Nucleophilic Substitution in Solution: Activation Strain Analysis of Weak and Strong Solvent Effects.

We have quantum chemically studied the effect of various polar and apolar solvents on the shape of the potential energy surface (PES) of a diverse collection of archetypal nucleophilic substitution reactions at carbon, silicon, phosphorus, and arsenic by using density functional theory at the OLYP/TZ2P level. In the gas phase, all our model SN 2 reactions have single-well PESs, except for the nucleophilic substitution reaction at carbon (SN 2@C), which has a double-well energy profile. The presence of the solvent can have a significant effect on the shape of the PES and, thus, on the nature of the SN 2 process. Solvation energies, charges on the nucleophile or leaving group, and structural features are compared for the various SN 2 reactions in a spectrum of solvents. We demonstrate how solvation can change the shape of the PES, depending not only on the polarity of the solvent, but also on how the charge is distributed over the interacting molecular moieties during different stages of the reaction. In the case of a nucleophilic substitution at three-coordinate phosphorus, the reaction can be made to proceed through a single-well [no transition state (TS)], bimodal barrier (two TSs), and then through a unimodal transition state (one TS) simply by increasing the polarity of the solvent.

Introduction

The bimolecular nucleophilic substitution (SN2) is one of the most studied and widely recognized elementary chemical reactions in organic chemistry; a typical example is shown in Scheme 1 for A=carbon, with chloride as nucleophile and leaving group.1 This reaction type has recently been reviewed2 and has been the subject of an exceptional number of experimental3 and theoretical4 studies over the past 70 years. In archetype SN2 processes, at least one charged species is present before and/or after the elementary reaction step. Often, such species react in a very different manner in the gas phase when compared to the solution phase, due to substantial stabilization of the charged species by the solvent. Hence, the behavior and rate of this reaction is contingent on the medium in which the reaction is conducted.3f, 5

Scheme 1

Model SN2 reactions at A=C, Si, P, or As.

The bimolecular nucleophilic substitution at carbon (SN2@C: see Scheme 1, A=C) proceeds through a backside attack of the Cl− nucleophile at the carbon atom, followed by a concerted expulsion of the Cl− leaving group. In the gas phase, this process occurs through a double‐well potential energy surface (PES) and a reactant and product complex (RC and PC, respectively) are separated by a pentacoordinate transition state (TS) (see Figure 1 b).3, 4 Solvation in aqueous solution transforms this double‐well PES to a unimodal PES (see Figure 1 c).3, 4 The mechanism behind this drastic solvent effect on the reaction profile is explained by differential solvation of the reactants, products, intermediates, and transition states.6

Figure 1

Typical reaction profiles [energy (E) vs. reaction coordinate (ζ)]. a) Single‐well, b) double‐well, c) unimodal barrier, and d) bimodal barrier. R=reactants, RC=reactant complex, TS=transition state, TC=transition complex, pre‐TS=transition state leading to the TC, post‐TS=transition state leading away from the TC, PC=product complex, P=products.

The overall structural transformation for a bimolecular nucleophilic substitution at silicon7 and phosphorus8 (SN2@Si and SN2@P, respectively: see Scheme 1, A=Si and A=P, respectively) is equivalent to that of SN2@C, however, the potential energy surface is noticeably different. Our understanding of the effect of solvation on these reactions is much less explored and as a result less concrete. What we do know is that in the gas phase, SN2@Si and SN2@P reactions proceed through a single‐well PES associated with a D 3 symmetric transition complex (TC), thereby proceeding without encountering a first‐order saddle point (see Figure 1 a). Aqueous solvation destabilizes the transition complex for SN2@Si and SN2@P reactions and turns the PESs into unimodal reaction profiles, with central transition states (see Figure 1 c).7b

Bimolecular nucleophilic substitution at arsenic (SN2@As: see Scheme 1, A=As) is even far less investigated and is included in the present study due to its chemical (valence isoelectronic) similarity to phosphorus, appearing just below arsenic on the periodic table. Arsenic has both a near identical electronegativity and atomic radius to phosphorus.9 Additionally, in biological systems, arsenic is thought to behave similarly to phosphorus.10 It has been proposed that in the presence of arsenate, a strain of Halomonas bacteria (GFAJ‐1) could incorporate arsenic into the backbone of DNA in competition with phosphorus.11 Auxiliary investigations, however, revealed that arsenate does not allow for incorporation of arsenic into Halomonas DNA when phosphate is limiting.12 The arsenate‐ester hydrolysis reaction (SN2@As4) has been studied computationally by Šponer et al. and they calculated a bimodal barrier for the reaction in the gas phase and in water.13 Furthermore, systematically modeling SN2@As adds an extra dimension to the more fundamental interest in investigating the shape of the PESs for nucleophilic substitution reactions at arsenic and how they compare to the other electrophilic centers.

Intrigued by the intricacies of solvation on the nature and rate of SN2 reactions, we have quantum chemically explored and analyzed the PESs of nucleophilic substitutions at various electrophilic centers and in a spectrum of solvents. The objective of the current research is to understand these fundamental processes in a variety of solvents. This is relevant for a wide range of disciplines, including organic, inorganic, (exo)planetary, and biological chemistry. For example, understanding how SN2@P changes in various solvents has direct implications for the backbone elongation concomitant with DNA replication and is a continuation of our ongoing research line into DNA stabilization and replication.14 Additionally, there have been many potential solvents discovered in our solar system to date in various forms, either liquid, icy mixtures, gas, or transiently.15 Understanding how solvent polarity affects the kinetics and the overall shape of the PES for archetypical nucleophilic substitution reactions on Earth as well as elsewhere in the cosmos has intrinsic value. A comprehensive analysis on the effect of systematically varying solvent polarity on SN2 substitution reactions at different electrophilic centers has, to the best of our knowledge, not yet been carried out.

