X. Chapuisat

Vector parametrization of the N-atom problem in quantum mechanics. I. Jacobi vectors

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

Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split Hamiltonian pseudospectral approach

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 s...

Vector parametrization of the N-atom problem in quantum mechanics. II. Coupled-angular-momentum spectral representations for four-atom systems

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 rotational) part of the problem.

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment.

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.

VECTOR PARAMETRIZATION OF THE THREE-ATOM PROBLEM IN QUANTUM MECHANICS II. VALENCE VECTORS

Abstract It is shown that the description of a three-atom molecular system by two valence relative position vectors is, within the framework of an adequate representation previously introduced for Jacobi vectors, also advantageous with regard to the criterion of maximal prediagonalization of the matrix representing the kinetic energy operator.

Wave packet propagation for constrained molecular systems: spectroscopic applications to triatomic molecules

A new numerical method for the calculation of parts of the vibrational spectra of polyatomic molecules is presented. In particular, this method accounts for the high-lying floppy states in which the molecule may be delocalized over several isomeric forms. For testing the validity of the method, i.e. for allowing comparisons with reliable results previously obtained, the method is applied to triatomic molecules, namely the molecules isoelectronic to HCN/CNH (HCP, HSiN and HSiP). But the method is obviously designed for larger systems. The potential energy surfaces of the four molecules studied are topologically strongly different, i.e. the repartitions of the minima and the transition states are changing significantly from one another, thus producing different spectral profiles.