[a,b]R. Aloisio

# The Terzina instrument onboard the NUSES space mission

L. Burmistrov  A. Di Giovanni  M. Heller  T. Montaruli  C. Trimarelli

###### Abstract

In this paper we will introduce the Terzina instrument, which is one of the
two scientific payloads of the NUSES satellite mission. NUSES serves as a
technological pathfinder, hosting a suite of innovative instruments designed
for the in-orbit detection of cosmic rays, neutrinos, and gamma rays across
various energy ranges. The Terzina instrument itself is a compact telescope
equipped with Schmidt-Cassegrain optics. Its primary objective is to detect
Cherenkov radiation emitted by Extensive Air Showers generated by the
interaction of high-energy (> 100 PeV) cosmic rays with the Earth’s
atmosphere. Terzina represents a critical step forward in the development of
future space-based instruments aimed at detecting upward-moving showers
induced by tau-leptons and muons resulting from the interaction of high-energy
astrophysical neutrinos with the Earth. In this paper, we will delve into the
key technical aspects of the Terzina instrument, its capabilities, and its
potential for detection.

##  1 Introduction

The NUSES (Neutrinos and Seismic Electromagnetic Signals) satellite mission is
a collaborative project led by the Gran Sasso Science Institute (GSSI) aimed
at exploring new scientific and technological pathways for future
astroparticle physics space-based detectors. This project is conducted in
collaboration with the Istituto Nazionale di Fisica Nucleare (INFN), the
Italian Space Agency (ASI), several Universities in Italy, the University of
Geneva in Switzerland and the University of Chicago in the USA. The NUSES
mission is supported by Thales Alenia Space Italy (TAS-I), industrial partner
providing the satellite platform 2MF/NIMBUS (New Italian Micro BUS) with a
modular and flexible design based on additive manufacturing techniques. The
NUSES satellite, scheduled to launch in the second half of 2025 under the
management of ASI, will be a ballistic mission without orbital control,
operating at a Low Earth Orbit (LEO), with an altitude at the Beginning of
Life (BoL) of 535 km, with a high inclination of 97.8° (LTAN = 18:00) in a
Sun-synchronous orbit along the day-night boundary. The nominal duration of
the NUSES mission is three years (End of Life, EoL).

The NUSES satellite will host two innovative scientific payloads: Zirè and
Terzina. In this proceedings paper, we will focus on the Terzina instrument,
while detailed information about the Zirè detector can be found in [1].

Terzina is a telescope specifically designed for the detection of Cherenkov
light emitted by Extensive Air Showers (EAS) induced by high-energy Cosmic
Rays (CR) and neutrinos in the Earth’s atmosphere. In astrophysical
environments, high-energy neutrinos are produced through the decay chain of
pions, leading to an equipartition (due to flavour oscillation) among the
three different leptonic flavours when observed at the Earth. At sufficiently
high energy ($E>1~{}PeV$), tau neutrinos and, to a lesser extent, mu neutrinos
passing through the Earth can produce $\tau$ and $\mu$ leptons, which can
emerge by decaying or interacting in the atmosphere when the elevation angles
of the neutrino momentum on the Earth’s surface are small (Earth skimming
events). As a result, Earth skimming neutrinos generate EAS moving in the
atmosphere from bottom to top [2], similar to the EAS produced by charged
particles (CR) impinging the atmosphere from above the Earth limb [2]. The
Cherenkov emission from these EAS can be detected by space-based instruments,
providing a unique signal for Low Earth Orbit (LEO) satellites [3, 4], which,
given the high exposures, could potentially revolutionise the observation of
high-energy neutrinos and CR. Terzina serves as a technological pathfinder,
aiming to detect the EAS Cherenkov emission demonstrating the viability of the
space-based detection technique.

This paper presents a general description of the Terzina telescope and its
observational capabilities.

##  2 Cherenkov emission observed from space

Figure 1: [Left panel] Schematic of the orbital configuration and the geometry
of an above-the-limb event. [Central panel] Distribution of the relevant line
of sight angles for different values of the proton EAS energy (as labelled).
[Right panel] Distribution of the Cherenkov photons produced by a proton EAS
of 100 PeV energy as function of the viewing angle and above the limb
altitudes of the first interaction point.

The Cherenkov emission produced by an EAS is mainly due to the high energy
($E>100$ MeV) electron-positron pairs generated in a large amount during the
shower development. Thus, the number of Cherenkov photons emitted by an EAS is
directly proportional to the shower energy, which corresponds to the energy of
the primary particle that initiated the cascade. Considering the specific
characteristics of the Terzina telescope, particularly the area of its primary
mirror (approximately $0.1~{}m^{2}$), as discussed in the next section, it is
capable of detecting the Cherenkov emission only from EAS with energies
exceeding 100 PeV. Consequently, Terzina is expected to predominantly observe
CR with trajectories above the Earth’s limb due to their higher flux compared
to neutrinos (roughly 4 orders of magnitude higher). Nevertheless, the
Cherenkov signal produced by these CR events, apart from the incoming
direction, exhibits nearly identical properties to the expected signal from
neutrino events occurring below the limb, such as similar wavelength spectra
of the arriving photons, as well as comparable spatial profiles and time
distributions. Thus, above-the-limb CR events serve as a reliable benchmark
for directly testing the various components of an in-orbit Cherenkov telescope
(e.g., optics, photo-sensor, electronics, and triggers) during the actual
mission. This strategic approach underpins the Terzina mission, which aims to
validate the detection technique through in-orbit testing.

In this section we will briefly review the nature of Cherenkov emission as
observed from a space based telescope in the case of above-the-limb EAS. The
results presented are based on the EASCherSim computational framework
(c4341.gitlab.io/easchersim/index.html), a simulator designed for modelling
the production and atmospheric transport of Cherenkov photons by EAS, build
upon the findings discussed in [2]. To provide an estimate of the expected
signal in the Terzina telescope, we consider the case of EAS generated by
protons. Due to the geometry of above-the-limb trajectories, a significant
portion of the particle cascade occurs at high altitudes in a rarefied
atmosphere. Consequently, the generation of optical Cherenkov emission is
limited, but so is its atmospheric attenuation during photon propagation.
Therefore, a detailed calculation of the Cherenkov signal strength and
geometry is necessary to determine the overall instrumental sensitivity to
such events.

Figure 2: [Left panel] Temporal evolution of the Cherenkov burst of a 100 PeV
proton EAS for different values of the altitude of the first interaction point
(as labelled). [Central panel] Total flux of Cherenkov photons at the Terzina
(BoL) altitude integrated over 100 ns as function of the distance from the EAS
axis, in the case of a proton EAS of 100 PeV energy for different altitudes of
the first interaction point of the proton (as labeled). [Right panel] Spectrum
of Cherenkov photons produced by a proton EAS of 100 PeV energy at the Terzina
(BoL) altitude for different altitudes of the first interaction point of the
proton (as labeled).

The results presented in figures 1, 2 show several important points. Given the
geometry of the observation from the Terzina altitude (figure 1 left panel)
and the characteristics of the atmosphere, Cherenkov emission can be observed
from a tiny layer of the atmosphere, with a angular size less than 1∘, which
corresponds to altitudes above the Earth’s limb that span from 20 km up to 50
km (the Earth’s limb is seen by Terzina at an elevation angle
$\theta_{d}=67.5^{\circ}$), as follows from the central and right panels of
figure 1. The Cherenkov signal is a burst with a typical duration of few tens
on nano seconds (left panel figure 2) of visible-UV photons distributed on a
cone with a very narrow aperture ($\delta\simeq 1^{\circ}$) around the EAS
axis, which corresponds to the direction of motion of the primary particle
that generated the EAS. At the operative altitudes of Terzina the cone has a
typical base radius of few tens of km, with a flux integrated over the burst
duration of about 100 photons per $m^{2}$, in the case of a proton EAS with
100 PeV energy (central panel figure 2). Finally, it is interesting the effect
of photons propagation across the Earth’s atmosphere that mainly suffer the
effect of absorption on the ozone layers that reduce the photons spectra
between wavelength of 500 nm and 700 nm, with a progressive attenuation of
this effect for EAS generated at increasing altitudes (due to the reduction of
the ozone layer traversed), as follows from the right panel of figure 2.

##  3 The Terzina instrument

The Terzina detector is composed by a near-UV-optical telescope, with a
Schmidt-Cassegrain optics, and the Focal Plane Assembly (FPA), figure 3 left
panel. The optical system of the telescope is based on a dual mirror
configuration composed of two parabolic mirrors: primary, with radius 394 mm,
and secondary, with radius 144 mm, placed at a relative distance of 280 mm.
The FPA has a maximum radius 121 mm and it is placed at a distance of 40 mm
from the primary mirror. This configuration is chosen to maximise the focal
length up to 925 mm in a compact telescope which, including the baffles needed
to obscure straight light propagation on the FPA (left panel figure 3), should
fit in an envelope of 600x600x730 mm3. The telescope will operate inclined by
$67.5^{\circ}$ with respect to nadir, with the optical axis pointing towards
the dark side of the Earth’s limb, the expected duty cycle is around $40\%$.
The star tracker system of the satellite platform maintains the optical axis
configuration with a high accuracy of 0.1∘. The total weight of the Terzina
instrument (telescope and FPA) is around 35 kg.

Figure 3: [Left panel] Scheme of the optics (M1, M2 primary and secondary
mirror) and the FPA of Terzina with the baffles structure to protect from
straight light pollution. [Central panel] Point spread function with the
encircled energy on the FPA produced by photons for different photons
incidence angles respect to the telescope focal axis (as labelled). [Right
panel] Scheme of the focal plane with the pixels structure, coloured bands
show the corresponding observed regions below (red band) and above (blue band)
the limb. The axis label the corresponding length in km probed at the Earth
along the limb line (x axis) and across it (y axis).

