A Fragment Diabatization Linear Vibronic Coupling Model For

A Fragment Diabatization Linear Vibronic Coupling Model for Quantum Dynamics of Multichromophoric Systems: Population of the Charge Transfer State in the Photoexcited Guanine Cytosine Pair

James A. Green,† Martha Yaghoubi Jouybari,‡ Haritha Asha,† Fabrizio Santoro,∗,‡ and Roberto Improta∗,†

†Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), via Mezzocannone 16, I-80136 Napoli, Italy ‡Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy

E-mail: [email protected]; [email protected]

Abstract We introduce a method (FrD-LVC) based on a fragment diabatization (FrD) for the parametrization of a Linear Vibronic Coupling (LVC) model suitable for studying the photophysics of multichromophore systems. In combination with effective quantum dynamics (QD) propagations with multilayer multiconfigurational time-dependent Hartree (ML-MCTDH), the FrD-LVC approach gives access to the study of the competition between intra-chromophore decays, like those at conical intersections, and inter-chromophore processes, like exciton local- ization/delocalization and the involvement of charge transfer (CT) states. We used FrD-LVC parametrized with TD-DFT calculations, adopting either CAM-B3LYP or ωB97X-D functionals, to study the ultrafast photoexcited QD of a Guanine-Cytosine (GC) hydrogen bonded pair, within a Watson-Crick arrangement, considering up to 12 coupled diabatic electronic states and the effect of all the 99 vibrational coordinates. The bright excited states localized on C and, especially, on G are predicted to be strongly coupled to the G→C CT state which is efficiently and quickly populated after an excitation to any of the four lowest energy bright local excited states. Our QD simulations show that more than 80% of the excited population on G and ∼50 % of that on C decays to this CT state in less than 50 fs. We investigate the role of vibronic effects in the population of the CT state and show it depends mainly on its large reorganization energy so that it can occur even when it is significantly less stable than the bright states in the Franck-Condon region. At the same time, we document that the formation of the GC pair almost suppresses the involvement of dark nπ∗ excited states in the photoactivated dynamics.

1 Introduction These systems are often described within an excitonic picture, where the focus is usually The excited state dynamics of multichro- on inter-molecular processes, like the transfer mophore systems rules many fundamental of energy or charge from one chromophore to biochemical and technological phenomena.1–9 another, or the delocalization of excited states

1 among many units or “sites”. Model Hamil- ure1). GC constitutes ∼40% of the hu- tonians have been proposed to describe these man genome and its photoactivated behav- processes accounting for electronic couplings ior has been thoroughly investigated in the (often considered independent of the nuclear gas phase,32–41 in chloroform solution,42–46 and coordinates) and vibrational motions, along in DNA duplexes,39,40,47,48 due to its possible “tuning modes” leading toward the energy min- involvement in the Proton Coupled Electron ima of the different states.7,8,10,11 However, in Transfer (PCET) processes in DNA.49–51 Time- many cases, each single chromophore is also resolved (TR) experiments in the gas phase characterized by a rich intrinsic dynamics, with show that when GC is in a WC arrangement, internal conversion or inter-system crossing be- after a UV pulse, the absorption of the infrared tween local excitations (LEs, such as bright probe is broad and featureless, suggesting an ππ∗ and dark nπ∗ states). For certain multi- ultrashort excited state lifetime.52 According to chromophore systems, for example DNA, these the seminal contributions by Sobolewski, Dom- intra-molecular decays of the individual units cke et al., a very effective PCET process is in- are actually competitive with inter-molecular deed operative.32,33 The lowest energy bright processes.1–4 When such molecular processes excited states of GC decay to an inter-molecular are ultrafast, they usually occur at Conical charge transfer (CT) quasi-dark excited state Intersections (CoIs) of the excited potential G+C− (G→C), which, in turn, can undergo to energy surfaces (PESs). If the chromophores a inter-molecular proton transfer (PT). The lat- are rigid enough, the essential features of the ter involves the transfer of the H1 atom from dynamics can be captured with simple vibronic Gua-N1 to Cyt-N3 (see Figure1), and is the coupling Hamiltonian models,12 like the lin- doorway for a sub-ps ground state recovery.32,33 ear vibronic coupling (LVC) model, where CoIs Such combined PCET process should be op- arise from the combined action of tuning modes erative also in low-polar solvents,42,43,45 and and coupling modes. its involvement in DNA is also matter of de- In this contribution, we introduce an auto- bate.1,47,48 Many computational dynamics stud- matic parametrization of a generalized LVC ies have thus been devoted to simulate the pho- model of multichromophore systems using a toactivated dynamics of GC in different envi- fragment based diabatization (FrD-LVC) that ronments,34–36,39,40,47 but, to the best of our allows the investigation of the competition be- knowledge, without considering quantum nu- tween intra-molecular and inter-molecular pro- clear effects. cesses. LVC models have attracted renewed In this study we focus on the first part of this interest recently, as a cost effective method process, i.e. the possible population of the CT to study nonadiabatic spectroscopy and in- state, using our FrD-LVC Hamiltonian in com- tramolecular excited state dynamics.8,9,13–28 On bination with quantum dynamics (QD) simula- the other side, fragment-based models are pop- tions to explore the excited state dynamics of ular approaches to study the excited state dy- GC following the excitation to the four lowest namics of multichromophore systems,8,9,22–31 energy bright excited states. The PCET reac- but in most of their implementations they con- tion occurs essentially on the PES of the CT sider each single chromophore (site) as charac- state,32,33 therefore it is fundamental to assess terized by a single relevant excited state, or few on which timescale it is populated, and what states but without an internal (nonadiabatic) are the main vibronic effects mediating this pro- dynamics. cess. As a first test application of the FrD-LVC This work gives us the opportunity to tackle method, we choose to study a minimal, yet another crucial issue in the field of the photo- extremely relevant, system: the dimer formed physics of nucleic acids, namely the effect that by Guanine and Cytosine connected by three WC hydrogen bond pairing has on the popu- hydrogen bonds in a Watson and Crick (WC) lation of the dark nπ∗ states localized on indi- arrangement, hereafter simply GC (see Fig- vidual nucleobases.1 Actually, there are several

