XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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General Coalescence Conditions for the Exact Wave Functions
Yusaku I. Kurokawa, Hiroyuki Nakashima, and Hiroshi Nakatsuji
Quantum Chemistry Research Institute, JST, CREST, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245, Japan
  We derived necessary conditions for exact wave functions of the time-independent Schrödinger equation that must be satisfied at a coalescence (or cusp) region. Some of such conditions are already known as the Kato's cusp conditions (CC) [1] and Rassolov and Chipman's CC [2]. In this study, we have generalized them to be relations among higher order derivatives of wave functions. Furthermore, we have extended them to be applicable not only to the Coulombic system but also to any systems where the interaction between two particles is represented in power series of inter-particle distance. We named these conditions to be General Coalescence Conditions (GCCs). Any wave functions must satisfy GCCs; otherwise they never become exact. The Kato's CC and Rassolov and Chipman's CC are included in GCCs as special cases.
  We applied the Free Complement (FC) wave functions [3] (which is nearly exact) of the hydrogen atom in the ground and excited states, the harmonic oscillator, a system with interacting potential of V = r, and the helium atom to GCCs and confirmed that the FC wave functions satisfy GCCs.

 [1] T. Kato, Commun. Pure Appl. Math. 10, 151 (1957).
 [2] V. A. Rassolov and D. M. Chipman, J. Chem. Phys. 104 (24), 9908 (1996).
 [3] H. Nakatsuji, Phys. Rev. Lett. 93 (3), 030403 (2004); H. Nakatsuji, Phys. Rev. A 72 (6), 062110 (2005).


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