Theoretical Methods

Computational details

The density functional theory (DFT)16‐based quantum chemical calculations were carried out by using the Amsterdam density functional (ADF 2014.01) program.17 A generalized gradient approximation (GGA) of DFT by using the OLYP functional was selected for the calculations. This GGA functional utilizes the optimized exchange (OPTX) functional proposed by Handy and co‐workers,18 and the Lee–Yang–Parr (LYP) correlation functional.19 This exchange and correlation functional reproduces SN2@C and SN2@Si barriers within a few kcal mol−1 compared to highly correlated ab initio benchmarks,4n, 7c providing sufficient accuracy to study the qualitative effects on the PES shapes upon varying the solvent polarity. Vibrational analysis confirmed energy minima (no imaginary frequencies) and transition states (a single imaginary frequency). The all‐electron TZ2P basis set used herein is of triple‐ζ quality and consists of a large uncontracted set of Slater‐type orbitals used to construct the molecular orbitals (MOs). The basis set has been augmented with two sets of polarization functions, that is, 2p and 3d on hydrogen, 3d and 4f on carbon, oxygen, silicon, phosphorus, and chlorine. The accuracy parameter of both the Becke grid integration and the Zlm fit scheme were set to EXCELLENT.20

All solution‐phase calculations employ COSMO to simulate solvent effects.21 Seven solvents in the range ϵ r=[2.4, 188.4] were considered to emulate a wide spectrum of solvents. The relative dielectric constants ϵ r of toluene, chloroform, ammonia, methanol, water, formamide, and methylformamide are 2.4, 4.8, 16.9, 32.6, 78.4, 109.5, and 188.4, respectively. Default parameters in ADF were used for all solvents except for water. In the case of water, the solvent radius (R s) was taken from experimental data for the macroscopic density (ρ) and the molecular mass (M m) with the formula R s 3=2.6752M m ρ −1, leading to an R s value of 1.9 Å for water. Atomic radii values were taken from the MM3 van der Waals radii,22 and scaled by 0.8333 (the MM3 radii are 20 % larger than the normal van der Waals radii due to the specific form of the van der Waals energy within the MM3 force field). The surface charges at the GEPOL93 solvent‐excluding surface23 were corrected for outlying charges. This setup provides a “non‐empirical” approach to including solvent effects with a dielectric continuum and works well for solvation processes, accurately reproducing experimental hydration energies of the chloride ion.24 A sample ADF input file involving a geometry optimization in water is provided in the Supporting Information.

Activation strain model

The activation strain model (ASM), also known as distortion/interaction model, is a useful tool for investigating the factors giving rise to activation barriers.25 The activation barrier, or well, results from the interplay between the strain energy (ΔE strain) and the interaction energy (ΔE int) [Eq. (1)].

The transition structure is separated into two fragments (the distorted substrate and the chloride ion), followed by single‐point energy calculations on each fragment. The difference in energy between the optimized ground‐state structure and the distorted structures is the strain energy (ΔE strain), whereas ΔE int refers to the interaction between the deformed reactants.

Furthermore, the ASM model has been extended to account for solvation, which is in line with previous work by De Cózar and co‐workers.4e In this framework, the ΔE solution (PES in solution) is decomposed into the energy of the solute (ΔE solute), specifically the reaction system in vacuum with the solution‐phase geometry, plus the solvation energy (ΔE solvation) [Eq. (2)].

ΔE strain and ΔE int make up the intrinsic energy of the solute (ΔE solute) and are augmented by the solvation term ΔE solvation, as shown in Equation (3).

Notably, ΔE strain and ΔE int refer to the strain of, and mutual interaction between, the solute reactant molecules in their solution geometries, but in the absence of the solvent. As such, the strain is computed as the energy difference between the solute reaction system relative to the solute reactants in vacuum. The ΔE solvation term accounts for interaction of the solute with both the solvent and the cavitation, that is, the formation of a cavity in the solvent by the presence of the solute. This approach to extending upon the ASM differs from a prior approach,26 in which all solvent effects were incorporated in either the strain or interaction terms.

Results and Discussion

The results of our OLYP/TZ2P calculations in the gas phase and seven selected solvents are presented in Tables 1 and 2 as well as in Figure 2. Reaction profiles for the SN2@C, SN2@Si, and SN2@P reactions in the gas and aqueous phase provided here are, where available, in line with previous studies.7b Driven to assess the effect of solvation on the shape of the PES and to provide new insights into the backside SN2 reaction mechanism, we systematically screened solvents of varying polarity. We observe dramatic variation in the shape of the PES in the range of vacuum to ammonia, followed by minimal deviations for polar solvents with dielectric constants greater than ϵ r=16.9 (ammonia). In addition, we find that an increase in the solvent polarity results in destabilization of the transition zone and rising of energy barriers. Under strongly polar conditions, the PES eventually becomes unimodal for SN2@C, SN2@P3, and SN2@P4 reactions and bimodal for SN2@Si and SN2@As4 reactions.

Table 1

Energies (in [kcal mol−1]) relative to the reactants of stationary points along the PES of the symmetric SN2 reactions in the gas phase and in solution.[a]

No.	Medium[b]	Reaction[c]	Shape of the PES[d]	Reactant complex/(pre‐transition state)	Transition state/(transition complex)
				ΔE RC (ΔE p‐TS)	ΔE TS (ΔE TC)
1 a	gas	Cl−+CH3Cl	double‐well	−9.1	−0.1
1 b	toluene		double‐well	−2.6	13.2
1 c	chloroform		double‐well	−1.0	18.0
1 d	ammonia		unimodal	–	21.5
1 e	methanol		unimodal	–	21.9
1 f	water		unimodal	–	22.1
1 g	formamide		unimodal	–	22.6
1 h	methylformamide		unimodal	–	22.7
2 a	gas	Cl−+SiH3Cl	single‐well	–	(−24.3)
2 b	toluene		single‐well	–	(−7.7)
2 c	chloroform		single‐well	–	(−1.6)
2 d	ammonia		bimodal	(3.1)	(2.9)
2 e	methanol		bimodal	(3.8)	(3.7)
2 f	water		bimodal	(3.9)	(3.8)
2 g	formamide		bimodal	(4.4)	(4.3)
2 h	methylformamide		bimodal	(4.5)	(4.4)
3 a	gas	Cl−+PH2Cl	single‐well	–	(−26.0)
3 b	toluene		single‐well	–	(−9.9)
3 c	chloroform		single‐well	–	(−4.0)
3 d	ammonia		bimodal	(0.9)	(0.3)
3 e	methanol		bimodal	(1.4)	(1.1)
3 f	water		unimodal	–	1.2
3 g	formamide		unimodal	–	1.7
3 h	methylformamide		unimodal	–	1.8
4 a	gas	Cl−+POH2Cl	single‐well	–	(−22.3)
4 b	toluene		single‐well	–	(−4.0)
4 c	chloroform		unimodal	–	2.9
4 d	ammonia		unimodal	–	7.9
4 e	methanol		unimodal	–	8.8
4 f	water		unimodal	–	8.9
4 g	formamide		unimodal	–	9.6
4 h	methylformamide		unimodal	–	9.7
5 a	gas	Cl−+AsH2Cl	single‐well	–	(−29.6)
5 b	toluene		single‐well	–	(−13.2)
5 c	chloroform		single‐well	–	(−7.1)
5 d	ammonia		single‐well	–	(−2.6)
5 e	methanol		single‐well	–	(−1.8)
5 f	water		single‐well	–	(−1.7)
5 g	formamide		single‐well	–	(−1.2)
5 h	methylformamide		single‐well	–	(−1.1)
6 a	gas	Cl−+AsOH2Cl	single‐well	–	(−29.6)
6 b	toluene		single‐well	–	(−10.7)
6 c	chloroform		single‐well	–	(−3.6)
6 d	ammonia		bimodal	(1.8)	(1.6)
6 e	methanol		bimodal	(2.7)	(2.6)
6 f	water		bimodal	(2.9)	(2.7)
6 g	formamide		bimodal	(3.4)	(3.3)
6 h	methylformamide		bimodal	(3.8)	(3.5)

