Molecular orbitals ordering

Iwasa Y, Takenobu T (2003) Superconductivity, Mott-Hubbard states, and molecular orbital order in intercalated fullerides. J Phys Condens Matter 15 R495-R519... 

Proposer (Ref.) Method used Rh—Rh bond order Molecular orbitals ordering... 

A correlation diagram can now be constructed (Fig. 6) with the molecular orbitals ordered by relative energies—a knowledge of absolute energies is not required—and assigned symmetries relative to Pi and Pz (S, symmetric and A, antisymmetric). In Fig. 6, the assignment SA, fOT example, means symmetric about Pi, and antisymmetric about Pz. 

Collman, J. R, Harford, S. T., Maldivi, R, Marchon, J.-C. (1998b). Unusual molecular orbital ordering in molybdenum-ruthenium heterometallic porphyrin dimers Structural and magnetic evidence, J. Am. Chem. Soc., 120 7999. 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

When computing UV visible spectra, you should do a Cl singles calculation, RHFor L H F ealcu lation s arc sufficient to reproduce the proper order of molecular orbitals in most complexes. 

You can order the molecular orbitals that arc a solution to etjtia-tion (47) accordin g to th eir en ergy, Klectron s popii late the orbitals, with the lowest energy orbitals first. normal, closed-shell, Restricted Hartree hock (RHK) description has a nia.xirnuin of Lw o electrons in each molecular orbital, one with electron spin up and one w ith electron spin down, as sliowm ... 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

The logical order in which to present molecular orbital calculations is ab initio, with no approximations, through semiempirical calculations with a restricted number of approximations, to Huckel molecular orbital calculations in which the approximations are numerous and severe. Mathematically, however, the best order of presentation is just the reverse, with the progression from simple to difficult methods being from Huckel methods to ab initio calculations. We shall take this order in the following pages so that the mathematical steps can be presented in a graded way. 

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

Alternative procedure Mathcad. Follow the procedure above except that where QMOBAS is indicated, use Mathcad instead. Enter the Huckel molecular orbital matrix, modified by subtracting xl, with some letter name. For example, call the modified matrix A. Type the command eigenvals(A) = with the name of the modified HMO matrix in parentheses. Mathcad prints the eigenvalues. The command eigenvecs(A) yields the eigenvectors, which are useful in ordering the energy spectrum. 

It is a truism (cliche ) that microcomputers have beeome more powerful on an almost exponential eurve sinee their advent more than 30 years ago. Molecular orbital calculations that I ran on a supercomputer a decade ago now run on a fast desktop mierocomputer available at a modest priee in any popular eleetionies store or by mail order eatalog. With this has eome a eomparable inerease in software sophistication. 

FIGURE 114 The TT molecular orbitals of benzene arranged in order of increasing energy and showing nodal surfaces The six tt electrons of benzene occupy the three lowest energy or bitals all of which are bonding... 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

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