Edited by Christopher C. Cummins, Massachusetts Institute of Technology, Cambridge, MA, and approved June 14, 2018 (received for review April 14, 2018)
Lanthanide borides constitute an important class of materials with wide industrial applications, but clusters of lanthanide borides have been rarely investigated. It is of great interest to study these nanosystems, which may provide molecular-level understanding of the emergence of new properties and provide insight into designing new boride materials. We have produced lanthanide boride clusters and probed their electronic structure and chemical bonding. Two Ln2B8− clusters are presented, and they are found to possess inverse sandwich structures. The neutral Ln2B8 complexes are found to possess D8h symmetry with strong Ln–B8 bonding. A unique (d–p)δ bond is found to be important for the Ln–B8–Ln interactions. The Ln2B8 inverse sandwich complexes broaden the structural chemistry of the lanthanide elements and provide insights into bonding in lanthanide boride materials.
While boron forms a wide range of metal borides with important industrial applications, there has been relatively little attention devoted to lanthanide boride clusters. Here we report a joint photoelectron spectroscopy and quantum chemical study on two octa-boron di-lanthanide clusters, Ln2B8− (Ln = La, Pr). We found that these clusters form highly stable inverse sandwich structures, [Ln–B8–Ln]−, with strong Ln and B8 bonding via interactions between the Ln 5d orbitals and the delocalized σ and π orbitals on the B8 ring. A (d–p)δ bond, involving the 5dδ and the antibonding π orbital of the B8 ring, is observed to be important in the Ln–B8 interactions. The highly symmetric inverse sandwich structures are overwhelmingly more stable than any other isomers. Upon electron detachment, the (d–p)δ orbitals become half-filled, giving rise to a triplet ground state for neutral La2B8. In addition to the two unpaired electrons in the (d–p)δ orbitals upon electron detachment, the neutral Pr2B8 complex also contains two unpaired 4f electrons on each Pr center. The six unpaired spins in Pr2B8 are ferromagnetically coupled to give rise to a septuplet ground state. The current work suggests that highly magnetic Ln…B8…Ln inverse sandwiches or 1D Ln…B8…Ln nanowires may be designed with novel electronic and magnetic properties.
Boron forms a wide variety of boride materials, ranging from the superconductor MgB2 to superhard transition metal borides (1, 2). In particular, lanthanide borides represent a class of highly valuable magnetic, optical, superconducting, and thermoelectric materials (3⇓⇓–6). In the past two decades, extensive experimental and theoretical studies have been conducted to elucidate the structures and chemical bonding of size-selected boron clusters (7⇓⇓⇓–11), resulting in the discoveries of novel graphene-like (borophene), fullerene-like (borospherene), and nanotubular structures (12⇓⇓⇓–16). However, there has been relatively less attention devoted to metal boride clusters, even though a number of transition metal-doped clusters have been characterized (11, 17⇓–19). In particular, there have been few experimental studies on lanthanide boron clusters.
The SmB6− and PrB7− clusters represent the first lanthanide (Ln) boron clusters reported (20, 21), each featuring a B6 or B7 cluster coordinated to the Ln atom. Here we present a joint photoelectron spectroscopy (PES) and quantum chemical study of the first di-Ln–doped boron clusters, La2B8− and Pr2B8−. We have found that these clusters have highly stable and symmetric inverse sandwich structures: a B8 ring sandwiched by the two Ln atoms, [Ln−B8−Ln]−. Both anionic complexes are found to have D4h symmetry, whereas upon electron detachment the neutral La2B8 and Pr2B8 complexes are found to possess perfect D8h symmetry. The interactions between the Ln atoms and the B8 ring are derived from strong Ln5d and B2p π and δ interactions. The bonding in the Ln2B8 inverse sandwich complexes can help us understand the bonding properties of bulk systems and the design of novel lanthanide boride materials.
The experiment was performed using a magnetic-bottle PES apparatus equipped with a laser vaporization supersonic cluster source (10) (see SI Appendix, Methods for more details). Briefly, lanthanide boron clusters were generated by laser ablation of a La/11B or Pr/11B mixed target, followed by supersonic expansion using a helium carrier gas seeded with 5% argon. Negatively charged clusters were extracted from the cluster beam and analyzed by a time-of-flight mass spectrometer. Clusters with different LaxBy− or PrxBy− compositions were produced. The La2B8− and Pr2B8− clusters of current interest were mass-selected and photodetached by the 193-nm radiation of an ArF excimer laser (6.424 eV). PES data at 193 nm were first obtained for the La2B8− cluster, which was found to exhibit a particularly simple spectral pattern (Fig. 1A), suggesting a highly symmetric structure. Subsequently, the spectrum of Pr2B8− was measured (Fig. 1B), revealing a similar spectral pattern as La2B8− and indicating that the two di-Ln–octa-boron clusters should have similar structures and bonding.
