Coupled cluster

About: Coupled cluster is a research topic. Over the lifetime, 6280 publications have been published within this topic receiving 301055 citations.

Coupled-cluster methods with internal and semi-internal triply excited clusters: Vibrational spectrum of the HF molecule

Abstract: The recently proposed, single-reference, coupled-cluster (CC) methods with singly, doubly, and triply excited clusters, in which triexcited clusters T3 are restricted to internal and semi-internal components defined through active orbitals, designated as the CCSD{t′} and CCSDt approaches [P. Piecuch, S. A. Kucharski, and R. J. Bartlett, J. Chem. Phys. 110, 6103 (1999)] have been used to obtain the potential energy function and the vibrational spectrum of the HF molecule, as described by the large, aug-cc-pvtz, basis set. A comparison has been made with the vibrational term values obtained at the very high, full CCSDT (CC singles, doubles, and triples), level and with the experimental (RKR) data. In spite of using the restricted Hartree–Fock reference, the calculated CCSD{t′} and CCSDt vibrational term values have been found to be in much better agreement with the full CCSDT and RKR data than the results of conventional CCSD (CC singles and doubles) calculations, which produce errors of an order of 2000 cm...

Particle-particle and quasiparticle random phase approximations: connections to coupled cluster theory.

Abstract: We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a “correct bosonization” in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call “crossed-ring” whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call “mosaic” terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA and qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.

The MP2 limit correction applied to coupled cluster calculations of the electronic dissociation energies of the hydrogen fluoride and water dimers

Abstract: The basis set convergence of ab initio computed electronic dissociation energies is reported for the hydrogen bonded complexes (HF)2 (H2O)2. At the level of CCSD(T) theory (coupled cluster model with singles, doubles, and approximate connected triples), the interaction energy is split into one- and two-body terms, and corrections such as the counterpoise (CP) and the MP2 limit are explored. The MP2-limit correction consists of substituting the second-order Moller-Plesset (MP2) perturbation theory contribution computed with the actual basis set by the limiting value that is obtained in a complete basis. Clearly the basis set convergence of the CCSD(T) calculations is improved by the MP2 limit correction. Moreover, the MP2-limit correction can be applied irrespective of whether or not the two-body term has been CP corrected beforehand. Little difference is found between the two possibilities, but the most accurate results are obtained by applying the MP2 limit correction to CP corrected CCSD(T) two-body ter...

Atomization energies from coupled-cluster calculations augmented with explicitly-correlated perturbation theory

Abstract: The atomization energies of the 105 molecules in the test set of Bakowies [D. Bakowies, J. Chem. Phys. 127 (2007) 084105] have been computed with an estimated standard deviation (from the values compiled in the Active Thermochemical Tables) of {+-}0.1 kJ/mol per valence electron in the molecule. Equilibrium geometries and harmonic vibrational frequencies were calculated at the all-electron CCSD(T)/cc-pCVTZ level, that is, at the level of coupled-cluster theory with singles, doubles and non-iterative triples in a correlation-consistent polarized core-valence triple-zeta basis. Single-point energy calculations were performed at the all-electron CCSD(T) level in a correlation-consistent polarized core-valence quadruple-zeta basis (cc-pCVQZ), and several corrections were added: (i) a correction for the basis-set truncation error, obtained from second-order perturbation theory using Slater-type geminals (MP2-F12 theory), (ii) a correction for the effect of anharmonicity on the zero-point vibrational energy, (iii) a relativistic correction, (iv) a correction for the difference between the full CCSDT model (coupled-cluster theory with singles, doubles and triples) and the CCSD(T) approximation, and (v) a correction for connected quadruple excitations obtained from CCSDT(Q) calculations. The correction for the basis-set truncation error was obtained from MP2-F12 calculations by scaling the MP2 basis-set truncation error by an empirically optimized 'interference factor' of f{submore » int} = 0.78. The reference values from the Active Thermochemical Tables for 73 molecules in the test set, the equilibrium geometries, the harmonic vibrational frequencies, and all of the energy corrections represent valuable data for performance assessments of additivity schemes that will be developed in the future, in which the basis-set truncation error will be calculated at the level of coupled-cluster theory using Slater-type geminals (CC-F12 theory). Such a scheme will be free of empirical corrections and scaling factors.« less

Integral-direct electron correlation methods

Abstract: Integral-direct implementations of Moller—Plesset perturbation theory up to fourth order (MP4(SDQ) without triple excitations), quadratic configuration interaction with single and double excitations (QCISD), coupled cluster (CCSD), multiconfiguration self-consistent field (MCSCF), second- and third-order multireference perturbation theory (MRPT2, MRPT3), and internally contracted multireference configuration interaction (MRCI) methods are described. All methods use the same three integral-direct kernels, namely direct calculation of Fock matrices, direct partial integral transformation, and direct evaluation of external exchange matrices. New algorithms for the latter two procedures are proposed and implemented, for which the memory requirement scales only linearly with basis set size. Test calculations with more than 500 basis functions are presented. It is demonstrated that integral prescreening can significantly reduce the scaling of the computational cost with molecular size N. For small polyglycine p...