Covalent bonds molecular orbital methods

In this chapter, the basic ideas related to the molecular orbital approach to covalent bonds have been presented. Other applications of the molecular orbital method will be discussed in Chapters 5 and 17. 

The nature of the chemical bond between ions is investigated in the perovskite-type hydrides, MMgH3 (M = Na, K, Rb), CaNiH3/ and SrPdH3 by the DV-Xx molecular orbital method. Also, the enthalpy changes in the dehydrogenation reactions are calculated using the pseudopotential method. It is found that the Mg-H bond is rather ionic, but the covalent interaction still remains to some extent. On the other hand, the M-H bond is further ionic. 

Resonance structures of molecules are more stable than the hypothetical static forms from which they are derived. When orbitals extend over an entire molecule, the electrons in the expanded orbitals can have longer wavelengths and correspondingly lower energy. The ideas behind delocalization led scientists to a more rigorous approach to understanding the covalent bond than the methods covered so far. That approach is called molecular orbital theory. 

Theoretical calculations of organolithium species have received considerable attention. The low atomic number of lithium is suitable for the most sophisticated molecular orbital methods. Although much debate exists over the degree of covalency within lithium carbon-bonding interactions, the presence of some covalent character in Li bonds of alkyllithinm componnds is widely accepted. 

The electronic state calculations of transition metal clusters have been carried out to study the basic electronic properties of these elements by the use of DV-Xa molecular orbital method. It is found that the covalent bonding between neighboring atoms, namely the short range chemical interaction is very important to determine the valence band structure of transition element. The spin polarization in the transition metal cluster has been investigated and the mechanism of the magnetic interaction between the atomic spins has been interpreted by means of the spin polarized molecular orbital description. For heavy elements like 5d transition metals, the relativistic effects are found to be very important even in the valence electronic state. 

We will now have a look at two possible ways of viewing a covalent bond between atoms. They are known as the valence bond method and the molecular orbital method. We will consider the theory of the methods separately and judge the merits of both approaches when we come to examples later. 

The mechanism of Si-O chemical bonding was analyzed for covalent and ionic bond orders in p- and Y-C2S. Each bond order was evaluated by an overlapping population calculated by the DV-Xa molecular orbital method (Xiuji et al. 1994). There are slight differences in computed covalent and ionic bond orders obtained for both dicalcium silicates. However, Xiuji et al. (1994) demonstrated that the differences in hydraulic activity between p- and Y-C2S do not arise from the difference of Si-O chemical bonding. Further investigation will be required to establish the relationship between these differences in the crystal structure to hydraulic activity of belite. 

The UHE wave function can also apply to singlet molecules. Usually, the results are the same as for the faster RHEmethod. That is, electrons prefer to pair, with an alpha electron sharing a molecular space orbital with a beta electron. Use the UHE method for singlet states only to avoid potential energy discontinuities when a covalent bond is broken and electrons can unpair (see Bond Breaking on page 46). 

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

The H7+ molecule-ion, which consists of two protons and one electron, represents an even simpler case of a covalent bond, in which only one electron is shared between the two nuclei. Even so, it represents a quantum mechanical three-body problem, which means that solutions of the wave equation must be obtained by iterative methods. The molecular orbitals derived from the combination of two Is atomic orbitals serve to describe the electronic configurations of the four species H2+, H2, He2+ and He2. 

COVALENT BOND FORMATION-MOLECULAR ORBITAL (MO) METHOD... 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

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