Topological and electronic influences on magnetic exchange coupling in Fe(III) ethynylbenzene dendritic building blocks

ARTICLE

pubs.acs.org/JACS

Topological and Electronic Influences on Magnetic Exchange

Coupling in Fe(III) Ethynylbenzene Dendritic Building Blocks

Wesley A. Hoﬀert,^†Anthony K. Rappꢀe, and Matthew P. Shores*

Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523-1872, United States

S Supporting Information

b

ABSTRACT: Signiﬁcant variance in the magnitude of reported exchange

coupling parameters (both experimental and computed) for paramagnetic

transition metalꢀethynylbenzene complexes suggests that nuances of the

magnetostructural relationship in this class of compounds remain to be

understood and controlled, toward maximizing the stability of high-spin

ground states. We report the preparation, electrochemical behavior, magnetic

properties, and results of computational investigations of a series of iron

ethynylbenzene complexes with coordination environments suitable for

metallodendrimer assembly: [(dmpe)₂FeCl(C₂Ph)](OTf) (1), [(dmpe)₄-

Fe₂Cl₂(μ-p-DEB)](BAr^F) (2), [(dmpe)₆Fe₃Cl₃(TEB)] (3), [(dmpe)₆-

4 2

Fe₃Cl₃(μ₃-TEB)](OTf)₃(4), and [(dmpe)₄Fe₂Cl₂(μ-m-DEB)](BAr^F) (5) [dmpe = 1,2-bis(dimethylphosphino)ethane;

4 2

p-H₂DEB = 1,4-diethynylbenzene; BAr^F₄= tetrakis[3,5-bis(triﬂuoromethyl)phenyl]borate; H₃TEB = 1,3,5-triethynylbenzene;

m-H₂DEB = 1,3-diethynylbenzene]. As expected, the ligand topology drives the antiferromagnetic coupling in 2 (J = ꢀ134 cm^ꢀ1

ꢀ1

using the H = ꢀ2JS₁S₂convention) and the ferromagnetic coupling in 4 and 5 (J = +37 cm , J⁰= +5 cm^ꢀ1for 4; J = +11 cm^ꢀ1for

^

^ ^

3

5); the coupling is comparable to but deviates signiﬁcantly from values reported for related Cp*-containing species (Cp* = η⁵-

C₅Me₅). The origins of these diﬀerences are explored computationally: a density functional theory (DFT) approach for treating the

coupling of three spin centers as a linear combination of single-determinantal descriptions is developed and described, and the

results of these computations can be generalized to other paramagnetic systems. Unrestricted B3LYP hybrid DFT calculations

performed on rotamers of 4 and 5 and related complexes, as well as Cp* analogues, provide J values that correlate with the

experimental values. We ﬁnd that geometric considerations dominate the magnetism of the Cp* complexes, while topology and

alkynyl ligand electronics combine more subtly to drive the magnetism of the new complexes reported here. These calculations

imply that substantial magnetic exchange parameters, with accompanying well-isolated high-spin ground states, are achievable for

ethynylbenzene-bridged paramagnetic metallodendrimers.

’ INTRODUCTION

ground state (S) and a negative molecular easy-axis magnetic

anisotropy (D), as deﬁned in eq 1:

In search of increased processor speeds, larger data storage

densities, and improved material and energy eﬃciencies, recent

eﬀorts have focused on the control of charge and/or spin at the

molecular level. Employing carbon-rich ligands as bridges for

metal ion species represents a promising route in that the ligands

are tunable by well-established synthetic methods and often dis-

play good orbital and energetic overlap with the metal ends.

Especially relevant to technological applications are polyyne

ligands bridging redox-active metal centers: they have been

shown to be exceptional conduits for electricity at the nanoscale,

and this discovery in turn has energized the relatively new ﬁeld of

molecular electronics.^1,2

Enhancing intramolecular communication is also vital to the

development of nanoscale magnets. Research in single-molecule

magnet (SMM) clusters has progressed from the discovery of

slow magnetic relaxation in a Mn₁₂O₁₂molecule³to the isolation

of hundreds of molecular species that show similar properties,^4,5

including a recent report of magnetic hysteresis in a dinuclear

terbium complex at a record-high temperature of 14 K.⁶The

origin of this phenomenon is rooted in the combination of a high-spin

2

^

H ¼ DS_zþ EðS_xþ S_yÞ

ð1Þ

Importantly, for species where exchange interactions dominate,

the coupling constants (J) must be maximized in order to avoid

populating lower-spin excited states. In this regard, rigid, highly

conjugated bridging ligands might be anticipated to generate

robust magnetic coupling over long distances as a result of

tailor-made orbital communication pathways.⁷We note that

SMM behavior was recently observed for the ﬁrst time in mono-

and dinuclear organometallic lanthanide complexes,^8,9but to our

knowledge, only one SMM where magnetic communication

occurs through a noncyanide carbon linkage is known.¹⁰

Here, arylalkynyl ligands based on 1,3,5-triethynylbenzene

(H₃TEB) avail themselves as potential candidates for generating

strong magnetic exchange coupling and perhaps negative zero-

ﬁeld splitting parameters.^11ꢀ13The deprotonated congeners

Received: July 26, 2011

Published: November 08, 2011

r

2011 American Chemical Society

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Journal of the American Chemical Society

ARTICLE

have been employed as bridging ligands in second- and third-row

transition-metal metallodendrimers because of their rigidity and

amenability to a regular spatial arrangement of many diamagnetic

transition metals around a C₆H₃core.^14ꢀ17Although some

paramagnetic ethynylbenzene-bridged complexes are known,

the reported coordination environments of the metal ions are

not suitable for elaboration to larger assemblies. It has been

shown that these ligands may permit signiﬁcant spin commu-

nication between transition-metal centers, but the strength of the

coupling appears to be dependent on subtle and not well under-

stood factors. Lapinte and co-workers synthesized an impressive

array of paramagnetic [(dppe)(Cp*)Fe^III]-containing complexes

[dppe =1,2-bis(diphenylphosphino)ethane; Cp* = η⁵-C₅Me₅)

with various acetylide connecting ligands in order to study their

magnetic and charge-transfer properties.^18ꢀ24The exchange cou-

pling constants extracted for the triferric complex [(dppe)₃-

(Cp*)₃Fe^III₃(TEB)](PF₆)₃are relatively small at 9.6 and 4.4 cm^ꢀ1

strong exchange coupling and well-isolated high-spin ground

states.

’ EXPERIMENTAL SECTION

Preparation of Compounds. Manipulations were performed

inside a dinitrogen-filled glovebox (MBRAUN Labmaster 130). Pentane

was distilled over sodium metal and subjected to three freezeꢀ

pumpꢀthaw cycles prior to use. Other solvents were sparged with

dinitrogen, passed over alumina, and degassed prior to use. The pre-

parations of [(dmpe)₄Fe₂Cl₂(μ-p-DEB)] (p-H₂DEB = 1,4-diethyny-

lbenzene),³⁰[(dmpe)₂FeCl(C₂Ph)],³⁰[(dmpe)₂FeCl(C₂SiMe₃)](PF₆),³³

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)],³³[(dmpe)₂FeCl₂],³⁴[Cp₂Fe]BAr^F

(Cp = η⁵-C₅H₅; BAr^F₄= tetrakis[3,5-bis(trifluoromethyl)phenyl]borate),³⁵⁴

[Cp₂Fe]PF₆,³⁶[Cp*₂Fe]PF₆,³⁶and H₃TEB³⁷have been described else-

where. All other reagents were purchased commercially and used without

further purification.

(using the H = ꢀ2JS₁S₂convention).¹⁹Meanwhile, in regard to

trans-[(dmpe)₂FeCl(C₂Ph)](OTf) (1). A solution of AgOTf

(33.4 mg, 0.130 mmol) in 5 mL of acetonitrile was added to a solution

of [(dmpe)₂FeCl(C₂Ph)] (61.1 mg, 0.124 mmol) in 5 mL of dichloro-

methane. The solution color immediately turned dark-blue-green. The

solution was stirred for 1 h and then filtered, and the filtrate was dried in

vacuo. The resulting solid was recrystallized by slow diffusion of diethyl

ether vapor into a concentrated solution of the crude product in

dichloromethane. After 1 day, large dark-blue-green crystals were iso-

lated by filtration, washed with diethyl ether (3 ꢁ 5 mL), and dried

under vacuum for 1 h at 293 K to afford 65 mg of product (0.101 mmol,

82%). IR (mineral oil mull) ν_CtC: 2031 cm^ꢀ1. ¹H NMR (CD₂Cl₂): δ

27.85 (br, 2H, m-ArꢀH), ꢀ20.35 (br, 16H, ꢀPCH₃, ꢀPCH₂), ꢀ23.74

(br, 12H, ꢀPCH₃), ꢀ24.38 (br, 4H, ꢀPCH₂), ꢀ27.32 (br, 2H,

o-ArꢀH), ꢀ28.06 (br, 1H, p-ArꢀH). ESI-MS(+) (CH₂Cl₂): m/z 492

([1 ꢀ OTf]⁺). UVꢀvis (CH₂Cl₂) λ_max/nm (ε_M/M^ꢀ1cm^ꢀ1): 361 (sh,

4930), 411 (1240), 544 (sh, 800), 606 (3290), 732 (9490). Anal. Calcd

for C₂₁H₃₇ClF₃FeO₃P₄S: C, 39.30; H, 5.81. Found: C, 39.30; H, 5.68.

