Spectroscopy and Excited States
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A Non-Equilibrium Molecular Dynamics Study of Infra-red Perturbed Electron Transfer Zheng Ma, Panayiotis Antoniou, Peng Zhang, Spiros Skourtis, and David N. Beratan J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00001 • Publication Date (Web): 13 Jul 2018 Downloaded from http://pubs.acs.org on July 14, 2018
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Journal of Chemical Theory and Computation
A Non-Equilibrium Molecular Dynamics Study of Infra-red Perturbed Electron Transfer
Z. Ma,a P. Antonioub, P. Zhang,*a S. Skourtis,*b and D.N. Beratan,*a, c, d
a
Department of Chemistry, Duke University, Durham, North Carolina, 27708, United States
b
Department of Physics, University of Cyprus, Nicosia, Cyprus
c
Department of Physics, Duke University, Durham, North Carolina, 27708, United States
d
Department of Biochemistry, Duke University, Durham, North Carolina, 27710, United States
Abstract
Infra-red (IR) excitation is known to change electron transfer kinetics in molecules. We use nonequilibrium molecular dynamics (NEqMD) simulations to explore the molecular underpinnings of how vibrational excitation may influence non-adiabatic electron-transfer. NEqMD combines classical molecular dynamics simulations with non-equilibrium semiclassical initial conditions to simulate the dynamics of vibrationally excited molecules. We combine NEqMD with electronic structure to probe IR effects on electron transfer in two molecular species, dimethylaniline-guanosine-cytidine-anthracene ensemble
(DMA-GC-Anth)
and
4-(pyrrolidin-1-yl)phenyl-2,6,7-triazabicyclo[2.2.2]octatriene-10-
cyanoanthracen-9-yl structure (PP-BCN-CA). In DMA-GC-Anth, the simulations find that IR excitation of NH2 scissoring motion, and the subsequent intramolecular vibrational energy redistribution (IVR), do not significantly alter the mean-squared donor-acceptor (DA) coupling interaction. This finding is consistent with earlier computational analysis of static systems. In PP-BCN-CA, IR excitation of the bridging C=N bond changes the bridge-mediated coupling for charge separation and recombination by ~ 30 - 40%. The methods described here enable detailed exploration of how IR excitation may perturb charge transfer processes at the molecular scale.
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I. INTRODUCTION Developing strategies for infra-red (IR) modulated electron transfer (ET) is an appealing goal because of the chemically innocent nature of IR excitation and its potential to control charge flow at the nanoscale.1-2 Early theoretical studies suggested that IR excitation might be able to change coupling pathway interferences and thus modify donor-acceptor interactions.3-4 Further theoretical studies of ET rates in donor-bridge-acceptor (DBA) model systems found that vibrational excitation of bridgelocalized modes can substantially modulate the ET rate when the tunneling barriers are not particularly high. In this case, the bridge can have sufficiently large electron population to enable coupling of the transiting electron to bridge vibrational modes that are excited by IR.1 To achieve substantial IR-induced ET rate perturbation, the ET time scale should be comparable to or faster than that of intramolecular vibrational energy redistribution (IVR), so that the IR excitation can influence the ET reaction before the excitation energy is dissipated.1 Early experimental studies of IR-perturbed ET in DMA-GC-Anth (Fig. 1)5 found that IR excitation of the H-bonded bridge slows the charge separation rate by ~67% and accelerates the charge recombination by ~3.5 fold.6 In contrast, IR-excitation accelerated charge separation was found in fac-[ReI(CO3)(DCEB)(3-DMABN)] (3DMABN is 3-dimethylaminobenzonitrile and DCEB is 4,4′- (dicarboxyethyl)-2,2-bipyridine)7. IR-excitation of the ring-stretching modes of DCEB (4,4’-dicarboxyethyl-2,2’-bipyridine) caused the rate of charge transfer from the initially prepared triplet metal-to-ligand charge transfer state (3MLCT) to a triplet ligand-to-ligand charge transfer state (3LLCT) to increase by ~28%. Weinstein and co-workers recently reported IR-modulated ET in a series structures with phenothiazine donors, naphthalene monoimide acceptors, and platinum(II)-trans-acetylide bridges. IR-excitation of bridge-localized –C ≡ C– stretching modes suppressed charge separation and accelerated charge recombination.8-12 1 ℏ ∫ ℏ
