scheme 5,

whereas the addition to the double bond of 16 is anti, as

could be used by layering 5−10 volumes of an organic solvent on

top of the aqueous solution. This was selective for the

crystallization of 12 with several organic solvents and for the

crystallization of 6 with DMF.³We have previously reported the

γ-ray-initiated reactions and structural chemistry of 6 to give 7.³

The γ-ray-initiated reactions and the results of an extensive study

of the structural chemistry of single crystals of 12 are described

below.

Samples of 12 were irradiated in capped vials under air for 2−

128 d at 5 kGy/day. The samples were dissolved in D₂O and

1

analyzed by H NMR spectroscopy, which showed increased

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diﬀusion of a layered acetone−magnesium trans-2-butenoate

aqueous solution; details may be found in the Experimental

Section. An X-ray structure determination of 12 prior to

exposure to ⁶⁰Co γ-rays showed it to crystallize in the triclinic

Scheme 6. Thermal Dimerization of 14 to Give rel-

(3S,4R,5S)-1-Hexene-3,4-dicarboxylate-2,5-d₂(15) and γ-

Ray-Initiated Dimerization of 16 to Give rel-(3S,4R,5R)-1-

Hexene-3,4-dicarboxylate-2,5-d₂(17)

̅

system, space group P1, with Z = 1. The asymmetric unit, which

consists of one-half of a hexaaquamagnesium dication, one

molecule of water of hydration, and a disordered trans-2-

butenoate anion, is shown in Figure 1. The magnesium ion

Figure 1. View of the asymmetric unit in 12. The water molecules in the

asymmetric unit are labeled; three additional symmetry-related water

molecules complete the coordination sphere about Mg. The major

component of the trans-2-butenoate moiety is shown with green C

atoms, while the minor component is shown with blue C atoms.

Disorder of atoms C101, O1, and O2 could not be resolved. Atoms

reﬁned using anisotropic displacement parameters are represented

using 50% probability ellipsoids (minor component atoms were reﬁned

using isotropic displacement parameters).

expected for an intermolecular hydrogen atom transfer in a

radical chain reaction.

A plausible mechanism for the formation of 17 (bisdeuterated

2b) is shown in Scheme 7. γ-Ray initiation by abstraction of a

Scheme 7. Radical Chain Mechanism for the Conversion of

16 to 17

occupies a center of symmetry; Figure 1 shows the full six-

coordinate cation for completeness. The anion disorder was

reﬁned with the constraint that the two fractional occupancies of

the anion (0.684(4)/0.316(4)) sum to 1.0. Only the disordered

CH₃CH=CH− portions of the anion could be resolved. Figure 1

shows the numbering scheme for the major component atoms

(C201, C301, and C401 in green) and minor component atoms

(C202, C302, and C402 in blue) that could be resolved.

Summary experimental details of the structure determination

appear in Table 1A; full details are available in the Supporting

Information. Unlike many salts and complexes of metals with

trans-2-butenoate, the metal in compound 12 is not bonded to

the oxygen atoms of the trans-2-butenoate anion. As shown in

the packing diagram (Figure 2), the trans-2-butenoate anions

reside in a cavity in the center of the unit cell along with two

water molecules of hydration and hexaaquamagnesium cations

at the eight unit cell corners. In discussion of the important

contacts for all of the structural chemistry in this paper, we will

use the atomic numbering system in the ﬁgures, deﬁning the

contact’s symmetry-related position once, and always designat-

ing the symmetry-related atom by a prime-symbol. Thus, here

the dashed line shows a contact distance of 3.792(3) Å between

atom C201 and symmetry-related atom C201′ (−x, −1−y, −1−

z). The facile γ-ray-induced dimerization process, by which 12 is

converted to 2b in the solid state, is consistent with the

hypothesis that crystalline 12 contains short C···C contacts and

that topochemical eﬀects, viz., C···C contacts less than 4.2 Å

(3.792(3) Å in the major component and 3.451(6) Å in the

minor component) and a favorable orientation of adjacent

molecules for reaction, are responsible for both the eﬃciency of

hydrogen atom of 16 gives allylic radical 18-d, which adds to a

second molecule of 16 in the ﬁrst propagation step to give

dimeric radical 19-d₂. The regio- and stereochemistry of the

addition are controlled topochemically. In the second

propagation step, a third molecule of 16 transfers a hydrogen

atom to the radical 19-d₂to generate the product 17, and a

second molecule of allylic radical 18-d that continues the chain.

Because this hydrogen atom transfer is intermolecular and the

molecular motion of 19-d₂is restricted by the crystal lattice, the

addition to the double bond should be stereospeciﬁcally anti as

is observed.

Structural Chemistry of Hexaaquamagnesium trans-

2-Butenoate Dihydrate. Single crystals of 12 were grown by

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a

Table 1A. Crystallographic Data for Crystal 1

crystal codes

0_1

8_1

16_1

7.5729(4)

7.8451(5)

7.8437(3)

104.505(4)

100.024(4)

105.945(5)

418.76(4)

1, 0.5

32_1

a (Å)

b (Å)

c (Å)

α (deg)

β (deg)

γ (deg)

V (Å³)

Z, Z′

7.6047(3)

7.8363(3)

7.8674(4)

7.5950(2)

7.8383(2)

7.8615(3)

105.902(2)

99.993(2)

105.158(2)

419.01(2)

1, 0.5

7.5673(3)

7.8510(3)

7.8306(3)

103.826(3)

100.118(3)

106.216(3)

418.85(3)

1, 0.5

106.515(4)

100.002(4)

104.777(3)

419.02(4)

1, 0.5

F.W., g mol⁻¹

space group

T (K)

169.3

P1

̅

294

P1

̅

P1

̅

P1

̅

294

λ (Å)

0.71073

1.342

0.158

0.71073

1.342

0.158

0.71073

1.342

0.158

0.71073

1.342

0.158

ρ_calc(g cm⁻³

)

μ (mm⁻¹

)

θ_max; trans. factors

R, R_w(I > 2σ(I))

R, R_w(all data)

30.4°; 0.87−0.91

0.0368, 0.0445

0.0465, 0.0593

1.042

30.4°; 0.88−0.91

0.0475, 0.0599

0.0593, 0.0784

1.046

30.4°; 0.88−0.91

0.0472, 0.0575

0.0603, 0.0780

1.020

30.4°; 0.88−0.91

0.0481, 0.0606

0.0607, 0.0800

1.035

S

no. reﬂ. (I > 2σ(I); all)

no. param.

2112; 2530

143

2047, 2529

153

2018, 2527

152

2037, 2526

152

major/minor reactant; ratio

major/minor product; ratio

extent of reaction

0.684(4)/0.316(4) 2.165

0.592(4)/0.273(2) 2.165

0.092(4)/0.043(2) 2.160

0.135(6)

0.387(4)/0.179(2) 2.162

0.297(4)/0.137(2) 2.168

0.434(6)

0.266(4)/0.123(2) 2.162

0.418(4)/0.193(2) 2.165

0.611(6)

0

a

R = ∑||F_o| − |F_c||/∑|F_o|; R_w= [∑w(|F_o| − |F_c|)²/∑w|(F_o)²]^1/2; S = [∑w(|F_o| − |F_c|)²/(n − m)]^1/2

molecular motion that must occur during the solid-state

dimerization process. There are eight strong hydrogen bonds

in the structure, involving all six coordinated water molecules as

well as the two molecules of hydrated water, with O···O contact

distances ranging from 2.74 to 2.85 Å and O−H···O angles

ranging from 160° to 174°; the full listing appears in Table S1.

Most of the hydrogen bonds are shown in Figure 3.

Figure 2. View of the crystal structure of 12 viewed down the

crystallographic a axis. Only the major components of the disordered

trans-2-butenoate are shown, with a contact distance of 3.792(3) Å

between α-carbon atoms C201 and C201′ (see text). The minor

component of the disorder (see Figure S1) has an α-carbon contact

distance of 3.451(6) Å between atom C202 and symmetry-related atom

C202′ (−x, −1−y, −1−z).

the process as well as the stereochemistry of the product as

discussed in detail below.

The disorder of the trans-2-butenoate groups is a consequence

of a “relatively spacious” cavity, with only the oxygen atom end

of the trans-2-butenoates held securely by strong hydrogen

bonds. The lack of restrictive contacts is expected to facilitate the

Figure 3. View of the hydrogen bonds in the crystal structure of 12,

viewed down the crystallographic a axis. Only the major components of

the disordered trans-2-butenoate are shown. All hydrogen bonds are

shown at least once except for the coordinated water-to-solvate water

hydrogen bond, O5−H81···O6.

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a

Single-Crystal-to-Single-Crystal Solid-State Reaction

of 12 to Give 2b. Past experience suggested that the crystals

would likely become amorphous as the reaction proceeded to

convert 12 to 2b in the solid state.^{1−4,15,16,23,24}After ⁶⁰Co γ-

irradiation of X-ray quality crystals, an exploratory X-ray

structure determination of a partially reacted crystal revealed

the presence of product in the area of the trans-2-butenoate

anions. Thus, we concluded that the cavity created by the eight

hexaaquamagnesium cations had suﬃcient free space to allow

reaction to occur without signiﬁcant disruption of the crystal.

Crystals of 12 were beautifully faceted and clear at the outset and

did not degrade optically upon irradiation. Therefore, we

decided to study the extent of the solid-state reaction versus

irradiation dose, hopefully in a set of three or four single crystals

that would survive the required months of γ-irradiation. The

composition of the material, with eight water molecules per unit

cell, was a concern over an extended period of irradiation, with

previously observed dehydration-cum-loss of crystal quality.

The six crystals were coated with perﬂuoropolyether, placed into

glass capillaries, and aﬃxed to the capillary walls with epoxy; the

capillaries were sealed using a hot wire. At the time of this

experimental work, a CCD machine was not available in our

laboratory, nor was a low-temperature device. (The latter

restriction was good fortune, as we later discovered that

compound 12 undergoes an enantiotropic, polymorphic phase

transition to a diﬀerent cell at ca. 274 K.⁵⁷) High-quality, high-

resolution data were collected at RT on an Enraf-Nonius CAD-4

Turbo diﬀractometer equipped with Mo Kα radiation. After data

collection, crystals were irradiated for various times with ⁶⁰Co γ-

rays at Brandeis University (Gammacell 220 Irradiator, Atomic

Energy of Canada, Ltd., dose rate 2.6 kGy/day). The crystals

were periodically removed from the γ-ray irradiator, and their

structures were redetermined. The process was repeated until

the crystals reached maximum conversion (ca. 5 cycles). Two

crystals degraded to an unidentiﬁed polycrystalline material,

owing to water loss after one or two cycles, and further studies of

those two samples were abandoned. For the four crystals

studied, irradiation was carried out for 8, 16, 32, 56, and 110 days

(20.8, 41.6, 83.2, 145.6, and 286 kGy, respectively). In order to

establish either completeness or plateauing of conversion after

the initial 286 kGy at Brandeis University, crystals 1 and 2 were

irradiated with an additional 650 kGy γ-ray dose at the Radiation

Laboratory, University of Massachusetts, Lowell (dose rate of 20

kGy/h).

