# Plasmonic enhancement of molecular hydrogen dissociation on metallic
magnesium nanoclusters

Oscar A. Douglas-Gallardo  Department of Chemistry, University of Warwick,
Gibbet Hill Road, Coventry, CV4 7AL, UK.  Connor L. Box  Department of
Chemistry, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK.
Reinhard J. Maurer<EMAIL_ADDRESS>Department of Chemistry, University
of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK.

###### Abstract

Light-driven plasmonic enhancement of chemical reactions on metal catalysts is
a promising strategy to achieve highly selective and efficient chemical
transformations. The study of plasmonic catalyst materials has traditionally
focused on late transition metals such as Au, Ag, and Cu. In recent years,
there has been increasing interest in the plasmonic properties of a set of
earth-abundant elements such as Mg, which exhibit interesting hydrogenation
chemistry with potential applications in hydrogen storage. This work explores
the optical, electronic, and catalytic properties of a set of metallic Mg
nanoclusters with up to 2057 atoms using time-dependent density functional
tight-binding and density functional theory calculations. Our results show
that Mg nanoclusters are able to produce highly energetic hot electrons with
energies of up to 4 eV. By electronic structure analysis, we find that these
hot electrons energetically align with electronic states of physisorbed
molecular hydrogen, occupation of which by hot electrons can promote the
hydrogen dissociation reaction. We also find that the reverse reaction,
hydrogen evolution on metallic Mg, can potentially be promoted by hot
electrons, but following a different mechanism. Thus, from a theoretical
perspective, Mg nanoclusters display very promising behaviour for their use in
light promoted storage and release of hydrogen.

##  I Introduction

Plasmonic properties arise when specific nanostructured materials interact
with incident electromagnetic radiation.[1, 2, 3, 4] This interaction produces
a collective and coherent oscillation of conduction band electrons, a
phenomenon known as localized surface plasmon resonance (LSPR).[1, 2, 3, 4]
The associated optical absorption signal (LSPR band) is often broad and
reaches a maximum when the incident light frequency ($\omega_{inc}$) is in
resonance with the natural frequency of plasmonic excitation ($\omega_{LSPR}$)
of the irradiated nanomaterial.[1, 2, 3, 4] This optical phenomenon leads to
highly efficient light absorption transferring large amounts of energy into
the nanomaterial. The absorption cross-section associated with these plasmonic
materials is often several orders of magnitude larger than most organic dye
molecules.[1, 2, 3, 5] Plasmonic nanomaterials have rapidly found different
applications in several fields such as optical-sensors,[6] enhanced
spectroscopies,[7] and even biomedical application.[8]

Recently, it has been reported that some plasmonic materials are able to
effectively produce highly energetic distributions of electron-hole-pair (EHP)
excitations upon non-radiative decay associated with dephasing of the
plasmonic excitation (Landau damping).[9, 10, 5, 11, 12, 13, 14] EHPs act as
hot-carriers and can potentially promote bond formation/dissociation events in
molecules adsorbed on or nearby the plasmonic material. This is often
discussed in terms of two possible mechanisms.[14, 13] EHPs created during the
plasmon decay can lead to direct charge transfer into molecular states. This
direct excitation mechanism depends strongly on the chemical interaction
between the adsorbed molecule and the metal surface and is closely related to
chemical interface damping (CID).[14, 15, 16, 17, 18] CID arises from the
hybridisation of adsorbate and metal states during molecular chemisorption and
leads to a reduction of plasmonic excitation lifetime.[15, 16, 14] Highly
excited non-equilibrium EHPs created upon plasmon decay will subsequently
thermalize into an equilibrium distribution associated with an elevated
electronic temperature that is higher than the lattice temperature.[1, 4, 19,
20, 13] These equilibrated hot electrons can exchange energy indirectly with
adsorbates. Finally, this electronic subsystem can subsequently transfer its
energy to the lattice subsystem by means of electron-phonon scattering.[1, 14,
13] This last stage is often modelled by a two-temperature model (TTM) which
connects the electronic and lattice subsystem by means of two non-linear
coupled thermal diffusion equations.[21] LSPR induced EHPs have shown to
increase rates of important surface chemical reactions such as the CO2
reduction,[22, 23] H2O splitting [24, 25, 26] and H2 dissociation
reaction.[27, 28, 29]

