Size-dependent superhalogenicity and ring currents of tantalum doped platinum clusters TaPt_n−1^−/0 (n = 2–21)

Abstract

The anionic and neutral TaPt_n−1^−/0 clusters, with n = 3–21, are systematically investigated using density functional theory (B3PW91/def2-TZVP). Their structural evolution is rationalized by four representative building units, TaPt₃^−/0, TaPt₇^−/0, TaPt₁₃^−/0 and Ta@Pt₁₈^−/0, corresponding to triangular, near triangular-pyramidal, basket-like and bipyramidal structures, respectively. The Ta dopant preferentially occupies a near-central site to maximize coordination and Ta–Pt bonding. An exohedral-to-endohedral transition occurs at n = 19, with full encapsulation established from Ta@Pt₁₈^−/0 onward. Ta doping markedly increases binding energies relative to pure Pt_n^−/0 clusters, with the anionic series generally being more stable. Pronounced electron affinity values in the range of ∼3.0–3.4 eV are obtained for TaPt₃, TaPt₇, TaPt₁₃ and Ta@Pt₁₈, indicating a quasi-superhalogen character of these magic sizes. Charge redistribution is strongly geometry-dependent, shifting from Ta → Pt donation in the exohedral TaPt₃⁻ to increasingly important Pt → Ta donation as the framework grows and Ta occupies an endohedral position in the TaPt₇⁻, TaPt₁₃⁻ and Ta@Pt₁₈⁻. Extensive multicenter electron delocalization is consistent with coherent ring currents in TaPt₁₃⁻, confirming active Ta participation in the coherent electronic motion.

The anionic and neutral TaPt_n−1^−/0 clusters, with n = 3–21, are systematically investigated using density functional theory (B3PW91/def2-TZVP).

1. Introduction

Platinum (Pt) nanomaterials are widely used as key catalysts in both heterogeneous catalysis and electrocatalysis, owing to their high intrinsic activity and broad reaction scope.^1,2 Their importance spans diverse technologies, from low-temperature fuel cells to fine-chemical synthesis and automotive emission control.^1,3,4 Beyond energy and chemical processing, Pt-based nanostructures have also attracted much interest for biomedical applications, including anticancer therapy.^1,5–7 Nevertheless, the practical use of Pt is still constrained by two persistent challenges, namely, lowering Pt loading without sacrificing performance and suppressing activity losses caused by surface poisoning, nanoparticle coarsening, Pt dissolution, and support corrosion effects that are often accelerated under dynamic operating conditions.^3,8,9 These inherent limitations motivate the development of Pt-efficient catalysts that simultaneously enhance activity, selectivity and long-term durability.

To address these issues, two complementary strategies are commonly pursued. The first approach is nanoscale engineering where catalytic behavior is tuned through controlled particle size, morphology and exposed facets.¹⁰ In this context, ultrasmall Pt clusters are especially attractive because the addition or removal of even a single atom can strongly affect their electronic structure and reactivity, making atomically precise synthesis particularly important.¹¹ The second approach is a chemical modification of Pt, such as alloying, heteroatom doping and interfacial engineering with functional supports to tune adsorption energetics and stabilize active sites.¹² Doping, in particular, can profoundly reshape the electronic and geometric structures of nanoclusters, providing an effective way to tailor performance for specific reactions and to address limitations of pure Pt catalysts.^13,14

Within this design landscape, the tantalum element (Ta) has emerged as a particularly effective modifier for Pt-based catalysts because of its strong oxophilicity¹⁵ and its tendency to form stable TaO_x/Ta₂O₅ phases and carbide/oxide interfacial structures,^16,17 that provide practical handles to regulate the local chemical environment around Pt active sites. In fuel-cell electrocatalysis, Ta is frequently introduced through Ta-doped oxide supports such as Ta–SnO₂ and Ta–TiO₂, which are reported to improve both Pt nanoparticle stability and the oxygen reduction reaction (ORR) activity.^18,19 A Pt/TaO_x/GC electrocatalyst prepared by sequential deposition of TaO_x and Pt on glassy carbon delivered ORR kinetic currents at 0.80 V that were more than 12 times higher than those of Pt/GC.¹⁷ Similarly, Ta-modified Pt electrodes in acidic media showed improved four-electron oxygen reduction as compared to bare Pt, an effect attributed to Pt–Ta oxide interfacial synergy and spillover-assisted diffusion of reaction intermediates.²⁰

Pt nanoparticles supported Ta-doped SnO₂ has been highlighted for its relatively high electronic conductivity as compared with undoped or alternatively doped oxides, which can benefit charge transport within practical electrodes.¹⁸ Moreover, the use of Ta-doped metal oxides as supports can mitigate carbon corrosion, one of the major failure modes of conventional Pt/C catalysts, thereby improving durability under dynamic conditions.²¹ Pt/TaO_x integrated with mesoporous carbon (Pt/TaO_x/MC) has been proposed to combine high surface area and transport with oxide-enabled stabilization, limiting Pt dissolution and agglomeration while alleviating carbon corrosion and enabling both high durability and high power output in polymer electrolyte fuel cells.²² Ta₂O₅ layers have been used as templates to direct the formation of uniform Pt microbead-like nanostructures on surfaces,²³ while Pt ion implantation into Ta substrates can generate shallow Pt-containing layers that improve corrosion resistance and reduce hydrogen embrittlement.²⁴

