# Measuring Happiness Around the World Through Artificial Intelligence

Rustem Ozakar  Department of Computer Engineering
Erzurum Technical University
Erzurum, Turkey
<EMAIL_ADDRESS>Rafet Efe Gazanfer  Department of Computer
Engineering
Erzurum Technical University
Erzurum, Turkey
<EMAIL_ADDRESS>Y. Sinan Hanay  Department of Computer
Engineering
Erzurum Technical University
Erzurum, Turkey
<EMAIL_ADDRESS>
###### Abstract

In this work, we analyze the happiness levels of countries using an unbiased
emotion detector, artificial intelligence (AI). To date, researchers proposed
many factors that may affect happiness such as wealth, health and safety. Even
though these factors all seem relevant, there is no clear consensus between
sociologists on how to interpret these, and the models to estimate the cost of
these utilities include some assumptions. Researchers in social sciences have
been working on determination of the happiness levels in society and
exploration of the factors correlated with it through polls and different
statistical methods. In our work, by using artificial intelligence, we
introduce a different and relatively unbiased approach to this problem. By
using AI, we make no assumption about what makes a person happy, and leave the
decision to AI to detect the emotions from the faces of people collected from
publicly available street footages. We analyzed the happiness levels in eight
different cities around the world through available footage on the Internet
and found out that there is no statistically significant difference between
countries in terms of happiness.

###### Index Terms:

human happiness, artificial intelligence, machine learning, facial emotion
recognition, happiness index

##  I Introduction

Emotions are a distinctive part of human nature. It is an essential element of
life, and it contributes to our interactions with other people. Our
intelligence attaches great importance to how we feel and distinguishes
between different emotions. It is not possible to define or measure emotions
in an exact manner, since they are abstract and subjective. However, social
scientists have used different indicators about how one feels and what affects
one’s feelings. Thus, measuring happiness is possible to some extent.

Happiness is a multidimensional complex fact [1]. It is a driving force and
natural goal for most people. Researchers in social sciences have different
methods on measuring happiness and variables that affect happiness.

Analyzing happiness levels or life satisfaction of countries attracted wide
interest in social sciences and media. Generally, social sciences use polls to
measure the level of happiness of society. Acquiring accurate results with
happiness levels is a desired goal in different research areas. Machine
learning can help with this problem by adding unbiased approach on measuring
happiness and add an extra dimension to researchers in social sciences. In
this mindset, our work examines the emotions from facial images collected from
publicly available street footages of eight different cities around the world.
Facial expressions from raw city footage are categorized into seven basic
emotions; Anger, Sad, Neutral, Disgust, Surprise, Fear, Happy.

Our approach is fundamentally different than that of indicators used by social
scientists. It is relatively unbiased, because it relies on machine learning
to determine the emotions of people. Machine learning has been a powerful tool
for solving problems in various domains such as medicine, economics and
robotics. It can accurately detect emotions by analyzing the facial images.

The organization of the paper is as follows; related works in this area are
discussed in Section II. Section III describes the proposed methods in detail.
Results are given in Section IV and Section V concludes the paper.

##  II Related Work

Understanding the factors that affect happiness have been studied extensively.
Veenhoven, Ruut and Ehrhardt [2] investigated if the data available on
happiness are in accordance with the three theories of happiness; comparison,
folklore and livability. In a previous study, the researchers concluded that
happiness is adversely affected for the people when their neighboring
countries becomes wealthier [3]. In another study [1], it is investigated
whether social capital has a significant effect on happiness. In [4],
researchers updated the Easterlin Paradox, the idea that happiness is
proportional to income, is valid for only developed countries. They concluded
that this paradox also holds for less developed countries. In [5], the effects
of different variables on the happiness (migration, health issues, income,
etc.) are investigated on both national and global scale. HSBC’s expat survey
[6] measured the satisfaction of expats in different aspects for various
countries.

There are varying approaches on the subject in literature for emotion
recognition ranging from examining brain signals to hybrid approaches like
analyzing audio and text input together with videos. Machine learning
algorithms such as Support Vector Machines (SVM) [7], Neural Networks and
K-nearest Neighbors (k-NN) can be used to predict emotions from face images.

Some of the notable works in this field are as follows; Ekman and Friesen [8]
developed a system which is called FACS (Facial Action Coding System), where
basic universal facial expressions are represented as combinations of
different action units. Black and Yacoob [9] used polynomials to represent
optical flow and extract the motion of the facial features. After that, they
used a rule-based classifier to classify basic emotions. Yacoob and Davis [10]
used optical flow of the detected facial features within rectangular regions
with rule-based classifier for recognition. Essa and Pentland [11] transformed
face images into mesh models, then calculated the optical flow from them to
recognize facial expressions. Donato et al. [12] compared different techniques
to extract and classify facial expressions. Cowie et al. [13] published a
survey about emotion recognition containing detailed information about both
audio and visual approaches. Cohen et al. [14] in their work used Naive Bayes
Classifiers with a Cauchy distribution together with HMM for facial expression
recognition. Ioannou et al. [15] used a combination of SVM, morphological
operators, neural networks and neuro-fuzzy system to classify facial
expressions. Gunes and Piccardi [16] used face and hand gestures in
combination to determine emotional expression. Mansoorizadeh and Charkari [17]
introduced a hybrid feature space from extracted features of speech and video
and performed emotion recognition. Dahmane and Meunier [18] used HOG and SVM
to classify emotions from videos containing face. Halder et al. [19] used
different combinations of fuzzy sets to classify emotions from faces. Poria et
al. [20] used Convolutional (CNN) and Recurrent Neural Networks (RNN) with
Multiple Kernel Learning to analyze sentiment from audio, video and text.
Zhang et al. [21] introduced a fusion approach using a Part-based Hierarchical
Bidirectional RNN (PHRNN) and a Multi-Signal CNN Network (MSCNN) on images to
recognize emotions. Jain et al. [22] also proposed a CNN-RNN hybrid model on
face images for recognition. Hossein and Muhammad [23] worked on audio and
image inputs together using CNN and SVM for emotion recognition.

