Vacancy‐Induced Atomic Diffusion in a Molecular Metal Cluster Complex

Abstract

The presence of atomic vacancies in a close‐packed material is believed to allow the migration of atoms adjacent to the vacancies, which induces dynamics of atoms. However, it is not known whether atoms in discrete molecules can undergo vacancy‐induced dynamics. We describe herein the generation of a close‐packed Pd₁₂ cluster complex [Pd₁₂(C₇H₇)₆][B(Ar^F)₄] _n (n = 2, 3) with a Pd‐atom vacancy, and the observation of the diffusion of Pd atoms. Variable‐temperature NMR analysis, X‐ray structure analysis, and theoretical calculations indicate that an atomic vacancy is located at the surface sites of the Pd₁₂ core, and that it migrates rapidly on the NMR timescale. This means that all 11 palladium atoms at the surface undergo self‐diffusion with a low energy barrier. These results demonstrate, for the first time, that atomic diffusion occurs within a molecule through the vacancy mechanism.

We report the formation and dynamic behavior of atomic vacancy in an organometallic palladium cluster complex. Variable‐temperature NMR analysis and theoretical calculations of the Pd₁₂ cluster [Pd₁₂(C₇H₇)₆][B(Ar^F)₄]₂ suggest that an atomic vacancy migrates rapidly at the surface of the metal cluster on the NMR timescale, leading to the vacancy‐induced atomic diffusion in a molecule.

Atomic defects or vacancies have been believed to have important effects on the properties of materials. For example, when atomic defects exist in close‐packed materials, diffusion of atoms is likely to occur via sequential migration to vacancy sites (Figure 1a).^{[ 1 ]} Nonetheless, it is generally difficult to track the atomic diffusion occurring with vacancy migration, even in electron microscopy analysis of low‐dimensional materials.^{[ 2} , ³ , ⁴ , ^{5 ]} If atomic vacancies can be precisely introduced into discrete molecules, their dynamic behavior can be studied with a finite number of possible positions, contributing to the fundamental understanding of the vacancy‐induced dynamics of atoms. To the best of our knowledge, however, there is no report of observations of atomic vacancy migration in close‐packed clusters at the molecular level. Furthermore, it is not known whether atomic diffusion occurs in molecules. This is probably due to the lack of suitable model molecules; that is, in order to observe the vacancy migration, not only must the molecule be able to hold a polyatomic packing structure with atomic vacancies, but also the molecular structure must be such that temperature‐dependent spectral changes associated with the migration of an atomic vacancy can be observed. In fact, it is difficult to find suitable polynuclear metal complexes of transition‐ or main‐group metal elements that satisfy these conditions, although numerous metal cluster complexes have been synthesized in previous thorough synthetic efforts.^{[ 6} , ⁷ , ⁸ , ^{9 ]} For group 11 metals, the 12‐atom mixed metal cluster complexes with copper as the major metal element, AuCu₁₁{S₂P(O ⁱ Pr)₂}₆(C≡CPh)₃Cl and MHCu₁₁{S₂P(O ⁱ Pr)₂}₆(C≡CPh)₄ (M = Pd, Pt), were recently prepared, and these compounds can be regarded as close‐packed metal clusters having an atomic vacancy.^{[ 10} , ¹¹ , ^{12 ]} However, dynamic vacancy migration has not been reported for these known cluster complexes.

Figure 1.

a) A schematic model for the vacancy mechanism of the atomic diffusion in a solid. b) The vacancy migration leads to atomic diffusion in the Pd₁₂ cluster complex 4.

We surmised that the organometallic cluster complexes recently developed by our group^{[ 13} , ^{14 ]} would provide a suitable molecular model for studying the dynamic properties of an atomic vacancy if a single metal‐atom vacancy could be introduced into the molecular framework. Here we report the generation and dynamic behavior of the organo‐Pd₁₂ cluster complex, which has a palladium‐atom vacancy. We found that the Pd₁₂ cluster complex exhibits rapid diffusion of palladium atoms through the vacancy mechanism (Figure 1b).

