Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points.

B.K. Carpenter, G.S. Ezra, S. C. Farantos, Z. C. Kramer, and S. Wiggins. Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points, Regular and Chaotic Dynamics, 23(1), 60-79 (2018).


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In this paper we analyze a two degree of freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical points. In addition, the model has an index one saddle between the potential wells. We study the dynamical mechanisms underlying transport between the two potential wells, with emphasis on the role of the flat region surrounding the wells. The model allows us to probe many of the features of the “roaming mechanism” whose reaction dynamics are of current interest in the chemistry community.

Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics

B.K. Carpenter, G.S. Ezra,  S. C. Farantos, Z. C. Kramer, and S. Wiggins. Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics. J. Phys. Chem. B. DOI: 10.1021/acs.jpcb.7b08707

Publication Date (Web): October 2, 2017.

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This paper uses trajectory data and machine learning approaches to “learn” phase space structures. Classical Hamiltonian trajectories are initiated at random points in phase space on a fixed energy shell of a model two degree of freedom potential, consisting of two interacting minima in an otherwise flat energy plane of infinite extent.  Below the energy of the plane, the dynamics are demonstrably chaotic.  However, most of the work in this paper involves trajectories at a fixed energy that is 1% above that of the plane, in which regime the dynamics exhibit behavior characteristic of chaotic scattering.  The trajectories are analyzed without reference to the potential, as if they had been generated in a typical direct molecular dynamics simulation.  The questions addressed are whether one can recover useful information about the structures controlling the dynamics in phase space from the trajectory data alone, and whether, despite the at least partially chaotic nature of the dynamics, one can make statistically meaningful predictions of trajectory outcomes from initial conditions.  It is found that key unstable periodic orbits, which can be identified on the analytical potential, appear by simple classification of the trajectories, and that the specific roles of these periodic orbits in controlling the dynamics are also readily discerned from the trajectory data alone.  Two different approaches to predicting trajectory outcomes from initial conditions are evaluated, and it is shown that the more successful of them has ~90% success.  The results are compared with those from a simple neural network, which has higher predictive success (97%) but requires the information obtained from the “by-hand” analysis to achieve that level.  Finally, the dynamics, which occur partly on the very flat region of the potential, show characteristics of the much-studied phenomenon called “roaming.” On this potential, it is found that roaming trajectories are effectively “failed” periodic orbits, and that angular momentum can be identified as a key controlling factor, despite the fact that it is not a strictly conserved quantity.  It is also noteworthy that roaming on this potential occurs in the absence of a “roaming saddle,” which has previously been hypothesized to be a necessary feature for roaming to occur.

CHAMPS – Kick off Meeting 15th & 16th January 2018

The Champs (Chemistry and mathematics in phase space) Kick off Meeting took place 15th & 16th January 2018.  This two-day conference was held at The Watershed in Bristol and launched the Chemistry and Mathematics in Phase Space project. 70 people from all over the world attended the event which had a stimulating set of talks from eminent speakers.

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It brought together an international group of distinguished speakers who gave first class talks to a large audience on a wide range of areas in Mathematics and Chemistry.

The conference dinner was held in the Bristol Museum and Art Gallery


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The kick off meeting was the first organized activity of Champs bringing together chemists and mathematicians. The success of this meeting reinforces our optimism that this is an opportune time for such an interdisciplinary collaboration of chemists and mathematicians and we expect that this will be the first of many such successful meetings  of Champs related topics.

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first contact with the AtMath collaboration

Dr. David Glowacki recently returned from Screen Shot 2017-11-28 at 18.59.12Levi in Finland (way up in Lapland!) where he was invited to give a plenary lecture (entitled “Non-equilibrium reaction dynamics in atmospheric chemistry”) at the kickoff meeting for the Finnish “AtMath” collaboration. AtMath (like CHAMPS) is a funded by a large grant, in order to bring together atmospheric scientists and mathematicians and make progress on difficult problems. David was specifically invited to the conference by Prof. Hanna Vehkamäki, whose group is involved in fundamental modeling of atmospheric particle formation and growth processes using both quantum chemistry and also large non-linear kinetics models. The conference was fantastic:  not only was the snow-covered Lapland landscape was amazing, but the relaxed conference programme facilitated great conversations with several of the conference participants who delivered a wide range of fascinating talks across several different areas. There were also a range of speakers invited from beyond the AtMath collaboration, including for example Prof. Jochen Schenk (CSUF) who gave a fascinating talk on the molecular-level transport of water in trees, and also Prof. Eric Vanden-Eijnden (Courant Institute, NYU), who is an applied mathematician who has made very well-known contributions to chemistry for path sampling high-dimensional systems.

efficient excited states in large systems

We recently published a paper titled “Pushing the Limits of EOM-CCSD with Projector-Based Embedding for Excitation Energies” where we calculated the interaction of light with some small molecules that are in solution using state of the art techniques. In this post, I’m planning on giving a general introduction to why we did this research and the ways impact it may have.

The interaction between light and molecules is eom-ccsdcentral to all branches of physical sciences, with our understanding of the physical process involved going back to the quantum revolution 100 years ago. Being able to work out the amount of energy needed for light to affect a molecule and the strength of that interaction is valuable in many areas that affect modern day life, such a photosynthesis, designing better solar cells or even how to build better phone screens.

The use of computers in chemistry makes it possible to predict how chemical reactions occur with little cost or damage to the environment and can be a helpful guide to experiment. Computational chemists aim to find ways to calculate many chemical properties as efficiently as possible without losing accuracy in our predictions.

In the case of light-chemical interactions, two methods that are commonly used are a quick and somewhat rough method called TD-DFT and a more accurate and expensive method called EOM-CCSD. Our work combines the methods in such a way that makes it possible to work our how light interacts with chemicals accurately and quickly.

The approach that we took was to treat different chemicals with different accuracy using a method called “Embedding” (placing one method inside another). By doing this we were able to accurately calculate the effect of light hitting a molecule in solvent between 100x and 1000x faster than possible before.

In the long term, our research may help enable highly accurate predictions of light-chemical interactions in academia and industry. For example, calculating how chlorophyll in plants absorbs light or how to test new solar cell designs without having to actually build them.