Adiabatic approximations to internal rotation

A number of subtle and confusing issues are addressed concerning large amplitude motion (LAM) coordinates ( χ ) for internal molecular motions, using the methyl rotation in acetaldehyde ( C H 3 C H O ) as a model problem. If the LAM coordinate is chosen to be one of the H-C-C-O dihedral angles ρ 1 , ρ 2 , or ρ 3 , it lacks the required 2 π ∕ 3 periodicity, and its use is thus undesirable. An excellent local internal coordinate for this model problem is τ 3 = 1 3 ( ρ 1 + ρ 2 + ρ 3 − 2 π ) . A similarly good but nonlocal coordinate for the adiabatic approximation of internal rotation is provided by the intrinsic reaction coordinate s . Comparison of the mass-independent V 0 ( τ 3 ) and the mass-dependent V 0 ( s ) internal rotation curves shows that the two are virtually identical for the parent isotopolog of acetaldehyde. A unified internal coordinate projection scheme for determining complementary vibrational frequencies and subsequently V ZPVE ( χ ) along a path for LAM has been formulated, where V ZPVE ( χ ) is the zero-point vibrational energy correction to the internal rotation curve. In addition to its simplicity, the projection scheme developed for a distinguished reaction path generated by constrained optimizations is appealing because the vibrational frequencies along the LAM path are invariant to chemically meaningful choices of the internal coordinates for the complementary modes.