# Hydride Migration within RhH2Ag19 Superatom: A Combined Neutron Diffraction and DFT Analysis

Tzu-hao Chiu, Michael N Pillay, Jian-Hong Liao, Xiaoping Wang, Hao Liang,

Samia Kahlal, Jean-Yves Saillard, C. W. Liu

► To cite this version:

Tzu-hao Chiu, Michael N Pillay, Jian-Hong Liao, Xiaoping Wang, Hao Liang, et al. Hydride Migration within RhH2Ag19 Superatom: A Combined Neutron Diffraction and DFT Analysis. Small, 2025, pp.2501583. 10.1002/smll.202501583. hal-05023854

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# Hydride Migration within RhH<sub>2</sub>Ag<sub>19</sub> Superatom: A Combined Neutron Diffraction and DFT Analysis

Tzu-Hao Chiu, Michael N. Pillay, Jian-Hong Liao, Xiaoping Wang, Hao Liang, Samia Kahlal, Jean-Yves Saillard,* and C. W. Liu*

An investigation combining neutron diffraction and DFT allows determining the most likely hydride migration pathway within the icosahedral metal framework of [RhH<sub>2</sub>Ag<sub>19</sub>{S<sub>2</sub>P(O<sup>η</sup>Pr)<sub>2</sub>}<sub>12</sub> (RhH<sub>2</sub>Ag<sub>19</sub>). Starting from the experimentally derived solid-state structures, a computational analysis is able to reveal an energetically favorable migration pathway with a maximum energy barrier of 4.2 kcal mol<sup>-1</sup>. The two hydrides migrate simultaneously within the Rh@Ag<sub>12</sub> icosahedral core, traversing several positional isomers. This study expands the understanding of hydride dynamics in nanoclusters and provides critical insights into the structural flexibility of the superatom framework. These findings have significant implications for hydrogen storage, catalysis, and the design of advanced hydride-containing materials.

## 1. Introduction

Atomically precise nanoclusters (NCs), unlike traditional nanoparticles with their broader size and structure distribution, offer a significantly more controllable platform for investigating the intricate interplay between structure, properties, and performances. This enables fine-tuning NC properties, making them highly attractive for diverse applications such as (electro)catalysis, sensing, and biomedicine.[1-3] As a result, developing novel NCs has become a focal point of research, motivated by the need to tune the NC properties for future

advancements.[4] Additionally, hydride-containing NCs offer a platform for physically quantifying metal-hydride interactions at the atomic level at resolutions not possible in bulk metal-hydrides.[5] Identification of the hydride positions within NCs is crucial, and single-crystal X-ray diffraction (SCXRD) has proven valuable in this endeavor.[6] Distortions in the metallic framework, such as changes in bond lengths or lattice expansion, can also serve as evidence for assigning hydride location.

Synthetically, doping silver or gold NCs with hetero-metals like palladium, platinum, or rhodium in the presence of borohydride as a reducing agent in a one-pot synthesis can induce hydrogen inclusion. Such hydrogen atom(s) lie(s) within the cluster core near the central hetero-metal and behave(s) somewhat as metallic in nature,[7] playing a crucial role in the formation of superatoms.[8] Hydride-containing gold-rich systems have been initially reported, with gold adept at stabilizing several heterometallic cores.[9-13] In terms of silver, comparatively fewer reports have been made to date. Our research group has successfully isolated examples, incorporating PdH, PtH, RhH, and RhH<sub>2</sub> into M@Ag<sub>19</sub>(dtp/dsep)<sub>12</sub> clusters (M = PdH, PtH, RhH<sub>2</sub>; dtp = dithiophosphate; dsep = diselenophosphate) and (RhH)@Ag<sub>20</sub>(dtp)<sub>12</sub>, all protected by dichalcophosphate ligands.[14-21] Likewise, Lee et al. have reported thiolate-stabilized NCs incorporating RhH, IrH, RuH<sub>2</sub>, and OsH<sub>2</sub> into the Ag<sub>12</sub> icosahedral core of Ag<sub>25</sub>(SR)<sub>18</sub> clusters.[22,23]