The summary of experimental details appears in Tables 1A

and 1B for crystal 1. The reaction takes place in a single crystal,

with no change in space group, and the unit cell constants

change gradually by small amounts. No new diﬀraction pattern

appears, and thus, the solid-state reaction takes place within a

single phase. In Tables 1A and 1B, each crystal is denoted by a

code n1_n2, where n1 is the number of exposure days, and n2 is

the crystal number. Thus, entry 32_1 is the column for data

collection on crystal 1 after 32 days (83.2 kGy exposure); for

crystals 1 and 2, which received an additional 650 kGy dose, the

codes are 110_65m_1 and 110_65m_2. In the Supporting

Information, the six Tables S2_0 through S2_110 each contain

all of the information presented in Tables 1A and 1B, with each

row given for each irradiation time of crystals 1−4, and Table

S2_110_65m presents the analogous data for the extra radiation

dose received by crystals 1 and 2. Inspection of all the tables

reveals a remarkable consistency in the crystallographic results

for the four crystals over a period of nearly four months (110

kGy γ-ray dose, plus the additional dose of 650 kGy for crystals 1

Table 1B. Crystallographic Data for Crystal 1

crystal codes

a (Å)

b (Å)

56_1

110_1

7.5620(3)

110_65m_1

7.5639(3)

7.8542(4)

7.8221(2)

103.461(3)

100.176(3)

106.330(4)

418.85(3)

1, 0.5

7.5303(3)

7.8573(3)

7.8219(3)

103.049(3)

100.170(3)

106.545(4)

417.56(3)

1, 0.5

169.3

P1

̅

294

0.71073

1.346

0.159

7.8564(3)

7.8178(4)

103.227(4)

100.216(4)

106.380(3)

418.98(3)

1, 0.5

c (Å)

α (deg)

β (deg)

γ (deg)

V (Å³)

Z, Z′

F.W., g mol⁻¹

space group

T (K)

169.3

P1

̅

P1

̅

294

λ (Å)

0.71073

1.342

0.158

0.71073

1.342

0.158

ρ_calc(g cm⁻³

)

μ (mm⁻¹

)

θ_max; trans. factors 30.4°; 0.88−0.91 30.4°; 0.90−0.91 30.4°; 0.90−0.91

R, R_w(I > 2σ(I))

R, R_w(all data)

S

0.0472, 0.0633

0.0582, 0.0833

1.003

0.0489, 0.0689

0.0612, 0.0934

0.970

0.0489, 0.0629

0.0662, 0.0978

0.965

no. reﬂ. (I > 2σ(I); 2081, 2528

all)

2058, 2528

1936, 2520

no. param.

152

major/minor

reactant ; ratio

0.184(4)/

0.085(2) 2.165

0.134(5)/

0.062(2) 2.161

0.157(7)/

0.073(3) 2.151

0.527(7)/

0.243(3) 2.169

2.169

0.770(11)

major/minor

product ; ratio

0.500(4)/

0.237(2) 2.110

0.550(5)/

0.254(2) 2.165

2.110

2.165

extent of reaction

0.731(6)

0.805(7)

a

R = ∑||F_o| − |F_c||/∑|F_o|; R_w= [∑w(|F_o| − |F_c|)²/∑w|(F_o)²]^1/2; S =

[∑w(|F_o| − |F_c|)²/(n − m)]^1/2

and 2). Below we ﬁrst consider the structural chemistry of

reactant and product and then examine the consistency of the

single-crystal-to-single-crystal reactions throughout the four-

crystal experiment.

Panels a and b of Figure 4 show the major and minor

components of the disordered trans-2-butenoate anions,

respectively, as observed in the structure of 12 prior to

irradiation. The pairs of molecules are related by a center of

symmetry and are chosen to show the shortest α-carbon to α-

carbon contacts for each component. Both distances are well

within the 4.2 Å limit of the Schmidt topochemical postulate for

photochemical reactions, which we and others have shown also

to be a highly useful criterion for radiation-induced radical

reactions in the solid state.^{2−4,16−24}The short distance, and the

centrosymmetric orientation of the reactants in each case, would

be expected to lead to the observed topochemical product,

magnesium rel-(3S,4R)-1-hexene-3,4-dicarboxylate (2b).

After the initial irradiation period, the structure of the mixed

reactant/product crystals could be solved by conventional

means. The structure, presented in Figures 5 and 6, involves a

complex four-component disorder, because each disordered

reactant component yields a diﬀerent product orientation, and

as can be seen in Tables 1A and 1B, the reaction does not

proceed to completion. Figures 5b and 6b show the numbering

scheme for the resolvable product major component atoms (C2,

C3, and C4) and the product minor component atoms (C21,

C31, and C41), respectively.

Thus, for example, at maximum conversion, the crystal

contains 20% of the two original monomer components and

80% of the two resultant product components. The successful

reﬁnement required a thoughtful analysis and consideration of a

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Figure 4. (a) View of a pair of major-component reactant molecules related by an inversion center and appropriately oriented to form 2b, a rel-(3S,4R)-

1-hexene-3,4-dicarboxylate moiety; (b) the analogous view for the minor component reactant pair.

Figure 5. (a) View of a pair of inversion-related, major-component reactant molecules of 12 superimposed on the major product component, rel-

(3S,4R)-1-hexene-3,4-dicarboxylate 2b; (b) the identical view with the reactant molecules removed. Reactants have green C atoms and gray H atoms,

while product molecules have yellow C atoms and black H atoms. Disorder of the product molecule is not shown, and disorder of the O atoms was not

resolved (view from 32-day irradiation). The bond distance between the α-carbon atoms C2 and C2′ (−x, −1−y, −1−z) is 1.558(6) Å.

proper set of constraints and restraints. Many diﬀerent

combinations of restraints were attempted, but in the end,

three general restraints helped ensure a stable and consistent

reﬁnement of all 26 determinations. The conditions applied

were as follows: (i) the occupancies of reactant and product

were restrained to sum to 1.0; (ii) the ratio of major/minor

product occupancies and the ratio of major/minor reactant

occupancies were restrained to be equal by restraining their

diﬀerence to be 0.0; and (iii) for carboxylate carbon atom C1 of

the product, where disorder could not be resolved, the

occupancy of C1 and the sum of the occupancies of the major

and minor product were restrained to be equal by restraining the

diﬀerence to be 0.0. An analogous restraint was applied to the

occupancy of reactant carboxylate carbon atom C101. The

equations used may be found in the deposited CIF ﬁles. In

simpler language, disorder of C1 and C101 could not be

resolved, so that (a) the occupancy of C1 is the sum of the

occupancies of the two components of product and (b) the

occupancy of C101 is the sum of the occupancies of the two

components of reactant.

The X-ray structure determination of the solid solution of 12

and 2b conﬁrms the stereochemistry of 2b assigned by

Naruchi²⁵by hydrogenation of acid 2c to give meso-2,3-

diethylsuccinic acid, mp 192 °C (lit.⁵⁸187−206 °C), rather than

( )-2,3-diethylsuccinic acid, mp 130−134 °C.⁵⁸We have the

rare opportunity to conﬁrm the structure of product 2b by

analysis of the X-ray data without puriﬁcation and crystallization

of the product. In our previous work¹⁻⁴with trans-2-butenoates,

the crystals became amorphous upon irradiation.

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S2_110_65m). Third, inspection of Tables S2_0 through

S2_110 for crystals 1−4 shows that there is a smooth change in

all cell constants versus irradiation and no evidence for a phase

transition. The cell data for crystals 1−4 are remarkably similar

in each table, along with the extent of conversion versus dose,

which demonstrates the reproducibility of these experiments.

Fourth, we note that the conversion rate of the single crystals of

12 sealed in capillaries is approximately twice as fast as that of

powdered 12 under air in vials, although both plateau at 80%

conversion. The irradiation time in days is comparable, but the

dose rate is 5 kGy/day for powdered 12 and 2.6 kGy/day for the

single crystals of 12, because the latter experiments were

conducted ﬁve years (i.e., one-half-life) later. Possible reasons

for this include shorter chain length resulting from termination

of the radical chain by adventitious oxygen in powdered 12,

partial decomposition of powdered 12 by loss of water leading to

shorter chain length, and better initial crystal quality of the single

crystals. Finally, we note that the smallest unit cell volumes are at

the 8−16 day exposure times. However, the maximum

diﬀerences are very small: for crystals 1−4, they are all less

than 0.1%. The values are 0.26(6), 0.27(6), 0.29(5) and

0.39(22) Å³, respectively. Compound 12 diﬀers from the others

we have studied in that the reactants are enclosed in a cavity, in

which molecular motion is possible, and retention of crystallinity

is thus considerably more likely.

Figure 6. (a) View of a pair of inversion-related, minor-component

reactant molecules of 12 superimposed on the minor product

component rel-(3S,4R)-1-hexene-3,4-dicarboxylate 2b; (b) the identi-

cal view with the reactant molecules removed. Reactants have blue C

atoms and gray H atoms, while product molecules have yellow C atoms

and black H atoms. Disorder of the product molecule is not shown, and

disorder of the O atoms was not resolved (view from 32-day

irradiation). The bond distance between α-carbon atoms C21 and

C21′ (−x, −1−y, −1−z) is 1.529(13) Å.

As mentioned in the ﬁrst section, the radiation-induced

dimerization of 12 yields only a single diastereomer, the rel-

(3S,4R)-1-hexene-3,4-dicarboxylate dianion 2b. As a top-

ochemical product, the diastereomer can be produced only by

a reactant pair consisting of either major/major or minor/minor

components. If a “cross-reaction” occurs, i.e., a major/minor pair

reacts, as illustrated in Figure 7, the product will be the

alternative diastereomer, rel-(3S,4S)-1-hexene-3,4-dicarboxy-

late. Thus, this is a rare case where “the reaction chemistry

Figure 5a shows the superposition of major component

reactant and product, while Figure 6a shows the analogous view

for minor component reactant and product. The complete

structure is a superposition of Figures 5a and 6a. The reader is

encouraged to view these two ﬁgures as PowerPoint animations

in the Supporting Information ﬁle Figures 5 and 6.pptx. It is

notable that the reacting C atom distance is longer for the major

component (Figure 4), but the amount of molecular motion is

greater for the minor component. Figures 5b and 6b show a

“partial” (i.e., undisordered) structure of the dimeric product,

rel-(3S,4R)-1-hexene-3,4-dicarboxylate. The dimer occupies a

center of symmetry, which results in a 1:1 disorder of the

CH₂=CH− and CH₃CH₂− ends of the molecule. The torsion

angles C1−C2−C2′−C3′ and C4−C3−C2−C2′ for the major

product are 60.5(11)° and 98.5(14)°, while torsion angles C1−

C21−C21′−C31′ and C41−C31−C21−C21′ for the minor

product are −54.6(11)° and 175.9(11)°, respectively. While

there are only a few structural analogues for the 98.5° and 175.9°

torsion angles, the two diﬀerent values appear to represent the

expected values for each “end” of the disordered product. The

major isomer is near to values observed for unsaturated

analogues²⁹LISVUG (124°),⁵⁹LISWAN (−129°),⁵⁹and

LISWIV (−122°),⁵⁹while the minor isomer value is in good

agreement with the saturated analogues JOKJOI (177°),⁶⁰

KAGJUX (161°),⁶¹and VODFOJ (−174°).⁶²

Examination of Tables 1A and 1B reveals some interesting

observations. First, the ratios of reactant and product disorder

versus total dose are equal within experimental error; a

conservative estimate of the standard uncertainties of the ratios

sets the range of values to 0.02−0.07 (see also Tables S2_0

through S2_110 for the entire crystal set). All values are within

3 standard uncertainties. Second, the extent of conversion

begins to plateau between 32 and 110 days of irradiation,

reaching a maximum value of ca. 80% after 110 days (286 kGy).

