solvent molecules play a role in an snar reaction

doi.org/10.26434/chemrxiv.7782797.v1

Solvent Molecules Play a Role in an SNAr ReactionYumiao Ma

Submitted date: 28/02/2019 • Posted date: 28/02/2019Licence: CC BY-NC-ND 4.0Citation information: Ma, Yumiao (2019): Solvent Molecules Play a Role in an SNAr Reaction. ChemRxiv.Preprint.

Reaction between 4-nitrobenzonitrile and sodium methoxide (MeONa) exhibits unexpectedly low conversionand puzzling kinetics behavior, which is in sharp contrast to the prediction that reaction would be rapid andthorough made by density functional theory (DFT) calculations under implicit solvation. Free energy surfaces(FES) obtained by explicit solvation model including 62 solvent molecules differ greatly from those with implicitsolvation. The real nucleophile is not methoxide anion but methanol-methoxide complex, and it is the entropyeffect due to solvent molecules that modifies the FES. It is the first work revealing the significant modificationof FES by explicit solvation for small molecule reactions.

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Solvent Molecules Play a Role in an SNAr Reaction

Yumiao Ma*

BSJ Institute, Beijing, 100084

Abstract

Reaction between 4-nitrobenzonitrile and sodium methoxide (MeONa) exhibits unexpectedly low

conversion and puzzling kinetics behavior, which is in sharp contrast to the prediction that

reaction would be rapid and thorough made by density functional theory (DFT) calculations under

implicit solvation. Free energy surfaces (FES) obtained by explicit solvation model including 62

solvent molecules differ greatly from those with implicit solvation. The real nucleophile is not

methoxide anion but methanol-methoxide complex, and it is the entropy effect due to solvent

molecules that modifies the FES. It is the first work revealing the significant modification of FES

by explicit solvation for small molecule reactions.

Introduction

Quantum chemistry computations have been used widely and successfully to gain both insights

and numbers into chemical reactions. Nearly all quantum chemistry calculations for reactions in

solution are based on implicit solvation model, which considers solvents as continuous medium,

and no dynamics of solvents is included. In 2016 Singleton reported that implicit solvation model

is insufficient to explain the regioselectivity of toluene nitration1. To the best of our knowledge it

is the only research revealing the importance of explicit solvation for small molecular reaction.

In this communication, the significant influence of explicit solvation on free energy surface (FES)

is observed. Implicit solvation gave completely wrong prediction for a seemingly simple SNAr

reaction, the reaction between sodium methoxide and 4-nitrobenzonitrile (1) in dimethyl sulfoxide

(DMSO) (Figure 1). The experimentally observed low conversion and “strange” kinetics

behaviors originate from the entropy effect due to the dynamics of solvation molecules, which

modified the FES in an astonishing extent.

Figure 1. Summary of this work

Results and Discussions

The work commenced with an incidentally performed reaction of 4-nitrobenzonitrile (1) and

sodium methoxide. The reaction gave cleanly a mixture of unreacted 1 and SNAr product 2, which

will be stated in detail later. There seems to be nothing interesting at the first look. However, when

the calculated free energy surface (FES) was examined (Figure 2), a puzzling inconsistence came

to appear. Under SMD implicit solvation model the reaction is fast and irreversible. Compound 1

undergoes a rapid addition by methoxide anion with barrier of 2.6 kcal/mol, leading to a

Messenheimer complex Int2. The transition state (TS) for elimination of NO2- is lower in energy

than Int2 after including correction to Gibbs free energy, indicating a dynamical dominating

behavior2. In a summary, the reaction was predicted to proceed smoothly and thoroughly. Pathway

involving benzyne is highly disfavored.

Figure 2. M06-2X/6-311+G(d,p)/SMD(DMSO)//M06-2X/6-31+G(d)/SMD(DMSO) calculated

FES. Gibbs free energies with harmonicity approximation are shown in black, and anharmonic

ones are shown in grey. DLPNO-CCSD(T)/aug-cc-pVTZ/SMD(DMSO)//M06-2X/6-

311+G(d,p)/SMD(DMSO) results are shown in brackets.

Experiments gave a very different picture. All reactions gave a clean mixture of 1 and 2, with no

detectable byproducts. Reaction with 1 eq MeONa gave no conversion of 1. Yield of 2 became

higher with large excess of MeONa, although even with 10 eq MeONa there is still 30% of

substrate unconverted (Figure 3a). Small amount of methanol raised final yields, but the yields

dropped sharply with more than 40 eq of methanol (equivalents calculated with respect to 1).

According to these observations, 5 eq of MeONa appeared to be a proper condition for kinetics

measurement. Reaction profile is depicted in Figure 3e. Initially the reaction was rapid and 25.1%

of 1 converted to 2 in the first 30 s. Order of MeONa was determined to be 2 by measuring initial

rates (Figure 3d). However, the reaction profile deviated significantly from what expected from an

r=k[1][MeONa]2 pattern. The kinetics equation was determined to be r=k[1]([1]0-[1]final-([1]0-[1])).

