Method for Molecular Electronic State Multiplet Structure Calculation in the Space of Xα-SW-Orbitals

1991 ◽  
Vol 02 (01) ◽  
pp. 510-514
Author(s):  
I.A. TOPOL ◽  
V.I. POLYAKOV
Keyword(s):  
Energy Levels ◽  
Scattered Wave ◽  
Open Shell ◽  
Hamiltonian Matrix ◽  
Matrix Elements ◽  
Multiplet Structure ◽  
Molecular Electronic ◽  
Present Scheme ◽  
Molecular Integrals ◽  
State Functions

The SCF-Xα-scattered wave method (Xα-SW) as well as other versions of the density function approach cannot give a proper description of the open-shell many-electron energy levels and thus it is not always possible to reproduce electron spectra adequately by this method. We propose the following way to overcome this drawback of the X α-SW method. First one- and two-particle molecular integrals with Xα-SW molecular orbitals (MO) are calculated numerically. Then these integrals are used to evaluate Hamiltonian matrix elements (both diagonal and off-diagonal) in the basis of configuration state functions. The present scheme allows us to describe molecular electronic spectra in various approximations: a) one-configurational frozen orbitals approach; b) ΔSCF; c) configuration interaction (CI). Our method gives an opportunity to go beyond the muffin-tin (MT) approximation for a potential; inherent in the X α-SW method. In the X α-SW-MO basis it is simple enough to construct the full electron Hamiltonian matrix elements for various open-shell systems.

ESR STUDY OF SPIN-HAMILTONIAN PARAMETERS AND CRYSTAL FIELD ENERGY LEVELS FOR THE LOW C3 SYMMETRY Fe3+ CENTER IN GREEN SAPPHIRE CRYSTALS AND POWDER

2007 ◽  
Vol 21 (04) ◽  
pp. 225-236 ◽  
Author(s):  
P. LIMSUWAN ◽  
N. UDOMKAN ◽  
P. WINOTAI
Keyword(s):  
Rotation Angle ◽  
Energy Levels ◽  
Heat Treating ◽  
Esr Spectra ◽  
Field Energy ◽  
Hamiltonian Matrix ◽  
Magnetic Field Direction ◽  
Spin Hamiltonian ◽  
Corundum Structure ◽  
Hamiltonian Parameters

In this report, Fe 3+ impurity ions present in green sapphire ( Al 2 O 3) were studied experimentally, by heating a light green sapphire in flowing oxygen atmosphere for 12 h from 1200, 1300, 1400, 1500 and 1600°C, respectively. Electron spin resonance (ESR) spectra in X-band (~9.45 GHz ) were recorded by mounting the crystal with the c-axis perpendicular (θ = 90°) to the magnetic field direction. The spectra were recorded and simulated by a numerical diagonalization of spin Hamiltonian matrix in the range from 0 to 180 degrees for every 15 degrees of rotation angle (φ). In our case, only the last two sets of peaks strongly depend on the rotation angle (φ), and each exhibits C 3 symmetry due to two magnetically inequivalent Fe 3+ sites in the corundum structure. For polycrystalline ESR spectra, seven main Fe 3+ ESR absorption peaks occur at the resonance magnetic fields of 100.20, 310.24, 486.80, 525.00, 550.60, 761.00 and 777.00 mT respectively. Specifically, ESR signals show that the number of paramagnetic Fe 3+ ions increase roughly linearly with the heat treating temperature, having the [Formula: see text] ratio ~1.41 at 1600°C.

scholarly journals Open shell electronic state calculations on quantum computers: A quantum circuit for the preparation of configuration state functions based on Serber construction

2019 ◽  
Vol 1 ◽  
pp. 100002 ◽  
Author(s):  
Kenji Sugisaki ◽  
Satoru Yamamoto ◽  
Shigeaki Nakazawa ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
...  
Keyword(s):  
Electronic State ◽  
Quantum Circuit ◽  
Open Shell ◽  
Quantum Computers ◽  
State Functions

State Functions for Many Electron Atoms: Eigenfunctions of L2 and S2 for One Open Shell Configurations

1974 ◽  
Vol 52 (17) ◽  
pp. 1672-1675
Author(s):  
Jacek Karwowski ◽  
Serafin Fraga
Keyword(s):  
Open Shell ◽  
New Formalism ◽  
State Functions

The construction of eigenfunctions of L2 and S2 using a new formalism, that represents an alternative to the Racah genealogical scheme, is discussed. The corresponding functions have been tabulated for all the states arising from pN, dN, and fN configurations; this tabulation, not presented here because of space restrictions, is available as indicated in the text.

scholarly journals Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Energy Levels ◽  
Form Factors ◽  
Model Space ◽  
Negative Parity ◽  
Matrix Elements ◽  
Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

Ab initio predictions of the zero field splittings and the singlet–triplet transition strengths for the n → π* transition of selenoformaldehyde

