Computational Photochemistry
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1 Computational Photochemistry Filipp Furche Department of Chemistry February 09, 2015 Turbomole Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
2 Acknowledgments Jefferson Bates (Temple) Henk Eshuis (Montclair) CHE Filipp Furche (UC Irvine) DE-SC Computational Photochemistry Enrico Tapavicza (CSULB) Turbomole 02/09/ / 27
3 Introduction Photocatalytic Water Splitting Enrico Berardo, Martijn Zwijnenburg (UCL) Can photochemical water splitting efficiently be catalyzed by TiO nanoclusters? (TiO 2 ) 4 +4 H 2 O model Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
4 Introduction Wish List for Computational Photochemistry 1 Enable calculations on systems with 100s of atoms, high density of excited states, multiple intersections, and near-degeneracies 2 Automatically explore relevant parts of configuration space 3 Account for nuclear quantum effects, such as non-radiative decay 4 Describe bond breaking 5 Require minimal user input ( black box ) Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
5 Introduction Outline 1 Introduction 2 Non-Adiabatic Dynamics 3 Time-Dependent Density Functional Theory 4 Implementation 5 Applications 6 Conclusions Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
6 Non-Adiabatic Dynamics Born-Oppenheimer Approximation Central assumption: Due to mass difference, nuclear kinetic energy is small compared to electronic energy differences. 1 Solve electronic Schrödinger equation for fixed nuclear positions R (adiabatic separation): Ĥ el (x R)Ψ n (x R) = E n (R)Ψ n (x R) 2 Solve nuclear Schrödinger equation using Born-Oppenheimer (BO) potential energy surface: ( ˆT nuc + E n (R))Φ kn (R) = E kn Φ kn (R) Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
7 Non-Adiabatic Dynamics Breakdown of Born-Oppenheimer BO breaks down if electronic excitation energies are comparable to nuclear kinetic energy Close to avoided crossings and conical intersections BO cannot describe non-radiative transitions and excited state decay C. Xie, J. Ma, X. Zhu, D. H. Zhang, D. R. Yarkony, D. Xie, H. Guo, J. Phys. Chem. Lett. 5 (2014), 1055 Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
8 Non-Adiabatic Dynamics Tully Surface Hopping MD Born-Oppenheimer expansion of time-dependent wavefunction: Ψ(t R) = n C n (t) Ψ n (R) Time-dependent Schrödinger equation: iċ = HC iσ(t)c Coupling matrix σ mn = Ṙ τ mn, non-adiabatic coupling τ mn = Ψ m ξ Ψ n Nuclei propagated classically on one surface using Verlet method Surface hop occurs if g mn = 2Re J. C. Tully, J. Chem. Phys. 93 (1990), t+ t t dt C nσ nm C m C n C m > rnd(0, 1) Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
9 Non-Adiabatic Dynamics Building Blocks for Non-Adiabatic Dynamics Excitation energies F. Furche, D. Rappoport in Computational Photochemistry, Ed. M. Olivucci, Elsevier, Amsterdam, 2005, p. 93 Analytical energy gradients F. Furche, R. Ahlrichs, J. Chem. Phys. 117 (2002), 7433 Analytical ground-to-excited state couplings R. Send, F. Furche, J. Chem. Phys. 132 (2010), Analytical excited-to-excited state couplings Q. Ou, G. D. Bellchambers, F. Furche, J. E. Subotnik, J. Chem. Phys., in press (2015) Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
10 Time-Dependent Density Functional Theory Time-Dependent Density Functional Theory Map interacting problem onto non-interacting time-dependent Kohn-Sham (TDKS) system: i t φ j(t) = ĤKS [ρ](t) φ j (t), ρ(t, x) = j φ j (t, x) 2 Time-dependent density uniquely determines exchange correlation (XC) potential: Ĥ KS [ρ](t) = ˆT + ˆV H [ρ](t) + ˆV XC [ρ](t) + ˆV en + V nn + ˆV ext (t) Adiabatic approximation: V XC [ρ](t, x) = δe XC [n] δn(x) n(x)=ρ(t,x) E. Runge, E. K. U. Gross, Phys. Rev. Lett. 52 (1984), 997 Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
11 Time-Dependent Density Functional Theory The TDKS Eigenvalue Problem Interacting excitation energies and transition densities are accessible from linear response of TDKS system Sympletic RPA eigenvalue problem/ Casida s Equations: [( ) ( )] ( ) A B 1 0 Xn Ω B A n = RPA pseudo-norm: X T n X n Y T n Y n = 1 Eigenvalues Ω n are excitation energies, eigenvectors (X n, Y n ) T are one-particle transition density matrices Dimension is N ph = N occ N virt N 2 Y n A. D. McLachlan, M. A. Ball, Rev. Mod. Phys. 36 (1964), 884 M. E. Casida, in Recent advances in density functional methods, Vol. 1, Ed. D. P. Chong, World Scientific, Singapore, 1995, 155 Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
12 Time-Dependent Density Functional Theory Orbital Rotation Hessians Hybrid TDDFT Orbital Rotation Hessians: (A + B) iajb = (ɛ a ɛ i )δ ij δ ab + 2(ia jb) + 2f XC++ iajb c x [(ib ja) + (ij ab)] (A B) iajb = (ɛ a ɛ i )δ ij δ ab + 2f XC iajb + c x [(ib ja) (ij ab)] Generalized XC kernels: Density matrix derivatives f XC±± µνκλ = 2 E XC D ± µν D ± κλ Special cases: TDHF (E XC = 0, c x = 1), TDA/CIS (B = 0), non-hybrid TDDFT (c x = 0) J. E. Bates, F. Furche, J. Chem. Phys. 137 (2012), Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
