Coupling Real-Time Time-Dependent Density Functional Theory with

Subscriber access provided by Gothenburg University Library

Letter

Coupling Real-Time Time-Dependent Density Functional Theory with Polarizable Force Field Greta Donati, Andrew Wildman, Stefano Caprasecca, David B Lingerfelt, Filippo Lipparini, Benedetta Mennucci, and Xiaosong Li J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02320 • Publication Date (Web): 10 Oct 2017 Downloaded from http://pubs.acs.org on October 11, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry Letters

Coupling Real-Time Time-Dependent Density Functional Theory with Polarizable Force Field Greta Donati,†,‡ Andrew Wildman,†,‡ Stefano Caprasecca,¶ David B. Lingerfelt,† Filippo Lipparini,∗,¶ Benedetta Mennucci,∗,¶ and Xiaosong Li∗,† †Department of Chemistry, University of Washington, Seattle, WA, 98195 ‡Authors contributed equally ¶Dipartimento di Chimica e Chimica Industriale, Universit` a di Pisa, Via G. Moruzzi 13, 56124 Pisa, Italy E-mail: [email protected]; [email protected]; [email protected]

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Page 2 of 13

Page 3 of 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A wide variety of theoretical models have been proposed to capture the essential aspects of the system-environment interactions while reducing the large number of degrees of freedom required to describe the environment. Among such approaches, continuum solvation models treat the environmental degrees of freedom implicitly, sacrificing any atomistic description thereof. The combination of continuum models and QM descriptions of the system has shown to give an accurate description of systemenvironment interactions, in all the cases where the latter can be represented in terms of an average effect. 20–23 However, an atomistic description of the environment becomes necessary when the change in the system’s properties are the result of specific system-environment interactions which strongly depend on the relative orientation and distance between the two (e.g. solute-solvent hydrogen bondings). 24 To preserve the atomistic nature of the environment, hybrid models were devised in which the system electronic degrees of freedom are treated quantum mechanically (QM), while the environment is described at a classical level (often through molecular mechanics (MM)). 25–27 The most common examples of hybrid QM/MM models include the effect of the classical environment on the QM system using fixed point charges to represent the environment atoms. This “electrostatic” embedding approach has shown to capture the large part of the environment effects, but obviously it cannot model any mutual polarization between the system and its environment. To overcome this limitation, in recent years hybrid QM/MM models have been generalized to include a “polarizable” embedding. Many approaches for including the polarization of the system by its environment (and vice versa) have been explored, including the so-called “Effective Fragment Potential Method”, 28,29 “induced dipoles”, 30–34 “fluctuating charges”, 35–38 and Drude oscillator-based models. 39 In this paper, the induced dipole formulation of polarizable MM (MMPol) is employed to describe the the environment degrees of freedom, while the system degrees of freedom are treated quantum mechanically via the time-dependent self consistent field approach.

In particular, the QM/MMPol formulation is here extended to RT-TDDFT for computations of spectroscopic quantities and simulations of the electronic dynamics of chemical systems embedded in a large polarizable force field. LRTDDFT calculations on QM/MMPol systems have already been performed and validated in previous works to simulate electronic spectra of (supra)molecular systems in complex environments. 30,40–43 Very recently, during the development of this paper, an example of the extension of MM polarizable embeddings to RTTDDFT has been presented within the software deMon2k that relies on auxiliary fitted densities. 44 In this work, we also consider the timedependent response of covalently bonded protein residues in addition to electrostatics of solvent. The time-dependent electronic degrees of freedom of the quantum subsystem are modeled with the RT-TDDFT approach, i

dP(t) = [K(t), P(t)] dt

(1)

where K and P are the Kohn-Sham/Fock and density matrices in the orthonormal basis, respectively. Equation (1) is integrated using the modified midpoint unitary transformation (MMUT) approach, a second order “leap-frog” style algorithm, 5,6,45,46 P(tk+1 ) = U(tk ) · P(tk−1 ) · U† (tk ) U(tk ) = C(tk ) exp [−i2∆t λ(tk )] C(tk ) (2) λ(tk ) = C† (tk ) · K(tk ) · C(tk ) where C and λ are the eigenvectors and eigenvalues of the Kohn-Sham/Fock matrix. To describe the many-electron dynamics embedded in a polarizable force field, one needs to integrate the mutual interaction and polarization between the TDDFT and MMPol subsystems during the reaction dynamics. The interaction between the polarizable environment and the quantum system is introduced via a density-dependent operator, VMMPol , in


