Group theory molecular orbitals

Widdifield and Schurko have written a a very useful pedagogical article on understanding shielding tensors using group theory, molecular orbital analysis, and density-functional theory. ... 

Cluster Compounds Inorganometalhc Compounds Containing Transition Metal Main Group Elements Electronic Stmcture of Main-group Compounds Molecular Orbital Theory Phosphorus Inorganic Chemistry. 

At the same time as Ballhausen cultivated the scientific activity at FKI did he also found time to write his influential books. Apart from the dissertation, the first of these was Introduction to Ligand Field Theory [16]. It is probably the publication for which he is best known to the broad audience of chemists. It is a classic in the world of inorganic chemistry. It contains chapters on atomic theory and group theory, crystal-field theory, molecular orbitals, spin-orbit coupling, and vibronic interactions. Last, but not least, it also contains an actual discussion of the properties of a number of inorganic complexes. In the preface, he writes, inter alia ... 

Each boron or carbon atom has sp hybridization. One of the hybridized orbitals of each atom forms a bond with the terminal hydrogen atom, and the remaining three orbitals (one sp and two p orbitals) give multicenter orbitals of the cluster grouping. The molecular orbital theory shows that borane polyhedra having n vertices have such symmetry that 3n atomic orbitals of the cluster possessing n skeletal atoms form +1 bonding molecular orbitals. ... 

It is recommended that the reader become familiar with the point-group symmetry tools developed in Appendix E before proceeding with this section. In particular, it is important to know how to label atomic orbitals as well as the various hybrids that can be formed from them according to the irreducible representations of the molecule s point group and how to construct symmetry adapted combinations of atomic, hybrid, and molecular orbitals using projection operator methods. If additional material on group theory is needed. Cotton s book on this subject is very good and provides many excellent chemical applications. 

Color from Transition-Metal Compounds and Impurities. The energy levels of the excited states of the unpaked electrons of transition-metal ions in crystals are controlled by the field of the surrounding cations or cationic groups. Erom a purely ionic point of view, this is explained by the electrostatic interactions of crystal field theory ligand field theory is a more advanced approach also incorporating molecular orbital concepts. 

The first line indicates that the syrrumetry could not be determined for this state (the symmetry itself is given as Sym). We will need to determine it ourselves. Molecular symmetry in excited states is related to how the orbitals transform with respect to the ground state. From group theory, we know that the overall symmetry is a function of symmetry products for the orbitals, and that only singly-occupied orbitals are... 

This could account for the paramagnetism, but esr evidence shows that the 2 cobalt atoms are actually equivalent, and X-ray evidence shows the central Co-O-O-Co group to be planar with an 0-0 distance of l3l pm, which is very close to the 128 pm of the superoxide, 02, ion. A more satisfactory formulation therefore is that of 2 Co atoms joined by a superoxide bridge. Molecular orbital theory predicts that the unpaired electron is situated in a rr orbital extending over all 4 atoms. If this is the case, then the jr orbital is evidently concentrated very largely on the bridging oxygen atoms. 

In the present work a theory for the facile construction of complex molecular orbitals from bond and group orbitals is presented and complemented by accurate drawings of the valence molecular orbitals for over one hundred molecules representing a wide range of connectivities and functional groupings. Direct applications to phenomena in organic chemistry are also discussed. 

Optically active 2-allylpiperidines and -pyrrolidines arc obtained by treating hydroxylactams containing the l-[(S)-l-arylethyl]substituent as an auxiliary (see Appendix) with tin(IV) chloride and trimethyl(2-propenyl)silane46. Interestingly, the moderate diastereoselection when the aryl group is phenyl decreases when 2-chlorophenyl is used, whereas the sense of the stereoselectivity reverses for 2,6-dichlorophenyl or pentachlorophcnyl. These results are rationalized by application of molecular orbital theory and substrate conformational preferences46. 

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. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

From 1933 85>, several theoretical approaches to the problem of the chemical reactivity of planar conjugated molecules began to appear, mainly by the Huckel molecular orbital theory. These were roughly divided into two groups 36>. The one was called the "static approach 35,37-40)j and the other, the "localization approach 41,42). in 1952, another method which was referred to as the "frontier-electron method was proposed 43> and was conventionally grouped 44> together with other related methods 45 48> as the "delocalization approach". 

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