# Digital Twins of the EM Environment:
Benchmark for Ray Launching Models

Michele Zhu∗ , Lorenzo Cazzella∗ , Francesco Linsalata∗ ,
Maurizio Magarini , Matteo Matteucci , Umberto Spagnolini
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di
Milano, Milan, Italy This work was partially supported by the European Union
under the Italian National Recovery and Resilience Plan (NRRP) of
NextGenerationEU, partnership on “Telecommunications of the Future”
(PE00000001 \- program “RESTART”) CUP: D43C22003080001.
∗These authors equally contributed to this research

###### Abstract

Digital Twin has emerged as a promising paradigm for accurately representing
the electromagnetic (EM) wireless environments. The resulting virtual
representation of the reality facilitates comprehensive insights into the
propagation environment, empowering multi-layer decision-making processes at
the physical communication level. This paper investigates the digitization of
wireless communication propagation, with particular emphasis on the
indispensable aspect of ray-based propagation simulation for real-time Digital
Twins. A benchmark for ray-based propagation simulations is presented to
evaluate computational time, with two urban scenarios characterized by
different mesh complexity, single and multiple wireless link configurations,
and simulations with/without diffuse scattering. Exhaustive empirical analyses
are performed showing and comparing the behavior of different ray-based
solutions. By offering standardized simulations and scenarios, this work
provides a technical benchmark for practitioners involved in the
implementation of real-time Digital Twins and optimization of ray-based
propagation models.

###### Index Terms:

Digital Twin, Radio Map, Radio Propagation, Ray Launching, Ray Tracing,
Wireless Communication

##  I Introduction

The accurate modeling of electromagnetic (EM) radio maps has significant
implications for improving key parameters in network design and deployment
[1]. Within this context, the concept of the Digital Twin (DT) emerges,
representing a sophisticated but interesting approach to constructing precise
digital replicas of physical entities or processes. These DTs provide real-
time insight into their corresponding physical counterparts, effectively
integrating simulations with existing databases [2]. This framework
necessitates the development of appropriate models for the continuous update
and enhancement of the virtual representations, ensuring their matching with
real-world entities. Achieving this correspondence enables a closed-loop
system in which decisions concerning the physical entity are informed by real-
time data derived from the DT.

In addressing the demands of modeling and designing radio maps tailored to the
dynamic and complex environments in the forthcoming sixth-generation (6G)
networks, the DT presents a compelling avenue. In fact, by leveraging high-
definition three-dimensional (3D) maps, DT-enabled network systems can achieve
precise real-time digital representations of the EM environment and radio
maps. DT effectiveness can be improved by incorporating multimodal sensory
data from different entities in the network, including user equipment,
connected vehicles, drones, in conjunction with a comprehensive description of
the state of the communication network [3].

Wireless propagation is notably featured by multipath propagation. Ray-based
propagation simulation stands as a versatile modeling tool, offering estimates
of path loss, angle of arrival/departure, propagation delay, and Doppler shift
for each multipath component. Functionally, ray-based propagation simulation
relies on the high-frequency approximation of Maxwell’s equations, which
results in the concept of ray. Furthermore, it allows for effective
integration with 3D scenarios maps to dynamically and faithfully model the
propagation environment with rich geometric features [4].

Different organizations have proposed computational engines to perform ray-
based propagation simulations, and by integrating those software into the DT-
enabled network systems, it is possible to better simulate the real-world
conditions of the EM environment in urban settings, where the propagation of
high-frequency signals is significantly affected by the urban landscape. By
accounting for different possible interactions with the environment— e.g.,
reflections, diffractions, and diffuse scattering— we can achieve more
accurate estimates and designs for wireless communication systems.
Specifically in dynamic scenarios, such as vehicular ones, traditional models
may fail to accurately represent channel characteristics [5]. As research on
DT-enabled network systems continues, it becomes incrementally more relevant
to assess and understand their integration with ray-based propagation
simulations.

Ray-based propagation simulations are expensive, and therefore substantial
research efforts have been directed towards enhancing computational speed [6,
7, 8, 9, 10]. In [6] a simplification of simulations based on ray-based models
is proposed and evaluated in end-to-end networks. An alternative dynamic ray-
based method that is in [7] alleviates the computational load of ray-based
models. An adaptive ray launching algorithm is proposed for urban environments
[8], reducing its computational burden. The high-fidelity 3D model of the city
of Boston, introduced in [9], offers easier integration into DT-enabled
systems. In [10] a simplification of building representation is proposed for
ray models.

The computational burden associated with ray-based propagation simulations can
easily become the bottleneck towards achieving real-time performance in the
update of a DT. In addition, the dynamism of the environment may render the
simulation outdated even before the end of its computation.

Contributions. In this paper, we aim to provide a technical benchmark to
evaluate the computational performance of different ray-based simulation
software. The main contributions are summarized below:

  * •

Definition of an empirical benchmark to evaluate and compare the computational
performance of ray-based simulation software in two different urban scenarios
characterized by their geometrical representation complexity.

  * •

Evaluation of time performance for a selection of ray-based simulation
software in the proposed urban scenarios and wireless link configurations—
i.e., single link vs. simultaneous multiple links; the latter is evaluated
with GPU acceleration (when applicable). The evaluation has been carried out
for increasing ray interaction depth, with/without diffuse scattering, and
variation in ray launching parameter.

  * •

The 3D meshes of the evaluation scenarios and the source code to replicate the
benchmark for the evaluated solutions are available111Source code and
scenarios are available in https://github.com/Michele-Zhu/ray-launching-
benchmark.. Fostering a repeatable benchmark with standardized approach to
evaluate the computational performance of diverse ray-based propagation
algorithms, spanning different implementations and hardware architectures.

By establishing shared simulation settings and scenarios, researchers and
developers gain a comprehensive framework for in-depth comparison and analysis
of the efficiency of their methodologies. The definition of a standardized
methodology promotes transparency and repeatability in research, driving
advances in ray-based propagation modeling, and addressing the evolving needs
wireless communication systems.

Organization. The remainder of this article is structured as follows: in Sec.
II, we provide an overview of the basic ray-based simulation algorithms.
Section III describes the 3D maps of the urban environments considered in our
simulations, the type of wireless link configurations, and the proposed
benchmark framework. Sec. IV provides a brief review of software that
implements ray-based models. In Sec. V, we report the simulation results on
the comparison of the selected ray-based simulation software. Section VI
provides an overview and some remarks about the compared solutions, while in
Sec. VII, we draw the conclusions.

##  II Ray-based propagation algorithms

Following the distinction done in [11], ray-based models can be differentiated
into exact ray computation (ray tracing) and approximated (ray launching):

  * •

Ray Launching (RL), which is an approximate algorithm based on spawning rays
from an EM emission source towards a set of angular discretized directions.
For each launched ray, after a number of interaction steps (usually a
simulation parameter) with the propagation environment, the reception of the
ray at a target receiver is checked—e.g., by means of ray-tube modeling [12]
or testing if the ray hits a sphere of given (possibly parametric) radius
centered at the receiver position. The goal of plain ray launching is not
exact point-to-point propagation modeling. Instead, ray launching is
particularly suitable for large-scale approximate propagation simulation. One
realization of ray launching is the shooting and bouncing rays method
discussed below.

