ultrafast dynamics of photo-excited 2- cite as: struct....
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Struct. Dyn. 7, 024101 (2020); https://doi.org/10.1063/1.5143228 7, 024101
© 2020 Author(s).
Ultrafast dynamics of photo-excited 2-thiopyridone: Theoretical insights intotriplet state population and proton transferpathways
Cite as: Struct. Dyn. 7, 024101 (2020); https://doi.org/10.1063/1.5143228Submitted: 20 December 2019 . Accepted: 29 February 2020 . Published Online: 17 March 2020
Jesper Norell , Michael Odelius , and Morgane Vacher
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Ultrafast dynamics of photo-excited2-thiopyridone: Theoretical insights into tripletstate population and proton transfer pathways
Cite as: Struct. Dyn. 7, 024101 (2020); doi: 10.1063/1.5143228Submitted: 20 December 2019 . Accepted: 29 February 2020 .Published Online: 17 March 2020
Jesper Norell,1,a) Michael Odelius,1,b) and Morgane Vacher2,3,c)
AFFILIATIONS1Department of Physics, AlbaNova University Center, Stockholm University, SE-106 91 Stockholm, Sweden2Department of Chemistry-Angstr€om Laboratory, Uppsala University, 75121 Uppsala, Sweden3Laboratoire CEISAM-UMR CNRS 6230, Universit�e de Nantes, 44300 Nantes, France
a)Author to whom correspondence should be addressed: [email protected])[email protected])[email protected]
ABSTRACT
Ultrafast non-adiabatic dynamics of the small heteroaromatic compound 2-thiopyridone has been studied with surface hopping simulationsbased on multi-configurational quantum chemistry. Initial excitation of the bright S2ðp;p�Þ state is found to promptly relax to S1ðn; p�)through in-plane motion. The subsequent dynamics are oppositely driven by out-of-plane motion, which results in both complex populationtransfers among all the available states and intersystem crossing predominantly through the “El-Sayed forbidden” S1ðn; p�) to T2ðn; p�)channel, through significant mixing of electronic excitation characters. Despite this complexity, the femto- to picosecond triplet population,expected from several spectroscopic measurements, is well described as a simple exponential decay of the singlet state manifold. No protontransfer is found in the reported trajectories, but two mechanisms for its possible mediation in previously reported experiments are proposedbased on the observed structural dynamics: (i) ultrafast intra-molecular transfer driven by the initially coherent in-plane motion and (ii)inter-molecular solvent-mediated transfer driven by the out-of-plane modes that dominate the later motion.
VC 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5143228
I. INTRODUCTION
Due to the importance of light induced processes in biomole-cules, in general, and in nucleic acids, in particular, the photo-chemistry of heteroaromatic compounds has been the subject ofextensive investigations.1 Among these, thiosubstituted (organosul-furic) compounds have gathered increasing interest from ultrafastscience due to their wide range of applications and rich excited-statedynamics.2–17 One such compound, 2-thiopyridone (2-TP, see Fig. 2),has primarily been studied as a compact model system for excited-state proton transfer (ESPT),18–24 which is related to, for instance,photo-protection mechanisms of DNA25 and pigmentation of thehuman skin.26
While it is long established that the nitrogen protonated 2-TPcan tautomerize into sulfur protonated 2-mercaptopyridine upon achange in the chemical environment (gas phase, solid, or solvated),27–31
it is only recently that time-resolved measurements18,20–22 have been
used to explicitly investigate the possibility for the corresponding UV-pumped process. In the measurement with the highest temporal resolu-tion, traces of N–H dissociation were found below picosecond (ps)timescales using N1s resonant inelastic x-ray scattering (RIXS), but, dueto limited statistics, the electronic states involved in the process couldnot be resolved.20 Two pico- to nanosecond (ns) measurements, per-formed using N1s22 and S1s21 near-edge x-ray absorption (NEXAFS),however, instead find the ESPT to be a nanosecond process, consistentwith previous vibrational measurements.18 In particular, our recentstudy,22 combining time-resolved N1s NEXAFS with spectrum simula-tions of valence-excited states, provided strong evidence for a dominantreaction pathway on these timescales, shared for S2 and S4 initial excita-tion, where ESPT results from nanosecond decay of the T1 state.Notably, none of the studies have been able to address whether theESPT occurs intra-molecularly or inter-molecularly through solvent-mediated formation of a deprotonated anion 2-TP�.