Traditionally, noble metal (Au and Ag) nanostructures have been most widely
studied as plasmonic catalyst materials primarily due to their chemical
stability and characteristic optical response.[1, 2, 4, 3, 8] Colloidal
solutions of these plasmonic materials often exhibit a strong optical
absorption band (LSPR band) which is located along the visible range of the
electromagnetic spectrum.[4, 1, 2, 3] The plasmonic excitation frequency can
be widely tuned by modifying the nanostructure morphology and its chemical
environment,[1, 2, 3, 8, 4] but is typically limited to wavelengths larger
than 400 nm for these specific noble plasmonic metals. In recent years the
study of optical and electronic properties of non-standard plasmonic materials
such as Al[30, 28, 29, 31, 23] and Mg[32, 33, 34, 35] has gathered increasing
interest as they can provide highly cost effective alternatives. Mg
nanoclusters emerge as very attractive systems in the context of plasmonics
hot-electron effects.[32, 33, 35] Metallic Mg is an earth-abundant element
that behaves as a pure plasmonic metal without sp to d interband transitions
(like Au and Cu) due to lack of d-electrons in its electronic groundstate band
structure. The plasmonic response for this type of material is only due to sp-
electrons and its dipole LSPR band can be easily detected even for relatively
small particle size. [36, 37]

From the point of view of catalysis, metallic Mg exhibits interesting
hydrogenation chemistry with high reactivity towards forming hydride compounds
(MgH2).[38, 39, 40, 41, 32, 35] Mg nanoparticles can switch from a metallic to
an insulating state by simple uptake and release of molecular hydrogen.[39,
40, 34, 35] Magnesium can store a large amount of H atoms reaching up to 7.6 %
by weight as bulk material representing a promising, efficient and cost-
effective alternative to store hydrogen molecules (chemical storage as metal
hydride; chemisorption).[42, 43, 44, 41] [45, 46, 47] However, the activation
energy associated with the H2 dissociation reaction on metallic Mg surfaces
(400 Å thick Mg film) is relatively high (0.75$\pm$ 0.15) eV.[38, 44, 48]
Different strategies have been explored to increase the effectiveness of this
chemical reaction including doping with transition metals and the use of
nanostructured particles.[49, 41, 50, 51] [45, 46, 47] However, the potential
effect of the Mg plasmonic activity on this particular chemical reaction has
not been fully explored. A suitable hot-carrier distribution can potentially
help to promote dissociative hydrogen adsorption on or release of molecular
hydrogen from magnesium.

We present a comprehensive computational study of the electronic and optical
properties of a set of metallic Mg nanoclusters and periodic Mg(0001) slabs
based on density functional theory (DFT) and time-dependent density functional
tight-binding (TD-DFTB)[52, 53] calculations to simulate the optical
absorption spectra and hot-electron distributions generated by incident light.
We compare and contrast the optical properties of Mg with a conventional
transition metal, namely Ag, before studying how hydrogen adsorption affects
the plasmonic response of the nanoparticle. By analysis of the electronic
structure and electron-nuclear response via electronic friction theory,[54,
55, 56] we qualitatively assess the potential for plasmonic enhancement
effects of dissociative hydrogen adsorption onto and hydrogen evolution from
Mg nanoparticles and surfaces, which we discuss in the context of CID and
Landau damping.

##  II Results and discussion

###  II.1 Optical absorption spectra and hot-carrier distribution on Mg
nanoclusters

Figure 1: Schematic representation of the set of icosahedral Mg nanoclusters
considered (labelled with the number of atoms) along with their respective
optical absorption spectrum. An extra x-axis was included to show the
wavelength of the respective dipole LSPR energy in units of nanometers.

The optical absorption response and ensuing hot-carrier distribution are
explored for a selected set of icosahedral Mg nanoclusters. The hot-carrier
distribution is produced under two different types of external electric
fields, namely constant and pulsed irradiation (cf. section IV). The number of
metallic atoms contained in each particle follow the natural progression of
icosahedral structures (with magic numbers: 13, 55, 147, 309, 561, 923, 1415,
2057). The largest particle size that we have considered is $\sim$ 5 nm in
diameter. The most stable crystal structure for Mg bulk is the hexagonal
closest packed (hcp) configuration, however, for nanoscale sized particles,
the icosahedral shape turns out to be the most stable geometric isomer.[57,
58] Figure 1 shows the optimized structures and the corresponding optical
absorption spectra as calculated with the time-dependent density functional
tight-binding (TD-DFTB) method (cf. section IV for computational details).

As can be seen in Figure 1, the main spectroscopic features of the
nanoclusters are located within a range of 3-5 eV ($\sim$ 400-250 nm). The
larger particles (561, 923, 1415 and 2057 atoms) are characterized by a strong
single dipole LSPR band located at $\sim$ 4 eV ($\sim$ 310 nm). The LSPR band
shows a strong dependence on particle size for the smaller particles, with the
LSPR band peaks shifting from 3.5 to 4.5 eV as a function of nanocluster size.
For small particle sizes ranging from 55 to 309 atoms, we find a slight blue
shift with increasing size. This may be related to a mixture of localised
molecular and collective pseudo-plasmonic response. For larger nanocluster
sizes, we observe a red shift, which is the expected behaviour for plasmonic
response. This optical behaviour is somewhat different from the case of Ag
where only a red-shift is observed when the particle size is increased. [15]
The excitation spectrum of the smallest Mg nanoparticle shows similarities
with very small nanoclusters between 2-5 and $\sim$ 10-100 metallic atoms
previously studied by correlated wavefunction theory[59] and time-dependent
DFT, [36, 37] respectively.

