# The mystery of sub-picosecond charge transfer following irradiation of hydrated uridine monophosphate

Aurélien de la Lande, Sergey Denisov, Mehran Mostafavi

► To cite this version:

Aurélien de la Lande, Sergey Denisov, Mehran Mostafavi. The mystery of sub-picosecond charge transfer following irradiation of hydrated uridine monophosphate. Physical Chemistry Chemical Physics, 2021, 23 (37), pp.21148-21162. 10.1039/D0CP06482C. hal-03868450

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Submitted on 17 Feb 2025

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# The Mystery of Sub-Picosecond Charge Transfer Following
# Irradiation of Hydrated Uridine Monophosphate

Aurélien de la Lande¹*,

Sergey Denisov¹, Mehran Mostafavi¹

1: Institut de Chimie Physique, CNRS, Université Paris Saclay (UMR 8000). 15 avenue Jean Perrin, 91405 France.

To whom correspondence should be addressed: aurelien.de-la-lande@universite-paris-saclay.fr

<figure><img src="image_2.png" /></figure>

## ABSTRACT

The early mechanisms by which ionizing rays damage biological structure by so-called direct effect are largely elusive. In a recent picosecond pulse radiolysis study of concentrated uridine monophosphate solutions [J. Phys. Chem. Lett. **2018**, 9, 5105], unexpected results have been regarding the oxidation of the nucleobase. The signature of the oxidized nucleobase couldn't be
detected 5 ps after the electron pulse, but only oxidized phosphate, raising intriguing interrogations
about the identity of charge transfer mechanisms that could explain the absence of U⁺.

We address here this question by means of advanced first principles atomistic simulations of
solvated uridine monophosphate, combining Density Functional Theory (DFT) to polarizable
embedding schemes. We contrast three very distinct mechanisms of charge transfer covering the
atto-, femto- and picosecond timescales. We first investigate the ionization mechanism and
subsequent hole/charge migrations on atto- to a few femtosecond time scales under the frozen
nuclei approximation. When then consider a nuclear-driven phosphate-to-oxidized-nucleobase
electron transfer, showing it is an uncompetitive reaction channel on the sub-picosecond time
scale, despite a high exothermicity and significant electronic coupling. Finally, we show non-
adiabatic charge transfers are enabled by femtosecond nuclear relaxation after ionization. We
show that electronic decoherence and electronic coupling strength are key parameters
determining hopping probabilities. Our results provide important insights on the interplay between
electronics and nuclear motions in the early stages of the multiscale responses of biological matter
subjected to ionizing rays.

INTRODUCTION

The complex molecular mechanisms by which ionizing radiation damages biomolecules via the
so-called direct effect are still largely undiscovered. While the chemical alterations caused by the
products of water radiolysis (e.g hydroxyl and hydrogen radicals, solvated electrons...), have been
investigated in depth.¹,² The cascade of physical-chemical and chemical processes triggered by
high energetic particles directly deposing energy within biomolecules are by contrast more
challenging to investigate.³,⁴ The reductive pathway involving the reactivity of low, or very low,
energy electrons has for example been thoroughly investigated by shooting electrons on DNA
films.<sup>4-6</sup> The oxidative pathway that is enabled following the creation of multiple oxidized moieties during the physical stage has also attracted great interest. DNA strand breakage is an example of deleterious lesion for cell viability that can result from irradiation.<sup>7,8</sup> Formation of radicals on the C5' atom of DNA is thought to be a major path to strand breakage<sup>9</sup>. Experimentally, the difficulty of addressing the formation of such lesions in native DNA/RNA has led researchers to investigate model systems, for example phosphoester compounds or nucleotides.<sup>9,10</sup> In this context, some of us recently reported new insights on the ultrafast responses of uridine monophosphate (thereafter abbreviated as USP, for Uridine, Sugar and Phosphate groups) by picosecond pulse radiolysis coupled to UV-visible probe spectroscopy.<sup>10</sup> Using a beam of accelerated electron with 5 ps duration, we found that the first species to be detected after irradiation were the oxidized phosphate (P<sup>+</sup>) and the reduced uracil base (U<sup>+</sup>). The former species could clearly be attributed to direct ionization of phosphate group by the radiation since the high redox potential of phosphate prevent oxidation by other chemical species.<sup>11 U<sup>+</sup> was, on the other hand, the result of electron attachment and was found to be stable over subsequent millisecond time range. Surprisingly though, oxidized uracil (U<sup>+</sup>) could not be detected in spite of its spectroscopic signature which was in principle accessible to our experimental set-up; at variance with S<sup>+</sup> that was not detected because it absorbs in far UV (Ultra Violet), a region of the electromagnetic spectrum our set-up is not able to probe. The non-observance of U<sup>+</sup> is particularly intriguing as the rule of thumb to predict ionization sites in radiolysis experiments is that ionization is proportional to the electron density on each site.<sup>12</sup> Ionization by high energy charged particles effectively involves so much energy that it is not chemically selective. All molecular fragments are expected to be ionized with a probability more or less proportional to their number of electrons. Alternatively said, the U, S and P subunits that comprise respectively 45, 54 and 47 electrons, are expected to be roughly responsible for 33, 37 and 30% of the total ionization of USP, respectively. Therefore, the non-observance of U<sup>+</sup> at the end of the electron pulse points toward the existence of an ultrafast charge transfer that would have restored the neutral oxidation state of U, for the fraction of USP molecules
irradiated at the level of the nucleobase. Such ultrafast electron transfers could not be time-
resolved experimentally though. Importantly, we note that inter-molecular charge transfer could
unequivocally be ruled out experimentally by comparing radiolysis of USP solutions with radiolysis
of uridine nucleobase in phosphoric acid solutions.¹⁰

The objective of this article is to explore possible mechanisms of ultrafast electron transfers toward oxidized U⁺ by means of computer simulations focusing on the as-ps time domain. In the first one, electron transfer is driven by electron correlation, *i.e.* by charge migration at fixed nuclear positions. Charge migration is a mechanism originally proposed by Prof. Cederbaum,¹³ that has gained strong momentum in the field of attosecond spectroscopy.¹⁴,¹⁵ For example, experimental (mass) spectra of small amino acids recorded in attosecond pump-probe experiments revealed beatings on the femtosecond time scale that could be understood from the analysis of hole migrations, some of which exhibited similar characteristic frequencies.¹⁶,¹⁷

In the context of condensed matter radiolysis, we proposed that charge migrations could be
responsible of the ultrafast charge transfer between the radical cation of water produced by
radiolysis and surrounding molecules.¹⁸ We recently reported simulations of large DNA models by
MeV charged particles (H⁺, He²⁺ or C⁶⁺) demonstrating that effectively, charged migrations were
expected to take place after irradiation.¹⁹ These previous works give credibility to the present
hypothesis that charge migration may explain ultrafast reduction of U⁺, and justification for further
investigation.

