$\mathcal{O}(\alpha_{s}^{3})$ corrections to semileptonic $b\to c$ decays in
the heavy daughter approximation

Kay Schönwald1$\star$

1 Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology
(KIT),

76128 Karlsruhe, Germany

*<EMAIL_ADDRESS>
15th International Symposium on Radiative Corrections:
Applications of Quantum Field Theory to Phenomenology,
FSU, Tallahasse, FL, USA, 17-21 May 2021 10.21468/SciPostPhysProc

## Abstract

We present our recent calculation of the third order corrections to the
semileptonic $b\to c$ and the muon decays. The calculation has been performed
in an expansion around the limit $m_{c}\sim m_{b}$, but shows decent
convergence even for $m_{c}=0$ from which the contribution to the muon decay
can be extracted. For the semileptonic $b\to c$ decay we find large
perturbative corrections in the on-shell scheme which can be significantly
reduced by changing to the kinetic scheme for the bottom quark mass. These
results are important input for the inclusive determination of $|V_{cb}|$ and
the Fermi coupling constant $G_{F}$.

##  1 Introduction

The Cabbibo-Kobayashi-Maskawa (CKM) matrix elements are fundamental constants
in the Standard Model (SM) which describe the flavor mixing in the quark
sector and provide the only source of charge-parity (CP) violation. It is
therefore important to determine these constants precisely. One way to
determine the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ are inclusive
semileptonic $B$ meson decays $B\to X_{c(u)}\ell\overline{\nu}$ using global
fits to the experimental values of the semileptonic decay widths and moments
of kinematical distributions [1, 2, 3, 4, 5]. Here, the presence of the heavy
bottom quark allows to describe the decay in the heavy quark effective theory
(HQET), where the decay rate can be given in an expansion in the strong
coupling constant $\alpha_{s}$ and in inverse powers of the heavy quark mass
$1/m_{b}$. The leading order in $1/m_{b}$ is given by the free quark decay
$b\to c\ell\overline{\nu}$ which had been known up to
$\mathcal{O}(\alpha_{s}^{2})$ [6, 7, 8] together with leading terms in the
large $\beta_{0}$ approximation to higher orders [9]. Higher terms in the
$1/m_{b}$ expansion are obtained from higher-dimensional operators in the HQE.
In these proceedings we review the calculation of the semileptonic decay rate
at leading order in $1/m_{b}$ to order $\alpha_{s}^{3}$ obtained in Ref. [10]
and report on recent progress on the extension of the calculation to inclusive
moments.

##  2 Calculation

|  |  |
---|---|---
(a) | (b) | (c)
|  |
(d) | (e) | (f)
Figure 1: Sample Feynman diagrams which contribute to the forward scattering
amplitude of a bottom quark at LO (a), NLO (b), NNLO (c) and N3LO (d-f).
Straight, curly and dashed lines represent quarks, gluons and leptons,
respectively. The weak interaction mediated by the $W$ boson is shown as a
blob.

We compute the process

$\displaystyle b(p)\to X_{c}(p_{x})l(p_{l})\overline{\nu}(p_{\nu}),$ (1)

where $X_{c}$ is a state containing charm, light quarks and gluons. The
calculation is based on the optical theorem, this means we have to compute the
imaginary part of 5-loop forward scattering diagrams. Some example diagrams
are given in Fig. 1. The total leptonic momentum is given by
$q=p_{\ell}+p_{\nu}$. For the global fits not only the total decay width but
also moments of kinematic distributions are used. In the following we will
focus on the recently proposed $q^{2}$-moments [11] which are defined by

$\displaystyle Q_{i}$ $\displaystyle=$ $\displaystyle\int{\rm
d}q^{2}(q^{2})^{i}\frac{{\rm d}\Gamma}{{\rm d}q^{2}}~{}.$ (2)

Note that $Q_{0}$ corresponds to the total decay rate $\Gamma$. Inclusively
these moments, including the total rate $\Gamma$, can be computed from the
imaginary part of the forward scattering diagrams by multiplying the
integrands of the individual Feynman diagrams with the appropriate power of
$q^{2}$ and then integrate. For global fits, moments of the total hadronic
invariant mass and the charged lepton energy have been used.

Since an analytic calculation retaining the full dependence on the charm and
bottom mass seems out of reach, we compute the diagrams in an asymptotic
expansion around

$\displaystyle\delta$ $\displaystyle=$ $\displaystyle
1-\frac{m_{c}}{m_{b}}\approx 0.7~{}.$ (3)

Although this limit seems unnatural for the physical values of the charm and
bottom quark masses it has been shown at $\mathcal{O}(\alpha_{s}^{2})$ in Ref.
[12] that this expansion converges quite fast at the physical point and can
even be extended to $\delta\to 1$. Furthermore, this limit has a couple of
technical advantages:

  * •

To calculate the asymptotic expansion we use the method of regions [13]. In
the limit $\delta\to 0$ the leptonic momentum has to be ultrasoft
$q\sim\delta\cdot m_{b}$. The number of regions to be considered is therefore
reduced.

  * •

When performing the $\delta$-expansion the leptonic system completely
factorizes and can be integrated out without any IBP reduction. In the end, we
are therefore left with 3-loop integrals, although starting from 5 loops.

The asymptotic expansion has been implemented in dedicated FORM [14] routines
and we made use of the program LIMIT [15] to implement partial fractioning and
the minimization of topologies. In the end we are left with integral families
where either all loop momenta are hard or ultrasoft. The first class of
integrals corresponds to on-shell propagator integrals which are well studied
in the literature [16, 17, 18]. The second class has recently be considered
for the relation between the kinetic and on-shell mass up to
$\mathcal{O}(\alpha_{s}^{3})$ [19, 20], Here, the relevant master integrals
are given to the necessary order in $\epsilon$ needed for the present
calculation. Due to the large expansion depth of our calculation, we aim at 8
terms of the $\delta$-expansion, huge intermediate expressions of
$\mathcal{O}(100\text{GB})$ had to be handled and $\mathcal{O}(10^{7})$ scalar
integrals with positive or negative indices up to $12$ had to be reduced. For
this task we used FIRE [21] in combination with LiteRed [22, 23].111We thank
A. Smirnov for providing a private version of Fire which was essential for the
reduction.

##  3 Results

We parametrize the total decay rate as

$\displaystyle\Gamma$ $\displaystyle=$
$\displaystyle\Gamma_{0}\left(X_{0}+C_{F}\sum\limits_{i=1}^{\infty}\left(\frac{\alpha_{s}}{\pi}\right)^{i}X_{i}\right)~{},$
(4)

with $\Gamma_{0}=A_{\rm ew}G_{F}^{2}|V_{cb}|^{2}m_{b}^{5}/(192\pi^{3})$,
$\alpha_{s}\equiv\alpha_{s}^{(5)}(\mu_{s})$,
$X_{0}=1-8\rho^{2}-12\rho^{4}\ln(\rho^{2})+8\rho^{6}-\rho^{8}$,
$\rho=m_{c}/m_{b}$ and $A_{\rm ew}=1.014$ is the leading electroweak
correction [24]. Our result for the total decay rate at
$\mathcal{O}(\alpha_{s}^{3})$ reads

$\displaystyle X_{3}$ $\displaystyle=$
$\displaystyle\delta^{5}\biggl{(}\frac{266929}{810}-\frac{5248a_{4}}{27}+\frac{2186\pi^{2}\zeta_{3}}{45}-\frac{4094\zeta_{3}}{45}-\frac{1544\zeta_{5}}{9}-\frac{656l_{2}^{4}}{81}+\frac{1336}{405}\pi^{2}l_{2}^{2}$
(5)
$\displaystyle+\frac{44888\pi^{2}l_{2}}{135}-\frac{9944\pi^{4}}{2025}-\frac{608201\pi^{2}}{2430}\biggr{)}+\delta^{6}\biggl{(}-\frac{284701}{540}+\frac{2624a_{4}}{9}-\frac{1093\pi^{2}\zeta_{3}}{15}$
$\displaystyle+\frac{391\zeta_{3}}{3}+\frac{772\zeta_{5}}{3}+\frac{328l_{2}^{4}}{27}-\frac{668}{135}\pi^{2}l_{2}^{2}-\frac{1484\pi^{2}l_{2}}{3}+\frac{4972\pi^{4}}{675}$
$\displaystyle+\frac{591641\pi^{2}}{1620}\biggr{)}+\mathcal{O}(\delta^{7}\ln^{2}(\delta))~{},$

where we specified the color factors to QCD, set $\mu_{s}=m_{b}$ and only show
the first two expansion terms. Furthermore we use the notations
$l_{2}=\ln(2)$, $a_{4}=\text{Li}_{4}(1/2)$ and $\zeta_{i}$ is Riemanns zeta
function. The full result expressed in terms of $SU(N)$ color factors and up
to $\mathcal{O}(\delta^{12})$ can be found in the ancillary file to Ref. [10].
Recently the results of three color factors up to $\mathcal{O}(\delta^{9})$
have been confirmed in Ref. [25].

