SIMaP, University of Grenoble-Alpes, 38042 Grenoble, France

# Probing the SO2 adsorption mechanism in Hofmann clathrates via inelastic
neutron scattering and density functional theory calculations

Ángel Fernández-Blanco  Institut Laue Langevin, 71 Avenue des Martyrs, CS
20156-38042, Grenoble, France  Lucía Piñeiro-López  IMDEA Nanociencia, Faraday
9, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain  Mónica Jiménez-
Ruiz  Institut Laue Langevin, 71 Avenue des Martyrs, CS 20156-38042, Grenoble,
France  Stephane Rols  Institut Laue Langevin, 71 Avenue des Martyrs, CS
20156-38042, Grenoble, France  José Antonio Real  Departamento de Química
Inorgánica, Insituto de Ciencia Molecular (ICMol), Universidad de Valencia,
Spain  J. Alberto Rodríguez-Velamazán<EMAIL_ADDRESS>Institut Laue
Langevin, 71 Avenue des Martyrs, CS 20156-38042, Grenoble, France  Roberta
Poloni<EMAIL_ADDRESS>Grenoble-INP, SIMaP, University of
Grenoble-Alpes, CNRS, 38042 Grenoble, France

###### Abstract

The adsorption mechanism of SO2 in the Hofmann-like coordination polymer
Fe(pz)[Pt(CN)4] is studied using inelastic neutron scattering and density
functional theory calculations. We find that the most important spectral
change upon gas adsorption is the blueshift of the low energy peak found at
100 cm-1, a feature that is fully confirmed by the computed neutron-weighted
phonon density of states. Our calculations suggest that the origin of this
change is twofold: i) an increase in the force constant of the cyanide out-of-
plane movement due to the binding of the gas onto the Pt(CN)4 plane, and ii)
the hampered rotation of the pyrazine due to steric hindrance. The high energy
region of the neutron scattering data whose spectral weight is dominated by
the internal vibrations of the pyrazine is negligibly affected by the presence
of the gas as expected from a physisorption type of binding.

###### keywords:

American Chemical Society, LaTeX

##  1 Introduction

Metal-organic frameworks (MOFs) are 3D nanoporous materials formed through
coordination bonds between metal cations and organic ligands. The great
variety of metal ions, organic linkers, combined with the structural topology,
allow to achieve an almost infinite number of possible combinations. Owing to
this exceptional tunability, combined with the larger surface area and
nanoscale porosity, the past 10-15 years have seen a rapid development in the
field of MOFs for efficient gas adsorption and separation 1, 2. In recent
years, adsorption and chemical sensing of toxic gas molecules using MOFs has
become a very active field of research 3, 4, 5. Among these, iron (II) spin-
crossover Hofmann-type clathrates represent an interesting class of MOFs with
sensing capabilities due to their bistability, meaning that they can be
switched between two different spin states 6, 7. These complexes undergo a
spin-state change under the influence of external stimuli such as light,
temperature, pressure or the incorporation of guest molecules. A relevant
feature is the presence of metallic centers with an “open” metal coordination,
i.e. metal centers exhibiting an unsaturated coordination. Interestingly,
these open-metal sites have been shown to exhibit a high affinity for many
gases, such as CO28, CH4 9, and CO10. Based on the well known Hofmann
clathrate compounds 11, these materials are built via cyanide (CN) bridging
ligands forming metallo-cyanide planes with different linkers acting as
bridges between the planes. The most representative example of this class of
compounds is the family Fe(pz)[M(CN)4], with M = Ni, Pd, Pt, and pz =
pyrazine12. The Fe(II) centers undergo a transition (spin crossover) from low
spin to high spin, yielding a change in the magnetic, optical, dielectric, and
structural properties of the material. This bistability coupled with the
presence of potentially high-affinity open metal sites makes them excellent
candidate materials for MOF-based gas sensing switches 4.

In 2013, Arcís-Castillo et al. 13 studied the adsorption of SO2 in the
Fe(pz)[Pt(CN)4] Hofmann-type clathrate by measuring the adsorption isotherms
and the x-ray diffraction patterns. The experimental results, combined with
the DFT calculations established that the SO2 binds strongly via
chemisorption. In this work, we combine inelastic neutron scattering data with
DFT calculations to further understand and clarify the SO2 adsorption
mechanism in the material. The most relevant signature of the binding occurs
in the spectral region between 100 cm-1 and 140 cm-1. The intense low energy
peak at around 100 cm-1 blueshitfs upon adsorption, a signature that we
attribute to both the hampered rotation of the pyrazine and the out-of-plane
movement of the cyanide. The well defined peaks in the high-energy region of
the spectra are associated with the internal vibrations of the pyrazine and
are negligibly affected by the adsorbed gas. These findings are well
reproduced by the computed generalized-phonon density of states and are
consistent with the analysis of a strong physisorption mechanism occurring via
the Pt(CN)4 plane and the pyrazine molecules. This work shows that INS
measurements provide a powerful tool to probe the gas adsorption mechanism in
this class of materials thus allowing to unambiguosly characterize the nature
of the interaction when supported by DFT calculations.

