Eric J. Sundstrom

Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks

A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π(*) shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.

Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: Theory and applications to intermolecular interactions involving radicals

Radical-closed shell and radical-radical intermolecular interactions are less well-understood than those between closed shell species. With the objective of gaining additional insight, this work reports a generalization of the absolutely localized molecular orbital (ALMO) energy decomposition analysis (EDA) to open shell fragments, described by self-consistent field methods, such as standard density functional theory. The ALMO-EDA variationally partitions an intermolecular interaction energy into three separate contributions; frozen orbital interactions, polarization, and charge transfer. The first examples involve comparison of the interactions of alkanes and alkyl radicals (methyl radical, methane, tertiary butyl radical, and isobutane) with sodium, potassium, hydronium, and ammonium cations. A second series of examples involve benzene cation interacting with a series of nucleophiles in both on-top and side-on geometries. The ALMO-EDA yields a variety of interesting insights into the relative roles of its component contributions as the interacting partners and their geometries are changed.

Computational and experimental study of the mechanism of hydrogen generation from water by a molecular molybdenum-oxo electrocatalyst.

We investigate the mechanism for the electrocatalytic generation of hydrogen from water by the molecular molybdenum-oxo complex, [(PY5Me(2))MoO](2+) (PY5Me(2) = 2,6-bis(1,1-bis(2-pyridyl)ethyl)pyridine). Computational and experimental evidence suggests that the electrocatalysis consists of three distinct electrochemical reductions, which precede the onset of catalysis. Cyclic voltammetry studies indicate that the first two reductions are accompanied by protonations to afford the Mo-aqua complex, [(PY5Me(2))Mo(OH(2))](+). Calculations support hydrogen evolution from this complex upon the third reduction, via the oxidative addition of a proton from the bound water to the metal center and finally an α-H abstraction to release hydrogen. Calculations further suggest that introducing electron-withdrawing substituents such as fluorides in the para positions of the pyridine rings can reduce the potential associated with the reductive steps, without substantially affecting the kinetics. After the third reduction, there are kinetic bottlenecks to the formation of the Mo-hydride and subsequent hydrogen release. Computational evidence also suggests an alternative to direct α-H abstraction as a mechanism for H(2) release which exhibits a lower barrier. The new mechanism is one in which a water acts as an intramolecular proton relay between the protons of the hydroxide and the hydride ligands. The calculated kinetics are in reasonable agreement with experimental measurements. Additionally, we propose a mechanism for the stoichiometric reaction of [(PY5Me(2))Mo(CF(3)SO(3))](+) with water to yield hydrogen and [(PY(5)Me(2))MoO](2+) along with the implications for the viability of an alternate catalytic cycle involving just two reductions to generate the active catalyst.

Useful lower limits to polarization contributions to intermolecular interactions using a minimal basis of localized orthogonal orbitals: Theory and analysis of the water dimer

The problem of describing the energy-lowering associated with polarization of interacting molecules is considered in the overlapping regime for self-consistent field wavefunctions. The existing approach of solving for absolutely localized molecular orbital (ALMO) coefficients that are block-diagonal in the fragments is shown based on formal grounds and practical calculations to often overestimate the strength of polarization effects. A new approach using a minimal basis of polarized orthogonal local MOs (polMOs) is developed as an alternative. The polMO basis is minimal in the sense that one polarization function is provided for each unpolarized orbital that is occupied; such an approach is exact in second-order perturbation theory. Based on formal grounds and practical calculations, the polMO approach is shown to underestimate the strength of polarization effects. In contrast to the ALMO method, however, the polMO approach yields results that are very stable to improvements in the underlying AO basis expansion. Combining the ALMO and polMO approaches allows an estimate of the range of energy-lowering due to polarization. Extensive numerical calculations on the water dimer using a large range of basis sets with Hartree-Fock theory and a variety of different density functionals illustrate the key considerations. Results are also presented for the polarization-dominated Na(+)CH4 complex. Implications for energy decomposition analysis of intermolecular interactions are discussed.

LOBA: a localized orbital bonding analysis to calculate oxidation states, with application to a model water oxidation catalyst

We propose a method for calculation of oxidation states in transition metal complexes, utilizing a bonding analysis based on localized molecular orbitals in conjunction with traditional population analyses. The localized orbital bonding analysis (LOBA) is seen to accurately produce both the oxidation state and chemically intuitive views of bonding in the complexes studied. This is in contrast to simple population analyses where the oxidation states are not reproduced for even simple systems and more complex analyses which break down on problematic systems. We report the application to a manganese complex with potential activity as oxygen-evolving catalyst, determining the location of the oxidations.

Degree of initial hole localization/delocalization in ionized water clusters.

The electronic structure of ionized bulk liquid water presents a number of theoretical challenges. Not the least of these is the realization that the detailed geometry of the hydrogen bonding network is expected to have a strong effect on the electronic couplings between water molecules and thus the degree of delocalization of the initially ionized system. This problem is approached from a cluster perspective where a high-level coupled cluster description of the electronic structure is still possible. Building on the work and methodology developed for the water dimer cation [J. Phys. Chem. A 2008, 112, 6159], the character and spectrum of electronic states of the water hole and their evolution from the dimer into higher clusters is presented. As the time evolution of the initially formed hole can in principle be followed by the systems transient absorption spectrum, the state spacings and transition strengths are computed. An analysis involving Dyson orbitals is applied and shows a partially delocalized nature of states. The issue of conformation disorder in the hydrogen bonding geometry is addressed for the water dimer cation.

Non-orthogonal configuration interaction for the calculation of multielectron excited states

We apply Non-orthogonal Configuration Interaction (NOCI) to molecular systems where multielectron excitations, in this case double excitations, play a substantial role: the linear polyenes and β-carotene. We demonstrate that NOCI when applied to systems with extended conjugation, provides a qualitatively correct wavefunction at a fraction of the cost of many other multireference treatments. We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree-Fock Slater determinants and the details for computing ⟨S(2)⟩ for the ground and excited states.

Wavefunction stability analysis without analytical electronic Hessians: Application to orbital-optimised second-order Møller-Plesset theory and VV10-containing density functionals

Wavefunction stability analysis is commonly applied to converged self-consistent field (SCF) solutions to verify whether the electronic energy is a local minimum with respect to second-order variations in the orbitals. By iterative diagonalisation, the procedure calculates the lowest eigenvalue of the stability matrix or electronic Hessian. However, analytical expressions for the electronic Hessian are unavailable for most advanced post-Hartree–Fock (HF) wave function methods and even some Kohn–Sham (KS) density functionals. To address such cases, we formulate the Hessian-vector product within the iterative diagonalisation procedure as a finite difference of the electronic gradient with respect to orbital perturbations in the direction of the vector. As a model application, following the lowest eigenvalue of the orbital-optimised second-order Møller–Plesset perturbation theory (OOMP2) Hessian during H2 dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a second independent unrestricted solution. We show that a single stable solution can be recovered by using the regularised OOMP2 method (δ-OOMP2), which contains a level shift. Internal and external stability analyses are also performed for SCF solutions of a recently developed range-separated hybrid density functional, ωB97X-V, for which the analytical Hessian is not yet available due to the complexity of its long-range non-local VV10 correlation functional.

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H2 insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O2, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.

Erratum: "Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks" [J. Chem. Phys. 141, 024102 (2014)].

Author(s): Zuev, Dmitry; Jagau, Thomas-C; Bravaya, Ksenia B; Epifanovsky, Evgeny; Shao, Yihan; Sundstrom, Eric; Head-Gordon, Martin; Krylov, Anna I