The two other charge transfer mechanisms we consider are driven by nuclear motion. One relies
on the Marcus theory of electron transfer which is now a well-established formalism to account for
the thermodynamics and the kinetics of ET reactions in chemistry, material sciences or in
biology.²⁰ The other is a non-adiabatic electron transfer that follow nuclear relaxation after
ionization by the radiation source.
Advanced simulations approaches are required to explore the relevance of each of the three mechanisms. For simulating charge migrations in large molecular systems, we devised an electron dynamics engine relying on Real-Time Time-Dependent Auxiliary Density Function Theory (RT-TD-ADFT).<sup>21</sup> On the other hand, nuclear motion driven electron transfer have been investigated with ab initio Molecular Dynamics (MD) simulations using Constrained DFT (cDFT), again with an in-house code.<sup>22</sup> cDFT permits to define *ad hoc* charge transfer states at the DFT level within the phenomenological Marcus theory picture<sup>23,24</sup>. All simulations (RT-TD-ADFT and cDFT) have been conducted in the framework of hybrid QM/MM (Quantum Mechanics/Molecular Mechanics) approaches with polarizable force fields<sup>25</sup>. Our approach thus accounts explicitly for the effect of the USP environment including electrostatic induction.

## METHODOLOGY

All DFT simulations have been carried out with deMon2k.<sup>26</sup> deMon2k implements Kohn-Sham DFT with localized Gaussian type atomic orbitals as basis sets. The program relies on variationally fitted densities<sup>27</sup> to significantly speed-up the simulations. Fitted electron densities are employed to evaluate Coulomb and Exchange-Correlation (XC) contributions.<sup>28</sup> Auxiliary DFT (ADFT) has been coupled to molecular mechanic (MM) force fields to describe explicitly the aqueous environment of the USP molecule. We utilized the in-deMon2k implementation of QM/MM methodology as described in Ref.<sup>25</sup>. Water is described either with the non-polarizable TIP3P model<sup>29</sup> or with the polarizable POL3 model.<sup>30</sup>

### System preparation

The system investigated experimentally is the doubly deprotonated uridine monophosphate. The system was prepared at MM level with the AMBER package.<sup>31</sup> The USP molecule was solvated in a 70 Å edge cubic water box. No counter-ions were added. The -2 charge from USP was
counter-balanced by a net-neutralizing plasma implicitly included in the Ewald summation
technique we used. The polarizable POL3 water model was employed at this stage. After
geometry optimization the system was equilibrated for 500 ps in the NVT (constant number of
particles, volume and temperature) ensemble at 300K followed by 300 ps of equilibration in the
NPT (constant number of particles, pressure and temperature) ensemble under 1 atm.

To run QM/MM simulations, we have considered the last structure generated by the MD
simulation, placing the USP molecule at the center of the simulation box by reimaging. As
deMon2k does not implement periodic boundary conditions, but enables DFT/MM/solvation
continuum schemes, we shaped the system as illustrated on Figure 1, retaining the USP molecule
solvated in a spherical water droplet with diameter of 33 Å.

<figure><img src="image_3.png" /><figcaption>Figure 1: left, Molecular simulation set-up employed in this study for DFT/MM/Continuum simulations. The QM region (DFT) encompasses only the USP molecule or USP plus its first solvation shell (see text for details). In MM partition is described by a polarizable force field. MM water molecules shown in green have their motion restrained during MD simulations to avoid evaporation. Right, partitioning of the USP molecule into uracil (green), ribose (red) and phosphate (orange) moieties, with atom labels. For clarity, hydrogen atoms are not shown.</figcaption></figure>

We carried out a 40 ps QM/MM MD simulation at 300 K of the system in the resting redox state,
i.e. before radiolysis (Figure 1). For these simulations, the QM region encompassed only the USP
molecule in order 1) to reduce the computational cost of the simulations and 2) to avoid difficulties
that would arise due to QM waters migrating toward the MM region (and vice versa). Structures
were extracted regularly along this MD trajectory to serve as starting geometries both for RT-TD-ADFT electron dynamics simulations and *ab initio* molecular dynamics simulations with constrained DFT (see details below).

## Electron dynamics simulations

We simulated charge migrations carrying out Electron Dynamics simulations (ED) by Real-Time-Dependent Auxiliary Density Functional Theory (RT-TD-ADFT).²¹ The QM subsystem encompassed the USP molecule and the first solvation layer (51 water molecules) for a total of 185 atoms (678 electrons). The water environment was described by the POL3 polarizable water model (3,526 molecules). The electron density was propagated numerically by the second order Magnus propagator coupled to a predictor-corrector scheme with a time-step of 1 as (attosecond).³² The induced dipoles on the MM regions were fully relaxed at every ED step. The exponential of the Kohn-Sham potential entering the Magnus propagator was evaluated by a Taylor expansion encompassing 40 terms. We employed the ScaLapack library for this task.³³ The DZVP-GGA basis set (Double Zeta with Valence Polarization optimized for Generalized Gradient Approximation XC functionals)³⁴ was chosen for all atoms except for water oxygen atoms for which the aug-cc-pVDZ was chosen³⁵. It was demonstrated that the amount of deposited energy upon collision of molecules by swift ions is sensitive to the basis set³⁶,³⁷. Our choice of basis set results from a compromise between cost and accuracy. We have repeated a set of simulations with a combination of TZVP³⁴ (all atoms) and aug-cc-pVDZ (oxygen water atoms) basis set, or a combination of cc-pVQZ³⁸ (all atoms) and aug-cc-pVDZ (oxygen water atoms). We found that although the amount of deposited energy is higher with the richest basis sets, the subsequent charge flows that are of interest for the present study are essentially basis set insensitive (Figure S1). The Coulomb and XC energies and potentials were computed with the help of fitted densities expanded over the automatically generated GEN-A2 auxiliary basis set for hydrogen atoms and over the GEN-A2* auxiliary basis set on phosphorous, oxygen, carbon and nitrogen atoms.
Regarding the auxiliary basis set, we have recently showed that the one chosen here ensure good reliability of the simulations³⁹. We used the PBE (Perdew–Burke-Ernzerhof) exchange correlation functional.⁴⁰ The auxiliary electron density was integrated numerically every 5 as to extract atomic charges following the Hirshfeld partition scheme.⁴¹ A complex absorbing potential (CAP) was added to the imaginary part of the Kohn-Sham potential to remove electrons, eventually reaching a threshold distance from the QM region. A CAP is needed with localized basis set quantum chemistry codes as secondary electrons produced by irradiation cannot be described at any arbitrary distance from the region of emission due to the finite spatial extension of local basis sets. We removed secondary electrons when they reached a distance of 7 Å from the QM region. Our tests showed that such a distance is a good compromise that avoids introducing unreliable biases in the propagation. Technically the CAP function is defined in deMon2k as a superposition of atom centered $CAP_a$ on each atom a, i.e. $CAP(R) = \min_a CAP_a(R)$, with :

$$CAP_a(R) = \begin{cases} V^{max} \sin^2\left(\frac{\pi}{2W}(R-R^\circ)\right) & \text{for } R < R^\circ \\ V^{max} & \text{for } R^\circ + W < R < R^\circ \\ V^{max} & \text{for } R > R^\circ + W \end{cases} \quad (1)$$

where $V^{max}$ is the maximum value of the absorbing potential, $W$ is the width of increase of the atomic CAP and $R^\circ$ is the distance threshold at which starts the atomic CAP. $V^{max}$, $W$ and $R^\circ$ were set to 10 Ha, 15 Å and 7 Å respectively.

We used three different schemes to define the initial conditions of electron dynamics (ED) simulations of hole dynamics. This will be detailed in the Results section. In the first two schemes, ionization was triggered by collision of the molecular system by 0.1 MeV alpha particles or by 50 eV electrons that we both describe as classical particles. In each simulation, the projectile was situated 70 Å away from the QM region defining, by convention, time zero. Schemes 1 and 2 allow for the simulation of ionization dynamics and subsequent charge migrations. By contrast the third scheme relies on the “sudden ionization” approximation without attempting to simulate ionization
*per se*. For example, a sub-set of selected MOs (Molecular orbitals) generated by the SCF (Self-Consistent-Field) procedure can be depopulated, leading to a non-stationary state from which ED can be launched. To operate the selection of MOs, we first localized the MOs according to the Pipek-Mezey method⁴². The initial state produced by this procedure does not correspond to a pure state of the Kohn-Sham system, and is therefore rather arbitrary.

## Marcus theory electron transfer modelling

The free energy curves associated to electron transfer from P to U⁺ have been built for eleven starting structures extracted from the 40 ps DFT/MM MD simulation for the resting redox state. The corresponding nuclear positions and velocities were used as initial conditions of cDFT/MM MD simulations in each of the (US)⁺P and (US)P⁺ redox states. Previous experimental results indicate that charge transfer has already taken place a 5 ps after the electron pulse,¹⁰ the cDFT/MM MD were thus carried out with the same duration. Charge transfer states were obtained by forcing the charge difference between the donor and acceptor to ±1, based on the Hirshfeld partition scheme. We then reprocessed each trajectory every 10 fs to determine the vertical energy gaps distribution and to build Electron transfer (ET) free energy curves (see SI). The polarizable water model was used for this reprocessing stage. It transpired that full convergence of both density and induced dipoles in cDFT/MMpol single point energy calculations were challenging to achieve for USP, a difficulty we traced back to the use of a polarizable water model. To circumvent this difficulty, we adopted a strategy commonly found in the literature,⁴³ consisting in turning off the MM induced dipoles update during the SCF procedure. Only once the SCF had converged, were the MM induced dipoles optimized in presence of partial charges on the QM atoms, the latter were derived from Hirshfeld population analyses.⁴¹ This approach captures most of the induction energy.⁴³,⁴⁴ The electronic coupling $H_{if}$ between the diabatic states were also computed every 10 fs. We chose BH&HLYP XC functional⁴⁵ for running all cDFT/MM calculations (MD trajectories
generation and reprocessing). This functional alleviates the risk of SCF convergence issues and
ensures reliable electronic coupling values.⁴⁶ More technical details are given in SI.

### ET characteristic times via a Mean First Passage

A similar procedure as above was followed to investigate relaxation of ionized USP on the (US)$^{+}$P potential energy surface. Contrary to the previous section, we don't attempt to build free energy curves, but a mean first passage through crossing points and the associated probability for electron hopping. We have considered 21 regularly spaced structures from the initial 40 ps BOMD simulation, and run cDFT/MM MD on the (US)$^{+}$P. More details will be given below and in SI.

### Data processing and data availability

The deMon2k developer versions utilized were the 4.4.5 and the 6.0.2, for RT-TD-ADFT/MMpol and cDFT/MMpol simulations respectively. They are readily available on request to the authors.
The computational data generated by deMon2k were analyzed with the R program for statistical analyses (using the graphical RStudio interface)⁴⁷, and the coda package.⁴⁸ Details on the computation of statistical uncertainties are detailed in Supplementary Information. All the Rstudio scripts used to produce the graphs and the tables reported in this article can be found in Supplementary Information. In addition, all the data generated by deMon2k and the scripts are freely available on the Zenodo data repository (DOI: 10.5281/zenodo.4290681).

## RESULTS AND DISCUSSION

### Charge migrations subsequent to collision with 0.1 MeV He$^{2+}$ ions

Firstly, we analyzed the response of the electron cloud after ionization of the USP molecule on the femtosecond time scale. The aim is to investigate the ionization mechanism and also whether charge migration could provide a relevant mechanism to account for sub-picosecond hole transfer
from the uracil nucleobase to the phosphate group. Charge migration was simulated by pure RT-
TD-ADFT simulations which we utilized under the frozen nuclei approximation (see the
methodology section). We adopted a QM/MMpol set-up in which the QM region comprises the
USP molecule and its first solvation layer while the MM region is described by a polarizable force
field (Figure 1). We have carried our three sets of electron dynamics simulations with different
initial conditions. In the first two sets we induced ionization by simulating the collision of USP with
either a 0.1 MeV α particle or a 50 eV β⁻ particle (an electron). The third set corresponds to
simulations assuming a sudden ionization has taken place, and will be detailed below. We chose
these energies because they are close to energies at which collisions lead to the highest ionization
probabilities. Here our objective is not to evaluate average stopping power or ionization cross
sections as function of incoming projectile kinetic energy but to generate holes in solvated USP in
order to examine subsequent charge migrations. The solvated USP molecule is initially prepared
in the ground state. As illustrated in Figure 2, we have considered five collision trajectories (named
CU1, CU2, CS, CP and CW). In CU1 and CU2 trajectories, the projectile strikes the aromatic ring
of the uracil base perpendicularly (CU1) or longitudinally (CU2), respectively. The projectile
passes through the center-of-mass of the nucleobase. In CS trajectory, the projectile traverses
the sugar group (S) roughly perpendicular, going through its center-of-mass, which is close to the
C2' and C3' atoms (see Figure 1 for atom labelling). In CP, the projectile strikes the phosphate
groups. Finally, trajectory CW triggers radiolysis of the first hydration layer without direct collision
with the USP molecule. This trajectory is intended to examine a possible charge transfer between
a H₂O⁺ cation formed upon radiolysis and the ribose. Three water molecules are successively
struck by the projectile in CW trajectories.
<figure><img src="image_4.png" /><figcaption>Figure 2: Four projectile trajectories considered in irradiation of USP. For clarity we only show atoms treated at the DFT level. Left is a side view of solvated USP, Right is a view from below.</figcaption></figure>

The energy profile associated to these collisions are shown in Figure S2. Between 80 and 300 eV are deposited into the electron cloud depending on the simulation. Such huge energy depositions are typical of the extreme perturbations caused by the incoming charged ion and explain molecule ionization. We note that no electrons are absorbed by the absorbing potential which is positioned 7 Å away from the QM region. Irradiation thus cause electron emission, but the emitted electrons remain within the QM region, being somehow confined by the MMpol environment. As we shall see below, secondary electrons are scattered over the solvation layer.