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(3)

the Kohn-Sham/Fock matrix,

Ep (P′ (t)) =

−

X

p′ 6=p

p′ 6=p (5) 3Rpp′ (Rpp′

Spp′

(3)

Spp′

+ +

X

Zi

qi

Rp − R i |Rp − Ri |3

Zi

R p − Ri |Rp − Ri |3

ρ(r, t)

Rp − r dr |Rp − r|3

(6)

In addition, we assume that the process of geometrical relaxation (reorientation) of the environment happens at a slower timescale than the one investigated, and therefore we keep the positions of the MM atoms frozen. The first case study is the solvatochromic dye coumarin 153, 51–60 a member of a class of molecules widely employed as sensitizers in solar cells. 61 The RT-TDDFT/MMPol electronic dynamics of the coumarin 153 dye in methanol solvent are simulated to resolve the absorption spectrum. All the calculations were performed by employing the PBE0 62 hybrid functional with the 6-31g(d) basis set. 63,64 Coumarin 153 was placed in a box of 175 methanol molecules and a schematic picture is given in Fig. 1. 65,66 The solvation box was previously equilibrated using the Amber parm99SB force field. 67–69 LRTDDFT and RT-TDDFT calculation were performed at QM/MMPol theory level in order to obtain absorption spectra that include solute/solvent mutual polarization. The real-time dynamics simulations were performed for 15 fs with an electronic time step of ∼0.25 attoseconds. The external electric field employed to perturb the system had an intensity of 0.0001

µp′ (t) |Rpp′ |3

· µp′ (t)) ) |Rpp′ |5

X i6=p

where we use R and R to indicate nuclear coordinates in the MM and QM regions, respectively. The bra-ket notation implicitly integrates over the electronic degrees of freedom r. We also use the index p and p′ to label the polarizable sites in the MM region. During the time-evolution of the quantum electronic dynamics, the Kohn-Sham/Fock matrix (Eq. (3)) is computed on-the-fly at every time step by including the time-dependent perturbing potential (Eq. (4)) arising from the induced MM dipoles µp (P′ (t)). The timedependence of the MM dipoles µp (t) arises from the fact that the dipoles are computed as the linear response to the electric field produced by the MM charges and time-dependent QM density, by solving the following linear system of equations X

(5)

Spp′ and Spp′ parameters used in the following case studies are tabulated in the Supplementary Information. In this work, we only consider static polarizabilities of the environment. This is a reasonable and useful approximation for cases where the electric field generated by the QM region is oscillating much slower than the response in the MM region. 50 In Eq. (5), we have assumed that the electronic degrees of freedom of the environment, modelled here by the induced dipoles, respond instantaneously to the electric field produced by the time-dependent electronic density of charge ρ(r, t) at each polarizable site p:

K′ (t) = K′0 (t, P′ (t)) + VMMPol (q, µ(P′ (t))) (3) where K′0 is the perturbation-free Hamiltonian matrix for the QM region. Note that primed notations reference corresponding matrices in non-orthogonal atomic orbital basis. VMMPol (q, µ(P′ (t))) is the time-dependent interaction potential induced by the MM charges and induced dipoles µ(t) from the MMPol region. This perturbation term represented in the atomic basis (λ, ν, ...) takes on the following form, 30,31 X qi MMPol |νi Vλν =− hλ| |r − Ri | i X µp (P′ (t)) · (Rp − r) |νi (4) − hλ| |r − Rp |3 p

µp (t) = αp (Ep (P′ (t)) +

Page 4 of 13

(5)

where αp is the static polarizability tensor at (5) (3) MM site p. Spp′ and Spp′ are screening factors depending on the MM topology which are introduced to avoid overpolarization effects. 47–49


