New derivation of the Waller-Hartree-Fock spatial wave function

1984 ◽  
Vol 25 (4) ◽  
pp. 707-713 ◽  
Author(s):  
Ruben Pauncz
Keyword(s):  
Wave Function ◽  
Hartree Fock ◽  
Spatial Wave Function

scholarly journals Evaluation of the one electron expectation values for different wave function of Be atom

2007 ◽  
Vol 4 (3) ◽  
pp. 393-396
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Slater Determinant ◽  
Open Shell ◽  
Expectation Values ◽  
Electronic Density ◽  
Expectation Value ◽  
Hartree Fock ◽  
Shell System ◽  
Electronic Wave Function ◽  
The One

The aim of this work is to evaluate the one- electron expectation value from the radial electronic density function D(r1) for different wave function for the 2S state of Be atom . The wave function used were published in 1960,1974and 1993, respectavily. Using Hartree-Fock wave function as a Slater determinant has used the partitioning technique for the analysis open shell system of Be (1s22s2) state, the analyze Be atom for six-pairs electronic wave function , tow of these are for intra-shells (K,L) and the rest for inter-shells(KL) . The results are obtained numerically by using computer programs (Mathcad).

Implementation of Membership Function using Spatial Wave-Function Switched FETs

2014 ◽  
Vol 23 (01n02) ◽  
pp. 1450007 ◽  
Author(s):  
Supriya Karmakar ◽  
John A Chandy ◽  
Faquir C. Jain
Keyword(s):  
Wave Function ◽  
Membership Function ◽  
Applied Voltage ◽  
Field Effect ◽  
Field Effect Transistor ◽  
Charge Carrier Concentration ◽  
Circuit Model ◽  
Digital To Analog Converter ◽  
Effect Transistor ◽  
Spatial Wave Function

Spatial wave-function switched field effect transistor (SWSFET) switches the current flow between different channels inside the FET based on the applied voltage in its gate terminal. SWSFET can be used to implement multi-valued logic circuit with less number of circuit elements. Recently we presented unipolar inverter circuit using SWSFET. In this paper we develop a circuit model of SWSFET based on BSIM 3.2.0 and BSIM 3.2.4 and implement membership function using that circuit model of SWSFET. The spatial wave-function switched field effect transistor (SWSFET) has two or three low band-gap quantum well channels inside the substrate of the semiconductor. Applied voltage at the gate region of the SWSFET, switches the charge carrier concentration in different channels from source to drain region. A circuit model of SWSFET is developed in BSIM 3.2.0. Membership function is implemented using the circuit model of the SWSFET. Membership function implementation using less number of SWSFET will reduce the device count in future analog-to-digital converter (ADC) and digital-to-analog converter (DAC) circuits.

Excitation Energies from a Partially Spin-Restricted Wave Function

2007 ◽  
Vol 3 (1) ◽  
pp. 65-69 ◽  
Author(s):  
V.N. Glushkov
Keyword(s):  
Wave Function ◽  
Excited States ◽  
Electron Correlation ◽  
Electronic Excitation ◽  
Slater Determinant ◽  
Molecular Orbitals ◽  
Reference Configuration ◽  
Excitation Energies ◽  
Hartree Fock ◽  
Natural Base

A singe Slater determinant consisting of restricted and unrestricted, in spins, parts is proposed to construct a reference configuration for singlet excited states having the same symmetry as the ground one. A partially restricted Hartree-Fock approach is developed to derive amended equations determining the spatial molecular orbitals for singlet excited states. They present the natural base to describe the electron correlation in excited states using the wellestablished spin-annihilated perturbation theories. The efficiency of the proposed method is demonstrated by calculations of electronic excitation energies for the Be atom and LiH molecule.

Projection of the wave function of the unlimited Hartree-Fock method on the doublet state in the case of benzyl radical

1974 ◽  
Vol 8 (3) ◽  
pp. 242-249
Author(s):  
I. I. Ukrainskii ◽  
Yu. A. Kruglyak ◽  
H. Preuss ◽  
R. Yanoshek
Keyword(s):  
Wave Function ◽  
Doublet State ◽  
Hartree Fock ◽  
Benzyl Radical

CALCULATION OF THEORETICAL ISOTROPIC COMPTON PROFILE FOR MANY PARTICLE SYSTEMS

2010 ◽  
Vol 24 (14) ◽  
pp. 1601-1614
Author(s):  
ALI A. ALZUBADI ◽  
KHALIL H. ALBAYATI
Keyword(s):  
Wave Function ◽  
Impulse Approximation ◽  
Particle Systems ◽  
Electron Interaction ◽  
Compton Profile ◽  
High Momentum ◽  
Atomic Systems ◽  
Hartree Fock ◽  
Hf Wave ◽  
Momentum Region

Theoretical isotropic (spherically symmetric) Compton profiles (ICP) have been calculated for many particle systems' He , Li , Be and B atoms in their ground states. Our calculations were performed using Roothan–Hartree–Fock (RHF) wave function, HF wave function of Thakkar and re-optimized HF wave function of Clementi–Roetti, taking into account the impulse approximation. The theoretical analysis included a decomposition of the various intra and inter shells and their contributions in the total ICP. A high momentum region of up to 4 a.u. was investigated and a non-negligible tail was observed in all ICP curves. The existence of a high momentum tail was mainly due to the electron–electron interaction. The ICP for the He atom has been compared with the available experimental data and it is found that the ICP values agree very well with them. A few low order radial momentum expectation values 〈pn〉 and the total energy for these atomic systems have also been calculated and compared with their counterparts' wave functions.

On the basis of orbital theories

1955 ◽  
Vol 232 (1188) ◽  
pp. 114-135 ◽  
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Singlet Ground State ◽  
New Techniques ◽  
Hartree Fock ◽  
Basic Set ◽  
Spin Eigenfunctions ◽  
Spin Degeneracy ◽  
One And Many ◽  
Reduced Density

In molecular theory the wave function is usually constructed from antisymmetrized products, or ‘Slater determinants’, of one-electron ‘orbitals’. A single determinant of suitably chosen, doubly occupied orbitals is often a fair approximation to a singlet ground state; but when more general products are admitted, as in ‘configuration interaction’ calculations, it is first necessary to resolve a high ‘spin degeneracy’ by constructing spin eigenfunctions (SE’s). In §1, the fundamental basis of recent methods (McWeeny 1954 b ) is clarified by a group theoretical approach. Next, in §2, the energy expression, using as wave function an arbitrary mixture of similar SE’s, is written very simply in terms of the reduced density matrices for one and two particles, and formulae for the calculation of these matrices are given. The remaining problem is to get a ‘best’ wave function, usually with limited configuration interaction, by (i) variation of SE coefficients and (ii) variation of the orbitals appearing in the SE’s; this problem is formally solved in §3. (i) is the usual configuration interaction process; but (ii) is new and leads, when the orbitals are expressed in terms of a standard basic set (e.g. of atomic orbitals), to a complete generalization of the Roothaan 1951) equations. These (matrix) equations are simple in appearance, but their numerical solution calls for new techniques; and it is possible that the Roothaan (i.e. Hartree–Fock) approach, followed by configuration interaction, provides about the best working compromise between (i) and (ii). In §4, some points of contact between one- and many-configuration theories are noted. In particular, certain density matrix elements provide appropriate generalizations of the ‘charges’ and ‘bond orders’ of Coulson and Longuet-Higgins and continue to describe the response of a system to changes in its ‘Coulomb’ and ‘resonance’ integrals.

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