| 1. |
- Baev, A., et al.
(författare)
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Quantum-classical modeling of nonlinear pulse propagation in a dissolved two-photon active chromophore
- 2006
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Ingår i: Journal of Physical Chemistry B. - : American Chemical Society (ACS). - 1520-6106 .- 1520-5207. ; 110:11, s. 5379-5385
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Tidskriftsartikel (refereegranskat)abstract
- In the present work we outline the implications of a quantum-classical approach for modeling two-photon absorption of organic chromophores in solution. The approach joins many-photon absorption dynamic simulations with quantum chemical first principles calculations of corresponding excitation energies and transition matrix elements. Among a number of conclusions of the study, we highlight three: (i) The use of either short- or long-pulse excitation is demonstrated to switch the absorptive capacity of the nonlinear medium owing to enhancement of the nonlinear stepwise processes; (ii) The two-photon cross section strongly depends on the way in which the dephasing rate decays when the laser frequency is tuned off-resonant with the corresponding molecular transition; (iii) The results of the pulse propagation simulations based on electronic structure data obtained with a new Coulomb attenuated functional is shown to be in much better agreement with the experimental results than those based on data received with traditional density functionals.
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| 2. |
- Bast, Radovan, et al.
(författare)
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Static and frequency-dependent dipole-dipole polarizabilities of all closed-shell atoms up to radium : A four-component relativistic DFT study
- 2008
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Ingår i: ChemPhysChem. - : Wiley. - 1439-4235 .- 1439-7641. ; 9:3, s. 445-453
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Tidskriftsartikel (refereegranskat)abstract
- We test the performance of four-component relativistic density functional theory by calculating the static and frequency-dependent electric dipole-dipole polarizabilities of all (ground-state) closed-shell atoms-up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically, shape-corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient-regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple-zeta quality are used. The results are compared to experimental data or to accurate ob initio results. The reference static electric dipole polarizability of palladium has been obtained by finite-field calculations using the coupled-cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape-corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare-gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptomatic correction is switched on in the core region.
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| 3. |
- Bondesson, Laban, et al.
(författare)
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A linear scaling study of solvent-solute interaction energy of drug molecules in aqua solution
- 2007
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Ingår i: Journal of Physical Chemistry B. - : American Chemical Society (ACS). - 1520-6106 .- 1520-5207. ; 111:34, s. 10320-10328
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Tidskriftsartikel (refereegranskat)abstract
- Solvent-solute interaction energies for three well-known drug molecules in water solution are computed at the Hartree-Fock and B3LYP density functional theory levels using a linear scaling technique, which allows one to explicitly include in the model water molecules up to 14 A away from the solute molecule. The dependence of calculated interaction energies on the amount of included solvent has been examined. It is found that it is necessary to account for water molecules within an 8 A radius around the drug molecule to reach the saturated solvent interaction level. Effects of electron correlation and basis set on solvent-solute interaction energies are discussed.
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| 4. |
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| 5. |
- Bondesson, Laban, et al.
(författare)
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Basis set dependence of solute-solvent interaction energy of benzene in water : a HF/DFT study
- 2008
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 29:11, s. 1725-1732
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Tidskriftsartikel (refereegranskat)abstract
- Solute-solvent interaction energies for the benzene molecule dissolved in water are computed using Hartree-Fock and B3LYP density functional theories. Explicit solvent molecules up to 14-angstrom away from the dissolved benzene molecule are included in the calculation of interaction energies. Both basis set dependence and basis Set Superposition errors are carefully examined. It is found that the use of a larger basis set for the region near the solute together with a smaller basis set for the outer region gives results very close to what would have been obtained if the larger basis set had been used for the whole system. It is also shown that a correction for the basis Set superposition error is a necessary component in this kind of calculations. With this correction, results obtained with different tested basis sets converge to within 1 kcal/mol.
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| 6. |
- Coriani, Sonia, et al.
(författare)
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Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 126:15, s. 11930-11935
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Tidskriftsartikel (refereegranskat)abstract
- A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.
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| 7. |
- Feifel, R., et al.
