— Physical Chemistry Chemistry Question
Atomic and molecular orbitals
It is known that molecular orbitals of H2 + are represented by the linear combination of atomic orbitals (LCAO). The molecular orbitals are
φa ∝ 1sA – 1sB
φb ∝ 1sA + 1sB
where 1sA is a ground-state hydrogen orbital centered on nucleus A, and 1sB is centered on nucleus B. The energies for the molecular orbitals are shown in Figure 1 as a function of the internuclear distance of H2 +. (Note that the potential energy between an electron and a proton is set zero, when an electron and proton is fully separated.) Write which energy curve is for φa .
Model Answer
The upper curve (2) in Fig. 1 shows the energy of the anti-bonding orbital, φa as a function of the internuclear distance.
Write the internuclear distance of stable H2 +.
Model Answer
The lower line in Fig. 1 shows the energy of the bonding orbital, φb . From the minimum of the energy curve, we are able to obtain the internuclear distance of stable H2 + to be 0.085 nm.
The two energy curves in Fig. 1 converge at E1 as the internuclear distance becomes infinity. Write which physical parameter of the hydrogen atom the energy |E1| equals to.
Model Answer
The two energy curves in Fig. 1 converge at E1 as the internuclear distance becomes infinity. Here, H2 + is regarded as totally separated one hydrogen atom and one proton. Hence, |E1| is the same as the ionization potential of the hydrogen atom.