www.pnas.org/cgi/doi/10.1073/pnas. 115 1

Supporting Information Appendix

A Critical Computational Analysis Illuminates the Reductive-Elimination Mechanism That Activates Nitrogenase for N2 Reduction Simone Raugei,(1) Lance C. Seefeldt(2) and Brian M. Hoffman(3)

(1) Pacific Northwestern National Laboratory, Richland, Washington 99352 (2) Department of Chemistry and Biochemistry, Utah State University, Logan, UT, 84322 (3) Department of Chemistry, Northwestern University, Evanston, Illinois 60208 *Corresponding authors: Simone Raugei, Ph. 509-372-6902, simone.raugei@pnnl.gov; Lance Seefeldt, Ph. 435-797-3964, lance.seefeldt@usu.edu; Brian M. Hoffman, Ph. 847-491-3104.

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2

Summary Section S1 – Figures and Table Cited in the Text

Figure S1. Models of the FeMo-co pocket adopted in the DFT calculations 3 Figure S2. Energetic of three possible spin configurations that maximizes the

antiferromagnetic spin coupling between in the E0 state 4

Figure S3. Energy ranking of possible E4 states and their schematic representation 5 Figure S4. Energy of FeMo-co in the E4(4H), E4(3H,CH) and E0 relative to that of the isolated

FeMo-co in the E0 state. 6

Figure S5. Energy profile for the dissociation of H2 from E4(2H;H2;N2) and E4(2H;H2) 7 Figure S6. Structure of relevant En states 8 Figure S7. B3LYP free energy of various E4 species potentially involved in FeMo-co

reductive activation and the breaking of the N2 triple bond 9

Table S1. The 35 spin configurations of the initial guesses for the broken symmetry calculations

10

Table S2. BP86 relative energy of broken symmetry solutions for the E0 11 Table S3. B3LYP relative energy of broken symmetry solutions for the E0 12 Table S4. BP86 relative energy of broken symmetry solutions for the E4(4H) 13 Table S5. B3LYP relative energy of broken symmetry solutions for the E4(4H) 14 Table S6. BP86 relative energy of broken symmetry solutions for the E4(4H)(b) 15 Table S7. B3LYP relative energy of broken symmetry solutions for the E4(4H)(b) 16 Table S8. BP86 relative energy of broken symmetry solutions for the E4(4H)(c) 17 Table S9. B3LYP relative energy of broken symmetry solutions for the E4(4H)(c) 18 Table S10. BP86 relative energy of broken symmetry solutions for the E4(2H; H2) 19 Table S11. B3LYP relative energy of broken symmetry solutions for the E4(2H; H2) 20 Table S12. Statistical data on the deviations from the crystal structure of the nearest-neighbor

Fe-Fe, Fe-C and Fe-S distances 21

Table S13. Deviation of bond distances of the En species studied in the present work from E0 22 Section S2 – Benchmark of DFT exchange and correlation functionals 23

Figure S8. Statistical data on the deviations from the crystal structure of the nearest-neighbor Fe-Fe distances in the E0 state

23

Section S3 – Protein environment and stability of the cofactor 24 Figure S9. Structure of the C-protonate E4(CHi) state found using the B3LYP functional 25 Figure S10. Structure of the high energy C-H protonated E4(CHo) state as obtained with the B3LYP functional

26

Section S4 – Natural Bond Orbitals Analysis of selected E4 States 27 Table S14. Coefficients and occupation of selected Natural Bond Orbitals 28 Table S15. Magnitude of the charge qCT transferred between selected NBO orbitals 29

Section S5 – Energy balance 30

Section S6 – Web Enhanced Object 31

Section S7 – Coordinates of the computed species 32

S1 Fig

Figure S1. the hydrogemodel (a), i356Gly-35leaving onlythe stabilizaoptimized Egray, H. Shchains and t-359Arg arelist of the fr

gures and

Models of the Fen bonding interit deletes all wat57Gly, 358Leu,-3y FeMo-co and ation (136 atomsE0 state (52 atomadowy red stickthe amino acid be indicated twiceozen atom is giv

d tables c

eMo-co pocket action at the actter molecules int359Arg (163 atomits ligands, the c

s). Model (e): mms). The color-coks represent hydrbackbone include). Ghostly asterven in Section SI

cited in th

adopted in the Dtive site, includinteracting with F

ms). Model (d): icharged resides,inimal model th

oding of atoms isrogen bond inter

ded in the modelrisks mark the atI 6.

he main t

DFT calculationsng those from weMo-co (176 atoit additionally om, -70Val, and that includes only

s as follows: rustractions. Black a, respectively (n

tom which were

text

s. Model (a): larwater molecules oms). Model (c)mits the side ch

he residues on toy FeMo-co and itt, Fe; yellow, S; and red labels arnote that, becausfrozen during th

rgest model adop(191 atoms). M

): it further deleain and the back

op of -70Arg ants ligands. The scyan, C (or Mo

re used to indicase of this choicehe geometry opti

pted that includeModel (b): startinetes the backbonkbone N-H of -nd -70Val, requistructures repres); red, O; blue, Nate the amino ac, residues -278imization. The d

3

es all of ng from ne of --278Ser, ired for sent the N; light cid side 8Ser and detailed

Figure S2. between theThe calculaenvironmen

Panel a. Relative Fe centers in thations were perfont. Panel b show

ve energetic of thhe E0 state for thformed on a struthe local environ

hree possible sphe FeMo-co Mo4uctural model thnment around Fe

pin configuration4+4Fe2+3Fe3+ oxi

hat includes all teMo-co and the

ns that maximizeidation state as othe H-bonding iFe atoms numbe

es the antiferromobtained from Dintegrations betwering (see also F

magnetic spin coDFT/BP86 calculween FeMo-co

Figure 1).

4

oupling lations. and its

Figure S3. Eenergy acco1) and correatoms are in

Energy ranking ording to the BP8ections for the pndicated in red an

of possible E4 st86 functional as protein environmnd green, respec

tates (a) and theievaluated from

ment described bctively.

ir schematic reprthe extended str

by a polarizable

resentation (b). Tructural model re

continuum. For

The relative eneeported in Figurr clarity, hydridi

ergy includes elere S1a (see also ic and protic hy

5

ectronic Figure

ydrogen

Figure S4. FeMo-co in

Electronic energthe E0 state (mo

gy of FeMo-co iodel (e)).

n the E4(4H), E44(3H,CH) and EE0 from models (

(a) to (e) relativee to that of the i

6

isolated

7

Figure S5. Energy profile for the dissociation of H2 from E4(2H;H2;N2) (black trace) and E4(2H;H2) (red trace) as obtained from constrained geometry optimizations. Energies relative to the corresponding equilibrium geometries.

1.5 2.0 2.5 3.0 3.5Fe2-H2 Distance (Å)

0

10

20

30

40

50

60

Ene

rgy

(kJ/

mol

)

Figure S6. chemical str(hydridic hy

Structure of releructure of FeM

ydrogens) and gr

evant En states. Ioco as seen froreen (protic hydr

In all of the stickm the top of throgens). Relevan

k structures, FeMhe Fe2, Fe3, Fe6,nt distances are r

Mo-co is viewed, and Fe7 face.reported in Å.

d from α-275Cys, The four added

with superimpod H+ are shown

8

osed the n in red

Figure S7. breaking of level of theo

B3LYP relativf the N2 triple boory the E4(4H)(b)

e free energy oond. Protic and ) (see Figure S6

of various E4 sphydridic hydrog) was not identif

pecies potentiallgens are indicatefied.

ly involved in Fed in green and

FeMo-co reductred, respectively

tive activation ay. Note that at B

9

and the B3LYP

10

Table S1. The 35 spin configurations of the initial guesses for the broken symmetry calculations for the E4 (S = 1/2) states according to an electron counting the Mo3+3Fe2+4Fe3+ E0 state. The number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. Initial Guess Spin Conf. AF Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All 1 9 11 2 9 11 3 9 11 4 8 10 5 8 10 6 8 10 7 8 10 8 8 10 9 8 10 10 8 9 11 7 9 12 7 9 13 8 9 14 7 9 15 7 9 16 6 9 17 8 9 18 7 9 19 7 9 20 7 8 21 6 8 22 5 8 23 5 8 24 6 8 25 7 8 26 5 8 27 7 8 28 6 8 29 6 7 30 6 7 31 6 7 32 6 7 33 6 7 34 6 7 35 3 3

11

Table S2. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E0 state (model a, Figure S1) as obtained for the BP86 functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

2 0.0 0.0 0.0 2.89 2.76 -2.24 -2.21 1.95 -2.32 2.05 -0.33 9 11 3 11.2 11.5 11.0 2.96 -2.34 2.67 -2.26 1.97 2.02 -2.25 -0.32 9 11

1 23.3 22.9 22.8 2.98 -2.43 -2.26 2.66 -2.16 2.09 2.00 -0.31 9 11

8 30.2 30.1 29.9 -2.84 2.25 1.46 1.58 1.11 -2.32 -1.32 -0.05 6 8

7 30.3 30.0 29.8 -2.84 2.25 1.45 1.58 1.10 -2.32 1.33 -0.05 6 8

4 32.8 32.7 32.5 -2.84 1.67 2.14 1.50 1.16 1.25 -2.29 -0.13 6 8

11 34.6 35.0 35.1 2.86 2.60 -1.75 -2.22 2.00 1.35 -1.91 -0.17 7 9

6 34.8 35.3 35.2 -2.86 1.56 1.44 2.18 -2.24 1.32 1.11 -0.05 6 8

18 37.5 37.7 37.6 2.86 2.55 -2.28 -1.80 -1.84 1.41 2.02 -0.09 7 9

25 40.5 40.0 39.7 -2.74 2.53 2.24 2.30 -1.93 2.23 -2.06 0.13 7 9

20 43.6 42.7 42.4 -2.75 2.42 2.33 2.33 -1.94 -1.99 2.13 0.19 7 9

15 45.9 46.6 46.7 2.92 -1.90 2.42 -2.25 2.02 -2.00 1.50 -0.12 7 9

12 46.6 47.2 47.3 2.96 -1.91 -2.21 2.44 1.31 -1.94 2.14 -0.06 7 9

14 50.2 49.2 48.9 2.90 -2.37 2.41 -1.73 -1.84 2.10 1.22 -0.11 7 9

27 50.7 49.5 49.1 -2.79 2.48 2.35 2.46 2.11 -2.08 -1.97 0.12 7 9

19 51.2 50.0 49.7 2.95 -2.39 -1.64 2.46 1.27 2.11 -1.89 -0.13 7 9

16 52.1 50.6 49.9 2.88 -2.21 -2.04 -2.13 2.28 2.29 2.28 -0.61 6 9

10 56.0 54.5 54.0 2.68 2.36 1.91 -2.45 2.19 -2.13 -1.99 0.14 8 10

35 56.1 54.6 54.0 2.68 2.35 1.91 -2.45 2.19 -2.13 -1.99 0.14 8 10

17 56.9 56.1 55.8 2.93 -2.59 1.65 2.13 -1.90 2.32 -2.00 0.13 8 10

13 58.3 57.6 57.4 2.97 2.43 -2.44 1.34 -1.80 -2.04 2.24 0.21 8 10

23 65.0 64.0 63.5 -2.88 -2.78 2.14 1.97 0.75 1.92 1.90 -0.44 5 8

31 71.3 69.6 69.0 2.76 2.64 0.34 -2.10 -1.07 -2.03 2.04 0.13 6 8

34 74.7 74.5 74.6 3.02 2.62 -2.13 0.29 2.01 -2.03 -1.04 0.09 6 8

5 75.2 76.1 76.1 -2.84 -2.50 2.59 2.45 -1.70 2.40 2.47 -0.27 8 10

30 75.6 75.3 0.0 2.97 -2.38 0.83 2.33 -1.85 -1.44 2.07 0.18 6 8

26 76.4 76.2 0.0 -2.93 2.05 -2.72 1.88 0.91 1.89 2.07 -0.47 5 8

29 76.7 75.8 75.4 2.58 1.71 2.01 -2.20 -1.27 1.94 -2.06 0.08 6 8

22 78.8 0.0 0.0 -2.68 -1.55 -2.12 2.39 2.42 2.44 2.33 -0.63 5 8

33 81.4 82.4 82.6 2.67 1.89 -2.21 2.02 -1.97 2.00 -1.59 0.14 6 8

21 81.8 82.5 82.6 -2.84 -2.17 2.46 2.40 2.23 -1.91 2.38 -0.17 6 8

9 82.3 81.7 81.4 -2.75 -2.09 2.52 2.48 2.32 2.34 -1.91 -0.33 8 10

32 82.7 82.1 81.8 2.97 -2.36 2.28 1.07 2.00 -1.56 -1.87 0.09 6 8

28 91.2 91.1 90.7 -2.74 2.35 -0.85 2.10 1.95 2.23 -2.07 -0.24 6 8

24 93.3 94.7 94.9 -2.94 2.63 2.35 -1.98 -1.67 2.34 2.09 -0.24 6 8

12

Table S3. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E0 state (model a, Figure S1) as obtained for the B3LYP functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

2 0.0 0.0 0.0 3.58 3.61 -3.43 -3.40 3.47 -3.53 3.45 -0.72 9 11 11 28.0 30.8 31.7 3.59 3.61 -3.47 -3.34 3.58 3.43 -3.43 -0.95 7 9 5 30.7 32.5 33.0 -3.58 -3.56 3.51 3.36 -3.49 3.49 3.45 -0.77 8 10 1 32.0 33.3 33.7 3.58 -3.50 -3.44 3.50 -3.47 3.45 3.41 -0.86 9 11 9 34.1 33.0 32.7 -3.56 -3.56 3.45 3.49 3.54 3.50 -3.39 -1.01 8 10 8 35.9 36.7 37.1 -3.59 3.52 3.61 -3.52 3.47 -3.49 3.45 -0.67 8 10 3 37.4 35.6 34.9 3.55 -3.45 3.66 -3.36 3.44 3.42 -3.42 -1.11 9 11

18 39.9 41.7 42.3 3.58 3.60 -3.47 -3.40 -3.51 3.46 3.48 -0.67 7 9 19 48.0 47.6 47.7 3.60 -3.55 -3.57 3.58 3.54 3.55 -3.38 -0.95 7 9 7 48.6 48.6 48.6 -3.57 3.46 -3.63 3.52 3.51 -3.46 3.46 -0.61 8 10 4 49.8 50.7 51.0 -3.59 3.61 3.47 -3.43 3.49 3.47 -3.42 -1.02 8 10