(författare)
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X-ray absorption and resonant Auger spectroscopy of O(2) in the vicinity of the O 1s ->sigma* resonance : Experiment and theory
- 2008
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Ingår i: Journal of Chemical Physics. - : American Institute of Physics (AIP). - 0021-9606 .- 1089-7690. ; 128:6
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Tidskriftsartikel (refereegranskat)abstract
- We report on an experimental and theoretical investigation of x-ray absorption and resonant Auger electron spectra of gas phase O(2) recorded in the vicinity of the O 1s ->sigma* excitation region. Our investigation shows that core excitation takes place in a region with multiple crossings of potential energy curves of the excited states. We find a complete breakdown of the diabatic picture for this part of the x-ray absorption spectrum, which allows us to assign an hitherto unexplained fine structure in this spectral region. The experimental Auger data reveal an extended vibrational progression, for the outermost singly ionized X (2)Pi(g) final state, which exhibits strong changes in spectral shape within a short range of photon energy detuning (0 eV>Omega>-0.7 eV). To explain the experimental resonant Auger electron spectra, we use a mixed adiabatic/diabatic picture selecting crossing points according to the strength of the electronic coupling. Reasonable agreement is found between experiment and theory even though the nonadiabatic couplings are neglected. The resonant Auger electron scattering, which is essentially due to decay from dissociative core-excited states, is accompanied by strong lifetime-vibrational and intermediate electronic state interferences as well as an interference with the direct photoionization channel. The overall agreement between the experimental Auger spectra and the calculated spectra supports the mixed diabatic/adiabatic picture.
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| 8. |
- Ferrighi, Lara, et al.
(författare)
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Density-functional-theory study of the electric-field-induced second harmonic generation (EFISHG) of push-pull phenylpolyenes in solution
- 2006
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Ingår i: Chemical Physics Letters. - : Elsevier BV. - 0009-2614 .- 1873-4448. ; 425:4-6, s. 5593-5603
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Tidskriftsartikel (refereegranskat)abstract
- Density-functional theory and the polarizable continuum model have been used to calculate the electric-field-induced second harmonic generation of a series of push-pull phenylpolyenes in chloroform solution. The calculations have been performed using both the Becke 3-parameter Lee-Yang-Parr functional and the recently developed Coulomb-attenuated method functional. Solvation has been investigated by examining the effects of the reaction field, non-equilibrium solvation, geometry relaxation, and cavity field. The inclusion of solvent effects leads to significantly better agreement with experimental observations.
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| 9. |
- Helgaker, Trygve, et al.
(författare)
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Self-consistent field methods applied to large molecular systems
- 2006
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Ingår i: RECENT PROGRESS IN COMPUTATIONAL SCIENCES AND ENGINEERING, VOLS 7A AND 7B. - : VSP BV-C/O BRILL ACAD PUBL. - 9789004155428 ; , s. 1297-1297
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Konferensbidrag (refereegranskat)abstract
- With recent developments in theory and in implementation, Hartree-Fock and density-functional theory (DFT) self-consistent field (SCF) methods can now be applied to large molecular systems, at a cost that scales linearly with system size. In the present talk, such developments are reviewed, with emphasis on the calculation of energy and molecular properties. In particular, it is demonstrated that energies and molecular properties can now be determined entirely in the atomic orbital (AD) basis, with no implicit or explicit introduction of canonical molecular orbitals in the course of the calculation. After a discussion of energy optimization and convergence of the self-consistent field iterations, some applications are presented, with emphasis on polarizabilities and excitation energies and on the comparison of results obtained by Hartree-Fock and DFT theories in extended systems.
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| 10. |
- Jansik, B., et al.
(författare)
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Cubic response functions in time-dependent density functional theory
- 2005
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 122:5
-
Tidskriftsartikel (refereegranskat)abstract
- We present density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively, the quasienergy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained only implicitly-through the time dependence of the density itself rather than through the form of the exchange-correlation functionals-it generalizes previous time-dependent implementations in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange correlation at the generalized-gradient approximation level and fractional exact Hartree-Fock exchange. With our implementation the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. As illustration we explore the use of various combinations of functionals for applications of nonlinear optical hyperpolarizabilities of a few centrosymmetric systems; molecular nitrogen, benzene, and the C-60 fullerene. Considering that vibrational, solvent, and local field factors effects are left out, we find in general that very good experimental agreement can be obtained for the second dynamic hyperpolarizability of these systems. It is shown that a treatment of the response of the density beyond the local density approximation gives a significant effect. The use of different functional combinations are motivated and discussed, and it is concluded that the choice of higher order kernels can be of similar importance as the choice of the potential which governs the Kohn-Sham orbitals.
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| 11. |
- Jonsson, Dan, et al.
