Claude Leforestier

Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with a split Wigner pseudo spectral approach

A novel and efficient pseudospectral method for performing fully coupled six-dimensional bound state dynamics calculations is presented, including overall rotational effects. 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 (up to over one million states for a given symmetry) in order to fully converge the calculations. The Lanczos scheme was conducted in a symmetry adapted spectral representation, containing Wigner functions attached to each monomer. The Hamiltonian operator has been split into different terms, each corresponding to an associated diagonal or nearly diagonal representation. The potential term is evaluated by a pseudospectral scheme of Gaussian accuracy, which guarantees the variational principle. Spectroscopic properties are computed with this...

Grid representation of rotating triatomics

A grid formulation is presented for the body‐fixed (BF) motion of a rotating triatomic molecule. The BF component of the wave function, described in terms of Jacobi coordinates, is discretized on a {Ri×rj×θα} grid. By use of the generalized discrete variable representation (DVR) of Light, Hamilton, and Lill [J. Chem. Phys. 82, 1400 (1985)] one can employ the same θ grid for the different Ω components of the wave function, Ω corresponding to the projection of the total angular momentum J onto the z BF axis. Such a unique grid definition allows one to define adiabatic states, with respect to the θ coordinate, independent of the Ω value considered. These states have been directly computed by means of a distributed 2D DVR, sampling only the relevant points in configuration space. Further reduction of the rovibrational basis set was achieved by defining new adiabatic states, with respect to the Ω component. This formation is applied to the calculation of bound rovibrational states of the HCN molecule for the J...

Determination of a flexible (12D) water dimer potential via direct inversion of spectroscopic data

We report the determination of two dimer water potential energy surfaces via direct inversion of spectroscopic data. The first surface, rigid, employs the MCY functional form originally fitted by Clementi and co-workers from ab initio calculations, modified by adjunction of a fifth, uncharged, site to improve the dispersion component. The vibration-rotation-tunneling energy levels were computed by means of the pseudospectral split Hamiltonian method that we developed previously. The fitted surface shows considerable improvement as compared to the original one: transitions among the ground-state manifold are in error by at most 0.2 cm−1, and excited state band origins (up to 150 cm−1) are reproduced to within 0.5 to 3 cm−1. For the second surface, flexible, we used the same modified MCY functional form, considered now to depend on the 12 internal degrees of freedom, and augmented by the monomer potential energy terms. The water dimer is described in its full dimensionality by collision-type coordinates in ...

Quantum exact three‐dimensional study of the photodissociation of the ozone molecule

We present an exact three‐dimensional quantum study of the dissociation of the ozone molecule on a single potential‐energy surface (1B2). The wave function has been discretized on a three‐dimensional grid, in conjunction with a mixed pseudospectral scheme in order to represent the action of the Hamiltonian operator on it. The correlation function (Fourier transform of the total cross section) has been computed within the time formulation. This function was obtained by means of the Lanczos algorithm, without any actual propagation of the initial wave packet on the upper surface. A calculation performed for the total angular momentum value J=0, reproduces the characteristic features of the experimental correlation function (recurrence times).

Accurate determination of a potential energy surface for CD3H

We present in this paper an application of the Lanczos algorithm to the fitting of a potential energy surface from the experimental spectrum. This method presents two definite improvements on the conventional approach: (i) the Lanczos algorithm allows to treat ultra‐large basis sets (120 000 states in this calculation) and (ii) it is possible to tune selectively the calculation to specific components of the spectrum (e.g., a given combination band nνi+mνj) thus reducing considerably the complexity of the fit. This method has been applied to the CD3H molecule, considering all the vibrational degrees of freedom. Converged line positions have been obtained for high overtones of the C–H stretching mode (up to 16 000 cm−1). The accuracy of the fitted surface is demonstrated by direct comparison of experimental and calculated spectroscopical parameters.