Analogously, we can give the result for $Q_{1}$:

$\displaystyle Q_{1}$ $\displaystyle=$
$\displaystyle\Gamma_{0}m_{b}^{2}\left(Y_{0}+C_{F}\sum\limits_{i=1}^{\infty}\left(\frac{\alpha_{s}}{\pi}\right)^{i}Y_{i}\right)$
(6)

with
$Y_{0}=3/10(1-\rho^{10})-9/2(1-\rho^{6})\rho^{2}-24(1-\rho^{2})\rho^{4}-18(1+\rho^{2})\rho^{4}\ln(\rho^{2})$.
Our result for the $\mathcal{O}(\alpha_{s}^{3})$ correction reads:

$\displaystyle Y_{3}$ $\displaystyle=$
$\displaystyle\delta^{7}\biggl{(}-\frac{52480a_{4}}{567}+\frac{4372\pi^{2}\zeta_{3}}{189}-\frac{8188\zeta_{3}}{189}-\frac{15440\zeta_{5}}{189}-\frac{6560l_{2}^{4}}{1701}+\frac{2672\pi^{2}l_{2}^{2}}{1701}$
(7)
$\displaystyle+\frac{89776\pi^{2}l_{2}}{567}-\frac{19888\pi^{4}}{8505}-\frac{608201\pi^{2}}{5103}+\frac{266929}{1701}\biggr{)}+\delta^{8}\biggl{(}\frac{26240a_{4}}{189}-\frac{2186\pi^{2}\zeta_{3}}{63}$
$\displaystyle+\frac{3910\zeta_{3}}{63}+\frac{7720\zeta_{5}}{63}+\frac{3280l_{2}^{4}}{567}-\frac{1336}{567}\pi^{2}l_{2}^{2}-\frac{2120\pi^{2}l_{2}}{9}+\frac{9944\pi^{4}}{2835}+\frac{591641\pi^{2}}{3402}$
$\displaystyle-\frac{284701}{1134}\biggr{)}+\mathcal{O}(\delta^{9}\ln^{2}(\delta))~{}.$

Since the leptonic momentum $q$ has to be ultrasoft, i.e. $q\sim\delta\cdot
m_{b}$, the $n$-th $q^{2}$ moment is suppressed by $2n$ additional powers of
$\delta$ as compared to the leading $\delta^{5}$ term in Eq. 5.

The convergence of the $\delta$-expansion is studied in Fig. 2. For both, the
total rate $\Gamma$ and the first $q^{2}$ moment $Q_{1}$, one observes that
the convergence at the physical point $\rho\sim 0.28$ is fast and does not
vary much starting from order $\delta^{9}$ for the total decay rate and
$\delta^{11}$ for $Q_{1}$. Also at $\rho\to 0$ one sees a convergence for the
high expansion terms, although much slower than at the physical point. We get:

$\displaystyle X_{3}(\rho=0.28)$ $\displaystyle=-68.4\pm 0.3~{},$
$\displaystyle Y_{3}(\rho=0.28)$ $\displaystyle=-14.41\pm 0.03~{}.$ (8)

The uncertainty due to the truncation of the series has been determined from
the difference of the last two expansion orders including a safety factor of
$5$. At 2-loop order this approach leads to a conservative error
approximation.

Using the on-shell masses $m_{c}=1.3\,\text{GeV}$ and $m_{b}=4.7\,\text{GeV}$
and setting the renormalization scale $\mu_{s}=m_{b}$, we find

$\displaystyle\Gamma(m_{b},m_{c})$ $\displaystyle=$
$\displaystyle\Gamma_{0}X_{0}\left[1-1.72\frac{\alpha_{s}}{\pi}-13.09\left(\frac{\alpha_{s}}{\pi}\right)^{2}-162.82\left(\frac{\alpha_{s}}{\pi}\right)^{3}\right]~{},$
(9) $\displaystyle Q_{1}(m_{b},m_{c})$ $\displaystyle=$
$\displaystyle\Gamma_{0}m_{b}^{2}Y_{0}\left[1-1.61\frac{\alpha_{s}}{\pi}-12.83\left(\frac{\alpha_{s}}{\pi}\right)^{2}-168.34\left(\frac{\alpha_{s}}{\pi}\right)^{3}\right]~{}.$
(10)

As expected we find a bad convergence of the perturbative series using the on-
shell scheme for the quark masses. To mitigate this problem various so-called
threshold masses have been proposed. We want to focus on the scheme used for
the latest extraction of $|V_{cb}|$. Here, the bottom mass is expressed in the
kinetic scheme, while the charm quark is expressed in the $\overline{\rm MS}$
scheme at the scale $\mu_{c}=3\,\text{GeV}$. With the input values
$m_{b}^{\text{kin}}=4.526\,\text{GeV}$ and
$\overline{m}_{c}(3\,\text{GeV})=0.993\,\text{GeV}$, we find

$\displaystyle\Gamma(m_{b}^{\text{kin}},\overline{m}_{c}(3\,\text{GeV}))$
$\displaystyle=$
$\displaystyle\Gamma_{0}X_{0}\left[1-1.67\frac{\alpha_{s}^{(4)}}{\pi}-7.25\left(\frac{\alpha_{s}^{(4)}}{\pi}\right)^{2}-28.6\left(\frac{\alpha_{s}^{(4)}}{\pi}\right)^{3}\right]~{},$
(11) $\displaystyle Q_{1}(m_{b}^{\text{kin}},\overline{m}_{c}(3\,\text{GeV}))$
$\displaystyle=$
$\displaystyle\Gamma_{0}Y_{0}\left(m_{b}^{\text{kin}}\right)^{2}\left[1-1.83\frac{\alpha_{s}^{(4)}}{\pi}-8.45\left(\frac{\alpha_{s}^{(4)}}{\pi}\right)^{2}-34.7\left(\frac{\alpha_{s}^{(4)}}{\pi}\right)^{3}\right]~{},$

where $\mu_{s}=m_{b}^{\text{kin}}$ is used. Note that the conversion to the
kinetic scheme also contains the renormalization of the HQET parameters
$\mu_{\pi}$ and $\rho_{D}$, which formally only enter at order $1/m_{b}^{2}$
and $1/m_{b}^{3}$ respectively. The scale dependence of the two quantities can
be studied in Fig. 3. One observes a much better behavior of the perturbative
series and a reduced dependence on the renormalization scale.

The results for the total cross section together with the improvement of the
relation between the on-shell and kinetic mass to
$\mathcal{O}(\alpha_{s}^{3})$ have recently been used to update the inclusive
determination of $|V_{cb}|$ [5]

$\displaystyle|V_{cb}|=42.16(30)_{th}(32)_{exp}(25)_{\Gamma}\times
10^{-3}~{}.$ (13)

The inclusion of the higher order calculations resulted in a small shift of
the central value and a reduced theory uncertainty. Especially the uncertainty
due to the width $\Gamma$ was halved.

Figure 2: The $\mathcal{O}(\alpha_{s}^{3})$ contribution to the total decay
rate $b\to s\ell\overline{\nu}$ (left) and its first $q^{2}$-moment (right)
for different expansions depths in $\delta$.

The heavy daughter limit allows us also to estimate the $O(\alpha_{s}^{3})$
correction to the $b\to u\ell\overline{\nu}_{\ell}$ decay by setting
$\delta\to 1$:

$X_{3}^{u}=-202\pm 20,$ (14)

where the relative 10% uncertainty is estimated for unknown higher $\delta$
terms in the expansion. We can study the convergence of the perturbative
series also in this case. We use the exact one and two loop results in the
massless limit from Ref. [26] and the three loop correction estimated above to
derive the total rate for $b\to u\ell\overline{\nu}_{\ell}$

$\Gamma_{b\to u}(m_{b}^{\mathrm{kin}},\overline{m}_{c}(3\text{
GeV}))=\Gamma_{0}X_{0}\Bigg{[}1-0.27\frac{\alpha_{s}^{(4)}}{\pi}+4.0\left(\frac{\alpha_{s}^{(4)}}{\pi}\right)^{2}+95.4\left(\frac{\alpha_{s}^{(4)}}{\pi}\right)^{3}\Bigg{]}~{}.$
(15)

We observe an apparent worse behavior of the $\alpha_{s}$ expansion compared
to $b\to c$. Note that the result depends in this case also on the Weak-
Annihilation scale entering in the Wilson coefficient of $\rho_{D}$ at order
$1/m_{b}^{3}$. We set $\mu_{\mathrm{WA}}=m_{b}^{\mathrm{kin}}/2$.

