The coupled-cluster method with a multiconfiguration reference state

The coupled-cluster approach to obtaining the bond-state wave functions of many-electron systems is extended, with a set of physically reasonable approximations, to admit a multiconfiguration reference state. This extension permits electronic structure calculations to be performed on correlated closed- or open-shell systems with potentially uniform precision for all molecular geometries. Explicit coupled cluster working equations are derived using a multiconfiguration reference state for the case in which the so-called cluster operator is approximated by its one- and two-particle components. The evaluation of the requisite matrix elements is facilitated by use of the unitary group generators which have recently received wide attention and use in the quantum chemistry community.     

Coulombic Basis for Relative Hydrogen-Bonding Basicities and Conformational Energies of Tertiary Amine Oxides and Phosphine Oxides

The structures, energies, and natural atomic charges of 2-dimethylaminophenol oxide, 2-Me₂N-(O)C₆H₄OH, and 2-dimethylphosphinylphenol, 2-Me₂P(O)C₆H₄OH, in three different conformations were computed at the ab initio MP2/6-31G* level. Computed natural charges indicate distributions of electron density in amine oxides and phosphine oxides that are quite different from what is normally assumed on the basis of the formal charges in the usual representations of these compounds. The charges on nitrogen and phosphorus in these compounds are typically computed to be approximately zero on nitrogen and +2 on phosphorus, and the oxygen is considerably more negative in the phosphine oxide than in the amino oxide. Electronegativity differences thus play a larger role and formal charges a smaller one in determining atomic charges in these compounds than is generally believed. Despite the more negative oxygen in phosphine oxides, amine oxides are computed to be considerably more basic when participating in hydrogen bonding. Calculations treating the computed natural charges on these six conformations as point charges for classical approximations of the coulombic energies support the idea that the quantum mechanically computed relative energies are largely determined by coulombic interactions.     

Equivalence of dimensional reduction and dimensional regularisation

For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the -functions calculated using DRED transform into those computed in DREG. TheS-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.     

Sessions of the Seminar “Algebra i Logika”

Sessions of the seminar algebra i logika     

The electric field gradient at111Cd in vanadium oxides

The electric field gradient (efg) of¹¹¹Cd in polycrystalline V₂O₅ was studied using perturbed angular correlation (PAC) spectroscopy, with the¹¹¹In activity ion-implanted at 400 keV. Between the individual steps of an isochronal annealing program, a distinct efg (v _Q 1=88.1(3) MHz, ₁=0.62(2)) was recorded the contribution of which increased with annealing temperature up to 74% at 870 K. Corresponding X-ray analysis of inactive V₂O₅ samples, which underwent the same annealing treatment, proved that the sample always stayed as V₂O₅. Since V₂O₅ has only one equivalent cation site, it is concluded that this efg belongs to¹¹¹Cd at this site. Oxidation of a vanadium foil atT=675 and 800 K at =200 mbar also yielded this efg. From PAC measurements in VO₂, two well-defined efg's were found above and below the metal-semiconductor transition at 340 K, which are tentatively attributed to the monoclinic and the tetragonal phase.Supported by Deutsche Forschungsgemeinschaft and DAAD.On leave from the University of Durban-Westville, South Africa.     

Soliton experiments in stimulated Raman scattering

Experimental observations of solitons in stimulated Raman scattering are reported. Soliton formation resulted from the introduction of a phase shift in the incident Stokes beam as predicted by theory. Pulse sharpening and retardation on propagation in the Raman medium have been observed along with amplitude diminution. The first two features were predicted and the third was not. Spontaneous soliton formation has been observed in the absense of any amplitude modulation or apparent phase shift in the optical fields, indicating that additional sets of initial conditions may result in soliton formation.Work performed under the auspices of the U.S. Department of Energy.