Photoelectron spectra of (A) La2B8− and (B) Pr2B8− at 193 nm and comparison with the simulated spectra for the (C) D4h La2B8− and (D) D4h Pr2B8−. See SI Appendix, Tables S4 and S5 for the detachment energies of the observed bands and their assignments for La2B8− and Pr2B8−, respectively.
The two spectra each displayed four well-resolved bands labeled as X, A, B, and C. PES involves electron detachment from the anions, resulting in neutral species. The lowest binding energy band (X) corresponds to detachment transition from the ground state of the Ln2B8− anion to that of the corresponding neutral, whereas bands A, B, and C correspond to detachment transitions to excited states of neutral Ln2B8. The broad widths of some of the detachment bands suggest that they may contain multiple detachment transitions. The X band yielded the first vertical detachment energy (VDE) of 1.76 eV for La2B8− and 1.75 eV for Pr2B8−. The adiabatic detachment energy (ADE) for band X was evaluated from its onset to be 1.64 ± 0.05 eV and 1.59 ± 0.05 eV, which represent the electron affinities (EAs) of neutral La2B8 and Pr2B8, respectively. The A band at 2.91 eV (La2B8−) and 2.94 eV (Pr2B8−) was broad and intense in both spectra. At around 4 eV, both spectra displayed a relatively sharp band B, closely followed by a weak band C. The signal/noise ratios above 5 eV were poor, and no specific detachment bands could be definitively identified. Some weak features appeared around bands A and B and also possibly above band C (labeled by *). These weak features were likely due to multielectron or shakeup processes, as a result of strong electron correlation effects expected for these systems (22). The well-resolved photoelectron spectral features served as electronic fingerprints to allow analyses of their structures and bonding by comparing with theoretical calculations.
The global minimum structure for La2B8− was searched using the Tsinghua Global Minimum (TGMin) package (23, 24) with a constrained basin-hopping algorithm (25) (see SI Appendix, Methods for the computational details). A D4h (2B2u) inverse sandwich structure was found to be the global minimum (SI Appendix, Fig. S1). The D4h structure of the La2B8− anion was distorted from the perfect D8h symmetry due to the Jahn–Teller effect. We optimized the neutral D4h La2B8, which led to the perfect D8h (3A2g) structure, as shown in Fig. 2. The structural differences between the anion and neutral are relatively small. The coordinates of the anion and neutral global minima are given in SI Appendix, Table S1. For the first two isomers, CCSD(T) calculations with the PBE0/TZP geometries were further carried out to obtain more accurate relative energies. The CCSD(T) results were deemed reliable because the multiconfigurational characters were not significant from the T1 diagnostic factors of CCSD calculations (0.018 for the global minimum of La2B8−).
Two views of the global minima of the neutral D8h Ln2B8. Bon lengths: Ln…Ln = 3.720 Å (La), 3.558 Å (Pr); Ln−B = 2.759 Å (La), 2.701 Å (Pr); B−B = 1.560 Å (La), 1.555 Å (Pr) at the PBE0/TZP level.
The closest isomer above the global minimum had Cs symmetry (SI Appendix, Fig. S1), which was 32.41 kcal/mol higher in energy at the CCSD(T) level, indicating the overwhelmingly high stability of the D4h symmetrical inverse sandwich structure. The isomer of La2B8− with a seven-atom ring and one B atom squeezed out was found to be the third isomer, which lies 36.37 kcal/mol above the global minimum at the PBE0/TZP level. The isomer with a pseudoC7v B©B7 moiety (the most stable structure for bare B8) (26), sandwiched by the two La atoms, is even higher in energy (67.07 kcal/mol at the PBE0/TZP level).
