Showing papers on "Coupled cluster published in 1987"

Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method

Abstract: Fourth‐order Mo/ller–Plesset perturbation theory (MP4) is formulated for localized internal orbitals of closed‐shell systems. Unlike previous localized perturbation theories, our formulation is strictly identical with canonical MP4 theory if no further approximations are made. In the local treatment, large savings can be achieved by two techniques: (1) neglecting or treating at a lower (second order) level pair correlation between distant pairs, and (2) restricting the correlation basis to the atomic orbitals in the spatial vicinity of the correlated pair. These techniques have been used in our previous local correlation treatment for variational CI, coupled electron pair (CEPA), and approximate coupled cluster (ACCD) wave functions. The MP4 method is more economical than these techniques because of the absence of iterative cycles. Implementation with single, double, and quadruple substitutions is discussed.

Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application

Abstract: The theory for the analytic evaluation of energy gradients for coupled cluster (CC) wave functions is presented. In particular, explicit expressions for the analytic energy gradient of the CC singles and doubles (CCSD) wave function for a closed‐shell restricted Hartree–Fock reference determinant are presented and shown to scale as N6 where N is the one‐electron number of atomic basis functions for the molecular system. Thus analytic CCSD gradients are found to be of the same magnitude in computational cost as is the evaluation of analytic gradients for the configuration interaction singles and doubles (CISD) wave function. Applications of this method are presented for the water molecule and the formaldehyde molecule using a double‐ζ plus polarization (DZ+P) basis set. The CCSD equilibrium geometries, dipole moments, and, via finite differences of gradients, CCSD harmonic vibrational frequencies and infrared intensities are reported. For H2O these results are compared to analogous CISD, CISDT, CISDTQ, and...

The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results

Abstract: A single and double excitation coupled cluster (CCSD) method restricted to closed‐shell single configuration reference functions is described in explicit detail. Some significant simplifications resulting from the restriction to closed‐shell systems are exploited to achieve maximum computational efficiency. Comparisons for energetic results and computational requirements are made with the single and double excitation configuration interaction (CISD) method. The specific molecules considered include N2, H2O, H3O+, H5O+2, HSOH, and s‐tetrazine (C2N4H2).

The description of N2 and F2 potential energy surfaces using multireference coupled cluster theory

Abstract: The ground state potential energy surfaces (PES’s) for diatomic nitrogen and fluorine are examined using a version of our recently published linearized multireference coupled cluster method (MR‐LCCM). Comparison calculations employing a variety of standard ab initio techniques such as single reference configuration interaction singles and doubles (CISD), many‐body perturbation theory (MBPT), coupled cluster single and doubles (CCSD), and multireference (MR)‐CISD were also performed. In addition, the PES’s were also investigated using the newly developed CCSDT‐1 method, which includes the dominant effect of T3. These single reference procedures fail in various ways (with the possible exception of the CCSDT‐1 method), while the MR‐LCCM method is shown to compare favorably to the more traditional MR‐CI techniques. Like the MR‐CIs, the MR‐LCCM energy curves dissociate correctly and the two are nearly parallel.

Property evaluation and orbital relaxation in coupled cluster methods

Abstract: Molecular electronic properties such as dipole moments, polarizabilities and hyperpolarizabilities and quadrupole moments and polarizabilities, and spin properties such as hyperfine splitting constants and nuclear magnetic coupling constants are predicted by ab initio coupled cluster (CC) methods for a variety of molecules. We compare the results of property evaluation using orbitals that have been allowed to relax in the presence of the perturbation and results obtained using nonrelaxed orbitals. It is demonstrated numerically, and proven formally, that the coupled cluster singles and doubles (CCSD) model using nonrelaxed orbitals is able to include most of the relaxation effects for the evaluation of first‐ and second‐order properties. Thus there is little reason to perform coupled (perturbed) Hartree–Fock calculations as a precursor to correlated CCSD calculations of such properties.

