Showing papers on "Coupled cluster published in 1988"

Recent Progress in MANY-BODY THEORIES

Abstract: Ludwig Boltzmann: Recent Applications of Boltzmann's Theory (D. Rainer). Cycles of the Transition Processes as Basic Idea of Ludwig Boltzmann (V.I. Belinicher). Quantum Fluids: Recent Progress in the Theory of Highly Correlated Quantum Fluids (C.E. Campbell). Systematics and Numerics in Manybody Systems (M. Suzuki). Quantum Chemistry: Research of Appropriate Treatments of the Various Aspects of the Electron Correlation in Molecules and Their Interplay (J.P. Malrieu). A Coupled Cluster Approach to the Electron Correlation Problem Using a Correlated Reference State (D. Mukherjee). Nuclear Physics: Realistic Microscopic Calculations of Nuclear Structure (B.R. Barrett et al.). Microscopic Theories of Atomic and Nuclear Optical Potentials (C. Mahaux). Lattice Hamiltonians: Microscopic Theories of Quantum Lattice Systems (R.F. Bishop). A Nonperturbative Microscopic Theory of Hamiltonian Lattice Gauge Systems (R.F. Bishop et al.). Complex Systems: Complexity, Correlations, and Fluctuations in Manyparticle Systems (P.A. Carruthers). Solids: High Temperature Superconductors: A Review (E. Dagotto). Feenberg Medal Presentation: Pathways to the Quantum Realm (J.W. Clark). 28 additional articles. Index.

Spin‐adapted multireference coupled‐cluster approach: Linear approximation for two closed‐shell‐type reference configurations

Abstract: An explicit form of the spin‐adapted multireference coupled‐cluster formalism in the linear approximation is developed for the special case of a two‐dimensional model space involving only closed‐shell‐type configurations. The formalism is applicable to a number of quasidegenerate systems with two valence orbitals of distinct spatial symmetry and should serve as a convenient testing ground for the suitability of the multireference coupled‐cluster theory. General problems of the multireference coupled‐cluster approach and its relationship with the corresponding configuration interaction formalism are discussed as well as the problems pertaining to a practical implementation of this formalism.

Molecular applications of multireference coupled-cluster methods using an incomplete model space: Direct calculation of excitation energies

Abstract: A multireference coupled‐cluster (MRCC) formulation for the direct calculation of excitation energies and ionization potentials is presented. The reference space connects a set of p–h excited determinants built from all the set of active particles and holes in the model space. This model space is incomplete, requiring a Fock‐space approach and the postulate of a ‘‘universal’’ wave operator to arrive at a linked diagram expression for the effective Hamiltonian Heff, whose eigenvalues are the excitation energies for the problem. Use of a normal‐ordered exponential cluster ansatz allows one to construct, hierarchically, the CC equations for the p–h model space starting from the ground state. We present an extension of an earlier formulation for excitation energies that allows us to have both active and inactive particles and holes in our method. Numerical applications are reported for the prototypical small molecules CO and N2.

A unitary multiconfigurational coupled‐cluster method: Theory and applications

Abstract: A unitary wave operator exp(G) is used to relate a multiconfigurational reference function Φ to the full, potentially exact, electronic eigenfunction Ψ=exp(G)Φ. If the reference function Φ is of a generalized complete‐active‐space (CAS) form, then the energy, computed as 〈Φ‖exp(−G)H exp(G)‖Φ〉 is size extensive; here H is the full N‐electron Hamiltonian. The Hausdorff expansion of exp(−G)H exp(G) is truncated at second order as part of our development. The parameters which appear in the cluster operator G are determined by making this second‐order energy stationary. Applications to the widely studied H2O (at the double zeta basis level) and lowest and first excited 1A1 states of BeH2 are performed in order to test this method on problems where ‘‘exact’’ results are known.

