Analysis of ab initio molecular dynamics

This section continues the discussion of the quasi-chemical theory, but incorporates AIMD ab initio molecular dynamics) calculations to develop the point that the central quantities of quasi-chemical theories can be obtained from simulation calculations. Additionally, we develop a variational perspective on the quasichemical partitioning of inner and outer shells. The calculations which provide the basis of this discussion treat liquid water (Asthagiri et al, 2003c). 

We discuss the latter topic - the variational character - first. The inner-shell and outer-shell terms displayed in Eq. (7.8) offer the possibility of balancing contributions. In fact, the sum of those two terms would be independent of the definition of the iimer shell if no further approximations were made. This is because the rearrangement induced by definition of the inner shell was entirely formal and correct, and the original problem was independent of the definition of the inner shell. 

When approximations are made in the evaluation of those distinct terms, the sum needn t be independent of definition of the iimer shell. We argue here that when the sum is insensitive to local adjustment of the inner shell then the inevitable approximations are well balanced. The quasi-chemical approach is variational in this sense. 

We now develop an example of this variational character. We utilize results from ab initio molecular dynamics (AIMD) for that purpose, and estimate fiquid water. The ab initio molecular dynamics simulations were carried out with the VASP (Kresse and Hafner, 1993 Kresse and Furthmiiller, 1996) simulation program, as described in detail in Asthagiri et al. (2003c). Ab initio molecular dynamics of aqueous solutions are recent activities compared with other simulation methods for aqueous solutions, and basic characterization of the new methods is still underway see Grossman et al. (2004) and Schwegler et al. (2004) for initial examples. 

We focus first on the outer-shell contribution of Eq. (7.8), p. 145. That contribution is the hydration free energy in liquid water for a distinguished water molecule under the constraint that no inner-shell neighbors are permitted. We will adopt a van der Waals model for that quantity, as in Section 4.1. Thus, we treat first the packing issue implied by the constraint Oy [1 i a (7)] of Eq. (7.8) then we append a contribution due to dispersion interactions, Eq. (4.6), p. 62. Einally, we include a contribution due to classic electrostatic interactions on the basis of a dielectric continuum model. Section 4.2, p. 67. 

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