We start by analyzing collisions with alpha particles. The graphs in Figure 3 depict charge variations of the molecular sub-units composing the QM region with respect to the ground state density, i.e. before collision. The charges on U, S and P fragments are shown in green, red and orange respectively while the total charge of the solvation water layer is shown in blue (Figure 3). We arbitrarily set time origin as the time at which the projectile is positioned 70 Å away from the QM region. Collisions CU1, CU2, CS and CP logically give rise to different charge evolutions but also exhibit common features. Starting with CU1, we observe a sharp decrease of the electronic charge of the nucleobase just before collision. This is followed by a very fast increase up to a
value of 0.5. This two-phase evolution is typical of the response of electron clouds collided by a
positively charged projectile. We named this an ebb-and-flow mechanism of ionization in a
previous work.¹⁹ During the ebb-phase, when the projectile is approaching the molecule, it strongly
polarizes the electron density, draining electrons from the surrounding atoms toward the fragment
about to be struck. On the graph corresponding to the CU1 trajectory, we clearly see a strong
decrease of the uracil charge with a concomitant increase of the total charge of water molecules
and to a lesser extent of the ribose moieties. Immediately after, the projectile leaves the uracil
fragment, the electron density experiences a backflow from U toward the surrounding moieties
which (flow-phase). The net flow of electron during the ebb-phase is smaller than during the flow-
phase, reflecting partial ionization of the collided fragment. The emitted fraction of electron
localizes on the water solvation shell as deduced from its charge, which then becomes negative.

The electronic motion that characterizes ionization of the collided fragment is extremely fast and
takes place within a few tens to a few hundreds of attoseconds. After this primary excitation step,
the fragment charges continue to fluctuate on longer time scales, reflecting the existence of charge
flows within the electron cloud, *i.e.* charge migrations. For example, a little bit less than a
femtosecond after collision, the charge on U decreases again while that of the sugar group
increases concomitantly. The total charge on the U+S pair (green dashed line), on the other hand,
is relatively constant. This indicates a flow of electron density from the sugar group toward the
base which is likely to be propelled by the strong correlation among electrons localized on these
two fragments. Recall however that we use a GGA functional (PBE) that suffers from self-
interaction-error. As such, charge flows might be overestimated in our simulations. On the other
hand, we do not observe significant ionization of the phosphate group which keeps more or less
constant charge over time.
<figure><img src="image_5.png" /><figcaption>Figure 3: Charge variations with respect to the ground state density of U (green), S (red), P (orange) and the solvation shell (blue) upon collision of USP with 0.1 MeV He²⁺ ions. The green dashed lines correspond for each simulation to the sum of the charge variations of U and S. The CU1, CU2, CS, CP and CW collision conditions are illustrated on Figure 2. For the CW case, the charges of the three molecules struck by the projectile are subtracted from the blue curve and shown separately as dashed-dotted light blue lines.</figcaption></figure>

Trajectory (CU2) reveals similar trends in the evolution of the different fragment charges except that the amplitude of ionization of U is much more pronounced during the ebb-phase. It reaches a charge of 1.3 vs. 0.5 with the CU1 trajectory. In CU2, the projectile propagation line is collinear to the aromatic plane and, consequently, the projectile traverses a wider slice of electron density.
This leads to a larger deposition of energy (196 eV vs. 111 eV in CU2 and CU1 respectively, Fig. S2). The electronic system, being more excited emits more electrons. As for the CU1 trajectory, the hole created on the nucleobase delocalizes over the sugar group after a few femtoseconds. Looking at the concomitant evolutions of the charge of the U+S moieties (green dashed lines) with the total charge of the hydration shell, we note a decrease of the former compensated by an increase of the latter between 4 and 7 fs. This trend is likely to reflect charge recombination between the hole formed on the U+S pair and secondary electrons localized on the solvation layer. For the CU2 trajectory, no ionization of the phosphate group was detected.

Trajectory CS involves direct collision of the sugar group, with an ebb-and-flow mechanism of ionization once again at play. A small transfer of the hole initially created on the sugar moieties toward the nucleobase is detected on the 4-7 fs time window. As for the previous case a significant amount of charge recombination is detected between the U+S pair and the water solvation shell. Conversely, the presence of a +1 charge on the sugar did not trigger any significant electron flow from the nearby phosphate group, which kept its initial charge, despite the geometrical proximity between the two moieties.

CP shows a marked ionization of the phosphate group. Emitted electrons localize, as previously, on water molecules. The hole created on the phosphate group continuously decays on the femtosecond time scale. Meanwhile both the U nucleobase and the sugar accumulate positive charge, and to a lesser extent the total charge of the solvation shell slightly increases. This correlated evolution indicates important flow of electron from the U-S group toward the phosphate group.

We finally consider the CW trajectory that involves irradiation of water solvation molecules. The three water molecules successively struck by the projectile are plotted separately from the ensemble of other water molecules. They are shown with dashed-dotted lines. The three waters are each partially ionized with charges comprised between 0.4 to 1.3 just after collision. Therefore,
the simulation suggests that the probability of formation of more than one ionized water molecules within a rather small volume is not negligible. The secondary electrons localize on the other water solvation shell and on the USP molecule, and essentially the U+S subunit. Slow but steady charge recombination between secondary electrons in USP and ionized water molecules are detected during the following femtoseconds.

Charge migration subsequent to collision with 50 eV e⁻

The first set of RT-TD-ADFT simulations has dealt with the eventuality of irradiation by a heavy ion ionizing radiation. Actually, most chemical damage is thought to proceed via the shower of secondary electrons produced by primary ionizations. We consider this eventuality in a second set, simulating irradiation by classical 50 eV electrons. Owing to the mass of the electron which is three orders of magnitude smaller than the mass of the helium nucleus used in the first set, its quantum nature is much more pronounced, making the simulation of irradiation technically more difficult⁴⁹. For the sake of simplicity, we make here the crude approximation that the incoming electron projectile can be modelled as a classical particle holding a -1 charge. The de Broglie wavelength of a 50 eV electron is 1.75 Å. We thus ignore exchange-correlation interactions between the projectile and the electrons composing the molecular electron cloud, and consider the projectile to be a punctual charge. A consequence of this is that no electron attachment can be simulated (electron attachment is however not likely at this energy), nor other subtle quantum effects. We depict on Figure 4 the outcomes of RT-TD-ADFT simulations reflecting the response of the electron cloud upon collision with such low energy electrons. We have considered the same irradiation conditions as for He²⁺ ions. Irradiation by 50 eV deposit also large fraction amount of energy (Figure S2), reaching several tens of eV.

Clear similarities with irradiation by He²⁺ ions appear on the graph depicting charge evolutions of the fragments (Figure 4) but also note qualitative differences. First of all, the ebb-and-flow mechanism is recovered but operates in an opposite direction. The charges of the moieties about
to be struck by the electron now increase when the incoming electron is approaching. Taking
trajectory CU1 as example, we see a first increase of the uracil base charge accompanied by a
decrease of the solvation layer charge (this was the reverse with He<sup>2+</sup> projectiles). This is easily
explained by the repulsive interaction between incoming electron and the electron cloud. Another
difference with irradiation by He<sup>2+</sup> ions, is that the backflow of electrons on the collided fragment
and the phase of electron emission becomes clearly resolved: the uracil base charge goes back
to zero after the initial polarization before increasing again as a result of electron emission.
Electrons emission is thus not instantaneous but occurs after a few tens of attoseconds after
collision. This “reversed” ebb-and-flow mechanism is seen on each CU1, CU2, CS, CP and CW
trajectories. Interestingly the subsequent responses are similar to the analysis with helium nuclei.
Firstly, when holes are initially formed on the uracil base (CU1, and CU2), they become shared
with the ribose moieties but do not migrate to the phosphate group. Secondly, slow charge
recombination takes place on the femtosecond time scale between the emitted electrons toward
the water shell and the (U+S) moieties.

