Modeling rate-controlling solvent effects. The pericyclic Meisenheimer rearrangement of N-propargylmorpholine N-oxide

Published on Web 04/29/2005

Modeling Rate-Controlling Solvent Effects. The Pericyclic

Meisenheimer Rearrangement of N-Propargylmorpholine

N-Oxide

Zolta´n Mucsi,*^,†Anna Szabo´,^‡Istva´n Hermecz,^‡AÄ rpa´d Kucsman,^†and

Imre G. Csizmadia*^,§,|

Contribution from the Department of Organic Chemistry, Eo¨tVo¨s Lora´nd UniVersity,

Budapest, H-1117, Hungary, Department of Organic Chemistry, Technical and Economical

UniVersity of Budapest, Budapest, H-1111, Hungary, Department of Chemistry, UniVersity of

Toronto, Toronto, Ontario, Canada, M5S 3H6, and Department of Chemistry and Chemical

Informatics, Faculty of Education, UniVersity of Szeged, Szeged, H-6725, Hungary

Received December 26, 2004; E-mail: zoltan_mucsi@freemail.hu; icsizmad@jgytf.u-szeged.hu

Abstract: The activation parameters of the pericyclic Meisenheimer rearrangement and a competitive

rearrangement of N-propargylmorpholine N-oxide were determined by experimental and computational

methods. A number of aprotic and protic solvents of different polarities and hydrogen bond-forming abilities

and the roles of electron-pair acceptor additives were investigated. The reaction kinetics were followed by

means of NMR. In protic solvents, isotope-labeling experiments revealed a novel inverse secondary kinetic

isotope effect (k_H/k_Dabout 0.8) for the rate-determining cyclization step, probably occurring because of a

C(sp) f C(sp²) change in hybridization at the reaction center. In molecular computations at the B3LYP/

6-31++G(d,p) level of theory, implicit, explicit, and joint explicit-implicit solvent models were used. The

explicit-implicit model and molecular dynamic simulations gave the most accurate results. The components

of the rate-controlling solvent effect are discussed, and general equations are proposed for accurate

prediction of the solvent-dependent activation parameters.

1. Introduction

wish to draw attention to the importance of appropriate chemical

modeling.

1.1. Preamble. In drug research, study of the rates of

metabolic processes is essential for the development of drugs

with the desired effects. If decomposition of the drug is too

fast, the compound cannot express its activity on the receptor;

if it is too slow, an overdose may occur. Our aim was a

quantitative study, using only theoretical considerations, of the

rate-determining step of a metabolically occurring process, the

Meisenheimer rearrangement of N-propargylmorpholine N-

oxide. Computed and experimentally determined parameters

were compared to validate the theoretical models.

Solvent effects are complex dynamic processes in which a

great number of solvent molecules take part and interact with

the solute molecules. A completely correct description of such

a system is impossible, but attempts can be made to design the

average effect in a static model. The most-preferred methods

are based on the different polarizable continuum medium

(PCM)^1-4and conductor-like screening models (COSMO).⁵

These implicit solvent models deal only with the solute molecule

embedded in the infinite polarizable or nonpolarizable con-

tinuum medium. However, the implicit model has been found

to be inaccurate in most cases because it does not deal explicitly

with the solvent molecules. Relatively few works take the

solvent molecules into account appropriately, and they do not

reflect the importance of this.^6-14Later in the article, we present

1.2. Background. The accurate prediction of different reac-

tion parameters has been a dream of numerous chemists for

many years. Currently, the fascinating improvement of com-

putational tools and methods has made theoretical prediction

an affordable, almost routine task. However, despite the accurate

ab initio and density functional theory (DFT) methods, many

theoretical results deviate considerably from the experimental

findings because the chemical environment (effects of solvent

molecules, such as hydrogen bonding (HB), self-association,

etc.) is not successfully taken into account. In this article, we

(1) Cance`s, M. T.; Mennucci, B.; Tomasi, J. J. Chem. Phys. 1997, 107, 3032-

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^†Eo¨tvo¨s Lora´nd University.

^‡Technical and Economical University of Budapest.

^§University of Toronto.

^|University of Szeged.

9

J. AM. CHEM. SOC. 2005, 127, 7615-7631

7615

A R T I C L E S

Mucsi et al.

Chart 1. Different Conformations of N-Propargylmorpholine

Scheme 1. Rearrangements of N-Propargylmorpholine N-Oxide

(1)

N-Oxide (1)

a dramatic rate acceleration when an electron-pair acceptor

(EPA) ionophore (e.g., LiClO₄or NaClO₄) is added to the

reaction mixture.^23,29,30These results were explained by the

enhanced polarity of the TSs, stabilized less effectively by HBD

solvents and EPAs, as compared with that in the reactants.

This unexpected solvent effect was a challenge to develop

theoretical methods for prediction of the effect of the reaction

medium. The Meisenheimer rearrangement of N-oxides is

additionally of biological importance. In vivo degradation of

the excellent irreversible monoamine oxidase (MAO) inhibi-

tors^31,32(e.g., MAO-A: Clorgyline, Abbott-21.855; MAO-B:

Selegiline, Pargyline), essentially tertiary amines with N-

propargyl and N-methyl substituents (for individual structures,

see Scheme S1 in the Supporting Information), starts with a

Meisenheimer rearrangement of the corresponding N-oxides.¹⁵

Furthermore, it has recently been discovered³³that Selegiline-

N-oxide is a very strong neuroprotective agent. This discovery

is suggestive of the promise of development of a potential new

drug.

1.3. Scope. In our present work, we started from the well-

established mechanism of the rearrangement of 1 that we

proposed earlier.^16,17To reveal the controlling role of the reaction

medium, we carried out the reaction not only in the previously

investigated HBD solvents (MeOH, EtOH, i-PrOH, and t-

BuOH), but also in other HBD solvents [H₂O, CF₃CH₂OH,

(CF₃)₂CHOH, CHCl₃, CHBr₃, CH₂Cl₂, and MeNO₂], in non-

HBD solvents (Me₂SO, MeCN, Me₂CO, pyridine, and dioxane),

in the presence of electron-pair acceptors (EPAs such as Li⁺,

Na⁺, nitro derivatives of benzene, BF₃:OEt₂and H⁺interacting

with the nonbonding electron pair of the N-oxide oxygen), and

in deuterated solvents (D₂O, CD₃OD, C₂D₅OD, CDCl₃, CDBr₃,

and CD₂Cl₂).

evidence that an explicit consideration of solvent molecules is

essential for an acceptable description of chemical processes.

To study the solvent effect, we have chosen the pericyclic

Meisenheimer rearrangement of N-propargylmorpholine N-oxide

1 in different solvents (Scheme 1). In earlier work,^15-17we

demonstrated that both the rate and the product distribution of

this pericyclic reaction, which proceeds through a cyclic-

activated complex (transition state: TS 2), are affected by the

nature of the solvent. In aprotic solvents (e.g., in diethyl ether)

a trisubstituted hydroxylamine, N-(propadienyloxy)morpholine

(3; “O-allenylhydroxylamine” in ref 16) was formed by N-C

bond cleavage as a result of the Meisenheimer rearrange-

ment.^18,19In protic solvents (e.g., in C₁-C₄alcohols), however,

the rate of the Meisenheimer rearrangement was markedly

decreased, and in a competitive rearrangement involving

N-O cleavage 3-(3-oxapentane-1,5-diyl) aminoacrylaldehyde

(4; “enamino aldehyde” in ref 16) was formed and became the

main component. In C₁-C₄alcohols, kinetic measurements were

performed to determine the rate constants and the activation

parameters for both rearrangements.¹⁶Preliminary theoretical

calculations were also carried out to reveal the mechanisms of

the competing reaction pathways.¹⁷

The fact that the rearrangements of N-oxide 1,^18,19involving

a pericyclic rate-determining step, exhibit a significant solvent

dependence was unexpected. Most pericyclic reactions that

proceed through an isopolar TS (differing in charge separation

very little, if at all, from the initial reactant) are not appreciably

affected by changes in the substituent or the reaction medium.^20-23

In a few cases, for example, in hetero Diels-Alder reactions,

the pericyclic step proceeds markedly faster in hydrogen-bond

donor (HBD) solvents than in non-HBD ones,^24-28and there is

In the models of solvent effects, the solvents and media are

divided into two groups. Type 1 media are non-HBD (aprotic)

solvents: Me₂SO, MeCN, Me₂CO, pyridine, dioxane, and

vacuum. For appropriate modeling, we divided the type 2

solvents into two subgroups: weak HBD solvents such as

CHCl₃,^34-37CHBr₃, CH₂Cl₂, and MeNO₂(prominently weak)

belong to type 2A, whereas strong HBD solvents such as H₂O,

MeOH, EtOH, CF₃CH₂OH, i-PrOH, (CF₃)₂CHOH, and t-BuOH

belong to type 2B.^38-40

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Ed.; Birkha¨user: Basel, 1999; pp 75-108.

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Med. Chem. 2004, 11, 2017-2031.

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9

7616 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

Scheme 2. Suggested Mechanism for the Rearrangements of N-Propargylmorpholine N-Oxide (1) in Type 1, Type 2A, and Type 2B

Solvents^a

^aCPE: conformational pre-equilibrium, SPE: solvent-solute pre-equilibrium, RC: ring-closure step, X-H ) OH or CH.

The reaction starts with the syn-clinal (gauche, 1c/1d)

rate ) k_EXP[1b] ) 0.5‚K_CPE‚k_RC[1b]

(1)

conformation, even though the anti-periplanar (1b) conformation

k

∆G_CPE∆G^q

^RC+ ln

is considerably more stable (Chart 1). The conformational pre-

ln ^EXP) -ln 2 -

-

(2a)

RT

h

equilibrium (CPE) is illustrated in Scheme 2.¹⁶

T

RT

While different PCM methods are effective in providing an

adequate model of the effects of type 1 solvents, it is difficult

to find an appropriate environmental and chemical model for

protic solvents. The question arises of how many solvent

molecules should be taken into account. If we focus only on

the first solvation shell around the N-oxygen of 1, are one or

two or three solvent molecules able to interact with the three

nonbonded electron pairs of the negative acceptor oxygen

atom?^32-34We carried out computations on models containing

zero or one or two solvent molecules of type 2; for one solvent

(MeOH), we also computed the model involving three solvent

molecules.

