Ground Wave Function Research Articles

The Energy Spectrum of an Ion Cr 3+ in Antiferromagnet Cr 2 O 3

The antiferromagnetic crystal Cr 2 O 3 contains magnetoactive ions Cr 3+ . In this crystal exist linear magnetoelectric effect, effect of polarization plane non-reciprocal rotation and ellipticity of light in reflection. It is necessary to know the energy levels and wave functions of an ion for exact simulation of this effect. In the present paper the problem of calculation of the crystaline field potential is solved in the single-ion model. For Cr 2 O 3 the splitting of energy levels are determined and wave functions for ground and exited states are calculated.

Electron Localization in the Insulating State

The insulating state of matter is characterized by the excitation spectrum, but also by qualitative features of the electronic ground state. The insulating ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is localized. We give a sharp definition of the latter concept, and we show how the two basic features stem from essentially the same formalism. Our approach to localization is exemplified by means of a two--band Hubbard model in one dimension. In the noninteracting limit the wavefunction localization is measured by the spread of the Wannier orbitals.

Effctive nonadiabatic calculations on the ground state of the HD+ molecule

AbstractThe nonadiabatic methodology, which is based on an effective elimination of the center‐of‐mass motion rather than explicit separation achieved by a coordinate transformation, is applied to the ground state of the HD+ molecule. The many‐body nonadiabatic wave function is generated in terms of explicitly correlated Gaussian functions. The analytical first and second derivatives of the variational functional with respect to the Gaussian exponents are applied in conjunction with the Newton–Raphson optimization method to find the nonadiabatic energy and the ground–wave function. The numerical results are compared with conventional nonadiabatic calculations. © 1995 John Wiley & Sons, Inc.

Reduced probabilities of gamma transitions in even-even deformed nuclei

The reduced probabilities of the E2 intraband and interband transitions in even-even erbium isotopes (A=158–170) andN=94 isotones (A=158–164) are analysed in the frame of the perturbation theory assuming the mixing of the wave functions of ground, beta- and gammavibrational states as well as different values of the intrinsic quadrupole moments of these states.

Computations of energy levels and wave functions of ground and excited states by the steepest-descent method.

The steepest-descent method is used for the computation of energies and wave functions of ground and excited states of some simple quantum-mechanical systems. The accuracy of numerical results gives hope that the method can be used also in nonperturbative quantum-field-theory calculations. By calculating the evolution of the wave function along the steepest-descent path we are using the finite-element method.

Theory for continuum resonance Raman scattering in diatomics using irreducible spherical tensors

AbstractA theory is presented which describes resonance Raman scattering via continuum electronic states of diatomic molecules. It is applied to the dissociative continuum of the bounded B(3Πo+u)‐state and the continuum of the repulsive 1Π1u state of the halogen molecules. Using spherical tensors and Wigner 3‐j symbols, closed forms for the resonance Raman intensities for different polarizations are given, which allow first principle calculations for molecules for which the vibrational wavefunctions of ground and electronic excited states as well as the oscillator strengths are known from absorption of fluorescence data.

Charge transfer excited states of hydroxyl ion impurities in alkali halide crystals

A theoretical investigation of the u.v. absorption anisotropy factor g and the transition energies of OH − molecule in alkali halide crystals is presented in terms of a charge transfer model and the free OH − ground wave-function. Comparison of calculated and observed transition energies for OH − in KBr and NaCl shows reasonable agreement between theory and experiment. For KCl:OH −, a reasonable result for the transition energy is also obtained through a confinement of the free K4 s function used for the one-electron transfer function. The model fails, however, to explain the value of about 0·3 for the anisotropy factor which is observed in a number of host crystals.

Vibrational and Electronic Oscillator Strengths of LiO.

Electronic energies and wave functions of ground and excited states of LiO are calculated in the Hartree-Fock approximation. The vibrational oscillator strengths of the X 2Π and A 2Σ+ valence states are calculated for v = 0 to 1 and 1 to 2 transitions. Electronic oscillator strengths are also presented for transitions to the quantum number two Li Rydbergs. Reasons are presented to support the use of the Hartree-Fock approximation.

Light Scattering of Transition-Metal Ions. I. Phonons of Three Normal Spinels and Electronic Raman Scattering of Co2+ in Co2GeO4

Polarized Raman studies of the three normal spinels Ag2MoO4, Co2GeO4, and ZnAl2O4 are reported. Electronic Raman scattering to levels of Co2+ in a surrounding of D3d symmetry is discussed and wave-functions of ground and excited states are given.

Molecular Orbital Study of NH2, NO2, and NF2

The orthogonality constrained basis set expansion method has been used to determine SCF wavefunctions for ground and lower excited doublet states of NH2, NO2, and NF2. The calculations on NO2 and NF2 were performed using a minimal basis set, while both minimal and extended bases were used in the study of NH2. Geometries and dipole moments of the various states were obtained and found to be in good agreement with available experimental data. Calculated vertical and 0–0 transition energies in these systems were also found to approximate the experimentally determined excitation energies.