Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

摘要: We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in linear response formalism exhibiting linear-scaling computational complexity with system size, without relying on simplifying Tamm-Dancoff approximation (TDA). The implementation relies representing occupied and unoccupied subspaces two different sets situ optimised localised functions, yielding very compact efficient representation transition density matrix excitation accuracy associated systematic basis set. TDDFT is solved using preconditioned conjugate gradient algorithm that memory-efficient. validated small test molecule good agreement results obtained from standard quantum chemistry packages found, preconditioner significant improvement convergence rates. method developed this work then used to reproduce experimental absorptionspectrum bacteriochlorophyll an organic solvent, where it demonstrated TDA fails main features low energyspectrum, while yields qualitative data. Furthermore, need for explicitly including parts solvent into calculations highlighted, making treatment large sizes necessary are well within reach capabilities introduced here. Finally, properties by computing lowest energy solution. largest systems considered same order magnitude as variety widely studied pigment-protein complexes, opening up possibility studying their having resort any semiclassical approximations protein environment.