Krylov-space algorithms for time-dependent Hartree-Fock and density
functional computations
V. Chernyak,a
M.F. Schulz,a
S. Mukamel,a
S. Tretiak,b
and E.V. Tsiperc
aDepartment of Chemistry, Univ Rochester, Rochester, NY 14627 bUniv Calif Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 cDepartment of Physics, SUNY at Stony Brook, Stony Brook, NY 11794
A fast, low memory cost, Krylov-space-based algorithm is proposed for
the diagonalization of large Hamiltonian matrices required in
time-dependent Hartree-Fock (TDHF) and adiabatic time-dependent
density-functional theory (TDDFT) computations of electronic
excitations. A deflection procedure based on the symplectic structure
of the TDHF equations is introduced and its capability to find higher
eigenmodes of the linearized TDHF operator for a given numerical
accuracy is demonstrated. The algorithm may be immediately applied to
the formally-identical adiabatic TDDFT equations.
Freixas, V.M., Tretiak, S. and Fernandez-Alberti, S.,
Infinitene: Computational Insights from Nonadiabatic Excited State Dynamics.
The Journal of Physical Chemistry Letters, 13, pp.8495-8501, 2022.
Freixas, V.M., Keefer, D., Tretiak, S., Fernandez-Alberti, S. and Mukamel, S.,
Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals.
Chemical Science, 13(21), pp.6373-6384, 2022.
Zamok, L., Coriani, S. and Sauer, S.P.,
A tale of two vectors: A Lanczos algorithm for calculating RPA mean excitation energies.
The Journal of Chemical Physics, 156(1), p.014102, 2022.
Non-adiabatic excited-state molecular dynamics: Theory and applications for modeling photophysics in extended molecular materials.
Chemical reviews, 120(4), pp.2215-2287, 2020.
Malone, W., Nebgen, B., White, A., Zhang, Y., Song, H., Bjorgaard, J.A., Sifain, A.E., Rodriguez-Hernandez, B., Freixas, V.M., Fernandez-Alberti, S. and Roitberg, A.E.,
NEXMD software package for nonadiabatic excited state molecular dynamics simulations.
Journal of Chemical Theory and Computation, 16(9), pp.5771-5783, 2020.
Vibronic quantum beating between electronic excited states in a heterodimer.
The Journal of Physical Chemistry B, 124(19), pp.3992-4001, 2020.
Alfonso-Hernandez, L., Athanasopoulos, S., Tretiak, S., Miguel, B., Bastida, A. and Fernandez-Alberti, S.,
Vibrational energy redistribution during donor–acceptor electronic energy transfer: criteria to identify subsets of active normal modes.
Physical Chemistry Chemical Physics, 22(33), pp.18454-18466, 2020.
Zhang, Y., Li, L., Tretiak, S. and Nelson, T.,
Nonadiabatic excited-state molecular dynamics for open-shell systems.
Journal of Chemical Theory and Computation, 16(4), pp.2053-2064, 2020.
Rodríguez-Hernández, B., Oldani, N., Martínez-Mesa, A., Uranga-Piña, L., Tretiak, S. and Fernandez-Alberti, S.,
Photoexcited energy relaxation and vibronic couplings in π-conjugated carbon nanorings.
Physical Chemistry Chemical Physics, 22(27), pp.15321-15332, 2020.
Freixas, V.M., Oldani, N., Franklin-Mergarejo, R., Tretiak, S. and Fernandez-Alberti, S.,
Electronic Energy Relaxation in a Photoexcited Fully Fused Edge-Sharing Carbon Nanobelt.
The Journal of Physical Chemistry Letters, 11(12), pp.4711-4719, 2020.
Rodrıguez-Hernández, B., Oldani, N., Martınez-Mesa, A., Uranga-Pina, L., Tretiakc, S. and Fernandez-Alberti, S.,
Photoexcited energy relaxation and vibronic couplings in p-conjugated carbon nanorings1.
Phys. Chem. Chem. Phys, 22, pp.15321-15332, 2020.
Freixas, V.M., Ondarse-Alvarez, D., Tretiak, S., Makhov, D.V., Shalashilin, D.V. and Fernandez-Alberti, S.,
Photoinduced non-adiabatic energy transfer pathways in dendrimer building blocks.
The Journal of Chemical Physics, 150(12), p.124301, 2019.