21 52.2 53.4 53.9 -3.56 -3.59 3.51 3.42 3.45 -3.48 3.50 -0.56 6 8 15 52.6 54.6 55.1 3.60 -3.52 3.74 -3.51 3.49 -3.49 3.42 -0.61 7 9 12 52.8 53.2 53.4 3.63 -3.54 -3.50 3.55 3.47 -3.48 3.52 -0.56 7 9 14 55.5 57.0 57.5 3.58 -3.51 3.66 -3.55 -3.48 3.57 3.47 -0.61 7 9 6 59.6 61.8 62.4 -3.57 3.58 -3.63 3.39 -3.44 3.50 3.38 -0.71 8 10

16 61.4 60.1 59.9 3.42 -3.32 -3.37 -3.18 3.64 3.66 3.66 -1.66 6 9 23 76.3 78.2 79.0 -3.78 -3.34 3.64 -3.45 3.61 3.68 3.57 -1.71 5 8 24 77.4 80.4 81.4 -3.62 3.53 3.55 -3.50 -3.51 3.47 3.46 -0.66 6 8 22 81.7 81.1 81.3 -3.71 -3.37 -3.40 3.54 3.61 3.72 3.65 -1.66 5 8 26 85.3 86.3 86.7 -3.82 3.58 -3.49 -3.49 3.64 3.58 3.58 -1.67 5 8 17 86.4 85.7 85.4 3.71 -3.55 3.53 3.45 -3.51 3.57 -3.41 -1.02 8 9 28 87.6 88.6 89.0 -3.59 3.50 -3.66 3.52 3.55 3.50 -3.36 -0.94 6 8 10 98.2 97.8 97.6 3.76 3.56 3.57 -3.45 3.49 -3.62 -3.46 -0.73 8 9 13 104.1 102.4 101.6 3.81 3.51 -3.58 3.60 -3.47 -3.54 3.41 -0.47 8 9 25 113.2 113.8 114.0 -3.44 3.57 3.46 3.52 -3.49 3.43 -3.44 -1.26 7 8 33 117.8 119.7 120.2 3.79 3.60 -3.60 3.75 -3.53 3.52 -3.38 -1.11 6 7 20 123.0 123.3 123.4 -3.42 3.48 3.55 3.39 -3.43 -3.57 3.39 -0.90 7 8 29 123.4 123.9 124.1 3.74 3.63 3.65 -3.43 -3.53 3.51 -3.44 -1.19 6 7 30 127.2 128.2 128.2 3.70 -3.57 3.57 3.40 -3.60 -3.44 3.46 -0.63 6 7 27 127.7 127.5 127.5 -3.43 3.51 3.46 3.55 3.45 -3.62 -3.41 -1.17 7 8 31 128.8 127.9 127.8 3.76 3.64 3.73 -3.45 -3.56 -3.53 3.42 -0.82 6 7 34 135.7 137.5 137.9 3.79 3.56 -3.52 3.80 3.53 -3.63 -3.35 -1.15 6 7 32 136.6 138.6 139.0 3.73 -3.54 3.59 3.48 3.58 -3.53 -3.37 -1.11 6 7 35 215.5 212.5 211.6 3.87 3.65 3.69 3.86 -3.54 -3.62 -3.43 -1.50 3 3

13

Table S4. Relative energy in the gas phase and = 4 and 10 of broken symmetry solutions (Table S1) for the E4(4H) state (model a, Figure S1) as obtained for the BP86 functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

1 0.0 0.0 0.0 2.92 -2.01 -2.12 2.91 -2.09 1.18 -0.20 0.21 8 10 4 2.1 1.0 0.6 -2.89 2.13 2.24 -2.87 2.05 1.67 -0.58 -0.36 8 10 5 6.5 4.2 3.4 -2.86 2.21 2.25 2.41 -2.29 0.99 -0.96 0.22 7 9

11 14.9 12.7 11.8 2.92 -2.15 -2.01 -2.34 2.08 1.64 0.44 -0.46 6 9 20 18.2 16.7 16.0 -2.77 2.46 2.43 2.46 -2.10 -1.15 -0.05 0.39 6 9 12 27.8 28.2 28.4 2.85 -2.19 -2.40 2.62 1.54 -2.07 -0.39 0.11 6 8 2 29.5 29.3 29.1 2.74 0.76 -2.34 -2.47 2.24 -1.08 0.85 -0.20 9 11

10 34.3 35.5 35.8 2.93 2.52 -2.17 -2.44 2.06 -1.79 -0.15 0.09 8 10 7 36.2 35.1 34.6 -2.92 2.38 -2.56 2.25 1.59 1.76 -0.53 -0.33 6 8

15 36.7 37.1 37.1 2.9 -2.45 2.50 -2.59 1.99 -1.95 -0.71 0.09 8 10 14 36.9 36.6 36.4 2.97 -1.68 2.72 -2.16 -1.62 1.05 -0.82 0.08 8 10 24 40.5 39.7 39.4 -2.85 2.41 2.37 -2.68 -0.70 2.36 1.24 -0.33 6 8 27 40.8 38.8 38.0 -2.9 2.16 2.05 1.82 0.65 -1.97 -0.87 0.24 7 9 3 42.7 41.9 41.5 2.83 -2.52 1.01 -2.57 2.24 -1.03 0.11 -0.19 7 9 9 44.2 42.9 42.3 -2.95 -2.79 1.97 2.06 1.43 1.48 -0.54 -0.37 8 10

21 50.6 50.5 50.3 -3.03 -2.95 2.38 2.61 2.03 -1.76 0.85 -0.16 6 8 18 51.2 52.0 52.2 3.03 3.05 -2.21 -2.18 -1.59 1.87 -0.12 0.09 6 8

14

Table S5. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(4H) state (model a, Figure S1) as obtained for the B3LYP functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

15 0.0 0.0 0.0 3.55 -3.49 3.56 -3.54 3.39 -3.19 2.43 -2.08 7 9 4 6.1 9.3 10.6 -3.57 3.42 3.35 -3.64 3.40 2.40 -2.21 -1.53 8 10 2 16.6 18.1 18.7 3.54 3.48 -3.50 -3.50 3.39 -2.77 2.21 -1.95 9 11 8 18.1 18.3 18.4 -3.60 3.49 3.53 -3.63 3.40 -2.76 2.43 -2.01 8 10 5 21.9 25.7 27.1 -3.58 -3.60 3.51 3.31 -3.44 3.05 2.53 -0.56 8 10

14 23.9 26.9 28.1 3.55 -3.62 3.53 -3.59 -3.40 3.16 2.52 -0.63 7 9 24 24.2 24.6 24.9 -3.59 3.45 3.42 -3.61 -3.27 3.33 2.76 -0.43 6 8 1 33.7 36.9 38.1 3.58 -3.58 -3.45 3.47 -3.38 3.17 2.19 -0.57 9 11

12 35.4 34.4 34.3 3.57 -3.48 -3.55 3.51 3.14 -2.92 2.16 -2.00 7 9 21 37.6 38.3 38.6 -3.57 -3.59 3.49 3.42 3.37 -3.04 2.43 -2.04 6 8 6 41.0 44.1 45.2 -3.49 3.63 -3.48 3.48 -3.35 3.36 2.29 -0.55 8 10 3 41.5 43.0 43.7 3.47 -3.74 3.46 -3.54 3.37 1.71 -2.53 -1.53 9 11

28 45.9 49.0 50.1 -3.55 3.30 -3.52 3.51 2.97 2.32 -2.49 -1.47 6 8 16 46.8 47.9 48.5 3.44 -3.43 -3.41 -3.25 3.52 3.44 2.49 -1.82 6 9 23 47.8 50.5 51.7 -3.72 -3.50 3.52 -3.48 3.50 3.34 2.78 -1.86 5 8 19 52.9 50.9 50.6 3.57 -3.72 -3.51 3.55 3.16 1.80 -2.59 -1.50 7 9 7 64.6 66.4 67.1 -3.55 3.58 -3.52 3.47 3.21 -2.90 2.16 -1.85 8 10

20 65.2 66.0 66.5 -3.45 3.50 3.26 3.27 -3.41 -3.35 2.37 -0.71 7 8 9 72.5 73.0 73.4 -3.57 -3.72 3.45 3.51 3.13 1.77 -2.47 -1.50 8 10

22 74.4 75.6 76.4 -3.60 -3.52 -3.42 3.56 3.50 3.40 2.64 -1.84 5 8 31 79.8 83.1 84.5 3.65 3.51 3.32 -3.59 -3.43 -3.29 2.45 -0.73 6 7 30 83.0 88.1 89.7 3.67 -3.73 3.51 3.39 -3.47 -3.86 2.10 -0.80 6 7 26 83.6 85.7 86.1 -3.64 3.60 -3.46 -3.47 3.54 3.10 3.28 -1.89 5 8 11 84.0 83.8 83.3 3.57 3.55 -3.52 -3.32 3.46 2.89 -2.85 -2.14 7 9 25 98.0 98.7 99.1 -3.42 3.43 3.40 3.32 -3.53 3.00 -2.43 -1.66 7 8 13 99.6 103.9 105.4 3.71 3.51 -3.62 3.49 -3.35 -3.15 1.72 -0.60 8 9 33 107.6 109.4 110.0 3.70 3.42 -3.51 3.44 -3.49 3.03 -2.58 -1.64 6 7 29 110.3 112.2 113.1 3.61 3.42 3.47 -3.53 -3.47 2.91 -2.44 -1.64 6 7 18 117.2 119.7 120.1 3.62 3.75 -3.43 -3.43 -3.36 3.32 3.23 -1.96 7 9 10 127.2 133.6 135.9 3.65 3.46 3.44 -3.56 3.19 -3.25 -3.14 -1.69 8 9 17 130.8 136.0 137.4 3.66 -3.41 3.46 3.54 -3.44 2.59 -3.26 -1.75 8 9 27 138.7 143.6 145.0 -3.64 3.34 3.33 3.46 3.32 -3.30 -3.11 -1.62 7 8 32 160.1 165.8 167.6 3.64 -3.88 3.36 3.29 3.18 -3.92 -3.46 -1.68 6 7 34 162.3 162.0 162.1 3.67 3.37 -3.52 3.57 3.27 -3.63 -2.87 -2.28 6 7 35 221.4 226.7 228.5 3.76 3.37 3.42 3.37 -3.48 -3.69 -3.53 -1.74 3 3

15

Table S6. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(4H)(b) state (model a, Figure S1) as obtained for the BP86 functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

5 0.0 0.0 0.0 -2.72 1.33 1.92 2.25 -1.61 2.08 -1.87 -0.13 7 9 27 6.1 6.0 5.8 -2.69 1.74 2.02 1.64 1.59 -1.33 -1.93 0.11 7 9 16 7.1 6.6 6.3 2.72 -1.35 -1.92 -2.19 2.02 -0.66 2.07 -0.23 7 9 14 17.0 18.6 19.1 2.62 -0.42 -1.80 -1.43 -1.69 1.74 2.01 -0.18 7 9 10 22.6 24.1 24.3 2.79 -1.34 2.32 -2.12 2.03 -1.50 -1.86 0.13 8 10 6 24.2 26.7 27.5 -2.64 1.86 -1.74 2.28 -2.06 2.03 1.84 -0.13 8 10 2 24.5 25.1 25.8 2.53 0.63 -1.90 -2.10 1.82 -1.87 1.71 -0.06 9 11

13 24.9 26.1 26.3 2.80 -1.24 -1.83 2.49 -1.87 -1.41 1.62 0.28 8 10 20 26.3 28.5 28.9 -2.76 1.76 2.30 2.08 -1.78 -1.81 1.75 0.18 7 9 9 33.6 34.8 35.0 -2.65 -1.58 1.98 1.68 1.52 1.63 -1.81 -0.17 8 10 4 34.1 35.6 35.9 -2.81 1.76 2.06 -2.14 1.99 1.88 -1.32 -0.26 8 10

29 35.5 37.9 38.5 2.74 -1.77 2.16 -1.89 -1.02 1.97 -1.46 0.01 8 10 11 36.5 39.8 40.6 2.69 0.77 -2.29 -2.24 2.04 1.48 -1.78 -0.16 7 9 7 38.6 39.7 40.0 -2.73 1.82 -1.88 2.07 1.28 -1.47 2.14 -0.08 8 10 8 44.2 46.1 46.4 -2.84 1.72 1.76 -2.36 1.81 0.24 1.42 -0.36 5 8

23 44.9 45.4 45.6 -2.83 1.69 1.77 -2.36 1.70 0.96 0.70 -0.33 5 8 22 47.0 47.4 47.3 -2.77 1.61 -2.37 1.69 0.77 0.62 1.96 -0.33 5 8 32 51.0 52.5 52.9 2.76 -1.35 -1.59 2.19 1.48 -1.79 -1.27 0.17 6 8 24 54.1 55.7 56.1 -2.83 1.58 2.08 -1.99 -1.41 2.03 2.23 -0.26 6 8 12 54.4 56.9 57.6 2.81 -1.92 -2.26 1.88 0.73 -2.08 1.18 0.00 7 7 21 54.6 58.8 60.0 -2.86 -1.87 2.29 2.00 1.30 -1.77 1.98 -0.24 6 8 17 68.2 69.7 70.1 2.74 -1.93 1.65 1.88 -1.72 -0.74 -1.72 0.37 5 8 19 68.9 71.3 71.8 2.85 -2.08 -2.35 2.15 0.35 1.21 -1.81 -0.01 7 9 26 86.6 90.1 90.3 -2.57 1.89 -1.80 -1.91 2.03 2.09 2.02 -0.60 5 8

16

Table S7. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(4H)(b) state (model a, Figure S1) as obtained for the B3LYP functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF

gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All 15 0.0 0.0 0.0 3.55 -3.49 3.56 -3.54 3.39 -3.19 2.43 -2.08 7 9 4 6.1 9.3 10.6 -3.57 3.42 3.35 -3.64 3.4 2.4 -2.21 -1.53 8 10 2 16.6 18.1 18.7 3.54 3.48 -3.5 -3.5 3.39 -2.77 2.21 -1.95 9 11 8 18.1 18.3 18.4 -3.6 3.49 3.53 -3.63 3.4 -2.76 2.43 -2.01 8 10 5 21.9 25.7 27.1 -3.58 -3.6 3.51 3.31 -3.44 3.05 2.53 -0.56 8 10

14 23.9 26.9 28.1 3.55 -3.62 3.53 -3.59 -3.4 3.16 2.52 -0.63 7 9 24 24.2 24.6 24.9 -3.59 3.45 3.42 -3.61 -3.27 3.33 2.76 -0.43 6 8 1 33.7 36.9 38.1 3.58 -3.58 -3.45 3.47 -3.38 3.17 2.19 -0.57 9 11