Figure 3. (a) Dependence of final yield on amount of MeONa. (b) Dependence of final yield on

amount of added MeOH, with 5 eq MeONa. (c) Dependence of final yield on amount of MeONa

with 50 eq MeOH. (d) Dependence of initial rate on amount of MeONa with no MeOH added. (e)

Reaction profile. Reaction profile predicted by several kinetic equations were shown in curve. (f)

Dependence of initial rate on added MeOH.

Some experiments were employed to determine whether the final mixture is in equilibrium.

Adding extra 3 eq of MeONa to a mixture with 2 eq of MeONa that has been stirred for 2 h after

mixed led to final yield comparable to that with 5 eq MeONa directly added (Table 1). However,

adding NaNO2 did not reduce the final yield, indicating no equilibrium involving NO2-. This

observation, along with the kinetic equation above, strongly suggested that the real nucleophile is

not MeONa but some species irreversibly generated from MeONa and with an initial

concentration of [1]0-[1]final.

Entry Variation on conditions Final yield (%)

1 None 44

2 2 eq MeONa, then add 3 eq MeONa 2 h later 43

3 5 eq MeONa and 5 eq NaNO2 49

4 5 eq MeONa and 5 eq 15-crown-5 71

5 MeOLi instead of MeONa 0

Table 1. Influence of additives on final yields.

Obviously the calculated FES based on implicit solvation model was unable to give even

qualitatively correct insight into the experimental observations. Then we turned our attention to

explicit solvation. DFT-derived transition state TS1 was placed at the center of a sphere on 62

DMSO molecules. Solvent molecules were treated by PM7 and the TS1 part was treated with

M06-2X/6-31+G(d). A two-dimensional potential mean field (2D-PMF) calculation was

performed to obtain the FES for the addition of MeO- to 1 (Figure 4a). The PMF surface indicated

a concerted addition-elimination process, in agreement with the extremely low energy of TS2

shown in Figure 2. Most importantly and surprisingly, the FES exhibited a barrier larger than 40

kcal/mol, in sharp contrast to the rapid reaction implied from Figure 2.

Some factors possible to cause wrong PMF surface were precluded by careful examination of the

calculated results. Then it came to the problem why it shows such a large difference from that

calculated from implicit solvation model. There may be several reasons. One is that the

insufficiency of SMD solvation model itself, and the other is the harmonious approximation used

in conventional DFT calculations.

Anharmonic free energies were obtained under implicit solvation model with VPT2 method

(Figure 2, grey). Anharmonicity made an unexpected difference on the relative free energies and

could not be corrected using correction factors, which is widely used for convenient inclusion of

anharmonicity. However, the anharmonic FES based on implicit solvation model also exhibits a

very low barrier. Thus there must be other factors contributing to the PMF FES. By comparing

PMF-FES and xtb electronic energies and PM7 enthalpies, we concluded that the 62 DMSO

molecules modified the shape of FESs through entropy. Detailed discussions, as well as the origin

of entropy effect, can be seen in Supporting Information.

The involvement of MeO- as nucleophile is precluded by the calculation results above, and then

came the problem what the true nucleophile is. We found that in the trajectories obtained, MeO -

did not exist in its free form. Instead, it always extracted a proton from DMSO (Figure 4d-f).

Methanol has been considered to show acidity 106 stronger than DMSO for a long time, and it

looks impossible that sodium methoxide can exist in such a form in DMSO solvation. However,

after diving deeply into the literature, we found that the acidity measurement of alchohols in

DMSO is actually scarce3, as well as the experimental studies about existing form of sodium

methoxide in solution4. Then it came to be a crucial problem how MeONa actually exists in a

DMSO solution.

MeONa dimer was chosen as a model. 49 trajectories were generated starting from equilibrated

cluster with a DFT optimized MeONa dimer surrounded by 62 DMSO molecules. Each of them

dissociated rapidly with O-Na distance longer than 8 angstrom. These trajectories with 98

methoxide anion in total gave two products, 68 MeOH (after proton transfer with DMSO) and 32

MeO- respectivel. These species are stable in a time period of 2 ps. On the other hand, all 39

trajectories from MeONa monomer in DMSO cluster gave MeOH with proton extracted from

DMSO, and average O-Na distance of 12 angstrom. Although surprising, the results were

validated by high accuracy methods (see Supporting Information).

Figure 4. (a) PMF-FES for reaction of methoxide and 1 with 62 DMSO molecules. (b, c)

Snapshots of trajectories with MeONa dimer in DMSO cluster, with harmonious force to keep O-

O distance at 2.3 and 6.0 angstrom respectively. (d-f) Snapshots of trajectories for reaction of 1

and MeONa, with harmonious force to keep C-O distance at 2.8, 2.0, 1.9 angstrom respectively.

(g) PMF-FES for dissociation of methanol-methoxide complex. (h) 1-D version of (a) (blue), and

the PMF-FES under implicit solvation (red). (g) PMF-FES with methanol-methoxide complex as

nucleophile. One CH2SOCH3- is included in the cluster for blue line.

