### Speaker

Antonio Lagana`
(1Department of Chemistry, University of Perugia)

### Description

We have implemented on the production grid of EGEE GEMS.0, a demo version
of our Molecular processes simulator that deals with gas phase atom diatom
bimolecular
reactions. GEMS.0 takes the parameters of the potential from a data bank
and carries out the dynamical calculations by running quasiclassical trajectories
[1].
A generalization of GEMS.0 to include the calculation of ab initio potentials and
the use of quantum dynamics is under way with the collaboration of the members
of COMPCHEM [2]. In this communication we report on the implementation of
quantum dynamics procedures.
Quantum approaches require the integration of the Schroedinger equation to calculate
the scattering matrix SJ (E). The integration of the Schroedinger equation
can be carried out using either time dependent or time independent techniques.
The structure of the computer code performing the propagation in time of the
wavepacket (TIDEP)[3] for the Ncond sets of initial conditions is sketched in Fig.
1.
Read input data: tfin, tstep, system data ...
Do icond = 1,Ncond
Read initial conditions: v, j, Etr, J ...
Perform preliminary and first step calculations
Do t = to, tfin, tstep
Perform the time step propagation
Perform the asymptotic analysis to update S
Check for convergence of the results
EndDo t
EndDo icond
Fig. 1. Pseudocode of the TIDEP wavepacket program kernel.
The TIDEP kernel shows strict similarities with that of the trajectory one
(ABCtraj)
already implemented in GEMS.0. In fact, for a given set of initial conditions,
the inner loop of TIDEP propagates recursively over time the wavepacket. The most
noticeable difference between this and the trajectory integration is the fact that
at
each time step TIDEP performs a large number of matrix operations which increase
memory and computing time requests of some orders of magnitude.
The structure of the time independent suite of codes [4] is, instead, articulated in
a different way. It is in fact made of a first block (ABM) [4] that generates the
local
basis set and builds the coupling matrix (the integration bed) using also the basis
set of the previous sector. This calculation has been decoupled by repeating for
each
sector the calculation of the basis set of the previous one (see Fig. 2). This
allows
to distribute the calculations on the grid. The second block is concerned with the
propagation of the solution R matrix from small to large values of the hyperradius
performed by the program LOGDER [4]. For this block, again, the same scheme
of ABCtraj can be adopted to distribute the propagation of the R matrix at given
values of E and J as shown in Fig. 3.
Read input data: in, fin, step, J, Emax, ...
Perform preliminary calculations
Do (rho) = (rho)in + (rho)step, (rho)fin, (rho)step
Calculate eigenvalues and surface functions for present and previous
(rho)
Build intersector mapping and intrasector coupling matrices
EndDo (rho)
Fig. 2. Pseudocode of the ABM program kernel.
Read input data: in, fin, step, ...
Transfer the coupling matrices generated by ABM from disk
Do icond = 1,Ncond
Read input data: J, E ...
Perform preliminary calculations
Do (rho) = (rho)in, (rho)fin, (rho)step
Perform the single sector propagation of the R matrix
EndDo (rho)
EndDo icond
Fig. 3. Pseudocode of the LOGDER program kernel.
References
1. Gervasi, O., Dittamo, C., Lagana', A.: Lecture Notes in Computer Science 3470,
16-22 (2005).
2. EGEE-COMPCHEM Memorandum of understanding, March 2005
3. Gregori, S., Tasso, S., Lagana', A: Lecture Notes in Computer Science 3044, 437-
444 (2004).
4. Bolloni, A., Crocchianti, S., Lagana', A.: Lecture Notes in Computer Science
1908, 338-345 (2000).

### Primary authors

Antonio Lagana`
(1Department of Chemistry, University of Perugia)
Osvaldo Gervasi
(2Department of Mathematics and Computer Science, University of Perugia)