Molecular orbital calculation-constrained

This is analogous to the simple Hiickel approximation in molecular orbital calculations (365). Since it is assumed that the electrons are constrained to a single chain, i.e., k is parallel to a, k-a is equal to ka. Vector notation is therefore discontinued. Because of the very small overlap assumed it is seen from Eq. 7 (with A = 0) that... 

Since the minimal basis model has only two basis functions with coefficients that can be varied and since molecular orbitals are constrained to be normalized, the minimal basis model has, in the general case, only one degree of freedom. An unrestricted solution, unlike the restricted solution, is not symmetry determined and a convenient way of incorporating this one degree of freedom into unrestricted calculations is to write the unrestricted occupied molecular orbitals and ij/ i as linear combinations of the restricted symmetry determined orbitals ij/i and 2 follows ... 

Doms, L., H. J. Geise, C. Van Alsenoy, L. Van den Enden, and L. Schafer. 1985. The Molecular Orbital Constrained Electron Diffraction (MOCED) Structural Model of Quadricyclane Determined by Electron Diffraction Combined with Ab Initio Calculations of Potential and Geometrical Parameters. J. Mol. Struct. 129, 299-314. 

Schafer, L., J. D. Ewbank, K. Siam, N. S. Chiu, and H. L. Sellers. 1988a. Molecular Orbital Constrained Electron Diffraction (MOCED) Studies The Concerted Use of Electron Diffraction and Quantum Chemical Calculations, in Stereochemical Applications of Gas-Phase Electron Diffraction, Hargittai, I., and Hargittai, M., eds., Vol. A, Chap. 9, 301-320. New York, VCH Publisher. 

Theoretical chemistry at UBC was further strengthened with the arrival of Delano Chong and Keith Mitchell in 1965 and 1966, respectively. Chong s interests in quantum chemistry have spanned the full range from semiempirical to ab initio molecular orbital methods. His long-standing interests in perturbation methods and constrained variations have figured prominently in his publications. He is probably best known for his attempts to calculate the X-ray and UV photoelectron spectra of molecules, often by means of perturbation corrections to Koopmans theorem.40 More recently he has shifted his focus to coupled pair functional methods and density functional methods, with a special interest in polarizabilities and hyperpolarizabilities.41... 

The stability of the trihalogen intermediate is greatest when the least electronegative atom is in the central position. This complex is expected to be bent by examination of the appropriate Walsh molecular orbital diagrams and it is possible that the reaction is constrained to take place only for certain preferred interaction geometries. Trajectory calculations [561] for Cl + Br2, I2 and Br + I2 could not reproduce the experimental results with any surface having a potential well that preferred collinear approach of the reagents. 

L. Schafer was the first to begin to use in the late 1970s the results from molecular mechanics and ab initio calculations to supplement GED structure analysis. He also coined the acronym MOCED (Molecular Orbital Constrained Electron Diffraction) for such a combination [211,212]. The major problem facing the direct incorporation of ab initio results (r structure) into electron-diffraction structure analysis is the same as it was for the (GED + MW) combination (see Sec. IV B) the different physical significance of the parameters involved. 

Another molecular orbital approach is to calculate the energy of a model in which the tt bonds are constrained to be localized double bonds by the definition of the wave function. The calculated energy of this model can then be compared with the computed energy of the molecule in which delocalization is permitted. By this definition, butadiene has a resonance stabilization of about 9.3 kcal/mol, while benzene has a resonance energy of about 56 kcal/mol. To compare this value with that obtained with the polyene reference, one must subtract a correction for the butadiene resonance energy (3 x 9.3), which gives a value of about 28 kcal/mol as the resonance stabilization of benzene. 

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