TaO_x-modified Pt electrodes can support larger methanol oxidation currents along with a favorable shift in onset potential relative to unmodified Pt,²⁵ and Pt nanostructures electrodeposited on Ta substrates display substantially enhanced ethanol electro-oxidation rates and improved stability compared to smooth Pt.²⁶ Pt supported on Ta₂O₅ was reported to be highly active and exceptionally stable for SO₃ decomposition, maintaining activity during continuous operation at 600 °C for 1800 h with minimal deactivation.²⁷ Pt supported on crystalline Ta₂O₅ nanotubes also enables efficient CO oxidation with high stability, with ultrasmall sputter-deposited Pt lowering the reaction temperature to below 200 °C.²⁸ Moreover, Ta can also be introduced as a carbide phase; Pt/TaC core–shell nanoparticles provide a versatile platform for durable catalyst design, with substantial room for further compositional and structural optimization across electrochemical and catalytic applications.²⁹

While previous studies highlight the advantages of Ta–Pt coupling at the nanoparticle and interface levels, the small-size cluster regime remains comparatively underexplored, despite being crucial for identifying size-dependent growth motifs and intrinsic electronic-structure effects that can govern catalytic behavior. The present study aims to conduct a systematic investigation of Ta-doped Pt nanoclusters across size and charge, focusing on the TaPt_n−1^−/0 clusters including n = 2–21, and exploring a comprehensive set of structural configurations for both anionic and neutral states. This size- and charge-resolved analysis provides us with mechanistic insights into cluster growth pattern and the factors governing their stability and electronic properties, thus offering a framework for understanding on how Ta incorporation tunes Pt cluster structure and reactivity at the small length scales.

2. Computational methods

All electronic structure calculations are carried out using the Gaussian 16 program package.³⁰ The def2-TZVP basis set³¹ is employed in this study because it provides a favorable balance between computational cost and accuracy for Pt-cluster systems.³² Previous studies on pure and doped Pt_n clusters showed that several density functionals including the B3PW91,^33,34 ωB97XD,³⁵ TPSSh,³⁶ PBE,^37,38 M06-L,³⁹ and BP86,^40,41 can reasonably describe Pt-based systems.^42–45 Therefore, these functionals, together with the def2-TZVP basis set, are selected for a benchmark assessment of relative energies and adiabatic electron affinities with respect to results obtained at the higher-level (U)CCSD(T)/def2-TZVP method for representative systems, including anionic and neutral TaPt^−/0, TaPt₃^−/0, and anionic TaPt₇⁻ clusters. The unrestricted formalism (UHF) is used for open-shell configurations.

The benchmark results, summarized in Tables S1–S5 of the SI file, indicate that the B3PW91 is among the functionals that show good agreement with those obtained by (U)CCSD(T) method. In addition, B3PW91 was reported to reliably describe pure and doped Pt_n cluster structures and to yield good agreement with available experimental results.^42–45 Accordingly, the B3PW91/def2-TZVP level is employed throughout this work to ensure methodological consistency, computational efficiency, and meaningful comparison with results reported in previous Pt-based cluster studies.

Low-energy isomers of TaPt_n−1^−/0 clusters are searched using a two-stage protocol. Initial candidate geometries are built by placing Ta atoms at different sites, via substitution or addition, within previously reported global-minimum frameworks of neutral and charged pure Pt clusters.^{32,42,45–59} These guess structures are first optimized with B3PW91/LANL2DZ computations.⁶⁰ To broaden configurational sampling beyond hand-built guesses, additional structures are produced using a stochastic generation approach⁶¹ derived from the random-kick method,⁶² following the procedure established in our earlier work.⁶³ All structures from this sampling step are optimized using B3PW91/LANL2DZ computations as well. For each converged geometry, optimizations are repeated for alternative spin multiplicities to ensure the lowest-energy spin state is identified. When nearly isoenergetic candidates are encountered, symmetry-constrained re-optimizations are carried out to confirm relevant structural assignment and symmetry.

All local energy minima lying within ∼3 eV (∼69 kcal mol⁻¹) from the global minimum for each size are subsequently re-optimized at B3PW91/def2-TZVP and verified as true minima by harmonic vibrational frequency calculations at the same level. Zero-point energy (ZPE) corrections obtained from these frequency calculations are included in the reported relative energies.

Natural electron configurations (NEC) and spin density distributions are evaluated using NBO 5.0,⁶⁴ enabling detailed analysis of charge transfer and bonding characteristics. Delocalized bonding patterns are further resolved using adaptive natural density partitioning (AdNDP)⁶⁵ as implemented in the Multiwfn program.⁶⁶

In the traditional concept of ring currents, delocalized π electrons in an aromatic system respond to an external static magnetic field by generating a circulating current along the ring. Depending on its direction, the induced current can be diatropic or paratropic, producing an induced magnetic field parallel or antiparallel to the applied field, respectively.^67,68

In contrast to the traditional picture, a coherent ring current arises from an optically allowed pair of degenerate (or quasi-degenerate) excited states, represented by the real-valued wavefunctions Φ₁ and Φ₂. The corresponding transition dipole moments from the ground state Φ₀, denoted M_x and M_y, are oriented along x- and y-axis. For a single-ring aromatic system, the superposition states and are eigenstates of the z-component of the angular momentum operator. When M_xM_y > 0, these states determine the rotational direction of π-electrons as counterclockwise (CCW) or clockwise (CW), respectively, viewed along the positive z-axis.⁶⁹