The CP trajectory deserves special discussion. As expected, the phosphate subsystem undergoes
a strong electronic depopulation with a charge variation of up to 0.7e-. However, in less than one
femtosecond, the charge on the phosphate group almost goes back to zero; i.e. it recovers the
number of electrons it held before collision. The charge of the (U+S) group is remarkably steady
after ionization, indicating that the water shell is absorbing the hole formed on the phosphate group
after collision.

Finally, the CW trajectory with 50 eV is found to be similar with 0.1 MeV helium nuclei, apart from
the “reversed” ebb-and-flow” mechanism at play during ionizations of the water molecules.
<figure><img src="image_6.png" /><figcaption>Figure 4: Charge variations with respect to the ground state density of U (green), S (red), P (orange) and the solvation shell (blue) upon collision of the USP molecule with 50 eV e⁻. The green dashed lines correspond to the sum of the charge variations of U and S. The CU1, CU2, CS, CP and CW collision conditions are illustrated on Figure 2. For the CW case, the charges of the three molecules struck by the projectile are subtracted from the blue curve and shown separately as dashed-dotted light blue lines.</figcaption></figure>

As an intermediate conclusion, recalling our initial motivation to account for reduction of U⁺, we noted that once a hole has been created on the base, on the ribose group or on a water solvation shell, it does not migrate to the phosphate group by charge migration. To verify this conclusion is
not an artefact coming from the choice of a specific nuclear geometry, we have repeated the He²⁺ collision trajectories CU1 and CU2 for eleven sets of nuclear coordinates extracted from a Born-Oppenheimer MD simulation (see Methods). Results can be found in SI (Fig. S3.). As expected, the set of initial geometries generates some scattering in the curves depicting charge fluctuations on different fragment. Nevertheless, all the conclusions that we have drawn beforehand remain true, ruling out the risk of an artefact caused a choice of one specific geometries.

## Charge migration after sudden ionization

Another point of caution has to be raised. RT-TD-ADFT is a mean-field approach. Thus, the conclusions drawn so far are correct within this average hypothesis. As a consequence, if only a few channels populated upon irradiation effectively lead to hole transfer from the base to the phosphate, they would be hidden in the average and not easily detected by the afore described RT-TD-ADFT simulations.

To explore this eventuality, we have carried out supplementary RT-TD-ADFT simulations in which ionization is not produced by explicit simulation of the interaction between the electron cloud and a projectile, but assumed to take place instantaneously. Technically, this can be achieved by depopulating completely or partially a set of molecular orbitals from the SCF solution and launching a RT-TD-ADFT simulation from the resulting fictitious state. We localized the MOs generated by the SCF procedure with a Pipek-Mezey procedure,⁴² and we selected MOs that are mainly localized mainly on the U, S or P groups respectively. The results and the analyses can be found in SI (Fig. S4). We observe a fast relaxation during the first tens of attoseconds with a decrease of the charge on the base and on the sugar, followed by a slower further decrease, and increase of the charge of the solvation shell. Globally, we recover a picture similar to the previous simulations, with not marks of significant phosphate group oxidation.
To summarize, we have seen that holes formed by direct ionization of the uracil base do not migrate to the phosphate group by a purely charge migration process. A charge migration mechanism at fixed nuclear position cannot account for the non-observance of ionized uracil a few picoseconds after the pulse. Actually, it is clear that on such a long-time scale compared to the attosecond time scales characterizing charge migrations, atom nuclei have time to move, and eventually induce charge migrations⁵⁰. In the next section we follow different simulation protocol of investigate the time scale of nuclear motion driven electron transfers.

## Electron transfer within the Marcus theory

In this section, we investigate whether reduction of the cationic uracil nucleoside by the phosphate group can be accounted for by a Marcus theory kind of mechanism. The Marcus theory formalism relies on the definition of phenomenological (diabatic) charge transfer states, hereafter labelled as initial (i), and final (f). In the high temperature limit and in the limit of weak electronic coupling the ET rate expression reads:

$$k_{ET} = \frac{2\pi}{\hbar} \langle H_{DA}^2 \rangle \frac{1}{\sqrt{4\pi\lambda^{St}/\beta}} \exp \left( \frac{-\beta(\Delta A^\circ + \lambda^{St})^2}{4\lambda^{St}} \right) \quad (2)$$

$\Delta A^\circ$ is the reaction free energy, $\lambda^{St}$ is the Stokes reorganization energy and $H_{DA}^2$ is the squared electronic coupling between the charge transfer states. $\beta = 1/k_B T$ with $k_B$ being the Boltzmann constant and T the temperature.

Within the Linear Response Approximation that underlies the Marcus theory, $\Delta A^\circ$ and $\lambda$ can be calculated from the average potential energy gap between the diabatic states, namely ($\Delta E_{if} = E_f - E_i$).⁵¹

$$\Delta A^\circ = \frac{1}{2} (\langle \Delta E_{if} \rangle_i + \langle \Delta E_{if} \rangle_f) \quad (3)$$
$$ \lambda^{\text{St}} = \frac{1}{2} (\langle \Delta E_{if} \rangle_i - \langle \Delta E_{if} \rangle_f) \qquad (4) $$

$$ \lambda_x^{\text{var}} = \frac{\beta \cdot \sigma_x^2 (\Delta E_{if})}{2} \qquad (5) $$

$\langle...\rangle_x$ and $\sigma_x^2(...)$ respectively denote the average and the variance of the energy gap emerging from the NVT ensemble corresponding to the electronic state $x$ ($i$ or $f$). For ergodic systems and provided sufficient conformation sampling for both diabatic states, $\lambda^{\text{St}} = \lambda_i^{\text{var}} = \lambda_f^{\text{var}}$. In practice the conformational space has been sampled by ab initio Molecular Dynamics (MD) simulations (see Methodology section). We have repeated the simulations for eleven starting structures extracted from a 40 ps BOMD simulation of the system in the resting state.

The electron dynamics simulations described in the previous section have shown that the +1 charge produced by radiolysis on the nucleobase delocalizes on the sub-femtosecond time scale over the U+S subsystems. We therefore shall consider as initial ($i$) and final ($f$) diabatic states the $(US)^+P$ and $(US)P^+$ forms respectively. We have used constrained DFT to access such ad hoc charge transfer states diabatic states. We enforce with cDFT the charge difference between the donor and the acceptor to be $\pm 1$, leaving the electron density the flexibility to relax within each group to minimize energy.

