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Model Hamiltonians derived from Kohn–Sham theory
Author(s) -
Fournier René,
Jiang Nan
Publication year - 2000
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 - 10.1002/1097-461x(2000)80:4/5<582::aid-qua7>3.0.co;2-k
Subject(s) - hamiltonian (control theory) , kohn–sham equations , eigenvalues and eigenvectors , atomic orbital , basis set , molecular orbital , atom (system on chip) , basis (linear algebra) , physics , computational chemistry , quantum mechanics , statistical physics , chemistry , molecule , density functional theory , mathematics , computer science , geometry , electron , mathematical optimization , embedded system
We discuss a general way to derive approximate molecular orbital (MO) methods starting from some reference MO theory. In particular, we present a model Hamiltonian that is based on a Kohn–Sham reference and that is free of adjustable parameters. This Hamiltonian is a linear combination of atom‐centered ket‐bra operators, each of which is easily derived from the results of Kohn–Sham atomic calculations. The resulting equations are similar to those of extended Hückel (eH) theory and are as efficient computationally as eH. Orbital energies for a few small molecules show that this method is more stable with respect to choice of basis set, and slightly more accurate, than eH. We improved the accuracy of our model Hamiltonian by introducing parameters fitted to the higher level of theory. These parameters define a basis of pseudoatomic orbitals that are, in a certain sense, optimal for the molecule used in the fitting procedure. We illustrate our method by calculating the eigenvalue spectrum of silicon clusters. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 582–590, 2000