1549380323-Statistical Mechanics Theory and Molecular Simulation

Problems 491

O O

H

O O

H

O O

H

-0.8 -0.4 0 0.4 0.8

d

c

(Å)

0

1

2

3

4

D

A

(kcal/mol)

Classical

Quantum

Quantum H

Fig. 12.14Top: Sketch of the internal proton transfer reaction in malonaldehyde. Bottom:
Classical, quantum, and quantum-H free energy profiles at 300 K.

effects by construction. Therefore, if such a model were used in conjunction with path
integrals, quantum effects would be “double counted.” By contrast, simulations per-
formed with potential models whose parameters are fit toab initiocalculations do not
contain quantum effects implicitly, and therefore, these models arestrictly correctonly
when used in conjunction with path-integral methods. An example of such a model
is the water potential of Xantheas and coworkers (Fanourgakis and Xantheas, 2006;
Fanourgakiset al., 2006; Paesaniet al., 2007), which yields accurate results when
simulated as a path integral. When nuclear quantum effects can be safely neglected,
then models such as these can be simulated using classical molecular dynamics or
Monte Carlo algorithms. Similarly, when potential energies and forces in a simulation
are computed “on the fly” from the electronic structure via theab initiomolecular
dynamics technique (Car and Parrinello, 1985; Marx and Hutter, 2009), these simula-
tions should, strictly speaking, be performed within the path-integral framework since
nuclear quantum effects are not implicitly included in this approach. Simulations us-
ing this technique have yielded important insights, for example, into the solvation and
transport of charge defects (in the form of hydronium and hydroxide ions) in aqueous
solution (Marxet al., 1999; Tuckermanet al., 2002).