2 computational indications that in the gas phase cytosine,15–17 no significant population trans- a significant population transfer to the dark nπ∗ fer to the dark nπ∗ states is predicted. This occurs for photoexcited Cytosine.14–17,53 More- study provides, at full QD level, new insights on over, the spectral signature of a dark state is the interplay between electronic and vibrational found for Cytosine and its derivatives in chlo- degrees of freedom in a process of crucial bio- roform54 and in water55,56 and it has been pro- chemical interest. At the same time, it shows posed that this state is populated also within that FrD-LVC, thanks to its flexibility and rel- DNA duplex.57 atively low computational cost, can be a very In this contribution we thus describe our useful tool for the study of the photoactivated methodological approach, focusing on the dynamics of multichromophore systems. new developments, and we use it to study the photoexcited state dynamics of the WC GC pair formed by 1-methylcytosine and 2 Methods 9-methylguanine, i.e. modeling the sugars The approach taken in the present work is present in the nucleotide by methyl groups. a combination of our fragment diabatization Thanks to the effectiveness of parametriza- scheme to parametrize a purely electronic ex- tion of the FrD-LVC Hamiltonian from time- citonic model in Ref. 63, and the diabatiza- dependent density functional theory (TD- tion scheme to parametrize a LVC model in DFT), and the potentiality of the multi-layer Refs. 14 and 15. The LVC Hamiltonian for a extension of the multiconfiguration time de- coupled set of diabatic electronic states |di = pendent Hartree (ML-MCTDH) method for (|d i , |d i ,..., |d i) may be written as wavepacket propagation, we included up to 1 2 N 12 electronic states and all the 99 vibrational X H = (K + V d(q) |d i hd |)+ modes of the system. However, since our Hamil- ii i i i tonian is not suited to describe CoIs at very (1) X d distorted geometries, our simulations do not in- Vij (q)(|dii hdj| + |dji hdi|), clude the decays to the ground state, which for i,j>i both the bases are known to occur at strongly where q are the dimensionless normal mode non-planar CoIs on the sub-ps timescale in coordinates, defined on the ground electronic gas-phase.1 Therefore, we will focus on the state S0, with conjugate momenta p. The ki- ultrafast timescale (∼ 100 fs) when large out- netic K and potential V terms of the Hamilto- of-plane deviations of the molecular structure nian are defined as are not expected, and the involvement of triplet 58–60 1 excited states is marginal. K = pT Ωp (2) We use TD-DFT as a reference electronic 2 method, with two different functionals: CAM- 61 62 1 B3LYP and ωB97X-D,. These two widely V d(q) = Ed(0) + λT q + qT Ωq (3) adopted, long range-corrected functionals pro- ii ii ii 2 vide a different estimate of the relative stabil- d d T ity of the lowest energy G→C CT state, thus Vij (q) = Eij(0) + λijq, (4) providing the opportunity of checking the de- with Ω the diagonal matrix of normal mode fre- pendence of our predictions on this seemingly quencies ωα, λij the vector of linear coupling crucial parameter. Quantum dynamical sim- d constants, Eii(0) the diabatic energy of state ulations, starting from the four lowest energy d i at the reference geometry (0), and Eij(0) an bright excited states, predict a fast (on the ≤ 50 electronic coupling constant between diabatic fs time scale) population transfer to the lowest states i and j at the reference geometry. No- energy CT state, which is particularly effective tice that this latter term does not appear in (≥80%) when exciting the bright excited states the standard LVC approach,12 however in the of G. In contrast to what happens with isolated FrD-LVC approach the diabatic states may be

3 Figure 1: Schematic drawing and atom labeling of the computational model of the Guanosine- Cytidine dimer in a Watson-Crick arrangement. Sugar rings are modelled by the methyl groups bonded at Gua-N9 and Cyt-N1. coupled electronically even at the reference ge- batic energies of the MC computed at the ref- ometry, as will be revealed below. erence geometry Following the procedure established in Ref. MC MC MC 63, we define diabatic states of some mul- H[a (0)] = diag(E1 (0),E2 (0), MC (6) tichromophoric complex (MC), consisting of ...,EM (0)), Nfrag fragments on the basis of reference states |Rfragsi of either the adiabatic states of the frag- to obtain the diabatic matrix ments (for LEs), or orbital transitions between T MC the fragments (for CT states). The diabatic H[d(0)] = D(0) H[a (0)]D(0), (7) states are then obtained via a transformation d which contains the diabatic energies Eii(0) on of the adiabatic states of the MC d the diagonal, and electronic couplings Eij(0) on |di = |aMCi D the off diagonal. In fact, while for a ‘standard’ (5) MC T T − 1 LVC approach it is customary to define the N = |a i S (SS ) 2 diabatic states to be identical to N adiabatic where S = hRfrags|aMCi is the overlap of the states at the reference geometry, in the FrD- reference states of the fragments with the adia- LVC approach diabatic states defined on the batic states of the MC. Notice that S is not nec- fragments are in general not eigenstates of the essarily a square matrix, and in general, in or- electronic Hamiltonian of the MC, and there- der to properly project the selected N diabatic fore they exhibit non vanishing couplings. states one will need to consider M adiabatic To obtain the linear coupling constants λij, states at the reference geometry with M > N. we displace each normal coordinate α by some The derivation of the transformation matrix D small value ±∆α and perform a numerical dif- in terms of the overlap matrix S uses Löwdin ferentiation re-orthogonalisation, and has been defined in d d d ∂Vij (q) Eij(∆α) − Eij(−∆α) our previous works.15,63 λij,α = ' . (8) ∂qα 2∆α Performing the transformation at the reference geometry, i.e. S(0) = hRfrags(0)|aMC(0)i, The diabatic energies and electronic couplings d yields the transformation matrix D(0). This at displaced geometries Eij(∆α) are obtained can be applied to the diagonal matrix of adia- by performing the diabatization based on max-

4 imum overlap of the reference states with the individual fragments at their own equilibrium diabatic states at displaced geometry. This geometry. Then, the normal mode coordinates amounts to computing the overlap of the ref- are those of the individual fragments. Option erence states at equilibrium geometry with the (i) is appropriate when vibrational modes are adiabatic states of the MC at displaced geom- strongly coupled between fragments, such as frags MC etry, i.e. S(∆α) = hR (0)|a (∆α)i, and when strong hydrogen bonds are present. The performing the transformation in Eq.5. The disadvantage would be an expensive optimisa- transformation matrix at displaced geometry tion and frequency calculation for a large MC. D(∆α), can be applied to the diagonal matrix Option (ii) is appropriate when the converse is of adiabatic energies of the MC at displaced ge- true, and vibrational modes are generally local- ometry ized to individual sites. This therefore neglects low frequency inter-fragment vibrations, how- MC MC MC H[a (∆α)] = diag(E1 (∆α),E2 (∆α), ever they could be re-introduced by deﬁning a MC (9) ...,EM (∆α)), proper number of degrees of freedom describ- ing such vibrations between rigid monomers. to obtain the diabatic matrix at displaced ge- It should be noted that option (ii) would still ometry capture the vibronic coupling between excita-

T MC tions located on different sites that are due to H[d(∆α)] = D(∆α) H[a (∆α)]D(∆α). the vibrations of a single site. One could also (10) imagine a combination of options (i) and (ii), This diabatic Hamiltonian matrix contains where the entire MC is divided into sub-systems d d Eii(∆α) on the diagonal and Eij(∆α) on the off of multiple fragments, and the sub-system is diagonal, exactly analogous to Eq.7 at the ref- parametrized according to option (i) and then erence geometry. These values can then be used the overall MC according to option (ii). Indeed, in Eq.8 to obtain the linear coupling constants. the flexibility of the fragment diabatization ap- In principle any electronic structure method proach allows one to choose the number of frag- can be used for this diabatization, provid- ments (and number of states) to include to best ing the reference states and overlap ma- balance accuracy and efficiency, as was demon- trix can be appropriately defined. Re- strated in our excitonic model application.63 cently, for instance, some of us adopted In the present application of the GC pair, we RASPT2/RASSCF to parametrize a LVC choose option (i) due to the relatively small 18 model to study photoexcited pyrene. How- size of the system, and the strong hydrogen ever, as previously done for DNA nucleobases bonds between the pair leading to vibrational 13–15,17,63 and G-quadruplexes, we define these modes that are not localized on either site.64 quantities within the framework of TD-DFT. The reference geometry is therefore the ground The derivation has been presented in previous state equilibrium geometry of GC. The FrD- 15,63 papers, and we also include it in the Sup- LVC approach is schematically shown in Fig- porting Information (SI, Section S1.1), as we ure.2, summarizing the main steps of our pro- have found a more computationally efficient cedure, i.e. (1) the choice of reference states, method of calculating the overlap matrix. (2) projection of the reference states onto the For the definition of the reference geometry MC at reference geometry, and (3) projection and normal mode coordinates, in principle two onto the MC at displaced geometries. choices could be made: (i) define the reference Our approach bears some similarity to the geometry as the ground state equilibrium ge- work of Tamura and Burghardt on conjugated ometry of the MC, and then the normal coordi- polymers and fullerene systems,8,9,22–28 however nates as those of the entire MC, or (ii) define the there are a number of differences in the imple- reference geometry as any arrangement of indi- mentation. Firstly, we calculate the overlap S vidual fragments, not necessarily at the equilib- via transition densities following Neugebauer,65 rium geometry of the overall MC, but with the rather than Slater determinants. Secondly, we