12 35.4 34.4 34.3 3.57 -3.48 -3.55 3.51 3.14 -2.92 2.16 -2 7 9 21 37.6 38.3 38.6 -3.57 -3.59 3.49 3.42 3.37 -3.04 2.43 -2.04 6 8 6 41.0 44.1 45.2 -3.49 3.63 -3.48 3.48 -3.35 3.36 2.29 -0.55 8 10 3 41.5 43.0 43.7 3.47 -3.74 3.46 -3.54 3.37 1.71 -2.53 -1.53 9 11

28 45.9 49.0 50.1 -3.55 3.3 -3.52 3.51 2.97 2.32 -2.49 -1.47 6 8 16 46.8 47.9 48.5 3.44 -3.43 -3.41 -3.25 3.52 3.44 2.49 -1.82 6 9 23 47.8 50.5 51.7 -3.72 -3.5 3.52 -3.48 3.5 3.34 2.78 -1.86 5 8 19 52.9 50.9 50.6 3.57 -3.72 -3.51 3.55 3.16 1.8 -2.59 -1.5 7 9 7 64.6 66.4 67.1 -3.55 3.58 -3.52 3.47 3.21 -2.9 2.16 -1.85 8 10

20 65.2 66.0 66.5 -3.45 3.5 3.26 3.27 -3.41 -3.35 2.37 -0.71 7 8 9 72.5 73.0 73.4 -3.57 -3.72 3.45 3.51 3.13 1.77 -2.47 -1.5 8 10

22 74.4 75.6 76.4 -3.6 -3.52 -3.42 3.56 3.5 3.4 2.64 -1.84 5 8 31 79.8 83.1 84.5 3.65 3.51 3.32 -3.59 -3.43 -3.29 2.45 -0.73 6 7 30 83.0 88.1 89.7 3.67 -3.73 3.51 3.39 -3.47 -3.86 2.1 -0.8 6 7 26 83.6 85.7 86.1 -3.64 3.6 -3.46 -3.47 3.54 3.1 3.28 -1.89 5 8 11 84.0 83.8 83.3 3.57 3.55 -3.52 -3.32 3.46 2.89 -2.85 -2.14 7 9 25 98.0 98.7 99.1 -3.42 3.43 3.4 3.32 -3.53 3 -2.43 -1.66 7 8 13 99.6 103.9 105.4 3.71 3.51 -3.62 3.49 -3.35 -3.15 1.72 -0.6 8 9 33 107.6 109.4 110.0 3.7 3.42 -3.51 3.44 -3.49 3.03 -2.58 -1.64 6 7 29 110.3 112.2 113.1 3.61 3.42 3.47 -3.53 -3.47 2.91 -2.44 -1.64 6 7 18 117.2 119.7 120.1 3.62 3.75 -3.43 -3.43 -3.36 3.32 3.23 -1.96 7 9 10 127.2 133.6 135.9 3.65 3.46 3.44 -3.56 3.19 -3.25 -3.14 -1.69 8 9 17 130.8 136.0 137.4 3.66 -3.41 3.46 3.54 -3.44 2.59 -3.26 -1.75 8 9 27 138.7 143.6 145.0 -3.64 3.34 3.33 3.46 3.32 -3.3 -3.11 -1.62 7 8 32 160.1 165.8 167.6 3.64 -3.88 3.36 3.29 3.18 -3.92 -3.46 -1.68 6 7 34 162.3 162.0 162.1 3.67 3.37 -3.52 3.57 3.27 -3.63 -2.87 -2.28 6 7 35 221.4 226.7 228.5 3.76 3.37 3.42 3.37 -3.48 -3.69 -3.53 -1.74 3 3

17

Table S8. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(4H)(c) state (model a, Figure S1) as obtained for the BP86 functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

3 0.0 5.3 4.1 2.85 -1.88 2.50 -2.31 2.24 -1.48 -1.46 0.09 8 10 5 8.1 0.0 0.0 -2.71 2.01 0.18 2.10 -2.35 0.86 1.33 -0.06 6 8 2 12.4 8.6 7.6 2.73 -1.96 -1.90 -1.96 1.97 0.25 1.83 -0.37 6 9

10 13.8 4.4 5.3 2.78 -1.77 2.28 -2.13 2.06 -1.15 -1.69 0.10 8 10 20 18.6 8.6 9.4 -2.71 1.94 1.19 1.97 -2.03 -0.48 1.35 0.11 7 9 6 21.5 12.5 13.6 -2.66 1.93 0.03 1.94 -2.15 0.87 1.46 -0.08 6 8

25 22.3 11.5 12.0 -2.74 1.84 1.91 1.97 -1.76 1.25 -1.33 0.10 7 9 1 22.9 11.3 11.6 2.78 -1.75 -1.95 2.42 -1.91 -0.92 1.67 0.21 8 10

27 24.0 12.5 12.7 -2.67 1.94 1.74 1.31 1.38 -1.03 -1.79 0.10 7 9 16 30.7 26.3 23.6 2.7 -1.73 -1.90 -1.96 1.97 0.56 1.70 -0.37 6 9 11 43.1 33.9 34.9 2.73 1.91 -1.75 -2.05 2.02 -0.47 -1.43 0.07 8 10 14 43.7 33.7 34.5 2.76 -1.97 2.30 -1.79 -1.03 1.12 -0.54 -0.03 8 9 29 43.9 33.7 34.4 2.76 -1.96 2.31 -1.79 -1.01 1.14 -0.61 -0.03 8 9 7 44.8 33.8 34.2 -2.78 1.82 -2.42 1.84 0.78 0.44 1.72 -0.30 5 8

28 46.0 35.4 35.9 -2.69 1.95 -2.03 1.88 2.00 1.57 -1.42 -0.26 6 8

18

Table S9. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(4H)(c) state (model a, Figure S1) as obtained for the B3LYP functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

1 0.0 0.0 0.0 3.61 -3.47 -3.35 3.53 -3.73 3.32 3.32 -2.39 9 11 6 1.2 1.0 0.9 -3.57 3.42 -3.44 3.5 -3.48 3.34 3.45 -2.28 8 10

18 4.6 4.4 4.3 3.56 3.49 -3.43 -3.21 -3.5 3.32 3.51 -2.27 7 9 5 5.1 5.0 5.0 -3.53 -3.5 3.55 3.43 -3.71 3.31 3.34 -2.37 8 10 4 5.5 5.4 5.2 -3.59 3.48 3.42 -3.5 3.5 3.15 -3.23 -1.51 8 10

26 5.7 5.5 5.4 -3.77 3.43 -3.5 -3.38 3.77 3.39 3.66 -2.15 5 8 24 6.2 5.8 5.5 -3.59 3.56 3.46 -3.35 -3.48 3.29 3.5 -2.27 6 8 16 7.1 7.0 7.0 3.47 -3.57 -3.45 -3.46 3.7 3.35 3.48 -2.19 6 9 25 7.9 7.7 7.5 -3.45 3.39 3.47 3.43 -3.69 3.08 -3.42 -1.63 7 8 14 9.6 9.5 9.5 3.58 -3.51 3.55 -3.51 -3.65 3.4 3.35 -2.31 7 9 11 9.7 4.0 3.6 3.56 3.45 -3.5 -3.39 3.68 3.24 -3.26 -2.12 7 9 23 10.7 11.0 11.0 -3.64 -3.54 3.44 -3.55 3.67 3.33 3.49 -2.18 5 8 33 11.0 11.3 11.4 3.69 3.31 -3.44 3.58 -3.68 3.09 -3.43 -1.61 6 7 29 11.3 11.4 11.4 3.71 3.39 3.57 -3.48 -3.68 3.08 -3.38 -1.62 6 7 28 12.6 12.3 12.2 -3.59 3.27 -3.6 3.46 3.65 3.03 -3.21 -1.43 6 8 3 12.8 12.7 12.7 3.57 -3.42 3.48 -3.44 3.51 2.39 -3.3 -1.53 9 11

15 13.8 14.4 14.7 3.58 -3.51 3.47 -3.57 3.44 -3.33 3.2 -2.34 7 9 2 14.4 14.4 14.4 3.54 3.53 -3.5 -3.45 3.6 -3.5 3.36 -2.27 9 11

22 14.5 14.3 14.2 -3.63 -3.54 -3.56 3.47 3.66 3.36 3.44 -2.20 5 8 8 15.1 15.1 15.2 -3.61 3.47 3.43 -3.54 3.58 -3.42 3.42 -2.26 8 10

12 18.4 18.2 18.1 3.59 -3.48 -3.49 3.31 3.04 -3.24 3.23 -2.31 7 9 30 19.4 20.3 20.5 3.76 -3.44 3.6 3.46 -3.81 -3.41 3.04 -2.45 6 7 17 20.0 19.5 19.4 3.77 -3.57 3.61 3.46 -3.78 2.79 -3.5 -1.70 8 9 9 20.8 20.2 20.0 -3.54 -3.56 3.39 3.4 3.21 2.74 -3.32 -1.53 8 10

21 21.0 20.8 20.7 -3.57 -3.39 3.38 3.13 3.43 -3.25 3.13 -2.30 6 8 20 21.4 20.6 20.3 -3.47 3.42 3.54 3.46 -3.71 -3.48 3.31 -2.24 7 8 31 23.8 23.4 23.3 3.68 3.57 3.57 -3.52 -3.68 -3.47 3.36 -2.29 6 7 7 24.4 23.9 23.8 -3.57 3.37 -3.54 3.5 3.66 -3.46 3.35 -2.23 8 10

13 25.0 24.2 24.0 3.67 3.33 -3.37 3.48 -3.7 -3.5 3.37 -2.21 8 9 19 25.0 24.3 24.1 3.61 -3.54 -3.43 3.55 3.55 3.39 -3.39 -2.42 7 9 10 29.1 28.9 28.8 3.66 3.5 3.5 -3.48 3.59 -3.43 -3.38 -2.32 8 9 32 38.1 37.5 37.3 3.73 -3.49 3.51 3.2 3.4 -3.44 -3.56 -2.46 6 7 34 39.2 38.1 37.6 3.66 3.5 -3.54 3.57 3.59 -3.47 -3.41 -2.39 6 7 27 41.4 40.1 39.5 -3.62 3.44 3.42 3.61 3.61 -3.34 -3.32 -2.36 7 8 35 54.2 53.3 53.0 3.76 3.6 3.6 3.51 -3.8 -3.46 -3.59 -2.63 3 3

19

Table S10. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(2H; H2) state (model a, Figure S1) as obtained for the BP86 functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

25 0.0 0.0 0.0 -2.71 0.97 2.03 2.25 -1.88 2.32 -1.63 -0.14 7 7 14 6.3 8.1 8.6 2.69 -0.87 -1.73 -1.39 -1.79 2.15 1.75 -0.18 7 9 8 6.5 7.9 8.3 -2.81 1.56 2.07 1.57 1.73 -2.09 -0.96 0.08 7 9 5 6.9 9.6 10.4 -2.63 -0.40 1.48 2.13 -2.12 2.19 0.68 -0.11 8 10 3 9.8 10.4 10.5 2.79 -1.45 -1.34 -2.18 1.87 2.20 -1.34 -0.20 7 9

10 11.4 13.9 14.7 2.81 -0.60 2.15 -2.25 2.15 -2.19 -1.60 0.20 8 10 21 14.2 8.0 8.3 -2.79 1.36 1.92 1.47 1.67 -2.12 -0.27 -0.03 7 8 15 19.8 23.2 24.3 2.82 -1.46 1.78 -2.43 2.10 -2.09 0.17 0.01 7 8 6 20.4 22.1 22.7 -2.76 1.69 -1.86 2.33 -2.15 2.33 1.58 -0.15 8 10

13 20.6 21.8 22.1 2.88 -1.19 -1.91 2.49 -1.80 -1.37 1.44 0.31 8 10 2 22.4 24.0 24.7 2.81 1.91 -1.69 -2.21 1.87 -2.21 0.48 -0.03 9 11

20 25.0 26.2 26.4 -2.81 1.54 2.51 2.28 -1.82 -2.13 1.74 0.18 7 9 27 26.0 26.8 27.2 -2.76 1.33 1.97 2.18 2.02 -2.10 -1.66 0.15 7 9 1 27.8 26.1 26.5 2.17 -1.51 -2.00 1.61 -1.96 2.17 0.38 -0.02 9 11

29 32.7 32.5 32.1 2.75 -1.13 2.07 -1.88 -1.43 1.76 -1.45 0.07 8 10 33 35.5 25.0 25.2 2.80 -1.16 -1.80 2.41 -2.01 1.53 -1.30 0.27 8 10 9 35.7 35.6 35.4 -2.76 -1.66 1.94 1.79 1.33 1.95 -1.64 -0.18 8 10

12 38.1 39.6 40.0 2.87 -1.69 -2.29 2.02 1.25 -2.29 1.05 0.05 7 8 32 38.6 40.6 41.0 2.83 -1.23 -1.77 2.10 1.67 -2.22 -0.81 0.18 6 8 23 39.7 40.7 40.9 -2.88 1.46 1.96 -2.37 1.56 1.44 0.17 -0.36 5 8 34 40.6 40.6 41.0 2.82 -0.97 -1.85 2.08 1.74 -2.20 -1.13 0.23 6 8 24 44.2 44.8 44.9 -2.89 1.92 2.21 -2.11 -1.60 2.29 1.37 -0.23 6 8 7 46.0 45.5 45.2 -2.81 1.61 -1.61 2.16 1.54 -1.53 1.88 -0.15 8 10

11 46.4 47.2 47.8 2.68 0.74 -2.44 -2.31 1.99 1.87 -1.78 -0.24 7 9 22 47.6 44.3 44.9 -2.75 0.39 -2.08 2.04 0.67 1.82 1.32 -0.38 5 8 4 51.1 25.6 25.7 -2.85 1.68 2.00 -2.09 1.89 2.36 -1.77 -0.33 8 10

16 51.7 52.6 53.1 2.46 -1.80 -2.42 -2.40 1.80 2.09 1.38 -0.44 6 9 18 55.7 8.1 8.6 2.79 1.34 -2.11 -2.14 -1.88 1.94 1.25 -0.24 7 9 28 61.5 41.9 42.1 -2.87 1.58 -2.07 1.97 1.33 2.36 -1.37 -0.33 6 8 17 61.9 62.4 62.6 2.81 -1.79 -0.41 2.13 -1.88 1.46 -1.52 0.07 8 10 26 67.7 67.7 67.4 -2.89 1.84 -1.35 -1.93 1.87 2.46 1.31 -0.55 5 8 19 69.7 71.1 71.7 2.90 -1.84 -2.38 2.25 0.46 0.67 -1.49 0.09 7 8 30 75.0 76.1 76.3 2.90 -1.90 1.24 2.01 -2.18 -2.44 1.28 0.23 6 8 31 78.3 48.9 49.6 2.57 1.31 1.93 -2.26 -1.38 -2.24 1.23 0.18 6 8 35 127.9 128.7 129.2 2.47 0.97 1.70 1.92 -2.18 -2.53 -1.79 0.52 3 6

20

Table S11. Relative energy in the gas phase and = 4 and 10 of the 35 broken symmetry solutions (Table S1) for the E4(2H; H2) state (model a, Figure S1) as obtained for the B3LYP functional. Mulliken spin densities of Fe and Mo atoms are listed according the FeMo-co standard numbering (Figure S2), along with the number of anti-ferromagnetic (AF) couplings between the Fe centers and the total number of coupling (both Fe and Mo centers).