  * •

Ray Tracing (RT), which aims at modeling point-to-point propagation by
determining the geometrically exact propagation paths between an EM emission
source and a target receiver location. According to Reif et al. in [13], ”the
exact solution of a 3D optical system consisting of linear reflective surfaces
and partially reflective surfaces is undecidable”. The computational time of
the ray tracing task can easily become intractable with the increase of the
number of surfaces to be taken into account or with the maximum number of
interaction points per ray to be considered. The image method, discussed
below, is a realization of the ray tracing method for reflection interaction
types.

Ray launching and ray tracing lead to a set of fundamental algorithms in high-
frequency computational EM, among which are the main ones discussed in the
following.

(a) Image method

(b) Shooting and Bouncing Rays

Figure 1: LABEL:sub@fig:_Image_method Image Method; T′ is the image of
transmitter T with respect to the reflection plane $\Sigma$.
LABEL:sub@fig:_SBR Shooting and Bouncing Rays method; R indicates reflection
points, D a diffraction point at an edge, and a path is considered at the
receiver if it satisfies the reception condition—exemplified by hitting a
reception sphere (red circle) at receiver P.

Image Method [RT]: The image method is a point-to-point propagation simulation
method. As such, it is a realization of the above-discussed ray tracing
method. We provide in Fig. 1a a graphical representation of the image method
for the single reflection case. Referring to Fig. 1a, the trajectory of the
ray reflected from a plane surface can be determined as follows: T′ is
computed as the image of transmitter T with respect to the reflection plane
$\Sigma$; then T′ and P are connected through a segment that intersects the
plane at point Q; the reflected ray is determined by the segments connecting
(T, Q, P). In case of multiple reflections, the method can be extended
recursively taking into consideration different reflection planes. The image
method becomes computationally taxing when the environment presents an
abundant number of reflecting surfaces or the number of sequential
interactions considered for a ray increases [4].

Shooting and Bouncing Rays (SBR) [RL]: is a realization of the ray launching
approach. A graphical representation is provided in Fig. 1b. A set of rays is
launched from the transmitter T with a given angular separation. In
conventional implementations, the launched rays are propagated in the
environment up to a maximum number of interactions with surfaces, and are
considered to reach the receiver P if they meet a reception condition— e.g.,
intersecting a sphere centered at the receiver P with radius proportional to
the distance traveled by the ray. SBR implementations can consider a variety
of environmental interactions, e.g., reflection, diffraction, and diffuse
scattering. The latter has been shown to be particularly relevant to
accurately model urban propagation environments[14].

Path correction methods [RL and RT]: In SBR, the exact reception of a ray at a
given target point in space is highly unlikely owing to the discrete angular
resolution of ray launching. For this reason, path correction methods [4] have
been proposed to exploit both the computational efficiency of SBR and the
exact geometric accuracy of the image method. This is achieved by slightly
changing the positions of the intermediate path interaction points on the
surfaces so that the launched ray can exactly hit the target point. Examples
of path correction methods are implemented in the SBR models proposed by [15]
and [16].

Differentiable Ray Tracing [RL or RT]: A new approach to ray modeling based on
differentiable rendering (DR) [17] has recently been proposed in [18]. The
developed procedure is based on Mitsuba 3 [19] DR system— which, in turn,
leverages the Dr.Jit just-in-time (JIT) compiler [20]. DR for ray simulation
brings as a key advantage differentiability with respect to environmental
(e.g., objects’ radio-materials parameters) and system (e.g., antenna arrays
positions) of the ray tracing procedure. In [18], both an exhaustive ray
tracing method and an approximate SBR-based approach are proposed. The
exhaustive method tests all the possible combinations of mesh triangles and
edges— leading to high accuracy but intractable computational time. The ray
launching method provides a trade-off between accuracy and complexity by means
of a sampling scheme on the ray launching sphere. In [21], the authors tackle
the challenges of integrating ray tracing into DR systems, proposing a new
fully differentiable framework with continuous loss function through local
smoothing.

##  III Benchmark framework

(a) Scenario1

(b) Scenario2

Figure 2: Details of the 3D meshes of the two proposed scenarios. The view in
LABEL:sub@fig:_Wireframe_Scenario1 highlights the level of detail in Carla
w.r.t. LABEL:sub@fig:_Wireframe_Scenario2, which is the view of the OSM
scenario characterized by a lower level of details. In
LABEL:sub@fig:_Wireframe_Scenario2, the main building of the High Frequency
campus, Italy is in green.

(a) Scenario1

(b) Scenario2

Figure 3: Top views of the selected evaluation scenarios along with the chosen
Tx (red spheres) and Rx (blue spheres) positions. In (b), the main building of
the High Frequency Campus in Milan, Italy is in green.

In what follows, we describe urban scenarios, wireless link configurations,
and the proposed benchmark framework to evaluate the ray-based method
considered.

###  III-A Evaluation scenarios

We have selected two urban evaluation scenarios, differentiated by the level
of complexity of the buildings’ meshes by which they are composed. Figure 2
shows the mesh complexity of the proposed scenarios.

  * •

CARLA High Definition Mesh (Scenario1): It is an environment composed by
complex realistic 3D buildings’ meshes retrieved from the Town 10 urban
scenario available within the realistic CARLA automotive simulator [22]. Town
10 represents a typical inner-city environment, composed of, e.g.,
skyscrapers, hotels, public buildings, and apartment blocks. We have
considered a selection of buildings in Town 10 that led to a diversified urban
environment, and we exported the corresponding 3D meshes using the CARLA
Unreal Engine editing interface. The resulting 3D mesh is represented in Fig.
2a.

  * •

OSM Low Definition Mesh (Scenario2): As the second test environment, we
consider a scenario composed by simplified 2.5D buildings’ meshes—i.e., meshes
defined by their outline on the ground and their height—retrieved from the
OpenStreetMap (OSM) [23] online service for the High Frequency Campus urban
geographical area in Milan, Italy. A section of the scenario is reported in
Fig. 2b, showing the simplicity of the building representation in this
setting.

###  III-B Wireless link configurations

Let $\mathcal{G}$ be a generic set of transceiver configurations,
$\mathcal{T}$ be the set of transmitters, $\mathcal{R}$ be the set of
receivers. A generic transceiver configuration is defined as $g_{k}\coloneq
a_{k}\cup b_{k}$ where $a_{k}\subseteq\mathcal{T}$ and
$b_{k}\subseteq\mathcal{R}$. Denoting $N_{Tx}=|\mathcal{T}|$,
$N_{Rx}=|\mathcal{R}|$ the number of transmitters and receivers.

