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  • Parkkinen, Pauli; Losilla, Sergio A.; Solala, Eelis; Toivanen, Elias A.; Xu, Wen-Hua; Sundholm, Dage (2017)
    A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid The integration of the bubbles part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H-2, H2O, and CO. Our calculations show that an accuracy of 10(-4) to 10(-7) E-h can be reached in HF-SCF calculations on general molecules.
  • Shao, Yihan; Mei, Ye; Sundholm, Dage; Kaila, Ville R. I. (2020)
    Quantum chemical calculations are important for elucidating light-capturing mechanisms in photobiological systems. The time-dependent density functional theory (TDDFT) has become a popular methodology because of its balance between accuracy and computational scaling, despite its problems in describing, for example, charge transfer states. As a step toward systematically understanding the performance of TDDFT calculations on biomolecular systems, we study here 17 commonly used density functionals, including seven long-range separated functionals, and compare the obtained results with excitation energies calculated at the approximate second order coupled-cluster theory level (CC2). The benchmarking set includes the first five singlet excited states of 11 chemical analogues of biochromophores from the green fluorescent protein, rhodopsin/bacteriorhodopsin (Rh/bR), and the photoactive yellow protein. We find that commonly used pure density functionals such as BP86, PBE, M11-L, and hybrid functionals with 20-25% of Hartree-Fock (HF) exchange (B3LYP, PBE0) have a tendency to consistently underestimate vertical excitation energies (VEEs) relative to the CC2 values, whereas hybrid density functionals with around 50% HF exchange such as BHLYP, PBE50, and M06-2X and long-range corrected functionals such as CAM-B3LYP, omega PBE, omega PBEh, omega B97X, omega B97XD, BNL, and M11 overestimate the VEEs. We observe that calculations using the CAM-B3LYP and omega PBEh functionals with 65% and 100% long-range HF exchange, respectively, lead to an overestimation of the VEEs by 0.2-0.3 eV for the benchmarking set. To reduce the systematic error, we introduce here two new empirical functionals, CAMh-B3LYP and omega hPBE0, for which we adjusted the long-range HF exchange to 50%. The introduced parameterization reduces the mean signed average (MSA) deviation to 0.07 eV and the root mean square (rms) deviation to 0.17 eV as compared to the CC2 values. In the present study, TDDFT calculations using the aug-def2-TZVP basis sets, the best performing functionals relative to CC2 are omega hPBE0 (rms = 0.17, MSA = 0.06 eV); CAMh-B3LYP (rms = 0.16, MSA = 0.07 eV); and PBE0 (rms = 0.23, MSA = 0.14 eV). For the popular range-separated CAM-B3LYP functional, we obtain an rms value of 0.31 eV and an MSA value of 0.25 eV, which can be compared with the rms and MSA values of 0.37 and -0.31 eV, respectively, as obtained at the B3LYP level.
  • Mera-Adasme, Raul; Xu, Wen-hua; Sundholm, Dage; Mendizabal, Fernando (2016)
    Solar power is a strong alternative to the currently used fossil fuels in order to satisfy the world's energy needs. Among them, dye-sensitized solar cells (DSSC) represent a low-cost option. Efficient and cheap dyes are currently needed to make DSSCs competitive. Computational chemistry can be used to guide the design of new light-absorbing chromophores. Here, we have computationally studied the lowest excited states of ZnPBAT, which is a recently synthesized porphyrinoid chromophore with high light-absorption efficiency. The calculations have been performed at ab initio correlated levels of theory employing second-order coupled clusters (CC2) and algebraic diagrammatic construction using second order (ADC(2)) methods and by performing density functional theory (DFT) calculations using the time-dependent DFT (TDDFT) approach for excitation energies. The ultraviolet-visible (UV-vis) spectrum calculated at the ADC(2) and CC2 levels agrees well with the experimental one. The calculations show that ZnPBAT has six electronic transitions in the visible range of the absorption spectrum. The ab initio correlated calculations and previously reported experimental data have been used to assess the performance of several well-known density functionals that have been employed in the present TDDFT study. Solvent effects have been estimated by using the conductor-like screening model (COSMO). The influence of the addition of a TiO2 cluster to the chromophore systems has also been investigated. The results indicate that both CAM-B3LYP and Becke's "half-and-half'' (BHLYP) density functionals are appropriate for the studies of excitation energies in the blue range of the visible spectrum for these kinds of porphyrinoid chromophores, whereas the excitation energies of the Q band calculated at the ab initio correlated level are more accurate than those obtained in the present TDDFT calculations. The inclusion of solvent effects has a modest influence on the spectrum of the protonated form of the studied chromophores, whereas solvent models are crucial when studying the absorption spectrum of the anionic chromophore. The calculated UV-vis spectrum for the chromophore anion is not significantly affected by attaching a TiO2 cluster to it.
  • Valiev, R. R.; Cherepanov, V. N.; Baryshnikov, G. V.; Sundholm, D. (2018)
    A method for calculating the rate constants for internal-conversion (k(IC)) and intersystem-crossing (k(ISC)) processes within the adiabatic and Franck-Condon (FC) approximations is proposed. The applicability of the method is demonstrated by calculation of k(IC) and k(ISC) for a set of organic and organometallic compounds with experimentally known spectroscopic properties. The studied molecules were pyrromethene-567 dye, psoralene, hetero[8]circulenes, free-base porphyrin, naphthalene, and larger polyacenes. We also studied fac-Alq(3) and fac-Ir(ppy)(3), which are important molecules in organic light emitting diodes (OLEDs). The excitation energies were calculated at the multi-configuration quasi-degenerate second-order perturbation theory (XMC-QDPT2) level, which is found to yield excitation energies in good agreement with experimental data. Spin-orbit coupling matrix elements, non-adiabatic coupling matrix elements, Huang-Rhys factors, and vibrational energies were calculated at the time-dependent density functional theory (TDDFT) and complete active space self-consistent field (CASSCF) levels. The computed fluorescence quantum yields for the pyrromethene-567 dye, psoralene, hetero[8]circulenes, fac-Alq(3) and fac-Ir(ppy)(3) agree well with experimental data, whereas for the free-base porphyrin, naphthalene, and the polyacenes, the obtained quantum yields significantly differ from the experimental values, because the FC and adiabatic approximations are not accurate for these molecules.
  • Solala, Eelis; Parkkinen, Pauli; Sundholm, Dage (2018)
    Canonical decomposition methods and the Tucker decomposition method have been applied to the cube part of the orbitals in the bubbles and cube framework for numerical electronic structure calculations on molecules. The iterative process of two variants of the alternating least squares method for performing canonical decomposition is found to converge rapidly to a given accuracy, whereas the accuracy is not significantly improved by continuing the iterations, implying that the studied canonical decomposition methods are not of practical use in our approach to numerical electronic structure calculations. The Tucker decomposition method of the orbitals is on the other hand found to have relative errors that are smaller than the numerical accuracy of the orbitals. The calculations also show that the reconstruction of the orbitals leads to errors that are well below the required accuracy.