[a] Computed at the OLYP/TZ2P level. [b] Solvent modeled with COSMO. [c] See the Supporting Information for structures and Cartesian coordinates. [d] See Figure 2 for PESs.

Table 2

Solvation energies (ΔE solvation in [kcal mol−1]), chlorine atomic charges (Q Cl in [a.u.]), and A−Cl distances (in [Å]) of the reactants, reactant complexes, pre‐transition states, transition complexes, and transition states.[a]

No.	Medium[c]	Reaction	Reactants[b]			Reactant complex (or pre‐transition state)			Transition state (or transition complex)
			ΔE solvation	Q Cl	A−Cl	ΔE solvation	Q Cl	A−Cl	ΔE solvation	Q Cl	A−Cl
1 a	gas	Cl−+CH3Cl	–	−0.128	1.79	–	−0.225	1.83	–	−0.543	2.35
						–	−0.854	3.38
1 b	toluene		−1.0	−0.149	1.80	−40.6	−0.184	1.81	−33.0	−0.562	2.35
							−0.943	3.93
1 c	chloroform		−1.5	−0.160	1.80	−56.9	−0.175	1.80	−45.2	−0.570	2.35
							−0.965	4.23
1 d	ammonia		−1.8	−0.168	1.80	–	–	–	−53.9	−0.577	2.35
1 e	methanol		−1.6	−0.169	1.80	–	–	–	−55.6	−0.578	2.35
1 f	water		−1.8	−0.170	1.80	–	–	–	−56.2	−0.579	2.35
1 g	formamide		−2.0	−0.170	1.80	–	–	–	−56.8	−0.579	2.35
1 h	methylformamide		−2.0	−0.171	1.80	–	–	–	−57.0	−0.579	2.35
2 a	gas	Cl−+SiH3Cl	–	−0.156	2.07	–	–	–	–	(−0.474)	(2.35)
2 b	toluene		−1.1	−0.178	2.08	–	–	–	(−30.0)	(−0.492)	(2.36)
2 c	chloroform		−1.6	−0.191	2.08	–	–	–	(−40.9)	(−0.501)	(2.37)
2 d	ammonia		−2.2	−0.202	2.09	(−51.7)	(−0.370)	(2.21)	(−48.8)	(−0.507)	(2.38)
							(−0.678)	(2.69)
2 e	methanol		−2.3	−0.204	2.09	(−52.3)	(−0.393)	(2.23)	(−50.4)	(−0.509)	(2.38)
							(−0.647)	(2.62)
2 f	water		−2.2	−0.205	2.09	(−52.5)	(−0.403)	(2.25)	(−50.8)	(−0.509)	(2.38)
							(−0.635)	(2.59)
2 g	formamide		−2.3	−0.205	2.09	(−52.9)	(−0.410)	(2.26)	(−51.4)	(−0.510)	(2.38)
							(−0.625)	(2.57)
2 h	methylformamide		−2.3	−0.206	2.09	(−53.1)	(−0.410)	(2.26)	(−51.7)	(−0.510)	(2.38)
							(−0.626)	(2.57)
3 a	gas	Cl−+PH2Cl	–	−0.140	2.08	–	–	–	–	(−0.497)	(2.42)
3 b	toluene		−1.1	−0.163	2.09	–	–	–	−30.4)	(−0.511)	(2.42)
3 c	chloroform		−1.7	−0.175	2.09	–	–	–	(−41.6)	(−0.517)	(2.42)
3 d	ammonia		−2.1	−0.184	2.10	(−61.3)	(−0.215)	(2.12)	(−49.5)	(−0.522)	(2.42)
							(−0.909)	(3.57)
3 e	methanol		−2.2	−0.187	2.10	(−61.6)	(−0.227)	(2.13)	(−51.1)	(−0.522)	(2.42)
							(−0.886)	(3.39)
3 f	water		−2.1	−0.188	2.10	–	–	–	−51.5	−0.523	2.42
3 g	formamide		−2.3	−0.188	2.10	–	–	–	−52.2	−0.523	2.42
3 h	methylformamide		−2.3	−0.188	2.10	–	–	–	−52.4	−0.523	2.42
4 a	gas	Cl−+POH2Cl	–	−0.094	2.04	–	–	–	–	(−0.447)	(2.37)
4 b	toluene		−5.1	−0.096	2.04	–	–	–	(−32.1)	(−0.468)	(2.36)
4 c	chloroform		−7.4	−0.097	2.04	–	–	–	−44.4	−0.471	2.36
4 d	ammonia		−9.4	−0.098	2.04	–	–	–	−53.4	−0.474	2.36
4 e	methanol		−9.8	−0.098	2.04	–	–	–	−55.1	−0.474	2.36
4 f	water		−9.9	−0.098	2.04	–	–	–	−55.8	−0.474	2.36
4 g	formamide		−10.1	−0.098	2.04	–	–	–	−56.4	−0.474	2.36
4 h	methylformamide		−10.1	−0.098	2.04	–	–	–	−56.6	−0.474	2.36
5 a	gas	Cl−+AsH2Cl	–	−0.180	2.21	–	–	–	–	(−0.517)	(2.53)
5 b	toluene		−1.3	−0.212	2.23	–	–	–	(−30.2)	(−0.534)	(2.54)
5 c	chloroform		−2.0	−0.228	2.24	–	–	–	(−41.4)	(−0.541)	(2.54)
5 d	ammonia		−2.6	−0.243	2.24	–	–	–	(−49.3)	(−0.547)	(2.54)
5 e	methanol		−2.7	−0.246	2.25	–	–	–	(−50.9)	(−0.548)	(2.55)
5 f	water		−2.6	−0.248	2.25	–	–	–	(−51.3)	(−0.548)	(2.55)
5 g	formamide		−2.8	−0.248	2.25	–	–	–	(−52.0)	(−0.549)	(2.55)
5 h	methylformamide		−2.8	−0.249	2.25	–	–	–	(−52.3)	(−0.549)	(2.55)
6 a	gas	Cl−+AsOH2Cl	–	−0.142	2.19	–	–	–	–	(−0.475)	(2.48)
6 b	toluene		−6.2	−0.152	2.19	–	–	–	(−32.8)	(−0.485)	(2.47)
6 c	chloroform		−9.3	−0.157	2.19	–	–	–	(−45.6)	(−0.489)	(2.47)
6 d	ammonia		−11.8	−0.160	2.19	(−57.8)	(−0.327)	(2.30)	(−55.0)	(−0.492)	(2.47)
							(−0.688)	(2.80)
6 e	methanol		−12.3	−0.161	2.19	(−58.3)	(−0.372)	(2.34)	(−56.8)	(−0.492)	(2.47)
							(−0.629)	(2.68)
6 f	water		−12.6	−0.161	2.19	(−58.6)	(−0.393)	(2.36)	(−57.6)	(−0.492)	(2.47)
							(−0.603)	(2.63)
6 g	formamide		−12.8	−0.161	2.19	(−58.8)	(−0.424)	(2.39)	(−58.2)	(−0.493)	(2.47)
							(−0.567)	(2.57)
6 h	methylformamide		−12.8	−0.161	2.19	(−59.0)	(−0.414)	(2.38)	(−58.5)	(−0.493)	(2.47)
							(−0.578)	(2.59)

