Configuration State Functions and Matrix Elements of the Hamiltonian

2019 ◽  
pp. 22-34
Author(s):  
Charlotte Froese Fischer ◽  
Tomas Brage ◽  
Per Jönsson
Keyword(s):  
Matrix Elements ◽  
State Functions

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.

State Functions of Nostalgia Scale

2012 ◽  
Author(s):  
Erica G. Hepper ◽  
Timothy D. Ritchie ◽  
Constantine Sedikides ◽  
Tim Wildschut
Keyword(s):  
State Functions

The light-scattering Mueller matrices for Rayleigh and Rayleigh-Gans-Debye approximation

1990 ◽  
Vol 55 (12) ◽  
pp. 2889-2897
Author(s):  
Jaroslav Holoubek
Keyword(s):  
Light Scattering ◽  
Theoretical Work ◽  
Matrix Elements ◽  
Elastic Light Scattering ◽  
Yield Information ◽  
Recent Theoretical Work ◽  
Particle Parameters ◽  
Complete Set ◽  
Single Matrix ◽  
Scattering Matrix Elements

Recent theoretical work has shown that the complete set of polarized elastic light-scattering studies should yield information about scatterer structure that has so far hardly been utilized. We present here calculations of angular dependences of light-scattering matrix elements for spheres near the Rayleigh and Rayleigh-Gans-Debye limits. The significance of single matrix elements is documented on examples that show how different matrix elements respond to changes in particle parameters. It appears that in the small-particle limit (Rg/λ < 0.1) we do not loose much information by ignoring "large particle" observables.

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