^

^ ^

3

related m-diethynylbenzene-bridged dinuclear complexes, the

ferromagnetic coupling for [(dppe)₂(Cp*)₂Fe^III₂(m-DEB)]-

(PF₆)₂(m-H₂DEB = 1,3-diethynylbenzene) was found to be

signiﬁcantly stronger (J = 65 cm^ꢀ1); a recent reinvestigation by

Paul and co-workers found that the triplet ground state is fully

populated at 300 K, implying a ferromagnetic exchange strength

of at least 150 cm^{ꢀ1 25}

Diﬀerences in the reported magnetic

.

exchange coupling values have been attributed to impurities^18,26

and to varying coordination geometries and relative orientations

of spin-containing orbitals.^27,28

Relevant to the incorporation of ﬁrst-row transition metals

into ethynylbenzene-based dendrimers, Field and others pre-

pared Fe^IIand Fe^IIIσ-acetylide complexes with a (P₄)(σ-C)(Cl)

ﬁrst coordination sphere and studied their electrochemical and

intervalence charge-transfer properties.^29ꢀ32Since these types of

species contain the necessary coordination geometry for stepwise

ligand substitution, an examination of the magnetic properties for

the individual “building blocks” is needed for the properties of

larger assemblies to be more easily understood. Berben has found

that trans,trans-[(dmpe)₄Fe₂Cl₂(m-DEB)](PF₆)₂[dmpe =1,2-

bis(dimethylphosphino)ethane] is consistent with a coupling

constant of 41 cm^ꢀ1, a value that is in line with Lapinte’s earliest

report on the Cp* analogue.³³All of these results suggest that

under certain circumstances, strong magnetic coupling may be

produced by alkynylbenzene bridging ligands, provided that

robust magnetostructural correlations can be established.

In view of the variance found in the magnetic and theoretical

treatments applied to a relatively small number of ethynylbenzene-

bridged complexes, a systematic study of the factors involved

in magnetic exchange is warranted. Herein we present the

syntheses, magnetic characterizations, and results of computa-

tional investigations of a family of di- and trinuclear complexes

containing [(dmpe)₂Fe^IIICl] units connected by DEB^2ꢀand

TEB^3ꢀbridging ligands. We compare magnetic data obtained

on the new complexes with those for the previously reported, struc-

turally similar species. We describe a novel density functional

theory (DFT) approach for treating the coupling of three spin

centers as a linear combination of single-determinantal descrip-

tions and place all of the complexes in the same computational

framework, allowing subtle diﬀerences in the geometries and

electronic structures of the complexes to be related to the

observed magnetic properties; the results of these computations

can be generalized to other paramagnetic systems. We ﬁnd that

[(dmpe)₂Fe^IIICl]-based alkynyl complexes oﬀer the potential for

[(dmpe)₄Fe₂Cl₂(μ-p-DEB)](BAr^F) (2). A solution of [Cp₂Fe]-

4 2

BAr^F₄(107 mg, 0.102 mmol) in 5 mL of dichloromethane was added to

a solution of [Cl₂(dmpe)₄Fe₂(μ-p-DEB)] (46 mg, 0.051 mmol) in 5 mL

of dichloromethane. The solution color immediately turned dark-green.

After the solution was stirred for 10 min, the solvent was removed in

vacuo. Pentane (5 mL) was added to precipitate a green solid. The solid

was isolated by filtration, washed with pentane (3 ꢁ 5 mL) to remove

residual [Cp₂Fe], and recrystallized by slow diffusion of pentane vapor

into a concentrated solution of the crude product in dichloromethane.

After 1 day, dark-green crystals were isolated by filtration, washed with

pentane (3 ꢁ 3 mL), and dried under vacuum for 1 h at 293 K to afford

109 mg of product (0.041 mmol, 81%). Crystals suitable for X-ray

analysis were obtained by allowing a solution of 2 in a 3:1 (v/v) pentane/

dichloromethane mixture to stand in a ꢀ40 °C freezer for 3 days. IR

(mineral oil mull) ν_CtC: 2017 cm^ꢀ1. ¹H NMR (CD₂Cl₂): δ 7.49 (br,

16H, BArꢀH), 7.44 (br, 8H, BArꢀH), ꢀ1.22 (br, 4H, ArꢀH), ꢀ14.99

(br, 24H, ꢀPCH₃), ꢀ15.22 (br, 8H, ꢀPCH₂), ꢀ18.11 (br, 32H, ꢀPCH₂,

ꢀPCH₃). UVꢀvis (CH₂Cl₂) λ_max/nm (ε_M/M^ꢀ1cm^ꢀ1): 403 (10 278),

475 (8442), 606 (4624), 747 (23 210), 837 (15 184). Anal. Calcd

for C₉₈H₉₂B₂Cl₂F₄₈P₈Fe₂: C, 44.69; H, 3.52. Found: C, 44.47; H,

3.55.

[(dmpe)₆Fe₃Cl₃(μ₃-TEB)] (3). Freshly distilled triethylamine

(0.2 mL, 1.43 mmol) was added to a solution of [(dmpe)₂FeCl₂]

(117 mg, 0.274 mmol) and freshly sublimed H₃TEB (13.7 mg,

0.0913 mmol) in methanol (12 mL). The solution color immediately turned

orange. After an additional 1 h of stirring, an orange solid precipitated.

This solid was isolated by filtration, washed with methanol (3 ꢁ 3 mL)

and pentane (3 ꢁ 3 mL), and then dried in vacuo for 1 h at 293 K to

afford 52 mg of product (0.039 mmol, 43% based on H₃TEB). IR

(mineral oil mull) ν_CtC: 2035 cm^ꢀ1. ¹H NMR (C₆D₆): δ 6.50 (s, 3H,

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Journal of the American Chemical Society

ARTICLE

Table 1. Crystallographic Data^afor the Compounds [(dmpe)₂FeCl(C₂Ph)](OTf) (1), [(dmpe)₄Fe₂Cl₂(μ-p-DEB)](BAr^F) (2),

4 2

and [(dmpe)₆Fe₃Cl₃(μ₃-TEB)](CF₃SO₃)₃(4)^b

1

2

4

formula

C₂₁H₃₇ClF₃FeP₈O₃F₃S

641.75

C₉₈H₉₂B₂Cl₂F₄₈Fe₂P₈

2633.70

C₅₀H₉₉Cl₃F₆Fe₃O₆P₁₂S₂

fw (g/mol)

color, habit

T (K)

1619.97

blue prism

120(2)

Pbcm

blue prism

100(2)

green block

100(2)

space group

Z

P2₁2₁2₁

4

P1

1

4

a (Å)

12.8296(3)

14.3749(4)

15.8508(4)

90

13.4127(7)

14.1127(7)

17.5241(10)

66.8130(10)

67.9560(10)

81.356(2)

2826.3(3)

1.547

15.5873(6)

28.0448(12)

21.4267(10)

90

b (Å)

c (Å)

α (deg)

β (deg)

90

γ (deg)

V (Å³)

d_calcd(g/cm³)

90

2923.3(1)

1.458

9366.5(7)

1.149

GOF

1.008

1.049

1.054

R₁^c(wR₂)^d(%) [I > 2σ(I)]

2.40 (5.40)

4.08 (10.45)

5.43 (17.83)

^aObtained with graphite-monochromatized Mo Kα radiation (λ = 0.71073 Å). ^bData for [(dmpe)₄Fe₂Cl₂(μ-m-DEB)](BAr^F) (5) are included in

4 2

Table S1 in the SI. ^cR₁= ∑||F_o| ꢀ |F_c||/∑|F_o|. ^dwR₂= {∑[w(F_oꢀ F_c²)²/∑[w(F_o) ]}^1/2

.

2

2 2

ArꢀH), 1.60 (br, 24H, ꢀPCH₂), 1.39 (br, 72H, ꢀPCH₃). ³¹P NMR

(C₆D₆): δ 66.33 (s, 12P, FeꢀP). ¹³C NMR (C₆D₆): δ 130.26 (s, 3C,

C_ArH), 127.21 (s, 3C, C_ArCtC), 120.84 (s, 3C, CtCꢀFe), 84.82 (d,

3C, CtCꢀFe), 30.64 (p, 12C, CH₂), 16.02 (s, 12C, CH₃), 13.76 (s,

12C, CH₃). ESI-MS(+) (CH₂Cl₂): m/z 1320.00 ([3]⁺). UVꢀvis

(CH₂Cl₂) λ_max/nm (ε_M/M^ꢀ1cm^ꢀ1): 248 (122 500), 363 (77 500),

466 nm (1800). Anal. Calcd for C₄₈H₉₉Cl₃P₁₂Fe₃: C, 43.61; H, 7.55.

Found: C, 43.34; H, 7.29.

into a concentrated solution of the crude product in dichloromethane.

After 2 days, dark-blue crystals were isolated by filtration, washed with

pentane (3 ꢁ 3 mL), and dried under vacuum for 1 h at 293 K to afford

53 mg of product (0.020 mmol, 80%). IR (ATR) ν_CtC: 2021 cm^ꢀ1. ¹H

NMR (CD₂Cl₂): δ 46.85 (br s, 1H, ArꢀH), 7.46 (s, 16H, BArꢀH), 7.41

(s, 8H, BArꢀH), ꢀ19.29 to ꢀ20.56 (br m, 32H, ꢀPCH₃, ꢀPCH₂),

ꢀ21.93 to ꢀ22.54 (br m, 8H, ꢀPCH₃, ꢀPCH₂), ꢀ24.15 to ꢀ24.42 (br

m, 24H, ꢀPCH₃, ꢀPCH₂), ꢀ55.79 (br s, 1H, ArꢀH), ꢀ57.35 (br s, 2H,

ArꢀH). Anal. Calcd for C₉₈H₉₂B₂Cl₂F₄₈P₈Fe₂: C, 44.69; H, 3.52.

Found: C, 44.93; H, 3.40.

[(dmpe)₆Fe₃Cl₃(μ₃-TEB)](OTf)₃(4). To an orange slurry of 3

(30 mg, 0.023 mmol) in acetonitrile (10 mL) was added a solution of

AgOTf (17.5 mg, 0.068 mmol) in acetonitrile (3 mL). The solution

immediately turned blue-green. The mixture was stirred for 20 min and

then filtered to remove silver metal, and the solvent was removed from

the filtrate in vacuo. The solid was stirred with diethyl ether (10 mL) for

30 min at 293 K. The blue-green solid was isolated by filtration and

recrystallized by slow diffusion of diethyl ether vapor into a concentrated

solution of the crude product in dichloromethane. After 1 day, blue-

green crystals were isolated by filtration, washed with diethyl ether

(3 ꢁ 3 mL), and dried in vacuo for 1 h at 293 K to afford 34 mg of

product (0.019 mmol, 83%). Although X-ray analysis suggested that as

many as six molecules of dichloromethane are included in crystals of

4 (see below), samples for elemental analysis were sealed under vacuum,

X-ray Structure Determinations. Compounds 1, 2, 4, and 5

were characterized by single-crystal X-ray analysis [Table 1 and Table S1

in the Supporting Information (SI)]. Crystals were coated in Paratone

oil prior to removal from the glovebox, supported on Cryoloops, and

mounted on a Bruker Kappa Apex 2 CCD diffractometer under a stream

of cold dinitrogen. All data collections were performed with Mo Kα

radiation and a graphite monochromator. Initial lattice parameters were

determined from a minimum of 112 reflections harvested from

36 frames; these parameters were later refined against all data. Data sets

were collected targeting complete coverage and fourfold redundancy.