13 Time-Dependent Density Functional Theory Locally Range-Separated Hybrids Locally range-separated PBE: E XC lrsh-pbe = E X sr-pbe + E X lr + E C PBE Long-range exchange: E X lr = σ Brandon Krull d 3 r 1 d 3 r 2 γ σ (r 1, r 2 ) 2 1 e ασ(r) r 1 r 2 2, r 1 r 2 where α σ (R) = c ρ σ (R) /ρ σ (R) Efficient semi-numerical integration A. V. Krukau, G. E. Scuseria, J. P. Perdew, A. Savin, J. Chem. Phys. 129 (2008), Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
14 Time-Dependent Density Functional Theory Locally Range-Separated Hybrids No tuning necessary Correct high density scaling possible Minimal self-interaction error Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
15 Implementation Generalized Symplectic Davidson Method An alternative which has not been tried is to allow B to be non-orthogonal and to solve the generalized eigenvalue problem in step 1. [E. R. Davidson, Comput. Phys. Commun. 53 (1989), 49] Minimize excitation energy on an iteratively expanded Krylov subspace using raw preconditioned residual vectors as basis No orthogonalization necessary Since residual norm decreases, (much) fewer integrals needed for later iterations Makes linear scaling exchange methods competitive Favorably combined with RI-J approximation Numerically stable Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
16 Implementation Performance System Sym. N at Method Property Speedup Rel. Error 1 C B3LYP/SV(P) α iso % 2 T 282 PBE0/SV(P) E(2 1 A) % 3 C 1 67 PBE0/SV(P) E(2 1 A) % Relative speedups of new algorithm using link+ri on 1 Intel X5560 core (2.80GHz) Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
17 Applications SH-TDDFT Simulations on TiO 2 -Water Clusters Enrico Berardo, Martijn Zwijnenburg (UCL) Simulations show heterolytic water splitting in S 1 state B3LYP/SV(P), 278 K Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
18 Applications Vitamin D Photochemistry Provitamin D (Pro) Lumisterol (Lumi) R:=C 9 H 17 (D 2 ) R:=C 8 H 17 (D 3 ) R:=CH 3 (this study) Previtamin D (Pre) Vitamin D (Vita) Toxisterols (Toxi) Tachysterol (Tachy) E. Tapavicza, A. M. Meyer, F. Furche, Phys. Chem. Chem. Phys. 13 (2011), Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
19 Applications Provitamin D Ring-Opening Typical trajectory: Dark (S 2 ) state is not involved Consistent with recent experimental detection of fluorescence K.-C. Tang, A. Rury, M. B. Orozco, J. Egendorf, K. G. Spears, R. J. Sension, J. Chem. Phys. 134 (2011), Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
20 Applications Excited State Decay Rates Comparison of cyclohexadiene (black), α-terpinene (orange), provitamin D (red) Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
21 Applications Origin of Biexponential Decay Comparison of lifetimes (fs) to experiment PBE0 Exp. Cyclohexadiene τ τ α-terpinene τ τ Provitamin D τ τ Biexponential decay caused by productive/non-productive pathway At 300 K, τ(pro) 5τ(CHD) K. Kosma, S. A. Trushin, W. Fuss, W. E. Schmid, Phys. Chem. Chem. Phys. 11 (2009), 172 K.-C. Tang, A. Rury, M. B. Orozco, J. Egendorf, K. G. Spears, R. J. Sension, J. Chem. Phys. 134 (2011), Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
22 Applications Quantum Yields Quantum yields for ring-opening (%): PBE0 Exp. Cyclohexadiene (Cyclohexane) α-terpinene 54 Provitamin D (EtOH) Lumisterol (EtOH) K. Kosma, S. A. Trushin, W. Fuss, W. E. Schmid, Phys. Chem. Chem. Phys. 11 (2009), 172 K.-C. Tang, A. Rury, M. B. Orozco, J. Egendorf, K. G. Spears, R. J. Sension, J. Chem. Phys. 134 (2011), Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
23 Applications Previtamin D Photochemistry Tachy formation: Z/E isomerization by Hula-twist mechanism Quantum yields (in %): Product Computed Exp. 303 nm 254 nm Pre 69 Lumi Pro Tachy Toxi Vita Total simulation time 0.2 ns(!), few weeks on 10 cluster nodes Embarrassingly parallel H. J. C. Jacobs, J. W. J. Gielen, E. Havinga, Tetrahedron Lett. 22 (1981), 4013 Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
24 Applications Acetaldehyde Photochemistry Dissociation into open shell fragments is common Conventional wisdom: Multi-reference methods needed K. H. J. Giesbertz, E. J. Baerends, Chem. Phys. Lett. 461 (2008), 338 Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
25 Applications Spin-Unrestricted Non-Adiabatic TDDFT Simulations Typical bond-breaking trajectory: PBE0/SV(P), 10 a.u. timestep, 157 nm excitation Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
26 Conclusions Conclusions and Outlook TDDFT-SH enables non-adiabatic MD simulations of molecules with up to 100 atoms Mechanisms, quantum yields, product distributions are obtained with qualitative accuracy Hybrid functionals are necessary Re-formulation of Davidson method in conjunction with RI-J yields speedup of up to 5 for hybrid functionals Non-adiabatic MD simulations using single-reference TDDFT can describe homolytic bond breaking Next steps: Double excitations, intersystem crossing, massively parallel implementation Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
27 Conclusions Further Reading E. Tapavicza, G. Bellchambers, J. C. Vincent, F. Furche, Phys. Chem. Chem. Phys. 15 (2013), F. Furche, R. Ahlrichs, C. Hättig, M. Klopper, F. Weigend M. Sierka, WIREs Comput. Mol. Sci. 4 (2014), 91 Furche group publication list: Filipp Furche (UC Irvine) Computational Photochemistry 02/09/ / 27
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