##  2 Methods

Sample preparation. [Fe(pz)Pt(CN)4]·nH2O precipitates when a solution of
K2[Pt(CN)4] in H2O is added with constant stirring to a solution which
contains stoichiometric amounts of pz and Fe(BF4)2·6H2O in MeOH/H2O (1:1)
under nitrogen at room temperature. A small amount of ascorbic acid was added
to prevent the oxidation of Fe(II). After stirring for 1h, the yellow
precipitate was collected by suction filtration, washed with water and
methanol and dried under ambient pressure 12. The sample was then heated in a
drying oven at a temperature of 100 $\degree$C.

Gas adsorption. The sample (722.9 mg, 1.6 mmol) was placed inside a
cylindrical aluminium sample holder allowing the gas injection, connected with
a capilar to a manifold gas pumping system. Temperature control was achieved
using either a closed cycle cryostat (IN1-LAGRANGE) or an Orange cryostat (IN5
and PANTHER). The empty MOF was measured at 30 K. The adsorption of SO2 was
performed near room temperature in two injection steps until reaching a total
of 1.6 mmol of SO2 adsorbed, that is, one molecule of SO2 per formula unit of
the host. Finally, the temperature of the sample was decreased to 30 K to
perform the measurements.

IN1-LAGRANGE. The INS experiment was performed in the indirect geometry-type
spectrometer IN1-LAGRANGE 14 installed on the hot neutron source of the high
flux reactor at the Institut Laue-Langevin (ILL) in Grenoble, France. The
incident neutron energy was determined using a combination of Cu and Si
monochromators for the intermediate and lower energy range respectively. Upon
scattering by the sample, neutrons enter a secondary spectrometer where a
beryllium filter is installed to remove higher-order harmonics in the analyser
reflections. Neutrons are then reflected to a He3 gas detector at fixed final
energy of 4.5 meV. This is done by using a focussing analyzer built around the
vertical sample-detector axis. The scattering angle, $\theta$, varies from
33.7∘ to 69.4∘ and the accesible kinematical range of the instrument, $Q$, is
defined as

$Q^{2}=k_{i}^{2}+k_{f}^{2}-2k_{i}k_{f}cos(\theta)$ (1)

Where ki ad kf are the initial and final scattering wave vectors that can be
related to neutron energy by E=$\frac{\hbar^{2}k^{2}}{2m_{n}}$, mn being the
neutron mass. To collect the data, the incident neutron energy was scanned
step-by-step by rotating the whole secondary spectrometer around the
monochromator allowing the measurement of a neutron energy loss spectra. The
monochromators were selected to provide the best relation between energy
transfer range and resolution: we employed Cu(220), Si(311), and Si(111),
respectively, for the energy transfers of [44 - 161] cm-1, [130 - 286] cm-1,
and [209 - 1500] cm-1. Data were collected at 30 K for both the empty and
loaded material.

IN5. INS data for the bare material were collected in the low energy region,
i.e. $<$ 100 cm-1, as a function of momentum transfer on the direct geometry
disk chopper time-of-flight spectrometer at the ILL (Grenoble, France). The
cold neutron flux from the neutron guide H16 is scattered by the sample after
being turned into a pulsed monochromatic beam by a set of 6 choppers. The
scattered neutrons are collected by a large cylindrical array of pixelated
position-sensitive detectors (PSD) mounted inside a vacuum time-of-flight
chamber, giving access to the dynamic structure factor $S(Q,\omega$). Data
were collected at 295 K (at low-spin state) using the standard configuration
with a wavelength of 5 Å (Ei $\approx$ 29.8 cm-1) and a Q range of $\backsim$
0.2 - 4.1 Å-1 for the angular detector coverage.

PANTHER. Complementary measurements for the low energy region were performed
in the high-flux direct-geometry time-of-flight spectrometer PANTHER installed
on the H12 thermal beam tube at the ILL. A double focusing pyrolytic graphite
monochromator determines the incoming energy in the range 7.5 - 112 meV. Short
neutron pulses produced by a slit Fermi chopper are scattered by the sample
and collected by PSD. Data were collected at 10 K using an initial energy of
50 meV.