Importantly, in several cases, we have noted the ability of the hydride in solution, often resulting in complex distribution of isomers. Isomers differing in the positions of their hydrides are common and can sometimes interconvert via hydride migration.[24-29] Indeed, weak interactions between hydrides and metals often lead to a dynamic hydride migration process. Although this migration was recently suggested from a density functional theory (DFT) investigation on bare (unligated) MHAg<sub>12</sub> cluster models,[30] efforts to experimentally reveal such processes are frequently hindered by the difficulty of capturing intermediate states. Recently, the replacement of hydrides with other more strongly bonded ligands to capture migration intermediates has been reported in Au<sub>22</sub>.[31] However, capturing hydride migration intermediates within superatomic cores remains challenging, as such hydrides cannot be replaced by other ligands. We have previously observed from low-temperature NMR studies that hydride can migrate inside NC icosahedral metallic kernels, leading to complex isomeric distributions in solution.[18]

T.-H. Chiu, M. N. Pillay, J.-H. Liao, C. W. Liu
Department of Chemistry
National Dong Hwa University
No. 1, Sec. 2, Da Hsueh Rd., Hualien 97401, Taiwan
E-mail: chenwei@gms.ndhu.edu.tw

X. Wang
Neutron Scattering Division
Neutron Sciences Directorate
Oak Ridge National Laboratory
Oak Ridge, Tennessee 37831, USA

H. Liang, S. Kahlal, J.-Y. Saillard
Univ Rennes, CNRS, ISCR-UMR 6226
Rennes 35000, France
E-mail: jean-yves@univ-rennes1.fr

ID The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/smll.202501583

© 2025 The Author(s). Small published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/smll.202501583
<figure><img src="image_3.png" /></figure>

**Scheme 1.** The two C₁ polymorphs of RhH₂Ag₁₉ obtained via differ-ent crystallization conditions and characterized by neutron diffraction (RhH₂Ag₁₉₀N, orthorhombic phase (this work); RhH₂Ag₁₉mN, mono-clinic phase.[¹⁸] Their configurational differences in ligand layer (S₂P) is highlighted by the red sticks. Color code: sky blue Agᵢₙco, green for Agᵢₙcap, yellow for S, orange for P.

The movement is made possible by the unique arrangement of
atoms inside the centered icosahedral NC kernel, which offers
several tetrahedral interstitial sites that are energetically favorable
for hydrogen occupancy. The relatively low energy barriers con-
necting the occupation of these sites, combined with the inherent
flexibility of the icosahedral structure, facilitate hydride migra-
tion or “hopping.” Importantly, the occupancy of these interstitial
sites leads to measurable distortions in the metallic framework, a
key factor we leverage in the following discussion to identify the
hydride positions.

We report below a neutron diffraction analysis of a new crys-
tal polymorph of the dihydride NC [RhH₂Ag₁₉ {S₂P(OⁿPr)₂}₁₂]
(RhH₂Ag₁₉). In combination with SCXRD data and DFT calcula-
tions, this study provides insights into the hydride migration pro-
cess within the icosahedral core. These findings not only expand
the library of available hydride-encapsulating NCs but also con-
tribute to our understanding of hydrogen behavior within metal-
rich systems.

In the preparation of heterometallic NCs, the solubility
of the metal precursors is crucial. As detailed in a previ-
ous report,[¹⁸] RhH₂Ag₁₉ was synthesized using a co-reduction
method. Organic-soluble metal precursors, [Ag(MeCN)₄]BF₄
and [Rh(COD)Cl]₂, were reduced by LiBH₄ in the presence
of (NH₄)[S₂P(OⁿPr)₂], (molar ratio: Ag⁺:Rh⁺:[S₂P(OⁿPr)₂]⁻:H⁻
of 40:1:10:20). This reaction yielded [RhH₂Ag₁₉ {S₂P(OⁿPr)₂}₁₂]
(RhH₂Ag₁₉), which was isolated in pure form by column
chromatography. Modifying the crystallization conditions of
RhH₂Ag₁₉ (Scheme 1), we were able to obtain a new crystal habit
in the orthorhombic *Pbca* space group (RhH₂Ag₁₉₀)[³²] (Figure
S1, Supporting Information), distinct from the previously re-
ported monoclinic *P*2₁*/c structure (RhH₂Ag₁₉m).[¹⁸] The molec-
ular structure of RhH₂Ag₁₉₀ differs from that of RhH₂Ag₁₉m in
the orientation and connectivity of four dtp ligands, yielding poly-
morphs (Scheme 1).

