Search

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 algorithms based on pseudospectral (PS) ab initio electronic structure methods for solving the first- and second-order Hartree–Fock/Kohn–Sham equations and evaluating molecular polarizabilities and first- and second-order hyperpolarizabilities in the spin-restricted and spin-unrestricted formalisms at the Hartree–Fock (HF) and density functional theory (DFT) levels. We carry out calculations on 50 small molecules to test the accuracy of the PS approach. Our results demonstrate that the molecular polarizability α computed by the PS method is essentially identical to the value obtained from conventional methods for both HF and DFT calculations, while the first-order hyperpolarizability β and second-order hyperpolarizability γ have mean unsigned percentage differences of 1.26% and 0.62% (HF) and 0.78% and 0.65% (DFT), respectively. We also present CPU timing comparisons between the PS and conventional methods at the 6-31 G** level for 14 molecules having 185 to 1185 basis functions. The timing results show that the PS method is 25 (PS-HF) and 13 (PS-DFT) times faster than the conventional method for a system with 500 basis functions. The PS methods are found scale as N2.70 (PS-HF) and N2.40 (PS-DFT), while the conventional methods scale as N2.93 (PRISM-HF) and N2.87 (PRISM-DFT), where N is the number of basis functions. [ABSTRACT FROM AUTHOR]