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Variational Metadynamics

Periodic Reporting for period 2 - VARMET (Variational Metadynamics)

Reporting period: 2017-07-01 to 2018-12-31

Molecular dynamics and Monte Carlo methods based on an atomistic description of matter are indispensable tools in modern science. They have the ability of simulating on the computer the microscopic behavior of matter. They help explain experimental results, provide insight, predict new phenomena and replace costly or impossible experiments. They find applications in almost all areas of science. Improving these method will help design new drugs, discover new materials with new properties, find greener chemical processes, and address the renewable energy problem, just to quote a few areas of great societal interest. In this project we plan to lift one of the limitations of these methods the limited time scale that can be explored. Typically with standard methods one can study phenomena that take place on the time scale of one millionth of a second, while many phenomena of interest occur on a much longer time scale, say seconds or more. Our objective is to use a recently derived variational principle to achieve this result. The variational principle allows obtaining a bias potential that when added to theHamiltonian of the system accelerate sampling. The variational principle allows a flexibility and power that is absent in other methods and, properly engineered, the bias allows calculating the rates of transitions between long lived metastable states. The objective of the method is to develop further the method, make the software needed to apply the method available to the scientific community, and apply the methods to topical problems of current interest, most noticeably in the area of nucleation and drug-ligand unbinding.
The project VARMET has so far reached the proposed objectives that in the space of time of 18 months were planned. This was facilitated by the previous experience with the ERC project PUSHBOUND and the working environment that was already in place for conducting ERC financed projects. The work plan submitted was divided into four different areas: Coarse Graining, Methods, Rates and Nucleation. I will discuss the project advance separately for each area.

Coarse Graining
In this area of work we have implemented the Variational Enhanced Sampling (VES) method into the plug in PLUMED that has been developed for standard metadynamics and that it is extremely popular. Its ability to be interfaced with many of the most popular ab-initio and standard MD codes allows an easy access to the VES method. In order to facilitate even more the diffusion of the method we have manage to find funds from a different source to run a very successful workshop aimed at young people with 51 participants most of whom (48) were from European research institution.
We have also realized that VES can be directly used to obtain coarse grained representations of microscopic systems. To this effect we have shown that one can use VES to compute the parameters of the Landau-Ginzburg free-energy, a well known coarse grained model that is used to describe in a coarse grained fashion the behavior of systems close to a second order phase transitions.
We are also applying VES to describe the behavior of small proteins. In order to calibrate the quality of our results we compare with the simulations performed on purposely build machines by the D.E. Shaw group. We found that reweighting the results using a bias that is multidimensional was a problem. To this effect we are introducing collective variable of novel design that will allow reducing the number of variable on which the bias is made to depend.

Methods
We have implemented a variety of basis set and we now use them as appropriate in different context. We have and still are exploring better methods of minimization. We have implemented and applied model bias potential whose coefficients can be optimized via VES. We have used a potential that is inspired by the shape of Marcus theory potential. This is now a fully implemented and is a new tool available for use whenever it is convenient.

Rates
In this area of research we use the extraordinary properties of VES to design bias potentials that have a preassigned free energy height. By biasing a system with such potential one facilitates transitions to other metastable states. The rates in the biased system can be simply related to the unbiased rates thus very long time scale can be reached. We have indeed proved this to be correct and we have applied this approach to chemical reactions.
In an important development we have found a way to optimize the collective variables, using the variationally accelerated configurational sampling method developed by Frank Noe and adapting it biased runs. We have tested so far this method in standard metadynamics. Extension to VES appears straightforward.

Nucleation
This is one of the main areas in which we want to apply VES. As promised we have applied expressions derived from classical nucleation theory to construct the bias to study nucleation. This application has been successful and has provided insight into the theory and how the finite size effects can effect the results. We have started working ahead of schedule on nucleation of crystals from the liquid state here another remarkable finding has been the identification of entropy, or better said a surrogate for entropy, as a collective variable. This variable does not prejudge the crystal structure the system is going to crystallize and mimics the physical process that in a first order phase transition results in a trade off between entropy and enthalpy.

In conclusion a number of important results have been obtained and most of them are already published in peer revie
All the results presented are novel and have pushed the state of the art. As discussed above we have made the code available to a vast community of users including the industrialist. The wide variety of possible applications ensure that the project will have lasting impact in many areas like material science, chemistry, biology, and drug design.
Free-energy surface profile , F(s), and flooded surface, F(s) +V(s), for the asymmetric CH3F + Cl- -