Recently, we noted the dynamic behavior of the hydrides
in solution, characterized by VT-NMR (Figure S2, Supporting

Information)[¹⁸] Crucially, the disorder observed within the crys-
tal lattices, as captured by neutron (RhH₂Ag₁₉₀N) and X-ray
diffraction, provides experimental support for a likely hydride mi-
gration pathway within metallic frameworks. In the solid-state
structures, the hydride atoms tend to avoid occupying intersti-
tial sites directly adjacent to capping metal atoms (Agᵢₙcap). This
preference arises from the increased rigidity of the capped tri-
angular faces of the Rh@(Agᵢₙco)₁₂ centered icosahedral kernel.
These specific faces, along with their capping atoms, constitute
the green (Agᵢₙco)₃Agᵢₙcap tetrahedra shown in Figure S1 (Support-
ing Information). In contrast, the hydride atoms prefer occupy-
ing the most deformable interstitial sites that involve Agᵢₙco atoms
distant from Agᵢₙcap.[⁶] The initial evidence of the hydride positions
was attained by first analyzing the distortions of the uncapped
(Agᵢₙco)₃ faces in the disordered X-ray structure of RhH₂Ag₁₉₀,
which exhibits Agᵢₙco partial occupancies that resolve to 55% and
45% (structures 2₀ and 4₀ in Figure 1a; Figure S3, Supporting In-
formation). Furthermore, the configurations of 2₀ and 4₀ are not
identical, and their ∠HRhH angles are different. 2₀ shows an an-
gle (102°) comparable to that observed in RhH₂Ag₁₉m (101° for
both X-ray and neutron structures), while 4₀ presents a smaller
angle (69°). The RhH₂Ag₁₉₀N neutron structure is also disordered
but differently from its X-ray RhH₂Ag₁₉₀ counterpart. Such a dif-
ference can be explained by the different conditions under which
the corresponding single crystals were grown. Two disordered
Agᵢₙco can result in four slightly different metal frameworks, with
the hydride positioned within the expanded tetrahedral cavities
of these four distinct metal frameworks. The two hydrides in
RhH₂Ag₁₉₀N exhibit disorder over five positions, with occupan-
cies of 0.6, 0.43, 0.36, 0.35, and 0.26, respectively, yielding to the
four different configurations 1₀, 2₀, 3₀, and 4₀ shown in Figure 1b,
with ∠HRhH angles of 93°, 96°, 66° and 46°, respectively (Table
1). Note that 2₀ and 4₀ are present in both X-ray and neutron struc-
tures. The Rh...H distances range from 1.67(6) to 1.86(10) Å, with
an average of 1.73(7) Å, which is comparable to that observed in
RhH₂Ag₁₉m.[¹⁸]

Starting from their solid-state structure as models, the geome-
tries of the four distinct configurations 1, 2, 3, and 4, were
optimized through density functional theory (DFT) calculations.
For the sake of computational limitations, the dtp ligands were
replaced by S₂PH₂ models, a simplification that has been proved
to be reasonable in many past investigations.[¹⁴⁻²⁰] The four struc-
tures were found to be minima on the potential energy surface
and, thus, are true isomers. The four isomers lie within a range of
only 3.5 kcal mol⁻¹, isomer 1, being the global minimum (Figure
2). The hydride connectivity in the DFT-optimized structure of
2, slightly differs from that observed in its solid-state counter-
part. In the solid-state structures of 2 (Figure S4, Supporting In-
formation), the two hydrides occupy the T4 and T7 RhAg₃ tetra-
hedral cavities identified in Figure 3, whereas, in the optimized
structure, they occupy the T4 and T6 cavities, T6 and T7 being
neighboring interstitial sites. The discrepancy between the opti-
mized and experimental structures can be attributed to the flat-
ness of the potential energy surface associated with hydride dis-
placements, rendering the ∠HRhH angle sensitive to any weak
structural perturbation. To address this, optimizations of the only
hydride positions within a frozen cluster cage having the ex-
perimental metrics were performed. Indeed, they show a better
alignment of the computed results with the experimental ones
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Metal-framework of a) $RhH_2Ag_{19o}$ b) $RhH_2Ag_{19oN}$, with their disorder deconvolution in individual molecular structures.</figcaption></figure>

(Tables S1 and S2, Supporting Information). In particular, the hydrides of the $2_o$ (partly) optimized structure now occupy the T4 and T7 cavities. A plausible hydride migration pathway was subsequently explored by investigating interconversions between these four closely related isomers. During our search for transition states, a fifth isomer, namely $IM_o$, was discovered. Al-

though this key intermediate has not been experimentally observed, it plays a crucial role in linking the entire migration pathway (Figure 2). The whole hydride migration pathway involves seven different tetrahedral cavities (Figure 3). In each transition state, the imaginary frequency corresponds to the vibration of the $\mu_3$-hydride, oscillating between two tetrahedral cavities within the