(författare)
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Kohn–Sham Time-Dependent Density Functional Theory with Applications to Linear and Nonlinear Properties
- 2006
-
Ingår i: Nonlinear optical properties of matter. - Dordrecht : Springer Netherlands. - 9781402048500 ; , s. 151-209
-
Bokkapitel (refereegranskat)abstract
- We review Kohn–Sham density-functional theory for time-dependent response functionsup to and including cubic response. The working expressions are derived from anexplicit exponential parametrization of the density operator and the Ehrenfest principle,alternatively the quasi-energy ansatz. While the theory retains the adiabatic approximation,implying that the time-dependency of the functional is obtained only implicitly—through the time-dependency of the density itself rather than through the form ofthe exchange-correlation functionals—our implementation generalizes previous timedependentapproaches in that arbitrary functionals can be chosen for the perturbed densities(energy derivatives or response functions). Thus, the response of the density canalways be obtained using the stated density functional, or optionally different functionalscan be applied for the unperturbed and perturbed densities, even different functionals fordifferent response order. In particular, general density functionals beyond the local densityapproximation can be applied, such as hybrid functionals with exchange–correlation atthe generalized gradient-approximation level and fractional exact Hartree–Fock exchange.We also review some recent progress in time-dependent density functional theory foropen-shell systems, in particular spin-restricted and spin restricted-unrestricted formalismsfor property calculations. We highlight a sample of applications of the theory
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| 12. |
- Keal, T. W., et al.
(författare)
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Choice of exchange-correlation functional for computing NMR indirect spin-spin coupling constants
- 2006
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Ingår i: Chemical Physics Letters. - : Elsevier BV. - 0009-2614 .- 1873-4448. ; 425:1-3, s. 163-166
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Tidskriftsartikel (refereegranskat)abstract
- The choice of exchange-correlation functional for the determination of indirect nuclear spin-spin coupling constants in density-functional theory is considered. In an assessment of one-bond (1)J(CH) couplings, the PBE functional was recently shown [S.N. Maximoff, J.E. Peralta, V. Barone, G.E. Scuseria, J. Chem. Theory Comput. 1 (2005) 541] to perform well, significantly outperforming B3LYP. For couplings involving N, 0, and F atoms in simple molecules, we demonstrate that the opposite is observed; PBE is considerably less accurate than B3LYP. By contrast, the B97-2 and B97-3 semi-empirical functionals provide good, consistent quality couplings for all these atom types in an extensive assessment.
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| 13. |
- Kjaergaard, Thomas, et al.
(författare)
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Gauge-Origin Independent Formulation and Implementation of Magneto-Optical Activity within Atomic-Orbital-Density Based Hartree-Fock and Kohn-Sham Response Theories
- 2009
-
Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 5:8, s. 1997-2020
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Forskningsöversikt (refereegranskat)abstract
- A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(omega) of the Faraday effect and the B term of magnetic circular dichroism. The approach is expressed in terms of an atomic-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the B term and divergence is encountered if this component is not projected out. Illustrative results are reported for the Verdet constant of H-2, HF, CO, N2O, and CH3CH2CH3 and for the B term of pyrimidine, phosphabenzene, and pyridine. The results are benchmarked against gauge-origin independent CCSD values
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| 14. |
- Lian, Ke-Yan, et al.
(författare)
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Density-functional studies of plasmons in small metal clusters
- 2009
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 130:17
-
Tidskriftsartikel (refereegranskat)abstract
- We study the formation of plasmon modes of small gold clusters by modeling the excitation spectra. The shape change of the longitudinal mode as a function of cluster size is studied using time-dependent Kohn-Sham theory and Gaussian basis sets. The presence of d electrons in gold atoms affect the plasmon formation process, resulting in a high excitation energy for transverse mode and a complicated spectra profile in general. The transverse mode can still be identified with the help of a frozen-orbital approximation.
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| 15. |
- Paterson, M. J., et al.
(författare)
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Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory
- 2006
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 124:5, s. 425-430
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Tidskriftsartikel (refereegranskat)abstract
- We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.
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| 16. |
- Peach, M. J. G., et al.
(författare)
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Assessment of a Coulomb-attenuated exchange-correlation energy functional
- 2005
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Ingår i: Physical Chemistry, Chemical Physics - PCCP. - : Royal Society of Chemistry (RSC). - 1463-9076 .- 1463-9084. ; 8:5
-
Tidskriftsartikel (refereegranskat)abstract
- The recently proposed CAM-B3LYP exchange-correlation energy functional, based on a partitioning of the r(12)(-1) operator in the exchange interaction into long- and short-range components, is assessed for the determination of molecular thermochemistry, structures, and second order response properties. Rydberg and charge transfer excitation energies and static electronic polarisabilities are notably improved over the standard B3LYP functional; classical reaction barriers also improve. Ionisation potentials, bond lengths, NMR shielding constants and indirect spin-spin coupling constants are comparable with the two functionals. CAM-B3LYP atomisation energies and diatomic harmonic vibrational wavenumbers are less accurate than those of B3LYP. Future research directions are outlined.
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| 17. |
- Peach, Michael J. G., et al.