On the necessity of f basis functions for bending frequencies

Abstract: The calculation of out‐of‐plane bending vibrations for π‐bonded systems appears to be extraordinarily sensitive to the choice of a one‐particle basis set. Ab initio predictions are reported for acetylene, an extreme example, at the self‐consistent field (SCF), singles and doubles configuration interaction (CISD), nth order Mo/ller–Plesset perturbation theory (MPn,n=2–4), coupled‐pair functional (CPF), and singles and doubles coupled cluster (CCSD) levels of theory. It is found that the addition of a set of f basis functions to the carbon atom changes the value of the SCF πg frequency by +45 cm−1, and the value of all correlated πg frequencies by more than +100 cm−1. Evidence is presented that this behavior is present in other π‐bonded systems. It is concluded that basis sets consisting of triple zeta plus two sets of polarization functions plus one set of f functions (TZ2P+f ) can predict highly accurate (∼1% average error) harmonic frequencies with the MP2, CPF, and CCSD methods, for a large number of m...

A coupled‐cluster method for quasidegenerate states

Abstract: A size-extensive, multireferences coupled-cluster method for studies of quasidegenerate states based on the Jeziorski–Monkhorst [16] ansatz for the cluster operator (Ω = ∑ePj, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., Tj ≈ Tj(2). The linear version of this method (MR L-CEPM) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) a model involving the C2ν insertion of Be into H2. For the first time in multireference coupled-cluster calculations, the nonlinear parts of the equations are completely accounted for. The MR CEPM results are very encouraging for strongly quasidegenerate states. The MR L-CEPM results are slightly below the accurate (FCI) values.

A systematic theoretical study of harmonic vibrational frequencies: The single and double excitation coupled cluster (CCSD) method

Abstract: Recently developed analytic CCSD gradient methods have been used to predict the harmonic vibrational frequencies of six molecules: CH4, NH+4, HCN, C2H2, HNC, and CO2. In every case a double zeta plus polarization (DZ+P) basis set of size C,N,O(9s5p1d/4s2p1d), H(4s1p/2s1p) was used. Previous analogous studies of H2O, H2CO, and NH3 are extended to form a statistical base of nine molecules. For these molecules 28 harmonic vibrational frequencies (out of total of 35 fundamentals) are thought to be known from experiment. The average errors with respect to experiment were found to be 9.1% (DZ+P self‐consistent field), 3.7% (DZ+P configuration interaction including single and double excitations), and 2.2% (DZ+PCCSD). These statistics should provide guidance for the use of the CCSD method in situations where experimental vibrational frequencies are not available. Infrared intensities are also compared with available experimental data.

Nuclear spin-spin coupling constant of hydrogen molecule with deuterium (HD)

Abstract: Using the coupled cluster, singles and doubles, polarization propagator approximation, the authors have calculated the nuclear spin-spin coupling constant of HD. They find that J/sub HD/ = 42.79 Hz, including all four terms (Fermi contact, spin-dipole, paramagnetic spin-orbit, and diamagnetic spin-orbit) as well as vibrational and Boltzmann averaging at 40 K. This is in good agreement with experiment, 42.94 +/- 0.04 Hz. Inclusion of very tight basis functions in the basic set is essential, as is a numerical determination of the vibrational correction amounting to 1.81 Hz. The improved treatment of the vibrational averaging also leads to an increase in literature values for the isotope shifts of J/sub HD/ (..delta..J/sub HD/ = 0.30 Hz).

The open‐shell coupled‐cluster method in general model space: Five states of LiH

Abstract: The open‐shell coupled‐cluster method is used to calculate the potential functions of the five lowest states of LiH, at internuclear separation of 2.0≤R≤10.0 bohr, with a 18σ9π2δ basis. The usual complete‐model‐space calculation diverges, and a general, incomplete model space, comprising the physically important 2σ 2, 2σ3σ, and 2σ1π configurations (but excluding the high‐energy determinants 3σ 2 and 1π 2 from the P space) is used. Good agreement with experimental molecular constants is obtained.

On expectation value calculations of one-electron properties using the coupled cluster wave functions

Abstract: The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (〈O〉=〈φ¦exp (T+)O exp (T)¦φ〉c) was truncated so that T1T2, T3, and (1/2) T2T2 clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T1, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.