Salimi, A., Cho, D., Lee, J.Y., Kang, S. and Mukamel, S.,
Signatures of Through‐Space Charge Transfer in Two‐Photon Absorption of Paracyclophane Derivatives.
Bulletin of the Korean Chemical Society, 40(11), pp.1076-1086, 2019.
Photoexcited nonadiabatic dynamics of solvated push–pull π-conjugated oligomers with the NEXMD software.
Journal of chemical theory and computation, 14(8), pp.3955-3966, 2018.
Hanson-Heine, M.W., George, M.W. and Besley, N.A.,
Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems.
Molecular Physics, 116(11), pp.1452-1459, 2018.
Ondarse-Alvarez, D., Nelson, T., Lupton, J.M., Tretiak, S. and Fernandez-Alberti, S.,
Let digons be bygones: The fate of excitons in curved π-systems.
The journal of physical chemistry letters, 9(24), pp.7123-7129, 2018.
Ondarse-Alvarez, D., Oldani, N., Roitberg, A.E., Kleiman, V., Tretiak, S. and Fernandez-Alberti, S.,
Energy transfer and spatial scrambling of an exciton in a conjugated dendrimer.
Physical Chemistry Chemical Physics, 20(47), pp.29648-29660, 2018.
Rodriguez-Hernandez, B., Ondarse-Alvarez, D., Oldani, N., Martinez-Mesa, A., Uranga-Piña, L., Tretiak, S. and Fernandez-Alberti, S.,
Modification of optical properties and excited-state dynamics by linearizing cyclic paraphenylene chromophores.
The Journal of Physical Chemistry C, 122(29), pp.16639-16648, 2018.
Bjorgaard, J.A., Sheppard, D., Tretiak, S. and Niklasson, A.M.N.,
Extended Lagrangian excited state molecular dynamics.
Journal of Chemical Theory and Computation, 14(2), pp.799-806, 2018.
Lystrom, L., Zhang, Y., Tretiak, S. and Nelson, T.,
Site-specific photodecomposition in conjugated energetic materials.
The Journal of Physical Chemistry A, 122(29), pp.6055-6061, 2018.
Sifain, A.E.,
Photoexcitation and Nonradiative Relaxation in Molecular Systems: Methodology, Optical Properties, and Dynamics.
Doctoral dissertation, University of Southern California, 2018.
Zheng, F., Fernandez-Alberti, S., Tretiak, S. and Zhao, Y.,
Photoinduced intra-and intermolecular energy transfer in chlorophyll a dimer.
The Journal of Physical Chemistry B, 121(21), pp.5331-5339, 2017.
Furche, F., Krull, B.T., Nguyen, B.D. and Kwon, J.,
Accelerating molecular property calculations with nonorthonormal Krylov space methods.
The Journal of Chemical Physics, 144(17), p.174105, 2016.
Fernandez-Alberti, S., Makhov, D.V., Tretiak, S. and Shalashilin, D.V.,
Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach.
Physical Chemistry Chemical Physics, 18(15), pp.10028-10040, 2016.
Shenai, P.M., Fernandez-Alberti, S., Bricker, W.P., Tretiak, S. and Zhao, Y.,
Internal conversion and vibrational energy redistribution in Chlorophyll A.
The Journal of Physical Chemistry B, 120(1), pp.49-58, 2016.
Franklin-Mergarejo, R., Alvarez, D.O., Tretiak, S. and Fernandez-Alberti, S.,
Carbon nanorings with inserted acenes: breaking symmetry in excited state dynamics.
Scientific reports, 6(1), pp.1-11, 2016.
Ondarse-Alvarez, D., Kömürlü, S., Roitberg, A.E., Pierdominici-Sottile, G., Tretiak, S., Fernandez-Alberti, S. and Kleiman, V.D.,
Ultrafast electronic energy relaxation in a conjugated dendrimer leading to inter-branch energy redistribution.
Physical Chemistry Chemical Physics, 18(36), pp.25080-25089, 2016.
Li, H., Wu, C., Malinin, S.V., Tretiak, S. and Chernyak, V.Y.,
Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules.
Chemical Physics, 481, pp.124-132, 2016.
Kilina, S., Kilin, D. and Tretiak, S.,
Light-driven and phonon-assisted dynamics in organic and semiconductor nanostructures.
Chemical reviews, 115(12), pp.5929-5978, 2015.
