Ta2+-mediated ammonia synthesis from N2 and H2 at

ambient temperatureCaiyun Genga, Jilai Lia,b,1, Thomas Weiskea, and Helmut Schwarza,1

aInstitut für Chemie, Technische Universität Berlin, 10623 Berlin, Germany; and bInstitute of Theoretical Chemistry, Jilin University, Changchun 130023,People’s Republic of China

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2018.

Contributed by Helmut Schwarz, September 20, 2018 (sent for review August 24, 2018; reviewed by R. Graham Cooks and Markus Reiher)

In a full catalytic cycle, bare Ta2+ in the highly diluted gas phase is

able to mediate the formation of ammonia in a Haber–Bosch-likeprocess starting from N2 and H2 at ambient temperature. This find-ing is the result of extensive quantum chemical calculations sup-ported by experiments using Fourier transform ion cyclotronresonance MS. The planar Ta2N2

+, consisting of a four-memberedring of alternating Ta and N atoms, proved to be a key intermedi-ate. It is formed in a highly exothermic process either by the re-action of Ta2

+ with N2 from the educt side or with two moleculesof NH3 from the product side. In the thermal reaction of Ta2

+ withN2, the N≡N triple bond of dinitrogen is entirely broken. A detailedanalysis of the frontier orbitals involved in the rate-determiningstep shows that this unexpected reaction is accomplished by theinterplay of vacant and doubly occupied d-orbitals, which serve asboth electron acceptors and electron donors during the cleavageof the triple bond of N≡N by the ditantalum center. The ability ofTa2

+ to serve as a multipurpose tool is further shown by splittingthe single bond of H2 in a less exothermic reaction as well. Theinsight into the microscopic mechanisms obtained may provideguidance for the rational design of polymetallic catalysts to bringabout ammonia formation by the activation of molecular nitrogenand hydrogen at ambient conditions.

gas-phase catalysis | ammonia synthesis | dinitrogen activation |hydrogen activation | quantum chemical calculation

The direct use of molecular nitrogen with its thermodynami-cally stable and kinetically inert triple bond as one of the very

few commodities that are freely available worldwide and in al-most unlimited quantities is essential for life on Earth (1–3).Nature utilizes nitrogen-binding enzymes, the nitrogenases, tocatalyze the conversion of nitrogen to ammonia at ambientconditions (4, 5). In contrast, its industrial production still relieson the highly energy-demanding Haber–Bosch process to bringabout the challenging chemical marriage of N2 and H2 to formNH3 (3, 6–8), which consumes ca. 1–2% of the world’s energyproduction (8–11). In addition, presently about 1.5 tons of thegreenhouse gas carbon dioxide are produced per ton of ammonia(9). To slow down global warming (12), it would, therefore, besensible, in addition to numerous other measures, to find aprocess for producing ammonia on an industrial scale from themolecular feedstock nitrogen and hydrogen in an economicallyviable and environmentally benign way.The greatest obstacle to the production of ammonia from N2

corresponds to the cleavage of the N≡N triple bond, which with abond energy of 945 kJ mol−1 (13), constitutes one of the stron-gest chemical bonds. While some progress has been made on thedaunting road to artificial nitrogen activation, the number ofwell-defined complexes that bind N2 and ultimately, lead to acomplete cleavage of the N≡N triple bond is rather limited sofar. For instance, complexes with single (14–32) and multiple(15, 33–39) transition metal centers, small metal clusters (40–48), and also, main group compounds (49–52) have been foundto be able to split dinitrogen. The activation of N–N bonds by

oriented external electric fields (53, 54) followed by insertion of,for example, a nitrogen atom in the C–C bonds of alkanes hasbeen reported as well (55, 56). Another promising approach isbased on the electrochemical cleavage of N2 to produce ammonia(11, 31, 32, 51, 57–60). There are indications that the cooperativeactivation of N2 by several transition metal atoms holds promiseas well (28, 34–39, 45, 61–64). Furthermore, the reactivity ofditantalum complexes of the type ([NPN]Ta(μ-H))2N2 ([NPN] =PhP(CH2SiMe2NPh)2) with dinitrogen (65) has also been ex-tensively investigated in the past (28, 34, 61–71).Mechanistically, the catalytic activity of the transition metals is

based on the interplay of vacant and filled d-orbitals during multi-electron rearrangements along the reaction coordinate. Here, thevacant orbitals of the metal center receive electrons from N2 andsimultaneously weaken (or cleave) the triple bond of dinitrogen bydonating electron density from the filled d-orbitals into the anti-bonding π*-orbitals of N2 (49, 50). According to the conceptualframework outlined by Fryzuk and coworkers (67), it was recognizedthat the ability of Ta compounds to store two electrons in a Ta–Tabond is a prerequisite for subsequent reductive transformations andis of paramount importance to split the N≡N triple bond completely.While the impressive progress made in recent decades is un-

deniable, a deep and comprehensive understanding of the vari-ous mechanistic details related to either fixation or activation ofN2 to ammonia is far from being complete. This also applies to aconsistent description of the elementary steps involved, with the

Significance

A combined experimental/computational approach providesdeep mechanistic insight into an unprecedented cluster-mediated N−H coupling mimicking the industrially extremelyimportant ammonia synthesis from N2 and H2 (the “Haber–Bosch” process) at room temperature. Crucial steps wereidentified for both the forward reactions (i.e., the activation ofN2) and the backward process (i.e., the Ta2

+-mediated de-composition of NH3). The central intermediate for either pathcorresponds to Ta2N2

+, a four-membered ring with alternatingTa and N atoms. The root cause of tantalum’s ability to bringabout nitrogen fixation and its coupling with H2 under mildconditions has been identified by state-of-the-art quantumchemical calculations.

Author contributions: J.L. and H.S. designed research; C.G. and J.L. performed research;C.G., J.L. and T.W. analyzed data; and J.L., T.W. and H.S. wrote the paper.

Reviewers: R.G.C., Purdue University; and M.R., Swiss Federal Institute of Technology.

The authors declare no conflict of interest.

Published under the PNAS license.

See QnAs on page 11657.1To whom correspondence may be addressed. Email: Jilai@jlu.edu.cn or helmut.schwarz@tu-berlin.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1814610115/-/DCSupplemental.

Published online October 23, 2018.

11680–11687 | PNAS | November 13, 2018 | vol. 115 | no. 46 www.pnas.org/cgi/doi/10.1073/pnas.1814610115

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

exception of the elegant elucidation of the mechanism of theHaber–Bosch process by Ertl and coworkers (7, 8, 72, 73).As has been shown time and again, gas-phase experiments

provide an ideal arena for tackling many challenging mechanisticissues at a strictly molecular level, such as investigating the de-tailed course of chemical reactions, including those that are in-dustrially relevant (74–88). Structurally properly characterizedgas-phase clusters have been chosen as prototypical models toprobe the active sites in (including but not limited to) hetero-geneous catalysis aimed at a better understanding of the intrinsicfactors that govern reactivity patterns in the condensed phase(89, 90). In addition, it has been shown that fundamental ques-tions can be addressed when complementing the experimentalfindings by quantum chemical (QC) calculations (91, 92).Given the enormous importance of the Haber–Bosch process,

the study of metal clusters capable of activating dinitrogen so as tosynthesize ammonia represents a worthy undertaking (39), not tomention the fundamental problems being addressed. Herein, wedescribe our findings on the unexpected, mechanistically uniqueammonia synthesis from its elements at ambient temperaturemediated by the cationic tantalum dimer Ta2

+ in the highly dilutedgas phase using advanced MS complemented by QC calculations.

