CHAMPS workshop – “Recent Developments and Possible Extensions to the World of the Exact Factorization and Bohmian Dynamics” 22nd April 2019


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…

CHAMPS Workshop – “Discovering Phase Space Structure and Reaction Mechanisms from Trajectory Data Sets” 19th March 2019

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.

Workshop Photo - 19.03.19 group IMG_2183

 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 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.

Workshop Photo - 19.03.19 PDRAs IMG_2183

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

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.



Upcoming CHAMPS workshop on Exact Factorization and Bohmian Mechanics

CHAMPS – Workshop on Exact Factorization and Bohmian Mechanics

Engineers House The Promenade Clifton Down, Bristol BS8 3NB

Monday 22nd April 2019

Methodologies for separating nuclear and electronic motions are fundamental to chemistry.

In recent years the notion of “Exact Factorization” has emerged as a compelling approach for analysing and interpreting the complete wave function for a system of nuclei and electrons evolving in a time-dependent external potential.

Another related approach is Bohmian mechanics, which is known for many years, but recently has received much of attention.

The purpose of this workshop is to bring together experts in this area to discuss the current “state-of-the-art” and the prospects for future development.

To register your interest in this event please email the Champs Project Manager for further information –


Event schedule 22.04.19


Upcoming CHAMPS Workshop on “Discovering Phase Space Structure and Reaction Mechanisms from Trajectory Data Sets”

CHAMPS – Workshop on “Discovering Phase Space Structure and Reaction Mechanisms from Trajectory Data Sets” 

Engineers House The Promenade Clifton Down, Bristol BS8 3NB

Tuesday 19th March 2019

Trajectories generated by Hamilton’s equations are a fundamental quantity for understanding reaction mechanisms in chemistry. Trajectories are an inherently phase space object, i.e. they describe the change in configuration space coordinates and momentum coordinates. Consequently, their behaviour is governed by phase space structures. Theoretical and computational advances now allow the generation of large sets of trajectories. Consequently, there has been significant activity in recent years in developing theoretical and computational strategies for discovering “structure” in these data sets. This is a “first of its kind”  workshop that will bring together  people in the applied mathematics and chemistry communities that are working on these issues.

To register your interest in this event please email the Champs Project Manager for further information –


19.03.19 Workshop Schedule of Talks

Congratulation to CHAMPS PDRA Lars Bratholm for being awarded a Alan Turing Institute Fellowship

Congratulation to CHAMPS PDRA Lars Bratholm for being awarded a Alan Turing Institute Fellowship

We are please that Dr. Lars Bratholm is in the first group of Alan Turing Institute fellows at the University of Bristol. This is a notable accomplishment and we anticipate that this will serve to  further develop links between CHAMPS and the Alan Turing Institute.

Information about the Alan Turing Institute can be found here:


Lars Bratholm - photo for website
L. Bratholm | Bristol