The involvement of methanol as primary product for dissociation of MeONa prompted us to

consider of methanol-methoxide complex. This complex is stable toward proton extraction from

DMSO in a trajectory of 8 ps, giving the possibility of its presence in real solution and we

proposed that the fate of MeO- produced in dissociation of MeONa dimer is either to form MeOH

by extracting a proton from DMSO, or form methanol-methoxide complex with another methanol

molecule in a non-equilibrium manner. The conversion of two MeOH molecules (together with

two CH2SOCH3- and two Na+) into methanol-methoxide complex has a barrier of 26 kcal/mol

(Figure 4g), indicating that methanol cannot be in equilibrium with methanol-methoxide complex.

In a summary, in our mechanistic model, sodium methoxide exists as two species unable to

interconvert in DMSO solution, namely MeOH and methanol-methoxide complex. The ratio of

them is determined upon the irreversible dissociation of MeONa aggregations or crystal. Some

NMR evidences were discussed in Supporting Information.

This insight gave us a hint that the actual nucleophile is possible to be methanol-methoxide

complex. An experimental kinetics isotopic effect (KIE) of 2.3 given by initial rate measurement

in DMSO-d6 gave us confidence on this proposal. TS for this process under implicit solvation was

located (Figure 1) and the predicted KIE is exactly 2.30. The PMF surface for the SNAr involving

methanol-methoxide complex exhibits a barrier of 24 kcal/mol. Although acceptable considering

the error of PMF, this pathway cannot explain the experimentally observed second order kinetics

on MeONa. After including one CH2SOCH3- anion, however, the barrier was reduced to 18

kcal/mol. It has to be carefully treated because there might be some hidden “resting state” since

any trajectory with finite length cannot promise there is no configuration of the cluster with lower

energy than B. However, this model shows best consistence with experiments. Thus it is suggested

that in real solvation environment the SNAr reaction between 1 and MeONa proceeds with

involvement of a methanol-methoxide complex and a CH2SOCH3- anion.

According to the discussion above, the initial concentration of methanol-methoxide complex is

determined during the solvation process, and is proportional to the amount of MeONa.

Furthermore, this complex cannot be in equilibrium with other species once MeONa has been

fully solvated. Thus the final yield of the SNAr reaction should reflect the concentration of this

complex. This accounts for the low conversion, since most methoxide anion is converted into

MeOH during solvation. The experimentally observed r=k[1]([1]0-[1]final-([1]0-[1])) kinetics has

r=k[1][methanol-methoxide][CH2SOCH3-] as its real form, where [CH2SOCH3

-], generated also

during the solvation of MeONa, is constant. The observed second-order dependence of initial rate

on amount of MeONa is reflected in the [methanol-methoxide][CH2SOCH3-] part. Our mechanistic

model is shown in Scheme 1.

Scheme 1. Summary of our mechanistic model.

In conclusion, we examined an SNAr reaction by combining experimental and computational

methods. The DFT calculated FES based on implicit solvation model gave an over-simplified and

qualitatively wrong picture. FESs obtained in the presence of 62 DMSO molecules showed huge

difference from those obtained under implicit solvation model. It is not electronic energy, but

entropy due to solvent molecules, that modified the shape of FES. Keeping this in mind, we found

that the real existing form of MeONa in DMSO is a mixture of MeOH and methanol-methoxide

complex which are not in equilibrium, and the latter is the true nucleophile. This work exhibits

that in some case solvent can influence the reaction in a way that is very different from what

people used to think. There is actually no method to fully account for entropy effect of solvent

molecules except molecular dynamics. Although this work is the first work revealing the huge

influence of explicit solvation on the shape of FES for reactions of small organic molecules to the

best of our knowledge, it is possible that there are more such cases unrealized, in which people

were misled by implicit solvation. Also it is still an open question how to explain the origin of this

effect in detail, and how to account for it in a way less time-consuming than molecular dynamics

simulations.

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Supporting Information

Solvent Molecules Play a Role in an SNAr Reaction

Yumiao Ma*

BSJ Institute, Haidian, Beijing, 100084, People’s Republic of China

[email protected]

Table of Contents

Supporting Information..................................................................................................1Experimental Procedure.................................................................................................3Computational Details....................................................................................................3

Conventional DFT calculations..................................................................................4PMF calculation for the reaction between nucleophilic and 4-nitrobenzonitrile.......4PMF calculation for the dissociation of methanol-methoxide complex.....................5PMF calculation for the dissociation of MeOH-MeONa complex............................6PMF calculation for the dissociation of MeONa dimer.............................................7Molecular dynamics simulations for the dissociation of MeONa dimer....................7

Discussions on the origin of explicit solvation effects...................................................8Benchmark on several methods for description of MeO-DMSO complex..................11NMR evidence for the existing form of MeONa in DMSO.........................................13Geometries for species involved in the article.............................................................15Supporting Information..................................................................................................1Experimental Procedure.................................................................................................3Experimental Procedure.................................................................................................3Computational Details....................................................................................................3Computational Details....................................................................................................3

