New Complete Orthonormal Sets of Exponential-Type Orbitals in Standard Convention and Their Origin

In standard convention, the new complete orthonormal sets of psi((alpha*))-exponential type orbitals (psi((alpha*))-ETOs) are introduced as functions of the complex or real spherical harmonics and L-(alpha*)-modified and L-(P*)-generalized Laguerre polynomials (L-(alpha*)-MLPs and L-(P*)-GLPs), psi((alpha*))(nlm)(zeta,(r) over right arrow) = (2 zeta)(3/2)e(-x/2)L(nl)((alpha*))(x)S-lm(theta,phi) [GRAPHICS] where, 0 < zeta < infinity, x = 2 zeta r, p* = 2l + 2 - alpha*, q* = n + l + 1 - alpha* and alpha* is the noninteger or integer (-infinity < alpha <= 2 for alpha* = alpha) frictional quantum number (-infinity < alpha* < 3 for alpha* not equal alpha). It is shown that the origin of the psi((alpha*))-ETOs, L-(alpha*)-MLPs and L-(p*)-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 psi((alpha*))-ETOs, L-(alpha*)-MLPs, and L-(p*)-GLPs, respectively, are established. We note that, in the case of disappearing frictional forces (for alpha* = 1 and zeta = Z/n), the psi((alpha*))-ETOs and eigenvalue are reduced to the Schrodinger's results in nonstandard convention for the hydrogen-like atom and, therefore, the psi((alpha*))-ETOs become the noncomplete, i.e., psi((1))(nlm) equivalent to psi(nlm). Here, the psi(nlm) is Schrodinger's wave function in nonstandard convention. As examples of an application of psi((alpha*))-ETOs as basis sets, the calculations have been performed for the total energies of some atomic and ionic systems.