##  III Methodology

In our work, we present an unbiased emotion detector through machine learning
using publicly available videos of the crowded streets in various countries.
We aimed to gather unbiased data from different cities around the world to
analyze the psychology of the general population. Footages from different
cities are converted to frames to be used as dataset. All methods mentioned
here are performed with Python language.

To detect facial emotion recognition, first we need to detect faces in each
frame in the dataset. For this purpose, we used Adam Geitgey’s [24] face
recognition model. With this model, it is possible to locate face in the frame
and crop the face region for further processing.

For each city, we traverse through all frames and detected faces are cropped,
turned into grayscale and resized to 48x48 pixels using OpenCV library. Then,
these images are sent to pre-trained deep learning model of Priya Dwivedi [25]
as inputs. Classification result belongs to one of these emotion categories;
Anger, Sad, Neutral, Disgust, Surprise, Fear, Happy. Finally, classification
results are exported to a CSV file categorized by city, emotion and value.

###  III-A Dataset

Our dataset contains eight cities, Barcelona, Copenhagen, Istanbul, Kiev,
London, New York, Paris and Tokyo. Footages were taken from various publicly
available videos online, containing crowded street scenes dated between July
2013 - October 2020. Each city contains 300 detected 48x48 pixel face images
in grayscale, thus complete dataset has 2400 images. It is made sure that
dataset doesn’t have any mistaken image for face, or, any sunglasses or
regular glasses present.

###  III-B Face Recognition

For face recognition, we used Adam Geitgey’s [24] CNN based face recognition
library. It is actually a Python adaptation of Dlib’s [26] face recognition
algorithm, a popular C++ library that consists of various machine learning
algorithms. CNN method can detect faces from different angles, unlike the HOG
based version in the Dlib library.

###  III-C Emotion Recognition

As previously mentioned, we used Priya Dwiedi’s model [25] for emotion
recognition. They trained their model with The Facial Expression Recognition
2013 (FER-2013) database which is a work of Pierre-Luc Carrier and Aaron
Courville [27]. This database consists of 28,709 face images for training in
48x48 pixel grayscale format.

A graphic representation of the CNN model prepared with visualkeras [28] can
be seen in the Fig. 1. Activation functions used in layers are ReLU, except
the last layer, which is softmax.

Figure 1: CNN architecture for emotion recognition

##  IV Experimental Results

Our results showed that most common emotions detected with the algorithm were;
Surprise, Fear, Happy and Anger. Sad and Neutral emotions were not detected in
any of the cities. In Table-I detailed results containing all emotions are
given. We notice that "surprise" emotion is very common. One explanation can
be due to the recording nature of video (i.e. a youtuber recording the video)
people might be surprised to notice a camera.

In Fig. 2, 95% confidence intervals for happiness proportion by cities are
shown. The intervals show that there is no statistically significant
difference between cities in terms of proportion of happy people. There can be
several explanations for that. First, even though we collected street footage,
the recordings used were not taken in an obscure manner and this might have
biased emotions. Another explanation could be that the proportion of happy
people in street is indeed similar across the world. Results are discussed in
Conclusion section.

TABLE I: Emotion results by city

Anger Disgust Surprise Fear Happy Barcelona 2 0 90 203 5 Istanbul 1 1 64 227 7
Kiev 2 0 79 215 4 London 1 0 115 182 2 New York 1 0 61 230 8 Paris 2 0 31 267
0 Tokyo 3 0 32 260 5 Copenhagen 1 0 69 227 3

Figure 2: Happiness distribution by city

##  V Conclusion

In our work, we proposed the use of public footage as a resource to determine
happiness levels in society. We collected footage from various cities around
the world together, then used artificial intelligence to recognize emotions
from facial expressions.

For the reason why surprise and fear are prevalent in results, we think that
it could be due to sun light directly hitting people outdoors, thus making
them grimace, or maybe they were in a rush to catch up something, or maybe
they were surprised when they noticed the camera recording. Another reason may
be different races have different facial structures which can give a way to
unintended classifications. It could be due to the neural network
architecture, or the learning method altogether, it may need more training
with different datasets or update in architecture.

For a future direction, further work needed in creating a more specialized
dataset for the purposed idea and different machine learning algorithms needs
to be explored in terms of performance and accuracy.

