Werner A. Bingel

Simulation of the influence of the core electrons by a pseudopotential I. atoms with one and two valence electrons

Abstract Alkali atoms in ground and Rydberg states are treated as one-electron systems in the field of a pseudopotential of cut-off-Coulomb type. The appropriate cut-off radii are determined empirically from the lowest ionization potentials and are compared with conventional ion radii. For ground states and excited states of alkaline earth atoms Hartree-Fock-calculations are performed for the two-valence-electron systems in the field of the pseudopotential determined from the corresponding singly positive ions. Good agreement with calculations that involve all electrons and with experiment is obtained.

The hartree-fock and the correlation energies of the H+3 ion and their dependence on the nuclear configuration

Abstract The method of solving the two-electron Schrodinger equation numerically by ??? calculation of approximate natural orbitals is applied to the H+3 ion for different nuclear configurations, using a basis of Gaussian lobe functions. For the equilateral triangular equilibrium configuration and the lowest-energy linear configuration total energies of −1.3359 and −1.2729 a.u. respectively are obtained. the accurate eigenvalues can be estimated to be −1.341 ± 0.001 and −1.278 ± 0.001 a.u. Most striking is the change in the correlation energy, which has been calculated to be −0.039 a.u. in the triangular and −0.047 a.u. in the linear configuration.

The Behaviour of the First-Order Density Matrix at the Coulomb Singularities of the Schrödinger Equation

The cusp conditions of KATO for a spinless n-electron wave function at the COULOMB Singularities of the SCHRÖDINGER Equation are used to derive corresponding conditions for the first-order density matrix. These results are applied to the united-atom expansion of the electronic energy of polyatomic molecules resulting in an exact relation between the coefficients of the quadratic and cubic terms in this expansion. Finally it is shown how the cusp condition for the first-order density matrix is modified if the wave function includes electron spin in a proper way.

The convergence of the Rayleigh-Ritz Method in quantum chemistry: II. Investigation of the convergence for special systems of Slater, Gauss and two-electron functions

The convergence of the Rayleigh-Ritz Method (RRM) or of CI calculations, respectively, for the non-relativistic electronic Hamiltonian of molecules is investigated using the conventional basis sets of Quantum Chemistry, such as systems of Slater, Gauss and two-electron functions. Conditions for the choice of orbitalexponents with respect to Slater and Gauss orbitals are especially given, such that the convergence is guaranteed. Inter alia, in Theorem 10 a proof of the convergence of the RRM for a Hylleraas basis in s,t,u-coordinates is presented, a question which is still being debated today.

Simulation of the influence of core electrons by a pseudopotential II

Pseudopotential theory is combined with the Hartree-Fock and natural expansion method to calculate the molecular constantsDe, Re andke for Na2, K2, NaCs and BeH2. We treat these molecules as two- or four-electron problems respectively in the pseudopotential field of their cores. We then analyze the energies and wave functions in terms of the contributions of the different natural orbitals to the correlation energy. The calculated equilibrium distances agree well with the experimental ones. The dissociation energies are in better agreement with experiment than those of previous calculations.РезюмеПсевдопотенциальная теория комбинируется с методом Харти-фока и методом естественного разложения в ряд с целью определения молекулярных постоянныхDe, Re иke для Na2, K2, NaCs и BeH2. Эти молекулы рассматривались как двух- и четырехэлектронные проблемы соответственно в псевдопотенциальном поле своих атомных остатков. Далее были анализированы энергии и волновые функции с точки зрения взноса различных натуральных орбит в корреляционную энергию. Вычисленные расстояния равновесия хорошо согласуутся с экспериментальными данными Соответствие диссоциационных энергий с экспериментальными данными лучше, чем в педыдущих вычислениях.

Correlation coefficients for electronic wavefunctions of atoms in S-states and linear molecules

Abstract The connection between the correlation coefficients previously discussed byKutzelnigg, del Re and Berthier and the correlation factors introduced by McWeeny is determined. the Correlation coefficients are then discussed for some special cases. It is shown that for atoms S-staes the angular correlation coefficientτ is completely determined by the ι = 0 and 1 contributions of the expansion of the pair denstity π(Γ1.π2 in Legendre polynomials. For linear molecules the equatorial correlation coefficient τe can be expressed solely by the λ = 0 and 1 contributions of the Fourier expansion of π(gG1-Γ2) in terms of cos λ(ϕ1-ϕ2).

Die Elektronenstruktur und Lichtabsorption des Benzylradikals

Es werden der Grundzustand und die ersten angeregten Elektronenzustände des Benzylradikals mit der Methode der Valenzstrukturen, der Methode der Molekülbahnen und dem Modell der freien Elektronen berechnet. Die Ergebnisse dieser drei Methoden sind untereinander und mit den spektroskopischen Daten in qualitativer Übereinstimmung. Mit den beiden letzten Methoden werden die Elektronenstruktur des Benzylkations und -anions im Grundzustand und die ersten angeregten Zustände derselben bestimmt.

The behaviour of the triplet θ and singlet θ energy of the H2 molecule for larger R as calculated with the wang function

Abstract The optimum scale factors ζ t and ζ s of the Wang function for the 3 Σ + u and 1 Σ + g states of H 2 are determined as a function of R . It is shown that the introduction of scale factors does not change the incorrect asymptotic behaviour for large R of the energies of these two states previously found with the Heitler-London treatment. The limiting behaviour of the triplet θ function for R → 0 is also discussed.

Note on the solution of secular problems with two non-orthogonal basis functions

A convenient trigonometric expression for the eigenfunctions and eigenvalues of 2 x 2 secular problems including overlap is presented.

The symmetry group of vibrationally distorted molecules

A recipe for the determination of the symmetry groupG(Q) of a vibrationally distorted molecule is given, using only group-theoretical knowledge about the irreducible representations of the groupG(O) of the molecule in itsequilibrium geometry. The method is illustrated with several examples. Ambiguities which can arise due to the freedom in the choice of a basis for degenerate representations as well as the choice of molecular axes are indicated.