Ludwik Adamowicz

A state‐selective multireference coupled‐cluster theory employing the single‐reference formalism

A new state‐selective multireference (MR) coupled‐cluster (CC) method exploiting the single‐reference (SR) particle‐hole formalism is described. It is an extension of a simple two‐reference formalism, which we presented in our earlier paper [N. Oliphant and L. Adamowicz, J. Chem. Phys. 94, 1229 (1991)], and a rigorous formulation of another method of ours, which we obtained as an approximation of the SRCC approach truncated at triple excitations (SRCCSDT) [N. Oliphant and L. Adamowicz, J. Chem. Phys. 96, 3739 (1992)]. The size extensivity of the resulting correlation energies is achieved by employing a SRCC‐like ansatz for the multideterminantal wave function. General considerations are supplemented by suggesting a hierarchy of approximate schemes, with the MRCCSD approach (MRCC approach truncated at double excitations from the reference determinants) representing the most important one. Our state‐selective MRCCSD theory emerges through a suitable selection of the most essential cluster components appearing in the full SRCCSDTQ method (SRCC method truncated at quadruple excitations), when the latter is applied to quasidegenerate states. The complete set of equations describing our MRCCSD formalism is presented and the possibility of the recursive intermediate factorization [S. A. Kucharski and R. J. Bartlett, Theor. Chim. Acta 80, 387 (1991)] of our approach, leading to an efficient computer algorithm, is discussed.

Multireference coupled‐cluster method using a single‐reference formalism

A multireference coupled‐cluster singles and doubles method utilizing two reference determinants which differ by a two electron excitation is proposed. One of these determinants is selected as the formal reference determinant. The proposed method includes single‐reference coupled‐cluster equations truncated after quadruples. These equations are graphically derived using Feynman diagrams. The appropriate restrictions are then placed on the triple and quadruple amplitudes to allow only those amplitudes which correspond to single and double excitations from the second reference determinant.

State‐selective multireference coupled‐cluster theory employing the single‐reference formalism: Implementation and application to the H8 model system

The new state‐selective (SS) multireference (MR) coupled‐cluster (CC) method exploiting the single‐reference (SR) particle‐hole formalism, which we have introduced in our recent paper [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)], has been implemented and the results of the pilot calculations for the minimum basis‐set (MBS) model composed of eight hydrogen atoms in various geometrical arrangements are presented. This model enables a continuous transition between degenerate and nondegenerate regimes. Comparison is made with the results of SR CC calculations involving double (CCD), single and double (CCSD), single, double, and triple (CCSDT), and single, double, triple, and quadruple (CCSDTQ) excitations. Our SS CC energies are also compared with the results of the Hilbert space, state‐universal (SU) MR CC(S)D calculations, as well as with the MR configuration interaction (CI) results (with and without Davidson‐type corrections) and the exact correlation energies obtained using...

The implementation of the multireference coupled-cluster method based on the single-reference formalism

A generalized version of the multireference coupled‐cluster method using a single‐reference formalism, which we presented in an earlier paper, has been implemented. Any number of determinants, that differ from the formal reference determinant by single or double excitations, can now be included in the reference space. In the present implementation, the single and double excitations from the secondary reference determinants have been truncated to include only those that correspond to triple excitations from the formal reference determinant. Calculations are done on a few model systems, LiH, BH, and H2O, at equilibrium and stretched geometries. Comparisons are made with full configuration interaction (CI) treatment for the single bond stretch in LiH and BH, and the results are quite promising. For the water molecule, comparisons are made with the results obtained with the coupled cluster method truncated at triple excitations (CCSDT), as well as with the full CI results. While the multireference method did not do as well for the simultaneous two‐bond stretch in H2O as it did for the single bond cases, it did at least as well as the CCSDT at representing the points on the full CI potential curve.

