Mathematical chemistry / W.I. Hong, editor.

Includes bibliographical references and index.

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MATHEMATICAL CHEMISTRY; CONTENTS; PREFACE; EXACT TREATMENT OF FINITE RANKMODIFICATIONS OF FINITE-DIMENSIONALAND INFINITE-DIMENSIONAL QUANTUM SYSTEMS; Abstract; 1. Introduction; 2. Description of Finite-Dimensional Systems; 3. Internal and External Modifications of Finite-DimensionalSystems; 4. LRM Treatment of External Modificationsof Finite-Dimensional Systems; 4.1. Interlacing of Modified Eigenvalues s f with Parent Eigenvalues in; 4.2. Cardinal Solutions of the Combined System; 4.3. Singular Solutions of the Combined System; 4.4. Numerical Considerations.

4.5. Normalization of Modified Eigenstates4.6. Numerical Example; 5. Internal Modifications of Finite-Dimensional Systems; 5.1. Interlacing of Modified Eigenvalues s f with Eigenvalues in; 5.2. Cardinal Solutions of the Modified System; 5.3. Singular Solutions of the Modified System; 5.4. Case P = 0; 5.5. Case V = 0; 6. LRM Treatment of the Vibrational IsotopeEffect in the Harmonic Approximation; 6.1. Out-Of-Plane Vibrations of Planar Molecules; 6.2. Interlacing Rule for out-of-Plane Vibrations of Planar Molecules; 6.3. Single Isotopic Substitutions; 6.4. Inversion Relations.

6.5. Interlacing of Out-of-Plane Vibrational Frequencies of Thiopheneand Deuterated Thiophenes6.6. Out-of-Plane Vibrations of Ethylene Isotopomers; 6.7. Out-of-Plane Vibrations of Benzene Isotopomers; 6.8. Equality of LRM and DFT out-of-Plane Frequenciesof Benzene (H, D)-Isotopomers; 6.9. Comparison of LRM, Frequency Scaled DFT and Experimental out-of-Plane Frequencies of Benzene (H, D)-Isotopomers; 7. External Modification as a Special Case of InternalModification; 8. Infinite Dimensional Systems; 9. Description of an Infinite-Dimensional System.

10. External Modifications of Infinite-Dimensional Systems11. General Properties of The Solutionsto the Infinite-Dimensional Combined System; 11.1. Fractional Shift; 11.2. Description of the Open System that Interacts with an Infinite System; 12. Characteristic and Derived Operators; 12.1. Calculation of the Derived Operators; 13. Isolated Solutions of the Infinite-Dimensional CombinedSystem; 13.1. Resonant Points; 13.2. Probabilities Associated with Isolated Cardinal Eigenstates; 14. Embeded Solutions of the Combined System; 14.1. Embedded Cardinal Solutions.

14.2. Embedded Singular Solutions15. Completeness Relations; 16. One Dimensional Open Systems; 17. Examples; 17.1. Example E1; 17.2. Example E2; 17.3. Example E3: Interaction of a Single State with one-Dimensional Solid inThe Nearest-Neighbor Tight-Binding Approximation; 18. Time-Dependent Systems; 19. One Dimensional Open Systems -- Time Dependent Case; 19.1. Decay of a Local State in the Weak Coupling Limit; 19.2. Transitions of the State K to The Eigenstates of the System A; 19.3. Transition of the Local State to The System A in the Weak CouplingLimit; 19.4. Example E4; 19.5. Example E5.

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