As seen on Fig. S6 showing the evolution of the vertical energy gaps, it takes less than 100 fs after ionization of solvated USP for the system to reach a new equilibrium. We have thus discarded the 10 first evaluations (100 fs) of $\Delta E_{if}$ and $H_{if}$ in all series to calculate the Marcus theory ET parameters. Table 1 collects the thermodynamic parameter considering all the 10 fs spaced snapshots from 100 fs to 5 ps. Electron transfer from P toward $(US)^+$ is always found to be strongly favorable with reaction free energies ranging from -1.26 to -1.56 eV. For comparison, we have calculated the change in free energy for an electron transfer between $(O_3POCH_3)^2-(H_2O)_2$ and the
uracil nucleoside at the DFT(ωB97XD)/PCM⁵² level of calculation with implicit solvation (see SI),
finding a value of -1.52 eV. The large driving forces obtained from our *ab initio* MD simulations are
thus in line with the difference of redox potentials between uracil nucleoside and phosphate
molecules calculated on small models with implicit solvation models.

The Stokes reorganization energies ($\lambda^{St}$) range from 3.14 to 3.51 eV, which are also rather large values. A deeper analysis shows that most of the reorganization comes from the solvation shell. Fig. S7 compares the radial distribution functions (RDF) of water molecule atoms around the USP molecule. The USP-phosphate-water-oxygen-atoms RDF indicates that the first two solvation layers of the phosphate group are more structured on the (US)$^+$P potential energy surface than on the (US)P$^+$ one, with three more water molecules present in the first hydration layer in the former case. Similarly, hydrogen bonds from water molecules toward the uracil O2 and O4 atoms are tightened in the (US)P$^+$ redox state. Besides the restructuration of the first solvation layer, the RDF plotted in Fig. S7 further indicates a modification of the bulk water structure up to 10 Å. The reorganization calculated from the variance of the energy gaps ($\lambda_i^{var}$ and $\lambda_f^{var}$) are seemingly larger than the Stokes reorganization energies, noticing however, that the associated statistical uncertainties are much larger.

We have plotted the Marcus free energy curves (see SI for details), showing in Figure 5 (Top) parabolas obtained for the representative fifth simulation. The ten other graphs can be found in SI (Fig. S8). The activation free energies calculated as $(\Delta A^{\circ} + \lambda^{St})^2/4\lambda^{St}$ amount to small fraction of eV. Small activation barriers are the combined consequence of strong driving forces and high reorganization energies.

The electronic coupling between the two redox states amounts to 0.076 ± 0.017 eV and 0.024 ± 0.014 eV on the (US)$^+$P to the (US)P$^+$ potential energy surfaces (Fig. S9). We note that the electronic coupling is significantly higher for the initial state than for the final state. Intuitively, one can understand this considering that the electron donor and acceptor should be closer in the
(US)⁺P state owing to the strong electrostatic attraction between the two partners which should favor lower donor-to-acceptor distances. However, we could not find a simple relationship between the electronic coupling and the distance. Nevertheless, as the electronic coupling is rather large, we should estimate the activation free energy (ΔA<sup>act</sup>) entering eq. 2 as (ΔA° + λ<sup>St</sup>)<sup>2</sup>/4λ<sup>St</sup> – ⟨H<sub>if</sub><sup>2</sup>⟩<sub>i</sub><sup>1/2</sup>. Results are reported in Table 1. They range between 0.16 and 0.24 eV with statistical uncertainties of the same order. The latter are thus significant given the rather good statistical knowledge of ΔA°, λ<sup>St</sup> and H<sub>if</sub> taken individually. The exponential function entering the definition of ΔA<sup>act</sup> is the origin of this high uncertainty.

The characteristic ET times ($\tau_{ET}^{NAM}$), defined as the inverse of the non-adiabatic Marcus theory expression, are reported in Table 1. They fall in the picosecond time domain, from a few ps, to a few hundreds of ps. This is an encouraging result, suggesting that ET between the phosphate group and the sugar-base could take place of very short time scales, not in the ns time scale, or longer, for instance. On the other hand, the $\tau_{ET}^{NAM}$ values estimated from our simulations seem too large to fully account for the non-observance of U⁺, 5 ps after the pulse. The origin of the discrepancy might come from an overestimation of $\tau_{ET}^{NAM}$ due to the absence of nuclear tunneling in our treatment. It should also be reminded that applying the Marcus Theory framework to ultrafast ET operating under non-thermodynamics equilibrium should be done with caution. Still, these results suggest that an electron transfer in the spirit of the Marcus theory is not the main physical-chemical process that can explain to non-observation of U⁺ at the end of the pulse in the radiolysis experiments. We will thus explore another reactive channel in the next section.
<table><caption>Table 1: Thermodynamics and kinetic parameters of electron transfer from phosphate to ionized (U+S) group within the framework of the Marcus theory. Statistical uncertainties correspond to a 95% confidence interval.</caption><thead><tr><th>set</th><th>ΔA° (eV)</th><th>λ<sup>St</sup> (eV)</th><th>λ<sub>i</sub><sup>var</sup> (eV)</th><th>λ<sub>f</sub><sup>var</sup> (eV)</th><th>ΔA<sup>act</sup> (eV)</th><th>τ<sub>ET</sub><sup>NAM</sup> (ps)</th></tr></thead><tbody><tr><td>1</td><td>-1.36 ± 0.07</td><td>3.49 ± 0.07</td><td>3.73 ± 1.71</td><td>3.98 ± 0.44</td><td>0.24 ± 0.41</td><td>167 ± 33</td></tr><tr><td>2</td><td>-1.35 ± 0.06</td><td>3.51 ± 0.06</td><td>3.79 ± 1.14</td><td>3.62 ± 0.94</td><td>0.24 ± 0.35</td><td>138 ± 26</td></tr><tr><td>3</td><td>-1.41 ± 0.05</td><td>3.34 ± 0.05</td><td>3.18 ± 1.08</td><td>3.29 ± 0.30</td><td>0.19 ± 0.25</td><td>24 ± 8</td></tr><tr><td>4</td><td>-1.41 ± 0.06</td><td>3.33 ± 0.06</td><td>3.26 ± 0.97</td><td>5.28 ± 1.07</td><td>0.17 ± 0.29</td><td>6 ± 4</td></tr><tr><td>5</td><td>-1.44 ± 0.06</td><td>3.38 ± 0.06</td><td>3.40 ± 1.03</td><td>3.76 ± 1.04</td><td>0.20 ± 0.32</td><td>31 ± 11</td></tr><tr><td>6</td><td>-1.50 ± 0.04</td><td>3.33 ± 0.04</td><td>2.91 ± 0.60</td><td>3.29 ± 0.55</td><td>0.16 ± 0.18</td><td>83 ± 3</td></tr><tr><td>7</td><td>-1.28 ± 0.05</td><td>3.35 ± 0.05</td><td>3.47 ± 0.85</td><td>4.09 ± 0.68</td><td>0.24 ± 0.24</td><td>386 ± 13</td></tr><tr><td>8</td><td>-1.56 ± 0.03</td><td>3.32 ± 0.03</td><td>2.45 ± 0.36</td><td>5.73 ± 0.79</td><td>0.23 ± 0.16</td><td>83 ± 4</td></tr><tr><td>9</td><td>-1.26 ± 0.11</td><td>3.14 ± 0.11</td><td>3.83 ± 0.32</td><td>7.35 ± 3.62</td><td>0.17 ± 0.49</td><td>386 ± 32</td></tr><tr><td>10</td><td>-1.46 ± 0.05</td><td>3.44 ± 0.05</td><td>3.12 ± 0.72</td><td>3.94 ± 0.80</td><td>0.24 ± 0.25</td><td>83 ± 30</td></tr><tr><td>11</td><td>-1.35 ± 0.03</td><td>3.17 ± 0.03</td><td>2.84 ± 0.31</td><td>3.27 ± 0.54</td><td>0.21 ± 0.13</td><td>386 ± 7</td></tr></tbody></table>
### Marcus Curve Set 5

