This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design.

We report an implementation of periodic boundary conditions for mixed quantum mechanics/molecular mechanics (QM/MM) simulations, in which atomic partial charges are used to represent periodic images of the QM region. These charges are incorporated into the Fock matrix in a manner that preserves the variational nature of the self-consistent field procedure, and their interactions with the MM charges are summed using the conventional Ewald technique. To ensure that the procedure is stable in arbitrary basis sets, the atomic charges are derived by least-squares fit to the electrostatic potential generated by the QM region. We formulate and implement analytic energy gradients for the QM/MM-Ewald method and demonstrate that stable molecular dynamics simulations are thereby obtained. As a proof-of-concept application, we perform QM/MM simulations of a hydrated electron in bulk liquid water at the level of Hartree-Fock theory plus empirical dispersion. These simulations demonstrate that the “cavity model” of the aqueous electron, in which the spin density of the anionic defect is localized within an excluded volume in the liquid, is stable at room temperature on a time scale of at least several picoseconds. These results validate cavity-forming pseudopotential models of e−(aq) that have previously been derived from static-exchange Hartree-Fock calculations, and cast doubt upon whether non-cavity-forming pseudopotentials are faithful to the underlying Hartree-Fock calculation from which they were obtained.

According to the conventional picture, the aqueous or “hydrated” electron, e –(aq), occupies an excluded volume (cavity) in the structure of liquid water. However, simulations with certain one-electron models predict a more delocalized spin density for the unpaired electron, with no distinct cavity structure. It has been suggested that only the latter (non-cavity) structure can explain the hydrated electron’s resonance Raman spectrum, although this suggestion is based on calculations using empirical frequency maps developed for neat liquid water, not for e –(aq). All-electron ab initio calculations presented here demonstrate that both cavity and non-cavity models of e –(aq) afford significant red-shifts in the O–H stretching region. This effect is nonspecific and arises due to electron penetration into frontier orbitals of the water molecules. Only the conventional cavity model, however, reproduces the splitting of the H–O–D bend (in isotopically mixed water) that is observed experimentally and arises due to the asymmetric environments of the hydroxyl moieties in the electron’s first solvation shell. We conclude that the cavity model of e –(aq) is more consistent with the measured resonance Raman spectrum than is the delocalized, non-cavity model, despite previous suggestions to the contrary. Furthermore, calculations with hybrid density functionals and with Hartree–Fock theory predict that non-cavity liquid geometries afford only unbound (continuum) states for an extra electron, whereas in reality this energy level should lie more than 3 eV below vacuum level. As such, the non-cavity model of e –(aq) appears to be inconsistent with available vibrational spectroscopy, photoelectron spectroscopy, and quantum chemistry.

The presence of a two-center, three-electron hemibond in the solvation structure of the aqueous hydroxl radical has long been debated, as its appearance can be sensitive to self-interaction error in density functional theory.