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# Signature of excitonic insulators in phosphorene nanoribbons

A. F. P. de Oliveira  Andréia L. da Rosa<EMAIL_ADDRESS>Institute of
Physica, Federal University of Goiás, Campus Samambaia, 74690-900, Goiânia,
Goiás, Brazil.  Alexandre C. Dias<EMAIL_ADDRESS>Institute of Physics
and International Center of Physics, University of Brasília, Brasília
$70919$-$970$, Distrito Federal, Brazil

###### Abstract

Phosphorene is a recently developed two-dimensional (2D) material that has
attracted tremendous attention because of its unique anisotropic optical
properties and quasi-one-dimensional (1D) excitons. We use first-principles
calculations combined with the maximally localized Wannier function tight
binding Hamiltonian (MLWF-TB) and Bethe-Salpeter equation (BSE) formalism to
investigate quasiparticle effects of 2D and quasi-1D blue and black
phosphorene nanoribbons. Our electronic structure calculations shows that both
blue and black monolayered phases are semiconductors. On the other hand black
phosphorene zigzag nanoribbons are metallic. Similar behavior is found for
very thin blue phosphorene zig-zag and armchair nanoribbon. As a general
behavior, the exciton binding energy decreases as the ribbon width increases,
which highlights the importance of quantum confinement effects. The solution
of the BSE shows that the blue phosphorene monolayer has an exciton binding
energy four times higher than that of the black phosphorene counterpart.
Furthermore, both monolayers show a different linear optical response with
respect to light polarization, as black phosphorene is highly anisotropic. We
find a similar, but less pronounced, optical anisotropy for blue phosphorene
monolayer, caused exclusively by the quasi-particle effects. Finally, we show
that some of the investigated nanoribbons show a spin-triplet excitonic
insulator behavior, thus revealing exciting features of these nanoribbons and
therefore provides important advances in the understanding of quasi-one
dimensional phosphorus-based materials.

##  I Introduction

Few-layer black phosphorus has recently attracted attention because of its
fascinating applications in several technological fields, including electronic
and optoelectronic devices 1; 2; 3 Monolayer phosphorene has been of
particular interest in exploring technological applications and investigating
fundamental phenomena, such as 2D quantum confinement and many-body
interactions. However, phosphorene monolayers are usually unstable against
oxidation and environmental attack under ambient conditions, making its
characterization challenging.4 Consequently, many important physical
properties of phosphorene, such as its excitonic nature, remain unclear.

Black phosphorus, an elemental phosphorus allotrope, was first synthesized in
$1914$ and was recently rediscovered as an exciting member of the 2D family,5.
In black phosphorene, each atom is bonded to three adjacent phosphorus atoms
in a puckered structure. It is possible to synthesize a monolayer black
phosphorene via chemical exfoliation, since bulk black phosphor is composed of
single atomic layers held together by van der Waals interactions. Black
phosphorus has a direct bandgap, which can be tuned from
$0.3\text{\,}\mathrm{eV}$ (bulk) to $2.0\text{\,}\mathrm{eV}$ (monolayer) as a
result of layer-dependent photoluminescence (PL) spectra.6 Single layer black
phosphorene has quasi-particle and optical gaps of $2.2\text{\,}\mathrm{eV}$
measured by photoluminescence spectroscopy.7 Near-band-edge recombinations are
observed at $2\text{\,}\mathrm{K}$, including dominant excitonic transitions
at $0.276\text{\,}\mathrm{eV}$ and a weaker one at
$0.278\text{\,}\mathrm{eV}$.8 This makes black phosphorene ideal for
optoelectronic applications such as broadband photodetection.9 First-
principles GW-BSE calculations shows the effect of strain on excitons in
pristine black phospherene monolayers10 reported $1.40\text{\,}\mathrm{eV}$
for the optical bandgap and $0.74\text{\,}\mathrm{eV}$ for the exciton binding
energy. Experimental results suggested $0.9\text{\,}$ and
$0.12\text{\,}\mathrm{eV}$.11 More recently a linearly polarized luminescence
emission owing to from edge reconstructions has been identified 12 However,
some of the structures shown in 12 reconstruct whereas other do not and
therefore the condition for edge reconstruction has no been completely
clarified. Here we do not find any spontaneous reconstruction of the edges;
thus, strain plays a minor role.

In addition to the black structure, phosphorene can be crystallized in
hexagonal symmetry (blue phosphorene). This structure is the most stable form
on noble metal substrates such as Au($111$) and Ag($111$), while black
phosphorene is the most stable phase on metal surfaces such as Al($111$) and
Sn($100$) 13. Similarly to black phosphorene, the fundamental bandgap of blue
phosphorene depends on the number of layers. Recently, the experimental
electronic bandgap structure of blue phosphorene on Au($111$) substrate was
determined to be $1.1\text{\,}\mathrm{eV}$ 14.

In addition to two-dimensional nanostructures, more recently quasi-one-
dimensional phosphorene has been reported. These long phosphorene chains were
synthesized on an Ag (111) surface by molecular beam epitaxy (MBE) and
characterized by scanning tunneling microscopy, showing a band gap of
$1.5\text{\,}\mathrm{eV}$, which makes them viable for possible applications
in nanoelectronics.15. In low-dimensional structures, the screening of the
Coulomb interaction is strongly reduced, which can have important consequences
such as the significant increase of exciton binding energies. Since reduced
electron screening in two plays a fundamental role in determining exciton
properties, understanding the optoelectronic and photonic properties of
phosphorene is fundamental in determining its device performance.