<figure><img src="image_7.png" /><figcaption>Figure 5: top, Marcus parabolas drawn for one set number 5. The free energy curves for the (US)$^+$P and (US)P$^+$ states are drawn in red and green respectively. The two curves result from a linear fit to a parabolic function taking the entire set of data points and considering the system to be ergodic. The grey dashed line are approximate adiabatic free energy curves (see SI).</figcaption></figure>

## Electron transfer via non-adiabatic relaxation

A close inspection of the evolution of the energy gap after ionization indicates the system is generally brought to a region of the conformational space where the (US)$^+$P state is higher in energy than the (US)P$^+$ state (Fig. S6). The system then relaxes within a few femtoseconds to the bottom of the initial potential well, crossing on the way the (US)P$^+$ charge transfer state. This observation suggests the existence of another charge transfer mechanism that doesn't need any activation barrier. The associated rate can be evaluated from the mean first passage through the seam, and accounting for the probability of the system to hop from the initial to the final charge transfer states.

$$k_{ET}^{MFP} = \langle P_h \rangle \cdot \frac{1}{\langle \tau_{crossing}^{MFP} \rangle} \qquad (6)$$
Where $\langle \tau_{crossing}^{MFP} \rangle$ is the average time taken for the system to reach a crossing point and $\langle P_h \rangle$ is an average hopping probability. We have evaluated $\langle \tau_{crossing}^{MFP} \rangle$ by running 21 cDFT/MM MD simulations on the (US)$^+$P charge transfer state, sampling the initial conditions every 2 ps (see Methods), and monitoring the vertical energy gap every 0.5 fs. In this approach we thus cDFT as a mean to define ad hoc average charge transfer states. We have tested four different hybrid functionals (BH&HLYP, PBE50$^{53}$, M06-2X$^{54}$, HSE06$^{55}$). The results are collected in Table 2. In 95% of the trajectories, the (US)$^+$P potential energy surface is higher in energy than the (US)$^+$P one just after ionization and cross each other in average after 4.5 fs, without subsequent re-crossings (Fig. S10). The timescale of first crossing is not sensitive of the XC energy functional.

We have next evaluated the hopping probability $\langle P_h \rangle$ either by the Landau-Zener-Stückelberg (LZS) formula$^{56,57}$ or by a decoherence-corrected transmission coefficient expression. The former reads $\langle P_h^{LZS} \rangle = \langle 1 - \exp[-2\pi H_{if}^2/\hbar |\Delta E_{if}|] \rangle$ with $|\Delta E_{if}|$ being the speed at which the system passes through the seam (sweeping rate). The latter was derived in Ref.$^{58}$ by analytically integrating the Rabi formula with a phenomenological decoherence function. It was found that $\langle P_h^{DC1} \rangle = 4\mu^2/(\hbar^2 + 4\mu^2)$ or $\langle P_h^{DC2} \rangle = 4(\mu^2/\hbar^2) \sum_{j=1}^{\infty} \frac{1}{(2j-1)!!} (-8\mu^2/\hbar^2)^{j-1}$ with $\mu = H_{if} \cdot \tau_{dec}$, and $\tau_{dec}$ being the characteristic decoherence time. DC1 or DC2 refers to the choice of mathematical form made for the decoherence function, either a first order$^{59}$ or a second order decay$^{60}$ function. For $\tau_{dec}$, we have followed the proposal of Prezhdo et al. that uses the difference of forces exerted on the n nuclei $(n, F_{n,x})$ between the two charge transfer states.$^{59}$

$$ \tau_{dec} = \left[ \left\langle \sum_n \frac{(F_{n,i} - F_{n,f})^2}{2a_n \hbar} \right\rangle_T \right] \quad (7) $$

where $a_n$ are (fixed) nuclear wave-packets widths.$^{61}$ This expression for the decoherence time has the further advantage that it relies on a nuclear-decoupling approximation, meaning that we
can identify nuclei that most contribute to electronic decoherence. All the quantities needed to evaluate $P_h^{LZS}$ or $P_h^{DC1,2}$ can be evaluated from our cDFT/MD simulations.

The LZS hopping probabilities are highly dependent on the choice of XC functional. They range from 0.07 (BH&HLYP) to 0.3 (M06-2X) and even 0.84 (HSE06). The electronic coupling at the crossing point is the main factor affecting $\langle P_h^{LZS} \rangle$. The HSE06 probably largely overestimates $H_{if}$ as this functional only incorporates 23% of exact exchange while a fraction of around 50% was shown to be necessary to obtain reliable $H_{if}$ with cDFT.⁴⁶ The three other functionals are, on the other hand probably reliable as they incorporate 50% (BH&HLYP and PBE50) and 54% (M06-2X) exact exchange. Still, a factor of three is found between M06-2X and BH&HLYP or PBE50, with consequently a much larger average hopping probability with the former. BH&HLYP or PBE50 produce rather similar $H_{if}$ but the slower sweeping rate with PBE50 permits to almost double $\langle P_h^{LZS} \rangle$. Another difficulty comes from the rapid increase $H_{if}$ over the first femtoseconds after ionization (Fig. S9). The origin of this trend is very likely to be electrostatic attraction between the phosphate and the nucleobase. I summary, it is hard to tell which one of the four tested functionals is the most adequate to describe both nuclear relaxation and hopping, but electron hopping is certainly not negligible.

Electronic decoherence times of around 0.6 fs are obtained with all functionals. Such short time scales strongly limit $\langle P_h^{DC1} \rangle$ below 0.05, except for HSE06, but this is due to a much larger $H_{if}$.

The hopping probabilities $\langle P_h^{DC2} \rangle$ and $\langle P_h^{DC1} \rangle$ are undistinguishable. The LZS formula can be seen as a limit regime where population exchanges are limited by the increase of the vertical energy gap as the system passes through the seam, neglecting electronic decoherence, while the DC expressions capture an opposite limit where population exchanges are limited by decoherence, assuming zero energy gap. The real value is likely to lie between these two extremes limits.

Interestingly, decoherence is roughly due for 50% to USP and for 50% to the solvent (see table
S1). This result is making sense considering that electronic decoherence is triggered in our approach by the diverging motion of atom nuclei on the (US)⁺P and (US)P⁺ potential energy surfaces. Both the USP nuclei and the solvent rearrange upon electron transfer and contribute to decoherence.

