The variational method of Djukic and Vujanovic and its relation to classical variational methods

1976 ◽  
Vol 27 (5) ◽  
pp. 525-544 ◽  
Author(s):  
Werner A. Schlup
Keyword(s):  
Variational Method ◽  
Variational Methods

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.

A Variational Method for Approximating the Response of Nonlinear Stochastic Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 353-357
Author(s):  
L. D. Zirkle ◽  
L. G. Clark
Keyword(s):  
Approximate Solution ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Variational Method ◽  
Variational Methods ◽  
Stochastic Systems ◽  
Random Variables ◽  
Nonlinear Stochastic Systems ◽  
Non Gaussian

A method is introduced for determining approximate properties of the response of nonlinear stochastic systems. The method is based in concept on the variational methods of mechanics and allows the consideration of classes of systems not readily subject to analysis by existing techniques. Three examples are presented illustrating the application to nonlinear systems with non-stationary inputs, non-Gaussian inputs and with time delay. The main limitation of the technique is the necessity for assuming a meaningful form for the approximate solution in terms of arbitrary random variables.

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.

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