In this work we use density functional theory combined with maximally
localized wannier functions tight binding (MLWF-TB) Hamiltonian and Bethe-
Salpeter formalism to investigate the the excitonic properties of pristine
phosphorene nanosheets and nanoribbons. Our calculations revealed strongly
bound excitons with anisotropic spatial delocalization. We show that the
exciton binding energies in both sheets and ribbons are highly anisotropic.
Furthermore, we suggest that phosphorene nanoribbons are an excitonic
insulator, arising from the spontaneous formation of electron-hole-bound
states. Our results provide a new feature of these materials and help to
understand the ground-state excitons. Localized emission from black
phosphorous edges motivates exploration of nanoribbons for tunable narrow band
light generation, with future potential to create nanostructures for quantum
information processing applications as well as exploration of exotic phases.

##  II Methodology

First-principle spin-polarized calculations have been performed using density
functional theory (DFT), within the generalized gradient approximation (GGA)
according to the Perdew-Burke-Ernzerhof (PBE) parameterization,16 to determine
the structural properties and phonon dispersion of materials based on
phosphorus. As DFT-PBE tends to underestimate the fundamental band gap due to
self-interaction errors,17; 18 we have used range-separated hybrid exchange-
correlation functional proposed by Heyd, Scuseria and Ernzerhof (HSE06)19; 20
to improve the electronic properties of the investigated nanostructures.

The projector augmented wave (PAW) method,21 as implemented in the Vienna ab
initio simulation package (VASP) 22; 23 has been used to describe the
electronic charge density. To obtain the electronic and structural properties,
we chose a plane wave energy cutoff of $400\text{\,}\mathrm{eV}$, with a total
energy convergence criterion of ${10}^{-6}\text{\,}\mathrm{eV}$. The ground
state properties have been obtained until the atomic forces were less than
$0.01\text{\,}\mathrm{eV}\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$.
These calculations were done considering a k-points density of
$40\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$ in each periodic lattice
vector direction. Further details on the atomic structures and the vacuum in
the non-periodic directions can be seen in the Support Information (SI).

Phonon dispersion has been obtained combining calculations performed with VASP
and Phonopy package,24. We chose the density functional perturbation theory
(DFPT) method, with a $4\times 3\times 1$($4\times 4\times 1$) supercell for
the pristine black(blue) phosphorene monolayer. We use the same energy cutoff
and automatic Monkhorst-Pack 25 k-mesh generation scheme of the electronic
properties.

In order to investigate the excitonic and optical properties, we first
generate a maximally localized Wannier function tight-binding (MLWF-TB)
Hamiltonian, directly obtained from DFT-HSE06 calculations using the Wannier90
package.26 Then we investigate the linear optical response at independent
particle approximation (IPA). Next, to include electron-hole interaction we
solve the Bethe-Salpeter equation (BSE) 27; 28 using the Rytova-Keldysh 2D
potential (V2DRK).29 The nanostructures are surrounded by a vacuum region. We
use a $120\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$ k-points density and
a smearing of $0.05\text{\,}\mathrm{eV}$ for the calculation of real and
imaginary parts of the frequency dependent dielectric tensor. Further details
about the parameters used in the BSE calculations are given in the SI. We
define the optical band gap as the lowest optical transition, with an
excitation energy greater than or equal to $0\text{\,}\mathrm{eV}$, with an
optical transition rate greater than
$0.1\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{2}$. Both IPA and BSE linear
optical response levels are obtained using WanTiBEXOS implementation.30

##  III Results

###  III.1 Structural and Electronic Properties

####  III.1.1 Pristine phosphorene monolayers

As a matter of completeness we show the band structure for Black phosphorene
monolayer has a puckered structure as shown in Fig. 1(a). The relaxed lattice
parameters are $a=4.62$ $\mathrm{\SIUnitSymbolAngstrom}$ and $b=3.30$
$\mathrm{\SIUnitSymbolAngstrom}$. Free-standing black phosphorene is not
planar, but shows a corrugation $\Delta=2.10$ $\mathrm{\SIUnitSymbolAngstrom}$
as seen in Fig. 1(a)(lower panel). Our results are in agreement with previous
works.12; 31; 8

Figure 1: Top (upper panel) and side view (lower panel) of (a) black and (b)
blue phosphorene monolayer. Buckling $\Delta$ and unit cell lattice parameters
$a$ and $b$ are shown.

Figure 2: Electronic band structure and phonon dispersion calculated within
HSE06 for (a) black and (b) blue phosphorene. The Fermi level is set at zero.

On the other hand, blue phosphorene has a honeycomb structure shown in Fig.
1(b). The relaxed lattice parameters are a= b=
$3.28\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. The buckling is $\Delta$ =
$1.23\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (lower panel).

Black phosphorene has been found to have an anisotropic behavior in its
thermal and electrical properties as reported previously 32. This anisotropic
behavior can be verified on phonon dispersion relations of black phosphorene
as seen in Fig. 2(a), right panel. The phononic band gap is
$2.5\text{\,}\mathrm{THz}$. The slope of the acoustic branches along the
Y-$\Gamma$ (armchair) and $\Gamma$-X (zig-zag) directions highlights the
thermodynamic anisotropy of this structure.

Once the atomic positions and lattice vectors have been optimized, we
calculated the electronic band structure as shown in Fig. 2(lower left panel).
We obtained a band gap of $0.91\text{\,}\mathrm{eV}$ with PBE and
$1.60\text{\,}\mathrm{eV}$ with HSE06 functional.