5 Figure 2: Schematic of the FrD-LVC approach, illustrated with two chromophores (circles) and the MC consisting of these two chromophores (oval). Yellow stars represent reference LEs of individual chromophores, whilst a CT reference state is represented by an arrow from an occupied orbital of one individual chromophore to a virtual orbital of the other (1). Projections of these reference states onto the MC are shown by arrows towards the MC at either the reference (2) or displaced (3) geometries. The moiety (i.e single chromophore or MC) involved in a given computational step (excited state calculation, projection, or normal mode displacement) is depicted in black, the one not involved in gray. Illustration of the diabatic Hamiltonian shown in the centre. do not use the “electron-hole” formalism to de- 3 Computational Details scribe local excitations. In this way we account for the possible existence of multi-orbital com- Electronic structure calculations have been per- ponents in the local excitations a case which, formed with DFT for the ground state, and for instance, does occur in DNA nucleobases. TD-DFT for the excited states, using two dif- Thirdly, we include a vibrational dependence ferent range-separated functionals that confer 61 on the diabatic couplings through the λij pa- diﬀerent CT state stability, CAM-B3LYP and rameter, and fourthly, we compute the reference ωB97X-D,62 and two basis sets 6-31G(d) and 6- states based on isolated chromophores, rather 31+G(d,p), using the Gaussian 16 program.66 than well-separated ones. The 6-31G(d) basis set is used in parametrization of the FrD-LVC models presented in the main text. Single point energy test calcula-

6 tions are performed with the 6-31+G(d,p) basis propriate for harmonic potentials. We checked set for both functionals, which is also used to convergence by monitoring the populations at build a test FrD-LVC model with the ωB97X- the beginning and end of the grid using the D functional. These results are shown in the rdgpop tool provided in Quantics, and ensur- SI, Section S6, to check the solidity of our con- ing that they did not exceed 10−9. For the ML clusion with respect to an increase of the size “tree” expansion, we chose the number of single of the basis set. TD-DFT computations were particle functions (SPFs) for each node based performed using tight SCF convergence, with a on the magnitude of the linear coupling con- −6 10 a.u. threshold. stants λii,α, with modes with larger couplings As a molecular model, we use 9-methylguanine assigned larger numbers of SPFs, as we have and 1-methylcytosine to represent GC in Wat- done in recent studies of single nucleobases.13–17 son Crick conformation (see Figure1), geom- Mode combination was also utilised for modes etry optimised with Cs symmetry, which per- with similar character. The eigenvalues of the mitted electronic decoupling of the A’ (ππ∗ density matrices of each node in the ML tree, and CT) and A” (nπ∗) states. The vibra- also known as the natural weights, were moni- tional frequencies obtained in the S0 state of tored, ensuring that the smallest natural weight GC are utilised for each of the excited states was always less than 1% to obtain a reasonable in the FrD-LVC models. Two different FrD- quality calculation, as indicated in the Quantics LVC models are parametrized for each of the manual. functionals: (i) a 12 diabatic state model, in- Absorption spectra of GC, G, and C were cluding 4 ππ∗, 2 CT and 6 nπ∗ states and both calculated following the procedure we have re- in-plane (A’) and out of plane (A”) modes for cently utilised, via the Fourier transform of a full-dimensional (99 mode) picture of GC, the auto-correlation function produced by the and (ii) a reduced-dimensionality (65 mode) 5 quantum dynamics calculations, weighted by state model, including 4 ππ∗ and 1 CT state, the transition dipoles.17,19 For GC, the tran- so that out-of-plane A” modes are not active sition dipoles of the diabatic states were ob- and have been neglected. These diabatic states tained by application of the transformation ma- were defined based on reference states of in- trix D(0) to the adiabatic transition dipole dividual G and C at the same geometry as in moments obtained by TD-DFT at the Franck- the GC pair, using the procedure described in Condon (FC) point, in the same manner as Section2, and then projected onto the calcula- Eq.7 and as previously described in Ref. 63. tion of 40 adiabatic states of GC by TD-DFT For monomeric G and C, the diabatic transition (see Eq.5). The diabatization was performed dipoles are equivalent to the adiabatic TD-DFT with an in-house code interfaced with Gaussian ones. The absorption spectra include contribu- 16 that is freely available upon request. LVC tions from initial excitation to each of the ππ∗ models for individual G and C have also been states, and are phenomenologically broadened parametrized at the same level of theory as GC, with a Gaussian of half-width half-maximum including 2 ππ∗ and 3 nπ∗ states for each base, HWHM=0.04 eV. Further details may be found following the procedure for individual bases we in the SI, Section S1.2. have recently used.15–17 Expectation values of the FrD-LVC diabatic d d Quantum dynamics calculations were per- potential diagonal (Vii ) and off diagonal (Vij ) formed with the ML-MCTDH method,67–69 terms are also calculated by integrating the adopting the implementation within the Quan- wavepacket over all normal modes. Since tics package.70 We used a variable mean field each diabatic potential is the sum of indepen- d (VMF) with a Runge–Kutta integrator of or- dent terms on the different modes Vij (q) = −7 P d der 5 and accuracy 10 , as in the provided α Vij (qα), it is straightforward to define examples for S2/S1 dynamics of pyrazine with the expectation value of such potential terms 68,71 d 24 normal modes. For the primitive basis hΨ|Vij (qα)|Ψi on each mode. set we adopted Hermite DVR functions, as ap-

7 4 Results agreement with the EOM-CCSD(T) results of Ref. 72 that are also shown in the Table. 4.1 Adiabatic and diabatic states: The ordering and relative energy gaps be- FC point and minima tween the states is quite similar for ωB97X- D and EOM-CCSD(T), with the main differ- The 12 lowest singlet state energies of GC, ence being that the stability of the C(ππ∗2) and calculated by the CAM-B3LYP and ωB97X-D G(Lb) states is switched. For CAM-B3LYP, ∗ functionals and 6-31G(d) basis set are shown as well as the C(ππ 2) and G(Lb) switch, the in Table1 (TD-DFT column). WC pairing G→C(CT)1 state is predicted to be the low- leads to a non-negligible mixing between the est energy excited state, and its relative sta- ππ∗ states on G and C (especially according bility to the other bright states is overesti- to ωB97X-D), and the CT state, as shown mated by ∼0.45 eV and ∼0.65 eV compared with the natural transition orbitals (NTOs) to ωB97X-D and EOM-CCSD(T), respectively. in the SI, Figures S1 and S2. Nonethe- The comparison with the results obtained for less, we can identify 2 ππ∗ states on C, 2 the isolated bases (see Ref. 17 and SI Table S1) ∗ ππ states on G (commonly referred to as La shows that WC pairing strongly destabilizes the ∗ ∗ ∗ and Lb following Platt’s nomenclature), 3 nπ nπ states, and, in particular the G(nOπ ) and ∗ ∗ states of C, 3 nπ states of G, and 2 G→C C(nOπ ) states. Confirming a trend already dis- CT states. The G→C(CT)1 state involves a cussed in the literature,1,73 the transfer of an HOMO(G)→LUMO(C) transition, whilst the electron from the lone pair involved in a hydro- G→C(CT)2 state a HOMO(G)→LUMO+1(C) gen bond towards a π∗ delocalized on the ring transition. Considering the differences in the weakens the hydrogen bonds and destabilizes basis set, CAM-B3LYP and, especially, ωB97X- the associated excited states. The strong hy- D provide a description of the FC region in good drogen bonding is also responsible for the mix-

d Table 1: Energies (eV) of the diabatic states from the FrD-LVC 12 state models Eii(0), compared with adiabatic energies with same predominant character from TD-DFT and via diagonalization of the FrD-LVC Hamiltonian (see text for details). State ordering in parentheses. Calculated on GC in Cs symmetry at equilibrium geometry by CAM-B3LYP/6-31G(d) and ωB97X-D/6-31G(d). Also shown are EOM-CCSD(T)/TZVP results from Ref. 72.