[a] Computed at the OLYP/TZ2P level. Q Cl values obtained in the corresponding medium with the Voronoi deformation density (VDD) method presented in [a.u.]27 (when two values are given, the top and bottom values are for the LG and the Nu, respectively). [b] Values refer to the substrate. ΔE solvation for Cl− is −45.3, −61.9, −73.7, −76.0, −76.6, −77.7, and −77.9 kcal mol−1, in toluene, chloroform, ammonia, methanol, water, formamide, and methylformamide, respectively. [c] Modeled with COSMO.

Figure 2

Reaction profiles of six SN2 reactions. a) SN2@C, b) SN2@Si, c) SN2@P3, d) SN2@P4, e) SN2@As3, and f) SN2@As4, computed at the OLYP/TZ2P level by using COSMO to simulate the effect of solvation. In each case, the order of the solvents remains the same, varying systematically from least polar to most polar.

Nucleophilic substitution at carbon

The first reaction we discuss is Cl−+CH3Cl (SN2@C, Table 1, entries 1 a–h, Figure 2 a). The PES for SN2@C shifts from a double‐well in the gas phase, as well as in non‐polar solvents, to unimodal as the solvent polarity increases. Specifically, the PES is characterized by a double‐well in vacuum, toluene, and chloroform, having a reactant complex that becomes less stabilized relative to the reactants as the polarity increases, which is in line with previous observations by Chandrasekhar et al.4m Thus, the energy of the reactant and product complexes (RC and PC, respectively) at the bottom of the double‐well relative to the separate reactants and products (R and P, respectively) increases from −9.1, −2.6, to −1.0 kcal mol−1 (Table 1, entries 1 a–c). The central barrier associated with reaching the D 3‐symmetric transition state (TS) rises significantly as the polarity increases. Initially, there is a slightly negative barrier of −0.1 kcal mol−1 in the gas phase and the barrier rises to 22.7 kcal mol−1 in the most polar solvent, that is, methylformamide. A significant change in the PES is observed in ammonia, as the double‐well transforms to a unimodal barrier with the reactant complex (RC) disappearing. This unimodal barrier persists in ammonia and more polar solvents and it coalesces with the ΔΔE TS varying only by 1.2 kcal mol−1. The ΔΔE TS is greatest (13.3 kcal mol−1) when changing from vacuum to toluene despite the fact that the Δϵ between vacuum and toluene is only 2.4. This reveals that a modest change in the solvent polarity compared to vacuum has a drastic effect on the shape of the PES, which indeed appears to be the case for all SN2 reactions studied herein.

Nucleophilic substitution at silicon

The energetics of the reaction Cl−+SiH3Cl (SN2@Si, Table 1, entries 2 a–h, Figure 2 b) are discussed next. The pentavalent [Cl‐SiH3‐Cl]− is a stable energy minimum, referred to as transition complex (TC), at variance with the labile transition state (TS) discussed for SN2@C above. As the polarity increases from the gas phase to chloroform, the single‐well PES becomes increasingly shallow (Table 1, entries 2 a–c). Unlike for SN2@C, the PES for SN2@Si in ammonia, turns into a bimodal barrier with a C 3‐symmetric pre‐transition state (pre‐TS) that is slightly higher (0.1–0.2 kcal mol−1) in energy than the D 3‐symmetric TC (Table 1, entries 2 d–h). In a previous communication from our group, it was reported that SN2@Si in water proceeds through a unimodal barrier, which, because of a numerical artifact, experienced a shift in the transition vector to a slightly positive value (38 cm−1).7b This may be an incomplete view of the surface topology because when using the highest quality numerical integration scheme and careful analysis, a bimodal barrier emerges. Note, however, that the PES around the transition complex is extremely shallow and locating the pre‐TS complexes proved non‐trivial. The activation barrier for SN2@Si is significantly lower than for SN2@C, by approximately 18 kcal mol−1, and increases monotonically from 3.1 to 4.5 kcal mol−1 when moving from ammonia to methylformamide (Table 1, entries 2 d–h).

