Write the Hamiltonian operator for the LiH molecule. Which of the terms in the Hamiltonian operator may be neglected when using the Born-Oppenheimer approximation? Step 1 of 7 List the terms that represent the kinetic energies of the nuclei. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V2, Use the following as necessary: mLi, mH, ALi, and AH-) 2m "Li 2m "H 1 1 ALi 2my Li 2mLi Are these terms positive or negative when used in the Hamiltonian operator? positive P negative

Principles of Modern Chemistry
8th Edition
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Chapter4: Introduction To Quantum Mechanics
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Problem 39P: Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a...
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Write the Hamiltonian operator for the LiH molecule. Which of the terms in the Hamiltonian operator may be neglected when using the Born-Oppenheimer approximation?
Step 1 of 7
List the terms that represent the kinetic energies of the nuclei. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V2. Use the following as necessary: mLi, mH, Ali, and AH.)
1
ALi ´2m
1
2m
1
ALi:
2mH
Li
Н
-AH
2mLi
Are these terms positive or negative when used in the Hamiltonian operator?
O positive
negative
Step 2 of 7
Assuming that the subscript "1" represents the electron on the hydrogen atom and the subscripts "2", "3", and "4" represent the electrons on the lithium atom, list the terms that represent the kinetic energies of the
electrons. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V². Use the following as necessary: A1, A2, A3, and A4.)
Δ1
2m
2m
(G) ». ()
() » ()
-
A2,
Li
H
Are these terms positive or negative when used in the Hamiltonian operator?
O positive
negative
Step 3 of 7
List the terms that represent the potential energies between the electrons ("1", "2", "3", and "4") and the hydrogen nucleus. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V2. Use
r#H to represent the distance between an electron and the hydrogen nucleus as necessary: r1H, r2H, r3H, and r4h-)
Are these terms positive or negative when used in the Hamiltonian operator?
O positive
O negative
Transcribed Image Text:Write the Hamiltonian operator for the LiH molecule. Which of the terms in the Hamiltonian operator may be neglected when using the Born-Oppenheimer approximation? Step 1 of 7 List the terms that represent the kinetic energies of the nuclei. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V2. Use the following as necessary: mLi, mH, Ali, and AH.) 1 ALi ´2m 1 2m 1 ALi: 2mH Li Н -AH 2mLi Are these terms positive or negative when used in the Hamiltonian operator? O positive negative Step 2 of 7 Assuming that the subscript "1" represents the electron on the hydrogen atom and the subscripts "2", "3", and "4" represent the electrons on the lithium atom, list the terms that represent the kinetic energies of the electrons. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V². Use the following as necessary: A1, A2, A3, and A4.) Δ1 2m 2m (G) ». () () » () - A2, Li H Are these terms positive or negative when used in the Hamiltonian operator? O positive negative Step 3 of 7 List the terms that represent the potential energies between the electrons ("1", "2", "3", and "4") and the hydrogen nucleus. (Enter your answers as a comma-separated list. Use A to represent the Laplace operator, V2. Use r#H to represent the distance between an electron and the hydrogen nucleus as necessary: r1H, r2H, r3H, and r4h-) Are these terms positive or negative when used in the Hamiltonian operator? O positive O negative
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