Within the framework of an adequate spectral representation, the geometrical description of an N-atom molecular system by n=N−1 Jacobi relative position vectors is shown to be particularly advantageous with regard to the criterion of prediagonalization of the matrix representing the kinetic energy operator.

No abstract

Since the conformation of physical systems is often advantageously described with the help of generalized (i.e. curvilinear) coordinates, the following questions are raised and general answers given to them: (i) What are the components of the momentum operators, those of the adjoint momentum operators and those of the hermitian momentum operators ? (ii) What is the general form of the hamiltonian operator ? (iii) What do the general forms of the momentum and hamiltonian operators become when expressed in terms of quasi-momentum operators (e.g. angular momentum component operators) ? (iv) How are the answers to the above questions affected by an arbitrary choice of normalization convention for the total wave-function ? A complete set of formulae (whatever the independent choices of coordinates, quasi-momentum operators and normalization) is given and various 'historical' formulae are shown to be particular instances of the general formulae proposed.

No abstract

An efficient pseudospectral method for performing fully-coupled six-dimensional bound state dynamics calculations is presented. A Lanczos-based iterative diagonalization scheme produces the energy levels in increasing energies. This scheme, which requires repetitively acting the Hamiltonian operator on a vector, circumvents the problem of constructing the full matrix. This permits the use of ultralarge molecular basis sets in order to fully converge the calculations. The Lanczos scheme was conducted in a symmetry adapted six-dimensional spectral representation. The Hamiltonian operator has been split into only four different terms, each being Hermitian and symmetry-adapted. The potential term is evaluated by a pseudospectral scheme of Gaussian accuracy, which guarantees the variational principle. Spectroscopic levels are computed with this method for one ammonia potential, and compared to experimental results. The results presented below are a direct application of our vector formulation. The latter has shown to be particularly well adapted to the split pseudospectral approach for it yields a compact and symmetry-adapted Hamiltonian.

No abstract

No abstract

Within the framework of adapted coupled-angular-momentum spectral representations, the geometrical description of a four-atom molecular system by three Jacobi relative position vectors is shown to result in matrices representing the kinetic energy operator, prediagonalized to a very large extent. A fully diagonal representation is built for the angular ͑internal and rotational͒ part of the problem.