BS Conf. E Mulliken spin densities (e) AF gas = 4 = 10 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Mo Fe only All

2 0.0 0.0 0.0 3.55 3.26 -3.36 -3.48 3.48 -3.47 3.41 -2.36 9 11 16 32.8 30.0 30.1 3.48 -3.41 -3.50 -3.61 3.50 3.65 3.51 -2.24 6 9 15 32.9 32.5 33.3 3.59 -3.27 3.47 -3.72 3.48 -3.53 3.37 -2.41 7 9 8 45.3 44.7 45.5 -3.67 3.31 3.51 -3.56 3.50 -3.46 3.40 -2.36 8 10

23 48.0 47.6 48.4 -3.71 -3.35 3.34 -3.78 3.52 3.59 3.47 -2.26 5 8 26 48.7 46.5 46.7 -3.76 3.17 -3.50 -3.61 3.54 3.70 3.49 -2.24 5 8 7 64.1 61.8 62.0 -3.55 3.29 -3.46 3.51 3.44 -3.45 3.35 -2.32 8 10

21 69.1 67.3 67.8 -3.54 -3.09 3.36 3.32 3.48 -3.42 3.34 -2.40 6 8 11 72.1 71.8 72.6 3.53 3.12 -3.41 -3.51 3.50 3.51 -3.42 -2.07 7 9 12 73.9 69.6 68.9 3.67 -3.12 -3.47 3.52 3.41 -3.48 3.37 -2.33 7 9 6 82.9 93.5 93.8 -3.43 3.46 -3.45 3.60 -3.33 3.62 3.47 -2.19 8 10

22 84.6 82.2 82.5 -3.7 -3.40 -3.72 3.38 3.48 3.61 3.46 -2.23 5 8 18 90.0 89.9 90.8 3.53 3.20 -3.39 -3.41 -3.39 3.52 3.54 -2.15 7 9 5 94.4 94.4 95.3 -3.55 -3.24 3.29 3.40 -3.55 3.61 3.41 -2.32 8 10 3 94.7 91.6 91.4 3.58 -3.39 3.45 -3.66 3.48 3.51 -3.45 -2.11 9 11 4 95.0 94.4 95.2 -3.68 3.20 3.46 -3.55 3.51 3.51 -3.43 -2.09 8 10

14 96.2 95.6 96.5 3.58 -3.31 3.45 -3.65 -3.43 3.56 3.50 -2.26 7 9 10 100.4 100.6 101.6 3.69 3.25 3.65 -3.51 3.44 -3.67 -3.54 -2.15 8 9 29 105.9 110.6 113.3 3.65 3.15 3.56 -3.50 -3.52 3.22 -3.46 -1.53 6 7 24 108.5 108.2 109.2 -3.67 3.27 3.50 -3.56 -3.40 3.47 3.47 -2.25 6 8 20 111.9 110.3 110.8 -3.48 3.39 3.48 3.55 -3.59 -3.57 3.33 -2.39 7 8 1 113.1 112.2 113.1 3.64 -3.22 -3.47 3.46 -3.56 3.66 3.47 -2.34 9 11

25 113.4 117.0 119.2 -3.5 3.16 3.40 3.39 -3.49 3.35 -3.45 -1.54 7 8 33 116.4 118.9 120.7 3.55 3.15 -3.46 3.38 -3.51 3.37 -3.39 -1.45 6 7 28 122.0 120.0 120.3 -3.58 3.16 -3.47 3.65 3.39 3.53 -3.42 -2.38 6 8 13 122.5 123.5 124.6 3.57 3.28 -3.49 3.36 -3.46 -3.61 3.19 -1.46 8 9 31 123.9 123.0 123.7 3.69 3.42 3.70 -3.42 -3.51 -3.64 3.36 -2.36 6 7 30 126.1 123.5 123.6 3.72 -3.15 3.41 3.56 -3.56 -3.58 3.24 -2.47 6 7 9 132.5 127.6 126.6 -3.56 -3.32 3.36 3.33 3.26 3.52 -3.44 -2.17 8 10

27 140.5 138.7 139.2 -3.48 3.35 3.46 3.60 3.39 -3.63 -3.60 -2.44 7 8 34 141.2 138.4 138.5 3.71 3.30 -3.35 3.78 3.32 -3.61 -3.58 -2.48 6 7 19 143.9 140.1 139.9 3.65 -3.42 -3.54 3.57 3.36 3.57 -3.41 -2.35 7 9 32 168.5 160.1 157.9 3.77 -3.18 3.58 3.55 3.30 -3.72 -3.57 -2.38 6 7 17 169.6 163.0 161.5 3.73 -3.27 3.49 3.61 -3.54 3.41 -3.50 -2.54 8 9 35 174.5 175.5 176.7 3.83 3.10 3.59 3.64 -3.52 -3.82 -3.49 -1.60 3 3

21

Table S12. Statistical data on the deviations from the crystal structure (PDB entry 3U7Q) (2) of the nearest-neighbor Fe-Fe, Fe-C and Fe-S distances (Å) in the E0 state calculated in previous and present studies using different exchange and correlation functionals: Standard deviation from the average (STDEV), mean absolute error (MAE) and maximum absolute deviation (MAX). The variations among different crystal structures (3U7Q (2), 2AFK (69), 1M1N (70)) are also reported in the column X-Ray. In the comparison with each X-Ray structure, the average distances in the two MoFe protein subunits were employed.

X-Ray Ref. (27) Ref. (26) Ref. (33) Present Work

S = 3/2 S = 1/2 S = 3/2 S = 3/2

M06-2X B3LYP TPSSh BP86 BLYP PBE B3LYP PBE0 M06 M06-2X

Fe-Fe STDEV 0.002 0.246 0.119 0.024 0.054 0.057 0.052 0.135 0.139 0.083 0.187

MAE 0.003 0.439 0.182 0.045 0.060 0.036 0.057 0.135 0.131 0.090 0.387

MAX 0.006 0.932 0.390 0.071 0.130 0.102 0.125 0.387 0.370 0.249 0.657

Fe-C STDEV 0.007 0.287 0.161 0.016 0.034 0.049 0.033 0.132 0.134 0.079 0.403

MAE 0.013 0.322 0.185 0.038 0.039 0.034 0.037 0.118 0.111 0.082 0.382

MAX 0.020 0.958 0.491 0.055 0.063 0.111 0.058 0.414 0.414 0.249 1.088

Fe-S STDEV 0.010 0.071 0.057 0.025 0.039 0.040 0.038 0.052 0.051 0.038 0.068

MAE 0.004 0.116 0.138 0.022 0.033 0.043 0.032 0.077 0.065 0.062 0.155

MAX 0.011 0.243 0.235 0.063 0.076 0.088 0.070 0.198 0.187 0.125 0.260

22

Table S13. Deviation of bond distances (Å) of the En species studied in the present work from E0. The last column reports the mean absolute deviation from E0. To facilitate the reading of the table the following color coding is employed: black, deviations smaller than or equal to 0.1 Å; green, deviation from 0.1 Å to 0.5 Å; blue, deviation from 0.5 to 1.0 Å; red, deviation greater than 1.0 Å. Data are also reported for the lowest-energy E2 state as obtained from our extended model (a) (one bridging hydride between Fe2 and Fe6, and protonated S2B).

E 0

E 2

E 4(4

H)

E 4(4

H)(b

)

E 4(4

H)(c

)

E 4(2

H;H

2)

E 4(4

H)(d

)

E 4(4

H)(e

)

E 4(4

H)(f

)

E 4(3

H;C

H)

E 4(4

H)(h

)

E 4(2

H;H

2;N

2)

E 4(2

H;N

2)

E 4(H

;N2H

)

E 4(N

HN

H)

MA

D

Fe1 S1A 2.337 -0.099 0.014 -0.078 -0.102 -0.061 -0.067 -0.125 -0.091 -0.056 -0.089 -0.054 0.042 -0.084 -0.085 -0.059 Fe1 S2A 2.298 -0.001 -0.063 -0.039 -0.041 -0.038 0.153 0.877 0.024 -0.026 0.089 -0.033 -0.048 -0.096 -0.063 0.048 Fe1 S4A 2.219 0.079 0.078 0.027 0.056 0.041 0.012 -0.039 0.114 0.080 0.056 0.029 0.083 0.069 0.050 0.056 Fe2 S1A 2.300 -0.027 -0.050 -0.063 -0.076 -0.069 0.001 -0.028 0.019 -0.129 -0.050 0.050 0.013 -0.068 -0.082 -0.040 Fe2 S2A 2.288 -0.058 0.017 -0.036 -0.017 -0.029 0.105 0.035 -0.030 0.024 0.042 -0.028 0.114 -0.100 -0.055 -0.003 Fe2 S2B 2.214 0.183 0.356 1.577 1.913 1.562 0.142 0.048 0.205 1.635 0.020 1.459 0.309 1.673 1.740 0.885 Fe3 S2A 2.196 0.092 0.086 0.038 0.040 0.047 0.296 0.183 0.103 0.005 0.460 0.029 0.010 0.037 -0.011 0.104 Fe3 S4A 2.244 0.032 -0.012 0.010 -0.152 0.021 -0.006 0.045 0.049 -0.002 -0.028 0.052 -0.026 0.014 0.045 0.011 Fe3 S5A 2.233 0.010 0.201 0.070 0.046 0.059 0.037 0.146 0.103 -0.025 0.031 0.022 0.059 0.053 -0.019 0.062 Fe4 S1A 2.248 0.047 0.089 0.010 0.002 0.017 0.008 0.041 0.084 1.218 0.052 -0.023 0.045 -0.020 -0.012 0.117 Fe4 S3A 2.193 0.008 0.021 0.005 -0.068 0.004 0.005 0.018 0.012 0.190 0.008 -0.001 0.020 -0.014 -0.028 0.019 Fe4 S4A 2.250 -0.046 0.045 0.006 -0.022 0.010 0.035 0.034 -0.020 0.096 0.034 0.000 0.047 0.015 -0.001 0.022 Fe5 S3A 2.188 -0.003 -0.001 0.004 -0.004 0.009 0.017 0.015 0.015 0.154 0.024 0.002 -0.005 0.008 0.002 0.017 Fe5 S1B 2.252 -0.002 0.001 -0.047 -0.055 -0.028 0.002 0.024 0.018 0.013 0.012 -0.018 -0.010 -0.011 -0.047 -0.008 Fe5 S4B 2.208 -0.003 0.004 -0.007 -0.020 -0.006 -0.006 0.025 0.025 0.046 0.050 -0.009 -0.004 -0.001 -0.003 0.007 Fe6 S1B 2.194 0.062 0.040 -0.005 0.054 0.003 0.010 -0.036 0.048 0.040 -0.013 0.104 -0.007 0.088 0.039 0.030 Fe6 S2B 2.209 0.097 0.111 0.271 0.404 0.274 0.152 0.011 0.143 0.176 0.024 0.290 0.000 0.073 0.155 0.142 Fe6 S3B 2.226 -0.048 -0.023 0.016 -0.009 0.000 -0.041 -0.048 -0.006 0.076 -0.017 0.034 -0.050 -0.003 0.026 -0.004 Fe7 S5A 2.229 0.009 0.088 0.081 0.069 0.032 0.030 0.091 0.030 -0.020 0.071 0.044 0.032 0.086 -0.001 0.046 Fe7 S3B 2.244 0.004 0.013 0.002 -0.011 -0.007 0.001 -0.024 0.888 -0.001 0.573 0.001 -0.021 -0.023 -0.026 0.097 Fe7 S4B 2.240 -0.009 0.034 -0.026 -0.032 -0.042 -0.030 0.051 -0.068 -0.017 -0.029 -0.032 -0.019 -0.005 -0.012 -0.010 Mo S1B 2.411 -0.015 -0.022 -0.004 -0.020 -0.013 -0.017 -0.010 -0.019 -0.012 -0.005 -0.020 -0.015 -0.024 -0.032 -0.016 Mo S3B 2.414 -0.031 -0.054 -0.008 -0.019 0.014 -0.014 -0.025 0.069 -0.044 0.089 -0.041 0.015 -0.030 -0.013 -0.009 Mo S4B 2.381 0.013 -0.007 0.005 0.011 0.009 0.010 -0.004 0.009 0.012 0.017 0.006 0.004 0.016 0.001 0.006 Fe2 C 1.950 -0.019 0.019 -0.011 -0.061 -0.015 -0.031 -0.049 -0.025 -0.074 -0.059 0.078 0.148 -0.077 -0.026 -0.017 Fe3 C 1.959 -0.001 0.017 0.005 -0.033 -0.019 -0.084 -0.037 -0.013 1.616 -0.074 -0.092 -0.012 -0.061 -0.017 0.090 Fe4 C 1.947 0.019 0.057 -0.049 0.046 -0.049 0.020 0.007 0.011 0.007 0.001 0.006 0.019 -0.041 -0.029 0.003 Fe5 C 1.944 0.003 -0.035 -0.018 -0.027 -0.009 0.009 0.002 -0.014 0.105 0.070 0.011 0.027 0.038 -0.012 0.011 Fe6 C 1.984 -0.033 -0.067 -0.008 0.026 0.021 -0.045 -0.075 -0.003 -0.027 -0.049 0.016 -0.105 0.348 0.178 0.011 Fe7 C 1.942 0.004 -0.02 0.011 -0.006 -0.030 -0.010 0.021 -0.043 1.350 -0.041 0.003 0.002 -0.069 -0.014 0.083

S2 BenWe exploB3LYP fuof the E0 (two functcoupling adopted w

Tability of nonethelefunctional

with the aSiegbahn found thastructure wIn contrasfunctionalparticularpresent reSiegbahn Tobtained wal. (27) creported idistances is rather plargest deB3LYP lemaximumhybrid fun