Results and DiscussionTa2

+ Cleaves the N≡N Triple Bond to Form Ta2N2+. The spectra in

Fig. 1 have been obtained by using Fourier transform ion cy-clotron resonance (FT-ICR) MS (details are in ExperimentalDetails) and show the results of the reactions of mass-selectedTa2

+ ions (m/z = 362) (refs. 93 and 94 have details) with 14N2,15N2, and a 1:1 mixture of 14N2 and 15N2. To properly ther-malize the precursor ion Ta2

+, it was allowed to interact withpulsed-in argon (ca. 2 × 10−6 mbar) before reacting with molec-ular nitrogen. A temperature of 298 K for the thermalized clusterswas assumed. Spectra resulting from the reactions with back-ground impurities as well as with argon, serving as an inert sub-strate, have been recorded as well (Fig. 1A).As displayed in Fig. 1A, when only argon was admitted to the

ion cyclotron resonance (ICR) cell, a signal B with Δm = +16relative to the precursor ion Ta2

+ appears; this corresponds tothe product ion Ta2O

+ generated by reactions with backgroundgases. On leaking N2 into the ICR cell, in Fig. 1B, a new signal C

with Δm = +28 appears, which has been identified as Ta2N2+

(Eq. 1). By using isotope-labeled 15N2, signal C from Fig. 1B isshifted by two mass units on the mass scale and shows up as peakD in Fig. 1C (Ta2

15N2+) (Eq. 2). If Ta2

+ is exposed to a 1:1mixture of 14N2 and

15N2, signals for both Ta214N2

+ and Ta215N2

+

are observed, but there are none containing both nitrogen iso-topes Ta2

14N15N+ (Eqs. 3 and 4). Mass-selected and properlythermalized Ta2

14N2+, when exposed to 15N2, does not react fol-

lowing one of the degenerate exchange reactions 3 and 4:

Ta2+ +N2 →Ta2N2+ [1]

Ta2+ + 15N2 →Ta215N2+ [2]

Ta214N2+ + 15N2↛Ta215N2

+ + 14N2 [3]

Ta214N2+ + 15N2↛Ta214N15N

++ 14N15N. [4]

The rate constant k(Ta2+/N2) for reaction 1 is estimated to

5.1 × 10−12 cm3 molecule−1 s−1; this corresponds to a collisionefficiency of ϕ = 0.8%. Owing to the uncertainty in the de-termination of the absolute N2 pressure, an error of ±30% isassociated with these measurements. In addition to the labelingexperiments, the elementary compositions of the charged parti-cles have been confirmed by exact mass measurements. Since14N/15N kinetic isotope effects (KIEs) are expected to be quitesmall (95) and as it was not possible to reproducibly adjust thepressure in the ICR cell to the required accuracy to obtain mean-ingful data, we have renounced the determination of the 14N/15NKIE for the formation of Ta2N2

+.The simplified 2D potential energy surface (PES) of the most

favorable pathway as well as selected structural parameters ofkey species (Fig. 2) reveals insight into the mechanism of theTa2

+-mediated activation of the N≡N triple bond at a molecularlevel. A Fortran-based genetic algorithm (96) to generate initialguess structures of Ta2N2

+ followed by optimizations at thelevel of the Becke-3–Lee–Yang–Par functional including thedef2–triple-zeta valence basis set with one set of polarization

340 362 420

A

A = Ta2+

B = Ta2O+

B

Ar

340 362 420

A

C = Ta2N2+

B

14N2

C

340 362 420

A

D = Ta15N2+

B

15N2

D

340 362 420

A

BCD

A B

C D

Fig. 1. Mass spectra for the thermal reactions of Ta2+ with Ar (A), 14N2 (B),

15N2 (C), and a 1:1 mixture of 14N2 and15N2 (D) at a pressure of ca. 2.0 × 10−7

mbar after a reaction time of 2 s. All x axes are scaled in m/z, and the y axesare normalized relative ion abundances.

0.01

-93

1/2 -55 2

-1042/3 -94

3 -453

247TaN

+ TaN+2.19

1.09

Ta N

TaN+: 1.66

TaN: 1.68

(Cs)

1.90

2.38

1.991.95 a b

b

a

(C1)

1.292.68

1.92 1.96

2.35a b

a b

1.57

2.37

1.99

(C2v)a b

a

b

1.32

2.50

1.901.82

(Cs)

2.08a b

ab

(D2h)

1.86

2.69

2.56

a bb

a

2[Ta2]+

N2

Ta2+

N2

Fig. 2. Simplified PES (ΔH298K) for the reactions of Ta2+ with N2. The cal-

culations were done at the B3LYP/def2-QZVPP//B3LYP/def2-TZVP level oftheory. Key ground-state structures with selected geometric parameters arealso provided. Charges are omitted for the sake of clarity, bond lengths aregiven in Å, and relative energies are in kJ mol−1.

Geng et al. PNAS | November 13, 2018 | vol. 115 | no. 46 | 11681

CHEM

ISTR

YINAUGURA

LART

ICLE

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

functions (B3LYP/def2-TZVP) could only identify the intermediates1–3 as the most stable species. (Additional computational details areprovided in SI Appendix.)Dinitrogen approaches the positively charged Ta2

+, which inits ground state, is a doublet (2Δg) (97), through the known side-on/end-on binding mode (μ-η1:η2-N2) (34, 63, 65–67) to formintermediate 1 (−93 kJ mol−1, Cs symmetry) in a barrier-freeprocess. The end-on bonded nitrogen atom (Na) in 1 has anNa−Taa bond length of only 1.82 A, while Tab binds side on to Na

(2.08 A) and end on to Nb (1.90 A). The N–N and Ta–Ta bonddistances are elongated by 0.23 and 0.31 A, respectively, com-pared with the isolated reactants; thus, on interacting with Ta2

+,the N≡N triple bond is already weakened, but the N2 unit assuch is still intact. These geometric properties closely resemblethose reported for the crystal structure of ([NPN]Ta(μ-H))2N2(65). During the next step, atom Nb, while still connected to Tab,approaches Taa, eventually binding to Taa via transition state 1/2(−55 kJ mol−1). This leads to the formation of intermediate 2(−104 kJ mol−1) having C2v symmetry; 2 displays a double side-on (μ-η2:η2-N2) “butterfly” geometry with an already significantlyelongated N–N bond distance amounting to 1.57 A, clearly in-dicating additional activation of the N2 molecule. Finally, theremaining bonding interaction between Na and Nb is disruptedentirely by passing through the low barrier of 2/3 (−94 kJ mol−1),thus giving rise to the global minimum 3 (−453 kJ mol−1); 3 aswell as its neutral counterpart (98) exhibit a slightly distortedplanar square with D2h symmetry. It has a cyclic structure con-sisting of alternating Ta and N atoms. Na and Nb in 3 are 2.56 Åapart from each other, indicating that the direct interaction be-tween the two N atoms is negligibly small; this is confirmed by aMayer bond order (99, 100) of less than 0.1. The energy re-quirements for dissociating 3 into various couples of, for exam-ple, TaN+/TaN, Ta2N

