ISSN:
1432-2234
Keywords:
Bessel functions, Slater-types-orbitals, addition theorems of ∼
;
Zeta function
;
Gegenbauer polynomials, spherical harmonics, expansions in ∼
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Abstract Addition theorems are derived for reduced Bessel functionsr N+1 k N (βr), wherek N is a modified spherical Bessel function, and for functionsr −N b N (βr) withb N being a spherical Bessel, Neumann, or Hankel function. Furthermore, addition theorems are derived for the logarithm, the Gaussian function, and the function (rcosθ) N , i.e. powers of the scalar product (e z ·r). With the help of the addition theorem of reduced Bessel functions one obtains a one-center expansion of Slater-types-orbitals, which can be compared with Barnett and Coulson's zeta function expansion. This yields a closed form expression of the zeta function. The given addition theorems for the functions considered, which in fact describe translations of these functions, are expansions in which the radial and angular dependencies are separated. The angular dependencies are expressed by spherical harmonics, as it is most appropriate for physical applications. For the derivations of the addition theorems use is made of the concept of generating functions for Gegenbauer polynomials. It turns out that the coefficientsT N l,k of the one-center expansion ofr N , which was given in the preceding paper, play a dominant role in all the expansions considered. Possible fields of applications of the theorems are scattering theory, the calculation of stationary states and other problems in molecular theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00963467
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