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## Hybrid Quantum Mechanics / Molecular Mechanics (QM/MM) Approaches to Biochemistry and Beyond

#### CECAM-HQ-EPFL, Lausanne, Switzerland

#### Organisers

The combination of quantum mechanics and molecular mechanics (QM/MM), since the seminal work of Warshel and Levitt (J. Mol. Biol. 103, 227 (1976)), accompanied by the increasing computational power of modern parallel, vector-parallel and hybrid CPU-GPU platforms, has been a real breakthrough in the simulations of realistic systems in condensed phases, with special emphasis on biomolecular structures and related reactions (for a review, see for instance H. M. Senn and W. Thiel Angew. Chem. Int. Ed. 48, 1198 (2009)). This made it possible to start an entirely new branch of biological chemistry, which, beside the traditional in vivo and in vitro experiments, offers the possibility of performing experiments on computers with appreciable accuracy virtual. This has even given rise to a new terminology, in silico, coined in 1989 by the Mexican mathematician Pedro Miramontes.

However, due to the generality and variety of QM/MM approaches, their specific choice and practical use by students and young researchers facing this field for the first time is difficult. Moreover, the availability of freely downloadable computer codes from the web hides a severe drawback. Users tend to use these packages as a sort of "black boxEwithout really knowing what kind of calculations a particular code does (or does not) and which is the underlying theory, not to mention the actual strength and crucial limitations of a particular QM/MM approach.

The scope of the present tutorial, which follows an analogous one held in February 2011, is to present the main features of QM/MM approaches for simulating biomolecular systems. Indeed, due to the large number of applications (82) received at the time of the first tutorial held on this subject, and the restricted number of students (29) who could be accepted, an analogous tutorial would be highly welcome by applicants, particularly by all those students who are still asking for it and who were excluded for the reasons mentioned above.

In this tutorial, special emphasis will be given to advantages and disadvantages, practical applications and new advanced techniques aimed at exploring the terrain beyond simple static relaxations and standard molecular dynamics simulations. The main goal will be to provide to neophytes a solid background to enable them to simulate complex systems of biological, medical and environmental relevance. The tutorial is organized with theoretical lessons and examples of successful (and unsuccessful) simulations, as well as with practical exercises, planned for the afternoon sessions. An initial set (two half days) of theoretical lessons has been planned to build-up a necessary minimal background enabling students to start QM/MM simulations autonomously. An important point, unfortunately still unclear to beginners and unexperienced users, is the fact that the chemistry of the biochemical system and the specific process that one plans to study crucially determine the QM approach, the type of QM/MM interface and the majority of the parameters (and their tuning) involved in the coupling of a classical force field with a quantum mechanical approach.

One of the major tasks of this tutorial is to make neophytes able to select a specific, small QM region in a large biomolecular system “as providedEby experiments and Protein Data Bank (http://www.pdb.org/) that will be handled at the QM level. This choice is always somehow arbitrary and dependent on the quantum process (chemical reactions, charge transfers, etc.) one wants to focus on. A second, equally important task, is the problem of the time scale. QM/MM simulations have in fact the same picoseconds time-scale problem as full quantum calculations; methods enabling the enhancement of the sampling of rare events (activated processes), such as metadynamics, Blue Moon sampling, etc. represent viable tools to overcome this problem, hence allowing to expand simulations not only with respect to the size of the system but also with respect to the time. The practical sessions will be performed with the codes CPMD and CP2K, which are among the few QM/MM codes that support ab initio molecular dynamics.

Day 1

Opening; introduction to QM/MM methods.

14:00 to 14:10 - Welcome

14:10 to 15:00 - How to set-up a QM/MM system and why using a QM/MM approach: From pristine crystallographic coordinates to the set-up for dynamical simulations.

15:00 to 15:50 - Practical aspects: QM size, initial structure (classical equilibration), QM/MM protocol. Computational needs.

15:50 to 16:10 - Coffee Break

16:10 to 17:00 - Partitioning the system: Hamiltonian and calculation of forces.

17:00 to 17:50 - Examples of (successful and unsuccessful) Applications 1

Day 2

Connections between the QM and the MM subsystems

09:00 to 09:50 - QM/MM border: Link Atoms (LA), Frontier Orbitals (FO), Optimized Effective Core Potentials (OECP), scaled-position link atom method (SPLAM)

09:50 to 10:50 - Interactions between the QM and MM subsystems: Restrained Electrostatic Potential (RESP) charge scheme, Polarized-Boundary Redistributed Charge (PBRC) and dipole (PBRCD).

10:50 to 11:10 - Coffee Break

11:10 to 12:00 - Real space multigrid QM/MM implementation.

12:00 to 12:45 - Examples of (successful and unsuccessful) Applications 2

12:45 to 14:00 - Lunch Break

14:00 to 18:00 - Terminal session (Exercises 1)

Day 3

Dynamics in the QM/MM environment

09:00 to 09:50 - (N,V,E) and (N,V,T) Molecular dynamics within QM/MM: crucial parameters controlling the dynamics.

09:50 to 10:50 - Efficient Treatment of Long-Range interactions in a QM/MM scheme

10:50 to 11:10 - Coffee Break

11:10 to 12:00 - Numerical integration schemes for the equations of motion, constants of motion, control of stability, accuracy.

12:00 to 12:45 - van der Waals corrections to DFT functionals

12:45 to 14:00 - Lunch Break

14:00 to 18:00 - Terminal session (Exercises 2)

Day 4

Advanced techniques

09:00 to 09:50 - Advanced techniques: Combining QM/MM with TD-DFT (1)

09:50 to 10:50 - Examples of (successful and unsuccessful) Applications 3

10:50 to 11:10 - Coffee Break

11:10 to 12:00 - Advanced techniques: Combining QM/MM with TD-DFT (part 2)

12:00 to 12:45 - Advanced techniques: Combining QM/MM with Metadynamics/Blue Moon Ensemble

12:45 to 14:00 - Lunch Break

14:00 to 18:00 - Terminal session (Exercises 3)

Day 5

Applications and examples

09:00 to 09:50 - Examples of (successful and unsuccessful) Applications 4

09:50 to 10:50 - Participants' presentations

10:50 to 11:10 - Coffee Break

11:10 to 12:30 - Participants' presentations

12:30 to 12:45 - Closing word

12:45 to 14:00 - Lunch Break

14:00 to 18:00 - Terminal session (Exercises 4)

Departure

## References

**France**

Mauro Boero (Univerity of Strasbourg-CNRS) - Organiser & speaker

Ari Paavo Seitsonen (Ecole Normale Supérieure) - Organiser & speaker

**Spain**

Carme Rovira (University of Barcelona) - Organiser & speaker