1993 ◽  
Vol 71 (10) ◽  
pp. 1706-1712 ◽  
Author(s):  
D.C. Moule ◽  
L. Chantranupong ◽  
R.H. Judge ◽  
D.J. Clouthier
Keyword(s):  
Energy Levels ◽  
Random Phase ◽  
Open Shell ◽  
Oscillator Strengths ◽  
Basis Set ◽  
Zero Field ◽  
Zero Field Splitting ◽  
Hartree Fock ◽  
Lower Valence ◽  
Polarization Functions

The energy levels of the lower valence and Rydberg states of selenoformaldehyde, CH2Se, have been calculated by the SCF/CI method. Wavefunctions for the ROHF (restricted open shell Hartree–Fock) states were obtained with the Binnings–Curtis double-ζ basis set, augmented with Rydberg and polarization functions. Configuration interaction was applied to the parent configurations, PCMO (parent configuration molecular orbital). Oscillator strengths were evaluated for the allowed electric dipole transitions by the RPA (random phase approximation), and SOPPA (second-order polarization propagator approximation) methods. The spin-orbit contribution to the zero field splitting of the first triplet state, 3A2(n,π*) as well as the oscillator strengths to the three spin components were calculated by perturbation theory. These calculations predict that the Sx, Sy, and Sz components are shifted by −96.091,−96.707, and + 29.167 cm−1, respectively, from their unperturbed position. The oscillator strengths for the three components fx, fy, and fz of the 3A2(n,π*) ← 1A1(g.s.) transition were calculated to be 3.45 × 10−7, 1.15 × 10−7, and 173.0 × 10−7.

MULTIBAND FINITE ELEMENT MODELING OF WAVEFUNCTION-ENGINEERED ELECTRO-OPTICAL DEVICES

1995 ◽  
Vol 04 (01) ◽  
pp. 191-243 ◽  
Author(s):  
L. R. RAM-MOHAN ◽  
J. R. MEYER
Keyword(s):  
Finite Element ◽  
Energy Levels ◽  
Optical Devices ◽  
General Concept ◽  
Semiconductor Heterostructures ◽  
Matrix Elements ◽  
Transition Matrix Elements ◽  
Band Mixing ◽  
Degree Of Control ◽  
Structure Engineering

Recent advances in the modeling of semiconductor heterostructures with complex geometries allow one to go beyond band-structure engineering to the more general concept of wavefunction engineering. In this work, we illustrate how tailoring the band mixing and spatial distribution of the carriers leads to an expanded degree of control over such properties as the dispersion relations, interband and intersubband transition matrix elements, nonlinear optical and electro-optical coefficients, and lifetimes. The computations are based on a multiband finite element method (FEM) approach which readily yields energy levels, electron and hole wavefunctions, and optical matrix elements for heterostructures with arbitrary layer thickness, material composition, and internal strain. Application of the FEM to laterally-patterned heterostructures is also discussed.

scholarly journals The effect of a nuclear spin on the optical spectra.—III

1930 ◽  
Vol 127 (805) ◽  
pp. 407-416 ◽  
Keyword(s):  
Interaction Energy ◽  
Nuclear Spin ◽  
Energy Levels ◽  
Optical Spectra ◽  
Wave Functions ◽  
Orbital Momentum ◽  
Multiplet Structure ◽  
Multiple Wave ◽  
First Approximation ◽  
Intensity Ratios

In two recent papers the author has discussed the effect of a nuclear spin on the optical spectra by the method of multiple wave-functions. In these papers the interaction energy of the nuclear and electron spins was not taken into account, as has been pointed out by Hill. By its omission the equations were simplified considerably, without affecting the intensity ratios of the lines of the multiplet. The problem of finding the relative intensities is a purely kinematical one, depending as it does, to the first approximation, on the un­perturbed wave-functions. In the papers cited we used the interaction energy of the nuclear spin and orbital momentum to find the 4 i n + 2 wave-functions ( i n being the number of quanta of nuclear spin) which must replace the two wave-functions necessary to describe the electron spin fine structure. In order to describe the multiple energy levels correctly we must calculate the interaction energy of the two spins in addition to the energy increments already calculated in I and II. This is the first purpose of the present paper, and the work is carried out for the cases i n = ½, 1, 1½, 4½. It is found that in the case of the p ½ levels the interaction energy of the two spins is equal to that of the nuclear spin and orbital momentum, while for the p 3/2 levels the ratio is — ⅕. It is further found that the energy levels of the S terms are correctly given in I and II. As regards comparison with Jackson’s results in the case of cæsium, it would seen that, the separation of the p -levels being very small in comparison with that of the S-level, he has been able to observe the multiplet structure of the lines due to the separation of the S-level only. If we make this assumption it will be seen on reference to I that our results agree quite well with his observations.

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