Marta Włoch

Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian.

Completely renormalized (CR) coupled-cluster (CC) approaches, such as CR-CCSD(T), in which one corrects the standard CC singles and doubles (CCSD) energy for the effects of triply (T) and other higher-than-doubly excited clusters [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], are reformulated in terms of the left eigenstates Phimid R:L of the similarity-transformed Hamiltonian of CC theory. The resulting CR-CCSD(T)(L) or CR-CC(2,3) and other CR-CC(L) methods are derived from the new biorthogonal form of the method of moments of CC equations (MMCC) in which, in analogy to the original MMCC theory, one focuses on the noniterative corrections to standard CC energies that recover the exact, full configuration-interaction energies. One of the advantages of the biorthogonal MMCC theory, which will be further analyzed and extended to excited states in a separate paper, is a rigorous size extensivity of the basic ground-state CR-CC(L) approximations that result from it, which was slightly violated by the original CR-CCSD(T) and CR-CCSD(TQ) approaches. This includes the CR-CCSD(T)(L) or CR-CC(2,3) method discussed in this paper, in which one corrects the CCSD energy by the relatively inexpensive noniterative correction due to triples. Test calculations for bond breaking in HF, F(2), and H(2)O indicate that the noniterative CR-CCSD(T)(L) or CR-CC(2,3) approximation is very competitive with the standard CCSD(T) theory for nondegenerate closed-shell states, while being practically as accurate as the full CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving the trimethylene biradical as a transition state show that the noniterative CR-CCSD(T)(L) approximation is capable of providing activation enthalpies which perfectly agree with experiment.

Coupled-cluster theory for excited electronic states: The full equation-of-motion coupled-cluster single, double, and triple excitation method

The equation-of-motion coupled-cluster method with the full inclusion of the single, double, and triple excitations (EOM-CCSDT) has been formulated and implemented. The proper factorization procedure ensures that the method scales as n8, i.e., in the same manner as the standard CCSDT method for ground states. The method has been tested on the vertical excitation energies of the N2 and CO molecules for several basis sets up to 92 basis functions. The full inclusion of the triple excitations improves the EOM-CCSD results by up to 0.2 eV for considered systems.

Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules

The general-purpose open-shell implementation of the completely renormalized equation-of-motion coupled-cluster approach with singles, doubles, and noniterative triples [CR-EOMCCSD(T)] is reported. Benchmark calculations for the low-lying doublet and quartet states of the CH radical show that the CR-EOMCCSD(T) method is capable of providing a highly accurate description of ground and excited states of open-shell molecules. This includes states with strong double excitation character, for which the conventional EOMCCSD approach fails.

Active-space equation-of-motion coupled-cluster methods for excited states of radicals and other open-shell systems: EA-EOMCCSDt and IP-EOMCCSDt

The previously developed active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods are extended to radicals and other open-shell systems by combining them with the electron attached (EA) and ionized (IP) EOMCC approaches. As illustrated by the calculations for the CH and OH radicals, the resulting EA-EOMCCSDt and IP-EOMCCSDt theories are capable of providing a highly accurate description of the electronic spectra of radical systems, including excited states displaying a manifestly multideterminantal nature, with the low costs that are not much greater that those characterizing the standard EOMCC singles and doubles method.

Stereoelectronic Effects on Molecular Geometries and State-Energy Splittings of Ligated Monocopper Dioxygen Complexes

The relative energies of side-on versus end-on binding of molecular oxygen to a supported Cu(I) species, and the singlet versus triplet nature of the ground electronic state, are sensitive to the nature of the supporting ligands and, in particular, depend upon their geometric arrangement relative to the O2 binding site. Highly correlated ab initio and density functional theory electronic structure calculations demonstrate that optimal overlap (and oxidative charge transfer) occurs for the side-on geometry, and this is promoted by ligands that raise the energy, thereby enhancing resonance, of the filled Cu dxz orbital that hybridizes with the in-plane pi* orbital of O2. Conversely, ligands that raise the energy of the filled Cu dz2 orbital foster a preference for end-on binding as this is the only mode that permits good overlap with the in-plane O2 pi*. Because the overlap of Cu dz2 with O2 pi* is reduced as compared to the overlap of Cu dxz with the same O2 orbital, the resonance is also reduced, leading to generally more stable triplet states relative to singlets in the end-on geometry as compared to the side-on geometry, where singlet ground states become more easily accessible once ligands are stronger donors. Biradical Cu(II)-O2 superoxide character in the electronic structure of the supported complexes leads to significant challenges for accurate quantum chemical calculations that are best addressed by exploiting the spin-purified M06L local density functional, single-reference completely renormalized coupled-cluster theory, or multireference second-order perturbation theory, all of which provide predictions that are qualitatively and quantitatively consistent with one another.

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.

Coupled-cluster theory for three-body Hamiltonians

We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of {sup 4}He. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.

Ab-initio coupled-cluster study of 16O.

We report converged results for the ground and excited states and matter density of 16O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0(+) state. Incorporation of triples has no effect on the latter finding.

Breaking Bonds of Open-Shell Species with the Restricted Open-Shell Size Extensive Left Eigenstate Completely Renormalized Coupled-Cluster Method

The recently developed restricted open-shell, size extensive, left eigenstate, completely renormalized (CR), coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as ROCCL, is compared with the unrestricted CCSD(T) [UCCSD(T)] and multireference second-order perturbation theory (MRMP2) methods to assess the accuracy of the calculated potential energy surfaces (PESs) of eight single bond-breaking reactions of open-shell species that consist of C, H, Si, and Cl; these types of reactions are interesting because they account for part of the gas-phase chemistry in the silicon carbide chemical vapor deposition. The full configuration interaction (FCI) and multireference configuration interaction with Davidson quadruples correction [MRCI(Q)] methods are used as benchmark methods to evaluate the accuracy of the ROCCL, UCCSD(T), and MRMP2 PESs. The ROCCL PESs are found to be in reasonable agreement with the corresponding FCI or MRCI(Q) PESs in the entire region R = 1-3Re for all of the studied bond-breaking reactions. The ROCCL PESs have smaller nonparallelity error (NPE) than the UCCSD(T) ones and are comparable to those obtained with MRMP2. Both the ROCCL and UCCSD(T) PESs have significantly smaller reaction energy errors (REE) than the MRMP2 ones. Finally, an efficient strategy is proposed to estimate the ROCCL/cc-pVTZ PESs using an additivity approximation for basis set effects and correlation corrections.

A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effects.

The CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.