Hartree-Fock, ab initio, computational

The usual ab initio Hartree-Fock computations lead to the canonical orbitals which allow a simple assignment of an energy quantity ("orbital energy") to each orbital. In particular, the contour surfaces of the highest (highest-energy) occupied (HOMO) and lowest unoccupied (LUMO) orbitals, and the frontier orbitals [96,97] are often used to interpret properties of molecules and reactions. 

Figure 1. Comparison of the second virial coefUcients from experiments and computations with empirical ST2 and ab-initio Hartree-Fock, MCY and CI(2) potentials.

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. 

The calculations were performed employing either pure ab initio Hartree-Fock (HF) methods, or hybrid HF-DFT functionals, in particular B3LYP [22]. The hybrid functionals have several advantages. One is that they are commonly applied with great success in computational studies of molecules and clusters, thus making it possible to benefit from the gathered experience from molecular studies. Another is their recently noted ability to accurately model band gaps in semiconductor compounds [57]. 

Because of the latter contradiction an ab initio Hartree-Fock calculation has been performed (61). To reduce the computer time only a linear Ni—CO molecule has been studied. Such a calculation cannot be assumed to give accurate ionisation potentials of a chemisorbed system, but if the surface molecule picture is valid, it may supply us with some relevant information. The calculation predicts similar to the CNDO calculation that the first CO peak is due to the 1 n and 5a orbitals and the second peak due to the 4a orbital of CO. The ordering of the In and 55 orbitals of chemisorbed CO is, however, different from the ordering... 

The cluster approach is, like the extended-surface approach, characterized by many different calculational schemes. A recent review stresses electronic aspects of bonding. In this review we have chosen to concentrate on geometric aspects. We shall discuss a number of major techniques in order of increasing computational complexity the extended H uckel theory, self-consistent Xa scattered wave calculations, and self-consistent ab initio Hartree-Fock and valence bond methods. In that order these techniques allow increasing accuracy. However, the cluster size must decrease simultaneously due to calculational complexity, ultimately reducing the degree of analogy with surfaces. 

Usually, the parent molecules M are confined to some limited size that allows rapid determination of the parent molecule density matrices within a conventional ab initio Hartree-Fock-Roothaan-Hall scheme, followed by the determination of the fragment density matrices and the assembly of the macro-molecular density matrix using the method described above. The entire iterative procedure depends linearly on the number of fragments, that is, on the size of the target macromolecule M. When compared to the conventional ab initio type methods of computer time requirements growing with the third or fourth power of the number of electrons, the linear scaling property of the ADMA method is advantageous. 

Veillard is not convinced that ab initio Hartree-Fock theory will ever lead to the kind of black box calculations now possible for some organic molecules. Tsipis is rather more positive recognising the possibilities for a complementary interplay between theory and experiment but is nevertheless of the opinion that there exists no general canon for the efficacious selection and application of the most eligible computational method for the study of a certain compound or series of compounds . This view does not appear to be shared by Ziegler or Comba who convey quite positive messages concerning the capabilities of Density Functional Theory and Molecular Mechanics respectively. 

The energy of this Dsd structure was later computed by Lin and Hall and compares quite well at the ab initio Hartree-Fock level with that of the dodecahedron for Y8C12 (-20.1 kcal mol ) and for Nb8Ci2 (+3.6 kcal moL ). 

The definition of the gas-phase acidity through reaction (7.3) implies that this quantity is a thermodynamic state function. Thus, one could use quantum chemical approaches to obtain gas-phase acidities from the theoretically computed enthalpies of the species involved. However, two points must be noted before one proceeds A chemical bond is being broken and an anion is being formed. Thus, one may anticipate the need for a proper treatment of electronic correlation effects and also of basis sets flexible enough to allow the description of these effects and also of the diffuse character of the anionic species, what immediately rules out the semi-empirical approaches. Hence, our discussion will only consider ab initio (Hartree-Fock and post-Hartree-Fock) and DFT (density functional theory) calculations. 

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