Ove Christiansen

The second-order approximate coupled cluster singles and doubles model CC2

Abstract An approximate coupled cluster singles and doubles model is presented, denoted CC2. The CC2 total energy is of second-order Moller-Plesset perturbation theory (MP2) quality. The CC2 linear response function is derived. Unlike MP2, excitation energies and transition moments can be obtained in CC2. A hierarchy of coupled cluster models, CCS, CC2, CCSD, CC3, CCSDT etc., is presented where CC2 and CC3 are approximate coupled cluster models defined by similar approximations. Higher levels give increased accuracy at increased computational effort. The scaling of CCS, CC2, CCSD, CC3 and CCSDT is N4, N5, N6, N7 and N8, respectively where N is th the number of orbitals. Calculations on Be, N2 and C2H4 are performed and results compared with those obtained in the second-order polarization propagator approach SOPPA.

The Dalton quantum chemistry program system

Dalton is a powerful general‐purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self‐consistent‐field, Møller–Plesset, configuration‐interaction, and coupled‐cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic‐structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge‐origin‐invariant manner. Frequency‐dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one‐, two‐, and three‐photon processes. Environmental effects may be included using various dielectric‐medium and quantum‐mechanics/molecular‐mechanics models. Large molecules may be studied using linear‐scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Response functions in the CC3 iterative triple excitation model

The derivation of response functions for coupled cluster models is discussed in a context where approximations can be introduced in the coupled cluster equations. The linear response function is derived for the approximate coupled cluster singles, doubles, and triples model CC3. The linear response functions for the approximate triples models, CCSDT‐1a and CCSDT‐1b, are obtained as simplifications to the CC3 linear response function. The consequences of these simplifications are discussed for the evaluation of molecular properties, in particular, for excitation energies. Excitation energies obtained from the linear response eigenvalue equation are analyzed in orders of the fluctuation potential. Double replacement dominated excitations are correct through second order in all the triples models mentioned, whereas they are only correct to first order in the coupled cluster singles and doubles model (CCSD). Single replacement dominated excitation energies are correct through third order in CC3, while in CCSD...

Response Functions from Fourier Component Variational Perturbation Theory Applied to a Time-Averaged Quasienergy

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann)Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2 n q 1 and 2 n q 2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self- consistent field, and second-order Moller)Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state

The CC3 model: An iterative coupled cluster approach including connected triples

An alternative derivation of many-body perturbation theory (MBPT) has been given, where a coupled cluster parametrization is used for the wave function and the method of undetermined Lagrange multipliers is applied to set up a variational coupled cluster energy expression. In this variational formulation, the nth-order amplitudes determine the energy to order 2n+1 and the nth-order multipliers determine the energy to order 2n+2. We have developed an iterative approximate coupled cluster singles, doubles, and triples model CC3, where the triples amplitudes are correct through second order and the singles amplitudes are treated without approximations due to the unique role of singles as approximate orbital relaxation parameters. The compact energy expressions obtained from the variational formulation exhibit in a simple way the relationship between CC3, CCSDT-1a [Lee et al., J. Chem. Phys. 81, 5906 (1984)] CCSDT-1b models [Urban et al., J. Chem. Phys. 83, 4041 (1985)], and the CCSD(T) model [Raghavachari et...

Vibrational coupled cluster theory

The theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a three-mode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational self-consistent-field, vibrational Møller-Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.

EXCITATION ENERGIES OF H2O, N2 AND C2 IN FULL CONFIGURATION INTERACTION AND COUPLED CLUSTER THEORY

Abstract Singlet excitation energies of H2O, N2 and C2 have been calculated in full configuration interaction (FCI) and in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3. Excitation energies are improved at each level in the coupled cluster hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the excitations in CCS, CC2, CCSD and CC3 are correct through higher and higher order in the fluctuation potential, and that more and more completer cluster treatments are used. Non-iterative triples corrections to the CCSD excitation energies are compared with the iterative triples models CC3 and FCI. The CCSDR(3) approach recovers the major part of the correlation improvement obtained in the CC3 model.

Excitation energies of BH, CH2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models

Abstract Excitation energies in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3 have been calculated for Ne, BH and CH 2 and compared with full configuration interaction (FCI) results. Single replacement dominated excitations are improved at each level in this hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the single replacement dominated excitations in CCS, CC2, CCSD and CC3 are correct through respectively first, second and third order in the fluctuation potential. The improvement from CC2 to CCSD is due to the fact that CCSD gives a full coupled cluster treatment in the singles, doubles space. Double replacement dominated excitations can only be described at the CCSD and CC3 levels, and are correct through first and second order, respectively. The CC3 double replacement dominated excitations have similar quality as the single replacement dominated excitations in CC2. The scaling of CCS, CC2, CCSD and CC3 is N 4 , N 5 , N 6 and N 7 , respectively, where N is the number of orbitals.

Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties

An atomic integral-direct implementation of molecular linear-response properties and excited-state one-electron properties is presented for the coupled cluster models CCS, CC2, and CCSD. Sample calculations are presented for the polarizability of N2 and for excited-state one-electron properties and transition-properties of furan.

Large‐scale calculations of excitation energies in coupled cluster theory: The singlet excited states of benzene

Algorithms for calculating singlet excitation energies in the coupled cluster singles and doubles (CCSD) model are discussed and an implementation of an atomic‐integral direct algorithm is presented. Each excitation energy is calculated at a cost comparable to that of the CCSD ground‐state energy. Singlet excitation energies are calculated for benzene using up to 432 basis functions. Basis‐set effects of the order of 0.2 eV are observed when the basis is increased from augmented polarized valence double‐zeta (aug‐cc‐pVDZ) to augmented polarized valence triple‐zeta (aug‐cc‐pVTZ) quality. The correlation problem is examined by performing calculations in the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3, as well as by using the CCSDR(3) perturbative triples corrections. The effect of triple excitations are less than 0.2 eV for all excitations except for the 2 1E2g state. The calculated excitation energies are compared with experiment and other theoretical results.