6D vibrational quantum dynamics: Generalized coordinate discrete variable representation and (a)diabatic contraction

A new discrete variable representation (DVR) in generalized vibrational coo rdinates is proposed together with a new mixed diabatic/adiabatic contracti on technique for the treatment of multidimensional vibrational problems up to high vibrational excitations. Formally based on the equidistant Chebyshe v DVR in the grid index the new formulation is particularly suitable for mu ltidimensional minimum energy paths. The new Z-matrix DVR proposed in this paper encompasses usual valence coordinates as well as nonlinear maps of co ordinates on optimal nonequidistant grids. The pointwise numerical calculat ion of all kinetic energy terms avoids the algebraic derivation of speciali zed analytical forms of the kinetic energy adding to the flexibility of the method. With efficient truncation schemes the generalized DVR allows for a compact representation of the time-dependent wave-packet dynamics in up to six dimensions. Vibrationally adiabatic approaches to the detailed modelli ng of multidimensional quantum-dynamics usually are hampered by the typical ly large number of (avoided) crossings in dense spectra. This problem is pa rticularly severe for discrete variable representations. A solution is prov ided by the new technique of diabatic rotations leading to a systematic con struction of locally diabatic channels. This allows the treatment of very d ense spectra where conventional truncation techniques fail. Applying the ne w approach to the vibrational problem of tetratomic molecules demonstrates its flexibility and efficiency. The examples of formaldehyde, ammonia, and hydrogen peroxide cover the whole range from semirigid (CH2O) to large ampl itude inversion (NH3) and torsional tunnelling dynamics (H2O2). In solving the full six-dimensional vibrational eigenvalue problems for CH2O and NH3 t he Z-matrix DVR shows at least comparable if not superior numerical efficie ncy compared with specialized techniques. In the case of H2O2 the technique of diabatic rotations and adiabatic contraction for the first time allows the treatment of the tunneling dynamics significantly above the dissociatio n threshold up to the fifth OH stretch overtone. The calculated decrease of the tunneling rate by about one order of magnitude agrees well with experi mental observations. (C) 2000 American Institute of Physics. [S0021-9606(00 )00128-8].