Ab initio approach

HCR and co-workers carried out a number of studies by employing 3D potential energy surfaces calculated by means of highly sophisticated ab initio approaches [88,91-101]. The results of these computations are in impressive agreement with the corresponding experimental findings. The discrepancies in the order of 100 wavenumbers, as in early ab initio studies [16,17], have been reduced in the HCR studies to only a few wavenumbers. In conclusion of their paper on the ( H ) system of NH2, Gabriel et al. state We believe... 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

Others report that the term first principles is being increasingly used because the Latin term ab initio can been seen as unnecessarily elitist and that there is no scientific significance in using one term rather than the other one. Others disagree, suggesting that first principles is favored by the DFT community since in this kind of work it is quite clear that some semi-empirical elements are introduced whereas the wavefunction or traditional ab initio approaches are less semi-empirical. 

Within these ab initio approaches the fact that certain elements... 

And yet in spite of these remarkable successes such an ab initio approach may still be considered to be semi-empirical in a rather specific sense. In order to obtain calculated points shown in the diagram the Schrodinger equation must be solved separately for each of the 53 atoms concerned in this study. The approach therefore represents a form of "empirical mathematics" where one calculates 53 individual Schrodinger equations in order to reproduce the well known pattern in the periodicities of ionization energies. It is as if one had performed 53 individual experiments, although the experiments in this case are all iterative mathematical computations. This is still therefore not a general solution to the problem of the electronic structure of atoms. 

Cao D, Lu GQ, Wieckowski A, Wasileski SA, Neurock M. 2005. Mechanisms of methanol decomposition on platinum A combined experimental and ab initio approach. J Phys ChemB 109 11622-11633. 

As was mentioned in Section 6.2.3, phenomenological CF models have been extensively used in the past to rationalize the electronic structure of lanthanide complexes [4, 40-50], and they are still in use nowadays [38, 39, 78, 79]. The ab initio approach described above is, in principle, able to provide accurate energies and wave functions of multiplets in lanthanide complexes. Nevertheless, even if ab initio calculations appear to be successful, CF description is still of great... 

Such a quantum ab-initio approach was initially performed by Csizmadia et al. 

A good computational test of the validity of OEMO theory is a high quality ab initio calculation6. However, other computational methods which are popular with chemists and which avoid the expense of ab initio approaches can also be useful, if judiciously applied, in testing the predictions of OEMO theory. These methods fall into two groups ... 

The issue of the chemical nature of graphene edges, and thus of (re)active sites, was addressed head-on by Radovic and Bockrath [29]. Density functional theory was used to minimize problems that truly ab initio approaches such as Hartree-Fock are known to have, but careful comparison with experimental results in several seemingly unrelated fields was also performed. The key argument of relevance here is that, rather than being H-terminated, the sites that are most relevant for the chemical (re)activity of sp2 hybridized carbon materials are of carbene- and carbyne-type, as illustrated below for the zigzag (a) and armchair edges (b). 

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