Data were integrated and corrected for absorption effects with the Apex

2 software package.³⁸Structures were solved by direct methods and

refined with the SHELXTL software package.³⁹Displacement para-

meters for all non-hydrogen atoms were refined anisotropically with the

exception of disordered carbon, phosphorus, and fluorine atoms. Hydrogen

atoms were added at the ideal positions and refined using a riding model

in which the isotropic displacement parameters were set at 1.2 times

those of the attached carbon atom (1.5 times for methyl carbons). Two

of the trifluoromethyl groups in the structure of 2 were disordered. The

CF₃disorder was modeled using a two-component treatment with an

independent free variable for each group; the occupancies for each group

refined to 85:15 and 79:21 ratios, respectively. After several attempts to

model extreme anion/solvent disorder in the structures of 4 failed, the

SQUEEZE routine in PLATON was applied.⁴⁰For 4, four 636 Å³voids

were found; each contained 249 electrons. This electron count roughly

corresponds to six dichloromethane molecules. The results for 4 pre-

sented in Table 1 reflect solvent-free data. Both of the triflate anions in

the asymmetric unit of 4 reside on a mirror plane. Refinement of the

allowing the solvent to escape. IR (mineral oil mull) ν_CtC: 2035 cm^ꢀ1

.

¹H NMR (CD₂Cl₂): δ 63.27 (br, 3H, ArꢀH), ꢀ16.69 (br, 36H, ꢀPCH₃),

ꢀ18.07 (br, 12H, ꢀPCH₂), ꢀ21.46 (br, 48H, ꢀPCH₃, ꢀPCH₂). ESI-

MS(+) (MeCN): m/z 1617.80 ([4 ꢀ OTf]⁺), 735.57 ([4 ꢀ 2OTf]²⁺).

UVꢀvis (CH₂Cl₂) λ_max/nm (ε_M/M^ꢀ1cm^ꢀ1): 301 (53 600), 401

(sh, 4290), 544 (sh, 1720), 609 (8100), 732 nm (12 940). Anal. Calcd

for C₅₁H₉₉Cl₃P₁₂F₉S₃O₉Fe₃: C, 34.62; H, 5.64. Found: C, 34.58;

H, 5.35.

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)](BAr^F) (5). A solution of [Cp₂Fe]-

4 2

BAr^F₄(52.3 mg, 0.050 mmol) in 5 mL of dichloromethane was added to

a solution of [Cl₂(dmpe)₄Fe₂(μ-m-DEB)] (22.6 mg, 0.025 mmol) in

5 mL of dichloromethane. The solution color immediately turned dark-

teal. After the solution was stirred for 10 min, the solvent was removed in

vacuo. Pentane (5 mL) was added to precipitate a green solid. The solid

was isolated by filtration, washed with pentane (3 ꢁ 5 mL) to remove

residual [Cp₂Fe], and recrystallized by slow diffusion of pentane vapor

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ARTICLE

positional disorder in one of the triflates was modeled with a two-

component model using a free variable. The occupancies of these two

positions refined to a 70:30 ratio; with the exception of the sulfur atom,

the minor component was refined isotropically. For the structure of 5,

the quality of the data was sufficiently low that only crude connectivity

could be established (Figure S1 in the SI). Crystal data for 5 are

presented in the SI.

were symmetrized; for the second, the [(dppe)(Cp*)Fe] fragments were

rotated about the (P P centroid)ꢀFeꢀ(phenyl plane) dihedral angle

3 3 3

j (see Figure 2c for definition) to align the magnetic orbitals with

the aryl π system. For the series of [(dXpe)₆Cl₃Fe₃(TEB)]³⁺complexes,

the geometry was optimized for X = H [i.e., for 1,2-diphosphinoethane

(dpe)]; XꢀC bond distances were fixed at idealized values.

The current three-center, three-electron doublet system is diﬃcult to

compute with standard literature techniques. The broken-symmetry

projection approaches of Noodleman⁵⁴and Soda⁵⁵are problematic

here: the present systems contain three low-spin broken-symmetry

states (ααβ, αβα, and βαα, corresponding to placing the β spin on

each of the three Fe centers) but only two actual doublets. Sum rules⁵⁶

and spin-ﬂip^57ꢀ59approaches are appropriate when the individual

determinants are degenerate (not generally true) but do not treat

coupling between the two doublet states. To estimate the magnetic

interactions, the high-spin quartet and three M_S= ¹/₂spin-ﬂip “doublet”

microstates were computed. Spin natural orbitals derived from the

Magnetic Susceptibility Measurements. Magnetic suscept-

ibility data were collected with a Quantum Design MPMS-XL SQUID

magnetometer. In the glovebox, finely ground samples were loaded into

gelatin capsules and inserted into straws. The straws were sealed in

plastic bags prior to removal from the glovebox and quickly loaded into

the instrument to minimize exposure to air. Data were corrected for the

magnetization of the sample holder by subtracting the susceptibility of

an empty container and for diamagnetic contributions of the sample by

using Pascal’s constants.⁴¹Theoretical fits to the susceptibility data for 2

and 5 were obtained using a relative error minimization routine (julX

1.4.1)⁴²with a Hamiltonian of the form H = ꢀ2JS₁S₂. The best fits to

^

ground-state quartet were used to generate starting guesses for the three

3

1

the data for trinuclear 4 were obtained with MAGFIT 3.1⁴³using a three-

possible single-spin-ﬂip M_S

=

/

states for each of the trinuclear

2

^

^ ^

complexes. Magnetic J values were estimated using eqs 2ꢀ4, and the

energy diﬀerences are deﬁned in eqs 5ꢀ7. Further details are provided

in the SI.

center isosceles spin Hamiltonian of the form H = ꢀ2J(S₁S₃) ꢀ

3

0

^ ^

^

2J(S₂S₃) ꢀ 2J (S₁S₂).

3

Other Physical Measurements. Electronic absorption spectra

were obtained in air-free cuvettes with a Hewlett-Packard 8453 spectro-

photometer. IR spectra were measured with a Nicolet 380 FT-IR

spectrophotometer using either mineral oil mulls sandwiched between

NaCl plates or a Smart Performer ZnSe attenuated total reflectance

(ATR) accessory. ¹H NMR spectra were recorded on a Varian INOVA

instrument operating at 300 MHz. Electron paramagnetic resonance

(EPR) spectra were obtained using a continuous-wave X-band Bruker

EMX 200U instrument outfitted with a liquid nitrogen cryostat. Com-

pounds were dissolved in a 1:1 mixture of dichloromethane and 1,2-

dichloroethane to form a glass at low temperature. Cyclic voltammetry

experiments were done in 0.1 M solutions of (Bu₄N)PF₆in dichlor-

omethane. Cyclic voltammograms (CVs) were recorded with a CH

Instruments potentiostat (model 1230A or 660C) using a 0.25 mm Pt

disk working electrode, Ag/Ag⁺reference electrode, and Pt mesh

auxiliary electrode. All CVs shown were measured at a scan rate of

0.1 V/s. Reported potentials are referenced to the [Cp₂Fe]⁺/[Cp₂Fe]

(Fc⁺/Fc) redox couple and were determined by adding ferrocene as an

internal standard at the conclusion of each electrochemical experiment.

Elemental analyses were performed by Robertson Microlit Laboratories

(Madison, NJ).

1

J₁₃

J₂₃

J₁₂

¼

ðΔE_ααβꢀ ΔE_αβαþ ΔE_βαα

ðΔE_ααβꢀ ΔE_βααþ ΔE_αβα

ðΔE_αβαꢀ ΔE_ααβþ ΔE_βαα

Þ

ð2Þ

ð3Þ

ð4Þ

2

1

2

1

2

ΔE_ααβ¼ E_ααβꢀ E_ααα

ΔE_αβα¼ E_αβαꢀ E_ααα

ΔE_βαα¼ E_βααꢀ E_ααα

ð5Þ

ð6Þ

ð7Þ

The quartet and doublet energies were obtained from eqs 8 and 9,

respectively:

1

E_Q¼ ꢀ ðJ₁₂þ J₁₃þ J₂₃Þ

ð8Þ

2

Electronic Structure Calculations. In general, unrestricted

B3LYP hybrid DFT studies⁴⁴and time-dependent DFT (TD-DFT)/

natural transition orbital (NTO) analyses were carried out using the

Gaussian 09 suite of electronic structure codes.⁴⁵Given the presence of

low-lying excited states, difficult-to-converge wave functions were con-

verged using a quadratically convergent procedure.⁴⁶The possible

presence of lower-energy wave function solutions was investigated using

a stability check protocol.⁴⁷LANL2⁴⁸basis sets and effective core

potentials were used for Fe and P atoms; the 6-31G* or polarized

Dunning valence double-ζ basis sets were used for the remaining atoms,

as noted.^49ꢀ52For [(dmpe)₆Cl₃Fe₃(TEB)]³⁺(the cation of 4), geome-

ꢀ

ꢁ

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1

2

E_{D =D}

¼

J₁₂þ J₁₃þ J₂₃( 2 J₁₂þ J₂₃þ J₁₃ꢀ J₁₂J₁₃ꢀ J₁₂J₂₃ꢀ J₁₃J₂₃

1

2

ð9Þ

It should be noted that when J₁₂= J₁₃= J and J₂₃= γJ, the doublet

energies reduce to the literature expressions^60ꢀ62E_D= 2J ꢀ γJ and

E_D= ³/₂γJ. When J₁₂= J₁₃= J₂₃= J, the doublet energie¹s simplify further

2

to E_{D /D}= ³/₂J.