We further conduct an initial assessment of the EHP distribution of Mg
produced under external laser irradiation (pulsed and continuous excitation).
The underlying electronic dynamics associated with the plasmonic excitation,
dephasing, and hot-carrier generation process are explored for a cluster with
1415 metallic atoms. Figure 2 shows the EHP distribution that arises from the
electronic dynamics following plasmonic excitation. A similar analysis has
been conducted for noble metals in other recent reports.[15, 5, 11] The
population and depopulation dynamics of ground state molecular orbitals (MO)
are distinguished with positive and negative population values, indicating hot
electron and hot hole generation, respectively. These MO population
differences are calculated with respect to the ground-state population at the
initial time $t=0$ ($\Delta\rho_{ii}$=$\rho_{ii}(t)-\rho_{ii}(0)$). This is
generated for both a continuous (panel a) and pulsed laser (panel b) source of
external electric field at the LSPR frequency ($\omega_{LSPR}$ = 4.069 eV).
Sources were chosen in order to cover two extreme cases. In both cases, the
same electric field intensity ($E_{0}$=0.02 V $\AA^{-1}$) was selected. The
pulsed laser source used here is different from a Dirac $\delta$ pulse used to
compute the optical absorption spectra in Fig. 1 (cf. section IV for more
details). For the pulsed source, the external electric field is modulated
using a sin2 function with a laser duration of $\tau=$5 fs.

Figure 2:  Evolution of molecular orbital (MO) population at different time
steps along the electronic dynamics with respect to the population at $t=0$.
Two different types of external perturbation laser are used: (a) constant and
(b) pulsed. An icosahedral Mg nanocluster with 1415 metallic atoms is
illuminated with both sinusoidal time-dependent and sin2 electric field tuned
to the LSPR frequency ($\omega_{LSPR}$ = 4.069 eV). The selected electric
field intensity was 0.02 V $\AA^{-1}$.

The electronic response of the Mg nanoparticle can be divided into two main
stages. The first stage (highlighted in blue in Figure 2) corresponds to
plasmonic excitation located $\sim$ 1 eV above and below the Fermi energy and
can be detected immediately after laser excitation has started. This
particular time step is highlighted as it is close to the computed lifetime
for plasmonic excitation associated with this Mg nanocluster (1.07 fs, vide
infra). The second stage involves EHP excitations that expand rapidly to
higher energies above and below the Fermi level, producing a transient
population and depopulation of a manifold of molecular states that evolves as
a function of time. This last stage can be seen more clearly when a pulsed
laser source is used. In this case, the finite energy intake leads to a
convergence of the distribution as the TD-DFTB simulation does not fully
capture thermalisation due to electron-electron scattering effects (vide
infra) and neglects equilibration with the lattice due to electron-phonon
coupling. On the other hand, the continuous laser source steadily provides
energy to the system and a continuous hot-carrier production is detected
simultaneously with the plasmonic excitation.

Plasmonic properties can be harnessed for catalysis in a continuous and pulsed
illumination regime. [60] In both cases, the largest concentration of high-
energy electrons builds up at $\sim$3 eV above the Fermi energy and the
largest concentration of holes is produced at $\sim$1 eV below the Fermi
level. This particular distribution of EHPs can be connected to the Mg
electronic bandstructure, which exhibits weakly dispersed valence bands close
to the Fermi energy between M and L and at $\Gamma$ high symmetry points from
which many electrons can be transferred into a high density of conduction
bands at around 2 to 4 eV above the Fermi level (see Supporting Figure S1).

The non-equilibrium electronic distribution at different time steps of the
dynamics for both external perturbations are shown on a logarithmic y axis
scale in Supporting Figure S3. In this representation, equilibrium Fermi-Dirac
distributions should appear as straight lines with the gradient governed by
the effective electronic temperature. A quasi-equilibrium distribution can be
found that ranges over few hundred meV above and below the Fermi level.
Outside of this range, both illumination regimes generate highly non-
equilibrium electron distributions that do not satisfy a Fermi-Dirac
distribution. We find a characteristic steplike structure in the distribution
with a step width of $\sim$ 4 eV. The non-equilibrium electronic distributions
show the general features of ultrafast electron dynamics in metals reported
from Boltzmann equation simulations.[19, 20, 1] It is important to state that
electronic thermalisation due to electron-electron scattering is not well
described with the TD-DFTB method as it does not sufficiently capture the
many-body correlation effects that give rise to such scattering events. For
this reason, even long-time propagation for times beyond 200 fs do not show
the electron thermalisation towards Fermi-Dirac distributions at elevated
temperatures that is generally expected.[4, 13, 14, 61] However, it is
illustrative to generate a rough estimate of the electronic temperature regime
that we expect to reach upon equilibration by computing the slope associated
with the external edge of the steplike structure. From Supporting Figure S3,
we estimate electronic temperature ranges of 9000$~{}\pm$ 3000 K and 4400
$\pm$ 600 K for constant and pulsed laser perturbation after about 100 and 240
fs, respectively. These values provide an estimate of the range of electronic
temperatures that can be expected upon equilibration. We will subsequently use
this in the discussion of plasmonic hydrogen evolution on Mg nanoparticles in
section II.3.