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The joint body of evidence for the ESPT pathway in 2-TP cur-rently contains several gaps, particularly with respect to the ultrafastdynamics that leads to triplet population. Highly related, as a culmina-tion of many previous experimental2–9 and theoretical10–17 efforts, thegroups of Crespo-Hern�andez and Gonz�alez recently offered a mecha-nistic explanation for the general trend of rapid and efficient tripletpopulation in thionated compounds as a stabilization that depends onthe localization of the electronic excitation.32 The spectroscopic mea-surements, based on UV absorption, were in this case supplementedwith ab initio simulations of the non-adiabatic molecular dynamics,where recent extensions of trajectory surface hopping methods33
allowed the authors to describe, with relative affordability, non-adiabatic dynamics with spin–orbit induced transitions.34–36 With acomputational description of the complete photo-chemical process, itcan, thereby, be interpreted in well-known chemical concepts such asmolecular orbitals, potential energy surfaces, and conical intersections,which may not be possible to similarly extract from measurements.
In the current work, we simulate the non-adiabatic moleculardynamics, including spin–orbit coupling induced transitions, ofphoto-excited 2-TP. This provides a link between the excited-statedynamics probed in previous time-resolved measurements18,20–22 andquantum chemical insights gained from previous simulations.18,22–24,31
Our main goal is to identify inherent aspects of the ultrafast dynamics,both electronic and structural, which result in the observed triplet pop-ulation and may drive ESPT along previously reported or alludedpathways at various timescales.
II. COMPUTATIONAL DETAILS
Non-adiabatic molecular dynamics of 2-TP was simulated by tra-jectory surface hopping33 as implemented in the SHARC code,34,35
version 1.01. The simulations included three singlet (S0, S1, and S2)and two triplet (T1 and T2) states, as denoted in the basis of molecularCoulomb Hamiltonian (MCH) states (i.e., with pure spin multiplicitiesas obtained directly from the electronic structure calculations) withpropagation performed in the spin-mixed basis of fully diagonal states.A time step of 0.5 femtoseconds (fs) was employed for the nucleardynamics, with 100 substeps for propagation of the electronic stateamplitudes. Non-adiabatic couplings were estimated from the overlapof electronic wave functions at different time steps, referred to as thelocal diabatic or overlap method.37–39 An energy based decoherencecorrection40 of 0.1 Hartree was further applied to correct for the artifi-cially high coherence between different electronic states otherwiseexpected in trajectory surface hopping frameworks. An ensemble of100 trajectories was simulated, with initial conditions sampled from aWigner distribution to reproduce the vibrational ground state of S0; allsimulations were initialized populating the S2 state.
The underlying electronic structure calculations were performedin OpenMolcas41 with a CASSCF(12, 10)42 setup that included: thefull p system (p1; p2; p3; pS; p�1; p�2; p�3) and the lone-pair nS todescribe the valence excitations, together with rN�H and r�N�H todescribe the potential breaking of the N–H bond, as visualized in Fig. 1.The same level of theory was also applied to (i) optimize the S0geometry and calculate its vibrational modes and vertical electronicexcitations and (ii) optimize pair-wise minimum energy crossingpoints (MECPs) [or, more specifically, minimum energy conicalintersections (MECIs) for states with the same spin multiplicity]between the electronic states. Second-order perturbation theory
corrections for the vertical excitation energies in theFranck–Condon geometry were additionally calculated using multi-state CASPT2.43,44 Scalar relativistic calculations using theDouglas–Kroll–Hess formulation45,46 was performed employing therelativistic ANO-RCC-VDZP47 basis set (which is shortly comparedto the larger ANO-RCC-VTZP basis in supplementary material Sec.S1) together with Cholesky factorization.48,49 Spin–orbit couplingelements were computed using an atomic mean field integral(AMFI)50 approach within the RASSI framework.51,52 Molecularorbitals were visualized with the luscus program.53
Further details of the complete computational setup, in the formof example inputs, are provided in the supplementary material.
