Quantum dynamics simulations using Gaussian wavepackets: the vMCG method

Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical mechanics, allowing a simple pictorial interpretation of an evolving wavepacket. They also have better...

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Published in	International reviews in physical chemistry Vol. 34; no. 2; pp. 269 - 308
Main Authors	Richings, G.W., Polyak, I., Spinlove, K.E., Worth, G.A., Burghardt, I., Lasorne, B.
Format	Journal Article
Language	English
Published	Abingdon Taylor & Francis 03.04.2015 Taylor & Francis Ltd
Subjects	Chemical Sciences Convergence direct quantum dynamics Dynamics Evolution Exact solutions Gaussian Gaussian wavepackets Mathematical analysis Mathematical functions Mathematical problems Normal distribution or physical chemistry Quantum chemistry quantum dynamics simulations Quantum physics Schrodinger equation Schroedinger equation Simulation Theoretical and theoretical chemistry Waveform analysis
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Abstract	Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical mechanics, allowing a simple pictorial interpretation of an evolving wavepacket. They also have better scaling with system size compared to conventional grid-based techniques. Here we review the variational multi-configurational Gaussian (vMCG) method. This is a variational solution to the TDSE, with explicit coupling between the Gaussian basis functions, resulting in a favourable convergence on the exact solution. The implementation of the method and its performance will be discussed with examples from non-adiabatic photo-excited dynamics and tunneling to show that it can correctly describe both of these strongly quantum mechanical processes. Particular emphasis is given to the implementation of the direct dynamics variant, DD-vMCG, where the potential surfaces are calculated on-the-fly via an interface to quantum chemistry programs.
AbstractList	Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical mechanics, allowing a simple pictorial interpretation of an evolving wavepacket. They also have better scaling with system size compared to conventional grid-based techniques. Here we review the variational multi-configurational Gaussian (vMCG) method. This is a variational solution to the TDSE, with explicit coupling between the Gaussian basis functions, resulting in a favourable convergence on the exact solution. The implementation of the method and its performance will be discussed with examples from non-adiabatic photo-excited dynamics and tunneling to show that it can correctly describe both of these strongly quantum mechanical processes. Particular emphasis is given to the implementation of the direct dynamics variant, DD-vMCG, where the potential surfaces are calculated on-the-fly via an interface to quantum chemistry programs. Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrodinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical mechanics, allowing a simple pictorial interpretation of an evolving wavepacket. They also have better scaling with system size compared to conventional grid-based techniques. Here we review the variational multi-configurational Gaussian (vMCG) method. This is a variational solution to the TDSE, with explicit coupling between the Gaussian basis functions, resulting in a favourable convergence on the exact solution. The implementation of the method and its performance will be discussed with examples from non-adiabatic photo-excited dynamics and tunneling to show that it can correctly describe both of these strongly quantum mechanical processes. Particular emphasis is given to the implementation of the direct dynamics variant, DD-vMCG, where the potential surfaces are calculated on-the-fly via an interface to quantum chemistry programs.
Author	Lasorne, B. Polyak, I. Spinlove, K.E. Worth, G.A. Richings, G.W. Burghardt, I.
Author_xml	– sequence: 1 givenname: G.W. surname: Richings fullname: Richings, G.W. organization: School of Chemistry, University of Birmingham – sequence: 2 givenname: I. surname: Polyak fullname: Polyak, I. organization: School of Chemistry, University of Birmingham – sequence: 3 givenname: K.E. surname: Spinlove fullname: Spinlove, K.E. organization: School of Chemistry, University of Birmingham – sequence: 4 givenname: G.A. surname: Worth fullname: Worth, G.A. email: g.a.worth@bham.ac.uk organization: School of Chemistry, University of Birmingham – sequence: 5 givenname: I. surname: Burghardt fullname: Burghardt, I. organization: Institute of Theoretical and Physical Chemistry, University of Frankfurt – sequence: 6 givenname: B. surname: Lasorne fullname: Lasorne, B. organization: Institue of Charles Gerhardt, University of Montpellier
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Snippet	Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has... Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrodinger equation (TDSE). They have an underlying trajectory picture that has...
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SubjectTerms	Chemical Sciences Convergence direct quantum dynamics Dynamics Evolution Exact solutions Gaussian Gaussian wavepackets Mathematical analysis Mathematical functions Mathematical problems Normal distribution or physical chemistry Quantum chemistry quantum dynamics simulations Quantum physics Schrodinger equation Schroedinger equation Simulation Theoretical and theoretical chemistry Waveform analysis
Title	Quantum dynamics simulations using Gaussian wavepackets: the vMCG method
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