We have also explored the effect of particle size on hot-carrier generation.
Supporting Figure S4 reports the electronic dynamics after 4.84 and 96.75 fs
for Mg nanoclusters with 147, 309, 561, 923, 1415, and 2057 metallic atoms
under constant illumination. All cluster sizes exhibit high energy hot
electron generation around 4 eV. As we reduce the nanocluster size, the energy
regime becomes more selective with a very pronounced peak between 3.5 and 4 eV
for clusters with 147 and 309 atoms. The generation of hot electrons within a
narrow energy regime could potentially be very useful for the selective
activation of chemical reactions and suggests a potentially measurable
dependence of this effect with respect to nanocluster size. Only clusters with
561 atoms or more exhibit the typical short-time plasmonic response of the EHP
distribution close to the Fermi level. This plasmonic decay behaviour is fully
established for larger clusters. Increasing the cluster size from 1415 to 2057
atoms does not further increase the population of hot electrons at 3.5 to 4
eV. This suggests that for Mg nanocluster sizes even larger than those
considered here (diameter $>$ 5 nm), the concentration of hot electrons may
effectively decrease, which would affect the ability to activate surface
chemical reactions by hot electron transfer. This size effect has been
previously shown for Ag nanoparticles.[62]

###  II.2 Comparison of plasmonic response of Mg and Ag nanoclusters

Figure 3:  Optical absorption spectra (top panel) and hot-carriers
distribution (bottom panel) for a Ag (black line) and Mg (red line)
nanocluster with 1415 metallic atoms. The MO population change for both
systems was obtained at 43.6 fs under a constant laser source. Both profiles
were normalized for their respective density of states (DOS). Inset: Fitting
of the absolute value of the dipole moment signal in x-direction for a Ag
(black line) and Mg (red line) nanocluster with 1415 metallic atoms when these
are illuminated at their respective plasmonic frequencies under constant laser
source.

We now briefly identify the similarities and differences in optical absorption
response between metallic Mg nanoclusters and more conventional plasmonic
metals such as Ag.[15, 5, 63] The optical and electronic properties of
icosahedral Mg and Ag nanoclusters with 1415 atoms are compared in Figure 3.
The optical absorption spectra for both particles are shown in Figure 3a. The
optical response in both metals is characterized by a single clearly defined
dipole LSPR band located at 2.71 and 4.07 eV for Ag and Mg, respectively. The
main spectroscopic features of the Ag nanocluster are largely localised in the
visible regime (2-3 eV), whereas for Mg they are in the UV region (3-5 eV).
Another key difference is the line width associated with the LSPR band, which
is significantly narrower in Ag than in Mg, associated with a longer lifetime
of the LSPR in the case of Ag (vide infra). The absorption is much more
intense for Mg than for Ag. With a strong plasmonic response in the UV range,
Mg nanoclusters could potentially complement conventional plasmonic materials,
which typically absorb in the visible or near UV range.[4, 3, 2, 1, 35, 32]

In order to further characterize the plasmonic behaviour of Mg nanoclusters,
we report the homogeneous linewidth ($\Gamma$) and lifetime (T2) associated
with its plasmonic excitation. The homogeneous linewidth can be calculated by
fitting the time-dependent dipole moment response ($\mu(t)$) when the
nanostructure is illuminated with a sinusoidal time-dependent electric field
as an external perturbation. [31, 15] The absolute value of the dipole moment
and its respective fitting curve are shown in the top part of Figure 3 as an
inset. The raw dipole moment response for both metals is shown in Supporting
Figure S5. The homogeneous linewidth and lifetime for Ag and Mg nanoclusters
computed in this way are $\Gamma_{Ag}$ =144.17 meV (9.13 fs) and $\Gamma_{Mg}$
= 1227.61 meV (1.07 fs), respectively. The homogeneous linewidth computed for
the Mg nanoclusters with 1415 metallic atoms is several times larger than that
for the Ag nanocluster. This suggests that plasmonic dephasing occurs much
more efficiently in nanostructured Mg than in Ag. An important quantity that
can be associated with the homogeneous linewidth ($\Gamma$) is the quality
factor (Q) which is defined as Q = $E_{LSPR}/\Gamma$.[64, 65] This quantity
accounts for the extent of the local field enhancement ($\sim Q^{4}$) and can
be used as a metric to judge the performance of a material for plasmonic
applications such as surface-enhanced Raman spectroscopy (SERS) and near-field
fluorescence quenching.[64, 65] The computed values for Ag and Mg nanoclusters
with 1415 atoms are QAg = 18.80 and QMg=3.32. These values indicate that the
Ag nanocluster can potentially produce higher local field enhancement than Mg.
On the other hand, the Mg nanoclusters show a LSPR in the UV region that
efficiently produces high energy hot electrons where Ag or Au are
plasmonically inactive. Therefore, specifically in the context of hot electron
chemistry, Mg may represent a suitable alternative to conventional plasmonic
materials.

