The Hellmann-Feynman theorem in the variational method

1963 ◽  
Vol 16 (2) ◽  
pp. 165-167 ◽  
Author(s):  
R. Gáspár
Keyword(s):  
Variational Method ◽  
Feynman Theorem

THE USE OF THE HELLMANN–FEYNMAN THEOREM TO CALCULATE MOLECULAR ENERGIES

1960 ◽  
Vol 38 (11) ◽  
pp. 2117-2127 ◽  
Author(s):  
Richard F. W. Bader
Keyword(s):  
Variational Method ◽  
Variational Methods ◽  
Present Method ◽  
Molecular Orbitals ◽  
Internuclear Separation ◽  
Electron Densities ◽  
Empirical Expression ◽  
Atomic Orbitals ◽  
Helium Atoms ◽  
Feynman Theorem

The Hellmann–Feynman theorem has been employed to calculate the repulsion between two helium atoms and the molecular energies of H2 and H3. The method of molecular orbitals was used to determine the necessary expressions for the electron densities. The screening constants of the atomic orbitals comprising the molecular orbitals were treated as functions of the internuclear separation according to an empirical expression which duplicates very closely the "best" values for these parameters as determined by the variational method. The results of the calculations indicate that the present method is capable of yielding estimates of molecular energies which are comparable to those obtained by the more elaborate and time-consuming variational methods.

Numerical Study of the Structure and Thermodynamics of Colloidal Suspensions by Variational Method

2014 ◽  
pp. 12-26
Author(s):  
Khalid Elhasnaoui ◽  
◽  
A. Maarouf ◽  
M. Badia ◽  
M. Benhamou ◽  
...  
Keyword(s):  
Variational Method ◽  
Numerical Study ◽  
Colloidal Suspensions

Variational Method for Estimating the Dipole Moment in the Second Excited State of Fluorescein Molecule from its Electronic UV Absorption Spectra

2019 ◽  
Vol 70 (10) ◽  
pp. 3538-3544
Author(s):  
Alina Costina Luca ◽  
Ana Cezarina Morosanu ◽  
Irina Macovei ◽  
Dan Gheorghe Dimitriu ◽  
Dana Ortansa Dorohoi ◽  
...  
Keyword(s):  
Dipole Moment ◽  
Excited State ◽  
Variational Method ◽  
Electronic State ◽  
Excited Electronic State ◽  
Spectral Band ◽  
Uv Absorption ◽  
Optical Parameters ◽  
Electrical Permittivity ◽  
Fluorescein Molecule

Electro-optical parameters of fluorescein molecule in the second excited electronic state and information on the interactions with solvents were obtained from a solvatochromic study. Parameters of the solvents such as the refractive index, electrical permittivity and Kamlet-Taft parameters (hydrogen bond acidity and basicity) were related with the experimentally recorded shifts of UV absorption spectral band of fluorescein dissolved in several solvents. Through a variational method, the electric dipole moment and polarizability in excited state of fluorescein molecule were estimated. The calculus requires some parameters of the fluorescein molecule in the ground electronic state, which were determined through a quantum-mechanical study.

scholarly journals Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

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