+/N, TaN2+/Ta, and Ta+/TaN2 are located

247, 288, 416, and 409 kJ mol−1, respectively, above the entrancelevel. To enable these reactions, external energy must be sup-plied, for instance, by collisional activation (101–104). Withoutexternal energy supply, intermediate 3 can only return to thereactants, or its lifetime can be increased by IR photon emission(105) or collisional cooling (106).To further substantiate the claim that, in Ta2N2

+, the bindinginteraction between the two nitrogen atoms originally tied to-gether by a triple bond has indeed completely disappeared, we

considered the following. If it were 1 that had been generated, adegenerate exchange of the N2 unit, according to Fig. 3, shouldbe possible, as all relevant species are located well below theentrance asymptote. However, this computational finding is inconflict with the experimental results (Eq. 3). Thus, the experi-mentally generated Ta2N2

+ does not have structure 1. Further-more, 2 is also not likely to be long lived along the reactioncoordinate. As an isolated species, it cannot dissipate its internalenergy of ca. 104 kJ mol−1 and will rather easily surmounttransition state 2/3 to form the global minimum 3. For this ion, inagreement with the experiments (Eq. 4), extensive calculations(SI Appendix, Fig. S1) reveal that, for the exchange reactionswith N2, prohibitive barriers are encountered. Finally, collisionalactivation (101–104) of Ta2N2

+ with argon leads to the loss of N2only at rather high excitation energies [E(coll.,CM) > 4.8 eV]. Thisindicates that strong chemical bonds must exist between Ta2

+

and N2. Although the direct dissociation of 3 to TaN+/TaN bycycloreversion may have an entropic advantage, obviously thisprocess cannot compete with the energetically favored multistepdissociation back to the starting reactants (3 → → → Ta2

+/N2).Thus, the cleavage of the N≡N triple bond of N2 by Ta2

+ forms3 and proceeds via the rate-limiting transition state 1/2. As therate-limiting transition state 1/2 is located below the entranceasymptote, activation of N2 is accessible at ambient temperature.

Establishing a Working Hypothesis—a Brief Detour. Recently,Arakawa et al. (107) have shown that Ta2N2

+ can also begenerated in the gas phase by the reaction of Ta2

+ with NH3at 298 K (Eq. 5). In our experiments, we found that Ta2

+

reacts with N2 to form Ta2N2+ as well (Eq. 1). Combining the

two reactions (Eq. 6) represents the reverse of the Haber–Bosch ammonia synthesis (Eq. 7). If the structures of the keyintermediates Ta2N2

+ generated in reactions 1 and 5 areidentical, the principal of microscopic reversibility requiresthat there must be a way by which N2 and H2, mediated byTa2

+, can form NH3 at ambient temperature (Eq. 7), since thereactions 1, 5, and 7 are exothermic (108):

Ta2+ + 2NH3 →Ta2N2+ + 3H2 [5]

2NH3 →N2 + 3H2 [6]

N2+3H2 → 2NH3. [7]

Crucial Intermediates Along the N2 ⇄ NH3 Reaction Coordinates.Next, we consider computationally (Fig. 4) the elementary stepsassociated with the Ta2

+-mediated reactions in Eq. 7. It is im-portant to stress that these processes turned out to be mechanis-tically rather complex, and as they do not form the main target ofour investigations, they are not discussed here in detail. Further-more, we are well aware that most likely not all conceivable in-termediates and sideways have been included that could beinvolved in the ammonia synthesis from molecular nitrogen andhydrogen mediated by Ta2

+. However, the intermediates andtransition states, shown in Fig. 4 (details are in SI Appendix, Fig.S6), already form a feasible road map to the formation of NH3 outof N2 and H2 mediated by Ta2

+ at room temperature.As the key step, a reaction with N2 takes place followed by the

sequential uptake of two H2 molecules. After liberation of thefirst NH3 molecule and subsequent uptake of a third H2 mole-cule, the second NH3 molecule is released, and Ta2

+ is regen-erated to be ready for another catalytic cycle. It is quiteimpressive to note how stable some of the intermediates are! Forexample, the global minimum (8, −690 kJ mol−1) is arrived atafter the uptake of two H2 molecules by Ta2N2

+. Ta2N2H4+,

after several intramolecular isomerizations, finally splits off one

1.89 1.951.29

1 0.0

3.1 -47

3.1/2 -32

3.2 -96

N2N2

3.1/2 -32

3.1 -47

2.341.13

2.861.16

2.14

1 0.0

2.341.13

2.861.16

2.14

Fig. 3. Simplified PES (ΔH298K) for the degenerate exchange reactions of 1with N2. Details are in Fig. 2.

11682 | www.pnas.org/cgi/doi/10.1073/pnas.1814610115 Geng et al.

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

molecule of NH3. The remaining intermediate 14, Ta2NH+, isable to catch another dihydrogen molecule. After a series ofadditional hydrogen migrations toward the NH group, a secondNH3 is formed and finally, liberated. Note that the generationof the terminal products Ta2

+ and NH3 corresponds to therate-determining step for the whole Ta2N2

+ hydrogenation–denitrogenation reactions; however and importantly, as it liesbelow the reaction entrance, a “Haber–Bosch” process transpiresat room temperature. The theoretically obtained value for theheat of formation of two NH3 molecules resulting at the end of

the catalytic cycle shown in Fig. 4 amounts to −101 kJ mol−1 andcompares well with the experimental one (−91.8 kJ mol−1) (108).To test experimentally the QC predictions of this catalytic cycle,

thermal reactions of Ta2+ with NH3 were examined. As can be seen

from Fig. 5A, Ta2+ on reacting with NH3 gives rise to Ta2NH

+ asthe main product (signal E), with Ta2N2

+ also emerging as a weaksignal C; the reaction efficiency amounts to ca. 90%. This confirmsthe results already obtained by Arakawa et al. (107). Next, whenTa2NH+ is mass selected and further reacted with another

+H2

1.342.30

1.78

(C2v)

+N2 +H2 +H2NH3 NH3

Ta2+Ta2+ [Ta2,N2]+ [Ta2,N2,H2]+ [Ta2,N2,H4]+ [Ta2,N,H]+ [Ta2,N,H3]+

1.78

1.02

1.76

1.89

1.38

2.29

14

-55 1/2 -94

2/3 -101

19 -249

-275 16/17

0

2 -104

3 4 -468

-468 4/5

-639

-498 6/7

7 -528

-526 7/8

-482 8/9

9 -613

-479 11/12

11 -510

12 -583

10 -577

-479 9/10 -490

10/1113

-493

-337

15 -365

-368 15/16

-473

17 -348

-346 17/18

18 -352

-397 12/13

1 -93

-148 18/19

-453

-6185

8-690

14

16

6

0.76 2.41

+ N2

+ 3H2

+ 2NH3

Fig. 4. Simplified PES (ΔH298K) for the reactions of Ta2+ with one molecule of N2 and three molecules of H2 and the reverse process Ta2

+ + 2NH3 → Ta2N2+ +

3H2. Details are in Fig. 2.

