Approximations of MO theory

Anomeric effect, 82, 310-311, 305 Antarafacial, 163 examples, 164 sigma bonds, 167 Anti-Bredt olefin, 102 Approximations of MO theory Born-Oppenheimer, 22 Hartree-Fock, 222 Huckel, 35, 86 independent electron, 35 LCAO, 229 nonrelativistic, 22 SHMO, 87... 

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

The molecular Schrodinger equation can be solved exacdy for the case of Hj when VAB is simply the sum of two hydrogen ion potentials. In general, however, an exact solution is not possible. Following the well-worn tracks of MO theory we look instead for an approximate solution that is given by some linear combination of atomic orbitals (LCAO). Considering the AB dimer illustrated in Fig. 3.1 we write... 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

The widespread application of MO theory to systems containing a bonds was sparked in large part by the development of extended Hiickel (EH) theory by Hoffmann (I) in 1963. At that time, 7r MO theory was practiced widely by chemists, but only a few treatments of a bonding had been undertaken. Hoffmann s theory changed this because of its conceptual simplicity and ease of applicability to almost any system. It has been criticized on various theoretical grounds but remains in widespread use today. A second approximate MO theory with which we are concerned was developed by Pople and co-workers (2) in 1965 who simplified the exact Hartree-Fock equations for a molecule. It has a variety of names, such as complete neglect of differential overlap (CNDO) or intermediate neglect of differential overlap (INDO). This theory is also widely used today. 

The approximations used in EH theory have included (1) neglect of core electrons, (2) use of atomic basis functions, (3) use of effective Hamiltonian resulting in arbitrariness in choice of matrix elements, (4) lack of explicit accounting for electron-electron and nuclear-nuclear repulsion, and (5) approximate energy calculation procedure. Although these approximations seems severe in light of Hartree-Fock treatments of MO theory, the important feature to remember is that EH theory has proved useful in several systems. 

Although the aufbau approach of MO theory is adequate in all that follows, it may be useful for the sake of completeness to mention the rather more complicated method developed by Heitler, London, Slater, Pauling and others, and to stress that the two theories do not conflict. Both lead to approximations to the same charge density the difference is superficial and the same Fcynman-Hellman interpretation applies in each case. To appreciate this, it is sufficient to consider the molecule Hg. From the MO standpoint, the full two-electron wave function would be the product... 

The approximate LCAO MO theory of nmr shielding by Karplus and Pople (151) contains contributions from (MO) excitation energies A ( - j) and from LCAO coefficients as well as electron densities, A reduction in A (i — j) increases the contribution of the corresponding component to whereas a... 

In order to make the mathematics tractable, a number of approximations are made. The choice of approximations has produced a variety of molecular orbital methods, the judicious application of which can provide a valuable insight into questions of bonding, structure, and dynamics. The discussion that follows will not be sufficiently detailed for the reader to understand fully how the calculations are performed or the details of the approximations. Instead, the nature of the information obtained will be described, as well as the ways in which organic chemists have applied the results of MO theory in an attempt to understand the structure and reactivity of organic molecules. For more detailed treatments, several excellent sources are available. ... 

Though much progress has been made by application of approximate SO MO theory to inorganic problems, MOVB theory has formal and conceptual advantageswhich promise to reveal facets of chemical bonding which have hitherto remained unrecognized. "Surprising" conclusions of MOVB theory have already been discussed in previous chapters. 

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