A further 650 kGy dose does not increase the amount of product.

It appears that, after 110 days of irradiation, further exposure

only contributes to radiation damage (see also Table

Figure 7. View of a pair of major-component reactant molecule of 12

(below) and a minor-component (above) molecule of 12, including the

α-carbon distance. If such a “cross-reaction” were to occur, the expected

topochemical product would be rel-(3S,4S)-1-hexene-3,4-dicarbox-

ylate, which was not observed by NMR analysis or by solution of the

crystal structure.

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tells us about the crystallography”. The overall disorder could

involve a 2.165:1 random mixture of carboxylates, above and

below the inversion center. However, the chemical result

precludes that option as long as the disorder is static. In a

separate study, we observed the identical ratio of components in

a pristine sample in the temperature range 274−320 K,

consistent with static disorder of the molecules.⁵⁷The chemistry

and the static nature of the disorder are consistent only with

inversion-paired reactants.

Structure−Reactivity Relationships for Hydrogen

Transfer in 12. In order to develop an understanding of

thermal and photochemical solid-state dimerization, we need

only to analyze the spatial orientation of two molecules of the

monomer as depicted in Figure 4. Crystal structure data from the

16-day and 32-day irradiations had reactant/product ratios

nearest to 1:1, and the data from the 32-day exposure were used

in the calculations and illustrations which follow. The radical

chain dimerization depicted in Schemes 6 and 7 involves three

molecules of monomer and further requires that radical 19

produced in propagation step 2 be appropriately oriented to

continue the chain. The deuterium-labeling experiment using 16

provides stereochemical information about the hydrogen atom

transfer (propagation step 2). To determine whether hydrogen

atom transfer is topochemical, we ﬁrst consider the relationships

for C−C bond formation beginning with each of the two

orientations of reactant, as illustrated in Figure 4. We then add

an additional trans-2-butenoate molecule by symmetry, with the

criteria for choice being simply that the added molecule

possesses the shortest intermolecular methyl hydrogen to β-

carbon atom distance. We then determine whether the predicted

stereochemistry of carbon−carbon bond formation and hydro-

gen atom transfer is consistent with the observed stereo-

chemistry of the deuterium-labeled dimer 16. As stated earlier,

the dimerization about a center of symmetry is expected to yield

magnesium rel-(3S,4R)-1-hexene-3,4-dicarboxylate, but we now

need to establish the topochemical nature of the hydrogen

abstraction. The nearest methyl H atom for propagation step 2 is

C3···H4012′ (1−x, −1−y, −1−z) at a distance of 4.521 Å, using

a dimer molecule for C3 and a monomer molecule for the

hydrogen atom transfer. Monomer−monomer (4.547 Å) and

dimer−dimer (4.043 Å) distances are similar, with a somewhat

shorter dimer−dimer distance.

The complete relationship for the geometrical course of the

reaction is shown in Figure 8. The reader is strongly encouraged

to view Figures 8 and 9 as annotated PowerPoint animations in

the Supporting Information ﬁle Mechanism.pptx. The anima-

tion presents the process in a much clearer fashion than can be

illustrated in a single ﬁgure. Initiation (INIT) occurs with

breaking of a C401−H bond and formation of radical 18 (see

Scheme 7) at atom C401. Propagation step 1 (label 1) involves

bond formation between the α-carbon atoms (green color, just

above and below the new bond) of the monomer to form the

C2−C2′ bond, along with the formation of radical 19 at atom

C3. Propagation step 2 (label 2) involves the abstraction of

hydrogen atom H4012 from a symmetry-related C401 atom

(see above). Another radical 18 is created in step 2, and a second

round of propagation begins with the ﬁrst step (label 3) forming

a C2−C2′ bond and radical 19 at C3, followed by the second

step 2 with abstraction of another H4012 atom from methyl

carbon atom C401 (label 4). The third round of propagation

begins in a like manner with bond formation and radical 19

generation (step 1, label 5) and the partially shown step 2 (label

Figure 8. View of the set of superimposed major-component reactant/

product molecules shown in Figure 5a, with two additional sets

translated by one and two unit cells along the a direction, in order to

show the likely geometrical mechanism of the radical chain reaction, as

described in the text.

6). The torsion angle of approach, C2′−C2−C3···H4012, is

excellent for anti-addition at 176.3°.

For the minor component reaction, the diagram must be

constructed in a diﬀerent fashion. Examination of a diagram

similar to that of Figure 8, but using all minor-component

reactants and products, shows an unsatisfactorily short

intermolecular γ-carbon to γ-carbon atom C41···C41′ (1−x,

−1−y, −1−z) contact of 2.640 Å for the products. With a

major/minor component ratio of ca. 2.2:1, the major-

component mechanistic reaction pathway (Figure 8) must be

considered, but we cannot use the same process to propose a

sensible mechanism for the minor component: the single-

crystal-to-single-crystal radical chain process cannot proceed

under those circumstances. Thus, we hypothesized that, if (a)

there were a minor component pair interleaved between two

major component pairs and (b) it could be shown that this

arrangement did not lead to unusually short contacts, the result

would be a consistent geometrical mechanism that includes the

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the ﬁrst step (label 3) forming a C21−C21′ bond (the two blue

monomer α-carbon atoms above and below C21 and C21′ are

the reacting atoms) and radical 19 at C31, followed by the

second step 2 with abstraction of a H4012 atom from methyl

carbon atom C401 (label 4). The third round of propagation

begins in a like manner with bond formation and radical 19

generation (step 1, label 5) and the partially shown step 2 (label

6). The torsion angle of approach C2′−C2−C3···H4021 is

166.6°, and the torsion angle C21′−C21−C31···H4012 is

111.2°, both consistent with anti-addition.

The 4.521 Å distance between the carbon radical and the

methyl hydrogen atom in propagation step 2 of the major−

major reaction (and the analogous distances of 4.090 and 4.034

Å for the major−minor reaction) are much longer than those

that we and others have observed in γ-ray initiated radical chain

reactions as taken from monomer−monomer distances which

are 3.13 Å for 4,³3.32 Å for 6,³3.31 or 3.55 Å for 8,⁴3.10 or 3.30

Å for 10,⁴3.09−3.30 Å for 2-deoxy-β-D-erythro-pentopyr-

anose,⁴¹3.4 Å for D-fructose,³⁹and 3.05−3.47 Å for a bis alkyne

dimerization.^42,63The only other hydrogen atoms that can be

abstracted by the alkyl radical of dimer 19 are either sp²

hydrogen atoms (bond strength 111 kcal/mol) or water

hydrogen atoms (bond strength 117 kcal/mol)⁶⁴that are too

strongly bound to be abstracted by an alkyl radical. It is likely

that the radical has a long lifetime in the crystal. The monomer

and dimer radical are not directly bound to magnesium but held

more loosely in a cavity so greater molecular motion may be

possible than is typical in solid-state reactions. Thus, in this case

a shorter abstraction distance than that calculated from the

crystal structure may be achieved.

Figure 9. View of the set of superimposed major-component (top and

bottom set) and minor-component (middle set, with blue C atoms for

monomer) reactant/product molecules shown in Figure 6a, with each

unit translated by one and two unit cells along the a direction, in order

to show the likely geometrical mechanism of the radical chain reaction,

as described in the text.

⁶⁰Co γ-Irradiation of Sodium trans-2-Butenoate (1). As

we have previously communicated,¹γ-irradiation of crystalline 1

followed by acidiﬁcation with aqueous hydrochloric acid and

ﬁltration of the precipitate gave crude tricarboxylic acid 3b in

55% yield (see Scheme 8); the structure of 3b was determined

observed minor component reactivity. The analogous γ-carbon

to γ-carbon atom C4···C41′ (1−x, −1−y, −1−z) product

“cross-contact”, is quite normal at 3.759 Å. The diagram

construction is somewhat more complicated, as this time we

again search for the shortest β-carbon to methyl H distance in

propagation step 2, but for both (i) the major product

abstraction from the minor reactant, and (ii) the minor product

abstraction from the major reactant. We ﬁnd these distances to

be (i) C3···H4021′ (1−x, −1−y, −1−z) at a distance of 4.090 Å

and (ii) C31 to H4012′ (1−x, −1−y, −1−z) at a distance of

4.034 Å. These use a dimer molecule for C3 and C31,

respectively, and monomer molecules for the hydrogen atom

transfer. The analogous monomer−monomer and dimer−dimer

distances for (i) are 4.045 and 4.043 Å, and for (ii) are 3.646 and

3.689 Å; we note that none of the contacts are unusually short.

The complete relationship for the geometrical course of the

mixed major−minor component “stack” is shown in Figure 9,

and we may describe the process in a manner analogous to that

for the major component. Note that the monomer molecules in

the middle of the stack are the minor component, with C atoms

colored blue; this pair will produce a minor component product,

as shown. Initiation (INIT) occurs with breaking of a C401−H

bond and formation of radical 18 (see Scheme 7) at atom C401.

Propagation step 1 (label 1) involves bond formation between

the α-carbon atoms (green color, just above and below the new

bond) of the monomer to form the C2−C2′ bond, along with

the formation of radical 19 at atom C3. Propagation step 2 (label

2) involves the abstraction of hydrogen atom H4021 from a

symmetry-related C402 atom (see above). Another radical 18 is

created in step 2, and a second round of propagation begins with

Scheme 8. γ-Ray-Induced Trimerization of 1

by X-ray crystallographic analysis. Crude acid 3b was treated

with diazomethane⁶⁵to form trimethyl ester 3c that was

estimated to be 94% pure by GC analysis. The ﬁltrate was

concentrated after the removal of precipitated 3b, taken up in

ether and treated with diazomethane to give a complex mixture

consisting of additional 3c (57%), dimer 20c⁶⁶(22%) with

unknown stereochemistry, and numerous minor products. The

total yield was determined to be 68% of 3c and 12% of 20c by

GC analysis of the ester mixture obtained by concentration of

the acidiﬁed mixture prior to ﬁltration, dissolution in ether, and

treatment with diazomethane.