With advances in laser control, a degenerate excited-state pair can be selectively excited using a circularly polarized (CP) laser pulse whose carrier frequency matches the transition energy from ground state to degenerate excited states. In particular, the desired superposition state can be prepared using either left- or right-handed CP pulses. The magnitude of coherent ring currents has been investigated in several quantum chemical studies.^69,70 Within this approach, the coherent current is evaluated analytically on a plane perpendicular to the bond axis connecting two atomic centers using time-dependent density functional theory (TD-DFT). This quantity is commonly referred to as the coherent bond current.⁷⁰ In the present work, the corresponding analytical expression is adopted and applied to, as for a typical case, the highly symmetric TaPt₁₃⁻ anion.

First, the superposition of the degenerate excited states is prepared by a CP pulse. The time-evolved electronic wave function, arising from the interaction between two components of the CP electric field and the pair of transition dipole moments, M_x and M_y, can be expresed as eqn (1):

Ψ(t) = c₀(t)Φ₀ + c₁(t)Φ₁ + c₂(t)Φ₂, 1

Here, c_k(t) is time-dependent expansion coefficient of k electronic state, k = 0, 1, and 2. For the state described by eqn (1), the coherent bond current is given by eqn (2):

2

Here, the coherent bond current J(t)_IK is evaluated on the surface (S) placed at the midpoint of the bond connecting atoms I and K, whose positions are R_I and R_K, respectively. The unit normal vector n_(s) = (R_I − R_K)/|R_I − R_K| defines the positive direction of current flow through (S).

In eqn (2), and are configuration-interaction coefficients associated with single excitations from occupied orbital a to virtual a′ (contributing to Φ₁), and from b to b′ (contributing to Φ₂), respectively. Within the linear combination of atomic orbitals (LCAO), each molecular orbital (MO) is expanded in terms of atomic orbital (AO) centered on all atoms in the system. χ_I(r − R_I) denotes an AO on atom I contributes to MO-a, and c_a,I is its coefficient in orbital a.

The target state, Ψ(T) ≡ Φ_ is generated by an appropriately designed CP pulse.⁶⁹ At the preparation time T, the time-dependent coefficients in eqn (1) satisfy and ; results in . The coherent bond currents are then evaluated for all I − K atomic pairs in the cluster system after the target time. In this case, the electron motion corresponds to a CW rotation around the z-axis.

3. Results and discussion

3.1. Structural evolution

For clarity, TaPt_n−1^−/0 isomers are labeled using the format x.n.y. Here, x indicates the charge state (a for anionic, n for neutral), n gives the cluster size (the total number of atoms), and y denotes the energetic ordering (z = 1, 2, 3,… for increasing relative energy). For example, a.4.1 designates the lowest-energy anionic isomer of TaPt₃⁻ cluster.

For comparison, the global energy minimum geometries of the pure Pt_n^+/0/– clusters (n = 2–21) are taken from our previous study on Pt clusters.³² It is worth noting that Lin et al. reported the Pt₂₁⁻ global minimum as a spheroidal, three-layer structure (7 atoms per layer) with D_6h symmetry at a sextet spin state.⁵⁹ Upon re-examination, however, this D_6h isomer is found not to be the lowest-energy structure. Instead, the distorted isomer identified in our earlier work, retaining a triangular-prism-like motif, lies significantly ∼30 kcal mol⁻¹ lower in energy than the D_6h candidate (cf. Fig. S1).

Fig. 1–4 present the three lowest-energy isomers for each cluster size in the anionic TaPt_n−1⁻ series. Additional low-lying structures for both anionic and neutral TaPt_n−1^−/0 clusters are provided in Fig. S2–S9 of the SI.

Fig. 1. Structures, multiplicities (M, in bracket) and relative energies (rE, kcal mol⁻¹) of the low-lying anionic TaPt_n−1⁻ isomers with n = 2–6 calculated using B3PW91/Def2-TZVP + ZPE computations.

Fig. 2. Structures, multiplicities (M, in bracket) and relative energies (rE, kcal mol⁻¹) of the low-lying anionic TaPt_n−1⁻ isomers with n = 7–11 calculated using B3PW91/Def2-TZVP + ZPE computations.

Fig. 3. Structures, multiplicities (M, in bracket) and relative energies (rE, kcal mol⁻¹) of the low-lying anionic TaPt_n−1⁻ isomers with n = 8–16 calculated using B3PW91/Def2-TZVP + ZPE computations.

Fig. 4. Structures, multiplicities (M, in bracket) and relative energies (rE, kcal mol⁻¹) of the low-lying anionic TaPt_n−1⁻ isomers with n = 17–21 calculated using B3PW91/Def2-TZVP + ZPE computations.

In general, owing to its larger atomic radius, the Ta atom preferentially occupies a near-central position in TaPt_n−1^−/0 clusters, where higher coordination with surrounding Pt atoms can be achieved and Ta–Pt bonding can be maximized. Consequently, Ta incorporation induces appreciable distortions relative to the corresponding initial Pt_n^−/0 frameworks. Overall, the structural evolution of TaPt_n−1^−/0 is not well described by a simple “Ta substitution” or “Ta addition” trends based on pre-existing Pt clusters. Instead, the Pt atoms are progressively assembled to generate a cage-like environment around a Ta-centered core.

