Spin adaptation of antisymmetrized geminal product wave functions

A spin-free polynomial representation of antisymmetrized geminal products is presented for several cases. In particular, products of identical geminals, which possess different spin multiplicity, are considered. The cases of singlet geminals, singlet geminals with one or two triplet geminals coupled to the lowest possible spin multiplet, and triplet geminals coupled to an arbitrary multiplet are considered in detail, and explicit polynomial representation is given.     

Self-consistent approximation to the polarization propagator

A theorem is presented that characterizes approximate states and truncated operator manifolds associated with self-consistent approximate propagators. This theorem establishes a natural relationship between Hermiticity, stationarity, nonredundance and completeness of operator manifolds, model time evolution, and the vacuum condition. For the case of the polarization propagator we describe algorithms by which we can construct states and manifolds that satisfy this theorem and the vacuum condition.     

Renormalization of the frozen Gaussian approximation to the quantum propagator

The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining "on the fly" quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to "on the fly" computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable "on the fly"; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.     

A polarization propagator analysis of the geminal 31P-31P coupling in bis(difluorophosphino)amine⋆

Inner projections of the polarization propagator (IPPP) are used to decompose in through-space and through-bond contributions the two-bond P-P coupling in PF₂-NH-PF₂. This study is carried out using a ground state INDO wavefunction. Results for a phosphorus sp and spd atomic basis sets are compared. Several experimental trends are correctly reproduced using either of them. It is concluded that the overlap of the lone pair of both P atoms constitutes a very efficient pathway for transmitting through-space the spin information associated to the Fermi contact term.Part of a PhD thesis (H.O.G.) to be presented to the University of Buenos AiresFellow of the Argentine National Research Council (CONICET)Member of the Argentine National Research Council (CONICET)     

The antisymmetrized product of weak nonorthogonal geminals

Most commonly the nonorthogonality of geminals is weakly expressed so that the exchange and overlap integrals ζ^(η), φ^(η) are negligible for large exchange parameters η. The conditions which allow the terms with large η to be discarded are considered. The integrals ζ^(η), φ^(η) are derived for η = 2, 3, 4.     

Construction of unique canonical coefficients for antisymmeterized geminal power states

Coefficients often defined to be canonical for a given geminal may not be unique. In this article we show by carefully examining a theorem by B. Zumino how to construct unique canonical coefficients for a geminal. This result leads to expansions of antisymmeterized geminal power states solely in terms of natural generalized spin orbitals and positive geminal occupation numbers. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

On the fixed-nuclei approximation as applied to rotational excitation of molecules by atoms

The applicability of the fixed-nuclei approximation to the rotational excitation of a diatomic molecule by an atom is investigated. The approximation is shown to predict accurate quantum cross sections for the model system H₂ + N₂ at thermal collision energies. A quasi-classical Monte-Carlo study of the same problem is also performed, and the success of the fixed-nuclei approximation is interpreted by investigating in detail a number of coplanar classical trajectories.     

Molecular photoionization cross sections in electron propagator theory: angular distributions beyond the dipole approximation

Corrections to dipole approximation results for angular distributions in photoionization of first-row hydrides have determined by using Dyson orbitals calculated with ab initio electron propagator theory and by considering the full multipole expansion for the incident photon representation. The relative importance of first-order corrections which consist of electric quadrupole and magnetic dipole terms and of higher-order terms has been estimated as a function of photon energy. Multipole corrections to the dipole approximation depend on photon energy and on the characteristics of the Dyson orbitals.     

Calculations of spin-spin coupling constants with the self-consistent polarization propagator approximation in non-singlet unstable wavefunctions

Nuclear spin-spin coupling constants are calculated with the self-consistent polarization propagator approximation method starting from a semi-empirical non-singlet unstable wavefunction. Effects on α and π transmitted components are separately analysed. Resultss show that this approximation is an adequate framework for the Fermi contact term when the corresponding HF state presents a non-singlet instability.     

Superoperator approach to propagator approximations

The superoperator formalism for matrix propagators is reviewed, with special attention to the validity of superoperator resolution of the identity. The equation of motion for the particle-hole propagator is discussed. Decoupling procedures based on inner projections and partitioning are examined showing the desirability of self-consistent approximations. The conditions under which a state can be a vacuum for a given linear manifold of operators are analyzed.     