We define two distinct link configurations, represented by $\mathcal{G}_{1}$
and $\mathcal{G}_{2}$:

  * •

Single Link (SL) configurations: the set $\mathcal{G}_{1}$ represents the set
of all Tx/Rx pairs. Ray computations and wall-clock time measurement are
performed for $g_{ij}$ with $i=1,2,...,N_{Tx}$ and $j=1,2,...,N_{Rx}$. This
approach captures the performance of the ray model without parallelization.

  * •

Multi Link (ML) configurations: a transceiver configuration
$g_{i}\in\mathcal{G}_{2}$ is defined as $g_{i}=T_{i}\cup\mathcal{R}$ with
$i=1,2,...,N_{Tx}$. Measurements and computations are performed for the
configurations in $\mathcal{G}_{2}$ simulating a channel propagation scenario
with one transmitter and multiple receivers. This allows the different ray
methods to exploit hardware parallelization and algorithmic optimization in
realistic use cases.

Generic link configurations can be defined and characterized by their set of
transceiver configurations $\mathcal{G}$, each different configuration can be
designed to suit different use cases and capture different properties of the
ray methods. The algorithm in 1 is the pseudo code for a generic simulation
with set $\mathcal{G}$, measurements of the wall-clock time are performed
after the transceivers in $g_{k}\in\mathcal{G}$ are loaded into memory. If
round-trip-time measurements are more desirable, include the loading of the
configuration $g_{k}$ within the simulation software.

The $N_{Tx}=6$ transmitters are placed in nodal positions in urban
environments at a height of 7 m, while the $N_{Rx}=51$ receivers are
distributed along roads at a height of 1.5 m. Each transmitter (Tx) and each
receiver (Rx) are equipped with the same type of isotropic antennas. In Fig. 3
the positions of the transmitters (red spheres) and receivers (blue spheres)
are shown. When required, the simulation boundary was set with a 50 m margin
with respect to the bounding box comprising all buildings. The simulation
boundary is assumed to be absorbing, so that only rays interacting with the
buildings and ground within the scenario are considered. The ITU
recommendation [24] has been considered as reference to determine the required
EM properties (relative permittivity and conductivity) of the radio materials.
The simulation parameters that are common for each scenario are summarized in
Table I.

1:$\mathcal{T}\coloneq$ set of transmitters, $\mathcal{R}\coloneq$ set of
receivers.
$\mathcal{G}\coloneq$ set of transceiver configurations, $g_{k}=a_{k}\cup
b_{k}$ with $g_{k}\in\mathcal{G}$, $a_{k}\subseteq\mathcal{T}$, and
$b_{k}\subseteq\mathcal{R}$.

2:$\boldsymbol{t}$ vector of wall-clock time measurements.

3:Initialize $\boldsymbol{t}\in\mathbb{R}^{|\mathcal{G}|}$

4:for all $g_{k}\in\mathcal{G}$ do

5: load_transmitters($a_{k}$)

6: load_receivers($b_{k}$)

7: $t^{\prime}=$ current_timestamp()

8: compute_paths($g_{k}$)

9: $t_{k}=$ current_timestamp() $-\ t^{\prime}$

10:end for

11:return $\boldsymbol{t}$

Algorithm 1 Simulation pseudocode. TABLE I: Simulation parameters. Parameter | Value
---|---
Antenna Type | Isotropic
Carrier frequency | 28 GHz
Buildings and ground material | Concrete
Material relative permittivity | 5.31
Material conductivity | 0.4838 S/m
Tx height, Rx height | 7 m , 1.5m
$N_{Tx}$, $N_{Rx}$ | 6, 51

###  III-C Benchmark workflow

Figure 4: Benchmark workflow. $\mathcal{G}$ is a set of transceiver
configurations and $g_{k}$ is a specific configuration containing transmitters
and receivers.

Given a ray-based simulation software, a scenario, and a configuration
$\mathcal{G}$. The benchmark workflow can be described as follows.

1\. Pre-process & load scenario. Ray-based model simulation requires 3D meshes
of the environment as input. These meshes may not be in a format compatible
with the specific ray-based simulation software. If necessary, the scenario is
converted from its original format into a supported one before loading it
within the simulation software. This ensures that the simulation software can
accurately interpret and utilize the environmental data.

2\. Setup of EM properties. In this step, the EM properties of the scenario
are configured. This includes defining parameters such as permittivity,
permeability, and conductivity of materials within the simulation environment,
according to the specifications in Table I.

3\. Setup of ray model parameters. Different software implementations of ray
models may offer various configurable parameters. This step involves aligning
and configuring these parameters to ensure consistency across different
simulations.

4\. Load configuration. Transmitters and receivers in the configuration are
loaded within the simulated scenario at positions provided from an external
file.

5\. Ray-model simulation. This step is the core computational step where the
actual simulation of the ray model is performed. The software computes the
paths that rays take as they propagate from the transmitters to the receivers.
The wall-clock time is measured in this step222In order to capture steady-
state performance a warm-up procedure is required. This means running the
simulation for few minutes without performing measurements..

Steps 4. and 5. are repeated until the configurations $g_{k}\in\mathcal{G}$
are exhausted. Figure 4 summarizes the benchmark workflow.

##  IV Comparison of ray-based simulation software

In this section, we review the examined ray-based simulation software. Open-
source and commercial software embeds ray-based models for EM propagation
modeling. Among the most widely used commercial software are Remcom Wireless
InSite [15], MathWorks RF Antenna Toolbox [16], Siradel Volcano [25], Altair
Feko [26], iBware Design and iBware Reach [27], and EDX SignalPro [28]. NVIDIA
Sionna [29] and Ns-3 mmWave Module [30] instead provide open source solutions.
Based on the availability of proprietary software, we evaluate the following
ray-based simulation software.

Remcom Wireless InSite (v3.3.3) [15] is a commercial software that provides
several methods for the analysis of radio propagation and wireless
communication systems in various conditions (i.e., indoor, outdoor, and rural
areas). Widely used for wireless propagation simulation in the relevant
literature [31, 32], it provides an efficient and accurate modeling of the
characteristics of the communication channel in complex EM propagation
environments. It offers two ray optical computation models allowing generic 3D
environments: (i) full 3D, supporting simulations in the 0.1-20 GHz frequency
range by means of SBR and Eigen Ray algorithms, and (ii) X3D, which supports
simulations in the 0.1-100 GHz frequency range and integrates SBR with a path
correction algorithm adjusting the interaction points to obtain exact
propagation paths between Tx and Rx. Moreover, X3D supports diffuse scattering
simulation, which has been shown to be particularly relevant for accurately
modeling urban propagation environments [14].

NVIDIA Sionna RT (v0.16.2) [18] is a recently proposed differentiable ray
optical engine that is part of the NVIDIA Sionna link-level simulation library
[29]. NVIDIA Sionna RT allows for accurate ray simulations taking account of
reflection, diffraction, and diffuse scattering interactions of propagation
paths with the environment. As reported in Sec. II, it implements
differentiable rendering providing a flexible framework that allows to include
the communication channel within end-to-end optimization procedures. Sionna RT
provides two ray-based methods: (i) an exhaustive method, which tests all
possible combinations of 3D primitives and paths and becomes computationally
intractable for high path depths—i.e., number of interaction points per
path—or number of surfaces in the scene, and (ii) a Fibonacci method, which
uses the SBR approach to efficiently compute the propagation paths and
implements a sampling procedure for ray launching that enables a trade-off
between simulation accuracy and computational time.