(författare)
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Structural and electronic properties of polyacetylene and polyyne from hybrid and coulomb-attenuated density functionals
- 2007
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Ingår i: Journal of Physical Chemistry A. - : American Chemical Society (ACS). - 1089-5639 .- 1520-5215. ; 111:46, s. 11930–11935-
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Tidskriftsartikel (refereegranskat)abstract
- The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-133LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-133LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional.
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| 18. |
- Reine, Simen, et al.
(författare)
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Variational and robust density fitting of four-center two-electron integrals in local metrics
- 2008
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 129:10
-
Tidskriftsartikel (refereegranskat)abstract
- Density fitting is an important method for speeding up quantum-chemical calculations. Linear-scaling developments in Hartree-Fock and density-functional theories have highlighted the need for linear-scaling density-fitting schemes. In this paper, we present a robust variational density-fitting scheme that allows for solving the fitting equations in local metrics instead of the traditional Coulomb metric, as required for linear scaling. Results of fitting four-center two-electron integrals in the overlap and the attenuated Gaussian damped Coulomb metric are presented, and we conclude that density fitting can be performed in local metrics at little loss of chemical accuracy. We further propose to use this theory in linear-scaling density-fitting developments.
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| 19. |
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| 20. |
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| 21. |
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| 22. |
- Rizzo, A., et al.
(författare)
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Density-functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase
- 2005
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 122:23
-
Tidskriftsartikel (refereegranskat)abstract
- A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej's triple-zeta basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene.
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| 23. |
- Rubensson, Emanuel H., et al.
(författare)
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A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations
- 2007
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 28:16, s. 2531-2537
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Tidskriftsartikel (refereegranskat)abstract
- A hierarchic sparse matrix data structure for Hartree-Fock/Kohn-Sham calculations is presented. The data structure makes the implementation of matrix manipulations needed for large systems faster, easier, and more maintainable without loss of performance. Algorithms for symmetric matrix square and inverse Cholesky decomposition within the hierarchic framework are also described. The presented data structure is general; in addition to its use in HartreeFock/Kohn-Sham calculations, it may also be used in other research areas where matrices with similar properties are encountered. The applicability of the data structure to ab initio calculations is shown with help of benchmarks on water droplets and graphene nanoribbons.
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| 24. |
- Rubensson, Emanuel H., et al.
(författare)
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Density matrix purification with rigorous error control
- 2008
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 128:7
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Tidskriftsartikel (refereegranskat)abstract
- Density matrix purification, although being a powerful tool for linear scaling construction of the density matrix in electronic structure calculations, has been limited by uncontrolled error accumulation. In this article, a strategy for the removal of small matrix elements in density matrix purification is proposed with which the forward error can be rigorously controlled. The total forward error is separated into two parts, the error in eigenvalues and the error in the occupied invariant subspace. We use the concept of canonical angles to measure and control differences between exact and approximate occupied subspaces. We also analyze the conditioning of the density matrix construction problem and propose a method for calculation of interior eigenvalues to be used together with density matrix purification. (C) 2008 American Institute of Physics.
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| 25. |
- Rubensson, Emanuel H., 1979-
(författare)
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Matrix Algebra for Quantum Chemistry
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns methods of reduced complexity for electronic structure calculations. When quantum chemistry methods are applied to large systems, it is important to optimally use computer resources and only store data and perform operations that contribute to the overall accuracy. At the same time, precarious approximations could jeopardize the reliability of the whole calculation. In this thesis, the self-consistent field method is seen as a sequence of rotations of the occupied subspace. Errors coming from computational approximations are characterized as erroneous rotations of this subspace. This viewpoint is optimal in the sense that the occupied subspace uniquely defines the electron density. Errors should be measured by their impact on the overall accuracy instead of by their constituent parts. With this point of view, a mathematical framework for control of errors in Hartree-Fock/Kohn-Sham calculations is proposed. A unifying framework is of particular importance when computational approximations are introduced to efficiently handle large systems. An important operation in Hartree-Fock/Kohn-Sham calculations is the calculation of the density matrix for a given Fock/Kohn-Sham matrix. In this thesis, density matrix purification is used to compute the density matrix with time and memory usage increasing only linearly with system size. The forward error of purification is analyzed and schemes to control the forward error are proposed. The presented purification methods are coupled with effective methods to compute interior eigenvalues of the Fock/Kohn-Sham matrix also proposed in this thesis.New methods for inverse factorizations of Hermitian positive definite matrices that can be used for congruence transformations of the Fock/Kohn-Sham and density matrices are suggested as well. Most of the methods above have been implemented in the Ergo quantum chemistry program. This program uses a hierarchic sparse matrix library, also presented in this thesis, which is parallelized for shared memory computer architectures. It is demonstrated that the Ergo program is able to perform linear scaling Hartree-Fock calculations.