The non-adiabatic ET rate, expressed in the time domain is =
(1)
is the reaction free energy, is the donor-acceptor (DA) coupling auto-correlation function at
is the DA energy gap auto-correlation function at thermal equilibrium thermal equilibrium and
(see SI for details).13-14 Molecular modes that modulate the DA energy gap are usually termed “promoting modes” and modes that modulate the DA couplings are called “inducing modes.” The excitation of promoting and inducing modes by IR or IVR can influence the ET rate. 2 ACS Paragon Plus Environment
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For ET reactions that are coupled to mixed classical-quantum promoting modes, IR-excitation can populate the first vibrational excited state of a quantum promoting mode. This can produce a change in the quantum Franck-Condon factor.6, 15-17 This quantum Franck-Condon factor produces rate slowing for near activationless ET and rate acceleration for highly activated ET. In our earlier studies,6 we found
that the most significant rate suppression effect occurs when the reaction free energy , the inner-
sphere reorganization energy , the outer-sphere reorganization energy and the vibrational frequency of the quantum promoting mode ℏ
satisfy the relation + + − ℏ
≈ 0.6 In cases where ET
reactions are coupled to classical promoting modes, IVR following IR excitation can excite classical promoting modes, creating non-equilibrium distributions that cause the donor-acceptor energy gap fluctuations to increase in frequency. For near activationless ET, the DA surface crossing occurs near the minimum of the reactant potential energy surface, and the IVR-injected energy can cause the system to have larger nuclear velocities near the crossing. As a result, the time scales and the probabilities for the donor and acceptor to remain in resonance are decreased, leading to expected ET rate slowing. For highly activated ET, IVR can increase the probability of the system to reach the surface crossing, producing ET rate acceleration.6 〉 approximation, the ET rate is given by = 2&/ℏ〈)*+ - , where - is the Franck Condon
IR-excitation and IVR can also change the DA couplings by exciting inducing modes. In the Condon factor, )*+ is the donor-acceptor (DA) coupling, and 〈… 〉 is )*+ averaged over molecular
conformations at thermal equilibrium.13-14, 18 When a quantum inducing mode is excited, the coupling / average should be performed over a non-equilibrium ensemble, and the ET rate becomes = 13, 19-24 〉 〉 2&/ℏ〈)*+ , and 〈)*+ / - . )*+ can be sensitive to the structural fluctuations / could be
〉 substantially different from 〈)*+ if )*+ varies asymmetrically along the IR-excited quantum
inducing mode coordinates. When the DA coupling fluctuation time scale is comparable or shorter than the DA energy gap fluctuations, the Condon approximation can fail, and the DA coupling correlation function is needed to describe the non-adiabatic ET rate, rather than the mean-squared DA coupling. The IR excitation of an inducing mode may accelerate or slow the ET rate. ET systems can have classical promoting and inducing modes that are not excited directly but can be excited by IVR. In this case, molecular dynamics (MD) simulations can help describe the IVR process and explore how non-equilibrium promoting and inducing mode populations influence the DA couplings 3 ACS Paragon Plus Environment
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and the ET rate. MD simulations that would describe the IR perturbed systems would need to begin with geometries that capture the initial IR-excitation of high-frequency modes. We describe a strategy to describe the vibrational energy cascade following initial excitation, using non-equilibrium MD methods. We describe a general approach to simulate the effect of vibrational excitation of classical promoting and inducing modes on nonadiabatic ET rates. The method computes non-equilibrium ET rates using the non-equilibrium version of Eq. 1
=
1 0 0 ∫ ℏ ℏ
(2)
where the energy gap and DA coupling correlation functions are computed by averaging over nonequilibrium MD trajectories of the molecule with initial conditions that describe the IR excited state. In this study, we apply the method to examine IR-perturbed DA coupling fluctuations and their influence on ET rates.
