Pauling valence-bond model

In the 1930s a theoretical treatment of the covalent bond was developed by, among others, Linus Pauling (1901-1994), then at the California Institute of Technology. The atomic orbital or valence bond model won him the Nobel Prize in chemistry in 1954. Eight years later, Pauling won the Nobel Peace Prize for his efforts to stop nuclear testing. 

Pauling- Wheland Valence-Bond Model 3.1 First Orthogonalization... 

The Knudsen effusion method In conjunction with mass spectrometrlc analysis has been used to determine the bond energies and appearance potentials of diatomic metals and small metallic clusters. The experimental bond energies are reported and Interpreted In terms of various empirical models of bonding, such as the Pauling model of a polar single bond, the empirical valence bond model for certain multiply-bonded dlatomlcs, the atomic cell model, and bond additivity concepts. The stability of positive Ions of metal molecules Is also discussed. 

The use of empirical models of bonding has been Invaluable for the interpretation of the experimental dissociation energies of diatomrLc Intermetallic molecules as well as for the prediction of the bond energies of new molecules. In the course of our work, conducted for over a decade, we have extended the applicability of the Pauling model of a polar single bond (31) and have developed new models such as the empirical valence bond model for certain multiple bonded transition metal molecules (32,33) and the atomic cell model (34). 

A comparison of experimental values for intermetallic diatomic molecules with gold with the corresponding value calculated by the Pauling model and by the atomic cell model has been given in Table 6 of Reference ( ). Table 7 of Reference ( ) shows a comparison between experimental dissociation energies with values calculated by the atomic cell model and the empirical valence bond model. Table 9 of Reference ( ) takes Mledema s refinements (43) of the atomic cell model into account In these comparisons. 

Empirical models have been developed to predict the bond energies of metallic and intermetallic molecules, such as the following the Pauling model of a polar single bond [174], the valence bond model for certain multiply bonded metallic molecules by Brewer [175] and Gingerich [176], and the macroscopic atom or atomic cell model by Miedema and Gingerich [177]. 

These results can be interpreted successfully in terms of Pauling s valence bond order concept. In the framework of this model, a chemical bond between X and H in diatomic molecule XH or between H and B in a HB molecule can be characterized by empirical valence bond orders Pxh and Phb decreasing exponentially with bond distance ... 

In the preceding section, we discussed the electron pair (2c-2e) bond and how it can be influenced by Pauli repulsion of the SOMOs with other electrons. In the three-electron (2c-3e) bond, Pauli repulsion plays an even more fundamental role, as we will see.72 The idea of the three-electron bond was introduced in the early 1930s by Pauling in the context of the valence bond (VB) model of the chemical bond.70 71 Since then, it has been further developed both in VB and in MO theory and has become a standard concept in chemistry.118-129 In VB theory,7°>71 118 123 the two-center, three-electron (2c-3e) bond between two fragments A and B is viewed as arising from a stabilizing resonance between two valence bond structures in which an electron pair is on fragment A and an unpaired electron on B (13a), or the other way around (13b) ... 

R.D. Harcourt in (a) Valence Bond Theory and Chemical Structure, D.J. Klein, N. Trinajstic, (eds.) Elsevier New York 1990, p. 251. (b) Quantum Mechanical Methods in Main-Group Chemistry, (T.M. Klapotke, A. Schulz) Wiley, Chichester 1998, p. 217. (c) Pauling s Legacy- Modern Theory (Modelling) of Chemical Bonding, Z.B. Maksic, W.J. Orville-Thomas, (eds.) Elsevier, New York 1999, p. 443. 

The Yamanouchi-Kotani basis is best suited if we want to solve the Heisenberg problem in the complete spin space. However, the number of spins that can be handled this way, soon reaches an end due to the rapid growth of the spin space dimension f(S,N). Even with the present day computers, the maximum number of spins that can be treated clusters around N = 30. For larger values of N one must resort to approximate treatments, one of which, as described hereafter, is based on the idea of resonating valence bonds (RVB) coming from the classical VB model developed by Pauling and Wheland back in the early 1930 s [37, 51]. In essence,... 

The chemist is accustomed to think of the chemical bond from the valence-bond approach of Pauling (7)05), for this approach enables construction of simple models with which to develop a chemical intuition for a variety of complex materials. However, this approach is necessarily qualitative in character so that at best it can serve only as a useful device for the correlation and classification of materials. Therefore the theoretical context for the present discussion is the Hund (290)-Mulliken (4f>7) molecular-orbital approach. Nevertheless an important restriction to the application of this approach must be emphasized at the start viz. an apparently sharp breakdown of the collective-electron assumption for interatomic separations greater than some critical distance, R(. In order to illustrate the theoretical basis for this breakdown, several calculations will be considered, the first being those for the hydrogen molecule. 

An understanding of the nature of the bond between the central ion and its ligands would have to await the development of Lewis shared-electron pair theory, and Pauling s valence-bond picture. We have already shown (Page 50) how hybridization of the d orbitals of the central ion creates vacancies able to accommodate one or more pairs of unshared electrons on the ligands. Although these models correctly predict the structures of transition metals, they are by themselves unable to account for several of their special properties ... 

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