Showing papers on "Coupled cluster published in 1984"

Generalized cluster description of multicomponent systems

Abstract: A general formalism for the description of configurational cluster functions in multicomponent systems is developed. The approach is based on the description of configurational cluster functions in terms of an orthogonal basis in the multidimensional space of discrete spin variables. The formalism is used to characterize the reduced density matrices (or cluster probability densities) and the free energy functional obtained in the Cluster Variation Method approximation. For the particular representation chosen, the expectation values of the base functions are the commonly used multisite correlation functions. The latter form an independent set of variational parameters for the free energy which, in general, facilitates the minimization procedure. A new interpretation of the Cluster Variation Method as a self-consistency relation on the renormalized cluster energies is also presented.

A linear response, coupled‐cluster theory for excitation energy

Abstract: Expressions for static and dynamic properties in coupled-cluster (CC) theory are derived. In the static case, using diagrammatic techniques, it is shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects. For the dynamic case, excitation energy expressions are obtained without consideration of orbital relaxation effects and shown to be equivalent to an equation of motion (EOM) approach subject to a coupled-cluster ground-state wave function and an excitation operator consisting of single and double excitations. Illustrative applications for excited states of ethylene are reported.

A coupled cluster approach with triple excitations

Abstract: The coupled‐cluster model for electron correlation is generalized to include the effects of connected triple excitation contributions. The detailed equations for triple excitation amplitudes are presented, and a simplified version implemented that retains the dominant terms. The model presented, CCSDT‐1, provides the energy correct through fourth order and the wave function through second order. The CCSDT‐1 model is illustrated by comparing with full CI results for HF, BH, and H2O, the latter at several geometries.

A study of Be2 with many‐body perturbation theory and a coupled‐cluster method including triple excitations

Abstract: The unusual potential energy curve for the 1∑+g ground state of Be2 is investigated using many‐body perturbation theory (MBPT) and coupled‐cluster (CC) methods. The curve, which has a ∼2 kcal/mol inner minimum at ∼2.6A and a van der Waals minimum at ∼5.0 A, is very difficult to describe accurately with even high‐level ab initio correlated methods. To resolve uncertainties in previous MBPT/CC studies, we have generalized CC theory to include effects of triple excitations. The present calculations are compared with recent full CI results to assess the relative importance of different contributions of electron correlation. MBPT (4) is found to be qualitatively correct, but to slightly exceed the correct full CI binding energy, while CC theory even with triple excitations, has no inner minimum. The latter follows from CC theory being exact for separated Be atoms (with frozen core) but to have a 1% correlation energy error in the binding region. Yet this 1% accounts for the ∼2 kcal/mol inner well. The possibil...

Analytical gradients for the coupled-cluster method†

Abstract: A nondiagrammatic formulation of the analytical first derivative of the coupled-cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree-Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first-order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non-perturbation-dependent set of equations can be solved instead. This and the first-order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. III. Coupled cluster treatment for He, Be, H2, and LiH

Abstract: Cižek’s coupled‐pair, many‐electron theory is formulated in a first‐quantized, basis set independent way. The resulting set of coupled integro‐differential equations for symmetry‐adapted spinless pair functions is then solved variationally using the basis set of explicitly correlated Gaussian geminals. In this way, accurate values of the correlation energies in both the linear and quadratic versions of the coupled‐pair theory are obtained for He, Be, H2, and LiH. These values are expected to be saturated up to within a fraction of 1%. For Be our results are practically identical with the basis set independent coupled‐pair energies obtained recently by Lindgren and Salomonson using an extensive partial‐wave expansion, two‐dimensional numerical integrations, and extrapolation techniques. For LiH, at the equilibrium separation of the nuclei, the correlation energy obtained using the complete coupled‐pair theory amounts to −81.5 mhartrees. Since the leading (fourth‐order) perturbation correction to this result is negative, this value can be viewed as a ‘‘perturbative’’ upper bound to the true nonrelativistic correlation energy. The linear coupled‐pair theory gives −82.7 mhartrees for the correlation energy of LiH; this value cannot be considered as an upper bound, however. The above results are to be compared with the estimated experimental correlation energy of LiH amounting to −83.2±0.1 mhartree. A simplified theory obtained by neglecting all four‐electron integrals in the quadratic part of the coupled‐pair equations has been tested. For both Be and LiH the correlation energies obtained differ by only a few hundredths of a mhartree from the complete coupled‐pair results.

Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. IV. A simplified treatment of strong orthogonality in MBPT and coupled cluster calculations

Abstract: A simplified strong orthogonality projection has been introduced for the use in the many body perturbation theory (MBPT) or coupled cluster method (CCM) calculations with explicitly correlated geminals. This approximate projection efficiently eliminates the undesired strong orthogonality violating components from the perturbative or CCM pair functions. Moreover it permits dropping the exact strong orthogonality projectors from the pair equations. This results in a dramatic simplification of atomic and molecular calculations with explicitly correlated geminals.

Coupled-cluster approach to electron correlation in one dimension. II. Cyclic polyene model in localized basis

Abstract: The many-electron correlation problem for one-dimensional metalliclike systems with Born--von K\'arm\'an boundary conditions, represented by the Pariser-Parr-Pople and the Hubbard Hamiltonian cyclic polyene models, ${\mathrm{C}}_{\mathrm{N}}$${\mathrm{H}}_{\mathrm{N}}$, N=2n=4\ensuremath{ u}+2, \ensuremath{ u}=1,2,..., is studied using the coupled-cluster approach in the localized Wannier basis representation. Various truncation schemes for the pair clusters are examined. It is shown that already the intracell pair-cluster approximation, which can be handled analytically and yields the same expression for the correlation energy as the variational approach of Ukrainskii, provides a reasonable approximation in the entire range of the coupling constant. Using all doubly excited clusters composed of locally excited particle-hole pairs, one obtains the exact correlation energy in the fully correlated limit assuming that the coupled-pair equations are corrected for the connected quadruply excited cluster contributions. This is achieved by using the recently developed approximate coupled-pair approach with corrections for the quadruply excited clusters (ACPQ), which is almost identical, except for a numerical factor of certain diagrams, with the standard approximate coupled-pair approach. The ACPQ approach removes the singularities which otherwise plague the standard coupled-pair approach and yields very good correlation energies in the entire range of the coupling constant even when the ${n}^{3}$ doubly excited pair clusters are truncated to only n+10 locally and quasilocally excited pair clusters in the localized Wannier basis representation.

Coupled-Cluster Methods for Molecular Calculations

Abstract: Coupled-cluster (CC) theory for the accurate treatment of electron correlation is presented including its similarities and differences from configuration interaction (CI). Topics addressed include computational aspects of the CC method; extended CC methods that include single, double, and triple excitation operators; and a multi-reference CC technique. Numerical examples illustrate CC results for correlation energies compared to those from full CI and multi-reference CI calculations.

Coupled-cluster method with optimized reference state

Abstract: We propose a variant of the coupled-cluster (CC) method in which spin orbitals of the reference Slater determinant are optimized in a self-consistent way This approach is a reformulation of the Brueckner–Hartree–Fock (BHF) method used in nuclear physics and known also as the exact SCF method We discuss the use of the reference-state determinants built of HF, natural, and Brueckner spin orbitals, with relations among them investigated in terms of the many-body perturbation theory (MBPT) It is shown that the Brueckner spin orbitals emerge as a convenient basis set in the coupled-cluster method and equations that determine these spin orbitals are found The Brueckner spin orbitals can be calculated as eigenvectors of a certain Hermitian one-electron operator which has a form of the Hartree–Fock operator plus a “correlation potential” depending linearly on two- and three- electron cluster amplitudes The usual decoupling scheme in the coupled-cluster method leads to a hierarchy of approximations; in the first nontrivial one the three-electron cluster amplitudes are neglected, and the two-electron ones are determined by solving Cižek's CPMET equations We also analyze the problem of spatial, spin, and time-reversal symmertry in the CC and BHF methods If (and only if) the reference-state determinant belongs to a one-dimensional representation of a certain symmetry subgroup of the system, the CC operator and the BHF one-electron operator are invariant with respect to this subgroup Thus the restricted (entirely symmetry-adapted) version of the BHF method can be formulated only for the closed-shell systems This is done for the above-mentioned approximate BHF method We discuss also the usefulness of the BHF method in application to extended metallic systems

A Full Coupled-Cluster Singles, Doubles, and Triples Model for the Description of Electron Correlation

Abstract: Equations for the determination of the cluster coefficients in a full coupled cluster theory involving single, double and triple cluster operators with respect to an independent particle reference, expressible as a single determinant of spin-orbitals, are derived The resulting wave operator is full, or untruncated, consistant with the choice of cluster operator truncation and the requirements of the connected cluster theorem A time-independent diagrammatic approach, based on second quantization and the Wick theorem, is employed Final equations are presented that avoid the construction of rank three intermediary tensors The model is seen to be a computationally viable, size-extensive, high-level description of electron correlation in small polyatomic molecules

Use of a unitary wavefunction in the calculation of static electronic properties

Abstract: A unitary coupled cluster method is advocated in this paper for the calculation of static properties. Corresponding to the perturbed Hamiltonian H(λ) including the relevant static property, a suitable unitary wavefunction is envisaged. It is shown that a specific nonvariational model of calculating various order static properties utilising this unitary ansatz results in simplifications compared to the previous Coupled Cluster Theories using only hole-particle excitation parameters formulated for this purpose.