CAM-B3LYP ωB97X-D d d Diab. State Eii(0) Ad. LVC TD-DFT Eii(0) Ad. LVC TD-DFT EOM-CCSD(T)

G→C(CT)1 5.17 5.12 (S1) 5.07 (S1) 5.54 5.56 (S3) 5.50 (S3) 5.36 ∗ C(ππ 1) 5.33 5.29 (S2) 5.27 (S2) 5.31 5.25 (S1) 5.28 (S2) 4.92

G(La) 5.42 5.36 (S3) 5.31 (S3) 5.42 5.31 (S2) 5.21 (S1) 4.85

G(Lb) 5.66 5.75 (S4) 5.69 (S4) 5.65 5.74 (S4) 5.69 (S4) 5.48 ∗ C(ππ 2) 5.92 5.96 (S7) 5.93 (S7) 5.89 5.93 (S6) 5.90 (S6) 5.37

G→C(CT)2 6.39 6.40 (S8) 6.33 (S8) 6.67 6.68 (S11) 6.60 (S11) ∗ C(nNπ ) 5.92 5.92 (S5) 5.79 (S5) 5.88 5.88 (S5) 5.77 (S5) 5.65 ∗ G(nOπ ) 5.94 5.93 (S6) 5.93 (S6) 5.95 5.94 (S7) 5.93 (S7) 5.76 ∗ G(nNπ 1) 6.50 6.46 (S10) 6.44 (S9) 6.47 6.43 (S8) 6.43 (S8) ∗ C(nOπ 1) 6.54 6.46 (S9) 6.45 (S10) 6.53 6.47 (S9) 6.46 (S9) 6.27 ∗ C(nOπ 2) 6.55 6.64 (S11) 6.60 (S11) 6.53 6.59 (S10) 6.56 (S10) 6.42 ∗ G(nNπ 2) 6.73 6.78 (S12) 6.71 (S12) 6.73 6.77 (S12) 6.70 (S12)

8 ing between the different excited states, as well ing that our model appropriately reproduces as the close proximity of the bases. the low-energy adiabatic states of the dimer at Single point energy calculations with the the FC point. The only exceptions are the or- ∗ ∗ larger 6-31+G(d,p) basis set are shown in the dering of the G(nNπ 1) and C(nOπ 1) states in SI, Table S14. They reveal a very similar en- the CAM-B3LYP model, and the C(ππ∗1) and ergy ordering, and the changes in the relative G(La) states in the ωB97X-D model. The en- stability of the different states are small. See ergies, however, are not greatly different, and it Section S6 of the SI for further details on the should be reminded that the TD-DFT C(ππ∗1) 6-31+G(d,p) basis set test. and G(La) ωB97X-D states are significantly Also shown in Table1 are the energies of the mixed. d diabatic states at the FC point, Eii(0), calcu- Inspection of Table2 and S2 in the SI shows lated by the FrD procedure and used in the LVC that diabatic states localized on G are more model. In contrast to the TD-DFT states, by significantly coupled with G→C CT states. In construction our LEs are fully localized either particular, G(La) is the excited state with the on G or on C. The mixing of LE and CT states largest coupling with G→C(CT)1, almost twice at the FC point is accounted for through the as large as those involving the other bright d constant coupling parameter Eij(0), see Table2 excited states. A similar trend is found for for a selected few, and Tables S2 and S3 in the G→C(CT)2, though in this case, the most cou- SI for all. The energies of the adiabatic states pled state is G(Lb). Interestingly, ωB97X- of the FrD-LVC model at the FC point, i.e. the D and CAM-B3LYP provides a similar pic- eigenvalues of the FrD-LVC Hamiltonian, are ture, i.e. G(La) has the largest coupling with reported in the ‘Ad. LVC’ column of Table1 G→C(CT)1, notwithstanding that according to (the corresponding eigenvectors are shown in ωB97X-D the G→C(CT)1 state is energetically the SI, Tables S8 and S9). These energies are closer to other bright excited states. Our analy- within ∼0.05-0.1 eV of the TD-DFT energies, sis thus suggests that ‘hole’ coupling is most im- and in predominantly the same order, indicat- portant than the ‘electron’ one. In other words,

Table 2: ππ∗-CT, excitonic, and intra-monomer ππ∗ mixing couplings between diabatic states at the d FC point (Eij(0), eV) as predicted by the 12 state FrD-LVC models parametrized by CAM-B3LYP and ωB97X-D.

Coupling CAM-B3LYP ωB97X-D ππ∗-CT

G(La):G→C(CT)1 0.065 0.067

G(Lb):G→C(CT)1 0.038 0.037 C(ππ∗1) : G→C(CT)1 0.022 0.023 C(ππ∗2) : G→C(CT)1 −0.039 −0.036 Excitonic ∗ G(La) : C(ππ 1) 0.002 0.002 ∗ G(La) : C(ππ 2) 0.053 0.052 ∗ G(Lb) : C(ππ 1) −0.020 −0.018 ∗ G(Lb) : C(ππ 2) 0.041 0.037 ππ∗ Mixing

G(La) : G(Lb) −0.171 −0.176 C(ππ∗1) : C(ππ∗2) 0.160 0.155

9 ad,m Table 3: Energies (eV, relative to S0 minimum) of adiabatic (coordinates qmin ) and diabatic d,i (coordinates qmin) excited state planar minima. In each minima, the diabatic energies from the d FrD-LVC model are shown (Vii (q) column) as well as the adiabatic energies predicted by TD-DFT, and the adiabatic energies from the FrD-LVC model (Ad. LVC column). Also shown is the RMSD ad,m d,i ˚ between the Cartesian coordinates of the qmin and qmin geometries in A. Further details in text.

ad,m d,i qmin qmin d d State Vii (q) Ad. LVC TD-DFT Vii (q) Ad. LVC TD-DFT RMSD CAM-B3LYP G→C(CT)1 4.04 4.03 4.00 3.94 3.93 4.00 0.060 C(ππ∗1) 4.95 4.95 4.94 4.94 4.95 4.95 0.007

G(La) 5.18 5.11 5.07 5.09 5.03 5.01 0.052 ∗ G(nOπ ) 5.57 5.56 5.42 5.50 5.50 5.45 0.054 ∗ G(nNπ 1) 6.02 5.79 5.68 5.93 5.81 5.74 0.030 ∗ C(nOπ 1) 5.91 5.56 5.40 5.66 5.57 5.54 0.052 ωB97X-D G→C(CT)1 4.48 4.47 4.40 4.39 4.39 4.36 0.045 C(ππ∗1) 4.94 4.94 4.91 4.93 4.92 4.92 0.006

G(La) 5.21 5.06 5.02 5.10 5.07 5.05 0.039 ∗ G(nOπ ) 5.59 5.59 5.44 5.53 5.52 5.47 0.059 ∗ G(nNπ 1) 5.94 5.73 5.65 5.87 5.75 5.69 0.025 ∗ C(nOπ 1) 5.70 5.48 5.36 5.56 5.48 5.45 0.044 that the LUMO’s of G and C are more coupled inter-monomer couplings of the nπ∗ states are than the HOMO’s. relatively small, consulting the eigenvectors of Table2 also shows that hydrogen bonding the nπ∗ FrD-LVC adiabatic states in Table S9 leads to a significant intra-monomer coupling shows some mixing of the states localized on between the bright excited states localized on G G and C at the FC point, in particular for the ∗ ∗ and C, i.e. G(La)-G(Lb) and C(ππ 1)-C(ππ 2), CAM-B3LYP model, due to the closeness in en- which we refer to as ππ∗ mixing couplings. This ergy of the nπ∗ diabatic states. This indicates effect, which we have discussed in detail in Ref. that the hydrogen bonding could induce a small 63, mirrors the changes in the shape of the ex- amount of delocalization of the dark states. cited states of the isolated chromophore due to The general trends in terms of the strength surrounding molecules and is crucial for the ap- of coupling are confirmed when considering the plication of excitonic Hamiltonians to closely effect of vibrations, which allows the coupling spaced MC assemblies. In contrast, the inter- between ππ∗ and nπ∗ states. Interestingly, as monomer excitonic couplings, i.e. those possi- shown in Tables S12 and S13 in the SI, nπ∗ bly promoting energy transfer between the ππ∗ states localized on C are significantly vibroni- states are much smaller, in particular for G(La)- cally coupled with G→C(CT)1. C(ππ∗1). As an additional characterisation and test of For the nπ∗ states, as shown in Table S3 in the the robustness of our approach, we have com- SI, hydrogen bonding affects the intra-monomer pared the energies and geometries of planar adi- mixing couplings in a similar manner to the ππ∗ abatic excited state minima from TD-DFT ge- ∗ ∗ ad,m states, in particular for G(nNπ 1)-G(nNπ 2) ometry optimisations (qmin for adiabatic state ∗ ∗ and C(nOπ 1)-C(nOπ 2) mixing. Whilst the m, see also Section S2.2 and S3.2.2 in the SI)

