In the BOA, we neglect the nuclear kinetic energy operators to solve the electronic problem. Below is the Hamiltonian of H2+. Which are the neglected terms? (A) (B) (C) (D) ra rb R

In the BOA, we neglect the nuclear kinetic energy operators to solve the electronic problem. Below is the Hamiltonian of H2+. Which are the neglected terms? (A) No, this is the electron kinetic energy operator (B) YES! (C) No, this is the potential energy coming from the Coulomb repulsion of the nuclei (D) No, this is the Coulomb attraction between the nuclei and the electron ra rb R

In the BOA, we treat the nuclear geometry as fixed and solve the TISE for each geometry to get the corresponding electronic energy. In the Hamiltonian of H2+, one term is thereby reduced to a (nonzero) constant that does not contribute to the electronic energy. Which one? (A) (B) (C) (D) ra rb R

In the BOA, we treat the nuclear geometry as fixed and solve the TISE for each geometry to get the corresponding electronic energy. In the Hamiltonian of H2+, one term is thereby reduced to a (nonzero) constant that does not contribute to the electronic energy. Which one? (A) The kinetic energy operator is obviously important for electronic motion! (B) These terms are already neglected (i.e., set to zero) (C) YES! The repulsion between the nuclei is an additive constant that plays no role for the motion of the electrons (D) This is the field in which the electrons move! ra rb R

What is the justification of the BOA? (A) The nuclear mass is much smaller than the electron mass, so we can neglect the motion of the nuclei. (B) The nuclear repulsion plays no role for the electron motion (see previous clicker question), so we can neglect the nuclear motion as well. (C) The nuclear mass is much greater than that of the electrons. Because the particle mass is in the denominator of the kinetic energy operator, the nuclear kinetic energy operator will be much smaller than the electron K.E. operator.

What is the justification of the BOA? (A) The nuclear mass is much smaller than the electron mass, so we can neglect the motion of the nuclei. NO! Other way around! (B) The nuclear repulsion plays no role for the electron motion (see previous clicker question), so we can neglect the nuclear motion as well. No! This is a completely separate argument! (C) The nuclear mass is much greater than that of the electrons. Because the particle mass is in the denominator of the kinetic energy operator, the nuclear kinetic energy operator will be much smaller than the electron K.E. operator.

What is the final Hamiltonian of H2+ to solve the electronic problem within the BOA? (A) (B)

What is the final Hamiltonian of H2+ to solve the electronic problem within the BOA? (A) No, this is everything we said plays no role for el. motion! (B) Let’s go with the book and keep the internuclear repulsion. However, it is just an additive constant, so we could solve the TISE without it and put it in later.