Computational details The DFT calculations were performed with the Quantum
Espresso package 15, 16, 17 (v. 6.4) within the generalized gradient
approximation (GGA) of Perdew, Burke and Ernzerhof (PBE)18 and long-range
interactions described with the semiempirical approach proposed by Grimme
(PBE+D2)19, 20. We use the Rappe-Rabe-Kaxiras-Joannopoulos ultrasoft (rrkjus)
pseudopotentials 21 without semicore states in valence. The convergence
threshold on forces is 0.0001 Ry/Bohr and the wavefunctions and charge density
cutoffs are set to 100 Ry and 1000 Ry, respectively. These are carefully
chosen to obtain converged phonon frequencies. The low temperature (low spin)
structure of the Hofmann clathrate was described by many authors as a
disordered orientation of the pyrazines 22, 12, 23, 24, 25. Recently, the
present authors employed neutron diffraction data collected at D20@ILL to show
an ordered configuration with the pyrazines perpendicular to each other 26, a
configuration that has already been observed in certain conditions 23, 24, 27,
28. To describe this perpendicular orientation a supercell with lattice
parameter $a^{\prime}$=$\sqrt{2}a$ and $b^{\prime}$=$\sqrt{2}b$ was used, with
$a$ and $b$ lattice parameters of the primitive cell. This impos implying a
disordered orientation (parallel in the calculations) of the pyrazines. The
PBE+D2 lattice parameters of the bare MOF are i.e. $a$ = 10.096 Å, $b$ =
10.097 Å and $c$ = 6.711 Å. The Brioullin zone is sampled using
3$\times$3$\times$3 Monkhorst-Pack k-points grid. A revised PBE approximation
for densely packed solids by Perdew et. al 29 (PBEsol+D2) and the nonlocal
functional rev-vdW-DF2 30 were used to study the effect of the functional
choice on the computed density of states (see text). For rev-vdW-DF2 we employ
PBE-generated pseudopotentials while for PBEsol+D2, since the convergence of
the electronic structure with the rrkjus was not reached, we employed
pseudopotentials from Garrity-Bennet-Rabe-Vanderbilt library (GBRV) 31.
Wavefunctions and charge density cutooffs used for PBEsol+D2 and rev-vdW-DF2
are 70 Ry and 700 Ry. Calculations are performed using the low spin (S=0)
electronic configuration.

Figure 1: Experimental inelastic neutron scattering data, S($\omega$),
collected at 30 K at IN1-LAGRANGE for the bare compound and upon SO2 uptake,
upper panel (a). The S($\omega$) computed using the PBE+D2 functional is
reported in the lower panel (a). Side and top view illustrations of unit cell
employed for the calculations containing neighboring pyrazine molecules
oriented perpendicularly. Color code: purple, orange, blue, silver, red, and
yellow are Pt, Fe, N, C, O, and S, respectively. H atoms are omitted for
clarity.

Generalized-phonon density of states. The phonon frequencies were obtained by
diagonalizing the dynamical matrix by employing the ph.x package in Quantum
Espresso15. The harmonic interatomic force constants are computed using
density functional perturbation theory 32, 33. The inelastic scattering data
collected at IN1-LAGRANGE are compared with the computed generalized-, or
neutron-weighted, phonon density of states. The $l$-atom contribution to the
total one-phonon density of states is given by

$g_{l}(\omega)=\sum_{q,j}|u_{l}(j,\textbf{Q})|^{2}\delta(\omega-\omega_{j}(\textbf{Q}))$
(2)

where $\omega_{j}(\textbf{Q})$ is the phonon frequency of the $j$-branch at Q
wavevector and $u_{l}(j,\textbf{Q})$ is the corresponding atomic displacement.
Thus, $g(\omega)d\omega$ gives the number of eigenstates in the frequency
interval ($\omega$, $\omega$+$d\omega$). The total generalized-phonon density
of states, G($\omega$), is then defined as the phonon density of states
weighted by the neutron scattering power of each atom $l$ and it is given by

$G(\omega)=\sum_{l=1}g_{l}(\omega)\frac{\sigma_{l}}{M_{l}}$ (3)

where $\sigma_{l}$ is the incoherent neutron scattering cross section and
$M_{l}$ is the mass. In the harmonic and incoherent approximation, this
density of vibrational states is related to scattering function $S(Q,\omega)$
by the following relation34, 35, 36

$S(Q,\omega)=e^{-2\overline{W}}\frac{Q^{2}\hbar}{2\overline{M}\omega}<n+1>G(\omega)$
(4)

where $\overline{M}$=$\sum_{l}$ Ml/N, $n$ is the thermal-equilibrium
occupation number of the vibrational state and
$<n+1>=\frac{exp(\hbar\omega\beta)}{exp(\hbar\omega\beta)-1}$ and
$\beta=\frac{1}{K_{B}T}$. We drop the vector symbol from the scattering
function because for powders we measure the average over momentum transfer.
The exponential term is the Debye-Waller factor for neutron attenuation by
thermal motion and 2W=$\frac{Q^{2}\bar{<u^{2}>}}{3}$. The average of the mean-
square displacements over all the atoms is $<\overline{u^{2}}>$ and it is
computed as