Blue phosphorene also shows an isotropic behavior for thermal and electrical
properties, measured by in Ref. 32. This isotropic behavior can be verified on
phonon dispersion relations of blue phosphorene shown in Fig. 2 (lower right
panel). The phonon band gap is $4.9\text{\,}\mathrm{THz}$ with the slope of
the acoustic branches being anisotropic. The computed electronic band gap is
$1.93\text{\,}\mathrm{eV}$ with PBE and $2.83\text{\,}\mathrm{eV}$ with HSE06.
HSE06 calculations shows a better agreement with previous work 12; 31; 8; 7
and will be therefore used in the calculations of properties of nanoribbons as
shown next.

###  III.2 Phosphorene nanoribbons

Quasi-one-dimensional phosphorene nanostructures have successfully been
fabricated on Ag($111$) substrates 15. Those structures are composed of
armchair chains made of black phosphorene as seen in Fig. 3. Placing two
nanochains of phosphorus oriented along the zigzag direction as shown in Fig.
3(a) can lead to spontaneous formation of nanoribbons. We find that up to a
distance of $4.00\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ the nanochains relax
in such a way as to form ribbons as shown in Fig.,3(b). This ribbon resembles
blue pristine phosphorene with armchair orientation. We notice that we have
investigated several possible configurations, and the ones shown here have the
lowest energy among them.

Phonon dispersion allows us to verify that for this geometry no imaginary
frequencies are found in Fig. 4 (a), which indicates the thermodynamic
stability of the structure at low temperatures. Acoustic and optical branches
are seen, and mixed modes are also seen. The band structure and phonon
dispersion are shown in Fig. 4. The evaluated band gap is
$2.20\text{\,}\mathrm{eV}$ with HSE06 as seen in Figs. 4(b). Our calculations
show that HSE06 overestimates the experimental gap of
$1.8\text{\,}\mathrm{eV}$.15 A possible explanation for this discrepancy is
the effect of the substrate reported experimentally, whose effect is out of
the scope of this paper.

Figure 3: (a) Schematic view of ribbon assembling. Top view before and (b)
after atomic optimization of two interacting nanochains for distance X less
than $4.0\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. Here the ribbon has
armchair edges. Figure 4: (a) Phonon dispersion of a thin phosphorene ribbon
shown in Fig. 3. Band structure calculated with b) PBE and c) HSE06 exchange-
correlation functionals.

When discussing nanoribbon electronic and optical properties, it is important
to investigate exciton quantum confinement effects. Therefore the ribbons
width L was varied in order verify strain and reconstruction effects. In
general, we find that strain plays a minor role in these nanostructures, and
spontaneous reconstruction does not occur.

Relaxed structures of black phosphorene nanoribbons are shown in Fig. 5(a) for
armchair termination and widths of
$2.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$5.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$6.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$8.2\text{\,}\mathrm{(}$L=5)Å and in Fig. 5(b) for zigzag termination and
widths of $4.8\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$7.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$8.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$12.5\text{\,}\mathrm{(}$L=5)Å. The black nanoribbons with armchair
termination and L= 2, 3, 4, 5 show indirect band gap, seen in Fig. 6 (upper
panel). On the contrary, the zigzag edge-terminated ribbons contribute to
metallic behavior for all widths. For smaller ribbons with L= 2 and zigzag
edges, a conductive behavior is found, as seen in the band structure of Fig. 6
(lower panel).

Relaxed structures of blue phosphorene nanoribbons are shown in Fig. 7(a) for
armchair termination and widths of
$5.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$8.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$12\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$15.3\text{\,}\mathrm{(}$L=5)Å and in Fig. 7(b) for zigzag termination and
widths of $5.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$6.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$10.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$12.5\text{\,}\mathrm{(}$L=5)Å. As seen in Fig. 8 (upper panel) blue armchair
ribbons with L = 2 have an indirect band gap, while for L = 3, 4 and 5 have
direct gap at the X-point.

Band structure of blue phosphorene ribbons with zigzag termination are shown
in Fig. 8(b). The smallest ribbon of width
$5.0\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (L=2) shown in Fig. 7 has a
conductive character as seen in Fig. 8 (lower panel). As we increase the width
L of the ribbons to $6.5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (L=3),
$10\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (L=4) and
$12.5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (L=5) as seen in Fig. 8 we find
indirect band gap semiconductors as seen in Fig. 8.

(a)

(b)

Figure 5: Relaxed geometries of black phosphorene nanoribbons. a) armchair
termination and widths of
$2.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$5.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$6.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$8.2\text{\,}\mathrm{(}$L=5)Å. b) zigzag termination and widths of
$4.8\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$7.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$8.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$12.5\text{\,}\mathrm{(}$L=5)Å.

Figure 6: HSE06 band structure of black phosphorene nanoribbons. Upper panel:
armchair termination and widths of a)
$2.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$5.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$6.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$8.2\text{\,}\mathrm{(}$L=5)Å. Lower panel: zigzag termination and widths of
a) $4.8\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$7.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$8.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$12.4\text{\,}\mathrm{(}$L=5)Å. Blue (red) lines represent the up (down) spin
channel. Fermi level is set at zero.

