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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,y Martha Yaghoubi Jouybari,z Haritha Asha,y Fabrizio Santoro,∗,z and Roberto Improta∗,y yConsiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), via Mezzocannone 16, I-80136 Napoli, Italy zConsiglio 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 photo- physics 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 !B97X-D func- tionals, 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 jdi = pendent Hartree (ML-MCTDH) method for (jd i ; jd i ;:::; jd 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) jd i hd j)+ 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)(jdii hdjj + jdji hdij); 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.
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