Section: New Results
The study of hybrid materials with a coupling method between molecular dynamics (MD) and quantum mechanism (QM) has begun in collaboration with IPREM (Pau) in the ANR CIS 2007 NOSSI. These simulations are complex and costly and may involve several length scales, quantum effects, components of different kinds (mineral-organic, hydro-philic and -phobic parts). Our goal is to compute dynamical properties of hybrid materials like optical spectra. The computation of optical spectra of molecules and solids is the most consuming time in such coupling. This requires new methods designed for predicting excited states and new algorithms for implementing them. Several tracks are investigated in the project and new results obtained as described bellow.
Optical spectra. Theory of electronic excitations contributes to our understanding of photovoltaic devices, dyes and photo-catalytic materials. Recent advances in polymer semiconductors pose new challenges for theoretical predictions because the size of the system and the absence of any symmetry in molecules of interest. Ab-initio approaches to the quantum theory of large molecules (hundreds of atoms) is often limited to density functional theory and its time-dependent counterpart (TDDFT) because these approaches allow for a favorable complexity scaling in practical computations. An essential ingredient of TDDFT—the Kohn-Sham response function—has a simple expression in terms of molecular orbitals, although disregarding its inherent locality leads to a poor complexity scaling O(N4) with the number of atoms N . Moreover, the applications of Kohn–Sham response function go beyond TDDFT, therefore we have been further developing of a fast method for the Kohn–Sham response function. The fast Kohn–Sham response function allows for a favorable O(N2) complexity scaling ( ,  ). Our implementation of the algorithm had been optimized and parallelized with the shared-memory approach ( ,  ). This work allowed us to compute the response function and corresponding absorption spectra of fullerene C60 . The overall complexity for the absorption spectra of O(N2) has been achieved due to usage of an iterative method (bi-orthogonal Lanczos or GMRES)  . An article is in preparation. Future work on Kohn–Sham response function shall be concentrated on distributed memory parallelization because of high memory demand of the response function. The symmetry properties of the response function must be necessarily exploited in the MPI parallelized version of the program.
QM/MM algorithm. For structure studies or dynamical properties, we intend to couple QM model based on pseudo-potentials (SIESTA code) with dynamic molecular (DL-POLY code). Therefore we have developed first a new algorithm to avoid to count twice the quantum electric field in the molecular model. Secondly, we have introduced an algorithm to compute faster the electric field which polarizes the quantum atoms. Now, we are implementing our algorithm in Siesta and DL-POLY codes.