Ab Initio Packages

It is traditional to divide quantum-mechanical molecular models into three broad bands depending on their degree of sophistication. There are sublevels within each band, and a great deal of jargon accompanied by acronyms. Many authors speak of the level of theory . The Hiickel independent electron model of Chapter 7 typifies the lowest level of theory, and authors sometimes refer to these models as empirical . The Hamiltonian is not rigorously defined, and neither are the basis functions. Nevertheless, these models have been able to produce impressive predictions and rationalizations. 

At the other end of the spectrum are the ab initio ( from first principles ) methods, such as the calculations already discussed for H2 in Chapter 4. I am not trying to imply that these calculations are correct in any strict sense, although we would hope that the results would bear some relation to reality. An ab initio HF calculation of the potential energy curve for a diatomic Aj will generally give incorrect dissociation products, and so cannot possibly be right in the absolute sense. The phrase ab initio simply means that we have started with a certain Hamiltonian and a set of basis functions, and then done all the intermediate calculations with full rigour and no appeal to experiment. 

In between come the semi-empirical models such as PPP or ZINDO. Here we start with a rigorous Hamiltonian and perhaps a well-defined basis set, but we then calibrate the difficult integrals against experiment. 

I have deliberately restricted the discussion to quantum-mechanical models, so molecular mechanics is excluded from the classification. 

Over the last thirty years, international collaboration and cooperation on a scale rarely witnessed in science has led to the development of several very sophisticated software packages for ab initio molecular electronic structure calculations. In the early days, such packages were freely distributed amongst workers in the field. Today, you buy executable code, a licence and professional documentation just as with any software package. 

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You will easily reproduce Table 14.1 if you have access to an ab initio package. 

Over the years, geometry optimization has become an essential part of ab initio methodology. Research papers simply don t get published unless they report a geometry optimization. Almost all of the early ab initio packages made use of internal coordinates (bond lengths, bond angles and dihedral angles), as defined by the Z-matrix discussed in Chapter 1. The reason for the popularity of the... 

Many ab initio packages use this route to calculate the dipole for wavefunctions where analytical derivatives are known. 

Many ab initio packages use the two key equations given above in order to calculate the polarizabilities and hyperpolarizabilities. If analytical gradients are available, as they are for many levels of theory, then the quantities are calculated from the first or second derivative (with respect to the electric field), as appropriate. If analytical formulae do not exist, then numerical methods are used. 

Step (1) defines a particular set of CASSCF Cl coefficients, so that, by using this Cl vector, step (2) may be carried out by most current CASSCF programs, such as the one available in the MOLPRO ab initio package [39-41]. 

An important question concerns the relation of the present method with the one using diabatic orbitals. Such methods are implemented in standard ab initio packages such as MOLPRO [27] with emphasis in multiconfiguration-reference Cl and related methods. These methods are based on the particle model. 

The growth of computational chemistry and the ready availability of commercial ab initio packages has had a dramatic effect on the way that physical chemistry is practiced in the contemporary research laboratory. The clear implication is that without integration of computational chemistry into our physical chemistry laboratory curriculum we will be failing to teach our students how contemporary research is conducted. Fortunately, a number of approaches to including computational chemistry in the physical chemistry laboratory have been developed. These range from modifications of the full course to individual computational chemistry exercises for the laboratory. These developments can be found in Table VII. 

A.2 IMPLEMENTATIONS OF VALENCE BOND METHODS IN STANDARD AB INITIO PACKAGES... 

Hartree-Fock-level ab-initio calculations can provide reliable potential energy diagrams for small clusters. Such calculations can be applied to the zeolite lattice if the clusters are chosen carefully and use is made of the property that bonding is highly localized in these materials. Calculations were done using the GAMESS ab-initio package. 

As far as the QM programs are concerned, they can be divided into two types according to the level of approximation they use There are ab initio packages, such as GAUSSIAN94 [24] series, GAMESS [25], a special Density Func-... 

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