Quantum-chemical methods valence bond method

Table 4 contains the X-ray structure analysis data obtained for A3 (interatomic distances and angles) in comparison with the results of A3 structure optimization by various quantum-chemical methods. The bond lengths and valence angles of the acridine nucleus are close to those of other acridine derivatives [46,47], On the whole, both calculation methods used reproduce the geometric parameters of the A3 molecule. 

This theory appears not to involve adjustable parameters (other than the nuclear radius parameters that were taken from the literature). In particular, it was criticized that the calibration approach involved a slope that is too high by about a factor of two. However, in actual calculations with the linear response approach, it was found that the slope of the correlation line between theory and experiment (dependent on the quantum chemical method) is close to 0.5. Thus, it also requires a scaling factor of about 2 in order to reach quantitative agreement with experiment. The standard deviations between the calibration and linear response approaches are comparable thus indicating that the major error in both approaches still stems from errors in the description of the bonding that is responsible for the actual valence shell electron distribution. 

Quantum chemists have developed considerable experience over the years in inventing new molecules by quantum chemical methods, which in some cases have been subsequently characterized by experimentalists (see, for example, Refs. 3 and 4). The general philosophy is to explore the Periodic Table and to attempt to understand the analogies between the behavior of different elements. It is known that for first row atoms chemical bonding usually follows the octet rule. In transition metals, this rule is replaced by the 18-electron rule. Upon going to lanthanides and actinides, the valence f shells are expected to play a role. In lanthanide chemistry, the 4f shell is contracted and usually does not directly participate in the chemical bonding. In actinide chemistry, on the other hand, the 5f shell is more diffuse and participates actively in the bonding. 

The theory of resonance should not be identified with the valence-bond method of making approximate quantum-mechanical calculations of molecular wave functions and properties. The theory of resonance is essentially a chemical theory (an empirical theory, obtained largely by induction from the results of chemical experiments). Classical structure theory was developed purely from chemical facts, without any help from physics. The theory of resonance was also well on... 

I think that the theory of resonance is independent of the valence-bond method of approximate solution of the Schrodinger wave equation for molecules. I think that it was an accident in the development of the sciences of physics and chemistry that resonance theory was not completely formulated before quantum mechanics. It was, of course, partially formulated before quantum mechanics was discovered and the aspects of resonance theory that were introduced after quantum mechanics, and as a result of quantum mechanical argument, might well have been induced from chemical facts a number of years earlier. [25]... 

However, there exists a vast literature of ab initio quantum chemical methods which are described in terms of either the molecular orbital (MO) or valence bond (VB) schemes for determining the electronic and geometric structure of molecules. The application of these methods to surface problems has advanced rapidly in recent years, as we shall discuss in this section. 

Computational methodology has been used to accompany or to anticipate experimental results for many classes of compounds. Such results are particularly helpful for transient species, for rationalization of physical and structural properties, and for simulation of reaction pathways and transition states. Semiempirical valence electron (CNDO/MNDO), ab initio, and nonquantum mechanical force field (molecular mechanics) calculations have mainly been used for the examination of structure and stability of moderately strained olefins, whereas many-electron quantum-chemical methods have been used for detailed discussion of electronic aspects. Excellent reviews of molecular mechanics calculations, the principal method used to describe geometrical and energy features in distorted double bond systems, have been written by Osawa and Musso (61). 

In between, the relationship of the two main quantum-chemical methods was established in the general sense by Slater [86] and later by Longuet-Higgins [87]. The fact that molecular orbital and valence bond methods must, if used with the same basis set and the... 

Quantum theory provides us with two fundamental methods for the study of the electronic structure of molecules the valence-bond method, whose simplified qualitative version is referred to frequently as the resonance theory, and the molecular-orbital method. Both represent approximate procedures for obtaining approximate solutions of the Schrddinger equation relative to molecules. This equation is the basic equation of the quantum theory and its resolution provides the electronic energy levels and the distribution of the electronic cloud in chemical systems. Approximate procedures are needed because we are unable, at present, to solve rigorously the Schro-dinger equation for any atomic or molecular system beyond the very simplest ones. 

This last sentence makes clear Slater s attitude toward quantum chemistry. Contrary to Pauling, who was definitely in favor of the valence bond method as the mathematical expression of a chemical theory such as resonance. Slater considered both methods as mathematical approximations used in order to gain access to more fundamental physical principles. What really attracted Slater was the search for a unified view of the problem of molecule formation, in which both approximate methods would be treated so that one would manage to get at the essential physical features of the problem situation, forgetting, in the process, the particular method of approximation used. 

Brief mention may be made of earlier bonding indices (often originating from Hiickel MO theory) whose usefulness can be enhanced in the modem ab initio context by using NAOs or NHOs. These allow a closer connection to be drawn between the qualitative Huckel-type concepts of elementary valence theory and the quantitative results of rigorous quantum chemical methods. 

R.D. Harcourt, (a) J. Phys. Chem. A, 101,2496,5962 (1997). (b) in Increased-valence Structures in Quantum Chemical Methods in Main-Group Chemistry (T.M. Klapdtke and A. Schulz, Wiley 1998), pp. 217-253. (c) in Pauling s Legacy Modem Modelling of the Chemical Bond , Theoretical and Computational Chemistry, Vol. 6 (Elsevier Science B. V., Z.B. Maksic and W.J. Orville-Thomas editors, 1999) pp. 449 80. 

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