Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, and their stable and unstable manifolds in molecular Hamiltonian have been an integral part of computing quantitative results such as the cumulative reaction probability and rate constants in chemical reactions. Thus, methods that can reveal the geometry of these invariant manifolds in high dimensional phase space (4 or more dimensions) need to be benchmarked by comparing with known results. In these articles, we assessed the capability of one such method called Lagrangian descriptor (LD) for revealing the aforementioned high dimensional phase space structures associated with an index-1 saddle in Hamiltonian systems. The LD based approach is applied to two and three degree-of-freedom quadratic Hamiltonian systems where the high dimensional phase space structures are known, that is as closed-form analytical expressions. This leads to a direct comparison of features in the LD contour maps and the phase space structures’ intersection with an isoenergetic two-dimensional surface, and hence provides a verification of the method. Next, the method of LD is applied to classical two and three degrees of freedom Hamiltonians that model features of dissociation reactions. The result of the LD based approach is compared with an established numerical method for computing unstable periodic orbit and tube manifolds of a two degrees of freedom system, and the results are in good agreement. We have also discussed the results in the context of three degrees of freedom extension of the same model Hamiltonian.
References:
Shibabrat Naik, Víctor J. García-Garrido, Stephen Wiggins, Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors, Communications in Nonlinear Science and Numerical Simulation, 2019, 79, 104907
https://doi.org/10.1016/j.cnsns.2019.104907

Shibabrat Naik and Stephen Wiggins, Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential, Phys. Rev. E, 2019, 100 (2), 022204
https://doi.org/10.1103/PhysRevE.100.022204

Related talk:
https://doi.org/10.6084/m9.figshare.8131958.v2

Chemistry and molecular dynamics of peptides colloquium.
School of Chemistry University of Leeds.
11.09.2019 Room: 1.53

15:00-15:45 Enzymatic manipulation of peptides to tackle the next generation therapeutic targets: Facilitating cyclisation of peptides and their membrane permeation
Wael Houssen, Institute of Medical Sciences, University of Aberdeen
15:45-16:00 Coffee break
16:00-16:45 Chemistry research with virtual reality: From speeding up molecular dynamics to reaction network discovery.
Robin Shannon, School of Chemistry University of Bristol and School of chemistry University of Leeds
16:45-17:30 Virtual Reality demonstration. Cyclising peptides with your own hands and more.

Abstracts

Enzymatic manipulation of peptides, to tackle the next generation therapeutic targets: Facilitating cyclisation of peptides and their membrane permeation
Dr Wael Houssen
Institute of Medical Sciences, University of Aberdeen

Recent advances in our understanding of disease biology have identified a set of challenging targets for drug discovery. One of these is the protein-protein interactions (PPIs) known to be implicated in many critical diseases that are as yet without an effective treatment option e.g. autoimmune disorders and cancer. Although biological drugs can interact with PPIs but they cannot penetrate cellular membranes because of their large size. There is currently a much growing evidence that cyclic and stapled peptides can modulate PPIs and thus hold a great promise in targeting intracellular PPIs for which the transformational potential is greatest. However, the challenges in their production at large scale and their poor cellular permeability have hampered the development of these remarkable compounds. In this talk, I will explain my insights in using synthetic biology, enzyme engineering and computational chemistry to address these challenges.

Chemistry research with virtual reality: From speeding up molecular dynamics to reaction network discovery.
Dr Robin Shannon
School of Chemistry University of Bristol and School of Chemistry, University of Leeds

With the release of the open source Narupa code (https://gitlab.com/intangiblerealities), it has become possible to interact with dynamical chemistry simulations in virtual reality. You can now submerge yourself into atomistic world where you can push and pull molecules and atoms with your own hands, steering molecular dynamics in a chosen direction. In this talk I will discuss two areas where Narupa is being used to aid or enable research in the general field of rare event simulation. In the first case I show how Narupa can aid the sampling of complex conformation changes, for example in the process of peptide cyclisation or nanotube permeation, in order to obtain quantitative thermodynamic information, and in the second case I will show some initial results where virtual reality and gamification are being used to explore reaction networks. After the talk you will be able to try VR chemistry yourself.

CHAMPS Research Day at the University of Bristol—10 June 2019

CHAMPS held a research day at the University of Bristol on Monday 10th June 2019. The focus of this year’s research day was to give each PDRA an opportunity to discuss the current status of their research and their plans for the future and to obtain feedback from the entire CHAMPS team.

A copy of the schedule for the day can be found here: Research Day 10.06.19 Schedule.

At the end of the we had dinner at Côte Brasserie in Clifton Village, which also provided an opportunity for a timely birthday celebration.

Lars Bratholm – CHAMPS PDRA:

 

A 1-day workshop, entitled “Recent Developments and Possible Extensions to the World of the Exact Factorization and Bohmian Dynamics” was held at the University of Bristol on Monday 22 April 2019. The workshop comprised a forum of eight 40-minute seminars with four breaks for discussion with world experts in the two related subjects of Bohmian Dynamics (BD) and Exact Factorization. This 1-day scientific encounter was intended to engage the CHAMPS team’s postdocs in these two topics, disseminate the recent work in these two areas performed by members of the CHAMPS team to the visiting world experts and inform all of the participants of the latest advances in these topics in the chemistry community.

To define the topics, Bohmian trajectories are meant to represent classical particle paths corresponding to quantum solutions when the quantum coupling constant h-bar has been set equal to zero in the 1927 Born-Oppenheimer (BO) approximation. J von Neumann’s 1931 approach (described in his textbook) is now called the “Exact Factorization” (EXF). The EXF approach generalised the formulation of the quantum-classical problem which has recently seen an active revival and development in numerical simulations of molecular chemistry.