Nucleophilic substitution at phosphorus

The shape of the PES for SN2@P3 Cl−+PH2Cl varies significantly based on the solvent polarity. A single‐well exists in vacuum, toluene, and chloroform that becomes increasingly shallow, in a systematic manner, ranging from −26.0 to −4.0 kcal mol−1 (Table 1, entries 3 a–c, Figure 2 c). In ammonia and methanol, the shape of the PES transforms into a bimodal barrier (Table 1, entries 3 d and e). Gilheany and co‐workers also observed a bimodal barrier for SN2@P depending on the solvent polarity by using NMR spectroscopic and computational techniques.8c Extremely low barriers of 0.9–1.4 kcal mol−1 associated with this pre‐TS lead to a slightly more stable (0.3–0.6 kcal mol−1) pentacoordinate TC, similar to the case of SN2@Si in solution when ϵ r≥16.9. Solvation in water and more polar solvents results in a unimodal PES (Table 1, entries 3 f–h). The pre‐TS no longer exists in these solvents and instead, a C 2‐symmetric TS associated with very low activation barriers ranging from 1.2 to 1.7 and 1.8 kcal mol−1 is observed, in water, formamide, and methylformamide, respectively (Figure 2 c). In short, by increasing the polarity of the solvent for SN2@P3, we recover both the shift from a single‐well PES to a bimodal PES that was observed for SN2@Si, and, continuing along the spectrum, the shift from a bimodal PES to a unimodal PES, similar to SN2@C.

In the case of the SN2@P4 reaction Cl−+POH2Cl, we find that the transition structures (either transition state or transition complex) are destabilized by 4–8 kcal mol−1 compared to the SN2@P3 reaction Cl−+PH2Cl, due to an increased coordination at the electrophilic center.7b We discuss the effect of increased coordination and the resulting effects it has on both the interaction and the strain energy below in the Activation Strain Analysis section. In vacuum and toluene, SN2@P4 occurs through a single‐well (Table 1, entries 4 a and b, Figure 2 d). Moving to chloroform and the other polar solvents, the PES shifts directly to a unimodal barrier, with a C 2‐symmetric TS (Table 1, entries 4 c–h). The bimodal PES is bypassed in this oxide system compared to the non‐oxide substrate (compare Figures 2 c and d). The barriers for SN2@P4 rise incrementally in ammonia and more polar solvents and vary from 7.9 to 9.7 kcal mol−1 (Table 1, entries 4 d–h).

Nucleophilic substitution at arsenic

The PES associated with the SN2@As3 reactions deviates significantly from the PES for SN2@P3 in ammonia and more polar solvents. This is the only SN2 reaction included in the present study that does not have a barrier even in the most polar of solvents. A single‐well PES is observed for SN2@As3 in every solvent (Table 1, entries 5 a–h) and is deepest for the reaction in the gas phase (−29.6 kcal mol−1). From the gas phase to solvation, and going to more polar solvents, we recover the same trend of a decreasing stability of the transition complex as we found for the other reactions, that is, the single‐well becomes increasingly shallow in a monotonic fashion as the solvent polarity increases, to a final ΔE TC of −1.1 kcal mol−1 in methylformamide (Table 1, entry 5 h).

The PES for SN2@As4 is a single‐well in the gas phase and in the non‐polar solvents, toluene and chloroform, with the stabilization of the TC relative to the reactants R varying greatly from −29.6 to −10.7 to −3.6 kcal mol−1, respectively (Table 1, entries 6 a–c). When transitioning to ammonia and increasingly polar solvents, the PES shifts to a bimodal barrier with a C 2‐symmetric TC (Table 1, entries 6 d–h). The bimodal PES has a C‐symmetric pre‐TS and post‐TS that connect the separated reactants/products and the TC. The pre‐TS and post‐TS are similar in shape to those occurring in the SN2@Si reaction. The transition structures (pre‐TS, TC, TS, and post‐TS) for SN2@As4 are all destabilized compared to the non‐oxide (SN2@As3) variants by 0–4 kcal mol−1. This relative destabilization caused by the oxide functionality is less extreme than was the case for SN2@P.

Solvent effects on the reaction PES

Now, we examine how solvation affects the shape of the PES of each reaction by decomposing the solution phase PES (ΔE solution) into two terms, namely, ΔE solute and ΔE solvation (see the Theoretical Methods section for details).4e The term ΔE solute refers to the energy of the solute (computed in the gas phase, but with its solution‐phase geometry), whereas ΔE solvation is the stabilization provided by the solvent. Overall changes in the shape of the PES can be explained in terms of differential solvation of the various stationary points (i.e., R, RC, PC, pre‐TS, post‐TS, TS, and TC).6 For nucleophilic substitutions involving an anionic nucleophile, such as the reactions studied in this work, it is known that a polar solvent stabilizes the reactants and products more strongly than the intermediate complexes that occur as the reaction progresses.7b,7d Solvation, therefore, generally results in a destabilization of the region around the central transition state or transition complex.

This can be understood already from the classical electrostatic Born equation for spherical ions in a dielectric continuum [Eq. (4)] in combination with a simplified model of our SN2 reaction systems.28

In Equation (4), Q is the charge of the ion, a is the radius of the ion, ϵ 0 is the dielectric constant in vacuum, and ϵ r is the relative dielectric constant of the solvent. The simplification involves the notion that the reaction systems consist of a relatively neutral central moiety (e.g., CH3) between a (partially) negatively charged nucleophile Cl1 and leaving group Cl2. The latter two groups have charges Q 1 and Q 2 that, in the course of the SN2 reaction, go from Q 1=−1 and Q 2≅0 to Q 1≅0 and Q 2=−1. This leads to the following Equation (5).

Equation (5) is, in fact, a crude approximation to the solvation energy as computed in our more sophisticated COSMO computations, but it catches the essence of the physics: solvation stabilization is strongest when the excess negative charge is localized mainly on one of the two ionic groups, that is, Q 1=−1 or Q 2=−1, and it is the least stabilizing in intermediate situations in which the charge is delocalized over both sides, that is, Q 1=Q 2≅− [Eq. (5)]. As a result, the central part of the PES is less strongly stabilized compared to the reactant and product sides.