In this article, we compute the Gibbs free energy of the rate-

determining step (∆G^q_TOT; see Section 3.3) and compare it with

the experimentally determined value (∆G^q_OBS). Equations 1-6

reveal the components of the experimentally determined Gibbs

free energies of activation of the processes shown in Scheme 2

and the associated thermodynamic levels.

k

RT

h

-RT‚ln ^EXP- RT ln 2 - ln

) ∆G_CPE+ ∆G^q_RC

)

(

)

T

∆G^q_EXP) ∆G_O^q_BS(2b)

In type 2A solvents (weak HBDs CHCl₃, CHBr₃, CH₂Cl₂, and

MeNO₂):

rate ) k^x_EXP[1b] ) 0.5‚K_S^x_PEK_C^x_PE‚k^x_RC[HBD][1b] (3)

k^x

∆G^x_SPE∆G^x_CPE∆G^xq

ln ^EXP) -ln 2 -

-

+

RC

T

RT

ln + ln[HBD] (4a)

h

k^x

-RT‚ln ^EXP- RT ln 2 - ln - ln[HBD] ) ∆G^x_SPE

+

RT

h

(

)

T

∆G_C^x_PE+ ∆G^xq) ∆G^xq) ∆G_O^q_BS+ ∆G_S^x_PE(4b)

RC

EXP

In vacuo and in type 1 solvents (non-HBDs Me₂SO, MeCN,

Me₂CO, pyridine, and dioxane):

In type 2B solvents (strong HBDs MeOH, EtOH, i-PrOH,

t-BuOH, H₂O, CF₃CH₂OH, (CF₃)₂CHOH):

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7617

A R T I C L E S

Mucsi et al.

rate ) k^/_EXP[1b] ) 0.5‚K_S^/_PEK_C^/_PE‚k^/_RC[ROH]²[1b] (5)

data, the cooled solutions of 1 were dried with molecule sieve (Aldrich,

4 Å, 5 µm, without extra activation), and the residual water content

(∼0.2%) was checked by NMR. H NMR spectroscopy was used for

1

k^/

∆G^/_SPE∆G^/_CPE∆G*_R^q_C

ln ^EXP) -ln 2 -

-

+ ln

+

RT

h

non-HBD solvents (Me₂SO, MeCN, PhNO₂, Me₂CO, pyridine, t-BuOH,

and dioxane) and for weak HBD solvents (MeNO₂, CH₂Cl₂, CHCl₃,

and CHBr₃). The NMR methods used, together with characteristic

chemical shifts, are listed in Table S1 in the Supporting Information.

GC measurements were applied for strong HBD solvents (H₂O, MeOH,

EtOH, CF₃CH₂OH, i-PrOH, (CF₃)₂CHOH, and t-BuOH). The experi-

mental conditions of GC measurements were the same as described in

ref 16. For the solvents MeCN, H₂O, MeOH, EtOH, i-PrOH, t-BuOH,

CH₂Cl₂, and CHCl₃, the Gibbs free energy (∆G^q_OBS), enthalpy

(∆H^q_OBS), and entropy (∆S_O^q_BS) of activation were calculated from the

reaction constants determined at various temperatures. The ∆G_O^q_BS

and ∆H^q_OBSvalues in other solvents were obtained through compari-

son of the rate constants with those determined in MeCN. To calculate

∆G^q, ∆H^q, and ∆S^qvalues, the Eyring equation was used.^16,41Rate

constants and activation parameters obtained for the transformation of

1 in MeOH, EtOH, and i-PrOH were published earlier.¹⁶Parameters

for other solvents are reported in this article (see Table 3).

T

RT

2 ln[ROH] (6a)

k^/

-RT‚ln ^EXP- RT ln 2 - ln - 2 ln[ROH] ) ∆G^/_SPE

+

RT

h

(

)

T

∆G_C^/_PE+ ∆G*_R^q_C) ∆G*_E^q_XP) ∆G_O^q_BS+ ∆G^/_SPE(6b)

where k_EXP, k^x_EXP, and k_E^/_XPrepresent the experimentally deter-

mined reaction rate for type 1, type 2A, and 2B solvents,

respectively; RDH stands for the symbols of C1-C4 alcohols.

In theory, a fourth possible solvation model may also exist,

where three solvation molecules coordinate the oxygen of 1,

because of the presence of three nonbonding electron pairs (eqs

7 and 8):

rate ) k^//[1b] ) 0.5‚K^//K^//‚k^//[ROH]³[1b] (7)

2.2. Computational Methods. 2.2.1. Ab Initio Methods and Basis

Set Error (BSE). The geometries and vibrational frequencies were

calculated by using the Gaussian03^1-4,42program in vacuo and in

solvents, using the default PCM method (integral equation formalism

polarizable continuum medium, IEF-PCM, or PCM in brief) at the same

B3LYP/6-31++G(d,p)⁴³theoretical level. The effects of the applied

computational method (HF, B3LYP, MP2(fc),⁴⁴and MP4(fc)⁴⁵) and

basis set were also examined (Table S2 in the Supporting Information).

The difference between the energy values obtained at the B3LYP/6-

311++G(2d,2p) and B3LYP/6-31++G(d,p) levels of theory was 1.95

kJ mol^-1, and we used this value (∆E_B^q_SE) to correct for BSE. Because

of convergence problems, in the case of the explicit-implicit solvent

model, the geometry optimization was halted when, after at least 50-

100 optimization steps, the energy differences within the last five

EXP

SPE CPE RC

//

k^//

∆G

∆G**^q

^RC+ ln

SPE

CPE

RT

h

ln ^EXP) -ln 2 -

-

+

T

RT

3 ln[ROH] (8a)

k^//

RT

h

-RT‚ln ^EXP- RT ln 2 - ln - 3 ln[ROH] ) ∆G^//

+

SPE

(

)

T

∆G^//+ ∆G**^q_RC) ∆G**^q_EXP) ∆G^q_OBS+ ∆G^//(8b)

CPE

SPE

It may be seen that all experimental activation parameters

contain the CPE contribution (∆G_CPE), where multiplication by

0.5 indicates that the formation of a pair of degenerate gauche

conformers is twice as fast as that of a single anti conformer.

In HBD (types 2A and 2B) solvents, the ∆G^q_EXPcontains the

solvent-solute pre-equilibrium (SPE) contribution (∆G_SPE),

originating from the complexing properties of the solvent

molecules. Since we are dealing with solutions, we can only

obtain the observable activation free energy (∆G^q_OBS) instead

of the experimental one (∆G^q_EXP) relating to the unsolvated/

uncomplexed form.

optimization steps were below 0.3 kJ mol^-1

.

2.2.2. Entropy Calculations. The entropy contribution of the

hindered rotation of the propargyl group in N-oxide 1 was taken into

account by using the free rotation entropy formula (eq 9) instead of

the vibration entropy (eq 10).^46-48The I ) h²/8π²Θk_B; (Θ ) hcω/k_B)

value, where Θ is the characteristic rotational temperature, h is the

Planck constant, k_Bis the Boltzmann constant, c is the speed of light,

and ω is the torsional vibration of the propargyl group (ω ) 87.4 cm^-1

) 8740 m^-1), which was obtained from frequency calculations. The

variable σ_intis the rotational symmetry number (σ_int) 1).

Solvents and additives (EPAs) may have two different

functions. They influence the rate of the reaction by differently

stabilizing the starting structure (1c/1d, 1c^x/1d^x, and 1c*/1d*)

and the TS (2, 2^x, and 2*), and they may stabilize the

intermediate (5, 5^x, and 5*) through protonation (5 f 6) or, in

the case of EPAs, through addition to C(9) of 5^x. It appears

that strong HBD (type 2B) solvents such as ROH have dual

functions: by forming hydrogen bonds with the oxygen of

N-oxide 1 (Scheme 2), they reduce the nucleophilicity of the

negatively charged oxygen atom, and they are also involved in

the C(9) protonation of the ring-closed isoxazolidine intermedi-

ate (5* f 6*). Weak HBD (type 2A) and EPA molecules have

only one function: they reduce the nucleophilicity of the oxygen.

Non-HBD (type 1) solvents influence the process only via their

relative permittivities (ꢀ_rel).

(8π³I_intk_BT)^1/2

1/2

1

2

πT

1

S_free.rot) R ln

+

) R ln

+ R )

2

{

}

[

(

)

σ²_intΘ

[

]

σ_inth

1/2

πk_BT

πk_B(313 K)

1

2

1

R ln

+ R ) R ln

+ R )

2

(

)

σ²_intcω_ih

ch(8740 m

)

-1

]

16.30 J mol^-1K^-1(9)

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2.1. Experimental Methods. By means of kinetic measurements,

we examined the rate-determining first step of transformation of N-oxide

1 in a number of solvents, and the rates of the reactions were measured

at different temperatures. Since traces of water may lead to false-positive

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9

7618 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

hcω_i

S_vib) R

- R ln[1 - exp(hcω_i/k_BT)] )

k_BT[exp(hcω_i/k_BT) - 1]

hc(8740 m^-1

)

R

k_BT{exp[hc(8740 m^-1)/k_B(313 K)] - 1}

- R ln{1 - exp[hc(8740 m^-1)/k_B(313 K)]} ) 9.19 J mol^-1K^-1

(10)

When the other frequencies were left fixed, the final corrected

entropy value of the ring-closure step was ∆S^q_CORR) -14.24 J mol^-1

K^-1in vacuo, which is near the observed experimental value. This

entropy value was used in the description of the ring-closure step.

2.2.3. Molecular Dynamic (MD) Simulations. The MD simulation

of the first solvation shell was carried out by using the Hyperchem 7.0

program⁴⁹with 256 equilibrated solvent molecules in a box under

periodic boundary conditions and correct dimensions (20-33 Å); the

shifted cutoffs⁴⁹were 12.5 and 16.5 Å. The Amber 99 force field⁵⁰

method was used, lasting for 300 ps - 1 ns after 20 ps of the

equilibrium process. For charge parametrizations of the 1a, 1b/1c, 2,

H₂O, MeOH, EtOH, i-PrOH, t-BuOH, CH₄, CH₂Cl₂, and CHCl₃

molecules in MD simulations, the B3LYP/6-31++G(d,p) level of

theory and natural bond orbital (NBO) version 3 analysis⁵¹were applied

(Table S3 in the Supporting Information).

Figure 1. Shift of the water proton signal during the Meisenheimer

transformation of N-oxide 1 in MeCN containing 2 equiv of water.

The radial distribution function (RDF)⁵²of the OH or CH proton

and that of the oxygen in N-oxide 1 and TS 2 for different solvents

was calculated by using eq 11:

N

δ[r - r_O-H] ‚V

∑

i

i)1

RDF(r) )

(11)

4πr²‚∆r‚N

Figure 2. The ν(NO) frequency of N-propargylmorpholine N-oxide (1) in

different solvents and in MeCN solutions containing LiClO₄. The arrow

indicates the shift in the IR band in MeCN after the addition of LiClO₄.

where N is the total number of OH or CH protons within the volume

element, δ is the Dirac delta function, r_O-His the radial distance of

the N-oxygen from the OH or CH of the solvent molecule, V is the

volume of the simulated box, and 4πr²∆r is the spherical shell.

i

solvents. The solubility of the N-oxide 1 was found to be

relatively high in solvents where the rearrangement proceeds

slowly, whereas it proved poor in solvents that increase the rate

of the rearrangement. For solubility data, see the Supporting

Information. The solubility of 1 increased significantly when

minimal amounts of water or EPA were added, pointing to the

complexation effects exerted by HBD solvents and EPAs.

NMR Spectroscopy. Convincing evidence of HB was

furnished by NMR. When the rearrangement of N-oxide 1 in

MeCN or CH₂Cl₂in the presence of 2 equiv of water or MeOH

was followed by NMR, the chemical shift of the OH proton

moved toward lower values as the reaction proceeded (i.e., the

concentration of 1 decreased; Figure 1).

3. Results

3.1. Hydrogen Bonding of N-O Functionality. As indicated

in Section 1.3, in HBD solvents three different solvations models

can be set up for which quite diverse kinetic and activation

parameters are assumed. Expectations were confirmed by

preliminary DFT [B3LYP/6-31++G(d,p)] calculations. For the

models with one, two, and three explicit solvating MeOH

molecules in vacuo, the computed ∆E^qvalues referring to the

rate-determining ring-closure (RC) step were 86.2,¹⁷101.5,¹⁷

and 120.1 kJ mol^-1, respectively. The different values clearly

indicate that the creation of a suitable chemical model with the

correct number of solvating molecules (solvation number, SN)

is essential for DFT calculations. This correct SN in various

solvents was determined by using theoretical MD simulations.