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The stereochemistry of the hydrogen atom transfer can be

easily determined using deuterium-labeled trans-2-butenoic acid

as described above and in earlier papers in this series.^3,4We need

to use trans-2-butenoic-2-d acid⁴because the hydrogen atom is

transferred to the 2-position rather than the 3-position as in the

thermal dimerization of 1. Crystalline sodium trans-2-

butenoate-2-d (21) was prepared and γ-irradiated in a partially

ﬁlled vial under air to give a mixture containing approximately

60% of starting material, only 20% of 22a, and 16% of sodium

trans-2,3-epoxybutanoate-2-d (23a) (see Scheme 9).⁶⁷The

Scheme 10. Radical Chain Mechanism for the Conversion of

21 to 22a

Scheme 9. γ-Ray-Induced Trimerization of 21

decreased yield and formation of the epoxide byproduct from

reaction of oxygen with radical intermediates is expected for

radical chain reactions. Epoxide formation was not observed in

earlier studies because we used less-precious unlabeled trans-2-

butenoate compounds, and reactions were carried out in full,

tightly packed, capped vials with little air space. Fortunately, γ-

irradiation of a sample of 21 sealed under vacuum followed by

acidiﬁcation aﬀorded a precipitate consisting of a 9:1 mixture of

22b and unreacted trans-2-butenoic-2-d acid. In the NMR

spectrum of 22b the vicinal coupling constant for the CHD

proton to the adjacent methine hydrogen is 11 Hz, consistent

with preferential conformations with the CO₂H group anti to

the large R(CO₂H)CD substituent as shown.⁶⁸This indicates

that the hydrogen atom is transferred anti to the previously

formed C−C bond.

The overall mechanism is shown in Scheme 10. γ-Irradiation

of 21 leads to loss of a hydrogen atom to give allylic radical 24,

which adds to a second molecule of 21 to give dimeric radical 25

in the ﬁrst propagation step. Addition of dimeric radical 25 to a

third molecule of 21 anti to the previously formed C−C bond

will give trimeric radical 26 in the second propagation step. In

the third propagation step, trimeric radical 26 abstracts a

hydrogen atom from a fourth molecule of 21 anti to the

previously formed C−C bond to give product 22a and another

molecule of allylic radical 24. This complex sequence of stereo-

and regiospeciﬁc reactions likely occurs under topochemical

control. The minor product dimer 27, the deuterium-labeled

analogue of 20a, can be formed from dimeric radical 25 by

hydrogen abstraction from 21.

trideuteroacetyl chloride.⁶⁹Great care was needed throughout

this process to prevent deuterium from washing out.

Unfortunately, the γ-irradiation of the 4,4,4-trideuterated

analogues of 1 and 12 proceeded in much lower yield than

that of the unlabeled compounds and gave product mixtures that

could not be analyzed completely.⁶⁹γ-Irradiation with a

deuterium atom at C₂or C₃should exhibit only small secondary

isotope eﬀects. Primary kinetic isotope eﬀects as large as 15.9

have been reported for hydrogen atom transfer in radical chain

reactions.⁷⁰Presumably, because a deuterium atom must be

transferred from the CD₃group, the radical chain reaction no

longer proceeds eﬃciently.

Structural Chemistry of Sodium trans-2-Butenoate (1).

While compound 1 may be prepared easily, the growth of single

crystals remains a challenging project to this day. Over a period

of three decades, many graduate and undergraduate research

personnel were asked to participate in our quest to grow high-

quality crystals. We had only three partially successful

experiments, which, in part, helped us to understand the solid-

state behavior of this remarkable material. We found two

diﬀerent structures, which, for the sake of simplicity, we will

designate as polymorph 1_I, and polymorph 1_II; the latter

polymorph was measured at 294 and 120 K, designated as RT

and LT in Table 2. Compound 1 invariably crystallizes as a very

thin, platelike material, a likely mixture of polytypes, resembling

mica in appearance: layers of the material easily split oﬀ from the

mass. Thus, one must be very careful in handling 1 in order to

preserve any single-crystal character. The rare crystals of 1 are

highly mosaic, with omega (Weissenberg or serial diﬀractom-

eter) widths of up to 2°. Summary crystal data appear in Table 2;

a full report appears in Table S3. The ﬁrst-discovered phase, 1_I,

has a short c-axis of 3.465 Å. The second-discovered phase, 1_II,

has cell constants equal to those of polymorph 1 at 294 K, except

that the c-axis is doubled and the space group has changed from

γ-Irradiation of compounds prepared from trans-2-butenoic-

4,4,4-d₃acid should give analogous products in which a

deuterium atom from the methyl group is transferred in the

ﬁnal propagation step. The spectra of these compounds should

be informative because coupling to the methyl groups will be

removed but all backbone hydrogen atoms will be present except

for the one replaced by a deuterium atom. We prepared trans-2-

butenoic-4,4,4-d₃acid in seven steps from Meldrum’s acid and

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Table 2. Summary of Crystallographic Data for Crystal 1

compound_form

1_I

1_II(RT)

1_II(LT)

a (Å)

b (Å)

c (Å)

β (deg)

V (Å³)

Z, Z′

28.354(8)

5.283(2)

3.465(1)

92.95(3)

518.3(3)

4, 0.5

108.07

C2/m

294

28.334(3)

5.2869(12)

6.9224(17)

93.007(13)

1035.6(4)

8, 1

108.07

C2/c

294

27.803 (7)

5.2864(10)

6.8607(15)

90.732(17)

1008.3(4)

8, 1

108.07

C2/c

120

F.W. (g mol⁻¹

space group

T (K)

)

C2/m to C2/c. Another crystal of 1_II was found later and

measured at 120 K. All three materials were far from ideal: 1_1

was triply twinned, with only partial resolution of the twinning,

and had a high R value of 0.137; 1_II(RT) had a high R value of

0.107 and reacted/decomposed (85.6%, decomposition correc-

tion applied) under Cu Kα irradiation before a complete data set

could be obtained. The best sample was twinned 1_II(LT), with

R = 0.0692 and 100% completeness. Our experience over the

long period of study indicates that 1 is a mixture of these two

phases, and likely other polytypes. We therefore choose to base

our discussion of the structural chemistry of the most well-

deﬁned material, polymorph 1_II, with a limited, brief

comparison to the structure of 1_I.

The coordination environment of the sodium ion in

polymorph 1_II is shown in Figure 10. The Na ion is ﬁve-

coordinate, with Na−O distances ranging from 2.337 to

2.424(3) Å, along with a longer contact of 2.638(3) Å to the

apical O2 atom. Similar coordination for Na is also present in the

closely related structures of sodium propynoate²³(Na−O

2.368−2.494 Å; 3.120 Å to apical O2) and the β-polymorph of

sodium acetate (Na−O 2.309−2.477 Å; 2.802 Å to apical O2).⁷¹

Coordination in the apical position is more symmetrical in 1_II

(2.424, 2.638 Å) than in the propynoate and acetate salts.

We note that the distance guidelines of the topochemical

postulate for the onset and control of reactivity do not generally

apply to thermal reactions,⁷²⁻⁷⁴where reactive materials may

have initial distances of ∼5 Å.⁷²However, in cases such as the

thermal dimerization of 1, where the partner molecules are

already within distances only slightly longer than a van der Waals

contact, we can expect that topochemical control and least-

motion considerations will prevail, and the product(s) will likely

reﬂect the observed intermolecular relationships. In the case of

1, however, the crystal structure of polymorph 1_I suggests that

1 is disordered by 180° rotation about the C1−C2 bond (see

Figure S2) so that dimer pairs with both eclipsed and alternating

trans-2-butenoates need to be considered.

Figure 10. Coordination environment of the Na ion in polymorph 1_II.

Contacts of 3.438 Å between α-carbon atoms along the crystallographic

c-axis are indicated by dotted lines. Note that the alkene bonds are

alternating rather than eclipsed.

As described earlier, heating solid 1 to 300 °C gives dimer 2a,

disodium rel-(3S,4R)-1-hexene-3,4-dicarboxylate, in 84% yield,

by a thermal ene reaction (see Schemes 5 and 6).^25,26

Compound 1 has short α-carbon atom C2···C2′ (x, 2−y, z−

1/2) contacts of 3.438(1) Å along the c-axis. Two such contacts

(dotted lines) are shown in Figure 10. In order to obtain product

2a, a rotation of 180° around the carboxylate carbon atom to α-

carbon atom bond (C1−C2) must ﬁrst occur. The reaction

takes place at 300 °C, and a rotation, possibly accompanied by a

phase transition, is thus plausible. Figure 11 shows a perspective

view of the two trans-2-butenoate anions at the bottom right of

Figure 10 and shows why a rotation of 180° must ﬁrst occur

before a concerted ene reaction can occur. We can examine the

likely transition states for the formation of either 2a or the rel-

Figure 11. View of two nearest neighbors (cf. Figure 10) showing

(dotted line) short C2−C2′ contact of 3.438 Å. A rotation of 180° must

occur around the C1′−C2′ bond before a concerted ene reaction can

occur. The C1−C2···C2′−C1′ torsion angle is −8°. An analogous view

of polymorph 1_I may be viewed in Figure S3.

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(3R,4R) diastereomer. In Figure 12, the left reaction shows the

thermal ene dimerization of crystalline 1 with eclipsed trans-2-

Finally, there remains the question of how the crystal structure

of 1 helps us understand the γ-ray-induced trimerization

reaction. The reaction occurs at ambient temperature, so that

any molecular reorientation or phase transition is unlikely. For

polymorph 1_II, Figure 13 shows the bilayer packing and short

intermolecular α-carbon to symmetry-related β′-carbon, C2···

C3′ (x, 2−y, z−1/2), contacts of 3.651(6) Å, all within one

section of the bilayer. The trans-2-butenoate moiety packs in a

head-to-head arrangement, with C1 and C2 directly above and

below the analogous carbon atoms along the c-axis; the alkene

carbon bonds have an alternating orientation in a single section

of the bilayer.

We can now consider the orientation of trans-2-butenoates

that leads to the observed product 3a in the trimerization of 1,

which is clearly shown in Scheme 10. The ﬁrst C−C bond in the

trimer 3a is formed from alternating trans-2-butenoates as

expected from the structure of polymorph 1_II, but the second

C−C bond is formed from eclipsed trans-2-butenoate species.

Unfortunately, the absence of a single-crystal-to-single-crystal

reaction for 1 leaves us without enough information to explain

the stereochemistry of the trimerization. One possibility is that

180° rotation about the C1−C2 bond to give the eclipsed

species needed for the second addition occurs readily after the

crystal structure is disrupted by the ﬁrst addition, and the

resultant molecular motion creates free space. We also cannot

explain why the reaction is selective for trimer 3a (68%) over

dimer 20 (12%) and tetramers (5%).

Figure 12. Left reaction shows the thermal ene dimerization of

crystalline 1 with eclipsed trans-2-butenoates after 180° rotation about

the C1−C2 bond to give 2a. The right reaction shows why the thermal

ene dimerization of the conformer of 1 with alternating trans-2-

butenoates observed in the crystal structure does not give the

diastereomer of 2a.

butenoates after 180° rotation about the C1−C2 bond to give

2a. The C1−C2···C2′−C1′ torsion angle in the transition state

(i.e., the E−C···C−E torsion angle at left in Figure 12) is about

−40°, a modest twist from the torsion angle of −8(3)° in the

crystal structure of 1_II (see Figure 11). The right reaction

shows why the thermal ene dimerization of the conformer of 1

with alternating trans-2-butenoates that is observed in the crystal

structure does not give the diastereomer of 2a. A C1−C2···C2′−

C1′ torsion angle of about 75° is required (cf. the E−C···C−E

torsion angle at the right in Figure 12), and that is unlikely to be

achieved in the crystal because it would require moving the

carboxylate ions away from the sodium atoms.