Conventional DFT calculations..................................................................................4PMF calculation for the reaction between nucleophilic and 4-nitrobenzonitrile.......4PMF calculation for the dissociation of methanol-methoxide complex.....................5PMF calculation for the dissociation of MeOH-MeONa complex............................6PMF calculation for the dissociation of MeONa dimer.............................................7Molecular dynamics simulations for the dissociation of MeONa dimer....................7

Discussions on the origin of explicit solvation effects...................................................8Discussions on the origin of explicit solvation effects...................................................8

S1

mailto:[email protected]

Benchmark on several methods for description of MeO-DMSO complex..................11Benchmark on several methods for description of MeO-DMSO complex..................11NMR evidence for the existing form of MeONa in DMSO.........................................13NMR evidence for the existing form of MeONa in DMSO.........................................13Geometries for species involved in the article.............................................................15Geometries for species involved in the article.............................................................15

S2

Experimental Procedure

All reagents used in this work are commercially available. Solvents were dried

before use. 4-nitrobenzonitrile was recrystallized with DCM/PE and dried under

vacuum. Other reagents are used without further purification. All the

experiments were performed in a short period during which the room

temperature is constantly 293 K.

Reaction between 4-nitrobenzonitrile and sodium methoxide

Given amount of MeONa (powder) and 3.0 mg (0.02 mmol) of 4-

nitrobenzonitrile was mixed under nitrogen atmosphere. Then 1.0 mL of DMSO

was added. The mixture was treated by ultrasonic for 2 s to accelerate the

solvating of MeONa (key for reproducibility), and then rigorously stirred for a

given time. Then the solution was quenched by saturated aqueous NaHCO3

and extracted by DCM. The yield was determined by 1H-NMR.

Reaction between 4-nitrobenzonitrile and sodium methoxide with

added methanol

Given amount of MeONa (powder) and 3.0 mg (0.02 mmol) of 4-

nitrobenzonitrile was mixed under nitrogen atmosphere. Given amount of

MeOH was added into 1.0 mL of DMSO. Then the mixed solvent is added into

the solid mixture. The mixture was treated by ultrasonic for 2 s to accelerate

the solvating of MeONa (key for reproducibility), and then rigorously stirred for

a given time. Then the solution was quenched by saturated aqueous NaHCO3

and extracted by DCM. The yield was determined by 1H-NMR.

Computational Details

DFT calculations were performed by Gaussian 09 program. Quasi-classical

molecular dynamics were performed using Singleton’s PROGDYN program.

MOPAC program was employed to run semi-empirical calculations. Grimme’s

xtb program was used to calculate electronic energy of snapshots of

S3

trajectories. ORCA 3.1 package was used for DLPNO-CCSD(T) calculations.

Conventional DFT calculations

For conventional DFT calculations, geometry optimizations and frequency

calculations were performed at M06-2X/6-31+G(d) level combining SMD

implicit solvation model to include the influence of DMSO. Harmonic

corrections to Gibbs free energy were obtained from frequency calculations.

Anharmonic corrections were obtained by freq=anharmonic keyword of

Gaussian. This keyword leads the program to run a VPT2 calculation and give

the anharmonic enthalpy and entropy. For species involving hydrogen bonds

such as Methanol-methoxide complex, M06-2X/6-31+G(d,p) level was also

tried and the results show minimal difference. Single point energies were

obtained under M06-2X/6-311+G(d,p) level (gas phase calculations). Solvation

free energies were obtained under M05-2X/6-31+G(d), and the final Gibbs free

energy is the sum of electronic energy from single point calculation, correction

to Gibbs free energy, and solvation free energy.

For comparison, DLPNO-CCSD(T)/aug-cc-pVTZ calculations were also

performed based on geometries optimized at M06-2X/6-

311+G(d,p)/SMD(DMSO) level. Solvation free energies under SMD model were

added to the DLPNO-CCSD(T) energies in the same way described above.

PMF calculation for the reaction between

nucleophilic and 4-nitrobenzonitrile

The PMF calculations followed three steps: model building, equilibrating, and

sampling.

TS1 (or TS1’) optimized at M06-2X/6-31G(d) level was placed in the center of

a sphere with radius of 13 angstrom, and 62 DMSO solvents were placed in

the sphere. The geometry of this cluster was optimized under PM7 level with

transition state part fixed.

Then the model was used to initiate a molecular dynamics trajectory using

PROGDYN program. An ONIOM model is employed; the transition state is

treated by M06-2X/6-31+G(d) method and DMSO molecules were treated by

PM7. An harmonic force of 0.30 Hartree/(Bohr·angstrom) is used to fix the

bond length between nucleophilic oxygen atom and attacked carbon atom in

substrate. Sphereon feature of PROGDYN is set to keep the density of this

cluster around 1.1. The first 1000 fs was run at 500 K.

