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Exercise: Pa and øp are chosen to be a normalized set of basic function for an LCAO wavefunction for a one-electron homonuclear diatomic system. It is found that the values for the integrals involving these functions are : Sфанфаdт %3D — S päĤ¢adt : SФаНфьdт %3D —1 а.и; SФЪНфьdт %3 - 2 а.и; JФафьdт %3D -2 а. и ; Note: For hydrogen like atoms, the orbitals are orthonormal: H21 = Hi2 (H is Hermitian operator) S12 = S21 (Integral differ only in order) a) Find an upper bound for the exact lowest electronic energy for the system. b) Find the approximate normalized wave function corresponding to LCAO

Exercise: Pa and øp are chosen to be a normalized set of basic function for an LCAO wavefunction for a one-electron homonuclear diatomic system. It is found that the values for the integrals involving these functions are : Sфанфаdт %3D — S päĤ¢adt : SФаНфьdт %3D —1 а.и; SФЪНфьdт %3 - 2 а.и; JФафьdт %3D -2 а. и ; Note: For hydrogen like atoms, the orbitals are orthonormal: H21 = Hi2 (H is Hermitian operator) S12 = S21 (Integral differ only in order) a) Find an upper bound for the exact lowest electronic energy for the system. b) Find the approximate normalized wave function corresponding to LCAO

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Exercise: Pa and øp are chosen to be a normalized set of basic function for an LCAO wavefunction for a one-electron homonuclear diatomic system. It is found that the values for the integrals involving these functions are : Sфанфаdт %3D — S päĤ¢adt : SФаНфьdт %3D —1 а.и; SФЪНфьdт %3 - 2 а.и; JФафьdт %3D -2 а. и ; Note: For hydrogen like atoms, the orbitals are orthonormal: H21 = Hi2 (H is Hermitian operator) S12 = S21 (Integral differ only in order) a) Find an upper bound for the exact lowest electronic energy for the system. b) Find the approximate normalized wave function corresponding to LCAO
Transcribed Image Text:Exercise: Pa and øp are chosen to be a normalized set of basic function for an LCAO wavefunction for a one-electron homonuclear diatomic system. It is found that the values for the integrals involving these functions are : Sфанфаdт %3D — S päĤ¢adt : SФаНфьdт %3D —1 а.и; SФЪНфьdт %3 - 2 а.и; JФафьdт %3D -2 а. и ; Note: For hydrogen like atoms, the orbitals are orthonormal: H21 = Hi2 (H is Hermitian operator) S12 = S21 (Integral differ only in order) a) Find an upper bound for the exact lowest electronic energy for the system. b) Find the approximate normalized wave function corresponding to LCAO
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