The FPA is designed to detect photons from both below and above the limb. It
has a rectangular shape with a $2:5$ aspect ratio. It is composed of 10
Silicon Photon Mutlipliers (SiPM) arrays [7] of $8\times 8$ pixels forming 2
rows of 5 arrays each (640 pixels overall, see figure 3 right panel). Given
the Schmidt-Cassegrain optics the upper row of 5 SiPM arrays will observe
events coming from below the Earth’s limb (red area in right panel of figure
3), this part of the FPA will perform a clear characterisation of the
background and is unlikely to observe neutrino-induced EAS. On the other hand,
the lower row of 5 SiPM arrays will observe events coming from EAS generate by
CR from above the limb, with the blue area in the right panel of figure 3
signalling the most contributing part of the atmosphere. The axis in the right
panel of figure 3 show the length probed by the telescope at the Earth, along
the limb line and across it. Terzina observes a vast volume of the atmosphere
with a section across the Earth’s limb of 360 × 140 km2. Given the focal
length of the telescope $F_{l}=925~{}mm$ and the SiPM pixels size
$r_{SiPM}\simeq 3~{}mm$, the Field-of-View (FoV) per pixel of the FPA can be
estimated as ${\rm FoV}_{pix}=\arctan(r_{SiPM}/F_{l})\simeq 0.18^{\circ}$,
with a telescope FoV of 7.20∘ (40 pixels) along the Earth’s limb and 2.88∘
across it (16 pixels). The point spread function (PSF) of the Terzina optical
system is compatible with the 3 × 3 mm2 pixel size chosen for the FPA, with
the overall encircled energy always contained inside 1.5 mm independently of
the inclination angle of the incoming photons (figure 3 central panel).

The SiPM sensors are provided by the Fondazione Bruno Kessler (FBK) and
briefly described below (see [5] for a detailed discussion). The camera
frontend electronics is composed of 10 Application Specific Integrated
Circuits (ASICs) [6], each reading one SiPM array with $8\times 8$ channels.
The ASIC has an input amplification stage and digitises signals, upon
validation of trigger conditions, as determined by the trigger logic
implemented in the ASICs and in a dedicated Field Programmable Gate Array
(FPGA). The ASIC digitises the signal on a programmable time interval (see
below) that spans from a minimum of 180 ns up to 1.280 $\mu$s, enabling pulse-
shape reconstruction [6].

In order to build a complete simulation chain of the Terzina detector it is
important to estimate the expected background. This is composed by: the Night
Glow Background (NGB) of visible light and the background radiation of charged
particles in the 100 keV - 100 MeV energy range. The rate per pixel due to the
NGB ($R_{pix}^{NGB}$) has been estimated using the formula [8]:
$R_{pix}^{NGB}=\eta\times\Delta\Omega\times\phi_{NGB}\times S\times PDE_{eff}$
where:

Figure 4: [Left panel] Photon detection efficiency versus photon wavelength
for different SiPM types by FBK (as labelled). [Right panel] Single pixel
trigger rate as a function of the threshold expressed in photo electrons
(p.e.) for DCR and NGB values estimated at different times during the mission
life (as labelled). The horizontal blue dashed line corresponds to the maximum
event rate of 120 Hz, see text. Horizontal blue line corresponds to the
maximum single pixel trigger rate (120 Hz/640 $\sim$ 0.18 Hz per pixel). The
horizontal red line corresponds to 1.25 kHz (maximum single pixel rate with
two pixels cluster in the hit-map). The vertical lines shows thresholds for
single (blue) and double coincidence (red) trigger logic.

$S=0.1~{}\mathrm{m^{2}}$ is the collecting area of the telescope’s primary
mirror; $PDE_{eff}=0.1$ is the total Photon Detection Efficiency (PDE)
calculated from the convolution of the SiPM PDE and the NGB spectrum (see
figure 4 left panel); $\Delta\Omega\simeq(FoV_{pix})^{2}$ is the pixel viewing
solid angle; $\phi_{NGB}=1.55\times 10^{4}~{}m^{-2}sr^{-1}ns^{-1}$ is the
total integrated NGB flux in the wavelengths range $\lambda=300~{}nm$
$\lambda=1000~{}nm$ [8]; $\eta=6$ is a conservative safety factor that takes
into account the expected large fluctuations of the NGB flux. The rate per
pixel due to the NGB estimated by these reference values is
$R_{pix}^{NGB}\sim$10 MHz.

The background radiation expected at the operating altitudes of Terzina were
estimated using the SPENVIS computation scheme (www.spenvis.oma.be), focusing
on the dominant component of electrons and protons in the 100 keV - 100 MeV
energy range, coupled with a Geant4 simulation (geant4.web.cern.ch/geant4) of
the full detector (mechanical structure, optics and FPA). The effect of the
in-orbit background radiation on the FPA is twofold: from one side it can
mimic events, as for Cherenkov emission produced by electrons inside the
telescope’s optical/mechanical parts and hitting on the SiPM layer, on the
other side it produces a progressive sensor damage with an increasing Dark
Current Rate (DCR) during the mission.

The in-orbit time evolution of the SiPMs characteristics and their related
power consumption are crucial factors that should be taken into account in
choosing the sensors technology [5]. The SiPMs chosen are the NUV-HD series
produced by FBK and designed for the near-UV visible wavelengths [9]. The NUV-
HD SiPM technology has typical operating parameters for 35 $\mu$m cell-size
given by: DCR $\simeq$ 100 kHz/mm2, after-pulsing AP $\simeq 5\%$ and optical
crosstalk CT $\simeq 5\%-20\%$. In figure 4 left panel, we plot the PDE of
different SiPM produced by FBK, our baseline solution is the NUV-HD without
coating (blue line in left panel of figure 4) [5, 7]. Given the SiPM choice we
can simulate the background rate due to NGB and DCR at different times of the
Terzina mission: at BoL, after the first and second years and at EoL, the
rates obtained are: 11 MHz, 22 MHz, 33 MHz, 44 MHz respectively [5]. In the
right panel of figure 4 we plot the trigger rate per pixel as function of the
number of photo-electrons (p.e.) produced by the SiPM at BoL, after one year,
after two years and at EoL. It is evident the effect on the expected trigger
rate of the increased DCR due to radiation effects.

At EoL, the power consumption of the sensors of the camera, operated at an
over-voltage of about 6 V, will reach 0.2 W. This figure does not include the
power consumption of the 10 ASICs, which are expected to consume 5 mW/channel
[6], 3.2 W for the 640 channels of the camera. The overall power needed to
operate the FPA is expected to be lower than 3.5 W.

The ASIC technology is discussed in [6], here we recall that each ASIC has 64
channels (8x8 pixels of a single SiPM array), each channel has a memory with a
total number of 256 cells (12bit resolution, sampling frequency 200 MHz)
arranged in 8 blocks of 32 cells each. Each ASIC has two programmable
thresholds (low $S_{0}$ and high $S_{1}$) and a clock cycle $T_{{\rm clk}}=5$
ns. The trigger scheme is based on the recognition of specific pixels
topologies in the hit-map of the ASIC depending on the (low or high) threshold
exceeded by multiple pixels (see [6] for a detailed discussion). If one
channel at the time $t_{S}$ exceeds $S_{0}$ ($S_{1}$), during the time
interval $\Delta t_{c}=16~{}T_{{\rm clk}}=80$ ns changes to the pixels state
are accepted, after $\Delta t_{c}$ the hit-map is transferred to the FPGA. The
event is accepted by the FPGA if the hit-map shows two (three) or more
adjacent pixels, with defined topologies, above $S_{1}$ ($S_{0}$). Once the
event is accepted it will be centred for digitisation at $t_{S}$ and digitised
through 32 time-samples of the signal spaced by $T_{{\rm clk}}$ for a total
sampled time interval $2\Delta t_{c}=160$ ns in the time interval
($t_{S}-\Delta t_{c},t_{S}+\Delta t_{c}$), occupying one memory block per
channel (pixel). The hit-map recognition chain has a total duration of 250 ns,
given by $\Delta t_{c}=80$ ns plus the time needed to transfer the hit-map to
the FPGA (140 ns) and the time needed by the FPGA to recognise the event and
communicating it back to the ASIC (30 ns). Each ASIC is able to manage in
parallel a maximum of 8 (number of memory blocks per channel) digitisation
processes [6].

The digitised signal in a single pixel is encoded in a number of bit:
12x32+header+padding = 434 bit. Thus, an event in a single ASIC is encoded in
64x434 = 27776 bit. The maximum downlink data stream for Terzina is 45
Gbit/day, which corresponds to an absolute maximum number of events per day
that can be sent for the offline analysis $1.29\times 10^{7}$ events/day,
roughly an event rate of 150 Hz. The possibility of reprogramming the ASICs
thresholds during the flight guarantees the opportunity to adjust $S_{0}$ and
$S_{1}$ to the changing response of the sensors, in order to maintain a fixed
event rate. In the right panel of figure 4, we show the variation of $S_{0}$
(red vertical lines) and $S_{1}$ (blu vertical lines) with the increasing
mission age. These estimations follows by defining $S_{0}$ as the threshold
corresponding to the maximum single pixel rate $120/640$ Hz (blu horizontal
line) and $S_{1}$ as the threshold corresponding to the maximum allowed single
pixel rate in the case of configurations with two pixels clustering 1.25 kHz
(red horizontal line) as discussed in [5].

##  4 Conclusions

In conclusion, we provide a preliminary estimation of the detection
capabilities of the Terzina instrument. When monitoring below the limb,
Terzina will perform background sampling with hit-map recording at a rate that
can reach several Hz. From above the limb, Terzina is capable of observing CR
events.

Figure 5: Expected Terzina aperture to protons’ EAS vs energy during the first
year of operation.

Figure 5 illustrates the expected detector’s aperture associated with CR
protons, calculated based on the BoL sensors’ response and a single threshold
trigger scheme with $S_{0}=7$ p.e. The results in figure 5 are obtained by
combining the Geant4 simulation scheme of the detector with the EASCherSim
computation scheme for generating protons’ EAS. Considering the observed CR
flux at energies exceeding 100 PeV, $\phi_{CR}\sim 6.6\times 10^{3}$ ${\rm
km}^{-2}{\rm sr}^{-1}{\rm y}^{-1}$ [10], assuming a proton fraction of 50$\%$
[10], and a detector duty cycle of $40\%$, the aperture shown in figure 5
demonstrates Terzina’s capability to observe a significant number of CR proton
events (with $E\geq 100$ PeV) already during the first year of operation, with
an estimated count of no less than 20 events per year. Achieving this level of
detection would serve as a clear validation of the experimental technique
employed by Terzina.

