## Section: New Results

### Material physics

#### Hybrid materials

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(N^{4}) 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(N^{2})
complexity scaling
([4] ,
[12] ).
Our implementation of the algorithm had been optimized and parallelized
with the shared-memory approach ([12] ,
[24] ). This work allowed us to compute
the response function and corresponding absorption spectra of
fullerene C_{60} . The overall complexity for the absorption
spectra of O(N^{2}) has been achieved due to usage of an iterative
method (bi-orthogonal Lanczos or GMRES)
[13] . 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.