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DTSTART:20180325T030000
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UID:5ba012785050b862018393@ist.ac.at
DTSTART:20181017T110000
DTEND:20181017T130000
DESCRIPTION:Speaker: Emil Zak\nhosted by Misha Lemeshko\nAbstract: In varia
 tional calculations of rotational-vibrational energy levels of polyatomic 
 molecules the total wave-function is typically represented as a linear com
 bination of basis functions. The size of the multidimensionaldirect-produc
 t basis grows exponentially with the number of atoms. As a result\, the me
 mory requirements forvariational calculations become prohibitive for molec
 ules with more than 4-5 atoms - this is often referred to asthe curse of d
 imensionality [1].Here we propose a method which circumvents the problem o
 f the exponential scaling of the basis set size.This is achieved through t
 he collocation approach [2]\, in which the Schrodinger equation is solved 
 at a set ofpoints\, avoiding the need for an accurate multidimensional qua
 drature.The new collocation method has the following advantages: 1) the si
 ze of the matrix eigenvalue problem isthe size of the required pruned (non
 -direct product) polynomial-type basis\; 2) it requires solving a regular\
 , andnot a generalized matrix eigenvalue problem\; 3) accurate results are
  obtained even if quadrature points andweights are not good enough to yiel
 d a nearly exact overlap matrix\; 4) the potential matrix is diagonal\; 5)
 the matrix-vector products required to compute eigenvalues and eigenvector
 s can be evaluated by doing sumssequentially\, despite the fact that the b
 asis is pruned\; 6) unlike in popular MCTDH and tensor rank-reductionmetho
 ds\, here no sum-of-product form of the potential energy surface (PES) is 
 required.To achieve these advantages we use sets of nested Leja grid point
 s and special hierarchical basis functions.Matrix-vector products needed f
 or iterative eigensolvers are inexpensive because transformation matrices 
 be-tween the basis and the grid\, and their inverses\, are lower triangula
 r. Vibrational energy levels of CH2NH arecalculated with the new method.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:swheatle@ist.ac.at
SUMMARY:Emil Zak: Overcoming the curse of dimensionality: a hierarchical co
 llocation method for solving the rotational-vibrational Schrödinger equat
 ion for polyatomic molecules
URL:https://talks-calendar.ista.ac.at/events/1415
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