Acknowledgements. NUSES is funded by the Italian Government (CIPE n. 20/2019),
by the Italian Minister of Economic Development (MISE reg. CC n. 769/2020), by
the Italian Space Agency (CDA ASI n. 15/2022), by the Swiss National
Foundation (SNF grant n. 178918) and by the European Union - NextGenerationEU
under the MUR National Innovation Ecosystem grant ECS00000041 - VITALITY - CUP
D13C21000430001.

## References

  * [1] M. Fernandez Alonso, et al. [NUSES Collaboration], this conference proceedings.
N. Mazziotta, et al. [NUSES Collaboration], this conference proceedings.
F. Nozzoli, et al. [NUSES Collaboration], this conference proceedings.

  * [2] A. L. Cummings, R. Aloisio and J. F. Krizmanic, Phys. Rev. D 103, no.4, 043017 (2021) A. Cummings, R. Aloisio, J. Eser and J. Krizmanic, Phys. Rev. D 104, no.6, 063029 (2021)
  * [3] A. V. Olinto et al. [POEMMA Collaboration], JCAP 06, 007 (2021)
  * [4] J.F. Krizmanic and J.W. Mitchell, Proceedings 32nd ICRC (2011), arXiv:1109.6544.
A. Neronov et al. Phys. Rev. D 95, no.2, 023004 (2017)

  * [5] L. Burmitrov et al. [NUSES Collaboration], EPJ Web of Conferences 283 (2023) 06006,
  * [6] M. Bertaina, et. al. [NUSES Collaboration], this conference proceedings.
  * [7] F. Corsi, et al. Nuclear Instruments and Methods in Phys. Res. Sect. A 572.1 (2007) 416-418.
  * [8] W. Hofmann, et al. Appl. Opt. 16 (1977) 3125-3130.
  * [9] A. Gola, et al. Sensor 19 (2019) 308.
F. Acerbi and S. Gundacker, Nucl. Instrum. Methods Phys. Res. A 926 (2019)
16–35.

  * [10] P. Abreu et al. [Pierre Auger], Eur. Phys. J. C 81, no.11, 966 (2021).
A. Aab et al. [Pierre Auger], [arXiv:1909.09073 [astro-ph.HE]].

## Full Authors List NUSES Collaboration

R. Aloisio1,2, C. Altomare3, F. C. T. Barbato1,2, R. Battiston4,5, M.
Bertaina6,7, E. Bissaldi3,8, D. Boncioli2,9, L. Burmistrov10, I. Cagnoli1,2,
M. Casolino11,12, A.L. Cummings13, N. D’Ambrosio2, I. De Mitri1,2, G. De
Robertis3, C. De Santis11, A. Di Giovanni1,2, A. Di Salvo7, M. Di Santo1,2, L.
Di Venere3, J. Eser14, M. Fernandez Alonso1,2, G. Fontanella1,2, P. Fusco3,8,
S. Garbolino7, F. Gargano3, R. A. Giampaolo1,7, M. Giliberti3,8, F.
Guarino15,16, M. Heller10, R. Iuppa4,5, J. F. Krizmanic17,18, A. Lega4,5, F.
Licciulli3, F. Loparco3,8, L. Lorusso3,8, M. Mariotti19,20, M. N. Mazziotta3,
M. Mese15,16, H. Miyamoto1,7, T. Montaruli10, A. Nagai10, R. Nicolaidis4,5, F.
Nozzoli4,5, A. V. Olinto14, D. Orlandi2, G. Osteria15, P. A. Palmieri6,7, B.
Panico15,16, G. Panzarini3,8, A. Parenti1,2, L. Perrone21,22, P. Picozza12,11,
R. Pillera3,8, R. Rando19,20, M. Rinaldi11, A. Rivetti7, V. Rizi2,9, F.
Salamida2,9, E. Santero Mormile6, V. Scherini21,22, V. Scotti15,16, D.
Serini3, I. Siddique1,2, L. Silveri1,2, A. Smirnov1,2, R. Sparvoli11, S.
Tedesco7,23, C. Trimarelli10, L. Wu1,2,†, P. Zuccon4,5, S. C. Zugravel7,23.

1Gran Sasso Science Institute (GSSI), Via Iacobucci 2, I-67100 L’Aquila, Italy
2Istituto Nazionale di Fisica Nucleare (INFN) - Laboratori Nazionali del Gran
Sasso, I-67100 Assergi, L’Aquila, Italy
3Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Orabona 4,
I-70126 Bari, Italy
4Dipartimento di Fisica, Università di Trento, via Sommarive 14 I-38123
Trento, Italy
5Istituto Nazionale di Fisica Nucleare (INFN) - TIFPA, via Sommarive 14
I-38123 Trento, Italy
6Dipartimento di Fisica, Università di Torino, Via P. Giuria, 1 I-10125
Torino, Italy
7Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Torino, I-10125
Torino, Italy
8Dipartimento di Fisica M. Merlin, dell’Università e del Politecnico di Bari,
via Amendola 173, I-70126 Bari, Italy
9Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi di
L’Aquila, I-67100 L’Aquila, Italy
10Département de Physique Nuclèaire et Corpusculaire, Université de Genève,
1205 Genève, Switzerland
11INFN Roma Tor Vergata, Dipartimento di Fisica, Universitá di Roma Tor
Vergata, Roma, Italy
12RIKEN, 2-1 Hirosawa, Wako, Saitama, Japan
13Departments of Physics and Astronomy & Astrophysics, Institute for
Gravitation and the Cosmos, Pennsylvania State University, University Park, PA
16802, USA
14Department of Astrophysics & Astronomy, The University of Chicago, Chicago,
IL 60637, USA
15Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, via Cintia,
I-80126 Napoli, Italy
16Dipartimento di Fisica E. Pancini dell’Università di Napoli Federico II, via
Cintia, I-80126 Napoli, Italy
17CRESST/NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
18University of Maryland, Baltimore County, Baltimore, MD 21250, USA
19Università di Padova, I-35122 Padova, Italy
20Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Padova, I-35131
Padova, Italy
21Dipartimento di Matematica e Fisica “E. De Giorgi", Università del Salento,
Via per Arnesano, I-73100 Lecce, Italy
22Istituto Nazionale di Fisica Nucleare - INFN - Sezione di Lecce, Via per
Arnesano, I-73100 Lecce, Italy
23Department of Electrical, Electronics and Communications Engineering,
Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
†Now at Institute of Deep Space Sciences, Deep Space Exploration Laboratory,
Hefei 230026, China


# Ultrafast excitonic dynamics in DNA:
Bridging correlated quantum dynamics and sequence dependence

Dennis Herb  Equal contribution  Institute for Complex Quantum Systems, Ulm
University, 89069 Ulm, Germany  Center for Integrated Quantum Science and
Technology (IQST) Ulm-Stuttgart, Germany  Mirko Rossini  Equal contribution
Institute for Complex Quantum Systems, Ulm University, 89069 Ulm, Germany
Center for Integrated Quantum Science and Technology (IQST) Ulm-Stuttgart,
Germany  Joachim Ankerhold  Institute for Complex Quantum Systems, Ulm
University, 89069 Ulm, Germany  Center for Integrated Quantum Science and
Technology (IQST) Ulm-Stuttgart, Germany

(August 28, 2024)

###### Abstract

After photo-excitation of DNA, the excited electron (in the LUMO) and the
remaining hole (in the HOMO) localized on the same DNA base form a bound pair,
called the Frenkel exciton, due to their mutual Coulomb interaction. In this
study, we demonstrate that a tight-binding (TB) approach, parametrized by ab
initio data, allows to correlate relaxation properties, average charge
separation, and dipole moments to a large ensemble of double-stranded DNA
sequences (all 16,384 possible sequences with 14 nucleobases). This way, we
are able to identify a relatively small sub-ensemble of sequences responsible
for long-lived excited states, high average charge separation, and high dipole
moment. Further analysis shows that these sequences are particularly T-rich.
By systematically screening the impact of electron-hole interaction (Coulomb
forces), we verify that these correlations are relatively robust against
finite-size variations of the interaction parameter, not directly accessible
experimentally. This methodology combines simulation methods from quantum
physics and physical chemistry with statistical analysis known from genetics
and epigenetics, thus representing a powerful bridge to combine information
from both fields.

Key words

Tight-binding model, Frenkel exciton, electron-hole interaction, exciton
decay, relaxation time, charge separation, dipole moment, DNA polarization,
fluctuations, and epigenetics.

##  I Introduction

Photoexcited energy and charge transfer in biologically relevant systems is
one of the fundamental processes in nature and the basis for all life on
earth. Exploring its microscopic mechanisms has been a major field of research
over the past decades in biology, chemistry, and physics. One prominent
example is the formation of electron-hole pairs (excitons) on complex
molecular structures under external radiation. It not only serves as a model
system to better understand molecular energy transport, e.g., in light-
harvesting complexes in photosynthesis [1, 2, 3, 4, 5] but has also triggered
the design of nature-inspired tools such as efficient organic solar cells [6,
7], energy storage devices [8], and organic photodetectors and
phototransistors [6].

In particular, photoexcited charge dynamics on DNA, the central repository of
genetic information in the cell, has been intensively studied because of its
relevance to induce DNA lesions, alter DNA binding properties, and trigger
carcinogenic mutations. As a result, a substantial body of literature has
appeared reviewing charge transfer processes in DNA [9, 10, 11, 12, 13, 14,
15] and proposing applications ranging from genetics, e.g., understanding DNA
damage and repair [16, 17, 18] and distinguishing pathogenic from non-
pathogenic mutations [19], to nanotechnology, e.g., designing nanosensors,
nanocircuits, and molecular wires [20, 21].

DNA is known to be photostable with rapidly decaying excitations. Improved
spectroscopic methods, such as pump-probe techniques, have made it possible to
experimentally study the dynamics of ultrafast excited states in DNA [22, 23].
These states can be generated naturally by ultraviolet (UV) radiation, for
example as a result of direct exposure to sunlight. In both cases, an electron
is excited from the highest occupied molecular orbital (HOMO) to the lowest
unoccupied one (LUMO), leaving a hole in the HOMO. These charge carriers
interact as a result of attractive Coulomb forces and, when bound to a single
nitrogenous DNA base, form an electron-hole pair known as a Frenkel exciton.
As a localized excitation, the Frenkel exciton plays an important role in
processes such as energy transfer in DNA-based systems [24, 25, 26].