MathWorks Ray tracing model (vR2023a U1) [16] is part of the MathWorks Antenna
Toolbox and offers two ray optical computation methods: (i) SBR implementation
with exact path correction, supporting up to 10 reflection and 2 edge
diffractions and providing an approximate number of propagation rays; (ii) a
ray tracing model based on the image method, supporting a maximum of 2 path
reflections and providing an exact number of rays featured by line-of-sight or
reflection with exact geometry. Both methods enable simulation in the 0.1-100
GHz frequency range and support generic 3D indoor and outdoor environments.

##  V Numerical results

In this section, we evaluate the computational time efficiency of the
considered ray-based methods in Scenario1 and Scenario2. Also we produce the
radio map from the different simulation software. Our simulations are
performed on a Windows 10 workstation equipped with Intel(R) Core(TM) i7-9700K
<EMAIL_ADDRESS>GHZ, 8 cores, 16 GB RAM, and NVIDIA GeForce GTX 1070 Ti GPU with 8GB
of dedicated memory.

###  V-A Computational Time

(a) SL Scenario2: WI X3D

(b) SL Scenario2: Sionna Fibonacci CPU

(c) SL Scenario2: MW SBR

(d) ML Scenario2: WI X3D

(e) ML Scenario2: Sionna Fibonacci GPU

(f) ML Scenario2: MW SBR

Figure 5: Single Link (SL) and Multi Link (ML) configurations in Scenario2
with 1$\sigma$ errorbar with respect to the maximum interaction depth, varying
angular separation (AS) or number of samples (NS), with (solid line) or
without (dashed line) Diffuse Scattering (DS).

(a) SL Scenario1: WI X3D

(b) SL Scenario1: Sionna Fibonacci CPU

Figure 6: Single Link configurations in Scenario1 with 1$\sigma$ errorbar with
respect to the maximum interaction depth, varying angular separation (AS) or
number of samples (NS), with (solid line) or without (dashed line) Diffuse
Scattering (DS).

(a) Scenario1: WI X3D

(b) Scenario1: Sionna Fibonacci GPU

Figure 7: Multiple Link configurations in Scenario1 with 1$\sigma$ errorbar
with respect to the maximum interaction depth, varying angular separation (AS)
or number of samples (NS), with (solid line) or without (dashed line) Diffuse
Scattering (DS).

As discussed in Sec. III we consider a set of transmitters $\mathcal{T}$, a
set of receivers $\mathcal{R}$. The wall-clock time $t_{k}$ is measured during
the ray computation, for each transceiver configuration $g_{k}\in\mathcal{G}$.
Sample mean $\mu$ and variance $\sigma^{2}$ are evaluated for the specific
Single Link (SL) and Multi Link (ML) simulation, with $K=|\mathcal{G}|$ as:

$\displaystyle\mu$ $\displaystyle=\frac{1}{K}\sum_{k=1}^{K}t_{k},$ (1)
$\displaystyle\sigma^{2}$
$\displaystyle=\frac{1}{K-1}\sum_{k=1}^{K}(t_{k}-\mu)^{2}.$

(a) Single Link configurations on Scenario1

(b) Single Link configurations on Scenario2

(c) Multiple Link configurations on Scenario1

(d) Multiple Link configurations on Scenario2

Figure 8: Comparison of the selected ray-based simulation software over a comparable initial number of rays at Tx. WI X3D AS $=0.5$ deg, MW SBR AS = Medium, Sionna Fibonacci NS $=1.6e5$.  TABLE II: Software-specific ray launching simulation parameters. Software | Parameter | Value
---|---|---
Remcom Wireless InSite (v3.3.3) | RT method | X3D
Angular separation | [0.25, 0.5, 1.0] deg
Diffractions num. | 1
Diffuse scattering | $(R=2,D=1)$
MathWorks Ray Tracing Model (vR2023a U1) | RT method | SBR
Angular separation | [low, medium, high]
Diffractions num. | 1
NVIDIA Sionna RT (v0.16.2) | RT method | Fibonacci
Num. of samples | [1e4, 1.6e5, 1e6]
Diffractions num. | True
Diffuse scattering | True

We consider the X3D model for Remcom Wireless InSite (WI X3D), the SBR with
exact path correction model for the MathWorks ray launching model (MW SBR),
and the Fibonacci model for NVIDIA Sionna RT. MW SBR has been performed within
its Graphical User Interface (GUI), adding a negligible overhead in terms of
computational time, and the software cannot handle Scenario1 on our
workstation.

Ray launching algorithms are significantly impacted by the initial number of
rays sampled at the Tx. Both WI X3D and MW SBR offer the flexibility to
specify the angular separation (AS) in degrees between the launched rays,
while Sionna Fibonacci allows for the specification of the number of samples
(NS)— e.g., the number of candidate rays split equally among the Tx during the
simulation. Simulations are performed for the two proposed scenarios, SL/ML
configurations, and increasing maximum interaction depth. For Sionna
Fibonacci, this parameter encompasses any type of ray interaction, whereas for
WI X3D and MW SBR, it specifically pertains to the maximum number of
reflections. The varying parameters for each ray launching methods are
summarized in Table II, while the unmentioned parameters are set to default
values.

CPUs and GPUs are different types of hardware resources. The former are
optimized to handle sequential tasks and general-purpose computing. The latter
are particularly useful for handling tasks that require parallel execution and
high throughput— Sionna framework allows for finer control of the type of
resource used in the computation, in SL configurations we do not enable GPU
acceleration, while for ML configurations we enable it.

In Fig. 5, the results of the SL and ML configurations are reported for
Scenario2. For SL configurations, it can be observed that for WI X3D and
Sionna CPU the addition of diffuse scattering interaction adds a negligible
overhead in the computation. MW SBR does not model diffuse scattering. For ML
configurations, the WI X3D model observes a significant increase in
computational time.

In Fig. 6, the results of the SL configurations for Scenario1 are reported.
Scenario1 is characterized by a higher number of meshes— i.e. number of
vertices, edges, and faces that defines the shape of the objects in the 3D
map. This complexity significantly impairs the ray computations. An inspection
between Fig. 5a and 6a highlights the impact of mesh complexity, specifically
the addition of diffuse scattering.

In Fig. 7, presents the results of ML configurations for Scenario 1. Figure 7a
reports of the computation for WI X3D without diffuse scattering. When diffuse
scattering is considered the overall average wall-clock time: is 440 s with
maximum interaction depth set to 1 and AS 1.0 deg, while 730 s with maximum
interaction depth set to 10 and AS 0.25 deg.