3.1.1. Experimental Observations Indicative of Hydrogen

Bonding (HB). Experimental evidence of existing HB may

provide a good tool to reinforce our theoretical results.

At the end of the reaction, the chemical shift of the water

proton reached the normal value of 2.15 ppm, because product

3 is much less capable of forming HB.

IR Spectroscopy. N-Oxide 1 in the solid state exhibits an

IR band at ∼950 cm^-1, assigned to the vibrational frequency

of the N-O group. This band is assumed to exhibit characteristic

shifts in solution, depending on the relative permittivity and

the HBD and EPA ability of the solvents. Figure 2 shows the

shifts of the ν(NO) band in non-HBD (dioxane and MeCN) and

HBD (H₂O, MeOH, EtOH, i-PrOH, t-BuOH, CH₂Cl₂, and

CHCl₃) solvents and in MeCN solutions containing an EPA

additive (LiClO₄). It may be seen that the ν(NO) band appears

at significantly higher frequencies in strong HBD solvents than

in non-HBD media, due to the existence of HB of different

strengths between the solute and solvent molecules. An ex-

Solubility. The simplest way to estimate the solvent effects

is to investigate the solubilities of a given compound in different

(49) Hyperchem, version 7.04; Hyperchem Inc.: Gainesville, FL, 2003.

(50) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.;

Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P.

A. J. Am. Chem. Soc. 1995, 117, 5179-5197.

(51) Carpenter, J. E.; Weinhold, F. J. Mol. Struct. (THEOCHEM) 1988, 169,

41-62.

(52) Cramer, C. J. Essentials of Computational Chemistry; Wiley & Sons: West

Sussex, England, 2001; Chapter 3, pp 63-94.

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7619

A R T I C L E S

Mucsi et al.

Figure 3. RDF for different solvents. (A) H₂O. (B) H₂O, MeOH, and EtOH. (C) i-PrOH and t-BuOH. (D) CHCl₃, CH₂Cl₂, and CH₄.

Table 1. Results of MD Studies on Different Conformers of N-Propargylmorpholine N-Oxide (1b, 1c/1d) and the TS (2) in Various Solvents

(SN ) Solvation Number)

1b

1c/1d

2

integral^aSN

max (Å)^b

width (Å)^c

integral^aSN

max (Å)^b

width (Å)^c

integral^aSN

max (Å)^b

width (Å)^c

exchange (ps)^d

H₂O

2.50

2.40

2.11

2.09

1.22^e

1.10

1.79

1.15

2.10

2.25

2.20

2.40

2.45

2.50

2.40

2.50

∼0.80

∼0.90

∼0.75

∼1.00

∼1.10

∼1.00

∼1.10

∼1.20

2.44

2.34

2.15

2.01

1.20^e

1.02

1.67

1.10

2.10

2.20

2.40

2.50

2.40

2.50

∼0.80

∼0.90

∼1.00

∼1.10

∼1.00

∼1.10

∼1.20

2.14

2.05

1.95

1.91

1.24^e

1.05

1.25

0.85

2.35

2.40

2.45

2.40

2.35

2.50

∼0.95

∼1.05

∼0.95

∼1.00

∼1.10

∼1.20

∼100

∼200

∼300

>300

∼80

MeOH

EtOH

i-PrOH

t-BuOH

CH₂Cl₂

CHCl₃

CH₄

∼100

∼35

^aIntegral value for the first solvating shell (1.9-∼3.0 Å). ^bMaximum extent of the first solvating shell. ^cApproximate width of the first solvating shell.

^dApproximate exchange rate of the solvating molecules in the first solvating shell. ^eOnly for the first solvating shell.

tremely high shift occurs when a complex is formed between

Li⁺ions and N-oxide molecules.

solvating shell and a smaller, broad peak relating to the second

solvating shell. The average O-H‚‚‚^-O-N⁺distance for all

the studied solvents was about 2.0-2.45 Å (Table 1). The

narrowest functions were obtained for water and MeOH,

whereas t-BuOH exhibited a much broader distribution. In all

strong HBD media except t-BuOH, roughly two OH groups

participated in a coordinative HB to the N-oxygen of 1b and

1c/1d.

In the case of t-BuOH, two first solvating shells exist at

different distances. The SN of the nearer one (2.45 Å) is 1.2,

while the farther one (3.2-5 Å) contains an additional 0.8 OH,

revealed as a small broad shoulder. This means that t-BuOH

has a specific solvating shell, probably due to the bulkiness of

its molecules (see also Section 3.2.2). Thus, t-BuOH represents

a special class of HBD solvents. The split of the first solvating

shell indicates that t-BuOH requires a more complex approach.

The significantly smaller ∆G^qin t-BuOH as compared with that

in i-PrOH may be explained by a sophisticated complexing

3.1.2. Molecular Dynamics Simulations. To answer the

question of how many solvent molecules are required for

accurate modeling of the Meisenheimer rearrangement of

N-oxide 1, MD simulations were performed. Since the activation

energy depends on the structure of both the starting structure

and the TS, the solvation of TS structures in different solvents

was also studied. To determine the XH-hydrogen-N-oxygen

RDF (eq 11, Figure 3) of the starting structures 1b, 1c/1d, and

2 in different solvents, calculations were carried out for strong

HBD solvents (H₂O, MeOH, EtOH, i-PrOH, and t-BuOH), and

weak HBD solvents (CHCl₃and CH₂Cl₂) at reaction tempera-

tures of 338 and 313 K. To study the RDFs of non-HBD

solvents, liquid methane (high pressure) was applied (Figure

3).

The shape of the RDF in different strong HBD solvents is

similar, containing a high, narrow peak that relates to the first

9

7620 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

Figure 4. (A) Change in the NBO charge of O(7) during the reaction (1c/1d f 2). (B) The number of solvent molecules (SN) in the first solvating shell,

obtained from the RDFs for 1c/1d and 2. (C) The number of solvent molecules (SN) in the first solvating shell when O(7) has a different charge.

equilibrium process between t-BuOH and the N-oxide (1b and

1c/1d).

structures 1b and 1c/1d. With the exception of t-BuOH, roughly

two HBD protic solvent molecules play important roles in the

solvation, whereas in the case of t-BuOH only one molecule

belongs closely to the first solvating shell. In summary, two

strong HBD solvent molecules must be considered in the

primary solvation shell model for direct solvation studies

involving DFT calculations.

For weak HBD, halogenated solvents, the TS structure (2) is

complexed with roughly 1 equiv of solvent molecules, indicating

that exact consideration for only one solvent molecule is

sufficient for the DFT calculations.

The exchange of the solvent molecules around the N-oxygen

proved to be very fast (∼10-100 ps). Accordingly, the separate

sign of the OH proton in the solvating molecule cannot be

observed in low-temperature NMR experiments since the time

scale is set in milliseconds.

3.1.3. DFT Study of HB. The strengths of HB (complexation

energies, ∆E₁and ∆E₂) between N-oxide 1 and different HBD

molecules were determined by theoretical methods, ignoring the

basis set superposition error (BSSE), which proved to be

marginally different, as shown in preliminary calculations. We

calculated ∆E₁and ∆E₂via eqs 12 and 13, respectively:

Surprisingly, CHCl₃displays a relatively high SN (1.6

molecules of solvent/solute), but this is still significantly smaller

than those of strong HBD solvents. CH₂Cl₂gives a very small

first solvating shell, composed of about 1.2 equiv of solvent

molecules. The peak of RDF proved to be very wide (2.2-3.5

Å), revealing a weak and unsure HB effect. The methane

solution chosen as non-HBD solvent reference gave a very broad

and uncertain first peak (2.2-3.6 Å), with roughly only one

hydrogen atom in the first solvating shell, at an appreciable

distance (2.5 Å) from O(7).

The DFT calculation [B3LYP/6-31++G(d,p)] shows that the

charge of O(7) decreases from the starting gauche structure 1c/

1d to TS 2, which may be associated with a difference in

solvation of 1c/1d and TS 2. To examine the change in the SN

of the water molecules around the N-oxygen during the reaction,

12 MD simulations (50 ps) were carried out in water with

decreasing C(10)-O(7) distances (3.8-1.6 Å), mimicking the

reaction coordinates from the starting gauche structure 1c/1d

to isoxazolidine 5 through TS 2 (Figure 4), with continuous

change of the charges (see the protocol in Section 2.2). The

number of solvating H₂O molecules significantly decreases

toward TS 2 and 5. However, there are two reasons for this

decrease: the first is the decreasing charge of O(7) (Figure 4),

and the second is the increasing steric hindrance of the

approaching propargyl group.

∆E₁) E_complex1 - (E_HBD/EPA+ E_N-oxide

)

(12)

(13)

∆E₂) E_complex2 - (2E_HBD/EPA+ E_N-oxide

)

All molecules were optimized in vacuo and with the PCM

method, using the appropriate relative permittivity (Table 2).

As shown in Table 2, the values obtained for the explicit solvent

In the case of the TS structure (2), the SN values of XH (X

) C or O) are significantly smaller than those of the starting

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7621

A R T I C L E S

Mucsi et al.

Table 2. Calculated Energies (kJ mol^-1)^aand O(7)···X^bDistances (Å)^aObtained by Different Computational Methods for Complexes Formed

between N-Propargylmorpholine N-Oxide (1) and Strong HBDs, Weak HBDs, and EPAs

explicit method

E₂

explicit

−

implicit method

∆E₁

d₁

∆

d₂

∆E

₂− ∆E₁

∆E₁

d₁

∆E₂

d₂

∆E₂− ∆E₁

H₂O

-68.12

-126.80

1.77

-58.67

-8.39

-8.14

1.71

1.70

1.71

1.59

1.76

1.56

1.77

2.05

1.91

2.07^c

6.50^c

1.09^c

1.84^c

2.22^c

1.51^c

-8.72

-8.48

-11.38

-6.57

-26.75

0.67

1.75

1.76

1.75

1.77

1.70

1.78

1.64

1.84

2.03

2.00

-0.33

-0.34

-2.22

1.07

H₂O^c

MeOH

EtOH

-42.56

-41.92

-62.77

-42.03

-64.16

-39.33

-24.91

-30.40

-31.37

-0.71

-966.74

-284.17

-208.23

-115.15

-79.03

1.71

1.73

1.61

1.76

1.54

1.76

2.02

1.93

2.05

2.53

1.06

1.76

2.12

1.56

-76.05

-73.45

-109.04

-70.59

-113.58

-68.05

-44.07

-53.45

1.78

1.79

1.69

1.82

1.65

1.83

2.06

1.99

-33.49

-31.54

-46.24

-28.57

-49.43

-28.71

-19.16

-23.05

-9.16

-7.64

CF₃CH₂OH

i-PrOH

(CF₃)₂CHOH

t-BuOH

CH₂Cl₂

CHCl₃

MeNO₂

CH₄

-5.28

-21.46

-3.39

4.07

-10.16

-3.36

-14.88

-4.72

6.08

-5.10

-8.61

2.73

-3.49

-8.59

-18.78

-10.17

-3.36^c

3.70^c

H⁺

-1157.61^c

-4.19^c

-5.48^c

-124.87^c

-70.74^c

Li⁺

Na⁺

BF₃

BF₃:OEt₂

^aSubscripts 1 and 2 relate to complexation with one or two HBD and EPA molecules. ^bX ) H for solvents (and acids) or alkaline ions or boron atom.