S4

Then the trajectory was copied into several directories, and applied force of

0.30 Hartree/(Bohr·angstrom) was set at difference bond lengths. For 1-D

calculation, harmonic force constants were set with minimum at 1.4, 1.6, 1.7,

1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.6, 2.8 angstrom (C-O bond length); for 2-D

calculations, a grid of C-O distance (between 1.4 and 2.8 angstrom) and C-N

distance (between 1.4 and 2.6 angstrom) was set. For the “1.9” and “1.7”

trajectories, the force constant was set to 1.0 Hartree/(Bohr·angstrom) in

order to enhance sampling in this region.

Each system was cooled down to 293 K by removing 0.1% of kinetic energy

per fs. Density, total energy and potential energy in each frame are recorded.

Typically these quantities tend to be stable after 3.5 ps. To avoid any problem

due to insufficient equilibration, all trajectories were equilibrated for 5 ps

before sampling.

Then 1000 fs of data was collected for each trajectory, and free energy

surface was obtained by WHAM program.

In addition to PM7, other semi-empirical methods available in MOPAC were

also tested. All the PM6-based methods led to an unphysical decomposition of

DMSO into DMS and dimethylsulfone even at 293 K. Grimme’s xtb was also

examined using a self-written python interface toward PROGDYN. Xtb

significantly underestimated the density of the cluster and the xtb-optimized

cluster geometry was quite sparse. In the contrast, PM7 gave very perfect

density and no unphysical decomposition.

PMF calculation for the dissociation of

methanol-methoxide complex

The DFT optimized geometry of methanol-methoxide complex was placed in

the center of a sphere with radius of 13 angstrom, and 62 DMSO solvents

were placed in the sphere. The geometry of this cluster was optimized under

PM7 level with methanol-methoxide part fixed.


PROGDYN program. An ONIOM model is employed; the complex is treated by

M06-2X/6-31+G(d) method and DMSO molecules were treated by PM7. An

harmonic force of 0.10 Hartree/(Bohr·angstrom) is used to fix the O-O

distance. Sphereon feature of PROGDYN is set to keep the density of this


Then the trajectory was copied into several directories. Harmonic applied

forces were set with minimum at 2.2, 2.3, 2.4, 2.5, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6,

3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0

angstrom (O-O distance). Since the large range of O-O distance, a ‘slow

S5

change’ strategy was employed. Trajectories with O-O distance near 2.2 to 4.0

angstrom was equilibrated first. Then the “4.0” trajectory was copied to

generate “4.2” to “6.0” trajectories. The equilibrated “6.0” trajectory was

then used to produce other trajectories.

Each system was cooled down to 293 K by removing 0.1% of kinetic energy

per fs. Density, total energy and potential energy in each frame are recorded.

All trajectories were equilibrated for 5 ps before sampling.



PMF calculation for the dissociation of MeOH-

MeONa complex

The M06-2X/6-31+G(d,p) optimized geometry of methanol-methoxide

complex was placed in the center of a sphere with radius of 13 angstrom, and

62 DMSO solvents were placed in the sphere. A sodium cation was placed

randomly in a place near both the two oxygen atoms. The geometry of this

cluster was fully optimized under PM7 level.



M06-2X/6-31+G(d,p) method and DMSO molecules were treated by PM7. An




Then the trajectory was copied into several directories. Harmonic force

constants were set with minimum at 2.2, 2.3, 2.4, 2.5, 2.6, 2.8, 3.0, 3.2, 3.4,

3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 6.5, 7.0, 7.5, 8.0,

8.5, 9.0 angstrom (O-O distance). The ‘slow change’ strategy was employed

as described above. Each system was cooled down to 293 K by removing

0.1% of kinetic energy per fs. Density, total energy and potential energy in

each frame are recorded. All trajectories were equilibrated for 5 ps before

sampling.



S6

PMF calculation for the dissociation of

MeONa dimer

The DFT optimized geometry of MeONa dimer was placed in the center of a

sphere with radius of 13 angstrom, and 62 DMSO solvents were placed in the

sphere. The geometry of this cluster is optimized under PM7 level with MeONa

dimer fixed.



M06-2X/6-31+G(d) method and DMSO molecules were treated by PM7. An




Then the trajectory was copied into several directories. Harmonic applied

forces were set with minimum at 2.1, 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5, 3.7, 3.9,

4.1, 4.3, 4.5, 4.7, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0 angstrom (O-O

distance). For O-O distance larger than 6.5 angstrom, the final value of

applied force was set to 0.05 Hartree/(Bohr·angstrom). The ‘slow change’

strategy was employed as described above. Each system was cooled down to

293 K by removing 0.1% of kinetic energy per fs. Density, total energy and

potential energy in each frame are recorded. All trajectories were equilibrated

for 5 ps before sampling.



