No abstract

Recently, usefulness of the noninteger principal quantum numbers for Bessel type orbitals was discussed by Weniger [1]. In this study, we analyzed the applicability and numerical accuracy of basis sets of noninteger Bessel type orbitals to electronic structure calculations. Both numerical and analytical approaches are applied to two-electron atomic systems. The results of the numerical test demonstrated the potential of the noninteger values of principal quantum number for the improving of Bessel type functions approach in use of LCAO methods. Nevertheless, the analytical approach is still not suitable and in development and needs to be investigated further. The performance of the presented basis functions is also compared to the numerical Hartree-Fock results.

Bu çalışmanın amacı, baş kuantum sayısı tamsayı olmayan Bessel tipli orbitallerin Hartree-Fock-Roothaan yöntemi ile atomik sistemlere uygulanabilirliğini ve literatürdeki diğer üstel tipli orbitallerden üstünlüklerini incelemektir. Birleşik Hartree-Fock-Roothaan yönteminde yeni önerilen Bessel tipli orbitaller kullanılarak, iki elektronlu atomik sistemlerin orbital ve temel durum enerji değerleri hesaplanmıştır. Minimal baz çerçevesinde oluşturulan yeni baz fonksiyonları ile elde edilen değerler tablolarda karşılaştırmalı olarak verilmiştir. Elde edilen sonuçlar, literatürde kullanılan benzer üstel tipli baz fonksiyonlarına göre daha iyi değerler vermekte ve sayısal Hartree-Fock değerleri ile çok iyi uyum sağlamaktadır.

Recently, we reported a new set of Bessel type orbitals, which include the radial part of generalized Bessel functions for LCAO calculations of atomic systems. In this study, to achieve further improvement of the performance of generalized Bessel type basis sets in the Hartree-Fock-Roothaan calculations, different hyperbolic cosine functions inserted into the radial part of those generalized Bessel functions. For this purpose, three different generalized hyperbolic cosine functions have been used to construct the generalized Bessel type hyperbolic cosine basis sets. The accuracies of generalized Bessel type hyperbolic cosine orbitals within the minimal basis sets approach are compared to show their superiority to conventional approaches those in the literature. The performance of the presented basis functions is also compared to the numerical Hartree-Fock results. Our virial ratios are in good agreement to within 8-digits of the -2. It is shown that the results obtained by the new basis sets surpass the quality and accuracy of existing BTOs basis sets

Recently, usefulness of the noninteger principal quantum numbers for Bessel type orbitals was discussed by Weniger [1]. In this study, we analyzed the applicability and numerical accuracy of basis sets of noninteger Bessel type orbitals to electronic structure calculations. Both numerical and analytical approaches are applied to two-electron atomic systems. The results of the numerical test demonstrated the potential of the noninteger values of principal quantum number for the improving of Bessel type functions approach in use of LCAO methods. Nevertheless, the analytical approach is still not suitable and in development and needs to be investigated further. The performance of the presented basis functions is also compared to the numerical Hartree–Fock results.