4

Page 5 of 13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


of the chromophore. Even small changes in the conformations of residues can significantly shift the absorption. 76 Including mutual polarization between the environment and RPSB is required in order to accurately recover the excitation energies, 76 and because RPSB undergoes a cis/trans photoisomerization, 77–80 accurate descriptions of the early-time electron dynamics are essential for understanding this process. The comparison between the LR- and RT-TDDFT for RPSB are shown in Fig. 4. Again, the spectra show excellent agreement, with all of the peaks showing the same positions and relative intensities between methods. It is also informative to investigate the dynamics of the net dipoles in both the QM and MM regions. As can be seen in Fig. 5, the net dipole in the MM region shows anti-oscillatory behavior compared to that in the QM region. Because the dipoles are being propagated instantaneously with the perturbed electronic density, this behavior is expected; the dipoles are responding to the changing electronic density by aligning to the lowest energy position against the dipole in the QM region.

Intensity (Arb. Units)

4.0 LR RT

3.0 2.0 1.0 0.0 0

2

4

6

8

Energy (eV)

Figure 4: Absorption spectrum of RPSB in bovine rhodopsin calculated with LR- and RTTDDFT/MMPol. Oscillator strengths from the LR-TDDFT calculation are shown as black sticks.

one peak centered at 3.27 eV and the other at 6.12 eV; the more energetic peak is about twice as intense as the first. In order to validate the developed method, the absorption spectrum is compared to the LR-TDDFT calculation coupled with the same MMPol approach. Figure 2 shows that the LR- and RT-TDDFT spectra are in excellent agreement. The coumarin model system provides good support for the validity of this model in the case of a solute/solvent system. However, simulating a heterogeneous environment such as that provided by a protein is much more challenging. In order to test the RT-TDDFT/MMPol method developed in this work, the 11-cis retinal protonated Schiff base (RPSB, Fig. 3) in bovine rhodopsin residues was investigated. Simulations were carried out at the CAMB3LYP 75 /6-31g(d) 63,64 level of theory. The structure was obtained from a cluster analysis of frames extracted from QM/MM molecular dynamics (MD) trajectories where the QM part was treated within DFT using the PBE exchange-correlation functional (see Ref. 40 for the details). The interactions with the surrounding residues strongly affect the optical properties

QM Dipole Change (µD)

300

100 QM MM

200

50 100 0

0

-100 -50 -200 -300

MM Dipole Change (nD)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 13

-100 0

2

4

6

8

10

12

14

Time (fs)

Figure 5: Evolution of the net dipole in both the QM and MMPol region. Note the different scales on left and right axes.

We conclude the discussion by commenting about the nature of the response of the environment included in the present RT-TDDFT formulation. Polarizable embeddings introduce a speci-


6

Page 7 of 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ficity which is not present in non-polarizable embeddings. 81–84 When we consider an electronic excitation in the QM subsystem, the electronic component of the environment response (here represented by the induced dipoles) can be determined by either the corresponding transition density or the change in the electronic density between ground and excited state. The former response is accounted for in a LRTDDFT approach while the latter requires going beyond the standard TDDFT formulation and calculating the relaxation of the electronic density upon excitation. To account for this State-Specific (SS) term within a TDDFT framework, different approximations have been proposed. 34,58,85,86 The simplest one is a perturbative correction to the excitation energy which is calculated in terms of the interaction between the change in the electronic density and the corresponding change in the electronic component of the environment polarization. Such an approach (commonly known as corrected LR, or cLR) was originally proposed for PCM, 85 but it has been more recently extended to the induced dipole formulation of polarizable MM, 34 and it is also used here (Tab. 1).

able models has not yet been achieved, we expect the RT formalism to be able to provide clearer insights into how to properly describe the response of environment to excited state dynamics. A detailed investigation of these aspects will be object of a future communication. Real-time TDDFT is coupled with a polarizable QM/MM model, connecting the propagation of a wave function with the mutual polarization between the QM system and the environment. The proposed method was successfully validated by comparing the spectrum calculated by both this method and LR-TDDFT of two completely different systems: a solvatochromatic dye in methanol solution and a chromophore in its protein environment. Until now RT-TDDFT simulations of solvated systems or protein environments were either based on computationally expensive full quantum mechanical time-dependent theory or coupled with the mean-field time-dependent polarizable continuum model. With the timedependent mutual polarization approach introduced in this work, the coupled RT-TDDFT and polarizable force field approach holds the potential to accurately probe the ultrafast nonequilibrium interaction between both the solvent and solute degrees of freedom and a chromophore embedded in its protein environment.

