Monika Musiał

Efficient computer implementation of the renormalized coupled-cluster methods: The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) approaches

Abstract The recently proposed renormalized (R) and completely renormalized (CR) coupled-cluster (CC) methods of the CCSD[T] and CCSD(T) types have been implemented using recursively generated intermediates and fast matrix multiplication routines. The details of this implementation, including the complete set of equations that have been used in writing efficient computer codes, memory requirements, and typical CPU timings, are discussed. The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) computer codes and similar codes for the standard CC methods, including the LCCD, CCD, CCSD, CCSD[T], and CCSD(T) approaches, have been incorporated into the gamess package. Information about the main features of this new set of CC programs is provided.

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.

Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT

The equation-of-motion (EOM) coupled cluster (CC) method with full inclusion of the connected triple excitations for ionization energies has been formulated and implemented. Using proper factorization of the three- and four-body parts of the effective Hamiltonian, an efficient computational procedure has been proposed for IP-EOM-CCSDT which at the EOM level requires no-higher-than nocc3nvir4 scaling. The method is calibrated by the evaluation of the valence vertical ionization potentials for CO, N2, and F2 molecules for several basis sets up to 160 basis functions. At the basis set limit, errors vary from 0.0 to 0.2 eV, compared to “experimental” vertical ionization potentials.

Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT

We extend the full triples equation-of-motion (EOM) coupled cluster (CC) method to electron attached states. Proper factorization of the three- and four-body parts of the effective Hamiltonian makes it possible to achieve for the EA-EOM part a scaling no higher than nocc2nvir5. The method is calibrated by the evaluation of the valence vertical electron affinities for the C2 and O3 molecules for several basis sets up to 160 basis functions. For C2, EA-EOM-CCSDT gives 3.24 eV at the extrapolated basis limit, while the experimental adiabatic EA is equal to 3.27±0.008 eV. For O3 the agreement is ∼1.9 eV compared to an adiabatic value of 2.1 eV.

Critical comparison of single-reference and multireference coupled-cluster methods: Geometry, harmonic frequencies, and excitation energies of N2O2

Calculated vertical excitation energies, optimized geometries, and vibrational frequencies of the nitric oxide dimer are reported. The “multireference” (MR) nature of the problem and weak bond between the monomers make a proper description of the system difficult, and standard methods are not as applicable to this system. In this study, recently developed methods such as the double-electron-affinity similarity-transformed equation-of-motion coupled cluster method (DEA-STEOM-CCSD), MR Brillouin–Wigner CCSD (MR-BWCCSD), MR average quadratic CCSD (MR-AQCCSD), and others are used along with a series of basis sets of increasing accuracy. The calculated excitation energies are consistent and convergent with respect to the basis set in DEA-STEOM-CCSD, MR-BWCCSD, and MR-AQCCSD methods. The geometries are highly sensitive to the basis set size and the challenge to obtain the right answers in the basis set limit remains. Nevertheless, we obtain qualitative agreement with the experimental geometry and harmonic vibra...

Multireference coupled-cluster theory: The easy way

The multi-ionization equation-of-motion coupled-cluster (CC) method is developed for multireference (MR) problems. It is operationally single reference, depending upon a formal matrix diagonalization step to define the coefficients in the wavefunction in an unbiased way that allows for important MR character. The method is illustrated for the autoisomerization of cyclobutadiene, which has a very large multireference effect and compared to other MR-CC results. The newly implemented methods are also used to obtain the vertical double ionization (DI) potentials of several small molecules (H(2)O, CO, C(2)H(2), C(2)H(4)). Also, the performance of the new methods is analyzed by plotting the potential energy curve for twisted ethylene as a function of a dihedral angle between two methylenes. Evaluation of the total molecular energy via MR-DI-CC calculations makes it possible to avoid an unphysical cusp.

Molecular applications of the intermediate Hamiltonian Fock-space coupled-cluster method for calculation of excitation energies.

The intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculate vertical excitation energies (EEs) for some molecular systems. The calculations are performed for several small molecules, such as H2O, N2, and CO, and for larger systems, such as C2H4, C4H6, and C6H6. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and model spaces are employed permitting a comparison of the calculated vertical EEs with the experimental data.

Fock space multireference coupled cluster method with full inclusion of connected triples for excitation energies.

We report the initial Fock space multireference coupled cluster method with the full inclusion of single, double, and triple excitations (FS-CCSDT) for the (1,1) sector. We present pilot applications for calculating excitation energies for the N(2) molecule and the Ne atom. The performance of the current model, along with the FS-CCSD one, has been studied in comparison with the equation-of-motion coupled-cluster and the similarity transformed methods.

Formulation and implementation of the full coupled-cluster method through pentuple excitations

Using the quasilinearized formulation of CC theory in terms of recursively computed intermediates, we present the detailed equations and implementation of coupled-cluster theory with single, double, triple, quadruple, and pentuple excitations, CCSDTQP. We illustrate its results by comparison with several full CI results in double zeta, polarized basis sets (DZP), at different geometries. The maximum error compared to full CI occurs for H2O at twice Re which is 0.026 mH. For all other cases, HF, SiH2, and CH2 in its singlet state, the largest errors are 0.001 mH. The magnitude of the connected T5 contribution is as large as 0.35 mH, but usually less than 0.1 mH for these examples.

Intermediate Hamiltonian Fock-space multireference coupled-cluster method with full triples for calculation of excitation energies.

The intermediate Hamiltonian multireference coupled-cluster (CC) method with singles, doubles, and triples within the excited (1,1) sector of Fock space (FS) is implemented and formulated to calculate excitation energies (EEs). Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, coupled to an efficient factorization strategy, relatively large basis sets and model spaces are employed permitting basis set converged comparisons of the calculated vertical EEs, which can be compared to the experimental data for the N(2) and CO molecules. The issue of charge-transfer separability is also addressed.