John D. Watts

Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open‐shell Hartree‐Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD...

Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods

Abstract In critical cases, single-reference correlated methods like coupled-cluster theory or its quadratic CI approximations fail because of the importance of additional highly excited excitations that cannot usually be included, like connected triple and quadruple excitations. Here we present the first, non-iterative method to evaluate the full set of fifth-order corrections to CCSD and QCISD and assess their accuracy compared to full CI for the very sensitive Be 2 curve and other cases.

The coupled‐cluster single, double, and triple excitation model for open‐shell single reference functions

The CCSDT model for general single determinant reference functions for open and closed‐shell electronic states has been implemented for the first time and has been used to compute the electron affinity of the F atom, the CH2, 3B1–1A1 energy difference, and the ionization potentials of 1A1 CH2. The results compare very well with FCI and are markedly superior to those of simpler coupled‐cluster methods.

Open-shell analytical energy gradients for triple excitation many-body, coupled-cluster methods: MBPT(4), CCSD+T(CCSD), CCSD(T),and QCISD(T)

Abstract Equations are derived for the derivatives of the contribution of triple excitations to the energy for the fourth-order many-body perturbation theory (MBPT(4)), quadratic configuration interaction with singles, doubles, and noniterative triples (QCISD(T)), and coupled-cluster with singles, doubles, and noniterative triples (CCSD+T(CCSD) and CCSD(T)) methods. Based on these equations, analytical gradients have been efficiently implemented for the four aforementioned methods for unrestricted Hartree-Fock (UHF) reference functions. This is the first implementation of open-shell analytical gradients for the QCISD(T), CCSD+T(CCSD), and CCSD(T) methods. The new analytical gradient techniques have been used to compute the structure and some properties of the ground state of the HOO radical with extended basis sets.

Economical triple excitation equation-of-motion coupled-cluster methods for excitation energies

Abstract Two triple excitation equation-of-motion coupled-cluster (EOM-CC) methods for excitation energies are derived, implemented, and tested. They are excited state analogues of the CC singles, doubles, and linearized triples (CCSDT-1) iterative method and the CCSD method with a noniterative inclusion of triple excitations (CCSD (T)). EOM-CCSDT-1 and EOM-CCSD(T) results are compared with full configuration interaction, EOM-CCSDT, and experimental data. The new methods describe two-electron transitions significantly better than EOM-CCSD, and are in reasonable agreement with the more complete EOM-CCSDT method.

A DIRECT PRODUCT DECOMPOSITION APPROACH FOR SYMMETRY EXPLOITATION IN MANY-BODY METHODS. I, ENERGY CALCULATIONS

An analysis of the matrix contractions involved in many‐body perturbation theory and coupled‐cluster calculations leads to a convenient strategy for exploiting point group symmetry, by which the number of floating point operations can be reduced by as much as a factor of h2, where h is the order of the molecular point group. Contrary to a statement in the literature, the significant reduction in computation time realized in coupled‐cluster calculations which exploit symmetry is not due to nonlinearities in the equations. Rather, the savings of the fully vectorizable direct product decomposition (DPD) method outlined here is associated with individual (linear) contractions, and is therefore applicable to both linear and nonlinear coupled‐cluster models, as well as many body perturbation theory. In addition to the large reduction in floating point operations made possible by exploiting symmetry, core memory requirements are also reduced by a factor of ≊h2. Implementation of the method for both open and clos...

Many-body perturbation theory with a restricted open-shell Hartree-Fock reference

Abstract A new, efficient ROHF based MBPT method is presented. The method, which is non-iterative, invariant to transformations among occupied or virtual orbitals, and generalizable to any order, is illustrated by application to the UHF spin contaminated CN radical and the H+OCH 2 transition state.

Analytic energy gradients for open-shell coupled-cluster singles and doubles (CCSD) calculations using restricted open-shell Hartree—Fock (ROHF) reference functions

Abstract The theory of analytic energy gradients for the open-shell single and double excitation coupled-cluster (CCSD) method based on restricted open-shell Hartree—Fock (ROHF) reference functions is presented. The new CCSD gradient method is applied to the dissociation of the 3 A″ state of formaldehyde (CH 2 O) to H and HCO. Complete geometry optimization is carried out for the initial reactant, the transition state of the reaction, and for the dissociation products. Non-iterative triples appropriate to ROHF are introduced and are used to define a new ROHF-CCSD(T) method. Using this approach and zero-point corrections, the activation energy is calculated to be 21.0 kcal/mol and the exit barrier height is predicted to be 6.1 kcal/mol, both in excellent agreement with experiment.

Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods

Abstract New iterative and non-iterative triple excitation corrections to EOM-CCSD are presented based upon the CCSDT-3 method. This method is recommended formally, since it fully employs the EOM-CCSD Hamiltonian H = exp [−(T 1 + T 2 )]H exp (T 1 + T 2 ) in its development. This permits defining iterative EOM-CCSDT-3 and non-iterative EOM-CCSD(T) corrections correct through second-order in H . Results for some full CI examples demonstrate average errors of 0.09 eV and 0.08 eV, respectively. We also study trans-butadiene as a more demanding example. We also consider a computationally simpler but accurate approximation to EOM-CCSD(T), EOM-CCSD(T′).

The inclusion of connected triple excitations in the equation‐of‐motion coupled‐cluster method

We report the implementation of connected triple excitations in the equation‐of‐motion (EOM) coupled‐cluster (CC) method for excitation energies for the first time. The reference state is described by the complete CC singles, doubles, and triples (CCSDT) method. Excited states are generated from the reference state wave function by the action of a linear excitation operator including single, double, and triple excitations. The excited state wave functions and energies are obtained by diagonalizing the effective Hamiltonian e−THeT, where T is the cluster operator for the reference state, in the space of singly, doubly, and triply excited determinants. Comparison is made with full configuration interaction excitation energies for several examples (CH+, Be, SiH2, and CH2). These show that EOM‐CCSDT is able to describe states which are doubly excited relative to the reference state, as well as singly excited states. Calculations of several excitation energies of BH using an extended basis set are also reporte...