Th¹e r²elative stabilities and characters of the ﬁve d orbitals of each

magnetic iron center were assessed using a TD-DFT/NTO analysis of

the mononuclear fragments [(dmpe)₂FeCl(C₂H)]⁺,[(dmpe)₂ClFe(C₂Ph)]⁺

(the cation of 1), and [(dppe)(Cp*)Fe(C₂Ph)]⁺. Fragment geometries

were extracted from the trinuclear complexes, with the exception that

the FeꢀC distance was varied from 1.800 to 2.300 Å for [(dppe)(Cp*)-

Fe(C₂Ph)]⁺and from 1.907 to 2.397 Å for [(dmpe)₂ClFe(C₂Ph)]⁺for

two dmpe rotamers, one parallel and the other perpendicular to the

phenylacetylide aromatic ring.

tries for four idealized (P P centroidꢀFe)ꢀ(phenyl plane) orienta-

3 3 3

tional isomers (having different values of the torsion angle j defined in

Figure 2c) were optimized for the quartet ground state. Except as noted,

the optimization studies used FeꢀP distances constrained to 2.28 Å.

For [(dmpe)₄Cl₂Fe₂(p-DEB)]²⁺(the cation of 2) and [(dmpe)₄Cl₂Fe₂-

(m-DEB)]²⁺(the cation of 5), geometries were optimized for the lowest-

energy (P P centroidꢀFe)ꢀ(phenyl plane) orientational isomers.

3 3 3

For [(dppe)₃(Cp*)₃Fe₃(TEB)]³⁺, two structures were considered: for

the first, the coordinates from the Fe(II) crystal structure⁵³were used

with C(sp³)ꢀH bonds set to 1.09 Å and C(sp²)ꢀH bonds set to 1.07 Å,

and CꢀC bond distances for the alkynylaromatic bridging framework

’ RESULTS AND DISCUSSION

Syntheses and Characterizations. The preparations of the

di- and triethynylbenzene-bridged complexes are outlined in

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Scheme 1. Syntheses of Ethynylbenzene Complexes 1ꢀ5

Figure 1. Cyclic voltammogram of 3 in dichloromethane.

and Berben; the CVs for the corresponding ferric complexes 1,

2, and 5 are identical to those except for the value of the rest

potential, consistent with oxidation of Fe^IIto Fe^III.

The previously reported electrochemical behavior of [(dmpe)₄-

Fe^IICl₂(μ-p-DEB)] shows two reversible one-electron redox

2

waves centered at ꢀ0.69 and ꢀ0.49 V vs Fc⁺/Fc.³⁰These waves

correspond to the formation of the mixed-valent [Fe^IIIFe^II] and

diferric [Fe^IIIFe^III] complex cations in solution. Interestingly, the

comproportionation constant is much larger for [(dppe)₂-

(Cp*)₂Fe₂(p-DEB)]ⁿ⁺(K_com= 2.6 ꢁ 10⁴)⁶³than for

[(dmpe)₄Cl₂Fe₂(p-DEB)]ⁿ⁺(K_com= 2.4 ꢁ 10³), indicating

stronger FeꢀFe electronic communication in the Cp*-ligated

species. On the basis of the CV data, the BAr^Fsalt 2 can be prepared

4

by oxidizing the neutral [Fe^II] complex with 2 equiv of [Cp₂Fe]PF₆.

2

Scheme 1. The neutral (diferrous) form of complex 2, [(dmpe)₄-

Fe^IICl₂(p-DEB)], was previously described by Field and co-

For the trinuclear complexes, Lapinte and co-workers pre-

viously reported the isolation of mono- and diferric derivatives of

[(dppe)₃Fe₃(Cp*)₃TEB)]ⁿ⁺complexes on the basis of the

presence of three well-separated redox waves (ΔE_1/2= 0.130 V)

for the neutral complex in dichloromethane solution.^53,30The m-

phenylene bridges in 3 and 5 would be expected to engender

weaker coupling than the p-phenylene and Cp* variants^53,63

because of the lack of cumulenic/quinoidal character in the

overall bonding structure for complexes with an m-DEB

bridge.^25,64Indeed, the CV for 3 shows one broad redox wave

centered at ꢀ0.59 V with a peak-to-peak separation of 186 mV

(Figure 1). The appearance of shoulders at ca. ꢀ0.61 and ꢀ0.64 V

indicates that multiple redox processes occur on the electro-

chemical time scale, but the lack of resolution is consistent with

weaker communication between metal centers, similar to the

behavior observed for the dinuclear complexes. On the basis of

the electrochemical data, the triferric complex 4 can be synthe-

sized by combining 3 with 3 equiv of AgOTf in acetonitrile. The

purity of 4 was conﬁrmed by microanalysis and ¹H NMR

spectroscopy. The ¹H NMR spectrum contains broad, paramag-

netically shifted peaks from aromatic, methyl, and ethylene protons,

and resonances from precursor 3 are not present in the ¹H NMR

spectrum of 4 (Figure S5a in the SI). The mononuclear ferric

complex 1 was prepared in a similar fashion.

2

workers;³⁰the synthesis of the trinuclear complex 3 was adapted

from that report. The hexafluorophosphate analogue of 5,

[(dmpe)₄Fe^IICl₂(p-DEB)](PF₆)₂, has been synthesized by

2

Berben,³³and a similar synthetic procedure was adopted here.

Related compounds with (Cp*)(dppe)Fe units coordinated to

bridging ethynylbenzene ligands have also been reported by

Lapinte.^19,23,53,63For the preparation of the ferrous compounds,

Field and co-workers’ efforts indicated that [(dmpe)₂FeCl₂]

undergoes solvolysis in methanol to generate [(dmpe)₂Fe-

(MeOH)Cl]⁺, which interacts with the ethynylbenzene ligand,

presumably forming a vinylidene complex. The vinylic proton is

then captured by triethylamine to form the iron acetylide

complex product, which precipitates cleanly from the reaction

mixture. The purity of 3 was verified by combustion analysis,

1

mass spectrometry, and H, ³¹P, and ¹³C NMR spectroscopy

(Figures S2ꢀS4, respectively, in the SI). The ¹H NMR spectrum

contains a sharp resonance corresponding to the aromatic protons in

addition to broad resonances from the ethylene and methyl protons

of the dmpe ligands. A single sharp resonance in the ³¹P spectrum

confirms the trans coordination geometry about each Fe(II) ion.

Cyclic voltammetry studies aﬀord the potentials required for

oxidation to Fe^IIIspecies and serve as a probe of the electronic

coupling between iron ions. CVs for the ferrous complexes

[(dmpe)FeCl(C₂Ph)],³⁰[(dmpe)₄Fe₂Cl₂(μ-p-DEB)],³⁰and

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)]³³have been reported by Field

All of the compounds were characterized by FT-IR spectros-

copy. As a result of π back-bonding from iron, the ethynylben-

zene-bridged complexes exhibit a single ν_CtCresonance at lower

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Figure 2. X-ray structures of the complex cations in (a) 1 and (b) 2,

with red, purple, green, and gray ellipsoids/spheres corresponding to Fe,

P, Cl, and C atoms, respectively. Thermal ellipsoids are rendered at 40%

probability. H atoms in all structural plots have been omitted for clarity.

A rendering for 5 is presented in Figure S1 in the SI. (c) Deﬁnition of the

torsion angle j as viewed down the ClꢀFeꢀC axis; Cl has been omitted

for clarity.

Figure 3. (a) X-ray structure of the complex cation in 4, with H

atoms removed for clarity. (b, c) Views of the cation along the (b) Cl1ꢀ

Fe1ꢀC₂and (c) Cl2ꢀFe2ꢀC₂axes, with H atoms and methyl groups

omitted for clarity. See Figure 2 for color coding. All thermal ellipsoids

are rendered at 40% probability.

energies relative to the free acetylene compounds. The acetylide

stretching frequency in 2 decreases to 2017 cm^ꢀ1versus

2042 cm^ꢀ1in the neutral complex. Coincidentally, the acetylide

stretches for redox-related 3 and 4 both occur at 2035 cm^ꢀ1

.

As expected, orange solutions of ferrous 3 quickly turn blue-

green in air, indicating oxidation of the Fe^IIcenters to Fe^III. In the

solid state, ferric 1, 2, 4, and 5 maintain their structural con-

nectivity in air for period of at least 1 day, as determined by IR

spectroscopy. A gradual change in color upon exposure to air for

dichloromethane solutions of ferric 1, 2, 4, and 5 from blue-green

to green was observed over several days; the identities of the

decomposition products were not determined.

X-ray Structures. The crystal structures of all of the complexes

presented herein reveal a pseudo-octahedral coordination geo-

metry around each iron center (Figures 2 and 3). The equatorial

positions are occupied by four phosphorus atoms from the

bidentate dmpe ligands, while the chloride and bridging-

acetylide-containing ligands are located at the axial positions.

The acetylide ligands in the cations of all of the structures impart

a rigid connectivity, leading to essentially linear CꢀCꢀFe angles;

the greatest deviation from linearity is 2.8° in the structure of 2.

The average FeꢀC bond lengths are 1.8750(12), 1.871(2), and

1.876(6) Å for complexes 1, 2, and 4, respectively. Other relevant

bond distances and angles are comparable to those of related

complexes in the literature.^24,29,63,65

roughly perpendicular to the central phenyl ring (j = 36.9°).

The Fe atoms reside at the vertices of an isosceles triangle; the

Fe1 Fe2 and Fe1 Fe2a distances are 10.184(1) Å, while

3 3 3

the Fe2 Fe2a distance is 10.389(1) Å. Examination of the

3 3 3

packing plot (Figure S6 in the SI) reveals that the cationic

complexes are arranged in two-dimensional layers parallel to the

crystallographic ab plane. These arrays are separated from one

another by triﬂate anions, and the interlayer distance as measured

from the aromatic ring is ∼10.713(2) Å. When viewed down the

c axis, the cations form inﬁnite stacks that are perfectly eclipsed.