The initial number of rays significantly impacts the computational performance
of the ray launching approach. In order to provide a direct comparison, a set
of equivalent values is used. The WI X3D AS is set at 0.5 degrees, the MW SBR
AS is set as Medium, Sionna Fibonacci NS is set to $1.6e5$. This creates an
equivalent starting condition. Figure 8 illustrate the results, showing in
each graph a different scenario and a wireless link simulation.

(a) WI X3D

(b) Sionna Fibonacci

(c) MW SBR

(d)

Figure 9: Channel Gain (dB) of the radio map produced using the evaluated ray-
based simulation software. Simulations are performed for a) WI X3D AS = 0.5
deg, b) Sionna Fibonacci NS = 1.6e5, c) MW SBR AS = Medium. WI and MW with
maximum 3 reflections and 1 diffraction. Sionna maximum path depth 4. The Tx
position is highlighted by a red diamond.

Comparison of Sionna in Fig. 8a and Fig. 8c reveals distinct behaviors in
Sionna’s computational time when utilizing CPU versus GPU across increasing
interaction depth. The CPU behavior exhibits a linear trend with increasing
path depth, whereas the GPU is not affected by path depth. In Fig. 8c Sionna
GPU for maximum interaction depth of 1 observes a slightly higher
computational time than the counterpart at depth of 5. This is due to the GPU
warm-up time and just-in-time compilation overheads. The differentiable ray
tracing implementation from Sionna supports the addition of diffuse scattering
interactions with the environment without significantly increasing the average
wall-clock time.

###  V-B Radio Map predictions

The three different simulation software are used to calculate the Channel Gain
in Scenario2, obtaining the radio maps reported in Fig. 9. These simulations
were conducted with the following parameters: for WI X3D, an angular
separation (AS) of 0.5 degrees; for MW SBR AS = Medium; and for Sionna, a
Fibonacci number of samples (NS) of 1.6e5. WI and MW were configured with a
maximum of three reflections and one diffraction, while Sionna was set to a
maximum path depth of four.

A single transmitter (Tx) was considered and is located on the top of the main
building of the High Frequency Campus in Milan, Italy at height of 21.7 m from
the ground. The receivers are uniformly distributed throughout the map area at
height of 1.5 m, forming a grid with a resolution of 10 × 10 meters. The
carrier frequency is set to 28 GHz, and the Tx and Rxs antennas are isotropic.

Overall, the results are consistent across the three simulators, with
differences of only a few dB at specific points. WI X3D and MW SBR offer more
detailed insights into the EM radio map, particularly where the Rxs are
located far from the Tx. The impact of buildings and obstacles is represented
more consistently by these two simulators compared to the Sionna Fibonacci.

The WI X3D, shown in Fig. 9a, integrates the SBR method with a path correction
algorithm that adjusts the interaction points to achieve precise propagation
paths between the Tx and each Rx. This enhancement is particularly evident in
non-line-of-sight points.

Sionna Fibonacci, illustrated in Fig. 9b, lacks channel characterization for
certain RX points on the map. This limitation may be due to the underlying
Mitsuba differentiable rendering system that is unable to compute the
propagation path and/or due to the absence of path correction methods for
Sionna Fibonacci.

Simulation | Software | Single Link | Multiple Link | Path Depth Behaviour | DS Behavior
---|---|---|---|---|---
| Performance | Performance | Single/Multiple Link | Single/Multiple Link
Scenario1 | Sionna Fibonacci | ✓✓ | ✓✓ | linear, constant |  $\times$(1.5 to 2), constant
WI X3D | ✓ | ✓ | linear, linear |  $\times$(1 to 1.5), $\times$(10 to 25)
Scenario2 | Sionna Fibonacci | ✓✓✓ | ✓✓ | linear, constant |  $\times$(1.5 to 2), constant
WI X3D | ✓✓ | ✓✓✓ | linear, linear |  $\times$(1 to 1.5), $\times$(20 to 30)
MW SBR | ✓ | ✓ | linear, linear | N/A
TABLE III: Summary of results over a comparable initial number of rays at Tx.
WI X3D AS $=0.5$ deg, MW SBR AS = Medium, Sionna Fibonacci NS $=1.6e5$. Single
Link and Multi Link simulation performance, their approximate behavior at
increasing maximum interaction depth, and the increase range with respect to
the same simulation condition with the diffuse scattering interaction. Each
extra tick indicates a better relative wall-clock time in the simulations
without diffuse scattering.

In Fig. 9c, the radio map predicted by the MW SBR is shown. The MW software
also utilizes an SBR implementation with exact path correction, resulting in a
comprehensive characterization of the EM environment.

##  VI Overview and Discussion

This section aims to summarize the main observations and notable points
derived from our simulations. Table III provides an overview of the results
evaluated with an equivalent initial number of rays. Each extra tick in the SL
and ML performance column indicates a better relative wall-clock time for the
given wireless link simulation without diffuse scattering. With an increase in
the maximum interaction depth, the behavior is approximately linear for most
of the simulations. The diffuse scattering behavior indicates the approximate
increase range with respect to the same simulation parameter without the
diffuse scattering interaction. Sionna and WI implement different models for
the diffuse scattering interaction, as can be observed by their distinct
behavior.

The computational performance for ray-based models is a multifaceted task.
This includes the meshes of the propagation environment, the underlying
computing infrastructure, and any type of algorithmic optimization. The type
and number of interactions also significantly affect the simulation times.
Conducting a comprehensive analysis from a computational theory standpoint of
all these factors is challenging and becomes unfeasible when the source code
is unavailable. Instead, benchmarks serve as a practical alternative for
evaluating algorithmic implementations and hardware configurations in a black-
box manner.

The simulations that compare the radio map using three different software in
similar simulations setting showcase consistent results across them with minor
discrepancies. WI X3D and MW SBR provided detailed insights into the EM radio
map, particularly for distant receiver points, while Sionna Fibonacci lacks
characterization for certain RX locations in non-line-of-sight condition.

##  VII Conclusions

This paper proposes a benchmark of different ray launching solutions,
considering several simulation parameters such as the angular
separation/number of samples and ray interactions with the environments. Two
different urban environments are considered, one with complex mesh detail and
one with simpler mesh detail. Two sets of transceiver configurations that
evaluate different use cases are tested. The proposed framework allows the
practitioner to make an informed decision when selecting the appropriate
solution for their application. The availability and reproducibility of the
benchmark333Source code and scenarios are available in
https://github.com/Michele-Zhu/ray-launching-benchmark. have the additional
advantage of providing a reference point to track advances, ensuring that
improvements in computational performance can be systematically monitored and
evaluated.

