Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality.

In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)].

Smolyak Algorithm Adapted to a System-Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions.

A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom.

Quantum dynamics with curvilinear coordinates: models and kinetic energy operator.

In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived for small systems or special kinds of coordinates, a and approach allows one to compute them in terms of sophisticated curvilinear coordinates.

Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach: general formulation and removal of singularities.

We present new techniques for an automatic computation of the kinetic energy operator in analytical form. These techniques are based on the use of the polyspherical approach and are extended to take into account Cartesian coordinates as well. An automatic procedure is developed where analytical expressions are obtained by symbolic calculations.

Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality.

Quantum dynamical approaches based on product-grids are limited to the studies of molecular systems with few degrees of freedom, typically less than ten. Recently, Avila et al. [G.

Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach.

We develop a new general code to automatically derive exact analytical kinetic energy operators in terms of polyspherical coordinates. Computer procedures based on symbolic calculations are implemented. Sets of orthogonal or non-orthogonal vectors are used to parametrize the molecular systems in space.

Torsional energy levels of nitric acid in reduced and full dimensionality with ElVibRot and Tnum.

The internal rotation (nu(9)) of nitric acid is studied using several ab initio models including 1D models and full dimensionality (9D) ones. For the 9D calculations, an adiabatic separation between the large amplitude motion, i.e.

A simple and efficient evolution operator for time-dependent Hamiltonians: the Taylor expansion.

No compact expression of the evolution operator is known when the Hamiltonian operator is time dependent, like when Hamiltonian operators describe, in a semiclassical limit, the interaction of a molecule with an electric field. It is well known that Magnus [N. Magnus, Commun.

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum.

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol.