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We have developed an algorithm based upon pseudospectral (PS) ab initio electronic structure methods for evaluating nuclear magnetic shielding constants using gauge-including atomic orbitals (GIAOs) in the spin-restricted and spin-unrestricted formalisms of Hartree–Fock (HF) theory and density-functional theory (DFT). The nuclear magnetic shielding constants for both 1H and 13C calculated using PS methodology for 21 small molecules have absolute mean errors of less than 0.3 ppm in comparison with analytic integral results. CPU timing comparisons between PS methods and conventional methods carried out for seven large molecules ranging from 510 to 1285 basis functions demonstrate that the PS methods are an order of magnitude more efficient than the conventional methods. PS-HF was between 9 and 26 times faster than conventional integral technology, and PS-DFT (Becke three-parameter Lee–Yang–Parr) was between 6 and 21 times faster. [ABSTRACT FROM AUTHOR]

We have developed and implemented pseudospectral time-dependent density-functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm-Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time-dependent density-functional theory with full linear response (PS-FLR-TDDFT) and within the Tamm-Dancoff approximation (PS-TDA-TDDFT) for G2 set molecules using B3LYP/6-31G** show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS-FLR-TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS-FLR-TDDFT and best estimations demonstrate that the accuracy of both PS-FLR-TDDFT and PS-TDA-TDDFT. Calculations for a set of medium-sized molecules, including Cn fullerenes and nanotubes, using the B3LYP functional and 6-31G** basis set show PS-TDA-TDDFT provides 19- to 34-fold speedups for Cn fullerenes with 450-1470 basis functions, 11- to 32-fold speedups for nanotubes with 660-3180 basis functions, and 9- to 16-fold speedups for organic molecules with 540-1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46-residue crambin protein, fullerenes up to C540 and nanotubes up to 14×(6,6), using the B3LYP functional and 6-31G** basis set with up to 8100 basis functions show that PS-FLR-TDDFT CPU time scales as N2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]