Showing papers on "Coupled cluster published in 1986"
TL;DR: In this article, the second and third orders of Moller-Plesset perturbation theory are reformulated in terms of arbitrary (e.g., localized) internal orbitals, and atomic orbitals in the virtual space.
Abstract: Based on the Hylleraas functional form, the second and third orders of Moller-Plesset perturbation theory are reformulated in terms of arbitrary (e.g., localized) internal orbitals, and atomic orbitals in the virtual space. The results are strictly equivalent to the canonical formulation if no further approximations are introduced. The new formalism permits the extension of the local correlation method to Moller-Plesset theory. It also facilitates the treatment of weak pairs at a lower (e.g., second order) level of theory in CI and coupled cluster methods. Based on our formalism, an MP2 gradient algorithm is outlined which does not require the storage of derivative integrals, integrals with three external MO indices, and, using the method of Handy and Schaefer, the repeated solution of the coupled-perturbed SCF equations.
474 citations
TL;DR: In this article, it is shown that if only excitation energies, rather than the full wave-operator Ω, are desired, then no theoretical error is made, and the theoretical status of earlier applications which had used formulae appropriate to IN, yet ignored disconnected diagrams, is analyzed.
151 citations
TL;DR: In this paper, the excitation energies can be obtained as eigenvalues of a generally non-Hermitian matrix characterizing the homogeneous part of a linear response equation and the explicit form of the required matrix elements in the orthogonally spin-adapted version of the theory is given for configuration spaces restricted to single and double excitations.
Abstract: In the time‐dependent coupled cluster approach the excitation energies can be obtained as eigenvalues of a generally non‐Hermitian matrix characterizing the homogeneous part of a linear response equation. This matrix consists of the Hermitian configuration interaction part as well as of a non‐Hermitian part which describes the ‘‘renormalization’’ due to ground state correlations. The relationship between a singular behavior of the ground state coupled cluster equations and the existence of vanishingly small excitation energies in the linear response formalism is pointed out. The explicit form of the required matrix elements in the orthogonally spin‐adapted version of the theory is given for configuration spaces restricted to single and double excitations. A numerical test of the formalism for π‐electron models of trans‐butadiene and benzene is carried out and the relationship of the time‐dependent coupled cluster approach with other many body approaches to excitation energies calculation is discussed.
131 citations
TL;DR: In this article, a coupled cluster doubles (CCD) reference state within the framework of perturbative propagator methods is applied to the lowest singlet and triplet excitations in CH+.
Abstract: A new approach to the direct evaluation of excitation energies and transition moments from the polarization propagator is presented. The method, which uses a coupled cluster doubles (CCD) reference state within the framework of perturbative propagator methods, is applied to the lowest singlet and triplet excitations in CH+. Comparison of the coupled cluster doubles polarization propagator approximation (CCDPPA) results with experiments and standard perturbative polarization propagator calculations shows that a significant improvement is obtained with a coupled cluster rather than a Rayleigh–Schrodinger reference state: the singlet excitation energy is improved by about 0.5 eV and the triplet instability of the standard second order approach is removed. The radiative lifetime of the v’=0 level of the A 1Π state is estimated to be very close to 800 ns. The improved performance of the coupled cluster propagator method over propagator calculations based on Rayleigh–Schrodinger expansion mainly stems from a en...
87 citations
01 Jan 1986
TL;DR: In this article, a diagrammatic derivation of the coupled-cluster (CC) linear response equations for gradients is presented, where MBPT approximations emerge as low-order iterations of the CC equations.
Abstract: A diagrammatic derivation of the coupled-cluster (CC) linear response equations for gradients is presented. MBPT approximations emerge as low-order iterations of the CC equations. In CC theory a knowledge of the change in cluster amplitudes with displacement is required, which would not be necessary if the coefficients were variationally optimum, as in the CI approach. However, it is shown that the CC linear response equations can be put in a form where there is no more difficulty in evaluating CC gradients than in the variational CI procedure. This offers a powerful approach for identifying critical points on energy surfaces and in evaluating other properties than the energy.