$<\overline{u^{2}}>=\frac{\hbar}{2\overline{M}N}\sum\frac{1}{\omega_{j}}coth(\frac{1}{2}\hbar\omega_{j}\beta)$
(5)

where $Q$ is the kinematical range of IN1-LAGRANGE (eq. 1). Because of the
small $Q$ range measured at each energy transfer, we compute phonons only at
$\Gamma$ to compare with experimental INS data, thus dropping the sum over the
phonon wavevector in eq. 2. Thus eq. 4 becomes $S(\omega)$. This should be a
fair approximation since we are measuring small $Q$ at low energy while at
high energy optical modes show small dispersion. Finally, the phonon density
of states is convoluted with a Gaussian function to account for the resolution
of the monochromators. We set the standard deviation of the Gaussian to 3.0
cm-1 for the range [0 - 478] cm-1 and 0.009$\omega$ for [478 - 4033] cm-1,
close to the experimental resolution of IN1-LAGRANGE 14.

##  3 Results and discussion

Figure 2: Total and partial (atom-specific) generalized phonon density of
states computed for the Hofmann clathrate with adsorbed SO2 molecules. The low
energy part and the high energy part are plotted separately in upper and lower
panels, respectively. The partial g($\omega$) of SO2 and Pt+Fe is multiplied
by a factor of 5 in order to be visualized in the same scale of the $y$ axis.

The INS spectra collected at IN1-LAGRANGE are shown in the upper panel of Fig.
1 for the empty and loaded MOF. The scattering function computed using eq. 4
is shown in the lower panel of Fig. 1. The full spectra including experimental
errors are reported in Fig. S1. We note the need to rescale the computed
$<\overline{u^{2}}>$ by a factor of 10 in order to reproduce the experimental
energy decay of the spectra. This deviation may derive from the fact that only
the normal modes are employed to compute eq. 5 which is a rough approximation
to the full density of vibrational states, especially in the low energy region
which dominates $<\overline{u^{2}}>$.

Since the IN1 measurement is not optimized below 100 cm-1 (see Fig. S1), we
studied this energy region for the bare material by using the the time-of-
flight spectrometer IN5. The data are reported in Fig. S2. These low-energy
vibrational modes are associated with the vibrations of the whole lattice and
with out-of-plane and in-plane vibrations of the Pt atom. Because of the
difference between the computed normal modes at $\Gamma$ and the experimental
data, the assignement of the modes within this region is somehow problematic.

Between 75 and 450 cm-1 of the measured INS data, two main peaks are observed
for the bare material, at 100 cm-1 and 393 cm-1, and in between these two a
less resolved region appears. Upon adsorption of SO2 the peak at 100 cm-1
becomes broader and shifts to higher energy, the maximum being found at 129
cm-1. The remaining part of the spectrum is negligibly affected by the
presence of the gas, even the strong excitation at 393 cm-1. This behavior is
in excellent agreement with the computational results.

The high energy region between 700 and 1500 cm-1 reveals several well defined
excitations which are very well reproduced by the simulations and whose nature
will be discussed later. The negligible change upon gas adsorption measured in
this region is also confirmed by the calculations.

###  3.1 Partial G($\omega$)

To better analyze the nature of the measured excitations we report in Fig. 2
the partial G($\omega$), i.e. the $g_{l}(\omega)\frac{\sigma_{l}}{M_{l}}$,
where $l$ represents the different atoms or molecules in the MOF, for the
Hofmann clathrate with adsorbed SO2 molecules.

Figure 3: Left panels: INS spectra measured at IN1 at 30 K for the empty
Fe(pz)[Pt(CN)4] (orange) and after SO2 adsorption (blue) in the upper figure.
The lower figure reports the computed S($\omega$). Rigth panel: zoom in the
region [130 - 160] cm-1 where the main change upon gas adsoprtion occurs.

In the low energy region, between 20 and 100 cm-1, the G($\omega$) is
dominated by the vibrations of the heavy atoms, Fe and Pt, and to a minor
extent by vibrations of the pyrazines and the CN groups. A few librational
modes of SO2 also appear between 20 and 120 cm-1 (see Fig. S3). Concerning the
SO2 molecule, the normal modes in the gas phase are predicted at 484 cm-1,
1107.7 cm-1 and 1303.5 cm-1 (see Fig. S3). These are respectively the
scissoring (i.e. the asymmetric bending), and the symmetric and asymmetric
stretches. All these modes are IR active and are found to change negligibly
upon SO2 adsorption (see Fig. S3). When the molecule is adsorbed in the MOF,
these are computed at 484.5 and 485.6 cm-1, 1042.2 and 1072.4 cm-1, and 1248.9
and 1250.4 cm-1 (2 molecules per unit cell).

Between 100 and 500 cm-1, all atoms contribute to the generalized density of
states as shown in the upper panel of Fig. 2. The peaks predicted at $ca.$ 140
cm-1 and 400 cm-1 have contributions mainly from the pyrazine and the CN
groups as explained in more detail below, while the peak computed at 107 cm-1
is mainly due to a vibration of the pyrazine. At high energy, between 600 and
1500 cm-1, the heavy atoms do not contribute any longer and the CN
contribution is almost negligible. Here the well defined peaks are associated
with vibrations of the pyrazine and their assignement is reported later. These
bands exhibit a strong spectral weight due to the contribution from H atoms.