10 with the diabatic minima predicted by the FrD- 0.8. Interestingly, a small fraction of the pop- d,i LVC models (qmin for diabatic state i). As ulation is ‘trapped’ on G(La) and then trans- shown in Table3, the geometries (see the low ferred to C(ππ∗1), whose population after 250 root-mean-square-deviation, RMSD) and rela- fs is non-negligible (∼0.05). tive energy of the two different sets of minima When exciting to C(ππ∗1), the population are quite similar. is also effectively transferred to G→C(CT)1, Moreover, in general, in its minimum each though the transfer is slower and less complete adiabatic state has a more predominant con- than when exciting the G La/Lb states. Af- tribution from a single diabatic state than in ter 60 fs, the population of C(ππ∗1) is still 0.5, the FC region, as shown by the comparison of and after 250 fs 0.15. Finally, excitation of the eigenvectors of the diabatization procedure C(ππ∗2) triggers an ultrafast decay to C(ππ∗1) in the different structures (see Tables S8-S11 and, then, to G→C(CT)1. In this case how- in the SI). For example, at the FC point the ever, a plateau is reached after ∼ 100 fs, with ∗ S1 and S2 states of ωB97X-D have significant C(ππ 1) and G→C(CT)1 exhibiting a similar mixing of the ππ∗ states localized on G with population (∼0.3 and ∼0.5, respectively). those localized on C (Table S8). However, at The picture provided by ωB97X-D is basi- ad,m d,i both qmin and qmin geometries of the G(La) and cally consistent with that of CAM-B3LYP. The C(ππ∗1) states, the FrD-LVC adiabatic states ∼0.4 eV larger energy of the G→C(CT)1 state are instead predominantly composed of either in the ωB97X-D model confers only a minor ∗ G(La) or C(ππ 1) diabatic states (Tables S10 slow down of the population transfer, and after and S11, respectively). These results support 100 fs the population of G→C(CT)1 is ≥ 0.8 the physical significance of the ‘monomer-like’ when exciting G(La) or G(Lb), and ≥ 0.4 when diabatic states, as well as benefitting the inter- exciting C(ππ∗1) or C(ππ∗2). In this latter pretation of the dynamics results in the follow- case the transfer to G→C(CT)1 is actually even ing section. larger than according to CAM-B3LYP, and a plateau in the populations of G→C(CT)1 and ∗ 4.2 Excited state dynamics of C(ππ 1) is reached at a later stage, after ∼150 fs. GC Figure3 also highlights that the population In Figure3 we report the excited state dy- of the dark nπ∗ excited states is extremely namics computed by using a FrD-LVC Hamil- small, their sum being ≤ 0.02 for all calcula- tonian including 12 states (solid lines) and tions except for an initial excitation to C(ππ∗2) parametrized with CAM-B3LYP or ωB97X-D where it is marginally larger (∼0.06 for the for initial excitations to each of the four low- CAM-B3LYP and ∼0.04 for the ωB97X-D mod- est bright excited states. When exciting G(La), els). WC pairing thus suppresses these deac- CAM-B3LYP predicts that, after an ultrashort tivation channels, which are active in the cy- 15,17 ‘spike’ due to the coupling with G(Lb) at the tosine monomer. Indeed, our recent QD FC point, an effective population transfer to studies on cytosine and 1-methylcytosine with G→C(CT)1 occurs. After ∼25 fs, the popu- a LVC Hamiltonian parametrized with CAM- lation of G→C(CT)1 is 0.5, and after 60 fs it B3LYP predict that after initial photoexcita- is 0.9, and the transfer is virtually complete. tion of ππ∗1 ∼20-25% of the population is No significant changes are then predicted until transferred to the nπ∗ states for cytosine and 250 fs, when the population of the other ex- ∼10% for 1-methylcytosine, while exciting ππ∗2 cited states is close to zero, the most populated the population transfer increases up to ∼50% ∗ one being C(ππ 1). When exciting to G(Lb), for cytosine and ∼30% for 1-methylcytosine. ∗ an ultrafast decay to G(La) is predicted, in Given the small participation of the nπ states line with the results obtained on G monomer.17 and the G→C(CT)2 state, it is unsurprising However, then G(La) acts as ‘doorway’ state to that the population dynamics predicted by the G→C(CT)1, whose population after ∼60 fs is reduced-dimensionality 5-state model, includ-

11 CAM-B3LYP ωB97X-D 1 a) 0.8 π G(La) G(nO *) G(L ) G(n π*1) 0.6 b Nπ C(ππ*1) G(nN *2) C(ππ*2) C(n π*) 0.4 Nπ G->C(CT)1 C(nO *1) G->C(CT)2 C(n π*2) 0.2 O

0 b) 0.8 12 State 0.6 5 State λ 0.4 5 State, i,CT=0 0.2

0 c) 0.8 Population 0.6

0.4

0.2

0 d) 0.8

0.6

0.4

0.2

0 0 50 100 150 200 0 50 100 150 200 250 Time (fs)

Figure 3: Diabatic state populations for FrD-LVC models with 12 states (solid line), 5 states ∗ (dotted line), and 5 states with λij = 0 for all the ππ states coupled to G→C(CT)1 (dashed line). ∗ ∗ Dynamics initiated on a) G(La), b) G(Lb), c) C(ππ 1) and d) C(ππ 2) states. Parametrized by CAM-B3LYP (left) and ωB97X-D (right).

∗ ing only the ππ and G→C(CT)1 states, and ter excitation to the G(Lb) state (where in this the 65 A’ vibrational modes, are similar to that case there is less trapping in the G(La) state). described above (dotted lines in Figure3). The Whilst part of the less effective population of main difference is the 5 state model predicts a the G→C(CT)1 state in the 12 state model can greater population transfer to the G→C(CT)1 be attributed to the small population of the nπ∗ state and reduced ‘trapping’ in the C(ππ∗1) states, the remainder may be attributed to this state after excitation to C(ππ∗2) in the CAM- trapping on the ππ∗ states. B3LYP model. Similar effects are seen, although to a lesser extent, in the ωB97X-D model, and also in the CAM-B3LYP model af-

12 4.2.1 Vibrational effects on the base that is initially excited, as well as the G→C(CT)1 state. The full figure may be In order to investigate the cause of the ‘trap- found in the SI, Figure S9. ping’ in the 12 state model, we have analysed For initial excitation to C(ππ∗2) in the CAM- the expectation values of the diabatic potentials B3LYP model, where the trapping effect is most of the different states, integrating over all nor- clearly observed, the left panel of Figure4d mal modes of the wavepacket as a function of shows that the potential of C(ππ∗1) in the time in Figure.4. For clarity, this figure only 12 state model almost plateaus after ∼50 fs, shows the potentials of the ππ∗ and nπ∗ states