Four key building units can be considered to interpret the structural growth mechanism of TaPt_n−1^−/0 clusters (n = 2–21), namely TaPt₃^−/0, TaPt₇^−/0, TaPt₁₃^−/0 and Ta@Pt₁₈^−/0. Accordingly, TaPt₃^−/0 adopts a triangular arrangement with Pt atoms surrounding Ta. Stepwise addition of Pt atoms to this framework leads to the near triangular-pyramidal geometry of TaPt₇^−/0, which further develops into the basket-like TaPt₁₃^−/0 structure upon continued Pt addition. Subsequent occupation of remaining growth sites yields the bipyramidal Ta@Pt₁₈^−/0 configuration, from which Ta@Pt₁₉^−/0 and Ta@Pt₂₀^−/0 are obtained by adding one and two Pt atoms, respectively. This stepwise growth pathway is summarized in Fig. 5 and S10. Notably, the anionic species adopt higher-symmetry structures than their neutral counterparts. This trend is consistent with the strong electron-accepting character of the neutral clusters, which facilitates formation of the corresponding highly stable anions (discussed in the following sections).

Fig. 5. Structural evolution of the anionic TaPt_n−1⁻ clusters with n = 2–21.

An exohedral-to-endohedral transition is observed at the size of eighteen Pt atoms. For smaller sizes, Pt atoms do assemble around Ta, however, because Pt is smaller than Ta and Ta–Pt bonding is favored, the Pt atoms remain relatively separated from one another. As a result, the resulting geometries upon doping are predominantly exohedral or at most half-endohedral. Fully endohedral encapsulation becomes established only from Ta@Pt₁₈^−/0 onward. This structural transition is accompanied by a corresponding change in preferred spin states.

In contrast to the host Pt_n clusters, which intrinsically exhibit relatively large magnetic moments and multiple spin states that are often close in energy,³² Ta doping tends to reduce both the preferred spin multiplicity and the span of energetically accessible spin states. Specifically, for most sizes below n = 19, the low-lying TaPt_n−1 structures are found in singlet or triplet states for the anions and doublet or quartet states for the neutrals. For larger sizes, from those containing eighteen Pt atoms onward where bipyramidal motifs and endohedral encapsulation occur, the preferred spin states become more structure-dependent and shift to higher multiplicities.

3.2. Thermodynamic stability

The thermodynamic stability of the TaPt_n−1^−/0 clusters is assessed using the average binding energy (E_b). In addition, the adiabatic electron affinity (EA_a) is also considered to quantify the tendency of the neutral clusters to accept an electron. Accordingly, the E_b, and EA_a values of the lowest-lying TaPt_n−1^−/0 (n = 2–21) are calculated using the expressions given in eqn (3)–(6):

Average binding energy (eV).

• For neutral TaPt_n−1 clusters.

E_b(TaPt_n−1) = [(n − 1)E(Pt) + E(Ta) − E(TaPt_n−1)]/n 3

• For anionic TaPt_n−1⁻ clusters:

E_b(TaPt_n−1⁻) = [(n − 2)E(Pt) + E(Pt⁻) + E(Ta) − E(TaPt_n−1⁻)]/n 4

or

E_b(TaPt_n−1⁻) = [(n − 1)E(Pt) + E(Ta⁻) − E(TaPt_n−1⁻)]/n 5

Adiabatic electron affinity:

EA_a(TaPt_n−1) = E(TaPt_n−1) − E(TaPt_n−1⁻) 6

In these equations, E(Ta) and E(Ta⁻) are the total energies of an isolated Ta atom and Ta anion, respectively. E(Pt) and E(Pt⁻) are the total energies of an isolated Pt atom and Pt anion, respectively. E(TaPt_n−1) and E(TaPt_n−1⁻) are the total energies of the of the lowest-energy neutral and anionic TaPt_n−1 clusters.

Both E(Ta⁻) and E(Pt⁻) are considered when evaluating E_b for the anionic TaPt_n−1⁻ clusters (cf.eqn (4) and (5)). As shown in Table S6 (SI), placing the excess electron on Pt leads to systematically smaller binding energies than placing it on Ta. This trend is consistent with the calculated dissociation energies (D_e), which indicate that loss of a Pt or a Pt⁻ fragment is more favorable than loss of a Ta or a Ta⁻ fragment. Such behavior aligns with the structural motif in which Ta preferentially occupies an interior site while Pt atoms are located at the periphery. Consequently, eliminating a peripheral Pt is energetically more accessible than extracting the central Ta. The corresponding expressions and D_e data are provided in Table S7 (SI). Accordingly, the E_b values referenced to the Pt⁻ are adopted for the discussion below and are plotted in Fig. 6A.

Fig. 6. (A) Average binding energy of Pt_n^−/0 and TaPt_n−1^−/0 clusters. (B) Adiabatic electron affinity of TaPt_n−1 clusters and (C) second-order energy difference of TaPt_n−1⁻ clusters (n = 3–21). Values are obtained from B3PW91/Def2-TZVP + ZPE computations.

