Finite-field many-body perturbation theory quadrupole polarizability of Be

Many-body perturbation theory is used for the calculation of the quadrupole polarizability of the Be atom within the finite-field perturbation scheme. The correlation corrections exhibit a considerable dependence on the f-type orbital exponents and the final results are in the range 287–294 au. The convergence of the correlation perturbation series is discussed.     

Finite-field many-body perturbation theory. VI. Multipole polarizabilities of beryllium. A comparative study

A high-resolution ESCA N1s spectrum from free p-aminobenzonitrile molecules is presented. The spectrum is very different from the corresponding spectrum from a solid sample. It shows one uncommonly intense shape-up line from the N1s ionization in the nitrile group, while ionization in the NH₂ group does not give rise to any such anomalous shake-up features. The spectrum is theoretically analyzed by means of a large-scale ab initio calculation by the CAS SCF method, in which a full π-orbital active space was employed for the ground and N1s ionic states. The calculations strongly underline the role of multiple excitations in the charge transfer following N1s(CN) ionization, as well as the importance of separate self-consistent treatment of all states involved. In particular, it is shown that an unsuitable choice of orbitals can lead to an apparent “shake-down”.     

Finite-field many-body perturbation theory IV. Basis set optimization in MBPT calculations of molecular properties. Molecular quadrupole moments

The choice of truncated basis sets and their optimization for MBPT calculations of molecular properties are discussed. It is pointed out that computing the correlation corrections to some kth order property by using the MBPT approach requires the knowledge of accurate perturbed orbitals through the kth order. Hence, it is argued that the basis set functions can be optimized with respect to the perturbed energies calculated within the coupled Hartree-Fock method. The proposed procedure is illustrated by MBPT calculations of quadrupole moments of H₂ and FH. Additionally, also some estimates of the quadrupole polarizability tensor components for these molecules are obtained.     

Finite-field many-body perturbation theory. Calculations of the dipole polarizability of the fluoride ion using electric-field-variant gaussian-type orbitals

The dipole polarizability of the fluoride ion, F^–, is calculated using finite-field many-body perturbation theory. The use of electric-field-variant basis sets in such calculations is investigated. Scaling of the zero-order Hamiltonian and the formation of Padé approximants are considered. Empirical and theoretical estimates of the polarizability of F^– are compared.Science Research Council Advanced Fellow.     

Electric dipole polarizability of the hydrogen molecule by many-body perturbation theory

Many-body perturbation theory is used to calculate the static electric dipole polarizability of the hydrogen molecule with a basis set of gaussian orbitals. Corrections complete through second order in electron correlation are calculated, and partial summation of certain classes of diagrams are extensively explored. The results are discussed in connection with the geometric approximation incorporating higher-order corrections.     

Sixth-order many-body perturbation theory. I. Basic theory and derivation of the energy formula

The general expression for the sixth-order Møller-Plesset (MP6) energy, E(MP6), has been dissected in the principal part A and the renormalization part R. Since R contains unlinked diagram contributions, which are canceled by corresponding terms of the principal part A, E(MP6) has been derived solely from the linked diagram terms of the principal part A. These have been identified by a simple procedure that starts by separating A into connected and disconnected cluster operator diagrams and adding terms associated with the former fully to the correlation energy. After closing all open disconnected cluster operator diagrams, one can again distinguish between connected and disconnected energy diagrams, of which only the former lead to linked diagram representations and, therefore, contributions to E(MP6). The connected diagram parts of A have been collected in four energy terms E(MP6)₁, E(MP6)₂, E(MP6)₃, and E(MP6)₄. The sum of these terms has led to an appropriate energy formula for E(MP6) in terms of first- and second-order cluster operators. © 1996 John Wiley & Sons, Inc.     

Use of noncanonical orbitals in many-body perturbation theory

A formalism for dealing with noncanonical Hartree–Fock spin orbitals is presented within the framework of many-body perturbation theory. A test calculation on the planar methyl radical is carried out which displays certain features of open-shell calculations and which demonstrates the viability of using noncanonical spin orbitals. Results are found to be in good agreement with a previous configuration interaction calculation.     

Applicability of multireference many-body perturbation theory to the Ne2+ molecule

The ground state as well as some low-lying excited states of the Ne₂⁺ molecule are calculated by means of the third-order multireference many-body perturbation theory with the “full” eight-orbital valence space using DZP and polarized valence TZ basis sets. The problem encountered with a large number of valence electrons is avoided by a proper definition of the Fermi vacuum. The calculated equilibrium distance of 1.721 Å and chemical dissociation energy D₀ = 1.283 eV are in good agreement with experimental results. A comparison with other ab initio techniques is also provided. © 1997 John Wiley & Sons, Inc.     

