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1. Derive the following expression for the bonding and antibonding orbitals of a heteronuclear diatomic molecule consisting of two electrons in a molecular orbital of the form y = cAA + CBB with atomic orbitals A and B. Let aA=HAA, AB=HBB, B=HAB=HBA, SAA=SBB=1, and, as a simplification, let SAB=SBA=S=0 (zero-overlap approximation). Note that the assumption of SAB=SBA=S=0 is used simply to get a more transparent expression. Show that the secular determinant is given by a, - E = 0 - E and energies are given by 1/2 2B E̟ = }(a, +a,)±±(a,- For B<0, E. is the lower energy solution.

1. Derive the following expression for the bonding and antibonding orbitals of a heteronuclear diatomic molecule consisting of two electrons in a molecular orbital of the form y = cAA + CBB with atomic orbitals A and B. Let aA=HAA, AB=HBB, B=HAB=HBA, SAA=SBB=1, and, as a simplification, let SAB=SBA=S=0 (zero-overlap approximation). Note that the assumption of SAB=SBA=S=0 is used simply to get a more transparent expression. Show that the secular determinant is given by a, - E = 0 - E and energies are given by 1/2 2B E̟ = }(a, +a,)±±(a,- For B<0, E. is the lower energy solution.

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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1. Derive the following expression for the bonding and antibonding orbitals of a heteronuclear diatomic molecule consisting of two electrons in a molecular orbital of the form y = CAA + CBB with atomic orbitals A and B. Let aa=HAA, aB=HBB, B=HAB=HBA, SAA-SBB=1, and, as a simplification, let SAB=SBA=S=0 (zero-overlap approximation). Note that the assumption of SAB=SBA=S=0 is used simply to get a more transparent expression. Show that the secular determinant is given by a,-E - E and energies are given by 1/2 2B E̟ = }(a, +a,)±(a,-a,) For B<0, E+ is the lower energy solution.
Transcribed Image Text:1. Derive the following expression for the bonding and antibonding orbitals of a heteronuclear diatomic molecule consisting of two electrons in a molecular orbital of the form y = CAA + CBB with atomic orbitals A and B. Let aa=HAA, aB=HBB, B=HAB=HBA, SAA-SBB=1, and, as a simplification, let SAB=SBA=S=0 (zero-overlap approximation). Note that the assumption of SAB=SBA=S=0 is used simply to get a more transparent expression. Show that the secular determinant is given by a,-E - E and energies are given by 1/2 2B E̟ = }(a, +a,)±(a,-a,) For B<0, E+ is the lower energy solution.
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