An Excited Electron Avoiding a Positive Charge - The Journal of

LETTER pubs.acs.org/JPCL

An Excited Electron Avoiding a Positive Charge Anthony D. Dutoi* and Lorenz S. Cederbaum Theoretische Chemie, Ruprecht-Karls-Universit€at, D-69120 Heidelberg, Germany

bS Supporting Information ABSTRACT: High-level ab initio calculations in the time domain reveal the effects of the chemistry in the vicinity of a chomophore unit on the dynamics of an initially localized electronic excitation. An all-electron wavepacket is propagated, and its one-body density matrix is used to divide the dynamic into particle and hole components that can be analyzed separately. The expectation that an excited electron will be attracted to a positively charged ammonium group is superseded by a dynamic in which the hole part of the excitation is driven away from this region, dragging the excited electron with it. These calculations illustrate the crucial role of the attraction between the particle and hole. Emerging timedomain electronic structure techniques hold much promise for unraveling the behavior of complex systems. SECTION: Molecular Structure, Quantum Chemistry, General Theory

T

he time-domain picture of electronic dynamics represents an exciting new way to approach chemical processes, and timeresolved experiments to follow electronic motion are quickly emerging.1 Little is known about what sort of purely electronic dynamics can occur in a molecule before the onset of nuclear motions. Such direct probes of the electronic structure of a system will provide a valuable tool for understanding energy transfer and chemistry in general. One of the most interesting electronic processes is charge separation. Until now, this has been understood mostly in the context of Marcus theory,2 where solvent coordinates relax to accommodate a charge, or in terms of charge-transfer stationary states.3 In recent work, we have studied some of the basic features of valence dynamics driven soley by electron correlation.4 In this Letter we explore the chemical factors that influence spontaneous (field-free) charge separation, starting from excitations localized on a chromophore group to represent the effect of a few-femtosecond perturbation. We find an interesting phenomenon, showing the preference of an excited electron to migrate toward a neutral acid group (OHOC
) rather than a positively charged ammonium group (
NH3+), as initially expected. A similar effect has also recently been noted in protonated tyrosine (TyrH+).5 TyrH+ has OHOC
and
NH3+ groups in equivalent positions relative to a chromophore ring. By comparing the time scales of specific fragmentation pathways in TyrH+ to those of related molecules (protonated tryptophan and decarboxylated analogues), it is presently presumed that, after an excitation on the ring, the electron goes not to the positively charged
NH3+, but rather to the neutral OHOC
group. This and recent related investigations6,7 on the gas-phase photofragmentation pathways of these molecules yield valuable clues about the nonradiative processes that quench fluorescence in vivo, important in both fundamental biochemical investigations8 and technology for disease diagnosis.9 These molecules may also be r 2011 American Chemical Society

ideal candidates for first experiments to follow electronic motion, which can test whether the picture presented for the simpler molecules in this work is valid there also. In order to study electronic dynamics in real time, we have developed a time-domain electronic structure method to follow the evolution of correlated multielectron wavepackets.10 The high level of theory automatically includes the particle
hole attraction, which is crucial when investigating charge separation. In order to visualize the electronic dynamics, the many-body wave function is reduced to time-dependent average densities of the excited electron (particle) and the vacancy it leaves behind (hole), as defined in the Computational Methods section, below. Our first system, NH3+-MeEteMe-F, is illustrated in Figure 1, which shows its optimized geometry and clarifies the abbreviated chemical formula. It contains a
NH3+ terminal group and our model chromophore is an ethenyl group (
CHdCH
), where the initial state is a projection of the πfπ* eigenstate of ethene. The dynamics of the particle and hole following the initial excitation are shown in this figure. Experience has already taught us to expect that the electronrich F atom will likely serve as an attractor for the hole,4 which it does. One of the lower-energy electronic modes is indeed the return of the electron it withdraws in the ground state. Already after the first half femtosecond, a substantial amount of the hole density is seen on the F atom. The subsequent femtosecond is characterized by a marked depletion of the hole density in the region of the original CdC excitation, which then resides mostly on the F atom and the C
H bonds of the methylene (
CH2
) linker during this time. Toward the end of the time shown, the hole again Received: July 1, 2011 Accepted: August 22, 2011 Published: August 22, 2011 2300