Our laboratory reported that the fcc‐close‐packed, cuboctahedral 13‐atom palladium cluster complexes having no atomic vacancy, [Pd₁₃Tr₆][B(Ar^F)₄]₂ [1; Ar^F = 3,5‐(F₃C)₂C₆H₃] and [Pd₁₃Tr₆][B(Ar^F)₄]₃ (2) (Figure 2), can be constructed by tetraarylborate‐induced reductive transformation of the Pd₃ sandwich complex [Pd₃Tr₂][B(Ar^F)₄]₂ (3).^{[ 13 ]} In 1 or 2, octahedrally arranged six Tr ligands well hold the Pd₁₃ core through μ₄‐facial coordination, where the octahedral arrangement of ligands is ideal for six‐coordinate metal complexes. These structural features led us to expect that a one‐atom‐deficient Pd₁₂ core will also be well retained within this organometallic face‐capping ligand shell. Importantly, the ¹H and ¹³C NMR resonance patterns of the Tr ligands in the homoleptic complex may provide insight into the structural changes occurring inside the ligand shell.

Figure 2.

The Pd₁₃ cluster complexes 1 and 2, and the Pd₁₂ cluster complexes 4 and 5. Deficiency of a surface metal atom of an fcc cuboctahedral Pd₁₃ core yields an fcc Pd₁₂ core with an atomic vacancy.

Although the Pd₁₃ complex 1 is formed by heating the neat trinuclear complex 3 ^{[ 15} , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ^{20 ]} at 160 °C overnight in the presence of an excess of cycloheptatriene (CHT) under vacuum and subsequent treatment with Et₃N,^{[ 13 ]} we found that a shorter reaction time resulted in the production of a mixture of 1 and the Pd₁₂ complex [Pd₁₂Tr₆][B(Ar^F)₄]₂ (4). The results of the treatment of 3 (22 µmol) at 140 °C are summarized in Figure 3. The reaction for 5 h gave a mixture of 1 and 4 in a 64:36 molar ratio, and a further reduction in the reaction time to 2 min increased the proportion of 4, giving a molar ratio of 40:60, albeit the total yield of 1 and 4 decreased from 17% for 5 h to 10% for 2 min. In a preparative‐scale reaction, a mixture of 1 and 4 in a molar ratio of 21:79 was obtained in a total yield of 10% by heating 3 at 140 °C for 3 min. The Pd₁₂ complex 4 was detected by ESI‐MS analysis (Figure 4a). Also, the Pd₁₂ complex 4 exhibited a distinct singlet ¹H or ¹³C NMR resonance for its Tr ligands at room temperature (Figure 4b,c). In the mechanism proposed for the formation of 1, which involves five steps—i) Ar^F group transfer, ii) Ar^F–Tr reductive coupling, iii) ligand exchange, iv) deprotonation or CHT elimination, and v) agglomeration (Scheme S1)^{[ 13 ]}—the agglomeration step (step v) involves the assembly of the transient trinuclear species Pd₃Tr₂ and [Pd₃Tr]⁺. In this agglomeration, an additional Pd⁰ atom must be captured to yield the Pd₁₃ complex 1; therefore, some of the intermediates must decompose during the reaction to become a source of Pd⁰. The short reaction time presumably suppressed incorporation of the additional Pd⁰ during the agglomeration, and the Pd₁₂ complex 4 formed instead of the Pd₁₃ complex 1. Although the Pd₁₂ complex 4 is stable in solution at room temperature for 1 day, it gradually decomposed on heating in C₂D₄Cl₂ at 70 °C (33% of 4 was consumed after 3 days). On the other hand, complex 1 remained intact even for 1 week under a similar condition. Addition of Pd₂(dba)₃ to a CD₂Cl₂ solution of 4 did not afford 1, indicating that the Pd₁₂ core in 4 is well protected by the hexakis‐Tr ligand shell.

Figure 3.

a) The reaction in a short time gave a mixture of the Pd₁₃ complex 1 and the Pd₁₂ complex 4. b) An ESI‐MS spectrum of 4 (black line = observed spectrum; deep blue line = simulated spectrum for [Pd₁₂(C₇H₇)₆]²⁺.

Figure 4.

a) Variable‐temperature ¹H NMR spectra of a mixture of 1 and 4 in THF‐d ₈. b) A ¹³C NMR spectrum of a mixture of 1 and 4 in THF‐d ₈ at −100 °C. For (a) and (b), △ = 1, ○ = 4, and × = impurities.