A ﬁnal note in this case concerns the crystal structure of triply

twinned polymorph 1_I. With a c-axis length of 3.465 Å, all

molecules are expected to be eclipsed. As detailed in the

Experimental Section, however, a further complication is that

the molecule has crystallographic m symmetry, with the mirror

plane containing the Na1, C1, and C2 atoms. With a 1:1

disorder, we do not know the disposition of a pair of adjacent

reactant molecules with certainty (see Figures S2 and S3 for

illustrations). With (a) the disorder, (b) the possibility of a high-

temperature molecular reorientation, and (c) the complications

arising from only partially corrected twinning, we will not

consider polymorph 1_I in the following discussion of the

trimerization of 1.

CONCLUSION

■

Irradiation of metal trans-2-butenoates with ⁶⁰Co γ-rays is a

powerful synthetic tool for the chemo-, regio- and stereospeciﬁc

preparation of dimers and trimers. In the present work, we have

discovered a sixth product that can be formed selectively by a γ-

ray-induced radical chain reaction of a crystalline alkali or

alkaline earth trans-2-butenoate.^3,4γ-Irradiation of crystalline

hexaaquamagnesium trans-2-butenoate dihydrate (12) aﬀords

rel-(3S,4R)-1-hexene-3,4-dicarboxylate (2) by a single-crystal-

to-single-crystal reaction by anti addition to the butenoate

double bond, as established by deuterium-labeling experiments.

Naruchi reported that the same dicarboxylate 2 is formed by

heating crystalline sodium trans-2-butenoate (1) at 300 °C, but

this thermal ene reaction has now been shown by deuterium

labeling to proceed by syn addition to the butenoate double

bond as expected. γ-Irradiation of sodium trans-2-butenoate

forms a single trimer chemo-, regio-, and stereospeciﬁcally, as

demonstrated by using deuterium labeling to establish the

Figure 13. View of the packing of polymorph 1_II viewed down the b-axis. The dotted lines show the favorable bilayer packing arrangement, and short

C2···C3′ (x, 2−y, z−1/2) contacts of 3.651 Å, each set within one section of the bilayer.

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12 to 2b over time: 2 d (0%), 4 d (1.8%), 8 d (7.4%), 16 d (23.1%), 32 d

(45.5%), 64 d (65.6%), and 128 d (80.3%). The spectrum of 2b was

determined from the 45.5:54.5 mixture of 2b and 12 obtained after 32 d

of γ-irradiation: ¹H NMR (D₂O) 5.82 (dd, 1, J = 17.2, 10.4, 10.1), 5.10

(br d, 1, J = 17.2), 5.02 (br d, 1, J = 10.1), 2.88 (dd, 1, J = 10.4, 10.4),

2.37 (ddd, 1, J = 10.4, 10.4, 4.6), 1.52−1.34 (m, 2), 0.86 (t, 3, J = 7.3);

¹³C NMR 184.0 (C), 182.8 (C), 137.8 (CH), 117.3 (CH₂), 59.4 (CH),

stereochemistry of hydrogen atom transfer. The crystal structure

of sodium trans-2-butenoate has been determined, and the

packing observed is consistent with the observed ene

dimerization and γ-ray-induced trimerization. As we showed

previously with the γ-irradiation of other trans-2-butenoates,^3,4

the formation of the carbon−carbon bond and hydrogen atom

transfer in the conversion of 12 to 2 is unequivocally topochemical,

stereospecific, and not the result of a random process.

55.6 (CH), 25.3 (CH₂), 12.8 (CH₃).

After longer γ-irradiation times, trace impurities were seen in the

spectra: (the percent is relative to 2b as 100%) δ 2.88 (8%, dd, 1, J =

11.6, 9.2), 2.55 (<1%, dd, 1, J = 10, 10), 0.98 (2%, d, 3, J = 7.3), 0.90

(5%, d, 3, J = 6.1), 0.83 (4%, d, 3, J = 7.5).

Apart from our work with trans-2-butenoates¹⁻⁴and early

work with carbohydrates,³⁶⁻⁴¹there are no systematic studies of

the chemo-, regio-, and stereospeciﬁc syntheses of small

molecules using ionizing radiation. We hope that our studies

will stimulate the search for new classes of these reactions.

An authentic sample of the sodium rel-(3S,4R)-1-hexene-3,4-

dicarboxylate (2a) was prepared by heating sodium trans-2-butenoate

(1) at 300 °C as described by Naruchi.^25,26The¹NMR spectrum of a

mixture of 2a and 2b indicated the presence of a single dicarboxylate.

Preparation of Dimethyl rel-(3S,4R)-1-Hexene-3,4-dicarbox-

ylate (2d). A sample of irradiated 12 (250 mg, 1.48 mmol) was

dissolved in 10 mL of 1 M HCl. The solution was extracted with ﬁve 10

mL portions of CH₂Cl₂. The combined organic layers containing acid

2c were dried (MgSO₄), ﬁltered, and treated dropwise with

diazomethane in ether.⁶⁵When the yellow color of diazomethane

persisted, dilute aqueous acetic acid was added and the solution was

washed with water, dried (MgSO₄), and concentrated to give 69.4

(47%) of 2d as an oil: ¹H NMR 5.78 (ddd, 1, J = 17.1, 9.6, 9.5) 5.16 (br

d, 1, J = 17.1), 5.12 (br d, 1, J = 9.6), 3.67 (s, 3), 3. 63 (s, 3), 3.22 (dd, 1, J

= 9.5, 9.5), 2.76 (ddd, 1, J = 9.5, 9.5, 4.7), 1.65−1.58 (m, 1), 1.48−1.39

(m, 1), 0.87 (t, 3, J = 7.4); ¹³C NMR (CDCl₃) 173.8 (C), 172.6 (C),

133.3 (CH), 119.0 (CH₂), 52.6 (CH), 52.0 (CH₃), 51.4 (CH₃), 49.6

(CH), 23.7 (CH₂), 11.7 (CH₃). A sample of 2a prepared by heating 1

EXPERIMENTAL SECTION

■

General Procedures. All commercially available reagents were

used without further puriﬁcation unless otherwise noted. NMR spectra

were recorded in CDCl₃, D₂O (referenced to the peak of dioxane at δ

3.75, the peak of HDO at δ 4.79, or the peak of acetone at δ 2.08), or

DMSO-d₆(referenced to residual solvent at δ 2.50) on a 400 MHz

spectrometer. The following abbreviations are used to indicate signal

multiplicity: s, singlet; d, doublet; t, triplet; q, quartet; br, broad.

Chemical shifts are reported in δ (ppm downﬁeld from TMS) and

coupling constants (J values) in Hz. A Gammacell 220 Irradiator

(Atomic Energy of Canada, Ltd.), equipped with a ⁶⁰Co source, was

used for γ-irradiation experiments. The nominal dose rate at the time of

these experiments varied from 10 kGy as of January, 1991, to 2.5 kGy/

day as of June, 2002 and 1.9 kGy/day as of April, 2004 because of the

decay of ⁶⁰Co (half-life of 5.26 years). A ⁶⁰Co Gamma reactor at the

University of Massachusetts, Lowell, nominal activity 18−20 kGy/h,

was also used for γ-irradiation experiments.

1

was converted to dimethyl ester 2d with identical H and ¹³C NMR

spectra.

Preparation of Sodium trans-2-Butenoate-3-d (14). A solution

of trans-2-butenoic-3-d acid³(300 mg, 3.44 mmol) in 4 mL of H₂O was

neutralized with 3 M NaOH to the phenolphthalein end-point. The

solution was evaporated at 20 Torr until cloudy. Acetone (6 mL) was

added to precipitate a transparent, cellophane-like polycrystalline

material. The precipitate was isolated by vacuum ﬁltration, washed with

acetone, and dried in vacuum over P₂O₅to give 240 mg (64%) of

Preparation of Hexaaquamagnesium trans-2-Butenoate

Dihydrate (12). A stock solution of magnesium trans-2-butenoate

was prepared using a 100 mL three-necked round-bottomed ﬂask

equipped with a thermometer, a condenser, and a stopper. The ﬂask was

charged with 30 mL of water and maintained at 75 °C using a heating

mantle. trans-2-Butenoic acid (5.319 g, 61.8 mmol) was added slowly to

the ﬂask. (MgCO₃)₄·Mg(OH)₂·5H₂O (3.000 g, 6.178 mmol) was

added in several portions. Each time that the bubbling subsided, a new

portion was added. After the addition was complete, the solution was

stirred for 1 h at 75 °C. The solution was ﬁltered through a preheated

funnel (∼75 °C) into a preheated ﬂask to give an aqueous stock

solution.

1

sodium trans-2-butenoate-3-d (14): H NMR (D₂O, referenced to

internal dioxane at δ 3.75) 5.81 (s, 1), 1.79 (s, 3).

Pyrolysis of 14. Preparation of Disodium rel-(3S,4R,5S)-1-

Hexene-3,4-dicarboxylate-2,5-d₂(15). A sample of sodium trans-2-

butenoate-3-d (75 mg, 14) was placed in a 3 mm inside diameter glass

tube and packed tightly using a glass rod. A septum was placed at the rim

of the glass tube, and the sample was evacuated for 3 min. The sample

was then placed under nitrogen for 3 min and sealed using an air/gas

ﬂame. The tube was heated at 300 °C for 4 h, taken out of the oven, and

allowed to cool to room temperature to give 68 mg of white solid. NMR

analysis of a small amount of product (10 mg) indicated that the solid

consisted of 45% unreacted 14 and 55% of disodium rel-(3S,4R,5S)-1-

Upon slow evaporation at room temperature, two diﬀerent types of

crystals, prismatic 12 and plate-like 6, grew within 1−2 weeks. Prismatic

crystals of 12 were separated and used for the single-crystal-to-single-

crystal dimerization studies.

Alternatively, the diﬀusion technique below was selective for the

crystallization of 12 with several organic solvents and for the

crystallization of 6 with DMF.³The aqueous stock solution (1 mL)

was placed in a Pyrex culture tube (18 × 150 mm). An organic solvent

(5 or 10 mL of ethyl acetate, cyclohexane, hexanes, ethyl ether, or

benzene) was layered carefully with a syringe on the top of the aqueous

solution and the tube was capped tightly. After 1−2 d, prismatic crystals

of 12 were formed. In optimal cases, 81 mg (23%) for ethyl acetate, 37

mg (11%) for ethyl ether, and 28 mg (8%) for hexanes were obtained

from the 1:10 mixtures of aqueous stock solution and organic solvent.

Addition of either 5 or 10 mL of acetone or acetonitrile to the 1 mL of

aqueous stock solution resulted in the formation of 12, 6, or a mixture of

both as could be determined by visual inspection of the crystals.

Although the use of these solvents did not lead exclusively to 12, the

yields of crystalline material were much higher than with other organic

solvents (276 mg with 5 mL of acetonitrile and 201 mg with 5 mL of

acetone).

1

hexene-3,4-dicarboxylate-2,5-d₂(15): H NMR (D₂O, referenced to

internal dioxane at δ 3.75) 5.09 (s, 1), 5.01 (s, 1), 2.87 (d, 1, J = 11.6),

2.37 (dd, 1, J = 11.6, 3.6), 1.38 (qd, 1, J = 7.3, 3.6), 0.85 (d, 3, J = 7.3).

Preparation of Hexaaquamagnesium trans-2-Butenoate-3-d

Dihydrate (16). A solution of trans-2-butenoic-3-d acid³(1.00 g, 11.5

mmol) in 6 mL of H₂O was warmed to 75 °C, and (MgCO₃)₄·

Mg(OH)₂·5H₂O (557 mg, 1.15 mmol) was added in small portions.