###  3.2 Low-energy region

The main change upon adsorption is found in the peak at 100 cm-1 (see Fig. 1).
The intensity of this peak decreases and a new broad feature appears centered
at about 129 cm-1. This result is confirmed by the INS data collected on
PANTHER which are shown in Fig. S4. The peak measured on PANTHER at 96.7 cm-1
for the bare material should correspond to the intense band measured at 94.4
cm-1 on IN1 (see Fig.S2). In this region, the most intense bands predicted by
the calculations for the bare material appear at 107.9 cm-1 and at 139 cm-1,
as shown in Fig. 3. The first one corresponds to the rotation of the pyrazine
around the $z$ axis, in agreement with calculations by Hochdörffer et al. 37
on a 3D molecular cluster composed of several repetitions of the clathrate
unit cell. The second band includes 3 vibrational modes at energies 137.8,
138.5, and 139.2 cm-1. We name this second intense peak A in Fig. 3 to assist
the analysis. The first peak at 137.8 is a collective mode involving a
movement of the CN group with contributions from in-plane and out-of-plane,
together with a rotation of the pyrazine around the $z$ axis. The second at
138.5 cm-1 involves a rigid out-of-plane twisting of the Fe(CN4)N2 octahedra
yielding a rigid twisting of the pyrazine about the $y$ axis. This vibrational
mode correponds to the one computed at 140 cm-1 in ref. 37. The vibration at
139.2 cm-1 involves a large out-of-plane vibration of the cyanide together
with a small libration of the pyrazine. The change in the eigenvectors is
illustrated in Fig. S5. Upon gas uptake, the vibration at 107.9 cm-1 blueshits
to 113.5 cm-1 possibly due to steric hindrance by the SO2 molecule and it
becomes coupled with a libration of SO2. Two new modes consisting of pure SO2
librations appear at 119.5 and 123.7 cm-1. Under peak A, the first mode barely
changes (i.e. 137.8 $\to$ 136.8 cm-1) while the second and third blueshift by
9 and 10 cm-1, respectively (i.e. 138.5 $\to$ 147.5 cm-1, and 139.2 $\to$
149.1 cm-1). The Pt atom does not participate in these vibrations for the bare
MOF, but upon gas adsorption the heavy atom contributes to the out-of-plane
bending of the cyanide for the mode at 149.1 cm-1. For the bare MOF the peak
named B in Fig. 3 includes two vibrations at 147.9 cm-1 and 152.2 cm-1. These
correspond to an in-plane movement of the Pt atoms together with a rigid in-
plane displacement of the pyrazines. Upon adsorption these slightly redshift
to 145.9 cm-1 and 150.4 cm-1, respectively. All of the vibrations found in
peaks A′ and B′ exhibit a negligible contribution from SO2.

Because the scattering cross section of hydrogen, $\sigma_{H}$ = 82.0 barn, is
significantly larger than any other atom (Fe and Pt for example have 11.62 and
11.71 barn, respectively), the gas adsorption mechanism is here probed mainly
through changes in the riding modes of H, i.e. those modes that involve
vibrations of the hydrogens 38. As described above, in this region, the
vibrations that imply the rotation of the pyrazine around the $z$ axis and the
cyanide out-of-plane movement shift to higher energy while those exhibiting
in-plane bendings of cyanides show a negligible shift. We attribute the
blueshift of this peak predicted at $ca.$ 139 cm-1 to an increase of the
cyanide out-of-plane bending force constant due to steric hindrance, similarly
to the hindered rotation of the pyrazine predicted at 107 cm-1.

While the assignement of the experimental peak at 400 cm-1 can be performed
without ambiguity based on the good agreement with the calculations, the
intense band at 100 cm-1 may be assigned either to the group of bands
predicted at 137.8, 138.5, and 139.2 cm-1, or to these bands together with the
peak at 107 cm-1. The intensity of the well defined peak predicted by DFT at
$ca.$ 400 cm-1 includes two normal modes at 403.5 and 405 cm-1 which are
associated with the torsion of the pyrazine. It undergoes a blueshift upon gas
adsorption of 0.8 cm-1 and a redshift of 2.06 cm-1 for the duplicated mode.
The predicted negligible change in the energy of this vibration by the DFT
calculations is in agreement with the small change found experimentally (see
Fig. 1).

