The basis-set convergence of the electronic correlation energy in the water molecule is investigated at the second-order Mo/ller–Plesset level and at the coupled-cluster singles-and-doubles level with and without perturbative triples corrections applied. The basis-set limits of the correlation energy are established to within 2 mEh by means of (1) extrapolations from sequences of calculations using correlation-consistent basis sets and (2) from explicitly correlated calculations employing terms linear in the interelectronic distances rij. For the extrapolations to the basis-set limit of the correlation energies, fits of the form a+bX−3 (where X is two for double-zeta sets, three for triple-zeta sets, etc.) are found to be useful. CCSD(T) calculations involving as many as 492 atomic orbitals are reported.

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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.

The linear and quadratic response functions have been determined for a coupled cluster reference state. From the response functions, computationally tractable expressions have been derived for excitation energies, first- and second-order matrix transition elements, transition matrix elements between excited states, and second- and third-order frequency-dependent molecular properties.

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 CCSDT-1a, CCSDT-1b, and CCSD they are only correct through second order. Calculations of excitation energies are reported for CH+, N2, and C2H4 to illustrate the accuracy that can be obtained in the various triples models. The CH+ results are compared to full configuration interaction results, the C2H4 results are compared with complete active space second order perturbation theory (CASPT2) and experiment, and the N2 results are compared to experiment. Double replacement dominated excitations are improved significantly relative to CCSD in all the triples models mentioned, and is of the same quality in CC3 and CCSDT-1a. The single replacement dominated excitation are close to full configuration interaction results for the CC3 model and significantly improved relative to CCSD. The CCSDT-1 results for the single replacement dominated excitations are not improved compared to CCSD.

We demonstrate that substantial computational savings are attainable in electronic structure calculations using a Cholesky decomposition of the two-electron integral matrix. In most cases, the computational effort involved calculating the Cholesky decomposition is less than the construction of one Fock matrix using a direct O(N 2 ) procedure.

An alternative derivation of many-body perturbation theory ͑MBPT͒ 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 2nϩ1 and the nth-order multipliers determine the energy to order 2nϩ2. 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 ͑1984͔͒ CCSDT-1b models ͓Urban et al., J. Chem. Phys. 83, 4041 ͑1985͔͒, and the CCSD͑T͒ model ͓Raghavachari et al., Chem. Phys. Lett. 157, 479 ͑1989͔͒. Sample calculations of total energies are presented for the molecules H 2 O, C 2 , CO, and C 2 H 4 . Comparisons are made with full CCSDT, CCSDT-1a, CCSDT-1b, CCSD͑T͒, and full configuration interaction ͑FCI͒ results. These calculations demonstrate that CC3 and CCSD͑T͒ give total energies of a similar quality. If results obtained by CC3 and CCSD͑T͒ differ significantly, neither method can be trusted. In contrast to CCSD͑T͒, time-dependent response functions can be obtained for CC3.