Time‐dependent coupled cluster method: A new approach to the calculation of molecular absorption spectra

Abstract: The time‐dependent coupled cluster method is developed to provide a formally exact theory of quantum‐mechanical motion of a vacuum state on multidimensional anharmonic surfaces with a view to calculate the molecular absorption spectra. The exact time evolution operator is represented as an exponential of creation operators. Since the separability requirments of many‐particle systems are built into such an ansatz, it is possible to develop approximations which can take into account any number of modes with much less computational effort than in a calculation by basis‐set expansion. The method gives a closed set of equations for harmonic surfaces and finite ordered equations for anharmonic surfaces when truncated at some finite rank.

Coupled cluster polarisation propagator study of the photodetachment cross section of Li

Abstract: The photodetachment cross section of the lithium anion is studied in the coupled cluster polarisation propagator approximation (CCPPA). The discrete pseudospectra are analysed by moment theoretical methods. The all-electron CCPPA cross section of this work differs considerably from older calculations that involve pseudopotential approximations for the inner-shell electrons. Similarly, differences with the less correlated random-phase approximation are found, which indicate that the random-phase approximation is not suitable for the calculation of cross sections of Li-. The above method is also used to obtain for the first time inner-shell photodetachment cross sections for Li-. For both the valence-shell and the inner-shell cross sections there seem to be no experimental data available.

Atomic clusters and cluster models in solid state physics

Abstract: Since it became possible to study experimentally the evolution of a metal and the transition from atomic and molecular to surface and bulk properties, the study of clusters, especially metal clusters due to their role in heterogeneous catalysis, represents a highly active research area. On the other hand, clusters serve also as very useful models in solid state physics to investigate impurity, surface, and interface problems. Both cluster aspects will be discussed in addition to the role of cluster calculations in aperiodic polymer and band structure computations. We also report results of Li-cluster studies. Correlation effects, calculated with the coupled cluster method, are discussed in connection with the onset of Pierls' distortion in Li-rings. Finally, it is demonstrated how the cluster model is used to investigate polymer-metal surface interactions and how these interactions influence and change the polymer conformation.

The open‐shell coupled‐cluster method: Effect of single excitations on electronic transition energies

Abstract: Ionization potentials (IP) of H2O and alkali atoms, excitation energies (EE) of H2O, and electron affinities (EA) of alkalies are calculated by the open‐shell coupled‐cluster method with double excitations only (CCD). Comparison with previously reported computations including single and double excitations (CCSD) gives the contributions of the singles. These are very small (0.02 eV) for alkali atom IPs, larger (up to 0.09 eV, or 20%) for alkali EAs, and about 0.2 eV for the water molecule IPs and EEs. One‐half of the effect in water is assigned to single excitations from the closed shells.

Two-component Fermi systems: II. Superfluid coupled cluster theory

Abstract: In this second paper of a series the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi superfluids using a Bardeen-Cooper-Schrieffer (BCS) ground state as a zeroth-order approximation. We concentrate on developing the formalism necessary for carrying out eventual numerical calculations on realistic superconducting systems. We do this by generalising the one-component formalism in an appropriate manner and by using the results in the first paper of this series, where we studied two-component Fermi fluids. We stress the previous successes of the CCM, both from the point of view of analytic and numerical results, and we further indicate its potential for studying superconductivity. We restrict ourselves here to a so-called ring plus single particle energy (RING+SPE) approximation for general potentials and show how it can be formulated as a set of four coupled, bilinear integral equations for the cluster-integrated amplitudes. These latter amplitudes are themselves derived from the four-point functions of the system which provide a measure of the two-particle/two-hole component in the true ground-state wavefunction with respect to the BCS model state. We indicate how to obtain possible analytic solutions.

An approximate coupled cluster doubles polarization propagator approximation

Abstract: A polarization propagator method based upon an approximate coupled cluster doubles (ACCD) wavefunction is presented and applied to CH+ and Be in calculations of excitation energies and radiative lifetimes. It is found that in these cases the computational results are nearly identical to results obtained using a similar method based on the full coupled cluster doubles (CCD) reference state. Since ACCD is far less time-consuming than CCD the approximate coupled cluster doubles polarization propagator approximatior (ACCDPPA) should be an effective method for large scale computations preserving the quantitative reliability of CCDPPA.