The shortest cationꢀanion distance is 3.3(3) Å and it occurs

between one of the Fe1 dmpe ethylene carbons (C14) and an

oxygen atom from one of the triﬂates (O1). The large estimated

standard deviation for this interatomic distance is likely the result

of libration eﬀects in the triﬂate molecule. While this is not an

obvious hydrogen-bonding interaction, the packing eﬀect never-

theless appears to inﬂuence the orientation of the dmpe ligands

on Fe1, causing them to be twisted out of registry with respect to

the dmpe ligands coordinated to Fe2 and Fe2a.

The structure solution for compound 5 established the atomic

connectivity and provided an estimate of relevant structural

metrics. However, the relatively poor resolution for crystals of

5 precluded a rigorous analysis of bond lengths from the X-ray

data, and the presence of dmpe ligand disorder could not be ruled

out. Similar crystallographic challenges were encountered by

Berben in the disclosure of the structure of the hexﬂuoropho-

sphate analogue of 5.¹⁵

For 4, two of the Fe atoms (Fe2 and Fe2a) are related by a

crystallographic twofold rotation axis, and the ethylene carbon

atoms of their bidentate dmpe ligands are essentially parallel to

the plane of the aromatic bridging ligand. The torsion angle j,

deﬁned by the P P centroid, the Fe ion, and the two adjacent

3 3 3

carbon atoms on the central aromatic ring, is 82.2° (see Figure 2c

for pictorial deﬁnition of j). In contrast to the environment

around Fe2 and Fe2a, the dmpe ligands coordinated to Fe1 are

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Figure 4. Temperature-dependent magnetic susceptibility data for 2

(blue 0) and the best ﬁt (solid red line).

Figure 5. Raw and TIP-corrected magnetic susceptibility data for 4

obtained in a 1 kOe dc ﬁeld, including best-ﬁt lines from one- and two-J

coupling models. See the text for details of the data adjustment and

ﬁtting procedures. Susceptibility values for [(dmpe)₂FeCl(C₂SiMe₃)]-

(PF₆) at 90, 105, 195, 210, and 225 K were not available for generating

adjusted data points.³³

Magnetic Properties. The magnetic susceptibilities (χ_M)

for all of the Fe^III-containing compounds presented here

(Figures 4ꢀ6 and Figure S13 in the SI) show significant

temperature-independent paramagnetism (TIP), manifested as a

linear increase in χ_MT with increasing temperature and higher-

than-expected room-temperature susceptibilities for the com-

pounds assuming g = 2.00. This issue has been noted previously

for pseudo-octahedral Fe^IIIcomplexes, and its origin has been

attributed to either unquenched orbital angular momentum or

small amounts of paramagnetic iron impurities present in the

sample.^18,22Considering that we used crushed crystalline sam-

ples for magnetic measurements and obtained consistent results

from multiple samples prepared at different times, we believe that

we minimized the paramagnetic impurities, so the magnetic in-

terpretations to be presented reflect intrinsic properties of the

compounds.

The dichloromethane/dichloroethane frozen glass X-band

EPR spectra of mononuclear 1, dinuclear 2, and trinuclear 4

show broad, axial signals at 100ꢀ110 K (Figures S8ꢀS10 in

the SI). The signals for 2 represent the triplet excited state rather

than the diamagnetic singlet ground state: they are similar to

resonances observed for trinuclear 4, albeit much weaker.

Detailed analyses of the spectra for the multinuclear complexes

are complicated by exchange coupling and the relative orienta-

tions of the Fe^III-containing units and will be discussed in a future

report. To ﬁnd a reasonable “isotropic” g value for anchoring the

magnetic susceptibility data ﬁts for the meta-bridged species 4

and 5, we analyzed the EPR spectrum of the mononuclear

phenylacetylide complex salt 1 using the EasySpin software

package.⁶⁶The simulated spectrum that best matched the data

gave the parameters g_x= 1.9419, g_y= 1.9415, and g_z= 2.5681 and

a Lorentzian line width of 75.31 mT. The average of the g_x, g_yand

g_zvalues is 2.150 (Figure S8 in the SI).

correlated in such a way that smaller g values are countered by

large TIP values and vice versa, all yielding comparable ﬁts to the

experimental data, with minor eﬀects on the magnitude of J (see

Table S2 in the SI for more details). When a small amount of

paramagnetic impurity was included to account for the nonzero

χ_MT product below 50 K (S = ¹/₂, 2.1%), the best ﬁt to the raw

data aﬀorded J = ꢀ134 cm^ꢀ1with g = 2.34 and TIP ﬁxed at 600 ꢁ

10^ꢀ6emu. While this coupling constant is robust, it is signiﬁ-

cantly smaller than that reported for similar Cp*-ligated com-

plexes.^24,25The diﬀerences in ligands for the complexes dis-

cussed here likely inﬂuence the propensity of the Fe^IIIion to form

FedC-type interactions.²²In addition, the relative orientations

of the “magnetic” d orbitals with respect to the aromatic π system

inﬂuence the observed J couplings; this will be explored in more

detail below.

For trinuclear 4 (Figure 5), the classical curve shape for a

ferromagnetically coupled system is obscured by the apparent

involvement of unquenched orbital angular momentum. The

susceptibility decreases from 2.00 emu K mol^ꢀ1at 300 K to a

local minimum of 1.79 emu K mol^ꢀ1at 40 K, followed by an

increase to 1.82 emu K mol^ꢀ1at 10 K. Below 10 K, the

susceptibility drops oﬀ rapidly, which may be due to a combina-

tion of weak intermolecular AF interactions, Zeeman splitting,

and/or zero-ﬁeld splitting eﬀects. The value of χ_MT at 10 K is

slightly smaller than the spin-only value expected for a ferro-

3

magnetically coupled S = /₂system with g = 2 (1.875 emu

K mol^ꢀ1).

A similar picture emerges from the raw data for dinuclear 5

(Figure 6). At 300 K, χ_MT is 1.67 emu K mol^ꢀ1. Cooling the

sample results in a monotonic susceptibility decrease to 1.15 emu

K mol^ꢀ1at 40 K. Below 7 K, a more rapid decrease occurs, and

χ_MT is 1.06 emu K mol^ꢀ1at 2 K.

To obtain a proper evaluation of the extent of magnetic com-

munication between the metal centers in 4 and 5, it was useful to

remove unquenched orbital angular momentum contributions

from the raw data to isolate the spin-only and exchange con-

tributions. It should be noted that these contributions, which

The susceptibility data for the para-bridged dinuclear complex

2 are presented in Figure 4. The χ_MT value of 0.79 emu K mol^ꢀ1

at 300 K is just slightly higher than the value of 0.75 emu K mol^ꢀ1

expected for two uncoupled S = ¹/₂centers with g = 2.00). As the

temperature is decreased, χ_MT decreases steadily to 0.07 emu

K mol^ꢀ1at 75 K and then drops more gradually to 0.02

emu K mol^ꢀ1at 4 K. The trend exhibited by 2 indicates that

antiferromagnetic (AF) coupling is operative. In the phenom-

enological ﬁtting protocol, we found that the g and TIP are

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used to analyze the magnetic properties of 5 provides a lower-

bound estimation of J.⁶⁷

The adjusted data for 4 (Figure 5) also show the expected

ferromagnetic coupling of Fe^IIIcenters. The χ_MT value at 300 K

is 1.07 emu K mol^ꢀ1, which is near the value expected for three

uncoupled S = ¹/₂centers with g near 2.00 (1.13 emu K mol^ꢀ1).

The susceptibility increases gradually upon cooling, reaching a

maximum of 1.77 emu K mol^ꢀ1at 8 K, and then decreases

slightly to 1.74 emu K mol^ꢀ1at 5 K. Considering that the Fe^III

ions are located at the vertices of an isosceles triangle and that

one of the (dmpe)₂Fe^IIIgroups is twisted out of registry with

respect to the other two, we ﬁt the data assuming two diﬀerent

exchange coupling constants. The best ﬁts to the 2J model gave

J

₁₂= J₁₃= 5 cm^ꢀ1and J₂₃= 37 cm^ꢀ1with g constrained at 2.15; a

small mean-ﬁeld correction (ꢀ0.84 K, ꢀ0.58 cm^ꢀ1) accounts for

very weak AF interactions between dinuclear complexes. Treat-

ing the data with a single exchange coupling constant between 6

Figure 6. Raw and corrected magnetic susceptibility data for 5 col-

lected in a 1 kOe dc measuring ﬁeld. See the text for details of the

data adjustment and ﬁtting procedures. Susceptibility values for

[(dmpe)₂FeCl(C₂SiMe₃)](PF₆) at 90, 105, 195, 210, and 225 K were

not available for generating adjusted data points.³³

and 300 K yielded a signiﬁcantly diﬀerent J value (J = 12 cm^ꢀ1

;

g = 2.15) and a much poorer ﬁt, especially at low temperature.

Comparison to structurally and magnetically characterized or-

ganic triradicals is meaningful: Iwamura applied an isosceles

model to the susceptibility data for 2-methoxy-1,3,5-benzenet-

riyltris(N-tert-butylnitroxide) and obtained J₁₂= J₁₃= 48 cm^ꢀ1

arise from the spinꢀorbit coupling brought about by near-

degenerate electronic conﬁgurations for each of the Fe^IIIcenters,

were also likely present in 2. However, the eﬀects appeared to be

quenched by the strong intramolecular AF interaction. The

orbital contributions of the low-spin Fe^IIIions in compounds 4

and 5 were eliminated from the data by the following protocol: n

equivalents of the susceptibility for [(dmpe)₂FeCl(C₂SiMe₃)]-

(PF₆)³³were subtracted from the raw data, and then the ligand

susceptibility and the expected spin-only value for n low-spin d⁵

centers with g = 2.15 were added (n = 3 for 4 and 2 for 5). Similar

procedures have previously been applied to magnetic data for

Fe^III-containing species in order to evaluate more accurately the

magnetic coupling interactions in systems where masking eﬀects

were present.^33,67ꢀ70Further details are provided in the SI.

