Multi-reference coupled-cluster study of the ionic-neutral curve crossing LiF

The recently developed exponential multi-reference wavefunction ansatz [J. Chem. Phys. 123 (2005) 84102] and the single-reference formalism multi-reference coupled cluster ansatz [J. Chem. Phys. 94 (1991) 1229] are applied to calculate the potential energy surface of LiF. The avoided crossing region for the ionic and the covalent ¹Σ⁺ states are analysed using plain self-consistent field and state averaged complete active space orbitals. Additionally, dipole moments are reported. All results are discussed and compared with full and multi-reference configuration interaction calculations.     

A state-specific multi-reference coupled-cluster approach with a cost-effective treatment of connected triples: implementation to geometry optimisation

Recently, we have suggested an approximate state-specific multi-reference coupled-cluster (SS-MRCC) singles, doubles and triples method based on the CCSDT-1a+d approximation applied to the single-reference CC approach, in which the contribution of the connected triple excitations is iteratively treated. The method, abbreviated as SS-MRCCSDT-1a+d is intruder-free and fully size-extensive. It has been employed for geometry optimisations of various systems possessing quasi-degeneracy of varying degrees (like N₂H₂ and O₃) by invoking numerical gradient scheme. The method is also applied to CH₂ and square cyclobutadiene in their excited states. For all systems under study, the computed values are in good accordance with state-of-the-art theoretical estimates indicating that the method might be a promising candidate for an accurate treatment of geometrical parameters of states plagued by electronic degeneracy in a computationally tractable manner.     

Benchmark calculations using the individually selecting configuration interaction method

Further progress is reported on the implementation of the configuration-selecting multi-reference configuration interaction method for massively parallel architectures with distributed memory which allows calculations with Hilbert spaces in excess of 10¹¹ configurations, 2 × 10⁷ of which can now be included in the variational subspace. This code makes it possible to elucidate the importance of the correlated treatment of triple and quadruple excitations into the (3s3p) shell of the oxygen molecule, to account quantitatively for its electron affinity. Also included are extensive calculations to elucidate the reaction pathways of members of the enediyne family.     

Structure and dynamics of cationic van-der-Waals clusters

The geometric structure and bonding properties of medium-sized ArnH+ clusters (n = 2–35), in which a proton is wrapped up in a number of Ar atoms, are investigated by applying a diatomics-in-molecules (DIM) model with ab-initio input data generated by means of multi-reference configuration-interaction (MRCI) computations. For the smaller complexes, n = 2–7, cross-checking calculations employing the coupled-cluster approach (CCSD) with the same one-electron atomic basis set as for the input data calculations (aug-cc-pVTZ from Dunning), show good agreement thus justifying the extension of the DIM study to larger n. Local minima of the multi-dimensional potential-energy surfaces (PES) are determined by combining a Monte-Carlo sampling followed, for each generated point, by a steepest-descent optimization procedure. For the electronic ground state of the ArnH+ clusters, the global minimum (corresponding to the most stable structure of the cluster) as well as secondary minima are found and analyzed. The structural and energetic data obtained reveal the building-up regularities for the most stable structures and make it possible to formulate a simple increment scheme. The low-lying excited states are also calculated by the DIM approach; they all turn out to be globally repulsive.     

State-specific multireference complete-active-space coupled-cluster approach versus other quantum chemical methods: dissociation of the N2 molecule

A comprehensive comparison of different quantum-chemical methods applied to calculate the N₂ ground state potential energy curve is presented. In the comparison we highlight the multireference state-specific (MRSS) coupled-cluster (CC) approach with the complete-active-space (CAS) reference and with single and double excitations from all reference determinants in the CC operator developed in our group. The method is called CASCCSD. The energy and amplitude equations for the method and the corresponding computer code have been generated using a computerized automative procedure that in the present work was extended to produce a parallel computer code. The complete CASCCSD wave function for N₂ includes some selected eight-fold excitations in the CC operator. An analysis of the wave function estimates the importance of those excitations at large internuclear separations.     