If we specify the color factors to QED and set $\delta=1-m_{e}/m_{\mu}\approx
0.005$ we obtain a prediction for the muon lifetime $\tau_{\mu}$ via

$\displaystyle\frac{1}{\tau_{\mu}}\equiv\Gamma(\mu^{-}\to
e^{-}\nu_{\mu}\overline{\nu}_{e})=\frac{G_{F}^{2}m_{\mu}^{5}}{192\pi^{3}}(1+\Delta
q).$ (16)

Precise measurements of the muon lifetime together with accurate QED
predictions therefore allow the extraction of the Fermi constant $G_{F}$. The
various correction terms, see for example Ref. [27] for a review, are usually
parametrized via

$\displaystyle\Delta q=\sum\limits_{i\geq 0}\Delta q^{(i)}.$ (17)

We find for the QED corrections

$\displaystyle\Delta
q^{(3)}\approx\left(\frac{\alpha(m_{\mu})}{\pi}\right)^{3}\left(-15.3\pm
2.3\right)~{},$ (18)

where the error is estimated from the convergence properties at 1- and 2-loop
order for which exact calculations are available [28, 29, 30]. This translates
to a shift in the muon lifetime of
$\Delta\tau_{\mu}\approx(-9\pm 1)\times 10^{-8}\,\text{$\mu$s}$. Comparing
this with the current experimental value given by
$\tau_{\mu}=(2.1969811\pm 0.0000022)\,\text{$\mu$s}$ [31], we see that the new
corrections are two orders of magnitude smaller than the current experimental
uncertainty. A new extraction of the Fermi constants therefore needs an
improvement of the experimental data.

Figure 3: The dependence on $\mu_{s}$ of the total rate $\Gamma$ (left) and
the first $q^{2}$-moment $Q_{1}$ (right) for different orders in the strong
coupling constants with the bottom quark expressed in the kinetic scheme and
the charm mass in the $\overline{\text{MS}}$ scheme. The scale of the charm
quark is set to $\mu_{c}=3\,\text{GeV}$.

##  4 Conclusions

In these proceedings we reviewed the calculation of the
$\mathcal{O}(\alpha_{s}^{3})$ corrections to the process $b\to
c\ell\overline{\nu}$ retaining finite charm quark effects through an expansion
around the equal mass case obtained in Ref. [10]. Furthermore, we showed an
extension of our method to inclusive $q^{2}$ moments, which can be used to
further constrain the global fits from which also $|V_{cb}|$ is extracted. We
showed that the expansions converge fast at the physical point and can even be
extended down to $\delta\to 1$. Although we find a badly converging prediction
using the on-shell masses for charm and bottom, the predictions are improved
by changing into the kinetic scheme for the bottom quark. Since the knowledge
of other moments, like moments of the lepton energy or the hadronic mass, is
desireable for the global fits we plan to extend our calculation. After
specifying our results to QED we also obtain $\mathcal{O}(\alpha^{3})$
predictions for the muon decay.

## Acknowledgements

I thank Matteo Fael and Matthias Steinhauser for their collaboration on the
presented work. This research was supported by the Deutsche
Forschungsgemeinschaft (DFG, German ResearchFoundation) under grant 396021762
— TRR 257 “Particle Physics Phenomenology after theHiggs Discovery”.

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# Ferroelectricity induced by the absorption of water molecules on double
helix SnIP

Dan Liu1 Corresponding author. E-mail<EMAIL_ADDRESS>Ran Wei1 Lin Han1
Chen Zhu1 and Shuai Dong1
1School of Physics, Southeast University, Nanjing 211189, China

###### Abstract

We study the ferroelectricity in a one-dimensional system composed of a double
helix SnIP with absorbing water molecules. Our $\it{ab~{}initio}$ calculations
reveal two factors that are critical to the electrical polarization. The first
one is the orientation of polarized water molecules staying in the R2 region
of SnIP. The second one is the displacement of I atom which roots from subtle
interaction with absorbed water molecules. A reasonable scenario of
polarization flipping is proposed in this study. In the scenario, the water
molecule is rolling-up with keeping the magnitude of its electrical dipole and
changing its direction, meanwhile, the displacement of I atoms is also
reversed. Highly tunable polarization can be achieved by applying strain, with
$26.5\%$ of polarization enhancement by applying tensile strain, with only
$4\%$ degradation is observed with $4\%$ compressive strain. Finally, the
direct band gap is also found to be correlated with strain.

Keywords: ferroelectricity, 1D double helix, electrical polarization, DFT

PACS: 77.80.-e, 77.84.-s, 73.22.-f

##  1 Introduction

Since the first experimental discovery of ferroelectricity in Rochelle salt
[1], in the past hundred years, for the perspective of application in sensors,
actuators and memories, a wide range of ferroelectric (FE) materials have been
intensively studied, such as the well known three dimensional (3D) BaTiO3 [2].
Interest in new, low-dimensional ferroelectrics has also been growing rapidly
due to their potential applications in electronics, such as recently emerged
ferroelectric two-dimensional (2D) layered structures including group-VI
monochalcogenides, In2Se3, CuInP2S6, etc [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16]. Besides these intrinsic 2D FE materials, ferroelectricity can be
also induced in non-FE 2D system through doping, manipulating defects and also
fabricating heterojunctions. For example, the hydroxyl-decorated graphene
systems exhibit a robust ferroelectricity [17, 18, 19]. The increasing demand
in high density in electronic device requests the further miniaturization of
FE materials. One method is to cut a one-dimensional (1D) nanoribbon from the
traditional 3D or 2D FE materials. However, there are two obvious drawbacks of
these 1D nanoribbons. One is the size of such nanoribbon is quite large. For
example, graphene nanoribbons fabricated by etching graphene using high-
resolution electron beam lithography range from 10 nm to 100 nm [20]. This
size is much larger than typical 1D structures, such as the (10, 10) carbon
nanotube (CNT) of which the diameter is only about 1.3 nm [21]. So these
nanoribbons can not be categorized as real 1D ferroelectricity, and thus the
reduction effect in electronic device size using these FE nanoribbons is
limited. The second concern is about the stability of these nanoribbons, while
cutting from their 3D or 2D parent compounds. The atoms staying on the edge
are electrical unsaturated, which will result in a structural distortion and
accordingly the FE behavior of these nanoribbons. In general, the optimum
method to reduce the size and increase the density of electronic devices
should be seeking real 1D ferroelectricity in atomic scale. Despite abundant
1D structures that have been explored since the successful synthesis of CNT
[22], intrinsic 1D FE materials are rarely found [23, 24, 25]. In analogy with
decorating graphene using hydroxyl to introduce electrical polarization, a
similar effect may be expecting in existed 1D structures through doping of
polarized molecules.

Fig. 1. Atomic structure of (a) 1D double-helix SnIP, (b) four configurations
of one water molecule attaching on region R1 of SnIP highlighted by
transparent blue area, on region R2 highlighted by red transparent red area.
Black dashed arrow represents the vector of unit cell.

Water molecule is a very common polarized molecule around us. However, little
attention has been focused on the ferroelectricity of water to date, because
it is not easy to make water molecules form a well-organized arrangement. To
solve the problem, we need to find an appropriate way to enforce water
molecules to form an expected arrangement. Previous study reported a unique
structure of quasi-1D water molecules confined in a 3D supramolecular
architecture. When the water molecules are frozen into special forms, this
quasi-1D water wire becomes ferroelectric [26]. In this study, we investigate
the electric polarization in 1D double-helix SnIP [36, 28] with absorption of
water molecules. Our density functional theory (DFT) calculations reveal that
there are two regions R1 and R2 in SnIP to anchor water molecules. And for
each region, there are also two energetic degenerate configurations holding
promise of the reversal of water molecule. We find that there are two factors
contributing to the emergence of ferroelectricity in the system. One is the
orientation of the polarized water molecules, the other is the displacement of
ions in SnIP originating from the interaction between water molecules and
SnIP. While flipping the orientation of water molecules from one degenerate
configuration to the other, the displacement of ions of SnIP will also be
reversed, which leads to the reversal of an entire electrical dipole. The
magnitude of polarization can be tuned mainly through applying tensile strain
along the axis of SnIP, while almost remaining constant under compressive
strain. The band gap of the system, remaining to be direct, can be tuned by
the axial strain as well.

##  2 Theoretical method

Our calculations of the stability, equilibrium structure, polarization and
energy changes during structural transformations have been performed using the
density functional theory (DFT) as implemented in SIESTA code [29]. The 1D
systems have been represented using periodic boundary conditions and separated
by 20Å. We have used the nonlocal Perdew-Burke-Ernzerhof (PBE) [30] and Local-
Density-Approximation (LDA) [42] exchange-correlation functional, norm-
conserving Troullie-Martins pseudopotentials [31], and a local numerical
double-$\zeta$ basis including polarization orbitals. The Brillouin zone of
periodic structures has been sampled by a fine grid of 1$\times$1$\times$12
k-points for 1D structures [32]. We find the basis, k-point grid, and mesh
cutoff energy of 180 Ry used in the Fourier representation of the self-
consistent charge density to be fully converged, providing us with a precision
in total energy of 2 meV/atom. Geometries have been optimized using the
conjugate gradient (CG) method [33], until none of the residual Hellmann-
Feynman forces exceeded $10^{-2}$ eV/Å. For the phonon spectrum calculation,
we use a much smaller force tolerance of $10^{-3}$ eV/Å to get the optimized
structure. The polarization is calculated using Berry phase method [34, 35].