Although attempts to separate 1 and 4 failed, the structure of the Pd₁₂ complex 4 was investigated by NMR analysis. Also, the structure of the one‐electron oxidized product of 4 was examined by X‐ray structure analysis (see below). An ¹H NMR analysis of a mixture of 1 and 4 in THF‐d ₈ at 20 °C showed that both complexes 1 and 4 exhibit a sharp singlet resonance for Tr protons at δ = 6.26 and at δ = 5.99, respectively. Interestingly, the Pd₁₂ complex 4 showed a temperature‐dependent behavior. The singlet resonance for the Tr protons of 4 at 20 °C decoalesced to three resonances with a relative intensity ratio of 1:1:1 at −100 °C (Figure 4a). This contrasts with the fact that the Pd₁₃ complex 1 showed no apparent change in its singlet resonance pattern at low temperatures down to −100 °C (Figure 4a). The ¹³C NMR analysis also supported this temperature‐dependent behavior, as three ¹³C resonances were observed for 4 at −100 °C (δ = 89.8, δ = 77.2, δ = 76.5), while 1 exhibited a sharp singlet signal at δ = 81.8 at the same temperature (Figure 4b). The observed patterns of the ¹H or ¹³C NMR resonances indicate that there are three chemically nonequivalent environments for the six Tr ligands in 4.

It is unlikely that the loss of one Pd atom would result in a significant change in the octahedral ligand geometry or the packing pattern of the metal atoms, partly because the cuboctahedral M₁₃ core in 1 is stereochemically adaptable to the octahedral ligand shell of the μ₄‐face‐capping ligands through square‐face augmentation.^{[ 14} , ^{21 ]} Rather, it might be reasonable to assume that 4 has a structure with one Pd atom missing from the Pd₁₃ core in 1, while almost maintaining an octahedral ligand geometry and the packing pattern of Pd atoms (fcc). In this case, there are two ways to remove one Pd atom from the Pd₁₃ complex 1: removal of one from the 12 surface atoms, yielding 4‐surf, or removal of the interstitial atom, yielding 4‐int (Figure 5). Complex 4‐surf has three types of Tr ligands (A‐, B‐, and C‐rings), depending upon the distance from the surface atomic vacancy (Figure 5a), whereas 4‐int has two types of Tr ligands (A‐ and B‐rings) when it distorts to a pseudo‐D _4h symmetric structure (Figure 5b), as discussed below. Thus, the structure of 4‐surf is consistent with the observed ¹H or ¹³C NMR resonance pattern of 4 at low temperatures, whereas that of 4‐int is not.

Figure 5.

The two possible vacant sites for the Pd₁₂ complex 4. The values indicate the relative potential energy (ΔE). a) The DFT‐optimized geometries of 4‐surf′. Selected optimized bond lengths (Å) for 4‐surf′: Pd2─Pd3 2.715, Pd2─Pd8 2.802, Pd2─Pd9 2.737, Pd3─Pd4 2.886, Pd3─Pd5 2.693, Pd4─Pd5 2.736, Pd4─Pd9 2.772, Pd4─Pd10 2.695, Pd5─Pd6 2.802, Pd5─Pd11 2.787, Pd6─Pd7 2.715, Pd6─Pd11 2.738, Pd7─Pd8 2.692, Pd7─Pd12 2.885, Pd8─Pd9 2.789, Pd9─Pd10 2.839, Pd10─Pd11 2.839, Pd_C─Pd2 2.675, Pd_C─Pd3 2.671, Pd_C─Pd4 2.779, Pd_C─Pd5 2.780, Pd_C─Pd6 2.676, Pd_C─Pd7 2.670, Pd_C─Pd8 2.780, Pd_C─Pd9 2.805, Pd_C─Pd10 2.679, Pd_C─Pd11 2.804, Pd_C─Pd12 2.779. b) The DFT‐optimized geometries of 4‐int′. Selected bond lengths (Å) for 4‐int′: Pd1─Pd2 2.697, Pd1─Pd3 2.818, Pd2─Pd2* 2.793, Pd2─Pd3 2.754, Pd2─Pd4 2.728, Pd3─Pd3* 2.653, Pd3─Pd4* 2.824.

The presence of a surface atomic vacancy was supported by the X‐ray structure analysis. That is, a single crystal was obtained by recrystallization of a mixture of the tricationic cluster complexes [Pd₁₃Tr₆][B(Ar^F)₄]₃ (2)^{[ 13 ]} and [Pd₁₂Tr₆][B(Ar^F)₄]₃ (5), which was generated by treating a mixture of 1 and 4 (the molar ratio of 1/4 = 23:77) with [H(OEt₂)₂][B(Ar^F)₄]. The X‐ray structure analysis^{[ 22 ]} of the crystal showed that the apparent decrease in occupancy was found at the surface sites of the cuboctahedral Pd core, rather than at the interstitial site, with the octahedral ligand shell retained (two surface sites showed occupancies of 0.58 and 0.73, respectively, indicating atomic deficiencies; see Figures S17 and S18). Such a decrease in occupancy was not observed for the X‐ray structure analysis of a pure sample of the Pd₁₃ cluster 2 (Figure S17).^{[ 13 ]} These results suggest that the crystal contains 2 and 5 and that the atomic vacancy in 5 is located at the surface position, consistent with the result of the low‐temperature NMR studies described above. It is noted that the X‐ray structure analysis showed no signs of vacancy migration in the crystalline state under the condition where the X‐ray data were collected at −183 °C (see below for the discussion on the vacancy migration based on the variable‐temperature NMR analysis in solution).

