Towards excitation energies and (hyper)polarizability calculations of large molecules. Application of parallelization and linear scaling techniques to time-dependent density functional response theory

We document recent improvements in the efficiency of our implementation in the Amsterdam Density Functional program (ADF) of the response equations in time-dependent density functional theory (TDDFT). Applications to quasi on e-dimensional polyene chains and to three-dimensional water clusters show t hat, using our all-electron atomic orbital (AO)-based implementation, calcu lations of excitation energies and (hyper)polarizabilities on molecules wit h several hundred atoms and several thousand basis functions are now feasib le, even on (a small cluster of) personal computers. The matrix elements, w hich are required in TDDFT, are calculated on an AO basis and the same line ar scaling techniques as used in ADF for the iterative solution of the Kohn -Sham (KS) equations are applied to the determination of these matrix eleme nts. Near linear scaling is demonstrated for this part of the calculation, which used to be the time-determining step. Transformations from the AO bas is to the KS orbital basis and back exhibit N-3 scaling, but due to a very small prefactor this N-3 scaling is still of little importance for currentl y accessible system sizes. The main CPU bottleneck in our current implement ation is the multipolar part of the Coulomb potential, scaling quadraticall y with the system size. It is shown that the parallelization of our code le ads to further significant reductions in execution times, with a measured s peed-up of 70 on 90 processors for both the SCF and the TDDFT parts of the code. This brings high-level calculations on excitation energies and dynami c (hyper)polarizabilities of large molecules within reach. (C) 2000 John Wi ley & Sons, Inc.