Calculation of Arbitrary Overlap Integrals over Slater Type Orbitals Using Basic Overlap Integrals

The recurrence relations are presented for the calculation of basic overlap integrals, by making use of which other overlap integrals are calculated analytically. These recurrence relations are especially useful for the calculation of any overlap integral for large quantum numbers. For the arbitrary values of screening constants of atomic orbitals and internuclear distances an accuracy of the computer results is satisfactory for the values of principal quantum numbers of Slater functions up to 50.     

Calculation of magnetic multipole moment integrals using translation formulas for Slater-type orbitals

Using translation formulas for Slater type orbitals (STO’s) the infinite series through the overlap integrals are derived for the magnetic multipole moment integrals. By the use of the derived expressions the magnetic multipole moment integrals, therefore, the magnetic properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of 10⁻⁵ for the computer results is obtained in the case 2 ^p -pole magnetic moment integrals for 1 ≤ v ≤ 5, and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

On the Evaluation of Two-Center Overlap Integrals over Integer and Noninteger -Center Overlap Integrals over Integer and Noninteger n-Slater-Type Orbitals

In this study, two-center overlap integrals over Slater-type orbitals (STOs) with integer and noninteger principal quantum numbers in unaligned coordinate systems have been calculated using formulas for overlap integrals in aligned coordinate systems obtained by the author's previous work (T. Ozdogan and M. Orbay, Int. J. Quant. Chem. 87(2002) 15). The obtained results for integer case have been found to be in excellent agreement with the prior literature.On the other hand, to the best of authors knowledge, because of the scarcity of the literatures on the use of noninteger n-STOs in unaligned coordinate systems, the results for noninteger case have been tested with the limit of integer case,and good agreement has been obtained too.     

Evaluation of Multicenter Nuclear Attraction Integrals by the Use of Translation Formula for Slater Type Orbitals

By the use of translation formula for Slater type orbitals (STOs), three-center nuclear attraction integralsare represented in terms of two-center overlap and nuclear attraction integrals. The computing results for the formulapresented here has been tested under wide changes in molecular parameters and good convergence has been obtainedwith the prior literature.     

On the Evaluation of Two-Center Overlap Integrals over Integer and Noninteger n-Slater-Type Orbitals

In this study, two-center overlap integrals over Slater-type orbitals (STOs) with integer and noninteger principal quantum numbers in unaligned coordinate systems have been calculated using formulas for overlap integrals in aligned coordinate systems obtained by the author's previous work (T. Özdogan and M. Orbay, Int. J. Quant. Chem. 87 (2002) 15). The obtained results for integer case have been found to be in excellent agreement with the prior literature. On the other hand, to the best of authors knowledge, because of the scarcity of the literatures on the use of noninteger n-STOs in unaligned coordinate systems, the results for noninteger case have been tested with the limit of integer case, and good agreement has been obtained too.     

Higher Electric Multipole Moments for Some Polyatomic Molecules from Accurate SCF Calculations

Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.     

On Evaluation of Overlap Integrals with Noninteger Principal Quantum Numbers

By use of complete orthonormal sets of ψ^α exponential-type orbitals (ψ^α-ETOs,α=1,0,-1,-2,...) the series expansion formulas for the noninteger n Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals (ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.     

Higher Electric Multipole Moments for Some Polyatomic Molecules from Accurate SCF Calculations

Higher electric multipole moments for the ground-state electronic configuration of some polyatomic molecules, i.e. CH₄, NH₃, H₂O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets. The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical and experimental ones.     

Electric Multipole Moments for Some First—Row Diatomic Hydride Molecules

As an example of the use of the analytical formulas derived for electric multipole moment integrals over STOs in our previous work(I.I.Guseinov,et al.,J.Mol.Struct(Theochem)465(1999)5),the 2ν-pole electric moments have been calculated for the ground electronic states of LiH,BH and FH of the first-row diatomic hydride molecules,Calculated electric multipole moment values are in agteement with literatures.By the use of these analytical formulas the 2^ν-pole moments for multiatomic molecules can be evaluated most efficiently and accurately by employing STOs as basis sets.     