^cObtained with MeCN solvent model.

model (in vacuo) differ significantly from the results ob-

tained with the implicit-explicit model, and the former does

not appear to be realistic. Thus, only the energies obtained with

the PCM method will be discussed. As expected, (CF₃)₂CHOH,

CF₃CH₂OH, and water undergo the strongest HB, the HB

strength decreasing significantly toward t-BuOH. Increase of

the number of chlorine atoms in the solvent molecule (from

CH₄to CHCl₃) significantly increases the complexation energies.

Surprisingly, the HB strength of CHCl₃proved to be very high

and was similar to those of strong HBD solvents. Large

differences can be observed if one or two solvating molecules

take part in the solvation in different strong HBD solvents,

indicating that the second solvation is higher in energy. This

energy has a + sign for EtOH (1.07 kJ mol^-1), i-PrOH (4.07

kJ mol^-1), and t-BuOH (6.08 kJ mol^-1). In the cases of H₂O,

Relative reaction constants at 313 K (k_rel) are also shown, as

compared with the standard k_relvalue of 1, referring to water-

free MeCN solution at 313 K (∆H^q_OBS) 94.7 kJ mol^-1, ∆G_O^q_BS

) 89.0 kJ mol^-1, ∆S^q) -17.1 J mol^-1K^-1). Solvents are listed

in the sequence of decreasing relative permittivities (ꢀ_rel).^54,55

In Figure 5, ∆G^q_OBSvalues are plotted against the relative

permittivity of the solvents.

In dry non-HBD media (type 1), the k_reland ∆G^q_OBSvalues

lie in the ranges 0.67-2.27 and 92.7-95.9 kJ mol^-1, respec-

tively, demonstrating fast reactions as compared with those in

other types of solvents. The Kirkwood-Onsager rules^23,56

predict a linear increase in ∆G^q_OBSaccording to 1/ꢀ_relfor ionic

molecules and 2(ꢀ_rel- 1)/(2ꢀ_rel- 1) for dipolar molecules, and

our experimentally obtained data for non-HBD solvents fit in

with this rule. As a consequence of its larger dipole moment,

the starting structure 1c/1d is better solvated than TS 2, which

results in a slight increase in ∆G^q_OBSas the ꢀ_relor 2(ꢀ_rel- 1)/

(2ꢀ_rel- 1) value of the solvent increases.

MeOH, and EtOH, the complexation energies [∆E₃) E_complex

3

- (3E_HBD+ E_N-oxide)] of the solvation by the third solvent

molecule were higher than ∆E₂. [∆E₃(H₂O) - ∆E₂(H₂O) )

1.18 kJ mol^-1; ∆E₃(MeOH) - ∆E₂(MeOH) ) 2.78 kJ mol^-1

;

In the absence of an exchangeable proton, in a non-HBD

(aprotic) solvent, only the Meisenheimer rearrangement takes

place and the product progressively decomposes to other

derivatives.¹⁶

∆E₃(EtOH) - ∆E₃(EtOH) ) 4.30 kJ mol^-1.] These values

suggest that unfavorable complexation effects may occur if a

third solvating molecule is considered. The energy values also

indicate that the first solvating shell with two solvent molecules

is preferred with H₂O, MeOH, EtOH, and i-PrOH as solvents

(∆E₂) -8.72, -11.38, -6.57, and +0.67 kJ mol^-1, respec-

tively), but in t-BuOH the effect of the second molecule is less

significant (Table 2).

3.2.2. Weak and Strong HBD Solvents. In contrast with

the non-HBD (aprotic) solvents, the reaction rates were sig-

nificantly lower in HBD (protic) media, reflecting the larger

∆G^q_OBS. In type 2A solvents (e.g., in dry CHBr_3,CHCl₃,

CH₂Cl₂, and MeNO₂), the k_reland ∆G^q_OBSvalues (0.67-0.22

and 96.0-98.8 kJ mol^-1, respectively) fall between those

observed for type 1 and 2B solvents, suggesting a weak HBD

effect. It should be mentioned that CH₂Cl₂and MeNO₂, with

EPAs also have very significant complexation energies (Table

2). H⁺and BF₃(corrected for the effect of diethyl ether, ∆E₁

) E_N-oxide-BF3+ E_OEt2- (E_BF3:OEt2+ ∆E_N-oxide-BF3) possess

the largest complexation energies, while Li⁺and Na⁺too have

significant effects.⁵³

k_rel) 0.67 and 0.52 and ∆G^q_OBS) 96.0 and 96.6 kJ mol^-1

,

respectively, exhibit a very weak HBD effect. In strong HBD

solvents of type 2B, the reactions proceed much more slowly:

k_rel) 0.032-1.98 × 10^-3, ∆G_O^q_BS) 104.6-111.0 kJ mol^-1, ∆

H^q_OBS) 97.6-107.3 kJ mol^-1, ∆S^q) (-9.6) - (-20.6) J

3.2. Experimental Kinetics. 3.2.1. Kinetic Studies in

Non-HBD (Aprotic) Solvents. Activation parameters (∆H_O^q_BS

,

∆G^q_OBS, and ∆S^q) calculated from the unimolecular rate con-

stants (k), obtained under standard conditions (see Section 2)

at given temperatures for the first step of the rearrangement of

N-oxide 1 in various aprotic solvents, are shown in Table 3.

mol^-1K^-1

.

(54) Abboud, J.-L. M.; Notario, R. Pure Appl. Chem. 1999, 71, 645-718.

(55) Evans, E.; McElroy, A. J. Solution Chem. 1975, 4, 413-430.

(56) Kirkwood, J. G. J. Chem. Phys. 1934, 2, 351-361.

(53) Maria, P.-C.; Gal, J.-F. J. Phys. Chem. 1985, 89, 1296-1304.

9

7622 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

Table 3. Rate Constants and Activation Parameters (∆G^q_OBS) Obtained for the First Step of the Rearrangement of N-Propargylmorpholine

N-Oxide (1) in Different Solvents (for Experimental Conditions, See the Supporting Information)

q

∆

H_OBS

∆

G_OBS

∆

S^q

a

1

b

1

c

1

solvent

ꢀ_rel

T (K)

k (s^-

)

k

°

(s^-

)

k_rel

(kJ mol^-

)

(kJ mol^-

)

(J mol^-¹K^-

)

D₂O

80.00

78.36

46.70

38.22

35.94

34.78^j

32.66

26.53^j

24.55

20.70

338

313

338

313

332

338

309

338

313

323

309

5.03 × 10^-5

3.92 × 10^-5

6.50 × 10^-4

4.51 × 10^-4

8.61 × 10^-4

1.31 × 10^-3

6.04 × 10^-5

5.00 × 10^-5

7.22 × 10^-5

1.86 × 10^-3

7.01 × 10^-5

1.63 × 10^-4

9.73 × 10^-4

4.70 × 10^-4

5.75 × 10^-4

1.91 × 10^-4

6.07 × 10^-4

1.15 × 10^-2

2.41 × 10^-6

1.70 × 10^-6

6.50 × 10^-4

4.51 × 10^-4

8.61 × 10^-4

1.31 × 10^-3

2.81 × 10^-6

1.98 × 10^-6

4.29 × 10^-6

1.86 × 10^-3

4.75 × 10^-6

8.59 × 10^-6

1.54 × 10^-3

1.99 × 10^-5

5.75 × 10^-4

1.91 × 10^-4

1.98 × 10^-4

8.00 × 10^-3

2.80 × 10^-3

1.98 × 10^-3

0.67

0.52

1.00

106.6

107.3

90.0

90.7

89.0

110.1

111.0

95.9

96.6

94.8

-9.6

-9.6^e

H₂O^d

Me₂SO^f

-17.1^g

-17.1

-17.1^g

-15.7

-17.1^g

-20.6

-17.1^g

-17.1^c

-17.1^g

f

MeNO₂

MeCN^f,h

f

PhNO₂

1.52

87.9

93.8

MeOHⁱ

3.26 × 10^-3

2.30 × 10^-3

4.98 × 10^-3

2.17

105.0

104.5

103.7

87.0

104.8

101.0

87.6

97.6

90.0

92.9

92.3

109.7

110.4

108.6

92.8

110.9

106.8

93.4

104.6

96.0

98.8

CF₃CH₂OH

EtOHⁱ

Me₂CO^f

(CF₃)₂CHOH

∼20^k

5.52 × 10^-3

9.98 × 10^-3

1.79

i-PrOHⁱ

19.92^j

12.91^j

10.36^j

8.93

pyridine^f

t-BuOHⁱ

0.0231

0.67

0.22

0.23

f

CH₂Cl₂

CHCl₃

f

4.90

f

CHBr₃

4.35^j

2.21

98.2

89.0

dioxane^f

0.11

83.1

^aTaken from the Gaussian03 program based on IUPAC data.^{54 b}Calculated for 313 K. ^cEstimated from ∆G^q_OBS, assuming that ∆S^qis constant (-17.1

J mol^-1K^-1) for different solvents. ^dValues corrected by taking the inverse R secondary isotope effect into account (see Section 3.2.3). ^eEstimated value

equal to that obtained for D₂O. ^fDeuterated solvent. ^gEstimated value equal to that obtained for MeCN. ^hReference solvent. ⁱTaken from ref 16. ^jTaken

from ref 17. ^kTaken from ref 55.

Figure 6. ∆G^q_OBSvalues as compared with R values,⁵⁷proportional to the

HBD ability of the given solvent. TFE ) CF₃CH₂OH; HFIPA )

(CF₃)₂CHOH.

Figure 5. ∆G^q_OBSvalues for the first step of the rearrangement of

N-propargylmorpholine N-oxide (1), obtained from kinetic measurements

in different solvents.

In Figure 6, the ∆G^q_OBSvalues are plotted against the R

values,^57-60which are proportional with the HBD ability of the

solvents. The R values were calculated by multilinear regression

of the solvatochromic effect values obtained for 4-nitroaniline

derivatives.

CH₂Cl₂, and MeNO₂) either. The special HB pattern of t-BuOH

may be attributed to the bulkiness of its molecules causing steric

hindrance around the N-oxygen.⁴⁰From the MD studies, we

concluded that the first solvating shell of t-BuOH is not

uniform: it splits into two parts, as described in Section 3.1.4.

The dual function of strong HBD solvents results in a slow

Meisenheimer reaction, allowing the competing reaction to

proceed, leading to the enamino aldehyde product (4) which

requires a protonation step 5* f 6* (Scheme 2). However, a

significant difference in the product distribution can be recog-

nized in the series of solvents ranging from H₂O to t-BuOH, as

a reflection of their different protonation and deprotonation

properties. The two extreme values were observed in t-BuOH

([3]/[4] ) 0.29) and in MeOH ([3]/[4] ) 1.21), with intermediate

data in EtOH ([3]/[4] ) 0.66) and in i-PrOH ([3]/[4] ) 0.50).¹⁶

Both the R and the acity⁶¹parameters (anion-solvating property,

obtained from nonlinear regression of numerous physical and

chemical properties of solvents) of the solvents display a good

relationship with the observed product distribution.¹⁶In weak

As expected, the two fluorinated solvents [CF₃CH₂OH and

(CF₃)₂CHOH] and water are involved in the strongest HB with

N-oxide 1, causing slow reactions as compared with other

solvents. It is interesting to compare the effects of the two

fluorinated solvents with those of the related nonfluorinated ones

(EtOH and i-PrOH); stronger HB significantly decreases the

reaction rate. The position of t-BuOH in Figures 5 and 6 is

rather special; t-BuOH does not closely belong to the strong

HBD solvents (the series from water to i-PrOH), but it cannot

be ranked among the weak HBD solvents (CHCl₃, CHBr₃,

(57) Laurence, C.; Nicolet, P.; Dalati, M. T.; Abboud, J.-L. M.; Notario, R. J.

