Subject: Re: CCL:Calculations without Born-Oppenheimer approximation "2nd Call"

From: "Dr. N. SUKUMAR" <nagams..at..rpi.edu>
Date: Tue, 16 Dec 2003 18:03:25 EST

On Tue, 16 Dec 2003 15:11:47 +0100 (MET) Giju Kalathingal wrote:

> Last week I had send the following message without 
> any success. So I am posting it again.
> 
> Dear CCL-all,
> 
> Could you please give me some info on programs
> that let me to do quantum chemical calculations
> (geometry optimzations and vibrational frequencies) 
> without Born-Oppenheimer approximation?
> 
> Thanks in advance.
> 
> Giju Kalathingal
> 
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
> 

Perhaps the reason you did not get any response was because your question
specifically dealt with programs for geometry optimzations and vibrational
frequencies. These concepts (molecular geometry and molecular vibrations)
are normally understood within the Born-Oppenheimer approximation. I do not
know of any readily available programs that deal with these outside of BO.
However quantities such as bond lengths and vibrational frequencies are
derivable from experiment and thus these concepts ARE defined beyond the
Born-Oppenheimer approximation: equilibrium bond lengths, for instance,
would be defined as the peaks in the two-particle radial distribution
functions for the two bonded nuclei. See the special issue of Israel
Journal of Chemistry, vol.19 (1980) for many papers (and much debate), e.g.
those of R.G.Woolley, pp.30-46 and of Carl Trindle, pp.47-53. L. Lathouwers
and P. Van Leuven (CPL 52, 439, 1977; PRA 18, 2150, 1978; IJQC S12, 371,
1978) demonstrated that the generator coordinate method could be employed
to avoid the BO separation and develop a non-adiabatic formulation of
molecular quantum theory.

In a series of pioneering papers on hydrides (CPL 3, 705, 1969; PS 185, 90,
1969; PRA 2, 728, 1200, 1675, 1970; PRA 3, 565, 1022, 1971; PRA 4, 457,
1971; PRA 5, 1104, 1972), I.L.Thomas put electrons into electronic orbitals
and protons into protonic orbitals (thereby avoiding the BO approximation),
antisymmetrized the two kinds of orbitals separately, performed SCF
computations and obtained molecular structures and spectra that
corresponded to experiment. For instance, the microwave transition
frequency of ammonia (conventionally explained by "umbrella flipping"
between two structures) is now obtained as the transition frequency between
protonic orbitals. Subsequently Thomas went on to become vice-president of
Occidental Petroleum and did not continue his protonic structure studies. I
wrote some programs to do similar computations as part of my candidacy work
at Stony Brook in the early 80s, but those are now lost on some magnetic
tape somewhere.

There are now several computations and programs that go beyond the BO
approximation by calculating the nonadiabatic coupling terms or performing
a diabatic transformation in multi-reference CI or CASSCF spaces (see e.g.
D.R.Yarkony in "Modern Electronic Structure Theory" Part I, World
Scientific, Singapore, 1995, pp.642-721; W.Domcke, et al. CPL 216,362,
1993; 226, 257, 1994; Neuheuser, Sukumar and Peyerimhoff, Chem.Phys., 194,
45-64, 1995; Mol.Phys. 95, 61-70, 1998) but none of these can be considered
as truly "without Born-Oppenheimer approximation"

(PRA=Phys.Rev A; CPL=Chem.Phys.Lett.; IJQC=Int.J.Quantum Chem)

N. Sukumar
RPI Department of Chemistry