As evident from Fig. 6A, a Ta doping results in markedly higher binding energies than the corresponding pure Pt_n^−/0 clusters for both neutral and anionic charge states, indicating that incorporation of a Ta atom intrinsically enhances the thermodynamic stability of the initial Pt clusters. In addition, the anionic Ta-doped clusters are generally more stable than their neutral counterparts, indicating a tendency to easily accept an extra electron. Within the anionic series, the four building units including TaPt₃⁻ (D_3h, ¹A₁′), TaPt₇⁻ (C₁, ³A″), TaPt₁₃⁻(C_4v, ¹A₁) and Ta@Pt₁₈⁻ (O_h, ⁷A₁U) emerge as especially stabilized sizes. This conclusion is further supported by the second-order energy difference (Δ²E) values that show pronounced stability enhancements at Pt counts of three, seven, thirteen, and eighteen, relative to neighboring sizes (cf.Fig. 6B and S11).

Notably, a Ta doping turns out to enhance the electron-accepting ability of the Pt_n host, as reflected by increased EA_a values. The most pronounced EA_a maxima occur for TaPt₃, TaPt₇, TaPt₁₃ and Ta@Pt₁₈, with values of approximately 3.0–3.4 eV (cf.Fig. 6C). These values are comparable to EA_a of halogen atoms and therefore suggest their quasi-superhalogen character. In general, a superhalogen species is considered to possess an adiabatic electron affinity comparable to, or greater than, those of halogen atoms,⁷¹ owing to an efficient stabilization of the excess electron through favourable geometry and/or electronic delocalization over the entire framework. Accordingly, electron attachment to the neutral TaPt_n clusters at n = 3, 7, 13 and 18 produces especially stabilized anions, consistent with their role as key building units in the structural growth sequence. The enhanced EA_a values at these sizes indicate particularly favourable electronic and geometric arrangements that allow the added electron to be effectively accommodated, while promoting higher symmetry, strong metal–metal bonding, and efficient charge delocalization, as discussed in detail in the following sections.

On the other hand, the Ta-doped clusters show sizable HOMO–LUMO gaps, with values of approximately 2.7 eV for TaPt₃⁻, 2.5 eV for TaPt₇⁻, 2.1 eV for TaPt₁₃⁻ and 1.3 eV for Ta@Pt₁₈⁻. Overall, the gap decreases as the number of Pt atoms increases, which can be attributed to the growing density of near-degenerate d-derived states in larger Pt frameworks. As Pt atoms are progressively added, more d electrons and d-type orbitals accumulate near the frontier region, leading to closer-lying occupied and unoccupied levels and hence a smaller HOMO–LUMO separation.

3.3. Chemical bonding

The density-of-states (DOS) for the four building-unit anions TaPt₃⁻, TaPt₇⁻, TaPt₁₃⁻ and Ta@Pt₁₈⁻ shown in Fig. S12 (SI file) indicate that Ta- and Pt-derived states extend over essentially the same energy range. However, the Pt contribution is much more intense than that of Ta, showing that the electronic structure is dominated primarily by Pt-derived s and d electrons.

The charge distribution and electron populations (detailed data given in Table S8, SI) of the four anions are basically governed by their geometries. The more exohedral the structure, the more positive the central Ta atom becomes, whereas increase of endohedral character drives the Ta atom toward a less positive and eventually a negative charge. In the clearly exohedral TaPt₃⁻ cluster, the negative charge is mainly localized on the Pt atoms, whereas Ta carries a positive charge. This is consistent with the slightly higher electronegativity of Pt than Ta (∼2.3 vs. ∼2.1), which favors electron accumulation on Pt. Quantitatively, each Pt atom bears a charge of about −0.6, while Ta carries approximately +0.8. Correspondingly, the electron population on each Pt atom increases by roughly 0.6 e, whereas that on Ta decreases by about 0.8 e, suggesting a Ta → Pt donor–acceptor bonding. Electron populations further indicate characteristic orbital mixing. On Pt, electron population on the 6s atomic orbital (AO) decreases by ∼0.6 e, accompanied by an increase of ∼0.2 e in the 5d-AO, suggesting a s–d hybridization. In contrast, the central Ta atom shows an s–p–d hybridization, with electron depletion from the 6s and 5d shells (about 1.0 e and 0.3 e, respectively) and a concomitant increase in the 6p population (about 0.6 e).

With increasing size and coordination, the charge on Ta shifts in the opposite direction. In TaPt₇⁻, TaPt₁₃⁻ and Ta@Pt₁₈⁻, the Ta center becomes progressively less positive and ultimately negative, with computed Ta charges of approximately +0.2, −0.6, and −1.1, respectively. This reversal can be rationalized by Ta's stronger ability to accept electron due to a greater availability of unfilled d-orbitals relative to Pt. As the cluster framework grows, more electron density becomes available for Pt → Ta donation, leading to negative charge on the Ta center. The Pt charge distribution is also non-uniform. Pt atoms farther from Ta, at longer Ta–Pt distances near the outer region, tend to be slightly positive, whereas Pt atoms closer to Ta remain slightly negative.

Electron distribution for the larger anions are consistent with this picture. For Pt atoms in TaPt₇⁻, TaPt₁₃⁻ and Ta@Pt₁₈⁻, a decrease of electron population in s-AO accompanied by increases in d and, in some cases, p-AOs indicates s–d or s–p–d mixing, while the total electron population on Pt sites remains nearly unchanged. In contrast, the Ta center shows size- and structure-dependent changes. In the exohedral TaPt₇⁻, the Ta atom exhibits 6s–5d–6p hybridization and only a slight reduction in its total electron population (∼0.2 e). In the half-endohedral TaPt₁₃⁻, mixing involving higher-lying orbitals (5d, 7p, 8s) is accompanied by an electron population increase of ∼0.6 e. In the fully endohedral Ta@Pt₁₈⁻ structure, a broader 6s–5d–6p–6d hybridization is observed together with an electron population increase exceeding ∼1 e.