###  3.3 The SO2 binding mechanism

The molecular orbital interaction of SO2 with this MOF was previously studied
by Arcís-Castillo et al. 13 using DFT calculations and it was reported before
by many authors for other metal complexes 39, 40, 41, 42. The results of our
calculations agree with those of Arcís-Castillo et al. except for the
interpretation: we do not identify the mixing between the hybridized Pt
d${}_{z^{2}}$-pz orbital 43 and the $\pi^{*}$ LUMO (lowest unoccupied
molecular orbital) of the SO2 as a $\pi$-backbonding because of the absence of
$\pi$ symmetry in this interaction 43. Below we discuss in more detail the
molecular orbital interaction between SO2 and the metal center.

When SO2 binds on top of a metal with square planar coordination, a strong
electron donor interaction may be achieved when the $\sigma$ HOMO (highest
occupied molecular orbital) of the molecule can donate electron density to the
empty d${}_{z^{2}}$ of the metal. In this case the expected binding
configuration is the $\eta^{1}$-planar 40 as illustrated and discussed in ref.
13. Because for a d8 electron count the d${}_{z^{2}}$ is doubly occupied, the
molecule can act only as an electron acceptor 42. Since the d${}_{z^{2}}$ is
fully occupied, the molecule orients in such a way to decrease the antibonding
$\sigma$-type of interaction between the HOMO of the molecule and the Pt
d${}_{z}^{2}$, thus adopting an $\eta^{1}$-pyramidal configuration 40 with the
angle between the Pt and the molecular plane of the SO2 being $\theta$=101.2∘
(PBE+D2). In this bent configuration, the LUMO of the molecule interacts with
a polarized molecular orbital of Pt (see Fig. S6) which is a hybridized Pt
d${}_{z^{2}}$-pz orbital, the polarized character resulting from the addition
(bigger lobe) and cancellation (smaller lobe) of the two d${}_{z^{2}}$ and pz
amplitudes 43. Such polarized character reduces the antibonding interaction.
Possibly because of the bent configuration that would reduce the $\pi$ type
overlap, the interaction of the $\pi$* LUMO does not occur with the dxz or dyz
orbitals of Pt.

Figure 4: Molecular orbital picture of the interaction between the SO2 LUMO and the polarized hybridized d${}_{z^{2}}$-pz orbital of Pt. Because this unoccupied electronic state involves a contribution from the Pt-d${}_{z^{2}}$ that is fully occupied in the bare material, such interaction results in a metal$\to$molecule charge transfer. |  Ebind(eV) | d(S-Pt) (Å) |  $\angle{\text{(Pt-S-O)}}$ ($\degree$) |  $\angle{\text{(O-S-O)}}$ ($\degree$)
---|---|---|---|---
PBE | 0.239 | 2.895 | 102.4 | 116.8
PBE+D2 | 0.769 | 2.933 | 101.2 | 117.2
PBE+D2+U | 0.683 | 3.470 | 95.2 | 118.2
PBE+D2[U] | 0.730 | 3.470 | 95.2 | 118.2
PBEsol+D2 | 0.911 | 2.786 | 102.1 | 116.8
Table 1: Comparison of the binding energy, bond distance and bond angles
computed using the different functionals. The PBE+D2 computed SO2 bond angle
for the isolated molecule is 119.4$\degree$.

On the basis of the discussed binding mechanism, SO2 is thus expected to act
as an electron acceptor. The Bader charge analysis peformed in this work using
PAW pseudopotentials reveals a rather small charge transfer from the MOF to
the molecule of 0.12 electrons, suggesting that other effects possibly related
to the MOF skeleton may contribute to the large value of the computed binding
energy per SO2 molecule, i.e. 0.769 eV (with PBE+D2). This value decreases to
0.210 eV upon full geometrical optimization after the D2 correction is
removed. We note the stronger binding computed by Arcís-Castillo et al. 13
using PBEsol+D2. They predict a binding energy of 0.977 eV, in agreement with
the value that we compute when using the same functional, i.e. 0.953 eV. To
corroborate this, we computed the binding energy of SO2 only with the two
Fe[Pt(CN)4] planes, respectively below and above the molecule, by fixing all
the atomic coordinates to the relaxed geometry in the MOF. The lattice
parameters in the plane are set to those of the MOF while we imposed a large
$c$ cell parameter in order to reduce interaction between the images along
$z$. The binding energy is 0.274 eV. This large energy difference between the
two cases points to a binding mechanism originating from a combined charge
transfer mechanism with the Fe[Pt(CN)4] planes via the SO2-Pt interaction,
together with a strong interaction with the rest of the MOF skeleton.