Finally, we compare the ability to generate energetic EHPs for Mg and Ag
nanoclusters in Figure 3b. Ag posseses a highly localised DOS below the Fermi
level associated with the d band, whilst its DOS above the Fermi level is
close to constant. Mg on the other hand shows a DOS that increases
monotonically with the square root of energy as is expected for a metal with
almost free electrons (see Supporting Figure S1). For a fair comparison
between both metals, the hot-carrier distribution was normalized by their
respective DOS computed at the DFTB level ($\Delta\rho^{Norm}_{ii}$). The non-
normalized hot-carrier distribution is shown in Supporting Figure S6. Both
metals exhibit a similar distribution of hot holes, but differ in the hot
electrons that can be generated. In the case of Mg, the highest concentration
of hot electrons is produced in the range of 3-4 eV, whereas Ag produces a
high concentration of hot electrons at $\sim$2.5 eV. In summary, the LSPR band
of Mg nanoclusters has a much shorter lifetime than Ag and produces a broader
distribution that reaches electron energies of up to 4 eV.

###  II.3  Plasmonic enhancement of hydrogen dissociation on Mg nanoclusters

Metallic Mg is highly reactive and readily forms a surface hydride when
exposed to molecular hydrogen (MgH2). [38, 40, 41, 43] This property has been
discussed in the literature in the context of hydrogen storage.[39, 34, 32,
35] In the following, we will interpret the predicted optical properties of Mg
nanoclusters in the context of plasmonic enhancement of hydrogen dissociative
adsorption and associative desorption (hydrogen evolution). In the previous
sections, we have shown that LSPR excitation of Mg nanoclusters produces hot
electrons with energies of up to 4 eV. By analysing the electronic structure
and nonadiabatic coupling of adsorbed hydrogen on Mg, we will study if these
hot electrons can efficiently couple with adsorbate degrees of freedom.

Figure 4:  (a) Optical absorption spectrum and (b) hot-carrier distributions
for a naked Mg nanocluster (dotted black line) with 561 metallic atoms, a Mg
nanocluster with 59 H2 molecules adsorbed (dotted gray line), and with 118
adsorbed H atoms (dotted red line). The hot-carrier distributions were
computed after 96.75 fs of electron dynamics with a constant laser source at
the respective plasmonic frequency.

We first turn our attention to the effect of hydrogen adsorption on the
optical properties of Mg nanoclusters. Figure 4 shows how hydrogen adsorption
changes the optical absorption spectrum and hot carrier distributions of a 561
atom Mg nanocluster. We compare the absorption spectrum of the bare cluster,
with the spectrum obtained for clusters covered by physisorbed molecular
hydrogen H2 and chemisorbed hydrogen atoms. We choose 59 H2 molecules and 118
H atoms to decorate the nanoparticle at random set of positions that would be
filled by the metal atom shell of the next largest icosahedral particle (923
Mg atoms). In all cases, stable absorption geometries have been obtained by
relaxing the structures of the adsorbate atoms while keeping the previously
optimized Mg atoms frozen in their positions. This allows a consistent
comparison with the naked Mg nanoclusters by avoiding any surface relaxation
effects. The optical and electronic properties associated with a full
optimization of Hydrogen covered nanocluster are discussed in the supplemental
material in Figure S11. We stress that determining the H adsorption positions
on Mg is a challenge.[46] Our approach represents an initial assessment to
evaluate the effect of H adsorption on the plasmonic properties of Mg.

In the case of molecular hydrogen physisorption, we find almost no effect on
the LSPR band or on the EHP distribution. As can be seen in Figure 4b, the
hot-electron distribution for the physisorbed case still leads to hot-
electrons with energies of up to $\sim$4 eV. On the other hand, a very strong
CID effect is found in the case of chemisorbed hydrogen atoms on Mg, which
reduces the LSPR lifetime (increase of the linewidth) and induces a blue-shift
of the maximum of the LSPR band. This optical behavior is opposite to what was
found for Ag nanoclusters, where strongly hybridised adsorbates produced a
red-shift of the LSPR band. [15]Likewise, the chemisorption of hydrogen atoms
reduces the number of hot electrons produced (Figure 4b), but reaches slightly
higher hot electron energies.