We then carried out density functional theory (DFT) calculations: Geometries were optimized using the B3PW91 functional^{[ 23} , ²⁴ , ²⁵ , ²⁶ , ^{27 ]} with the Grimme's empirical dispersion correction^{[ 28} , ^{29 ]} and the Beck–Johnson damping factor D3(BJ),^{[ 30} , ³¹ , ^{32 ]} where the LANL2DZ basis set was used for Pd atom with the corresponding effective core potentials (ECPs),^{[ 33 ]} and the 6‐31G(d) basis sets were used for other atoms. Single‐point calculations were performed to obtain better energy changes using the same functional, where the Stuttgart–Dresden–Bonn basis set^{[ 34 ]} and the corresponding ECPs were used for Pd atoms, and 6‐311G(d) basis sets^{[ 35 ]} were used for other atoms. The Gaussian 16 program^{[ 36 ]} was used; details of calculations are presented in the Supporting Information. The DFT calculations indicated that the surface‐defect dication [Pd₁₂Tr₆]²⁺ (4‐surf′) is more stable than the interstitial‐defect dication 4‐int′ by ΔE = 31.9 kcal mol⁻¹, where ΔE is the potential‐energy difference. This also supports that the Pd₁₂ complex 4 has a surface atomic vacancy. Note that all twelve surface Pd sites in the Pd₁₃ cluster [Pd₁₃Tr₆]²⁺ are equivalent, as supported by the X‐ray structure^{[ 13 ]} and electronic structure analysis,^{[ 37} , ^{38 ]} including topological analysis of the computed electron density (see the Supporting Information).^{[ 39 ]} This means that generating an atomic vacancy at any surface atomic site of the Pd₁₃ cluster results in the formation of an equivalent structure. The optimized geometry shown in Figure 5a indicates that the surface atomic vacancy in 4‐surf′ results in three chemically nonequivalent environments for the six Tr rings (A‐, B‐, and C‐rings). The A‐rings coordinate to the Pd₁₂ core in a μ₃‐η²:η¹:η²‐bridging mode with one C═C moiety of the Tr ligand remaining uncoordinated. The B‐ and C‐rings coordinate to the Pd₁₂ core in a μ₄‐η¹:η²:η²:η²‐bridging mode. This difference in the Tr coordination mode might be related to the fact that the ¹³C chemical shift of one resonance (δ = 89.8) is markedly shifted downfield compared with those of the other two resonances, which exhibit similar chemical shifts (δ = 77.2 and 76.5) (Figure 4b). In general, a decrease in the number of metal atoms bound to an unsaturated hydrocarbon ligand results in a downfield shift of a ¹³C resonance.^{[ 40 ]} Consistently, the calculated ¹³C NMR chemical shifts suggested that A‐rings exhibit a low‐field shifted resonance compared to B‐ and C‐rings (Table S10). The Pd₁₂ cluster core in 4‐surf′ maintains an fcc close‐packed structure, although the presence of the vacancy site at a surface position results in slight distortion about the Pd─Pd bonded skeleton (Figure 5a). In the cuboctahedral Pd₁₃ core in 1, the interstitial Pd atom (Pd_C) is bonded to the surface Pd atoms with approximately equal Pd─Pd lengths (the radial Pd─Pd bond lengths are 2.72 Å (av); calcd. 2.77 Å (av)). In contrast, in the optimized geometry of 4‐surf′, the radial Pd─Pd bonds are shortened to 2.67 Å (av) for the surface Pd atoms adjacent to the vacancy site (Pd2, Pd3, Pd6, and Pd7) and the Pd atom trans to the vacancy site (Pd10). There is little change in the lengths of the other radial Pd─Pd bonds (2.78 Å (av)).