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| 26. |
- Rubensson, Emanuel H., et al.
(författare)
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Rotations of occupied invariant subspaces in self-consistent field calculations
- 2008
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 49:3, s. 032103-
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Tidskriftsartikel (refereegranskat)abstract
- In this article, the self-consistent field (SCF) procedure as used in Hartree-Fock and Kohn-Sham calculations is viewed as a sequence of rotations of the so-called occupied invariant subspace of the potential and density matrices. Computational approximations are characterized as erroneous rotations of this subspace. Differences between subspaces are measured and controlled by the canonical angles between them. With this approach, a first step is taken toward a method where errors from computational approximations are rigorously controlled and threshold values are directly related to the accuracy of the current trial density, thus eliminating the use of ad hoc threshold values. Then, the use of computational resources can be kept down as much as possible without impairment of the SCF convergence. (C) 2008 American Institute of Physics.
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| 27. |
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| 28. |
- Rubensson, Emanuel H., et al.
(författare)
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Truncation of Small Matrix Elements Based on the Euclidean Norm for Blocked Data Structures
- 2009
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 30:6, s. 974-977
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Tidskriftsartikel (refereegranskat)abstract
- Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.
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| 29. |
- Rubensson, Emanuel, 1979-
(författare)
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Sparse Matrices in Self-Consistent Field Methods
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n3). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n).A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method.
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| 30. |
- Rubensson, Emanuel, et al.
(författare)
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Sparse matrix algebra for quantum modeling of large systems
- 2007
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Ingår i: Applied Parallel Computing - STATE OF THE ART IN SCIENTIFIC COMPUTING. - Berlin, Germany : Springer-Verlag. - 9783540757542 ; , s. 90-99
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Konferensbidrag (refereegranskat)abstract
- Matrices appearing in Hartree-Fock or density functional theory coming from discretization with help of atom-centered local basis sets become sparse when the separation between atoms exceeds some system-dependent threshold value. Efficient implementation of sparse matrix algebra is therefore essential in large-scale quantum calculations. We describe a unique combination of algorithms and data representation that provides high performance and strict error control in blocked sparse matrix algebra. This has applications to matrix-rnatrix multiplication, the Trace-Correcting Purification algorithm and the entire self-consistent field calculation.
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| 31. |
- Rubensson, Emanuel, et al.
(författare)
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Systematic sparse matrix error control for linear scaling electronic structure calculations
- 2005
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 26:15, s. 1628-1637
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Tidskriftsartikel (refereegranskat)abstract
- Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy.
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| 32. |
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| 33. |
- Rudberg, Elias, et al.
(författare)
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Automatic Selection of Integral Thresholds by Extrapolation in Coulomb and Exchange Matrix Constructions
- 2009
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 5:1, s. 80-85
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Tidskriftsartikel (refereegranskat)abstract
- We present a method to compute Coulomb and exchange matrices with predetermined accuracy as measured by a matrix norm. The computation of these matrices is fundamental in Hartree-Fock and Kohn-Sham electronic structure calculations. We show numerically that, when modern algorithms for Coulomb and exchange matrix evaluation are applied, the Euclidean norm of the error matrix e is related to the threshold value tau as epsilon C tau(alpha). The presented extrapolation method automatically selects the integral thresholds so that the Euclidean norm of the error matrix is at the requested accuracy. This approach is demonstrated for a variety of systems, including protein-like systems, water clusters, and graphene sheets. The proposed method represents an important step toward complete error control throughout the self-consistent field calculation as described in [J. Math. Phys. 2008, 49, 032103].
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| 34. |
- Rudberg, E, et al.
(författare)
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Calculations of two-photon charge-transfer excitations using Coulomb-attenuated density-functional theory
- 2005
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 123:18
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we show that an implementation of Coulomb-attenuated density-functional theory leads to considerably better prospects than hitherto for modeling two-photon absorption cross sections for charge-transfer species. This functional, which corrects for the effect of poor asymptotic dependence of commonly used functionals, essentially brings down the widely different results for larger charge-transfer species between Hartree-Fock and density-functional theory (DFT)-B3LYP into a closer range. The Coulomb-attenuated functional, which retains the best aspects of the Hartree-Fock and DFT-B3LYP methods, proves to be very promising for further modeling design of multiphoton materials with technical applications.
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| 35. |
- Rudberg, Elias, et al.
