Nous avons le plaisir d’accueillir le Pr Tucker Carrington de Queen’s University , Kingston, Ontario les 2 et 3 mai. Il donnera un séminaire le 2 mai à 14h – Amphi du LABRI
Titre
New variational methods for computing vibrational spectra of molecules with up to 11 atoms
Abstract
I shall present two new variational methods for computing vibrational spectra. Both rely on the Hamiltonian being a sum of products (SOP). To use a variational method one represents wavefunctions in a basis and uses methods of numerical linear algebra to determine the basis function coecients. A direct product basis has the advantage that it enables one to efficiently calculate the eigenvalues and eigenvectors of the Hamiltonian matrix using an iterative eigensolver. A direct product basis has the crucial disadvantage that the memory cost of a calcultion scales exponentially with the number of atoms in the molecule. One of the new methods uses an expanding basis of products of 1D functions and an iterative eigensolver. For ethylene oxide (7 atoms), converged results are obtained with a basis that is many orders of magnitude smaller than the direct product basis with which similar results would be obtained. The second new method uses sum-of-product basis functions stored in canonical polyadic (CP) tensor format and generated by evaluating matrix-vectorproducts. The memory cost scales linearly with the number of atoms in the molecule. Recent improvements make it possible to compute the spectrum of cyclopentadiene (11 atoms).