An efficient way to improve the treatment of electronic correlations in DFT is
to adopt the DFT+U approach where the Hubbard $U$ correction is computed in
terms of some localized Hubbard states. We employ the simplified rotationally
invariant formulation44 as implemented in Quantum Espresso. To study how the
change in hybridization 45 of the localized d states of Pt upon $U$ correction
affects the binding mechanism46, we employ ortho-atomic projectors to compute
self-consistently the linear-response $U$ parameters associated to the $d$
states of Pt (5.2 eV) and Fe (7.5 eV), using density functional perturbation
theory 47. By setting the atomic coordinates to the optimized PBE+D2, we
compute a DFT+U binding energy of 0.617 eV. When the geometry is allowed to
fully relax using PBE+D2+U, we predict a SO2 binding energy of 0.680 eV. The
full optimization with Hubbard $U$ gives a significantly different SO2 binding
geometry with respect to PBE+D2 case. Tab. 1 reports the binding energy, bond
distance and bond angles computed with the different schemes. The S-Pt bond
distance changes from 2.933 Å (PBE+D2) to 3.460 Å (PBE+D2+U) and the Pt-S-O
angle from 101.2$\degree$ to 95.0$\degree$. The SO2 bond angle, O-S-O,
slighlty increases upon $U$ correction (see Tab. 1). The projected density of
states shown in Fig. S7 reveals a lower contribution from the polarized Pt
atoms (see Fig. 4) to the states associated with the LUMO of the molecule,
consistent with a reduced charge transfer mechanism and larger SO2 bending
angle. We note that the reported experimental Pt-S bond distance at 120 K is
2.585 Å 13, significantly shorter than the PBE+D2+U one. This elongation of
bond lengths upon $U$ correction has already been reported and discussed by
some of us 45 and is the reason behind the choice of the PBE+D2 geometry in
the calculation of the vibrational modes. Because of this and because of the
use of DFT+U may lead to a bias when computing total energy differences48, we
also report the binding energy computed using a DFT+U density-corrected
approach. This consists in using the PBE+D2 total energy evaluated on the
PBE+D2+U electronic density, an approach that we have named PBE+D2[U]. Using
the PBE+D2 geometry we obtain a value of 0.730 eV.

This result together with the above analysis of the binding mechanism indicate
that the SO2 adsorption occurs via a physisorption mechansim, the high value
of the computed binding energy arising from a combination of stabilizing
electrostatic and van der Walls forces.

Experiment (INS) | DFT - pz@MOF | DFT - gas phase pz | Assignment
---|---|---|---
- | 3168 3167 3165 3164 | 3059 3067 | CH stretching
- | 3155 3153 3152 3150 | 3088 3092 | CH stretching
1601 | 1597 1596 | 1551 | CH in-plane bending, CC stretch
1482 | 1487 1486 | 1525 | CN and CC stretch
1472 | 1459 1458 | 1472 | CH in-plane bending, CN stretch
1430 | 1426.8 1426.3 | 1389 | CH in-plane bending, CN and CC stretch
1338 | 1323 1322 | 1324 | CH in-plane bending, CN stretch
1220 | 1263.9 1263.6 | 1225 | CN and CC stretch
1220 | 1211 1208 | 1209 | CH in-plane bending, CN and CC stretch
1105 | 1105 1104 | 1058 | CH in-plane bending, CN and CC stretch
1105 | 1099 1093 | 1128 | CH in-plane bending, CN stretch
1105 | 1047 1045 | 996 | CN in-plane bending
1105 | 1032 1031 | 1009 | Breathing mode
959 | 960 959 | 967 | CH out-of-plane bending, CNC twisting
959 | 949.9 949.4 | 959 | CH out-of-plane bending, CNC wagging
876 | 862 857 | 913 | CH out-of-plane bending, CNC twisting
817 | 820 819 | 725 | CH out-of-plane bending, CNC wagging
749 | 735.6 735.5 | 757 | CH out-of-plane bending, CNC wagging
696 | 687 685 | 690 | CNC in-plane bending
674 | 680 676 | 580 | CNC in-plane bending
394 | 403 404 | 312 | CH out-of-plane bending, CNC twisting
- | 566 525 | 413 | CH out-of-plane bending, CNC wagging
Table 2: Energy position of the peaks measured from the INS data for the bare
MOF, the calculated values in the bare MOF and for pyrazine in gas phase, and
their assignement. We could not find a correspondance for the modes whose
energy is re

###  3.4 High-energy region

The high energy region, which is dominated by the vibrations of the pyrazine,
negligibly changes upon gas adsorption. We have computed the G($\omega$) of
the pyrazine in gas phase and we report the comparison with the partial
G($\omega$) of the pyrazine in the compound in Fig. S8. The complexation of
the pyrazine in the MOF slightly modifies the position of the vibrational
modes with respect to the gas phase. A comparison and a brief description of
the modes is reported in Table 2. These were studied by various authors by
employing IR and Raman spectroscopies 49, 50, 51, 52, 53, 54, 55 and INS 56.
Three different spectral regions can be identified for the free and complexed
pyrazine: (i) in-plane CH bendings and ring stretching motions in [990 - 1600]
cm-1, (ii) intense bands associated with the CH out-of-plane deformation
vibrations at [700 - 990] cm-1, and (iii) CH stretching near 3000 cm-1. The
vibrations with predominant CC and CN character can be further divided into
C-C and C-N stretching modes at 1058 - 1551 cm-1, in-plane bending modes at
580 cm-1 and 690 cm-1 and out-of-plane bending in the region 750 - 990 cm-1
and bellow 500 cm-1 like 413 cm-1 and 312 cm-1. The characteristic breathing
mode of the pyrazine appears at 1009 cm-1. As a general trend the complexation
with Fe(II) blueshifts the vibrational modes of the free pyrazine. This effect
is possibly driven by an electron-acceptor effect of the pyrazine from the
occupied d orbitals of the metal 57 that increases the $\pi$ cloud of the
ring: thus the stronger double bond character increases the vibrational
frequencies 58. We note that the CH out-of-plane bending mode at 913 cm-1
undergoes the opposite effect and redshifts to $ca.$ 859 cm-1 thus appearing
in the gap between [760 - 910] cm-1 of the free pyrazine (see Fig. 2).