Striving to go one step beyond this general observation and explain how, and when, solvation can lead to PES shapes with different qualitative features (i.e., a labile TS or a stable TC, or the appearance of pre‐ and post‐TSs), we have numerically recreated all occurring PES shapes by using generic Gaussian functions f(x)=ae (Figure 3). In each of the four graphs in Figure 3, an identical single‐well ΔE solute profile is represented by the solid black line. In addition, various ΔE solvation profiles are modeled (colored dotted lines in Figure 3), by varying the peak width and peak height of the Gaussian functions. The colored solid lines are the sum of the modeled ΔE solute profile and the ΔE solvation model curves of the corresponding color, and represent the overall solution‐phase PES profiles ΔE solution.

Figure 3

Analytical solution‐phase PESs ΔE solution (colored solid lines: ΔE solution=ΔE solute+ΔE solvation) based on generic Gaussian functions f(x)=ae to represent ΔE solute (black solid lines: a=−1.2, b=0.30) and f(x)=ae −3.2 to represent ΔE solvation (colored dotted lines: shifted vertically by −3.2 to result in negative, that is, stabilizing, ΔE solvation values; with various values for a and b). In all graphs, ΔE solute is represented by the same Gaussian function, whereas the different ΔE solvation profiles are obtained by varying the parameters a (peak height) and b (peak width). Graph a) shows the effect of varying peak width, graphs b), c), and d) show the effect of varying the peak height with the peak widths of ΔE solvation chosen equal to, narrower than, and wider than that of ΔE solute, respectively.

First, we discuss the effect of varying the peak width for the ΔE solvation profiles. Our analysis reveals that when the ΔE solute and ΔE solvation profiles have roughly the same width, the resulting ΔE solution PES will feature no stationary points other than the central TC or TS (red lines in Figure 3 a). Due to the maximum of the ΔE solvation curve in the middle, where it is the least stabilizing, the central point along the solution‐phase PES ΔE solution is destabilized relative to the central point along the solute PES ΔE solute in vacuum. Whether this central point is a labile TS or stable TC also depends on the peak heights, which will be addressed hereafter. When the profile of ΔE solvation is much wider than that of ΔE solute, the solution‐phase PES ΔE solution [Eq. (2)] will develop pre‐TS and post‐TS barriers separating a central minimum or transition complex (TC) from the reactants and products. The reason is that near the reactants and products, the derivative |dΔE solvation/dζ|>|dΔE solute/dζ|, but nearer the central point |dΔE solvation/dζ|<|dΔE solute/dζ|. In other words, in early and late stages of the SN2 reaction, ΔE solution follows the destabilization of ΔE solvation relative to the reactants and products, whereas, in the central region, it follows the stabilization, that is, the drop in energy stemming from ΔE solute. This leads to the appearance of the aforementioned pre‐TS and post‐TS at points where the derivatives of ΔE solute and ΔE solvation are equal but of opposite sign: dΔE solvation/dζ=−dΔE solvation/dζ (yellow lines in Figure 3 a). A narrower ΔE solvation profile, on the other hand, provides a labile central TS, with stable RC and PC (green lines in Figure 3 a).

Now, turning to variation of the peak heights of the modeled ΔE solvation profiles, we provide in Figure 3 a series of solvation energy profiles that have the same width as ΔE solute (Figure 3 b), are narrower than ΔE solute (Figure 3 c), or are wider than ΔE solute (Figure 3 d). For each situation, a small peak height does not lead to any change in the qualitative features of the solution phase ΔE solution PES: the single well remains a single well (red lines in Figure 3 b–d). A sufficiently large ΔE solvation curve, does, however, change the single‐well ΔE solution PES to a unimodal profile with a central barrier (green lines in Figure 3 b–d). When the peak heights of the ΔE solute and ΔE solvation curves are comparable, the final reaction profile can contain stable RC and PC structures, separated by a TS (yellow lines in Figure 3 c, ΔE solvation peak width narrower than ΔE solute), or the inverse situation can occur: the central point can be a stable minimum, with maxima appearing before and after, resembling a pre‐TS and post‐TS (yellow lines in Figure 3 d, ΔE solvation peak width broader than ΔE solute peak width).

We now return to the actual chemical reactions that are investigated in this work. First, we recall that solvation raises the transition zone relative to the solvated reactants, for every SN2 reaction included in this study. The total solvation energy for the reactants is dominated by the chloride ion with its localized charge: ΔE solvation for this anion ranges from −45.3 to −77.9 kcal mol−1 from toluene to methylformamide, respectively (see Table 2, footnote [b]). The increased degree of stabilization (i.e., a more negative ΔE solvation) is directly correlated with the polarity of the solvent, with more polar solvent systems leading to amplified charge stabilization. Due to their lack of net charge, the neutral reactants are weakly solvated compared to Cl−, ranging from −1.0 to −2.8 kcal mol−1 for non‐oxide‐based reactants (Table 2, entries 1 a–h, 2 a–h, 3 a–h, 5 a–h) and −5.1 to −12.8 kcal mol−1 for the more polar and moderately solvated tetracoordinate phosphorus and arsenic compounds (Table 2, Entries 4 a–h, 6 a–h). The RCs, pre‐TSs, and central TCs/TSs display less strong solvation than the two separate reactants, with solvation energies ranging from −30.0 to −61.6 kcal mol−1, and always becoming more stabilizing as the polarity of the solvent increases (Table 2). Overall, the difference in the stabilization between the reactants and the intermediate structures becomes greater for more polar solvents, thus leading to larger changes in the PES shapes. This is graphically shown in Figure 4 a–c, where the ΔE solute, ΔE solvation, and ΔE solution terms are indicated for SN2@P3 in toluene, ammonia, and methylformamide. For the apolar solvent toluene, we only find a minor change from the single‐well PES for ΔE solute to a shallower single‐well PES for ΔE solution (Figure 4 a). Increasing the solvent polarity, as in the case of ammonia, we find that the single‐well ΔE solute curve is changed to a bimodal PES and even to a unimodal PES for the most polar solvent methylformamide (Figures 4 b and c, respectively).

Figure 4

Solvent effects on the PESs for a,b,c) SN2@P3 and d,e,f) SN2@As4 reaction in solvents of varying polarity: toluene (a and d), ammonia (b and e), and methylformamide (c and f). As described in Equation (2), the ΔE solution term (solution: colored solid curves) is comprised of the ΔE solute term (solute: black solid curves) and the ΔE solvation term (solvation: colored dotted curves).

