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Problem 6 Consider two hydrogen atoms that form molecular orbitals through their 1s atomic orbitals. The atomic orbitals are written as ), where i = {a, b} are labels to indicate the different atoms. The overlap integral is S : (e laba). The H2 molecule is then ionized, forming H. (Walwe) %3D a) Give expressions for the normalized bonding V+ and anti-bonding V– orbitals. b) Draw an molecular orbital diagram, and indicate the energies of V+ and V- in terms of the Coulomb integral a, resonance integral 3 and overlap integral S. Indicate the electron occupation in the diagram. c) Assume that a = -7.2 ev, 8 = -3.5 eV and S following: = 0.1. Determine the The energies of E4 and E-. The energy splitting AE between E, and E_. d) Which of the integrals a, B and S do you expect to depend on the inter- atomic distance? Briefly motivate.

Problem 6 Consider two hydrogen atoms that form molecular orbitals through their 1s atomic orbitals. The atomic orbitals are written as ), where i = {a, b} are labels to indicate the different atoms. The overlap integral is S : (e laba). The H2 molecule is then ionized, forming H. (Walwe) %3D a) Give expressions for the normalized bonding V+ and anti-bonding V– orbitals. b) Draw an molecular orbital diagram, and indicate the energies of V+ and V- in terms of the Coulomb integral a, resonance integral 3 and overlap integral S. Indicate the electron occupation in the diagram. c) Assume that a = -7.2 ev, 8 = -3.5 eV and S following: = 0.1. Determine the The energies of E4 and E-. The energy splitting AE between E, and E_. d) Which of the integrals a, B and S do you expect to depend on the inter- atomic distance? Briefly motivate.

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Problem 6 Consider two hydrogen atoms that form molecular orbitals through their 1s atomic orbitals. The atomic orbitals are written as ), where i = {a, b} are labels to indicate the different atoms. The overlap integral is S : (e laba). The H2 molecule is then ionized, forming H. (Walwe) %3D a) Give expressions for the normalized bonding V+ and anti-bonding V– orbitals. b) Draw an molecular orbital diagram, and indicate the energies of V+ and V- in terms of the Coulomb integral a, resonance integral 3 and overlap integral S. Indicate the electron occupation in the diagram. c) Assume that a = -7.2 ev, 8 = -3.5 eV and S following: = 0.1. Determine the The energies of E4 and E-. The energy splitting AE between E, and E_. d) Which of the integrals a, B and S do you expect to depend on the inter- atomic distance? Briefly motivate.
Transcribed Image Text:Problem 6 Consider two hydrogen atoms that form molecular orbitals through their 1s atomic orbitals. The atomic orbitals are written as ), where i = {a, b} are labels to indicate the different atoms. The overlap integral is S : (e laba). The H2 molecule is then ionized, forming H. (Walwe) %3D a) Give expressions for the normalized bonding V+ and anti-bonding V– orbitals. b) Draw an molecular orbital diagram, and indicate the energies of V+ and V- in terms of the Coulomb integral a, resonance integral 3 and overlap integral S. Indicate the electron occupation in the diagram. c) Assume that a = -7.2 ev, 8 = -3.5 eV and S following: = 0.1. Determine the The energies of E4 and E-. The energy splitting AE between E, and E_. d) Which of the integrals a, B and S do you expect to depend on the inter- atomic distance? Briefly motivate.
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