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1. Two-photon absorption in solution by means of time-dependent density-functional theory and the polarizable continuum model.

Author

Frediani L, Rinkevicius Z, and Agren H

Subjects
Absorption, Cyclohexanes chemistry, Isomerism, Models, Theoretical, Solutions chemistry, Solvents chemistry, Time Factors, Water chemistry, Algorithms, Photons, Stilbenes chemistry
Abstract

We present the first study of two-photon absorption (TPA) of solvated molecules based on direct evaluation of TPA cross sections from the quadratic response of time-dependent perturbations. A set of prototypical two-photon (TP) chromophores has been selected and analyzed: a pure pi system (t-stilbene) and its substituted homologs obtained employing a donor (D) and an acceptor (A) group to probe the solvent effects along the series pi, D-pi-D, A-pi-D, and A-pi-A. For the selected systems we have calculated the TPA cross sections in different environments by means of the polarizable continuum model. The data have been analyzed to evaluate how the structural and environmental parameters contribute to the final two-photon absorption cross section. These include molecular structure, geometry relaxation in solution, polarity, and refractive index of the solvent. The performances of the three common functionals SVWN, BLYP, and B3LYP have been compared. The results show a significant solvent dependence of the TPA cross section and an unusual trend when passing from cyclohexane to water. The data have also been rationalized in terms of the main orbital excitations leading to the transitions. Finally, trends along the series have been described and comparison with experiments and previous calculations has been drawn.

Published
2005
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2. The Dalton quantum chemistry program system