On the basis of their similar PE spectra, we expected that Pr2B8− should have a similar global minimum as La2B8−. Indeed, we found that Pr2B8− has a D4h structure with a sextet ground state (6B2u). Neutral Pr2B8 upon electron detachment was found to have a perfect D8h symmetry with six unpaired electrons (7A2g). The structural parameters for the D8h Pr2B8 are also shown in Fig. 2, together with those of La2B8, and its coordinates are given in the SI Appendix, Table S2. We have obtained preliminary PES data for a late lanthanide, Tb2B8− (SI Appendix, Fig. S2), which also gives a similar spectral pattern as those of La2B8− and Pr2B8−. Hence, we expect that many lanthanide elements may form the highly symmetric Ln−B8–Ln inverse sandwich structures, as confirmed for La2B8− and Pr2B8− by comparison between experiment and theory.
To validate the global minima of La2B8− and Pr2B8−, we calculated their ADEs and VDEs using the ΔSCF–TDDFT formalism. Fig. 1 C and D present the simulated spectra for the D4h global minimum structures, showing excellent agreement with the experimental spectral patterns. The computed ADE/VDEs at the CCSD(T) level are 1.47/1.52 eV and 1.53/1.64 eV for La2B8− and Pr2B8−, respectively, in good agreement with the experimental data of 1.64/1.76 eV and 1.59/1.75 eV (SI Appendix, Table S3). All of the computed detachment channels for La2B8− and Pr2B8− (including the electron configurations and final state symmetries) and their comparison with the experimental data are given in SI Appendix, Tables S4 and S5, respectively. As expected, each observed PES band corresponds to multiple detachment channels.
According to the valence molecular orbital (MO) correlation diagram of La2B8 and La2B8− (SI Appendix, Fig. S3) and the MO contours of the La2B8− anion (SI Appendix, Fig. S4), the bonding patterns of the neutral and anion species are similar. The lower symmetry of the anion is due to the Jahn–Teller effect, as a result of the extra electron in the 1e2u MO (1e2u3) in a D8h anion, leading to the slight distortion to the D4h symmetry. Electron detachments from the primarily 5d-type 1b2u and 1b1u MOs of La2B8− give rise to three detachment channels with very close computed VDEs from 1.597 to 1.661 eV, corresponding to the X band in the PE spectrum (Fig. 1C and SI Appendix, Table S4). The remaining MOs are all B8 ring-based fully occupied σ and π orbitals. Detachments from the 4eu and 2eg MOs give rise to four detachment channels with close computed VDEs from 2.798 to 2.856 eV, corresponding well to the A band around 3 eV. Detachments from the 4a1g and 3a2u MOs give rise to band B, whereas detachment from the 1a2g MO gives rise to the weaker band C.
The MOs of Pr2B8− are similar to those of La2B8−, except the two half-filled 4f-based 5eu and 3eg MOs (SI Appendix, Fig. S5), which contributed to the broad A band (SI Appendix, Table S5). Other detachment channels and assignments of Pr2B8− are similar to those of La2B8−. Overall, the theoretical VDEs from the D4h La2B8− and Pr2B8− and the simulated PE spectra agree well with the experimental data, providing considerable credence for the identified D4h global minima for the anions and the D8h global minima for the two Ln2B8 neutral complexes.
Inverse sandwich structures represent a fascinating class of inorganic compounds, consisting of two metal atoms sandwiching an aromatic hydrocarbon molecule (27⇓⇓⇓⇓⇓⇓⇓–35). The central aromatic molecule forms interesting chemical bonds to the metals on both sides of the molecular plane. Specifically, a δ-bond has been identified to be critical for the arene-bridged diuranium inverse sandwich complexes (32⇓–34). The current La2B8− and Pr2B8− species are the first inverse sandwich structures observed for lanthanide borides. Because of the high symmetry of the corresponding neutral species, we will use the neutral Ln2B8 to discuss the stability and bonding of the lanthanide boron inverse sandwiches. The Ln−B bond lengths are around 2.70−2.76 Å (Fig. 2), indicating strong bonding between the Ln and the boron atoms. The Ln−B8−Ln binding energies calculated for Ln2B8 → 2Ln + B8 are quite large, 403.89 kcal/mol for La2B8 and 456.16 kcal/mol for Pr2B8 (SI Appendix, Table S6). It should be reiterated that the B8 ring in the Ln2B8 inverse sandwiches is quite different from the bare B8 cluster, which has a D7h B©B7 wheel structure (26). The isomer involving this B8 wheel is much higher in energy, 67.07 kcal/mol above the global minimum (SI Appendix, Fig. S1).