Finite-field many-body perturbation theory II. SD-MBPT study of the nuclear charge dependence of the electron correlation contribution to the dipole polarizability of 10-electron atomic systems

The finite-field many-body perturbation theory limited to intermediate states involving single and double substitutions in the reference HF determinant is applied to the calculation of dipole polarizabilities of 10-electron atomic systems. The nuclear charge dependence of the convergence of the SD-MBPT series for correlation corrections to the dipole polarizability is investigated. It is concluded that the fourth-order SD-MBPT scheme is quite appropriate for neutral and positively charged species. For negatively charged systems the convergence of the SD-MBPT series becomes much poorer and including higher-order substitutions may be necessary. The role of the renormalization contributions to the SD-CI polarizability results is also considered. It follows that the corresponding data need to be corrected for the erratic treatment of unlinked clusters. The size inconsistency effects make quite important contributions to the SD-CI values of the correlation corrections to dipole polarizabilities.     

Calculation of correlation energy by many-body diagrammatic perturbation theory

The many-body diagrammatic perturbation theory is used for calculation of the correlation energy of closed-shell molecular systems. We apply Brueckner's concept of the two-particle renormalized interaction defined by a non-linear diagrammatic expression containing all possible (diagonal and/or non-diagonal) particle-particle, hole-hole and particle-hole intermediate elementary processes. Then, a “second-order” simple diagrammatic expression for the correlation energy can be formed, where the correlation energy is approximated by all the diagrams with biexcited intermediate states. An illustrative numerical application for the LiH molecule is presented. This article is dedicated to the memory of our friends and colleagues Dr. Jarka Surá and Dr. Marta Černayová, who tragically died in July 1976.     

Application of the many-body perturbation theory by using localized orbitals

Diagrammatic formulation of the many-body perturbation theory is investigated when both the occupied orbitals and the virtual ones are localized, i.e., they are unitary transforms of the canonical Hartree–Fock orbitals. All diagrams representing ground state correlation energy can be generated through fifth order. For cyclic polyenes C₆H₆ and C₁₀H₁₀ as model systems, the energy corrections are calculated in the Pariser–Parr–Pople approximation for a wide range of the coupling constant β^?1, through fourth order including some fifth order terms. The results are compared to those obtained by other methods: perturbation theory by using canonical orbitals and full CI. The effect of neglecting contributions from orbitals localized into neighboring sites is also studied.     

A note on the convergence of multiconfigurational many-body perturbation theory

The convergence of multiconfigurational many-body perturbation theory (MC MBPT ) is discussed in connection with the intruder state. Its convergence properties are first examined with a fictitious three-level system employing a Hermitian version of MC MBPT , which permits a general model space. It is then applied to the H₂—H₂ and N₂ systems. The results suggest that a more extensive model space is likely to embrace new intruder states and the space extension be executed with due caution.     

Comparison of high-order many-body perturbation theory and configuration interaction for H2O

Diagrammatic many-body perturbation theory, coupled with a recursive computational procedure, is employed to obtain the correlation energy of H₂O within a 39-STO basis set by evaluating all double-excitation diagrams through twelfth order without any approximations. This provides, for the first time, the complete double-excitation diagrams contributions to the correlation energy, which is ?0.28826 hartree, compared with a correlation energy of ?0.27402 hartree obtained from a configuration interaction calculation which includes all double excitations. The difference of 0.0142 hartree includes the “size consistency” correction to the all-double-excitations CI energy, due to the “pathological” unliked-diagram terms remaining in that result, but also involves certain fourth- and higher-order rearrangement diagrams. Contrary to conventional belief, the unshifted, or Møller-Plesset partitioning of the hamiltonian provides a much more rapid convergence of the perturbation series that does the shifted, or Epstein-Nesbet partitioning. In both cases. Padé approximants enhance the convergence of the series considerably. A simple variation-perturbation scheme based on the first-order MBPT wavefunction is sufficient to provide 97.5% of the all-doubles CI correlation energy.     

Electric and magnetic properties of LiH molecule according to Hartree-Fock perturbation theory

Applying perturbative techniques to Hartree-Fock (HF) equations for the LiH molecule in the presence of external electric and magnetic fields, first order corrections to the molecular orbitals in the fields have been obtained, solving coupled HF equations. The calculated observables, i.e. electric dipole polarizability and hyperpolarizability, magnetic susceptibility, and magnetic shielding constants for the Li and H nuclei, are compared with other calculations and, when possible, with experimental data. The problem of gauge-invariance of the calculated results is examined in some detail for magnetic observables.