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# GN-z11-flash in the context of Gamma-Ray Burst Afterglows

D. A. Kann IAA-CSIC, Glorieta de la Astronomía, s/n, 18008 Granada, Spain  M.
Blazek IAA-CSIC, Glorieta de la Astronomía, s/n, 18008 Granada, Spain  A. de
Ugarte Postigo IAA-CSIC, Glorieta de la Astronomía, s/n, 18008 Granada, Spain
DARK, Niels Bohr Institute, University of Copenhagen, Lyngbyvej 2, DK-2100
Copenhagen Ø, Denmark  C. C. Thöne IAA-CSIC, Glorieta de la Astronomía, s/n,
18008 Granada, Spain

###### Abstract

The recently discovered rapid transient GN-z11-flash has been suggested to be
the prompt-emission ultraviolet flash associated with a gamma-ray burst
serendipitously exploding in the ultra-high-$z$ galaxy GN-z11. We here place
the flash into the context of the early ultraviolet emission of gamma-ray
bursts, and find it is in agreement with the luminosity distribution of these
events.

High-redshift galaxies (734), Gamma-ray bursts (629)

## 1

Gamma-Ray Bursts (GRBs) are among the most powerful explosions in the
Universe, and their optical emission at very early times can be dominated by
extremely luminous ultraviolet (UV) flashes (Akerlof et al., 1999; Racusin et
al., 2008; Bloom et al., 2009; Vestrand et al., 2014), which may be directly
linked to the higher-energy prompt emission (e.g., Blake et al., 2005;
Vestrand et al., 2005). Such prompt flashes are the most luminous UV/optical
sources known (Kann et al., 2007; Perley et al., 2011), implying GRBs are
detectable across a broad wavelength range up to the highest studied redshifts
(Tanvir et al., 2009; Salvaterra et al., 2009; Cucchiara et al., 2011; Tanvir
et al., 2018). This makes them highly interesting probes of cosmology, and the
main target of mission concepts such as the Gamov Explorer (White, 2020) and
THESEUS (Amati et al., 2018).

Recently, Jiang et al. (2020b) reported a spectroscopic redshift for the
ultra-high-$z$ candidate galaxy GN-z11 (Oesch et al., 2016), finding it to lie
at $z=10.957$, confirming it to be the most distant object known at the time.
Serendipitously, as Jiang et al. (2020a, J20 hereafter) report, a single (2D
spectrum) image of their 5.3 hr $K$-band spectrum contains a strong signal
that is not seen in the previous or the subsequent integration. They exclude
atmospheric, terrestrial, and Solar System sources and present evidence that
the transient is very likely associated with GN-z11 and therefore at the same
redshift. This implies extreme luminosity, and they therefore argue that
GN-z11-flash is most likely the prompt flash of a GRB exploding while they
were observing the galaxy. It is extremely unlikely that such an incidence
would occur, however, all other explanations J20 present are even more
unlikely, mostly significantly so.

Assuming GN-z11-flash is indeed associated with the $z\approx 11$ galaxy, we
here compare its luminosity with a large sample of GRB afterglows (Kann et
al., 2006, 2010, 2011, Kann et al. 2021a,b, in prep.). J20 report the redshift
($z=10.957$), a lack of dust extinction, and the spectral slope they measure
from their calibrated spectrum ($\beta=-1.2\pm 0.4$ assuming
$F_{\nu}\propto\nu^{-\beta}$). Following J20, we here assume the emission is
synchrotron radiation and this spectral slope can be extrapolated. We neglect
Galactic foreground extinction, as this galaxy is in the GOODS/Hubble Deep
Field North, and it is negligible (a few millimag). We use a $\lambda$CDM
concordance cosmology with $H_{0}=72$ km/s/Mpc, $\Omega_{M}=0.27$, and
$\Omega_{\lambda}=0.73$. J20 report a slit-loss corrected flux density in the
$K$ band of $0.1-0.2$ mJy, we assume $0.15\pm 0.05$ mJy. This corresponds to
$K=18.46^{+0.44}_{-0.31}$ mag (AB system, $K=16.59$ mag in Vega). From the
spectral slope, we find $K-R_{C}=1.54$ mag (AB; $K-R_{C}=-0.15$ mag Vega).
Using the redshift and spectral slope, we find a magnitude correction to $z=1$
of $dRc=-1.98^{+0.78}_{-0.76}$ mag (the blue spectrum and the large distance
partially cancel each other out) following Kann et al. (2006). In total, this
yields $R_{C}=14.46^{+0.90}_{-0.82}$ mag at $z=1$, Vega system. Following J20,
the non-detection in the following spectrum implies a flux density at least
ten times fainter, giving us a corresponding $R_{C}>17.0$ mag. J20 did not
find a coincident GRB detection. We assume the GRB began ($t=T_{0}$) with the
end of the previous spectral integration, this yields logarithmic central
points of 14.0 s for the detection and 53.9 s for the upper limit, in the
$z=1$ frame. For these times, the decay slope is $\alpha\gtrsim 1.7$
($F(t)\propto t^{-\alpha}$), a reasonable value for early GRB flashes.

We plot the final result (red) in Fig. 1, highlighting a sample of $z>6$ GRB
afterglows (Kann et al. 2021a, in prep.). It can clearly be seen that
GN-z11-flash is in full accordance with the luminosity distribution of early
GRB optical emission, supporting the interpretation of J20. Considering no
further emission was detected in subsequent spectra, we even infer this was a
quite faint afterglow. In the sample of Kann et al. (2021a, in prep.), we find
70 GRB afterglows with detections at the time of the upper limit from J20
(assuming our $T_{0}$; note some are extrapolations), 63/70 (90%) are brighter
than the upper limit of $R_{C}>17$ mag.

Figure 1: GN-z11-flash (red) compared to a large sample of GRB afterglows
shifted to $z=1$. We also highlight afterglows of high-redshift GRBs at $z>6$.
GN-z11-flash is seen to agree with the early luminosity distribution of GRB
afterglows.

DAK acknowledges support from the Spanish National Research Project
RTI2018-098104-J-I00 (GRBPhot). MB acknowledges funding associated to a
personal técnico de apoyo fellowship (PTA2016-13192-I). AdUP and CCT
acknowledge support from Ramón y Cajal fellowships RyC-2012-09975 and
RyC-2012-09984.

## References

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  * White (2020) White, N. E. 2020, arXiv e-prints, arXiv:2003.01592


#  Synthesis technique and electron beam damage study of nanometer-thin
single-crystalline Thymine

Hazem Daoud∗ Department of Physics, University of Toronto, Toronto, Ontario,
M5S 1A7, Canada  * These authors contributed equally to this work  Sreelaja
Pulleri Vadhyar∗ Department of Physics, University of Toronto, Toronto,
Ontario, M5S 1A7, Canada  Department of Chemistry, University of Toronto,
Toronto, Ontario, M5S 3H6, Canada  Ehsan Nikbin∗ Department of Materials
Science and Engineering, University of Toronto, Toronto, Ontario, M5S 1A7,
Canada  Cheng Lu  R. J. Dwayne Miller  Department of Physics, University of
Toronto, Toronto, Ontario, M5S 1A7, Canada  Department of Chemistry,
University of Toronto, Toronto, Ontario, M5S 3H6, Canada

###### Abstract

Samples suitable for electron diffraction studies must satisfy certain
characteristics such as having a thickness in the range of 10 - 100 nm. We
report, to our knowledge, the first successful synthesis technique of
nanometer-thin sheets of single-crystalline thymine suitable for electron
diffraction and spectroscopy studies. This development provides a well defined
system to explore issues related to UV photochemistry of DNA and high
intrinsic stability essential to maintaining integrity of genetic information.
The crystals are grown using the evaporation technique and the nanometer-thin
sheets are obtained via microtoming. The sample is characterized via x-ray
diffraction (XRD) and is subsequently studied using electron diffraction via a
transmission electron microscope (TEM). The electron damage threshold is
determined to be a factor of 10 higher than similar molecular moieties, which
further highlights the extremely fast relaxation processes of electron
scattering-induced excited states, extending the concept of radiation
hardening beyond photoexcited states. The high stability of thymine in
particular opens the door for further studies of these ultrafast relaxation
processes giving rise to the high stability of DNA to UV radiation.