A theoretical description of the propagation of charges through DNA is rather
challenging. It is sensitive not only to extrinsic effects, such as the
surrounding aqueous solution, but also to intrinsic influences, such as
fluctuations in the dynamical structure [27, 28, 29], including the phosphate
backbone. As a consequence, the complexity of the DNA molecule and its
environment renders atomistic ab initio calculations even in equilibrium not
feasible for any structures beyond 3-4 nucleotides, that is, far from
capturing long-range charge transfer in double-strand aggregates. Therefore,
so-called tight-binding models have been developed as powerful alternatives
[30, 29].

Here, we follow this strategy with the goal of combining two methodologies,
namely, mesoscopic modeling that captures the essential features of excited-
state charge dynamics and a statistical analysis of sizable sets of double-
strand DNA sequences. With model parameters taken from first-principle
calculations [31, 32], we achieve sufficiently accurate results with the
required high numerical efficiency to screen larger ensembles.

Most of the previous studies have focused on the hole transfer along the DNA
strand for various reasons: First, experiments aimed at investigating the
motion of charges along DNA often make use of DNA oxidation [33, 18] (lack of
an electron) to create an initial charge carrier; second, ab initio
calculations (such as DFT) proved to be more accurate in retrieving low energy
structures and properties of HOMO molecular orbitals. However, more recent
literature [32] reports a comprehensive collection of structural data such as
binding energies and overlap integrals which provides the basis to develop
models including both electron and hole motion.

In this work, we go beyond by promoting a simplistic, yet relatively accurate,
unified model to analyze the dynamics of electrons and holes along DNA double
strands. In contrast to similar models discussed in the literature, we refine
the model by adding two crucial ingredients, namely the Coulomb interaction
among both charge carriers and the finite lifetime of excitons due to local
charge recombination.

Our hypothesis for this study is that there is a direct relation between
effective exciton lifetime and, induced by the mobility of electron and hole
along the DNA, their mean spatial separation; the latter depends on the
specificities of the DNA sequences encoded in the tight-binding parameters. If
this were true, at least for a sub-ensemble of DNA sequences of certain
length, the consequences could be far-reaching: A relatively stable charge
distribution resulting from charge delocalization within pockets of the DNA
molecule would result in the emergence of electrical dipole forces that, in
turn, may affect local conformational structures of the DNA complex and its
local electrical properties. Both phenomena could in principle have an impact
on the likelihood of binding of regulatory proteins to the DNA [34], a crucial
aspect of gene regulation and transcriptional processes.

In order to test this hypothesis, we combine efficient quantum dynamical
simulations with the screening of a large set of DNA sequences. More
specifically, our systematic analysis using advanced computational
implementation includes up to 16,384 possible DNA double strand sequences of
length seven bases such that, based on a statistical analysis, we are able to
combine information from quantum physics/physical chemistry with that from
genetics or epigenetics. This way, we aim to identify DNA sequences which may
be of particular interest to be explored further in experimental settings of
genetics/epigenetics.

Remarkably, we first find that our predictions in terms of exciton lifetime
and spatial separation for the most stable species are in good agreement with
data obtained in previous experiments [22, 35, 36, 23, 37]. Our results show
further that it is only a small subset of sequences that stands out as
responsible for relatively long-lived excited states and high-average charge
separation. The role of the electron-hole interaction is very decisive:
Assuming that the Coulomb interaction between charge carriers is completely
screened (no interaction) leads statistically to significantly different
subsets compared to the case when it is finite. However, if it is taken as
finite and is varied in a reasonable window of values [31, 38], the
interesting subset turns out to be relatively robust. This is important since
the precise value of this Coulomb interaction is not known and is
experimentally not directly accessible.

Although still in the embryonic stage, we hope that the presented methodology
may trigger future research by, for example, developing even more elaborate
tight-binding models and optimized numerical tools based on AI [39, 40] for
even larger sets of DNA.

The present manuscript is organized as follows: in Sec. II we provide a
description of the model used in our study. In Sec. III.1 we systematically
investigate exciton lifetime and average charge separation without e-h
interaction. We introduce a Coulomb interaction between the charges in Sec.
III.2 and present its effect on exciton lifetime and average charge separation
in Sec. III.3. We conclude in Sec. IV.

##  II Theoretical modeling

We consider each of the four DNA bases (A, C, G, T) as a site in a (two-
dimensional) tight-binding lattice (see Fig. 1) and numerate the sites by an
index tuple $(ij)$ where $i\in\\{1,2\\}$ refers to the upper or lower strand,
and $j\in\\{1,...,N\\}$ denotes the base index for each DNA strand with $N$
being the number of bases per strand. Two charges (electron and hole) are
created by an initial excitation. This is reflected in the Hilbert space of
the system $\mathcal{H}_{S}=\mathcal{H}_{e}\otimes\mathcal{H}_{h}$ with basis
states $\ket{e_{ij}h_{kl}}$ that describe all possible electron-hole
configurations on the lattice.

Figure 1:  Extended ladder model (ELM) with on-site energies and interaction
parameters, including the diagonal interstrand interaction parameters
$r_{\pm}$.

The overlap of the LUMO (and HOMO) orbitals of neighboring DNA bases allows an
electron (and a hole) to move and spread along the DNA molecule. The
Hamiltonian for both the electron and hole dynamics can be described by two
terms, $H_{\mathrm{self}}^{p}$ and $H_{\mathrm{trans}}^{p}$ (where
$p\in\\{e,h\\}$ describes either electron or hole), containing, respectively,
the on-site and transfer energies:

$\displaystyle H_{\mathrm{self}}^{p}$ $\displaystyle=$
$\displaystyle\sum_{j=1}^{N}\left(\epsilon_{1j}^{p}\ket{p_{1j}}\bra{p_{1j}}+\epsilon_{2j}^{p}\ket{p_{2j}}\bra{p_{2j}}\right)$
(1) $\displaystyle H_{\mathrm{trans}}^{p}$ $\displaystyle=$
$\displaystyle\sum_{j=1}^{N-1}\left(t_{1j}^{p}\ket{p_{1j}}\bra{p_{1,j+1}}+t_{2j}^{p}\ket{p_{2j}}\bra{p_{2,j+1}}\right)+\mathrm{h.c.}$
$\displaystyle+$
$\displaystyle\sum_{j=1}^{N}h_{j}^{p}\ket{p_{1j}}\bra{p_{2j}}+\mathrm{h.c.}$
$\displaystyle+$
$\displaystyle\sum_{j=1}^{N-1}\left(r_{j}^{+p}\ket{p_{1j}}\bra{p_{2,j+1}}+r_{j}^{-p}\ket{p_{1,j+1}}\bra{p_{2,j}}\right)+\mathrm{h.c.}$

This model is commonly known as the Extended Ladder Model (ELM) [29]. We can
now build the Hamiltonian for the electron and hole dynamics along the DNA
double-strand as
$H_{e}=(H_{\mathrm{self}}^{e}+H_{\mathrm{trans}}^{e})\otimes\mathbb{I}_{h}$
and
$H_{h}=\mathbb{I}_{e}\otimes(H_{\mathrm{self}}^{h}+H_{\mathrm{trans}}^{h})$.

To account for electron-hole attraction due to the Coulomb forces, we
introduce two-particle interaction terms of the form:

$\displaystyle
H_{\mathrm{int}}=\sum_{i,k=1}^{2}\sum_{j,l=1}^{N}U_{ijkl}\ket{e_{ij}h_{kl}}\bra{e_{ij}h_{kl}}.$
(3)

Normally, to account for these many-body interaction terms requires
investigating an exponentially large Hilbert space with respect to the
dimension of the system (number of DNA bases). In this case, however, we are
able to enforce the constraint that there is always either one exciton or no
exciton in the system, allowing us to investigate only a quadratically large
Hilbert space.

More specifically, for the interaction matrix elements we assume an algebraic
spatial decay according to $U_{ijkl}=J/(1+r/r_{0})$ with
$r_{0}=1.0\,\text{\AA}$ following [25, 26]. Since two neighboring DNA bases
are separated (in the intrastrand and interstrand direction) by $D\sim
3.4\,\text{\AA}$, we simplify in the tight-binding description the distance
dependence to be of the form
$r/r_{0}\approx(D/r_{0})\cdot\left(|i-k|+|j-l|\right)$ and only include
interactions between next-neighbor bases in agreement with a short-range
approximation used in the literature, i.e.,

$\displaystyle U_{ijkl}=\begin{cases}J&\mathrm{if}\quad(|i-k|+|j-l|)=0\\\
J/(1+D/r_{0})&\mathrm{if}\quad(|i-k|+|j-l|)=1\\\ 0&\mathrm{else}\end{cases}\,$
(4)

The first case describes the two charges being located at the same base, while
the second holds when electron and hole are sitting on neighboring bases. In
this way, we arrive at the interacting TB Hamiltonian for the ELM:
$H=H_{e}+H_{h}+H_{\text{int}}$. The parameters for this model are taken from
ab initio simulations in Ref. [32] and are given in the Supplementary material
[41].

Typical energies that are needed to create an excitation on the DNA are given
by the energy difference between HOMO and LUMO and range between
$3.5\,\mathrm{eV}$ and $4.5\,\mathrm{eV}$ [32]. The typical temperature
$T\approx 310\,\mathrm{K}$ for DNA under ambient conditions instead
corresponds to energies in the range of the meV, much too small to
spontaneously induce excitons, thus reflecting the stability of native DNA.
Hence, external stimuli give rise to excitonic phenomena. In this sense, in a
minimal setting, intrinsic loss mechanisms, i.e. exciton recombination, are
the only relevant impact of residual degrees of freedom to which energy from
the charge sector can be dissipated. In the spirit of quantum optical
modeling, these can be described by operators of the form

$A_{ij}=\sqrt{\gamma_{ij}}\ket{0}\bra{e_{ij}h_{ij}}\,$ (5)

with $\ket{e_{ij}h_{ij}}$ denoting an electron $e$ (hole $h$) at site $i$ on
strand $j$ and local (monomer) transition rates $\gamma_{ij}$. They act as
dissipators with the tendency to destroy quantum coherences in a Lindblad-type
equation for the reduced density operator of the exciton, namely,

$\frac{\mathrm{d}}{\mathrm{d}t}\rho(t)=-\frac{\mathrm{i}}{\hbar}[H,\rho]+\sum_{i,j}A_{ij}\rho
A_{ij}^{\dagger}-\frac{1}{2}\left(A_{ij}^{\dagger}A_{ij}\rho+\rho
A_{ij}^{\dagger}A_{ij}\right).$

Here, the total Hamiltonian enters the deterministic part while the second
part describes local exciton recombination to the monomer groundstate, see
Fig. 2 (for further details see below).

