# P.W. Ayers

## The influence of orbital rotation on the energy of closed-shell wavefunctions

### Abstract

The orbital dependence of closed-shell wavefunction energies is investigated by performing doubly-occupied configuration interaction (DOCI) calculations, representing the most general class of these wavefunctions. Different local minima are examined for planar hydrogen clusters containing two, four, and six electrons applying (spin) symmetry-broken restricted, unrestricted, and generalised orbitals with real and complex coefficients. Contrary to Hartree-Fock (HF), restricted DOCI is found to properly break bonds and thus unrestricted orbitals, while providing a quantitative improvement of the energy, are not needed to enforce a qualitatively correct bond dissociation. For the beryllium atom and the BH diatomic, the lowest possible HF energy requests symmetry-broken generalised orbitals, whereas accurate results for DOCI can be obtained within a restricted formalism. Complex orbital coefficients are shown to increase the accuracy of HF and DOCI results in certain cases. The computationally inexpensive AP1roG geminal wavefunction is proven to agree very well with all DOCI results of this study.

## Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals

### Abstract

A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surjan et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N-2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2.

## A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals

### Abstract

We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

## A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals

### Abstract

Inspired by the wavefunction forms of exactly solvable algebraic Hamiltonians, we present several wavefunction ansatze. These wavefunction forms are exact for two-electron systems; they are size consistent; they include the (generalized) antisymmetrized geminal power, the antisymmetrized product of strongly orthogonal geminals, and a Slater determinant wavefunctions as special cases. The number of parameters in these wavefunctions grows only linearly with the size of the system. The parameters in the wavefunctions can be determined by projecting the Schrödinger equation against a test-set of Slater determinants; the resulting set of nonlinear equations is reminiscent of coupled-cluster theory, and can be solved with no greater than O (N^{5}) scaling if all electrons are assumed to be paired, and with O (N^{6}) scaling otherwise. Based on the analogy to coupled-cluster theory, methods for computing spectroscopic properties, molecular forces, and response properties are proposed.

## Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices

## The sharp-G N-representability condition

### Abstract

The G-condition for the N-representability of the two-electron reduced density matrix is tightened by replacing the semidefiniteness constraint with the true upper and lower bounds of the G-type Hamiltonian operator. The lower bound is not easily computed (in contrast to the sharp P- and Q-conditions), but maps onto a well-known integer programming problem. The sharp-G, sharp-P, and sharp-Q conditions are just three members of a much broader class of conditions based on exactly solvable model Hamiltonians.

## Hirshfeld-E partitioning: AIM charges with an improved trade-off between robustness and accurate electrostatics

### Abstract

For the development of ab-initio derived force fields, atomic charges must be computed from electronic structure computations, such that (i) they accurately describe the molecular electrostatic potential (ESP) and (ii) they are transferable to the force-field application of interest. The Iterative Hirshfeld (Hirshfeld-I or HI) scheme meets both requirements for organic molecules. For inorganic oxide clusters, however, Hirshfeld-I becomes ambiguous because electron densities of nonexistent isolated anions are needed as input. Herein, we propose a simple Extended Hirshfeld (Hirshfeld-E or HE) scheme to overcome this limitation. The performance of the new HE scheme is compared to four popular atoms-in-molecules schemes, using two tests involving a set of 248 silica clusters. These tests show that the new HE scheme provides an improved trade-off between the ESP accuracy and the transferability of the charges. The new scheme is a generalization of the Hirshfeld-I scheme and it is expected that its improvements are to a large extent applicable to molecular systems containing elements from the entire periodic table.

## ACKS2: Atom-Condensed Kohn-Sham DFT approximated to second order

### Abstract

A new polarizable force field (PFF), namely atom-condensed Kohn-Sham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from Kohn-Sham density functional theory (KS-DFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the Kohn-Sham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc. 108, 4315 (1986)]10.1021/ja00275a013 in which two major EEM shortcomings are fixed: ACKS2 predicts a linear size-dependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atoms-in-molecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.

## Automated Parametrization of AMBER Force Field Terms from Vibrational Analysis with a Focus on Functionalizing Dinuclear Zinc(II) Scaffolds

### Abstract

A procedure for determining force constants that is independent of the internal redundant coordinate choice is presented. The procedure is based on solving each bond and angle term separately, using the Wilson B matrix. The method only requires a single ab initio frequency calculation at the minimum energy structure and is made available in the software "parafreq". The methodology is validated with a set of small molecules, by showing it can reproduce ab initio frequencies better than other methods such as taking the diagonal terms of the Hessian in internal coordinates or by using standard AMBER force fields. Finally, the utility of the method is demonstrated by parametrizing the dizinc scaffold of bis-dipicolylamine (BDPA) bound to phosphotyrosine, which is then functionalized into promising antitumor drug proteomimetics.