Figure 7: Relaxed structure of blue phosphorene nanoribbons. a) growth along
the zigzag direction with armchair edges and widths of
$5.4\text{\,}\mathrm{(}$L=2),
$8.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$12\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$15.3\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{5}\mathrm{)}$$\mathrm{\SIUnitSymbolAngstrom}$.
b) growth along armchair direction with zigzag edges and widths of
$5.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
$6.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$,
$10.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and
$12.5\text{\,}\mathrm{(}$L=5) $\mathrm{\SIUnitSymbolAngstrom}$.

Figure 8: HSE06 band structure of blue phosphorene nanoribbons. Upper panel:
growth along the zigzag direction with armchair edges and width of a)
$5.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$8.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$12\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$15.3\text{\,}\mathrm{(}$L=5)Å. Lower panel: growth along the armchair
direction with zigzag edges and widths of a)
$5.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$6.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$10.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$12.5\text{\,}\mathrm{(}$L=5)Å. Blue (red) lines represent the up (down) spin
channel. Fermi level is set at zero.

Finally, we would like to mention that black phosphorus nanoribbons with
armchair orientation have the lowest formation energy per atom, which is in
agreement with the STM pictures reported in reference 33.

##  IV Excitonic and optical Properties

###  IV.1 Pristine phosphorene monolayers

From the exciton band structure shown in Fig. 9 we can see that both
monolayers have an indirect excitonic ground state located between $\Gamma$-S
for black phosphorene with $1.03\text{\,}\mathrm{eV}$ and between K’-$\Gamma$
points for blue phosphorene with $0.78\text{\,}\mathrm{eV}$, which results,
when comparing with the fundamental band gap, in an exciton binding energy of
$564.18\text{\,}\mathrm{meV}$($1957.95\text{\,}\mathrm{meV}$) for the
black(blue) phosphorene. The direct excitonic ground state for blue(black)
phosphorene has excitation energies of
$1.06\text{\,}\mathrm{eV}$($0.96\text{\,}\mathrm{eV}$). Although blue and
black phosphorene have the same chemical composition, we can see that the
exciton binding energy in blue phosphorene is approximately four times higher
than their black counterpart, with indicates that the Coulomb interaction is
much stronger in the hexagonal buckled phase.

Figure 9: Exciton band structure of (a) black and (b) blue phosphorene
monolayers Figure 10: Absorption coefficient of (a) black and (b) blue
phosphorene monolayers, at IPA (dashed lines) and BSE (solid lines)
considering light polarization along $\hat{x}$ (blue curves) and $\hat{y}$
(red curves) directions.

In Fig. 10 we show the absorption coefficients for both black and blue
phosphorene monolayers within BSE (with excitonic effects) and IPA (without
excitonic effects) approximations. Comparing the dashed (IPA) and solid (BSE)
curves, we find that the excitonic effects are significant for both phases.
For the black phosphorene, we can see an optical anisotropy within both the
IPA and BSE levels. This results in an optical band gap of
$2.27\text{\,}\mathrm{eV}$ for the polarization of $\hat{x}$ and
$1.59\text{\,}\mathrm{eV}$ for the polarization of $\hat{y}$ at the IPA level.
Within BSE, despite the huge differences in the absorption spectrum for both
directions of light polarization, the optical band gap is located at
$1.06\text{\,}\mathrm{eV}$. Excitons in black phosphorene were found to be
highly anisotropic and strongly bound using polarization-resolved
photoluminescence measurements at room temperature. Moreover, in this
material, a quasiparticle bandgap of $2.2\text{\,}\mathrm{eV}$ and an exciton
binding energy of $0.9\text{\,}\mathrm{eV}$.7 This corroborates with our
results reported here, when the optical bandgap at IPA and BSE levels is
compared, remembering that it is difficult to experimentally measure the
indirect excitonic states.

On the other hand, for blue phosphorene we see that within IPA level, the
system is optically isotropic, which means that regardless the light
polarization, the optical response is the same. However, if excitonic effects
are considered, we see significant changes in the absorption coefficient for
peaks, which allows us to infer that the quasi-particle effects causes a small
anisotropy in the optical response. The optical band gap is located in this
case at $2.97\text{\,}\mathrm{eV}$ within IPA and $1.27\text{\,}\mathrm{eV}$
within BSE. .

###  IV.2 Phosphorene nanoribbons

In Fig 11 we shown the excitonic band structure of black phosphorene armchair
(upper panels) and zigzag (lower panels) nanoribbons. The armchair terminated
nanoribbons has an indirect excitonic ground state. This means that the lowest
excitonic state are formed for electrons and hole pairs at different k-points,
the exciton binding energy, as shown in Table 1, decreases as the nanoribbon
becomes wider. This is expected due to the reduction of the quantum
confinement in the non-periodic direction. Similar behaviour is found for the
nanoribbons with zig zag edges.

Despite the metallic behavior of the black zigzag nanoribbons, we obtained an
exciton binding energy, higher than $0\text{\,}\mathrm{meV}$. This means that
the exciton binding energy is higher than the band gap, which suggests that
these zig-zag nanoribbons becomes an excitonic insulator 34; 35; 36. Due to
the spin composition of the lowest conduction and valence bands, our
structures can be classified as a spin-triplet excitonic insulator.37 This
excitonic insulator behavior can explain why the exciton binding energy for
black zigzag nanoribbons becomes much smaller than that for black phosphorous
monolayers. As the quantum confinement is reduced, a possible semiconductor-
excitonic insulator phase transition occurs.

