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DTSTART:20180325T030000
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DTSTAMP:20191212T070210Z
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
T Austria
ORGANIZER:swheatle@ist.ac.at
SUMMARY:Overcoming the curse of dimensionality: a hierarchical collocation
method for solving the rotational-vibrational SchrÃ¶dinger equation for po
lyatomic molecules
URL:https://talks-calendar.app.ist.ac.at/events/1415
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