Next, we move to the effect of varying the central atom in the reaction system. We limit our discussion here to the results for the most polar solvent, namely methylformamide. For each reaction, we find a favorable solvation for the reactants, in all cases predominantly due to the Cl− ion, which varies from −80.0 to −91.5 kcal mol−1 (Table 3). For SN2@C, the ΔE solvation term becomes smaller during the reaction (−57.0 kcal mol−1 in the TS), combined with the high intrinsic barrier caused by steric congestion around the small carbon atom, this is enough to transform the double‐well PES to a unimodal PES with a central barrier of +22.8 kcal mol−1.

Table 3

Relative energies in solution (ΔE solution), solvation energies (ΔE solvation), and solute energies (ΔE solute) (all in [kcal mol−1], relative to the gas‐phase reactants) in methylformamide.[a]

No.	Reaction	Reactants[b]			Reactant complex/(pre‐transition state)			Transition state/(transition complex)
		ΔE solution	ΔE solvation	ΔE solute [c]	ΔE solution	ΔE solvation	ΔE solute	ΔE solution	ΔE solvation	ΔE solute
1 h	Cl−+CH3Cl	−80.0	−80.0	0.0	–	–	–	−57.2	−57.0	−0.2
2 h	Cl−+SiH3Cl	−80.5	−80.5	0.0	(−76.0)	(−53.1)	(−22.9)	(−76.1)	(−51.7)	(−24.4)
3 h	Cl−+PH2Cl	−80.3	−80.3	0.0	–	–	–	−78.4	−52.3	−26.1
4 h	Cl−+POH2Cl	−88.5	−88.5	0.0	–	–	–	−78.8	−56.6	−22.2
5 h	Cl−+AsH2Cl	−81.0	−81.0	0.0	–	–	–	(−82.1)	(−52.3)	(−29.8)
6h	Cl−+AsOH2Cl	−91.5	−91.5	0.0	(−87.9)	(−59.0)	(−28.9)	(−88.0)	(−58.5)	(−29.5)

[a] Energies computed at the OLYP/TZ2P level. [b] Comprises both Cl− and the substrate. [c] Value set to 0.0 kcal mol−1.

For SN2@Si and SN2@As4, solvation in methylformamide results in a bimodal PES (Figures 2 b and f). From our results, we find a correlation between the slope of the solvation energy (dΔE solvation/dζ, see Figure S2 in the Supporting Information) and the nature of the central atom: dΔE solvation/dζ becomes smaller, that is, the curve becomes less steep, as one moves down in the periodic table. This leads to a wider ΔE solvation profile and consequently, the appearance of a pre‐TS and post‐TS (see Figure 3 d). Why the ΔE solvation profile becomes broader for larger central atoms, can be understood from an examination of the various ARCl fragments (see Figures S3 and S4 in the Supporting Information). The LUMO of ARCl grows progressively more diffuse as one moves down in the periodic table (i.e., C to Si, P to As). This trend in the size of the LUMO coincides nicely with the electronegativity of the central atoms, with the larger, less electronegative ones (Si and As) displaying a relatively diffuse LUMO. A more diffuse LUMO (i.e., a relatively large amplitude at large distance from the central atom) allows for both charge transfer and HOMO /LUMO overlap to develop in a more gradual fashion along the reaction coordinate ζ, and thus, a wider ΔE solvation profile. This situation is schematically indicated by the red lines in Figure 5: an earlier, more gradual charge transfer from the nucleophile to the substrate leads to smaller values of Σ(Q ) at an earlier stage during the reaction, and, as also follows from an approximation based on the Born equation [Eq. (4)],27 to an earlier rise (i.e., becoming less stabilizing) of the solvation energy profile ΔE solvation. Analysis of the chloride Voronoi deformation density (VDD) charges (Q Cl) along the various PESs confirms that as the LUMO becomes larger, the chloride charge delocalizes indeed in a more gradual manner (similar trends emerge if instead we use, e.g., Hirshfeld charges, see Figure S5 in the Supporting Information).

Figure 5

Qualitative relationship between the rate at which the charges of the chlorides (Q Cl, nucleophile=dashed curve, leaving group=solid curve) change along the reaction coordinate and, through the sum of Q , effect on the solvation energy term.

Examination of the Mulliken gross population of the LUMOs of ARCl (see Figure S4 in the Supporting Information) further supports this relationship between the size of the LUMO and charge transfer. It is important to note that for SN2@As3 a single‐well PES persists in all solvents, because, due to the large LUMO and the strong stability of the central TC, the PES is virtually resistant towards solvation‐induced changes (Figures 4 d–f). And conversely, a more compact LUMO (as observed for small central atoms, such as in SN2@C and SN2@P) is associated with a delayed but fast charge transfer that occurs in the proximity of the transition structure. Such a situation leads to a narrow ΔE solvation profile, as indicated by green lines in Figure 5, and is more likely to convert a stable TC into a TS.

Activation strain analysis

Lastly, an activation strain analysis (ASA) on the solute, ΔE solute, (i.e., the reaction system in solution, but with the solvent taken away) transition structure (either TS or TC) for each of the SN2 reactions is presented. Decomposing the ΔE solute term into the ΔE strain and ΔE int terms, yields insight into how the barrier or well arises.4e Results from the ASA are collected in Table 4.

Table 4

Activation strain analysis (in [kcal mol−1]) of the solute (optimized in methylformamide) in the gas phase for all studied SN2 reactions.

No.	Reaction	Transition state(transition complex)
		ΔE strain	ΔE int	ΔE solute
1	Cl−+CH3Cl	31.6	−31.8	−0.2
2	Cl−+SiH3Cl	(25.2)	(−49.5)	(−24.4)
3	Cl−+PH2Cl	(13.4)	(−39.4)	(−26.1)
4	Cl−+POH2Cl	(26.9)	(−49.1)	(−22.3)
5	Cl−+AsH2Cl	(11.0)	(−40.8)	(−29.8)
6	Cl−+AsOH2Cl	(20.4)	(−50.0)	(−29.6)

[a] Computed at the OLYP/TZ2P level.