<table><caption>**Table 1.** Selected experimental distances (Å) and angles (deg.) for X-ray and neutron structure $1_o$, $2_o$, $3_o$, and $4_o$.</caption><thead><tr><th>Comp.</th><th>1<sub>o</sub>[neutron]</th><th>2<sub>o</sub>[neutron]</th><th>3<sub>o</sub>[neutron]</th><th>4<sub>o</sub>[neutron]</th><th>2<sub>o</sub>[X-ray]</th><th>4<sub>o</sub>[X-ray]</th></tr></thead><tbody><tr><td>CSM</td><td>0.37</td><td>0.43</td><td>0.29</td><td>0.22</td><td>0.43</td><td>0.28</td></tr><tr><td>Rh-Ag<sub>ico</sub></td><td>2.75(2)-2.92(4)<br>avg. 2.83(3)</td><td>2.75(2)-2.92(4)<br>avg. 2.83(3)</td><td>2.75(2)-2.91(3)<br>avg. 2.82(3)</td><td>2.76(2)-2.90(2)<br>avg. 2.82(3)</td><td>2.770(1)-2.883(2)<br>avg. 2.822(3)</td><td>2.770(1)-2.871(2)<br>avg. 2.819(3)</td></tr><tr><td>Ag<sub>ico</sub>-Ag<sub>ico</sub></td><td>2.82(2)-3.43(3)<br>avg. 2.98(3)</td><td>2.79(3)-3.46(3)<br>avg. 2.97(3)</td><td>2.79(3)-3.46(3)<br>avg. 2.97(3)</td><td>2.82(2)-3.38(3)<br>avg. 2.95(3)</td><td>2.799(2)-<br>3.483(2)<br>avg. 2.968(2)</td><td>2.819(1)-3.423(2)<br>avg. 2.963(2)</td></tr><tr><td>Ag<sub>ico</sub>-Ag<sub>cap</sub></td><td>2.89(2)-3.16(3)<br>avg. 3.04(3)</td><td>2.89(2)-3.16(3)<br>avg. 3.04(3)</td><td>2.89(2)-3.11(2)<br>avg. 3.03(3)</td><td>2.89(2)-3.10(2)<br>avg. 3.03(3)</td><td>2.886(1)-<br>3.230(1)<br>avg. 3.027(2)</td><td>2.886(1)-3.081(1)<br>avg. 3.014(1)</td></tr><tr><td>Rh-H</td><td>1.67(6)-1.72(4)<br>avg. 1.69(5)</td><td>1.67(6)-1.72(4)<br>avg. 1.69(5)</td><td>1.67(6)-1.71(6)<br>avg. 1.69(6)</td><td>1.67(7)-1.86(10)<br>avg. 1.79(8)</td><td>1.64 (4)-1.77(10)<br>avg. 1.71 (10)</td><td>1.62(4)-1.63(4)<br>avg. 1.63(6)</td></tr><tr><td>Ag<sub>ico</sub>-H</td><td>1.77(8)-2.27(7)<br>avg. 1.96(7)</td><td>1.81(6)-2.09(7)<br>avg. 1.95(6)</td><td>1.80(6)-2.09(7)<br>avg. 1.92(6)</td><td>1.70(9)-2.26(10)<br>avg. 1.95(9)</td><td>1.84<br>(10)-2.06(10)<br>avg. 1.94 (18)</td><td>1.89(5)-1.94(4)<br>avg. 1.91(10)</td></tr><tr><td>H-Rh-H</td><td>93</td><td>96</td><td>66</td><td>46</td><td>102</td><td>69</td></tr></tbody></table>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 2.** Proposed hydride migration within icosahedron, with configurations **1**<sub>o</sub>, **2**<sub>o</sub>, **3**<sub>o</sub>, and **4**<sub>o</sub> observed experimentally (ligands omitted for clarity).</figcaption></figure>