(författare)
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Efficient implementation of the fast multipole method
- 2006
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 125:8, s. 084106-
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Tidskriftsartikel (refereegranskat)abstract
- A number of computational techniques are described that reduce the effort related to the continuous fast multipole method, used for the evaluation of Coulomb matrix elements as needed in Hartree-Fock and density functional theories. A new extent definition for Gaussian charge distributions is proposed, as well as a new way of dividing distributions into branches. Also, a new approach for estimating the error caused by truncation of multipole expansions is presented. It is found that the use of dynamically truncated multipole expansions gives a speedup of a factor of 10 in the work required for multipole interactions, compared to the case when all interactions are computed using a fixed multipole expansion order. Results of benchmark calculations on three-dimensional systems are reported, demonstrating the usefulness of our present implementation of the fast multipole method.
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| 36. |
- Rudberg, Elias, 1976-
(författare)
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Fock Matrix Construction for Large Systems
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This licentiate thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree--Fock calculations.The methods described are also applicable in Kohn--Sham Density FunctionalTheory calculations, where the Coulomb and exchange matrices areparts of the Kohn--Sham matrix. Screening techniques for reducing the computational complexity of bot Coulomb and exchange computations are discussed, as well as the fast multipole method, used for efficient computation of the Coulomb matrix. The thesis also discusses how sparsity in the matrices occurring in Hartree--Fock and Kohn--Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them. As an example of a possible type of application, the thesis includes a theoretical study of Heisenberg exchange constants, using unrestricted Kohn--Sham Density Functional Theory calculations.
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| 37. |
- Rudberg, Elias, et al.
(författare)
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Hartree-Fock calculations with linearly scaling memory usage
- 2008
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 128:18
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Tidskriftsartikel (refereegranskat)abstract
- We present an implementation of a set of algorithms for performing Hartree-Fock calculations with resource requirements in terms of both time and memory directly proportional to the system size. In particular, a way of directly computing the Hartree-Fock exchange matrix in sparse form is described which gives only small addressing overhead. Linear scaling in both time and memory is demonstrated in benchmark calculations for system sizes up to 11 650 atoms and 67 204 Gaussian basis functions on a single computer with 32 Gbytes of memory. The sparsity of overlap, Fock, and density matrices as well as band gaps are also shown for a wide range of system sizes, for both linear and three-dimensional systems. (C) 2008 American Institute of Physics.
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| 38. |
- Rudberg, Elias, et al.
(författare)
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Heisenberg Exchange in Dinuclear Manganese Complexes : A Density Functional Theory Study
- 2006
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 2:4, s. 981-989
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Tidskriftsartikel (refereegranskat)abstract
- This work presents a systematic investigation of the performance of broken symmetry density functional theory for the evaluation of Heisenberg exchange constants. We study dinuclear MnIV-MnIV complexes with bis(μ-oxo), bis(μ-oxo)(μ-carboxylato), and tris(μ-oxo) cores for this purpose, as these are of fundamental biological interest as well as being potential precursors for molecular magnets based on manganese complexes, the so-called Mn12 magnets. The obtained results indicate that quantitative agreement with available experimental data for the Heisenberg exchange constants can be achieved for most of the investigated complexes but also that there are significant failures for some compounds. We evaluate factors influencing the accuracy of obtained results and examine effects of different mappings between broken symmetry and Heisenberg Hamiltonian states in an attempt to formulate a reliable recipe for the evaluation of magnetic coupling in these complexes. An assessment of the bonding situation in the molecular system under investigation is found crucial in choosing the appropriate scheme for evaluation of the Heisenberg exchange constants.
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| 39. |
- Rudberg, Elias, et al.
(författare)
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Nonlocal exchange interaction removes half-metallicity in graphene nanoribbons
- 2007
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Ingår i: Nano letters (Print). - : American Chemical Society (ACS). - 1530-6984 .- 1530-6992. ; 7:8, s. 2211-2213
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Tidskriftsartikel (refereegranskat)abstract
- Band gap studies of zigzag-edge graphene ribbons are presented. While earlier calculations at LDA level show that zigzag-edge graphene ribbons become half-metallic when cross-ribbon electric fields are applied, our calculations with hybrid density functional demonstrate that finite graphene ribbons behave as half-semiconductors. The spin-dependent band gap can be changed in a wide range, making possible many applications in spintronics.
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| 40. |
- Rudberg, Elias, 1976-
(författare)
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Quantum Chemistry for Large Systems
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree-Fock calculations. Density matrix purification, which is a method used to construct the density matrix for a given Fock matrix, is also discussed. The methods described are not only applicable in the Hartree-Fock case, but also in Kohn-Sham Density Functional Theory calculations, where the Coulomb and exchange matrices are parts of the Kohn-Sham matrix. Screening techniques for reducing the computational complexity of both Coulomb and exchange computations are discussed, including the fast multipole method, used for efficient computation of the Coulomb matrix. The thesis also discusses how sparsity in the matrices occurring in Hartree-Fock and Kohn-Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them.