We have recently rationalized the physical origins of IR-induced rate changes in the DMA-GC-Anth structure.6 By sampling geometries along normal coordinates and computing DA couplings, the DA couplings were found to be only weakly perturbed by IR excitation. Our earlier analysis6 did not allow explorations of how IVR following initial excitation may transiently influence the DA couplings. The study of non-equilibrium molecular dynamics (NEqMD) described enables this direct examination and 〉 IR excitation), time-dependent geometry analysis, and analysis of 〈)*+ for equilibrium and non-
combines classical molecular dynamics simulation with non-equilibrium initial conditions (simulating
equilibrium ensembles. This NEqMD approach is motivated by earlier studies of Stock and coworkers.25-27 We apply the methods to DMA-GC-Anth and to PP-BCN-CA (Fig. 1).
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(a)
(b)
Figure 1. Molecular structures. (a) DMA-GC-Anth. Dimethylaniline (DMA) is the electron donor. Anthracene (Anth) is linked to cytidine via an alkyne group and it is the electron acceptor. R is 2’, 3’, 5’-tri-O-(tert-butyldimethylsilyl)ribofuranosidyl and it does not participate in the photochemistry. (b) PP-BCN-CA. The electron donor is 4-(pyrrolidin-1-yl)phenyl and the electron acceptor is 10cyanoanthracene-9-yl. Both the donor and acceptor fragments are connected to the bridge, a 2,6,7triazabicyclo[2.2.2]octatriene fragment, via an alkyne group.
II. THEORETICAL AND COMPUTATIONAL METHODS The workflow of the NEqMD method has three elements (Scheme 1): preparation of the nonequilibrium initial state, MD simulation, and post-MD analysis. The post-MD analysis includes quantum chemical analysis of molecular snapshots, donor-acceptor coupling analysis, and time-dependent structural analysis.
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Scheme 1. The combined NEqMD and electronic structure computation workflow. Green arrows denote the MD trajectories (labeled with Traj #) simulated from the non-equilibrium initial conditions (NEqIC, grid ( = 0, , 2 , …). Based on these snapshots, quantum chemistry calculations and DA coupling
blue block). After the MD simulation, structural snapshots (orange circles) are recorded at each time
()*+ ) calculations are performed. Ensemble averaged squared couplings are computed at each time grid
point. Time-dependent geometry analysis is also performed on the snapshots.
A. Non-Equilibrium Initial Conditions (NEqIC). The non-equilibrium initial conditions (NEqIC) describe the initial IR-excited vibrational state. The positions and momenta of this excited state are sampled using the semiclassical Wigner phase space distribution function for quantum harmonic oscillators.28-29 The position and momentum distributions are derived from harmonic oscillator eigenstates. Compared to the action-angle sampling technique that retains ensemble-averaged energies,25-27 the Wigner phase space distribution sampling more accurately represents the atomic positions associated with low-energy vibrational motion.28-29 An accurate description of IR-induced molecular structural distortions is an essential starting point to evaluate DA coupling fluctuations. Action-angle sampling places more weight on nuclear distributions near the classical turning points, regardless of vibrational quantum numbers. However, for a quantum harmonic oscillator occupying low-lying vibrational states, the wave function dictates that the probability near the 6 ACS Paragon Plus Environment
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Journal of Chemical Theory and Computation
classical oscillator turning points does not dominant the distribution of nuclear geometries. In the case where the squared DA coupling varies in an asymmetric manner with respect to the geometry distortion from the equilibrium geometry, the position probability distribution described by action-angle sampling could cause inaccuracy in computed ensemble averaged squared DA couplings.
The mass-weighted normal-mode coordinates and momenta are defined as
1
2 = 34 ⋅ 6 27 = 34 ⋅ 67
(3)
where 4 is the reduced mass and 6 is the normal coordinate. The joint probability distribution function for the mass-weighted normal coordinate displacement Δ2 = √4 ⋅ 6 − 6 and momentum 27 is
approximated (for vibrational excited states) as the product of the probability distribution for position and for momenta29:
ℙ0 : 2, 27 < = |>0 2| ?@0 :27