The above time evolution equation is now represented in the above site basis.
Time-dependent expectation values are obtained from the respective density
operator $\rho(t)$ at time $t$. For example, the population in the electron
(hole) sector only follows from

$P_{ij}^{p}(t)=\bra{p_{ij}}\rho_{p}(t)\ket{p_{ij}}\ $

with the partial trace $\rho_{p}=$ Tr${}_{p^{\prime}}[\rho],p\neq
p^{\prime}\in\\{e,h\\}$. The exciton population at the same site is given by

$P_{ij}^{ex}(t)=\bra{e_{ij}h_{ij}}\rho(t)\ket{e_{ij}h_{ij}}$

To incorporate the possibility for e-h recombination, the underlying Hilbert
space is expanded by adding the state $\ket{0}$ to the set of above basis
states. It represents the ground state of the DNA sequence, as illustrated in
Fig. 2, with a population given by $P_{0}(t)=\bra{0}\rho(t)\ket{0}$.

Based on this modelling, the effective exciton lifetime as well as the charge
separation on the lattice is determined. For the latter, we introduce the
charge separation operator $\hat{d}$

$\bra{e_{ij}h_{kl}}\hat{d}\ket{e_{ij}h_{kl}}=D\cdot(|i-k|+|j-l|).$

whose time-average is an estimate for the amount of charge separation during
the dynamics, i.e.

$\bar{d}=\frac{1}{T}\int_{0}^{T}\ {\rm Tr}\\{\rho(t)\,\hat{d}\\}.$

When the electron and hole are temporarily separated in space, they form an
electric dipole with an effective dipole moment, which is directly determined
by the average charge separation.

Figure 2:  HOMO and LUMO for excited state and ground state of the DNA
molecule. Whenever electron and hole are located at the same base they
recombine with a rate $\gamma_{i}$ such that the DNA relaxes to its ground
state.

##  III Results

###  III.1 Excited-state lifetime and average dipole moment

Figure 3:  Top 30 DNA sequences with the longest exciton lifetime (subset
$S_{\rm time}$) (a) and the highest average charge separation (subset $S_{\rm
space}$) (b) from the analysis of all possible double-strand sequences with
seven DNA base pairs for each strand $S_{7}$. We assume a uniform relaxation
rate $\gamma=2\,\mathrm{meV}/\hbar$ and perfect charge screening (no e-h
interaction $J=0$). The letters denote the DNA bases on the upper strand in
the 5’-3’ direction.

In this section, we explore the exciton dynamics with particular focus on
lifetime and spatial separation, which in turn allows to reveal their
correlations with respect to DNA sequences. Our analysis of exciton lifetimes
as such appears to be of relevance in the context of pump-probe experiments
presented in the literature [10, 22, 42], thus addressing the yet not fully
understood topic of relatively long-lasting charge-hole excitations (in the
range of ps) after photo-exciting specific DNA strands. The second observable,
related to exciton mobility, provides information about the charge
distribution along DNA strands and sheds light on the question over which
length scales (number of bases) quantum coherences may survive, a topic that
has been discussed but not yet conclusively answered in previous work [35,
43]. In fact, possible implications are far-reaching since long-range spatial
separation of electron-hole pairs may give rise to relatively strong
electrical dipole forces, which in turn may open pathways for conformational
changes or modify the binding affinity for CpG methylation or other enzymatic
reactions.

More specifically, we conducted a systematic screening of lifetime and charge
separation for all double-strand DNA sequences ranging between $N=3$ and $N=7$
bases in each strand (i.e. total number of bases between 6 and 14), thus
covering up to $S_{7}\equiv 4^{7}=16,384$ DNA sequences. Each sequence has its
individual footprint in form of a specific set of parameters for the ELM, see
Eqs. (II), (3), obtained from atomistic calculations [32, 31]. Monomer exciton
recombination rates in Eq. (5) are not known theoretically and have thus been
inferred from pump-probe experiments in [22]. There, values have been reported
in the range of hundreds of femtoseconds for the recombination of an exciton
confined within a single DNA base. We have then chosen to assume a constant
rate for all modeled bases corresponding to an average lifetime of 300 fs.
Variations on these time scales do not significantly affect the quantitative
results for lifetime and charge separation, and thus have only a marginal
impact on relative dependencies between different DNA sequences (see
Supplementary material [41]).

We observed that exciton lifetimes vary substantially within the total set
$S_{N}$ of DNA sequences, with several sequences showing lifetimes on the
order of picoseconds (e.g., $>2.5\,\text{ps}$ for TTTTTAA) versus many other
sequences showing lifetimes comparable to the monomer lifetime of
approximately $300\,\text{fs}$ (see Supplementary material [41]). The range
between the longest and shortest lifetimes spanned nearly one order of
magnitude. Data of the top 30 sequences (ordered accordingly in a subset
$S_{\rm time}\subset S_{7}$) are shown in Fig. 3(a) with typical lifetimes of
the order of 2 ps and a variation of approximately 25%.

The charge separation analysis revealed a wide range of results among
different sequences, with some exhibiting negligible separation, while others
displaying charge separations exceeding $10\,\text{\AA}$, equivalent to an
average separation of approximately three base pairs. Following a similar
analysis to the one above, we identified an ordered set $S_{\rm space}\subset
S_{7}$ of 30 sequences with variations of approximately 20%, see Fig. 3(b).
Notably, charge separations within $D_{\rm large}$ qualitatively match
previous findings in [36, 23, 37, 35], where a mixed diffusion mechanism for
charge transfer along DNA strands is proposed in which quantum delocalization
plays a relevant role in patches of up to $3-4$ base pairs, i.e. approximately
$\sim 10\,-\,13\,\text{\AA}$.

Now, based on this analysis we turn to consider correlations between lifetime
and charge separation. Indeed, within the total set $S_{7}$, we find robust
correlations with correlation factor exceeding $\chi\gtrsim 0.95$ (see
Supplementary Material [41]). However, when considering only the respective
top subsets $S_{\rm time}$ and $S_{\rm space}$ a remarkably weaker correlation
appears: less than $\chi\approx 0.4$. For these specific sequences, a strong
correspondence between lifetime and dipole moment is not clearly recognizable.
The first finding is intuitive: Excitonic recombination is substantially
inhibited when electron and hole sit on different sites (bases) as they are
then efficiently screened by the surrounding background. This implies that
larger charge mobility along the chain leads in general to a longer excitonic
lifetimes. The second finding suggests though that details are more subtle
and, among the top sequences, additional mechanisms besides the mere particle
separation play a crucial role such as onsite energies.

A general trend can be found when relative distributions of A-T versus G-C
base pairs in $S_{7}$ are studied (see Fig. 4). Sequences containing regions
rich in G-C base pairs are more likely to feature long-lived excitations than
sequences rich in A-T base pairs. In all these data, increasing (decreasing)
monomer relaxation rates within a window around $300\,\mathrm{fs}$ leads to a
mere shift of absolute values towards smaller (larger) exciton relaxation
times but overall preserving relative relations.

Figure 4:  Relative distribution of base-pairs (A-T pair and G-C pair) in
sequences of seven base pairs over the expected exciton lifetime. We obtain
the distribution at time $t$ by counting the base pairs in all sequences with
a lifetime greater than $t$ and dividing by the number of base pairs. Since it
is necessary to average over several sequences before the results become
relevant, we have omitted the first 10 sequences with the largest exciton
lifetimes.

###  III.2 Electron-hole interaction and charge distribution

While single charge transfer along DNA has been largely investigated [38, 44,
31], the role of charge-charge interactions has received much less attention.
In the context of the current work, this is particularly true for electron-
hole correlations due to attractive Coulomb forces. In fact, to include this
interaction may be decisive for the dynamics of excitons as it implies to
account for two competing processes: Electron-hole interaction with the
tendency to localize charge pairs on individual sites (nucleotides) and the
mobility of both charge carriers in LUMO and HOMO with the tendency for
delocalization. Details thus depend on energy profiles, strength of
hybridization, and screening properties (range of Coulomb interaction) of a
specific DNA sequence.

Here, we start this analysis considering the impact of electron-hole
correlations within the so-called wire model [30]. The latter is a simplified
version of the ELM in which the bases forming a base pair are treated as one
macro-molecule of two adjacent molecules with electronic overlap such that
HOMO and LUMO are localized only on one of the bases of a pair [32]. This
model has been previously studied in the literature and thus provides
benchmark data that we used to validate our modeling. It further allows to
achieve a transparent dynamical understanding of electron-hole interaction
which will serve as the basis to consider it in the full ELM in the next
section.

Coulomb forces are usually considered as well-established and well-known
interactions, whose intensity can be easily evaluated given specific boundary
conditions. However, the situation in macro-molecular aggregates such as DNA
is more complex, though, because the strength of this interaction can vary due
to several factors inherent to surrounding degrees of freedom. An aqueous
environment acts as a polarizable medium (water has a relatively high
dielectric constant of about 80 at physiological temperatures), thus
influencing and screening the Coulombic forces in various ways. Additionally,
factors such as local hydration and the presence of counter-ions can
contribute to variations in the effective dielectric constant of the
surroundings. Structural deformations, which encompass mechanical stress,
temperature changes, and interactions with surrounding biomolecules or macro-
molecules, as well as conformational changes such as bending or twisting of
the DNA helix, can further impact the spatial arrangement of the charge
carriers and modify the strength and range of the Coulombic forces.
Consequently, the strength of the Coulomb interaction within DNA can exhibit
considerable variability. Due to these reasons, in our study, we investigate a
comprehensive range of interaction strengths, ranging from considerably weaker
to stronger with respect to the DNA hopping energies.

