Gas-liquid phase transition and singularities

A new model for the space of undercritical states of a gas-liquid system is proposed. Simple, physically motivated mathematical hypotheses among which stsbility plays an essential role, determine differential types of germs of pressure and temperature at the critical point. They are connected with the class D⁺₄ of Arnold's classification. The general configuration of vaporization and condensation curves is examined. As a result, Guggenheim's one-third law is obtained.     

Basis set generation for the SCF calculation

A method for basis set generation for SCF calculations is proposed. Using SCF orbitals and orbital energies obtained in the extended basis set the Fock operator can be expressed as its spectral resolution. The sum of differences between occupied orbital energies and corresponding eigenvalues obtained by the diagonalization of this operator in the new smaller basis set is a criterion of the quality of this new set. The present method consists of the minimization of this sum by changing the parameters that determine the new basis functions. An example of the optimization of the different Gaussian basis sets for the LiH molecule is described.     

Theoretical study of PO and PO−

The diatomic systems, PO and PO^– are studied, using numerical Hartree-Fock (NHF) and coupled-cluster calculations. The latter employs a hybrid NHF and Slater orbital basis set. Highly accurate CCSD methods predict bond lengths accurate to <0.004 Å and frequencies to 60 cm^–1. In addition the electron affinity of PO is computed to be 0.89 eV compared to an experimental value of 1.09±0.01. Comparisons are made with SCF and MBPT(2) results for PO⁺ using conventional basis sets.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayGuggenheim Fellow     

Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations

The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the internuclear distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD(+) ion.     

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.     

Reaction of diethylhydroxyborane with trialkylaluminium

The reaction of diethylhydroxyborane with trialkylaluminium has been studied. Trialkylboranes and diethyltriisobutyldialuminium dioxide were isolated and characterized. A two-stage mechanism is proposed for the formation.     

A free particle in noncommutative space-time

By examining some known wave equations it is shown that the dynamics of a free quantum particle in a slightly noncommutative space-time is equivalent to that of a charged particle moving in a self-generated (weak) electromagnetic field.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.     

Theoretical modeling of the nonenzymatic solvolysis of CMP-NeuAc in an acidic environment

A density-functional-theory investigation of the nonenzymatic solvolysis of the cytydine 5′-monophosphate N-acetylneuraminic acid and its derivatives in the acidic environment is presented. The theoretical calculations of the second stage of the reaction mechanism are in agreement with the hypothesis of a dissociative oxocarbenium-like transition state with proton transfer as a key part of the reaction. The geometries of the transition states of the reactions yielding -methyl and β-methyl glycosides are essentially different. This study provides new theoretical data that can be helpful in elucidating the mechanism of the carbohydrates hydrolysis as well as other reactions catalyzed by the glycosyltransferases.     

Polarization of Molecular ions in NaTCNQ and TTF. TCNQ Crtstals

Self-consistent electrostatic intersite potentials and atomic charges have been calculated. Lattice cohesion energy for NaTCNQ has been reproduced when polarization of TCNQ- anion in the lattice was taken into account.     

Accurate one-dimensional potential energy curve of the linear (H2)2 cluster

We present a sub-0.3 K accuracy, ground-state one-dimensional potential energy curve of the metastable linear configuration of the (H(2))(2) cluster calculated exclusively with explicitly correlated Gaussian functions with shifted centers. The H(2) internuclear distance is kept at the isolated H(2) vibrational ground-state average value of 1.448 736 bohr and the intermonomer separation is varied between 2 and 100 bohrs. The analytical gradient of the energy with respect to the nonlinear parameters of the Gaussians (i.e., the exponents and the coordinates of the shifts) has been employed in the variational optimization of the wave function. Procedures for enlarging the basis set and for adjusting the centers of the Gaussians to the varying intermonomer separation have been developed and used in the calculations.