340 362 420

A

E

NH3

340 420

ENH3

C

A = Ta2+

C = Ta2N2+

E = Ta2NH+

F = Ta2NH2+

377 377

CF

A B

Fig. 5. Mass spectra for the thermal reactions of (A) Ta2+ with NH3 at an NH3

pressure of ca. 2.0 × 10−9 mbar after a reaction time of 2 s and (B) Ta2NH+ with

NH3 at an NH3 pressure of ca. 2.8 × 10−9 mbar after a reaction time of 1 s. Thex axes are scaled in m/z, and the y axes are normalized relative ion abundances.

Ta2+

0.0

6.1 -25

6.1/2 -23

1.90

(C2v)

1.031.83 2.22

6.2 -134

0.79

2.07

H2

Fig. 6. Simplified PES (ΔH298K) for the reactions of Ta2+ with H2. Details are

in Fig. 2.

Geng et al. PNAS | November 13, 2018 | vol. 115 | no. 46 | 11683

CHEM

ISTR

YINAUGURA

LART

ICLE

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

molecule of ammonia, the only product obtained is Ta2N2+(ϕ ≈

0.95), thus connecting 3 with 14 (Fig. 4). Starting the reaction fromthe product side has the benefit that part of the excess energygained in the course of the exothermic reaction steps can be dis-sipated by the loss of neutral hydrogen molecules, thus increasingthe lifetime of the remaining charged counterparts. We have alsoperformed numerous experiments aimed at obtaining additionaldetails for the forward reaction (i.e., the system Ta2

+/N2/H2).However, these experiments were not conclusive, most likelydue to limited sensitivity and a lack of a sufficiently long life-time of the intermediates. Nevertheless, the combined experimental/computational findings show the existence of a catalytic roomtemperature cycle in the conversion of N2/H2 to NH3.

Brief View on the Reaction of Ta2+ with H2.Although less exothermic

than in the reaction with N2, as shown computationally (Fig. 6),Ta2

+ also is able to react with H2, and the rate-determining stepcorresponds to transition state 6.1/2 (−23 kJ mol−1). In a concerted,almost barrier-free way, the C2v-symmetric, butterfly-shapedintermediate 6.2 (−134 kJ mol−1) is generated, which strongly re-sembles structure 2 in the Ta2N2

+ system; 6.2 is able to react furtherwith another molecule of H2 (SI Appendix, Fig. S2). In contrast tothe Haber–Bosch process where H2 poisoning constitutes an im-portant issue (109), in this system, for all clusters Ta2(H2)x

+ (x = 1,2, 3) investigated, N2 is able to displace molecular hydrogen andthus, suppress H2 poisoning of the catalyst as shown in SI Appendix,Figs. S3 and S5.

Fig. 7. Schematic orbital diagrams based on a frontier orbital analysis. Only representative orbitals are shown. The structures are oriented such that the x axisis along the Ta–Ta vector and that the y axis is confined to the Ta2N2 plane. The πv- and πv*-orbitals of the dinitrogen molecule are vertical (v) to this plane,whereas the πp- and πp*-orbitals are lying within this plane. The magenta borders refer to π-backdonation; the green ones represent metal centers that acceptelectron density from N2. The more intense the color, the more electron density is transferred.

11684 | www.pnas.org/cgi/doi/10.1073/pnas.1814610115 Geng et al.

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

Closer Inspection of the Mechanism of the N≡N Triple-Bond Cleavageby a Frontier Orbital Analysis. To obtain a more detailed mecha-nistic insight into the splitting of the N≡N triple bond as the keystep of the whole reaction sequence, a frontier orbital analysisfor the rate-determining step has been performed (110–117).Fig. 7 shows the detailed evolution of the electronic structuresalong the reaction coordinates.According to Fig. 7, the multiple bonding in the cationic

tantalum dimer, having a doublet ground-state Ta2+ (6s25d7),

comprises two doubly occupied σ-bonds [σ(6s-6s) and σ(dx2-dx2)],two doubly occupied π-bonds [π(dxz-dxz) and π(dxy-dxy)], and asingly occupied δ-bond [δ(dyz-dyz)]. In 1, the approaching N2molecule lies in the same plane as the metal dimer, and thestrong interaction between these two fragments mainly resultsfrom the π-backdonation from the metal centers to N2 (i.e.,electron density relocates from the metal–metal π-bonding to thevacant antibonding orbitals of the N2 ligand); as a consequence,weakening of the N≡N triple bond occurs to a certain extent. Inreturn, although relatively small, donation of electron densityfrom the N–N π-bonds to the vacant metal–metal orbitals can befound as well. On its way to 2, the N2 molecule gradually rotatesperpendicular to the Ta–Ta axis while simultaneously adjustingthe metal–metal orbitals. After conversion to 2, only a smallbarrier of 10 kJ mol−1 precludes the four atoms to be trapped inthe deep potential well to form 3. This process is accompanied byboth π-backdonation from the metal dimer to the σ*- andπ*-orbitals of N2 and partial donation of bonding electrons fromN2 to the metal dimer. It is this electronic reorganization thateventually leads to the complete rupture of the N≡N triple bond,which is accompanied by generating strong Ta–N bonds in 3.As shown in Fig. 7, the orbital components of the antibondingorbitals of N2 are dominant in π*(dxz/dxz)_πv*, π(dxz/dxz)_σ*, andδ(dyz/dyz)_πv* in 3; once again, this clearly indicates the cleavageof the N≡N triple bond. Furthermore, the components of allthree N2-based bonding orbitals greatly shrink in going from2 to 3, sharing their electrons now within the four-memberedring. In sharp contrast, for the cleavage of the single bond of adihydrogen molecule by Ta2

+, the frontier orbital interactionmainly concerns the π(dxy/dxy)-orbital of the metal dimer center andthe antibonding σ*(H–H)-orbital of H2 (SI Appendix, Fig. S8).An even deeper understanding of the intrinsic reactivity can be

obtained by a comparison of the “naked” cationic tantalum di-mer with the ligated ditantalum core in the ([NPN]Ta(μ-H))2N2complex (65). The cationic Ta dimer is characterized by a Ta–Tamultiple bond with a Wiberg bond index (WBI) of 4.5. In con-trast, in the ligated complex, the WBI amounts to only 1.7 due tosignificant binding interactions between the metal atoms andthe coordinating N and P atoms of the ligands and the twobridging hydrido ligands. SI Appendix, Fig. S7 displays repre-sentative frontier orbitals dominating the metal atoms insidethe complex. Only two doubly occupied orbitals are left. As themetal–metal σ-bonding orbital is not a good electron donor, theπ-backdonation is expected to be rather small. More importantly,these orbitals are highly localized at one of the two metal cen-ters, and their lobes are leaning toward the ligands; in addition,they are not regarded as potential electron acceptors, as an op-timal overlap is difficult to achieve. Thus, the reactivity of thecationic ditantalum cluster toward dinitrogen can be attributedto the interplay of empty and doubly occupied d-orbitals at themetal center, which on the one hand, accepts electrons from N2

and on the other hand, weakens the N≡N triple bond further byπ-backdonation of electron density from the metal center intothe antibonding orbitals of N2 (50).