Phys. Chem. 1994, 98, 5807-5816.

(58) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J. Org.

Chem. 1983, 48, 2877-2887.

(59) Marcus, Y. Chem. Soc. ReV. 1993, 22, 409-416.

(60) Cramer, C. J. Essentials of Computational Chemistry; Wiley & Sons: West

Sussex, England, 2001; Chapter 7, p 433.

(61) Swain, C. G.; Swain, M. S.; Powell, A. L.; Alunni, S. J. Am. Chem. Soc.

1983, 105, 502-513.

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7623

A R T I C L E S

Mucsi et al.

HBD solvents (CHCl₃, CHBr₃, CH₂Cl₂, and MeNO₂), just as

in the non-HBD solvents, the formation of 4 is precluded

because of the absence of an acidic proton.

3.2.3. Kinetic Isotope Effect (KIE). Isotope-labeling experi-

ments carried out in the solvent pairs CH₃OH-CD₃OD and

C₂H₅OH-C₂D₅OD by the standard GC method demonstrated

significant inverse secondary KIEs (k_H/k_D) 0.80 and 0.78,

respectively) for the rate-controlling first step of the Meisen-

heimer rearrangement of N-oxide 1. These experiments proved

that there is no observable difference in the kinetic parameters

measured in aprotic deuterated or aprotic nondeuterated solvents.

However, in the case of deuterium oxide, we corrected the

measured reaction rate constant by multiplying by a factor of

0.78 due to the observed secondary isotope effect.

Deuterated strong HBD solvents exert two effects on the

reaction. When the reaction was performed in deuterated strong

HBD solvents, 70-80% of the exchangeable C(sp)-H(10)

exchanged to D(10) (the NMR signal of H(10) rapidly decreased

to 20-30% of its original value),¹⁵which influenced the rate-

determining step. It is known⁶²that such a KIE may be detected

if a change in the geometry from sp²to sp³hybrid states occurs

during the reaction. Although to the best of our knowledge there

are no relevant literature data, it is reasonable to assume that

the present inverse secondary KIE is a consequence of a novel

type of hybridization that changes from sp to sp², affecting the

terminal C(10) sp atom of the propargyl group of N-oxide 1 as

reaction center. If we suppose that H(10) f D(10) exchange

occurs for 1, we can estimate the KIE from a simple theoretical

description (eq 14),⁶²where only the average IR frequencies of

C(sp)-H of N-oxide 1 and those of C(sp²)-H of TS 2 are

considered. The calculation gave practically the same result as

the experiments.

Figure 7. Increase in ∆G^q_OBSvalues calculated for the rearrangement of

N-propargylmorpholine N-oxide (1) in MeCN solutions on the addition of

different amounts of water (see text for experimental conditions).

This process influences only the product distribution step and

has no effect on the examined rate-controlling step.

3.2.4. Titration with EPA and Water in MeCN. To

demonstrate the role of HB in decreasing the rate of the

rearrangement of N-oxide 1, we carried out titration experiments

with standard MeCN solutions, adding different amounts of

water to the reaction mixture (0.1, 0.3, 0.8, 1.3, 1.9, 6.2, 8.8,

58, and 100 molar equiv as compared with the substrate). We

found a significant decrease in the reaction rate, which undoubt-

edly indicates the effect of HB. For example, 1.9 equiv of water

(ca. 0.7%) reduced the reaction rate to one-fifth, and the rate in

a 1:1 (v/v) mixture of MeCN and water (100 equiv) almost

reached the rate observed in pure water. Figure 7 illustrates the

increase in the free energy of activation during titration relating

to “solvent sorting” or “selective solvation”.^63,64The calculated

∆G^q_OBSchanged from 94.8 kJ mol^-1(pure MeCN) to 111.0 kJ

mol^-1(pure water) during titration. This type of experiment is

suitable to determine the water concentration when the 1:1

complex formed between the N-oxide and water predominates

(see Section 3.3.4). The fitted curve is proportional to a ln

function that relates to the dependence of ∆G^q_OBSon ln([H₂O])

(see Section 1.3).^63,64

0.7195³ⁿ

_A-6

exp

[ν_i(AH) - ν_i(AD)]

∑

0.7195³ⁿ

{

}

k_H

k_D

T

i)1

)

^--7

exp

[ν_i(H)^-- ν_i(D)^-]

∑

}

T

i)1

0.7195

exp

[ν(AH) + 2δ(AH) - ν(AD) - 2δ(AD)]

{

}

T

)

0.7195

exp

[ν(H)^-+ δ₁(H)^-+ δ₂(H)^-- ν(D)^-- δ₁(D)^-- δ₂(D)^-]

Product 4, which forms in protic (strong HBD) media, appears

only in the 2:1 mixture of MeCN/H₂O (ca. 60 equiv of water

as compared to 1). In the case of the higher water content, this

compound did not even form at below 10 equiv of water (ca.

3.0 v/v%). The product ratio [3]/[4] is unpredictable because

of the following degradation steps.

{

}

T

0.7195

exp

(3300 + 2‚630 - 2444 - 2‚467)

[

]

338

) 0.73

(14)

0.7195

338

(3020 + 1300 + 810 - 2237 - 963 - 600)

[

]

In eq 14, k_Hand k_Ddenote the reaction rate constants in

HBD molecules belong to the larger family of EPAs. Hence,

similar rate-reducing effects can be expected from other known

EPA molecules. In the present study, certain aromatic com-

pounds (such as pyridine, different nitro derivatives of benzene),

LiClO₄, NaClO₄, BF₃:OEt₂, and HCl were investigated as shown

in Table 4.

nondeuterated and deuterated solvents, respectively, ν_iis the

IR frequencies of molecules containing hydrogen or deuterium,

ν(AH), ν(AD), δ(H), and δ(D) are the bond stretching and

bending frequencies of the C-L group (L ) H or D) for

structure 1 (estimated from literature data for propargyl groups),

and ν(AH)^q, ν(AD)^q, δ₁(H)^q, and δ₂(H)^qare the bond stretching

and bending frequencies of TS 2 (estimated from literature data

for molecules containing a similar bond pattern, >CdCL-O).

The second effect of deuterated solvents on this reaction

appears during the protonation process 5* f 6*, where a proton

binds to C(9) of 5* (Scheme 2). In deuterated solvents,

deuterium atom takes part in this process, and the resulting 4

contains a deuterium on C(9)¹⁵in addition to that on C(10).

BF₃and H⁺proved to be the strongest EPA additives since

the addition of 1 equiv of BF₃or H⁺practically halted the

reaction. One equivalent of Li⁺decreased the rate to ap-

(62) Ruff, F.; Csizmadia, I. G. Organic Reactions: Equilibria, Kinetics and

Mechanism; Elsevier: Amsterdam, 1994; Chapter 8, pp 232-239.

(63) Abboud, J.-L. M.; Douhal, A.; Arin, M. J.; Diez, M. T.; Homan, H.;

Guihe´neuf, G. J. Phys. Chem. 1989, 93, 214-220.

(64) Marcus Y. In SolVent Mixtures: Properties and SelectiVe SolVation; Marcel

Dekker: New York, 2002; Chapter 5, pp 180-234.

9

7624 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

Table 4. Rate Constants and ∆G^q_OBSValues Obtained for the Rearrangement of N-Propargylmorpholine N-Oxide (1) in MeCN Solutions

Containing EPA Molecules (for Experimental Conditions, See Text)

q

1

b

1

EPA

EPA added^a

T (K)

k (s^-

)

k°

(s^-

)

k_rel

∆

G_OBS(kJ mol^-

)

H⁺

BF₃

LiClO₄

NaClO₄

1

0.8

1

2

5

1

2

5

1

343

352

343

323

338

323

338

313

309

313

0^c

0

-

7.35 × 10^-4

7.69 × 10^-4

5.09 × 10^-4

4.39 × 10^-4

4.34 × 10^-3

2.16 × 10^-3

8.43 × 10^-4

2.03 × 10^-3

1.98 × 10^-3

2.89 × 10^-4

2.78 × 10^-3

1.97 × 10^-3

5.92 × 10^-4

1.31 × 10^-3

9.73 × 10^-4

8.61 × 10^-4

1.98 × 10^-5

2.07 × 10^-5

1.32 × 10^-5

3.72 × 10^-6

1.38 × 10^-4

6.42 × 10^-5

2.29 × 10^-5

6.46 × 10^-4

2.50 × 10^-4

1.29 × 10^-4

7.92 × 10^-4

6.11 × 10^-4

2.84 × 10^-5

1.31 × 10^-3

1.54 × 10^-3

8.61 × 10^-4

0.023

0.024

0.015

0.0043

0.16

0.075

0.027

0.75

0.29

0.15

0.92

0.71

104.3

104.2

105.4

108.6

99.3

101.3

103.9

95.5

96.0

105.4

95.1

95.6

103.4

93.8

93.4

94.8

NaClO₄

1 equiv of TNB^e

2 equiv of TNB^e

cc.TNB^e

2

∼10

1 equiv of DNB^d

2 equiv of DNB^d

cc.DNB^d

1

2

∼10

p.s.^f

0.033

1.52

1.79

PhNO₂

pyridine

MeCN^g

1.00

^aEquivalent amount of EPA as compared with N-oxide 1. ^bCalculated for 313 K. ^cNot measurable. ^d1,3-Dinitrobenzene (DNB). ^e1,3,5-Trinitrobenzene

(TNB). ^fPure solvent. ^gReference solvent.

proximately the same extent as observed in alcoholic solutions

(k_rel) 0.023, ∆G^q_OBS) 104.3 kJ mol^-1), although the molar

ratio of complexing ROH and N-oxygen is much larger in the

latter case, as it appeared that two ROH molecules were

coordinated to the N-oxygen instead of one species (see Section

3.3.4). The rate-decreasing effect of Na⁺is approximately 1

order of magnitude weaker (k_rel) 0.16, ∆G^q_OBS) 99.3 kJ

mol^-1) than that of Li⁺.

Our data reveal that only saturated solutions of 1,3,5-

trinitrobenzene (TNB) and 1,3-dinitrobenzene (DNB) (200 mg/

750 µL; ∼10 equiv) have such effects on the protic solvents

(k_rel) 0.015 and 0.033, ∆G^q_OBS) 105.4 and 103.4 kJ mol^-1

,

respectively). TNB displays a larger rate-decreasing effect than

DNB, but TNB is only in a concentrated solution as effective

as t-BuOH or i-PrOH. One equivalent amount of TNB decreases

the rate only 0.75-fold; this effect is similar to that of 1 equiv

of ROH in a standard solution. Nitrobenzene and pyridine could

be investigated only as pure solvents. They acted as very weak

EPAs, but the effects are negligible. The rate-decreasing effects

of various EPAs and HBDs on ∆G^q_OBSfor the rearrangements

of N-oxide 1 are depicted in Figure 8.

