Vladimir V. Ivanov

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.

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...

State-specific multireference complete-active-space coupled-cluster approach versus other quantum chemical methods: dissociation of the N2 molecule

A comprehensive comparison of different quantum-chemical methods applied to calculate the N2 ground state potential energy curve is presented. In the comparison we highlight the multireference state-specific (MRSS) coupled-cluster (CC) approach with the complete-active-space (CAS) reference and with single and double excitations from all reference determinants in the CC operator developed in our group. The method is called CASCCSD. The energy and amplitude equations for the method and the corresponding computer code have been generated using a computerized automative procedure that in the present work was extended to produce a parallel computer code. The complete CASCCSD wave function for N2 includes some selected eight-fold excitations in the CC operator. An analysis of the wave function estimates the importance of those excitations at large internuclear separations.

Excited states in the multireference state-specific coupled-cluster theory with the complete active space reference.

The recently proposed multireference state-specific coupled-cluster theory with the complete active space reference has been used to study electronically excited states with different spatial and spin symmetries. The algorithm for the method has been obtained using the computerized approach for automatic generation of coupled-cluster diagrams with an arbitrary level of the electronic excitation from a formal reference determinant. The formal reference is also used to generate the genuine reference state in the form of a linear combination of determinants contracted to a configuration with the spin and spatial symmetries of the target state. The natural-orbital expansions of the one-electron configuration inferaction density matrix allowed us to obtain the most compact orbital space for the expansion of the reference function. We applied our approach in the calculations of singlet and triplet states of different spatial symmetries of the water molecule. The comparisons of the results with values obtained using other many-particle methods and with the full configuration interaction results demonstrate good ability of the approach to deal with electronic excited states.

New scheme for solving the amplitude equations in the state-specific coupled cluster theory with complete active space reference for ground and excited states

A new scheme for solving the coupled cluster (CC) amplitude equations for ground and excited electronic states in the state-selective multireference (MR) CC method based on the complete active space (CAS) reference wave function (CASCC) is proposed. The CASCC wave function is generated using a single formal reference determinant, which is one of the CAS determinants, as the origin of the configuration expansion. Some single and double excitations from other CAS determinants may be triple, quadruple, and higher excitations from the reference determinant. We show that one may include the contribution from these higher excitations indirectly by modifying the coupled cluster amplitude equations corresponding to the single and double excitations. The modification involves including projections against the higher excitations in the equations for the singles and doubles. Test calculations for the ground and the first excited state of the H8-model system and for the singlet–triplet splitting of the CH2-biradical ...

New indices for describing the multi-configurational nature of the coupled cluster wave function

New cumulative indices which describe the configurational structure and the degree of ‘multi-configurationality’ of the coupled cluster (CC) wave function have been proposed and tested on some model systems. The indices calculated for the coupled cluster wave functions generated with the CCSD (single and double excitations) and CCSDT (single, double, and triple excitations) models were compared with the corresponding values obtained with the full configuration interaction (FCI) method. The test calculations have concerned cases where the multi-reference character of the wave function increases due to bond stretching.

Dipole polarizabilities and hyperpolarizabilities of the small conjugated systems in the π-electron coupled cluster theory

In this work, π-electron dipole polarizabilities and hyperpolarizabilities of some organic systems with double and triple bonds (polyenes, polyynes, and condensed hydrocarbons) have been calculated using the coupled-cluster (CC) π-electron method. It is shown that the CC approach gives the polarizabilities and hyperpolarizabilities which are considerably closer to the full configuration interaction (FCI) results than the results of the Hartree–Fock method and the second order perturbation theory. A correct description of (hyper)polarizabilities of polyenes can be achieved at the CC level of theory with the inclusion of only single and double electron excitations from the Hartree–Fock determinant (the CCSD approach). However, for systems with triple bonds (acetylenes), higher level excitations need to be explicitly included in the calculations to correctly describe their (hyper)polarizabilities.

Molecular dipole static polarisabilities and hyperpolarisabilities of conjugated oligomer chains calculated with the local π-electron coupled cluster theory

A new semi-empirical π-electron local coupled cluster theory has been developed to calculate static dipole polarisabilities and hyperpolarisabilities of extended π-conjugated systems. The key idea of the approach is the use of the ethylene molecular orbitals as the orbital basis set for π-conjugated compounds (the method is termed the Covalent Unbonded Molecules of Ethylene method, cue). Test calculations of some small model organic conjugated compounds demonstrate high accuracy of the version of the cue local coupled cluster theory developed in this work in comparison with the π-electron full configuration interaction (FCI) method. Calculations of different conjugated carbon-based oligomer chains (polyenes, polyynes, polyacenes, polybenzocyclobutadiene, etc.) demonstrate fast convergence (per π-electron) of the polarisability and hyperpolarisability values in the calculations when more classes of orbital excitations are included in the coupled cluster single and double (CCSD) excitation operator. The results show qualitatively correct dependence on the system size.

Discontinuities-free complete-active-space state–specific multi–reference coupled cluster theory for describing bond stretching and dissociation

The earlier proposed multi-reference state-specific coupled-cluster theory with the complete active space reference [CASCC; Lyakh et al., J. Chem. Phys. 122, 024108 (2005)] suffered from a problem of energy discontinuities when the formal reference state was changing in the calculation of the potential energy curve (PEC). A simple remedy to the discontinuity problem is found and is presented in this work. It involves using natural complete active space self-consistent field active orbitals in the complete active space coupled-cluster calculations. The approach gives smooth PECs for different types of dissociation problems, as illustrated in the calculations of the dissociation of the single bond in the hydrogen fluorine molecule and of the symmetric double-bond dissociation in the water molecule.

Electronic Excited States in the State-Specific Multireference Coupled Cluster Theory with a Complete-Active-Space Reference

The multireference state specific coupled cluster theory with CAS reference (CASCCSD) is generalized for calculations of electronically excited states. Test calculations have demonstrated high effectivity of the approach in comparison with other approximate approaches and with the full configuration interaction method.