Comparison of free energy methods for molecular systems

Abstract

We present a detailed comparison of computational efficiency and precision for several free energy difference (∆F ) methods. The analysis includes both equilibrium and non-equilibrium approaches, and distinguishes between uni-directional and bi-directional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration and single-ensemble path sampling, to more established methodologies. As test cases, we study relative solvation free energies, of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation ∆F estimates as compared to other methods used in this report, while also offering rapid estimation of ∆F . The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the uni-directional, "fast-growth" non-equilibrium case. Closer examination of the path sampling approach on a twodimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.

Stability of solid phases in the dipolar hard sphere system

“…The reliability of the calculation relies on the choice of the paths selected to calculate the average in Eq. (1) [33][34][35]. As mentioned above, by associating to the variation of h α,β the relaxation of the sphere configurations, it is possible to prevent overlap of the hard cores to interrupt the transition from one phase to the other.…”

Determining equilibrium constants for dimerization reactions from molecular dynamics simulations

“…[1][2][3][4] Also nonequilibrium methods have been successfully applied to calculate free energies of molecular systems. [5][6][7][8][9][10] To study the energetics of self-assembly processes, such as the binding of two (or more) molecules, the umbrella sampling technique 11 is often applied, in which harmonic (umbrella) potentials drive the system along a pre-defined reaction coordinate, for example the distance between the molecules.…”

Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds

“…11,23,24,25 A wide range of theoretical and numerical methods has been developed for assessing free energy changes. 26 The standard toolbox of free energy calculations includes the thermodynamic integration (TI) and free energy perturbation (FEP) techniques. The theory behind these methods was developed long ago by Kirkwood, 27 Landau and Lifshitz, 28 Zwanzig, 29 and others.…”