## Final Activity Report Summary - GRID-COMPCHEM (Grid Computational Chemistry)

The challenges in modern Computational Chemistry which covers phenomena of long time scales, from femtoseconds to seconds, and large spatial scales, from small molecules to biopolymers, can be answered by the emerging Grid computational technology. This paradigm of distributing computing allows one to employ hundreds-to-thousands of computers as a seamless, integrated, computational and collaborative environment embracing different categories of distributed systems. The endeavour of the ToK program, was to develop algorithms and computational codes in the field of Molecular Dynamics for efficiently running in the Grid environment.

The computational chemistry group of the University of Perugia which has created and maintains the Italian Chemistry Grid, part of GRID.IT, and the corresponding virtual organisation (VO) COMPCHEM was the main training partner. With their help as well as the theoretical support from the Department of Mathematics and Informatics of the University of Antwerp, we were able to develop efficient algorithms and codes in Quantum and Classical Molecular Dynamics to harness the current European computational Grid productive infrastructure, Enabling Grid for E-sciencE (EGEE).

In Phase 1, a cluster of more than 100 Intel and Sun CPUs was constructed and it was used to acquire experience in installing the middleware gLite and working under the Grid environment. This project was performed with the assistance of the University of Perugia.

In Phase 2, an algorithm for solving the molecular time dependent Schroedinger equation and a Fortran code highly parallelised were developed and tested with the assistance of the University of Antwerp. The N-atom molecular Hamiltonian is formulated in 3N-3 Cartesian coordinates usually defined by Jacobi vectors. The separation and conservation of the total angular momentum is obtained not by transforming the Hamiltonian in internal curvilinear coordinates but instead, by keeping the Cartesian formulation of the Hamiltonian operator and projecting the initial wave function onto the proper irreducible representation angular momentum subspace. The increased number of degrees of freedom from 3N-6 to 3N-3, compared to previous methods for solving the Schroedinger equation, is compensated by the simplicity of the kinetic energy operator and its finite difference representations which result in sparse Hamiltonian matrices. A parallel code in Fortran 95 has been produced (GridTDSE) and tested for model potentials of harmonic oscillators and realistic triatomic molecules. Moreover, we compared data obtained for the three dimensional hydrogen molecule and the six dimensional water molecule with results from the literature.

In Phase 3, computer codes were developed that assist one to harness the current computational Grid infrastructure for carrying out extended samplings of phase space and integrating the classical mechanical equations of motion for long times. A bundle of shell scripts has been written (GMDmult) to automatically submit and propagate trajectories in the Grid and to check and store large amounts of intermediate results. We reported our experience in employing the Enabling Grids for E-sciencE production infrastructure for investigating the dynamics and free energy hypersurfaces of enzymes such as Cytochrome c Oxidases. The proposed method can be adopted in any intensive computational campaign, which involves the scheduling of a large number of long time running jobs.

Phase 4, which spanned a period of three years was devoted to applications. Molecular dynamics calculations of Cytochrome c Oxidase enzymes from Paracoccus denitrificans (aa3) and Thermus thermophilus (ba3) have been carried out in the EGEE Grid through SEE and COMPCHEM VOs. Other applications involve thermodynamic perturbation theory calculations for comparing structures and kinetic behaviours of several CcOs. With respect to quantum Molecular dynamics project, calculations for H2O, SO2 and N2O have also been published.

The computational chemistry group of the University of Perugia which has created and maintains the Italian Chemistry Grid, part of GRID.IT, and the corresponding virtual organisation (VO) COMPCHEM was the main training partner. With their help as well as the theoretical support from the Department of Mathematics and Informatics of the University of Antwerp, we were able to develop efficient algorithms and codes in Quantum and Classical Molecular Dynamics to harness the current European computational Grid productive infrastructure, Enabling Grid for E-sciencE (EGEE).

In Phase 1, a cluster of more than 100 Intel and Sun CPUs was constructed and it was used to acquire experience in installing the middleware gLite and working under the Grid environment. This project was performed with the assistance of the University of Perugia.

In Phase 2, an algorithm for solving the molecular time dependent Schroedinger equation and a Fortran code highly parallelised were developed and tested with the assistance of the University of Antwerp. The N-atom molecular Hamiltonian is formulated in 3N-3 Cartesian coordinates usually defined by Jacobi vectors. The separation and conservation of the total angular momentum is obtained not by transforming the Hamiltonian in internal curvilinear coordinates but instead, by keeping the Cartesian formulation of the Hamiltonian operator and projecting the initial wave function onto the proper irreducible representation angular momentum subspace. The increased number of degrees of freedom from 3N-6 to 3N-3, compared to previous methods for solving the Schroedinger equation, is compensated by the simplicity of the kinetic energy operator and its finite difference representations which result in sparse Hamiltonian matrices. A parallel code in Fortran 95 has been produced (GridTDSE) and tested for model potentials of harmonic oscillators and realistic triatomic molecules. Moreover, we compared data obtained for the three dimensional hydrogen molecule and the six dimensional water molecule with results from the literature.

In Phase 3, computer codes were developed that assist one to harness the current computational Grid infrastructure for carrying out extended samplings of phase space and integrating the classical mechanical equations of motion for long times. A bundle of shell scripts has been written (GMDmult) to automatically submit and propagate trajectories in the Grid and to check and store large amounts of intermediate results. We reported our experience in employing the Enabling Grids for E-sciencE production infrastructure for investigating the dynamics and free energy hypersurfaces of enzymes such as Cytochrome c Oxidases. The proposed method can be adopted in any intensive computational campaign, which involves the scheduling of a large number of long time running jobs.

Phase 4, which spanned a period of three years was devoted to applications. Molecular dynamics calculations of Cytochrome c Oxidase enzymes from Paracoccus denitrificans (aa3) and Thermus thermophilus (ba3) have been carried out in the EGEE Grid through SEE and COMPCHEM VOs. Other applications involve thermodynamic perturbation theory calculations for comparing structures and kinetic behaviours of several CcOs. With respect to quantum Molecular dynamics project, calculations for H2O, SO2 and N2O have also been published.