59 citations
TL;DR: In this paper, an open-shell coupled-cluster method for the direct calculation of excitation energies is presented, with exact inclusion of T 1 and T 2, operators and lowest-order inclusion of t 3.
54 citations
TL;DR: In this paper, a local space approximation for the Hartree-Fock model of electronic structure is extended to configuration interaction and coupled cluster wave functions, which makes it feasible to study localized electronic structure changes in large systems.
Abstract: A local space approximation developed originally for the Hartree–Fock model of electronic structure is extended to configuration interaction and coupled cluster wave functions. In doing so many features employed by Saebo and Pulay in their local CI method are used to advantage. The computational effort is reduced to operations primarily on the local space (≡interaction complex) thereby making it feasible to study localized electronic structure changes in large systems. Charge transfer and polarization effects due to embedding the interaction complex in the surrounding medium are taken into account.
51 citations
TL;DR: In this paper, an open-shell coupled-cluster method for the direct calculation of excitation energies is presented and applied to excitations of atomic Mg and Ar. The so-called CCSD + T approximation involves the exact inclusion of T1 and T2 operators and the lowest-order inclusion of t3.
Abstract: An open-shell coupled-cluster method for the direct calculation of excitation energies is presented and applied to excitations of atomic Mg and Ar. The so-called CCSD + T approximation involves the exact inclusion of T1 and T2 operators and the lowest-order inclusion of T3. Quasi-complete model spaces, built from determinants with one valence hole and one valence particle, are used. Two ionization potentials and 20 excitation energies are calculated. Good agreement with experiment (˜0.2 eV) is obtained. The T3 effects are less important than for the Be and Ne atoms.
48 citations
TL;DR: In this paper, a variational open-shell coupled-cluster method was applied to the calculation of H2O and N2 ionization potentials in the T ≈ T2 approximation.
Abstract: A hermitian, variational open-shell coupled-cluster method is described and applied to the calculation of H2O and N2 ionization potentials in the T ≈ T2 approximation. A nonvariational calculation is also carried out, with the inclusion of T1 and T3 in addition to T2. Both methods give fair agreement with experiment when only T2 is taken into account. T3, which is included at present in the nonvariational scheme only, has a considerable effect on the results and gives good agreement with experiment.
48 citations
TL;DR: In this article, the authors reported the coupling constants calculated for the HD and HF molecules obtained by the infinite-order coupled cluster singles and doubles (CCSD) methods and MBPT(4).
Abstract: In nuclear spin–spin coupling constant determinations, correlation corrections to the Fermi contact term are significant. In this paper we report the coupling constants calculated for the HD and HF molecules obtained by the infinite‐order coupled cluster singles and doubles (CCSD) methods and MBPT(4). These are in good agreement with the experimentally estimated value for the Fermi‐contact term. In addition, it is well known that the coupled perturbed Hartree–Fock (CPHF) scheme fails for multiply bonded molecules because the closed shell Hartree–Fock solution is triplet unstable. A CCSD method using ordinary nonrelaxed SCF orbitals is presented in order to circumvent this problem, and illustrated by application to the C2H4 molecule. It is shown that CCSD results based upon ordinary SCF orbitals include effectively all the effect of orbital relaxation and reproduce the experimental values for most of the coupling constants. Unlike previous results, the 3J(H–H) constant is positive in agreement with experiment.
46 citations
TL;DR: The first ab initio molecular applications of the open-shell coupled cluster (CC) method for direct calculation of energy differences are reported in this article, starting from the zero-valence ground-state problem, various one-, two-, ⋯ m -valence problems are hierarchically generated.
TL;DR: In this article, it was shown that the open-shell coupled cluster (CC) theory is not inconsistent with the assumption of intermediate normalization, and that all the discussions on the appearance of unlinked diagrams based on the implicit use of normalization are invalid.