Figure 8. Effects of EPAs and HBDs on ∆G^q_OBSvalues for the rearrange-

ment of N-propargylmorpholine N-oxide (1) in different solvents. (A) Pure

MeCN. (B) 1 equiv of H₂O in MeCN. (C) 1 equiv of Na⁺in MeCN. (D)

Concentrated DNB-MeCN solution. (E) 1 equiv of Li⁺in MeCN. (F)

Concentrated TNB-MeCN solution. (G) Pure H₂O. (H) 1 equiv of BF₃:

OEt₂in MeCN. (I) 1 equiv of H⁺in MeCN.

Comparison of the titration curves of the EPAs (Li⁺, Na⁺,

DNB, and TNB) and water (Figure 9) allows the conclusion

that Li⁺and Na⁺reach their saturation point near 5 equiv, while

the weaker DNB and TNB do not attain their maximum effect

even at 10 equiv. The water curve lies between the pairs Li⁺/

Na⁺and DNB/TNB, demonstrating a moderate EPA effect.

Saturation is reached at around 2-3 equiv.

The presence of different EPAs in non-HBD MeCN solutions

has a significant effect on the rate reduction, but the lack of

protonating ability of these species means that product 3 is

formed exclusively. This is connected with their single function

(see Section 1.3) relative to the weak HBD solvents (CHCl₃,

CH₂Cl₂, and CHBr₃).

Figure 9. Comparison of the titration curves of different EPAs and water.

energies of activation when N-oxide 1 is transformed in solvents

belonging to different classes. Extreme ∆k_relvalues (∆k_rel

)

3.2.5. Energetic and Mechanistic Concepts. The results

observed for the rate constant and product ratio can be related

to the dual function of the strong HBD (protic) solvents, the

single function of the weak HBD and EPA molecules, and the

zero function of the non-HBD (aprotic) solvents. The experi-

mental data indicate large differences in reaction rates and free

8.71 × 10^-4, corresponding to ∆∆G_O^q_BS) 18.6 kJ mol^-1

characterize such reactions as those conducted in dioxane (type

1) or water (type 2B). On the other hand, the differences between

the solvents are rather small within a given class (∆∆G_O^q_BS

)

1-6 kJ mol^-1). If the series of different solvents are considered,

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7625

A R T I C L E S

Mucsi et al.

Table 5. Computed Activation Parameters (kJ mol^-1) and Atomic Distances (Å) Obtained with the Implicit Solvent Model (1) for the

Rearrangement of N-propargylmorpholine N-oxide (1) in Different Solvents, as Compared with the Experimental Data (2)

implicit method (1)

experiment (2)

∆∆G^q

(1) (2)

q

b

b,c

d

c,d

e

c,e

solvent

solvent type^a

∆

E^q

∆

E_CORR

∆

H_CORR

∆

G_CORR

∆

H_CPE

∆

G_CPE

∆

H_TOT

∆

G_TOT

d (O‚‚‚C)^f

∆

H_OBS

∆

G_OBS

−

H₂O

MeOH

2B

2A

1

83.95

83.73

82.86

82.63

81.29

80.49

77.19

83.76

83.83

83.74

83.68

82.63

81.40

72.74

66.75

85.9

84.36

84.03

83.18

83.01

81.62

80.87

75.41

84.10

84.19

84.08

84.05

83.01

81.51

73.32

67.39

89.06

88.73

87.88

87.71

86.32

85.57

80.11

88.8

88.89

88.78

88.75

87.71

86.21

78.02

72.09

2.93

3.46

4.12

4.21

5.15

5.45

6.74

3.41

3.47

3.44

4.21

4.98

8.86

3.25

3.61

4.27

4.47

5.09

5.47

6.73

3.66

3.75

3.69

3.65

4.47

4.82

8.67

9.70

87.29

87.49

87.3

92.31

92.34

92.15

92.18

91.41

91.04

86.84

92.46

92.64

92.47

92.4

2.05

2.06

2.05

2.06

2.07

2.04

107.3 111.0 -18.69

105.0 109.7 -17.36

103.7 108.6 -16.45

104.5 110.4 -18.25

101.0 106.8 -14.62

104.8 110.9 -18.72

97.6 104.6 -13.19

85.68

84.81

84.58

83.24

82.44

79.14

85.71

85.78

85.69

85.63

84.58

83.35

74.69

68.7

EtOH

CF₃CH₂OH^g

i-PrOH

87.3

87.22

86.77

86.32

82.15

87.51

87.66

87.52

87.49

87.22

86.49

82.18

77.69

(CF₃)₂CHOH^g

t-BuOH

CH₂Cl₂

CHCl₃

90.0

92.9

90.7

90.0

89.0

87.9

87.0

87.6

83.1

96.0

-4.96

98.8 -11.96

MeNO₂

Me₂SO

MeCN

96.6

95.9

94.8

93.8

92.9

93.4

89.1

-4.14

-3.26

-2.33

-1.40

-0.72

-2.37

-2.41

PhNO₂

Me₂CO

pyridine

dioxane

in vacuo^h

92.18

91.03

86.69

81.79

10.30

^a1: Non-HDBs, 2A: weak HDBs, 2B: strong HDBs. ^bIncluding ZPE and BSE. ^cEstimated from ∆H^qon the assumption that ∆S^q(-14.61 J mol^-1

K^-1) is constant in different solvents. ^dDifference between the gauche and anti conformers (pre-equilibrium). ^eWith consideration of BSE, dispersion, and

pre-equilibrium effect. ^fO(7)‚‚‚C(10) atomic distance in TS 2. ^gCalculated data equal to those computed for EtOH and i-PrOH, respectively. ^hTaken from

ref 17.

∆G^q_TOTof +81.79 kJ mol^-1is close to the value measured in

a decrease in the rate of reaction and an increase in the free

energy of activation can be observed on increase of the polarity

dioxane (∆G^q_OBS) 92.9 kJ mol^-1, see Table 5), but seems very

low in comparison with the value (∆G^q_OBS) 111.0 kJ mol^-1

,

of the solvent according to the theoretical Kirkwood-Onsager

rules.^23,56

see Table 5) obtained experimentally in aqueous solvents.

The very large difference in the case of water does not stem

from the low efficiency of the theoretical methods, but is rather

due to the inappropriate application of chemical modeling to

HB.

The data obtained on HBD solvents (types 2A and 2B) reveal

the relative importance of the solvent polarity and the ability

of HBD to control the rate of reaction. The relative permittivities

(ꢀ_rel) of MeCN and MeOH are comparable, whereas the ∆G^q

OBS

values determined for the rearrangements differ markedly (ꢀ_rel

However, the relatively small deviations point to the influence

of the relative permittivities (ꢀ_rel) of the solvent molecules, which

are present in large amount under the experimental conditions.

To model aprotic solvents, we chose the PCM method^1-4from

the implicit solvation method family. Using the implicit PCM

model, we first calculated the energies of the N-oxide 1

conformers in different solvents, including the activation

parameters for the conformational anti/gauche equilibrium

reaction. Data indicative of a significant solvent dependence

are found in Table 5 (see columns ∆H^q_CPEand ∆G_C^q_PE).

) 35.94 and 32.66; ∆G^q_OBS) 94.8 and 109.7 kJ mol^-1

,

respectively). The situation is similar when the solvents Me₂CO,

i-PrOH, and (CF₃)₂CHOH are compared (ꢀ_rel) 20.70, 19.92,

and ∼20; ∆G^q_OBS) 92.9, 106.8, and 108.2 kJ mol^-1, respec-

tively). The reaction rate in CH₂Cl₂is somewhat smaller than

those in aprotic solvents (e.g., in Me₂CO) that have similar

relative permittivities. The relative k(Me₂CO)/k(CH₂Cl₂) value

of 3.23 points to a moderate rate-reducing effect of very weak

HB between CH₂Cl₂and N-oxide 1 molecules. It may be

concluded unequivocally that the marked decrease in reaction

rate is due to the HBD ability of the solvents.

To obtain the corrected activation parameters (∆E_C^q_ORR

,

∆H^q_CORR, and ∆G^q_CORR), we used eqs 15-19 for the PCM

models:

The three types of solvents (types 1, 2A, and 2B) each exhibit

different behavior. Non-HBD solvents give only one intermedi-

ate in a rapid reaction. The kinetic data revealed that strong

HBD solvents and EPA molecules could be substituted for each

other. Both of them gave rise to similar rate-decreasing effects,

but EPA molecules have only a single functionality, which does

not permit formation of the non-Meisenheimer product (4), due

to the absence of the exchangeable proton that is essential in

step 5* f 6*. Protic solvents allow the formation of 4*, which

results in a lower reaction rate as compared with other solvent

types.

3.3. Computational Kinetics. 3.3.1. Calculations in the Gas

Phase and in Non-HBD Solvents (in Vacuo and PCM

Model). As mentioned earlier, the computed activation param-

eters of the RC step of the rearrangement of N-oxide 1 in vacuo

are as follows: ∆E^q_RC) +66.7 kJ mol^-1, ∆H_R^q_C) +65.4 kJ

mol^-1, ∆G^q_RC) +69.7 kJ mol^-1, and ∆S_R^q_C) -14.61 J mol^-1

K^-1. When CPE and BSE are included, the calculated

∆E^q_CORR) ∆E^q+ ∆E_B^q_SE) ∆E^q+ 1.95 kJ mol^-1(15)

∆H^q_CORR) ∆H^q+ ∆E_B^q_SE) ∆H^q+ 1.95 kJ mol^-1(16)

∆G^q_CORR) ∆H^q_CORR- T∆S^q_CORR

)

∆H^q_CORR- (-14.24 J K^-1mol^-1)‚T (17)

The final (TOT) activation parameters are composed of two

terms related to CPE and the correction introduced previously

(CORR).

∆H^q_TOT) ∆H^q_CORR+ ∆H_CPE

∆G^q_TOT) ∆G^q_CORR+ ∆G_CPE

(18)

(19)

In applying the PCM model, we calculated the activation

parameters for rearrangement of N-oxide 1 in all the solvents

9

7626 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

Table 6. Computed Activation Parameters (kJ mol^-1) and Atomic Distances (Å) Obtained with the Explicit (1) and the Explicit-Implicit

Solvent Model (2) for the Rearrangement of N-Propargylmorpholine N-Oxide (1) in Different Solvents, as Compared with the Experimental

Data (3)

explicit method (1)

explicit

−

implicit method (2)

experiment (3)

∆∆G^q

(1) (3)

