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Register a new userTargeted free energy perturbation revisited: Accurate free energies from mapped reference potentials
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We present an approach that extends the theory of targeted free energy perturbation (TFEP) to calculate free energy differences and free energy surfaces at an accurate quantum mechanical level of theory from a cheaper reference potential. The convergence is accelerated by a mapping function that increases the overlap between the target and the reference distributions. Building on recent work, we show that this map can be learned with a normalizing flow neural network, without requiring simulations with the expensive target potential but only a small number of single-point calculations, and, crucially, avoiding the systematic error that was found previously. We validate the method by numerically evaluating the free energy difference in a system with a double-well potential and by describing the free energy landscape of a simple chemical reaction in the gas phase.
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Free energy perturbation (FEP) was proposed by Zwanzig 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 Free Energy Perturbation, uses a high-dimensional mapping in configuration space to increase 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 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.
Inspired by the recent development on calculating the free energy change via a relaxation process [Nat. Phys. 14, 842 (2018)], we investigate the role of heat released in an irreversible relaxation following a large perturbation. Utilizing a derivation without microscopic reversibility, we arrive at a new free energy estimator that employs a volume term to account for missing important rare events. Applications to harmonic oscillators and particle insertion in Lennard-Jones fluid agree well with the (numerical) exact solutions. Our study hence suggests an alternative interpretation to the insufficient sampling problem in free energy calculations.
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Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. However, the theories employed have reached a high degree of sophistication and have become complex, making it difficult to gain insights into microscopic processes and biologically significant questions. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and criteria by which the necessity of the vibrational assistance is considered.
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