A Practical Diabatisation Scheme for Use with the Direct-Dynamics Variational Multi-Configuration Gaussian Method

Richings, Gareth W.; Worth, Graham A.

doi:10.1021/acs.jpca.5b07921

Cited by 60 publications

(71 citation statements)

References 77 publications

(137 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nuclear dynamics on the groundstate and first excited state of the cation have been studied using TSH [40], MCTDH [41] and DD-265 vMCG [22]. Furthermore, the butatriene cation was previously used to demonstrate the efficacy of the propagation diabatisation scheme outlined above [28].…”

Section: Resultsmentioning

confidence: 99%

“…[28] In the next section we present the necessary theory behind each aspect 100 of the method: grid-based dynamics, the method used to interpolate the PESs, and the diabatisation scheme. Subsequently, some technical details of the implementation are presented followed by results of a test calculation on the dynamics of the 105 butatriene cation.…”

mentioning

confidence: 99%

“…Previously one of us published a method for generating quasi-diabatic PESs on-the-fly, within the context of DD-vMCG [28]. The approach is based on the idea of the propagation of the transformation matrix between the adiabatic and diabatic representations [34], A, using line integrals of the non-adiabatic coupling terms (NACTs) between adiabatic states ψ i and ψ j ,…”

mentioning

confidence: 99%

“…However, to maintain the unitarity of A between consecutive points, equation (11) is rearranged as [28,34] A (q + ∆q) = exp 1 2…”

mentioning

confidence: 99%

See 3 more Smart Citations

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Richings

Habershon

2017

Chemical Physics Letters

Self Cite

100

View full text Add to dashboard Cite

We present a method for performing non-adiabatic, grid-based nuclear quantum dynamics calculations using diabatic potential energy surfaces (PESs) generated "on-the-fly". Gaussian process regression is used to interpolate PESs by using electronic structure energies, calculated at points in configuration space determined by the nuclear dynamics, and diabatising the results using the propagation diabatisation method reported recently [J. Phys. Chem. A, 119, 12457 -12470 (2015)]. To test this new method, the nuclear dynamics on the ground and first electronic excited states of the butatriene cation is studied using a grid-based method. The evolution of diabatic state populations is in very good agreement with those produced using a fitted potential. Overall, our scheme offers a route towards accurate quantum dynamics on diabatic PESs learnt on-the-fly.Keywords: Direct-dynamics, Diabatisation, Grid-based quantum dynamics, Butatriene 2010 MSC: 00-01, 99-00The study of nuclear quantum dynamics of nuclei is of great importance in helping to understand of the time-evolution of molecular systems upon excitation of the electronic degrees-of-freedom (DOFs); such simulations can make direct connections to the states. [6,7] One can model these non-adiabatic transitions using classical mechanics, as in the trajectory surface hopping (TSH) algorithm, [2,[8][9][10] but as the dynamics are inherently quantum mechanical, it is better to use a quantum mechani-25 cal method such as the multi-configuration timedependent Hartree (MCTDH) approach [1, 11,12] where possible.The major bottleneck in performing quantum dynamics calculations is usually not the wavefunc-30 tion time-propagation, but the creation of an appropriate PES on which to run the dynamics. As quantum mechanics is non-local, one needs a PES which is known everywhere in the configuration space of the nuclear motion prior to running the 35 dynamics. For the fully quantum mechanical study of non-adiabatic systems it is usually necessary to convert the PESs from the adiabatic representation to a diabatic representation. The adiabatic representation of the potential is an energy-ordered set 40 of PESs, and corresponds to the energies generated by electronic structure programs. However, at points in configuration space where adiabatic surfaces become degenerate, such as at conical interePreprint submitted to Chemical Physics Letters December 20, 2016 sections (CIs), there is a discontinuity in the gradi-45 ent of the states, such that the adiabatic states are no longer smooth; furthermore, the coupling between the states at these points is also infinite. Neither property of the adiabatic PESs is conducive to performing wavepacket dynamics, so transforma-50 tion to the diabatic representation is performed, resulting in smoothly varying surfaces with finite couplings. Diabatic representations are not unique for a given set of adiabatic states, so an appropriate diabatisation scheme must be chosen before the 55 PES can be used in a dynamics calculation. PESs are usua...

show abstract

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…However, to maintain the unitarity of A between consecutive points, equation (11) is rearranged as [28,34] A (q + ∆q) = exp 1 2…”

mentioning

confidence: 99%

See 2 more Smart Citations

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Richings

Habershon

2017

Chemical Physics Letters

Self Cite

100

View full text Add to dashboard Cite

show abstract

“…As a result, we are currently investigating the combination of GPR with diabatization schemes which are suited to direct quantum dynamics methods. 87 Given the improved performance of GPR, as well as its lower computational cost compared to second-order Taylor expansion methods in particular, our results suggest that, beyond the (relatively minor) problem of choosing the value of the GPR parameters, there is little reason to continue to use Taylor expansion methods to evaluate PES matrix elements for GWP-based quantum dynamics methods.…”

Section: Discussionmentioning

confidence: 87%

Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

Alborzpour

Tew

Habershon

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression The Journal of Chemical Physics 141, 144310 (2014); 10.1063/1.4897486Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation The Journal of Chemical Physics 148, 241704 (2018); 10.1063/1.5009347 THE JOURNAL OF CHEMICAL PHYSICS 145, 174112 (2016) Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each timestep; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

show abstract

Gaussian Wave Packets and the DD‐vMCG Approach

Worth

Lasorne

2020

Quantum Chemistry and Dynamics of Excited States

View full text Add to dashboard Cite

A Practical Diabatisation Scheme for Use with the Direct-Dynamics Variational Multi-Configuration Gaussian Method

Cited by 60 publications

References 77 publications

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

Gaussian Wave Packets and the DD‐vMCG Approach

Contact Info

Product

Resources

About