The Use of Perturbation Methods for the Study of the Effects of Configuration Interaction

A variant (here after called Epstein-Nesbet) of Rayleigh-Schrödinger perturbation treatment, corresponding to a new definition of the zeroth-order Hamiltonian leads to a faster convergence than the usual partition (here after called Møller-Plesset) of the exact Hamiltonian, when applied to the correlation problem. An illustration is given for the π system of the butadiene molecule. Some remarks are proposed concerning the convergence rate after the third order. On décrit une variante (appellée ici Epstein-Nesbet) de la méthode des perturbations de Rayleigh-Schrödinger, qui correspond à une nouvelle définition de l'Hamiltonien d'ordre zéro, et qui donne pour le problème de corrélation une convergence plus rapide que la partition ordinaire (appellée ici Møller-Plesset). On en donne une illustration pour le système π de la molécule de butadiène. On fait enfin quelques remarques sur la rapidité de convergence après le troisième ordre. Es wird eine Variante (hier Epstein-Nesbet genannt) der Rayleigh-Schrödingerschen Störungsmethode beschrieben, die eine neue Definition des Hamiltonoperators nullter Ordnung entspricht, and die zu einer schnelleren Konvergenz für das Korrelationsproblem als die gewöhnliche Teilung (hier Møller-Plesset genannt) des exakten Hamiltonoperators, führt. Eine Illustration wird für das π-System des Butadienmoleküls gegeben. Schliesslich wird die Konvergenzgeschwindigkeit nach der dritten Ordnung diskutiert.     

Size-consistent multireference configuration interaction method through the dressing of the norm of determinants

A new determinant-specific, effective change (‘dressing’) of the norm of the multireference configuration interaction (MRCI) wavefunction is proposed in order to achieve the size-consistency of the MRCI method. The new approach provides a unifying framework for analysis of size-consistent extensions of the MRCI method that are based on the coupled pair functional (CPF) strategy and lead to simplified computations of the analytical gradients. Using the new framework, a generalized multireference full coupled pair functional (MR-FCPF) method is introduced. The MR-FCPF method may be viewed as a functional counterpart of the recently proposed generalized (‘full’) coupled electron pair approximation (CEPA), referred to as the size-consistent self-consistent CI ((SC)²CI) method. A straightforward extension of the MR-FCPF method leads to a pseudo-functional form of the coupled cluster (CC) type formalisms. Therefore, the new approach may be used to introduce a simple alternative to existing CC-type gradient techniques. The new procedure is formally derived and compared with similar methods from the literature. Model systems calculations (H₂O, LiF, CH⁺ ₂) are further used to demonstrate the effect of various approximations and to elucidate the hierarchy of functional MR-CEPA schemes.     

Theoretical and experimental study of quadrupolar echoes for half-integer spins in static solid-state NMR

Numerical simulations of powder spectra produced by a two-pulse sequence applied to a quadrupolar nuclei system of half-integer spin number make it possible to propose simple experimental instructions to record static echo spectra with minimum lineshape distortion. Calculations take into account quadrupolar (first and second orders), shielding, scalar and inhomogeneous dipolar interactions as well as the radiofrequency pulse specifications (strength, duration, phase). The suggested instructions have been checked experimentally in different cases: for a large spin number system with Li⁹³NbO₃, when two interactions are present with a ^63/65Cu complex, and in the two-site system of ⁸⁷Rb₂SO₄.     

Molecular dynamics of polymers with explicit but frozen hydrogens

A new form of holonomic constraint, called a conic constraint, is introduced for the purpose of eliminating the fast vibrations of hydrogen atoms in molecular simulations of systems of aliphatic chains. It can easily be combined with bond constraints in SHAKE/RATTLE algorithms for which a unified tolerance criterion is defined. The new form of constraint allows the use of rather large time steps (in the 2–3 fs range). The procedure is illustrated for a full atomic model of polypropylene.