The Coupled Cluster Method

Abstract: The coupled cluster method (CCM) is nowadays widely recognised as providing one of the most powerful, most universally applicable, and numerically most accurate at attainable levels of implementation, of all available ab initio methods of microscopic quantum many-body theory. The number of successful applications of the method to a wide range of physical and chemical systems is impressively large. In almost all such cases the numerical results are either the best or among the best available. A typical example is the electron gas, where the CCM results for the correlation energy agree over the entire metallic density range to within less than one millihartree per electron (or <1%) with the essentially exact Green’s function Monte Carlo results.

The open‐shell coupled‐cluster method: Excitation energies and ionization potentials of H2O

Abstract: The open‐shell coupled cluster method is used to calculate directly several electronic excitation energies and ionization potentials of the water molecule. Correlation effects are included by summing single and double virtual excitations to infinite order. Triple excitations are treated approximately, to the lowest order they appear. Their contribution is significant, 0.2–0.4 eV for excitation energies and 0.5–0.7 eV for ionization potentials. The calculated energies are in good agreement (∼0.15 eV) with experiment.

Extended coupled-cluster method. II. Excited states and generalized random-phase approximation

Abstract: This article gives a discussion of the application of the extended coupled-cluster method (ECCM) to the excited states of a general quantum many-body system. The direct eigenvalue equations for the excitation amplitudes of both the ket and the bra eigenstates are derived in the biorthogonal basis obtained by a double similarity transformation. The equations correspond to the diagonalization of a matrix involving second-order functional derivatives of the average-value functional for the Hamiltonian with respect to the basic ECCM amplitudes. The same excitation spectrum is obtained by considering small oscillations around the equilibrium. The problem with its associated effective Hamiltonian has the structure of a generalized random-phase approximation. By diagonalizing the effective Hamiltonian we perform a canonical or symplectomorphic coordinate transformation into normal coordinates in the symplectic ECCM phase space. In this coordinate system the exact average-value functional for the Hamiltonian has a structure analogous to that of classical lattice dynamics or the phenomenological Ginzburg-Landau theory. At all stages the method satisfies the property of quantum locality, which in real space shows up as a definite quasilocality. Due to this property the method allows, for example, the treatment of mesonlike excitations in the presence of topological objects or in other symmetry-broken equilibrium states.

The quartic force field of H2O determined by many‐body methods. II. Effects of triple excitations

Abstract: Ab initio coupled cluster and many‐body perturbation theory methods that include triple excitation effects are applied to the determination of the quartic force field of the water molecule using an extended Slater‐type basis set. Predictions of fundamental, overtone, and combination vibrational frequencies, rotational constants, and vibration–rotation coupling constants are reported for H2O and its isotopomers. The best predicted harmonic frequencies for the stretching modes of H2O are accurate to 3 cm−1, while the bending mode has an error of 28 cm−1. The mean absolute error for all frequencies reached by two quanta is 0.6%, while the anharmonic constants xi j have a mean absolute error of less than 3%. The important role of triple excitation effects in the surface determination is discussed, and is compared with the effects of quadruple excitations.

Intraatomic correlation effects for the He–He dispersion and exchange–dispersion energies using explicitly correlated Gaussian geminals

Abstract: The coupling of the intermolecular interaction with the intramolecular correlation effects is considered using the coupled cluster (CC) formalism. The CC equations for the dispersion energy are presented and their relation to the double perturbation theory is analyzed. An approximate scheme based on partial decoupling of the CC equations is applied for the He–He interaction. Numerical results are obtained using explicitly correlated Gaussian geminal basis set. They confirm the importance of the intraatomic (apparent) correlation effects and agree very well with the experimentally derived potential.