Once addition was complete, the reaction mixture was heated at 75 °C

for 1 h and cooled to room temperature, and excess (MgCO₃)₄·

Mg(OH)₂·5H₂O was removed by gravity ﬁltration. A portion (1 mL) of

the ﬁltrate was placed in a test tube, and then a layer of less dense

solvent was carefully added with a syringe on the top of the aqueous

solution. The tube was capped tightly and kept at 0 °C for 2 d. The

weight of crystalline 16 varied using diﬀerent solvents: acetone, 250 mg;

ethyl ether, 67 mg; hexanes, 40 mg; 85 mg of crystal can be obtained

without adding a second solvent: ¹H NMR (D₂O, referenced to internal

dioxane at δ 3.75) 5.70 (s, 3), 1.67 (s, 1).

γ-Irradiation of 12. Magnesium rel-(3S,4R)-1-Hexene-3,4-

dicarboxylate (2b). Samples of 12 were irradiated in capped vials

under air for 2−128 d at 5 kGy/day. The samples were dissolved in D₂O

and analyzed by ¹H NMR. The spectra showed increased conversion of

γ-Irradiation of 16. Magnesium (3S,4R,5R)-1-Hexene-3,4-

dicarboxylate-2,5-d₂(17). Crystalline magnesium trans-2-bute-

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noate-3-d (40 mg, 16) was placed in a 3 mm inside diameter glass tube

and packed tightly using a glass rod. A septum was placed at the rim of

the glass tube, and the sample was evacuated for 3 min. The sample was

then placed under nitrogen for 3 min and sealed using an air/gas ﬂame.

Several tubes prepared in this manner were subjected to γ-rays. The

tubes were periodically removed from the γ-ray irradiator and NMR

analysis of product indicated that the solid consisted of unreacted

starting material and the magnesium rel-(3S,4R,5R)-1-hexene-3,4-

dicarboxylate-2,5-d₂(17). The conversion was about 3% after 12 d, 28%

after 30 d, and 53% after 90 d (1.9 kGy/d). Data for salt 17 were

out using the Enraf-Nonius EXPRESS software,⁷⁵while data reduction

and absorption corrections were performed using the Enraf-Nonius

MolEN package.⁷⁶Cell constants were obtained using the SET4

procedure (25 reﬂections).⁷⁷Data collection was carried out at 294 K.

Completeness for all data collections was 100%. From the systematic

absences, the observed metric constants, and intensity statistics, space

̅

group P1 was considered initially; subsequent solution and reﬁnement

conﬁrmed the correctness of this choice. The asymmetric unit of the

pristine crystal contains one-half of a hexaaquamagnesium cation, one

hydrate water molecule, and one disordered trans-butenoate anion (for

the title complex, Z′ = 0.5). The structure was solved using SIR-92⁷⁸

and reﬁned (full-matrix-least-squares) using the Oxford University

Crystals for Windows program.⁷⁹All non-hydrogen atoms were reﬁned

using anisotropic displacement parameters. After location of H atoms

on diﬀerence maps, H atoms attached to O were reﬁned using isotropic

displacement parameters, while H atoms attached to C were ﬁxed at

calculated positions and reﬁned using riding contraints.⁸⁰The solution

and reﬁnement process is of two types: (i) two-component disorder of

reactant butenoates in the four pristine crystals and (ii) four-

component disorder for all of the remaining 22 reﬁnements; there are

two disordered orientations of reactant butenoates as before, but now

there are also two orientations of product hexenedicarboxylates (see

Figures 5 and 6 in the main text). For the pristine crystals the only

constraint needed was that the sum of the occupancies of the two

disordered butenoates sum to 1.0. For the remaining 22 determi-

nations, three general restraints, as described in Results and Discussion,

ensured a stable and consistent reﬁnement. The restraint that the ratio

of major/minor product occupancies and the ratio of major/minor

reactant occupancies are expected to be equal was tested by a free

reﬁnement of the two ratios; no signiﬁcant diﬀerence was observed.

Additionally, a small number (ca. 10−15) of distance and angle

restraints (but no vibrational parameter restraints) were used in all of

the four-component disorder reﬁnements (i.e., all of the crystals

irradiated with γ-rays). Results of the reﬁnements may be seen in the

tables cited, and additional details of the standard geometric restraints

applied appear in the individual CIF ﬁles.

1

determined from the mixture: H NMR (D₂O, referenced to internal

dioxane at δ 3.75) 5.09 (s, 1), 5.02 (s, 1), 2.88 (d, 1, J = 11.0), 2.37 (dd,

1, J = 11.0, 11.0), 1.41 (qd, 1, J = 7.3, 11.0), 0.85 (d, 3, J = 7.3).

X-ray Data Collections for Pristine and Irradiated Hexaa-

quamagnesium trans-2-Butenoate Dihydrate (12). Initial experi-

ments suggested that, unlike other metal trans-2-butenoate materials we

studied, 12 undergoes a crystal-to-crystal solid-state reaction.¹⁻⁴The

experimental plan involved using six crystals, with the hope that three to

four would survive the required months of γ-irradiation without

degradation (dehydration-cum-loss of crystal quality had been

previously observed). Six crystals were selected and coated with

̈

perﬂuoropolyether (Riedel-de Haen, RS 3000). The coated crystals

were then placed into glass capillaries (Charles Supper Company),

aﬃxed to the capillary walls with epoxy and the capillaries sealed using a

hot wire. The capillaries were then set into specially designed 1/8 in.

brass pins, modeled after those used in the early Philips PAILRED

diﬀractomter (Figure 14). The capillaries were epoxied to the pin at the

Preparation of Sodium trans-2-Butenoate (1). A solution of

trans-2-butenoic acid (3.000 g, 34.8 mmol) in 20 mL of H₂O was

neutralized with 3.0 M sodium hydroxide to the phenolphthalein end-

point. The solution was concentrated under reduced pressure (20

Torr) until a cloudy mixture formed. Acetone (25 mL) was added to

precipitate a transparent, cellophane-like polycrystalline material. The

precipitate was isolated by ﬁltration, washed with acetone, and dried in

vacuo (0.25 Torr) over CaSO₄to aﬀord 3.748 g (99.6%) of 1: ¹H NMR

(D₂O) 6.65 (dq, 1, J = 15.5, 6.8), 5.83 (dq, 1, J = 15.5, 1.6), 1.79 (dd, 3, J

= 6.8, 1.6); IR (KBr) 3040, 1660, 1560, 970 cm⁻¹.

γ-Irradiation of 1. Preparation of rel-(2S,3S,4R,5S)-2,4-

Dimethyl-6-heptene-1,3,5-tricarboxylic Acid (3b). Salt 1 (3.24

g, 29.9 mmol) was γ-irradiated for 13 d (150−250 kGy). The resulting

colorless powder was dissolved in water (20 mL) to give a

homogeneous solution that was acidiﬁed with concentrated hydro-

chloric acid (3.5 mL) to give a colorless precipitate. The precipitate was

isolated by ﬁltration and dried in vacuo (0.25 Torr) over CaSO₄to give

1.40 g (55%) of 3b as a colorless powder. mp 203−205 °C; ¹H NMR

(DMSO-d₆) 12.2 (s, 3, OH), 5.85 (ddd, 1, J = 16.5, 10.9, 8.6), 5.11 (br

d, 1, J = 10.9), 5.10 (dd, 1, J = 16.5, 2.9), 2.89 (dd, 1, J = 8.6, 6.4), 2.37−

2.29 (m, 3), 2.10 (ddq, 1, J = 6.4, 7.1, 7.1), 1.88 (dd, 1, J = 15.3, 10.5),

0.95 (d, 3, J = 6.7), 0.93 (d, 3, J = 6.7); ¹³C NMR (DMSO-d₆) 174.8

(C), 173.8 (C), 173.4 (C), 136.0 (CH), 117.5 (CH₂), 53.9 (CH), 52.2

(CH), 36.6 (CH₂), 35.4 (CH), 28.3 (CH), 19.1 (CH₃), 13.3 (CH₃); IR

(KBr) 1721, 1706, 990, 906 cm⁻¹. Anal. Calcd for C₁₂H₁₈O₆: C, 55.81;

H, 7.02. Found: C, 56.08; H, 7.05. Irradiation of the peak at δ 2.89

changed the peaks at δ 5.85 (dd, 1, J = 16.5, 10.9) and 2.10 (dq, 1, J =

7.1, 7.1). Irradiation of the peak at δ 2.10 changed the peaks at 2.89 (d,

1, J = 8.6), 2.33 (sharper), and 0.93 (s, 3).

Figure 14. Glass capillary mounting pin used in this work.

drilled opening, and also at a milled-out opening halfway down the pin

body. One side of the pin had previously been milled ﬂat so that the

crystal and its pin could be removed for placement in the irradiator, and

later replaced in the goniometer with the setscrew against the ﬂat

surface, such that the original orientation matrix could be used to quickly

align the crystal and begin a data collection. At the time of this

experimental work, a CCD machine was not available in our laboratory,

nor was a low-temperature device. Data were collected at RT on an

Enraf-Nonius CAD-4 Turbo diﬀractometer equipped with Mo Kα

radiation. After data collection, crystals were irradiated for various times

with ⁶⁰Co γ-rays at Brandeis University (Gammacell 220 Irradiator, as

described in the main paper), and two crystals were given a further dose

of 650 kGy at University of Massachusetts, Lowell. A summary of

experimental details appears in Tables 1A and 1B, and full data for

crystals 1−4 appear in Tables S2_0 through S2_110_65m.

A total of 26 structure determinations were carried out (4 crystals × 6

irradiation periods + 2 crystals × 1 irradiation at University of

Massachusetts, Lowell). The careful reader will notice that around/

after the 16-day irradiation point, the unit cell axes, which have been

undergoing small changes, change from their original order of a < b < c

to a < b > c. CheckCIF assigns an Alert C error (“The unit cell is not

reduced”) at this time, but of course we need to retain the original axis

setting in order to provide a straightforward comparison of each stage of

the reaction. All operations were performed on an Enraf-Nonius CAD-4

Turbo diﬀractometer, using a normal-focus sealed tube (graphite-

monochromated Mo Kα radiation). A 1.0 mm collimator was used for

all experiments, as crystals were large (0.6−0.8 mm) and could not be

cut without shattering. All diﬀractometer manipulations were carried

Trimethyl rel-(2S,3S,4R,5S)-2,4-Dimethyl-6-heptene-1,3,5-

tricarboxylate (3c). A solution of triacid 3b (0.180 g, 0.698 mmol)

in 5 mL of isopropanol was treated with diazomethane in ether⁶⁵until

the light-yellow color of diazomethane persisted. The solution was

dried (MgSO₄) and concentrated in vacuo to aﬀord 205 mg (98%) of

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3c as a colorless oil: mp 27−30 °C; ¹H NMR (CDCl₃) 5.89 (ddd, 1, J =

17.0, 10.3, 9.0), 5.16 (br d, 1, J = 10.3), 5.13 (br d, 1, J = 17.0), 3.68 (s,

3), 3.67 (s, 3), 3.65 (s, 3), 2.99 (dd, 1, J = 9.0, 5.9), 2.56−2.34 (m, 3),

2.29 (ddq, 1, J = 5.9, 6.7, 6.7), 2.09 (dd, 1, J = 15.3, 10.6), 1.02 (d, 3, J =

6.8), 0.98 (d, 3, J = 6.4); ¹³C NMR 174.2 (C), 173.5 (C), 173.0 (C),

134.6 (CH), 118.6 (CH₂), 54.6 (CH), 53.1 (CH), 51.7 (CH₃), 51.6

(CH₃), 51.1 (CH₃), 36.2 (CH₂), 21.8 (CH), 19.2 (CH₃), 14.2 (CH₃);

IR (neat) 3080, 1745, 1740, 1640, 995, 915 cm⁻¹.