##  I Introduction

Thymine is one of the four molecular building blocks comprising human DNA. It
is thus of major interest to study its photochemical dynamics, owing to the
importance of mutagenic and carcinogenic effects caused by UV radiation on
DNA.[1] The structure of a DNA molecule is stabilized with two hydrogen bonds
between thymine and another nucleobase adenine. Thymine plays a vital role in
the storage and transfer of genetic features to build living cells. An
understanding of its structural relationship and dynamics in conserving
genetic information will shed light on the mechanisms of the biological
functions of DNA.[2] Thymine is particularly important in this regard as it is
typically T-T neighboring dimers that undergo photocyclization and is the weak
point in DNA with respect to photostability. The quantum yield for this
process is less than 5% but still a significant factor. [3] Understanding the
structural dynamics responsible for this degree of photochemical response is
important as there is likely some similar mechanism at play for the other
bases that makes them more immune to photochemical disruption in the genetic
sequence. Hence, due to its significance there have been many x-ray
diffraction, gas phase electron diffraction and spectroscopy studies on
thymine.[4, 5, 6] Studies on solid thymine are mainly limited to second
harmonic generation, coherent anti-Stokes Raman scattering, and electron
energy loss spectroscopy. [7, 8, 9] However, to our knowledge, no time-
resolved studies of single-crystalline thymine, which would simulate close
contact of T-T pairs in DNA, have been carried out yet. Here, there are
important questions regarding the ultrafast non-radiative relaxation of
excited states that have been determined to occur through a conical
intersection (CI).[10] The occurrence of CI’s in this class of planar aromatic
molecules is unique to DNA nucleobases. It has been speculated that this
ultrafast non-radiative relaxation and violation of the ”energy gap” law
conveys inherent ”radiation hardening” to UV critical to conserving the
genetic code.[1, 11] Moreover, the intersystem crossing and excited state
dynamics of cyclobutane pyrimidine dimer (CPD) formed from photo-dimerization
of thymines[3] in DNA is of great importance since the formation of
photolesions leads to the damage of DNA and interrupts normal cellular
processes.[12, 13] Thus, thymine represents an important system for UED
studies and making single crystals is critical to obtaining the highest
possible spatial resolution to directly observe the role of the CI in this key
non-radiative relaxation process.[14] Static structures are essential starting
points.
In this regard, high-resolution transmission electron microscopy (HRTEM) is an
efficient technique for crystal structure determination, the requirement of a
sufficiently thin sample sets limitation for this approach. The process of
HRTEM imaging consists of two sequential stages. The first step involves
interaction of high energy electrons with the sample, producing complex exit
wave at the exit surface of the sample. The next step is the navigation of
these diffracted waves through the electron optical system where they interact
with each other creating recordable images. An increase in specimen thickness,
not only reduces the transmission beam but also increases the degree of
dynamic scattering of the diffracted beam leading to significant loss of
information in image reconstruction. The sample thickness thus plays a crucial
role in electron multi-scattering taking place during electron transmission
inside the specimen and in exit waves resulting in image formation. [15]
Hence, to achieve the goal of studying this process via electron diffraction,
the studied samples must satisfy certain thickness requirements. Preparation
of single-crystalline nanometer-thin sheets of thymine for electron
diffraction studies has proven particularly difficult owing mainly the the
water-solubility of thymine, which renders traditional microtoming ineffective
for sample preparation. Cryomicrotome methods could be used. The issues of
photostability require studies under ambient conditions relevant to DNA
functions. Cryo condition will freeze out potentially important structural
relaxation processes. For the most part, studies of thymine via electron
diffraction have typically been limited to gas-phase studies.[5]
The purpose of this paper is twofold: (1) We report a successful method for
creating nanometer-thin sheets of single-crystalline thymine. (2) We study the
electron damage threshold of the sample paving the way to ultrafast electron
diffraction studies as well as other pump-probe x-ray diffraction and
spectroscopy studies. Although the radiation damage of x-irradiated DNA base
pairs has been studied using electron paramagnetic resonance, electron nuclear
double resonance, and electron spin resonance spectroscopy [16, 17], no
radiation damage study using electron diffraction on single-crystalline
thymine has been carried out.
Studying well defined single crystals could allow for a better understanding
of the much debated excited state structural dynamics of thymine involving
inter-system crossing at the atomic level without solvent fluctuations.[18]

(a) Molecular structure.

(b) Crystal unit cell structure.

Figure 1: Molecular and crystal structure of single crystalline thymine were determined by x-ray diffraction analysis. The study revealed that the grown crystal belongs to monoclinic system, with P21/c space group. The cell parameters are a=12.72 Å, b= 6.84 Å, c= 6.62 Å, $\beta$=104.35°and V= 557.9 Å3, Z= 4, which is in close agreement with the reported values.[19, 20] Table 1: Crystal data and structure refinement. Empirical formula | C5 H6 N2 O2 |
---|---|---
Temperature | 150(2) K |
Wavelength | 0.71073 Å |
Crystal system | Monoclinic |
Space group | P21/c |
Unit cell dimensions | a = 12.722(3) Å |  $\alpha$ = 90o
| b = 6.8380(14) Å |  $\beta$ = 104.354(7)o
| c = 6.6202(13) Å |  $\gamma$ = 90o
Volume | 557.9(2) Å3 |
Z | 4 |
Density (calculated) | 1.501 Mg/m3 |
Absorption coefficient | 0.119 mm-1 |
Crystal size | 0.720 $\times$ 0.420 $\times$ 0.040 mm3 |

##  II Preparation of single-crystalline nanometer-thin sheets of thymine

In this section we describe the full procedure for preparing single-
crystalline thymine samples.