Table 1: First excitation energy of RPSB calculated with different TDDFT formulations. Method

Energy (eV)

LR/Vacuo LR/MMPol RT/MMPol cLR/MMPol

2.4775 2.6581 2.6647 2.7635

Acknowledgement The development of the solvated electronic dynamics is funded by the US Department of Energy (DE-SC0006863 to XL). The development of ab initio linear response theory is supported by the US National Science Foundation (CHE-1565520 to XL). Computations were facilitated through the use of advanced computational, storage, and networking infrastructure provided by the Hyak supercomputer system at the University of Washington, funded by the Student Technology Fee, and the National Science Foundation (MRI-1624430).

The setup of the real time simulation, i.e., the system in the ground state is perturbed with a very short pulse and then left to evolve, is consistent with the assumptions made in LRTDDFT. Consequently, the RT-TDDFT results match the LR-TDDFT ones, while the statespecific (SS) corrected shift is larger. This discrepancy is of particular interest for understanding the different regimes modeled by the LR and SS approach. Since a complete consensus on how to describe excited states of solvated (or embedded) systems using classical polariz-

References (1) Stratmann, R. E.; Scuseria, G. E.; Frisch, M. J. An Efficient Implementation of Time-dependent Density-functional


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 13

(10) Ding, F.; Kuiken, B. E. V.; Eichinger, B. E.; Li, X. An Efficient Method for Calculating Dynamical Hyperpolarizabilities Using Real-Time Time-Dependent Density Functional Theory. J. Chem. Phys. 2013, 138, 064104.

Theory for the Calculation of Excitation Energies of Large Molecules. J. Chem. Phys. 1998, 109, 8218–8224. (2) Dreuw, A.; Head-Gordon, M. SingleReference ab Initio Methods for the Calculation of Excited States of Large Molecules. Chem. Rev. 2005, 105, 4009– 4037.

(11) Wislicenus, W. Ueber die Isomerie der Formylphenylessigester. Leibigs Ann. Chem. 1896, 291, 147–216.

(3) Lestrange, P. J.; Nguyen, P. D.; Li, X. Calibration of Energy-Specific TDDFT for Modeling K-edge XAS Spectra of Light Elements. J. Chem. Theor. Comput. 2015, 11, 2994–2999.

(12) Stobbe, H. Studien u ¨ber Tautomerie, insbesondere an einem semicyklischen 1,3Diketon der Pentamethylenreihe. Leibigs Ann. Chem. 1903, 326, 347–370.

(4) Petrone, A.; Goings, J. J.; Li, X. Quantum Confinement Effects on Optical Transitions in Nanodiamonds Containing Nitrogen Vacancies. Phys. Rev. B 2016, 94, 165402.

(13) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry; VCH Publishers: Weinheim, 1988. (14) Coetzee, J. F.; Ritchie, C. D. SoluteSolvent Interactions; Dekker: New York, 1969 and 1976; Vol. 1 and 2.

(5) Li, X.; Smith, S. M.; Markevitch, A. N.; Romanov, D. A.; Levis, R. J.; Schlegel, H. B. A Time-dependent Hartree-Fock Approach for Studying the Electronic Optical Response of Molecules in Intense Fields. Phys. Chem. Chem. Phys. 2005, 7, 233–239.

(15) Abraham, M. H.; Grellier, P. L.; Abboud, J. L. M.; Doherty, R. M.; Taft, R. W. Solvent Effects in Organic Chemistry - Recent Developments. Can. J. Chem. 1988, 66, 2673–2686.

(6) Liang, W.; Chapman, C. T.; Li, X. Efficient First-principles Electronic Dynamics. J. Chem. Phys. 2011, 134, 184102.

(16) Amis, E. S. Solvent Effects on Reaction Rates and Mechanisms; Academic Press: New York, 1966.