III. RESULTS AND DISCUSSIONA. Electronic states
To describe and rationalize the non-adiabatic dynamics, we firstintroduce the electronic states that will be involved. An overview ofthe first four excited states of 2-TP and their potential energy surfacesin the region of the explored dynamics, schematically constructed inaccordance with our later drawn conclusions, are given in Fig. 2. Theelectronic excitation energies computed in the Franck–Condon geom-etry at CASSCF and CASPT2 levels of theory are gathered in TableI(a). The singlet manifold consists of the dark S1ðn; p�Þ and the brightS2ðp; p�Þ, whereas the triplet manifold contains T1ðp; p�Þ andT2ðn; p�Þ. Including dynamic correlation with perturbation theoryleads to energy differences of less than 0.2 eV for singlet states and abit larger for triplet states. Importantly, the electronic state charactersand their energy ordering remain the same upon adding dynamic cor-relation. It is interesting to remark that the energy ordering of excita-tion characters (ðn; p�Þ and ðp; p�Þ) is inverted between the twomanifolds (singlet and triplet) and all states are found in a narrowenergy range, in particular, the lowest three, at both levels of theory.While the excitation characters may be strictly identified for all statesin the currently presented Franck–Condon analysis, we note thatthe same does not hold through the later presented trajectories. Fordiscussion of the non-adiabatic dynamics, the states will, therefore, ingeneral, simply be denoted by their energy ordered MCH state labels,i.e., without specified excitation character.
In a single-electron picture, all the states nominally result fromexcitation into the lowest unoccupied molecular orbital (LUMO) p�1,
FIG. 1. Active molecular orbitals in the CASSCF calculations, here shown for theS0 optimized geometry. The studied valence states can nominally be assigned toexcitation from the sulfur dominated pS (S2 and T1) and the sulfur lone-pair nS (S1and T2) into p�1 .
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S2 and T1 from the sulfur-dominated pS, S1 and T2 from the in-planesulfur lone-pair nS. Of particular relevance for later interpretation,we note that pS and nS correspond to the nearly degenerate highestoccupied molecular orbital (HOMO) and HOMO-1 in a single-determinant description, respectively,23 where the sulfur dominance ofthe former makes it comparable to an out-of-plane lone-pair.Visualizations of all the active molecular orbitals are found in Fig. 1.
B. Electronic dynamics
Non-adiabatic molecular dynamics simulations were performedto investigate the relaxation upon the population of the S2 bright state,with CASSCF as the underlying electronic structure method. A num-ber of studies, based on ab initiomultiple spawning,54–63 in particular,but also on other methods,17,64 have previously demonstrated the abil-ity of CASPT2 based simulations of non-adiabatic dynamics to yield
even quantitative results. Yet, due to both the difficulty in the imple-mentation of CASPT2 gradients and their steep computational cost,simulations that include spin–orbit coupling have instead mainly beenbased on the CASSCF level of theory.65–68 Due to the lack of dynamiccorrelation in the current description, later conclusions will primarilybe drawn about qualitative rather than quantitative aspects of the sim-ulated dynamics. The simulated trajectories were all started in thebright S2ðp; p�Þ state, which has previously been experimentallypumped with 343nm (Ref. 22) and 400 nm (Ref. 21) lasers and sharesa common reaction pathway on picosecond timescales and longerwith the second bright S4ðp;p�Þ state,22 pumped instead with 258nm(Ref. 18) and 266nm (Ref. 22) lasers.
From the ensemble of trajectories, we first consider the kineticsof the electronic state population transfers. The relative populations ofthe MCH states as a function of time are shown in Fig. 3 together witha kinetic model fit. Comparison of different state representations (seesupplementary material Sec. S3) displays only small differences for theoverall evolution of the populations, which thereby demonstrates astability of the populations themselves despite later discussed compli-cations in the electronic state characters. The main clues to the reac-tion pathway are found in Table I(b), which enumerates the numberof surface hops between the states. The dominant pathway is, in thisway, readily identified as a sequential decay in reverse energy order,i.e., S2 to S1 to T2 to T1, hereafter referred to as the “main” pathway.Yet, the total kinetics cannot be so easily described for at least tworeasons: first, because of the numerous “backward” transitions withinthe main pathway, which disallows the population transfer to be accu-rately modeled with a simple exponential “forward” decay and second,due to the existence of several “minority” pathways, which, forinstance, partially re-populates S0 at very early times.