Coupled‐cluster method truncated at quadruples

The coupled‐cluster (CC) equations including single, double, triple, and quadruple excitation amplitudes (CCSDTQ) are derived diagramatically, and the complete set of CCSDTQ equations are presented. These equations have been programmed and an iterative reduced linear equation method is used to solve these equations. The potential curves for the dissociation of a model system with a single bond (Li2 and LiH) is calculated using CC doubles (CCD), singles and doubles (CCSD), singles, doubles, and triples (CCSDT), and CCSDTQ. These calculations demonstrate the magnitude of the CC contributions arising from single, double, triple, and quadruple excitation amplitudes to the stretching of a chemical bond.

Optimized virtual orbital space for high‐level correlated calculations

The second order Hylleraas functional and a Newton–Raphson orbital optimization technique have been used to generate an active, optimized virtual orbital space (OVOS) of substantially reduced dimension for correlated calculations. Numerical examples for CH2(1A1), C6H6, and potential curves for B2H6 and H2O2 using MBPT and coupled‐cluster theory demonstrate that most of the correlation energy can be obtained with a much smaller number of optimized virtual orbitals, and effectively ∼100% of the correlation energy if the OVOS result is combined with the exact second‐order energy that is evaluated as a byproduct of the OVOS generation. This suggests a potentially wide applicability of the OVOS method in high accuracy quantum mechanical calculations.

Improved computational strategy for the state‐selective coupled‐cluster theory with semi‐internal triexcited clusters: Potential energy surface of the HF molecule

The recently developed state‐selective (SS) multi‐reference coupled‐cluster (CC) method involving all singly and doubly, and semi‐internal triply excited clusters from the formal reference configuration [SSCCSD(T) approach] is tested in the calculation of the potential energy surface (PES) of the HF molecule. Both double zeta and double zeta plus polarization basis sets are employed and a few different choices of active space are considered. The SSCCSD(T) method provides an accurate description of the entire PES at low cost even for the bond breaking region, contrary to the results obtained with the perturbative single‐reference CCSD(T) method or various limited configuration interaction approaches. This is the first application of the new SSCC code, which uses an improved computational strategy for handling the semi‐internal triexcited clusters. Details of this new implementation of the SSCCSD(T) method are discussed.

CASCCD: Coupled-cluster method with double excitations and the CAS reference

A new multireference coupled-cluster method which includes double excitations and is based on the complete active space (CAS) multiconfigurational reference wave function is proposed. By partitioning the CAS orbitals into active and nonactive sets a two-component, coupled-cluster wave function involving excitations into orbitals of the different sets was constructed. The first component includes all the CAS excitations and the second component, which has the exponential form, consists of double external and semi-external excitations. The coupled-cluster equations for the energy and for the amplitudes involved in the two components of the wave function were derived and illustrated using a diagrammatic formalism. Several numerical tests were performed, and the results demonstrate a very good performance of the method as compared to the full configuration interaction results.

The infrared spectra of matrix isolated uracil and thymine : an assignment based on new theoretical calculations

Abstract The IR spectra of uracil and thymine predicted theoretically at the ab initio Hartree-Fock level with 6-31G basis set are reported and compared with Ar matrix experimental spectra. The IR spectra computed at the SCF/6-31G level reproduce the experimental spectra with an accuracy which allows a reliable vibrational assignment. A split valence basis set, augmented with polarization functions on all atoms, was found to be quite sufficient for a reliable prediction and assignment of the IR absorption bands in the spectra of medium-sized molecules.

New approach to the state-specific multireference coupled-cluster formalism

A new development is presented in the framework of the state-specific multireference (MR) coupled-cluster (CC) theory (MRCC). The method is based on the CASSCF (complete active space self-consistent field) wave function and it is designed specifically for calculating excited electronic states. In the proposed approach, the cluster structure of the CC wave operator and the method to determine this operator are the key features. Since the general formulation of the CASCC method is uncontracted, i.e., allows the interaction between the nondynamic and dynamic correlation effects to affect both the CAS reference function and the CC correlation wave operator, the method is expected to perform better than contracted perturbative approaches such as the CASPT2 (second-order perturbation theory based on the CAS wave function) method. Also, the CASCC method is not a perturbative approach and is not based on selection of an unperturbed Hamiltonian, which in the case of the CASPT2 method often leads to the “intruder s...