###  3.5 Choice of the supercell

Several authors have reported a specific long range ordering of the pyrazine
ligands within these materials as a consecuence of gas adsorption 24, 23, 28.
In the absence of diffraction data, we assessed the ordering of the pyrazine
upon SO2 adsorption using DFT calculations. We performed two supercell
calculations where we impose that the pyrazines are oriented either
perpendicularly with neighboring ones or parallel. We find negligible energy
differences between these two configurations when the material is loaded with
one SO2 molecule per Pt atom. We recall that for the bare material such energy
difference becomes 39 meV/f.u. 26. The comparison between the corresponding
generalized phonon density of states and that of the bare material, however,
shows that the configuration with all pyrazines oriented parallel with one
another results in a predicted G($\omega$) exhibiting some deviations from the
bare material that are not observed experimentally. The comparison between the
empty (pyrazine perpendicular) and the loaded material is reported in Fig. 5.

Figure 5: Total G($\omega$) in the low (upper panel) energy and high energy
(lower panel) computed for the bare material with perpendicularly oriented
pyrazines (yellow), and for the material loaded with one SO2 per Pt site
computed by employing perpendicular (blue) or parallel (red) pyrazines.

The configuration with parallel pyrazines upon SO2 adsorption results in a
noticeable change in the intense peak at 400 cm-1 with respect to the bare
material, a feature that is not observed in the experiment. Similarly, the
high energy features between 800 and 1000 cm-1 redshift in the configuration
with parallel pyrazines, suggesting that the INS data may correspond to a
configuration with pyrazines oriented perpendicularly with each other both
before and after gas adsorption.

We tested a few functional choices on the computed G($\omega$) for the bare
material. For this we employed the primitive cell (thus imposing parallel
pyrazines) and the exchange and correlation functionals PBEsol+D2, rev-vdW-
DF2, and PBE+D2. The three functionals give very similar results. At high
energy, the spectra negligibly depend on the specific choice while at low
energy, as expected, they are more strongly affected by the approximation to
the exchange and correlation energy 59, as shown in Fig. S9. Specifically, we
see a tendency to predict higher frequencies in this region using PBEsol+D2,
as compared with PBE+D2, consistent with shorter bond distances and smaller
lattice parameters.

##  4 Conclusion

The SO2 adsorption mechanism in the Fe(pz)[Pt(CN)4] Hofmann clathrate is here
probed by combining inelastic neutron scattering experiments and DFT
calculations. The most noticeable change upon adsorption is the blueshift of
the peak measured at $ca.$ 100 cm-1 which we attribute to an increase of the
cyanide out-of-plane bending force constant due to steric hindrance and to the
hindered rotation of the pyrazine around the $z$ axis. The experimental
observations are consistent with an adsorption mechanism being a combined
charge transfer, electrostatic and dispersion interactions, as predicted by
the DFT calculations. The high-energy peaks which are associated with the
internal vibrations of the pyrazine molecule are negligibly affected by the
presence of the physisorbed gas molecule. Based on these findings we expect a
different signature of the adsorption of different molecules such as CO or CO2
on the INS data and are confident that the present joint computational and
experimental scheme will allow to characterize the gas interaction mechanism
in these family of materials.

This work benefited from the support of the project ANR-15-CE06-0003-01 funded
by the French National Agency for Research. Calculations were performed using
resources granted by GENCI under the CINES and TGCC grant numbers A0020907211
and A0110907211. Additionally, the froggy and Dahu platform of the CIMENT
infrastructure, which is supported by the Rhone-Alpes region (GRANT CPER07 13
CIRA) and the Equip@Meso project, was employed for the calculations. We thank
the ILL for the PhD contract of A.F.B. and for the beamtime allocation under
experiment numbers 7-02-108, 7-05-513, and 7-05-430 (doi.ill.fr/10.5291/ILL-
DATA.7-05-430). J.A.R. acknowledges resources from Grant PID2019-106147GB-I00
funded by MCIN/AEI/10.13039/501100011033.

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