ConclusionAs shown above, our working hypothesis about a tantalum-mediated coupling of N2 and H2 finally has been confirmed bygas-phase experiments and QC calculations. Here, we describethe concept of an ammonia synthesis from molecular N2 and H2catalyzed by a bare metal cluster cation at ambient temperature(118). The key step consists of the complete rupture of the N≡Ntriple bond, rendered possible by the interplay of vacant anddoubly occupied d-orbitals at the ditantalum center of Ta2

+ toform Ta2N2

+ as the central intermediate. This combined exper-imental/computational study further improves our knowledgeabout mechanistic details of the catalytic action of transitionmetals and emphasizes the crucial role that electron-donatingand -accepting orbitals play (49, 50). These findings mightserve as a base to improve or even invent “real world” catalysts tosave economic and ecologic resources in the future (73).

Materials and MethodsExperimental Details. The ion/molecule reactions were performed with aSpectrospin CMS 47X FT-ICRmass spectrometer equippedwith an external ionsource as described elsewhere (119–121). In brief, Ta2

+ was generated bylaser ablation of a tantalum disk using a neodymium-doped yttrium alumi-num garnet (Nd:YAG) laser operating at 532 nm and seeded in helium; thelatter serves as a cooling and carrier gas. Using a series of potentials and ionlenses, the ions were transferred into the ICR cell, which is positioned in thebore of a 7.05-T superconducting magnet. To properly thermalize the precursorion Ta2

+, it was allowed to take a bath in pulsed-in argon (ca. 2 × 10−6 mbar)before its reaction with dinitrogen. After thermalization, the reactions ofmass-selected Ta2

+ were studied by introducing isotopologues of dinitrogen(N2 and 15N2) and ammonia via leak valves at stationary pressures. A tem-perature of 298 K for the thermalized clusters was assumed. Before theexchange reactions between unlabeled and 15N-labeled N2, the precursorion Ta2N2

+ was thermalized by pulsed-in argon (ca. 2 × 10−6 mbar). In thecollision-induced dissociation (102–104) experiments, mass-selected, prop-erly thermalized Ta2N2

+ ions were reacted with argon.

Computational Details. The unbalanced treatment of static and dynamic cor-relation makes the transition metal chemistry hard to handle for any densityfunctional. We, therefore, carried out extensive investigations, even usingmultireference perturbation theory [like the n-electron valence state pertur-bation theory (NEVPT2)] (122–124) as well as a comparison of many densityfunctionals before deciding to base our conclusions on B3LYP calculations(125–128). The geometry optimization was conducted at the B3LYP/def2-TZVPlevel of theory. Subsequently, the electronic energies were refined by usingthe B3LYP functional with def2–quadruple-zeta valence basis set and two setsof polarization functions (B3LYP/def2-QZVPP//B3LYP/def2-TZVP) (129).

Additional information with regard to the computational details can befound in SI Appendix.

ACKNOWLEDGMENTS. We thank the following fellow colleagues forhelpful suggestions on the computational work: Prof. Dr. Frank Neese(Max Planck Institut für Kohlenforschung), Prof. Dr. Wenli Zou(Northwest University), and Dr. Jun Zhang (University of Illinois atUrbana–Champaign). We thank the reviewers for their thorough reviewand appreciate the comments and suggestions. This research wassponsored by the Deutsche Forschungsgemeinschaft, in particular theCluster of Excellence “Unifying Concepts in Catalysis,” and the Fondsder Chemischen Industrie. The work at Jilin University was supportedby National Natural Science Foundation of China Grants 21473070and 21773085.

1. Canfield DE, Glazer AN, Falkowski PG (2010) The evolution and future of Earth’s

nitrogen cycle. Science 330:192–196.2. Erisman JW, et al. (2008) How a century of ammonia synthesis changed the world.

Nat Geosci 1:636–639.3. Haber F (1920) The synthesis of ammonia from its elements. Nobel Lecture. Available

at https://www.nobelprize.org/uploads/2018/06/haber-lecture.pdf. Accessed October

11, 2018.

4. Hoffman BM, Lukoyanov D, Yang ZY, Dean DR, Seefeldt LC (2014) Mechanism of

nitrogen fixation by nitrogenase: The next stage. Chem Rev 114:4041–4062.5. Burgess BK, Lowe DJ (1996) Mechanism of molybdenum nitrogenase. Chem Rev 96:

2983–3012.6. Cheng T, Wang L, Merinov BV, Goddard WA, 3rd (2018) Explanation of dramatic pH-

dependence of hydrogen binding on noble metal electrode: Greatly weakened

water adsorption at high pH. J Am Chem Soc 140:7787–7790.

Geng et al. PNAS | November 13, 2018 | vol. 115 | no. 46 | 11685

CHEM

ISTR

YINAUGURA

LART

ICLE

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

7. Schlögl R (2008) Ammonia synthesis. Handbook of Heterogeneous Catalysis,eds Ertl G, Knözinger H, Schüth F, Weitkamp J (Wiley-VCH, Weinheim, Ger-many), pp 2501–2575.

8. Schlögl R (2003) Catalytic synthesis of ammonia-a “never-ending story”? AngewChem Int Ed Engl 42:2004–2008.

9. Pfromm PH (2017) Towards sustainable agriculture: Fossil-free ammonia. J RenewSustain Energy 9:034702.

10. Cherkasov N, Ibhadon AO, Fitzpatrick P (2015) A review of the existing and alter-native methods for greener nitrogen fixation. Chem Eng Process Process Intensif 90:24–33.

11. Licht S, et al. (2014) Ammonia synthesis by N2 and steam electrolysis in molten hy-droxide suspensions of nanoscale Fe2O3. Science 345:637–640.

12. Steffen W, et al. (2018) Trajectories of the earth system in the anthropocene. ProcNatl Acad Sci USA 115:8252–8259.

13. Tang X, Hou Y, Ng CY, Ruscic B (2005) Pulsed field-ionization photoelectron-photoion coincidence study of the process N2+hnu-->N++N+e-: Bond dissociationenergies of N2 and N2+. J Chem Phys 123:074330.

14. Gao Y, Li G, Deng L (2018) Bis(dinitrogen)cobalt(−1) complexes with NHC ligation:Synthesis, characterization, and their dinitrogen functionalization reactions afford-ing side-on bound diazene complexes. J Am Chem Soc 140:2239–2250.

15. Sekiguchi Y, et al. (2018) Catalytic reduction of molecular dinitrogen to ammoniaand hydrazine using vanadium complexes. Angew Chem Int Ed Engl 57:9064–9068.

16. Nishibayashi Y (2018) Development of catalytic nitrogen fixation using transitionmetal-dinitrogen complexes under mild reaction conditions. Dalton Trans 47:11290–11297.