Figure 5:  Accumulated average populations
$P_{k}^{\text{acc}}=\sum_{i=0}^{k}\langle P_{i}\rangle$ of (a) GCGCGC and (b)
GCGCG with initial excitation on the left base pair according to the wire
model description. The hopping parameters are as follows: GC
$-10\,\mathrm{meV}$, CG $-8\,\mathrm{meV}$ for the electron and GC
$-10\,\mathrm{meV}$, CG $50\,\mathrm{meV}$ for the hole.

More specifically, we investigate the effect of e-h interaction on time-
averaged populations for GC periodic sequences, modeled as one-dimensional
chains whose base units model the G-C DNA nucleobase pair. A similar analysis
is shown in the Supplementary Material [41] (Fig. 3), where we report results
for a uniform G sequence. Since the base units of the chain are the same (G-C
nucleobase pairs), we note that the difference between the alternating GC
sequence and the uniform G sequence lies in the staggered (or uniform) site-
site overlap parameters along the chain. Accordingly, within this wire model,
this sequence becomes degenerate with respect to on-site energies but not with
respect to coupling energies as the 5’-3’ DNA directionality implies that the
G-C molecular overlap is different from C-G one. When we set the e-h
interaction strength to zero, i.e. $J=0$ in Eq. (4), our results match the
findings of the above-mentioned works [38, 44, 31]: The electron spreads over
all DNA bases, while the hole is either distributed between the left and right
edges (consider $J=0$ for even-length chains, Fig. 5(a)) or localized on the
left edge ($J=0$ for odd-length chains, Fig. 5(b)). This different behavior
can be easily explained by considering the physics of one-dimensional
topological systems, such as the Su-Schrieffer-Heeger (SSH) chain [45]. By
inspecting the interaction energies of electrons and holes in Tab. VII in the
Supplementary material [41], one notices that in the electronic sector one has
$|t_{GC}|>|t_{CG}|$, while the opposite applies to holes. In SSH chains this
in turn induces two different regimes, namely a trivial and topological one,
characterized by exactly the two dynamical scenarios seen for electrons and
holes here.

Now, when switching on the e-h interaction $J\neq 0$, we observe the tendency
to wash out these differences, and two different regimes can be distinguished:
In the intermediate regime ($J$ is of the same order as the site-site overlap
parameters), the electron population at the edges increases slightly while the
hole spreads across the molecule and populates the bases in the bulk, very
similar to the behavior of the electron in the uncorrelated regime. While the
excitonic population (population of electron and hole sitting at the same
base) thus increases, the spreading of the hole along the chain is suppressed.
With increasing interaction strength, the role of electron and hole switch,
with the hole pulling the electron towards the edges. In this strongly
interacting regime, both charges display a similar localized distribution,
leading to the observed increase in the excitonic population.

Interestingly, we can identify an even-odd effect by comparing results shown
in Fig. 5(a) and Fig. 5(b). Sequences with an even or odd number of sites
(base pairs) show a rather different behavior in the hole sector. In "even-
length" sequences, the hole tends to be distributed at the edges of the
strand, not populating the bulk, in both cases when it is not interacting with
the electron and when it does so strongly. The same is true for the excitonic
distribution in the strong interaction regime. In contrast, in "odd-length"
sequences, both charges tend to localize only at the very first site of the
chain, where the exciton has been created by an external stimulus. Different
studies on the delocalization of quantum particles in "SSH-like" topological
systems confirm this even-odd duality that we observe in this context [45,
46]. These findings support the fact that the mobility of charge carriers and
of more elaborate structures like Frenkel excitons, is way more likely to be
influenced by long-range transport when placed in a wire-sequence with an even
number of sites rather than an odd number, in agreement with [29].
Nonetheless, both cases show very similar values for the total excitonic
population along the strand.

###  III.3 Electron-hole interaction and exciton lifetime

We now come back to the statistical analysis presented in Sec. III.1 and
extend it by including electron-hole interaction in the ELM. Inspired by the
discussion in the previous Section, as illustrative scenarios two specific
values for the interaction parameter, namely, $J=50\,\mathrm{meV}$ and
$J=100\,\mathrm{meV}$ are chosen.

Fig. 6 shows the top 30 sequences with the longest excitonic lifetimes $S_{\rm
time}^{J\neq 0}$. One immediately sees the tendency that lifetimes are
slightly reduced for all sequences compared to the situation with $J=0$ (see
also the Supplementary material [41]). This is easily understood by the fact
that an attractive electron-hole interaction promotes local exciton
recombination. However, quite unexpected is the finding that the sets $S_{\rm
time}^{J\neq 0}$ of DNA sequences for finite $J$ are strongly correlated while
correlations to the set for $J=0$ ($S_{\rm time}$) are considerably weaker.
This in turn implies that the mere insertion of a finite charge-charge
correlation is relevant (within a reasonable window) but not the precise value
of the interaction parameter. Since the latter is not directly accessible
experimentally, estimated values may already provide sufficiently reliable
predictions for sequence dependences.

Figure 6:  Expected values of excitonic lifetimes for different values of the
e-h interaction strength: $0\,\mathrm{meV}$, $50\,\mathrm{meV}$ and
$100\,\mathrm{meV}$. The colors of the sequences indicate the copresence of
the sequence in different plots. Red: sequence present in all three plots;
Green: sequence present in the first two plots; Blue: sequence present in the
second and third plots. Figure 7:  Correlation plots between lists of
lifetimes of DNA sequences, for different values of the e-h interaction
strength (see legend). The right plot is a zoom into the first 100 sequences
of the left plot. The correlation between different non-zero e-h interactions
is always higher than the correlations with zero e-h interactions. Figure 8:
Relative distribution of base pairs (A-T pair and G-C pair) in sequences of
seven bases per strand during the expected exciton lifetime, for the e-h
interaction = 50 (top) or 100 (bottom) meV. We obtain the distribution at time
$t$ by counting the base pairs in all sequences with a lifetime greater than
$t$ and dividing by the total number of base pairs. Since it is necessary to
average over several sequences before the results become relevant, we have
omitted the first 10 sequences with the largest exciton lifetimes.

Details of this analysis are shown in Fig. 7. The left panel shows
correlations for the entire list $S_{7}$ of DNA sequences discussed already in
Sec. III.1. The correlations between the non-interacting and either of the two
interacting lists (blue and green) are weak to absent within the subsets
$S_{\rm time}$ resp. $S_{\rm time}^{J\neq 0}$ of the longest lifetimes, but
moderate between the subsets of shorter lifetimes. As mentioned above, most
strikingly, the correlations between lists with finite $J$ are, instead,
permanently very strong, independent of the value of $J$. Even in the right
panel of Fig. 7, where data for the 100 DNA sequences with the longest
lifetimes are shown, correlations lie constantly above $\chi\sim 0.9$, except
for the top sequences where still $\chi>0.7$. Very similar results are
obtained by performing the same analysis for the mean charge distribution as
reported in Fig. S4 of the Supplementary Material [41].

We thus conclude that, with respect to the observables under analysis,
considering the effects of e-h interactions is crucial for a realistic
description of the dynamics of charges and excitons along DNA strands. The
mere introduction of electron-hole interactions into the model seems to be
much more relevant than the actual tuning of interaction strength.

In Fig. 8 we report the same analysis as in Fig. 4 for the relative
distribution of base pairs over the excitonic lifetime, for the two scenarios
with finite e-h interaction. We find that the effect of the e-h interaction
translates into a much greater influence of the TA base pair to ensure a
higher lifetime of an exciton within a given sequence. This reversal of
tendency also appears in Fig. 6, when considering the sequences that newly
appear in $S_{\rm time}^{J\neq 0}$ as compared to the set with $J=0$. This
suggests that T-rich sequences may more strongly support long-lived dipole
structures and may thus be more susceptible to reveal properties that are of
potential relevance for epigenetic processes due to photo-excitation (e.g. UV
radiation in skin cells).

##  IV Discussion

In this work we established a methodological bridge between quantum dynamical
simulations of electron-hole charge transfer along double-stranded DNA and the
statistical analysis of a large ensemble of DNA sequences. Although single
charge transfer has been studied quite frequently, correlated electron-hole
dynamics including recombination has rarely been investigated [25, 26, 47,
48]. By using a tight-binding model with parameters taken from ab initio
calculations, we are able to obtain results for all possible permutations of
DNA segments of up to 7 bases in each strand, far beyond what is feasible in
atomistic calculations. The efficiency of this method allows us to correlate
specific physical parameters to the entire ensemble of corresponding DNA
sequences, thus to establishing relative dependences between them. This way,
predictions can be made for subsets that support relatively long-lived,
delocalized charge-hole pairs which, in turn, imply relatively strong
electrical dipole moments over distances of 3-4 base pairs. Notably, these
sequences display a particular enrichment in thymine (T) bases. The resulting
charge imbalance within the DNA molecule induces molecular polarization, which
has the potential to influence various biological processes, such as sequence-
and conformation-dependent protein binding and transcriptional regulation.

Our findings are quantitatively in agreement with experimental data in terms
of exciton lifetimes (about 2-3 ps) [10, 22, 42] and coherence lengths (about
10 Å) [35, 43]. However, the tight-binding model presented is still too
simplistic to allow quantitative predictions for individual DNA sequences,
e.g., including a realistic description of the DNA backbone, but it does allow
the model to characterize relative correlations within an ensemble of
sequences. In particular, it turns out that most subsets are relatively robust
against variations of the charge-hole interaction parameter, as long as it
remains finite, within a broad window of values.

Finally, we want to discuss some implications that can be cast into the
following questions: Might some DNA-binding proteins use DNA-mediated
(correlated) charge transfer (CT) for long-range signaling or activation? CT
chemistry provides an approach to detect base stacking perturbations and
lesions: Might nature take advantage of this chemistry? Telomeric DNA (the
region of DNA at the ends of all linear chromosomes) and regions flanking
protein-coding exons are guanine-rich: Could the higher degree of degeneracy
(due to repeated Gs) in these areas facilitate the tunneling of excess charges
to these non-coding regions, thus avoiding dangerous complications (as
speculated in [49])? We believe that the methodology presented in this work
and its extension to larger system sizes resp. larger ensembles of DNA
sequences may open new avenues to address these questions from a perspective
which combines quantum dynamics with the large scale screening of DNA base
compositions. Thus, this research may complement existing techniques from
physical chemistry, bio-chemistry and genetics to achieve a broader
understanding of properties of DNA with potential applications in fields such
as nanotechnology [21], epigenetics [34] and DNA-related studies including DNA
damage, repair and mutagenesis.