Molecular dynamics simulations for the

dissociation of MeONa dimer

The DFT optimized MeONa dimer was placed in the center of a sphere with 62

DMSO molecules and the cluster was optimized at PM7 level with geometry of

MeONa dimer fixed. Then the cluster was used to initiate a trajectory. Two Na

and two O atoms in dimer were fixed by fixedatom feature of PROGDYN. The

cluster was equilibrated at 500 K for 1000 fs, and then cooled to 293 K. The

S7

system was equilibrated at 293 K for 5 ps.

While the trajectory above still running, a python script was used to copy the

trajectory with an interval of 50 fs. The copied trajectories were continued for

2000 fs without fixedatom, and the distance from the nearest hydrogen is

recorded for each of the two oxygen atoms in Methanol-methoxide complex.

Discussions on the origin of

explicit solvation effects

Single-point energy calculations for some snapshots (with all solvent molecules included) of

several trajectories used in 2D-PMF procedure (Figure 3a) were performed in xtb and PM7 levels.

The average xtb single point energies and enthalpies were shown in Figure S2, much similar to the

implicit solvation model-derived energies. Combining with the fact that the Hamiltonian of PM7

is fitted to reproduce experimental enthalpies, we concluded that the change in free energies arose

from entropy effects due to dynamics of solvent molecules.

S8

Figure S1. 2D PMF-FES shown in Figure 3a. For three of these trajectories, the

averaged xtb electronic energies, PM7 electronic energies and PM7 enthalpies

were shown in the format xtb / PM7 electronic energy / PM7 enthalpy.

In order to give a graphical description of entropy effects, we tried to

characterize the entropy due to solvent molecules by some statistical

amounts. For each of the trajectory generated for 2D-PMF corresponding to

reaction of methoxide anion and 1, the following procedure was performed:

For each frame, 62 vectors were defined as the orientation of S-O bond in

each DMSO. Then these vectors are averaged into one “average” vector:

v i , average=

162

∑ (x1−x2)

162

∑ ( y1− y2)

162

∑ (z1−z2)

Where subscript 1 and 2 means the oxygen and sulfur atom in each DMSO

molecule, and i means the frame number.

The “std” vector is defined as followings:

v i , std=

√ 162

∑ (x1−x2−x i ,average)2

√ 162∑ ( y1− y2− yi ,average)

2

√ 162

∑ (z1−z2−zi , average)2

Where x i ,average means the x component of v i , average , and so does the other

two components.

For the 1000 v i , std and v i , average vectors, the average value were

calculated and represented as v std and vmean vectors. Also calculated

were the v std− std and v std−mean vectors, meaning the standard deviations

for v i , std and v i , average respectively. Then the norm of each vector is

calculated. Then for each trajectory we have four statistical amounts to

describe the distribution of S-O dipole of DMSO. The plots of four amounts

versus their corresponding bond length (the zero point for harmonic applied

force) are shown in Figure S2.

The “mean” value for each trajectory is very close to zero, which should hold

for any successful trajectory without external electric field. The “std” values

vary point to point. However, in order to statistically describe the entropy of a

system, these “static” amounts are insufficient. The “std-mean” and “std-std”

values reflect the ability of the orientation of S-O dipoles to fluctuate within

the 1000 ps, and should be a much better probe for entropy. Figure S2c and

S2d show these two amounts. They have a column-like distribution; with a

larger C-O distance these amounts rise, indicating a more flexible solvent

S9

cage and thus a more favorable entropy.

Please recall the difference between PMF free energy surface and that under

implicit solvation model. The former exhibits a much higher free energy in the

side with shorter C-O distance. The picture above shows that the entropy

caused by the orientation of DMSO molecules is able to give an interpretation

for this observation, although it might not be a strict causality.

Then came to the problem why this could happen. Entropy came unfavorable

with a larger C-O distance, indicating that the DMSO cage seems to

entropically dislike a significant charge separation. The same trend can also

be seen in the case of dissociation of MeONa dimer. We propose that this

comes from an effect similar to hydrophobic effect. In these process, a cavity

is generated around the dissociating bond, and the other part of the bulky

solution has to be compressed in order to keep the total density constant,

leading to a tighter combination of solvent molecules and thus a lower

entropy.

In a summary, we propose that highly dipolar solvents might disfavor

“limited” charge separation, although it is well-known that polar solvent

favors “extensive” charge separation. When the two dissociated parts are

separated in a distance not adequate for solvent molecules to insert between

them, a cavity is generated and some entropy effects may come to appear.

This effect is expected to be more significant if the two parts are hard and

with high charges. Apparently more evidence is needed to validate this

proposal.

S10

Figure S2. Plot of four statistical amounts reflecting orientation of DMSO

molecules versus their corresponding C-O and C-N distance.

Benchmark on several methods

for description of MeO-DMSO

complex

The result that methoxide is prior to deprotonate DMSO is astonishing. In

order to preclude the possibility that inaccuracy of calculations led to a wrong

result, a benchmark was done for several methods employed in this work.

Relative gas-phase electronic energies of three species were used as testing

S11

examples, with DLPNO-CCSD(T)/aug-cc-pVTZ results as standard. Both PM7

and M06-2X/6-31+G(d,p) gave very excellent results. Removal of p functions

led to underestimate the stability of proton transfer products, but is not vital.

