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Nonadiabatic singer polymal wave functions for three‐particle systems
Author(s) -
Poshusta R. D.
Publication year - 1983
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560240106
Subject(s) - wave function , adiabatic process , physics , total angular momentum quantum number , excited state , angular momentum , quantum mechanics , atomic physics , quantum , symmetry (geometry) , helium , degrees of freedom (physics and chemistry) , momentum (technical analysis) , quantum number , geometry , mathematics , finance , economics
A method for nonadiabatic many‐particle quantum‐mechanical calculations is described and illustrated for the special case of three particles. The method uses a basis of explicitly correlated Singer‐type exponential quadratic function (polymals) of the internal degrees of freedom. Rigorous symmetry states are projected from the basis: linear momentum of the center of mass, total angular momentum, and permutational symmetry under interchange of indistinguishable particles. The nonadiabatic wave functions are interpreted via purely quantum‐mechanical criteria of interparticle correlation as measured by average values of powers of interparticle distances and angles. The illustrations are made on H 2 + which is easily treated in the Born–Oppenheimer and adiabatic approximations, on helium, muonic helium, and on ( e + , e − , e + ) which are poorly described in adiabatic methods. The ground and lowest bound excited states of these systems are studied with up to 256 tempered Singer polymals for which we find energies too high by 0.0011 a.u. in H 2 + , 0.0017 a.u. in muonic helium, 0.0009 a.u. in 4 He, and 0.0002 a.u. in ( e + , e − , e + ); the corresponding relative errors are 1800, 4, 300, and 200 ppm, respectively.