First, we analyze the SN2@C reaction Cl−+CH3Cl (Table 4, entry 1). The transition state marks the top of a central barrier that connects reactant and product complexes. Note, however, that ΔE solute(TS) is below the separate reactants by −0.2 kcal mol−1. This is because the initial interaction energy is very favorable. This leads to the occurrence of rather stable reactant complexes from which the actual substitution process proceeds. In general, this can but does not have to lead to pronouncedly negative overall barriers.4j In the present case, there is near cancellation of the favorable interaction energy between the nucleophile and the substrate by the strain energy required to distort the CH3Cl to the geometry it adopts in the TS.

The stabilizing nucleophile–substrate interaction is much stronger for SN2@Si (ΔΔE int=−17.7 kcal mol−1), whereas the strain energy is decreased compared to SN2@C (ΔΔE strain=−6.4 kcal mol−1). These are direct results of the decreased steric congestion at the silicon atom (i.e., all bonds are elongated in SiH3Cl compared to CH3Cl).7b The combination of a greater ΔE int and a reduced ΔE strain result in a single‐well, with a pronouncedly stable TC instead of a central barrier for SN2@Si (Table 4, entry 2).

The ΔE strain for SN2@P3 amounts to +13.4 kcal mol−1 and is thus lower compared to SN2@C (+31.6 kcal mol−1) and SN2@Si (+25.2 kcal mol−1) reactions. This is due to the decreased coordination of the phosphorous atom.8f The ΔE int (−39.4 kcal mol−1) is three times greater (in absolute terms) than ΔE strain, thus resulting in a deep single‐well PES (ΔE solute=−26.1 kcal mol−1). Increasing the coordination at the phosphorus (POH2Cl) for SN2@P4 directly doubles the strain energy (+26.9 kcal mol−1) of the TC. The ΔE int is also enhanced and is more favorable than for trivalent phosphorus (ΔΔE int=−9.7 kcal mol−1). The more favorable interaction energy results in a single‐well that is −22.3 kcal mol−1 below the reactants.

The depths of the single‐well PESs for the SN2@As3 and SN2@As4 reactions are nearly equivalent, with a ΔE solute of −29.8 and −29.6 kcal mol−1, respectively. Nonetheless, the ΔE strain and ΔE int follow similar trends as previously described for the SN2@P3 and SN2@P4 reactions, specifically the ΔE strain in the [Cl‐AsOH2‐Cl]− TC is double that of the tricoordinate TC and the interaction is more favorable. Comparing SN2@As4 to SN2@As3, we see the energetic penalty associated with the strain term (ΔΔE strain=9.4 kcal mol−1) is completely negated by the more favorable interaction energy (ΔΔE int=−9.2 kcal mol−1).

The above analyses demonstrate how the interplay of strain and interaction energies determines the course and barrier height/well depth of the solute in these SN2 reactions. They suggest that by either decreasing the steric congestion at the central atom, or by strengthening the nucleophile–substrate interaction in the solute, the SN2 barrier can disappear. This is what happens when moving from Cl−+CH3Cl to SN2@Si, SN2@P3, SN2@P4, SN2@As3, and SN2@As4 reactions. The solute TS turns into a stable TC because the strain energy associated with reaching the transition structure is decreased and the interaction energy is enhanced significantly. Furthermore, by comparing SN2@P3 with SN2@P4 and SN2@As3 with SN2@As4, we see that the extra oxygen substituent results in extra steric congestion, yet the penalty associated with strain is compensated by increased favorable interactions.

Conclusion

Solvation can dramatically modify not only the rate of SN2 substitutions, but also the shape of their reaction potential energy surface and, thus, the nature of this reaction mechanism. The effect strongly depends on the polarity of the solvent and the type of the SN2 system, as follows from our DFT study of six anionic model SN2 reactions, Cl−+ARCl, at various Group 14 (C, Si) and Group 15 (P, As) electrophilic centers, each modeled in the gas phase as well as seven solvents of varying polarity.

General trends can be gleaned from our results, in that all barriers increase in a monotonic fashion as the solvent polarity increases. In the gas phase, all but the SN2@C model substitutions proceed through a single‐well PES without a TS, whereas the former, that is, SN2@C shows the known double‐well potential. In the limit of strong solvation, the PES becomes eventually unimodal for the SN2@C, SN2@P3, and SN2@P4 reactions and bimodal for the SN2@Si and SN2@As4 reactions. The gas‐phase single‐well PES for SN2@P3 transforms into a bimodal reaction profile in ammonia, before it shifts to a unimodal barrier in methanol and increasingly polar solvents. All solvent effects, not only the raise in the barrier but also the transformation of the PES shapes can be understood in terms of differential solvation, that is, the stronger solvation stabilization of reactants and products (especially Cl−, but also reactant and product complexes) and weaker solvation stabilization of hypercoordinate intermediates (e.g., [Cl‐AsH2‐Cl]−) or transition states (e.g., [Cl‐CH3‐Cl]−≠).

The size or spatial distribution of the LUMO on the ARCl substrate controls the width (and shallowness) of the solvation energy profile ΔE solvation: this orbital determines how early and gradual, or late and abrupt, charge flows from the nucleophile to the leaving group. Diffuse LUMOs, as present on substrates with heavier central atoms, allow for an earlier and more gradual charge delocalization. Delocalization of charge at an early stage of the reaction, results, in accordance with the Born equation, in a wide ΔE solvation profile, whereas more abrupt delocalization, occurring only closely around the central point of the reaction, results in a narrow ΔE solvation profile. These principles can lead to the following situations for a single‐well ΔE solute, a curve with one minimum, and the unimodal ΔE solvation, a curve with one maximum: 1) a combination of a narrow ΔE solute profile and a broad ΔE solvation profile is likely to provide a PES with a pre‐TS and post‐TS surrounding a stable minimum; 2) a combination of a broad ΔE solute profile and a narrow ΔE solvation profile more often leads to a central TS; and 3) when the ΔE solute and ΔE solvation profiles have similar widths, the transition region contains either a TC or a TS (no other stationary points), determined by the height of the ΔE solvation curve. For example, solvation of SN2@C and SN2@P (relatively compact LUMOs on the central atom) is more likely to result in a solution‐phase PES with a central TS. On the other hand, solvation of SN2@Si and SN2@As (relatively diffuse LUMOs on the central atom) tends to provide a stable central TC, which may be flanked by a pre‐ and post‐TS depending on the height of the ΔE solvation profile.

Conflict of interest

The authors declare no conflict of interest.

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Supplementary

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