###### Acknowledgements.

The authors gratefully acknowledge Marco Trenti for his assistance with
numerical simulations. The authors appreciate the financial support of the
Center for Integrated Quantum Science and Technology (IQST) and the BMBF
through the QCOMP project in Cluster4Future QSens.

## References

  * Fassioli  _et al._ [2014] F. Fassioli, R. Dinshaw, P. Arpin, and G. Scholes, Photosynthetic light harvesting: excitons and coherence, R Soc Interface 11, 20130901 (2014).
  * Mirkovic  _et al._ [2017] T. Mirkovic, E. E. Ostroumov, J. M. Anna, R. van Grondelle, Govindjee, and G. D. Scholes, Light Absorption and Energy Transfer in the Antenna Complexes of Photosynthetic Organisms, Chemical Reviews 117, 249 (2017).
  * Chenu and Scholes [2015] A. Chenu and G. D. Scholes, Coherence in Energy Transfer and Photosynthesis, Annual Review of Physical Chemistry 66, 69 (2015).
  * Cao  _et al._ [2020] J. Cao _et al._ , Quantum biology revisited, Science Advances 6, eaaz4888 (2020).
  * Mattoni [2020] A. Mattoni,  _Theory and modeling of excitonic energy transfer in biological and bio.inspired photosynthesis_ , Ph.D. thesis, Ulm University (2020).
  * Ostroverkhova [2016] O. Ostroverkhova, Organic Optoelectronic Materials: Mechanisms and Applications, Chemical Reviews 116, 13279 (2016).
  * Inganäs [2018] O. Inganäs, Organic Photovoltaics over Three Decades, Advanced Materials 30, 1800388 (2018).
  * Lu  _et al._ [2021] X. F. Lu, Y. Fang, D. Luan, and X. W. D. Lou, Metal–Organic Frameworks Derived Functional Materials for Electrochemical Energy Storage and Conversion: A Mini Review, Nano Letters 21, 1555 (2021).
  * Improta  _et al._ [2016] R. Improta, F. Santoro, and L. Blancafort, Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases, Chemical Reviews 116, 3540 (2016).
  * Crespo-Hernandez  _et al._ [2004] C. Crespo-Hernandez, B. Cohen, P. Hare, and B. Kohler, Ultrafast Excited-State Dynamics in Nucleic Acids, Chem. Rev. 104, 1977 (2004).
  * Middleton  _et al._ [2009] C. T. Middleton, K. de La Harpe, C. Su, Y. K. Law, C. E. Crespo-Hernández, and B. Kohler, Dna excited-state dynamics: From single bases to the double helix, Annual Review of Physical Chemistry 60, 217 (2009).
  * Kleinermanns  _et al._ [2013] K. Kleinermanns, D. Nachtigallová, and M. S. de Vries, Excited state dynamics of DNA bases, International Reviews in Physical Chemistry 32, 308 (2013).
  * Schreier  _et al._ [2015] W. J. Schreier, P. Gilch, and W. Zinth, Early Events of DNA Photodamage, Annual Review of Physical Chemistry 66, 497 (2015).
  * Schuster [2004] G. Schuster,  _Long-Range Charge Transfer in DNA_ (Springer, New York, 2004).
  * Endres  _et al._ [2004] R. G. Endres, D. L. Cox, and R. R. P. Singh, Colloquium: The quest for high-conductance DNA, Rev. Mod. Phys. 76, 195 (2004).
  * Rajski  _et al._ [2000] S. R. Rajski, B. A. Jackson, and J. K. Barton, DNA repair: models for damage and mismatch recognition, Mutation Research/Fundamental and Molecular Mechanisms of Mutagenesis 447, 49 (2000).
  * Rajski and Barton [2001] S. R. Rajski and J. K. Barton, How Different DNA-Binding Proteins Affect Long-Range Oxidative Damage to DNA, Biochemistry 40, 5556 (2001).
  * Giese [2006] B. Giese, Electron transfer through DNA and peptides, Bioorganic & Medicinal Chemistry 14, 6139 (2006).
  * Shih  _et al._ [2011] C.-T. Shih, Y.-Y. Cheng, S. A. Wells, C.-L. Hsu, and R. A. Römer, Charge transport in cancer-related genes and early carcinogenesis, Computer Physics Communications 182, 36 (2011).
  * Chakraboty [2007] T. Chakraboty,  _Charge Migration in DNA: Perspectives from Physics, Chemistry, and Biology_ (Springer, Berlin, Heidelberg, 2007).
  * Albuquerque  _et al._ [2014] E. L. Albuquerque, U. L. Fulco, V. N. Freire, E. W. S. Caetano, M. L. Lyra, and F. A. B. F. de Moura, DNA-based nanobiostructured devices: The role of quasiperiodicity and correlation effects, Physics Reports 535, 139 (2014).
  * Crespo-Hernandez  _et al._ [2005] C. Crespo-Hernandez, B. Cohen, and B. Kohler, Base stacking controls excited-state dynamics in A·T DNA, Nature 436, 1141 (2005).
  * Takaya  _et al._ [2008] T. Takaya, C. Su, K. de La Harpe, C. E. Crespo-Hernández, and B. Kohler, Uv excitation of single dna and rna strands produces high yields of exciplex states between two stacked bases, Proceedings of the National Academy of Sciences 105, 10285 (2008).
  * Wang  _et al._ [2022] X. Wang, R. Sha, W. B. Knowlton, N. C. Seeman, J. W. Canary, and B. Yurke, Exciton Delocalization in a DNA-Templated Organic Semiconductor Dimer Assembly, ACS Nano 16, 1301 (2022).
  * Bittner [2006] E. R. Bittner, Lattice theory of ultrafast excitonic and charge-transfer dynamics in DNA, Journal of Chemical Physics 125, 094909 (2006).
  * Bittner [2007] E. R. Bittner, Frenkel exciton model of ultrafast excited state dynamics in AT DNA double helices, Journal of Photochemistry and Photobiology A: Chemistry 190, 328 (2007).
  * Gutiérrez  _et al._ [2009] R. Gutiérrez, R. A. Caetano, B. P. Woiczikowski, T. Kubar, M. Elstner, and G. Cuniberti, Charge transport through biomolecular wires in a solvent: Bridging molecular dynamics and model hamiltonian approaches, Physical Review Letters 102, 208102 (2009).
  * Gutiérrez  _et al._ [2010] R. Gutiérrez, R. Caetano, P. B. Woiczikowski, T. Kubar, M. Elstner, and G. Cuniberti, Structural fluctuations and quantum transport through DNA molecular wires: A combined molecular dynamics and model hamiltonian approach, New Journal of Physics 12, 023022 (2010).
  * Lambropoulos and Simserides [2019] K. Lambropoulos and C. Simserides, Tight-binding modeling of nucleic acid sequences: Interplay between various types of order or disorder and charge transport, Symmetry 11, 968 (2019).
  * Cuniberti  _et al._ [2007] G. Cuniberti, E. Maciá, A. Rodríguez, and R. A. Römer, Tight-Binding Modeling of Charge Migration in DNA Devices, in  _Charge Migration in DNA: Perspectives from Physics, Chemistry, and Biology_, edited by T. Chakraborty (Springer Berlin Heidelberg, Berlin, Heidelberg, 2007) pp. "1–20.
  * Simserides [2014] C. Simserides, A systematic study of electron or hole transfer along DNA dimers, trimers and polymers, Chemical Physics 440, 31 (2014).
  * Hawke  _et al._ [2010] L. Hawke, G. Kalosakas, and C. Simserides, Electronic parameters for charge transfer along DNA, The European Physical Journal E 32, 291 (2010).
  * Giese [2002] B. Giese, Long-distance electron transfer through dna, Annual Review of Biochemistry 71, 51 (2002).
  * Siebert  _et al._ [2023] R. Siebert, O. Ammerpohl, M. Rossini, D. Herb, S. Rau, M. Plenio, F. Jelezko, and J. Ankerhold, A quantum physics layer of epigenetics: a hypothesis deduced from charge transfer and chirality-induced spin selectivity of DNA, Clin. Epigenet. 15, 145 (2023).
  * Genereux and Barton [2010] J. C. Genereux and J. K. Barton, Mechanisms for DNA charge transport, Chemical Reviews 110, 1642 (2010).
  * Buchvarov  _et al._ [2007] I. Buchvarov, Q. Wang, M. Raytchev, A. Trifonov, and T. Fiebig, Electronic energy delocalization and dissipation in single- and double-stranded DNA, Proceedings of the National Academy of Sciences 104, 4794 (2007).
  * Kadhane  _et al._ [2008] U. Kadhane, A. I. S. Holm, S. V. Hoffmann, and S. B. Nielsen, Strong coupling between adenine nucleobases in DNA single strands revealed by circular dichroism using synchrotron radiation, Phys. Rev. E 77, 021901 (2008).
  * Lambropoulos  _et al._ [2016a] K. Lambropoulos, M. Chatzieleftheriou, A. Morphis, K. Kaklamanis, R. Lopp, M. Theodorakou, M. Tassi, and C. Simserides, Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of a wire model versus an extended ladder model, Physical Review E 94, 062403 (2016a).
  * Korol and Segal [2019] R. Korol and D. Segal, Machine Learning Prediction of DNA Charge Transport, The Journal of Physical Chemistry B 123, 2801 (2019).
  * Ullah and Dral [2022] A. Ullah and P. O. Dral, Predicting the future of excitation energy transfer in light-harvesting complex with artificial intelligence-based quantum dynamics, Nature Communications 13, 1930 (2022).
  * [41] See Supplementary material.
  * Trifonov  _et al._ [2005] A. Trifonov, M. Raytchev, I. Buchvarov, M. Rist, J. Barbaric, H.-A. Wagenknecht, and T. Fiebig, Ultrafast energy transfer and structural dynamics in dna, The Journal of Physical Chemistry B 109, 19490 (2005).
  * Boon and Barton [2002] E. M. Boon and J. K. Barton, Charge transport in DNA, Current Opinion in Structural Biology 12, 320 (2002).
  * Lambropoulos  _et al._ [2016b] K. Lambropoulos, K. Kaklamanis, A. Morphis, M. Tassi, R. Lopp, G. Georgiadis, M. Theodorakou, M. Chatzieleftheriou, and C. Simserides, Wire and extended ladder model predict THz oscillations in DNA monomers, dimers and trimers, Journal of Physics Condensed Matter 28, 495101 (2016b).
  * Asbóth  _et al._ [2016] J. K. Asbóth, L. Oroszlány, and A. Pályi, The Su-Schrieffer-Heeger (SSH) Model, in  _A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions_ (Springer International Publishing, 2016) pp. 1–22.
  * Cramer  _et al._ [2004] T. Cramer, S. Krapf, and T. Koslowski, DNA Charge Transfer: An Atomistic Model, The Journal of Physical Chemistry B 108, 11812 (2004).
  * Tornow  _et al._ [2010] S. Tornow, R. Bulla, F. B. Anders, and G. Zwicknagl, Multiple-charge transfer and trapping in DNA dimers, Physical Review B - Condensed Matter and Materials Physics 82, 195106 (2010).
  * Conwell  _et al._ [2008] E. M. Conwell, P. M. McLaughlin, and S. M. Bloch, Charge-Transfer Excitons in DNA, The Journal of Physical Chemistry B 112, 2268 (2008).
  * Delaney and Barton [2003] S. Delaney and J. K. Barton, Long-Range DNA Charge Transport, The Journal of Organic Chemistry 68, 6475 (2003).
  * Mehrez and Anantram [2005] H. Mehrez and M. P. Anantram, Interbase electronic coupling for transport through DNA, Phys. Rev. B 71, 115405 (2005).