(7) Ding, F.; Lingerfelt, D. B.; Mennucci, B.; Li, X. Time-dependent Non-equilibrium Dielectric Response in QM/Continuum Approaches. J. Chem. Phys. 2015, 142, 034120.

(17) Amis, E. S. Solvent Effects on Chemical Phenomena; Academic Press: New York, 1973; Vol. 1. (18) Abraham, M. H. Solvent Effects on Reaction Rates. Pure Appl. Chem. 1985, 57, 1055–1064.

(8) Pipolo, S.; Corni, S.; Cammi, R. Equation of Motion for the Sovent Polarization Apparent Charges in the Polarizable Continuum Model: Application to TimeDependent CI. J. Chem. Phys. 2017, 146, 064116–064124.

(19) Connors, K. A. Chemical Kinetics - The Study of Reaction Rates in Solution; VCH Publishers: Weinheim, 1990.

(9) Pipolo, S.; Corni, S. Real-Time Description of the Electronic Dynamics for a Molecule Close to a Plasmonic Nanoparticle. J. Phys. Chem. C 2016, 120, 28774– 28781.

(20) Tomasi, J.; Persico, M. Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent. Chem. Rev. 1994, 94, 2027– 2094.


8

Page 9 of 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(21) Cramer, C.; Truhlar, D. Implicit solvation models: Equilibria, structure, spectra, and dynamics. Chem. Rev. 1999, 99, 2161–2200.

Model. J. Chem. Theor. Comput. 2009, 5, 1838–1848. (31) Caprasecca, S.; Jurinovich, S.; Viani, L.; Curutchet, C.; Mennucci, B. Geometry Optimization in Polarizable QM/MM Models: The Induced Dipole Formulation. J. Chem. Theor. Comput. 2014, 10, 1588– 1598.

(22) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999– 3094.

(32) Caprasecca, S.; Jurinovich, S.; Lagardère, L.; Stamm, B.; Lipparini, F. Achieving Linear Scaling in Computational Cost for a Fully Polarizable MM/Continuum Embedding. J. Chem. Theor. Comput. 2015, 11, 694–704.

(23) Klamt, A. The COSMO and COSMO–RS solvation models. WIREs Comput. Mol. Sci. 2011, 1, 699–709. (24) Mennucci, B. Modeling Environment Effects on Spectroscopies through QM/Classical Models. Phys. Chem. Chem. Phys. 2013, 15, 6583–6594.

(33) Mao, Y.; Demerdash, O.; HeadGordon, M.; Head-Gordon, T. Assessing Ion-Water Interactions in the AMOEBA Force Field Using Energy Decomposition Analysis of Electronic Structure Calculations. J. Chem. Theor. Comput. 2016, 12, 5422–5437.

(25) Gao, J. Hybrid Quantum and Molecular Mechanics Simulations: An Alternative to Solvent Effects in Organic Chemistry. Acc. Chem. Res. 1996, 29, 298–305. (26) Lin, H.; Truhlar, D. G. QM/MM: What Have We Learned, Where Are We, and Where Do We Go from Here? Theor. Chem. Acc. 2006, 117, 185–199.

´ Caprasecca, S.; La(34) Loco, D.; Polack, E.; gardère, L.; Lipparini, F.; Piquemal, J.P.; Mennucci, B. A QM/MM Approach Using the AMOEBA Polarizable Embedding: From Ground State Energies to Electronic Excitations. J. Chem. Theor. Comput. 2016, 12, 3654–3661.

(27) Senn, H. M.; Thiel, W. QM/MM Methods for Biomolecular Systems. Angew. Chem. 2009, 48, 1198–1229. (28) Day, P. N.; Jensen, J. H.; Gordon, M. S.; Webb, S. P.; Stevens, W. J.; Krauss, M.; Garmer, D.; Basch, H.; Cohen, D. An Effective Fragment Method for Modeling Solvent Effects in Quantum Mechanical Calculations. J. Chem. Phys. 1996, 105, 1968–1986.

(35) Rick, S. W.; Stuart, S. J.; Berne, B. J. Dynamical Fluctuating Charge Force Fields: Application to Liquid Water. J. Chem. Phys. 1994, 101, 6141–6156. (36) Rick, S. W.; Berne, B. J. Dynamical Fluctuating Charge Force Fields: The Aqueous Solvation of Amides. J. Am. Chem. Soc. 1996, 118, 672–679.

