455 research outputs found
Comment on Hartree Fock Roothaan Calculations for Ground States of Some Atoms Using Minimal Basis Sets of Integer and Noninteger n STOs
Recently published formulas for the one-center integrals arising in atomic
Hartree-Fock-Roothaan (HFR) calculations with noninteger n STOs (S.Gumus, T.
Ozdogan, Chin. J. Chem., 22 (2004) 1262) are critically analyzed. The purpose
of this note is to point out that the presented in these work relations for the
integer n -nuclear attraction and kinetic energy integrals which are available
in the literature (C.C.J. Roothaan, J. Chem. Phys., 19 (1951) 1445) can not be
used for noninteger STOs. In addition, the formulas for two-electron integrals
can be obtained from the published in the literature (T. Koga, K. Kanayama,
Chem.Phys.Let., 266(1997)123; I.I. Guseinov, B.A. Mamedov, Theor. Chem.
Acc.,108 (2002) 21) relations by changing the indices. It should be noted that
the accuracy of computer values for ground states energy of some closed and
open shell atoms in the case of noninteger n STOs is not guaranteed since the
calculations were performed by the use of integer n -one electron integrals. It
is argued that the paper sheds no new light on the subject and that it is
altogether misleading.Comment: 2 page
Response to Comment on "Combined open shell Hartree-Fock theory of atomic-molecular and nuclear systems" [I.I.Guseinov, J. Math. Chem., 42 (2007) 177] by B. N. Plakhutin and E. R. Davidson
This article is a thorough critique to the Plakhutin-Davidson's comments made
to our paper published in the recent year. A detailed critical examination of
the arguments that led to the suggested comments by Plakhutin and Davidson
reveals some serious flaws. It is demonstrated that the principle of the
indistinguishability of identical particles is not taking into account in
Roothaan's open shell theory. This principle leads to the fact that the
orbital-dependent energy functional and, therefore, the Hartree-Fock and
Hartree-Fock-Roothaan equations for open shell systems presented by Roothaan
and others are not, in general, invariant under unitary transformation of the
combined closed-open shells orbitals. From a mathematical point of view this
statement is fundamentally flawless. It is shown that the Plakhutin-Davidson's
personal views about our assumptions concerning the insufficiencies of classic
Roothaan's open-shell theory are undisputedly wrong.Comment: 3 page
New development in theory of Laguerre polynomials
The new complete orthonormal sets of -Laguerre type polynomials (-LTP,) are
suggested. Using Schr\"odinger equation for complete orthonormal sets of
-exponential type orbitals (-ETO) introduced by the author, it is shown that
the origin of these polynomials is the centrally symmetric potential which
contains the core attraction potential and the quantum frictional potential of
the field produced by the particle itself. The quantum frictional forces are
the analog of radiation damping or frictional forces suggested by Lorentz in
classical electrodynamics. The new -LTP are complete without the inclusion of
the continuum states of hydrogen like atoms. It is shown that the nonstandard
and standard conventions of -LTP and their weight functions are the same. As an
application, the sets of infinite expansion formulas in terms of -LTP and
L-Generalized Laguerre polynomials (L-GLP) for atomic nuclear attraction
integrals of Slater type orbitals (STO) and Coulomb-Yukawa like correlated
interaction potentials (CIP) with integer and noninteger indices are obtained.
