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Enabling Quantum dynamics with or without Potential Energy Surfaces by removing extra fitting

Banff International Research Station for Mathematical Innovation and Discovery

One of the bottlenecks preventing routine quantum dynamics calculations on systems with more than about five degrees of freedom is the absence of potential energy surfaces. When PESs are available, they often need to be expressed in a form suitable for quantum dynamics, such as the sum– of–products form frequently used with MCTDH. Conversion to a sum–of–products form in dynamically suitable coordinates from e.g. inverse interatomic distances is itself a source of error and introduces extra human and computational cost. We present two approaches addressing this problem. One directly obtains a sums–of–products repre- sentation of the potential right at the point of fitting to ab initio data. The other eliminates the PES and makes it possible to obtain observables (such as the vibrational spectrum) directly from ab initio data. Both approaches have in common the removal of a step between ab initio calculations and the calculation of observables. They involve the use of parameterized basis functions in the expressions for the PES and the wavefunction, respectively.

Mathematics; Quantum theory; Partial differential equations; Mathematical physics

video/mp4

Author affiliation: National University of Singapore

2014-08-06

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49350

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/