Due to the similarity in the electronic structure and bonding between the anion and neutral species (SI Appendix, Fig. S3), we chose the more symmetric neutrals (D8h) to discuss the chemical bonding in the inverse sandwiches. We first analyzed the B8 ring using the localized coordinate system (Fig. 3). The 32 2s–2p valence orbitals of B8 can be divided into four categories using a Hückel-type approach—σs, σ(t)p, σ(r)p, and πp—where “t” and “r” denote tangential and radial bonding, respectively. The occupied σs and σ(t)p orbitals constitute the eight B−B bonds in the B8 ring. Of particular importance are the two sets of delocalized σ(r)p and πp orbitals, which primarily participate in bonding with the two Ln atoms above and below the B8 ring. These two sets of orbitals have smaller energy-level splitting because of less overlap between the B atoms as a result of the relatively large ring size (∼4.2 Å).
The localized coordinate system (LCS) of the B8 moiety from PBE/DZP calculations. The 32 valence orbitals are divided into four types: σs, σ(t)p, σ(r)p, and πp. The “t” means tangential and “r” means radial. The σ and π orbitals are labeled with a subscript number from 0–4 according to the number of their orbital nodes. The orbital occupancy is also indicated. The occupied and unoccupied orbitals are color-coded.
Fig. 4 presents the MO correlation diagram of La2B8 derived from the La…La and B8 moieties. The exceptional stability of La2B8 is evident by the large energy gap between the HOMO (1e2u) and LUMO (5a1g). The 4f orbitals are well known to be radially too contracted in lanthanide elements to participate in chemical bonding. They form a nonbonding f-band in between the HOMO–LUMO region, giving rise to interesting magnetic properties for the Ln2B8 complexes (for Ln > La). The Ln 5d orbitals are much more extended than the 4f orbitals radially. Thus, the 5dπ and 5dδ orbitals of the two Ln atoms are significantly stabilized via bonding with the σ1 and π2 orbitals of the B8 ring. Chemical bonding of the anionic Ln2B8− and neutral Ln2B8 differs only in the electron occupation in the 1e2u HOMO: It is half-filled (1e2u2) in the neutral, whereas it has a 1e2u3 occupation in the anion. Thus, the symmetry of Ln2B8− is reduced from D8h to D4h due to the Jahn–Teller effect, and the 1e2u orbital is split to 1b2u and 1b1u under D4h symmetry (SI Appendix, Table S7). The occupied valence MOs for La2B8− and Pr2B8− are shown, respectively, in SI Appendix, Figs. S4 and S5. Our bonding analyses will focus on the more symmetric neutral Ln2B8.
The MO bonding scheme of D8h La2B8 at the level of PBE0/TZP, illustrating the bonding interactions between the La…La and B8 fragments.
In La2B8, the two La atoms provide four electrons to fill the σr1 orbital of B8, which is transformed to the 3e1u MO in La2B8 (Fig. 4). This (d–p)π type bonding orbital contributes the most (74.6%) to the total orbital interactions between La…La and B8, as revealed through EDA–NOCV analyses [see ΔEorb(1) and ΔEorb(1)' in SI Appendix, Table S8]. The La…La d–σg orbital interacts with the σr0 of B8 to form the 4a1g (d–p)σ MO, which only accounts for 2.2% of the total bonding [see ΔEorb(3) in SI Appendix, Table S8]. The d–πg orbital of La…La only bonds marginally with the π1 orbital of B8 due to symmetry compatibility, accounting for 2.6% of the orbital interactions [see ΔEorb(4) and ΔEorb(4)′ in SI Appendix, Table S8]. Remarkably, the d–δu orbital of La…La and the π2 orbital of B8 are significantly stabilized because of favorable energy matching and effective orbital overlap to form the 1e2u bonding MO occupied with two unpaired electrons. This bond is reminiscent of the δ bond that plays a key role in stabilizing diuranium inverse sandwiches (32⇓–34). This unique (d–p)δ bond is also important for the La2B8 inverse sandwich, contributing 17.6% to the total orbital interactions [see ΔEorb(2) and ΔEorb(2)′ in SI Appendix, Table S8].