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LETTER

Figure 1. Particle and hole dynamics of systems studied [white: H; black: C; purple: F; orange: N; red: O]. At the center of both molecules is an ethenyl unit (Ete,
CHdCH
), where an initial πfπ* excitation is created, isolated by two methylene (Me,
CH2
) linkers. The resultant particle and hole densities are shown evolving in time using a logarithmic color scale. On the left, the
NH3+ group is mostly avoided by the excitation, including the negatively charged particle, whereas a migration of the particle density toward the neutral OHOC
group is seen on the right. In both systems, the hole density is seen oscillating between the CdC bond and the F atom. The densities are integrated in the out-of-page (z) direction.

accumulates on the CdC bond. Over the entire time shown, only a small amount ever goes to the methylene linker on the left, and only a smaller, transient amount ever visits the
NH3+ group itself. The expectation that the excited electron may go in the direction opposite to the hole, toward the positive
NH3+ group, proves to be false. The most obvious trend is that, to the lesser extent that it moves at all, the particle follows the hole. Its density on the F is highest when the density of the hole is highest there, likewise with the methylene linker to the F atom. When the density of the hole collects back onto the CdC group, so does the density of the particle. Similar to the hole, the occupation of the particle of the space near the
NH3+ is small, diffuse, and transient. In order to quantify the extent to which the particle and hole charges separate, we monitor the time-dependent difference of the system dipole moment Δμ, relative to that of the ground state. This is essentially a measure of the distance between the particle and hole centroids (weighted by charge). This is plotted as a trajectory in the xy plane (negligible z component) in the top panel of Figure 2. It begins near the origin because the initial state is a local excitation. It is seen clearly that the (approximately unit) charges do separate to the extent of a few atomic units (Bohr radii) for NH3+-MeEteMe-F. The left-pointing dipole Δμ that arises uses the chemistry convention, which means that the electron is to the left of the

hole (in the orientation that we have shown the molecules). On the basis of what we see from the real-space visualization of the dynamics in Figure 1, this is because the hole has traveled to the right to a larger extent than the particle. This has also been confirmed numerically; the trajectory of the difference dipole largely tracks the travel of the centroid of the hole density, with the particle centroid moving much less. Qualitatively, we say that the charge separation here is hole-driven, or dominated by the dynamic of the hole. Recalling that our previous simulations had emphasized the role of valence vacancy structure, and inspired by the suggestion that the excited electron in TyrH+ tends toward the acid group, we built another test case, OHOC-MeEteMe-F. In this molecule, the central acidic C atom has a Mulliken charge of +0.96, reflecting that its pz electron is withdrawn to the neighboring O and C atoms. This is similar to the electron deficiency of B atoms, which we earlier observed to allow free passage for the travel of an excited electron in π-conjugated systems.4 This system and its dynamics over the same time scale are shown alongside those of NH3+-MeEteMe-F in Figure 1. Indeed, the OHOC
substituent does act as an effective attractor for the particle. A steady increase in the density of the particle on the CdO bond is seen over the interval shown. With the exception of the F atom at short times, no other sites accumulate as much particle density. The fastest motion is a 2301

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Figure 2. Dynamic charge-separation trajectories. (Top) The difference in the dipole moment (relative to the ground state) is plotted as a trajectory for each of NH3+-MeEteMe-F and OHOC-MeEteMe-F, with the molecules in the coordinate frame shown in Figure 1. The times shown in the snap-shots of Figure 1 are indicated by filled circles here, starting near the origin. (Bottom) An extra proton is placed at varied separation in H+ 3 3 3 OHOC-MeEteMe-F. Most striking is the similarity of the trajectory for the 1 Å case to that of NH3+-MeEteMe-F, reflecting the common dynamic when the hole is repelled by the nearby charge.

