Anna I. Krylov

Q-Chem 2.0: A High-Performance Ab Initio Electronic Structure Program Package

Q‐Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function‐based methods. A review of the technical features contained within Q‐Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance.

Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space

The equation-of-motion coupled-cluster (EOM-CC) approach is a versatile electronic-structure tool that allows one to describe a variety of multiconfigurational wave functions within single-reference formalism. This review provides a guide to established EOM methods illustrated by examples that demonstrate the types of target states currently accessible by EOM. It focuses on applications of EOM-CC to electronically excited and open-shell species. The examples emphasize EOMs advantages for selected situations often perceived as multireference cases [e.g., interacting states of different nature, Jahn-Teller (JT) and pseudo-JT states, dense manifolds of ionized states, diradicals, and triradicals]. I also discuss limitations and caveats and offer practical solutions to some problematic situations. The review also touches on some formal aspects of the theory and important current developments.

The spin–flip approach within time-dependent density functional theory: Theory and applications to diradicals

An extension of density functional theory to situations with significant nondynamical correlation is presented. The method is based on the spin–flip (SF) approach which is capable of describing multireference wave functions within a single reference formalism as spin–flipping, e.g., α→β, excitations from a high-spin (Ms=1) triplet reference state. An implementation of the spin–flip approach within the Tamm–Dancoff approximation to time-dependent density functional theory (TDDFT) is presented. The new method, SF-TDDFT/TDA or simply SF-DFT, describes target states (i.e., closed- and open-shell singlets, as well as low-spin triplets) by linear response from a reference high-spin triplet (Ms=1) Kohn–Sham state. Contrary to traditional TDDFT, the SF-DFT response equations are solved in a subspace of spin–flipping operators. The method is applied to bond-breaking (ethylene torsional potential), and equilibrium properties of eight diradicals. The results demonstrate significant improvement over traditional Kohn–...

Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model

Abstract A new approach to the bond-breaking problem is proposed. Both closed and open shell singlet states are described within a single reference formalism as spin-flipping, e.g., α → β , excitations from a triplet ( M s =1) reference state for which both dynamical and non-dynamical correlation effects are much smaller than for the corresponding singlet state. Formally, the new theory can be viewed as an equation-of-motion (EOM) model where excited states are sought in the basis of determinants conserving the total number of electrons but changing the number of α and β electrons. The results for two simplest members of the proposed hierarchy of approximations are presented.

Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study

The spin-flip approach has been applied to calculate vertical and adiabatic energy separations between low-lying singlet and triplet states in diradicals. The spin-flip model describes both closed- and open-shell singlet and (low-spin) triplet states within a single reference formalism as spin-flipping, e.g., α→β, excitations from a high-spin triplet (Ms=1) reference state. Since both dynamical and nondynamical correlation effects are much smaller for the high-spin triplet states than for the corresponding singlet states, the spin-flip models yield systematically more accurate results than their traditional (non-spin-flip) counterparts. For all the diradicals studied in this work, the spin-flip variant of the coupled-cluster model with double excitations yields energy separations which are within less than 3 kcal/mol of the experimental or the highly accurate multireference values. In most cases the errors are about 1 kcal/mol.

Equation-of-motion spin-flip coupled-cluster model with single and double substitutions: Theory and application to cyclobutadiene

While the equation-of-motion coupled-cluster (EOM-CC) method is capable of describing certain multiconfigurational wave functions within a single-reference framework (e.g., open-shell type excited states, doublet radicals, etc.), it may fail in cases of more extensive degeneracy, e.g., bond breaking and polyradicals. This work presents an extension of the EOM-CC approach to these chemically important situations. In our approach, target multiconfigurational wave functions are described as spin-flipping excitations from the high-spin reference state. This enables a balanced treatment of nearly degenerate electronic configurations present in the target low-spin wave functions. The relations between the traditional spin-conserving EOM models and the EOM spin-flip method is discussed. The presentation of the formalism emphasizes the variational properties of the theory and shows that the killer condition is rigorously satisfied in single-reference EOM-CC theories. The capabilities and advantages of the new approach are demonstrated by its application to cyclobutadiene.

Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O 4

We describe an alternative procedure for obtaining approximate Brueckner orbitals in ab initio electronic structure theory. Whereas approximate Brueckner orbitals have traditionally been obtained by mixing the orbitals until the coefficients of singly substituted determinants in the many-electron wave function become zero, we remove singly substituted determinants at the outset and obtain orbitals which minimize the total electronic energy. Such orbitals may be described as variational Brueckner orbitals. These two procedures yield the same set of exact Brueckner orbitals in the full configuration interaction limit but differ for truncated wave functions. We consider the simplest variant of this approach in the context of coupled-cluster theory, optimizing orbitals for the coupled-cluster doubles (CCD) model. An efficient new method is presented for solving the coupled equations defining the energy, doubles amplitudes, and orbital mixing parameters. Results for several small molecules indicate nearly iden...

Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model

The nondynamical correlation energy may be defined as the difference between full configuration interaction within the space of all valence orbitals and a single determinant of molecular orbitals (Hartree–Fock theory). In order to describe bond breaking, diradicals, and other electronic structure problems where Hartree–Fock theory fails, a reliable description of nondynamical correlation is essential as a starting point. Unfortunately, the exact calculation of nondynamical correlation energy, as defined above, involves computational complexity that grows exponentially with molecular size and is thus unfeasible beyond systems of just two or three heavy atoms. We introduce a new hierarchy of feasible approximations to the nondynamical correlation energy based on coupled-cluster theory with variationally optimized orbitals. The simplest member of this hierarchy involves connected double excitations within the variationally optimized valence active space and may be denoted as VOO-CCD, or VOD. VOO-CCD is size-...

Spin-flip configuration interaction: an electronic structure model that is both variational and size-consistent

A new formulation of the configuration interaction (CI) method is presented. It is based on the recently introduced spin-flip (SF) approach. SF-CI target states are described as spin-flipping excitations from the reference Hartree–Fock high-spin, e.g., Ms=1 (|αα〉), determinant. The resulting model is both variational and size-consistent. Moreover, the SF-CI model can describe within a single-reference formalism some inherently multi-reference situations, such as single bond-breaking and diradicals. Initial benchmarks for the SF-CI model with single and double substitutions (SF-CISD) are presented.

Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals

We present perturbative corrections to a recently introduced spin–flip self-consistent field (SF-SCF) wave function. The spin–flip model describes both closed and open shell singlet states within a single reference formalism as spin–flipping, e.g., α→β, excitations from a triplet (Ms=1) reference state for which both dynamical and nondynamical correlation effects are much smaller than for the corresponding singlet state. The simplest spin–flip model employs a SCF wave function for the reference state, and the resulting equations for target states are therefore identical to configuration interaction singles (in spin–orbital form). While being a qualitatively correct zero-order wave function, SF-SCF should be augmented by dynamical correlation corrections to achieve a quantitative accuracy. The results demonstrate that the second-order approximation to the more theoretically complete spin–flip coupled-cluster model (truncated at double substitutions) represents a systematic improvement over the SF-SCF model.