The relativistic many body problem in molecular theory

Abstract: The essential features of current methods to take care of correlation effects in non-relativistic calculations are reviewed, with special attention to configuration interaction (CI) and coupled cluster (CC) methods. It is stressed that most of these methods start from a Fock space Hamiltonian. Then relativistic many-electron Hamiltonians are discussed, especially concerning their accuracy, problems related to the definition of electronic and positronic states and to variational collapse. Special attention is given to `no-pair' Hamiltonians, as well as to various choices of the electron interaction. After some comments on the adaptation of standard methods for electron correlation to the relativistic case, the state of the art of molecular relativistic many-electron theory is described. In an appendix a semiclassical derivation of a relativistic many-electron Hamiltonian is outlined.

Open‐shell coupled‐cluster method: Electron affinities of Li and Na

Abstract: The open-shell coupled-cluster method and the diagrams needed for its implementation are described. The method is applied to the electron affinities of Li and Na, which are calculated in two ways: as the ionization potential of the anions or as the energy of adding the second electron to the cations. The two schemes give essentially the same results, in very good agreement (<0.02 eV) with experiment. Three-body effects are negligible.

Coupled cluster studies. IV. Analysis of the correlated wavefunction in canonical and localized orbital basis for ethylene, carbon monoxide, and carbon dioxide

Abstract: An a posteriori analysis of the correlated wavefunctions of three small molecules using canonical and localized orbitals shows that, while more excitations are nearly zero for canonical orbitals than for localized ones, in the latter case a straightforward way exists for a priori selection of negligible excitations. In the case of the larger molecule cytosine the same observation is made. However, in this case 99% of the correlation energy is obtained already with ≈ 10% of the excitations when localized orbitals are used, while ≈ 36% of them are necessary in canonical basis. Furthermore it is shown that, using localized orbitals, the excitations can be split into subsets which can be calculated individually. The results suggest that 80–90% of the correlation energies given by MP2, CCL, or CCD can be obtained from the contributions of individual chemical bonds and their interactions. A simple derivation of the orbital invariant formalism of Pulay and Saebo for the calculation of MP2 and MP3 correlation energies is given.

The open‐shell coupled‐cluster method: Ionization potentials and electron affinities of the alkali atoms, Li to Cs

Abstract: The open‐shell coupled‐cluster method with single and double excitations (CCSD) is applied to the alkali atoms, Li to Cs, with moderately large basis sets. The calculated electron affinities are all within 0.01 eV of experiment, with valence‐shell correlation contributing almost all the correction to the (poor) Hartree–Fock results. Errors in the 2S ionization potentials range from 0.02 (Li) to 0.22 eV (Cs); with relativistic corrections estimated from numerical Hartree–Fock, IPs are within 0.1 eV of experiment. 2P IPs are even more accurate (0.02–0.04 eV).

Calculation of spectra and spin–spin coupling constants using a coupled–cluster polarization propagator method

Abstract: We present a coupled-cluster polarization propagator method based on a coupled cluster singles and doubles reference state. Applications to the Be atom show that we may calculate electronic excitation energies with an average absolute error of about 0.08 eV using this method. We have also calculated the nuclear spin–spin coupling constant of 1H19F to be 524.4 cps, in good agreement with experiment. For Be there is a large effect of using coupled-cluster rather than a low-order Rayleigh–Schrodinger expansion, whereas the coupling constant of HF is less sensitive to this improvement in the reference state.

The electronic spectrum of s‐tetrazine: Structures and vibrational frequencies of the ground and excited electronic states

Abstract: The ground and excited electronic states of the s‐tetrazine molecule have been studied using the methods of ab initio electronic structure theory. In particular, complete self‐consistent field (SCF) optimizations of the equilibrium structures on the X 1Ag, a 3B3u, and A 1Au(C2h)/1B3u (D2h) surfaces using both double‐ζ (DZ) and DZ+polarization (DZ+P) basis sets have been carried out. Harmonic vibrational frequencies have been analytically evaluated at these stationary points. DZ SCF results for higher excited electronic states are also reported with the optimizations on these surfaces having been restricted to D2h symmetry. Single point configuration interaction energies including single and double excitations relative to the SCF references (CISD) have been used to predict both vertical and adiabatic electronic excitation energies for all states investigated herein. In addition the Davidson correction [CISD(+Q)] and the closed shell coupled cluster singles and doubles (CCSD) method have been used to app...

Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: A comparison with configuration interaction (CCSD, CISDT, and CISDTQ) results for the harmonic vibrational frequencies, infrared intensities, dipole moment, and inversion barrier of ammonia

Abstract: The analytic energy gradient method that we have recently implemented for CCSD wave functions is applied to fully optimize the pyramidal C3v and planar D3h structures of ammonia. Using a double-zeta plus polarization basis set, results for harmonic vibrational frequencies, infrared intensities, and dipole moments have been obtained. Comparison with different levels of truncated configuration interaction suggests that CCSD values are of better than CISD quality and generally closer to CISDTQ results.

A coupled cluster study of the stability of lithium clusters

Abstract: Coupled cluster studies on Li2, on the Li6 ring and on other Li6 clusters are reported. In its linear approximation the coupled cluster method gives a larger fraction of the correlation energy for Li2 than the nonlinear version, although other physical properties like force constant and bond length are described unsatisfactory. The planar Li6 ring is predicted to be stable in the equidistant form. Larger rings tend to have a Peierl’s distorted alternant geometry on the Hartree–Fock level. Thus Li behaves somewhat similar to (CH)n, while for Hn also the n=6 ring is distorted. The stability of equidistant six‐membered rings is therefore attributed to the existence of rather delocalized 2s electrons. The comparison of the results for Li6 clusters of different symmetry (D6h,Oh,C5v) with similar calculations reported in the literature indicates that the inclusion of p‐functions is essential, whereas the size of the s function subspace is not very important.

Extended coupled cluster method: Quantum many-body theory made classical

Abstract: We focus attention in this paper on how the general quantum many-body problem can be cast in the form of a variational principle for a specified action functional. After some preliminary discussion in Section 2 concerning the algebra of the many-body operators and the development of a convenient shorthand notation to describe it, we show in Section 3 how each of the configuration-interaction (CI)1 method, the normal coupled cluster method (CCM),2–6 and an extended version of the CCM,7,8 can be derived by specific parametrisations of the ground-state bra and ket wavefunctions in the action functional. In each case we make contact and comparison with time-independent perturbation theory, and we discuss the various “tree-diagram” structures that emerge in each case.

Use of molecular symmetry in coupled‐cluster theory

Abstract: It is shown that intermediate arrays resulting from the quasilinearization of coupled‐cluster theory with double excitations, and having the form of pseudointegrals 〈ab‖ij〉n, retain symmetry properties of the ordinary two‐electron integrals 〈ab‖ij〉. The 〈ab‖ij〉n elements vanishing on symmetry grounds may be eliminated a priori, as well as contributions to nonvanishing 〈ab‖ij〉n pseudointegrals from vanishing 〈ab‖ij〉n−1 or 〈ab‖ij〉 terms. A program using molecular symmetry in this way has been coded and its speed compared with that of gaussian 82.

The coupled-cluster approach to non-relativistic and relativistic many-body calculations

Abstract: A review is given of the atomic many-body theory in the coupled-cluster approach or exponential-Ansatz formulation Explicit equations and corresponding graphical representations are given in the pair-approximation, where the one- and two-body parts of the cluster (exponent) operator are considered Also the effect of a small, additional perturbation is considered The technique of evaluating diagrams by means of one- and two-particle functions, satisfying inhomogeneous differential equations, is reviewed Illustrative numerical results are given for the electron correlation energy, electron binding energy, hyperfine separation and specific mass shift of simple atomic systems The extension of the non-relativistic procedure to the relativistic regime is discussed by considering the effect of the exchange of one and two virtual, transverse photons between the electrons In lowest order this leads to the "no-virtual-pair approximation"