17. Chalkley MJ, Del Castillo TJ, Matson BD, Roddy JP, Peters JC (2017) Catalytic N2-to-NH3 conversion by Fe at lower driving force: A proposed role for metallocene-mediated PCET. ACS Cent Sci 3:217–223.

18. Thompson NB, Green MT, Peters JC (2017) Nitrogen fixation via a terminal Fe(IV)nitride. J Am Chem Soc 139:15312–15315.

19. Del Castillo TJ, Thompson NB, Peters JC (2016) A synthetic single-site Fe nitrogenase:High turnover, freeze-quench 57Fe Mössbauer data, and a hydride resting state.J Am Chem Soc 138:5341–5350.

20. Kuriyama S, et al. (2016) Catalytic transformation of dinitrogen into ammonia andhydrazine by iron-dinitrogen complexes bearing pincer ligand. Nat Commun 7:12181.

21. Ung G, Peters JC (2015) Low-temperature N2 binding to two-coordinate L2Fe(0)

enables reductive trapping of L2FeN2(-) and NH3 generation. Angew Chem Int EdEngl 54:532–535.

22. Creutz SE, Peters JC (2014) Catalytic reduction of N2 to NH3 by an Fe-N2 complexfeaturing a C-atom anchor. J Am Chem Soc 136:1105–1115.

23. Anderson JS, Rittle J, Peters JC (2013) Catalytic conversion of nitrogen to ammoniaby an iron model complex. Nature 501:84–87.

24. Schrock RR (2008) Catalytic reduction of dinitrogen to ammonia by molybdenum:Theory versus experiment. Angew Chem Int Ed Engl 47:5512–5522.

25. Avenier P, et al. (2007) Dinitrogen dissociation on an isolated surface tantalum atom.Science 317:1056–1060.

26. Hendrich MP, et al. (2006) On the feasibility of N2 fixation via a single-site FeI/FeIVcycle: Spectroscopic studies of FeI(N2)FeI, FeIV[triple bond]N, and related species.Proc Natl Acad Sci USA 103:17107–17112.

27. Schrock RR (2005) Catalytic reduction of dinitrogen to ammonia at a single molyb-denum center. Acc Chem Res 38:955–962.

28. Pool JA, Lobkovsky E, Chirik PJ (2004) Hydrogenation and cleavage of dinitrogen toammonia with a zirconium complex. Nature 427:527–530.

29. Yandulov DV, Schrock RR (2003) Catalytic reduction of dinitrogen to ammonia at asingle molybdenum center. Science 301:76–78.

30. Laplaza CE, Cummins CC (1995) Dinitrogen cleavage by a three-coordinate molyb-denum(III) complex. Science 268:861–863.

31. Pickett CJ, Talarmin J (1985) Electrosynthesis of ammonia. Nature 317:652–653.32. Chatt J, Pearman AJ, Richards RL (1975) The reduction of mono-coordinated mo-

lecular nitrogen to ammonia in a protic environment. Nature 253:39–40.33. Lindley BM, et al. (2018) Mechanism of chemical and electrochemical N2 splitting by

a rhenium pincer complex. J Am Chem Soc 140:7922–7935.34. Burford RJ, Yeo A, Fryzuk MD (2017) Dinitrogen activation by group 4 and group 5

metal complexes supported by phosphine-amido containing ligand manifolds. CoordChem Rev 334:84–99.

35. Wang B, et al. (2017) Dinitrogen activation by dihydrogen and a PNP-ligated tita-nium complex. J Am Chem Soc 139:1818–1821.

36. Tanaka H, Nishibayashi Y, Yoshizawa K (2016) Interplay between theory and ex-periment for ammonia synthesis catalyzed by transition metal complexes. Acc ChemRes 49:987–995.

37. McWilliams SF, Holland PL (2015) Dinitrogen binding and cleavage by multinucleariron complexes. Acc Chem Res 48:2059–2065.

38. Shima T, et al. (2013) Dinitrogen cleavage and hydrogenation by a trinuclear tita-nium polyhydride complex. Science 340:1549–1552.

39. Gambarotta S, Scott J (2004) Multimetallic cooperative activation of N2. AngewChem Int Ed Engl 43:5298–5308.

40. Hübner O, Himmel H-J (2018) Metal cluster models for heterogeneous catalysis: Amatrix-isolation perspective. Chemistry 24:8941–8961.

41. Teng Y-L, Xu Q (2008) Matrix isolation infrared spectroscopic studies and densityfunctional theory calculations of the MNN, (MN)2 (M = Y and La), and Y3NN mole-cules. J Phys Chem A 112:3607–3613.

42. Liu F, Li M, Tan L, Armentrout PB (2008) Guided ion beam studies of the reactions ofCon

+ (n=1-18) with N2: Cobalt cluster mononitride and dinitride bond energies.J Chem Phys 128:194313.

43. Zhou M, Jin X, Gong Y, Li J (2007) Remarkable dinitrogen activation and cleavage bythe Gd dimer: From dinitrogen complexes to ring and cage nitrides. Angew Chem IntEd Engl 46:2911–2914.

44. Gong Y, Zhao Y, Zhou M (2007) Formation and characterization of the tetranuclearscandium nitride: Sc4N4. J Phys Chem A 111:6204–6207.

45. Himmel HJ, Reiher M (2006) Intrinsic dinitrogen activation at bare metal atoms.Angew Chem Int Ed Engl 45:6264–6288.

46. Himmel HJ, Hübner O, Klopper W, Manceron L (2006) Cleavage of the N2 triple bondby the Ti dimer: A route to molecular materials for dinitrogen activation? AngewChem Int Ed Engl 45:2799–2802.

47. Himmel HJ, Hübner O, Bischoff FA, Klopper W, Manceron L (2006) Reactivity of ti-tanium dimer and molecular nitrogen in rare gas matrices. Vibrational and elec-tronic spectra and structure of Ti2N2. Phys Chem Chem Phys 8:2000–2011.

48. Tan L, Liu F, Armentrout PB (2006) Thermochemistry of the activation of N2 on ironcluster cations: Guided ion beam studies of the reactions of Fe(n)

+ (n = 1-19) with N2.J Chem Phys 124:084302.

49. Légaré M-A, et al. (2018) Nitrogen fixation and reduction at boron. Science 359:896–900.

50. Broere DLJ, Holland PL (2018) Boron compounds tackle dinitrogen. Science 359:871.51. Lv C, et al. (2018) Defect engineering metal-free polymeric carbon nitride electro-

catalyst for effective nitrogen fixation under ambient conditions. Angew Chem IntEd Engl 57:10246–10250.

52. Melen RL (2018) A step closer to metal-free dinitrogen activation: A new chapter inthe chemistry of frustrated lewis pairs. Angew Chem Int Ed Engl 57:880–882.

53. Geng C, et al. (September 10, 2018) Oriented external electric fields as mimics forprobing the role of metal ions and ligands in the thermal gas-phase activation ofmethane. Dalton Trans, 10.1039/C8DT03048K.

54. Shaik S, Mandal D, Ramanan R (2016) Oriented electric fields as future smart re-agents in chemistry. Nat Chem 8:1091–1098.

