Theories of Bonding

Molecular-orbital theory treats molecule formation from the separated atoms as arising from the interaction of the separate atomic orbitals to form new orbitals (molecular orbitals) which embrace the complete framework of the molecule. The ground state of the molecule is then one in which the electrons are assigned to the orbitals of lowest energy and are subject to the Pauli exclusion principle. Excited states are obtained by promoting an electron from a filled molecular orbital to an orbital which is normally empty in the ground state. The form of the molecular orbitals depends upon our model of molecule formation, but we shall describe (and use in detail in Sec. IV) only the most common, viz., the linear combination of atomic orbitals approximation. 

In any molecule, the potential close to a nucleus approximates that of the free atom (in the correct valence state) consequently, in these regions the molecular orbitals lie near the free atomic orbitals. Accordingly, it is generally assumed that the molecular orbitals may be expressed as linear combinations of the separate atomic orbitals, the LCAO approximation. The total electronic energy of the molecule may then be minimized with respect to the coefficients in this approximation and the form of the molecular orbitals thus determined. If the molecular orbitals 0, are expressed in terms of the set of atomic orbitals b. .., f N as 

Evaluation of these integrals and expansion of the above determinant leads to a polynomial of degree N in , the roots of which give the energies of the molecular orbitals constructed in the above manner. The coefficients Cfj may be determined by substitution of the particular E into the simultaneous linear equations covered by the above determinant together with the normalization equation 

However, even for simple molecules it is difficult to evaluate //, and it is not until the form of the wave functions is specified that H can be defined, except that it be a one-electron operator, since the molecular orbitals /r,- are one-electron functions. 

The most common procedure is that of semiempirical theory, which treats Hi as a parameter assumed reasonably constant for a given series of compounds. For example, in the case of aromatic hydrocarbons, each carbon atom is in a similar state and contributes one orbital (a 2orbital with its nodal plane corresponding to the molecular plane) to the above linear combination. Hiickel theory applied to these compounds assumes 

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In theories of bonding the term is often used to indicate the probability of finding an electron at a particular point. 

The detailed theory of bonding in transition metal complexes is beyond the scope of this book, but further references will be made to the effects of the energy splitting in the d orbitals in Chapter 13. 

Two theories of bonding valence bond and molecular orbital theory,... 

Twentieth century theories of bonding m benzene gave us a clearer picture of aromatic ity We 11 start with a resonance description of benzene... 

Boron Monoxide and Dioxide. High temperature vapor phases of BO, B2O3, and BO2 have been the subject of a number of spectroscopic and mass spectrometric studies aimed at developiag theories of bonding, electronic stmctures, and thermochemical data (1,34). Values for the principal thermodynamic functions have been calculated and compiled for these gases (35). 

The shapes of the monomeric molecules of the Group 2 halides (gas phase or matrix isolation) pose some interesting problems for those who are content with simple theories of bonding and molecular geometry. Thus, as expected on the basis of either sp hybridization or the... 

The outermost electrons are used in the formation of chemical bonds (Chapter 2), and the theory of bond formation is called valence theory hence the name of these electrons. 

The Lewis structures encountered in Chapter 2 are two-dimensional representations of the links between atoms—their connectivity—and except in the simplest cases do not depict the arrangement of atoms in space. The valence-shell electron-pair repulsion model (VSEPR model) extends Lewis s theory of bonding to account for molecular shapes by adding rules that account for bond angles. The model starts from the idea that because electrons repel one another, the shapes of simple molecules correspond to arrangements in which pairs of bonding electrons lie as far apart as possible. Specifically ... 

There are two major theories of bonding in d-metal complexes. Crystal field theory was first devised to explain the colors of solids, particularly ruby, which owes its color to Cr3+ ions, and then adapted to individual complexes. Crystal field theory is simple to apply and enables us to make useful predictions with very little labor. However, it does not account for all the properties of complexes. A more sophisticated approach, ligand field theory (Section 16.12), is based on molecular orbital theory. 

The two selenium atoms are attached to the low-coordinated phosphorus atom, with two lengthened dative bonds (2.788 and 2.637 A). Interestingly the phosphorus atom is here strongly pyramidalized, the Z SePSe angle was 80.6°. In other words the lone pair orbital at the electrophilic phosphorus atom remains stereo chemically active, as one would expect on the basis of the quantum chemical theory of bonding within this species. 

It has long been known that iodine dissolves in solvents possessing electron lone pairs and that the colors of these solutions are related to the solvent s basicity. Explaining this simple observation has required decades of work and has consistently required the application of the most sophisticated experimental tools available. The observation has also continually challenged theories of bonding, and even today taxes the capabilities of the fastest computers in efforts to provide accurate descriptions of its origin. 

This definition of a molecule soon gained popularity. Before modern theories of bonding were developed, Tyndall had clearly assimilated Cannizarro s definition of a molecule when he described the way atoms assemble, when he said, A molecule is a group of atoms drawn and held together by what chemists term affinity . 

Twenty years ago many chemists would have defended the theory of bond arms as a satisfactory explanation because they had become accustomed to thinking of it as unique and as ultimate. 8... 

An understanding of the limitations of the Kirkwood-Vinti approximation should therefore lead to considerable advances in the theory of bonding. In its absence, we shall here use diamagnetic susceptibility as the principal method of measuring yms and use refractive index only as a secondary method. 

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