The DFT‐optimized geometry of 4‐int′ showed that the interstitial atomic vacancy gives rise to a large distortion (Figure 5b). The distance (2.97 Å) between the two square faces (the Pd2─Pd3─Pd3*─Pd2* face and the Pd2**─Pd3**─Pd3***─Pd2*** face) is shorter by 0.88 Å than the corresponding distance in 1 (3.85 Å), giving an ellipsoidal Pd₁₂ core with a pseudo‐D _4h symmetry. As a result, 4‐int′ offers two chemically nonequivalent environments (the A‐ and B‐rings) for the Tr ligands. Both A‐ and B‐rings in 4‐int′ coordinate in a μ₄‐fashion, but the Pd₄ faces bound to the B‐rings are largely distorted to a rhombic structure; the acute angle of the Pd₄ rhombus capped by the A‐ring is 65°, whereas that of the Pd₄ square capped by the B‐ring is 89°.

To gain an insight as to why 4‐surf′ is much more stable than 4‐int′, we compared the stability of the bare Pd₁₂ cores and their interaction energy. The bare Pd₁₂ core in 4‐surf′, which contains a surface vacancy, is more stable than the interstitial‐defect Pd₁₂ core in 4‐int′ by 22.1 kcal mol⁻¹. This result can be understood by considering that the interstitial defect leads to a loss of 12 radial Pd─Pd bonds, whereas the surface defect loses only five Pd─Pd bonds (one radial and four surface Pd─Pd bonds). The Wiberg bond indices for radial Pd─Pd bonds (0.098 (av)) are slightly larger than those for surface ones (0.073 (av)) in 1′,^{[ 37} , ^{38 ]} supporting the disadvantage of the loss of radial Pd─Pd bonds.

On the other hand, the interaction energy between the Pd₁₂ core and the [Tr₆]²⁺ ligand shell is slightly larger (more negative; that is, more stable in energy) in 4‐surf′ than in 4‐int′ by 3.1 kcal mol⁻¹. This difference in the interaction energy might be caused by several factors. In 4‐surf′, two A‐rings coordinate to the distorted Pd₃ site in a μ₃‐fashion, whereas the other B‐ and C‐rings coordinate to the Pd₄ site in a μ₄‐fashion. In 4‐int′, all six Tr ligands maintain a μ₄‐coordination to the Pd₄‐site, where the four Pd₄ sites capped by the A‐ring are largely distorted to the rhombic face. A μ₄‐coordination bond is much stronger than a μ₃‐bond,^{[ 37 ]} but the distortion of the Pd₄ sites at the A‐ring could decrease the stabilization energy by μ₄‐coordination in 4‐int′. These differences in the coordination manner of the Tr ligands and the distortion of the cluster surfaces could cause a slight difference in the interaction energy between 4‐surf′ and 4‐int′. We conclude that the relative stability of 4‐surf′ over 4‐int′ results mainly from the stabilization energy of the Pd₁₂ core. Notably, the interaction energy between the Pd₁₂ core and the ligand shell for 4‐surf′ and 4‐int′ is less than that of 1′ by 45.5 and 48.6 kcal mol⁻¹, respectively.

Next, we discuss the observed dynamic NMR behavior of 4‐surf. The coalescence of three ¹H or ¹³C NMR resonances upon raising the temperature suggests that 4‐surf undergoes a rapid dynamic behavior accompanied by the exchange of all Tr ligands on the NMR timescale. Line‐shape analysis of the temperature‐dependent ¹H NMR spectra allowed us to estimate the activation parameters, ΔG ^‡ ₂₉₈ = 9.4(4) kcal mol⁻¹, ΔH ^‡ = 10(1) kcal mol⁻¹, and ΔS ^‡ = 1.9(4) e.u.

There are three possible mechanisms for the exchange of the Tr ligands: (i) rapid migration of the atomic vacancy using all surface positions, (ii) rapid interconversion between 4‐surf and 4‐int through migration of the atomic vacancy between the surface and interstitial positions, and (iii) rapid migration of the Tr ligands on the rigid Pd₁₂ surface. We note that the internal space of the ligand shell, which the octahedrally arranged six Tr ligands surround, is almost filled with the Pd₁₂ or Pd₁₃ cluster core, leaving no room for Pd to move except by the above mechanisms involving the atomic vacancy migration (see the Supporting Information for the percent buried volume analysis^{[ 41 ]} around each Pd atom). Theoretical results confirm that the migration of the atomic vacancy at the surface positions (mechanism (i)) proceeds with a low barrier (ΔG ^‡ ₂₉₈ = 9.8 kcal mol⁻¹) (Figure 6), which agrees well with the experimentally observed value (ΔG ^‡ ₂₉₈ = 9.4(4) kcal mol⁻¹). On the other hand, the other two mechanisms are unlikely to occur at room temperature: for the mechanism (ii), the large energy difference between 4‐surf′ and 4‐int′ (ΔE = 31.9 kcal mol⁻¹) is inconsistent with the experimental ΔG ^‡ ₂₉₈ value; for the mechanism (iii), the ligand migration results in large destabilization and thus is energetically inaccessible (see the Supporting Information and Figure S15 for discussion). These experimental and theoretical results strongly suggest that an atomic vacancy moves around the surface of the Pd₁₂ core in 4‐surf on the NMR timescale (mechanism (i)).