∆∆G^q

(2) (3)

q

b

c

c,d

b

c

c,d

solvent

solvation^a

∆

E_CORR

∆

H_TOT

∆

G_TOT

d (O‚‚‚C)^e

∆

E_CORR

∆

H_TOT

∆

G_TOT

d (O‚‚‚C)^e

∆

H_OBS

∆

G_OBS

−

H₂O

1

2

1

2

1

2

1

2

1

2

1

2

1

2

88.08

103.93

88.17^f

103.65^f

87.30

103.58

115.58

88.18

102.87

121.22

87.79

102.01

70.56

89.06

105.75

89.29

105.18

88.11

105.54

117.32

89.83

104.52

122.73

88.99

103.54

70.77

82.27

87.35

94.29

90.94

99.09

94.45

1.87

1.78

1.88

1.79

1.88

1.80

1.75

1.88

1.84

1.79

1.89

1.84

2.02

1.93

1.89

1.9

93.18

104.41

94.16

106.23

99.55

111.45

1.96

1.88

107.3 111.0 -16.55 -14.45

110.97

94.51

110.4

93.33

110.76

122.54

94.3

109.85

127.21

94.00

108.55

75.99

92.11

92.44

99.38

96.00

104.15

-0.03

109.7 -16.46

0.7

0.45

MeOH

EtOH

105

104.11

105.64

110.86

1.92

1.16

103.7 108.6 -16.55

103.13

116.01

105.09

117.75

110.31

122.97

1.92

1.85

2.16

1.71

CF₃CH₂OH

i-PrOH

104.5 110.4

101.0 106.8

12.44

12.57

101.83

119.35

90.87

101.1

85.58

88.61

87.8

103.48

120.91

92.07

102.63

85.79

84.28

90.3

108.81

126.24

97.08

107.64

91.01

95.34

95.39

1.93

1.85

1.92

2.05

2.02

2.01

3.05

16.30

2.01

15.34

-7.52

3.04

(CF₃)₂CHOH

t-BuOH

104.8 110.9

97.6 104.6

3.95

CH₄

MeNO₂

CH₂Cl₂

85.38

84.85

93.79

87.15

90.7

90.0

96.6

96.0

-4.49

-3.56

3.38

-1.26

-0.61

-

CHCl₃

89.17

92.96

98.02

1.98

92.9

98.8

-2.8

-5.35

-0.78

96.30

1.84

^aNumber of solvent molecules. ^bIncluding ZPE and BSE. ^cWith consideration of BSE, dispersion, and pre-equilibrium effect. ^dEstimated from ∆H^qon

the assumption that ∆S^q(-14.61 J mol^-1K^-1) is constant in different solvents. ^eO(7)‚‚‚C(10) atomic distance in the TS 2. ^fUsing ∆E^qdata taken from ref

17.

at a given reaction temperature for the rearrangement of 1. We

investigated the activation energy calculations with one and two

of the explicit solvent molecules listed in Table 6 to verify our

prediction. As may be seen from Table 6, the computed ∆G_T^q_OT

of the explicit-implicit values confirmed the experimental

∆G^q_TOTresults.

The solvent molecules may assume different conformations.

We chose the conformers with lowest energy, estimating the

conformational energies by using the B3LYP/6-31G(d) method.

Direct computation of the activation entropy is impossible

because of the many low-frequency motions originating from

the solvent molecules; accordingly, the value of ∆S_C^q_ORR

(-14.61 J mol^-1K^-1) was used, as introduced in Section 2.2.3.

The ∆G^q_TOTvalues were calculated in the same way as

described for the implicit method in eqs 15-17. The values of

∆G_CPEin different solvents were considered to be equal to those

obtained with the implicit model.

Figure 10. Dependence of ∆G^q_CORR, ∆G_CPE, and ∆G^q(see eqs 15-19)

on the relative permittivities of the solvents used, as^TOc^Talculated with the

implicit solvent model (IEF-PCM) for the rearrangement of N-propargyl-

morpholine N-oxide (1). 1: dioxane. 2: pyridine. 3: Me₂CO. 4: PhNO₂.

5: MeCN. 6: Me₂SO. 7: MeNO₂. 8: CHCl₃. 9: CH₂Cl₂.

Table 6 lists the activation parameters calculated with the

explicit model in the solvents H₂O, MeOH, EtOH, CF₃CH₂OH,

i-PrOH, (CF₃)₂CHOH, t-BuOH, CHCl₃, CH₂Cl₂, and MeNO₂,

where one or two solvent molecules form a solvation complex

with the negatively charged oxygen in N-oxide 1. Extreme ∆

G^q_TOTdata can be observed for the fluorinated solvents, which

yielded the largest deviations from the experimental values.

These solvents comprise a separate group in the family of strong

HBD solvents. In nonfluorinated solvents, ∆∆G^qvalues of less

than 3.95 kJ mol^-1reveal that the explicit solvent model is more

capable of describing a protic (HBD) solvent effect than the

implicit variation.

The ∆G^q_TOTvalues computed by using the explicit solvent

models were individually quite close to those measured experi-

mentally for HBD solvents. The trend is undoubtedly similar

to that observed in the experiments where the ∆G^q_TOTvalues

decreased with increase of the relative permittivities of the

strong HBD solvents, with the exception of fluorinated sol-

vents. It is striking, however, that the relative ∆G^q_TOTvalues

[∆G^q_TOT(ROH) - ∆G_T^q_OT(H₂O)] calculated for different protic

used in the kinetic measurements. The data in Table 5 indicate

that the calculated ∆G^q_TOTvalues for non-HBD solvents are

very close to the measured ones [∆∆G^q) (-0.72) - (-3.26)

kJ mol^-1], whereas the data for strong HBD (type 2B) solvents

[∆∆G^q) (-18.72) - (-13.19) kJ mol^-1)] differ significantly.

Weak HBD solvents (type 2A) exhibit intermediate deviations

[∆∆G^q) (-4.96) - (-11.96) kJ mol^-1].

Figure 10 depicts the dependence of the calculated ∆G^qdata

(∆G^q_TOT, ∆G_C^q_PE, and ∆G^q_RC) on the relative permittivities

according to the Kirkwood-Onsager rule [2(ꢀ_rel- 1)/(2ꢀ_rel

-

1)]^23,56for different (non-HBD and weak HBD) solvents. All

∆G values (∆G_T^q_OT, ∆G_C^q_PE, and ∆G_R^q_C) are in good agreement

with the Kirkwood-Onsager rules, but ∆G^q_CPEand ∆G_R^q_Chave

opposite slopes, demonstrating conflicting changes with the

dipole moment in the processes 1b f 1c/1d and 1c/1d f 2.

3.3.2. Kinetics in HBD Solvents (Explicit and Joint Explicit

and Implicit Solvent Models). (A) Calculations with Explicit

Solvent Model. MD studies allow the conclusion that two strong

HBD or one weak HBD solvent molecules form the first shell

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7627

A R T I C L E S

Mucsi et al.

(B) Calculations with Joint Explicit-Implicit Solvent

Model. The explicit solvent model takes into account only the

effects of HB, other solvent effects, such as the relative

permittivities on which the implicit PCM model is based, being

neglected. From the results obtained separately with the implicit

and explicit models, we concluded that a suitable way to obtain

correct activation parameters is joint application of the two

methods. Unfortunately, the joint method has the serious

disadvantage that the convergence of the optimization process

becomes very labile and occasionally turns into an oscillating

cycle that requires a considerable amount of calculation time.

On the other hand, application of the joint method leads to

accurate and realistic results. Table 6 summarizes the data

obtained and demonstrates better agreement with the experi-

mental data than for the explicit solvent model alone.

Figure 11. Comparison of the differences ∆G^q_TOT(ROH) - ∆G^q_TOT(H₂O)

obtained from the implicit, explicit, and explicit-implicit solvent models

with the experimental results.

Relative ∆G^q_TOTvalues less than 3.04 kJ mol^-1reveal that

the joint model describes the strong HBD solvent effect well.

In the series from H₂O to t-BuOH, omitting the fluorinated

solvents, the relative ∆G^q_TOTvalues between the two extreme

data are 2.42, 3.81, and 6.4 kJ mol^-1, as computed with the

explicit solvent model or the joint model and measured

experimentally, respectively (Figure 11). The largest deviation

in relative ∆G^q_TOTwas observed for t-BuOH, where the solvent

model with two solvent molecules is an overestimate, and the

solvent model with one solvent molecule is an underestimate

of the experimental value. With reference to the MD study, the

experimental value can be estimated from a consideration of

the models with one or two t-BuOH molecules.

In Figure 12, the ∆G^qvalues obtained experimentally and

the ∆G^q_TOTcalculated for the rearrangement of N-oxide 1

with the implicit and joint implicit-explicit methods are

shown in different solvents, depending on the relative permit-

tivities.

The similar ∆∆G^q_TOTvalues obtained with the explicit and

joint explicit-implicit solvent models for protic solvents permit

the conclusion that the first solvation shell is involved to the

highest degree in the solvent effect.

solvents were smaller than the differences between the experi-

mental ones. In the solvent series from water to t-BuOH, the

computed relative ∆G_T^q_OTvalue is only 2.42 kJ mol^-1, while it

was measured to be 6.40 kJ mol^-1(Figure 11). This marked

deviation may be a result of the dominating HB and the neglect

of the relative permittivities of the solvents in controlling the

rate of rearrangement of N-oxide 1 when the explicit solvent

model is used.

Calculations for different protic and HBD solvents gave the

atomic distances between the reacting O(7) and C(10) atoms,

that is, the negatively charged N-oxygen and the terminal C

atom of the propargyl group in TS 2, as 1.75 (CF₃CH₂OH),

1.84 (t-BuOH), 1.90 (CHCl₃), and 1.93 Å (CH₂Cl₂) (Table 6).

This means that TS 2 in CF₃CH₂OH was the farthest and CH₂Cl₂

was the nearest to the substrate state, which is in accordance

with the relative reaction rates. The atomic distances in HBs of

different strengths, calculated for the various protic solvents,

were also in agreement with the different reactivities of the

N-oxide complexes. It may be concluded that the explicit solvent

model, in contrast with the implicit model, affords acceptable

results in describing the reactivity in different protic solvents.

Still, the exclusive role of the HBs in controlling the reactivities

may be criticized. For fluorinated solvents, the large activation

energies can be explained by the strong HB abilities of these

solvents, which is reflected in the O(7)-C(10) distance. The

agreement between the experimental and computed values is

weak, demonstrating an additional solvent effect.

For fluorinated solvents, the agreement between the ex-

perimental and computed values is weak as compared with that

for nonfluorinated solvents, indicating the existence of an

additional solvent effect that has yet to be described. In these

cases, the second solvation shell (-C-F‚‚‚H-O-) may also

Figure 12. (A) Dependence of ∆G^q_TOT(see eq 19) on the relative permittivities of the solvents used, as measured and calculated with the joint implicit-

explicit solvent model for the rearrangement of N-propargylmorpholine N-oxide (1). (B) Correlation between the experimental and theoretical values. 1:

dioxane. 2: pyridine. 3: Me₂CO. 4: PhNO₂. 5: MeCN. 6: Me₂SO. 7: MeNO₂. 8: CHCl₃. 9: CH₂Cl₂. 10: t-BuOH. 11: i-PrOH. 12: EtOH. 13: MeOH.

14: H₂O.

9

7628 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

possibly play a significant role.^65,66The construction of a more

reliable solvation model for further consideration will be

required.

Scheme 3. Equilibria in Mixed H₂O-MeCN Solutions Used for

Determination of the Species Distributions^a

3.3.3. Calculated Kinetic Isotope Effect. As estimated in

Section 3.2.3, using eq 14, we found that k_H/k_Dwas indeed 0.73,

which is in good agreement with the measured value, despite

the fact that only average IR frequencies from the literature were

applied. In isotope-labeling experiments involving use of the

solvent pairs MeOH-MeOD-d₃and EtOH-EtOD-d₅, we

observed an inverse secondary KIE (k_H/k_D) 0.78 and 0.80,

respectively) for the rate-determining RC step (1 f 2). To

achieve a more accurate determination of KIE, we used the

calculated IR frequencies of 1 and TS 2. On substituting the

calculated IR frequencies for nondeuterated and deuterated 1c/

1d and 2 into eq 14, we obtained a value of 0.82, which is in

very good agreement with the experimental value.

3.3.4. Calculations in Mixed Solvent. The ∆G^qvalues for

the rearrangement of N-oxide 1 can be easily measured for the

free form (e.g., in MeCN) and for the 2:1 water-N-oxide

complex (in H₂O). However, the calculation for mixed H₂O-

MeCN solvents required a more sophisticated approach. First,

the equilibrium constants for the formation of water-MeCN

and different water-N-oxide complexes (Scheme 3) were

calculated from the heats of formations (see Table 6).

