arXiv subjects

I. I. Guseinov

Publications and source records attributed to I. I. Guseinov.

At least 19 recordsLinked to original sources

arXiv2013

One-Range Addition Theorems in Terms of -ETOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices

In this study, the one-center expansion formulas in terms of complete orthonormal sets of -exponential type orbitals (-ETOs,) are established for the Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) of integer and noninteger indices. These relations are used in obtaining the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb-Yukawa like CIPs. The final results are especially useful in the calculations of multicenter multielectron integrals of STOs and CIPs occurring when Hartree-Fock-Roothaan (HFR) and explicitly correlated method are employed.

physics.chem-ph↗

arXiv2013

Unified treatment of complex and real rotation-angular functions for two-center overlap integrals over arbitrary atomic orbitals

The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, nuclei and solids when the integer and noninteger n complex and real atomic orbitals basis sets are emploed. This work presented the development of our previous paper (I.I. Guseinov, Phys. Rev. A, 32 (1985) 1864).

physics.chem-ph↗

arXiv2012

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.

physics.gen-ph↗

arXiv2012

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.

physics.gen-ph↗

arXiv2012

Use of group theory and Clifford algebra in the study of generalized Dirac equation for particles with arbitrary spin

Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin particles, this equation is reduced to the sets of two-component independent matrix equations. It is shown that the relativistic scalar and integral spin particles are described by component equation.

physics.gen-ph↗

arXiv2012

New development in theory of Laguerre polynomials

The new complete orthonormal sets of -Laguerre type polynomials (-LTP,) are suggested. Using Schrödinger 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.

math-ph↗

arXiv2012

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.

math-ph↗

arXiv2010

Expansion and one-range addition theorems for complete orthonormal sets of spinor wave functions and Slater spinor orbitals of arbitrary half-integral spin in position, momentum and four-dimensional spaces

The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater spinor orbitals of arbitrary half-integral spin. These theorems are expressed through the corresponding nonrelativistic expansion and one-range addition theorems of the spin-0 particles introduced by the author. The expansion and one-range addition theorems derived are especially useful for the computation of multicenter integrals over exponential type spinor orbitals arising in the generalized relativistic Dirac-Hartree-Fock-Roothaan theory when the position, momentum and four-dimensional spaces are employed.

math-ph↗

arXiv2009

Evaluation of potential energy of interaction between molecules using one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials

Using one-range addition theorems for noninteger n Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials with noninteger indices obtained by the author with the help of complete orthonormal sets of exponential type orbitals, the series of expansion formulas are established for the potential produced by molecule, and the potential energy of interaction between molecules through the radius vectors of nuclei of molecules, and the linear combination coefficients of molecular orbitals. The formulae obtained are useful especially for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the Hartree-Fock-Roothaan and explicitly correlated methods are employed. The relationships obtained are valid for the arbitrary values of indices and screening constants of orbitals and correlated interaction potentials.

math-ph↗

arXiv2009

Expansion formulae for one- and two-center charge densities over complete orthonormal sets of exponential type orbitals and their use in evaluation of multicenter-multielectron integrals

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations are expressed through the two-center overlap integrals between -orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter-multielectron integrals occurring when the complete orthonormal sets of exponential type orbitals are used as basis functions in the Hartree-Fock-Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter-multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants and location of orbitals.

physics.chem-ph↗

arXiv2008

Combined theory of two- and four- component complete orthonormal sets of spinor wave functions and Slater type spinor orbitals in position, momentum and four-dimensional spaces

By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two- and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin- 1/2 particles by the quasirelativistic and Dirac's relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four-component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the quasirelativistic and relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.

physics.chem-ph↗

arXiv2008

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.

physics.gen-ph↗

arXiv2008

Use of Combined Hartree-Fock-Roothaan Theory in Evaluation of Lowest States of K [Ar]4s^0 3d^1 and Cr+ [Ar]4s^0 3d^5 Isoelectronic Series Over Noninteger n-Slater Type Orbitals

By the use of integer and noninteger n-Slater Type Orbitals in combined Hartree-Fock-Roothaan method, self consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K [Ar]4s^0 3d^1 2(D) (Z=19-30) and Cr+ [Ar] 4s^0 3d^5 6(S) (Z=24-30). The results of calculations for the orbital and total energies obtained from the use of minimal basis sets of integer- and noninteger n-Slater Type Orbitals are given in tables. The results are compared with the extended-basis Hartree-Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results are accurately and considerably can be useful in the application of non-relativistic and relativistic combined Hartree-Fock-Roothaan approach for heavy atomic systems.

physics.chem-ph↗

arXiv2008

Combined theory of complete orthonormal sets of quasirelativistic and relativistic sets of wave functions, and Slater orbitals of spin -1/2 particles in position, momentum and four dimensional spaces

By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin - 1/2 particles by the quasirelativistic and relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the quasirelativistic and relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.

physics.chem-ph↗

arXiv2007

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.

physics.chem-ph↗

arXiv2007

Combined Extended Rejoinder to "Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys., Vol. 309 (2005), pp. 209-213)"

This article is a thorough critique to the Weniger's comments made to our papers published in prestigious journals in the recent years. A detailed and critical examination of the arguments that led to the suggested comment by Weniger reveals some serious flaws. In our published papers we have shown that the unsymmetrical and symmetrical one-range addition theorems for Slater type orbitals, Coulomb-Yukawa like correlated interaction potentials (CIPs) and their derivatives are derived from the expansions in terms of -ETOs that are complete and orthonormal sets of exponential type orbitals in corresponding Hilbert spaces, where The concrete criticism raised in Weniger's comment against our papers actually touches a very minor aspect of the works that are not relevant at all for the conclusions, which are made. As can be seen from our papers, all of the formulas for different kinds of multicenter integrals over Slater type orbitals with integer and noninteger principal quantum numbers obtained by the use of unsymmetrical and symmetrical one-range addition theorems were tested by computer calculations. We reject the Weniger's personal views about papers published by Guseinov and his coworkers from 1978 to 2006 and respectable referees on one-range addition theorems and multicenter integrals. All claims of inconsistencies and flaws in the theoretical framework are rejected as unfounded. This rejoinder paper contains all of the answers to Weniger's comments.

physics.chem-ph↗

arXiv2007

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.

physics.chem-ph↗

arXiv2007

On the accurate evaluation of overlap integrals over Slater type orbitals using analytical and recurrence relations

In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals (STOs) is presented. The proposed procedure guarantees a highly accurate evaluation of the overlap integrals with arbitrary values of quantum numbers, screening constants and internuclear distances. It is demonstrated that the computational accuracy of the proposed procedure is not only dependent on the efficiency of formulas, as has been discussed previously, but also on a number of other factors including the used program language package and solvent properties. The numerical results obtained using the algorithm described in the present work are in a complete agreement with those obtained using the alternative evaluation procedure. We notice that the program works without any restrictions and in all range of integral parameters.

physics.chem-ph↗