Consistently, Wiberg bond indices reveal a steady increase in the overall bonding contribution of the Ta center, rising from approximately 6.0 in TaPt₃⁻ to 6.8, 7.7 and 8.1 in TaPt₇⁻, TaPt₁₃⁻ and Ta@Pt₁₈⁻, respectively (cf. Table S8, SI). This trend indicates that the Ta atom forms an increasing number of coordination interactions and contributes more strongly to the bonding network as the cluster size grows. In parallel, the average Ta–Pt bond length increases with cluster size, from about 2.3 to 2.5, 2.6 and 2.7 Å, respectively.

Electron delocalization in the TaPt₃⁻ and TaPt₁₃⁻ is further examined. For TaPt₃⁻, its 36 valence electrons can be described in terms of a set of nine (2c–2e) bonds together with nine (3c–2e) bonds, which collectively reinforce the interactions among one Ta and three Pt atoms (cf.Fig. 7). The (2c–2e) bonds describe conjugated π-type interactions associated with overlaps of d_xz, d_yz and d_z² orbitals between Ta and Pt, while the (3c–3e) bonds relate to σ-type interactions dominated by d_xy and d_x²−y² overlaps, both contribute to the rigidity of the triangular framework. In contrast, delocalization in the TaPt₁₃⁻ is distributed over much larger set of centers. Because the TaPt₁₃⁻ geometry can be viewed as an assembly of interconnected five-vertex pyramidal caps, a prominent set of thirty (5c–2e) bonds is obtained, indicating electron delocalization over five-atom fragments through predominantly d-orbital overlap involving both Ta and Pt. In addition, thirty-eight (14c–2e) bonds are identified, emphasizing a substantial delocalization across the entire cluster framework (cf. Fig. S13, SI).

Fig. 7. A metallic aromaticity arising from nine (2c–2e) and nine (3c–2e) bonds of the triangular TaPt₃⁻ cluster via AdNDP analysis (B3PW91/Def2-TZVP).

Overall, these bonding characteristics exhibit specific metallic aromaticity and differ from those commonly found in pure Pt_n clusters. In previous studies,^32,43 small- and medium-sized Pt_n clusters often retain a portion of more localized electron density that does not contribute strongly to multicenter bonding. By contrast, Ta incorporation drives the bonding toward more extensive multicenter delocalization across the cluster skeleton.

3.4. Coherent ring current in the TaPt₁₃⁻ cluster

In this section, the TaPt₁₃⁻ anion is selected for a coherent ring-current analysis due to the fact that it is a key growth unit with a compact three-dimensional C_4v high-symmetry structure and enhanced electronic stability. Perhaps more importantly, its singlet ground state enables a clearer identification of the relevant excited states, allowing a more reliable interpretation of coherent electron circulation.

The atomic structure of the TaPt₁₃⁻ anion is re-plotted from the optimized Cartesian coordinates, as shown in Fig. 8. For clarity, the cluster is divided into three approximately parallel layers, labeled A, B and C. Layer A contains Pt1–Pt4, layer B contains Pt6–Pt9, and layer C contains Pt10–Pt13. It should be noted that Pt5 does not belong to layer A, and the Ta atom located on the z-axis is below layer B. In addition to the in-plane bonds within each layer, interlayer coherent bond currents are evaluated along two representative zigzag pathways. Here, S1 (lower panel) connects layers B and C, whereas S2 (upper panel) connects both layers A and B. The positive current direction is defined as clockwise (CW) about the z-axis. Based on TD-DFT calculations (B3PW91/def2-TZVP), the first three optically allowed degenerate pairs of excited states, denoted E1, E2 and E3, are selected in order of increasing excitation energy (Table 1). The x- and y-components of the transition dipole moments are used to assign the two real excited states Φ₁ and Φ₂ in eqn (1) of the section computational method.

Fig. 8. (a) Optimized geometry of the TaPt₁₃⁻ anion. (b) Atomic arrangement re-plotted in the Oxyz coordinate system. The structure is divided into three approximately parallel layers: layer A (Pt1–Pt4, red), layer B (Pt6–Pt9, yellow), and layer C (Pt10–Pt13, orange). Pt5 lies outside layer A, and the Ta atom located on the z-axis is below layer B. The interlayer “zigzag” pathways are defined as S1 = Pt6–Pt10–Pt7–Pt11–Pt8–Pt12–Pt9–Pt13 and S2 = Pt6–Pt1–Pt7–Pt2–Pt8–Pt3–Pt9–Pt4.

Table 1. Three pairs of degenerate excited state E1, E2, and E3 obtained by TD-DFT (B3PW91/DEF2TZVP). In each pair, the excited states Φ₁ and Φ₂ have non-zero transition dipole moment of M_x and M_y, respectively.