Our attempts to fit the obtained populations with a kinetic modelare described in more detail in the supplementary material, Sec. S4. Inshort, we find that a model with nine different rate constants (threemain forward, three main backward, and three minority forward tran-sitions), as schematically depicted in Fig. 2 and with the resulting fitshown in Fig. 3, is necessary to capture all qualitative aspects of thekinetics. Consequently, the lifetime of individual electronic states can
FIG. 2. Schematic potential energy surfaces in the region of 2-TP photo-excitation(left). Schematic of the kinetic model derived from the simulations and fitted to theelectronic state populations. Solid lines indicate the main pathway and dashed linesthe minority pathways (right).
TABLE I. (a) Excitation energies of the electronic states in the Franck–Condonregion. Upper row: directly from CASSCF calculations, as employed for the dynam-ics. Lower row in parentheses: with added multistate CASPT2 correction. (b) Totalnumber of surface hops from the old MCH state (rows) to a new MCH state (col-umns) found in the 100 trajectories. Only hops with 10 or more occurrences areshown, and the forward transitions of the main pathway are emphasized in bold.
(a) Excitation energies in units of eV.
S1ðn;p�Þ S2ðp;p�Þ T1ðp; p�Þ T2ðn;p�Þ
3.16 3.82 2.64 2.90(3.34) (3.64) (2.92) (3.31)
(b) Total number of MCH surface hops.
From To S0 S1 S2 T1 T2
S0 … … … … …S1 13 … 348 … 298S2 … 441 … … 10T1 … … … … 4849T2 … 251 … 4869 …
FIG. 3. Electronic state populations from the 100 trajectory ensemble (thick shadedlines) compared to the fit obtained with the full kinetic model (thin opaque lines, seesupplementary material Sec. S4 for further details).
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be neither simply nor robustly extracted, as they result from a complexbalance between backward and forward transfers of population andare highly sensitive to changes of the fitted model. We assign the com-plexity in the population kinetics to primarily result from large similar-ities between the states, both in their excitation energies and excitationcharacters, as elaborated in this section and Sec. IIIC.
The small energy splitting of the electronic states, already notedfrom their vertical excitations, is presumably the main cause for thesignificant contribution of backward transitions within the main path-way. An estimate of how the energy splittings develop over time, basedon the spin–orbit coupled state representation wherein the SHARCdynamics are propagated, is presented in supplementary material Sec.S2. In short, following large fluctuations within the first �100 fs, themean values of the splittings stabilize toward roughly 0.4 eV (S1 to T2)and 0.3 eV (T1 to T2). As a result, the S1, T1, and T2 states share com-parable populations at 1 ps, in contrast to multiple studies of similarsystems where a single T1 state dominates at such timescales.14,17,32
The increased tendency for backward transitions can also arise fromlimited “funneling” toward the associated conical intersection in the“upper” state and subsequently away from it in the “lower” state, aspreviously observed for LiH2.