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| 41. |
- Salek, Pawel, et al.
(författare)
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A comparison of density-functional-theory and coupled-cluster frequency-dependent polarizabilities and hyperpolarizabilities
- 2005
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Ingår i: Molecular Physics. - : Informa UK Limited. - 0026-8976 .- 1362-3028. ; 103:2-3, s. 439-450
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Tidskriftsartikel (refereegranskat)abstract
- The frequency-dependent polarizabilities and hyperpolarizabilities of HF, CO, H2O and para-nitroaniline calculated by density-functional theory are compared with accurate coupled-cluster results. Whereas the local-density approximation and the generalized gradient approximation (BLYP) perform very similarly and overestimate polarizabilities and, in particular, the hyperpolarizabilities, hybrid density-functional theory (B3LYP) performs better and produces results similar to those obtained by coupled-cluster singles-and-doubles theory. Comparisons are also made for singlet excitation energies, calculated using linear response theory.
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| 42. |
- Salek, Pawel, et al.
(författare)
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A self-contained and portable density functional theory library for use in ab initio quantum chemistry programs
- 2007
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 28:16, s. 2569-2575
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Tidskriftsartikel (refereegranskat)abstract
- A major unresolved problem of density functional theory is the yet unknown exchange-correlation functional, which leads to a proliferation of its less or more successful approximations. A practical implementation of these numerous functionals can present a substantial challenge particularly if the higher order functional derivatives are required. We present a systematic method of functional implementation. The method allows a clean handling of a large number of functionals in a mutually independent way. We developed an extensive set of automatic test routines to facilitate functional and derivative testing with respect to the implementation correctness and numerical stability. An integral part of the presented solution is a program for automatic code generation from analytical formulas that uses only freely available tools. Code for evaluation of functionals and their first, second, third, and fourth derivatives can be generated, which accelerates the development, implementation, and testing of new functionals.
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| 43. |
- Salek, Pawel, et al.
(författare)
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Linear response at the 4-component relativistic density-functional level : application to the frequency-dependent dipole polarizability of Hg, AuH and PtH2
- 2005
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Ingår i: Chemical Physics. - : Elsevier BV. - 0301-0104 .- 1873-4421. ; 311:1-2, s. 187-201
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Tidskriftsartikel (refereegranskat)abstract
- We report the implementation and application of linear response density-functional theory (DFT) based on the 4-component relativistic Dirac-Coulomb Hamiltonian. The theory is cast in the language of second quantization and is based on the quasienergy formalism (Floquet theory), replacing the initial state dependence of the Runge-Gross theorem by periodic boundary conditions. Contradictions in causality and symmetry of the time arguments are thereby avoided and the exchange-correlation potential and kernel can be expressed as functional derivatives of the quasienergy. We critically review the derivation of the quasienergy analogues of the Hohenberg-Kohn theorem and the Kohn-Sham formalism and discuss the nature of the quasienergy exchange-correlation functional. Structure is imposed on the response equations in terms of Hermiticity and time-reversal symmetry. It is observed that functionals of spin and current densities, corresponding to time-antisymmetric operators, contribute to frequency-dependent and not static electric properties. Physically, this follows from the fact that only a time-dependent electric field creates a magnetic field. It is furthermore observed that hybrid functionals enhance spin polarization since only exact exchange contributes to anti-Hermitian trial vectors. We apply 4-component relativistic linear response DFT to the calculation of the frequency-dependent polarizability of the iso-electronic series Hg, AuH and PtH2. Unlike for the molecules, the effect of electron correlation on the polarizability of the mercury atom is very large, about 25%. We observe a remarkable performance of the local-density approximation (LDA) functional in reproducing the experimental frequency-dependent polarizability of this atom, clearly superior to that of the BLYP and B3LYP functionals. This allows us to extract Cauchy moments (S(-4) = 382.82 and S(-6) = 6090.89 a.u.) that we believe are superior to experiment since we go to higher order in the Cauchy moment expansion.
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| 44. |
- Salek, Pawel, et al.
(författare)
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Linear-scaling implementation of molecular electronic self-consistent field theory
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 126:11, s. 85-98
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Tidskriftsartikel (refereegranskat)abstract
- A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.
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| 45. |
- Salek, Pawel, et al.