##  3 Results and Discussion

Fig. 2. Atomic structure of (a) (H2O)7@SnIP with 7 H2O attaching on SnIP, (b)
stretched SnIP with the same unit cell size of (H2O)7@SnIP in (a). (c) Phonon
spectrum of (H2O)7@SnIP. The red arrow with solid line represent the shift of
the atoms transforming the stretched SnIP in (b) to SnIP in (H2O)7@SnIP of
(a).

### Atomic structure of 1D double-helix SnIP and water@SnIP

The bunch of SnIP has been synthesized successfully in experiment [36]. The
single rod of double-helix SnIP is composed of the inner Phosphorus (P) helix
and the outer Tin(Sn)-Iodine(I) helix, which contains seven P, Sn and I atoms
in one primitive unit cell. The double helix of SnIP can be either right-
handed or left-handed with the same energetic stability. Here, we focus on the
right-handed SnIP to study the electrical polarization, since the left-handed
SnIP will possess the same FE properties as the right-handed one. Our DFT
calculation indicates the lattice constant of $\vec{a}$ as shown in Fig. 1(a)
is 8.12 Å which is slightly larger than the experimentally observed value of
bunched SnIP by 0.19 Å [36]. Considering the interaction between each rod in
the bunch will reduce the length along $\vec{a}$, our calculation result is
quite reliable. We analyze the Mulliken population of each atom of SnIP, and
find that Sn carries 0.45 positive charges while P and I get 0.22 and 0.23
more electrons respectively. This result clearly shows SnIP is an ionic
compound, and it could be a potential candidate of FE materials. However the
space group of $P2$ of SnIP shows a $180^{\circ}$ rotation symmetry in the
direction along the axis perpendicular to the helix, which prohibits the
polarization in this pristine system. Further modification of the structure is
needed to induce ferroelectricity.

Fig. 3. Electronic band structure ($E_{k}$) and density of states (DOS)
including its projection on individual atoms (left panels) for (a) optimum 1D
double-helix SnIP, (b) (H2O)7@SnIP. (c) Illustration of flipping
ferroelectricity of (H2O)7@SnIP, FE(+) sate and FE(-) state are energetic
eigenvalue states with opposite polarization direction. PE state is the
intermediate paraelectric state. (d) The change of energy and polarization in
the process of transformation from FE(+) to FE(-) state.

An in-depth analysis of the double-helix SnIP reveals that for the outer helix
SnI, there are two types of regions namely $R1$ and $R2$, which are
highlighted by blue and red shadows respectively in Fig. 1(b). In one
primitive unit cell of SnIP, there are seven alternatively arranged $R1$ and
$R2$ regions. For each region, it is surrounded by two Sn atoms and two I
atoms. $R1$ is enclosed by I1-Sn1-I2-Sn2, and $R2$ is enclosed by
Sn2-I2-Sn3-I3. In $R1$, the distance $d$ between two I atoms $d$(I1-I2)=4.92
Å, and $d$ between two Sn atoms $d$(Sn1-Sn2)=5.41 Å, while in $R2$,
$d$(I3-I2)=5.81 Å and $d$(Sn3-Sn2)=4.42 Å. These two different regions offer
two different potential spaces. Then we investigate the absorption of water
molecules on the surface of the outer helix SnI. We first put one water
molecule in $R1$ and $R2$ to see which region the water molecule prefers to
stay. When water molecules are absorbed in $R1$ or $R2$, the two hydrogen (H)
atoms of water molecule are attracted by two I atoms, and the oxygen (O) atom
tilts to one of the two Sn atoms. In other words, $R1$ and $R2$ provide a
double-well potential for water molecules. As a result, there are two
configurations for one water molecule attached in $R1$ or $R2$, labeled by
$R1-1$, $R1-2$, $R2-1$ and $R2-2$ shown in Fig. 1(b). Our DFT-PBE calculations
indicate that the cohesive energy of ${\Delta}E_{PBE}(R1-1)=275$ meV,
${\Delta}E_{PBE}(R1-2)=277$ meV, ${\Delta}E_{PBE}(R2-1)=298$ meV and
${\Delta}E_{PBE}(R2-2)=299$ meV. Taking the DFT calculation error of energy
into consideration, we can conclude that the configuration of $R1-1$ is as
energetically stable as $R1-2$ and $R2-1$ is as energetically stable as
$R2-2$. Considering SIESTA uses pseudo-atomic-orbital basis sets, the cohesive
energy will be overestimated due to the basis set superposition error (BSSE).
We have done correction calculations for BSSE (BSSEc), and find that
${\Delta}E_{PBE-BSSEc}(R2)=150$ meV and ${\Delta}E_{PBE-BSSEc}(R1)=135$ meV.
We also use DFT-LDA to calculate the cohesive energy with BSSE correction
taken in account, and find that ${\Delta}E_{LDA-BSSEc}(R2)=426$ meV and
${\Delta}E_{LDA-BSSEc}(R1)=398$ meV. Both the results of DFT-PBE and DFT-LDA
show that the configuration of water molecule staying in $R2$ is more stable
than in $R1$. From previous works [40, 41], we should claim here that the real
cohesive energy of ${\Delta}E(R2)$ should be between 150 meV and 426 meV. The
mulliken charge analysis of configurations in $R2$ shows a charge transfer
from water molecule to SnIP with $0.03$ e.

Then we investigate two molecules absorbed in two neighboring $R2$ regions of
SnIP separately. We find that the two water molecules aligning in the same
direction are more stable than aligning in the opposite direction by 34 meV.
Next, we focus on the water molecules aligning in the same direction while
staying on SnIP. As mentioned above, in one primitive unit cell of SnIP, there
are seven $R2$ regions available for water molecules to stay. We assume the
simplest case that each $R2$ region only absorbs one water molecule. The
formed chemical formula is written as (H2O)7@SnIP as the atomic structure
shown in Fig. 2(a). The cohesive energy of absorbing seven water molecules in
$R2$ regions in one unit cell is ${\Delta}E(R2)=295$ meV. The cohesive energy
${\Delta}E(R2)$ is stronger than a typical van der Waals interaction, which
not only locks the molecule in a specific orientation, but also results in the
distortion in atomic structure of SnIP. After absorbing seven water molecules
in one unit cell, the system is elongated by $4.4\%$. The dynamic stability of
(H2O)7@SnIP is confirmed by the phonon spectrum shown in Fig. 2(c).

Fig. 4. (a) Band gap value $E_{g}$ and the polarization as function of the
axial strain. (b) The change of energy in the process of transformation from
FE(+) to FE(-) state with axial strain of $-4\%$, $0\%$ and $+4\%$.

### Band structure and ferroelectric behavior of (H2O)7@SnIP

The isolated SnIP is a semiconductor with a direct band gap of $1.32$ eV at
$Z$-point shown in Fig. 3(a). We should claim here that the bandgap is
underestimated by DFT-PBE calculation, but still provides useful insights into
the trend in the electronic structures. For (H2O)7@SnIP, a direct band gap of
$1.48$ eV at $Z$-point is shown in Fig. 3(b). The dispersion relation at the
top of valence bands and bottom of conduction bands is similar for both
systems, which may come from SnIP but not water molecule. This is confirmed by
the partial density of state in Fig. 3(a) and (b), where we can see that the
contribution from water is almost zero in the energy range from $-2$ eV to $2$
eV. So while the SnIP is stretched after absorbing water molecules, the
orbital hopping of SnIP is reduced, which results in an increase of bandgap by
$0.16$ eV.

To study the ferroelectricity, we first analyze the detailed shift of each
atoms of the system. After combining water molecules and SnIP, besides the
oriented arrangement of water molecules and the stretch of SnIP resulted by
the interaction, there is also a local displacement of atoms. We compare the
atomic structure of SnIP in (H2O)7@SnIP with the isolated SnIP stretched by
$4.4\%$. We find an obvious displacement of I atoms by $0.3$ Å along the axis
direction, while the displacement of Sn and P atoms can be ignored. The
illustration of the shift of I atoms is represented by the red arrow in Fig.
2(a). Besides the displacement of I atoms along the axis direction, there is
also a slight shift of I atoms in the plane perpendicular with the axis. These
distortions of atomic structure make the space group $P2$ of pristine SnIP
change to space group $P1$ of SnIP in (H2O)7@SnIP.