Figure 11:  Exciton band structure of black phosphorene nanoribbons. Upper
panel: ribbons with armchair edges and width of a)
$2.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$5.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$6.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$8.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{5}\mathrm{)}$Å. Lower
panel: ribbons with zigzag edges and L of a)
$4.8\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$7.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$8.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$12.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{5}\mathrm{)}$Å.

Figure 12: Exciton band structure of blue phosphorene. Uppper panel: ribbons
with armchair edges and width of a)
$5.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$8.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$12.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$15.3\text{\,}\mathrm{(}$L=5)Å. The same for ribbons with zigzag edges and
width of a) $5.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$,
b) $6.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$10.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$12.5\text{\,}\mathrm{(}$L=5)Å.

The excitonic band structure for the blue phosphorene nanoribbons are shown in
Fig 12, for the armchair (upper panels) and zig-zag (lower panels)
terminations, the excitonic ground state indirect for all systems. From the
armchair nanoribbons, regardless of the ribbon width, all armchair structures
are excitonic insulators, with the same classification as the black
phosphorene zigzag nanoribbons. Furthermore, an interest feature is found: the
exciton binding energy $E_{\rm x}^{\rm b}$ shows negligible change with
respect to the ribbon width, as reported in Table 1. This behaviour is the
same shown for the electronic band gap of these systems, which suggests that
the electron and hole pairs that compose these lower energy excitonic states
are mostly edge states, resulting in high localized edge excitons.

For blue phosphorene nanoribbons with zigzag edges, we find an indication of
an excitonic insulator behavior for L = 2 and a trivial semiconductor behavior
for larger widths. The excitonic insulator phase in L=2 occurs due the band
gap closing as an effect of the quantum confinement. Our results indicates a
phase transition from excitonic insulator to semiconductor in a width between
L=2 to L=3, where one expects a band gap opening. For L larger than 3, the
exciton binding energy decreases as the quantum confinement decreases, as
shown in Table 1.

Table 1:  MLWF-TB+BSE electronic and excitonic properties for phosphorene nanoribbons: fundamental band gap $E_{\rm g}$, direct band gap, $E^{\rm d}_{\rm g}$, exciton ground state, $E_{\rm x}^{\rm gs}$, direct exciton ground state, $E_{\rm x}^{\rm gs}$ (d), and exciton binding energy, $E_{\rm x}^{\rm b}$, obtained from $E_{\rm g}-E_{\rm x}^{\rm gs}$. L is the ribbon width (see text). Structure | edges | L |  $E_{\rm g}$ ($\mathrm{eV}$) |  $E^{\rm d}_{\rm g}$ ($\mathrm{eV}$) |  $E_{\rm x}^{\rm gs}$ ($\mathrm{eV}$) |  $E{\rm x}^{\rm d}_{\rm gs}$ ($\mathrm{eV}$) |  $E_{\rm x}^{\rm b}$ ($\mathrm{meV}$)
---|---|---|---|---|---|---|---
Black | armchair | 2 | 1.68 | 2.12 | 1.00 | 1.61 | 677.83
Black | armchair | 3 | 1.59 | 1.62 | 0.96 | 1.09 | 628.03
Black | armchair | 4 | 1.48 | 1.63 | 0.96 | 1.12 | 525.71
Black | armchair | 5 | 1.43 | 1.60 | 0.92 | 1.12 | 502.69
Black | zigzag | 2 | 0.00 | 0.00 | $-0.41$ | $-0.08$ | 412.63
Black | zigzag | 3 | 0.00 | 0.00 | $-0.25$ | $-0.14$ | 253.03
Black | zigzag | 4 | 0.00 | 0.00 | $-0.36$ | $-0.08$ | 363.97
Black | zigzag | 5 | 0.00 | 0.00 | $-0.17$ | $-0.12$ | 175.75
Blue | armchair | 2 | 1.76 | 1.78 | $-0.30$ | $-0.30$ | 2056.62
Blue | armchair | 3 | 1.80 | 1.80 | $-0.31$ | $-0.31$ | 2115.68
Blue | armchair | 4 | 1.76 | 1.77 | $-0.24$ | $-0.24$ | 2005.38
Blue | armchair | 5 | 1.76 | 1.77 | $-0.26$ | $-0.26$ | 2026.57
Blue | zigzag | 2 | 0.00 | 0.00 | $-0.28$ | $-0.13$ | 277.06
Blue | zigzag | 3 | 1.29 | 1.65 | 0.40 | 0.61 | 885.35
Blue | zigzag | 4 | 1.19 | 1.60 | 0.40 | 0.69 | 786.01
Blue | zigzag | 5 | 1.17 | 1.51 | 0.46 | 0.77 | 709.43

In Table 1 is possible to realize that the exciton binding energy does not
vary significantly for blue nanoribbons with armchair edges. This might be an
indication of strong localization of the electron-hole pair in the nanorribon
edges. Recently, it it pointed out in Ref. 12 that black phosphorous edges
atomic reconstructions can strongly confine excitons resulting in distinct
emission features. The explanation is that local strain and screening can
mediate such interactions, thus reducing the PL emission lines. Here we notice
negligible bond length distortion between edge and bulk phosphorous atoms for
L = 2-5 ribbons and therefore we can state that emission from edge states are
not due to edge reconstruction.