Sophya Garashchuk discussed finite-dimensional representations of Bohmian trajectories and numerical difficulties in the implementation of Bohmian dynamics.

Salvador Miret-Artes discussed stochastic Bohmian particle trajectories as a possible representation of solutions of the Schrödinger-Langevin equation. In one of the discussion sessions which followed this lecture, the idea of stochasticity as a means of quantifying uncertainty in numerical simulations of the dynamics of molecular chemistry was a prominent topic.

Werner Koch discussed Bohmian trajectories whose space and time parameters and complex. This intriguing concept led to considerable discussion.

Cesare Tronci discussed a new mathematical formulation of EXF in terms of density matrices. In this new formulation, an analogue of the Bohmian trajectories arises as the Lagrangian paths of quantum complex-fluid parcels. The talk was based on a paper co-authored with a CHAMPS co-PI (Holm), which is to appear in Acta Mathematica Applicandae.

Eberhard Gross surveyed the modern development of the EXF approach and many of its successful applications in computational simulations of molecular chemistry processes during the past few years.

Ivano Tavernelli surveyed a series of standard applications of Bohmian trajectories in the BO framework, obtained upon setting the quantum coupling constant h-bar equal to zero.

Basile Curchod surveyed recent applications of the more modern EXF which involved the effects of h-bar at linear order. He also discussed many successful applications of EXF in computational simulations of molecular chemistry and explained the strategy of design of modern computational algorithms for these applications. Also

Mike Robb discussed recent applications of the BO approximation to computational simulations of atto-second processes in quantum molecular chemistry.

The many computational results displayed during the workshop raised the question of quantifying the uncertainty in these solutions. The discussions of these questions among the participants raised issues about how to model the combination of theoretical and computational errors in the quantum-classical interaction problem at the foundations of molecular chemistry which has an intrinsic uncertainty. We hope that the workshop will stimulate our efforts in improving the understanding of mathematical features of Bohmian Dynamics and Exact Factorization and creating new computational simulation techniques for use in chemistry.

 

Abstracts and slides for the lectures can be found here soon…

Report on the CHAMPS (Chemistry and Mathematics in Phase Space) Workshop

19th March 2019 – “Discovering Phase Space Structure and Reaction Mechanisms from Trajectory Data Sets” held at Engineers House, Clifton Bristol.

 This one day workshop was very much in the spirit of the CHAMPS project in that it brought together a group of chemists, mathematicians, and physicists all concerned with different aspects of the fundamental problem of revealing the phase space structures governing reaction dynamics using trajectory based diagnostics. The trajectory based diagnostic used by most of this group was the method of Lagrangian descriptors (a brief description of this approach was given in https://champsproject.com/2018/03/01/lagrangian-descriptors-from-fluid-dynamics-to-mathematics-to-chemistry/). This method has emerged as a flexible and “easy to code” method that can be used in a wide variety of settings relevant to chemical reaction dynamics.

Ana Mancho gave the first talk and discussed the basic ideas behind the method of Lagrangian descriptors and the different settings in which they can be applied. In particular, it was demonstrated how they could be applied to complex data sets in  geophysical fluid dynamics settings.  She was followed by Victor Garcia Garrido how the method could be applied in higher dimensional settings in order to detect periodic orbits and normally hyperbolic invariant manifolds (NHIMs) in general. Next Florentino Borondo showed how the method of Lagrangian descriptors could be applied to a study of  lithium cyanide isomerization. He showed how the method revealed the stable and unstable manifolds of a hyperbolic periodic orbit that mediated the isomerization reaction. Intriguingly, he demonstrated the existence of a parabolic periodic orbit in the reaction region and argued that it played an important role in the isomerization reaction. The full implications of this observation required further study. Rigoberto Hernandez  showed that the method of Lagrangian descriptors could be extended to completely new situations for reaction dynamics. In particular, he considered dissipative systems where the time dependence is stochastic and driven systems where the  dividing surfaces vary in time. This theme was extended by Fabio Revuelta who considered the situation where the environment exhibits memory effects and is modelled by colored noise. Thomas Bartsch considered the reaction dynamics of a system with three reactive channels that is known to be strongly chaotic at all energies—the monkey saddle.  He discussed the phase space structures controlling reaction dynamics in this situation. Joerg Main  concluded the main talks by discussing  how neural networks could be used to reveal the phase space structures, such as NHIMs,  that  govern the reaction dynamics. He showed how this approach could be used to locate time dependent NHIMs in driven systems and, from this, compute rate constants in multidimensional systems.

The day was concluded by a lively series of “lightning talks” (20 slides, 15 seconds per slide, for a total of 5 minutes) presented by the CHAMPS postdocs.

The small size of the workshop encouraged much interaction amongst the participants and encouraged further collaborations amongst the participants.  We hope to hear more about the fruits of these interactions in a follow-on workshop in the near future.

 

The Chesnavich Model for Ion-Molecule Reactions: A Rigid Body Coupled to a Particle

Gregory S. Ezra and Stephen Wiggins

International Journal of Bifurcation and Chaos, Vol. 29, No. 2 (2019) 1950025

DOI: 10.1142/S0218127419500251

 In this paper, we present a derivation of Chesnavich’s Hamiltonian for a model ion-molecule reaction. The model system has the basic structure of a rigid body coupled to a structureless particle. Using the form of the potential energy of interaction given by Chesnavich, we derive the equilibria, determine their stability, and construct two, two-dimensional invariant manifolds and determine their stability.