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Variational calculation of quantum mechanical/molecular mechanical free energy with electronic polarization of solvent
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10.1063/1.3699234
/content/aip/journal/jcp/136/13/10.1063/1.3699234
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/13/10.1063/1.3699234

Figures

Image of FIG. 1.
FIG. 1.

Potential energy profile of the Finkelstein reaction (Cl + CH3Cl → ClCH3 + Cl) in the gas phase. Zero of energy is set at the infinitely separated reactants. The basis sets are 6-311++G(3df,3p) for CCSD(T) and MP2 and 6-31+G(d,p) for B3LYP, BHHLYP, and HF methods. For comparison, the energy profile at the HF/6-31G(d) level is also shown.

Image of FIG. 2.
FIG. 2.

Potential of mean force (PMF) of the Finkelstein reaction Cl + CH3Cl → ClCH3 + Cl in aqueous solution. The result obtained with the mean-field QM/MM method is compared to those obtained from direct QM/MM calculations (see text for details). The QM calculation is performed at the HF/6-31G(d) level. The water is represented by the TIP3P model. The circles depict raw data points obtained by integrating the free energy gradient in Eq. (30). The statistical error of the PMF is comparable to the width of the plotted curve (see the supplementary material116 for more details).

Image of FIG. 3.
FIG. 3.

PMF of the Finkelstein reaction Cl + CH3Cl → ClCH3 + Cl in water and acetone solutions calculated with the mean-field QM/MM method. Solvents are described with the TIP3P and OPLS models in the nonpolarizable case (dashed lines) and with the CRK model in the polarizable case (solid line). The QM calculation is performed at the BHHLYP/6-31+G(d,p) level.

Image of FIG. 4.
FIG. 4.

Solvent electrostatic potentials (ESPs) acting on the solute atoms, 〈V α〉, for the Finkelstein reaction in (a) water and (b) acetone solutions. The results obtained with the polarizable and nonpolarizable solvent models are shown by solid and dashed lines, respectively. Cl* and Cl indicate the attacking and leaving chloride atoms, respectively. The curve labeled with CH3 shows the mean value of ESP acting on the methyl group. Panel (c) displays the solvation free energy calculated with the linear response approximation (see the main text). The ESP values in panels (a) and (b) include the contribution of the Wigner potential.

Image of FIG. 5.
FIG. 5.

PMF of the Finkelstein reaction in various solvents calculated with (a) the mean-field QM/MM method and (b) the COSMO continuum solvation model. In panel (a), all the solvents are described with the polarizable CRK model. The QM calculation is performed at the BHHLYP/6-31G+(d,p) level.

Image of FIG. 6.
FIG. 6.

Potential energy profile of the Menshutkin reaction NH3 + CH3Cl → NH3CH3 + + Cl in the gas phase. The basis sets are 6-311++G(3df,3p) for CCSD(T) and MP2 methods and 6-31+G(d,p) otherwise.

Image of FIG. 7.
FIG. 7.

PMF of the Menshutkin reaction NH3 + CH3Cl → NH3CH3 + + Cl in water, DMF, and cyclohexane solutions calculated with the mean-field QM/MM method. Solvents are described with the TIP3P and OPLS models in the nonpolarizable case (dashed lines) and with the CRK model in the polarizable case (solid line). The QM calculation is performed at the BHHLYP/6-31+G(d,p) level.

Image of FIG. 8.
FIG. 8.

Solvent electrostatic potentials (ESPs) acting on the solute atoms, 〈V α〉, for the Menshutkin reaction in (a) water, (b) DMF, and (c) cyclohexane solutions. The results obtained with the polarizable and nonpolarizable solvent models are shown by solid and dashed lines, respectively. Panel (d) displays the solvation free energy calculated with the linear response approximation (see the main text). In panel (c), the ESP value calculated with the OPLS-UA model for cyclohexane is identically zero because the latter has no partial charge on the united CH2 atoms.

Image of FIG. 9.
FIG. 9.

PMF of the Menshutkin reaction in various solvents calculated with (a) the mean-field QM/MM method and (b) the COSMO continuum solvation model. In panel (a), all the solvents are described with the polarizable CRK model. The QM calculation is performed at the BHHLYP/6-31+G(d,p) level.

Image of FIG. 10.
FIG. 10.

