Use of noninteger n-Slater type orbitals in combined Hartree-Fock-Roothaan theory for calculation of isoelectronic series of atoms Be to Ne

2009 ◽  
Vol 109 (2) ◽  
pp. 176-184 ◽  
Author(s):  
I. I. Guseinov ◽  
M. Ertürk
Keyword(s):  
Slater Type Orbitals ◽  
Slater Type ◽  
Hartree Fock ◽  
Isoelectronic Series

scholarly journals UNSYMMETRICAL AND SYMMETRICAL ONE-RANGE ADDITION THEOREMS FOR SLATER TYPE ORBITALS AND COULOMB–YUKAWA-LIKE CORRELATED INTERACTION POTENTIALS OF INTEGER AND NONINTEGER INDICES

2008 ◽  
Vol 07 (02) ◽  
pp. 257-262 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Basis Functions ◽  
Slater Type Orbitals ◽  
Addition Theorems ◽  
Slater Type ◽  
Interaction Potentials ◽  
Hartree Fock ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Multicenter Multielectron Integrals ◽  
Exponential Type Orbitals

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer nSTOs derived in this study with the help of ψa-exponential type orbitals (ψa-ETOs, a = 1, 0, -1, -2,…), the general formulas through the integer nSTOs are established for the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb–Yukawa-like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for the computations of arbitrary multicenter multielectron integrals that arise in the Hartree–Fock–Roothaan (HFR) approximation and also in the correlated methods based upon the use of STOs as basis functions.

scholarly journals A Hartree - Fock Program for Atomic Structure Calculations

1999 ◽  
Vol 52 (6) ◽  
pp. 973 ◽  
Author(s):  
J. Mitroy
Keyword(s):  
Open Shell ◽  
Fortran Program ◽  
Basis Functions ◽  
Slater Type Orbitals ◽  
Matrix Equations ◽  
Slater Type ◽  
Hartree Fock ◽  
The Matrix ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The Hartree–Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals.

Calculations of Isoelectronic Series of He Using Nonintegern-Slater Type Orbitals in Single and Double Zeta Approximations

2008 ◽  
Vol 26 (1) ◽  
pp. 213-215 ◽  
Author(s):  
Israfil GUSEINOV ◽  
Murat ERTÜRK ◽  
Ercan SAHİN ◽  
Hüseyin AKSU
Keyword(s):  
Slater Type Orbitals ◽  
Slater Type ◽  
Isoelectronic Series ◽  
Double Zeta

Momentum-Density Studies of Some Compounds with Triatomic Linear Anions

1993 ◽  
Vol 48 (1-2) ◽  
pp. 325-333
Author(s):  
R. O. Horenian ◽  
W. Weyrich
Keyword(s):  
Form Factors ◽  
Momentum Density ◽  
Basis Sets ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Interionic Interaction ◽  
Hartree Fock ◽  
Free Ions ◽  
Different Types ◽  
Powder Samples

Abstract High-purity powder samples of lithium and sodium azide (LiN3 , NaN3), cyanate (LiOCN, NaOCN) and hydrogen fluoride (LiFHF, NaFHF) were studied by means of 59.54 keV Compton spectroscopy. The measured isotropic Compton profiles were corrected for multiple scattering and transformed to spherically averaged reciprocal form factors Ba(s).The experimental results are compared with theoretical reciprocal form factors obtained from Hartree-Fock calculations with different types of basis sets (Gaussian-and Slater-type orbitals, with and without polarisation functions) both for the free ions and for several kinds of clusters. The importance of intraionic and interionic interaction for the description of chemical bonding in these compounds is pointed out and discussed.

scholarly journals Nonlinear approximations for electronic structure calculations

2013 ◽  
Vol 469 (2158) ◽  
pp. 20130231 ◽  
Author(s):  
G. Beylkin ◽  
T. S. Haut
Keyword(s):  
Electronic Structure ◽  
Functional Form ◽  
Integral Form ◽  
Electronic Structure Calculations ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Hartree Fock ◽  
Nonlinear Approximations ◽  
Novel Algorithms ◽  
Structure Calculations

We present a new method for electronic structure calculations based on novel algorithms for nonlinear approximations. We maintain a functional form for the spatial orbitals as a linear combination of products of decaying exponentials and spherical harmonics centred at the nuclear cusps. Although such representations bare some resemblance to the classical Slater-type orbitals, the complex-valued exponents in the representations are dynamically optimized via recently developed algorithms, yielding highly accurate solutions with guaranteed error bounds. These new algorithms make dynamic optimization an effective way to combine the efficiency of Slater-type orbitals with the adaptivity of modern multi-resolution methods. We develop numerical calculus suitable for electronic structure calculations. For any spatial orbital in this functional form, we represent its product with the Coulomb potential, its convolution with the Poisson kernel, etc., in the same functional form with optimized parameters. Algorithms for this purpose scale linearly in the number of nuclei. We compute electronic structure by casting the relevant equations in an integral form and solving for the spatial orbitals via iteration. As an example, for several diatomic molecules we solve the Hartree–Fock equations with speeds competitive to those of multi-resolution methods and achieve high accuracy using a small number of parameters.

Canonical two-range addition theorem for slater-type orbitals

2012 ◽  
Vol 113 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Daniel Gebremedhin ◽  
Charles Weatherford
Keyword(s):  
Addition Theorem ◽  
Slater Type Orbitals ◽  
Slater Type
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