metal framework (Figure S5, Supporting Information). The energy barriers connecting the isomers range as low as nearly 0 to 3.6 kcal mol⁻¹ (Figure 2). These small energy differences help explain the dynamic disorder observed experimentally. Notably, as the two hydrides migrate from **1**<sub>o</sub> to **2**<sub>o</sub>, **IM**<sub>o</sub>, **3**<sub>o</sub>, and **4**<sub>o</sub>, and eventually return to **1**'<sub>o</sub>', their positions are exchanged. This observation indicates that the two hydrides are equivalent (Figure S6, Supporting Information). Based on the hydride migration pathway of **RhH<sub>2</sub>Ag<sub>19</sub>**, we thus propose a possible hydride migration pathway for **RhH<sub>2</sub>Ag<sub>19m</sub>**. In addition to **1<sub>m</sub>**, which shows good alignment with both neutron and X-ray structures (**RhH<sub>2</sub>Ag<sub>19mN</sub>** and **RhH<sub>2</sub>Ag<sub>19m</sub>**), we identified three additional distinct intermediates: **2<sub>m</sub>**, **3<sub>m</sub>**, and **4<sub>m</sub>** (Figure 4; Table S3, Supporting Information). Similar results were observed in the hydride migration pathway of **RhH<sub>2</sub>Ag<sub>19m</sub>**, characterized by minimal energy

barriers and the ability of two hydrides to exchange positions via migration (Figure 4; Figure S7, Supporting Information).

The TD-DFT-simulated UV-vis spectra computed at the CAM-B3LYP/Def2-TZVP level for all the isomers of **RhH<sub>2</sub>Ag<sub>19</sub>** and **RhH<sub>2</sub>Ag<sub>19m</sub>** are shown in Figures S8 and S9 (Supporting Information). The simulated spectra for each isomer have two bands, the one at the lowest energy being sometimes reduced to a shoulder peak. These two bands are of 1P → 1D nature. The variations in the peak profile for each isomer highlight the significant influence of minor geometrical differences on the optical/absorption properties. Notably, when the simulated spectra of all the isomers are averaged, the resulting spectrum shows a good correlation to the experimental spectrum of **RhH<sub>2</sub>Ag<sub>19</sub>** (Figure S9, Supporting Information). This suggests that **RhH<sub>2</sub>Ag<sub>19</sub>** contains a mixture of isomers in solution, correlating to the proposed behavior described herein.

In summary, we obtained isomers of **RhH<sub>2</sub>Ag<sub>19</sub>**[**S<sub>2</sub>P(OPr)<sub>2</sub>**]₁₂ by controlling crystallization conditions and determined its atomically precise structure through X-ray and neutron diffraction. For the first time, a visual slice of hydride migration pathways within an enclosed icosahedral core of atomically precise nanoclusters is reported. The experimentally observed lattice disorder supports a possible mechanism for the hydride migration predicted by DFT calculations. This work thus provides valuable justification for future studies that may include dynamic techniques, such as variable-temperature neutron diffraction or quasielastic neutron scattering, potentially providing direct confirmation of hydride motion. This contributes to our understanding of hydride-metal interactions and the design of advanced hydride-containing superatomic systems for tailored applications.

## 2. Experimental Section

All chemicals were purchased from commercial sources and used as received. Solvents were purified following standard protocols. All reactions were carried out under N₂ atmosphere by using standard Schlenk techniques. [RhH₂@Ag₁₉ {**S₂P(OⁿPr)₂**}]₁₂ was prepared by the same procedure reported earlier.[¹⁸] The purified product was recrystallized under two

<figure><img src="image_7.png" /><figcaption>**Figure 3.** The seven tetrahedral cavities of **RhH₂Ag₁₉** selected for the DFT optimization study with five tetrahedra determined experimentally T1, T2, T4, T6, and T7 (red text); two assigned based on proximity T3, T5 (black text). The tetrahedral cavity where the hydride is located in the solid-state structure: 1o: (T1, T4), 2o: (T7, T4), 3o: (T2, T7), 4o: (T1, T6).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 4.** Hydride migration of $RhH_2Ag_{19m}$. (ligands omitted for clarity).</figcaption></figure>

different conditions: pure MeOH and a MeOH:hexane (1:1) mixture. Under the pure MeOH condition, black rod-like crystals of $RhH_2Ag_{19o}$ were obtained after approximately one week. Under the MeOH:hexane (1:1) condition, black prismatic crystals of $RhH_2Ag_{19m}$ were obtained after approximately one week.