Figure 6.

Geometry and energy changes in the atomic vacancy migration in [Pd₁₂Tr₆]²⁺. Rotation of the A1 ring assists the migration of the Pd6 atom to the original vacancy site.

We performed distortion/interaction analysis^{[ 42} , ⁴³ , ^{44 ]} to find the origin of the activation energy. On going from 4‐surf′ to the transition state 4‐surf′‐TS, the energy changes of the Pd₁₂ core, the [Tr₆]²⁺ ligand shell, and the interaction energies are +3.7, −2.7, and +8.4 kcal mol⁻¹, respectively, where potential energies are employed and a positive value means the term contributes to an increase in the activation barrier. These values indicate that a change in the interaction energy is the major contributor to the activation barrier. Movement of the Pd6 atom on approaching 4‐surf′‐TS is accompanied by cleavage of the Pd6−(B1 ring) coordination bonds. This might cause a reduction in the interaction energy at 4‐surf′‐TS. Notably, the A1‐ring maintains coordination bonds to Pd6 on the way to the transition‐state structure (see Figure 6 for the atom label). On going from 4‐surf′ to 4‐surf′‐TS, the Pd6─Pd11 bond is cleaved and a Pd6─Pd3 bond is formed. The radial Pd6─Pd_C bond is retained in 4‐surf′‐TS. A further shift of the Pd6 atom to the original vacant site accompanies the formation of Pd6─(A2 ring) coordination bonds, with retention of the attachment of the original A1 ring to the Pd6 atom. Also, the Pd6─Pd5 bond is cleaved and the Pd6─Pd2 bond is formed for completion of the vacancy migration.

The present results indicate that atomic diffusion proceeds facilely in a molecular metal complex through the vacancy mechanism. Notable is the fact that the atomic vacancy migrates rapidly and randomly within a finite number of positions in a molecule, i.e., 12 surface positions in the present case. Such vacancy‐induced atomic diffusion in discrete molecules is unprecedented, although there are a few reports of the dynamic skeletal rearrangement of metal cluster complexes.^{[ 45} , ^{46 ]} The use of the organometallic cluster supported by a small number of ligands provided a molecular platform with high symmetry and organometallic π‐coordinating nature, leading to the present observation of atomic diffusion. It is also valuable to note that the present results provide the quantification of the energy barrier to atomic‐vacancy migration, although its experimental evaluation is difficult in the bulk systems, where other mechanisms such as the interstitial mechanism and concerted exchange mechanism may also be involved in atomic diffusion.^{[ 47 ]} The energetically unfavorable migration of the atomic vacancy from the surface to internal position in the present cluster complex may also provide insight into the positional preference of atomic vacancies in matter; however, to generalize this, further investigation is needed with other examples.

In summary, by introducing a single atomic vacancy into an organopalladium cluster complex, we have achieved the first experimental observation showing that atomic diffusion occurs rapidly in a discrete molecule through the vacancy mechanism. This is not only an unprecedented type of dynamic behavior of molecules but also provides a new aspect of the atomic dynamics.

Supporting Information

The authors have cited additional references within the Supporting Information.^{[ 48} , ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² , ⁵³ , ⁵⁴ , ⁵⁵ , ⁵⁶ , ⁵⁷ , ⁵⁸ , ^{59 ]}

Conflict of Interests

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supporting Information

Iwata K., Miyazawa K., Kurashima K., Yamaura H., Zhu B., Tian Y., Takahira Y., Yamamoto K., Omoda T., Hashizume D., Sakaki S., Murahashi T., Angew. Chem. Int. Ed. 2025, 64, e202507444. 10.1002/anie.202507444

Data Availability Statement

The data that support the findings of this study are available in the Supporting Information of this article.