Analysis of 3c by capillary GC (Heliﬂex, 30 m × 0.25 mm; 60−150

°C at 10 degrees/min, 5 min isothermal, 150−190 °C at 20 degrees/

min, 8 min isothermal; detector temperature 280 °C, injector

temperature 240 °C) gave 6 peaks (% of total integration): 11.8 min

(1%), 12.4 min (94%, 3c), 12.8 min (2%), 14.0 min (1%), 15.0 min

(1%), and 15.8 min (2%). This indicates that crude 3c is 94% pure and

that triacid 3b precipitates in similar purity.

γ-Irradiation of 21 Under Air. Crystalline 21 (100 mg, 0.90

mmol) was placed in a glass vial, capped, and subjected to 650 kGy

(32.5 h, University of Massachusetts, Lowell) γ-rays. A 10 mg portion of

the sample was dissolved in water and acidiﬁed with concentrated HCl

(2 drops). No precipitate was observed. Another 10 mg of sample was

dissolved in D₂O for NMR analysis. Integration of the spectrum

indicated that the major component (60%) was starting material 21.

Approximately 21% of trimer 22a was also observed. Another product

(16%) was sodium trans-2,3-epoxybutanoate-2-d (23a): ¹H NMR

(D₂O) 3.10 (q, 1, J = 4.9), 1.33 (d, 3, J = 4.9). This data matches the

published data for the potassium salt of trans-2,3-epoxybutanoate:⁶⁷¹H

NMR (D₂O) 3.17 (d, 1, J = 2.4), 3.11 (dq, 1, J = 2.4, 5.1), 1.35 (d, 3, J =

5.1). Finally, other peaks (4−5%) were observed from uncharacterized

products: ¹H NMR (D₂O) 4.59 (d, J = 6.1), 4.21 (d, J = 4.2), 1.17 (d, 3,

J = 6.7).

Preparation and Crystal Growth for Polymorphs of Sodium

trans-2-Butenoate (1). Form 1_I. Sodium trans-2-butenoate was

readily prepared by neutralizing a solution of trans-2-butenoic acid with

NaOH (1 M) to the phenolphthalein end-point. The solubility was

assessed, and numerous methods for crystal growth were attempted,

including crystallization from water and methanol as well as mixtures of

those solvents with EtOH, DMSO, DMF, triethylene glycol, acetone,

CHC1₃, and Et₂O. Methods included slow evaporation between −10

and 50 °C, doping (dyestuﬀs) of aqueous solutions,⁸¹evaporation at

reduced pressure, and crystal growth in gels/Sephadex G-25. The

highest-quality crystals were obtained by slow evaporation of a 1:1

H₂O:DMSO solution at room temperature. Salt 1 is highly soluble in

H₂O (solubility = 720 g L⁻¹), and nucleation almost invariably occurs at

the solution suface. The result is very thin “cellophane-like” crystals

with a high degree of mosaicity (ω ≈ 2° from Weissenberg

photography). The chosen mixed solvent system appears to decrease

the rate of crystallization, and thus, higher-quality crystals form.

Form 1_II (for Room-Temperature Structure Determination).

Sodium hydroxide (0.80 g, 20 mmol) was added to a stirred solution of

trans-2-butenoic acid (1.96 g, 20 mmol) in 40 mL of 1:1 EtOH: H₂O.

The mixture was stirred at 25 °C for 4 h and ﬁltered. The ﬁltrate was

placed in a 100 mL glass crystallizing dish and allowed to evaporate at

RT. The dish was covered with a Kimwipe held in place with a rubber

band. Several holes were punctured in the Kimwipe with a needle.

Crystals of 1_II are very thin and fragile, so extra care was needed to

avoid deformation. Colorless thin plate-like crystals were observed on

the surface of the solution after 2 weeks. The crystals were carefully

removed from the glass dish using a spatula and dried on ﬁlter paper.

Form 1_II (for Low-Temperature Structure Determination).

Sodium hydroxide (0.811 g, 0.0203 mol) was dissolved in 40 mL of a

1:1 mixture of ethanol and H₂O. To the solution, 1.958 g (0.0227 mol)

of trans-2-butenoic acid and 3 mL of dimethyl sulfoxide were added; the

reaction mixture was stirred for 4 h, ﬁltered, and allowed to evaporate

slowly. Colorless, very thin ﬁlm-like crystals of Form 1_II were

obtained from the top of the solution after 3 weeks of slow-evaporation.

The crystals were carefully transferred to a glass slide and immediately

covered with Paratone oil prior to the X-ray analysis.

X-ray Data Collection, Solution, and Reﬁnement for 1_I. All

operations were performed on a Syntex P2₁serial diﬀractometer, a

graphite-monochromator, and normal-focus, sealed tube Mo Kα

radiation. A 1.5 mm collimator was used for all experiments, as the

crystals were large (max. dimension ca. 1.2 mm), mica-like in

appearance and physical nature, and could not be cut without

deformation. Data collection was carried out at 294 K. All

diﬀractometer manipulations, including data collection, integration,

scaling, and absorption corrections, were carried out using the Syntex

data collection software.⁸²Initial data reduction, absorption correc-

tions, solution, and reﬁnement were performed using the Syntex XTL

package on a Nova 1200 32k computer.⁸³Completeness was 100%.

From the systematic absences, the observed metric constants and

intensity statistics, space groups P2₁or P2₁/m (both with Z′ = 2) were

considered initially. However, while a plausible structure was obtained,

reﬁnements would not yield R factors below ca. 22%. Further work on

the problem was abandoned at that time. We decided to re-examine the

data and solution at the time that this paper was in preparation. We

Gas Chromatographic Analysis of γ-Irradiated 1. Another

irradiated sample of 1 was acidiﬁed, concentrated without removal of

the precipitated 3b, taken up in ether, and treated with diazomethane to

give a mixture of methyl esters. GC analysis as above gave 8 peaks (% of

total integration): 4.6 min (0.4%), 5.2 min (12%, 20c), 5.7 min (1.2%),

11.8 min (6%), 12.4 min (68%, 3c), 12.8 min (7%), 15.0 min (2%), and

15.8 min (3%). Samples eluting at 4.6−5.8 min (100−120 °C) are

dimers; samples eluting at 11.8−12.8 min (150 °C) are trimers, and

samples eluting at 15.0−15.8 min (150−170 °C) are tetramers.

Capillary GC analysis of methyl 3-hydroxybutanoate (4.8 min), diester

2d (4.9 min), dimethyl (E)-2-ethylidene-3-methylpentandioate (5.3

min),⁶⁶and dimethyl (Z)-2-ethylidene-3-methylpentandioate (7.2

min)⁶⁶gave peaks distinct from those observed in the chromatograms

obtained from samples of irradiated 1. A sample of both diastereomers

of dimethyl 2-ethenyl-3-methylpentanedioate (20c)⁶⁶eluted with the

major byproduct at 5.2 min in the samples of irradiated 1. Therefore,

acid 3b is the major product (68%) and precipitates selectively upon

acidiﬁcation.

The mother liquor resulting from acidiﬁcation of irradiated 1 and

removal of the precipitated 3b by ﬁltration was concentrated, taken up

in ether, and treated with diazomethane to give a mixture of methyl

esters. GC analysis as above gave 8 peaks (% of total integration): 4.6

min (1%), 5.2 min (22%, 20c), 5.7 min (1%), 11.8 min (5%), 12.4 min

(57%, 3c), 12.8 min (11%), 15.0 min (1%), and 15.8 min (2%). Not all

of the triacid 3b precipitates upon acidiﬁcation because it is still the

major product in solution after removal of all the precipitated 3b.

Preparation of Sodium trans-2-Butenoate-2-d (21). trans-2-

Butenoic-2-d acid⁴(1.00 g, 12 mmol) was dissolved in 20 mL of water

and sodium hydroxide (0.47 g, 12 mmol) was added. The reaction

mixture was stirred at room temperature for 1 h and concentrated under

reduced pressure to give a colorless solid that was washed with acetone

to remove any excess acid and dried to give 1.2 g (96%) of 21 as a

colorless solid, mp >220 °C.

γ-Irradiation of 21 Under Nitrogen. Preparation of rel-

(1R,2S,3S,4R,5S)-2,4-Dimethyl-6-heptene-1,3,5-tricarboxylic-

1,3,5-d₃Acid (22b). Crystalline 21 (100 mg, 0.90 mmol) was placed

in a 3 mm inside diameter glass tube and packed tightly using a glass

rod. A septum was placed at the rim of the glass tube, and the sample

was evacuated for 3 min. The sample was then placed under nitrogen for

3 min and sealed using an air/gas ﬂame. The sample was subjected to

500 kGy (25 h, University of Massachusetts, Lowell) γ-rays. The

product was isolated by dissolving the sample in 2 mL of water and

adding a few drops of concentrated hydrochloric acid to form a

colorless precipitate that was collected and dried to give 11 mg of a 9:1

mixture of triacid 22b and unreacted acid trans-2-butenoic-2-d acid as a

colorless solid: ¹H NMR (DMSO-d₆) 5.83 (dd, 1, J = 10.4, 17.0), 5.10

(br d, 1, J = 10.4, 1.8), 5.09 (dd, 1, J = 17.0, 1.8), 2.22 (dq, 1, J = 11, 6.7),

2.07 (q, 1, J = 6.9), 1.85 (d, 1, J = 11.0), 0.933 (d, 3, J = 6.9), 0.918 (d, 3,

J = 6.7). Residual peaks for trans-2-butenoic-2-d acid were observed at δ

6.81−6.86 (m, 1) and 1.83 (d, 3, J = 6.7). Irradiation of the peak at δ

0.91 showed NOEs to the peaks at δ 1.85, 2.07, 2.22. Irradiation of the

peak at δ 2.07 showed an NOE to the peak at δ 0.918. Irradiation of

peak at δ 2.22 showed NOEs to the peaks at δ 1.85 (small), 0.918, and

0.933. Irradiation of the peak at δ 5.83 showed NOEs to the peaks at δ

5.09 and 5.10.

