VALENCE-ELECTRON CORRELATION IN EXTENDED SYSTEMS - A NONPARAMETRIC EXPONENTIAL TRANSFORMATION OF MOLECULAR-ORBITALS INTO VALENCE-BOND WAVE-FUNCTIONS

From the exact solution of the homoatomic two-center problem one may define a bond factor rho-1 (hereafter named bond correlance) characterizing the reduction of the ionic valence-bond component in the correlated wave function: rho-1 = 1n(C(ionic)exact/C(ionic)uncorrelated), for any t/U (delocalization versus electronic repulsion) ratio. For an N-center problem, an excellent correlated wave function may be obtained by decomposing the single-determinantal wave function phi-0 into its valence-bond components phi-I and then multiplying C(I) = <phi-I/phi-0> by exp(- SIGMA-i,j q(i)Iq(j)I-rho-ij(eff)), where q(i)I and q(j)I are the net charges (0, +/- 1) of the atoms i and j in phi-I, and rho-ij(eff) is obtained by combining the bond correlances of the bonds between atoms i and j according to Kirchhoff's laws for the electrical resistances. This nonparametric wave function gives at least 90% of the correlation energy for a large series of structures involving up to 12 atoms, and is able to treat heterogeneous systems involving bonds of various t/U ratios.