Symbol of pair states	Excited state	Energy [eV]	Transition dipole moment vector (a.u.)		Dominant transition MOs	with large weightb
			M x	M y	o MO → v MOa
E1	S2	1.128	0	0.013	123 → 127	−0.331
					124 → 125	0.511
	S3		0.013	0	122 → 127	0.331
					124 → 126	0.511
E2	S9	1.353	0	−0.222	117 → 126	0.367
					123 → 127	0.322
	S10		−0.222	0	117 → 125	0.367
					122 → 127	−0.322
E3	S12	1.392	0	0.323	118 → 125	0.431
					119 → 125	−0.220
	S13		0.323	0	118 → 126	0.430
					119 → 126	0.220

^ao MO and v MO denote for occupied and virtual molecular orbital, respectively.

^bCI coefficients of two transitions MOs have largest weights in configuration of excited states Φ₁ and Φ₂.

Coherent bond currents are then computed using eqn (2). For symmetry-equivalent bonds within the same layer, identical current values are obtained. Accordingly, J_A,J_B, and J_C denote the representative in-plane coherent bond currents for layers A, B and C, respectively. Similarly, the zigzag pathways yield equivalent current values along each path, and the corresponding interlayer currents are denoted as J_S1 and J_S2.

When only p_z atomic orbitals are included (cf.Table 2), negative current values indicate a counterclockwise (CCW) current flow because CW is defined as the positive direction. Since electrons carry negative charge, CCW current corresponds to CW electron rotation. For all three excited-state pairs (E1–E3), the electron rotation is therefore CW, consistent with the Φ_ state as M_xM_y > 0 for three pairs (cf.Table 1). The current magnitudes range from several tens of nA to the µA scale. In all three cases, the in-plane current magnitudes follow |J_B| < |J_A| < |J_C|, while the zigzag currents approximately equal to each other J_S1 ∼ J_S2. Notably, no appreciable bond current is obtained between the Ta center and other atoms in the p_z-only treatment.

Table 2. Coherent bond current (nA). J_A, J_B and J_C denote the in-plane coherent bond currents in layers A, B, and C, respectively. J_S1 and J_S2 represent the coherent bond currents along the interlayer zigzag pathways S1 and S2, respectively. Ta–Pt denotes the bond current between the Ta atom and the surrounding Pt atoms.

Symbol of state	In-plane of layers			Zigzag bond paths		Center Ta to Pt atomsa
	J A	J B	J C	J S1	J S2	Ta–Pt
(a) p z only
E1	−765.04	−346.55	−1112.08	−263.98	−301.78	0
E2	−149.95	−33.47	−175.54	−31.15	−29.55	0
E3	−486.09	−322.03	−683.38	−245.53	−173.19	0
(b) p x + p y + p z
E1	527.30	−1037.35	1323.20	897.54	−228.52	3146.43
E2	−5.07	−40.58	72.96	110.06	−50.25	371.18
E3	270.12	−882.38	981.96	516.29	204.58	2608.24

^aThe bond currents Ta–Pt between the Pt atoms located in layer B and Ta atom are nonzero, whereas all other Ta–Pt bond current values are zero.

When the full p-orbital set (p_x, p_y and p_z) is included (cf.Table 2), the current pattern changes substantially. The in-plane currents in layer C reverse sign for all three excited-state pairs. In layer A, a similar sign reversal occurs for E1 and E3, whereas for E2 the current magnitude is strongly reduced. In contrast, the currents in layer B preserve their direction and increase markedly in magnitude, leading to a new amplitude ordering |J_A| < |J_B| < |J_C|. Importantly, these sign inversions do not imply a reversal of the overall electron rotation, because the in-plane currents in layer B retain the direction required by the selected eigenstate. The preservation of the coherent bond current direction in layer B (J_B) can be rationalized from the LCAO coefficients of the molecular orbitals that dominate eqn (2). Table 1 shows that, for E1 and E2, the largest contributions arise from overlaps involving occupied MOs 122 and 123 and virtual MOs 125 and 126, whereas for E3 the dominant contribution is mainly associated with the virtual MOs 125 and 126. For Pt atoms in layer B (Pt6–Pt9), the relevant MO coefficients are essentially zero for the p_x components of MOs 122 and 125 and for the p_y components of MOs 123 and 127 (SI). Thus, p_x and p_y orbitals contribute negligibly to the dominant transitions for these atoms, and ∣J_B∣ remains primarily controlled by the p_z components even when the full p-set is used.

In addition, the p_z-AOs contributions in layer C are generally larger than those in layers A and B, explaining the larger ∣J_C∣ values. For the zigzag currents, including p_x and p_y breaks the near-balance observed in the p_z-only results. Along S1 (between layers B and C), J_S1 reverses sign and increases strongly in magnitude. Along S2 (between layers A and B), sign inversion occurs only for E3 and the amplitude changes are much smaller. Consequently, ∣J_S1∣ and ∣J_S2∣ deviates significantly from unity when the full p-orbital set is used.

A key additional feature which is emerged only in the full-p treatment, is that sizable coherent bond currents appear between the Ta atom and the four Pt atoms in layer B, with the largest amplitudes in the entire system. These Ta-centered currents are approximately 2.7–5.0 times as large as the maximum currents along the in-plane or zigzag pathways. The current originating at Ta flows outward toward two opposite Pt atoms in layer B, whereas the currents associated with the other two Pt atoms flow in the opposite direction. This finding demonstrates that a restricting consideration only to p_z orbitals is insufficient for capturing the radial bond-current components between the Ta center and the surrounding Pt framework.