Molecular hydrogen dissociation is a highly activated process on Mg. We have
calculated a minimum energy path for the dissociative adsorption reaction of a
small Mg nanocluster (55 atoms) and a p(3x3) Mg(0001) periodic surface slab
using DFT (See Figure 5a and Supporting Figure S7a). Along this path, we
identify three key geometries, the initial physisorbed state (IS), the
transition state (TS), and the final chemisorbed state (FS). We find an
activation energy of 0.71 eV and 0.89 eV for hydrogen dissociation on the
nanocluster and the surface, respectively. This is in good agreement with a
measured activation energy of 0.75$\pm$0.15 eV)[38] and with other theoretical
reports. [43, 44, 48] We further analyse the electronic structure of the 3 key
geometries by visualising the projected DOS (pDOS) associated with a single
physisorbed H2 molecule on Mg nanoparticle and on a clean Mg(0001) surface in
Supporting Figure S8. In both cases, the IS shows little hybridisation and
state coupling. The unoccupied $\sigma^{*}$ state of $H_{2}$ shows some level
of state splitting in the range of 3 to 6 eV above the Fermi level, which
suggests some coupling to metallic states. This is in contrast to the FS,
where the projected DOS shows that the electronic states of adsorbed hydrogen
atoms strongly couple to the metallic states of Mg leading to a homogeneous
distribution of H contribution across a wide range of energies.

For plasmonic enhancement of hydrogen dissociation on Mg nanoclusters, hot
electrons need to be able to effectively transfer into the antibonding
$\sigma^{*}$ MO of a physisorbed H2 molecule, which requires sufficient
molecule-metal coupling and alignment of the molecular levels with the
energetic distribution of hot electrons created by LSPR decay. Both
requirements are reached for Mg nanoclusters. Hot electrons are efficiently
created with high energies of 3-4 eV for a wide range of nanocluster sizes,
which is an energy region that overlaps with unoccupied adsorbate states.
Therefore, our calculations point towards effective plasmonic enhancement of
hydrogen dissociation on Mg nanoclusters and surfaces, which is yet to be
corroborated in experiments.

###  II.4  Plasmonic enhancement of hydrogen evolution from Mg nanoclusters

To address the question if plasmonic excitation can also enhance hydrogen
evolution, we need to study the reverse reaction, namely the recombination of
chemisorbed H atoms into molecular hydrogen. Here, the situation is less clear
as the electronic states of chemisorbed hydrogen atoms are heavily hybridised
and homogeneously embedded into the DOS of the metal (see Supporting Figure
8). Therefore, there are no clear resonances which promote the reaction. This
is a case that is well described by Fermi’s golden rule where EHPs will couple
with hydrogen atom motion proportional to the magnitude of the DOS and the
nonadiabatic coupling strength between molecular motion and electronic states.
[66, 54] In this limit, nonadiabatic energy dissipation effects during
dynamics on surfaces can be described by molecular dynamics with electronic
friction (MDEF), [67, 55] where we describe the effect of EHPs on molecular
motion as frictional and random force governed by an electronic friction
tensor. This approach is well justified and common for the study of hydrogen
atom dynamics on metals [68, 69] and has also been applied to study light
driven diffusion and desorption dynamics in combination with TTM. [70, 71]
Using first order time-dependent perturbation theory on Kohn-Sham DFT, we can
calculate the relaxation rates and vibrational lifetimes associated with
different directions of atomic and molecular motion along the minimum energy
path. [56]

Figure 5:  (a) Minimum energy path (MEP) for the molecular hydrogen
dissociation reaction on a Mg nanocluster with 55 metallic atoms and the (b)
vibrational relaxation rates of molecular adsorbate motion due to hot
electrons for geometries along this reactive path. Rates are given along
internal coordinates of the molecule defined in Ref. [72] Inset: Electronic
temperature computed for Mg by means of TTM at three different laser fluences.

In Figure 5b and Supporting Figure S7b, we report the nonadiabatic relaxation
rates of hydrogen motion due to coupling with EHPs along the minimum energy
path of H2 dissociation. Similar to the previously reported case of H2
dissociation on Ag(111), we find the strongest coupling to EHPs for the
intramolecular stretch motion of H2 ($\Gamma_{dd}$) at the TS, [56] however
the relaxation rate on the Mg nanocluster and the Mg(0001) surface is
significantly higher reaching about 8 ps-1, which corresponds to a vibrational
lifetime of the internal stretch of about 100 fs. In the FS, nonadiabatic
relaxation rates are comparable between Ag(111) and Mg(0001) with the biggest
components of the relaxation rate tensor corresponding to about 2 ps-1 (or a
lifetime of 0.5 ps).