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

ABSTRACT

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H²-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.     

High-performance algorithm for calculating non-spurious spin- and parity-dependent nuclear level densities

A new high-performance algorithm for calculating the spin- and parity-dependent shell model nuclear level densities using methods of statistical spectroscopy in the proton-neutron formalism was recently proposed. When used in valence spaces that cover more than one major harmonic oscillator shell, this algorithm mixes the genuine intrinsic states with spurious center-of-mass excitations. In this Letter we present an advanced algorithm, based on the recently proposed statistical moments method, that eliminates the spurious states. Results for unnatural parity states of several sd-shell nuclei are presented and compared with those of exact shell model calculations and experimental data.     

Testing a New Class of Phonon Operators for RPA-Like Calculations Within an Exactly Solvable Model

Working in a boson formalism, we introduce a phonon operator different from that commonly used in RPA calculations. As a major feature, this new phonon operator has a vacuum carrying only a limited number of particle-hole excitations. Therefore, the form of this vacuum is quite different from the exponential one of the RPA. In addition, multiphonon excitations have a particle-hole structure never exceeding in complexity that of this vacuum, no matter how large is the number of phonons involved. We present the results of some preliminary tests performed within the exactly solvable two-level Lipkin model.     

Molecular cluster perturbation theory. I. Formalism

We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.     

Theoretical overview of atomic parity violation

Recent advances in interpreting the most accurate-to-date measurement of atomic parity violation in Cs are reviewed. The inferred nuclear weak charge, Q _W( ^133Cs ) = - 72.65(28)_expt(36)_theor , agrees with the prediction of the standard model at 1σ level. Further improved interpretation is limited by an accuracy of solving the basic correlation problem of the atomic structure. We report on our progress in solving this problem within the relativistic coupled-cluster formalism. We include single, double and triple electronic excitations in the coupled-cluster expansion. Numerical results for energies, electric-dipole matrix elements, and hyperfine-structure constants of Cs are presented.     

Variable operator technique and the min-max theorem

We investigate a variation method where the trial function is generated from the application of a variable operator on a reference function. Two conditions are identified, one for obtaining a maximum and another for a minimum. Although the conditions are easy to understand, the overall formulation is somewhat unusual as each condition gives rise to a two-step variation process. As an example, projection operators are used to form the variable operator, and by this tactics one obtains the new interpretation that the pseudopotential formalism is in fact equivalent to a minimax procedure. The two-step variational process is nevertheless more flexible than the pseudopotential formalism, for it can also be used when the variable operator is not manifestly expressed in terms of projectors. This is illustrated by a comparison of the two-step method with the variational solution of Dirac’s relativistic electron equation. The same comparison leads to an alternative proof that the process of maximizing energy by varying the u–l coupling operator eliminates all negative-energy contributions from a trial spinor. The latter observation is crucial for the derivation of the min-max theorem in relativistic quantum mechanics.     

On the computation of electronic excitations in solids

An approximation scheme is proposed for calculating electronic excitations in solids. It is described within a projection operator formalism of the Mori-Zwanzig type. The approximation consists in successively limiting the space of dynamical variables which are treated. The selection of the variables is done by making use of the local character of the correlation hole which is surrounding an electron. The method is distinct from a perturbation expansion and can be related to a variational ansatz via the Sauermann functional. The computation of the spectral density of the Green's function is reduced to the diagonalization of matrices. Their dimension depends on the required degree of accuracy of the calculations. The present method can be considered as an extension to excited states of a previously developed. Local Approach for ground state calculations.Dedicated to Prof. S. Methfessel on the occasion of his 60th birthday     