G(L ) G->C(CT)1 C(n π*) a π Nπ G(Lb) G(nO *) C(nO *1) C(ππ*1) G(n π*1) C(n π*2) Nπ O C(ππ*2) G(nN *2) CAM-B3LYP ωB97X-D

3 a) 2 1 12 State 0 5 State -1 3 b) 2 1 0

> (eV) -1 Ψ c) (q)|

d ii 2 |V Ψ < 1

d) 2

0 50 100 150 200 0 50 100 150 200 250 Time (fs)

d d Figure 4: Expectation of diabatic state potential energies, (hΨ|Vii (q)|Ψi) shifted by −ECT1(0) − P 1/4 α ωα so that the G→C(CT)1 energy is 0 initially. For the 12 state (solid lines) and 5 state (dotted lines) FrD-LVC models for GC, parametrized by left: CAM-B3LYP and right: ωB97X-D ∗ ∗ for dynamics initiated on a) G(La), b) G(Lb), c) C(ππ 1) and d) C(ππ 2) states. For clarity, only the potentials of the G→C(CT)1 state, and the ππ∗ and nπ∗ states localized on the base that is initially excited are shown.

13 whereas in the 5 state model it is destabilised. largest trapping is observed. Many vibrations are slightly more active in the Figure.4 also reveals that the n π∗ states 5 state than the 12 state model, resulting in are immediately destabilised upon excitation, this destabilisation of C(ππ∗1) and, therefore, within ∼10 fs the diabatic potential of the to a larger transfer to the G→C(CT)1 state lowest nπ∗ state on each base reaches a value for the 5 state model. The expectation of > 0.5 eV larger than at the FC point. In par- the C(ππ∗1) diabatic potential along a repre- ticular, when the initial excitation is close in ∗ sentative few normal modes is shown in Fig- energy to the nπ state, so to either G(Lb) or ure5, with the displacement vectors of the vi- C(ππ∗2), the ππ∗ state of initial excitation is brations illustrated in the SI Figure S6. In the immediately stabilised and the closest nπ∗ state 12 state model there is a larger bath of vibra- destabilised. This helps to explain why there is tional modes where the excess energy deposited only small population transfer to the nπ∗ states, when exciting C(ππ∗2) can be dissipated (as the as by the time the vibrational motions bring ∗ ∗ ∗ 12 state model includes all 99 A’ and A” modes, the G(Lb)/G(nOπ ) or C(ππ 2)/C(nNπ ) states whereas the 5 state model includes only the 65 close in energy once more, after ∼20 fs, the pop- A’ modes), cooling down the vibrations that ulation has already been deposited to the lower ∗ ∗ destabilize the C(ππ 1) state. In contrast, cool- G(La) or C(ππ 1) states and subsequently to ing down these vibrations does not affect the the G→C(CT)1. G→C(CT)1 state as significantly. This expla- Whilst this is very much a multi-vibrational nation correlates with the fact that the energy mode effect, we have identified two normal gap between initial excitation and G→C(CT)1 modes that provide a large contribution to this ∗ ∗ state is largest for initial excitation to C(ππ 2) process, q76 for the G(Lb)-G(nOπ ) gap, and q77 ∗ ∗ in the CAM-B3LYP model, hence this is the for the C(ππ 2)-C(nNπ ) gap. The q76 mode is case where the largest amount of energy has predominantly localized on G, and consists of to be dissipated in the vibrational modes in an N1-H1 and C8-H8 bending motion, whilst the subsequent reorganisation, and where the q77 is predominantly localized on C, and consti-

q q q q 1.4 07 76 80 95 q14 q77 q92 q97 1.2

1 > (eV) Ψ )|

α 0.8 (q *1)

ππ 0.6 d C(

|V 0.4 Ψ < 0.2

0 0 50 100 150 200 250 Time (fs) Figure 5: Expectation of diabatic state potential energy along various normal modes for the C(ππ∗1) d ∗ state (hΨ|VC(ππ∗1)(qα)|Ψi), after initial excitation to the C(ππ 2) state for the 12 state (solid lines) and 5 state (dotted lines) CAM-B3LYP parametrized FrD-LVC models. Each mode oﬀset by diﬀerent values so that they do not overlap.

14 tutes a combined NH2 bend, C4-C5 ring stretch to zero (dotted lines in Figure6). and C5-H5 and C6-H6 bend. The expectation In the SI we show that the results for the of the diabatic potentials along the q76 mode CAM-B3LYP model are the same, the effect of after initial excitation to G(Lb), and along the these modes after initial excitation to the other ∗ q77 mode after initial excitation to C(ππ 2) are states, and their value for the full 250 fs of the shown in Figure6, panels a) and b) respec- propagation (Figures S10 and S11). Interest- tively, for the first 25 fs of the calculation with ingly the mode q77, despite being localized on the ωB97X-D FrD-LVC model. In this Fig- C, significantly affects the states localized on G. ure we observe, indeed, that after initial ex- Another interesting vibrational effect is the ∗ citation, the G(Lb)/C(ππ 2) states are imme- large reorganisation energy of the G→C(CT)1 ∗ ∗ diately stabilised, whilst the G(nOπ )/C(nNπ ) state after it is populated, leaving it ∼0.5 eV states are destabilised within half a vibrational more stable after 250 fs than at the FC point, period (∼10 fs). After the vibrational period is whilst the ππ∗ states are > 0.5 eV destabilised, complete (∼20 fs) and the ππ∗ and nπ∗ states leaving the gap between the G→C(CT)1 and ∗ are close in energy once more, the population lowest ππ state > 1 eV (Figure4). The q76 ∗ from the G(Lb)/C(ππ 2) states is already close and q77 modes previously mentioned contribute

G(La) C(ππ*1) G(Lb) C(ππ*2) π π G(nO *) C(nN *) G->C(CT)1 1 0.6 a) 0.8 0.4

> (eV) Potential

Ψ 0.6 )| 0.2 Population 76 ) Population (q 0.4 d ii b

|V 0 Ψ 0.2 G(L < −1 -0.2 ω76 = 1586 cm 0 0.6 b) 0.8 0.4 > (eV) 0.6 Ψ

)| 0.2 77

(q 0.4 d ii 0 *2) Population |V ππ Ψ

0.2 C( < -0.2 −1 ω77 = 1607 cm -0.4 0 0 5 10 15 20 25 Time (fs)

Figure 6: Left: Expectation of diabatic state potential energies (solid lines) along the a) q76 normal ∗ mode after initial excitation to G(Lb) and b) q77 normal mode after initial excitation to C(ππ 2). Calculated with the 12 state FrD-LVC model for GC parametrized by ωB97X-D. For clarity the d potentials are shifted so that the G→C(CT)1 energy is 0 initially, i.e. by −ECT1(0) − 1/4ω76/77, and only the potentials of the G→C(CT)1 state, and the ππ∗ and lowest nπ∗ states localized on the base that is initially excited are shown. The dotted lines show the population of the G(Lb) state ∗ in a) and the C(ππ 2) state in b). On the right hand side are the displacement vectors of the q76 and q77 normal modes and their frequencies.