The ferroelectricity of the system can be divided into two main parts. The
first one is the arrangement of the dipole of water molecules. Since the H2O
is an ionic molecule, the polarization of water molecule $P$(H2O) can be
defined as the charge of O ion times the distance between the center of
positive and negative charge. Since the center of positive and negative charge
is overlapped in the pristine SnIP, there is no net polarization. After
absorbing the water molecules, we see the displacement of I ion carrying
$0.22$ negative charges, then $P(SnIP)$ is defined as the charge of I ion
times the shift of I ion. $P_{Z}$ is the decomposition of $P$ in the Z
direction. In the DFT calculation, we usually use berry phase method installed
in the software to calculate the polarization directly. From Fig. 2(a), we see
the component of water dipole along axis $P_{Z}$(H2O) is in the negative
$Z$-direction, and the shift of I atoms in the negative $Z$-direction results
in an electric dipole $P_{Z}$(SnIP) in the positive $Z$-direction. If we do
not consider the charge redistribution between atoms caused by absorbing water
molecule on SnIP, the total net electric polarization $P_{Z}$ should be the
difference between $P_{Z}$(SnIP) and $P_{Z}$(H2O). We first separate the 1D
water wire and the SnIP, and then calculate $P_{Z}$. We find that
$P_{Z}$(H2O)=$3.61\times 10^{-8}$ pC and $P_{Z}$(SnIP)=$6.53\times 10^{-8}$ pC
respectively, so $P_{Z}=2.92\times 10^{-8}$ pC. However, the charge
redistribution can not be neglected, and it will modify $P_{Z}$(H2O) and
$P_{Z}$(SnIP). We study the charge $Q$ of atoms before and after absorbing
water molecules on SnIP. $Q$(O) decrease from -0.78 to -0.73, $Q$(H) of half
of H atoms decrease from 0.39 to 0.36, while the charge of other half keeps
the same, the decrease of charges of H and O results in the decrease of
electric dipole of the water molecule. Instead, $Q$(Sn) increases from 0.45 to
0.47 and $Q$(I) increases from -0.23 to -0.27, which makes an increase of
dipole moment of SnIP. As a result, the increase of $P_{Z}$(SnIP) and the
decrease of $P_{Z}$(H2O) lead to a larger $P_{Z}$ than $2.92\times 10^{-8}$
pC. In order to get a reliable result, we use the standard Berry phase method
and get $P_{Z}=4.98\times 10^{-8}$ pC, which confirms the effect of charge
redistribution on the polarization. This electrical polarization of
(H2O)7@SnIP is comparable with the value in BaTiO3 of $3.2\times 10^{-8}$ pC
[37]. Besides the shift along the axial direction, I atoms also shift in the
plane perpendicular to the axis, however these shift are so small that the
resulted polarization is negligible.

Fig. 5. (a) Band structure $E_{k}$ of (H2O)7@SnIP under axial strain. The top
valence band is marked by red dashed line and the bottom conduction band is
marked by blue dashed line. (b) Charge density associated with valence state
$\rho_{vc}$ and conduction state $\rho_{cc}$ of optimum (H2O)7@SnIP is present
in the up and bottom panel respectively. The energy range associated with
$\rho_{vc}$ is indicated by the red transparent region in the band structure
of optimum (H2O)7@SnIP extends from $E_{F}-0.94<E<E_{F}$, and the energy range
associated with $\rho_{cc}$ is indicated by the blue transparent region in the
band structure of optimum (H2O)7@SnIP extends from $E_{F}<E<E_{F}+0.94$. The
isosurface values of $\rho_{vc}$ and $\rho_{cc}$ are $1{\times}10^{-3}$e/Å3
and $0.5{\times}10^{-3}$e/Å3.

While applying an external electric field in the opposite direction with the
polarization of a FE material, the polarization can be turned over by
$180^{\circ}$. In the process of flipping the polarization, the system starts
from the initial FE state FE(+), goes through a PE phase in which there is no
net polarization, and arrives at the final FE state FE(-). FE(-) has an
opposite polarization but the same energetic stability as FE(+). In the
traditional 3D or 2D FE materials like BaTiO3, the PE phase is typically
around the midpoint of a linear combination of the FE(+) and FE(-). However,
in the PE phase acquired through this way in our system, the bond angle of
H-O-H in the water molecule is around $180^{\circ}$, far from the optimum bond
angle. As expected, the energy of PE phase is much higher than FE phase by
4.65 eV/H2O, which means the PE phase obtained through linear combination is
not acceptable.

We propose here another reasonable scenario of flipping the electrical
polarization as shown in Fig. 3(c). In this scenario, the water molecule is
rolling-over while keeping the dipole constant, but changing the direction. In
the PE phase, the dipole of water molecule lies in the radial direction of the
double helix. In other words, there is no decomposition of dipole of water in
the axis direction. In the process of rolling-over of water molecules, due to
the interaction between water molecule and SnIP, the atomic structure of SnIP
is also changing. In the PE phase, the shift of I atoms and also the
associated polarization disappears. As a result of vanishing of the
polarization of water molecule and SnIP, there is no net polarization of the
whole system in the axis direction. As mentioned above, we know the adjacent
water molecules staying in R2 regions prefer to align in the same direction.
In the process of transformation from FE(+) to FE(-), once one water molecule
starts to turn over, the other neighboring water molecules will follow to turn
over. In other words, the seven water molecules flip collectively in the
transformation process. The changes of energy and net polarization along the
axis in the process of flipping the polarization are shown in Fig. 3(d). The
energy barrier is about 140 meV/H2O which is about thirty-three times smaller
than that of the linear combination scenario.

### Strain effect on Ferroelectricity and band structure

We also study the response of ferroelectricity and band structure to the axial
strain to explore the perspective of the materials in application. The
response of $P_{Z}$ to the tensile strain is more obvious than the compressive
strain. From red dashed line in Fig. 4(a), we see $P_{Z}$ increases
significantly by $26.3\%$ with $4\%$ stretch strain, but decreases very
slightly by $4.4\%$ with $4\%$ compress strain. The band gap $E_{g}$ of the
system is also decreased to $1.49$ eV with the $4\%$ axial compression and
increased to $1.63$ eV with $4\%$ axial stretching. The effect of strain on
the band gap is shown with blue dotted line in Fig. 3(c). The deformation
energy ${\Delta}E$ with strain of $4\%$ is about 70 meV, which means this
double-helix can be deformed easily by applying an axial stress. The energy
barrier ${\Delta}E$ in the process of transformation from FE(+) to FE(-) is
also affected by the strain. As shown in Fig. 4(b), from $4\%$ compressive
strain to $4\%$ tensile strain, ${\Delta}E$ is increased from 112 meV/H2O to
177 meV/H2O.

The change of the band gap with applying strain may come from the change of
band width. In order to explore the physics behind, we calculate the band
structures of (H2O)7@SnIP with different stress conditions as shown in Fig.
5(a). Comparing with the band structure of the system without strain, we find
the top valence band highlighted by the red dashed line almost remains
unchanged. The width of bottom conduction band highlighted by blue dashed line
changes but still keeps the dispersion relation. In Fig. 5(b), the energy
range between $E_{F}$ and 0.2 eV below the top of valence band indicated by
the red region, and the 0.2 eV above the bottom of conduction band indicated
by the blue region, are used to identify the valence and conduction frontier
states. We characterize the charge density associated with valence frontier
state $\rho_{vc}$ and conduction frontier state $\rho_{cc}$ in the lower panel
of Fig. 5(b). The valence frontier states encircled by red dashed line is
mainly occupied by the lone pair orbital of Sn and $p_{z}$ orbital of P. The
conduction frontier states encircled by blue dashed line contain the overlap
of orbital of one P atom and two nearest-neighboring Sn atoms. While applying
strain on the system, the distances between atoms are changed. Since the
valence frontier state has little relation with overlap of orbital of atoms,
there should be little change of the top valence band. However, the change of
distance affects the overlap of orbital between P and Sn atoms, so we see the
change of conduction band. While stretching the system, the distance between
two nearest-neighbor Sn atoms is enlarged from $4.54$ Å to $4.61$ Å, and the
distance between P atom and its nearest-neighbor Sn atom is enlarged from
$3.46$ Å to $3.56$ Å. As a result, the overlap between orbital and the
resulted width of conduction band is decreased, and vice versa for the
compressive strain.

### Discussion

When we study the ferroelectric behavior, band structures and their response
of axial strain in 1D (H2O)7@SnIP, one basic question may arise. Is SnIP
hydrophilic or hydrophobic and could SnIP attract water molecule from a water
cluster? The answer is determined by the competition between the absorption
energy of water molecule on SnIP and the interaction between water molecules
in water cluster. There are many configurations of water clusters, such as the
well known water dimmer. Using PBE-BSSEc, we calculate the interaction between
water molecules $E_{PBE-BSSEc}$ in the dimmer configurations. It ranges from
$46$ meV to $246$ meV. In our system, the interaction energy between water and
SnIP is about $150$ meV, which holds a great promise for water molecule to
stay.