On the hierarchy equations of the wave-operator for open-shell systems

Starting with the open-shell analogue of the Gell Mann-Low theorem of many-body perturbation theory, a non-perturbative linear operator equation is derived for the linked part of the wave-operatorW for open-shell systems. It is shown that, for a proper treatment of the linked nature of the wave-operator, a separation into its connected and disconnected components has to be made, and this leads to a hierarchy of equations for the various connected components. It is proved that the set of equations can be cast into a form equivalent to the non-perturbative equations of the wave-operator recently derived by Mukherjee and others in a coupled-cluster or exp(T) type formalism if a consistent use is made of a ‘core-valence separability’ condition introduced earlier. A comparison of the coupled-cluster representation ofW with the perturbative representation reveals that various alternative forms ofW in the coupled-cluster representation are possible and these reflect alternative ways of realising the core-valence expansion of the wave-operator. In particular it is emphasised how the use of Mandelstam block-ordering simplifies the coupled-cluster theories to a considerable extent and a comparison is made with coupled-cluster methods for open-shells put forward very recently by Ey and Lindgren. Finally, it is shown how difference energies of interest may be derived in a compact manner using the Mandelstam block-ordering of the wave-operator.     

Interpretation of the electronic spectra of phthalocyanines with transition metals from quantum-chemical calculations by the density functional method

Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of some metal phthalocyanines of transition metals and of their anionic forms with different electron localization are studied quantum chemically. It is shown that, in all the cases studied, calculations using the B3LYP functional with even a comparatively narrow basis set (6–31G) are quite consistent with the previous calculations of the same objects by the ZINDO/S-CI semiempirical method taking into account double excitations. For a number of particular examples, it is shown that a lack of consideration of doubly excited configurations in the calculation of excited states by the TDDFT method can be compensated by the contribution from single excitations, which proves to be more significant due to the presence of the correlation component of the exchange-correlation functional.     

Coupled-cluster and configuration-interaction calculations for odd-A heavy nuclei

We compare coupled-cluster (CC) and configuration-interaction (CI) results for 55Ni and 57Ni obtained in the pf-shell basis, focusing on the practical equation-of-motion (EOM) CC approximations that can be applied to systems with dozens of correlated fermions. The weight of the reference state and the strength of correlation effects are controlled by the gap between the f7/2 orbit and the f5/2, p3/2, p1/2 orbits. Independent of the gap, the CC methods with up to 2p-2h components in the cluster operator and 3p-2h/3h-2p components in the EOMCC excitation operator are more accurate than the computationally more demanding CI approach with up to 3p-3h excitations and almost as accurate as the even more demanding CI approach truncated at 4p-4h excitations.     

Highly accurate excited-state energies from direct computation of the 2-electron reduced density matrix by the anti-Hermitian contracted Schrödinger equation

ABSTRACT

Directly solving for the 2-electron reduced density matrix (2-RDM) via the anti-Hermitian contracted Schrödinger equation (ACSE) enables computations for excited states energies without the N-electron wave function. Of particular interest are excitations and dissociation curves that exhibit strong multi-reference correlation effects. The ground and excited states of the molecules HF, H₂O, and N₂ are examined at both equilibrium and non-equilibrium geometries to compare the ability of the ACSE and widely used ab initio techniques to treat strong multi-reference electron correlation. Calculations are performed with double-ζ basis sets for calibration with full configuration interaction (FCI). Multi-reference second-order perturbation theory (MRPT2) and the ACSE both provide qualitative precision with respect to FCI data, although the ACSE's capability to include higher order correlation effects permits near-FCI accuracy for ground and excited states and excitation energies.     

Vacuum-ultraviolet plasma Frenkel excitons: Elementary excitations of polymerized fullerene

The high-frequency excitations of the molecular insulator C₆₀ are investigated theoretically. The model of a quantum well rolled into a sphere is used to calculate the dipole (multipole in the general case) modes of an individual C₆₀ cluster. If the spectrum and oscillator strengths of the collective modes of an individual cluster are known, the microscopic continuum approach can be used to calculate the spectrum of delocalized excitations in a cluster crystal. Then the ordinary dielectric constant formalism permits calculation of the optical characteristics of the material in the vacuum ultraviolet region studied. Fiz. Tverd. Tela (St. Petersburg) 40, 913–915 (May 1998)