Basis sets (from Computational Chemistry-Introduction to the Theory and Applications of Molecular and Quantum Mechanics 2ed,Errol Lewars)精品.pdfVIP

232 5 Ab initio Calculations variety of mathematical tricks. Among these are: the use of symmetry to avoid duplicate calculation of identical integrals; testing two-electron integrals quickly to see if they are small enough to be neglected (as is the case for functions on distant nuclei; this decreases the time of a calculation from an n4 dependence on the number of basis function to about an n2.3 dependence); recalculating integrals to avoid the bottleneck of hard-drive access (direct SCF, Section 5.3.2); representing the MOs as a set of gridpoints in space (in addition to a basis set expansion), which eliminates the need to explicitly calculate two-electron integrals. This pseudospectral method speeds up ab initio calculations by a factor of perhaps 3 or 4. Methods of speeding up calculations are explained, with references to the literature, by Levine [33]. The method of calculating wavefunctions and energies that has been described in this chapter applies to closed-shell, ground-state molecules. The Slater determinant we started with (Eq. 5.12) applies to molecules in which the electrons are fed pairwise into the MO’s, starting with the lowest-energy MO; this is in contrast to free radicals, which have one or more unpaired electrons, or to electronically excited molecules, in which an electron has been promoted to a higher-level MO (e.g. Fig. 5.9, neutral triplet). The Hartree–Fock method outlined here is based on closed-shell Slater determinants and is called the restricted Hartree–Fock method or RHF method; “restricted” means that the electrons of a spin are forced to occupy (restricted to) the same spatial orbitals as those of b spin: inspection of Eq. 5.12 shows that we do not have a set of a spatial orbitals and a set of b spatial orbitals. If unqualified, a Hartree–Fock (i.e. an SCF) calculation means an RHF calculatio