The resulting plot for dinuclear 5 (Figure 6) shows tempera-

ture-dependent magnetic behavior in line with the expected

ferromagnetic coupling of low-spin Fe^IIIions. The value of

χ_MT at 300 K is 0.77 emu K mol^ꢀ1, corresponding to two

uncoupled electrons with a g value slightly larger than 2. The

susceptibility gradually increases upon cooling, reaching a max-

imum value of 0.98 emu K mol^ꢀ1at 6 K. This behavior is entirely

consistent with an S = 1 ground state at low temperature. Unlike

the para-bridged compound 2, where the raw data were used for

ﬁtting, g and J are inversely correlated for the corrected data ﬁt for

5. Thus, gaining insight is possible only when one of the values

can be determined independently. Analysis of the EPR spectrum

for mononuclear 1 (Figure S8 in the SI) aﬀorded an independent

determination of g_iso. Fitting the data with g ﬁxed at 2.15 aﬀorded

J = +11 cm^ꢀ1. In the ﬁt, a small mean-ﬁeld correction (ꢀ0.48 K,

ꢀ0.3 cm^ꢀ1) accounts for very weak AF interactions between

dinuclear complexes. The data for 5 are comparable to those for

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)](PF₆)₂obtained by Berben.³³The

magnetic susceptibility data for both compounds were treated

and J₂₃= 3 cm .

^{ꢀ1 62}Interestingly, the ﬁt to the data for 4 indicates

signiﬁcantly stronger magnetic coupling than determined for the

Cp*-containing TEB-bridged triiron complex, where the two

J values were reported to be 9.6 and 4.4 cm .

^{ꢀ1 65}The geometric

and electronic origins of this behavior are explored in the next

section.

Magnetization data collected in direct current (dc) ﬁelds up to

3

5 T support the assignment of an S = /₂ground state for 4

(Figure S7 in the SI), as the magnetization appears to saturate at

∼3 Nμ_B. The presence of axial magnetic anisotropy is evidenced

by a slight non-overlap of the isoﬁeld lines and tracking of all of

the magnetization data below the Brillouin function predicted for

S = ³/₂, g = 2.13. For comparison, a slight non-superposition of

isoﬁeld lines was observed by Holland and co-workers⁷²in a low-

coordinate Fe(II) complex: there it was reported that both |D|

and |E| were very large (E ≈ D/3). Preliminary alternating

current (ac) susceptibility studies for 4 carried out at zero applied

dc ﬁeld showed no frequency dependence in the out-of-phase

susceptibility component, indicating that at least at zero applied

dc ﬁeld, 4 does not behave as an SMM.

Magnetostructural Correlations in the TEB-Bridged Com-

plexes. A comparison of the electrochemical data for 3 and

[(dppe)₃(Cp*)₃Fe₃(TEB)] suggests that electronic communica-

tion between the Fe ions should be much weaker in the former

complex. We might expect that to translate into weaker magnetic

coupling for 4 versus [(dppe)₃(Cp*)₃Fe₃(TEB)]³⁺. For related

acetylide and nitrile-containing dinuclear complexes, it has been

argued that J scales with the amount of spin that is delocalized on

the bridging ligand.^25,73While this may explain the behavior of

p-DEB-bridged species, where the cumulenic form can be trans-

mitted across the bridge, it is not as helpful for the m-DEB- and

TEB-bridged complexes, where such resonance structures are

not supported. Notwithstanding, the coupling in trinuclear 4 is

clearly much stronger than that found in the Cp-containing

species. In the following, our aims are to explore the magneto-

structural correlations in the m/p-DEB- and TEB-bridged Fe^III

systems and come to a general understanding of spin delocaliza-

tion in ethynylbenzene-bridged complexes.

identically, yet J for the hexaﬂuorophosphate salt is +41 cm^ꢀ1

,

signiﬁcantly higher than the value found for 5. X-ray structural data

for [(dmpe)₄Fe₂Cl₂(μ-m-DEB)](PF₆)₂were not available for

detailed analysis, but the ancillary ligand conformations appear to

be similar to those in 5.³³Comparison to Cp*-containing m-DEB-

bridged Fe^IIIsystems is also telling: coupling constants in those

molecules range from 65 cm^ꢀ1to apparently >150 cm^{ꢀ1 19,25,71}

.

It should be noted that the subtractionꢀreplacement protocol

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Although the crystallographic twofold symmetry in the struc-

ture of 4 justiﬁes use of a two-J ﬁtting model, the more signiﬁcant

contribution to the ferromagnetic coupling in the trinuclear

complex originates from orbital symmetry considerations.

Lapinte and co-workers have interpreted the AF coupling in

polyenediyl-bridged diradicals using criteria developed by

Borden, where the degree of overlap between metal dπ and

ligand π orbitals has a large inﬂuence on the sign and magnitude

of magnetic exchange.^24,27,60,74Berke has nicely illustrated the

dependence of the singletꢀtriplet energy gap on the relative

orientation of the spin centers in a Mn₂C₂complex.²⁸However,

correlation of the exchange to the geometry has not been

considered in detail for the ethynylbenzene-bridged systems.

As described in the SI, a number of computational studies have

been carried out to probe the nature of bridge-mediated mag-

netic coupling, the ﬁrst being a TD-DFT/NTO analysis of the

mononuclear fragment [(dmpe)₂FeCl(C₂H)]⁺(Figure S14 in

the SI). With a B3LYP LANL2/6-31 g* hybrid density functional,

the ground state was found to possess a low-spin d⁵conﬁguration

with one member of the “t_2g” set singly occupied. This magnetic

orbital is has π symmetry with respect to the four phosphorus

centers and is directed between the chelate rings (interchelate).

The lowest-energy excitation takes an electron from the doubly

occupied perpendicular dπ orbital (intrachelate) and places it in

the singly occupied dπ orbital; this excited state is computed to

be 7 kcal/mol above the ground state. Since this energy roughly

corresponds to a 2700 T applied ﬁeld, the only magnetically

accessible state places the unpaired electron in a dπ orbital

directed between the chelate rings. To probe the impact of the

bridging phenyl ring, the above-mentioned TD-DFT/NTO

analysis was repeated for [(dmpe)₂FeCl(C₂Ph)]⁺as a function

of the FeꢀC distance and the orientation (j = 0 and 90°). When

j = 0°, the interchelate dπ orbital is aligned with the phenyl π

system, whereas when j = 90°, the intrachelate dπ orbital is

aligned with the phenyl π system. For j = 0°, the interchelate dπ

orbital was computed to remain singly occupied in the ground

state as the FeꢀC distance was varied from 1.907 to 2.397 Å

(Figure S15a in the SI). For j = 90°, the intrachelate dπ orbital

was computed to be singly occupied in the ground state for short

FeꢀC distances (d_FeꢀC) from 1.907 to roughly 2.020 Å (Figure

S15b). For d_FeꢀC> 2.020 Å, the ground state reverts to the

conﬁguration wherein the interchelate dπ orbital is magnetic

(Figure S15c). When d_FeꢀC= 1.907 Å, the intrachelate dπ orbital

conﬁguration is favored by nearly 7 kcal/mol, whereas when

d_FeꢀC= 2.397 Å, the singly occupied interchelate dπ orbital

conﬁguration is favored by nearly 8 kcal/mol (Figure S15d).

Thus, for short FeꢀC distances, the dπ interaction with the

aromatic π system dominates, while at longer FeꢀC distances

this interaction is diminished and ancillary ligand-ﬁeld eﬀects

control the spin orientation.

dinuclear species are collected in Table S3 in the SI. For the

para-substituted complex 2, the computed J value is roughly half

the magnitude of the observed value. For the meta-substituted

complex 5, J was computed to be nearly the same as the measured

value and half as large as the value reported for the PF₆salt

analogue.³³Empirically, pure density functionals tend to under-

estimate magnetic interactions, though inclusion of exact ex-

change in hybrid functionals such as B3LYP tends to reproduce

magnetic behavior more precisely.⁴⁷

For both the para- and meta-substituted complexes, the

computed conformation maximizes the communication between

the Fe^IIIcenters (j = 6 and 8°, respectively), whereas for the

experimental structures, j = 26° for para-substituted 2 and

deviates signiﬁcantly from j = 0° for meta-bridged 5.⁷⁵It appears

that the diﬀerences between the calculated and observed cou-

pling values are largely the result of diﬀerent orientational geo-

metries.

To understand the magnetism of 4, with the goal of generating

increased interaction, a number of rotational and substitutional

isomers were computationally investigated with d_FeꢀCset to

1.873 Å; UB3LYP energies were computed for the individual

1

quartet and M_S= /₂microstates, and eqs 2ꢀ9 were used to

estimate J as well as the Heisenberg energies (Table S4; see the SI

for details). For the X-ray conformation of [(dmpe)₆Cl₃Fe₃(TEB)]³⁺,

two of the Fe interchelate dπ orbitals are nearly perpendicular

to the aromatic π system. As discussed in the SI, two sets

of low-lying quartet and M_S= ¹/₂microstates were found. The

set consistent with experiment is summarized here. The com-

puted J values are smaller than the observed ones, similar to

the dinuclear calculations. Signiﬁcantly, the pattern of computed

J values (two small, one large) is consistent with experiment

(see Table 2). The presence of one large J value is not consistent

with a model that exclusively uses interchelate magnetic orbitals,

as two of the interchelate dπ orbitals are oriented in the plane

of the aromatic ring rather than being arranged perpendicular

to it, yet a large J remains. Spin density plots for the quartet and

1

individual M_S

=

/ microstates (Figure S17 in the SI)

2

suggest that the same orbitals are spin-active for the quartet

1

and the M_S= /₂microstates. For all four single-determinant

models, the spin density plots of the quartet and spin-ﬂipped

M_S= ¹/₂conﬁgurations (Figure 7 and Figure S17) reveal that one

of the Fe centers utilizes an intrachelate dπ orbital to generate a

signiﬁcant FeꢀFe exchange interaction (Fe2). In eﬀect, from a

structural point of view, one “wrong” orbital is used for coupling.

