MSC'99 Seminar D6: Friday, 19 March 1999, 11:05 am

Continuum Solvent Methods for Quantum Mechanics,

Molecular Dynamics and Monte Carlo Simulations

**Daniel T. Mainz** & William A. Goddard III

*Materials and Process Simulation Center, Caltech, Pasadena, CA
91125*

**Presentation Materials**:

- Seminar slides: HTML, PostScript (600 dpi) file (GZipped, 2.7 MB)

**Abstract**:

Solvation effects are of tremendous importance to molecular simulation,
and are a primary research concern at the MSC, where several collaborators
are studying peptide folding statistics, novel dendritic polymer structures
and functionalities, and developing new force fields based on quantum
chemistry results in solution. Several methods of including solvation
effects in *ab initio* quantum mechanics and classical molecular
dynamics will be addressed, including explicit solvent studies and force
field parameterizations. The argument is made that continuum dielectric
methods best balance the competing needs for acceptable accuracy and
computational efficiency. The use of the Poisson-Boltzmann equation for
solvation, based on Debye-Hückel theory, is presented, and serves as
the foundation for computational packages which use finite element
approaches (PBF) and Generalized Born (GB) algorithms. PBF works
exceptionally well with *ab initio* programs, yielding solvation free
energies within 0.4 kcal/mol at little additional cost to a gas-phase
calculation. Because it is a faster algorithm, GB methods are a better fit
for molecular dynamics simulations with the MSC-developed program MPSim.
The S-GB program significantly improves upon the GB formulation; in
addition to being faster and scaling better with system size, it reduces
absolute energetic errors from 10% of the total energy of ribonuclease A
conformers obtained through standard GB methods to only 1% error. S-GB is
especially amenable to computational parallelization; this shall bring
solvated dynamical simulations with MPSim to be only marginally more
expensive than solute-only calculations.

**Funding:** ARO/MURI, NSF Chemistry

**Figure 1**: The physical picture of continuum solvent methods. All
of the solvent atoms are eliminated from the system, and replaced with a
dielectric continnum; the electrostatic effects are governed by the
Poisson-Boltzmann equation.

GBSA |
S-GB |
||||

Chain length |
Natoms |
Abs. error |
Rel. sq. error |
Abs. error |
Rel sq. error |

4 |
58 |
10.229 |
9.137 |
2.027 |
6.273 |

18 |
280 |
23.703 |
38.811 |
2.213 |
22.869 |

22 |
362 |
45.414 |
22.278 |
2.931 |
1.891 |

30 |
620 |
65.929 |
37.954 |
10.801 |
8.946 |

**Table 1**: (from Ghosh, et al.) Comparison of conventional GB model
with new S-GB method for peptides of different lengths. S-GB is markedly
better at achieving accurate absolute and relative energies with respect to
high-quality numerical solution of the PB equation.

**References**:

`SCRF methods`: Tannor, et al.,*J. Am. Chem. Soc.*,**116**, 11875 (1994)`PB Solvation`: Cortis, et al.,*J. Comput. Chem.*,**18**, 1591 (1997)`GB Solvation`: Ghosh, et al.,*J. Phys. Chem. B.*,**102**, 19083 (1998)`MPSim`: Lim, et al.,*J. Comput. Chem.*,**18**, 501 (1997)