ISSN:
1573-935X
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Abstract Quantum-chemical calculations show that in the Roothaan method, even when the Hartree-Fock energy limit is achieved, the basis set extension can significantly influence other molecular characteristics. In this work we study the influence of an additional (orthogonal to an initial basis set) orbital χ on one-electron levels, total energy, and quantities that are calculated as average values of one-electron operators. We assume that the initial M-dimensional basis is sufficiently good, so that adding orbital χ does not lead to the redistribution of occupied and virtual levels. Then, each occupied (M+1)-dimensional MO φi is approximately the same as the corresponding M-dimensional MO φi 0 and differs from it only by admixture of the other orbitals φk 0 and the function χ. The coefficients of φk 0 and χ in φi are considered to be small parameters, and molecular characteristics of interest are expanded in power series with respect to them. It has been established that a decrease in the total energy during the basis extension corresponds to the quadratic in these parameters terms while quantities calculated as average values of one-electron operators change linearly during the basis extension. A shift of one-electron levels εi during the basis extension is examined. It is shown that the MacDonald rule is satisfied if integrals containing the energy shift operator for electron interaction are small with respect to integrals 〈χ∣F0∣φj 0〉 where F0 is the Fock operator in the initial basis. An an illustration, results of calculations for H2 and HeH+ molecules in an ellipsoidal basis are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00525297
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