Due to considerations of both accuracy and timing, we decided to use M06-

2X/6-31+G(d) for QM part of PMF involving 1, and M06-2X/6-31+G(d,p) for

others. The surprisingly excellent result given by PM7 gave us great

confidence.

Figure S3. Species used as testing examples

Method E (EnolateO ) E (DMSO_MeO ) E (EnolateC )

M06-2X/6-311+G(d,p) 0.65 0.0 -0.99

M06-2X/6-31+G(d,p) 1.99 0.0 -0.38

M06-2X/6-31+G(d) 4.81 0.0 2.28

PM7 1.27 0.0 -0.08

DLPNO-CCSD(T)/aug-cc-pVTZ 1.12 0.0 -0.31

Table S1. Relative electronic energies for testing examples.

S12

NMR evidence for the existing

form of MeONa in DMSO

(a)

S13

(b)

Figure S4. NMR for MeONa in DMSO-d6. (a) Full spectrum. (b) The part related

to MeONa.

NMR spectroscopy of MeONa in DMSO-d6 gave cleanly two peaks. One at 3.16

ppm corresponds to methanol, and the peak at 3.20 ppm was proposed to be

methoxide-methanol complex. The integral ratio was 12.5:1, in good

consistence with the experimental observation that 44% conversion of 1 was

achieved with 5 equivalents of MeONa.

Although it supports our model, this NMR should be carefully treated due to

the possibly presence of water in DMSO-d6. Also the calculations

underestimated the chemical shift of methanol by 0.14 ppm. This difference

could come from both systematic error for DFT calculation and the

conformational diversity of species in solution.