**X-Ray Crystallography:** Single crystals suitable for X-ray diffraction analysis of $RhH_2Ag_{19o}$ was obtained by evaporating MeOH solution at 4 °C within a week. The single crystals were mounted on the tip of glass fiber coated in paratone oil, then frozen. Data were collected on a Bruker APEX II CCD diffractometer using graphite monochromated Mo $\alpha$ radiation ($\lambda$ = 0.71073 Å) at 100 K. Absorption corrections for area detector were performed with SADABS[32] and the integration of raw data frame was performed with SAINT.[33] The structure was solved by direct methods and refined by least-squares against $F^2$ using the SHELXL-2018/3 package,[34,35] incorporated in SHELXTL/PC V6.14.[36] All non-hydrogen atoms were refined anisotropically. Selected X-ray crystallographic data is listed in Table S5 (Supporting Information).

**Single-Crystal Neutron Diffraction:** The hydride locations in $[RhH_2Ag_{19} \{S_2P(O^{\prime\prime}Pr)_2\}_{12}] (RhH_2Ag_{19oN})$ were confirmed by a single-crystal neutron diffraction experiment using the TOPAZ single-crystal neutron time-of-flight (TOF) Laue diffractometer at ORNL's Spallation Neutron Source.[37] Single crystals suitable for neutron diffraction were obtained by slow evaporation of methanol at ambient temperature within two weeks. A black, block-shaped crystal of $RhH_2Ag_{19oN}$ (2.95 mm × 1.06 mm × 0.85 mm, Figure S10, Supporting Information) was attached to a MiTeGen loop using a perfluorinated grease (Krytox GPL 205) and transferred to TOPAZ goniometer for data collection at 100 K. A total of 28 crystal orientations optimized with CrystalPlan software[38] were used to ensure better than 95% coverage of a hemisphere of reciprocal space (Figure S12, Supporting Information). The data were collected for ≈136 h with 20 C of proton charge each at the beam power of 1.4 MW. Raw peaks intensities were obtained using the 3-D ellipsoidal Q-space integration method available in Mantid.[39] Data normalization, including Lorentz, neutron 6 TOF spectrum, and detector efficiency corrections, were carried out with the ANVRED3 program.[40] A Gaussian numerical absorption correction was applied with $\mu$ = 1.1716 + 1.1088 $\lambda$ cm$^{-1}$. The reduced data were saved in SHELX HKLF2 format, in which the neutron wavelength for each reflection was recorded separately. Non-hydrogen atom positions in the X-ray structure were used for the initial refinement of the neutron structure. Hydrogen atoms on carbon atoms are placed using the riding model available in SHELXL-2014.[41] The position of hydride was located from the difference Fourier map calculated using the

neutron data. All non-hydrogen atoms and the interstitial hydride atoms were refined anisotropically, and the neutron structure was then refined successfully to convergence using the SHELXL-2014 program. Selected neutron crystallographic data is listed in Table S6 (Supporting Information). The neutron structures reported herein have been deposited at the Cambridge Crystallographic Data Centre. CCDC 2410768 (RhH$_2$Ag$_{19oN}$) contains the supplementary crystallographic data. This data can be obtained free of charge from the Cambridge Crystallographic Data Centre via https://www.ccdc.cam.ac.uk/data_request/cif.

**Computational Details:** Geometry optimizations were carried out within the formalism of the density functional theory (DFT) with the Gaussian 16 package,[42] using the BP86 functional[43,44] and the Def2-TZVP basis set from EMSL Basis Set Exchange Library.[45,46] All the optimized geometries were characterized as true minima or transition states by vibrational analysis. The compositions of the molecular orbitals were calculated using the AOMix program.[47] The natural atomic orbital (NAO) charges and Wiberg bond indices were computed with the NBO 6.0 program.[48] The UV-visible transitions were calculated on the above-mentioned optimized geometries by means of time-dependent DFT (TD-DFT) calculations, with the CAM-B3LYP functional[49] and the Def2-TZVP basis set. The UV-visible spectra were simulated from the computed TD-DFT transition energies and their oscillator strengths by using the SWizard program,[50] each transition being associated with a Gaussian function of half-height width equal to 2000 cm$^{-1}$.

[CCDC 2410767 (for RhH$_2$Ag$_{19o}$) and 2410768 (for RhH$_2$Ag$_{19oN}$) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif].

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

This work was supported by the National Science and Technology Council of Taiwan (113-2123-M-259-001) and the GENCI French National Computer Resource Center (A0030807367). Single-crystal neutron diffraction
performed on TOPAZ used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory, under contract no. DE-AC05-00OR22725 with UT-Battelle, LLC. H.L. thanks the China Scholarship Council for a Ph.D. grant.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.

## Keywords

hydrides, isomers, migration, rhodium, silver

Received: February 9, 2025

Revised: March 11, 2025

Published online:

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