Consistent calculation of the Hamiltonian matrix for systems with image potential induced by abrupt interface

1993 ◽  
Vol 87 (11) ◽  
pp. 1023-1026 ◽  
Author(s):  
V.A Shakin ◽  
E Hanamura
Keyword(s):  
Hamiltonian Matrix ◽  
Consistent Calculation ◽  
Abrupt Interface

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.

Self-consistent calculation of excited3P state wave functions of atoms

1971 ◽  
Vol 5 (6) ◽  
pp. 647-655 ◽  
Author(s):  
P. K. Mukherjee ◽  
A. K. Bhattacharya ◽  
A. Mukherji
Keyword(s):  
Wave Functions ◽  
Consistent Calculation ◽  
State Wave ◽  
Self Consistent

scholarly journals Reduction of the molecular hamiltonian matrix using quantum community detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Susan M. Mniszewski ◽  
Pavel A. Dub ◽  
Sergei Tretiak ◽  
Petr M. Anisimov ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Community Detection ◽  
Slater Determinant ◽  
Hamiltonian Matrix ◽  
Approximate Methods ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Molecular Hamiltonian ◽  
Structure Problem ◽  
Modularity Maximization ◽  
Chemical Knowledge

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

Self-consistent calculation of the interactions of lightest nuclei with6Li

1992 ◽  
Vol 18 (2) ◽  
pp. 379-392 ◽  
Author(s):  
M Kamal ◽  
V T Voronchev ◽  
V I Kukulin ◽  
V M Krasnopolsky ◽  
Y Nakao ◽  
...  
Keyword(s):  
Consistent Calculation ◽  
Self Consistent

The microwave spectrum of the OH X2Π radical in the ground and vibrationally-excited (ν ≤ 6) levels

1979 ◽  
Vol 57 (5) ◽  
pp. 619-634 ◽  
Author(s):  
J. A. Coxon ◽  
K. V. L. N. Sastry ◽  
J. A. Austin ◽  
D. H. Levy
Keyword(s):  
Absorption Spectrum ◽  
Parallel Plate ◽  
Microwave Spectrum ◽  
Hamiltonian Matrix ◽  
Centrifugal Distortion ◽  
Linear Least Squares ◽  
Vibrationally Excited ◽  
Hyperfine Constants ◽  
Vibrational Levels ◽  
Astrophysical Significance

The microwave absorption spectrum of the OH X2Π radical has been observed in all vibrational levels up to ν = 6. Experimental details are described of the tunable cavity and parallel plate Stark-modulated spectrometers employed for transitions below and above 23 GHz, respectively. The observed line frequencies, together with those reported by other workers, have been fitted using a non-linear least-squares routine with numerical diagonalization of the Hamiltonian matrix. Pseudo high-order corrections for centrifugal distortion of the Λ-doubling are required for the ν = 0 data, which now extend to J = 19/2 in the 2Π1/2 component. The various adjustable parameters of the Hamiltonian are compared with those of other similar models. The Λ-doubling and magnetic hyperfine constants for the different vibrational levels are reported, and several line frequencies of potential astrophysical significance are predicted.

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