As for a visualization, the coherent bond-current directions for the E1 pair are illustrated in Fig. 9 using arrows, where identical colors denote equal current magnitudes.

Fig. 9. (a) Directions of the in-plane coherent bond currents in layers A (green), B (blue) and C (purple) for E1 excited state pair, calculated using a full set of p-AOs from atoms; (b) coherent bond currents flowing along the “zigzag” bond path S1 (between layers B and C), and the “zigzag” bond path S2 (between layers A and B), and (c) the bond currents between Ta center atoms and four Pt atoms on layer B. The positive current direction is defined as clockwise (CW) when viewed along the z-axis.

4. Concluding remarks

In the present theoretical study, the anionic and neutral TaPt_n−1^−/0 clusters (n = 2–21) are systematically investigated using density functional theory with the B3PW91 functional and the def2-TZVP basis set, leading to the following main conclusions:

• The structural growth pattern of TaPt_n−1^−/0 with n = 2–21 can be rationalized in terms of four key building units, TaPt₃^−/0, TaPt₇^−/0, TaPt₁₃^−/0 and Ta@Pt₁₈^−/0, which correspond to triangular, triangular-pyramidal, basket-like and bipyramidal motifs, respectively. Across the size range, Ta preferentially occupies a near-central site to maximize coordination and Ta–Pt bonding. An exohedral-to-endohedral transition is observed at the size of eighteen Pt atoms, with fully endohedral encapsulation established from Ta@Pt₁₈^−/0 onward.

• Thermodynamically, Ta incorporation markedly enhances stability relative to the corresponding pure Pt_n^−/0 clusters, as reflected by higher binding energies for both neutral and anionic charge states, with the anionic Ta-doped clusters generally being the most stable. In addition, TaPt₃, TaPt₇, TaPt₁₃⁻ and Ta@Pt₁₈ exhibit pronounced adiabatic electron affinity maxima of approximately 3.0–3.4 eV, indicating their quasi-superhalogen character, showing that electron attachment to these radicals produces stabilized anions, consistent with their role as key growth motifs.

• The charge distribution and electron populations are, as expected, strongly geometry-dependent. Exohedral structures tend to place a positive charge on the Ta center, whereas increase of endohedral character drives Ta toward less positive and eventually negative charge. Accordingly, TaPt₃⁻ is characterized by Ta → Pt donor–acceptor interactions (consistent with Pt's slightly higher electronegativity), whereas TaPt₇⁻, TaPt₁₃⁻ and Ta@Pt₁₈⁻ possess increasing Pt → Ta donation as the Pt framework grows, and Ta's available d-acceptor character reinforces the negative charge on the central site.

• The bonding in TaPt₃⁻ and TaPt₁₃⁻ are dominated by extended multicenter electron delocalization. For TaPt₃⁻, metallic aromaticity is associated with a network of nine (2c–2e) π-type and nine (3c–2e) σ-type interactions arising primarily between Ta and Pt's d-orbital overlap, which stabilizes the triangular framework. For TaPt₁₃⁻, delocalization extends over larger fragments and the full skeleton, described by thirty (5c–2e) and thirty-eight (14c–2e) interactions, giving a delocalized metallic bonding pattern in the basket-like motif.

• The coherent bond-current analysis shows that TaPt₁₃⁻ anion supports a well-defined optically driven coherent circulation, consistent with preparation of the Φ_ superposition state (CW electron rotation for M_xM_y > 0). The use of only p_z orbitals reproduces the qualitative in-plane current trends but fails to capture Ta–Pt currents, indicating an incomplete description. When the full p-AOs set (p_x, p_y and p_z) is included, the current pattern is substantially reshaped and strong radial Ta–Pt bond currents emerge as the largest contributions, showing that the Ta dopant actively participates in the coherent electronic motion.

Conflicts of interest

There are no conflicts to declare.

Data availability

The quantum chemical program Gaussian 16 has been used. Reference of this program is given in the list of references. The additional datasets supporting this article are given as part of the supplementary information (SI). Supplementary information: (i) benchmark comparison of relative energies and adiabatic electron affinities of low-energy TaPt^−/0, TaPt₃^−/0, and TaPt₇^−/0 clusters calculated using different functionals against CCSD(T) results; (ii) the structures, multiplicities (M, in bracket) and relative energies (rE, kcal mol⁻¹) of the low-lying TaPt_n−1^−/0 (n = 2–21) clusters; (iii) structural evolution of the neutral TaPt_n−1 (n = 2–21) clusters; (iv) the average binding energy, dissociation energies and second-order energy difference of the low-lying TaPt_n−1^−/0 (n = 2–21); (v) calculated density of states (DOS) for the a.4.1, a.8.1, a.14.1 and a.19.1 isomers; (vi) natural electron configuration (NEC), natural charge and Wiberg bond index of the a.4.1, a.8.1, a.14.1 and a.19.1 isomers at their most stable spin state; (vii) AdNDP analysis showing multi-center bonds in the a.14.1 isomer; (viii) LCAO coefficients for Pt atoms in MOs 122, 123, 125, and 126 of the a.14.1 isomer; and (ix) coordinates of the lowest-lying TaPt_n−1^−/0 (n = 3–21) clusters. See DOI: https://doi.org/10.1039/d6ra02901a.