A simple way to test for collinearity in spin symmetry broken wave functions: general theory and application to generalized Hartree Fock.

We introduce a necessary and sufficient condition for an arbitrary wavefunction to be collinear, i.e., its spin is quantized along some axis. It may be used to obtain a cheap and simple computational procedure to test for collinearity in electronic structure theory calculations. We adapt the procedure for Generalized Hartree Fock (GHF), and use it to study two dissociation pathways in CO2. For these dissociation processes, the GHF wave functions transform from low-spin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to high-spin UHF type states, phenomena that are succinctly illustrated by the constituents of the collinearity test. This complements earlier GHF work on this molecule.

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.

Spin-flip non-orthogonal configuration interaction: a variational and almost black-box method for describing strongly correlated molecules.

In this paper, we report the development, implementation, and assessment of a novel method for describing strongly correlated systems, spin-flip non-orthogonal configuration interaction (SF-NOCI). The wavefunction is defined to be a linear combination of independently relaxed Slater determinants obtained from all possible spin-flipping excitations within a localized orbital active-space, typically taken to be the singly occupied orbitals of a high-spin ROHF wavefunction. The constrained orbital optimization of each CI basis configuration is defined such that only non-active-space orbitals are allowed to relax (all active space orbitals are fixed). A number of simplifications and benefits arise due to the fact that only a restricted number of orbital rotations are permitted, (1) basis states cannot coalesce during SCF, (2) basis state optimization is better conditioned due to a larger effective HOMO-LUMO gap, (3) smooth potential energy surfaces are easily obtained, (4) the Hamiltonian coupling between two basis states with non-orthogonal orbitals is greatly simplified. To illustrate the advantages over a conventional orthogonal CI expansion, we investigate exchange coupling constants of bimetallic complexes, the avoided crossing of the lowest singlet states during LiF dissociation, and ligand non-innocence in an organometallic complex. These numerical examples indicate that good qualitative agreement can be obtained with SF-NOCI, but dynamical correlation must be included to obtain quantitative accuracy.

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 ß-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.

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.

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 system's 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.