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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 one‐dimensional polyene chains and to three‐dimensional water clusters show that, using our all‐electron atomic orbital (AO)‐based implementation, calculations of excitation energies and (hyper)polarizabilities on molecules with several hundred atoms and several thousand basis functions are now feasible, even on (a small cluster of) personal computers. The matrix elements, which are required in TDDFT, are calculated on an AO basis and the same linear scaling techniques as used in ADF for the iterative solution of the Kohn–Sham (KS) equations are applied to the determination of these matrix elements. Near linear scaling is demonstrated for this part of the calculation, which used to be the time‐determining step. Transformations from the AO basis to the KS orbital basis and back exhibit N3 scaling, but due to a very small prefactor this N3 scaling is still of little importance for currently accessible system sizes. The main CPU bottleneck in our current implementation is the multipolar part of the Coulomb potential, scaling quadratically with the system size. It is shown that the parallelization of our code leads to further significant reductions in execution times, with a measured speed‐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 dynamic (hyper)polarizabilities of large molecules within reach. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1511–1523, 2000