Solvation Lies Within: Simulating Condensed-Phase Properties from Local Electronic Structures

TL;DR

Solvation shifts in condensed phases arise from local electronic-structure perturbations that are difficult to isolate with conventional cluster or continuum models. The authors develop an exact decomposition of KS-DFT energies into localized molecular-orbital contributions for a central monomer, yielding a solvated energy term $\\Delta E^{(n)}_{\\mathcal{K}} = \\\\mathcal{E}^{(n)}_{\\mathcal{K}} - E^{\\text{vac}} + (E^{(0)}_{\\mathcal{K}} - E^{(0,\\text{G})}_{\\mathcal{K}})$, and embed the system in a QM/AMOEBA environment with finite-temperature sampling. The approach shows rapid convergence with the number of neighboring monomers for water, ethanol, and acetonitrile, with weak basis-set dependence and strong dependence on the density functional, notably performing best with $\\omega$B97M-V/aug-pcseg-1 and aligning with experimental enthalpies of vaporization. The framework provides a physically transparent, efficient route to quantify bulk solvation effects from local electronic structure and opens avenues for heterogenous solvation and excited-state solvation studies, while connecting to alchemical free-energy concepts and future extensions beyond ground-state properties.

Abstract

In transitions between different environmental settings, a molecular system inevitably undergoes a range of detectable changes, and the ability to accurately simulate such responses, e.g., in the form of shifts to molecular energies, remains an important challenge across physical chemistry. Based on an exact decomposition of total energies from Kohn--Sham density functional theory in a basis of spatially localized molecular orbitals, the present work outlines a robust protocol for sampling the effect of solvation within homogeneous condensed phases by focusing on perturbations to local electronic structures only. We report chemically intuitive results for binding energies of water, ethanol, and acetonitrile that all display fast convergence with respect to the bulk size. Results stay largely invariant with respect to the choice of basis set while reflecting differences in density functional approximations, and our protocol thus allows for a physically sound and efficient estimation of general effects related to bulk solvation.

Figures (11)

• Figure 1: Changes to donor (D) and acceptor (A) energies in a water dimer upon forming and breaking hydrogen bonds. The monomer energies are decomposed using both MO- (left) and AO-based (right) schemes. Representative structures are provided in the upper-left panel.
• Figure 2: Individual steps and calculations involved in the solvation protocol of the present work. For comparison, the protocol of Ref. eriksen_local_condensed_phase_jpcl_2021 has also been highlighted in dark magenta.
• Figure 3: Convergence of binding energies ($\Delta E^{(n)}_{\mathcal{K}}$) obtained using Eq. \ref{['solv_energy_eq']} for 200 individual snapshots of bulk water. The level of theory is $\omega$B97M-V/aug-pcseg-1 and the QM/AMOEBA-based protocol depicted in panel $\bm{3}$ of Fig. \ref{['protocol_fig']} is used in all calculations.
• Figure 4: Two alternatives to Eq. \ref{['solv_energy_eq']}. Average ($\bm{1}$) and incremental ($\bm{2}$) solvation energy shifts are derived from successively larger bulk models according to Eqs. \ref{['average_energy_eq']} and \ref{['inc_energy_eq']}, respectively.
• Figure 5: Comparison of the three different protocols for computing the binding energy of water studied herein, namely, the present MO-based, decomposed approach in Eq. \ref{['solv_energy_eq']}, $\Delta E^{(n)}_{\mathcal{K}}$, the averaged approach in Eq. \ref{['average_energy_eq']}, $\Delta E^{(n)}_{\text{av}}$, and the incremental approach in Eq. \ref{['inc_energy_eq']}, $\Delta E^{(n)}_{\text{inc}}$. All the results using Eqs. \ref{['solv_energy_eq']}--\ref{['inc_energy_eq']} are obtained at the $\omega$B97M-V/(aug-)pcseg-1 level of theory, and those based on Eq. \ref{['solv_energy_eq']} are obtained from QM/AMOEBA calculations (cf. panel $\bm{3}$ of Fig. \ref{['protocol_fig']}).