Importance of the Intermolecular Pauli Repulsion in Embedding Calculations for Molecular Properties: The Case of Excitation Energies for a Chromophore in Hydrogen-Bonded Environments

Abstract

In embedding methods such as those labeled commonly as QM/MM, the embedding operator is frequently approximated by the electrostatic potential generated by nuclei and electrons in the environment. Such approximation is especially useful in studies of the potential energy surface of embedded species. The effect on energy of neglecting the non-Coulombic component of the embedding operator is corrected a posteriori. The present work investigates applicability of such approximation in evaluation of electronic excitation energy, the accuracy of which depends directly on that of the embedding potential. For several model systems involving cis-7-hydroxiquinoline hydrogen-bonded to small molecules, we demonstrate that such truncation of the embedding operator leads to numerically unstable results upon increasing the size of the atomic basis sets. Approximating the non-Coulombic component of the embedding potential using the expression derived in Frozen-Density Embedding Theory ([Wesolowski and Warshel, J. Phys. Chem.1993, 97, 8050] and subsequent works) by means of even a simple bifunctional dependent on the electron density of the chromophore and its hydrogen-bonded environment, restores the numerical stability of the excitation energies that reach a physically meaningful limit for large basis sets.

Subsystem density‐functional theory

“…In contrast, most other subsystem methods, such as QM/MM approaches, employ additional approximations for these contributions. The embedding potential also contains short‐range quantum mechanical effects. Among these, the exchange–correlation effects can be treated within the same approximations as used in KS‐DFT calculations. In addition, also effects usually referred to as Pauli repulsion are included through the kinetic energy contribution . For this part, one can either employ additional approximations, or the kinetic energy contributions can be treated exactly with reconstruction methods.…”

Excited states in large molecular systems through polarizable embedding

“…It is related to the lack of non-electrostatic repulsion, i.e., exchange-repulsion or Pauli repulsion, which introduces substantial errors at short distances when there is significant wave-function overlap. 114,115 In the PDE model, this issue is remedied by introducing a projection operator, based on the work by Huzinaga and Cantu, 116 that models wave-function orthogonality between the quantum region and the fragments in its environment. This non-electrostatic repulsion operator is defined aŝ…”

Response to “Comment on ‘Solvatochromic shifts of polar and non-polar molecules in ambient and supercritical water: A sequential quantum mechanics/molecular mechanics study including solute-solvent electron exchange-correlation”’ [J. Chem. Phys. 138, 217101 (2013)]

“…Therefore, we consider further including the full solvent polarization effect is still insufficient for describing the excited states of such systems in which dispersion as a quantum correlation effect dominates the interactions between the solute and solvents. In view of the above facts that results by both simple point charge embedding and ground-state polarizable EFP and FMO methods deviate much from the experimental determinations for aqueous benzene and solvent polarization in response to the solute excitation for such a system is also very small, we conclude that only improving the Coulombic electrostatic potential and including solvent polarization effect are [16][17][18][19] also addressed the importance of exchange interaction (Pauli repulsion, non-Coulombic interaction) in embedding calculations for molecular properties. Therefore, we reconfirm that the inclusion of the solvent molecules within the first solvation shell into the QM region to account for exchange interaction between a solute and its nearby solvents is highly recommended for accurate electronic spectral shift calculations of non-polar solutes dissolved in water.…”