##  Appendix A Tight-binding parameters

Tight-binding parameters for electrons and holes calculated using ab initio
methods have been proposed in several works in the literature [50, 32, 31]. We
have decided to use the set proposed by Hawke et al. [32] for the description
at the single-base level (wire model) and the set proposed by Simserides [31]
for the description at the base pair level (extended ladder model).

The LUMO and HOMO energies of the stacked DNA bases characterize the on-site
energies for electrons and holes. These energies differ from the on-site
energies of the isolated bases as stacked bases get slightly deformed due to
base-base interactions. The energy needed to create an exciton (that means
providing $\Delta E$ to excite an electron from the HOMO to the LUMO) is given
by the energy difference between HOMO and LUMO.

###  A.1 Extended ladder model

Table 1:  HOMO and LUMO energies of paired DNA bases. The HOMO energies are taken as on-site energies $\epsilon_{h}$ of the holes and the LUMO energies as on-site energies $\epsilon_{e}$ of the electrons. The energy difference $\Delta E$ between HOMO and LUMO equals the energy needed to create an exciton and is given in the last row. The parameters taken from [32, Table I] and given in $100\,\mathrm{meV}$. | A | T | G | C
---|---|---|---|---
LUMO (electrons) | -44 | -49 | -45 | -43
HOMO (holes) | -83 | -90 | -80 | -88
$\Delta E$ (exciton) | 39 | 41 | 35 | 45
Table 2:  Tight-binding parameters for the direct interstrand transfer $h_{e}$ ($h_{h}$) of electrons (holes). The parameters taken from [32, Table IV] and given in $\mathrm{meV}$. A-T | -9 (-12) | G-C | 16 (-12)
---|---|---|---
Table 3:  Tight-binding parameters for the intrastrand transfer $t_{e}$ ($t_{h}$) of electrons (holes). The table is to be read in such a way that the parameter in row $X$ and column $Y$ corresponds to the transfer parameter from base $X$ to base $Y$ in 5’-3’ direction (or the transfer parameter from base $Y$ to base $X$ in 3’-5’ direction). The parameters are taken from [32, Table V] and given in $\mathrm{meV}$. | A | T | G | C
---|---|---|---|---
A | 16 (-8) | 7 (68) | 1 (-5) | -3 (68)
T | -7 (26) | -30 (-117) | -17 (28) | 22 (-86)
G | 30 (-79) | -32 (73) | 20 (-62) | 43 (80)
C | -12 (5) | 63 (-107) | 15 (-1) | -47 (-66)
Table 4:  Tight-binding parameters for the diagonal interstrand transfer $r_{e}^{+}$ ($r_{h}^{+}$) of electrons (holes) in 5’-5’ direction. The table is to be read in such a way that the parameter in row $X$ and column $Y$ corresponds to the transfer parameter from base $X$ to base $Y$ in 5’-5’ direction (or the transfer parameter from base $Y$ to base $X$ in 3’-3’ direction). The parameters taken from [32, Table VII] and given in $\mathrm{meV}$. | A | T | G | C
---|---|---|---|---
A | 6 (2) | 2 (9) | 3 (4) | -2 (5)
T | 2 (9) | 2 (4) | 3 (5) | -2 (2)
G | 3 (4) | 3 (5) | -2 (3) | -3 (4)
C | -2 (5) | -2 (2) | -3 (4) | 2 (1)
Table 5:  Tight-binding parameters for the diagonal interstrand transfer $r_{e}^{-}$ ($r_{h}^{-}$) of electrons (holes) in 3’-3’ direction. The table is to be read in such a way that the parameter in row $X$ and column $Y$ corresponds to the transfer parameter from base $X$ to base $Y$ in 3’-3’ direction (or the transfer parameter from base $Y$ to base $X$ in 5’-5’ direction). The parameters taken from [32, Table VI] and given in $\mathrm{meV}$. | A | T | G | C
---|---|---|---|---
A | 29 (48) | 3 (-3) | -6 (-3) | -3 (-5)
T | 3 (-3) | 0.2 (0.5) | 2 (5) | -0.2 (0.5)
G | -6 (-3) | 2 (5) | -5 (-44) | -4 (4)
C | -3 (-5) | -0.2 (0.5) | -4 (4) | 0.3 (1)

###  A.2 Wire model

Table 6:  HOMO and LUMO energies of paired DNA bases. The HOMO energies are taken as on-site energies $\epsilon_{h}$ of the holes and the LUMO energies as on-site energies $\epsilon_{e}$ of the electrons. The energy difference $\Delta E$ between HOMO and LUMO equals the energy needed to create an exciton and is given in the last row. The parameters taken from [31, Table I] and given in $100\,\mathrm{meV}$. | A-T | G-C
---|---|---
LUMO (electrons) | -49 | -45
HOMO (holes) | -83 | -80
$\Delta E$ (exciton) | 34 | 35
Table 7:  Tight-binding parameters for the intrastrand transfer $t_{e}$ ($t_{h}$) of electrons (holes). The table is to be read in such a way that the parameter in row $X$ and column $Y$ corresponds to the transfer parameter from base $X$ to base $Y$ in 5’-3’ direction (or the transfer parameter from base $Y$ to base $X$ in 3’-5’ direction). The parameters taken from [31, Table II] and given in $\mathrm{meV}$. | A | T | G | C
---|---|---|---|---
A | -29 (20) | 0.5 (-35) | 3 (30) | 32 (-10)
T | 2 (-50) | -29 (20) | 17 (10) | -1 (110)
G | -1 (110) | 32 (-10) | 20 (100) | -10 (-10)
C | 17 (10) | 3 (30) | -8 (50) | 20 (100)

##  Appendix B Extra plots

In this section, we provide additional plots and data that complement and
extend the analyses presented in the main text. These supplementary figures
aim to offer a more comprehensive understanding of the key findings discussed
in the primary research manuscript.

In particular, we present the results of our analysis of the average charge
separation between electrons and holes in the time interval between
photoexcitation and relaxation of the DNA double strand. Fig. S9 shows that,
as discussed in the main text, the composition of the top 30 sequences changes
with increasing interaction strength toward a higher amount of thymine (T).
This is true for both the exciton lifetime and the average charge separation,
although the sequences themselves are different in both analyses. In Fig. S10
we show all DNA sequences of seven base pairs ordered by exciton lifetime
(left) and average charge separation (right) for selected interaction
strengths. We find that for the vast majority of DNA sequences (more than
10,000 sequences, especially strongly non-symmetric and non-uniform) the
excitation decays on the same time scale as for an isolated single base and
the charges show almost no separation, supporting the well-known result that
DNA is photostable. Fig. S11 shows the same kind of analysis on the mean-over-
time population with varying interaction strength as in Fig. 5 of the main
text, performed on uniform guanine sequences. Fig. S12 shows the correlations
for the dipole moment in the same way as in Fig. 7 of the main manuscript.

Figure 9:  Top 30 DNA sequences showing the highest exciton lifetime (upper
row) and average charge separation (lower row) for no interaction,
intermediate interaction ($J=50\,\mathrm{meV}$) and strong interaction
($J=100\,\mathrm{meV}$). Figure 10:  Results of all sequences consisting of
seven base pairs ordered by exciton lifetime (left) and average charge
separation (right) for no interaction, intermediate interaction
($J=50\,\mathrm{meV}$) and strong interaction ($J=100\,\mathrm{meV}$). Figure
11:  Accumulated average populations $P_{k}^{\text{acc}}=\sum_{i=0}^{k}\langle
P_{i}\rangle$ of (a) GGGGG and (b) GGGGGG with initial excitation on the left
base pair according to the wire model description. The hopping parameters are
as follows: $t_{e}=20\,\mathrm{meV}$ for the electron and
$t_{h}=100\,\mathrm{meV}$ for the hole. Figure 12:  Correlation plots between
lists of DNA sequence dipole moments, for different values of the e-h
interaction strength (see legend). The right plot is a zoom into the first 100
sequences of the left plot. The correlation between different non-zero e-h
interactions is always higher than the correlations with zero e-h interaction.
Figure 13: Excitonic lifetime plots for S4 sequences with different relaxation
rates for the release of energy into the environment. For different rates of
excitonic escape, the different resulting sequences show strong correlations
and very similar behavior, confirming the robustness of this phenomenon to
this parameter. The correlation of $\chi=0.97$ shown refers to the two
sequences with $\gamma=0.01-0.02$ and that of $\chi=0.92$ refers to the two
sequences with $\gamma=0.05-0.02$.