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observed the tell-tale signature of twinning in a plot of F_oversus F_cand

noted both (a) that many of the h + k odd reﬂections were weak and (b)

that the two “independent” molecules in the asymmetric unit were

almost perfectly C-centered. A reasonable hypothesis appeared to be

that the crystals were twinned and that the lattice was NOT primitive,

rather C-centered, with h + k odd reﬂections nonzero owing to twinning

and/or stacking faults. Accordingly, the space group was changed to

C2/m, which has one-half molecule in the asymmetric unit (Z = 4; Z′ =

0.5), with the Na atom and the C1−C2 bond residing on the

crystallographic mirror plane, and the β- and γ-carbon (C3 and C4)

collection, integration, scaling, and absorption corrections, were carried

out using the Bruker Apex2 software.⁸⁸Preliminary cell constants were

obtained from three sets of 12 frames. Data collection was carried out at

120 K, using a frame time of 40 s and a detector distance of 60 mm. The

optimized strategy used for data collection consisted of two phi and two

omega scan sets, with 0.5° steps in phi or omega; completeness was

100.0%. A total of 1730 frames were collected. Final cell constants were

obtained from the xyz centroids of 402 reﬂections after integration.

From the systematic absences, the observed metric constants and

intensity statistics, space group C2/c was chosen initially; subsequent

solution and reﬁnement conﬁrmed the correctness of this choice. The

structure was solved using SIR-92,⁷⁸and reﬁned (F², full-matrix-least-

squares) using the Oxford University Crystals for Windows program.⁷⁹

The asymmetric unit contains one molecule of the title complex (Z = 8;

Z′ = 1). Reﬁnement led quickly to a ﬁnal R value of 0.0857; however, a

plot of F_oversus F_csuggested that the crystal was a twin. The structure

was then analyzed using ROTAX;⁸⁴a TLQS twin⁸⁵with a 180° rotation

about [100]⁸⁶and an obliquity^85,86of 0.732° was chosen and reﬁned

with the constraint that the scale factors for the two twin laws sum to

1.0. At the conclusion of the reﬁnement, the twin laws and their

occupancies were ([1 0 0/0 1 0/0 0 1], 0.939(6); [1 0 0/0 −1 0/−0.006

0 −1], 0.061(6)). After location of H atoms on electron-density

diﬀerence maps, the H atoms were initially reﬁned with soft restraints

on the bond lengths and angles to regularize their geometry (C−H in

the range of 0.93−0.98 Å and U_iso(H) in the range 1.2−1.5 times U_eqof

the parent atom), after which the positions were reﬁned with riding

constraints.⁸⁰The atom C1 was reﬁned by using a thermal similarity

restraint to atom C2. The ﬁnal least-squares reﬁnement converged to R

= 0.0692 (I > 2σ(I), 416 data) and R_w= 0.1172 (F², 794 data, 65

parameters). The ﬁnal CIF is available in the deposited CIF ﬁles.

atoms disordered. The data were then analyzed using ROTAX;⁸⁴

a

TLQS twin⁸⁵with three twin laws was found: in addition to the parent

crystal, a 180° rotation about (100) or [502]⁸⁶and an obliquity^85,86of

0.15° and a rotation about [413] or (100) with an obliquity of 3.52°

were chosen and reﬁned with the constraint that the scale factors for the

three twin laws sum to 1.0. At the conclusion of the reﬁnement, the twin

laws and their occupancies were ([100/010/001], 0.703(2); [0.980

0.497 1.491/0.017 −0.996 0.013/0.010 0.002 −0.993] 0.089(2); 1 0

0.843/0 −1 0/0 0 −1], 0.208(2)). The structure was solved using SIR-

92⁷⁸and reﬁned on F (full-matrix least-squares) using the Oxford

University CRYSTALS for Windows package.⁷⁹All non-hydrogen atoms

were reﬁned using anisotropic displacement parameters. After location

of H atoms on diﬀerence maps, H atoms were initially reﬁned with soft

restraints on the bond lengths and angles to regularize their geometry

(C−H in the range 0.93−0.98 Å) and U_iso(H) (in the range of 1.2−1.5

times U_eqof the parent atom); then H atom positions were reﬁned by

using riding constraints.⁸⁰The ﬁnal R value including the h + k odd data

is 0.1376, a decrease of ca. 9% from the previous solution. R for the C2/

m model without the h + k odd reﬂections is 0.0672, suggesting that the

twin model is incomplete, but likely represents the major chemical

features of the structure. R for the model reﬁned with I_obsﬁltering is

0.0870,⁸⁷which, once again, suggests an incomplete model. The ﬁnal

ﬁle is available in the deposited CIF ﬁles.

ASSOCIATED CONTENT

* Supporting Information

The Supporting Information is available free of charge at

https://pubs.acs.org/doi/10.1021/acs.cgd.0c01466.

■

sı

X-ray Data Collection, Solution, and Reﬁnement for 1_II at

Room Temperature. All diﬀractometer manipulations were carried

out at 294 K on a CAD-4U diﬀractometer, equipped with graphite-

monochromator and a normal-focus Cu Kα sealed tube. Data collection

was managed with the Enraf-Nonius EXPRESS software,⁷⁵while data

reduction and absorption corrections were performed using the Enraf-

Nonius MolEN package.⁷⁶Cell constants were obtained using the

SET4 procedure (25 reﬂections).⁷⁷From the systematic absences, the

observed metric constants, and intensity statistics, space group C2/c

was chosen initially; subsequent solution and reﬁnement conﬁrmed the

correctness of this choice. Inspection of the three standard reﬂections

indicated that the crystal had decayed dramatically (intensity decreased

by 85.6%) during the data collection; a decay correction was applied

during data reduction, but the data collection had to be abandoned at

ca. 75% completeness; additional suitable crystals were not available.

The structure was solved using SIR-92⁷⁸and reﬁned (F, full-matrix-

least-squares) using the Oxford University Crystals for Windows

program.⁷⁹The asymmetric unit contains one molecule of the title

complex (Z = 8; Z′ = 1). Although a plot of F_oversus F_csuggested

twinning was present, either trying a few low-obliquity laws observed in

other crystals or using ROTAX⁸⁴failed to ﬁnd any applicable twin laws.

No twinning was observed. After location of H atoms on electron-

density diﬀerence maps, the H atoms were initially reﬁned with soft

restraints on the bond lengths and angles to regularize their geometry

(C−H in the range 0.93−0.98 Å and U_iso(H) in the range 1.2−1.5 times

U_eqof the parent atom), after which the positions were reﬁned with

riding constraints.⁸⁰The ﬁnal least-squares reﬁnement converged to R

= 0.1073 (I > 1.96σ(I), 373 data) and R_w= 0.2638 (F, 841 data, 65

parameters). The ﬁnal CIF is available in the deposited CIF ﬁles. This

determination, with its faults, is included to provide evidence of the

similarity in cell constants of Polymorphs 1_I and 1_II. No signiﬁcant

diﬀerences were observed between the distances and angles observed

for 1_II at 294 and 120 K.

Figures S1 through S3; Tables S1, S2_0 through

S2_110_65m, S3; correspondence between structure ID

and CCDC number (Table S4); ¹H NMR spectra of 2a,

3b, 15, 17, and 22b (PDF).

Figures 5 and 6.pptx: animations of the “before and after”

positions for the major and minor organic reactants and

products from γ-irradiation of crystalline hexaaquamag-

nesium trans-2-butenoate dihydrate (ZIP)

Mechanism.pptx: animations of the radical chain

mechanism for the major and minor organic reactants

and products from γ-irradiation of crystalline hexaaqua-

magnesium trans-2-butenoate dihydrate (ZIP)

Accession Codes

CCDC 2039295−2039323 contain the supplementary crystallo-

graphic data for this paper. These data can be obtained free of

charge via www.ccdc.cam.ac.uk/data_request/cif, or by email-

ing data_request@ccdc.cam.ac.uk, or by contacting The Cam-

bridge Crystallographic Data Centre, 12 Union Road, Cam-

bridge CB2 1EZ, UK; fax: +44 1223 336033.

AUTHOR INFORMATION

Corresponding Authors

■

Barry B. Snider − Department of Chemistry, Brandeis

University, Waltham, Massachusetts 02453-2728, United

States; orcid.org/0000-0002-2680-6104; Email: snider@

brandeis.edu

Bruce M. Foxman − Department of Chemistry, Brandeis

University, Waltham, Massachusetts 02453-2728, United

States; orcid.org/0000-0001-5707-8341;

Email: foxman1@brandeis.edu

X-ray Data Collection, Solution, and Reﬁnement for 1_II at

Low Temperature. All operations were performed on a Bruker-

Nonius Kappa Apex2 diﬀractometer, using graphite-monochromated

Mo Kα radiation. All diﬀractometer manipulations, including data

679

https://dx.doi.org/10.1021/acs.cgd.0c01466

Cryst. Growth Des. 2021, 21, 663−682

Crystal Growth & Design

Authors

Wen Shang − Department of Chemistry, Brandeis University,

Waltham, Massachusetts 02453-2728, United States;

orcid.org/0000-0002-6984-3060

Roxana F. Schlam − Department of Chemistry, Brandeis

University, Waltham, Massachusetts 02453-2728, United

States; orcid.org/0000-0003-3322-1750

Magali B. Hickey − Department of Chemistry, Brandeis

University, Waltham, Massachusetts 02453-2728, United

States

Jingye Zhou − Department of Chemistry, Brandeis University,

Waltham, Massachusetts 02453-2728, United States

Kraig A. Wheeler − Department of Chemistry, Brandeis

University, Waltham, Massachusetts 02453-2728, United

States; orcid.org/0000-0001-6752-7542

pubs.acs.org/crystal

Article

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Graciela C. Diaz de Delgado − Department of Chemistry,

Brandeis University, Waltham, Massachusetts 02453-2728,

United States; orcid.org/0000-0001-5511-4230

Chun-Hsing Chen − Department of Chemistry, Brandeis

University, Waltham, Massachusetts 02453-2728, United

States; orcid.org/0000-0003-0150-9557

Complete contact information is available at:

https://pubs.acs.org/10.1021/acs.cgd.0c01466

Notes

The authors declare no competing ﬁnancial interest.

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ACKNOWLEDGMENTS

■

We thank Dr. David Watkin and Professor Richard Cooper of

Oxford University for helpful discussions and guidance on

complex reﬁnement issues involving disorder and twinning,

Professor Gerhard Wegner of the Max Planck Institut fur

̈

Polymerforschung for stimulating discussions and suggestions

which led to the deuterium-labeling experiments, the late

Professor Howard Flack of the University of Geneva for helpful

discussions on twinning, and the late Professor Dan Sandman

for facilitating the use of the ⁶⁰Co γ-irradiator at the University of

Massachusetts, Lowell. The work described here spanned three

decades and was supported in part by the National Science

Foundation, Grants DMR 8812417, 9221487, 9629994,

0089257, and 0504000; we are most grateful for that support.

(19) Lauher, J. W.; Fowler, F. W.; Goroff, N. S. Single-Crystal-to-

Single-Crystal Topochemical Polymerizations by Design. Acc. Chem.

Res. 2008, 41, 1215−1229.

(20) Hall, A. V.; Yufit, D. S.; Apperley, D. C.; Senak, L.; Musa, O. M.;

Hood, D. K.; Steed, J. W. The crystal engineering of radiation-sensitive

diacetylene cocrystals and salts. Chem. Sci. 2020, 11, 8025−8035.

(21) Matsumoto, A.; Furukawa, D.; Mori, Y.; Tanaka, T.; Oka, K.

Change in Crystal Structure and Polymerization Reactivity for the

Solid-State Polymerization of Muconic Esters. Cryst. Growth Des. 2007,

7, 1078−1085.

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