# Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation

## Abstract

We give an account of a computationally tractable and efficient procedure for the calculation of potentials of mean force using mixed Hamiltonian models of electronic structure where quantum subsystems are described with computationally intensive ab initio wavefunctions. The mixed Hamiltonian is mapped into an all-classical Hamiltonian that is amenable to a thermodynamic perturbation treatment for the calculation of free energies. A small number of statistically uncorrelated (solute-solvent) configurations are selected from the Monte Carlo random walk generated with the all-classical Hamiltonian approximation. Those are used in the averaging of the free energy using the mixed quantum/classical Hamiltonian. The methodology is illustrated for the micro-solvated SN2 substitution reaction of methyl chloride by hydroxide. We also compare the potential of mean force calculated with the above protocol with an approximate formalism, one in which the potential of mean force calculated with the all-classical Hamiltonian is simply added to the energy of the isolated (non-solvated) solute along the reaction path. Interestingly the latter approach is found to be in semi-quantitative agreement with the full mixed Hamiltonian approximation.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (US), Environmental Molecular Sciences Laboratory (EMSL)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 15006814

- Report Number(s):
- PNNL-SA-38525

1813; 2403; KC0301020

- DOE Contract Number:
- AC06-76RL01830

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Molecular Structure - Theochem, 632(1-3):173-183

- Country of Publication:
- United States

- Language:
- English

- Subject:
- environmental molecular sciences laboratory

### Citation Formats

```
Dupuis, Michel, Schenter, Gregory K., Garrett, Bruce C., and Arcia, Edgar E.
```*Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation*. United States: N. p., 2003.
Web. doi:10.1016/S0166-1280(03)00297-5.

```
Dupuis, Michel, Schenter, Gregory K., Garrett, Bruce C., & Arcia, Edgar E.
```*Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation*. United States. doi:10.1016/S0166-1280(03)00297-5.

```
Dupuis, Michel, Schenter, Gregory K., Garrett, Bruce C., and Arcia, Edgar E. Fri .
"Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation". United States. doi:10.1016/S0166-1280(03)00297-5.
```

```
@article{osti_15006814,
```

title = {Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation},

author = {Dupuis, Michel and Schenter, Gregory K. and Garrett, Bruce C. and Arcia, Edgar E.},

abstractNote = {We give an account of a computationally tractable and efficient procedure for the calculation of potentials of mean force using mixed Hamiltonian models of electronic structure where quantum subsystems are described with computationally intensive ab initio wavefunctions. The mixed Hamiltonian is mapped into an all-classical Hamiltonian that is amenable to a thermodynamic perturbation treatment for the calculation of free energies. A small number of statistically uncorrelated (solute-solvent) configurations are selected from the Monte Carlo random walk generated with the all-classical Hamiltonian approximation. Those are used in the averaging of the free energy using the mixed quantum/classical Hamiltonian. The methodology is illustrated for the micro-solvated SN2 substitution reaction of methyl chloride by hydroxide. We also compare the potential of mean force calculated with the above protocol with an approximate formalism, one in which the potential of mean force calculated with the all-classical Hamiltonian is simply added to the energy of the isolated (non-solvated) solute along the reaction path. Interestingly the latter approach is found to be in semi-quantitative agreement with the full mixed Hamiltonian approximation.},

doi = {10.1016/S0166-1280(03)00297-5},

journal = {Journal of Molecular Structure - Theochem, 632(1-3):173-183},

number = ,

volume = ,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2003},

month = {Fri Aug 01 00:00:00 EDT 2003}

}