<table><caption>Table 2: Mean First Passage analysis of the phosphate-to-uracil electron transfer. Characteristic times are given in fs, the electronic coupling in eV and sweeping rates in eV/fs. Statistical uncertainties correspond to a 95% confidence interval, assuming normal distributions of the data.</caption><thead><tr><th rowspan="2">XC</th><th rowspan="2">EXX</th><th rowspan="2">τ<sub>dec</sub></th><th rowspan="2">⟨τ<sup>MFP</sup><sub>cross</sub>⟩</th><th rowspan="2">⟨ΔE<sub>if</sub>/Δt⟩<sub>cross</sub></th><th rowspan="2">⟨H<sub>if</sub>⟩<sub>cross</sub></th><th colspan="2">⟨P<sub>h</sub>⟩</th></tr><tr><th>⟨P<sup>LZS</sup><sub>h</sub>⟩</th><th>⟨P<sup>DC1</sup><sub>h</sub>⟩</th></tr></thead><tbody><tr><td>BH&HLYP</td><td>50%</td><td>0.61</td><td>4.9 ± 0.4</td><td>0.13</td><td>0.027</td><td>0.08</td><td>0.016</td></tr><tr><td>PBE50</td><td>50%</td><td>0.60</td><td>4.6 ± 0.4</td><td>0.10</td><td>0.022</td><td>0.14</td><td>0.013</td></tr><tr><td>M06-2X</td><td>54%</td><td>0.64</td><td>4.8 ± 0.4</td><td>0.15 ± 0.02</td><td>0.066 ± 0.007</td><td>0.30</td><td>0.038</td></tr><tr><td>HSE06</td><td>23%</td><td>0.74</td><td>7.0</td><td>0.30</td><td>0.251</td><td>0.84</td><td>0.35</td></tr></tbody></table>

DISCUSSION AND CONCLUSION

Researches to identify the mechanisms of formation of chemical damages to DNA and other biomolecules have largely focused on the reactivity of the product of water radiolysis such as the hydroxyl radical with biological molecules...¹ These reaction pathways are usually referred to as the indirect effect of ionizing radiations on biological matter.

On the other hand, chemical damages triggered by direct irradiation of biomolecules remain largely elusive, in particular all redox pathways opened by ionization of molecular components of DNA and proteins. The starting point of the present study was a recent picosecond pulse radiolysis study of concentrated solutions of uridine monophosphate that pointed toward intramolecular sub-
picosecond charge transfer from the phosphate moieties to the oxidized base. However, the time
resolution limitation of our experimental set-up didn't allow to access the underlying reaction
mechanisms.

We have explored here the possible reaction mechanisms by means of realistic simulations of
solvated USP relying on advanced first-principles algorithms using in-house codes. Electron and
molecular dynamics simulations have been carried out at the hybrid DFT/MM level with polarizable
embedding. We have ruled out pure charge migrations at fixed nuclear position as a possible
mechanism to account for reduction of U+. On the other hand, our RT-TD-ADFT/MMpol
simulations revealed interesting insights on charge migrations following ionization; for example,
hole delocalization over the entire U+S after ionization either of the nucleobase or of the ribose
group. This finding is reminiscent from previous simulations of solvated DNA that we recently
reported¹⁹. Another worth mentioning result is the very fast resorption of holes generated on the
phosphate group upon electron irradiation. This may sign an intrinsic protection mechanism of
phosphate groups against ionization by ionizing rays. More work will be needed to address this
hypothesis more in depth, especially in view of the classical approximation made on the projectile
(classical electron). It should be also recalled that we used a GGA functional (PBE) that is prone
to self-interaction-errors. Our conclusions will deserve confirmation with simulations relying for
instance on hybrid or range-separated functionals that are less SIE contaminated.

Assuming that electronic and vibrational relaxation had time to take place before U+ reduction, we
have next characterized the phosphate-to-uracil electron transfer within the framework of the
Marcus theory. The reaction was found to be strongly exergonic, in line with the redox potentials
of the two redox moieties, and associated to large reorganization energies. Despite significant
electronic coupling values afforded by the proximity of the redox partners, the estimated activation
free energies limit the kinetics of the reaction to the picosecond regime. Therefore, a ground-state
electron transfer is not likely to be the dominant mechanism accounting for the experimental
observations.

Finally, we have considered a non-adiabatic charge transfer decay. We found that most
geometries of the system in the resting states correspond at room temperature, to situations for
which the (US)⁺P state is higher in energy than the USP⁺ after ionization. A channel without
activation barrier is therefore accessible for femtosecond electron transfer. The hopping
probability between the two charge transfer states is delicate to evaluate with accuracy but is
probably significant. Nuclear motion induces fast variations of the electronic coupling within the
first femtoseconds and are further expected to cause electronic decoherence, both effects strongly
modulating hopping probabilities. All in all, this channel seems to offer the most plausible charge
transfer relaxation mechanism of U⁺ that could account for its sub-picosecond disappearance. The
time scales provided by our Born-Oppenheimer MD simulations on charge transfer states fall into
the femtosecond regime, which is close to the typical timescales of the so-called physical stage of
irradiation that we have simulated with purely RT-TD-ADFT. This highlights the tight connection
between electronic and nuclear degrees of freedom in the very early stage of biological matter
irradiation.

Guided by the experimental results we wished to understood, we have investigated a small RNA
model in solution. However, the physical-chemical processes we have analyzed here are likely to
also take place in larger molecular systems such as long DNA or RNA strands or in proteins.
Charge transfers along DNA/RNA strands have been investigated thoroughly and accounted for
by hopping or flickering resonance models⁶²⁻⁶⁴. We have characterized here a very fast charge
transfer showing that holes produced by irradiation on nucleobases can already be displaced from
the sites of production on the femtosecond timescale. The respective position and slopes of
potential energy surfaces certainly play a great role in modulating the ultrafast non-adiabatic
decays of irradiated nucleobases. In our experimental and computation study phosphate was
doubly deprotonated, providing high driving forces to drag the electron cloud toward the oxidized
base, hence the ultrafast time scales for phosphate-to-nucleobase electron transfer. In natural
DNA/RNA, phosphates generally hold a unique negative charge, and eventually host counter-ions
or structured water solvation shells⁶⁵. These characteristics of natural DNA certainly influence the
processes taking place during the physical-chemical stage of DNA radiolysis, and should stimulate
further studies.

We have focused in this article to the oxidative stage following irradiation of uridine
monophosphate. The experimental data also revealed unexpected behavior along the reductive
pathway. ¹⁰,⁶⁶ We are currently attempting to understand these results by numerical simulations.
Our results will be reported in due course.

SUPPLEMENTARY INFORMATION

Energy deposition profiles. Molecular relaxation during cDFT/MM simulations on initial and final electron transfer diabatic states; fluctuations and histograms of electronic coupling values. Marcus free energy profiles. Estimations of statistical uncertainties during data treatment within the framework of the Marcus theory. Raw computational data and all Rstudio scripts written to generate all the Figures and Tables produced for this article.

AUTHOR INFORMATION

Corresponding Authors

AdL E-mail: <aurelien.de-la-lande@universite-paris-saclay.fr>

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS
We are grateful to GENCI and compute Canada for providing us with generous computational resources. This work was funded by the Institut de Chimie of CNRS (project Emergence@INC 2018) and by the French Agence Nationale de la Recherche (Project RUBI, number: ANR-19-CE29-0011-01). We kindly thank Denise Humfress in the preparation of the manuscript.

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