(29) Kairys, V.; Jensen, J. H. QM/MM Boundaries across Covalent Bonds: A Frozen Localized Molecular Orbital-Based Approach for the Effective Fragment Potential Method. J. Phys. Chem. A 2000, 104, 6656–6665.

(37) Lipparini, F.; Barone, V. Polarizable Force Fields and Polarizable Continuum Model: A Fluctuating Charges/PCM Approach. 1. Theory and Implementation. J. Chem. Theor. Comput. 2011, 7, 3711– 3724.

(30) Curutchet, C.; Mu˜ noz-Losa, A.; Monti, S.; Kongsted, J.; Scholes, G. D.; Mennucci, B. Electronic Energy Transfer in Condensed Phase Studied by a Polarizable QM/MM

(38) Lipparini, F.; Cappelli, C.; Barone, V. Linear Response Theory and Electronic


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 13

dependent Density Functional Theory. J. Chem. Phys. 2016, 145, 104107.

Transition Energies for a Fully Polarizable QM/Classical Hamiltonian. J. Chem. Theor. Comput. 2012, 8, 4153–4165.

(47) Thole, B. T. Molecular Polarizabilities Calculated with a Modified Dipole Interaction. Chem. Phys. 1981, 59, 341–350.

(39) Boulanger, E.; Thiel, W. Solvent Boundary Potentials for Hybrid QM/MM Computations Using Classical Drude Oscillators: A Fully Polarizable Model. J. Chem. Theor. Comput. 2012, 8, 4527–4538.

(48) van Duijnen, P. T.; Swart, M. Molecular and Atomic Polarizabilities: Thole’s Model Revisited. J. Phys. Chem. A 1998, 102, 2399–2407.

(40) Daday, C.; Curutchet, C.; Sinicropi, A.; Mennucci, B.; Filippi, C. ChromophoreProtein Coupling beyond Nonpolarizable Models: Understanding Absorption in Green Fluorescent Protein. J. Chem. Theor. Comput. 2015, 11, 4825–4839.

(49) Wang, J.; Cieplak, P.; Li, J.; Hou, T.; Luo, R.; Duan, Y. Development of Polarizable Models for Molecular Mechanical Calculations I: Parameterization of Atomic Polarizability. J. Phys. Chem. B 2011, 115, 3091–3099.

(41) Steindal, A. H.; Ruud, K.; Frediani, L.; Aidas, K.; Kongsted, J. Excitation Energies in Solution: The fully Polarizable QM/MM/PCM method. J. Phys. Chem. B 2011, 115, 3027–3037.

(50) Nørby, M. S.; Vahtras, O.; Norman, P.; Kongsted, J. Assessing FrequencyDependent Site Polarisabilities in Linear Response Polarisable Embedding. Mol. Phys. 2017, 115, 39–47.

(42) Juronovich, S.; Curutchet, C.; Mennucci, B. The Fenna-Matthews-Olson Protein Revisited: A Fully Polarizable (TD) DFT/MM Description. ChemPhysChem 2014, 15, 3194–3204.

(51) Maroncelli, M.; Fleming, G. R. Picosecond Solvation Dynamics of Coumarin 153: The Importance of Molecular Aspects of Solvation. J. Chem. Phys. 1987, 86, 6221– 6239.

(43) Curutchet, C.; Novoderezhkin, V. I.; Kongsted, J.; Mu˜ noz-Losa, A.; van Grondelle, R.; Scholes, G. D.; Mennucci, B. Energy Flow in the Cryptophyte PE545 Antenna Is Directed by Bilin Pigment Conformation. J. Phys. Chem. B 2013, 117, 4263–4273.

(52) Lewis, J. E.; Maroncelli, M. On the (Uninteresting) Dependence of the Absorption and Emission Transition Moments of Coumarin 153 on Solvent. Chem. Phys. Lett. 1998, 282, 197–203. (53) Kovalenko, S. A.; Ruthmann, J.; Ernsting, N. P. Ultrafast Stokes Shift and Excited-State Transient Absorption of Coumarin 153 in Solution. Chem. Phys. Lett. 1997, 271, 40–50.