Figure S8. (Ref. 2) of tdifferent exabsolute dev

nchmarkred the sevenunctionals. A(S = 3/2) statetionals predibetween the

with all of the The geometry

a functional tess, the abilityl. Structural d

available X-r(26, 29), Rao

at GGA funcwith mean abst, all of the l used by Bj, the B3LYP

esults for the h(26, 29), obta

The comparisowith M06-2Xclaimed to fiin the Supporthe agreemenpoor for otheeviation is foevel the large

m 4% deviationctionals in d

Statistical data the nearest-neigh

xchange and corviation. If not oth

k of DFT n exchange ans described ine and selectedct the same Fe centers teother functioof the E0 rest

to reproduce gy to reproducdata obtained

ray structureso et al. (27) actionals, notabsolute errors hybrid functornsson et al

P functional hybrid functioained with theon between e

X and B3LYP ind a good arting Informatnt is good. Hoer distances, aound for theest deviation on observed fdescribing the

on the deviationhbor Fe-Fe distarrelation functioherwise specifie

exchangnd correlationn Methods, thd E4 (S = 1/2)

lowest-energends to be m

onals. ting state of Fgeometrical pce them repred with our ca

s and with strnd Bjornssonably the BP8from the cry

tionals we tril. (32, 33), pyields very onals reprodue M06-2X anexperimental is also shown

agreement betion of their powever, as eaas shown her nearest-neigis for the Fe

for the Fe4-Feinteratomic d

ns from the cryances (Å) in the nals: Standard d

ed, data refer to t

ge and con functionals lhese two were) isomers. Congy E0 (S = 3maximized (T

FeMo-co is kparameters is esents a first alculations for

ructures obtain et al. (33) ar86 and PBE ystallographicied, with the predict unacclong Fe-to-c

uce recently pd B3LYP funstructural pa

n in Figure Setween crystapaper only a fasily seen fromre in Table Sghbor Fe3-Fe4e1-Fe2 distance5 distance usdistances of th

stal structure (PE0 state obtainedeviation from the spin state S =

rrelationlisted in Methe first used tonsistent with 3/2) BS state

Table S1I, SI2

known with hnot the best istep in testin

r the present

ined for othere reported in

functionals,c atomic dista

exception ofeptably long

central carbonpublished E0 snctionals. arameters an

S8 and Table allographic afew selected m their publisS11. For inst4 distance (oce (overestimsing BP86. Thhe E0 state is

PDB entry 3U7Qed in previous anthe average, me

= 3/2. (1) Ref. 34

n functionhods, focusino explore all oprevious stude where the 2 and SI3). T

high precisionindicator of itng an exchanstructural mo

er models recn Figure S8 a reproduce w

ances (2) far sf the hybrid m

nearest neign and Fe-to-structures by

nd the correspS11. It is sur

and calculatedistances, anshed coordinatance, at the Moverestimated

mated by 15%he origin of tnot clear and

Q, average over nd present DFT ean absolute err4; (2) Ref. 33; (3

nals ng on the BP8of the 35 BS dies (22, 33),

antiferromagThis BS state

n (2). Althougts overall accunge and correodel are com

cently proposand Table S1well the FeMsmaller than 0meta-GGA T

ghbor distanc-Fe distancesRao et al. (27

ponding quanrprising that Red distances. d indeed, for ates, the agreeM06-2X leve

d by 35%); a%), as comparthe failure of

d certainly des

the two subunicalculations usiror and maximu3) Ref. 39.

23

86 and states these gnetic e was

gh the uracy,

elation mpared

sed by 1. We

Mo-co 0.1 Å.

TPSSh es. In

s. The 7) and

ntities Rao et

They those

ement el, the at the red to

f these serves

ts)ng

um

24

further detailed investigation, as these functionals are widely used as a de facto state-of-the-art in computational chemistry of organometallic complexes. Because energy considerations are generally more important than such structural features, the structure and the corresponding energetics of various critical E4 protonation states were calculated at both BP86 and B3LYP level of theory. As we will show, the two functionals provide a consistent picture, although having differences that will also be discussed. Because BP86 predicts a low-spin Mo(III) state for both E0 and E4, consistent with the available ENDOR data, as well as for other reasons to be given below, the energies discussed in subsequent subsections refer to this functional unless noted; B3LYP energies are given as appropriate.

S3 Protein environment and stability of the cofactor Previous investigations by Siegbahn(26), Rao et al.(27) and McKee(28) documented the protonation of the central carbon of FeMo-co, and Siegbahn(26) even showed that protonation can ultimately lead to the formation of CH3, which he proposed to be central to the nitrogenase function. The analysis reported in the main text clearly shows that this is a result of the inadequacy of the model adopted by these authors in describing the interaction at the active site. In this section, we present more details on the role of the interactions at the active on the FeMo-co.

The model adopted by Siegbahn(26) and Rao et al.(27) are similar to our models (c) and (d), in that they lack the majority of the H-bond cage around FeMo-co, while McKee's model (28) is identical to our minimal model (e) (Figure S1). In particular, although Rao et al. (27) performed a multiscale quantum chemical study (ONIOM), which included the full protein scaffold, they still missed the majority of the active site interactions, as they simply adopted one of the available the X-Ray structure and completely neglected the presence of water, which is known to be abundant near the FeMo-co.(31)

The analysis that follows focusses on some of the possible E4 states, and specifically the di-hydride E4(4H) state and the possible C-protonated E4 states as obtained using the BP86, B3LYP, and M06-2X exchange and correlation functionals. Before starting the discussion, we recall that the FeMo-co structures obtained from the various hybrid functionals we tested (including B3LYP and M06-2X) deviates significantly from the crystallographic structures (Table S12). In particular, some of the Fe-C distances deviates a lot from the references high-accuracy X-Ray references, with the M06-2X and B3LYP functionals deviating as much as 1.0 Å and 0.4 Å, respectively.

Using the extended model a (Figure S1), at BP86, B3LYP and M06-2X DFT levels, we found that E4(4H) state is the most stable. This state has two hydridic hydrogen atoms located in a semi-bridged position between Fe2-Fe6 and Fe3-Fe7, and two protic hydrogen atoms preferentially bound to the bridging m2-S atoms S5A and S2B. Other structures very close in free energy, which differs on the location of the hydridic hydrogen on the Fe2, Fe3, Fe6, and Fe7 face, are also possible as discussed in the main text. We found that protonation at locations other than those mentioned above is very unfavorable. For instance, protonation of bridging m3-S atoms is unfavorable as extensively discussed elsewhere. (25) In particular, in contrast to the results reported by Siegbahn(26) using a simplified structural model, protonation of S3A is also energetically unfavorable as this atom is located in the FeMoco docking cleft (Figure 1) and it interacts with various N-H backbone groups. Most important, protonation at the central carbon was not found feasible at BP86 level. Instead, using the hybrid functionals B3LYP and M06-2X, we found various stable, high-energy E4 states with a protonated central carbon. Single protonation of the central carbon leads to the partial disruption of FeMoco. Some of these C-protonated states, such as the state E4(3H;CHi) reported in Figure S9 (left), upon re-optimization using the BP86 functional, spontaneously evolved to species with bridging hydrides similar to E4(4H) as shown in Figure S9 (right). The E4(3H;CHi) structures (see Error! Reference source not found., left) are located at 146 kJ/mol (B3LYP) and 53 kJ/mol (M06-2X) above the “canonical” E4(4H), respectively. The structure of E4(3H;CHi) is similar to the C-protonated structure found by Rao et al. (27) using the hybrid M06-2X functional. We believe that the formation of such intermediate is a consequence of the expanded FeMoco

structure promptly

Nhere indicE4(4H) w(Figure SSiegbahn lacks of tgroups hya-359Arg; discussed characteriand BP86central caligands, p

Bclear that simplifiedthe surrou

Figure S9. B3LYP struspontaneoushomocitrate

yielded by hexpelled out

Notably, usingcated as E4(3

where the C-HS10). The ge(26) as the lothe hydrogenydrogen bondmodel (b) in

in the maiized undergo 6 levels. We aarbon. In addiprotonation ofBy comparing

the favorabled structural munding protein

Left: Structure ucture using thsly breaks and te end.

hybrid functiwhen the BP

g both BP86 a3H;CH) stateH resides on teometry of thowest-free enn bonding neded to FeMoc

Figure S1), n text. Usinan appreciab

also found thaition, using thf the central ca

structural moe protonation

model adoptedn matrix in sta

of the C-protonhe BP86, the Fthe hydride mov

onals, which86 functionaland B3LYP fu, located at the surface ofhe cofactor iergy structure

etwork aroundco (i.e., residuthis C-proton

ng model b, le additional

at, in the reduhe minimal marbon is founodels increasof the carbide

d in previous abilizing the c

nate E4(CHi) staFe2-Fe6 distanceves to a bridging

h allows H tol is used. unctionals, w121.4 kJ/molf the cofactorin E4(3H;CHe for the E4 std FeMoco. Rues a-358Leu, nated E4 (Figu

we observeopening, and

uced model b,model (e) (Fignd even more ing complexie center to yieinvestigation

cofactor.

ate found using e reduces consig position betwe

o be accomm

we found a secl (BP86) andr at the cente

H) is virtuallytate for a sim

Remarkably, a-357Gly, andure S9) beco

ed that all thd the structure, it is very easgure S1), comfavorable. ity optimizedeld a methyl ins, which hig

the B3LYP funiderably (from een the Fe2 and

modated insid

cond C-protond 68.9 kJ/moer of the Fe2,y identical to

mplified moderemoving fro

d a-356Gly, anomes the lowehe C-protonae are now stabsy to add a se

mposed only b

d at various leintermediate

ghlights the fu

nctional. Right: 4.10 Å to 2.7Fe6. The FeMo

de the cluste

nated intermeol (B3LYP), a Fe6, Fe4, Fe

o that reporteel of protein, wom our modend the backboest-energy staated E4 stateble at both B3econd protonby FeMoco a

evel of theoryis an artifact undamental ro

upon relaxation

72 Å), the C-Hoco is viewed fr

25

er, but

ediate, above 5 face ed by which el the one of ate, as es we 3LYP to the

and its

y, it is of the ole of

n of the H bond rom the

Figure S10on the surfa

. Structure of thace of the cofacto

e high energy Cor and it is symm

C-H protonated Emetrical located b

E4(CHo) state as between four Fe

obtained with the atoms.

he B3LYP functtional. The C-H

26

resides

27

S4 Natural Bond Orbitals Analysis of selected E4 States The natural bond orbital (NBO) analysis was developed to study hybridization and covalency in molecules in terms of concepts similar to Lewis chemical structures, then extended to the analysis of intermolecular charge transfer due to localized orbital interactions. In this appendix, we will briefly review a few main concepts and quantities of NBO theory, which we used to characterize and quantify bonding and orbital interactions in the E4 catalytic intermediates involved in the N2 reduction by nitrogenase. For consistency all of the NBO analysis was performed on species obtained from the extended structural model reported in Figure S1a.

The NBO of a localized orbital, , between two atoms A and B is formed by a linear combination of two orthonormal hybrid orbitals, hA and hB, defined in terms of atomic orbitals centered on A and B:

(A-B) = cAhA + cBhB

where |cA|2 + |cB|2 = 1. The relative magnitude of the coefficients cA and cB can be taken as a measure of the bond polarization due to the different electronegativity of A and B. For a perfectly apolar bond cA = cB = 2-1/2 ≈ 0.707. The coefficients cA and cB for selected (A-B) orbitals of key E4 species are listed in Table S13.

The strength of the interaction between non-covalent complexes can be estimated within the NBO framework. In fact, the magnitude E(2) of charge transfer interaction 1(A-B) 2(C-D) between two orbitals can be obtained from the second order perturbative formula

∆ 2 where is the Fock operator, and 2 and 1 are the NBO energies associated to 1 and 2. In turn, from E(2) the charge qCT transferred from 1(A-B) to 2(C-D) is obtained as qCT = |E(2)|/(2 - 1) (in electron charge, e). Here we discuss the results of the NBO analysis for E4(4H) and , the key N2-bond E4 species and along with the diazene intermediate along with E4(NHNH). The E4(4H) is characterized by two asymmetrically bridging hydrides between Fe2-H-Fe6 and Fe3-H-Fe7. The bonds Fe2-H and Fe7-H are shorter than Fe6-H and Fe3-H bonds (Error! Reference source not found.) and accommodate 1.8 and 1.7 e, respectively (Table S13). The magnitude of the coefficients cFe and cH indicate that these bonds are polarized toward the H atoms, while the coefficients for the S-H bonds show that these bonds are less polarized. The adduct is clearly characterized by a well-defined H-H bond, which hosts about 1.5 e, and a weak Fe2-H bonds, which host less than 0.9 e. The NBO analysis on double adduct does not show any covalent bond between FeMoco and either H2 nor N2. In this adduct the H2 is basically fully formed with a H-H bond hosting 1.9 e. As reported in Table S14, H2 connects to Fe2 via a strong (H-H) *(Fe2) charge transfer interactions and smaller (Fe2) *(H2) back donation. Here with we indicate either a d orbital or a hybrid orbital resulting from mixing of Fe2 d orbitals and S atoms orbitals. In this adduct, the N2 molecule is also intact, with the (N-N) and the two (N-N) orbital containing exactly two electrons each. However, the corresponding antibonding orbitals have an appreciable population deriving from FeMoco-to-N2 charge transfer (Table S14). The FeMoco/N2 interaction in formed upon H2 is release, are similar to those in , as can be seen from Table S13 and S14, with the only exception being that here N2 interacts head-on only with Fe2, rather than both Fe2 and Fe6 as in We conclude by commenting on the bonding properties of E4(NHNH). As discussed in the main text, the diazene moiety interacts with FeMo-co via -to-d*(Fe2) and -to-d*(Fe3) charge donation forming strong binding interactions that considerably contribute to stabilize this highly energetic species. Because of these strong interactions with the Fe2 and Fe6 centers, the character of the N-N bond is lost and replaced with Fe-N covalent bonds resulting from 3d(Fe) (with a smaller extend of s(Fe)) and p(N) mixing (Table S13).