(författare)
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Quantum chemical studies of three-photon absorption of some stilbenoid chromophores
- 2005
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Ingår i: Journal of Physical Chemistry A. - : American Chemical Society (ACS). - 1089-5639 .- 1520-5215. ; 109:48, s. 11037-11042
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Tidskriftsartikel (refereegranskat)abstract
- Three-photon absorption of a series of donor-acceptor trans-stilbene derivatives is studied by means of density functional theory applied to the third-order response function and its residues. The results obtained by using different functionals are compared with experimental data for similar systems obtained from the literature. With a Coulomb attenuated, asymptotically corrected functional, the excitation energy to the first resonance state is much improved. Comparison with experiment indicates that this is the case for the three-photon cross section as well. In particular, the overestimation of the cross sections and underestimation of excitation energies offered by the density functional theory using common density functionals is corrected for. It is argued that a reliable theory for three-photon absorption in charge transfer and other chromophore systems thereby has been obtained. Further elaboration of the theory and its experimental comparison call for explicit inclusion of solvent polarization and pulse propagation effects.
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| 46. |
- Simon, M., et al.
(författare)
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Elastic peak of K shell excited HCl molecule : Comparison HCl-DCl - Experiment and theory
- 2007
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Ingår i: Journal of Electron Spectroscopy and Related Phenomena. - : Elsevier BV. - 0368-2048 .- 1873-2526. ; 155:1-3, s. 91-94
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Tidskriftsartikel (refereegranskat)abstract
- Fermosecond dynamics has been recently observed by resonant X-ray Raman scattering (RXRS) after excitation along the dissociative Cl 1s -> 6 sigma* resonance of gas phase HCl. In this paper, we show a method to take into account and correct for self-absorption of the elastic peak, in order to allow for quantitative comparison with theory. We have performed measurements on the DCl molecule exhibiting ultrafast nuclear motion. A comparison between HCl and DCl is presented.
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| 47. |
- Simon, M., et al.
(författare)
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Femtosecond nuclear motion of HCl probed by resonant x-ray Raman scattering in the Cl 1s region
- 2006
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 73:2, s. 020706(R)-
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Tidskriftsartikel (refereegranskat)abstract
- Femtosecond dynamics are observed by resonant x-ray Raman scattering (RXS) after excitation along the dissociative Cl 1s -> 6 sigma(*) resonance of gas-phase HCl. The short core-hole lifetime results in a complete breakdown of the common nondispersive behavior of soft-x-ray transitions between parallel potentials. We evidence a general phenomenon of RXS in the hard-x-ray region: a complete quenching of vibrational broadening. This opens up a unique opportunity for superhigh resolution x-ray spectroscopy beyond vibrational and lifetime limitations.
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| 48. |
- Skomorowski, Wojciech, et al.
(författare)
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Electronic circular dichroism of disulphide bridge : Ab initio quantum-chemical calculations
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 127:8
-
Tidskriftsartikel (refereegranskat)abstract
- Electronic circular dichroism (ECD) parameters of the disulphide chromophore have been calculated for dihydrogen disulphide, dimethyl disulphide, and cystine using density-functional theory, coupled-cluster theory, and multiconfigurational self-consistent field theory. The objective is twofold: first, to examine the performance of the Coulomb-attenuated CAM-B3LYP functional for the calculation of ECD spectra; second, to investigate the dependence of the ECD parameters on the conformation around the disulphide bridge. The CAM-B3LYP functional improves considerably on the B3LYP functional, giving results comparable to CCSD theory and to MCSCF theory in an extended active space. The conformational dependence of the ECD parameters does not change much upon substitution, which is promising for the application of ECD in structural investigations of proteins containing disulphide bridges.
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| 49. |
- Thogersen, L., et al.
(författare)
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The trust-region self-consistent field method in Kohn-Sham density-functional theory
- 2005
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 123:7
-
Tidskriftsartikel (refereegranskat)abstract
- The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.
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| 50. |
- Velkov, Yasen, et al.
(författare)
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Origin of fine structures on the dissociative 1s ->sigma* resonance in X-ray absorption spectra of O-2
- 2009
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Ingår i: Chemical Physics Letters. - : Elsevier BV. - 0009-2614 .- 1873-4448. ; 476:4-6, s. 147-150
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Tidskriftsartikel (refereegranskat)abstract
- We attempt to explain a puzzling long-tailed peak shape of the X-ray absorption spectrum of the oxygen molecule in the energy region around 539 eV taking into account the Rydberg-valence and vibronic couplings. The long-tailed feature is found to arise from two dissociative sigma* states and the sudden drop in intensity is related to decrease in transition dipole near the crossing point between the repulsive sigma* and weak 3s Rydberg states with the quartet ion cores. This is supported by numerical wave-packet simulations allowing for all interchannel couplings between the Rydberg and valence manifolds with the quartet and doublet ion cores in a diabatic representation of the core-excited states.
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