Strictly Ab Initio Methods

Exclusively ab initio methods have been rarely employed on CPs other than P(Ac). An example is a calculation, by Tanaka and Tanaka [232]. For the very detailed methodology used, reference is made to the original source [232]. 

5 Representative Combination Ab Initio/Semi-Empirical Methods 

In other work of the Br6das group [235], geometry optimizations up to the tetramer level using the semi-empirical AMI method were used, which were then (i.e. in reverse order to the above) input to restricted Hartree-Fock (RHF) 3-21G basis set calculations of the total energy of different rotational conformations for undoped and doped polymer forms. 

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While these approaches show much promise, they are not strictly ab initio methods as they require an a priori knowledge of the unit cell. However, they may prove useful in the structure solving packages used to interpret powder diffraction patterns where the unit cell is obtained early in the analysis but where it is not possible to use traditional structure determination methods. 

While some attempts were made to parameterize such semiemprrical methods to reproduce the results of ab initio methods, Dewar insisted that we should not fit to the results that way, rather we should fit directly to experimental results. His view was that this would be the only approach actually useful to chemists. While ab initio methods might fit to experiment eventually, they did not fit at all well at the lower levels of calculation that were possible at the time. If semiempirical methods could be adequately developed and fit to experiment, perhaps one could really reach chemical accuracy with orders of magnitude with less work than would be required by strictly ab initio methods. 

The current situation is that while quantum mechanics cannot calculate accurate heats of formation for molecules containing more than a few atoms by strictly ab initio methods, much of the difficulty can be circumvented empirically (later). 

The scaled-opposite-spin MP2 (SOS-MP2) method omits the E l contribution entirely and takes E = 1.3 os [Y. Jung et al., /. Chem. Phys., 121, 9793 (2004) J. Comput. Chem., 28, 1953 (2007)]. The SOS-MP2 method gives results slightly less accurate than the SCS-MP2 method, but is faster and can be applied to larger molecules than SCS-MP2. Of course, the use of empirical parameters makes the SCS-MP2 and SOS-MP2 methods no longer strictly ab initio methods. 

Molecular Orbital Calculations. The most sophisticated and theoretically rigorous of the molecular orbital methods are ab initio calculations. These are performed with a particular mathematical function describing the shape of the atomic orbitals which combine to produce molecular orbitals. These functions, or basis sets, may be chosen based on a convenient mathematical form, or their ability to reproduce chemical properties. Commonly used basis sets are a compromise between these two extremes, but strict ab initio calculations use only these mathematical functions to describe electronic motion. Representative of ab initio methods is the series of GAUSSIAN programs from Carnegie-Mellon University (11). In general, these calculations are computationally quite intensive, and require a large amount of computer time even for relatively small molecules. 

Finally, heats of reaction can be calculated by ab initio methods with the aid of isodesmic reactions (Section 5.5.2.2a), as indicated in Fig. 5.28 (actually, the scheme in Fig. 5.28 is not strictly isodesmic - for example, only on one side of the isodesmic equation is there an H-H bond). From this scheme... 

In recent years, density functional theory (DFT) has become the most widely used electronic structure method for large molecular systems. The Kohn-Sham DFT method accounts for exchange and correlation effects via a particular exchange correlation functional. In its present form, Kohn-Sham DFT is not, strictly speaking, an ab initio method, since the functionals contain empirical parameters. 

The idea of the quality of a theoretical calculation is difficult to quantify but can be notionally separated into two parts. First, and from a strictly computational viewpoint, one must discover how sensitive the computed quantities are to the user-defined features of a given computational scheme (e.g. basis set size and electron correlation treatment in ab initio methods, parameter values in empirical and semi-empirical methods). Secondly, how well does the method reproduce actual experiment. 

Quantum-chemical calculations on such a grand scale pose special requirements to the computational scheme. Clearly, the task is far beyond the scope of sophisticated ab initio methods of quantum chemistry. To solve the problem, we devised a specialized semiempirical method dubbed strictly local gemi-nals (SLG) [18-21]. The method is based on geminals... 

Some areas of computational electronic-structure theory are not treated in this book. All methods discussed are strictly ab initio. Semi-empirical methods are not treated nor is density-functional theory discussed all techniques discussed involve directly or indirectly the calculation of a wave function. Energy derivatives are not covered, even though these play a prominent role in the evaluation of molecular properties and in the optimization of geometries. Relativistic theory is likewise not treated. In short, the focus is on techniques for solving the nonrelativistic molecular... 

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. 

The only notable difference between classical ab initio VB and modem ab initio VB lies in the one-electron orbitals. As we already mentioned, in the classical ab initio VB method, all one-electron orbitals are strictly atomic orbitals. In contrast, in modem ab initio VB methods, one-electron orbitals are not restricted to atomic orbitals anymore and are allowed to extend over the whole molecule in the form of OEOs... 

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