Bricker, W.P., Shenai, P.M., Ghosh, A., Liu, Z., Enriquez, M.G.M., Lambrev, P.H., Tan, H.S., Lo, C.S., Tretiak, S., Fernandez-Alberti, S. and Zhao, Y.,
Non-radiative relaxation of photoexcited chlorophylls: theoretical and experimental study.
Scientific reports, 5(1), pp.1-16, 2015.
Bjorgaard, J.A., Kuzmenko, V., Velizhanin, K.A. and Tretiak, S.,
Solvent effects in time-dependent self-consistent field methods. I. Optical response calculations.
The Journal of Chemical Physics, 142(4), p.044103, 2015.
Fan, G.H., Han, K.L. and He, G.Z.,
Time‐dependent Density Functional‐based Tight‐bind Method Efficiently Implemented with OpenMP Parallel and GPU Acceleration.
Chinese Journal of Chemical Physics, 26(6), p.635, 2014.
Ondarse-Alvarez, D., Oldani, N., Tretiak, S. and Fernandez-Alberti, S.,
Computational study of photoexcited dynamics in bichromophoric cross-shaped oligofluorene.
The Journal of Physical Chemistry A, 118(45), pp.10742-10753, 2014.
Oldani, N., Tretiak, S., Bazan, G. and Fernandez-Alberti, S.,
Modeling of internal conversion in photoexcited conjugated molecular donors used in organic photovoltaics.
Energy & Environmental Science, 7(3), pp.1175-1184, 2014.
Li, H., Catanzaro, M.J., Tretiak, S. and Chernyak, V.Y.,
Excited-state structure modifications due to molecular substituents and exciton scattering in conjugated molecules.
The journal of physical chemistry letters, 5(4), pp.641-647, 2014.
Nelson, T., Fernandez-Alberti, S., Roitberg, A.E. and Tretiak, S.,
Nonadiabatic excited-state molecular dynamics: Treatment of electronic decoherence.
The Journal of chemical physics, 138(22), p.224111, 2013.
Nelson, T., Fernandez-Alberti, S., Roitberg, A.E. and Tretiak, S.,
Artifacts due to trivial unavoided crossings in the modeling of photoinduced energy transfer dynamics in extended conjugated molecules.
Chemical Physics Letters, 590, pp.208-213, 2013.
Fan, G.H. and Han, K.L.,
Efficient implementation of time-dependent density functional-based tight-bind method on multi-core and GPU system.
Commun. Comput. Chem., 1, pp.124-131, 2013.
Ullrich, C.A.,
Time-dependent density-functional theory: concepts and applications.
Oxford University Press. ISBN 978---19-956302-9, 2012.
Fernandez-Alberti, S., Roitberg, A.E., Nelson, T. and Tretiak, S.,
Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules.
The Journal of chemical physics, 137(1), p.014512, 2012.
Nonadiabatic excited-state molecular dynamics: numerical tests of convergence and parameters.
The Journal of chemical physics, 136(5), p.054108, 2012.
Fernandez-Alberti, S., Roitberg, A.E., Kleiman, V.D., Nelson, T. and Tretiak, S.,
Shishiodoshi unidirectional energy transfer mechanism in phenylene ethynylene dendrimers.
The Journal of chemical physics, 137(22), p.22A526, 2012.
Soler, M.A., Roitberg, A.E., Nelson, T., Tretiak, S. and Fernandez-Alberti, S.,
Analysis of state-specific vibrations coupled to the unidirectional energy transfer in conjugated dendrimers.
The Journal of Physical Chemistry A, 116(40), pp.9802-9810, 2012.
Furmanchuk, A.O., Leszczynski, J., Tretiak, S. and Kilina, S.V.,
Morphology and optical response of carbon nanotubes functionalized by conjugated polymers.
The Journal of Physical Chemistry C, 116(12), pp.6831-6840, 2012.
Petrenko, T., Kossmann, S. and Neese, F.,
Efficient time-dependent density functional theory approximations for hybrid density functionals: Analytical gradients and parallelization.
The Journal of chemical physics, 134(5), p.054116, 2011.
Nonadiabatic excited-state molecular dynamics modeling of photoinduced dynamics in conjugated molecules.
The Journal of Physical Chemistry B, 115(18), pp.5402-5414, 2011.
Bartell, L.A., Reslan, R., Wall, M.R., Kennedy, R.D. and Neuhauser, D.,
Electron transfer with TD-Split, a linear response time-dependent method.
