Molecular orbital theory electron correlation

The symposium on which this book is based presented recent advances in the theory and computation of systems containing d and f electrons and applications to a number of the complex systems that have recently been examined using these techniques. Leading experimentalists presented work that would greatly benefit from advanced theory. The latest developments in molecular orbital theories, in correlation... 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

Hartree-Fock (HF), molecular orbital theory satisfies most of the criteria, but qualitative failures and quantitative discrepancies with experiment often render it useless. Methods that systematically account for electron correlation, employed in pursuit of more accurate predictions, often lack a consistent, interpretive apparatus. Among these methods, electron propagator theory [1] is distinguished by its retention of many conceptual advantages that facilitate interpretation of molecular structure and spectra [2, 3, 4, 5, 6, 7, 8, 9]. 

For many years, the lectures of Yngve Ohrn on the theory of chemical bonding have been models of clarity and incisiveness to graduate students at the University of Florida and at various topical schools. Their success in introducing the assumptions and conclusions of molecular orbital theory, group theory, electron correlation methods and related subjects has engendered a critical, but liberal attitude toward competing doctrines. 

The application of ab initio molecular orbital theory to suitable model systems has led to theoretical scales of substituent parameters, which may be compared with the experimental scales. Calculations (3-21G or 4-31G level) of energies or electron populations were made by Marriott and Topsom in 1984164. The results are well correlated with op (i.e. 07) for a small number of substituents whose op values on the various experimental scales (gas phase, non-polar solvents, polar solvents) are concordant. The nitro group is considered to be one of these, with values 0.65 in the gas phase, 0.65 in non-polar solvents and 0.67 in polar solvents. The regression equations are the basis of theoretical op values for about fifty substituents. The nitro group is well behaved and the derived theoretical value of op is 0.66. 

Including Electron Correlation in Molecular Orbital Theory... 

The observed spectra of some duroquinone-nickel complexes with olefins have been correlated by means of semiquantitative molecular-orbital theory by Schrauzer and Thy ret (48). In the case of n complexes of polynuclear hydrocarbons, such as naphthalene and anthracene, although their spectra are recorded, no conclusions have been drawn with regard to structure nor has any theoretical work been reported. Similar remarks apply to complexes of nonalternant hydrocarbons such as azulene. Although innumerable complexes of olefins with various transition metals are known and admirably reviewed (84), no theoretical discussion of even a qualitative nature has been provided of their electronic spectra. A recent qualitative account of the electronic spectra of a series of cyclopentadienone, quinone, and thiophene dioxide complexes has been given by Schrauzer and Kratel (85). 

Chemical Properties. Simple molecular-orbital theory predicts that many organometallic molecules should show electronic effects similar to conjugated systems, since the electronic structure is generally expressed in terms of molecular orbitals which involve both ring and metal orbitals. The ESR spectra (Sec. III.C) provide physical evidence for this formulation however correlation between chemical reactivities and theoretical quantities, such as charge densities and localization energies, which has been of use in aromatic systems (60) has not been attempted. Indeed, very few detailed kinetic studies of organometallic compounds have been reported with which to compare theory. We consider the different classes of compounds in turn. 

Out of each pair of states correlated in this way only one corresponds to an energy minimum. For example, simple molecular orbital theory predicts that CH2 will be linear or nearly linear in its lowest triplet state (Lennard-Jones and Pople, 1951 Walsh, 1953a) the stable state is then 3ZB and the bent configuration then represents the turning-points of vibrational motion in the bending mode of the electronic state. 

Aromatic systems play a central role in organic chemistry, and a great deal of this has been fruitfully interpreted in terms of molecular orbital theory that is, in terms of electrons moving more-or-less independently of one another in delocalized orbitals. The spin-coupled model provides a clear and simple picture of the motion of correlated electrons in such systems. The spin-coupled and classical VB descriptions of benzene are very similar, except for the small but crucial distortions of the orbitals. The localized character of the orbitals allows the electrons to avoid one another. Nonetheless, the electrons are still able to influence one another directly because of the non-orthogonality of the orbitals. 

Semiempirical molecular orbital methods23-25 incorporate parameters derived from experimental data into molecular orbital theory to reduce the time-consuming calculation of two-electron integrals and correlation effects. Examples of semiempirical molecular orbital methods include Dewar s AMI, MNDO, and MINDO/3. Of the three quantum chemical types, the semiempirical molecular orbital methods are the least sophisticated and thus require the least amount of computational resources. However, these methods can be reasonably accurate for molecules with standard bond types. 

There are a number of different approaches to the description of molecular electronic states. In this section we describe molecular orbital theory, which has been by far the most significant and popular approach to both the qualitative and quantitative description of molecular electronic structure. In subsequent sections we will describe the theory of the correlation of molecular states to the Russell Saunders states of the separated atoms we will also discuss what is known as the united atom approach to the description of molecular electronic states, an approach which is confined to diatomic molecules. 

A useful development has been the hybridization of molecular orbital theory and density functional theory.46 The latter uses a relatively simple equation to estimate the electron correlation as a function of the electronic density. With the electronic density described by the basis sets discussed above, a quicker approximation for electron correlation can be attained. There are numerous exchange and correlation functional pairs, but a commonly used set is the Becke 3-parameter exchange functional and the Lee-Yang-Parr correlation functional.47-43 This approximation for electron exchange and correlation is simply designated B3LYP in Gaussian 98 46... 

A number of physical methods have found support in molecular orbital theory, or have provided evidence that the deductions of molecular orbital theory have some experimental basis. Electron affinities correlate moderately well with the calculated energies of the LUMO, ionisation potentials correlate moderately well with the calculated energies of the HOMO, and spectroscopic methods reveal features that support molecular orbital theory. 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

Some of the first applications of molecular-orbital theory in mass spectrometry were in calculations of ionization potentials of n-alkanes (see Streitwieser, 1961, for leading references). Strictly, these ionization potentials are a property of both the molecule and the ion produced, but often the effect of electron correlation in the ion is ignored (Koopmans, 1933) and resort is then made to adjustment of parameters to give good agreement between theory and practice. In the absence of experimental confirmation, such calculations must be viewed cautiously. 

K. Raghavachari, R. A. Whiteside, J. A. Pople, and P. v. R. Schleyer, ]. Am. Chem. Soc., 103, 5649 (1981). Molecular Orbital Theory of the Electronic Structure of Organic Molecules. 40. Structures and Energies of C1-C3 Carbocations, Including Effects of Electron Correlation. 

---