15 d somewhat to this effect (see SI, Figures S10 and the diabatic coupling terms (i.e. Vij (q)) be- S11), however a much larger contribution arises tween the ππ∗ and G→C(CT)1 states is in- from a low frequency mode q07, that involves stead more limited. In particular, Figure S13 a shearing motion between the bases. An ex- in the SI shows after an excitation to G(La) ample of its affect on the expectation of the or G(Lb) the coupling between the doorway diabatic potential energies following initial ex- state G(La) and the G→C(CT)1 does not sig- ∗ citation to a) G(La) and b) C(ππ 1) is shown nificantly deviate from its initial value at the in Figure7 for the ωB97X-D model. It is not FC point (Table2). An analogously weak active for the first 50 fs of the calculation, how- time-dependence is observed for the coupling of ever when the G→C(CT)1 state is significantly C(ππ∗1) with G→C(CT)1 after an initial ex- populated it becomes active and stabilises the citation to C(ππ∗1) and C(ππ∗2). As a conse- G→C(CT)1 state, whilst destabilising the oth- quence, the dashed lines Figure.3 show that ne- d ers. The effect of this mode on the diabatic po- glecting the dependence of Vij (q) on coordinate tentials following excitations to the other ππ∗ for the ππ∗-G→C(CT)1 couplings (i.e. setting states is shown in the SI, Figure S12 along with the linear terms λij = 0 for i, j=G→C(CT)1) the CAM-B3LYP results, and the effect is much produces no discernible difference to the dy- the same. namics of the 5 state FrD-LVC models. The impact of the vibrational motion on The excitonic couplings, i.e. those between

G(L ) G->C(CT)1 C(n π*) a π Nπ G(Lb) G(nO *) C(nO *1) C(ππ*1) G(n π*1) C(n π*2) Nπ O C(ππ*2) G(nN *2) 2 a) 1.5

0.5

0 > (eV) Ψ )| -0.5 07 (q

d ii b) |V

Ψ 1

< −1 ω07 = 115 cm 0.5

-0.5 0 50 100 150 200 250 Time (fs)

Figure 7: Left: Expectation of diabatic state potential energies along the q07 normal mode (i.e. d hΨ|Vii (q07)|Ψi) from the 12 state FrD-LVC model for GC parametrized by ωB97X-D after initial ∗ excitation to a) G(La) and b) C(ππ 1). For clarity the potentials are shifted so that the G→C(CT)1 d energy is 0 initially, i.e. by −ECT1(0) − 1/4ω07, and only the potentials of the G→C(CT)1 state, and the ππ∗ and nπ∗ states localized on the base that is initially excited are shown. On the right hand side are the displacement vectors of the q07 normal mode and its vibrational frequency.

16 ππ∗ states localized on each base, are similarly the substitution of the five ’exchangeable’ pro- unaffected by the vibrations, see Figure S14 in tons (the amino and imino ones) by deuterium. the SI. In particular, the excitonic coupling be- Many TR studies on DNA are performed in ∗ 50 tween the doorway states, G(La)-C(ππ 1), re- deuterated solvents, and isotope substitution mains very small during the propagation, ex- has been suggested to affect the PCET pro- plaining the limited population transfer from cesses.74 As shown in Figure S7 of the SI the states localized on one base to ones localized population dynamics is very little affected by on the other. deuteration, which decreases the transfer to On the contrary, the couplings between the G→C(CT)1 by ≤5%. As a consequence the bright states localized on the same base are first step of the PCET reaction is not expected strongly affected by vibrational motions, see to be very sensitive to isotope effect, at least in Figure S15 in the SI. A tangible consequence, the gas phase. for example, is that the strong mixing of G(La)- ∗ ∗ G(Lb) and C(ππ 1)-C(ππ 2) states observed in 4.2.2 GC absorption spectrum the adiabatic states at the FC point decreases during the propagation, such that the adiabatic We have also computed the absorption spec- states end up resembling much more the refer- trum of the GC pair, based on our 12 state ence states on isolated monomers. FrD-LVC model calculations, using the proce- Finally, we have analysed how the excited dure described in the Computational Details, state dynamics is affected by deuteration, i.e. and SI, Section S1.2. These are shown in Fig- ure8, with panel a) illustrating the individ-

CAM-B3LYP ωB97XD 2.5 ππ a) GC: Total GC: C( *1) GC: G(L ) GC: C(ππ*2) 2 a GC: G(Lb)

1.5

1 ) -1 0.5 cm -1 (M

4 0 G+C G: G(L ) /10 b) a ε G G: G(Lb) 2 C C: C(ππ*1) C: C(ππ*2) 1.5

0.5

0 200 220 240 260 280 300 320 200 220 240 260 280 300 320 Wavelength (nm)

Figure 8: Absorption spectra of GC calculated from the 12 state FrD-LVC models (solid black line) with a) individual diabatic state components (solid blue, red, light and dark green lines) and b) compared to monomeric spectra of G (purple) and C (turquoise) with individual state components (dashed red, blue, light and dark green lines) and the sum of G and C (grey). LVC models parametrized by CAM-B3LYP (left) and ωB97X-D (right). All spectra shifted by -0.75 eV and broadened with Gaussian HWHM=0.04 eV.

17 ual state components of the GC spectrum, and 5 Concluding remarks panel b) comparing it to absorption spectra of isolated G and C and their sum. The absorp- In this contribution we have introduced a tion spectra of isolated G and C are calculated method for an automatic parametrization using 5 state LVC models, including 2 ππ∗ and of a generalised LVC Hamiltonian suitable 3 nπ∗ states for each base, in the same man- for studying the photophysics of multichro- ner as our recent work on single nucleobases.17 mophoric assemblies, exploiting TD-DFT. Its All spectra are shifted by -0.75 eV to match main methodological novelty concerns the pos- the onset of the GC spectrum in chloroform,42 sibility of defining the reference diabatic states (see Figure S18 in SI) and plotted on the wave- on the basis of isolated fragments. In combi- length scale. The parametrizations with CAM- nation with effective wavepacket propagations, B3LYP and ωB97X-D predicted quite similar for instance with the ML-MCTDH method, our spectra, therefore our analysis below applies to approach makes it rather straightforward to de- both models. scribe the competition between inter- and intra- Figure8a shows that the region of the chromophore photophysical pathways within maximum absorption at ∼ 250-260 nm is a fully quantum dynamical approach. This dominated by the contribution of the G(Lb). method is thus an attractive option to study At shorter wavelengths it is reinforced and phenomena where the timescale of internal con- then slightly overcome by the contribution of version processes on individual chromophores C(ππ∗2). Whilst on the red-wing, at longer is expected to be similar to that of energy and wavelengths, most of the signal arises from charge transfer between multiple chromophores. ∗ G(La) and C(ππ 1). In this red wing, accord- Furthermore, it can also account for the possi- ing to our computations most of the wavepacket ble coupling between these processes. should be located on G in the ∼280-295 nm Due to the efficiency of the parametriza- window, whilst the contribution from C(ππ∗1) tion of the LVC Hamiltonian and capability is only predominant at ≥ 295 nm. of ML-MCTDH propagations, it is possible Comparison with the results in Figure8b in- to include many electronic states (> 10) and dicate that the contribution of each individ- dozen/hundreds of normal coordinates in the ual state is broader in GC than the individual model. This permits the investigation of the ul- monomers, due to the large ππ∗ mixing cou- trafast vibronic dynamics following a photoex- plings and coupling to the G→C(CT)1 state citation in significantly broad energy ranges. in GC. Furthermore, the GC spectrum exhibits For example, in the present study we focused on interesting differences with respect to the sum the region above ∼220 nm, i.e. that ‘covered’ of monomer spectrum (G+C). First, the G+C by the four lowest energy bright states of a GC spectrum exhibits a longer red wing tail, com- pair. However, we have simulated the dynamics ing from the C contribution, which disappears considering up to 12 excited states (i.e. includ- in GC. This outcome is due to blue shifting of ing also the lowest energy dark states). This C(ππ∗1) due to hydrogen bonding.75 Second, is typically more than can be considered with the maximum of the absorption band of GC ‘on-the-fly’ dynamics calculations, such as sur- is weakly red-shifted with respect to G+C one face hopping (although, one should remember and it is more intense in the region 260-290 nm. that the number of adiabatic states to describe A similar effect is observed, although to a lesser the same dynamics could be smaller).76 There- extent, in experiment.42 Here we assign it par- fore, even in cases where an LVC Hamiltonian tially to the blue shifting of C(ππ∗1), and par- cannot capture all the details of the adiabatic tially due to weak red-shifting of the G(Lb) con- PES explored with surface hopping methods, tribution. this approach could complement these calculations by providing a relatively quick assessment of the role of higher excited states and/or the role quantum dynamics effects. Indeed, the pro-