quick but strong fluctuation of the particle density in the direction of the F atom. This is most easily understood by observing the dynamic of the hole at this same time. Similar to NH3+-MeEteMe-F, a strong coupling moves both the particle and hole parts to the F atom. However, in this system, this fluctuation is much shorter lived, and the hole, and especially the particle, do not stay on this atom to a large extent. On the longer time scale with which the particle moves to the CdO bond, the hole is also seen moving to the two O atoms of the OHOC
group, suggesting that it is following the particle. To move the hole to the left, electrons cannot be taken from the relatively empty central C atom, but rather from those atoms that had withdrawn them in the ground state. In Figure 2, we see that the charge separation achieved in the OHOC
system is of a similar magnitude as seen for the NH3+ system, and it is continuing to grow. From Figure 1, we note for OHOC-MeEteMe-F that, beyond the very first moments, the particle has a clear bias toward the left of the molecule, whereas the long-time bias of the hole is ambiguous. A more detailed analysis, following the individual particle and hole centroids, makes clear that the dynamic of the total dipole moment is dominated by the contribution for the particle, and so we say that this is particle-driven charge separation. The discrepancy in the behavior of essentially identical chromophore excitations when the neighboring substituent is changed is a new and interesting result, for which we would like to extract the most intuitive and transferable explanation. In order to investigate whether the electron avoiding the
NH3+ group is some counterintuitive effect of having a positive charge as part of the system, we compute the dynamics for the otherwise neutral OHOC-MeEteMe-F in the presence of an additional proton. This proton is nominally attached to the carbonyl oxygen with varied H+ 3 3 3 OdC distance (at 120°, opposite the rest of the molecule). An analysis of the particle and hole centroids shows that the travel of the excited electron to the OHOC
group is, in fact,

LETTER

suppressed when the proton is close. In short, when the proton is close to the OdC, only the hole is moving substantially, and with a strong tendency away from the H+, toward the F atom. At larger separation, only the excited particle moves much, tending toward the OHOC
group. At intermediate distances of 5 to 10 Å, the particle can transfer to the proton, and the hole is dragged along, to the left of the molecule. As a condensed result of this analysis, the bottom panel of Figure 2 shows difference dipole trajectories for representative H+ 3 3 3 OHOC-MeEteMe-F separations. Most striking is how similar the trajectory at a separation of 1 Å is to the dynamic of NH3+-MeEteMe-F. This is indicative of the fact that, in both systems with a close positive charge, neither the particle nor the hole visits the left-hand part of the molecule, and so the dynamic is not very sensitive to the identity of this group. After about 5 Å, the trajectory takes on some qualitative similarity to the infinitedistance case. Already at 20 Å (not shown), there is only a slight (∼10%) deviation from the asymptotic trajectory (i.e., no proton). It is critical to mention that as the proton approaches the OdC, the Mulliken charge on the central acidic C atom is effectively constant (even growing a little, by ∼0.1); the valence vacancy there is still available to the excited electron, in principle. In light of the foregoing, we arrive at the conclusion that the lack of tendency of the excited electron toward the
NH3+ group is related purely to the presence of the positive charge, which appears to chase away the combined particle
hole pair. The similarity of scale of the charge separation in all systems draws attention to a key point, being that one of the major physical drivers is the particle
hole attraction. With a fixed amount of energy input, there is a limit to the extent of particle
hole separation that can be achieved. Foremostly, the particle
hole pair is an overall neutral unit, composed of two mutually attracting charges, and whether it can approach a charged entity will generally be highly dependent on geometrical parameters (both the spatial extent of each charge and relative orientation). We believe that the time-domain picture presented here provides substantial insight into how a particle
hole pair interacts with the charges and valence vacancies that surround it. Whereas the dynamics of our systems can probably be comprehended in terms of many eigenstates with mixed local and chargetransfer character, the language of Coulombic forces balancing valence occupancy arguments is more insightful. In larger systems, there will be very many eigenstates near any energy, and these can be strongly mixed even by small interactions. The dynamic picture should be more transferable between systems with similar local structures when the global eigenstates are not easily comparable.