We can use this number for an approximate calculation of how much energy LSPR
excitation can transfer into an adsorbed hydrogen atom. We do this by
performing Langevin dynamics within MDEF where we neglect the underlying
potential energy surface and take the friction coefficient that describes the
coupling between hot electrons and adsorbate as constant. We couple these
equations with the simulated TTM temperature profiles shown in the inset of
Figure 5 to mimic how the electronic temperature changes as a function of
time. By propagating the relevant equation in time, we can calculate the
kinetic energy that will be transferred from the EHPs into the H atoms. (for
details see supporting section S9). [73] As shown in the inset of Figure 5b,
depending on the laser fluence, electronic temperatures of 2000-8000 K can be
generated (see supporting section S8 for details). According to the relaxation
rates we find for the FS in Figure 5, we select a friction coefficient that
corresponds to a relaxation rate of 2 ps-1. We find that a laser pulse with a
raw laser fluence of 10 J/m2 (100 J/m2) leads to peak electronic temperatures
of 2500 K (8000 K) and an increase of hydrogen kinetic energy by 0.17 eV (0.55
eV) over 250 fs. The DFT-PBE predicted energy required to overcome the barrier
for desorption is 0.71 eV and 0.89 eV on the 55 atom nanocluster and the
Mg(0001) surface slab, respectively. These results suggest that significant H2
desorption should be observed for fluences between 50-100 J/m2 as two H atoms
will be able to gain sufficient energy to overcome the barrier for hydrogen
evolution. Fluences in this range can be achieved by laser irradiation and
have been reported previously in ultrafast laser driven photodesorption
studies.[74, 75, 76] We note that this simple calculation neglects the
underlying energy landscape and other effects, such as the dependence of
nonadiabatic coupling rates $\gamma$ on the coordinates and the electronic
temperature. [54, 77]

##  III Conclusion

Earth-abundant materials are becoming increasingly important as catalysts as
they are more cost effective than traditional catalyst materials. In the
context of plasmonic catalysis, Mg nanoclusters may provide interesting
complementary properties to conventional plasmonic materials such as gold and
silver. In this work, we study the plasmonic properties of Mg nanoclusters
using electronic structure and TD-DFTB calculations, with a particular focus
on how the plasmonic behaviour could be used to catalyze hydrogen absorption
and release in the context of hydrogen storage.

Electron dynamics simulations show that Mg nanoclusters are able to produce
hot-carrier distributions with hot electrons at energies of $\sim$ 4 eV.
Therefore Mg nanoclusters produce higher concentrations of high energy hot
electrons than silver nanoclusters of the same size. We have studied the
optical absorption properties and the hot-carrier production on pristine and
hydrogen-covered Mg nanoclusters of various size. By analysis of the
electronic structure of physisorbed molecular hydrogen and chemisorbed atomic
hydrogen on Mg, we conclude that it is highly likely that hydrogen
dissociation can be selectively promoted by plasmonic excitation of Mg
nanoclusters. On the other hand, hydrogen evolution from Mg nanoclusters is
expected to be less sensitive to plasmonic excitation but generally effective
in the presence of high temperature thermalised hot electrons at least for an
early H adsorption stage where the plasmonic properties and metallic character
are still held. This scenario can occur during constant illumination or local
surface heating. As the dissociative adsorption and hydrogen evolution
reactions couple to hot electrons differently, we speculate that it may be
possible to realise experimental strategies where one or the other are more
preferentially promoted. Our results confirm that nanostructured metallic Mg
is a promising plasmonic material for applications in photocatalysis and
hydrogen storage.

##  IV Computational Methods

###  IV.1 Electronic structure of Mg nanoclusters

The ground-state electronic structure of Mg nanoclusters has been computed
using a self-consistent-charge density-functional-tight-binding (SCC-DFTB)
approach.[78, 79, 80] This method is based on a second order expansion of the
Kohn-Sham DFT total energy around a non-interacting reference density built
from a superposition of atomic densities.[78, 79, 80] The SCC-DFTB method has
been successfully employed to describe the electronic structure and quantum
properties of large organic, inorganic and biological systems in the past.[80,
81, 82] This semi-empirical method can overcome inherent computational
limitations associated with DFT calculations.[81, 80, 83, 82] We employ the
DFTB+ package[84, 52] to describe the ground-state and time-dependent
electronic properties of Mg nanoclusters. The 3ob-3-1 DFTB[85] parameter set
is used and the reliability in the predicting band structure and DOS for bulk
Mg has been verified against DFT calculations using the FHI-Aims[86] quantum
chemistry package and the Perdew, Burke, and Ernzerhof (PBE) functional[87]
(see validation section in ESI and Supporting Figure S1). This validation
study was also extended to compute the density of states (DOS) associated with
very small Mg nanoclusters containing 13, 55, 147, 309 atoms (see Supporting
Figure S2).