Usually, for a semiconductor, while using strain to improve one physical
property, other properties will be degraded. In this study, we find that the
modification of polarization by axial strain is very prominent, while the
effect of strain on band structure including the dispersion relation and band
gap is negligible. So with strain, the polarization is changed while other
physical properties are intact. Besides the strain along axis direction, the
other common strain occurs frequently in 1D system is bending. In theoretical
models of DFT calculation, it will contain too many atoms to study the bending
effect on physical properties. However, we can analysis the bending effect
qualitatively through the studying effect of axial tensile/compressive strain.
The diameter of 1D (H2O)7@SnIP is about $8.2$ Å, which is the same as (6,6)
carbon nanotube. When applying the bending strain, the outer part of this 1D
double-helix is stretched and the inner part is compressed. If we consider the
bending 1D tube as a part of a circle, then the extent of stretch of the outer
part is the same with the extent of compression of the inner part. From Fig.
3(c), the response of polarization to tensile strain is much more significant
than the response to compressive strain. As a result, we can conclude that the
polarization will also be increased by bending the 1D (H2O)7@SnIP.

The special atomic structure of SnIP makes it to be a promising candidate to
explore ferroelectricity in 1D. Here we use water molecule to introduce
electrical polarization in SnIP. The double potential well in $R2$ of SnIP
enforces the water molecule to arrange in a special orientation. We can use
other polarized molecules to replace water molecules, and it will have similar
results. In addition, we can use transition metal atoms to dope SnIP. With
appropriate choice of transition metal element, the atoms will stay in one of
the double-potential wells of SnIP to generate the ferroelectricity. Besides,
the doping of transition metal element will also bring magnetism to the 1D
system.

##  4 Conclusion

In conclusion, we have identified ferroelectricity induced in 1D direct-gap
semiconductor (H2O)7@SnIP through absorbing water molecule in SnIP. Our
$\it{ab~{}initio}$ DFT calculations indicate that there are two double-
potential well regions $R1$ and $R2$ of SnIP for water molecule to stay, and
water molecule prefer to attach in $R2$. The water molecules are arranged in a
special orientation due to the double-potential well of $R2$. On the other
hand, the interaction between water molecule and SnIP will lead to the
distortion of the atomic structure of SnIP and also a charge redistribution
between atoms. Comparing with the pristine SnIP with space group of $P2$,
(H2O)7@SnIP with space group of $P1$ loses the $180^{\circ}$ rotation
symmetry. For polarization flipping mechanism, we propose a scenario in which
the water molecules rotate while keeping the magnitude of the dipole but
changing the direction. The rotation of water molecule also leads to the
deformation of atomic structure of SnIP. When the dipole of water molecule
lies in the radial direction, SnIP is transformed back to the phase with space
group of P2. As a result, the net polarization along the axis direction
disappears. The effect of external axial strain on polarization is quite
remarkable, with 4$\%$ stretching, the polarization is enhanced by about
26$\%$. However the response of $E_{g}$ of the band structure to the axial
strain is not significant, since only the bottom of conduction band, instead
of top of the valence band, correlates with orbital overlap of atoms.

## Acknowledgment

D. Liu, R. Wei and L. Han acknowledges financial support by the Natural
Science Foundation of the Jiangsu Province Grant No. BK20210198. S. Dong
acknowledge financial support by the National Natural Science Foundation of
China (NNSFC) Grant No. 11834002. Computational resources for most
calculations have been provided by the Michigan State University High
Performance Computing Center.

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## Collaborative Design for Job-Seekers with Autism:
A Conceptual Framework for Future Research

Sungsoo Ray Hong†, Marcos Zampieri†, Brittany N. Hand‡, Vivian Motti†, Dongjun
Chung‡, and Ozlem Uzuner† 111 Dr. Sungsoo Ray Hong is an Assistant Professor
in Information Sciences & Technology at George Mason University. He
specializes in Human-Computer Interaction (HCI) and Computer-Supported
Cooperative Work (CSCW<EMAIL_ADDRESS>http://www.rayhong.net/). Dr. Marcos
Zampieri is an Assistant Professor in Information Sciences & Technology at
George Mason University. His domain of research is computational linguistics
and Natural Language Processing<EMAIL_ADDRESS>https://www.gmu.edu/profiles/mzampier). Dr. Brittany N. Hand is an Associate
Professor in Health Outcomes and Injury Prevention Sciences at the Ohio State
University. Her expertise includes health services and primary care for
autistic adults<EMAIL_ADDRESS>https://hrs.osu.edu/faculty-and-
staff/faculty-directory/hand-brittany). Dr. Vivian Motti is an Associate
Professor in Information Sciences & Technology at George Mason University. Her
research domain includes HCI and accessibility computing<EMAIL_ADDRESS>https://volgenau.gmu.edu/profiles/vmotti). Dr. Dongjun Chung is an Associate
Professor in the Department of Biomedical Informatics at the Ohio State
University. His research focuses on developing statistical and computational
models for the analysis of biomedical big data<EMAIL_ADDRESS>https://sites.google.com/site/statdchung/). Dr. Ozlem Uzuner is a Professor of
Information Sciences & Technology at George Mason University. She specializes
in Natural Language Processing, Artificial Intelligence, and Machine Learning
<EMAIL_ADDRESS>https://volgenau.gmu.edu/profiles/ouzuner).

†George Mason University, Fairfax, VA, USA
‡Ohio State University, Columbus, OH, USA

#### Abstract

The success of employment is highly related to a job seeker’s capability of
communicating and collaborating with others. While leveraging one’s network
during the job-seeking process is intuitive to the neurotypical, this can be
challenging for people with autism. Recent empirical findings have started to
show how facilitating collaboration between people with autism and their
social surroundings through new design can improve their chances of
employment. This work aims to provide actionable guidelines and conceptual
frameworks that future researchers and practitioners can apply to improve
collaborative design for job-seekers with autism. Built upon the literature on
past technological interventions built for supporting job-seekers with autism,
we define three major research challenges of (1) communication support, (2)
employment stage-wise support, and (3) group work support. For each challenge,
we review the current state-of-the-art practices and possible future
solutions. We then suggest future designs that can provide breakthroughs from
the interdisciplinary lens of human-AI collaboration, health services, group
work, accessibility computing, and natural language processing.

##  1 Introduction

In April 2023, the employment rate in the US was historically low at 3.4%. At
the same time, more than 85% of people with autism were unemployed [1]. Past
studies have largely focused on understanding how employers can implement more
neurodiversity-inclusive hiring environments and open workplace culture [2, 3,
4]. However, in 2024, it is estimated that over 5 million people with autism
will be unemployed in the US [5]. Unemployment can reduce the quality of life
among people with autism in many ways, for example, by preventing independent
living, isolating them from peer groups and communities, or contributing to
poor mental health [6, 7].

Collaborative design is an emerging direction of research that aims to lead to
better outcomes for job seekers with autism by facilitating collaboration
between them and their social surroundings [8]. When people seek a job, they
naturally collaborate with their social surroundings—colleagues, family,
friends, career advisors, employers, and other relevant parties [9, 10, 11].
Well-shaped communication and organized collaboration with their social
surroundings are crucial for success in job seeking [12, 13]. However, job-
seekers with autism may have disadvantages in collaborating with others
compared to the neuromajority [14]. One possible reason can be a different
communication style; people with autism are “literal thinkers” who minimize
using contextual language [8]. For example, someone with autism may have
difficulty answering a job interview question of “Where do you imagine
yourself in 3 years?” as they may not know whether they will get the job, and
if so, whether they will still work there in 3 years [8]. Other reasons may
include executive dysfunction [15] and emotional dysregulation [16].

Literature on collaborative job-seeking for people with autism has
predominantly focused on gaining an empirical understanding of their current
practice and challenges while having relatively less emphasis on devising new
interventions to provide better strategies. To provide actionable guidelines
and future research directions in the problem space of collaborative design
with job seekers with autism, we synthesize the existing findings in the
literature and define major research challenges using interdisciplinary
viewpoints that combine human-AI collaboration, group work, natural language
processing, clinical health services, and beyond. Consequently, we define
challenges in the conceptual framework of Collaborative Design for Job Seekers
with Autism as follows:

  * •

Communication Support Challenge: The language of people with autism is more
likely to be literal compared to neurotypical peers. How can we leverage
technology to help them decode various linguistic devices hidden in
neurotypical language, such as euphemism, sarcasm, simile, structure mapping,
metaphor, and context, when reading and listening?

  * •

Employment Stage-wise Support Challenge: Arguably, the current job-seeking
support tools have been built from the perspectives of neurotypicals. Such
design cannot fully accommodate the needs of people with autism in specific
stages of the hiring process, such as reading job calls, resume preparation,
or interviews. How can we redesign technology to provide autism-congruent
solutions that reduce cognitive burdens and facilitate job-seeking in
collaboration with their social surroundings efficiently and effectively?