69 Indeed, comparing the MECIs (whichrepresents well the hopping geometries as shown in Sec. IIIC) forS2–S1 and T2–T1, the former is categorized as peaked and bifurcatingand the latter as a sloped single-path.70 That is, the singlet transition(with fewer backward occurrences) takes place around a minimum ofthe upper state surface with multiple preferred relaxation directions onthe lower surface (which should both promote funneling), whereas thetriplet transition (with more backward occurrences) takes place on aslope of the upper state with a single downwards pathway in the lowerstate (which may both inhibit funneling). The tendency for backwardtransfer of population, in general, would likely be reduced in a solventby rapid dissipation of kinetic energy and thereby not be directly relat-able to previous experiments.18,20–22
In contrast to the energies, the similarities in excitation charactercannot at all be captured within a Franck–Condon picture. The effectis instead most clearly demonstrated by how intersystem crossing(ISC) is in the current case dominated by S1 to T2 transfer, which isEl-Sayed forbidden as the two states share the same nominal electronicconfiguration.71,72 The ISC must, therefore, be driven by symmetry-breaking in the structural dynamics, where the already noted similarityin both energy and localization of the nS and pS orbitals then allowsfor significant mixing of the electronic characters. Based on a singlepoint calculation of the MECP geometry between the S1 and T2 states(which represents well the hopping geometries as shown in Sec. III C),we find as leading terms of the configuration expansions for the statesS1¼ 0:69ðnS;p�Þþ0:58ðpS;p�Þ and T2¼ 0:73ðnS;p�Þ�0:58ðpS;p�Þ.The two states are, thereby, essentially orthogonal in their spatial wavefunctions, similarly as expected for the “El-Sayed allowed” transitions,but consist, in contrast, of heavily mixed contributions from in-planeand out-of-plane excitation characters. Similarly, for a sampling overfive randomly selected hop-inducing geometries (as introduced in theSec. IIIC) for the same transition, the weight of the dominant configu-ration has a mean (standard deviation) of 0.63 (60.13) and 0.81(60.14) for the S1 and T2 states, respectively. It can, for these reasons,also be assumed that all the electronic states, as they all nominallyinvolve excitations between the same orbitals, similarly carry a mixedcharacter throughout parts of the non-adiabatic dynamics.
While the kinetics of the individual electronic states appear to bedifficult to model, a simple trend emerges when they are summedtogether according to their spin multiplicities. The decay of the singletmanifold population, as shown in Fig. 4, can be almost as welldescribed with a single exponential fit as with the full kinetic model.The simplified fit allows us to better quantify the triplet state popula-tion transfer, with the rate constant that translates into an �1 pslifetime of the singlet manifold. The result is consistent with x-raymeasurements in solutions, where T1 appears to be dominantly popu-lated within the time resolution of �20 ps.21,22 The trend of the effi-cient triplet population upon thionation observed for a number ofcompounds,32 thereby, appears to hold also with the active involve-ment of more electronic states in the reaction pathway. Further extrap-olated within the 2-TP system, this trend would explain why thesame reaction pathway was also observed for S4 excitation at pico- tonanosecond scales,22 through similar ultrafast relaxation to the tripletmanifold.
C. Structural dynamics
With an overview of the population transfer kinetics, we nowturn to the structural dynamics. To rationalize how the structuraldistortions drive the electronic transitions, we first consider the “hop-inducing” geometries. Figure 5 shows, for each forward transitionwithin the main and the minority pathways, the mean value l andstandard deviation r of all geometries that precede the correspondingsurface hops. The backward transitions, as shown in supplementarymaterial Fig. S6, show no appreciable differences. The geometriesare expressed in normal mode coordinates, some of which are visual-ized in Fig. 6, while the rest can be found in supplementary materialFigs. S7–S9. The data are further compared with pair-wise MECPgeometries, visualized in supplementary material Fig. S5.
Starting with the main pathway, the initial internal conversion(IC) from S2 to S1 occurs through minimal structural distortion.This can be rationalized by their small energy gap already in theFranck–Condon region and is consistent with the ultrafast populationtransfer from S2 to S1 (see Fig. 3). In contrast, the S1 to T2 ISC is driven
FIG. 4. Singlet and triplet state populations (summed over individual MCH states,thick shaded lines) compared to the full kinetic model fit (thin full lines, see supple-mentary material Sec. S4 for further details) and a simple exponential fit with a life-time of s ¼ 1058 fs �1 ps of the singlet manifold (dashed lines).
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by strong distortions in almost all out-of-plane modes (blue dots inFig. 5). This is, as previously discussed, necessary to enable the spin-flip through mixing of electronic state characters, which would, other-wise, be highly inefficient between a singlet and triplet state of thesame configuration.71,72 A large number of apparent transitions withinthe triplet manifold then proceed through similar out-of-planemotion. Yet, considering the minuscule energy separation of the T1
and T2 states already in the Franck–Condon region and the charactermixing induced by the symmetry breaking, it is likely that most ofthese reflect a rapid and erratic energy re-ordering rather than transi-tions between well distinguishable states.