###  II.1 Preparation of thymine crystals

Thymine compound purchased from Sigma Aldrich was dissolved in water and the
saturated solution was allowed to slowly evaporate at room temperature. Well
developed thymine crystals obtained after three weeks were confirmed by single
crystal x-ray diffraction (XRD) analysis. Fig. 1 and table 1 show the results
of the XRD analysis. The study revealed that the grown crystal system is
monoclinic, with a P21/c space group. The cell parameters are a=12.72 Å, b=
6.84 Å, c= 6.62 Å, $\beta$=104.35°and V= 557.9 Å3, Z= 4, which is in close
agreement with the reported values.[19, 20]

###  II.2 Ultramicrotomy of thymine crystals

Ultramicrotomy is a standard method for ultra thin sample preparation.
However, for wet sectioning of water-soluble samples this method is deemed
ineffective as the samples dissolve in water before one is able to pick them
up from the knife boat and place them on grids. Here, we demonstrate a simple
technique to overcome this bottleneck in sample preparation. Thymine crystals
were carefully embedded into an epoxy resin and cleaved using the Leica
Ultracut Ultramicrotome equipped with a PELCO diamond knife. To prevent
dissolution of the crystal sections, a saturated aqueous solution of thymine
was prepared, and, as opposed to water, we filled the diamond knife boat with
the filtered solution in order to collect the sections. Under solution
saturation, no crystal dissolution was observed and the uniform thin sections
($\sim$100 nm) remained intact. The sections were carefully picked up and
placed over Cu 400 mesh transmission electron microscope (TEM) grids with
lacey carbon coating. The initial sections cut were 300 nm thin and they were
discarded till perfect flat crystal sections were obtained. Then the thickness
setting was reduced in steps of 50 nm. Finally, 100 nm sections were used for
the experimental electron damage studies. The crystals were indexed and the
orientation was determined to be (1 0 0). This sample preparation procedure
provides a novel and reliable way of obtaining thin sections for many water-
soluble samples from its bulk crystals for electron diffraction and
spectroscopy studies.
The obtained thymine samples were studied via a TEM. The diffraction pattern
is shown in Fig. 2. The samples proved to be robust under vacuum conditions
and lasted for many weeks without any signs of degradation. This observation
alone illustrates the robust nature of thymine.

Figure 2: TEM diffraction image on single-crystalline thymine.

##  III TEM electron damage study

To study the electron damage threshold of the thymine samples we subjected
them to various fluences. The intensity of each diffraction spot was recorded
over time. The electron damage threshold was determined.

###  III.1 Experimental setup and procedure

Single crystal, 100 nm thin, thymine samples were loaded into a Hitachi
HT-7700 TEM, which was operated at a voltage of 80 kV, and is equipped with an
X-Spectrum Amber 750K direct electron detector. The diffraction patterns were
acquired automatically using a custom written Python script to control the
electron beam intensity and the detector image acquisition. The control of the
microscope and the detector was enabled using the hihi package developed by
Hitachi High-Tech Inc. Canada. Various beam intensities were achieved by
focusing the beam on the sample and the sequences of diffraction patterns over
time were acquired. The diffraction spots were identified using a custom
script. The total intensities within a radius of 5 pixels were added up and
tracked over time.

###  III.2 Analysis

####  III.2.1 Effect of accumulated electron dose

Fixing the electron voltage, we monitored the effect of the accumulated
electron dose on different diffraction spots in the diffraction pattern. Fig.
3 shows the intensity changes for spots (0 -1 3) and (0 5 1) as a function of
time for an electron dose rate of 7.3 e/(Å2s) at 80 kV. The graphs show
exponential decay in intensity for both spots. The spot (0 -1 3) corresponds
to the inter-planar d-spacing of 2.0 Å, while (0 5 1) is a higher resolution
spot corresponding to the d-spacing of 1.3 Å. The higher resolution spot fades
away faster. The intensity of the (0 -1 3) spot reduces to 1/e of its initial
value at the accumulated electron dose of 80 e/Å2 compared to 58 e/Å2 for the
spot (0 5 1). The beam damage threshold was tested at the dose rates of 14.3
e/(Å2s) and 3.9 e/(Å2s) and similar results were obtained. Other studies have
shown that solving the structure of small molecules like acetaminophen,
biotin, carbamazepine, etc. at $\sim$1 Å resolution requires keeping the
electron dose as low as 3 e/Å2 at cryogenic temperatures at an electron energy
of 200 keV. [21] The typical electron dose for structure determination of
protein nanocrystals at cryogenic temperatures at $\sim$1.7 Å resolution is
around 1 e/Å2 to 5 e/Å2. [22, 23] Electron radiation damage, due to knock-on
damage, at 200 keV is typically twice the damage at 80 keV for the elements
carbon, nitrogen and oxygen.[24] Additionally, at cryogenic temperatures the
electron beam-induced damage is considerably reduced as compared to room
temperature.[25] Taking these points into consideration, we observe that the
threshold for electron radiation damage for thymine is at least over an order
of magnitude larger than similar classes of molecules. This observation likely
involves very fast relaxation of electron excited upper states in the
scattering process via the inverted conical intersection connecting upper
electronic states in this interesting molecular system. We see here already
intrinsic radiation hardening that is intrinsic to the thymine structure.

We observe that the intensity of the diffraction spot (0 5 1) at 1.3 Å
resolution drops to 1/e its initial value at an approximate dose of 58 e/Å2.
In a UED experiment with 106 electrons per pulse at 1 kHz and a beam diameter
of 100 $\mu$m the electron dose rate is $\sim$1.3 $\times$ 10-3 e/Å${}^{2}s$,
so it would take more than 4.5 $\times$ 104 s to induce substantial damage on
the sample, which is more than enough time to obtain a strong signal.

(a) Spot (0 -1 3) at 2.0 Å resolution.

(b) Spot (0 5 1) at 1.3 Å resolution.

Figure 3: Thymine sample degradation as a function of time for different
diffraction spots at 7.3 e/(Å2s) electron dose rate: a) For spot (0 -1 3) at
2.0 Å resolution. b) For spot (0 5 1) at 1.3 Å resolution.

##  IV Conclusion

We have successfully prepared the first single-crystalline nanometer-thin
thymine samples that are suitable for electron diffraction studies. The
samples are robust in vacuum and did not show any signs of degradation over a
span of several months. The crystal structure and characteristics were
determined using XRD. The crystals were studied using electron diffraction via
a TEM and the electron damage threshold was determined. Thymine was found to
be extremely robust in terms of stability under vacuum conditions at room
temperature. The degree of robustness was further exemplified in the one order
higher threshold with respect to electron dose for radiation damage. This
extraordinarily high threshold for electron-induced damage is likely related
to similar relaxation pathways through conical intersection within electronic
surfaces that rapidly converts excited states from either photo-induced or
electron scattering-induced excitation. This non-radiative conversion of
excited states to heat occurs faster than the slower photo-induced chemistry.
Thymine is exceptionally robust even for high energy electrons. Hence, this
study opens the door for conducting structure time resolved serial diffraction
studies to directly observe the excited state relaxation processes leading to
the exceptional UV stability of DNA nucleobases and the prospect to direct
imaging of conical intersection processes in this important class of
molecules.

##  V Acknowledgement

The authors acknowledge the Open Center for Characterization of Advanced
Materials (OCCAM) facility for the TEM support and Hitachi High-Tech Canada
Inc. for providing the tools for automated data acquisition.

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