  * •

Group Support Challenge: When working in groups, handling the communication
load, synchronizing situational awareness and knowledge among members, and
making consensus-driven decisions can be hard for people with autism. Such
difficulties can get harder in multi-tasking scenarios such as job-seeking. In
supporting the collaborative effort between people with autism and their
social surroundings, our framework’s last challenge is understanding how to
facilitate group collaboration through intelligent design.

In elaborating on each challenge space, we start by synthesizing the existing
work to define a set of possible directions of research that correspond to an
application-driven challenge. Based on our multidisciplinary expertise, we
provide our viewpoint on how different domains of researchers can collaborate
to make progress. This work provides opinion contributions across the fields
of Human-Compouter Interaction (HCI), Computer-Supported Cooperative Work
(CSCW), Natural Language Processing (NLP), Autism research, and Health Service
explaining how they can practically support job-seekers with autism by
providing novel future solutions.

##  2 Related Work

People with autism can meaningfully contribute to their workplace with several
skills, such as hyperfocus and consistency [17]. They can pay close attention
to critical details others often miss, think outside the box, and are more
likely to report and address problems that could otherwise be unaddressed
[18]. Despite such potential, the census shows that the unemployment rate for
adults with autism was over 80% for a decade [19, 1]. Since employment is
essential for maximizing the quality of life and independence for people with
autism, research has focused on building autism awareness and acceptance in
the workplace or providing accommodations to lower employment barriers [20].
For instance, Lorenz et al. found the lack of sensitivity and awareness about
workers on the autism spectrum can introduce a “formality problem” at an
organizational level and impede workers with autism from being productive
[21]. Annabi and Locke reviewed the literature on the employment of people
with autism and developed a theoretical framework for assessing IT workplace
readiness [22].

While there is a “macroscopic” approach to reducing unemployment among adults
with autism by increasing awareness and neurodiverse-friendly workplace
culture [8], other studies attempted to build new technological
interventions—though we have “limited volume” of research and unestablished
“quality of methodology” [23]. For example, one review study conducted in 2014
found only 10 articles focused on employment-related intervention for adults
with autism over 18 years old among 3,874 autism intervention articles [23].
While there is relatively less volume of studies for adults with autism,
empirical studies found people with autism transitioning from secondary
education to the workplace are in a precarious position due to a dramatic
reduction of formal supports and services [24]. Motivated by such findings,
more researchers committed efforts to developing better technological
interventions for reducing barriers for job seekers with autism. For example,
a survey conducted in 2022 found 48 studies that propose employment-based
interventions [25].

Collaborative design is an emerging direction of intervention for facilitating
autistic employment through collaboration with their social surroundings [8].
Existing employment interventions for adults with autism have leveraged social
support, such as by job seekers eliciting feedback, guidance, or obtaining
job-related video tips from volunteers [25, 26]. However, we have identified
the three gaps we aim to address in our framework. First, social collaboration
has a variety of formations—synchronous or asynchronous, and distributed or
co-located. Additionally, activities entailed in job-seeking can be highly
diverse, including writing e-mails, deciding where to apply, preparing for
interviews, or emotionally recovering from the arduous process of job-seeking.
While approaches exist that apply social support in employment intervention,
collaborative design has not been systemically and comprehensively analyzed in
terms of how it can benefit people with autism in varying job-seeking
situations. In developing the scope of collaborative design, we synthesize the
literature and define the major directions that can create synergy between
people with autism and their social surroundings. Second, job-seeking is a
longitudinal effort that requires consistent and recurring support. Finding
volunteers who can commit such consistent help can be challenging. To make
future endeavors more practical, our framework confines the social
surroundings as two types: (1) family or close colleagues of the job-seeker
with autism, or (2) professionals working with job-seekers with autism, such
as occupational therapists or career advisors. Third, we are witnessing the
burgeoning growth of interest in applying AI to various tasks. While extensive
conversation has started to reveal how to benefit various user groups using
AI, we lack investigation regarding how AI, such as Large Language Models
(LLMs), can benefit people with autism and their social surroundings when
conducting job-seeking-related activities.

##  3 Research in Collaborative Job-seeking for People with Autism

In laying out the main directions in our framework, we collected noteworthy
findings from three areas of literature: (1) reviews of interventions for job-
seekers with autism (e.g., [24, 27, 25, 23]), (2) empirical studies that
provide insights into how people with autism leverage technology in seeking
jobs (e.g., [14, 28, 8]), and (3) technical papers that propose interventions
to improve job-seeking experiences for people with autism, with or without
social supports(e.g., [29, 30] ). In our analysis, the first author coded the
papers regarding any noteworthy empirical insights and opinions. Using these
codes as an initial resource, every author participated in affinity
diagramming and theme-generation process following qualitative research [31,
32]. In shaping our final themes, each of the authors built their structure
based on their expertise and compared the structures to identify commonalities
and discrepancies The discussion continued multiple rounds until every author
reached a consensus. Consequently, we identified the three
directions—Communication Support, Employment Stage-wise Support, and Group
work support—as imminent and important problems that can yield practical
impact on the collaborative design for job-seekers with autism.

###  3.1 Communication Support

#### Background and State-of-the-Art

One of the most common challenges discussed in the literature is the different
communication styles between people with autism and neurotypicals. In
particular, people with autism tend to be literal thinkers whereas
neurotypical language uses various implicit language devices, such as
abstraction, metaphor, mapping, sarcasm, or euphemisms. Past research has
identified such bidirectional communication breakdown as a core reason for
people with autism to be not successful in the employment market [21, 8] Some
communication challenge examples featured in the previous literature include:
interpreting implicit language such as metaphors, analogies, and idioms in the
intended way; handling casual topics (i.e. small talk unrelated to the job
search); adjusting language and level of formality depending on the
conversational context; and taking turns (i.e., balancing conversational flow
between two or more people). A recent study found how different styles of
communication can cause unsuccessful outcomes in every stage of job-seeking;
when reading job calls, asking for details about jobs to hiring managers,
conducting interviews, and negotiating the offer [8].

Mitigating the bidirectional communication gap is the core to building up
social skills related to their career [24]. Therefore, it is imperative to
devise technological intervention to mitigate the gap between literal language
and contextual language [23]. Such language translation is relatively scarce
in literature but is emerging. For instance, Pouliot et al. devised a
communication supporting method [30].

#### Research Directions

In developing a new intervention for conversational support, the requirements
will be different between the following two cases of conversational
decoding—people with autism understanding neurotypical language—and
encoding—people with autism using neurotypical language. In decoding, it is
crucial to develop ways to detect the implicit use of language and translate
it to the explicit language. Recent advances in generative AI, more
specifically LLMs combined with prompt engineering, can be applied in
developing encoding scenarios. In encoding, language style transfer and tone
changing can be useful. One aspect of communication that is difficult for
people with autism is their anxiety about being perceived as rude or being
misunderstood [8]. In many cases, people with autism get help from their
social surroundings to check the “tone and manner” of their writing style [8].
While social surroundings can proofread writing and guide people with autism
to formulate answers to expected interview questions, providing such feedback
across the whole period of the job-seeking process can be time and resource
intensive. Therefore, designing intelligent interventions that can support
social surroundings will be perceived as useful. Finally, we note that such
decoding and encoding support will be equally important and useful for
neurotypicals in their collaboration.

In developing such intelligent group-AI collaboration interfaces in both
directions of conversation, we list a few more related challenges. To build AI
models that can be specifically accurate for conversational encoding and
decoding, characterizing the common cases of misalignment using numerous cases
of conversation made in employment contexts is essential. Such case collection
and classification are under the domain of data annotation. There has been
extensive research in interactive data annotation [33]. However, few
approaches have been proposed for making the annotation efficient and
effective in job-seeking scenarios for people with autism. In addition, in
developing interactive user interfaces used for conversational encoding and
decoding, strictly applying a human-centered and/or participatory methodology
by closely communicating with multi-stakeholders involved (i.e., people with
autism and various social surrounding groups) can increase the chance of
building the intervention that is perceived as practical, useful, and be
adopted in situ to create impact.

###  3.2 Employment Stage-wise Support

#### Background and State-of-the-Art

Employment is a process with multiple stages. While such a process can be
challenging for everyone, numerous articles explain why and how each stage has
greater barriers for people with autism than their neurotypical peers [8],
from reading a job advertisement to negotiating an offer. A few empirical
studies identified the importance of step-by-step, end-to-end support such as
writing cover letters, resumes, and intelligent tutoring [14].

In terms of state-of-the-art supports and interventions, DreamGig helps
underserved job-seekers find job openings that align with their career goal
and supports them in identifying skills they need to achieve to reach their
dream jobs [34]. there have been another line of interactive systems built for
supporting employment stages, such as Review-Me that supports resume editing
and Interview4 that elicit feedback on interviews from volunteers [14]. While
there are not many technological interventions specifically focusing on job-
seekers with autism as a user group, past studies’ results imply developing a
dedicated feature specifically focusing on stage-wise support may improve the
performance of job-seekers with autism.