The first minority pathway results from S2 to T2 ISC throughsmall structural distortions. It, thereby, represents the “El-Sayedefficient”71,72 ðp;p�Þ to ðn; p�Þ ISC, in contrast to the El-Sayed forbid-den ðn;p�Þ to ðn;p�Þ ISC of the main pathway. In further contrast,this ISC channel also competes with the S2 to S1 IC, as S2 is not thelowest state within the manifold of excited singlets. An appreciableISC yield already from the S2 state, thereby, appears to directly reflectthe increased ISC rate by the heavy atom effect of the sulfur. Still, asignificant majority of ISC occur after relaxation within the singletmanifold to S1, as traditionally expected.
The second minority pathway results from S1 to S0 IC. To sepa-rate this from the main pathway that instead proceeds through ISC,we denote the minority pathway trajectories with an alternative speciesS01. While the split between S1 and S01 is for fitting purposes imple-mented in the decay from S2, we deduce that it actually occurs in thesubsequent dynamics on the S1 surface as presented in Fig. 2. This asS1 and S
01 are reached through highly comparable geometries [compare
Figs. 5(a) and 5(d)] but decays through more distinguishable geome-tries [compare Figs. 5(b) and 5(e)] on different timescales: S01 to S0occurs on average after 114 fs, whereas S1 to T2 occurs on average after
369 fs. The splitting is, therefore, likely to be (partially) induced by thebifurcating character of the S2–S1 MECI, mentioned in Sec. III B.
The dynamical picture based on the hop-inducing geometriescan be compared with a static perspective provided by the MECPgeometries also presented in Fig. 5. We note that the MECP data forout-of-plane modes, due to the planar symmetry that makes their signarbitrary, must be compared to the total distortions enabled by boththe mean values and standard deviations of the hop statistics. Theexception to this is mode 8 and any other mode coherently phased toit, to which the signs were aligned to facilitate comparison. For themain pathway, we mainly note that the results appear to be in overallacceptable agreement, i.e., the transitions appear to, in most cases,occur “close” to the MECP, which thereby validates the argumentationabout electronic state characters for the associated ICs and ISCinvoked in the last section, based on single point calculations at theMECPs (MECIs). Regrettably, the S2 to T2 MECP of the first minoritypathway could not be converged, due to the complications that arisefrom S1 being energetically situated between the two states. Finally, theS1 to S0 MECI predicts much larger distortion, in several modes, thanseen in the dynamics. This can be understood by how the transitions,on average, occur for a potential energy of 1.33 eV above the MECIand results in a 0.69 eV increase in kinetic energy, which shows thatthe transitions typically occur far from both the MECI and any degen-eracy between the two surfaces.
Finally, we consider the structural dynamics also in a fully time-dependent picture. Figure 6 presents the time-evolution of selectednormal mode coordinates (i.e., those that display notable changes inamplitude over time and/or clear coherence) over the whole ensembleof trajectories. To gain some measure of the coherence between trajec-tories, we compare the mean values of the signed and unsigned coordi-nates. Equal amplitudes (of, e.g., a periodic oscillation or systematic
FIG. 5. Transition-inducing molecular geometries: comparison of the molecular geometries that precede a surface hop in the SHARC simulations (hop) to MECP geometries.The geometries are expressed as distortions along the normal mode coordinates of the electronic ground state, with each data point as the projection (12� 3 dimensional sca-lar product) pi ¼ hD~r geo � Dr NM;ii between the molecular geometry distortion D~r geo ¼~r geo �~r Franck�Condon and the normalized normal mode displacement vector Dr NM;i ofmode i. Green dots mark in-plane modes and blue dots out-of-plane modes. The out-of-plane modes were, for each geometry, if needed, aligned to a positive phase of mode8 by a mirroring through the molecular plane, to facilitate comparison to the MECPs.
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drift) of the two then signal a completely coherent motion, whereasa vanishing average of the signed coordinates oppositely signals a com-plete dephasing.