28

NBO Orbital, (A-B) cA cB Occupation (e)

(Fe2-H) 0.59 0.80 1.81 (Fe7-H) 0.58 0.82 1.73 (S5A-H) 0.76 0.65 2.00 (S2B-H) 0.78 0.63 2.00

(Fe2-H) 0.83 0.85 0.89 (H-H) 0.72 0.69 1.53

(Np-Nd) 0.74 0.68 2.00 (Np-Nd) 0.71 0.70 2.00 (Np-Nd) 0.72 0.69 2.00 (Np-Nd) -0.67 0.74 0.11 (Np-Nd) -0.70 0.71 0.25 (Np-Nd) -0.69 0.72 0.37 n(Np) 0.85 n(Nd) 0.98 (H-H) 0.71 0.71 1.89

(H-H) 0.71 -0.71 0.16

No covalent bonds between FeMoco and H2 or N2 detected

(Np-Nd) 0.72 0.70 2.00 (Np-Nd) 0.71 0.70 2.00 (Np-Nd) 0.70 0.70 2.00 (Np-Nd) 0.71 -0.70 0.08 (Np-Nd) 0.71 -0.70 0.23 (Np-Nd) 0.72 -0.69 0.24 n(Np) 0.90 n(Nd) 0.98 No covalent bonds between FeMoco and N2 detected

(Fe2-N2) 0.54 0.84 1.81 (Fe2-N6) 0.56 0.83 1.79 (Fe6-N6) 0.42 0.92 1.94 (N2-N6) 0.68 0.73 1.99 (N2-N6) 0.73 -0.68 0.03 n(N2) 0.96 () n(N6) 0.94 ()

Table S14. Coefficients (cA and cB) and occupation of selected Natural Bond Orbitals, (A-B) = cAhA + cBhB, where = (sigma bonding), (sigma antibonding), (pi bonding), * (pi antibonding), and n (lone pair). The coefficients cA and cB are the spin up/spin down orbitals average. The occupation is the sum of the spin up and spin down orbitals. In ) and ), Np stands for proximal N atom and Nd stands for distal N atom; instead, in NHNH), N2 and N6 indicates the N atoms close to Fe2 and Fe3, respectively.

29

Table S15. Magnitude of the charge qCT transferred from the NBOs 1 and to the NBO 2, 1(A-B) 2(C-D), for selected species and orbitals, where 1,2 = (sigma bonding), (antibonding), * (pi antibonding), and n (lone pair); indicates a Fe2 d orbitals or mixed Fe2 d and S orbitals. Both spin up and spin down orbital have been considered for the calculation of qCT.

Interaction qCT (e)

(H-H) *(Fe2) 0.27 (Fe2) *(H2) 0.06 (Fe2) *(N2) 0.18 (Fe6) *(N2) 0.20 n(Np) *(Fe2) 0.08 n(Np) *(Fe6) 0.02

(Fe2) *(N2) 0.29 n(Np) *(Fe2) 0.10

30

S5 Energy balance The adenosine triphosphate (ATP)-dependent reduction of N2 to yield NH3 follows the limiting stoichiometry (1) N2(g) + 8 e- + 8 H+ + 16 ATP + 16H2O → 2 NH3(g) + H2(g) + 16 ADP + 16 Pi, where ADP stands for adenosine diphosphate and Pi for inorganic phosphate.

In order to make an assessment of the energetic associated with the formation of the various En states, it is necessary to have an estimate of the free energy associated with the [e-/H+] pair. This represents a challenging computational problem, which can be circumvented quite easily as follows. By definition, at pH = 0 and T = 298 K, under H2 at 1 atm, the free energy of the reaction

2 e- + 2 H+(aq) → H2 is

DG0(H+/H2(g)) = 2G0(H2(g)) - 2G0(e-) - G0(H+) = 0 kJ/mol. The free energy of H2 is known with high accuracy. Using the most accurate electronic energy estimate (NIST database), along with enthalpy and entropy contributions, we obtain G0(H2) = -3074.487 kJ/mol. From G0(H2) we easily obtain that G0(e-) + G0(H+) = G0(H2(g))/2 = -1537.2 kJ/mol vs. NHE. Assuming that protons come from the cellular cytosol at pH = 7 and electrons are delivered by the Fe protein at a potential of E0(FeP) = -0.430 V vs. NHE (71), we need to correct the previous values as G(e-) + G(H+) = G0(e-) + G0(H+) + eRTpH + FE0(FeP) = -1455.8 kJ/mol. It is important to point out that working with the [e-/H+] pair, using the standard hydrogen electrode as a reference, allows one to avoid the use of the ill-defined absolute free energy of solvated proton and, even worse defined, free energy of the electron. Finally, for each electron and proton pair delivered to FeMoco, two molecules of ATP are hydrolyzed, which must be taken into account in the energetic balance. The free energy of hydrolysis of ATP to ADP and Pi is extremely sensitive to the pH and ionic strength of the solution.* The ionic strength of the cellular cytosol is difficult to assess since it strongly depends on the concentration of all ionic species, including proteins. To the best of our knowledge, no values have been reported for nitrogen metabolizing bacteria. Here we use the value DG(ATP) = -36.1 kJ/mol suggested for the ATP hydrolysis at pH = 7 and ionic strength I = 0.25 mol/kg, a typical value for cellular environments.‡

In summary, the overall free energy associated to the uptake of one [e-/H+] pair can be estimated to be

DG(e-/H+) = G(e-) + G(H+) + 2DG(ATP) = -1528.0 kJ/mol. The energetic of the reactions considered in the present work accounts for the amount DG(e-/H+) lost for each [e-/H+] pair transferred to FeMoco. In the manuscript, the notation e-/H+ indicates “2e-(FeP) + 2H+(pH=7) + 2ATP(aq) + 2H2O(aq)”, at pH = 7 and I = 0.25 mol/kg, with 2e-(FeP) indicating the reduced Fe protein yielding the oxidized Fe protein and ATP yielding ADP + Pi.

The reaction free energies reported in Figure 3 are calculated using the estimate for DG(e-/H+) given above. We also remark that using estimate for DG(e-/H+), we can also provide the conservative estimate DG(N2/NH3) = -622.9 kJ/mol for the free energy of N2 reduction to NH3 catalyzed nitrogenase (equation 1) at p = 1 bar, T = 25oC, pH = 7 and I = 0.25 mol/kg, making use of the standard state free energy of formation of N2 (0 kJ/mol), NH3 (-33.5 kJ/mol) and H2 (0 kJ/mol). This estimate can be extended to any conditions using simple thermodynamic considerations. Similarly, we can give an estimate of the free energy of H2 production catalyzed by nitrogenase under the same conditions DG(H+/H2) = -147.3 kJ/mol. This estimates are obtained using most accurate electronic * Alberty RA (2001) Effect of Temperature on Standard Transformed Gibbs Energies of Formation of

Reactants at Specified pH and Ionic Strength and Apparent Equilibrium Constants of Biochemical Reactions. The Journal of Physical Chemistry B 105(32):7865–7870.

31

energy estimate for the H2 molecule as given above, G0(H2(g)). Using, instead the DFT/BP86 reference as calculated from the computational set up adopted in the present manuscript, G0DFT(H2(g)), we have DG(N2/NH3) =-646.1 kJ/mol and DG(H+/H2) = -170.5 kJ/mol, being the difference between the G0(H2(g)) - G0DFT(H2(g)) = 23.2 kJ/mol (5.6 kcal/mol).

S6 Web Enhanced Object Movie S1 shows the re of H2 starting from E4(4H) induced by the N2 binding. The movie was generated by a linear interpolation of the structures calculated in the present study. The initial position of N2 was inferred from previous MD simulations (32).

32

S7 Coordinates of the computed species Optimization was performed constrained the position of the atoms where the protein fragments were cut. The entry ID of the fixed atoms of models (a) in the xyz coordinates list below are: 19, 20, 21, 29, 33, 43, 63, 64, 74, 140, 160, 161, 171. The fixed atoms the smaller models (b) – (e) are those in common with model (a). All coordinates are given in Å.

33

Electron counting according to E0 Mo4+4Fe2+3Fe3+ E0 - Mo4+4Fe2+3Fe3+ (S=3/2) - BP86 Fe 36.916 -7.894 -5.780 Fe 35.980 -6.200 -3.834 Fe 34.317 -7.505 -5.351 Fe 35.702 -5.554 -6.340 Fe 33.858 -3.942 -5.680 Fe 34.143 -4.553 -3.212 Fe 32.507 -5.825 -4.746 S 37.688 -5.739 -5.304 S 34.094 -2.494 -3.971 S 35.684 -8.467 -3.927 S 35.882 -5.051 -1.944 S 34.966 -3.892 -7.566 S 32.138 -5.298 -2.596 S 35.369 -7.546 -7.332 S 31.737 -4.289 -6.182 S 32.122 -7.913 -5.428 Mo 31.842 -3.353 -3.996 C 34.433 -5.611 -4.865 C 37.387 -5.536 3.511 C 37.484 -6.901 4.210 C 40.411 -5.910 0.080 N 40.672 -6.110 -1.294 C 39.640 -5.596 -2.022 H 39.522 -5.642 -3.105 N 38.754 -5.061 -1.163 H 37.729 -4.798 -1.461 C 39.200 -5.250 0.141 H 38.625 -4.910 0.995 C 37.895 -10.983 -6.749 H 37.035 -11.283 -6.128 H 37.562 -10.861 -7.791 S 38.639 -9.394 -6.114 C 42.505 -7.998 -5.954 C 42.086 -8.106 -4.476 O 42.431 -7.255 -3.601 N 41.389 -9.242 -4.163 H 40.842 -9.677 -4.920 C 39.505 -9.518 -2.491 O 38.773 -10.580 -3.130 H 38.582 -10.247 -4.050 N 35.210 -0.380 -6.868 H 34.637 -1.169 -7.199 C 36.429 -1.000 -6.294 H 36.944 -0.261 -5.646 H 36.143 -1.856 -5.662 C 37.429 -1.418 -7.390 O 37.562 -0.702 -8.434 N 38.202 -2.534 -7.168 H 37.953 -3.174 -6.408 C 39.282 -2.911 -8.084 H 39.410 -2.052 -8.768 H 40.224 -3.054 -7.527 C 39.109 -4.174 -8.951 O 40.114 -4.623 -9.578 N 37.853 -4.722 -9.043 H 37.144 -4.426 -8.353 C 37.657 -6.045 -9.656 H 38.605 -6.304 -10.163 C 36.505 -6.083 -10.663 O 35.954 -7.184 -11.002 N 36.166 -4.881 -11.201 H 36.586 -4.065 -10.754 C 35.068 -4.721 -12.150 C 32.024 -5.535 -9.889 N 31.546 -6.885 -9.545

H 32.243 -7.643 -9.706 C 30.544 -7.089 -8.664 N 29.917 -6.041 -8.070 H 30.534 -5.246 -7.830 H 29.316 -6.240 -7.244 N 30.046 -8.354 -8.490 H 30.511 -9.115 -9.006 H 29.762 -8.582 -7.535 C 28.805 -1.783 -5.986 C 30.080 -0.997 -5.913 N 31.241 -1.389 -5.215 C 32.153 -0.427 -5.410 H 33.179 -0.426 -5.057 N 31.640 0.570 -6.202 H 32.166 1.374 -6.529 C 30.328 0.224 -6.530 H 29.695 0.846 -7.154 C 30.012 -2.900 -0.486 C 29.963 -2.291 -1.910 C 29.094 -3.203 -2.824 O 29.738 -3.725 -3.866 O 27.870 -3.411 -2.590 O 31.299 -2.206 -2.430 C 29.347 -0.871 -1.883 H 28.303 -0.914 -1.525 H 29.946 -0.227 -1.215 C 41.017 -9.598 -2.785 H 41.765 -8.478 -6.617 H 43.483 -8.494 -6.090 H 42.608 -6.939 -6.231 H 32.613 -5.617 -10.814 H 32.669 -5.105 -9.099 H 31.164 -4.868 -10.069 H 28.127 -1.323 -6.726 H 28.280 -1.829 -5.017 H 29.001 -2.827 -6.283 H 29.365 -0.433 -2.896 H 39.356 -9.633 -1.400 H 41.585 -8.925 -2.119 H 41.348 -10.636 -2.590 H 39.104 -8.528 -2.791 H 30.527 -3.876 -0.516 H 28.990 -3.038 -0.092 H 30.581 -2.224 0.179 H 37.450 -6.809 -8.887 H 35.412 -4.203 -13.063 H 34.240 -4.142 -11.704 H 34.715 -5.729 -12.418 H 38.669 -11.768 -6.702 H 41.099 -6.233 0.852 H 35.533 0.082 -7.731 H 37.966 -6.815 5.201 H 38.076 -7.620 3.614 H 36.483 -7.342 4.368 H 38.389 -5.087 3.374 H 36.789 -4.821 4.103 H 36.907 -5.623 2.521 H 41.467 -6.578 -1.762 O 31.638 -10.309 -10.001 H 32.413 -9.780 -10.350 H 31.817 -11.235 -10.259 O 28.997 -6.181 -5.303 H 29.885 -6.566 -5.133 H 29.060 -5.303 -4.845 O 32.492 -10.719 -7.239 H 32.095 -10.482 -8.110 H 32.411 -9.895 -6.698 O 33.699 -8.688 -10.279 H 34.428 -8.133 -10.675 H 34.188 -9.271 -9.614

O 34.875 -10.409 -8.579 H 34.109 -10.595 -7.964 H 35.379 -9.718 -8.092 C 31.358 -7.824 3.950 C 31.752 -8.374 2.583 O 30.897 -8.601 1.710 N 33.081 -8.601 2.394 H 33.725 -8.360 3.148 C 33.691 -8.940 1.088 H 32.962 -8.663 0.309 C 34.977 -8.084 0.899 H 35.652 -8.285 1.770 C 35.712 -8.465 -0.400 H 35.081 -8.275 -1.285 H 36.612 -7.841 -0.530 H 36.016 -9.526 -0.422 C 34.602 -6.585 0.925 H 34.145 -6.283 1.885 H 35.489 -5.959 0.738 H 33.897 -6.346 0.108 C 33.881 -10.473 0.971 O 33.081 -11.198 0.356 N 34.961 -10.989 1.621 H 35.647 -10.345 2.015 C 35.286 -12.417 1.574 C 29.601 -7.466 -1.094 N 30.525 -8.062 -2.079 H 30.956 -7.420 -2.758 C 31.165 -9.230 -1.887 N 30.764 -10.092 -0.898 H 30.256 -9.637 -0.139 H 31.536 -10.660 -0.512 N 32.199 -9.568 -2.689 H 32.327 -9.046 -3.589 H 32.554 -10.519 -2.642 C 27.466 -12.000 -1.778 C 27.670 -11.370 -0.405 O 27.253 -10.225 -0.149 N 28.351 -12.102 0.522 H 28.579 -11.625 1.415 H 28.735 -13.019 0.310 O 28.477 -9.983 2.395 H 27.868 -9.773 1.644 H 29.258 -9.410 2.217 H 30.542 -8.439 4.365 H 30.962 -6.801 3.817 H 32.189 -7.790 4.676 H 28.186 -11.545 -2.481 H 26.453 -11.765 -2.138 H 27.614 -13.094 -1.782 H 34.377 -12.963 1.286 H 35.626 -12.763 2.564 H 36.074 -12.628 0.827 H 29.243 -6.516 -1.516 H 30.101 -7.269 -0.131 H 28.728 -8.124 -0.936 E0 - Mo4+4Fe2+3Fe3+ (S=3/2) – B3LYP Fe 37.112 -8.115 -5.574 Fe 35.908 -6.180 -3.615 Fe 34.127 -7.596 -5.203 Fe 35.573 -5.601 -6.274 Fe 33.691 -3.820 -5.645 Fe 34.034 -4.421 -2.989 Fe 32.282 -5.732 -4.661 S 37.638 -5.726 -5.100 S 33.902 -2.324 -3.869 S 35.614 -8.474 -3.650 S 35.804 -4.963 -1.703 S 34.888 -3.904 -7.563