The bonding patterns are similar in all Ln2B8 inverse sandwich complexes, albeit a different number of 4f electrons will give rise to different magnetic properties. The total charge and spin densities of both the anion and neutral Ln2B8 species were computed using several methods (SI Appendix, Table S9). The spin densities indicate that each Pr holds two unpaired 4f electrons, while no 4f electron is on La. The B atoms also have spin densities because of the two unpaired electrons in the (d–p)δ bonding orbitals. Upon one electron detachment from the 1b1u orbital of (d–p)δ character, the reduction of electrons on Ln is more than that on the B atoms, suggesting that the (d–p)δ bond is contributed slightly more by the Ln–5d orbitals. The B8 ring acts as a doubly aromatic motif to form the inverse sandwich Ln−B8−Ln complexes. Interestingly, we found some nonnegligible Ln…Ln interactions via the σ and π delocalized orbitals of the B8 ring (SI Appendix, Table S6). The distance between the two Ln atoms is about 3.6∼3.7 Å, which is remarkably close to the Ln−Ln single bond length (3.60 Å for La−La and 3.52 Å for Pr−Pr based on the self-consistent covalent radii of Pyykkö) (36).
The chemical bonding in Ln2B8 can be further understood using AdNDP analyses (37), as shown in Fig. 5 for La2B8. The AdNDP results show clearly eight two-center two-electron (2c–2e) bonds in the B8 ring. The remaining bonds are all delocalized 10c–2e bonds. The three delocalized bonds in the first row represent in-plane σ bonds within the B8 ring involving interactions with the La 5dσ/π orbitals. These bonds give rise to σ aromaticity because they fulfill the Hückel 4N+2 rule. The five delocalized bonds in the second row represent π bonds in Ln2B8, giving rise to π aromaticity for triplet states (38), because of the two single-electron bonds corresponding to the two singly occupied (d–p)δ MOs. Adding two electrons to these MOs would result in a filled (d–p)δ bonding MO and a closed-shell La2B82− with 10 π electrons. The B2p orbitals and the Ln4f orbitals are close in energy. This energetic factor and the fact that boron has low electronegativity make it difficult for Pr or other Ln elements with 4f electrons to donate more electrons to the B8 ring to fill the (d–p)δ bonding MOs. Hence, even though Pr is known to reach a maximum oxidation state of +V with highly electronegative elements (39), in the Pr2B8 inverse sandwich complex each Pr center still retains two 4f electrons (SI Appendix, Fig. S5).
AdNDP bonding analyses for La2B8 at the PBE0/cc-pVTZ level. Occupation numbers (ON) are shown.
The La2B8 inverse sandwich is magnetic due to the two unpaired electrons in the (d–p)δ (e2u) orbitals. Ferromagnetism was observed in La-doped CaB6 crystals at high temperatures (40) and has stimulated intense interests due to the many fundamental issues associated with this novel phenomenon (41⇓–43). The divalent CaB6 is a semiconductor with a band gap of ∼1 eV (44). The observed ferromagnetism in La-doped CaB6 is due to the partially filled impurity band formed by the La 5d orbitals (45), analogous to the half-filled (d–p)δ orbitals in La2B8.
The Pr2B8 inverse sandwich has more complicated and interesting magnetic properties due to the partially filled 4f shells. We carried out a series of calculations to determine the electron configurations and spin states of Pr2B8− and Pr2B8 (SI Appendix, Table S10). The isomers with the promotion of a 4f electron to the 5d orbital, …(d–p)δ2Pr(4f2)Pr(4f2), is energetically preferable to the isomer with the …(d–p)δ4Pr(4f1)Pr(4f1) configuration by 42.77 kcal/mol at the CCSD(T)/VTZ level. Thus, the bonding in Pr2B8 remains the same as in La2B8, as discussed above. We also examined the relative energies of possible ferromagnetic and antiferromagnetic configurations and found that the state with septuplet multiplicity is most favorable energetically with the two unpaired electrons in the (d–p)δ bonding MO and the four 4f electrons ferromagnetically coupled. The corresponding antiferromagnetic state (triplet) lies 12.12 kcal/mol higher in energy, calculated using the PBE0/TZP broken-symmetry approach. As expected, the energy differences are small for different occupations of the 4f manifold of orbitals (SI Appendix, Table S10). For example, the energy difference between the septuplet …(d–p)δ2Pr(4fδ2)Pr(4fδ2) and septuplet …(d–p)δ2Pr(4fϕ2)Pr(4fϕ2) configurations is only 4.99 kcal/mol at the PBE0 level.