Response to "Comment on ‘Electric Multipole Moments for Some First-Row Diatomic Hydride Molecules' [Commun. Theor. Phys. 38 (2002) 256]"

The comment of Guseinov is irrelevant and also unjust. In contrast to his comment, we show that theobtained electric multipole moment values for some first-row diatomic molecules are original and better than his values(I.I. Guseinov, E. Akin, and A.M. Rzaeva, J. Mol. Struct. (Theochem) 453 (1998) 163) with respect to Hartree-Fockvalues. Moreover, it must be noted that all the formulas are cited in our paper (M. Orbay and T. Ozdogan, Commun.Theor. Phys. (Beijing, China) 35 (2001) 585) and corrigendum (M. Orbay and T. Ozdogan, Commun. Theor. Phys.(Beijing, China) 37 (2002) 768).     

On the Evaluation Overlap Integrals with the Same and Different Screening Parameters Over Slater Type Orbitals via the Fourier-Transform Method

In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.     

On Evaluation of Overlap Integrals with Noninteger Principal Quantum Numbers

By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals(ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.     

Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of Ψα-exponential type orbitals(α = 1,0,1,2,...),this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree-Fock-Roothaan equations for molecules.The final results are expressed through multicentre charge density expansion coefficients and basic integrals.The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.     

On the Calculation of Two-Center Overlap Integrals with STO's Using Zeta-Function Method and Multipole Moments

One electron two-center overlap integrals are re-derived using Barnett's -function method and Guseinov electric-multipole-moments translation technique. To evaluate these integrals a computer program has been constructed. The obtained results are in good agreement with literature.     

Evaluation of Coulomb Energy Difference for Light Mirror Nuclei Using Slater—Type Orbitals

Behavior of the Coulomb energy difference for light nuclei is explained in terms of the different values of the average Coulomb interaction between two particles.Coulomb energy difference according to shell model of light mirror nuclei in the Coulomb and exchange integrals in the formula can be explained with exponential-type wavefunctions.In this study,using the one-center expansion of exponential-type wavefunctions in terms of Slater-type orbitals with the same center,we derived formula for Coulomb energy difference of light mirror nuclei.     

The Symmetry Properties of Linear Combination Coefficients for Molecular Orbitals of Diatomic Molecules

In this paper, the symmetry properties of linear combination coefficients for molecular orbitals of diatomicmolecules, using Slater type orbitals, are presented with the help of the symmetry operations in group theory. In order totest the presented symmetry properties, the linear combination coefficients of molecular orbitalsfor the ground electronicstate of pilot molecules F2 and CO are calculated using constructed computer programs for Hartree-Fock-Roothaanequation. It is seen that the obtained computing results satisfy the presented symmetry properties.     

Identities for Hypergeometric Integrals of Different Dimensions

Given complex numbers m₁, I₁ and nonnegative integers m₂, I₂, such that m₁+m₂ = I₁+ I₂, we define I₂-dimensional hypergeometric integrals I_a,b(z; m₁, m₂, I₁, I₂), a,b = 0,. . . ,min)(m₂,I₂), depending on a complex parameter z. We show that I_a,b(z;m₁, m₂,I₁, I₂) = I_a,b(z;I₁, I₂,m₁,m₂), thus establishing an equality of I₂ and m₂-dimensional integrals. This identity allows us to study asymptotics of the integrals with respect to their dimension in some examples. The identity is based on the ( _k, _k,) duality for the KZ and dynamical differential equations.Mathematics Subject Classifications (2000). 33C70, 33C80, 81R10     

Path Integrals for a Class of P-Adic Schrödinger Equations

The theme of doing quantum mechanics on all Abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-Archimedean locally compact division ring, it is of interest to examine the structure of dynamical systems defined by Hamiltonians analogous to those encountered over the field of real numbers. In this Letter, a path integral formula for the imaginary time propagators of these Hamiltonians is derived.     

Quadratic Integrals of Motion for the Systems of Identical Particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in Hamilton-Jacobi equation is clarified.