Abstract: In this paper we have demonstrated the following aspects of the open-shell coupled cluster (CC) theory when the model space consists ofmp-mh determinants: (I) If no other subsidiary conditions (besides the ‘minimality’ requirementPSP=0) on the normalization of the wave functions are imposed, then the demand that the wave operator admits of the corevalence separation of energy is inconsistent with the assumption of intermediate normalization. Thus all the discussions on the appearance of unlinked diagrams based on the implicit use of intermediate normalization are invalid. (ii) The open-shell CC developments of Mukherjeeet al are independent: of the normalization of the wavefunctions and the linked cluster theorems and the core-valence separation derived by them are valid formp-mh model space functions. In particular it has been shown that there are two different cluster ansatz for which the aspect (iii) above is valid. For a valence-universal wave operator ω admitting of a corevalence separation, it has been proved that the CC equations are linked as a consequence of the multicommutator nature of the expressions. There is a choice between two alternative schemes: one in whichS operators connecting all thekp-kh determinants withk m are retained, and another in which transitions fork
TL;DR: The anharmonic oscillator model is treated both in the maximum-overlap condition and in the Hartree approximation, and the ground-state energy is reproduced very well for all values of the coupling strength and already for a low-order truncation scheme.
Abstract: Recent applications of the coupled-cluster method to the (${\ensuremath{\varphi}}^{4}$${)}_{2}$ quantum field theory showed the necessity of a detailed analysis of its convergence behavior. The anharmonic oscillator has always served as a good test case for different approximation schemes. We treat the model both in the maximum-overlap condition and in the Hartree approximation. The ground-state energy is reproduced very well for all values of the coupling strength and already for a low-order truncation scheme. The expansion in correlation amplitudes can be carried out in extremely high order and shows a divergent tendency of the amplitudes. Introducing temperature dependence allows us to select the stable ground state out of a variety of solutions of the hierarchy of equations.
TL;DR: An analysis of some of the coupled-cluster methods has been undertaken for the calculation of first-order properties and it has been shown that Arponen's variational extended exp(T) method truncated to the quadratic power in the cluster amplitudes gives a result identical to the average value of the property operator with the linearized coupled-Cluster doubles (L-CCD) stationary state.
Abstract: An analysis of some of the coupled-cluster methods has been undertaken for the calculation of first-order properties. In particular, it has been shown that Arponen's variational extended exp(T) method truncated to the quadratic power in the cluster amplitudes gives a result identical to the average value of the property operator with the linearized coupled-cluster doubles (L-CCD) stationary state truncated to the quadratic power in amplitudes in the model where only two-body excitations have been included in the cluster amplitudes. In the same model it is also shown that Monkhorst's nonvariational method gives results identical to the previously mentioned average value again truncated to the quadratic power in amplitudes with a full CCD stationary-state wave function.
TL;DR: In this article, the interaction energy of two water molecules is evaluated at several levels of theory in a better than double zeta plus polarization basis set, and the CCSD+T(CCSD) results should be quite close to the full CI result in this case.
Abstract: The interaction energy of two water molecules is evaluated at several levels of theory in a better than double zeta plus polarization basis set. Our CCSD+T(CCSD) results should be quite close to the full CI result in this case. Results are compared with variation–perturbation results for the dispersion energy. Counterpoise-corrected correlated results are used to examine the importance of basis set superposition effects in this system.
TL;DR: The (nonperturbative) coupled cluster method is applied to the pion-nucleon system and a reasonable description of the deuteron is obtained.
Abstract: The (nonperturbative) coupled cluster method is applied to the pion-nucleon system. After solving the vacuum and one-nucleon problem, a reasonable description of the deuteron is obtained.
TL;DR: It is shown that the set of stationarity equations of scrJ H λ with respect to arbitrary variation of the cluster parameters of T(λ) and T"(λ) corresponding to any power of λ is the same for certain conditions and furnishes all the relevant values of cluster parameters.