Author

Aidas, Kestutis, Angeli, Celestino, Bak, Keld L., Bakken, Vebjørn, Bast, Radovan, Boman, Linus, Christiansen, Ove, Cimiraglia, Renzo, Coriani, Sonia, Dahle, Pal, Dalskov, Erik K., Ekström, Ulf, Enevoldsen, Thomas, Eriksen, Janus J., Ettenhuber, Patrick, Fernández, Berta, Ferrighi, Lara, Fliegl, Heike, Frediani, Luca, Hald, Kasper, Halkier, Asger, Hättig, Christof, Heiberg, Hanne, Helgaker, Trygve, Hennum, Alf Christian, Hettema, Hinne, Hjertenæs, Eirik, Høst, Stinne, Høyvik, Ida-Marie, Iozzi, Maria Francesca, Jansík, Branislav, Jensen, Hans Jørgen Aa., Jonsson, Dan, Jørgensen, Poul, Kauczor, Joanna, Kirpekar, Sheela, Kjærgaard, Thomas, Klopper, Wim, Knecht, Stefan, Kobayashi, Rika, Koch, Henrik, Kongsted, Jacob, Krapp, Andreas, Kristensen, Kasper, Ligabue, Andrea, Lutnæs, Ola B., Melo, Juan I., Mikkelsen, Kurt V., Myhre, Rolf H., Neiss, Christian, Nielsen, Christian B., Norman, Patrick, Olsen, Jeppe, Olsen, Jógvan Magnus H., Osted, Anders, Packer, Martin J., Pawlowski, Filip, Pedersen, Thomas B., Provasi, Patricio F., Reine, Simen, Rinkevicius, Zilvinas, Ruden, Torgeir A., Ruud, Kenneth, Rybkin, Vladimir V., Sałek, Pawel, Samson, Claire C. M., Sanchez de Merás, Alfredo, Saue, Trond, Sauer, Stephan P. A., Schimmelpfennig, Bernd, Sneskov, Kristian, Steindal, Arnfinn H., Sylvester-Hvid, Kristian O., Taylor, Peter R., Teale, Andrew M., Tellgren, Erik I., Tew, David P., Thorvaldsen, Andreas J., Thøgersen, Lea, Vahtras, Olav, Watson, Mark A., Wilson, David J. D., Ziolkowski, Marcin, Ågren, Hans, Aidas, Kestuti, Angeli, Celestino, Bak, Keld L., Bakken, Vebjørn, Bast, Radovan, Boman, Linu, Christiansen, Ove, Cimiraglia, Renzo, Coriani, Sonia, Dahle, Pål, Dalskov, Erik K., Ekström, Ulf, Enevoldsen, Thoma, Eriksen, Janus J., Ettenhuber, Patrick, Fernández, Berta, Ferrighi, Lara, Fliegl, Heike, Frediani, Luca, Hald, Kasper, Halkier, Asger, Hättig, Christof, Heiberg, Hanne, Helgaker, Trygve, Hennum, Alf Christian, Hettema, Hinne, Hjertenæs, Eirik, Høst, Stinne, Høyvik, Ida-Marie, Iozzi, Maria Francesca, Jansík, Branislav, Jensen, Hans Jørgen Aa, Jonsson, Dan, Jørgensen, Poul, Kauczor, Joanna, Kirpekar, Sheela, Kjærgaard, Thoma, Klopper, Wim, Knecht, Stefan, Kobayashi, Rika, Koch, Henrik, Kongsted, Jacob, Krapp, Andrea, Kristensen, Kasper, Ligabue, Andrea, Lutnæs, Ola B., Melo, Juan I., Mikkelsen, Kurt V., Myhre, Rolf H., Neiss, Christian, Nielsen, Christian B., Norman, Patrick, Olsen, Jeppe, Olsen, Jógvan Magnus H., Osted, Ander, Packer, Martin J., Pawlowski, Filip, Pedersen, Thomas B., Provasi, Patricio F., Reine, Simen, Rinkevicius, Zilvina, Ruden, Torgeir A., Ruud, Kenneth, Rybkin, Vladimir V., Sałek, Pawel, Samson, Claire C. M., de Merás, Alfredo Sánchez, Saue, Trond, Sauer, Stephan P. A., Schimmelpfennig, Bernd, Sneskov, Kristian, Steindal, Arnfinn H., Sylvester-Hvid, Kristian O., Taylor, Peter R., Teale, Andrew M., Tellgren, Erik I., Tew, David P., Thorvaldsen, Andreas J., Thøgersen, Lea, Vahtras, Olav, Watson, Mark A., Wilson, David J. D., Ziolkowski, Marcin, Ågren, Hans, Dipartimento di Chimica, Università degli Studi di Ferrara (UniFE), Centre for Theoretical and Computational Chemistry [Oslo] (CTCC), Department of Chemistry [Oslo], Faculty of Mathematics and Natural Sciences [Oslo], University of Oslo (UiO)-University of Oslo (UiO)-Faculty of Mathematics and Natural Sciences [Oslo], University of Oslo (UiO)-University of Oslo (UiO), Groupe Méthodes et outils de la chimie quantique (LCPQ) (GMO), Laboratoire de Chimie et Physique Quantiques (LCPQ), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC), Department of Physics, Chemistry and Biology, Amsterdam Center for Multiscale Modeling, Vrije Universiteit Amsterdam [Amsterdam] (VU), Laboratory of the Department of Oncology (DEPARTMENT OF ONCOLOGY), Herlev and Gentofte Hospital, Norwegian Meteorological Institute [Oslo] (MET), Teoretisk Kemi, Aarhus University [Aarhus], Centre for Biodiversity Dynamics, Norwegian University of Science and Technology [Trondheim] (NTNU), Norwegian University of Science and Technology (NTNU)-Norwegian University of Science and Technology (NTNU), Karlsruhe Institute of Technology (KIT), Department of Theoretical Chemistry, University Düsseldorf, Department of Mathematics, Tokyo University of Science, Institut Jean-Pierre Bourgin (IJPB), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Department of Environmental Engineering, Technical University of Denmark [Lyngby] (DTU), Computer Services Networks and Systems, Università degli Studi di Modena e Reggio Emilia (UNIMORE), Hammersmith Hospital, Imperial College, London, Department of Haematology, Niels Bohr Institute [Copenhagen] (NBI), Faculty of Science [Copenhagen], University of Copenhagen = Københavns Universitet (KU)-University of Copenhagen = Københavns Universitet (KU), Centre d'études biologiques de Chizé (CEBC), Centre National de la Recherche Scientifique (CNRS), Centre for Theoretical and Computational Chemistry, University of Tromsø (UiT), Department of Electronics Materials and Devices, Ivanovo State University of Chemistry and Technology, Department of Chemistry [Copenhagen], Institut für Nukleare Entsorgung (INE), Karlsruher Institut für Technologie (KIT), Department of Pharmacology, Skaggs School of Pharmacy & Pharmaceutical Sciences, University of California [San Diego] (UC San Diego), University of California-University of California, School of Chemistry, University of Nottingham, UK (UON), Theoretical Chemistry, Royal Institute of Technology [Stockholm] (KTH ), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Norwegian Meteorological Institute, Bakke, Vebjørn, Hjertenaes, Eirik, Høyvik, Ida Marie, Jensen, Hans Jørgen A. a., Kjaergaard, Thoma, Lutnaes, Ola B., Sánchez de Merás, Alfredo, Sylvester Hvid, Kristian O., Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)

