Gaussian series

All of these methods use just the new and current points to update the inverse Hessian. The default algorithm used in the Gaussian series of molecular orbital programs [Schlegel 1982] makes use of more of the previous points to construct the Hessian (and thence the inverse Hessian), giving better convergence properties. Another feature of this method is its use... 

The emphasis thus far has been upon classical approaches to evaluating GC CC,rostatic (although quantum-mechanical methods might be used in some instances to obtain atomic charges or solute molecule electronic densities.) However continuum models lend themselves very well to quantum-mechanical treatments of solute-solvent interactions, and have indeed been incorporated into several standard codes, such as the Gaussian series.29 GC CCtrostatiC is now given by,... 

The new and user-friendly tool created a subdiscipline of computational chemists who explored the molecular world with the GAUSSIAN series and many of the other packages, which sprouted alongside the dominant one. Today leading textbooks hardly include VB theory anymore, and when they do, the theory is misrepresented (59,60). Advanced quantum chemistry courses regularly teach MO theory, but books that teach VB theory are rare. This development of user-friendly ab initio MO-based software and the lack of similar VB software put the last nail in the coffin of VB theory and substantiated MO theory as the only legitimate chemical theory. 

In general the reported calculations used standard ab initio methods as implemented in the Gaussian series of programs. Details can be found in [4] and in our papers quoted in the text. 

Presently the most complete PCM implementation is available in the Gaussian series of programs [68] (Gaussian98 and the development version, Gaussian99, which will be distributed in the next future), allowing for ... 

Except as otherwise specified, all the results described in this subsection have been obtained by ab initio SCF calculations, at the 4-31G level. The geometry of each species has been fully optimized using the gradient techniques of the Gaussian series of programs (Binkley et al., 1981). 

SCF-type (see section 6.1) SE theories are based to a large extent on the approximate MO theory (see the book of this title [10]) developed by Pople and coworkers. The Pople school, however, went on to concentrate on the development of ab initio methods, and indeed it is for his contributions to these, which are largely encapsulated in the Gaussian series of programs [21], that Pople was awarded the 1998 Nobel Prize in chemistry [22] (shared with Walter Kohn, a pioneer in density functional theory see... 

We will illustrate the stages involved in the Roothaan-Hall approach using the helium hydrogen molecular ion, HeH, as an example. This is a two-electron system. Our objective here is to show how the Roothaan-Hall method can be used to derive the wavefunction, for a fixed internuclear distance of 1 A. We use HeH rather than H2 as our system as the lack of symmetry in HeH makes the procedure more informative. There are two basis functions, Isa (centred on the helium atom) and Isg (on the hydrogen). The numerical values of the integrals that we shall use in our calculation were obtained using a Gaussian series approximation to the Slater orbitals (the STO-3G basis set, which is described in Section 2.6). This detail need not concern us here. Each wavefunction is expressed as a linear combination of the two Is atomic orbitals centred on the nuclei A and B ... 

Quantum chemists have devised efficient short-hand notation schemes to denote the basis set used in an ab initio calculation, although this does mean that a proliferation of abbreviations and acronyms are introduced. However, the codes are usually quite simple to understand. We shall concentrate on the notation used by Pople and co-workers in their Gaussian series of programs (see also the appendix to this chapter). 

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