Exploring the ab initio/classical free energy perturbation method: The hydration free energy of water

Sakane, Shinichi; Yezdimer, Eric M.; Liu, Wenbin; Barriocanal, Jose A.; Doren, Douglas J.; Wood, Robert H.

doi:doi:10.1063/1.1305862

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On the temperature, equipartition, degrees of freedom, and finite size effects: Application to aluminum clusters

The relationship between statistical ensembles (especially microcanonical ensemble) and dynamics, the equipartition theorem, and the notion of dynamical temperature are reexamined with an emphasis on finite size effects. A (dynamical) equipartition ansatz (postulate) is formulated and the notion of dynamical degrees of freedom is introduced. The utility of the dynamical degrees of freedom as an analysis tool is discussed and illustrated in applications to model aluminum clusters. © 2000 American...

Direct iterative solution of the generalized Bloch equation. II. A general formalism for many-electron systems

A general nonperturbative formulation of the recently proposed [H. Meißner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997); Part I] quadratic iterative scheme for the wave function expansion coefficients (WECs), enabling a direct solution of the generalized Bloch equation, is given for the ab initio electronic Hamiltonians, thus enabling the computation of the molecular electronic structure. The method exploits the concepts of a multidimensional reference or model space, a (non-Hermiti...

The ab initio/classical free energy perturbation (ABC-FEP) method proposed previously by Wood et al. [J. Chem. Phys. 110, 1329 (1999)] uses classical simulations to calculate solvation free energies within an empirical potential model, then applies free energy perturbation theory to determine the effect of changing the empirical solute–solvent interactions to corresponding interactions calculated from ab initio methods. This approach allows accurate calculation of solvation free energies using an atomistic description of the solvent and solute, with interactions calculated from first principles. Results can be obtained at a feasible computational cost without making use of approximations such as a continuum solvent or an empirical cavity formation energy. As such, the method can be used far from ambient conditions, where the empirical parameters needed for approximate theories of solvation may not be available. The sources of error in the ABC-FEP method are the approximations in the ab initio method, the finite sample of configurations, and the classical solvent model. This article explores the accuracy of various approximations used in the ABC-FEP method by comparing to the experimentally well-known free energy of hydration of water at two state points (ambient conditions, and 973.15 K and 600 kg/m³). The TIP4P-FQ model [J. Chem. Phys. 101, 6141 (1994)] is found to be a reliable solvent model for use with this method, even at supercritical conditions. Results depend strongly on the ab initio method used: a gradient-corrected density functional theory is not adequate, but a localized MP2 method yields excellent agreement with experiment. Computational costs are reduced by using a cluster approximation, in which ab initio pair interaction energies are calculated between the solute and up to 60 solvent molecules, while multi-body interactions are calculated with only a small cluster (5 to 12 solvent molecules). Sampling errors for the ab initio contribution to solvation free energies are ±2 kJ/mol or less when 50–200 configurations are used. Using the largest clusters and most accurate ab initio methods, ABC-FEP predicts hydration free energies of water at both state points that agree with equations of state, within the sampling error. These results are the first calculation of a free energy of solvation at extreme conditions from a fully atomistic model with ab initio methods. © 2000 American Institute of Physics.