Chemical Physics, 391(1), pp.62-68, 2011.
Baroni, S., Gebauer, R., Malcioğlu, O.B., Saad, Y., Umari, P. and Xian, J.,
Harnessing molecular excited states with Lanczos chains.
Journal of Physics: Condensed Matter, 22(7), p.074204, 2010.
Bartell, L.A., Wall, M.R. and Neuhauser, D.,
A time-dependent semiempirical approach to determining excited states.
The Journal of chemical physics, 132(23), p.234106, 2010.
Tretiak, S., Isborn, C.M., Niklasson, A.M. and Challacombe, M.,
Representation independent algorithms for molecular response calculations in time-dependent self-consistent field theories.
The Journal of chemical physics, 130(5), p.054111, 2009.
Yan, S., Lee, S.J., Kang, S. and Lee, J.Y.,
Computational approaches in molecular recognition, self-assembly, electron transport, and surface chemistry.
Supramolecular Chemistry, 19(4-5), pp.229-241, 2007.
Tsiper, E.V.,
Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.
Physical review letters, 97(7), p.076802, 2006.
Mondal, C.K. and Lee, J.Y.,
Understanding of molecular functions: Computational approaches.
Journal of Theoretical and Computational Chemistry, 5(04), pp.857-869, 2006.
Tsiper, E.V.,
Computer simulation of resonant tunneling through quantum antidot in the fractional quantum Hall regime: evidence of fractional quantization of electric charge.
Nanostructures: physics and technology, p.127, 2006.
Furche, F. and Rappoport, D.,
III. Density functional methods for excited states: Equilibrium structure and electronic spectra.
Computational photochemistry, 16, pp.93-128, 2005.
Furche, F. and Burke, K.,
Time-dependent density functional theoryin quantum chemistry.
Annual reports in computational chemistry, 1, pp.19-30, 2005.
Kim, W.S., Kim, J., Park, J.K., Mukamel, S., Rhee, S.K., Choi, Y.K. and Lee, J.Y.,
Stacking effect of polyfluorene on the chemical shift and electron transport.
The Journal of Physical Chemistry B, 109(7), pp.2686-2692, 2005.
Furche, F. and Burke, K.,
Time-dependent density functional theory in quantum chemistry.
In Annual Reports in Computational Chemistry 1, 19-30, 2005.
Lee, J.Y., Cho, E.J., Mukamel, S. and Nam, K.C.,
Efficient fluoride-selective fluorescent host: Experiment and theory.
The Journal of organic chemistry, 69(3), pp.943-950, 2004.
Ottonelli, M., Musso, G., Comoretto, D. and Dellepiane, G.,
Theoretical investigation of the charge injection effects on the electronic properties of substituted oligodiacetylenes.
The Journal of Physical Chemistry B, 108(31), pp.11291-11300, 2004.
Tretiak, S. and Chernyak, V.,
Resonant nonlinear polarizabilities in the time-dependent density functional theory.
The Journal of chemical physics, 119(17), pp.8809-8823, 2003.
Marques, M.A. and Gross, E.K.,
Time-dependent density functional theory.
In A Primer in Density Functional Theory (pp. 144-184). Springer, Berlin, Heidelberg, 2003.
Choi, S., Chernyak, V. and Mukamel, S.,
Mechanical response functions of finite-temperature Bose-Einstein condensates.
Physical Review A, 67(4), p.043602, 2003.
Choi, S., Berman, O., Chernyak, V. and Mukamel, S.,
Nonlinear response functions of strongly correlated boson fields: Bose-Einstein condensates and fractional quantum hall systems.
arXiv preprint cond-mat/cond-mat/0307718, 2003.
Tretiak, S. and Mukamel, S.,
Density matrix analysis and simulation of electronic excitations in conjugated and aggregated molecules.
Chemical reviews, 102(9), pp.3171-3212, 2002.
Hutchison, G.R., Ratner, M.A. and Marks, T.J.,
Accurate prediction of band gaps in neutral heterocyclic conjugated polymers.
The Journal of Physical Chemistry A, 106(44), pp.10596-10605, 2002.
Nguyen, K.A., Day, P.N., Pachter, R., Tretiak, S., Chernyak, V. and Mukamel, S.,
Analysis of Absorption Spectra of Zinc Porphyrin, Zinc m eso-Tetraphenylporphyrin, and Halogenated Derivatives.
The Journal of Physical Chemistry A, 106(43), pp.10285-10293, 2002.