^a(A) -8.48 kJ mol^-1, K₁) 20.4. (B) -0.34 kJ mol^-1, K₂) 1.14. (C)

-0.21 kJ mol^-1, K_ACN) 1.08; at 323 K.

The concentration of the 1:1 water-N-oxide complex reached

its maximum at 7 equiv of water (Figure 13) as revealed by the

measurements (∆G_T^q_OT) 99.55 kJ mol^-1obtained with the

joint implicit-explicit method). The slow convergence of the

titrated curve to the final value also observed in pure water may

be ascribed to the presence of three different components (free

N-oxide 1, 1:1 and 2:1 water-N-oxide complexes) in the same

solution. Thus, the relatively rapid rearrangements of the free

form and the 1:1 complex determine the reaction rate in the

initial (0-7 equiv of water) and middle (7-60 equiv of water)

portions of the titrating curve, respectively.

From the equilibrium constants and the initial experimental

concentration of 1, we calculated the distribution of different

water-N-oxide complexes in various H₂O-MeCN mixtures,

as shown in Figure 13A.

3.3.5. Effects of Electron-Pair Acceptors. As discussed in

Section 3.2.5, measurements carried out in the presence of

typical EPA species (DNB, TNB, Na⁺, Li⁺, BF₃, and H⁺)

demonstrated a strong decrease in the reaction rates, which can

be ascribed to the formation of different complexes between

N-oxide 1 and EPA additives. The results of the theoretical

calculations correlate well with the experimental observations

for the Lewis acids Na⁺, Li⁺, BF₃, and H⁺. As is to be seen in

Table 7, the calculated activation energies increased in ac-

cordance with the strengths of the Lewis acids.

As expected for the ionic complexes of Li⁺, Na⁺, and H⁺

with N-oxide 1, there are large differences between the values

calculated in vacuo and with the PCM method. The results

obtained with the PCM method are in good agreement with the

experimental data. The very high activation energies of the H⁺

and BF₃complexes confirm that that rearrangement does not

proceed even at very high temperatures in the presence of only

1 equiv of a strong Lewis acid. The distance between O(7) and

C(10) in the TS structure (2) decreases in accordance with

increasing strength of the Lewis acids, in agreement with the

observed activation energies.

By applying the calculated concentrations of water-N-oxide

complexes (Figure 13A) in different H₂O-MeCN mixtures and

using the calculated ∆G_T^q_OTvalues for the free form of the

N-oxide, 1:1 and 2:1 water-N-oxide complexes [∆G^q_TOT(0) )

92.47, ∆G^q_TOT(1) ) 99.55, and ∆G_T^q_OT(2) ) 111.45 kJ mol^-1

respectively; see Sections 3.3.1 and 3.3.2], we calculated

∆G^q_AVin different H₂O-MeCN mixtures (Figure 13B,C) by

using eqs 20-22:

rate ) k_AV{[1] + 1^{H O}+ 1^{(H O)}} )

2

k₀[1] + k₁1^{H O}+ k₂1^{(H O)}(20)

2

-∆G^q_AV

exp

)

RT

-∆G^q_TOT(0)

-∆G^q_TOT(1)

- ∆G^q_TOT(2)

[1^{H O}] + exp

[1^{(H O)}

]

2

exp

[1] + exp

RT

(21)

{[1] + [1^{H O}] + [1^{(H O)}²]}

2

For MeCN solutions containing 1 equiv each of Li⁺and Na⁺,

the calculated ∆G^qvalues are higher than those found experi-

mentally. This divergence may be interpreted in terms of the

common presence of the free and complexed forms of N-oxide

1. Since the reaction rate for the free form is thousands of times

faster than that for the complexed form, even a minimal amount

of free N-oxide 1 can markedly accelerate the observed reaction

rate.

∆G^q_AV

)

-∆G^q_TOT(0)

[1] + exp

-∆G^q_TOT(1)

-∆G^q_TOT(2)

[1^{H O}] + exp

[1^{(H O)}

]

2

exp

RT

2

RT

-RT ln

{

}

{[1] + [1^{H O}] + [1^{(H O)}²]}

2

(22)

where k_AVand ∆G^q_AVare the calculated average reaction rate

and activation free energy in mixed solvents, and [1], [1^x], and

[1*] are the concentrations of N-oxide 1, 1:1 and 2:1 water-

N-oxide 1 complexes in mixed solvents, respectively.

4. Generalized Description of Solvent Effect

As in many other reactions, the overall solvent effect for the

overall reaction may be separated into different parts, depending

on the consecutive reaction steps (eq 23), composed of ∆G_CPE

(65) O’Hagan, D.; Rzepa, H. S. Chem. Commun. 1997, 7, 645-652.

(66) Guidry, M.; Drago, R. J. Am. Chem. Soc. 1973, 95, 759-763.

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7629

A R T I C L E S

Mucsi et al.

Figure 13. (A) Calculated distribution of different complexes of water-N-oxide 1. (B) The calculated activation energy curve (eqs 20-22) for different

water-MeCN mixtures in comparison with the experimental points. (C) Correlation between experimental and theoretical values.

Table 7. Computed Activation Parameters (kJ mol^-1) and Atomic Distances (Å) Obtained in Vacuo (1) and with the Implicit Solvent Model

(2) for the Rearrangement of N-Propargylmorpholine N-Oxide (1) Dissolved in MeCN Containing EPAs, as Compared with the Experimental

Data (3)

in vacuo (1)

implicit method (2)

experiment (3)

d

∆∆G^q

q

a

b

a

b

EPA

∆

E_CORR

∆

G_TOT

O(7)‚‚‚C(10)^c

∆

E_CORR

∆∆G_TOT

O(7)‚‚‚C(10)^c

∆

G_OBS

(1)

−

(3)

(2)

−

(3)

H⁺

BF₃

Li⁺

Na⁺

185.45

180.45

181.75

157.35

192.61

187.61

187.91

164.51

1.50

1.80

1.92

2.37

217.65

187.65

111.75

99.85

224.81

194.85

118.71

106.83

1.55

1.59

1.65

n.r.^d

108.6

103.9

79.31

60.61

10.11

2.93

^aIncluding ZPE and BSE. ^bWith consideration of BSE, dispersion, pre-equilibrium, and entropy (-14.61 J mol^-1K^-1) values. ^cO(7)‚‚‚C(10) atomic

distance in TS 2. ^dNot recordable.

Table 8. Parameters and Their Errors (kJ mol^-1) for the

and ∆G^q_RC. Both ∆G values can be correlated with the solvent

Theoretically Calculated ∆G_CPEand ∆G^qValues Obtained

RC

from the Kamlet-Taft Multilinear Regression^67,68

parameters Π* and R by using the Kamlet-Taft multilinear

regression method (eqs 24 and 25, Table 8):^67,68

∆G₀

error

Π*

error

R

error

R²

CPE

RC

8.024 1.459 -3.500 1.769 -1.612 0.999 0.605

84.290 3.362 1.360 4.121 22.842 2.074 0.986

∆G^q_sum) ∆G_CPE+ ∆G^q_RC

(23)

∆G_CPE) ∆G_0CPE+ S_CPEΠ* + A_CPER )

(8.024 - 3.500Π* - 1.610R) kJ mol^-1(24)

∆G^q_RC) ∆G₀^q_RC+ S_RCΠ* + A_RCR )

model, and the parameter R is very small, indicating that CPE

is practically independent of the HBD properties of the solvents.

In the case of the RC step, Π* is small and positive, as predicted

earlier, while R is large as an indication of the significant effect

of HB. The correlation between the theoretically computed and

predicted ∆G^q_TOTvalues is good (Figure 14).

(84.290 + 1.360Π* + 22.842R) kJ mol^-1(25)

The signs of the parameters reinforce our conclusions

concerning the solvent effects. In the case of CPE, the parameter

Π* is negative, similarly as predicted by the Kirkwood-Onsager

(68) Konnors, K. A. Chemical Kinetics: The Study of Reaction Rates in Solution;

Wiley & Sons: New York, 1990; Chapter 8.4, pp 442-446.

(67) Kamlet, M. J.; Taft, R. W. J. Am. Chem. Soc. 1976, 98, 2886-2894.

9

7630 J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005

Modeling Rate-Controlling Solvent Effects

A R T I C L E S

Figure 14. (A) Correlation between the theoretically computed (∆G^q_TOT; the sum of CPE and RC) and predicted values (A) and that between the

experimentally measured (∆G^q_OBS) and predicted values (B) for the rearrangement of N-propargylmorpholine N-oxide 1 using parameters obtained from the

multilinear regression (eqs 23-25) (see text). 1: Dioxane. 2: Pyridine. 3: Me₂CO. 4: MeCN. 5: Me₂SO. 6: MeNO₂. 7: CHCl₃. 8: CH₂Cl₂. 9: t-BuOH.

10: i-PrOH. 11: EtOH. 12: MeOH. 13: H₂O.

Figure 15. Schematic representation of the procedure applied for appropriate modeling of the solvent effects.

5. Conclusions

their assistance toward the linguistic improvement of this article.

One of the authors (I.G.C.) wishes to thank the Ministry of

Education for a Szent-Gyo¨rgyi Visiting Professorship, and the

Hungarian Scientific Research Fund for financial support

(OTKA T046861). This article is dedicated to Professor Andra´s

Lipta´k on the occasion of his 70th birthday.

Our aims were to find an all-purpose way with which to

predict the kinetic parameters of reactions in different solvents

(Figure 15) and which would be useful for both general

chemistry and preclinical development processes in the phar-

maceutical industry. As demonstrated here, the exchange of

aprotic solvents for protic ones can lead to great alterations in

chemical processes as concerns both the mechanism and the

reaction parameters. We have demonstrated that halogenated

hydrocarbons form a distinct solvent group because they exhibit

a weak but significant HBD ability in addition to aprotic

behavior. The commonly used PCM solvent models are ap-

plicable for the modeling of aprotic solvents. When HB may

occur and play a significant role, the number of solvating

molecules can be determined by using MD simulations. Starting

from this basis, the joint explicit-implicit solvent model gives

accurate results.

Supporting Information Available: Explanation and details

of experimental and theoretical methods used. Scheme S1:

chemical structures of selected MAO inhibitors. Table S1: NMR

chemical shifts of N-oxide 1 recorded in various solvents and

at different temperatures. Table S2: the energy values of

N-oxide 1 obtained by different computational methods. Table

S3: the parameters of MD simulations. Tables S4-S45: kinetic

raw data measured by NMR and GC. Figures S2-S43:

evaluation of kinetic raw data and experimental errors. Tables

S46-S49: equilibrium and transition state energies and ZPEs,

together with the corresponding geometries in xyz files. Refer-

ence 42 in completed form. This material is available free of

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

Acknowledgment. The authors are grateful to Professor

Ferenc Ruff for his interest and stimulating discussions. We

thank Dr Lelle Vasva´ri-Debreczy and Dr David Durham for

JA042227Q

9

J. AM. CHEM. SOC. VOL. 127, NO. 20, 2005 7631

Article Doi

Modeling rate-controlling solvent effects. The pericyclic Meisenheimer rearrangement of N-propargylmorpholine N-oxide

DOI: 10.1021/ja042227q

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Article abstract of DOI:10.1021/ja042227q

Full text of DOI:10.1021/ja042227q

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