Based on the described analysis, the following picture emerges:the dynamics are initially dominated by coherent in-plane H rocking,particularly in modes 17 and 22. As the S1 state reaches its peak popu-lation and starts to decay, these modes dephase, as signaled by a rapiddecrease in amplitude for the signed coordinates, whereas the ampli-tudes of the unsigned coordinates remain comparable. Concurrently,out-of-plane motion steadily increases over the first 100 fs and thereaf-ter remains comparable throughout the remainder of the simulations.This is primarily seen from N–H centric modes 7 and 8 with unsignedvalues that drastically increase before flattening out. Due to the arbi-trariness in the sign of the out-of-plane modes, however, the signedvalues appear to be artificially dephased. Within the same time frame,mode 30, which is essentially a pure N–H stretch, decreases notably inamplitude, i.e., the bond contracts from the S1 state and on. Finally, anadditional number of H rocking modes, in particular, 2, 20, and 21,display coherent motion over the whole time range. A partial dephas-ing, from the initially high coherence, occurs steadily over time, seenfrom a larger decrease in the sign than the unsigned coordinates, butwith clear oscillations that remain even to the end of the simulations.
D. Proton transfer
A complete ESPT is not found in any of the currently presentedtrajectories. Yet, large variations in the bonding structure are stillobserved, as demonstrated by the maximal rN�H value of 1.41 A andthe minimal rS�H value of 1.99 A, as compared to their means (withstandard deviations) of 1.03 (60.06) A and 2.78 (60:22Þ A. Whilelimitations in the statistics still cannot be excluded as a possible cause,this suggests that the absence of ESPT, in the current work, mightinstead be the result of limitations in the computational model. Suchlimitations could include (but not necessarily be limited to) exclusionof solvent molecules (which might, in fact, mediate both the protondetachment and reattachment in the measurements), insufficient flexi-bility in the electronic structure method, or limitations imposed by theclassical dynamics. Nevertheless, the observed electronic and structuraldynamics still allow us to speculate about which aspects of the photo-dynamics could promote ESPT.
Starting from the Franck–Condon picture, it is unclear why anyof the electronic excitations should promote ESPT, as they all appearto transfer electronic density from the sulfur to the nitrogen site, whichshould increase the basicity of the former and acidity of the latter. AMulliken analysis, in fact, shows that the initial �0.46 net charge ofthe sulfur site increases notably to �0.04 (S1), �0.25 (S2), �0.19 (T1),and �0.09 (T2) upon excitation, with smaller effects for the nitrogensite. This clearly suggests that the ESPT must instead result fromdynamical or external factors.
In terms of the structural dynamics that occur on short timescales(�100 fs), mode 22 is most likely to promote ESPT as it clearly rocksthe N–H and C–S bonds with respect to each other, which could pro-vide a channel for ultrafast intra-molecular ESPT before the dephasingof modes 17 and 22 sets in. Such a mechanism would be consistentwith the weak signature of N–H cleavage previously observed usingfemtosecond RIXS.20 It could, however, prove to be difficult to satisfac-torily investigate using computational models, as it may require both aquantum description of the dynamics (to, for instance, account for
FIG. 6. Time evolution of selected normal mode coordinate projections pi (asdescribed in Fig. 5). The blue colored heat plots represent the binned trajectorydensity for a given time. Orange lines mark the ensemble average and blacklines the ensemble average of the absolute values. The normal mode coordi-nates are visualized to the right, as an orange distortion of the optimizedgeometry.
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tunneling of the proton through a classically forbidden barrier) andsignificant statistics to either confirm or reject. Modes 2, 20, and 21could similarly participate in an intra-molecular transfer as they alsoaffect the S–H distance, but they all exhibit time periods of roughly150 fs, i.e., comparable to the time point where out-of-plane motioninstead sets in to dominate.