34

S 31.924 -5.176 -2.448 S 35.473 -7.772 -7.170 S 31.443 -4.078 -6.036 S 31.831 -7.889 -5.350 Mo 31.641 -3.189 -3.786 C 34.333 -5.572 -4.682 C 37.387 -5.536 3.511 C 37.484 -6.901 4.210 C 40.411 -5.910 0.080 N 40.686 -6.138 -1.280 C 39.675 -5.639 -2.026 H 39.570 -5.700 -3.101 N 38.787 -5.092 -1.192 H 37.809 -4.793 -1.476 C 39.212 -5.251 0.116 H 38.631 -4.895 0.948 C 37.895 -10.983 -6.749 H 37.007 -11.260 -6.175 H 37.589 -10.653 -7.744 S 38.857 -9.645 -5.893 C 42.505 -7.998 -5.954 C 42.180 -8.167 -4.466 O 42.363 -7.256 -3.621 N 41.752 -9.409 -4.111 H 41.330 -9.971 -4.842 C 39.993 -9.810 -2.338 O 39.282 -10.894 -2.937 H 39.011 -10.595 -3.833 N 35.245 -0.322 -6.846 H 34.612 -1.054 -7.159 C 36.429 -1.000 -6.294 H 36.978 -0.299 -5.647 H 36.114 -1.838 -5.670 C 37.410 -1.454 -7.384 O 37.530 -0.782 -8.445 N 38.186 -2.550 -7.132 H 37.965 -3.142 -6.340 C 39.274 -2.948 -8.019 H 39.434 -2.114 -8.710 H 40.193 -3.098 -7.445 C 39.092 -4.219 -8.861 O 40.101 -4.731 -9.403 N 37.827 -4.700 -9.021 H 37.101 -4.327 -8.409 C 37.588 -6.027 -9.595 H 38.524 -6.351 -10.063 C 36.469 -6.054 -10.627 O 35.904 -7.141 -10.944 N 36.164 -4.872 -11.204 H 36.586 -4.053 -10.787 C 35.068 -4.721 -12.150 C 32.024 -5.535 -9.889 N 31.515 -6.865 -9.533 H 32.172 -7.638 -9.706 C 30.485 -7.053 -8.701 N 29.870 -6.006 -8.113 H 30.463 -5.227 -7.825 H 29.181 -6.204 -7.383 N 29.955 -8.298 -8.557 H 30.387 -9.057 -9.083 H 29.629 -8.535 -7.627 C 28.805 -1.783 -5.986 C 29.930 -0.852 -5.677 N 31.032 -1.182 -4.878 C 31.810 -0.107 -4.825 H 32.751 -0.036 -4.308 N 31.271 0.908 -5.557 H 31.703 1.803 -5.715 C 30.078 0.448 -6.106 H 29.453 1.058 -6.735

C 29.846 -2.762 -0.254 C 29.842 -2.111 -1.654 C 28.935 -2.939 -2.600 O 29.554 -3.476 -3.634 O 27.708 -3.067 -2.390 O 31.172 -2.095 -2.169 C 29.309 -0.665 -1.583 H 28.277 -0.657 -1.217 H 29.945 -0.080 -0.908 C 41.480 -9.800 -2.724 H 41.803 -8.559 -6.579 H 43.522 -8.359 -6.145 H 42.453 -6.941 -6.219 H 32.642 -5.651 -10.780 H 32.642 -5.099 -9.094 H 31.189 -4.866 -10.117 H 28.138 -1.321 -6.723 H 28.220 -2.031 -5.096 H 29.177 -2.726 -6.392 H 29.338 -0.203 -2.575 H 39.924 -9.945 -1.250 H 42.037 -9.108 -2.085 H 41.880 -10.809 -2.570 H 39.527 -8.848 -2.591 H 30.287 -3.762 -0.307 H 28.825 -2.838 0.135 H 30.454 -2.152 0.424 H 37.321 -6.750 -8.819 H 35.405 -4.194 -13.049 H 34.238 -4.161 -11.704 H 34.728 -5.719 -12.429 H 38.538 -11.863 -6.850 H 41.083 -6.216 0.862 H 35.559 0.139 -7.700 H 37.863 -6.799 5.234 H 38.158 -7.579 3.672 H 36.502 -7.385 4.269 H 38.366 -5.040 3.481 H 36.699 -4.866 4.038 H 37.021 -5.640 2.486 H 41.480 -6.607 -1.721 O 31.512 -10.283 -10.112 H 32.297 -9.780 -10.430 H 31.680 -11.207 -10.348 O 28.695 -6.097 -5.329 H 29.560 -6.509 -5.178 H 28.763 -5.241 -4.869 O 32.185 -10.710 -7.250 H 31.871 -10.468 -8.138 H 32.115 -9.893 -6.722 O 33.654 -8.694 -10.292 H 34.398 -8.138 -10.626 H 34.083 -9.300 -9.637 O 34.681 -10.523 -8.536 H 33.912 -10.701 -7.957 H 35.168 -9.832 -8.050 C 31.294 -7.970 3.975 C 31.752 -8.374 2.583 O 30.947 -8.415 1.652 N 33.060 -8.683 2.461 H 33.643 -8.599 3.284 C 33.767 -8.923 1.188 H 33.098 -8.614 0.382 C 35.035 -8.030 1.157 H 35.609 -8.235 2.083 C 35.930 -8.341 -0.052 H 35.405 -8.179 -0.997 H 36.796 -7.673 -0.058 H 36.295 -9.374 -0.051 C 34.596 -6.552 1.187

H 34.077 -6.297 2.118 H 35.454 -5.888 1.072 H 33.935 -6.328 0.344 C 33.981 -10.437 1.014 O 33.218 -11.135 0.349 N 35.019 -10.985 1.683 H 35.704 -10.389 2.125 C 35.286 -12.417 1.574 C 29.601 -7.466 -1.094 N 30.304 -8.226 -2.146 H 30.538 -7.757 -3.018 C 30.929 -9.386 -1.930 N 30.836 -9.998 -0.728 H 30.654 -9.395 0.068 H 31.571 -10.668 -0.514 N 31.571 -10.010 -2.944 H 31.760 -9.441 -3.784 H 32.291 -10.669 -2.688 C 27.466 -12.000 -1.778 C 27.638 -11.369 -0.407 O 27.172 -10.260 -0.146 N 28.353 -12.074 0.507 H 28.589 -11.602 1.380 H 28.778 -12.960 0.283 O 28.481 -9.835 2.353 H 27.833 -9.707 1.634 H 29.203 -9.227 2.126 H 30.428 -8.578 4.255 H 30.962 -6.926 3.944 H 32.068 -8.072 4.742 H 28.216 -11.578 -2.458 H 26.480 -11.744 -2.170 H 27.585 -13.089 -1.765 H 34.394 -12.987 1.843 H 36.101 -12.680 2.252 H 35.568 -12.689 0.551 H 29.138 -6.603 -1.571 H 30.288 -7.113 -0.323 H 28.815 -8.086 -0.651 E0 - Mo4+4Fe2+3Fe3+ (S=3/2) – M06 Fe 37.040 -8.047 -5.739 Fe 35.979 -6.275 -3.790 Fe 34.185 -7.583 -5.382 Fe 35.615 -5.591 -6.426 Fe 33.771 -3.855 -5.702 Fe 34.109 -4.540 -3.091 Fe 32.345 -5.780 -4.749 S 37.699 -5.761 -5.267 S 34.019 -2.418 -3.894 S 35.640 -8.565 -3.879 S 35.853 -5.140 -1.827 S 34.906 -3.856 -7.658 S 31.999 -5.230 -2.532 S 35.436 -7.729 -7.369 S 31.552 -4.143 -6.158 S 31.939 -7.980 -5.249 Mo 31.741 -3.265 -3.939 C 34.395 -5.624 -4.804 C 37.387 -5.536 3.511 C 37.484 -6.901 4.210 C 40.411 -5.910 0.080 N 40.808 -6.098 -1.254 C 39.813 -5.703 -2.073 H 39.813 -5.755 -3.156 N 38.816 -5.264 -1.314 H 37.849 -5.004 -1.659 C 39.150 -5.389 0.021 H 38.463 -5.098 0.799 C 37.895 -10.983 -6.749

35

H 36.928 -11.125 -6.253 H 37.729 -10.834 -7.820 S 38.799 -9.533 -6.039 C 42.505 -7.998 -5.954 C 42.063 -8.046 -4.496 O 42.308 -7.130 -3.685 N 41.456 -9.202 -4.117 H 40.984 -9.735 -4.848 C 39.520 -9.182 -2.509 O 38.743 -10.315 -2.859 H 38.494 -10.200 -3.797 N 35.211 -0.424 -6.868 H 34.635 -1.220 -7.154 C 36.429 -1.000 -6.294 H 36.972 -0.225 -5.732 H 36.163 -1.788 -5.580 C 37.388 -1.526 -7.356 O 37.487 -0.944 -8.462 N 38.182 -2.581 -7.018 H 37.937 -3.158 -6.218 C 39.290 -3.001 -7.858 H 39.535 -2.155 -8.511 H 40.166 -3.218 -7.237 C 39.100 -4.221 -8.747 O 40.109 -4.764 -9.245 N 37.826 -4.630 -8.992 H 37.090 -4.246 -8.395 C 37.588 -5.946 -9.571 H 38.527 -6.269 -10.038 C 36.484 -5.985 -10.601 O 35.982 -7.087 -10.947 N 36.122 -4.811 -11.154 H 36.497 -3.974 -10.723 C 35.068 -4.721 -12.150 C 32.024 -5.535 -9.889 N 31.630 -6.873 -9.442 H 32.335 -7.610 -9.596 C 30.649 -7.091 -8.567 N 29.948 -6.070 -8.046 H 30.466 -5.203 -7.900 H 29.354 -6.264 -7.229 N 30.259 -8.361 -8.293 H 30.737 -9.113 -8.789 H 30.040 -8.546 -7.317 C 28.805 -1.783 -5.986 C 30.046 -0.971 -5.877 N 31.173 -1.316 -5.125 C 32.066 -0.357 -5.310 H 33.065 -0.326 -4.902 N 31.580 0.598 -6.146 H 32.103 1.392 -6.479 C 30.296 0.221 -6.513 H 29.681 0.804 -7.180 C 29.898 -2.750 -0.436 C 29.889 -2.220 -1.872 C 29.040 -3.154 -2.753 O 29.658 -3.637 -3.800 O 27.844 -3.391 -2.487 O 31.214 -2.166 -2.357 C 29.286 -0.814 -1.932 H 28.242 -0.825 -1.597 H 29.877 -0.150 -1.288 C 41.012 -9.425 -2.744 H 41.769 -8.478 -6.609 H 43.464 -8.519 -6.058 H 42.632 -6.957 -6.259 H 32.742 -5.667 -10.702 H 32.520 -4.963 -9.090 H 31.151 -4.987 -10.259 H 28.116 -1.304 -6.692

H 28.291 -1.903 -5.026 H 29.029 -2.795 -6.343 H 29.337 -0.430 -2.959 H 39.349 -8.987 -1.439 H 41.620 -8.772 -2.109 H 41.228 -10.465 -2.469 H 39.194 -8.291 -3.072 H 30.372 -3.739 -0.402 H 28.875 -2.827 -0.050 H 30.483 -2.064 0.190 H 37.330 -6.684 -8.798 H 35.432 -4.226 -13.056 H 34.212 -4.160 -11.758 H 34.761 -5.740 -12.398 H 38.503 -11.881 -6.601 H 41.049 -6.155 0.911 H 35.501 0.001 -7.750 H 37.932 -6.810 5.207 H 38.095 -7.603 3.629 H 36.489 -7.347 4.332 H 38.377 -5.073 3.409 H 36.756 -4.842 4.076 H 36.944 -5.639 2.512 H 41.661 -6.498 -1.646 O 31.800 -10.315 -9.902 H 32.507 -9.780 -10.317 H 32.073 -11.235 -10.016 O 28.885 -6.117 -5.240 H 29.680 -6.604 -4.981 H 28.976 -5.254 -4.787 O 32.640 -10.654 -7.133 H 32.293 -10.346 -7.985 H 32.556 -9.889 -6.537 O 33.787 -8.577 -10.261 H 34.514 -8.016 -10.622 H 34.252 -9.157 -9.621 O 34.970 -10.571 -8.673 H 34.295 -10.705 -7.978 H 35.538 -9.889 -8.281 C 31.282 -8.037 3.975 C 31.752 -8.374 2.583 O 30.983 -8.360 1.632 N 33.063 -8.692 2.458 H 33.660 -8.653 3.276 C 33.710 -8.957 1.167 H 32.997 -8.650 0.391 C 34.975 -8.101 0.998 H 35.690 -8.349 1.811 C 35.617 -8.393 -0.358 H 34.940 -8.103 -1.173 H 36.530 -7.800 -0.497 H 35.873 -9.451 -0.503 C 34.603 -6.622 1.131 H 34.297 -6.363 2.154 H 35.443 -5.983 0.836 H 33.782 -6.369 0.444 C 33.880 -10.472 1.032 O 33.017 -11.173 0.521 N 34.997 -10.990 1.590 H 35.724 -10.357 1.895 C 35.286 -12.417 1.574 C 29.601 -7.466 -1.094 N 30.562 -8.119 -1.990 H 30.983 -7.556 -2.730 C 31.153 -9.277 -1.726 N 30.668 -10.110 -0.772 H 30.038 -9.675 -0.108 H 31.391 -10.663 -0.304 N 32.248 -9.643 -2.412 H 32.459 -9.152 -3.290