55. Ayrton ST, Jones R, Douce DS, Morris MR, Cooks RG (2018) Uncatalyzed, re-gioselective oxidation of saturated hydrocarbons in an ambient corona discharge.Angew Chem Int Ed Engl 57:769–773.

56. Li G, Li X, Ouyang Z, Cooks RG (2013) Carbon-carbon bond activation in saturatedhydrocarbons by field-assisted nitrogen fixation. Angew Chem Int Ed Engl 52:1040–1043.

57. McEnaney JM, et al. (2017) Ammonia synthesis from N2 and H2O using a lithiumcycling electrification strategy at atmospheric pressure. Energy Environ Sci 10:1621–1630.

58. van der Ham CJM, Koper MTM, Hetterscheid DGH (2014) Challenges in reduction ofdinitrogen by proton and electron transfer. Chem Soc Rev 43:5183–5191.

59. Lan R, Irvine JTS, Tao S (2013) Synthesis of ammonia directly from air and water atambient temperature and pressure. Sci Rep 3:1145.

60. Marnellos G, Stoukides M (1998) Ammonia synthesis at atmospheric pressure.Science 282:98–100.

61. Burford RJ, Fryzuk MD (2017) Examining the relationship between coordinationmode and reactivity of dinitrogen. Nat Rev Chem 1:0026.

62. Knobloch DJ, Lobkovsky E, Chirik PJ (2010) Dinitrogen cleavage and functionaliza-tion by carbon monoxide promoted by a hafnium complex. Nat Chem 2:30–35.

63. Fryzuk MD (2009) Side-on end-on bound dinitrogen: An activated bonding modethat facilitates functionalizing molecular nitrogen. Acc Chem Res 42:127–133.

64. MacKay BA, Fryzuk MD (2004) Dinitrogen coordination chemistry: On the bio-mimetic borderlands. Chem Rev 104:385–401.

65. Fryzuk MD, et al. (2001) New mode of coordination for the dinitrogen ligand: For-mation, bonding, and reactivity of a tantalum complex with a bridging N(2) unit thatis both side-on and end-on. J Am Chem Soc 123:3960–3973.

66. MacKay BA, Munha RF, Fryzuk MD (2006) Substituent effects in the hydrosilylationof coordinated dinitrogen in a ditantalum complex: Cleavage and functionalizationof N2. J Am Chem Soc 128:9472–9483.

67. Studt F, MacKay BA, Fryzuk MD, Tuczek F (2004) Spectroscopic properties andquantum chemistry-based normal coordinate analysis (QCB-NCA) of a dinucleartantalum complex exhibiting the novel side-on end-on bridging geometry of N2:Correlations to electronic structure and reactivity. J Am Chem Soc 126:280–290.

68. Fryzuk MD, MacKay BA, Patrick BO (2003) Hydrosilylation of a dinuclear tantalumdinitrogen complex: Cleavage of N2 and functionalization of both nitrogen atoms.J Am Chem Soc 125:3234–3235.

69. Fryzuk MD, MacKay BA, Johnson SA, Patrick BO (2002) Hydroboration of co-ordinated dinitrogen: A new reaction for the N2 ligand that results in its function-alization and cleavage. Angew Chem Int Ed Engl 41:3709–3712.

70. Fryzuk MD, Johnson SA (2000) The continuing story of dinitrogen activation. CoordChem Rev 200–202:379–409.

71. Fryzuk MD, Johnson SA, Rettig SJ (1998) New mode of coordination for the dini-trogen ligand: A dinuclear tantalum complex with a bridging N2 unit that is bothside-on and end-on. J Am Chem Soc 120:11024–11025.

72. Ertl G (2008) Reactions at surfaces: From atoms to complexity (Nobel Lecture).Angew Chem Int Ed Engl 47:3524–3535.

73. Ertl G (1980) Surface science and catalysis—Studies on the mechanism of ammoniasynthesis: The P. H. Emmett award address. Catal Rev Sci Eng 21:201–223.

74. Dillinger S, et al. (2018) Cryo IR spectroscopy of N2 and H2 on Ru8+: The effect of N2

on the H-migration. J Phys Chem Lett 9:914–918.75. Schwarz H (2017) Ménage-à-trois: Single-atom catalysis, mass spectrometry, and

computational chemistry. Catal Sci Technol 7:4302–4314.76. Armentrout PB (2017) Methane activation by 5d transition metals: Energetics,

mechanisms, and periodic trends. Chemistry 23:10–18.77. O’Hair RAJ (2015) Mass spectrometry based studies of gas phase metal catalyzed

reactions. Int J Mass Spectrom 377:121–129.

11686 | www.pnas.org/cgi/doi/10.1073/pnas.1814610115 Geng et al.

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0

78. Schwarz H (2014) How andwhy do cluster size, charge state, and ligands affect the courseof metal-mediated gas-phase activation of methane? Isr J Chem 54:1413–1431.

79. Schlangen M, Schwarz H (2012) Effects of ligands, cluster size, and charge state ingas-phase catalysis: A happy marriage of experimental and computational studies.Catal Lett 142:1265–1278.

80. Lang SM, Bernhardt TM (2012) Gas phase metal cluster model systems for hetero-geneous catalysis. Phys Chem Chem Phys 14:9255–9269.

81. Schwarz H (2011) Chemistry with methane: Concepts rather than recipes. AngewChem Int Ed Engl 50:10096–10115.

82. Castleman AW, Jr (2011) Cluster structure and reactions: Gaining insights into cat-alytic processes. Catal Lett 141:1243–1253.

83. Roithová J, Schröder D (2010) Selective activation of alkanes by gas-phase metal ions.Chem Rev 110:1170–1211.

84. Schröder D, Schwarz H (2008) Gas-phase activation of methane by ligated transition-metal cations. Proc Natl Acad Sci USA 105:18114–18119.

85. Böhme DK, Schwarz H (2005) Gas-phase catalysis by atomic and cluster metal ions:The ultimate single-site catalysts. Angew Chem Int Ed Engl 44:2336–2354.

86. Schwarz H, Schröder D (2000) Concepts of metal-mediated methane functionaliza-tion. An intersection of experiment and theory. Pure Appl Chem 72:2319–2332.

87. Schröder D, Schwarz H (1995) C−H and C−C bond activation by bare transition-metaloxide cations in the gas phase. Angew Chem Int Ed Engl 34:1973–1995.

88. Eller K, Schwarz H (1991) Organometallic chemistry in the gas phase. Chem Rev 91:1121–1177.

89. Freund H-J, Meijer G, Scheffler M, Schlögl R,Wolf M (2011) CO oxidation as a prototypicalreaction for heterogeneous processes. Angew Chem Int Ed Engl 50:10064–10094.

90. Castleman AW, Keesee RG (1986) Clusters: Bridging the gas and condensed phases.Acc Chem Res 19:413–419.

91. Schwarz H, Shaik S, Li J (2017) Electronic effects on room-temperature, gas-phase C−Hbond activations by cluster oxides and metal carbides: The methane challenge. J AmChem Soc 139:17201–17212.

