Free energy perturbation (FEP) was proposed by Zwanzig [J. Chem. Phys. 22, 1420 (1954)] more than six decades ago as a method to estimate free energy differences and has since inspired a huge body of related methods that use it as an integral building block. Being an importance sampling based estimator, however, FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted FEP, uses a high-dimensional mapping in configuration space to increase the overlap of the underlying distributions. Despite its potential, this method has attracted only limited attention due to the formidable challenge of formulating a tractable mapping. Here, we cast Targeted FEP as a machine learning problem in which the mapping is parameterized as a neural network that is optimized so as to increase the overlap. We develop a new model architecture that respects permutational and periodic symmetries often encountered in atomistic simulations and test our method on a fully periodic solvation system. We demonstrate that our method leads to a substantial variance reduction in free energy estimates when compared against baselines, without requiring any additional data.
We propose a new algorithm for non-equilibrium molecular dynamics simulations of thermal gradients. The algorithm is an extension of the heat exchange algorithm developed by Hafskjold and co-workers [Mol. Phys. 80, 1389(1993 Mol. Phys. 81, 251 (1994)], in which a certain amount of heat is added to one region and removed from another by rescaling velocities appropriately. Since the amount of added and removed heat is the same and the dynamics between velocity rescaling steps is Hamiltonian, the heat exchange algorithm is expected to conserve the energy. However, it has been reported previously that the original version of the heat exchange algorithm exhibits a pronounced drift in the total energy, the exact cause of which remained hitherto unclear. Here, we show that the energy drift is due to the truncation error arising from the operator splitting and suggest an additional coordinate integration step as a remedy. The new algorithm retains all the advantages of the original one whilst exhibiting excellent energy conservation as illustrated for a Lennard-Jones liquid and SPC/E water.
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Using non-equilibrium molecular dynamics simulations, it has been recently demonstrated that water molecules align in response to an imposed temperature gradient, resulting in an effective electric field. Here, we investigate how thermally induced fields depend on the underlying treatment of long-ranged interactions. For the short-ranged Wolf method and Ewald summation, we find the peak strength of the field to range between 2 × 10 7 and 5 × 10 7 V/m for a temperature gradient of 5.2 K/Å. Our value for the Wolf method is therefore an order of magnitude lower than the literature value [J. Chem. Phys. 139, 014504 (2013) and 143, 036101 (2015)]. We show that this discrepancy can be traced back to the use of an incorrect kernel in the calculation of the electrostatic field. More seriously, we find that the Wolf method fails to predict correct molecular orientations, resulting in dipole densities with opposite sign to those computed using Ewald summation. By considering two different multipole expansions, we show that, for inhomogeneous polarisations, the quadrupole contribution can be significant and even outweigh the dipole contribution to the field. Finally, we propose a more accurate way of calculating the electrostatic potential and the field. In particular, we show that averaging the microscopic field analytically to obtain the macroscopic Maxwell field reduces the error bars by up to an order of magnitude. As a consequence, the simulation times required to reach a given statistical accuracy decrease by up to two orders of magnitude.
We present a mean-field theory to explain the thermo-orientation effect in an off-center Stockmayer fluid. This effect is the underlying cause of thermally induced polarization and thermally induced monopoles, which have recently been predicted theoretically. Unlike previous theories that are based either on phenomenological equations or on scaling arguments, our approach does not require any fitting parameters. Given an equation of state and assuming local equilibrium, we construct an effective Hamiltonian for the computation of local Boltzmann averages. This simple theoretical treatment predicts molecular orientations that are in very good agreement with simulation results for the range of dipole strengths investigated. By decomposing the overall alignment into contributions from the temperature and density gradients, we shed further light on how the nonequilibrium result arises from the competition between the two gradients.
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