In less than 100 fs, the N–H bond on average contracts, whichshould inhibit its cleavage. ESPT on longer timescales is, therefore,likely to be mediated by external factors, which strongly points towardinteractions with one or several solvent molecules. The bond contrac-tion onsets together with the strong out-of-plane motions, in particu-lar, N–H centered modes 7 and 8, which, in a solution environment,could strongly affect the proton’s coordination with the solvent. In ourpreviously mentioned Born–Oppenheimer molecular dynamicsstudy,23 we further found both that the compound exhibits stronghydrogen bonding with aqueous solutions and that the nitrogen sitecoordinated water molecule of the anion species 2-TP� interchangedthrough a rotation that realigned the molecular plane with respect tothe solvent. A similar mechanism, i.e., solvent re-coordination throughout-of-plane motion, could, therefore, also be responsible for solvent-mediated ESPT at timescales above 100 fs. This would be consistentwith pico- to nanosecond NEXAFS measurements, which find theESPT to be a rare event, presumably mediated by large fluctuationsthat concurrently result in T1 to S0 relaxation.
Based on currently presented and recent insights,23,24 we finallywant to point out two clear ways that time-resolved spectroscopycould be constructively employed to shed further light on the ESPT of2-TP: (i) femtosecond timescale measurements, with a probe capableof resolving either electronic states or vibrational modes, would be par-ticularly useful to evaluate speculations about the ESPT mechanismand pathway from current and previous work.18–20 (ii) Gas phase mea-surements on any timescale from femto- to pico- to nanoseconds,with a probe sensitive to the nitrogen and/or sulfur protonation, couldconclusively determine whether a solvent is necessary to mediate theESPT. Insights derived from such experiments could, possibly, fill allthe significant gaps in the current understanding of the pathway tofully “solve” the ESPT process of 2-TP.
IV. CONCLUSIONS
Non-adiabatic dynamics of 2-TP have been simulated by surfacehopping simulations including spin–orbit induced transitions, model-ing the UV-induced excited-state dynamics probed in multiple previ-ous time-resolved spectroscopic measurements.18,20–22
An ultrafast S2 to S1 population transfer, mediated by coherentin-plane vibrations, is followed by complex population kinetics thatappreciably populates all the energetically available states throughmultiple pathways. The complexity results from out-of-plane struc-tural dynamics that onset in the S1 state and significantly mixes theexcitation character of the electronic states, which, in particular, drivesISC through the El-Sayed forbidden S1ðn; p�) to T2ðn; p�) channel.The transfer of the population from singlets to triplets, once summedover the individual states, can nevertheless be well described as a sim-ple exponential decay with a lifetime of �1 ps. This follows the trendof efficient triplet population observed for multiple similar thio-substituted compounds and offers rationalization for why the sameexcited-stated dynamics have been previously observed for both S2and S4 excitation of the system, on picosecond scales and longer.22
While no ESPT was observed in the current work, two aspects ofthe structural dynamics are suggested as possible mediators for it inpreviously reported experiments: initial coherent in-plane motion forultrafast (�100 fs) intra-molecular transfer and out-of-plane motionfor solvent-mediated transfer at longer timescales. With this in mind,we suggest two ways in which time-resolved spectroscopy could beemployed to address important remaining questions about the ESPTpathway.
SUPPLEMENTARY MATERIAL
See the supplementary material for comparison to dynamics per-formed with a larger basis set, estimation of state energy splittings inthe dynamics, comparison of electronic state populations in other staterepresentations, comparison to other kinetic model fits, visualizationof the MECP geometries, visualization of hop-inducing geometries forbackward transitions, visualization of normal modes of the electronicground state, and example input files for the OpenMolcas andSHARC computations.
ACKNOWLEDGMENTS
This work was supported by the Swedish Research Council(Contract No. VR 2015-03956), the Carl Tryggers Foundation(Contract No. CTS18:285), and the Helmholtz Virtual InstituteVI419 “Dynamic Pathways in Multidimensional Landscapes.” Thecomputations were performed on resources provided by theSwedish National Infrastructure for Computing (SNIC) underallocation SNIC2019-1-9 at the Swedish National SupercomputerCenter (NSC), the High Performance Computer Center North(HPC2N), and the Chalmers Centre for Computational Science andEngineering (C3SE). We thank Markus Kowalewski for helpfuldiscussions and Sebastian Mai for assistance in using SHARC.
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