THEORETICAL CALCULATIONS OF THE TRANSITIONS OF PHOTOCOLORED FORMS OF CHROMENES

Abstract— –Theoretical prediction (MO-SCF-CI) of numbers, energies and intensities of transitions are compared with experimental data for the photocolored products of three types of chromenes. Generally good results are obtained. Several conclusions resulted from variation of parameters: (1) When all carbon-carbon bonds are considered equal in length, there is good agreement between experiment and theory regarding band locations and intensities, however, very poor correlation exists between theory and experiment when calculations are done on a model where the carbon-carbon bonds are alternately single and double, (2) theoretical calculations employing the Mataga approximation for the two-center repulsion integrals gives superior correlation with the experimental spectra in comparison with the Pariser-Parr approximation, and (3) variation of certain parameters (as I.P., E.A., β) did produce changes in the results, especially in the oscillator strengths, but there was no clear best choice, and therefore, conventional parameters were used.     

Some Observations on Boundary Conditions for the Shallow-water Equations in Two Space Dimensions

This paper is concerned with the specification of suitable boundaryconditions to ensure the well-posedness of the linearized shallowwater equations in a semi-infinite region. The authors applyKreiss's (1970) theory which enables results to be obtainedfor the case of variable coefficients in a general geometryonce the half-plane problem has been analysed. The entire setof possible boundary conditions consisting of linear relationsbetween the flow variables is considered and the effects ofthe boundary conditions on the well-posedness of the initial-boundary-valueproblem are discussed. The results indicate a fundamental similaritybetween the cases of outflow and inflow. They also emphasizethe very special nature of the case of no normal flow acrossthe boundary. They results are compared with those which theClassical Energy Method provides for uniqueness. This comparisonshows that there may be a relationship between the two methodsand further illustrates the similarity between outflow and inflow.     

Use of the Lanczos Method for Finding Complete Sets of Eigenvalues of Large Sparse Symmetric Matrices

A way of using the Lanczos method to find all the eigenvaluesof a large sparse symmetric matrix is described, and some empiricalobservations on the manner in which the method works in practiceare given. The method seems to be accurate, fast, and not verydemanding on storage. A formula for the number of iterationsnecessary to get the eigenvalues is proposed.     

Atom-pair formulation of the rotational and vibrational motions of molecules

We have expressed the angular momentum and the internal kinetic energy of a molecule (a system of point masses) in terms of atom-pair contributions, paralleling the use of pairwise additive potential energy functions. The partitioning of the internal kinetic energy into rotational and vibrational contributions is then made following the analysis of Jellinek, J., and Li, D. H., 1989, 98, Phys. Rev. Lett., 62, 241. The resulting expressions contain pair position and velocity variables whose redundancy may be removed by transformation to Jacobi vector coordinates. These expressions should prove especially useful for describing the internal motions of clusters of like atoms.