Subject: Atomic or nuclear masses for He2?

From: Robert Gdanitz <[email-masked]>
Date: Wed, 30 Sep 1998 19:06:03 +0200 (MET DST)

Dear collegues:

I have calculated the interaction potential of He2 with (explicitly correlated)
r12-MR-ACPF. When computing the molecular constants (R_0 and D_0), the question
arises whether to use atomic or nuclear masses. As you know, He2 is so weakly
bound that these different approaches have a quite noticeable influence on, e.g.
R_0 of 0.5 Angstroms.

While nuclear masses are clearly the correct choice in the Born-Oppenheimer
(clamped-nuclei) approximation, I am not sure, if the (traditional) use of
atomic masses would not result in more accurate molecular constants.

My arguments follow from the work of Bunker and Moss [Mol. Phys. 33 (1977) 417]
who *derived* a Hamiltonian of a vibrating and rotating singlet-sigma diatomic
which accounts for the effects of excited states and which contains *effective*
reduced masses for vibration (u_v) and rotation (u_r). Using the accurate
adiabatically corrected H_2 potential of Kolos and Wolniewicz, Bunker et al.
[Mol. Phys. 33 (1977) 425] fitted this Hamiltonian to the experimental vibra-
tion-rotation energy levels of the ground state of D_2 by adjusting u_v and
fixing u_r to the nuclear reduced mass. Of course, since there is no rotationa-
lly excited state of He2, u_r is not needed here.

The resulting u_v was found to be close to the atomic reduced mass. Thus, by the
use of the atomic reduced mass in the treatment of the vibrating D_2 (at least),
one approximately accounts for the non-adiabatic corrections due to the break-
down of the Born-Oppenheimer approximation.

In principle, from the comparable nuclear masses, this argument might also hold
for He2. In this case, however, the vibrational zero-point energy is very low
(~ 11 K ~ 35 uHartree) and thus it is difficult to understand that the electrons
cannot instantaneously follow the nuclear motion.

So what is the right choice for He2: atomic or nuclear masses?

Best Regards
Robert 
-- 
Robert J. Gdanitz               Institut f. Physikalische u.Theoretische Chemie
Phone: +49 531 391-5370         Technische Universitaet Braunschweig
Fax:   +49 531 391-5832         Hans-Sommer-Str. 10
email: [email-masked]       D-38106 Braunschweig, Germany