Maitra, N.T., Burke, K., Appel, H., Gross, E.K.U. and van Leeuwen, R.,
Ten topical questions in time-dependent density functional theory.
In Reviews in Modern Quantum Chemistry: A Celebration of the Contributions of R.G. Parr, 2002.
Starikov, E.B.,
Quantum chemistry of nucleic acids: how it could help and when it is necessary.
Journal of Photochemistry and Photobiology C: Photochemistry Reviews, 3(2), pp.147-164, 2002.
Ottonelli, M., Musso, G., Comoretto, D. and Dellepiane, G.,
Optical and electronic properties of neutral and charged oligodiacetylene clusters.
Physical Chemistry Chemical Physics, 4(12), pp.2754-2761, 2002.
Skone, J.H. and Curotto, E.,
Two Krylov space algorithms for repeated large scale sparse matrix diagonalization.
The Journal of chemical physics, 116(8), pp.3210-3222, 2002.
Chernyak, V. and Mukamel, S.,
Geometric picture for coupled electron–nuclear dynamics.
International journal of quantum chemistry, 90(2), pp.799-811, 2002.
Tommasini, M., Chernyak, V. and Mukamel, S.,
Electronic density‐matrix algorithm for nonadiabatic couplings in molecular dynamics simulations.
International Journal of Quantum Chemistry, 85(4‐5), pp.225-238, 2001.
Tsiper, E.V.,
A classical mechanics technique for quantum linear response.
Journal of Physics B: Atomic, Molecular and Optical Physics, 34(12), p.L401, 2001.
Toury, T., Zyss, J., Chernyak, V. and Mukamel, S.,
Collective Electronic Oscillators for Second-Order Polarizabilities of Push−Pull Carotenoids.
The Journal of Physical Chemistry A, 105(23), pp.5692-5703, 2001.
Tretiak, S., Saxena, A., Martin, R.L. and Bishop, A.R.,
Collective electronic oscillator/semiempirical calculations of static nonlinear polarizabilities in conjugated molecules.
The Journal of Chemical Physics, 115(2), pp.699-707, 2001.
Chernyak, V., Volkov, S.N. and Mukamel, S.,
Electronic structure-factor, density matrices, and electron energy loss spectroscopy of conjugated oligomers.
The Journal of Physical Chemistry A, 105(10), pp.1988-2004, 2001.
Toury, T., Zyss, J., Chernyak, V. and Mukamel, S.,
Collective Electronic Oscillators for Second-Order Polarizabilities of Push−Pull Carotenoids.
The Journal of Physical Chemistry A, 105(23), pp.5692-5703, 2001.
Goldmann, E., Asher, S.A. and Mukamel, S.,
Electronic excitations of polyalanine; test of the independent chromophore approximation.
Physical Chemistry Chemical Physics, 3(14), pp.2893-2903, 2001.
Tommasini, M., Zerbi, G., Chernyak, V. and Mukamel, S.,
Excited-state molecular dynamics simulations of conjugated oligomers using the electronic density matrix.
The Journal of Physical Chemistry A, 105(29), pp.7057-7071, 2001.
Tretiak, S.,
Random phase approximation/semiempirical computations of electronic structure of extended organic molecules.
Recent Research Developments in Physical Chemistry, 5, pp.721-45, 2001.
Zyss, J., Ledoux, I., Volkov, S., Chernyak, V., Mukamel, S., Bartholomew, G.P. and Bazan, G.C.,
Through-space charge transfer and nonlinear optical properties of substituted paracyclophane.
Journal of the American Chemical Society, 122(48), pp.11956-11962, 2000.
Tretiak, S., Middleton, C., Chernyak, V. and Mukamel, S.,
Bacteriochlorophyll and carotenoid excitonic couplings in the LH2 system of purple bacteria.
The Journal of Physical Chemistry B, 104(40), pp.9540-9553, 2000.
Tretiak, S., Saxena, A., Martin, R.L. and Bishop, A.R.,
Interchain electronic excitations in poly (phenylenevinylene)(PPV) aggregates.
The Journal of Physical Chemistry B, 104(30), pp.7029-7037, 2000.
Tretiak, S., Saxena, A., Martin, R.L. and Bishop, A.R.,
CEO/semiempirical calculations of UV–visible spectra in conjugated molecules.
Chemical Physics Letters, 331(5-6), pp.561-568, 2000.