92. Neese F (2017) High-level spectroscopy, quantum chemistry, and catalysis: Not just apassing fad. Angew Chem Int Ed Engl 56:11003–11010.

93. Li J, et al. (2015) On the role of the electronic structure of the heteronuclear oxidecluster [Ga2Mg2O5 ](.+) in the thermal activation of methane and ethane: An un-usual doping effect. Angew Chem Int Ed Engl 54:5074–5078.

94. Li J, et al. (2016) Mechanistic variants in gas-phase metal-oxide mediated activationof methane at ambient conditions. J Am Chem Soc 138:11368–11377.

95. Laplaza CE, et al. (1996) Dinitrogen cleavage by three-coordinate molybdenum(III)complexes:Mechanistic and structural data. J Am Chem Soc 118:8623–8638.

96. Ding X-L, Li ZY, Meng JH, Zhao YX, He SG (2012) Density-functional global optimi-zation of (La2O3)n clusters. J Chem Phys 137:214311.

97. Du J, Sun X, Jiang G (2012) A theoretical study on Ta(n)+ cluster cations: Structural

assignments, stability, and electronic properties. J Chem Phys 136:094311.98. Kumar Yadav M, Mookerjee A (2010) Nitrogen absorption and dissociation on small

tantalum clusters. Phys B 405:3940–3942.99. Mayer I (1984) Bond order and valence: Relations to Mulliken’s population analysis.

Int J Quantum Chem 26:151–154.100. Mayer I (1983) Charge, bond order and valence in the AB initio SCF theory. Chem

Phys Lett 97:270–274.101. Cooks RG, Yan X (2018) Mass spectrometry for synthesis and analysis. Annu Rev Anal

Chem (Palo Alto Calif) 11:1–28.102. McLafferty FW (2011) A century of progress in molecular mass spectrometry. Annu

Rev Anal Chem (Palo Alto Calif) 4:1–22.103. Cooks RG (1995) Special feature: Historical. Collision-induced dissociation: Readings

and commentary. J Mass Spectrom 30:1215–1221.104. Levsen K, Schwarz H (1983) Gas-phase chemistry of collisionally activated ions. Mass

Spectrom Rev 2:77–148.105. Dunbar RC, Chen JH, So HY, Asamoto B (1987) Infrared fluorescence relaxation of

photoexcited gas-phase ions by chopped-laser two-photon dissociation. J Chem Phys86:2081–2086.

106. Gerlich D, Borodi G (2009) Buffer gas cooling of polyatomic ions in rf multi-electrodetraps. Faraday Discuss 142:57–72.

107. Arakawa M, et al. (2018) The role of electronegativity on the extent of nitridation ofgroup 5 metals as revealed by reactions of tantalum cluster cations with ammoniamolecules. Phys Chem Chem Phys 20:13974–13982.

108. Chase MW, Jr (1998) NIST-JANAF thermochemical tables, 4th edition, monograph 9.J Phys Chem Ref Data Monogr 9:1–1951.

109. Kitano M, et al. (2012) Ammonia synthesis using a stable electride as an electrondonor and reversible hydrogen store. Nat Chem 4:934–940.

110. Li J, et al. (2015) Distinct mechanistic differences in the hydrogen-atom transfer frommethane and water by the heteronuclear oxide cluster [Ga2 MgO4](.). Angew ChemInt Ed Engl 54:12298–12302.

111. Li J, et al. (2015) On the mechanisms of hydrogen-atom transfer from water to theheteronuclear oxide cluster [Ga2Mg2O5]

•+

: Remarkable electronic structure effects.Angew Chem Int Ed Engl 54:11861–11864.

112. Sun X, et al. (2014) Large equatorial ligand effects on C-H bond activation by non-heme iron(IV)-oxo complexes. J Phys Chem B 118:1493–1500.

113. Sun X, Sun X, Geng C, Zhao H, Li J (2014) Benchmark study on methanol C-H and O-Hbond activation by bare [Fe(IV)O](2+). J Phys Chem A 118:7146–7158.

114. Li JL, Zhang X, Huang XR (2012) Mechanism of benzene hydroxylation by high-valent bare Fe(IV)=O2+: Explicit electronic structure analysis. Phys Chem Chem Phys14:246–256.

115. Sun XL, Huang XR, Li JL, Huo RP, Sun CC (2012) Mechanism insights of ethane C-Hbond activations by bare [Fe(III)═O]+: Explicit electronic structure analysis. J PhysChem A 116:1475–1485.

116. Geng C, Ye S, Neese F (2010) Analysis of reaction channels for alkane hydroxylationby nonheme iron(IV)-oxo complexes. Angew Chem Int Ed Engl 49:5717–5720.

117. Neese F (2006) Importance of direct spin-spin coupling and spin-flip excitations forthe zero-field splittings of transition metal complexes: A case study. J Am Chem Soc128:10213–10222.

118. Hölscher M, Leitner W (2017) Catalytic NH3 synthesis using N2/H2 at moleculartransition metal complexes: Concepts for lead structure determination using com-putational chemistry. Chemistry 23:11992–12003.

119. Engeser M, Weiske T, Schröder D, Schwarz H (2003) Oxidative degradation of smallcationic vanadium clusters by molecular oxygen: On the way from Vn

+ (n = 2 - 5) toVOm

+ (m = 1, 2). J Phys Chem A 107:2855–2859.120. Schröder D, et al. (1997) Activation of hydrogen and methane by thermalized FeO+

in the gas phase as studied by multiple mass spectrometric techniques. Int J MassSpectrom 161:175–191.

121. Eller K, Schwarz H (1989) Organometallic chemistry in the gas phase. A comparativefourier transform-ion cyclotron resonance/tandem mass spectrometry study. Int JMass Spectrom 93:243–257.

122. Angeli C, Cimiraglia R, Malrieu J-P (2002) n-electron valence state perturbationtheory: A spinless formulation and an efficient implementation of the stronglycontracted and of the partially contracted variants. J Chem Phys 117:9138–9153.

123. Angeli C, et al. (2001) Introduction of n-electron valence states for multireferenceperturbation theory. J Chem Phys 114:10252–10264.

124. Angeli C, Cimiraglia R, Malrieu J-P (2001) n-electron valence state perturbationtheory: A fast implementation of the strongly contracted variant. Chem Phys Lett350:297–305.

125. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vi-brational absorption and circular dichroism spectra using density functional forcefields. J Phys Chem 98:11623–11627.

126. Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange.J Chem Phys 98:5648–5652.

127. Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energyformula into a functional of the electron density. Phys Rev B Condens Matter 37:785–789.

128. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid corre-lation energies for local spin density calculations: A critical analysis. Can J Phys 58:1200–1211.

129. Li JL, Mata RA, Ryde U (2013) Large density-functional and basis-set effects for theDMSO reductase catalyzed oxo-transfer reaction. J Chem Theory Comput 9:1799–1807.

Geng et al. PNAS | November 13, 2018 | vol. 115 | no. 46 | 11687

CHEM

ISTR

YINAUGURA

LART

ICLE

Dow

nloa

ded

by g

uest

on

Dec

embe

r 1,

202

0