In addition, the magnetic orbital at Fe1 is canted out of the aryl

π plane. The generality of this observation was conﬁrmed by

comparing computational results for four idealized orientational

conformers: three singly-occupied magnetic orbitals parallel (PPP),

two parallel and one perpendicular (PPA), one parallel and two

perpendicular (PAA), and three perpendicular (AAA) to the central

aryl π system. A schematic representation is presented in Figure 8;

the data are collected in Table S5 in the SI, and the spin density plots

are presented in Figures S18ꢀS21 in the SI. The idealized PPP

conformation with all three iron centers oriented to maximize the

magnetic interactions does yield a substantially stabilized quartet

state, three nearly equivalent J values, and equivalent spin density

Turning to the dinuclear DEB-bridged diradical systems,

unrestricted B3LYP (UB3LYP) DFT was used to compute the

lowest triplet and broken-symmetry M_S= 0 states for the cationic

portions of 2 and 5 at their optimized geometries. The sum-rules

approach of Ziegler, Rauk, and Baerends was used to estimate the

tripletꢀsinglet gap and hence the Heisenberg exchange coupling

constant J (see eq 10):⁵⁶

1

delocalization of each of the three M_S= /₂microstates (Figure

S18). Rotating one interchlelate magnetic orbital out of registry

(PPA) does nearly quench two FeꢀFe interactions, substantially

reducing the doubletꢀquartet gap (Figure S19) and leaving a

1

2J ¼ ΔE ¼ E_ααꢀ ðE_αβþ E_βαÞ

ð10Þ

2

1

The ﬁnal J parameters are presented in Table 2 along with

single M_S= /₂microstate (the one wherein the spin-ﬂipped

experimental values; complete computational results for the

magnetic orbital is in the aryl plane) with signiﬁcant α spin density

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Table 2. Key Experimental and Computed Magnetostructural Parameters for Di- and Trinuclear Ethynylbenzene-Bridged Fe(III)

Complexes

complex

E/C^a

j (deg)

J (cm^ꢀ1

)

ref

[(dmpe)₄Fe₂Cl₂(μ-p-DEB)](BAr^F₄)₂(2)

[(dmpe)₄Fe₂Cl₂(μ-p-DEB)]²⁺

E

28.1, 24.3

ꢀ134

ꢀ83

ꢀ191 (Paul)

ꢀ1 (Lapinte)

ꢀ255

37, 5, 5

36, 2, 2

49, 47, 47

48, 2, 2

51, 2, 2

2, 2, ꢀ2

J = 9.6, J⁰= 4.4

34, 18, 9

67, 67, 66

85, 83, 83

113, 111, 109

11

b

C

E

3.9, 12.5

43.2

b

[(dppe)₂(Cp*)₂Fe₂(μ-p-DEB)](PF₆)₂

25

18

25

b

E

[(dHpe)₂(Cp)₂Fe₂(μ-p-DEB)]²⁺

[(dmpe)₆Fe₃Cl₃(μ-TEB)](OTf)₃(4)

[(dmpe)₆Fe₃Cl₃(μ-TEB)]³⁺X-ray

[(dmpe)₆Fe₃Cl₃(μ-TEB)]³⁺PPP^c

[(dmpe)₆Fe₃Cl₃(μ-TEB)]³⁺PPA^c

[(dmpe)₆Fe₃Cl₃(μ-TEB)]³⁺PAA^c

[(dmpe)₆Fe₃Cl₃(μ-TEB)]³⁺AAA^c

[(dppe)₃(Cp*)₃Fe₃(TEB)](PF₆)₃

[(dppe)₃(Cp*)₃Fe₃(TEB)]³⁺X-ray^d

[(dppe)₃(Cp*)₃Fe₃(TEB)]³⁺PPP^c

[(dHpe)₃(Cp)₃Fe₃(TEB)]³⁺PPP^c

[(dHpe)₃(Cp)₃Fe₃(TEB)]³⁺PPP ^e

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)](BAr^F₄)₂(5)

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)](PF₆)₂

[(dmpe)₄Fe₂Cl₂(μ-m-DEB)]²⁺

C

E

36.9, 83.2, 83.2,

37.4, 83.1, 83.5,

1.3, 5.5, 14.5

7.4, 12.9, 89.4

5.5, 89.2, 87.6

87.5, 88.6, 89.8

0.5, 53.6, 60.7

0.7, 62.3, 62.3

0.7, 1.5, 2.2

0.0, 4.1, 4.2

∼21, 86 ^f

C

E

b

19

b

C

E

b

E

∼30, 80 ^g

5.3, 8.5

41

33

b

C

E

24

[(dppe)₂(Cp*)₂Fe₂(μ-m-DEB)](PF₆)₂

61.7, 59.0

>150 (Paul)

65.3 (Lapinte)

256

25

19

25

b

E

[(dHpe)₂(Cp)₂Fe₂(μ-m-DEB)]²⁺

[(dppe)₂(Cp*)₂Fe₂(μ-m-DEB)]²⁺

[(dHpe)₂(Cp)₂Fe₂(μ-m-DEB)]²⁺X-ray^h

[(dHpe)₂(Cp)₂Fe₂(μ-m-DEB)]²⁺Tⁱ

[(dHpe)₂(Cp)₂Fe₂(μ-m-DEB)]²⁺Sⁱ

C

0, 4.5

0.7, 1.5

0.4, 0.4

0, 4.5

36

47

b

66

b

63

b

^aE = experimental, C = computed. ^bThis work. ^cIdealized structure: P = magnetic orbital parallel to the central aryl π system; A = magnetic orbital

perpendicular to the π system. ^dThese angles were measured from an idealized structure for the triferrous complex [(dppe)₃(Cp*)₃Fe₃(TEB)].

^eGeometry constructed on the basis of the X-ray structure of the dinuclear species in ref 25; approximate C₃symmetry. ^fSee ref 75. ^gA CIF ﬁle was not

available for analysis, and the dmpe ligands are rotationally disordered in the structure. ^hThe geometry was constructed from the X-ray structure in ref 23.

ⁱThe geometry was constructed from the calculated triplet structure in ref 25.

delocalization (Figure S19d). This leads to a large J_Fe1,Fe2and small

J_Fe1,Fe2aand J_Fe2,Fe2a. As discussed above for the X-ray-oriented

calculations, rotating a second interchelate magnetic orbital out of

registry (PAA) does not further reduce J, as again a state is found

where one of the Fe centers, Fe2a, uses an intrachelate magnetic

orbital to maintain the magnetic coupling (note the spin density

plots in Figure S20, where Fe2a uses the structurally incorrect

orbital). Rotation of all three sets of interchelate magnetic orbitals

out of registry (AAA) nearly quenches the magnetic coupling;

nevertheless, the spin density plots for this conﬁguration (Figure

S21) illustrate that a single dπꢀaryl π interaction involving Fe2a

can be maintained. Consistently, spin delocalization of at least one

Fe-based magnetic orbital into the aryl π system can be operative in

the [(dmpe)₂FeCl]²⁺-based molecules, irrespective of the Feꢀ

acetylide orbital orientation. From the standpoint of maximizing J,

however, it is noted that the presence of even one perpendicularly

oriented magnetic orbital gives rise to a low-energy doublet state,

precluding robust isolation of high ground-state spins.

structure vs 23 cm^ꢀ1for the X-ray-determined orientation and

59 cm^ꢀ1as determined experimentally). Whereas ferromagnetic

coupling in organic polyradicals is not perturbed by increased

nuclearity,^10,60others have observed weakened ferromagnetic

coupling as the complex nuclearity increases;⁷⁶if this were operative

in the TEB-bridged system, elaboration to larger metallodendri-

mers would lead to a deleterious diminishment of the stabiliza-

tion of high-spin ground states. To understand these diﬀerences,

a model complex with the dmpe methyl substituents replaced by

H atoms [i.e., using dHpe (more commonly denoted as dpe)

rather than dmpe] was constructed. It should be noted that

Paul and co-workers replaced phenyl groups with H atoms in

their Cp* calculations.²⁵Hydrogen substitution can impact the

sterics of the model as well as the phosphine donor capacity.

Gratifyingly, a near doubling of J as well as the doubletꢀquartet

gap was computed (the energy gap increased from 142 to

220 cm^ꢀ1) without a signiﬁcant change in geometry (Table S6

and Figure S22 in the SI). The lack of a geometry change suggests

that H substitution does not sterically impact this system.

Moreover, the increase in J suggests that hydrogen substitution

does lead to better energy alignment between the Fe magnetic

orbitals and the aromatic-bridge π* orbitals, increasing the magnetic

coupling.

While the doubletꢀquartet gap for the orbitally aligned

rotamer is signiﬁcantly larger than that found for the X-ray con-

formation, it is substantially smaller than (computed or experi-

mental) tripletꢀsinglet gaps reported by Paul for the dinuclear

Cp*-containing species (142 cm^ꢀ1for the geometry-optimized

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Figure 8. Idealized orientations of the “magnetic” dπ and acetylide

pπ orbitals relative to the aryl π system in the cation of trinuclear

4: (a) PPP; (b) PPA; (c) PAA; (d) AAA. Structurally, 4 would be

expected to behave like (c), but its magnetism is most consistent with

orbital arrangement (b).

the PPP structure, where all of the Fe^IIImagnetic orbitals are

aligned with the aryl π system, was computed to be 5 kcal/mol

more stable than the PPA rotamer, whereas for the parent

complex [(dmpe)₆Cl₃Fe₃(TEB)]³⁺, the PPP structure is stabi-

lized by only 0.5 kcal/mol relative to the PPA rotamer.

Several computations were undertaken to investigate the

impact of nuclearity on J (Figure S25 and Table S8 in the SI).

First, [(dHpe)₆Cl₃Fe₃(TEB)]³⁺was reduced by one electron to

give [(dHpe)₆Cl₃Fe₃(TEB)]²⁺, leading to two magnetic orbitals

and a singletꢀtriplet gap. Equation 10 was used to compute a J

value of 59 cm^ꢀ1, slightly larger than but comparable to the

m-DEB-bridged case studied above (48 cm^ꢀ1; Table S3 in the SI).

In a second study, when one of the [(dHpe)₂ClFe]²⁺fragments

was replaced by H, J was computed to drop to 44 cm^ꢀ1, almost

identical to the m-DEB-bridged complex. For comparison, the

average J value for [(dHpe)₆Cl₃Fe₃(TEB)]³⁺was calculated to

be ∼73 cm^ꢀ1(Table S6 in the SI). Computationally, an increase

from two spin-active electrons to three does not appear to

adversely aﬀect J, suggesting that the assembly of higher-nuclearity

species does not on its own lead to weaker exchange coupling.