18 posed parametrization is quite effective: TD- ings and anharmonicity. Several strategies may DFT calculations for the diabatization with 6- be employed to ameliorate these deficiencies, 31G(d) basis set in the present work took only such as moving to a quadratic vibronic cou- ∼24 hours using 28 cores, whilst the diaba- pling model (or at least some quadratic correc- tization took ∼30 minutes on 12 cores. For tions like done in Refs. 16,71,77), fitting with the quantum dynamics calculations themselves non-harmonic functions when anharmonicity is the computation times ranged between 100-300 confined to a few degrees of freedom, and mixed hours on a single core for the 12 state calcu- quantum classical approaches to deal with large lations, and 20-100 hours for the 5 state cal- amplitude motions.78 Such developments fall, culations. These values could be feasibly re- however, outside the aim of the present contri- duced through appropriate tuning of param- bution and will be tackled in future studies. eters in the ML-MCTDH computations, such In the present, first, application of FrD-LVC as choice of integrator, mode combination, and we have studied the excited state dynamics of multilayer ‘tree’, or by discarding smaller terms GC adopting a WC hydrogen bond arrange- in the FrD-LVC Hamiltonian. ment, after exciting each of the four lowest The application of FrD-LVC is most suited energy bright states. We predict a substan- when couplings between the different monomers tial and fast population transfer from the ini- are not excessively strong, and more in general tially excited bright state towards the low- when it is conceivable or interesting to hypoth- est energy G→C CT state. This transfer is esize to have prepared an initial state localized more effective for initial excitations on G bright on one single monomer. In those cases, the states, with ∼80% of the population trans- proposed approach also has the advantage to ferred in ∼50 fs. However, also when excit- be naturally allied with the chemical point of ing C(ππ∗1) and C(ππ∗2), in less than 100 fs view that breaks the investigated photophysi- ∼50% of the population is transferred to the cal event into elementary processes on the in- G→C(CT)1 state. Therefore, the fact that dividual molecular components and their possi- our Hamiltonian does not include the monomer ∗ ble interactions. For example, this is typically G(La) and C(ππ 1) decay channels to S0, in- done, more or less implicitly, for charge sep- volving large out-of-plane distortions,1 does not aration/migration/recombination in multichro- bias the qualitative reliability of our conclusion, mophore assemblies. given that the transfer to the CT states occurs The application of FrD-LVC should be han- on a time-scale (<100 fs) for which the decay dled with more care when the coupling be- to S0 of the bright states should play a minor tween the different units is so strong to make role. any connection with the behavior of the sepa- Our dynamical calculations are thus consis- rated unit too weak. The analysis of the results tent with the experimental picture in the gas of the fragment diabatization procedure, such phase,52 with the population of the bright ex- as calculated couplings and predicted minima, cited states disappearing on a <100 fs time and/or of the subsequent dynamics can provide scale. Considering that on the CT PES the pro- useful diagnostics to identify these ’problem- ton transfer is barrierless, our study also seems atic’ cases. However, it is important to stress to support the reliability of the mechanism pro- that FrD-LVC could still be used even in these posed by Sobolweski and Domcke .32,33 A forth- cases by considering initial states coherently ex- coming work will be devoted to study in depth cited on more than one diabatic state or, alter- the quantum dynamics of the coupling between natively, performing propagations by explicitly the CT formation and the PT process. including the interaction with the pump laser FrD-LVC provides interesting insights on the pulse in the dynamics. effects ruling the yield of the CT population. Our approach also obviously suffers from all For example, G(La) appears to be the excited the limitations of LVC models, such as lack state most strongly coupled to G→C(CT)1, and of large amplitude motions, Duschinsky mix- permits the fastest and most effective popula-

19 tion of G→C(CT)1. This is true even when the ergy than with CAM-B3LYP. Numerical experi- G→C(CT)1 state is closer in energy to other ments in the SI Section S4.5 indicate that, in or- ππ∗ states, such as predicted with the ωB97X- der to overcome this effect and make population D functional. Moreover, the extremely fast transfer to G→C(CT)1 significantly smaller, G(Lb)→G(La) decay suggests that G(La) is the the diabatic energy gap between the CT state ‘main’ doorway state to G→C(CT)1. and doorway state should be ≥ 0.6 eV. Despite the smaller coupling of the C ππ∗ WC pairing, besides allowing the formation states to the G→C(CT)1 state, we still observe of the CT states, has another important effect effective (albeit slightly slower) population on the photoactivated dynamics of G and C, transfer when the initial excitation is localized almost suppressing any population transfer to on C. The extremely fast C(ππ∗2)→C(ππ∗1) the dark nπ∗ states. This internal conversion ∗ decay, combined with the small C(ππ 1)-G(La) route is significant for isolated bases in the gas excitonic coupling indicates that C(ππ∗1) acts phase, in particular for C in the context of the as a secondary doorway state to G→C(CT)1. present work.14–17,53 As well as the significant These evidences lead us to conclude that a dra- destabilization of nπ∗ transitions by hydrogen matic dependence of the CT process on the bond formation, we have identified N-H bend- excitation wavelength should not be expected. ing vibrations that further destabilise the nπ∗ Interestingly, vibrational motions play only states upon initial excitation, whilst conversely minor role in modulating the coupling between stabilising the ππ∗ states. local excitations on different chromophores and The results of our dynamical simulations are with CT states. This does not mean, how- strictly valid only in the gas phase, nonethe- ever, that vibrations do not drastically affect less some of the effects we have discussed are the yield of the population transfer, since they likely operative also for a GC pair in solution determine the reorganization energy of any ex- and within DNA. For example, we can expect cited state and, therefore, the relative stabil- that the nπ∗ states should also not be signifi- ity of their minima. In Section S4.4 in the cantly populated within a duplex, since there is SI, we show that a trivial purely electronic dy- no reason to believe that a polar environment namics with nuclei frozen at the FC position would increase their stability. Analogously, would provide a much smaller average popula- G→C(CT)1 should also be significantly popu- tion of G→C(CT)1, even when it is the lowest lated in solution. On the other hand, within a energy excited state in the FC region. Further- duplex, the population of additional CT states more, the purely electronic dynamics with the involving the adjacent, stacked, bases to G, can ωB97X-D model also predicts a significant exci- become competitive46,50,79 and we will investi- tonic transfer between the doorway G(La) and gate the interplay of intra- and inter-strand CT C(ππ∗1) states, in contrast with the vibronic states in future work. dynamics in Figure3. As shown in the present contribution, the Our calculations indicate that the large re- FrD-LVC approach can thus provide many in- organisation energy of the G→C(CT)1 is the teresting insights into complex phenomena in- key to explain its population. As shown in volving both intra- and inter-chromophoric ex- Table3, the predicted planar adiabatic and cited states, in a fully quantum dynamical pic- diabatic minima of the G→C(CT)1 state are ture. Furthermore, in cases when an LVC PES ∼1 eV more stable than those of the ππ∗ states does not suffice to completely describe the dy- according to CAM-B3LYP, and ∼0.6 eV more namics, it can give useful indications on the rel- stable according to ωB97X-D. This stability ative importance of the different excited states results in similar population transfer to the and be used as a ‘first’ check before apply- G→C(CT)1 state by both CAM-B3LYP and ing more computationally expensive dynamical ωB97X-D models, despite the G→C(CT)1 state calculations, such as the ‘on-the fly’ methods, not being the lowest lying state at the FC point on reduced dimensionality systems. Alterna- with ωB97X-D, and it lying 0.4 eV higher in en- tively, the FrD-LVC approach can be used as a

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