The above single-configurational theoretical results are further examined using the wavefunction theory in the ab initio multiconfigurational framework. State-averaged CASSCF calculations indicate that the ground state of Pr2B8 is dominated by the …(d–p)δ2Pr(4f2)Pr(4f2) configuration (CI weight: ∼98%), even though the four 4f electrons distribute on almost every type of the near-degenerate 4f orbitals. The corresponding antibonding (d–p)δ* natural orbitals are shown to have occupation numbers only on the order of 0.03 (SI Appendix, Fig. S6). The CASPT2 results (SI Appendix, Table S11) confirm the septuplet ground state with a CI weight of 94%, which has two unpaired 4fδ and 4fϕ electrons on each Pr atom and two electrons in the degenerate singly occupied (d–p)δ bonding orbitals coupled ferromagnetically. Other calculations based on different occupation situations in the 4f orbitals were further performed. Overall, the septuplet …(d–p)δ2Pr(4f2)Pr(4f2) configuration is favored, no matter which type of 4f orbitals is occupied within an energy range of 5 kcal/mol (SI Appendix, Table S11). The triplet state dominated by the …(d–p)δ4Pr(4f1)Pr(4f1) configuration has shorter Pr…Pr distance (3.30 Å at the PBE0/TZP level) due to the enhanced (d–p)δ bonding, but it lies 38.79 kcal/mol higher in energy than the …(d–p)δ2Pr(4f2)Pr(4f2) septuplet ground state.
The antiferromagnetic coupling exhibits strong multiconfigurational characters due to configuration mixing. The lowest antiferromagnetic triplet excited state with two spin-up and two spin-down 4f electrons was evaluated to be 8.73 kcal/mol higher in energy than the septuplet ground state from the CASPT2 calculation (SI Appendix, Table S11). The ferromagnetic coupling in the Pr2B8 inverse sandwich involves the two f2 centers and the (d–p)δ bonding diradical (e2u)2 on the central B8 ring, which is highly unusual and is quite different from most Ln compounds with only Ln-centered unpaired spins. We further calculated the relative energies of a ferromagnetic and an antiferromagnetic 1D chain using the periodic VASP code with constrained D8h Pr…B8…Pr repeating units. The ferromagnetic coupling is found to be more favorable by 11.90 kcal/mol, with nearly 2 μb magnetization on each Pr atom and the B8 ring. If such a highly magnetic nanowire can be realized, it could have potential applications in magnetoresistance or quantum computing, in particular for the Gd…B8…Gd system with seven f electrons per Gd.
In conclusion, we report the first di-lanthanide octa-boron inverse sandwich complexes. The photoelectron spectra of two representative systems, Ln2B8− (Ln = La, Pr), show similar and relatively simple spectral patterns, suggesting that they have similar high-symmetry structures. Theoretical calculations showed that the Ln2B8− anions have D4h symmetry due to the Jahn–Teller effects, whereas the neutral Ln2B8 complexes have perfect D8h symmetry. Strong chemical bonding is found between the Ln atoms and the 2s and 2p MOs of the B8 ring. Neutral La2B8 has a triplet ground state, displaying diradical characters on the B8 ring, whereas Pr2B8 carries six unpaired spins with each Pr atom retaining two 4f electrons. The ground state of Pr2B8 is ferromagnetically coupled to give a septuplet spin state. All Ln2B8 complexes are expected to display similar structures and bonding, providing opportunities to design highly magnetic Ln2B8 sandwich complexes, as well as 1D magnetic nanowires.
The calculations were performed using supercomputers at Tsinghua National Laboratory for Information Science and Technology and the Supercomputing Center, Computer Network Information Center of the Chinese Academy of Sciences. The experimental work at Brown University was supported by National Science Foundation Grant CHE-1763380. The theoretical work at Tsinghua University was supported by National Natural Science Foundation of China Grants 21590792, 91426302, and 21433005.
↵1W.-L.L. and T.-T.C. contributed equally to this work.
Author contributions: J.L. and L.-S.W. designed research; W.-L.L., T.-T.C., D.-H.X., and X.C. performed research; W.-L.L. and T.-T.C. analyzed data; and W.-L.L., T.-T.C., J.L., and L.-S.W. wrote the paper.
The authors declare no conflict of interest.
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