Orbitals molecular, Huckel

In spite of the success of this method it was later felt that the calculation of the charge distribution in conjugated r-systems should be put on a less empirical basis. To achieve this, a modified Huckel Molecular Orbital (HMO) approach (Section 7.4) was developed. Again, the charge distribution in the r-skeleton is first calculated by the PEOE method. 

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 Bom-Oppenheimer approximation is not peculiar to the Huckel molecular orbital method. It is used in virtually all molecular orbital calculations and most atomic energy calculations. It is an excellent approximation in the sense that the approximated energies are very close to the energies we get in test cases on simple systems where the approximation is not made. 

In summary, we have made three assumptions 1) the Bom-Oppenheimer approximation, 2) the independent particle assumption governing molecular orbitals, and 3) the assumption of n-molecular orbital theory, but the third is unique to the Huckel molecular orbital method. 

HUCKEL MOLECULAR ORBITAL THEORY I EIGENVALUES by the matrix... 

The Jacobi method is probably the simplest diagonalization method that is well adapted to computers. It is limited to real symmetric matrices, but that is the only kind we will get by the formula for generating simple Huckel molecular orbital method (HMO) matrices just described. A rotation matrix is defined, for example. 

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. 

Refer to Computer Project 7-2. Calculate p in units of electron volts using Wheland s extension of Huckel molecular orbital theory. 

K. Yates, Huckel Molecular Orbital Theory Academic Press, New York (1978). 

Sandstrom et al. (65) evaluated the Kj value for 4,5-dimethyl-A-4-thiazoline-2-thione (46) in water (Scheme 19) K-j= 10. A-4-Thiazoline-2-thiones are less basic in the first excited state (61) than in the ground state, so application of Forster s cycle suggests that the thione form is even more favored in the first excited state. Huckel molecular orbital (HMO) calculations suggest that electronic effects due to substitution in... 

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

F. Heilbronner and P A. Straub, Huckel Molecular Orbitals, Springer-Verlag, Berlin, 1966 C. A. Coulson and A. Streitwieser, Dictionary of n-Electron Calculations, W. H. Freeman, San Franeisco, 1965. 

The Huckel molecular orbitals for acenaphthylene are shown below. The atomic coefficients for the orbital which is the LUMO in the neutral compound and the... 

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