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A momentum‐space picture of the chemical bond
Author(s) -
Avery John,
Hansen Tom Børsen
Publication year - 1996
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/(sici)1097-461x(1996)60:1<201::aid-qua22>3.0.co;2-g
Subject(s) - orthonormality , fock space , basis (linear algebra) , position and momentum space , orthonormal basis , quantum mechanics , reciprocal lattice , space (punctuation) , coulomb , wave function , atomic orbital , reciprocal , basis set , physics , kernel (algebra) , schrödinger equation , basis function , mathematics , mathematical physics , pure mathematics , geometry , molecule , linguistics , philosophy , diffraction , electron
The derivation of the reciprocal‐space Schrödinger equation is reviewed, as well as Fock's method for solving it for hydrogenlike atoms. It is shown that Fock's solutions (which represent Fourier transformed hydrogenlike orbitals in terms of 4‐dimensional hyperspherical harmonics) can be used as basis sets for solving other problems in quantum chemistry. Such basis sets are of the Sturmian type (i.e., all the members of the set correspond to the same energy), and they obey weighted orthonormality relations in both direct and reciprocal space. The kernel of the reciprocal‐space Schrödinger equation is expanded in terms of Sturmian basis sets, and this expansion is used to solve the problem of a particle moving in a many‐center potential. Both Coulomb and non‐Coulomb potentials are treated, and a new method for evaluating the necessary integrals is discussed. © 1996 John Wiley & Sons, Inc.