Adiabatic pseudospectral methods for multidimensional vibrational potentials

We describe a new algorithm for computing eigenvalues, spectral intensities, and selected eigenvectors of multidimensional vibrational potential surfaces. The method involves a synthesis of pseudospectral and sequential adiabatic reduction methods and merges the storage and computational advantages of the former with the improved basis set generated by the latter. The recursive residue generation method, which utilizes a Lanczos‐based diagonalization procedure, is employed to calculate the observables. As a test case, we apply the method to computation of the infrared and stimulated emission pumping spectra for the HCN molecule and demonstrate a very large (one to three orders of magnitude) reduction in computational effort (for comparable accuracy) as compared to discrete variable representation (DVR)/adiabatic reduction or standard collocation approaches. We expect that this advantage will be increased considerably for larger (e.g., tetra‐atomic) systems and will permit accurate basis set calculations o...

Classical trajectories using the full abinitio potential energy surface H−+CH4→CH4+H−

The classical trajectory method has been coupled with the gradient evaluation of the ab initio potential energy with respect to nuclear coordinates to study molecular dynamics. Trajectories, starting from a known transition state, can be computed in the full space of Cartesian coordinates in order to provide information on the reaction dynamics. The nucleophilic substitution reaction H−+CH4→CH4+H− is treated as an example and is shown to occur via a nonadiabatic path where initial vibrational energy of the methane molecule is essential for reaction.

Grid method for the Wigner functions. Application to the van der Waals system Ar–H2O

We present a method to switch back and forth between a basis set of Wigner functions and an associated three‐dimensional grid of Euler angles. The grid‐spectral transformation is not one to one as more grid points are used than Wigner functions, and thus departs from the Fourier method of Kosloff or the discrete variable representation method of Light and collaborators, but this extra number of grid points allows one to achieve a numerically exact integration of all the potential matrix elements in the Wigner basis set. As an example, we apply this method to the determination of the bound states of the H2O–Ar van der Waals system, already studied by Cohen and Saykally [J. Chem. Phys. 98, 6007 (1993)]. The calculation consists of coupling a Lanczos scheme with a split representation of the Hamiltonian. The iterative scheme is formulated entirely within the spectral representation in which the kinetic energy operator terms are analytic, the potential term being evaluated in the grid representation. Using th...

Spectroscopic determination of the water dimer intermolecular potential-energy surface

Two polarizable six-dimensional water dimer intermolecular potential surfaces have been determined by fitting the distributed multipole ASP (anisotropic site potential) potential form to microwave, terahertz, and midinfrared cavity ringdown (D2O)2 spectra via a rigorous calculation of the water dimer eigenstates with the PSSH (pseudo-spectral split Hamiltonian) method. The fitted potentials accurately reproduce most ground-state vibration-rotation-tunneling spectra and yield excellent second virial coefficients for both H2O and D2O. The calculated dimer structure and dipole moment are close to those determined from microwave spectroscopy and high level ab initio calculations, except that the O–O distance (2.952 A) is significantly shorter than the currently accepted experimental value. The dimer binding energy (4.85 kcal/mol) is considerably smaller than the accepted experimental result, but in excellent agreement with recent theoretical results, as are the acceptor switching and donor–acceptor interchang...

Hyperspherical formulation of the photodissociation of ozone

In a preceding paper [J. Chem. Phys. 92, 247 (1990)], we reported a preliminary three‐dimensional quantum calculation of the dissociation of the ozone molecule in the Hartley band. We present here a fully converged calculation of the autocorrelation function on the excited 1B2 potential energy surface of Sheppard and Walker. The study has been reformulated in terms of hyperspherical coordinates, in order to make use of the permutation‐inversion symmetry of the ozone molecule. The wave‐function has been discretized on a three‐dimensional hyperspherical grid. The autocorrelation function 〈φ0‖φt〉 has been computed within the time formulation, by means of the Lanczos algorithm. A calculation performed for the total angular momentum value J=0 shows a good agreement with the experimental results of Johnson and Kinsey, except for the overall intensity of the recurrence peaks. The calculated photodissociation spectrum reproduces the same oscillation pattern as observed experimentally.