###  IV.2 Electron dynamics

The 2020 release version of DFTB+ has been used[52, 53] to simulate the
electron dynamics associated with the plasmonic excitation and thus to obtain
the optical absorption spectra and other related dynamics properties such as
the hot-carrier distribution and the plasmonic lifetime. This is made possible
with a new implementation to describe the electron dynamics based on time-
dependent SCC-DFTB (TD-SCC-DFTB).[53, 52] Within this theoretical framework,
the electron dynamics is driven under the influence of an external time-
varying potential $(V_{ext}(t))$ or electric field ($E(t)$)

$H(t)=H_{GS}+V_{ext}(t)=H_{GS}-E(t)\mu$ (1)

Where $H_{GS}$ is the ground state Hamiltonian and $\mu$ is the dipole moment
operator.[52, 53] Two different kinds of external electric field have been
used to drive the electron dynamics. For the optical absorption spectra, a
Dirac $\delta$ pulse was used as external perturbation
($E(t)=E_{0}\delta(t-t_{0})$). The optical absorption spectrum is proportional
to the imaginary part of frequency-dependent dynamic polarizability
($\alpha(\omega)$) which can be obtained from a Fourier transform of the time-
dependent dipole moment, within the linear response regime (small electric
fields). To determine the plasmonic resonance (LSPR peak) frequency, we select
the main spectroscopic resonance by inspection. The LSPR band is often the
most intense peak within the computed optical absorption spectrum. To explore
the photophysics associated with plasmonic excitation, a sinusoidal time-
dependent electric field ($E(t)=f(t)E_{0}sin(\omega_{LSPR}^{Mg}t)$) in tune
with the plasmonic frequency was selected as external perturbation to drive
the electronic dynamics and to calculate different emerging dynamical
properties such as the plasmonic excitation lifetime and the hot-carrier
distribution. The $f(t)$ function is used to modulate the external electric
field for the second type of external perturbation. Two different shapes have
been considered, a continuous laser source with $f(t)=1$ and a pulsed laser
source with $f(t)=sin^{2}(\pi(t-t_{0})/\tau)$ if $t_{0}<t<t+\tau$ and $f(t)=0$
otherwise.[52] All nuclear positions have been frozen at their respective
optimized geometries during the electron dynamics simulations.

###  IV.3 CI-NEB and electronic friction calculations

The non-adiabatic effects during H2 dissociation on metallic Mg have been
characterized by computing the electronic friction tensor elements
($\Lambda_{ij}$) for geometries along the MEP for two different systems, a
periodic Mg(0001) slab and a small Mg nanocluster.[54, 56] To compute the
electronic friction tensor, the current implementation within FHI-aims has
been used.[86, 54] This implementation calculates nonadiabatic coupling matrix
elements to calculate the relaxation rates on adsorbate motion due to coupling
with hot electrons in the metal. The MEP was obtained by using the climbing-
image nudged elastic band (CI-NEB) method implemented in ASE[88] with FHI-
aims. The MEP path contains 7 and 9 images for the Mg nanocluster and periodic
Mg(0001) slab, respectively. The set of images was optimized with a maximum
force threshold of 0.05 eV/$\AA$. For the Mg nanocluster case, a small
iscohedral Mg particle containing 55 metallic atoms was considered. For the
periodic Mg(0001) slab a $3\times 3$ surface unit cell with 4 atomic layers
(36 atoms) was employed with the bottom two atomic layers frozen in order to
retain bulk properties. A Mg lattice constant for PBE previously published
(a=3.19 c=5.12)[89] was employed for the periodic system. The calculated
lattice constants are in good agreement with the experimental ones (a
=3.21$\mathrm{\AA}$ and c=5.21 $\mathrm{\AA}$).[90] To compute the MEP and the
electron friction components, a Monkhorst-Pack k-point mesh of $12\times
12\times 1$ was chosen for the periodic systems. This particular k-point grid
produced converged results for the relaxation rates associated with the
electronic friction elements (see Supporting Figures S7c and S7d). We use a
broadening of the electronic states of 0.6 eV when calculating relaxation
rates. The details of this procedure are explained in Ref. [54] In both
studied systems, PBE and ”tight” basis set option were chosen as suitable
choices to carry out these calculations.

## Acknowledgements

O.A.D-G and R.J.M acknowledge funding from the UKRI Future Leaders Fellowship
programme (MR/S016023/1). C.L.B. is supported by an EPSRC-funded Ph.D.
studentship. High performance computing resources were provided via the
Scientific Computing Research Technology Platform of the University of
Warwick, the EPSRC-funded Materials Chemistry Consortium for the ARCHER UK
National Supercomputing Service (EP/R029431/1), and the EPSRC-funded HPC
Midlands+ computing centre (EP/P020232/1). The authors want to thank James
Gardner and Franco P. Bonafé for fruitful discussions.

## Author contributions

R.J.M. supervised the project. R.J.M. and O.A.D-G. conceived the project.
O.A.D-G. carried out TD-DFTB and DFT calculations. C. L. B. and R.J.M. carried
out electronic friction calculations. O.A.D-G., C. L. B. and R.J.M. discussed
and interpreted the data and wrote the manuscript.

## Competing Interests

The authors declare no competing interests.

## Data Availability

The input and output files of all electronic structure calculations have been
uploaded to the NOMAD repository and are available as a data set at doi:
10.17172/NOMAD/2021.03.29-1. The data shown in all figures has been uploaded
to figshare at doi: 10.6084/m9.figshare.14339687.

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