#### Research Directions

Literature shows how people with autism can have difficulties in regulating
their attention and prioritizing employment-related tasks [8]. Several
challenges occur during the employment process, those are related to the way
in which the job is presented, regarding the description of the position and
the required qualifications of the candidate. Other issues emerge due to the
numerous steps required to prepare the materials, manage the scheduling, and
go through a selection process as detailed below.

Searching job ads: First of all, it is crucial to help people with autism to
easily narrow down job calls based on what they are looking for. There exists
a misalignment between what people with autism commonly look for and what
current “go-to” search tools are providing. To people with autism,
environmental factors, such as noise level, team-related activity factors,
such as the frequency and intensity of communication for finishing up their
main responsibility, and the organization’s culture about Diversity, Equality,
and Inclusion (DEI)—either they put the DEI statement in their job ads as
“boilerplate” or the statement truly represent their culture and a company can
work flexibly with their employees to accommodate their needs—can be crucial
factors [27]. Additionally, some positions require drastic life changes, such
as re-location. However, a change in routine is particularly challenging for
many people with autism. While many search tools—or the majority of job
advertisements—don’t provide these factors, one aspect that future design can
consider is to identify how to efficiently categorize numerous job calls based
on such factors. The factors that job-seekers with autism are looking for can
be highly individualized and may evolve over time. Interactive searching
environments that flexibly accommodate their ideal job criteria can
significantly reduce their effort.

Reading job ads: Developing a reading environment that minimizes the chance of
long reading of text, which may be challenging for some people with autism,
can provide aid. Job ads often describe roles and responsibilities
purposefully vague to invite a large number of candidates. They also provide a
long text to cover every aspect of the new job opportunity. That, summed with
people with autism tending to be “literal thinkers”, may result in hesitancy
to apply if they feel like they do not sufficiently meet all job requirements.
In developing an autism-friendly environment, recent advances in large AI
models can provide several solutions that can meaningfully improve job seekers
with autism’s job search-related productivity. For instance, modern
summarization and simplification models can convert job ads to less lengthy
forms written in language that will be easier for people with autism to
understand. Text-based Question Answering techniques can provide aid by
helping people with autism to comprehend job ads step-by-step through making
questions subsequently. comprehend job ads step-by-step by making subsequent
questions using their language.

Writing cover letter, resume, and preparing materials: Finetuning cover
letters and resumes can be also challenging for job-seekers with autism
especially because they may likely apply for multiple jobs simultaneously. An
interactive co-editing design between people with autism, an AI agent, and
their social surroundings that can easily convert their findings from job ads
reading into cover letters and resume editing can become useful in such a
scenario. In addition, the preparation of the job materials can be
overwhelming for job seekers with autism. Unfortunately, in many cases, the
required materials for application are not presented in a structured way with
templates. Additionally, not describing the expected contents and specific
steps entailed in the hiring process incurs anxiety during the application
process. Not only do they face challenges preparing and submitting the
documents required, but also contact the HR personnel to seek help and
interview through calls or in-person. Designing, developing, and evaluating
intelligent agents who can support people with autism and their social
surroundings to navigate these steps can help job seekers with autism to be
better prepared and more successful in their efforts.

Conducting interviews: For job seekers with autism, participating in the
interview is one of the most challenging steps in the hiring process. Some
candidates may also face challenges due to required improvisation when the
interview questions are not known upfront. For them, it can be hard to project
themselves into situations that are not yet experienced (imagined scenarios).
On top of the unanticipated questions, making conversation with an unknown
group of people adds to the challenge. In the case where a script with
interview questions is not available, developing the mock interview or shadow
interview environment that enables (1) people with autism to be exposed to a
variety of questions related to the job while (2) social surroundings can
easily review and provide their comments can help them. Also, people with
autism may benefit from practicing conversational turn-taking in the interview
context, with emphasis on estimating the right duration and depth of answers
to fit within the interview timeframe. Moreover, for the candidate to feel
comfortable, they may benefit from prompting to take regular breaks. In
helping support the aspects mentioned above, current research in using
wearable devices that can measure anxiety levels in real-time or applying
devices that provide immersive environments can provide practical future
interventions. Gamification design blended with multimodal guidance of
providing unique visual and audio feedback depending on how people with autism
answer the question or providing cues for time-related information can make a
difference.

Networking and communication with employers: Finally, devising a future
networking design that people with autism can leverage in reaching out to
volunteers can be helpful. However, volunteering in a job-seeking situation
expects longitudinal and heavy commitment. The networking feature should
carefully consider why both parties can readily agree to work together. In
doing so, recent research shows that people with autism have a strong
preference for seeking people who have commonalities in the neurodiverse
spectrum and cultural fit [8].

###  3.3 Groupwork Support

#### Background and State-of-the-Art

Groupwork is the subdomain of CSCW where the aim is to understand how a group
of people work together on a certain task using technology in different modes
of situations; working synchronously or asynchronously, and at the same space
or in a distributed manner [35]. As one of the most social beings on Earth
[36], humans can collaborate on almost any task under the shared vision. While
one could imagine that groupware can aid groups easily, Grudin’s early work in
CSCW has identified that boosting a group’s productivity using socialware is
extremely challenging [37, 38]. Despite the challenges entailed in designing
successful groupware, decades of research have found how groupwork support can
create a tremendous impact on several domains that would have been not
possible otherwise [39], enabling advancing democracy, motivating DEI,
regulating disinformation, realizing international scientific collaboration,
and more [40, 41].

As we briefly mentioned in Section 2, we found few studies that systemically
leverage groupwork as an intervention to facilitate the job-seeking process
for people with autism. Meanwhile, recent studies started to show evidence of
how groupwork can be a promising direction as a new intervention. For
instance, using better technology, one study found how underresourced job-
seekers can make a difference in their outcomes with career advisors [14].
With a more productivity-centered groupware design, career specialists can
support more people who require help [21]. This may contribute to making
professionals more available to a broader population of autism who could
receive benefits [14]. Another study found varying contexts that tell us how
people with autism collaborate with their social surroundings, describing
various technological barriers that block them from collaboration [8].

#### Research Directions

Supporting group collaboration using technology is challenging because any
matters that happen between humans are context-dependent and change every
moment. Since technology is especially effective for handling similar and
repetitive activities, Ackerman coined his notion of “social-technical gap”
which explains why we may never be able to resolve problems that require
social collaboration using technology [42]. In recent years, advances in large
language models and intelligent agents demonstrated meaningful breakthroughs.
Therefore, this section will explain the directions of AI-driven collaboration
support that could lead to a successful collaborative design for job seekers
with autism.

AI agents that help executive planning and multi-tasking: One of the most
challenging aspects of job-seeking for people with autism is to cope with
handling multiple job opportunities that have strict deadlines. Once they
focus on one task, they may easily fall into time-blindness and be late on the
interview or miss deadlines [8]. Handling the deadlines, and helping the group
to understand what will come and what needs to be done is a complex task that
intelligent agents can support human groups.

AI agents that can soften between-member dynamics and relationships: Conflict
resolution is one of the most challenging aspects in groupwork [43]. A variety
of conflicts can arise while working on a high-stakes task with impact, such
as job-seeking. There are several reasons that conflict can arise; caring for
other members can be seen as meddling, and asking for information on each
member’s activity can be perceived as violating privacy. Managing disagreement
on the decision can be also an important topic [44].

AI agents that manages the volume of communication and coordinates
dependencies for reduced work: Finally, the core competency of groupware is to
enable the group to achieve their goal in a high quality using reduced effort.
One downside of groupwork is the necessity of communicating with others to
synchronize their situational and group awareness [41]. In many cases, they
must coordinate their group work to manage dependencies between activities
[45]. Understanding how to effectively resolve such activities using the AI-
empowered agent can create useful solutions. One of the most challenging
aspects of job-seeking for people with autism is to cope with handling
multiple job opportunities that have strict deadlines. Once they focus on one
task, they may easily fall into time-blindness and be late on the interview or
miss deadlines [8]. Handling the deadlines, and helping the group to
understand what will come and what needs to be done is a complex task that
intelligent agents can support human groups.

##  4 Conclusions

In this work, we proposed a conceptual framework of Collaborative Design for
Job-seekers with Autism that future researchers and practitioners can leverage
in supporting people with autism in the job market. We discussed how recent
advances in HCI, CSCW, NLP, Autism Research, Health Service Research, and
neighboring areas can be applied to support individuals in three major
challenges: (1) communication support, (2) employment stage-wise support, and
(3) group support. We hope the challenges and opportunities analyzed here can
trigger meaningful technological intervention that can improve the independent
living and quality of life of people with autism.

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