Figure 13: Absorption coefficient for black phosphorene armchair nanoribbons
calculated within IPA (blue dashed lines) and BSE (red solid lines). Upper
panel: ribbon width of a)
$2.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$5.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$6.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$8.2\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{5}\mathrm{)}$Å (armchair
edges). Lower panel: ribbon width of a)
$4.8\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$7.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$8.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$12.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{5}\mathrm{)}$Å (zigzag
edges).

Figure 14: Absorption coefficient of the blue phosphorene armchair nanoribbons
calculated within IPA (blue dashed lines) and BSE (red solid lines). Upper
panel: Ribbon width of a)
$5.4\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$8.7\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$12.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$15.3\text{\,}\mathrm{(}$L=5)Å (armchair edges) and Lower panel: Ribbon width
of a) $5.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{2}\mathrm{)}$, b)
$6.5\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{3}\mathrm{)}$, c)
$10.0\text{\,}\mathrm{(}\mathrm{L}\mathrm{=}\mathrm{4}\mathrm{)}$ and d)
$12.5\text{\,}\mathrm{(}$L=5)Å (zigzag edges).

The absorption coefficient of the investigated nanoribbons is shown in Figs.
13 and 14, within both BSE and IPA levels of theory. Regardless of the
nanoribbon we can observe that the quasi-particle effects are significant in
the absorption spectrum shape and peaks, resulting in a red-shift.
Interestingly enough, the excitonic insulators nanoribbons behave as
semiconductor, having an optical band gap, as shown in Table 2 higher than
$0\text{\,}\mathrm{eV}$. The relation between optical band gap and the
nanoribbon width are shown in Table 2. We notice that within IPA and BSE
levels, the optical band gap has the lowest optical excitation. We consider
the onset as the photon energy equals or higher than $0\text{\,}\mathrm{eV}$
with an oscillator force higher than
$0.1\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{2}$.

Table 2: Optical band gap within IPA ($E_{\rm gopt}^{\rm IPA}$) and BSE ($E_{\rm gopt}^{\rm BSE}$) levels for phosphorene nanoribbons. The optical band gap is defined as the first optical transition, with photon energy higher or equals to $0\text{\,}\mathrm{eV}$. The oscillator force is set to be higher than $0.1\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{2}$. L is the ribbon width (see text). structure | edge | L |  $E_{\rm gopt}^{\rm IPA}$ ($\mathrm{eV}$) |  $E_{\rm gopt}^{\rm BSE}$ ($\mathrm{eV}$)
---|---|---|---|---
Black | armchair | 2 | 2.12 | 1.61
Black | armchair | 3 | 1.62 | 1.09
Black | armchair | 4 | 1.63 | 1.21
Black | armchair | 5 | 1.61 | 1.11
Black | zigzag | 2 | 1.14 | 0.50
Black | zigzag | 3 | 0.15 | 0.28
Black | zigzag | 4 | 1.60 | 0.88
Black | zigzag | 5 | 1.73 | 1.27
Blue | armchair | 2 | 1.78 | 0.01
Blue | armchair | 3 | 1.80 | 0.38
Blue | armchair | 4 | 1.76 | 0.03
Blue | armchair | 5 | 1.77 | 0.02
Blue | zigzag | 2 | 1.01 | 0.52
Blue | zigzag | 3 | 2.19 | 1.15
Blue | zigzag | 4 | 2.11 | 1.15
Blue | zigzag | 5 | 2.16 | 2.10

##  V Conclusions

Our electronic structure calculations shows that both monolayered phases are
semiconductors. For the nanoribbons we see that black phosphorene zig-zag
nanoribbons are metallic. Similar bheavior is found for thin blue phosphorene
zig-zag and armchair nanoribbon also metallic. For the semiconductor
nanoribbons the electronic band gap decreases as the nanoribbon width
increases.

The solution of the Bethe-Salpeter equation shows that blue phosphorene
monolayer has an exciton binding energy four times higher than the black
phosporene counterpart. Furthermore, both monolayers shows a different linear
optical response due light polarization, being black phosphorene highly
anisotropic. We find a similar, but less pronounced, optical anisotropy is
also seen in blue phosphorene monolayer, caused exclusively by the quasi-
particle effects.

As a general behavior, the exciton binding energy decreases as the ribbon
width increases, which highlights the importance of quantum confinement
effects. In addition to large band gap found for some of the investigated
structures, blue nanoribbons with zig-zag and armchair edges shows a spin-
triplet excitonic insulator behavior. Our calculations reveal exciting
features in these nanomaterials and therefore provides important advances in
the understanding of quasi-one- dimensional black phosphorus.

##  VI Acknowledgements

We acknowledge the financial support from the Brazilian funding agency CNPq
under grant numbers 313081/2017-4, 305335/2020-0, 309599/2021-0 and
408144/2022-0. We thank computational resources from LaMCAD/UFG, Santos
Dumont/LNCC, CENAPAD-SP/Unicamp (project number 897) and Lobo Carneiro HPC
(project number 133). A.C.D also acknowledge FAPDF grants numbers
00193-00001817/2023-43 and 00193-00002073/2023-84.

##  VII Electronic Support Information

The atomic structures data, complementary data for the figures shown in
manuscript and additional technical details are reported within the Electronic
Support Information (SI).

##  VIII Conflict of interest statement

The authors declare no conflict of interest.

##  IX Data availability statement

The atomic structures data, complementary data for the figures shown in
manuscript and additional technical details are reported within the Electronic
Support Information (SI).

##  X Ethics statement

It does not apply.

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