Multiconfiguration thermodynamic integration

A modified thermodynamic integration technique is presented to obtain free energy differences from molecular dynamics simulations. In this multiconfiguration thermodynamic integration technique, the commonly employed single configuration (slow growth) approximation is not made. It is shown, by analysis of the sources of error, how the multiconfiguration variant of thermodynamic integration allows for a soundly based assessment of the statistical error in the evaluated free energy difference. Since ensembles of configurations are generated for each integration step, a statistical error can be evaluated for each integration step. By generating ensembles of different lengths, the statistical error can be equally distributed over the integration. This eliminates the difficult problem in single configuration thermodynamic integrations of determining the best rate of change of the Hamiltonian, which is usually based on equally distributing the free energy change. At the same time, this procedure leads to a more efficient use of computer time by providing the possibility of added accuracy from separate calculations of the same Hamiltonian change. The technique is applied to a simple but illustrative model system consisting of a monatomic solute in aqueous solution. In a second example, a combination of multiconfiguration thermodynamic integration and thermodynamic perturbation is used to obtain the potentials of mean force for rotation of the sidechain dihedral angles for valine and threonine dipeptides with restrained backbones in aqueous solution.