(44) Wu, X.; Teuler, J.-M.; Cailliez, F.; Clavaguéra, C.; Salahub, D. R.; de la Lande, A. Simulating Electron Dynamics in Polarizable Environments. J. Chem. Theor. Comput. 2017, DOI:10.1021/acs.jctc.7b00251. (45) Isborn, C. M.; Li, X.; Tully, J. C. TDDFT Ehrenfest Dynamics: Collisions Between Atomic Oxygen and Graphite Clusters. J. Chem. Phys. 2007, 126, 134307.

(54) Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. Subpicosecond Measurements of Polar Solvation Dynamics: Coumarin 153 Revisited. J. Phys. Chem. 1995, 99, 17311–17337.

(46) Goings, J. J.; Kasper, J. M.; Egidi, F.; Sun, S.; Li, X. Real Time Propagation of the Exact Two Component Time-

(55) Kumar, P. V.; Maroncelli, M. Polar Solvation Dynamics of Polyatomic Solutes: Simulation Studies in Acetonitrile and


10

Page 11 of 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Methanol. J. Chem. Phys. 1995, 103, 3038–3059.

lar Orbital Hydrogenation Energies. Theoret. Chim. Acta 1973, 28, 213–222.

(56) Reynolds, L.; Gardecki, J. A.; Frankland, S. J. V.; Horng, M. L.; Maroncelli, M. Dipole Solvation in Nondipolar Solvents: Experimental Studies of Reorganization Energies and Solvation Dynamics. J. Phys. Chem. 1996, 100, 10337– 10354.

(64) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. SelfConsistent Molecular Orbital Methods. XXIII. A PolarizationType Basis Set for SecondRow Elements. J. Chem. Phys. 1982, 77, 3654– 3665.

(57) Cave, R. J.; E. W. Castner, J. TimeDependent Density Functional Theory Investigation of the Ground and Excited States of Coumarins 102, 152, 153, and 343. J. Phys. Chem. A 2002, 106, 12117– 12123.

(65) Jacquemin, D.; Planchat, A.; Adamo, C.; Mennucci, B. TD-DFT Assessment of Functionals for Optical 0-0 Transitions in Solvated Dyes. J. Chem. Theor. Comput. 2012, 8, 2359–2372. (66) Improta, R.; Barone, V.; Santoro, F. Ab Initio Calculations of Absorption Spectra of Large Molecules in Solution: Coumarin 153. Angew. Chem. 2007, 119, 409–412.

(58) Improta, R.; Barone, V.; Scalmani, G.; Frisch, M. J. A State-Specific Polarizable Continuum Model Time Dependent Density Functional Theory Method for Excited State Calculations in Solution. J. Chem. Phys. 2006, 125, 054103.

(67) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 1995, 117, 5179–5197.

(59) M¨ uhlpfordt, A.; Schanz, R.; Ernsting, N. P.; Farztdinov, V.; Grimme, S. Coumarin 153 in the Gas Phase: Optical Spectra and Quantum Chemical Calculations. Phys. Chem. Chem. Phys. 1999, 1, 3209–3218.

(68) Wang, J. M.; Cieplak, P.; Kollman, P. A. How Well Does a Restrained Electrostatic Potential (RESP) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules? J. Comput. Chem. 2000, 21, 1049–1074.

(60) Kurashige, Y.; Nakajima, T.; Kurashige, S.; Hirao, K.; Nishikitani, Y. Theoretical Investigation of the Excited States of Coumarin Dyes for Dye-Sensitized Solar Cells. J. Phys. Chem. A 2007, 111, 5544–5548.

(69) Hornak, V.; Abel, R.; Okur, A.; Strockbine, B.; Roitberg, A.; Simmerling, C. Comparison of Multiple Amber Force Field and Development of Improved Protein Backbone Parameters. Proteins 2006, 65, 712–725.

(61) O’Regan, B.; Grätzel, M. A Low-Cost, High-Efficiency Solar Cell Based on DyeSensitized Colloidal TiO2 Films. Nature 1991, 353, 737–740. (62) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158–6170.