Potential energy profiles of the phosphoryl dissociation reaction CH3OPO3 2 − → CH3O + PO3 in the gas phase. The basis sets are 6-311++G(3df,3p) for CCSD(T) and MP2 methods and 6-31+G(d,p) otherwise.

Image of FIG. 11.
FIG. 11.

PMF of the phosphoryl dissociation reaction CH3OPO3 2 − → CH3O + PO3 in (a) acetone and (b) cyclohexane solutions calculated with the mean-field QM/MM method. For comparison, PMF obtained with the COSMO model and the potential energy profile in the gas phase are also shown. The QM calculation is performed at the MPW1PW91/6-31+G(d,p) level.

Image of FIG. 12.
FIG. 12.

Solvent electrostatic potentials (ESPs) acting on the solute atoms, 〈V α〉, for the phosphoryl dissociation reaction in (a) acetone and (b) cyclohexane solutions. The results obtained with the polarizable and nonpolarizable solvent models are shown by solid and dashed lines, respectively. Panel (c) displays the solvation free energy calculated with the linear response approximation (see the main text). The ESP values in panels (a) and (b) include the contribution of the Wigner potential.

Tables

Generic image for table
Table I.

Free energy barrier ΔA (in kcal/mol) for the Finkelstein reaction (Cl + CH3Cl → ClCH3 + Cl) obtained with the mean-field QM/MM method. ΔA is calculated as A(ξ = 0.0) − A(ξ = −4.0). The solvents are described with the polarizable CRK model. Values in parentheses are obtained with the nonpolarizable solvent models. The basis sets are 6-311++G(3df,3p) for MP2 and 6-31+G(d,p) for BHHLYP method.

Generic image for table
Table II.

Free energy correction for statistical fluctuations of the QM wave function [namely, the second term in Eq. (C1)] calculated for the Finkelstein reaction in solution (in kcal/mol). The QM level is BHHLYP/6-31+G(d,p) and the solvents are described with the polarizable CRK model. Values in parentheses are obtained with the nonpolarizable solvent models.

Generic image for table
Table III.

Activation free energy ΔG (in kcal/mol) for the Finkelstein reaction Cl + CH3Cl → ClCH3 + Cl calculated with the mean-field QM/MM method. The QM calculation is performed at the BHHLYP/6-31+G(d,p) level, and the solvents are described with the polarizable CRK model. The values include the corrections for solute thermal motions (4.3 kcal/mol, see the main text) and statistical fluctuations of the QM wave function (Table II). Values in parentheses are the results obtained with the nonpolarizable models. refers to the experimental estimate.85

Generic image for table
Table IV.

Dielectric constants and molecular polarizability of water, methanol (MeOH), acetonitrile (MeCN), acetone, N,N-dimethylformamide (DMF), and cyclohexane (CHX).

Generic image for table
Table V.

Density ρ (in g/cm3) and vaporization enthalpy ΔH v (in kcal/mol) of bulk solvents calculated with the CRK and empirical (nonpolarizable) models. Vaporization enthalpy was calculated as ΔH v ≃ −⟨E⟩ + RT, where ⟨E⟩ is the average interaction energy per molecule and R is the gas constant.

Generic image for table
Table VI.

Density ρ (in g/cm3) and vaporization enthalpy ΔH v (in kcal/mol) of bulk water and acetone at 298 K and 1 atm calculated with the polarizable and nonpolarizable models. “pol-TIP3P” refers to the CRK water model derived from the TIP3P model, while “pol-SPC” refers to the CRK water model derived from the SPC model. The CRK model for acetone is derived from the OPLS-AA model. “TIP3P,” “SPC,” and “OPLS-AA” refer to the standard empirical models. The value of Coulomb damping parameter A is given in parentheses. In the main text, A was set to 2.7 for water and 2.6 for other solvents. The ΔA stands for the free energy barrier (in kcal/mol) for the Finkelstein reaction Cl + CH3Cl → ClCH3 + Cl calculated with the mean-field QM/MM method at the BHHLYP/6-31+G(d,p) level. The CRK matrix was calculated with the B3LYP/aug-cc-pVTZ method unless otherwise noted.

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/content/aip/journal/jcp/136/13/10.1063/1.3699234
2012-04-04
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Variational calculation of quantum mechanical/molecular mechanical free energy with electronic polarization of solvent
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/13/10.1063/1.3699234
10.1063/1.3699234
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