S14

Geometries for species involved

in the article

1

C -0.31103800 -1.22116100 -0.00030500

C 1.07815400 -1.21802800 -0.00051100

C 1.76879000 0.00001600 -0.00000100

C 1.07817200 1.21805400 0.00053800

C -0.31103400 1.22120900 0.00038600

C -0.97301100 0.00003100 0.00006100

H -0.87919700 -2.14374500 -0.00038200

H 1.63097300 -2.15125000 -0.00109000

H 1.63098200 2.15128000 0.00108700

H -0.87916400 2.14380600 0.00047800

C 3.21009500 -0.00000600 -0.00002700

N 4.36707000 -0.00002700 -0.00004300

N -2.45098600 -0.00000400 0.00009100

O -3.00974600 -1.08063600 0.00103500

O -3.00987200 1.08056600 -0.00119300

Imaginary frequency: 0

Int1

C 0.00889500 -0.56149000 -1.17446200

C -1.36779400 -0.40650300 -1.19326800

C -2.06553300 -0.22761100 0.01290600

C -1.38292200 -0.18485000 1.23277400

C -0.00006400 -0.33309700 1.25242300

C 0.67257000 -0.51070000 0.04918100

H 0.56919900 -0.70127500 -2.09070200

H -1.90880900 -0.43102100 -2.13404200

H -1.92917100 -0.04425400 2.16025400

H 0.54753900 -0.30745000 2.18703400

C -3.49423600 -0.08068000 -0.00840600

N -4.64683200 0.03690500 -0.02756100

N 2.11444900 -0.79477900 0.08619700

O 2.65657900 -1.13114400 -0.95305000

S15

O 2.67153300 -0.78719800 1.17381700

O 1.94378300 1.61192600 -0.46878500

C 1.00135700 2.46609300 -0.00413000

H 1.10486500 3.51170000 -0.38778200

H -0.05114900 2.17905000 -0.27477900

H 0.98539900 2.58271600 1.11160100


TS1

C 0.04495200 -0.59179000 -1.15609000

C -1.33460500 -0.50964200 -1.16393100

C -2.03649700 -0.24651000 0.02785300

C -1.33171900 -0.06409700 1.22747800

C 0.05160200 -0.14470800 1.24358700

C 0.74125200 -0.34656500 0.03966600

H 0.59636800 -0.80902700 -2.06269900

H -1.88187400 -0.66811400 -2.08856100

H -1.87344200 0.12040700 2.15056900

H 0.60322000 -0.02176800 2.16793200

C -3.46528100 -0.17661500 0.01780300

N -4.62454100 -0.11907600 0.00869900

N 2.15862400 -0.75943000 0.11883200

O 2.71016500 -1.11174900 -0.90908600

O 2.69376900 -0.77523200 1.21645400

O 1.77808000 1.51999300 -0.43294600

C 0.80806400 2.44787700 -0.18770000

H 1.09021500 3.45943000 -0.54868000

H -0.16207200 2.21611700 -0.69132900

H 0.56628400 2.58070800 0.89268200


TS2

C -0.06635200 0.33672700 1.22591100

C 1.29169500 0.15041400 1.21751700

C 2.00779400 0.00926400 0.00132900

C 1.29386000 0.14471500 -1.21675500

C -0.06423700 0.33038700 -1.22842200

C -0.83946500 0.29486400 -0.00186700

H -0.60542400 0.47035300 2.15912800

H 1.83846200 0.13837900 2.15788700

H 1.84229400 0.12844500 -2.15609200

H -0.60166500 0.45945600 -2.16323500

C 3.41248800 -0.16948200 0.00295700

N 4.56874200 -0.32220100 0.00424900

S16

N -1.73218600 -1.25371800 0.00170000

O -2.02084800 -1.75710200 1.07714600

O -1.99267100 -1.77922300 -1.07032000

O -2.03339500 1.04831500 -0.00497200

C -1.80951600 2.45063100 -0.00633400

H -2.79671700 2.91730800 -0.00863800

H -1.25914200 2.76935000 0.88737300

H -1.25599700 2.76710100 -0.89891700


TS1’

C -0.91736300 1.43411300 0.59270900

C -2.20272100 0.93027000 0.60077800

C -2.54162600 -0.18123700 -0.19446100

C -1.56102800 -0.76938200 -1.01302800

C -0.26956700 -0.27699700 -1.02559400

C 0.08555800 0.77219300 -0.15005800

H -0.65589900 2.29953200 1.18991000

H -2.96582100 1.41003500 1.20748900

H -1.82548900 -1.60400600 -1.65645900

H 0.48519100 -0.71171600 -1.67036200

C -3.87692200 -0.68592600 -0.19443500

N -4.96310400 -1.09764900 -0.19347800

N 1.29738600 1.56950600 -0.51372900

O 1.43677200 2.66670300 -0.00182200

O 2.07705300 1.08758100 -1.31483500

O 1.33371600 -0.02870300 1.20714300

C 0.56274600 -0.90456500 1.94994100

H 1.19567500 -1.56337200 2.56941600

H -0.12529200 -0.38475400 2.64284400

H -0.05476200 -1.57114600 1.31333300

H 2.66688100 -0.83857100 0.69831400

O 3.39117800 -1.46280600 0.39801500

C 2.86268900 -2.19013800 -0.68308200

H 3.54774200 -3.01310800 -0.91728900

H 1.87969000 -2.62742200 -0.44568900

H 2.75175000 -1.57064900 -1.58569900


Int2

C 0.32114500 -0.53015700 -0.98384700

C -1.04130800 -0.56023500 -1.06225000

C -1.88223000 -0.18543900 0.02162800

C -1.23276000 0.20566400 1.23024000

S17

C 0.12218200 0.25463700 1.34875200

C 1.05024400 -0.04736300 0.22514800

H 0.91820800 -0.79018300 -1.85534900

H -1.50983500 -0.88508200 -1.99087900

H -1.85037500 0.46399300 2.08963600

H 0.59827200 0.54461600 2.28254900

C -3.28950600 -0.22463600 -0.08569700

N -4.45562000 -0.25468100 -0.17501500

O 1.88065400 1.12119200 -0.10096400

C 1.15481100 2.21232300 -0.60489400

H 1.86949400 3.03097200 -0.73998100

H 0.68160100 1.97862700 -1.56899600

H 0.36722800 2.52785700 0.09420800

C 2.97532600 -1.41625800 -0.21347700

H 3.75099500 -1.94247800 0.35164900

H 2.52432000 -2.12267700 -0.92560600

H 3.43194500 -0.58577400 -0.76612500

O 2.03685400 -0.95723100 0.72601100


2

C -0.56131000 -1.21197200 -0.23601700

C 0.81960200 -1.21437200 -0.08387700

C 1.51250800 -0.00007600 -0.00398400

C 0.82055400 1.21486700 -0.08234200

C -0.56036300 1.21373800 -0.23443600

C -1.24720300 0.00120300 -0.30995400

H -1.11959000 -2.13992600 -0.31295900

H 1.36769000 -2.14956300 -0.03032600

H 1.36938300 2.14955200 -0.02754400

H -1.11803200 2.14215900 -0.31006900

C 2.94349700 -0.00072600 0.15332900

N 4.09415000 -0.00124200 0.28181700

O -2.60456700 0.00204700 -0.49193900

C -3.34305300 -0.00250500 0.72454300

H -4.39725100 -0.00096000 0.44719200

H -3.11545600 -0.89952400 1.31293700

H -3.11465300 0.88964600 1.31998400


Methanol-methoxide complex

O 1.07569700 0.68317700 -0.01692600

H 0.13971400 0.14828900 -0.01311600

C 2.12212600 -0.24856800 0.01399100

S18

H 3.08973900 0.27496000 0.00639100

H 2.10580400 -0.88381500 0.91957400

H 2.11697500 -0.93030700 -0.85723600

O -1.03585000 -0.62209400 -0.02063900

C -2.15619300 0.18060100 0.01415800

H -3.10415300 -0.40156900 -0.00534600

H -2.22842100 0.82133700 0.92634100

H -2.23403000 0.89024300 -0.84498100


S19

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solvent molecules play a role in an snar reaction

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