Hartree-Fock method basis sets used

We have used the terms SCF wave function and Hartree-Fock wave function interchangeably. In practice, the term SCF wave function is applied to any wave function obtained by iterative solution of the Roothaan equations, whether or not the basis set is large enough to give a really accurate approximation to the Hartree-Fock SCF wave function. There is only one true Hartree-Fock wave function, which is the best possible wave function that can be written as a Slater determinant of spin-orbitals. With current computer power, one can use very large basis sets for small molecules and obtain wave functions that differ negligibly from the true Hartree-Fock wave functions. Because of deficiencies in properties calculated from Hartree-Fock wave functions, several methods that go beyond the Hartree-Fock method are widely used (see Chapter 16). 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

Whereas there are only two different bond lengths in Ceo, short between atoms 1 and 2 and long between atoms 2 and 3, there are seven different bond lengths in C. The Crobond lengths have been calculated here and previously [12] by the restricted Hartree-Fock method using an STO-3G basis set and are discussed in some detail... 

Historically, Hartree-Fock methods were the first to attack many-particle problems, with considerable success for atoms and molecules. Cluster calculations can be employed to study impurities in this scheme. Ab initio Hartree-Fock methods are very computationally intensive, however, and thus restricted to small clusters. Correlation effects are neglected. The use of expanded basis sets (only a first step towards configuration-interaction analysis) rapidly increases computation time. 

Results for the other open-shell atoms are encouraging. One would expect the P3 method to be considerably less accurate when an unrestricted Hartree-Fock reference state is used. The lowest MAD for B -Ar obtains with the largest of the Dunning sets examined here, i.e. cc-pVQZ. The 6-311++G(3df,3pd) and well-tempered basis sets (WTBS) are roughly equivalent, with MADs of 0.50 eV and 0.57 eV, respectively. 

Table 3. Measured (Black and Law 2001) and ab initio vibrational frequencies for methyl chloride, C CX.Ab initio frequencies are calculated with GAMESS, using the Hartree-Fock method and 6-31G(d) basis set. The ratio of each measured and model frequency is also shown.

Accordingly, dipole moment and polarizability calculations are sensitive to both the quantum chemistry method and the basis set used. Accurate calculations typically require the use of D FTor Hartree-Fock methods with the inclusion of M P2 treatment of electron correlation [53, 54]. Furthermore, Gaussian basis sets should be augmented with diffuse polarization functions to provide an adequate description of the tail regions of density (the most easily polarized regions of the molecule). 

If the basis set used is finite and incomplete, solution of the secular equation yields approximate, rather than exact, eigenvalues. An example is the linear variation method note that (2.78) and (1.190) have the same form, except that (1.190) uses an incomplete basis set. An important application of the linear variation method is the Hartree-Fock-Roothaan secular equation (1.298) here, basis AOs centered on different nuclei are nonorthogonal. Ab initio and semiempirical SCF methods use matrix-diagonalization procedures to solve the Roothaan equations. 

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