A sodium atom and a chlorine atom collide head-on with the same kinetic energy in two…
PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra
Deriving the Spectrum, Ch The Born-Oppenheimer separation and the chemical bond
Problem
A sodium atom and a chlorine atom collide head-on with the same kinetic energy in two experiments that differ only in the sodium nucleus: ordinary 23Na in one, and in the other a hypothetical heavy isotope Na∗ with several times its mass. In both, the pair passes through the covalent-ionic avoided crossing at Rc=9.4A˚. The electronic gap and coupling at the crossing are the same in both experiments, since they are fixed by the electronic structure alone. Call a passage adiabatic when the pair follows one adiabatic curve through the crossing, and so swaps covalent for ionic character, and diabatic when it jumps to the other adiabatic curve and keeps the character it arrived with.
((a)) In which experiment do the nuclei pass through the crossing more slowly?
((b)) The probability of a diabatic jump grows with the speed of the nuclei through the crossing (the content of the Landau-Zener formula, quoted but not derived in the chapter). Predict which pair more reliably follows the adiabatic curve and ends up ionic, the first step of the harpoon mechanism, and which is more likely to jump.
((c)) Why is the single-curve (Born-Oppenheimer) picture under the most strain at Rc in both experiments, and why does it still work better for the heavier pair?