1969 ◽  
Vol 24 (12) ◽  
pp. 1964-1965 ◽  
Author(s):  
D.E. Freeman

Abstract The occurrence of a stationary or extremal diagonal compliance constant in the general secular equation for molecular vibrations leads to pecularities in the normal coordinates, in the distribution of potential energy among the compliance constants, and in the secular determinant which then possesses a linear factor.


A secular determinant for the determination of vibration frequencies of lithium has been set up by Launay’s method which takes the electron gas into account. Theoretical elastic constants have been used in the calculation of the force constants. Frequencies have been calculated for 47 points of the first Brillouin zone which gives the value of 3 x 1000 = 3000 frequencies by symmetry. Specific heats have been calculated by numerical computation in the range 300 to 6°K and show good agreement with the experimental data. The agreement below liquid-air temperatures is surprising in view of the known phase transformation of lithium.


2001 ◽  
Vol 71 (3) ◽  
pp. 460-465
Author(s):  
Biljana B. Arsic ◽  
Jovica V. Urosevic ◽  
Miroslav M. Mitic

Very often the application of quantum mechanics into chemistry represents a challenging task for chemistry students. However, this can be very usual exercise, and we have shown the easiness on the molecule of 3-aminopropenal, which is an interesting example because of the existence of the conjugation system consisting of the carbonyl group, alkenyl system and the lone electronic pair on nitrogen without any symmetry. Coefficients obtained using the Huckel secular determinant were -2.0484, -1.7328, -0.7827, +0.4892 and +1.5747.


1973 ◽  
Vol 26 (4) ◽  
pp. 501 ◽  
Author(s):  
SJ Joshua ◽  
D Morgan

A brief discussion is given of the symmetry properties of the energy band structure and the method of constructing orthogonal matrices at high symmetry points for group IV and III-V semiconductors. By means of examples it is shown how to factorize the n x n secular determinant formed by using the pseudopotential form factors of Cohen and Bergstresser (1966), thereby permitting easy numerical solution.


Author(s):  
Vikram R. Jadhav ◽  
Jamdhade Madhuri ◽  
Wadhawane Pooja ◽  
Y.R. Baste

In this study, characteristics of Hückel strategy, were abused so as to acquire some significant outcomes, through a theoretical technique with which it is conceivable to get secular equations, π energy, wave functions, electron density and charge density, as an account of cyclopentadienyl system i.e. C5H5+ (cation), C5H5- (anion), and C5H5. (radical) and permitting the expression of delocalization energy of conjugated cyclopentadienyl ring framework. Here, it was presented the secular determinant of the Hückel technique and applied to cyclopentadienyl system framework so as to communicate their orbital energies of cyclopentadienyl system, also to communicate its electron and charge density in terms of stable configuration of a system. It is settled by the Hückel strategy and applied by the assumptions for nearby comparability such as coulomb integrals, exchange integrals and overlap integrals. This simple way hypothetical strategy will allow to graduate and post graduate understudies to understanding the investigation of stable configuration, electron and charge density and also other parameters.


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