Abstract: A bivariational coupled-cluster method is advocated for the calculation of static electronic properties for closed-shell atomic and molecular systems. The proposed method uses a perturbed form of the Hamiltonian H(λ) which includes the field with which the system interacts, giving rise to the response in various orders. Higher-order properties can be calculated without the use of excited states. A novel linked energy functional scrJ H λ [T,T"] is used with two different types of cluster parameters T(λ) and T"(λ), each of which is a power series in λ. Unlike the Euler energy functional proposed in one of our earlier works, this functional is a terminating series in cluster parameters. It is shown that the set of stationarity equations of scrJ H λ with respect to arbitrary variation of the cluster parameters of T(λ) and T"(λ) corresponding to any power of λ is the same for certain conditions and furnishes all the relevant values of cluster parameters. The equations are derived for calculating static properties to any order with these stationary optimum values.
TL;DR: In this article, the approximate coupled cluster doubles (ACCD) approximation is tested, both at the infinite-order level and at the fourth order of many-body perturbation theory, and it is found that in the presence of strong pair coupling, there is a substantial deviation between the ACCD and the full representation of unlinked clusters of double substitutions at the additive fourth order level.
TL;DR: In this paper, the three lowest states of LiF − have been studied using a combination of numerical Hartree-Fock orbitals and Slater type orbitals as a basis set for coupled cluster calculations.
TL;DR: In this article, it was shown that for the beryllium atom most of the valence electron correlation energy can be obtained with only three equivalent excitations, and that this is possible also with one primitive set of p-type gaussians, provided their exponent is carefully optimized.
01 Jan 1986
TL;DR: In this paper it is assumed that the authors want to calculate the wave function of one or many body systems by using some simple “starting wave functions” φ to describe the Hamiltonian H.
Abstract: In this paper it is assumed that we want to calculate the wave function of one or many body systems. If the Hamiltonian H is sufficiently complicated, the standard approach is by using some simple “starting wave functions” φ. On top of them one puts those parts which are complicated and typically require sophisticated and/or extended numerical methods.
01 Jan 1986
TL;DR: Very accurate methods that combine purely numerical solutions to Hartree-Fock and Bethe-Goldstone equations for orbitals, with coupled-cluster and many-body perturbation methods for electron correlation, are able to obtain 99% of the correlation energy of LiH and 97% for FH as mentioned in this paper.
Abstract: Correlation energies and electron affinities for ground and excited states of polar diatomic systems are investigated. Very accurate methods that combine purely numerical solutions to Hartree-Fock and Bethe-Goldstone equations for orbitals, with coupled-cluster and many-body perturbation methods for electron correlation, are able to obtain 99% of the correlation energy of LiH and 97% for FH. Such methods are thought to be sufficiently accurate that it is meaningful to use these techniques to obtain correlated electron affinities for excited states of diatomic molecules. The first results for excited state affinities are reported for BeO and LiH.
TL;DR: In this article, the results of outer and inner valence IP calculations for the HF molecule using two different many-body methods for the direct evaluation of energy differences are reported, using a Huzinaga-Dunning (9s5p→ 5s3p/3s) basis.
Abstract: We report in this paper the results of outer and inner valence IP calculations for the HF molecule using two different many-body methods for the direct evaluation of energy differences. The first is the nonperturbative coupled-cluster based linear response theory (LRT) and the second is the hermitian open-shell many-body perturbation theory (MBPT). A Huzinaga-Dunning (9s5p→ 5s3p/3s) basis has been used. LRT uses an "ionization operator" S as in the equation of motion method (EOM) to generate the ionized states from a coupled-cluster type of ground state. S is chosen to consist of single ionization and ionization-cum-shake-up operators, thus treating the Koopmans as well as the shake-up states on equal footing. LRT would thus be capable of computing both the outer and the inner valence regions with equal facility. This is borne out by the results. For the open-shell MBPT, the model space is chosen to be spanned by the singly ionized determinants. The convergence of the results for the inner valence region is slow, and the results obtained from the [2, 1] Pade' approximants are presented. Unlike the LRT, the inner valence region is not reproduced with full complexity in MBPT, indicating that it is essential to modify the theory by way of expanding the model space to contain the shake-up determinants also.