To connect the present work to previously reported studies on

Cp*-containing complexes,^{18,24,25,63,65,71,79}unrestricted B3LYP

energies were computed for the individual quartet and M_S= ¹/₂

microstates for [(dppe)₃Cp*₃Fe₃(TEB)]³⁺. The computed

J values are signiﬁcantly larger than those observed experimen-

tally (Table 2), although the computed values are based on

symmetrized atomic coordinates from the Fe(II)-containing

complex, since a structure of the Fe(III) analogue has not been

reported. Strong pinning of the magnetic orbital identity by the

Cp*(dppe) ligand set suggests that exchange interactions via

bridge delocalization should be signiﬁcantly enhanced by align-

ing the Fe magnetic orbitals with the aryl π system. For

[(dppe)₃Cp*₃Fe₃(TEB)]³⁺, the orientational dependence of J

was investigated by constructing a rotamer wherein the three

magnetic orbitals were aligned with the aryl π system (j = 0°;

Figure S27 in the SI). J was computed to increase dramatically,

from a minimum of 34 cm^ꢀ1to a maximum of 66 cm^ꢀ1(Table S9

Figure 7. Illustrative spin density plots generated from UB3LYP

calculations for the (top) ααα and (bottom) αβα microstates of

[(dmpe)₆Cl₃Fe₃(TEB)]³⁺based on the experimentally determined

structure of 4. All four spin density plots are provided in Figure S16 in

the SI. Blue and green shading correspond to α and β spins, respectively;

the 0.003 electron density |isovalue| surface is displayed. It should be

noted that the lower-right iron uses an intrachelate magnetic orbital to

maximize overlap with the aryl π system, whereas the other two Fe

groups use interchelate magnetic orbitals.

To probe this hypothesis further, a series of substitutionally

related model complexes were studied; the results are collected in

Table S6 and Figure S23 in the SI. Replacing H with F or Cl again

doubles J and the doubletꢀquartet gap. Substitution with OCH₃

yields only a modest increase relative to H. This computed trend

correlates with the chelating phosphine HOMO orbital energy

(Figure S24 in the SI), which serves as a measure of phos-

phine donor ability. The alternative MESP analysis⁷³provided a

reduced correlation due to the wide span in electronegativity of

the phosphine substituents.^77,78Notably, the HOMO analysis

coupled with the orbital energy data in Table S7 in the SI suggests

that J for dppe should be slightly larger than that for dmpe but

signiﬁcantly smaller than that for dHpe.

Two other computational studies were aimed to inform future

dendrimer syntheses. First, to probe the impact of axial halide

replacement on coupling, we found that substitution of Cl by

either F or Br provides only a modest perturbation of J (Table S6

in the SI). Second, as an electronic eﬀect, replacement of TEB^3ꢀ

as the bridging ligand with the anionic form of 2,4,6-triethynyl-

mesitylene (Me₃TEB^3ꢀ) causes only a modest perturbation of

J. However, a more signiﬁcant geometric stabilization is realized:

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ARTICLE

in the SI). Since coupling for the Cp* system is so highly

dependent on the relative Cp*(dppe)Fe orientation, it is likely

that the as-isolated Fe^IIIcomplex features rotation of one or more

[(dppe)FeCp*]²⁺units further out of registry with the aryl π

system.

a single favorable exchange interaction in the triplet is replaced

by three favorable exchange interactions in the quartet.

The arylalkynyl π* system provides three orbitals (two e and

one a) that can support three orthogonal delocalizations, each of

which increases the magnetic exchange while lowering the energy

of the system.

In summary, the computational studies provide evidence for

strong orientational and phosphine donor strength dependencies

of J and comparable exchange coupling parameters for (dmpe)₂

and (dppe)(Cp*) ligand frameworks as well as evidence against

the suggestion that an increase in nuclearity leads to a decrease in

magnetic coupling. In fact, at least for the system studied here,

the opposite was found: for oriented rotamers, J was universally

computed to increase by nearly a factor of 2 in going from two

spins to three.

Notably, the maximum J value for the spin-aligned species

[(dppe)₃Cp*₃Fe₃(TEB)]³⁺(66 cm^ꢀ1; Table S9 in the SI) is still

appreciably smaller than that reported by Paul et al.²⁵for

[(dHpe)₂Cp₂Fe₂(m-DEB)]³⁺(256 cm^ꢀ1). Several computa-

tional experiments were employed to probe this discrepancy;

the results are summarized in Table 2, and details are provided in

Tables S10 and S11 and Figures S26ꢀS30 in the SI. From these

computational studies, it was found that the same general trends

apply to the Cp*/Cp-containing systems as to the (dmpe)₂-

containing species presented here: ﬁrst, the magnetic orbital

orientation directly aﬀects J; second, altering the ancillary ligand

substituents modiﬁes J but to a lesser extent than changing the

magnetic orbital orientation. In addition, we found that regard-

less of the relative orientation of [Cp*(dppe)Fe]²⁺units, triplets

are more stable than singlets, with maximum J values in the

50ꢀ70 cm^ꢀ1range. There is no computational support either for

large geometry changes upon magnetic excitation in these di-

’ CONCLUSIONS AND OUTLOOK

The syntheses, structures, magnetic properties and results of

electronic structure calculations for a series of Fe^IIIethynylben-

zene complexes have been described. Consistent with established

topology rules, meta-bridged complexes 4 and 5 display S = ³/₂

and S = 1 ground states, respectively, at low temperatures,

whereas para-bridged 2 shows antiferromagnetic interactions

that lead to an S = 0 ground state. The relative strengths of the

intramolecular exchange interactions are inﬂuenced by more

subtle structural features. By means of DFT calculations, the

orbital pathways responsible for the magnetic exchange interac-

tions in Fe^IIIacetylide complexes have been determined and

compared with those in Cp*-containing analogues. Whereas the

Cp* complexes provide a robust structural handle connecting the

relative geometry of ancillary ligand sets to the strength of

intramolecular magnetic interactions, magnetic orbital control

is more complex in the new complexes reported herein: the

interplay between dπ/aromatic-π interactions, geometry, and

ligand-ﬁeld eﬀects signiﬁcantly impact the magnitude of the

magnetic coupling. Nevertheless, the various factors can be de-

convoluted for the Fe^IIImonomers and in principle applied to the

understanding of higher-nuclearity species.

Importantly, substantial magnetic coupling strengths are fore-

seen for this class of complexes, provided that the magnetic

orbitals can be tuned geometrically and electronically; the results

of the preliminary computational exploration presented herein

oﬀer several synthetically accessible target molecules. The ability

to manipulate J is expected to have profound implications for the

preparation of low-dimensional metal complexes with well-

isolated high-spin ground states, potentially resulting in molec-

ular magnets with enhanced properties. Synthetic eﬀorts to

optimize the magnetic interactions in these and related com-

plexes are underway.

nuclear complexes or for J to be as large as 250 cm^ꢀ1

.

A ﬁnal question to be addressed is the nature of the exchange

pathway for the m-DEB- and TEB-bridged complexes. For

p-DEB-bridged species, transmission of the cumulenic form across

the bridge explains the strong AF exchange. For m-DEB- and

TEB-bridged complexes, this valence-bond pathway is absent,

and exchange/delocalization uses three fragment orbitals: the

alkynyl π and π* orbitals and the Fe-centered singly occupied

magnetic orbital. Two hypotheses for exchange delocalization are

the following: (1) direct delocalization from the singly occupied

Fe dπ orbital into the alkynyl π* orbital, leading to spin

delocalization onto the aryl π system, and (2) donation from

the doubly occupied alkynyl π orbital into the singly occupied Fe

dπ orbital followed by a secondary back-donation from the singly

occupied magnetic orbital (now Fe dπꢀC pπ antibonding in

character) into the alkynyl π* orbital, leading to spin delocaliza-

tion onto the aryl π system. The Jꢀphosphine HOMO correla-

tion investigation and a comparison of the spin natural orbitals

for [Cl(dmpe)₂Fe]²⁺and [Cl(dFpe)₂Fe]²⁺support the latter

hypothesis (Figure S31 in the SI). Regarding the Jꢀphosphine

HOMO correlation, decreased σ donation from the phosphine

to the metal (via electron-withdrawing substituents) stabilizes

the metal d orbital set by removing charge density from the metal

center, leading to an increase in the interaction between the

magnetic and aryl π system orbitals. If the interaction of the

magnetic orbital with the aryl π* system were the determining

factor, electron-donating substituents would be expected to

increase the J value, as this would destabilize the metal d orbital

set and increase interaction with the aryl π* system. The former

trend was computationally observed for J. Visually, going from

CH₃to F, the set of nearly doubly occupied spin natural orbitals

gain signiﬁcant Fe dπꢀC pπ bonding character and the set of

nearly empty spin natural orbitals gain signiﬁcant Fe dπꢀC pπ

antibonding character. The occupation numbers of the nearly

ﬁlled orbitals decrease, while the nearly empty correlative orbitals

gain electron density; this pattern is consistent with increased

metalꢀligand π bonding. The singly occupied magnetic orbitals

display an increase in aryl π character. This model also provides

an explanation for the increase in J as the nuclearity increases.

In going from a dinuclear triplet to a trinuclear quartet system,

’ ASSOCIATED CONTENT

S

Supporting Information. X-ray structural data for 1, 2,

b

and 4 (CIF); details of computational work; complete ref 45;

crystal data for 5; spectral data; details of ﬁtting procedures;

computed data and spin density plots. This material is available

free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION

Corresponding Author

matthew.shores@colostate.edu

20834

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Journal of the American Chemical Society

ARTICLE

Present Addresses

^†Paciﬁc Northwest National Laboratory, Richland, WA 99352.

(31) We note that replacement of the axial chloride in these complexes

is not facile. However, Field and co-workers have achieved stepwise ligand

substitution starting with structurally analagous [(dmpe)₂FeCH₃(C₂R)]

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(32) Field, L. D.; Turnbull, A. J.; Turner, P. J. Am. Chem. Soc. 2002,

124, 3692.

’ ACKNOWLEDGMENT

This research was supported by Colorado State University and

ACS-PRF (44691-G3).

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Topological and electronic influences on magnetic exchange coupling in Fe(III) ethynylbenzene dendritic building blocks

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