Subjects
Materials Chemistry2506 Metals and Alloys, Software Focus, Ab initio electronic structure methods structure methods, ab initio calculations, VDP::Mathematics and natural science: 400::Chemistry: 440::Theoretical chemistry, quantum chemistry: 444, Computer Science Applications1707 Computer Vision and Pattern Recognition, Quantum chemistry program, Ab-initio methods, Scientific Software, Quantum Chemistry, Molecular properties, Biochemistry, Algorithms, [Electronic Structure Theory], Algorithm, Molecular propertie, [CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry, Computational Chemistry, Computational Mathematic, Faculty of Science, Physical and Theoretical Chemistry, VDP::Matematikk og Naturvitenskap: 400::Kjemi: 440::Teoretisk kjemi, kvantekjemi: 444
Abstract

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms. © 2013 John Wiley & Sons, Ltd. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, (CC BY-NC-ND 3.0)

Published
2014
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3. Fully adaptive algorithms for multivariate integral equations using the non-standard form and multiwavelets with applications to the Poisson and bound-state Helmholtz kernels in three dimensions.

Author

Frediani, Luca, Fossgaard, Eirik, Flå, Tor, and Ruud, Kenneth

Subjects
*ALGORITHMS, *MULTIVARIATE analysis, *NUMERICAL solutions to integral equations, *WAVELETS (Mathematics), *FUNCTIONAL analysis, *GAUSSIAN function
Abstract

We have developed and implemented a general formalism for fast numerical solution of time-independent linear partial differential equations as well as integral equations through the application of numerically separable integral operators ind≥ 1 dimensions using the non-standard (NS) form. The proposed formalism is universal, compact and oriented towards the practical implementation into a working code using multiwavelets. The formalism is applied to the case of Poisson and bound-state Helmholtz operators ind= 3. Our algorithms are fully adaptive in the sense that the grid supporting each function is obtained on the fly while the function is being computed. In particular, when the functiong=O fis obtained by applying an integral operatorO, the corresponding grid is not obtained by transferring the grid from the input functionf. This aspect has significant implications that will be discussed in the numerical section. The operator kernels are represented in a separated form with finite but arbitrary precision using Gaussian functions. Such a representation combined with the NS form allows us to build a sparse, banded representation of Green’s operator kernel. We have implemented a code for the application of such operators in a separated NS form to a multivariate function in a finite but, in principle, arbitrary number of dimensions. The error of the method is controlled, while the low complexity of the numerical algorithm is kept. The implemented code explicitly computes all the 22dcomponents of thed-dimensional operator. Our algorithms are described in detail in the paper through pseudo-code examples. The final goal of our work is to be able to apply this method to build a fast and accurate Kohn–Sham solver for density functional theory. [ABSTRACT FROM AUTHOR]

Published
2013
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4. Wavelet formulation of the polarizable continuum model.

Author

WEIJO, VILLE, RANDRIANARIVONY, MAHARAVO, HARBRECHT, HELMUT, and FREDIANI, LUCA

Subjects
INTEGRAL equations, POLARIZATION (Electricity), WAVELETS (Mathematics), ELECTROSTATICS, MATRICES (Mathematics)
Abstract

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF-PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010 [ABSTRACT FROM AUTHOR]

Published
2010
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5. Adaptive order polynomial algorithm in a multiwavelet representation scheme.

Author

Durdek, Antoine, Jensen, Stig Rune, Juselius, Jonas, Wind, Peter, Flå, Tor, and Frediani, Luca

Subjects
*POLYNOMIALS, *ALGORITHMS, *MULTIVARIATE analysis, *MATHEMATICAL functions, *APPROXIMATION theory
Abstract

We have developed a new strategy to reduce the storage requirements of a multivariate function in a multiwavelet framework. We propose that alongside the commonly used adaptivity in the grid refinement one can also vary the order of the representation k as a function of the scale n . In particular the order is decreased with increasing refinement scale. The consequences of this choice, in particular with respect to the nesting of scaling spaces, are discussed and the error of the approximation introduced is analyzed. The application of this method to some examples of mono- and multivariate functions shows that our algorithm is able to yield a storage reduction up to almost 60%. In general, values between 30 and 40% can be expected for multivariate functions. Monovariate functions are less affected but are also much less critical in view of the so called “curse of dimensionality”. [ABSTRACT FROM AUTHOR]

Published
2015
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