scholarly journals A Semi-empirical Approach to the Self-consistent Molecular Orbitals

1954 ◽  
Vol 27 (8) ◽  
pp. 565-566 ◽  
Author(s):  
Hideo Kon
Keyword(s):  
Molecular Orbitals ◽  
Empirical Approach ◽  
The Self ◽  
Self Consistent ◽  
Semi Empirical

Contemplating Transport Characteristics by Augmenting the Length of Molecule

2013 ◽  
Vol 05 (03) ◽  
pp. 1350010 ◽  
Author(s):  
Milanpreet Kaur ◽  
Ravinder Singh Sawhney ◽  
Derick Engles
Keyword(s):  
Electron Tunneling ◽  
Tight Binding ◽  
Steady State Solution ◽  
The Self ◽  
Molecular Device ◽  
Hückel Theory ◽  
Single Electron Tunneling ◽  
Self Consistent ◽  
Semi Empirical ◽  
Non Equilibrium Green’S Function

In this paper, we contemplated the transport characteristics of a single molecular device junction by augmenting the length of the molecule in the scattering region. The molecules considered here belongs to class of alkanedithiols ( C n H 2n+2 S 2). Specifically, we used a tight binding semi-empirical model to compute the transport characteristics of butanedithiol, pentanedithiol, hexanedithiol and heptanedithiol connected to semi-infinite gold electrodes through thiol anchoring elements. The exploration of transport properties of considered alkanes was completed for different bias voltages within the sphere of Keldysh's Non Equilibrium Green's Function (NEGF) and Extended Hückel Theory (EHT), for studying the self-consistent steady-state solution, analyzing the out-of-equilibrium electron distribution, and the behavior of the self-consistent potential. We perceived that the current and conductance retrenches with aggravation with the increase in length of the molecule with exhibition of single electron tunneling. We observed that the coupling regime shifts from strong coupling to weak for higher order alkanedithiols and the transmission is function of evenness or oddness of the carbon atoms forming an alkane.

scholarly journals Lα X-ray satellites for 31 ≤ Z ≤ 38: Systematization

2019 ◽  
Vol 8 (4) ◽  
pp. 5275-5278
Keyword(s):  
Atomic Number ◽  
Empirical Method ◽  
The Self ◽  
Sufficient Data ◽  
Number Range ◽  
X Ray ◽  
Self Consistent ◽  
Consistent Method ◽  
Semi Empirical ◽  
First Time

An examination of the problem of the energy values, their interpretation and the origin of the Lα x - ray satellites in the atomic number range Z = 31-38 reveals non existence and lack of sufficient data for the purpose. The energies of these satellites where not available are obtained using suitable semi-empirical method for the elements under investigation and the available systematization procedures namely Mosley plot and the self consistent doubly modified Mosley plot are considered. It is concluded that the self consistent method is not applicable in the present scenario. The energy values for the satellites Lα5 , Lα6 and Lα7 are calculated using Mosley plot for the atomic number range Z= 31 to 35 and are reported for the first time.

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

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