(70) Bruner, A.; LaMaster, D.; Lopata, K. Accelerated Broadband Spectra Using Transition Dipole Decomposition and Padé Approximants. J. Chem. Theor. Comput. 2016, 12, 3741–3750.

(63) Hariharan, P. C.; Pople, J. A. The Influence of Polarization Functions on Molecu-


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(71) Goings, J. J.; Lingerfelt, D. B.; Li, X. Can Quantized Vibrational Effects Be Obtained from Ehrenfest Mixed QuantumClassical Dynamics? J. Phys. Chem. Lett. 2016, 7, 5193–5197.

Page 12 of 13

(79) González-Luque, R.; Garavelli, M.; Bernardi, F.; Merchán, M.; Robb, M. A.; Olivucci, M. Computational Evidence in Favor of a Two-State, Two-Mode Model of the Retinal Chromophore Photoisomerization. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 9379–9384.

(72) Egidi, F.; Sun, S.; Goings, J. J.; Scalmani, G.; Frisch, M. J.; Li, X. Two-Component Non-Collinear TimeDependent Spin Density Functional Theory for the Excited States Calculations. J. Chem. Theor. Comput. 2017, 13, 2591–2603.

(80) Frutos, L. M.; Andruniów, T.; Santoro, F.; Ferré, N.; Olivucci, M. Tracking the Excited-State Time Evolution of the Visual Pigment with Multiconfigurational Quantum Chemistry. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 7764–7769.

(73) Caprasecca, S.; Curutchet, C.; Juronovich, S.; Mennucci, B. PolChat: A Polarisation-consistent Charge Fitting Tool. Molecolab Tools, Pisa, Italy, 2017.

(81) Cammi, R.; Corni, S.; Mennucci, B.; Tomasi, J. Electronic Excitation Energies of Molecules in Solution: State Specific and Linear Response Methods for Nonequilibrium Continuum Solvation Models. J. Chem. Phys. 2005, 122, 104513.

(74) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H. et al. Gaussian Development Version Revision I.10++. Gaussian Inc., Wallingford CT 2016.

(82) Corni, S.; Cammi, R.; Mennucci, B.; Tomasi, J. Electronic Excitation Energies of Molecules in Solution within Continuum Solvation Models: Investigating the Discrepancy between State-Specific and Linear-Response Methods. J. Chem. Phys. 2005, 123, 134512.

(75) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid ExchangeCorrelation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57.

(83) Lunkenheimer, B.; Köhn, A. Solvent Effects on Electronically Excited States Using the Conductor-Like Screening Model and the Second-Order Correlated Method ADC(2). J. Chem. Theor. Comput. 2013, 9, 977–994.

(76) Guareschi, R.; Valsson, O.; Curutchet, C.; Mennucci, B.; Filippi, C. Electrostatic Versus Resonance Interactions in Photoreceptor Proteins: The Case of Rhodopsin. J. Phys. Chem. Lett. 2016, 7, 4547–4553.

(84) Schwabe, T. General Theory for Environmental Effects on (Vertical) Electronic Excitation Energies. J. Chem. Phys. 2016, 145, 154105.

(77) Polli, D.; Altoé, P.; Weingart, O.; Spillane, K. M.; Manzoni, C.; Brida, D.; Tomasello, G.; Orlandi, G.; Kukura, P.; Mathies, R. A. et al. Conical Intersection Dynamics of the Primary Photoisomerization Event in Vision. Nature 2010, 467, 440–443.

(85) Caricato, M.; Mennucci, B.; Tomasi, J. Solvent Polarity Scales Revisited: a ZINDO-PCM Study of the Solvatochromism of Betaine-30. Mol. Phys. 2006, 104, 875–887.

(78) Kim, J. E.; Tauber, M. J.; Mathies, R. A. Wavelength Dependent Cis-Trans Isomerization in Vision. Biochem. 2001, 40, 13774–13778.

(86) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Guido, C. A.; Mennucci, B.;


12

Page 13 of 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Scalmani, G.; Frisch, M. J. Practical Computation of Electronic Excitation in Solution: Vertical Excitation Model. Chem. Sci. 2011, 2, 2143–2161.


13

Coupling Real-Time Time-Dependent Density Functional Theory with

Recommend Documents