Application of the extended geminal theory to the BH molecule

Extended geminal theory is applied to the ground state of BH at R=2.329 bohr. It is found that the inclusion of only one-electron transfer configurations leads to a lowering in the energy of 0.01 hartree, compared to the antisymmetrized geminal product wavefunction. This improvement is >90% of that achieved by a full configuration-interaction wavefunction. A contracted doublezeta basis set is also found to be quite good.

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Zusammenfassung Die erweiterte Geminaltheorie wird auf den Grundzustand des BH für R=2,329 Bohr angewendet. Es wird gefunden, da der Einschlu von nur Ein-Elektron-Transfer-Konfigurationen zu einer Energieerniedrigung von 0,01 Hartree, verglichen mit der antisymmetrisierten Geminal-Produkt-Wellenfunktion, führt. Diese Verbesserung beträgt mehr als 90% gegenüber dem Wert, der mit einer vollen CI-Funktion erreicht wird. Ein kontrahierter doppelt-zeta-Basis-Satz liefert ebenfalls gute Ergebnisse.

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Résumé La théorie des géminales généralisée est appliquée à l'état fondamental de BH pour R=2,329 bohr. On trouve que l'introduction des seules configurations à «un transfert d'électron» conduit à un abaissement de l'énergie de 0,01 hartree, par rapport à celle correspondant à un simple produit antisymmétrisé de géminales. Cette amélioration est supérieure à 90% de celle obtenue par I.C. complète. Une base double zèta «contractée» s'avère aussi fort bonne.

     

Vibrational excitation and dissociation of a diatomic molecule in the diffusion approximation

A numeric solution is given for the excitation of vibration and dissociation in the diffusion approximation for an O₂-Ar (oxygen-argon) mixture. The time of vibrational relaxation is calculated, and also the rate constant for dissociation. The diffusion approximation describes the processes satisfactorily for a gas whose particles differ little in mass.I am indebted to B. V. Kuksenko, A. I. Osipov, and M. N. Safaryan for discussions and valuable advice.     

Determination of excitation energies and transition moments in a second order polarization propagator approach. Application to the Be atom and the CH+ molecule

Excitation energies and transition moments have been determined from a second order polarization propagator and the effect of including energy shifted denominators has been investigated. Results for Be and CH⁺ show a change of 2–5% for the transition moments and of 0–20% for the singlet excitation energies in a second order approach compared to a first order (time-dependent Hartree-Fock) approximation. Both Be and CH⁺ are triplet unstable in the time-dependent Hartree-Fock approximation. The triplet instability is removed for Be but not for CH⁺ in a second order polarization propagator approach.     

Access to 5-fluoroisoxazoles via the nitrosation of geminal bromo-fluoro arylcyclopropanes

A new method for the synthesis of 3-aryl-5-fluoroisoxazoles via the reaction of nitrosonium chlorosulfate with 2-aryl-1-bromo-1-fluorocyclopropanes containing acceptor substituents in the aromatic ring has been developed. The reaction proceeds highly regioselectively thus providing 3-aryl-5-fluoroisoxazoles in good yields. The structure of isoxazoles was corroborated by the DU8+ hybrid DFT/parametric computational approach.     

The first aldehyde-derived crystalline geminal diol lacking internal electronic stabilization

The first stable crystalline geminal diol of an aldehyde lacking electron-withdrawing groups on the-carbon was synthesized fromd-sorbitol and characterized by¹H and¹³C nuclear magnetic resonance (NMR) and single-crystal x-ray studies. Each hydroxyl is a donor for a single, unique intermolecular hydrogen bond. Only one hydroxyl acts as an acceptor. No intramolecular hydrogen bonding is observed in the crystal.     

Core-level electronic spectra in ADC(2) approximation for polarization propagator: Carbon monoxide and nitrogen molecules

An effective ab initio approach to core-level electronic spectral studies is discussed. The approach uses polarization propagator theory in a second-order algebraic diagram construction ADC(2) approximation for calculating the characteristics of electron transitions; it also uses the linear vibronic model LVM for investigating the vibrational structure of transitions. The core excitation specialization of ADC(2) is achieved by introducing the core valence separation (CVS) approximation. K-excitation spectra of CO and N₂ molecules are calculated to examine the potential of the approach. The calculated spectra and the available experimental data are analyzed to characterize the method. A number of additional facts of methodological and practical value are found, and new transitions are predicted. It is concluded that ADC(2)/CVS/LVM is a promising approach to problem solving in core level spectroscopy, which requires qualitatively reliable theoretical estimations. Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, May–June, 2000, pp. 590-604.