H 32.562 -10.598 -2.328 C 27.466 -12.000 -1.778 C 27.716 -11.314 -0.463 O 27.410 -10.140 -0.290 N 28.326 -12.042 0.502 H 28.591 -11.560 1.362 H 28.606 -12.999 0.354 O 28.592 -9.729 2.210 H 27.971 -9.589 1.474 H 29.305 -9.092 2.044 H 30.428 -8.678 4.225 H 30.921 -7.003 3.980 H 32.052 -8.148 4.745 H 28.238 -11.673 -2.485 H 26.500 -11.678 -2.174 H 27.494 -13.093 -1.713 H 34.355 -12.949 1.369 H 35.678 -12.736 2.544 H 36.011 -12.670 0.792 H 29.308 -6.524 -1.565 H 30.056 -7.252 -0.123 H 28.701 -8.081 -0.974 E0 - Mo4+4Fe2+3Fe3+ (S=3/2) – M06-2X Fe 37.486 -8.243 -5.690 Fe 36.242 -6.108 -3.705 Fe 34.325 -7.567 -5.227 Fe 35.975 -5.581 -6.601 Fe 33.814 -4.041 -5.723 Fe 34.049 -4.639 -2.814 Fe 31.537 -6.136 -4.619 S 38.012 -5.780 -5.228 S 33.685 -2.458 -3.908 S 35.950 -8.427 -3.702 S 36.087 -4.985 -1.710 S 34.883 -3.817 -7.727 S 31.714 -4.955 -2.449 S 35.621 -7.952 -7.241 S 31.466 -4.150 -6.038 S 32.153 -8.362 -4.966 Mo 31.303 -2.935 -3.893 C 34.570 -5.654 -4.798 C 37.387 -5.536 3.511 C 37.484 -6.901 4.210 C 40.411 -5.910 0.080 N 40.922 -6.154 -1.202 C 40.052 -5.703 -2.126 H 40.169 -5.789 -3.199 N 39.028 -5.171 -1.474 H 38.103 -4.862 -1.868 C 39.210 -5.295 -0.112 H 38.464 -4.950 0.581 C 37.895 -10.983 -6.749 H 36.926 -10.978 -6.246 H 37.769 -10.635 -7.773 S 39.122 -9.925 -5.862 C 42.505 -7.998 -5.954 C 42.118 -8.060 -4.483 O 42.261 -7.088 -3.711 N 41.669 -9.257 -4.038 H 41.328 -9.915 -4.730 C 39.742 -9.208 -2.410 O 38.989 -10.391 -2.626 H 38.790 -10.435 -3.579 N 35.268 -0.459 -7.017 H 34.778 -1.278 -7.381 C 36.429 -1.000 -6.294 H 36.923 -0.192 -5.742 H 36.089 -1.739 -5.562 C 37.462 -1.602 -7.244

36

O 37.674 -1.071 -8.359 N 38.169 -2.675 -6.810 H 37.892 -3.167 -5.970 C 39.339 -3.163 -7.517 H 39.730 -2.337 -8.119 H 40.098 -3.469 -6.794 C 39.161 -4.357 -8.448 O 40.164 -5.024 -8.763 N 37.916 -4.611 -8.943 H 37.132 -4.127 -8.510 C 37.690 -5.887 -9.613 H 38.645 -6.203 -10.040 C 36.660 -5.896 -10.718 O 36.348 -7.005 -11.235 N 36.122 -4.743 -11.138 H 36.342 -3.902 -10.618 C 35.068 -4.721 -12.150 C 32.024 -5.535 -9.889 N 31.956 -6.935 -9.462 H 32.763 -7.519 -9.736 C 31.183 -7.361 -8.467 N 30.350 -6.506 -7.838 H 30.647 -5.537 -7.749 H 29.850 -6.835 -7.015 N 31.123 -8.672 -8.154 H 31.737 -9.315 -8.666 H 31.051 -8.865 -7.152 C 28.805 -1.783 -5.986 C 30.073 -1.032 -6.200 N 31.167 -1.216 -5.363 C 32.164 -0.484 -5.837 H 33.174 -0.437 -5.462 N 31.756 0.177 -6.948 H 32.353 0.766 -7.503 C 30.431 -0.159 -7.194 H 29.877 0.222 -8.032 C 29.445 -2.717 -0.607 C 29.089 -2.361 -2.052 C 28.645 -3.630 -2.811 O 29.309 -3.846 -3.922 O 27.733 -4.363 -2.390 O 30.236 -1.827 -2.722 C 27.972 -1.313 -2.083 H 27.069 -1.724 -1.624 H 28.299 -0.431 -1.527 C 41.242 -9.442 -2.654 H 42.121 -8.855 -6.509 H 43.596 -7.963 -6.028 H 42.099 -7.084 -6.392 H 32.498 -5.515 -10.870 H 32.624 -4.931 -9.195 H 31.014 -5.121 -9.972 H 28.028 -1.413 -6.660 H 28.459 -1.681 -4.957 H 28.956 -2.851 -6.167 H 27.747 -1.009 -3.108 H 39.585 -8.916 -1.365 H 41.850 -8.765 -2.049 H 41.472 -10.468 -2.354 H 39.385 -8.383 -3.047 H 30.247 -3.460 -0.586 H 28.563 -3.123 -0.103 H 29.783 -1.814 -0.093 H 37.386 -6.676 -8.911 H 35.452 -4.365 -13.109 H 34.260 -4.067 -11.817 H 34.699 -5.738 -12.272 H 38.261 -12.011 -6.773 H 40.938 -6.189 0.971 H 35.656 -0.015 -7.849

H 37.956 -6.813 5.192 H 38.073 -7.606 3.616 H 36.490 -7.335 4.355 H 38.379 -5.093 3.374 H 36.790 -4.833 4.097 H 36.914 -5.632 2.530 H 41.781 -6.607 -1.493 O 32.884 -10.581 -9.519 H 33.372 -9.867 -9.969 H 33.634 -11.108 -9.159 O 29.338 -6.269 -4.859 H 28.879 -6.817 -4.212 H 29.141 -5.327 -4.577 O 32.939 -11.155 -6.490 H 32.699 -10.784 -7.351 H 32.831 -10.411 -5.877 O 34.298 -8.297 -10.082 H 34.999 -7.941 -10.674 H 34.709 -8.232 -9.194 O 35.134 -11.360 -8.166 H 34.639 -11.433 -7.330 H 35.474 -10.452 -8.132 C 31.227 -8.151 3.984 C 31.752 -8.374 2.583 O 31.032 -8.216 1.605 N 33.046 -8.741 2.481 H 33.606 -8.825 3.318 C 33.710 -8.963 1.194 H 32.999 -8.667 0.420 C 34.961 -8.084 1.037 H 35.670 -8.310 1.856 C 35.620 -8.355 -0.318 H 34.945 -8.072 -1.131 H 36.518 -7.746 -0.450 H 35.891 -9.406 -0.473 C 34.553 -6.608 1.155 H 34.224 -6.352 2.167 H 35.380 -5.958 0.861 H 33.735 -6.389 0.457 C 33.905 -10.475 1.052 O 33.038 -11.198 0.571 N 35.032 -10.981 1.588 H 35.783 -10.353 1.835 C 35.286 -12.417 1.574 C 29.601 -7.466 -1.094 N 30.858 -7.974 -1.635 H 31.450 -7.303 -2.116 C 31.343 -9.183 -1.415 N 30.649 -10.088 -0.679 H 29.975 -9.693 -0.034 H 31.250 -10.779 -0.237 N 32.548 -9.514 -1.924 H 32.776 -9.099 -2.835 H 32.839 -10.473 -1.801 C 27.466 -12.000 -1.778 C 27.692 -11.182 -0.530 O 27.417 -9.987 -0.494 N 28.251 -11.821 0.524 H 28.483 -11.268 1.348 H 28.487 -12.798 0.485 O 28.563 -9.395 1.985 H 27.976 -9.232 1.228 H 29.308 -8.780 1.877 H 30.315 -8.739 4.113 H 30.958 -7.097 4.090 H 31.943 -8.417 4.762 H 28.301 -11.814 -2.461 H 26.551 -11.662 -2.263 H 27.407 -13.072 -1.581 H 34.357 -12.942 1.792

H 36.030 -12.661 2.332 H 35.647 -12.748 0.594 H 29.393 -6.508 -1.575 H 29.683 -7.296 -0.020 H 28.783 -8.162 -1.304 E0 - Mo4+4Fe2+3Fe3+ (S=3/2) – PBE Fe 36.919 -7.903 -5.790 Fe 35.984 -6.227 -3.837 Fe 34.309 -7.527 -5.349 Fe 35.693 -5.564 -6.342 Fe 33.855 -3.952 -5.667 Fe 34.150 -4.579 -3.199 Fe 32.504 -5.841 -4.732 S 37.688 -5.744 -5.310 S 34.096 -2.514 -3.948 S 35.690 -8.497 -3.935 S 35.889 -5.087 -1.938 S 34.954 -3.897 -7.561 S 32.142 -5.317 -2.581 S 35.360 -7.560 -7.339 S 31.731 -4.300 -6.164 S 32.110 -7.934 -5.394 Mo 31.847 -3.376 -3.978 C 34.432 -5.630 -4.859 C 37.387 -5.536 3.511 C 37.484 -6.901 4.210 C 40.411 -5.910 0.080 N 40.682 -6.105 -1.290 C 39.648 -5.606 -2.022 H 39.539 -5.652 -3.105 N 38.752 -5.084 -1.169 H 37.726 -4.831 -1.469 C 39.191 -5.268 0.135 H 38.607 -4.938 0.986 C 37.895 -10.983 -6.749 H 37.032 -11.263 -6.125 H 37.563 -10.881 -7.793 S 38.650 -9.393 -6.149 C 42.505 -7.998 -5.954 C 42.079 -8.090 -4.480 O 42.433 -7.238 -3.611 N 41.362 -9.210 -4.162 H 40.824 -9.651 -4.920 C 39.461 -9.475 -2.517 O 38.746 -10.547 -3.151 H 38.565 -10.225 -4.075 N 35.208 -0.394 -6.869 H 34.635 -1.189 -7.181 C 36.429 -1.000 -6.294 H 36.946 -0.251 -5.660 H 36.150 -1.847 -5.648 C 37.422 -1.431 -7.387 O 37.546 -0.732 -8.442 N 38.198 -2.539 -7.153 H 37.953 -3.171 -6.386 C 39.278 -2.921 -8.062 H 39.416 -2.063 -8.744 H 40.216 -3.070 -7.499 C 39.104 -4.179 -8.931 O 40.110 -4.637 -9.545 N 37.845 -4.713 -9.037 H 37.134 -4.412 -8.354 C 37.648 -6.032 -9.649 H 38.596 -6.293 -10.153 C 36.502 -6.072 -10.657 O 35.955 -7.173 -10.996 N 36.159 -4.874 -11.197 H 36.578 -4.055 -10.755 C 35.068 -4.721 -12.150

37

C 32.024 -5.535 -9.889 N 31.565 -6.882 -9.526 H 32.261 -7.638 -9.692 C 30.566 -7.091 -8.646 N 29.931 -6.047 -8.057 H 30.538 -5.248 -7.813 H 29.325 -6.252 -7.239 N 30.082 -8.357 -8.460 H 30.542 -9.117 -8.979 H 29.813 -8.583 -7.501 C 28.805 -1.783 -5.986 C 30.093 -1.022 -5.921 N 31.239 -1.412 -5.202 C 32.165 -0.468 -5.411 H 33.185 -0.470 -5.044 N 31.677 0.513 -6.232 H 32.219 1.299 -6.573 C 30.366 0.178 -6.566 H 29.749 0.792 -7.212 C 30.006 -2.912 -0.473 C 29.969 -2.314 -1.899 C 29.104 -3.230 -2.809 O 29.745 -3.745 -3.853 O 27.883 -3.446 -2.569 O 31.305 -2.234 -2.410 C 29.355 -0.896 -1.889 H 28.308 -0.936 -1.543 H 29.946 -0.250 -1.217 C 40.975 -9.550 -2.788 H 41.762 -8.471 -6.617 H 43.476 -8.507 -6.082 H 42.623 -6.942 -6.237 H 32.615 -5.622 -10.812 H 32.663 -5.083 -9.107 H 31.156 -4.882 -10.079 H 28.137 -1.320 -6.732 H 28.279 -1.806 -5.017 H 28.979 -2.834 -6.269 H 29.387 -0.465 -2.903 H 39.297 -9.575 -1.427 H 41.530 -8.866 -2.123 H 41.307 -10.583 -2.574 H 39.058 -8.491 -2.835 H 30.517 -3.889 -0.491 H 28.980 -3.043 -0.088 H 30.571 -2.234 0.191 H 37.441 -6.798 -8.882 H 35.413 -4.206 -13.063 H 34.236 -4.144 -11.711 H 34.719 -5.730 -12.416 H 38.660 -11.774 -6.685 H 41.098 -6.224 0.856 H 35.525 0.052 -7.742 H 37.964 -6.815 5.201 H 38.075 -7.619 3.613 H 36.483 -7.341 4.366 H 38.389 -5.090 3.371 H 36.793 -4.820 4.105 H 36.903 -5.623 2.524 H 41.484 -6.562 -1.751 O 31.650 -10.321 -9.995 H 32.419 -9.792 -10.349 H 31.847 -11.249 -10.227 O 28.998 -6.207 -5.279 H 29.886 -6.591 -5.114 H 29.062 -5.329 -4.824 O 32.510 -10.723 -7.219 H 32.111 -10.476 -8.084 H 32.432 -9.907 -6.669 O 33.712 -8.689 -10.282

H 34.440 -8.132 -10.673 H 34.200 -9.274 -9.623 O 34.893 -10.426 -8.584 H 34.134 -10.611 -7.964 H 35.397 -9.732 -8.104 C 31.350 -7.846 3.954 C 31.752 -8.374 2.583 O 30.907 -8.578 1.698 N 33.080 -8.606 2.402 H 33.719 -8.387 3.166 C 33.694 -8.945 1.102 H 32.968 -8.665 0.321 C 34.980 -8.096 0.910 H 35.663 -8.303 1.773 C 35.697 -8.472 -0.398 H 35.049 -8.290 -1.271 H 36.589 -7.842 -0.547 H 36.009 -9.530 -0.426 C 34.614 -6.597 0.950 H 34.175 -6.300 1.918 H 35.501 -5.976 0.752 H 33.897 -6.351 0.147 C 33.873 -10.477 0.991 O 33.051 -11.201 0.407 N 34.967 -10.991 1.614 H 35.666 -10.346 1.981 C 35.286 -12.417 1.574 C 29.601 -7.466 -1.094 N 30.521 -8.076 -2.070 H 30.944 -7.448 -2.764 C 31.157 -9.242 -1.870 N 30.738 -10.113 -0.901 H 30.170 -9.681 -0.174 H 31.504 -10.662 -0.480 N 32.218 -9.568 -2.643 H 32.353 -9.043