The arrange and rearranged power series of a general power function are also
investigated. The convergence of these series is tested by calculating concrete
cases for arbitrary values of parameters of orbitals and power function.Comment: 10 pages, 2 figure
New complete orthonormal sets of exponential type orbitals in standard convention and their origin
In standard convention, the new complete orthonrmal sets of exponential type
orbitals (ETOs) are introduced as functions of the complex or real spherical
harmonics and modified and -generalized Laguerre polynomials (MPLs and GLPs),
where, and is the noninteger or integer (for) frictional quantum number. It is
shown that the origin of the ETOs, MLPs and GLPs is the self-frictional quantum
forces which are analog of radiation damping or self-frictional forces
introduced by Lorentz in classical electrodynamics. The relations for the
quantum self-frictional potentials in terms of ETOs, MLPs and GLPs,
respectively, are established. We note that, in the case of disappearing
frictional forces, the ETOs are reduces to the oringers wave functions for the
hydrogen-like atoms in standard convention and, therefore, become the
noncomplete.Comment: 6 page
Nonrelativistic, Quasirelativistic and Relativistic Sets of Wave Functions, and Slater Orbitals of Particles with Arbitrary Spin
Using the complete orthonormal basis sets of nonrelativistic and
quasirelativistic orbitals introduced by the author in previous papers for
particles with arbitrary spin the new analytical relations for the -component
relativistic tensor wave functions and tensor Slater orbitals in coordinate,
momentum and four-dimensional spaces are derived, where. The relativistic
tensor function sets are expressed through the corresponding nonrelativistic
and quasirelativistic orbitals. The analytical formulas for overlap integrals
over relativistic tensor Slater orbitals with the same screening constants in
coordinate space are also derived.Comment: 9 pages, 3 table
Comment on Unified treatment for the evaluation of arbitrary multielectron multicenter molecular integrals over Slater-type orbitals with noninteger principal quantum numbers
Ozdogan (Int. J. Quantum Chem., 92 (2003) 419) published formulas for
evaluating the multielectron multicenter molecular integrals over Slater-type
orbitals (STOs). It is demonstrated that the formulas presented in this work
are not original and they can easily be derived by means of a simple algebra
from the relationship of our published papers (I.I.Guseinov,
J.Mol.Struct.(Theochem), 417(1997)117; J.Mol.Struct.(Theochem), 593 (2002) 65;
I.I.Guseinov,B.A.Mamedov,F.Oner,S.Huseyin, J.Mol.Struct.(Theochem),
545(2001)265; I.I.Guseinov,B.A.Mamedov, J.Mol.Model., 8(2002)272;
Theor.Chem.Acc., 108(2002)21).Comment: 5 page
Combined Theory of Basis Sets of Spinors for Particles with Arbitrary Spin in Position, Momentum and Four-Dimensional Spaces
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin
particles are established in position, momentum and four-dimensional spaces,
where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and
half-integral spins are reduced to the independent sets of one- and
twocomponent spinors, respectively. Relations presented in this study can be
useful in the linear combination of atomic orbitals approximation for the
solution of generalized Dirac equation of arbitrary spin particles introduced
by the author when the orthogonal basis sets of relativistic exponential type
spinor wave functions and Slater type spinor orbitals in position, momentum and
four -dimensional spaces are employed.Comment: 28 pages; 3 tables. arXiv admin note: substantial text overlap with
arXiv:1008.526
Comment on Formulas and numerical table for the radial part of overlap integrals with the same screening parametres of Slater-type orbitals
Recently published formulas for the calculation of radial part of overlap
integrals (E.Oztekin, M.Yavuz, S.Atalay, Theor.Cmem.Acc., (2001), 106, 264) are
critically analyzed. It is demonstrated that the presented in this work
formulas are not original and they can be easily be obtained from the formulas
already established in our papers.Comment: 3 page
New Complete Orthonormal Basis Sets of Relativistic Exponential Type Spinor Orbitals and Slater Spinor Functions of Particles with Arbitrary Half-Integral Spin in Position, Momentum and Four-Dimensional Spaces
Using the complete orthonormal sets of radial parts of nonrelativitistic
exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical
harmonics of rank s the new formulae for the 2(2s+1)-component relativistic
spinors useful in the quantum mechanical description of the arbitrary
half-integral spin particles by the generalized Dirac equation introduced by
the author are established in position, momentum and four-dimensional spaces,
where 1/ 2, 3 / 2, 5 / 2, ... s = . These spinors are complete without the
inclusion of the continuum. The 2(2s+1)component spinors obtained are reduced
to the independent sets of two-component spinors defined as a product of
complete orthonormal sets of radial parts of orbitals and twocomponent spinor
type tensor spherical harmonics. We notice that the new idea presented in this
work is the unified treatment of half-integral spin and scalar particles in
position, momentum and four-dimensional spaces. Relations presented in this
study can be useful in the linear combination of atomic orbitals approximation
for the solution of different problems arising in the relativistic quantum
mechanics when the orthonormal basis sets of relativistic exponential type
spinor wave functions and Slater type spinor orbitals in position, momentum and
four -dimensional spaces are employed.Comment: 27 pages, 4 figure
Unsymmetrical and symmetrical one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices
Using one-center expansion relations for the Slater type orbitals (STOs) of
noninteger principal quantum numbers in terms of integer n STOs derived in this
study with the help of - exponential type orbitals (-ETOs, the general formulas
are established for the unsymmetrical and symmetrical one-range addition
theorems of STOs and Coulomb-Yukawa like correlated interaction potentials
(CIPs) with integer and noninteger indices. The final results are especially
useful for computations of arbitrary multicenter multielectron integrals over
STOs that arise in the Hartree-Fock-Roothaan (HFR) approximation and also in
the correlated methods which play a significant role in theory and application
to quantum mechanics of atoms, molecules, and solids.Comment: 5 page
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