Quantifying Fluctuations of Average Solvent Environments for Embedding Calculations

Abstract

The viability and effectiveness of replacing an ensemble of embedded solute calculations by a single calculation using an average description of the solvent environment are evaluated. This work explores the fluctuations of the average description of the system obtained in two ways: from calculations on an ensemble of geometries and from an average environment constructed from the same ensemble. To this end, classical molecular dynamics simulations of a rigid acetone solute in SPCE water are performed in order to generate an ensemble of solvent environments. From this ensemble of solvent configurations, a number of different approaches for constructing an average solvent environment are employed. We perform a thorough numerical analysis of the fluctuations of the electrostatic potential experienced by the solute, as well as the resulting fluctuations of the solute’s electronic density, measured through its dipole moment and fitted atomic point charges. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed method for generating the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum confinement effects, which may be important in certain cases, the fluctuations in the shift due to the interaction with the solvent are evaluated using frozen-density-embedding theory. Our results demonstrate that, for normally distributed environments, the constructed average environment is a reasonably good representation of a fluctuating molecular solvent environment. We then provide guidance for future comparisons between these theoretical treatments of solute/solvent systems to experimental measurements.

Embedding Nonrigid Solutes in an Averaged Environment: A Case Study on Rhodopsins

“…1−3 At the atomistic representation of the solvent -i.e. if the ensemble of instantaneous structures R Recently, we have reported the statistical analysis of the fluctuations for solvated acetone, 18 confirming the validity of the use of an average electrostatic potential.…”

“…This trend influences the weighted average emb K 1,..., to an extent which is determined by the weight of the basin with the Our analysis of FDET-based calculations with averaged liquid environments showed a deterioration of the results below a certain number of frames. 18 Such a threshold cannot be directly applied to drastically different systems, such as protein environments, where the movement may be different in the entity and speed. An excessively low number of frames may be a necessary but not sufficient condition for a relatively large error.…”

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

“…Instead, what is known as an “electrostatic embedding” is necessary: The DFT computations are performed in the presence of a counter-charge that is derived from the MM phase-space sampling, in analogy to the coupling between molecular and electronic DFT . Electrostatic embedding for determining solvation energies has been mostly explored for neutral molecular systems. − Only very recently (and independently from us), such an approach has been applied to electrified interfaces. , Even though charged interfaces are common, not only for electrified systems but also for oxide surfaces as a function of pH, electrostatic embedding is only rarely available in plane-waves codes, with the notable exceptions being GPAW, Quantum Espresso, , and CPMD.…”

Machine learning based implicit solvent model for aqueous-solution alanine dipeptide molecular dynamics simulations

“…Clearly, this opens the possibility of acquiring the corresponding forces on the solute atoms (at geometry r ) by extensively sampling solvent configurations, w ( m ) ( m = 1, 2, …, M ), around the solute,where M is the number of solvent configurations. Furthermore, if both solute and solvent molecules are described by fixed-charge force fields, the solute is essentially interacting in this expression with the average solvent environment configuration (ASEC) potential, 72–80 where the solvent environment is represented by M frames of solvent configuration. For each solvent configuration, w ( m ) ′, the solvent atomic charges are scaled by and van der Waals epsilon values by (due to the geometric combination rule).…”