Degeneracy and coupled-cluster approaches

Abstract: Problems which arise in the application of closed-shell coupled-cluster approaches to quasidegenerate or almost degenerate situations are discussed and the basic classification of quasidegeneracy types is outlined. Recent coupled-cluster results obtained for the cyclic polyene model, particularly in the strongly correlated limit, are briefly discussed and the unexpected features of approximate and localized coupled-pair approaches are pointed out.

A variational method to calculate static electronic properties

Abstract: Using a coupled cluster form of the wave function, a variational method is formulated for calculation of static properties of any order. Corresponding to an appropriate perturbed hamiltonian H(λ) including the relevant static property, a size consistent functional is set up. In a hierarchical fashion, properties of different orders may be found out using a variational method.

The Treatment of Electron Correlation: Where do We Go from Here?

Abstract: While substantial progress has been made in recent years in the methods and implementation of quantum chemical calculations, the results of such calculations still fall short, in many cases, of requirements. Generally, single-reference methods have difficulties in handling nondynamical correlation effects (which are due to near degeneracies of the reference function). The configuration interaction method easily deals with these effects by the use of multireference expansions, but has much greater difficulty than MBPT and coupled cluster methods in handling dynamical correlation because of its inability to treat disconnected cluster effects adequately. The most effective approach should combine a multiconfiguration reference function for the treatment of nondynamical correlation with a coupled cluster treatment (or a good approximation thereof) of dynamical correlation.

Use of cluster expansion techniques in quantum chemistry. A linear response model for calculating energy differences

Abstract: In this paper we have reviewed the theoretical framework of the coupled-cluster (cc) based linear response model as a tool for directly calculating energy differences of spectroscopic interest like excitation energy (ee), ionisation potential (ip) or electron affinity (ea). In this model, the ground state of a many-electron system is described as in a coupled cluster theory for closed shells. The electronic ground state is supposed to interact with an external photon field of frequencyw, and the poles of the linear response function as a function ofw furnish with the elementary excitations of the system. Depending on the general form of the coupling term chosen, appropriate difference energies like ee, ip or EA may be generated. Pertinent derivations of the general working equations are reviewed, and specific details as well as approximations for ee, ip or ea are indicated. It is shown that the theory bears a close resemblance to the equation of motion (eom) method but is superior to the latter in that the ground state correlation is taken to all orders and may be looked upon as essentially a variant of renormalisedtda. A perturbative analysis elucidating the underlying perturbative structure of the formulation is also given which reveals that the theory has a hybrid structure: the correlation terms are treated akin to an open shellmbpt, while the relaxation terms are treated akin to a Green function theory. A critique of the methodvis-a-vis other cc-based approaches for difference energies forms the concluding part of our review.

Coupled cluster equations for superconducting systems

Abstract: The coupled cluster formalism is combined with the Bogoljubov transformation to describe superconducting systems One obtains the well known BCS-formula $$\Delta _0 (k) = \smallint d^3 k'V_{eff} (k,k')\Delta _0 (k')/E(k')$$ as an exact result, valid for both weak and strong coupling superconductors The effective interaction can be calculated as a sum over some clusters

Linear coupled-cluster method. I. Exchange-correlation effects in atoms

Abstract: The linear coupled-cluster method and a hierarchy of its approximations are employed to investigate the Slater $X\ensuremath{\alpha}$ method and to study the exchange-correlation effects in the beryllium atom. An analysis of the various contributions to the exchange-correlation corrections to the total energy is made using the approximations to the coupled-cluster model. The total dominance of the valenceshell exchange-correlation corrections, the role of the single-particle excitation terms, and the relative importance of the ring- and ladder-diagram terms are gleaned from these calculations. The exchange parameter $\ensuremath{\alpha}$, for the calculation of the reference state, i.e., the $X\ensuremath{\alpha}$ orbitals, is chosen using the criterion that the total energy computed by the $X\ensuremath{\alpha}$ method be equal to the Hartree-Fock total energy for the atom. For this reference state, the total energy of the beryllium atom, with the inclusion of the exchange-correlation correction, is found to be - 14.663 598 hartrees, a value very close to the experimental energy of - 14.669 hartress. The $X\ensuremath{\alpha}$ method is seen to provide good single-particle reference states for many-body calculations.