’ COMPUTATIONAL METHODS Our aim here is to understand well the behavior of simple systems, using high-level calculations that proceed in a linear state space and include electron correlation size consistently. Since we are investigating spontaneous charge separation, the well-known charge-transfer failure11 of common density-functional methods is unacceptable. The field-free time-dependent Schr€odinger equation is integrated using the effective Hamiltonian derived from the extended, second-order algebraic diagrammatic construction12 [ADC(2)-x] for the particle
hole propagator. This propagation of a many-electron state includes correlation between all electrons in both the ground and excited states. In addition to the 2302

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hole pair that characterizes a single excitation, relaxations of the “unexcited” electrons are also included. The associated numerical methods have been presented at varying depth of detail in recent publications.4,10 The many-body wave function is an enormous amount of information that needs to be distilled to a simpler picture for visualization. Our main analysis tool involves dividing the overall dynamic into contributions for the particle and the hole. The spinless one-body difference density matrix ΔG is decomposed as GðtÞ
G0 ¼ ΔGðtÞ ¼ Gp ðtÞ
Gh ðtÞ where G is the density matrix for the evolving excited wavepacket and G0 is the same quantity for the ground state. The partitioning of the difference matrix into particle and hole components, Gp and Gh, is done by projecting it into two orthogonal subspaces, where the particle space is spanned by all single-electron states that increase in occupancy upon excitation, and the hole space is spanned by all states that decrease in occupancy. The particle and hole spaces are obtained by diagonalizing ΔG to obtain the natural particle and hole orbitals, which are identified by the sign of their associated eigenvalue; these states are used to span the respective particle and hole spaces. From this partitioning, the change in any one-electron observable, relative to the ground state, can be divided into particle and hole contributions. The densities we render here are individual contributions to the change in the spatial electron density. These are more commonly known as attachment
detachment densities,13 generalized to the time domain.10 Such densities are most familiar from energy-domain computations with wave functions that involve maximally single substitutions (primarily linear-response density functional theory), but this analysis technique is applicable to excitations on top of arbitrary correlated wave functions. For all computations, a 6-31+G* basis was used, which has previously been shown4 to provide an optimum of accuracy and cost for the kinds of excitations considered here, by reproducing the πfπ* excitations of ethene and hexatriene to within ∼0.1 eV using ADC(2)-x. All structures were optimized using secondorder Møller
Plesset theory with the same basis. The resolution-of-identity method was used to generate the electron repulsion integrals, with an RIMP2-aug-cc-pVDZ fitting basis. A time step of 1 au (∼0.024 fs) was used in a Lanczos time integration scheme, and the wave function at each step was converged to less than 10
6 in the L2 norm of the deviation of the wave function. The 1s core electrons of second-row elements are frozen (uncorrelated) after the initial Hartree
Fock calculation, along with a similar number of spuriously high virtual orbitals.

LETTER

’ ACKNOWLEDGMENT This work was funded by the Deutsche Forschungsgemeinschaft. We thank S. Brøndsted Nielsen for directing us to the story of protonated tyrosine. ’ REFERENCES (1) Goulielmakis, E.; Loh, Z.-H.; Wirth, A.; Santra, R.; Rohringer, N.; Yakovlev, V. S.; Zherebtsov, S.; Pfeifer, T.; Azzeer, A. M.; Kling, M. F.; et al. Real-Time Observation of Valence Electron Motion. Nature 2010, 466, 739–744. (2) Wasielewski, M. R. Energy, Charge, and Spin Transport in Molecules and Self-Assembled Nanostructures Inspired by Photosynthesis. J. Org. Chem. 2006, 71, 5051–5066. (3) Klinkusch, S.; Klamroth, T.; Saalfrank, P. Long-Range Intermolecular Charge Transfer Induced by Laser Pulses: An Explicitly TimeDependent Configuration Interaction Approach. Phys. Chem. Chem. Phys. 2009, 11, 3875–3884. (4) Dutoi, A. D.; Wormit, M.; Cederbaum, L. S. Ultrafast Charge Separation Driven by Differential Particle and Hole Mobilities. J. Chem. Phys. 2011, 134, 024303
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’ ASSOCIATED CONTENT

bS

Supporting Information. Animations of the particle and hole dynamics in real time for all systems studied. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel: +49-622154 5217. Fax: +49-6221-54 5221. 2303

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