One-center Wave Functions Research Articles

Electron-induced double ionization of oriented methane molecules

We report here a theoretical study of the target orientation effect on the total cross sections for the double ionization of methane molecules impacted by electrons. The theoretical description is performed within the first Born approximation. The initial state of the collisional system is composed of an electron projectile modeled by a plane wave and a molecular target described by a one-center wave function while the final state is constituted by a scattered electron described by a plane wave and two ejected electrons both represented by a Coulomb wave and coupled with a Gamow factor. Secondary electron energetic distributions and total cross sections are reported for particular target configurations. Strong orientation effects on the double-ionization process are pointed out in particular when scrutinized orbital by orbital.

Floating type wave functions in molecular pseudopotential calculations

Electronic structure, dissociation energy and equilibrium nuclear separation have been determined for the molecules CuH, AgH, AuH, ZnH+, CdH+, HgH+, NaH, KH, RbH, CsH, MgH+, CaH+, SrH+, BaH+ and RaH+ with the aid of the pseudopotential method. In such XH-type molecules two valence electrons are moving in the field of a proton and a positive ion X+, the interaction energy of these valence electrons and the positive ion being taken into account by a Hellmann-type pseudopotential. As a first approximation, floating hydrogen-type 1s one-center wave functions are used to describe the closed-shell and open-shell molecular bonding functions.

Molecular Density Matrices from One-Center Wavefunctions

The 1- and 2-matrices of the 10-electron polyhydrides, methide ion, ammonia, and oxonium ion, computed from one-center expansion wavefunctions with configuration interaction, are examined. The results are discussed in relation to the utility and limitations of one-center expansion wavefunctions. An explanation of Rutledge and Saturno's result, that methide ion and ammonia are planar, is proposed.

Correlated one-center wavefunctions for two-electron molecules

Correlated one-center wavefunctions for two-electron molecules

Electric Field Gradient for 14N in Ammonia from One-Center Wavefunctions

The electric field gradient has been computed for 14N in ammonia, employing the one-center SCF wavefunctions of Moccia, Joshi, and Rutledge and Saturno. It is found that the calculated values are comparable to that of a multicenter SCF wavefunction. Influence of configuration interaction on the electric-field-gradient calculation also is discussed.

Photo-Ionization of the Hydrogen Molecule

One-center wave functions are employed to investigate the photo-ionization of the hydrogen molecule from its ground state $X(1s\ensuremath{\sigma}{^{1}\ensuremath{\Sigma}_{g}}^{+})$, from 700 to 300 \AA{}. It is assumed that the residual ion is left in its ground state, and the free electron is in a $p\ensuremath{\sigma} or p\ensuremath{\pi}$ orbital. Using the one-center wave functions for $\mathrm{H}_{2}^{}{}_{}{}^{+}$ for the internuclear distance equal to $1.4{a}_{0}$, the free-electron wave functions are obtained by solving the integrodifferential equations in exchange and polarized-orbital approximations. The oscillator strengths obtained in the polarized-orbital approximation are found to be in satisfactory agreement with the experimental data.

Correlated one-center wavefunctions for two-electron molecules

Correlated one-center wavefunctions for two-electron molecules

Correlated one-center wavefunctions for two-electron molecules

Correlated one-center wavefunctions for two-electron molecules

Excitation of Hydrogen Molecules by Electron Impact

Using one-center wave functions of Huzinaga for the hydrogen molecule together with the Born and Ochkur approximations, the excitation of the molecule from the ground state to the $B$ and $C$ electronic states by electron impact has been investigated. The shape of the curves for the differential cross section and for the oscillator strength is in accord with the experimental results of Geiger. The effect of exchange is to reduce the scattering cross sections.

Magnetic Properties of Molecules from One-Center Wavefunctions. Theory and Application to the Hydrogen Molecule

A variational procedure is proposed for the purely theoretical calculation of the diamagnetic susceptibility and nuclear magnetic shielding constants of a molecule, given a one-center electronic wavefunction for it in the absence of a magnetic field. One performs a linear variational calculation, mixing in just those Slater determinants which the field causes to interact with the Slater determinants in the original wavefunction. A simple model is proposed, whereby one can simply estimate the magnetic properties from the original wavefunction. To illustrate the method, the susceptibility of the hydrogen molecule is computed from one simple and one more complex wavefunction expanded about the molecular center. The diamagnetic susceptibility and proton shielding constant for hydrogen then are calculated from a new single-center wavefunction expanded about one of the protons. The detailed behavior of the computed paramagnetic contribution to the magnetic properties is discussed and the results indicate that these terms are well accounted for by the proposed method. The calculated values for the susceptibility and proton shielding constant are —4.05×10—6 emu (—4.03×10—6 emu experimental) and 2.67×10—5 (2.66×10—5 experimental), respectively. Various other properties of hydrogen as calculated from the proton-center wavefunction are also given.

Treatment of the H 2 + -ion by means of one-, two- and three-center wave functions

The ground state energy of H 2 + is calculated with one- and multi-center wave functions by means of the variational method. By using hydrogen-like one-center wave functions a bound state is found even with Is function if it is centered-near one of the nuclei. Results can be improved by taking the linear combination of two or three of the one-center wave functions of the type 1s, 2s, 2p 2, 3d 2. By varying the position of the center we get the best results when the center is either located in one of the nuclei or in the middle point between the nuclei. A better approximation can be obtained with the two-center linear combination of 1s type wave functions centered on the two nuclei. The results can be essentially improved with the three-center wave function which is a linear combination of 1s wave functions centered on the two nuclei and on the middle point. In this case the energy and the internuclear distance areE = −0.5972e 2/a 0 andR = 2a 0, respectively, corresponding to the exact values − 0.60263e 2/a 0 and 2a 0.

Application of one-center wave functions to tetrahedral symmetric hydrid molecules II. Numerical computations for methane

Two different types of one-center wave functions are used to calculate several physical constants of the CH4 molecule. In spite of the great simplifications fairly good results are obtained for energy, bond length and vibrational frequency etc. The method, however, cannot predict a correct binding energy.

Application of one-center wave functions to tetrahedral symmetric hydrid molecules I. Theoretical basis of the method

The quantitative treatment of the polyatomic molecules encounters serious difficulties of mathematical nature. A considerable part of these may be overcome by the use of one-center wave functions. In case of molecules with high degree of symmetry this method seems to be successful. In the present work the application of the method to tetrahedral hybrid molecules is examined. It gives methods for the building up of the wave function and the simplification of the computations.