A. V. Bibikov

Basis set convergence studies of Hartree–Fock calculations of molecular properties within the resolution of the identity approximation

Within the resolution of the identity (RI) method, the convergence of the Hartree-Fock (HF) total molecular energy and the multipole moments in the course of the combined regular expansion of the molecular and auxiliary (RI) basis sets is studied. Dunnings cc-pVXZ series is used for both the molecular and the RI basis sets. The results show the calculated quantities converge to the HF limit when both the molecular and the RI basis sets are expanded from correlation-consistent polarized valence double zeta to correlation-consistent polarized valence sextuple zeta. Combinations of molecular/RI basis sets sufficient for convergence of the total energy and of the multipole moments at various accuracy levels have been determined. A measure of the RI basis set incompleteness is suggested and discussed. As it is significantly faster than the standard HF algorithm for small and midsize molecules, the RI-HF method, together with appropriate expanding series of both molecular and RI basis sets, provide an efficient tool to estimate and control the error of the Hartree-Fock calculations due to the finite basis set.

Electron capture beta decay of Be-7 encapsulated in C-60: Origin of increased electron density at the Be-7 nucleus

We offer a new theoretical interpretation for the effect of enhanced electron density at the 7 Be nucleus encapsulated in fullerene C 60 . Our ab initio Hartree-Fock calculations show that the electron density at the 7 Be nucleus in 7 Be@C 60 increases due to the attractive effective potential well generated by the fullerene. The 2s state in the isolated Be atom turns into a 3s state in the joint potential. This new state has higher energy and slightly larger amplitude at the Be nucleus than the previous 2s state. Moreover the 3s wave function has an additional node that appeared at a distance r ≃ 5a B from the center. The node imitates repulsion between the Be electron and the fullerene wall because the electron has zero probability to occupy this region. Such an imitation of the repulsion by means of the node in an attractive potential has a direct physical analogy in the theory of α-α and N-N nuclear interactions.