Journal
MOLECULAR PHYSICS
Volume 116, Issue 23-24, Pages 3701-3709Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00268976.2018.1473652
Keywords
Torsional level; methanol; kinetic energy operator; on-the-fly
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In quantum dynamics, physically well-adapted curvilinear coordinates are coordinates that lead to a Hamiltonian operator as separable as possible, in order to simplify the resolution of the corresponding time-independent or time-dependent Schrodinger equations. Various equivalent curvilinear expressions of the kinetic energy operator (KEO) are well known. They can be used in either an analytical or a numerical approach. The latter has the feature of allowing to straightforwardly compute the KEO in terms of sophisticated (yet easy to define) physically well-adapted curvilinear coordinates. Nevertheless, the number of terms to be computed on a full grid, scales as n(2)/2 (n being the number of degrees of freedom), so that, for systems with n > 10, the memory storage of the KEO's becomes extremely demanding and therefore often unrealistic. We show here that it is possible, starting from the basic quantum expression of the KEO as a curvilinear Laplacian operator, to reduce the memory storage bottleneck by numerically computing the KEO on-the-fly, i.e. each time it is required, without computing the extrapotential term. This new approach opens the way to rigorous quantum studies of systems with many degrees of freedom. The comparison of torsional levels of methanol obtained by the present on-the-fly method with our previous results shows excellent agreement. [GRAPHICS] .
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