Recent progress in many-body theories : proceedings of the Third International Conference on Recent Progress in Many-Body Theories held at Odenthal-Altenberg, Germany, August 29-September 3, 1983

Abstract: Quark clusters in nuclei.- Stochastic solution of nuclear models having sub-nuclear degrees of freedom.- Coupled-cluster theory of pions in nuclear matter and the EMC effect.- ?-Excitations and many-body theory of nuclear matter.- Random walk in fock space.- Nuclear matter properties in the BHF approximation with the Paris N-N potential and models of 3n interactions.- Three-body forces, relativistic effects, isobars and pions in nuclear systems.- Properties of matter in stellar collapse.- Hydrodynamics of ultra-relativistic heavy ion collisions.- Variational treatment of ? -condensed neutron matter in a realistic potential model.- Proton mixing in neutron star matter under ? condensation.- Tensor forces and the Fermi liquid properties of nuclear matter.- The effective mass in nuclear matter and in nuclei.- Deformations and correlations in nuclei.- Correlated pairs near the fermi surface.- Effective interactions and elementary excitations in electron and Helium liquids.- Old dogs and new tricks: Beyond the ground state with CBF theory.- Solution of the Ornstein-Zernike equation for non-uniform systems.- Jastrow-Slater trial energy for the low density hard sphere fermi gas.- Variational Monte Carlo approach on atomic impurities in 4He.- Density-fluctuation spectra of 3He-HeII mixtures at T=0 K.- Quantum-mechanical calculations of the properties of liquid He droplets.- Variational approach to two-component coulomb liquids.- Spin polarized 3He.- The properties of pauli enhanced normal Fermi liquids in finite magnetic fields.- Linear and non linear response.- Correlations and the possibility of a charge-density-wave (CDW) instability in quantum electron liquids.- CBF theory of metal surfaces: Chemisorption.- Melting of electrons on corrugated surfaces-structural and dynamical properties in liquid and solid phases.- Correlations in the layered electron-hole liquid.- Dense coulomb plasmas: Quantum statistics and ordering.- A conserving dynamic theory for the electron gas in metallic systems.- What present theory of superconductivity needs from many-body physicists.- Coupled cluster equations for superconducting systems.- Coupled cluster approach with explicitly correlated cluster functions.- Perturbation theory in a correlated basis.- Recent developments in a correlated theory of linear response.- Sum rules and a coupled cluster formulation of linear response theory.- Variational EXP S methods.- Computational quantum mechanics and the basis set problem.- Parquet perturbed.- Crossing symmetric rings, ladders, and exchanges.- New perturbation scheme for quantum fluids based on low-density expansions.- A direct access to many-body perturbation theory.- Beyond the Thomas-Fermi-Weizsacker-Dirac theory of electronic structure.- The closed time-path Green's function formalism in many-body theory.- Monte Carlo evaluations in finite fermionic systems.- Application of Green's function Monte Carlo to one-dimensional lattice fermions.- On the inverse problem in many body systems: From correlations to distribution function.- The interpolating equations method in quantum fluids.- Third International Conference on recent progress in many-body theories summary talk.

MULTICONFIGURATION COUPLED-CLUSTER CALCULA TIONS FOR EXCITED ELECTRONIC STATES: APPLlCATIONS TO MODEL SYSTEMS

Abstract: A multieonfigurational eoupled-cluster method previously developed in our laboratory is used to study excited states of the same spatial and spin symp1etry as the ground state. Applieations are made, with rather smali atomie orbital basis sets, to molecular systems whieh are highly eorrelated. These small-basis calculations are viewed on model ealculations whose value lies in the faet that one ean also obtain the exact (fuli configuration interaetion) energy in sueh eases. The results show that even though the eoupled-cluster equations may have many spurious solutions, one can locate solutions corresponding to the desired excited states by using proeedures similar to those utilized for ground states. To aehieve this success, one should include in the reference funetion all of the dominant eonfigurations of the state under eonsideration. Next, oneshould use the unique solution of the linearizedeoupled-cluster equations as the initial estimate to begin the solution of the non-linear eoupled-cluster equaCons. If the solution of these non-linear equations gives rise to one or more large t amplitudes one should repeat this proeedure but with the configuration eorresponding to the large / amplitude included in the referenee funetion.