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Zusammenfassung Auf die Hartree-Fock (HF)-Gleichung des LiH-Moleküls in Gegenwart von äußeren elektrischen und magnetischen Feldern wurden störungstheoretische Verfahren angewendet und es wurden Korrekturen 1. Ordnung zu den Molekülorbitalen durch die Lösung gekoppelter HF-Gleichungen berechnet. Die berechneten Observablen, nämlich die elektrische Dipol-Polarisierbarkeit und Hyperpolarisierbarkeit, magnetische Susceptibilität und magnetische Abschirmkonstanten für den Lisowie den H-Kern, werden mit Werten aus anderen Berechnungen sowie, wenn möglich, mit experimentellen Daten verglichen. Das Problem der Invarianz der berechneten Ergebnisse gegenüber der Wahl des Bezugssystems wird für die magnetischen Observablen untersucht.

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Résumé Par application de techniques de perturbation aux équations de Hartree-Fock pour la molécule LiH en présence de champs électrique et magnétique externes, on obtient les corrections du premier ordre pour les orbitales moléculaires dans ces champs comme solutions d'équations HF couplées. Les observables calculées (polarisabilité et hyperpolarisabilité dipolaires électriques, susceptibilité magnétique, constante d'écran magnétique pour les noyaux Li et H) sont comparées à d'autres valeurs théoriques et si possible aux valeurs expérimentales. Le problème de l'invariance de jauge des résultats calculés est étudié avec détail pour les observables magnétiques.

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This work was performed with the financial support of the Consiglio Nazionale delle Ricerche through the Laboratorio di Chimica Quantistica ed Energetica Molecolare-Pisa.     

GPU acceleration of many-body perturbation theory methods in MOLGW with OpenACC

Quasiparticle self-consistent many-body perturbation theory (MBPT) methods that update both eigenvalues and eigenvectors can calculate the excited-state properties of molecular systems without depending on the choice of starting points. However, those methods are computationally intensive even on modern multi-core central processing units (CPUs) and thus typically limited to small systems. Many-core accelerators such as graphics processing units (GPUs) may be able to boost the performance of those methods without losing accuracy, making starting-point-independent MBPT methods applicable to large systems. Here, we GPU accelerate MOLGW, a Gaussian-based MBPT code for molecules, with open accelerators (OpenACC) and achieve speedups of up to $$ over 32 open multi-processing (OpenMP) CPU threads.     

Applicability of quasi-degenerate many-body perturbation theory to the ground state of the F2 molecule

The ground-state potential energy curve of the F₂ molecule as well as spectroscopic constants were calculated by means of the second-order quasi-degenerate many-body perturbation theory within a full (eight) valence orbital space using a DZP basis set. The problem encountered with a large number of valence electrons is avoided by a proper redefinition of the Fermi vacuum. A comparison with other related multireference techniques is also provided. © 1995 John Wiley & Sons, Inc.     

Dual-basis analytic gradients. 1. Self-consistent field theory

Analytic gradients of dual-basis Hartree-Fock and density functional theory energies have been derived and implemented, which provide the opportunity for capturing large basis-set gradient effects at reduced cost. Suggested pairings for gradient calculations are 6-31G/6-31G**, dual[-f,-d]/cc-pVTZ, and 6-311G*/6-311 + +G(3df,3pd). Equilibrium geometries are produced within 0.0005 A of large-basis results for the latter two pairings. Though a single, iterative SCF response equation must be solved (unlike standard SCF gradients), it may be obtained in the smaller basis set, and integral screening further reduces the cost for well-chosen subsets. Total nuclear force calculations exhibit up to 75% savings, relative to large-basis calculations.     

Applicability of nondegenerate many-body perturbation theory to quasi-degenerate electronic states. II. A two-state model

In reply to Kaldor's [Int. J. Quantum Chem. XX, XXX (1985)] criticism of our study of simple four-electron models, in which the degree of quasi-degeneracy can be continuously varied, by the finite-order nondegenerate many-body perturbation theory, we examine in more detail a simple two-state model that the used to substantiate his claim that “the low order sum of the perturbation series is not very meaningful” in view of its divergence. It is shown that in contrast to Kaldor's claim, the partitioning used increases the radius of convergence of the considered perturbation series and is in principle capable to make it convergent. It is also shown that the convergence of the series is not very essential and that even divergent series can provide useful estimate of the exact result, particularly when the resummation techniques, such as Padè approximants or continued fractions, are employed. Finally, the shortcomings of the existing multi-reference perturbation approaches, which Kaldor advocates, are pointed out.