Trinuclear and Tetranuclear Ruthenium Carbonyl Nitrosyls: Oxidation of a Carbonyl Ligand by an Adjacent Nitrosyl Ligand

Trinuclear and tetranuclear ruthenium carbonyls of the types Ru3(CO)n(NO)2, Ru3(N)(CO)n(NO), Ru3(N)2(CO)n, Ru3(N)(CO)n(NCO), Ru3(CO)n(NCO)(NO), Ru4(N)(CO)n(NO), Ru4(N)(CO)n(NCO), and Ru4(N)2(CO)n related to species observed experimentally in the chemistry of Ru3(CO)10(µ-NO)2 have been investigated using density functional theory. In all cases, the experimentally observed structures have been found to be low-energy structures. The low-energy trinuclear structures typically have a central strongly bent Ru–Ru–Ru chain with terminal CO groups and bridging nitrosyl, isocyanate, and/or nitride ligands across the end of the chain. The low-energy tetranuclear structures typically have a central Ru4N unit with terminal CO groups and a non-bonded pair of ruthenium atoms bridged by a nitrosyl or isocyanate group.


Introduction
A noteworthy feature of the chemistry of ruthenium is its propensity to form a variety of nitrosyl derivatives.The experimental approach to the subset of such ruthenium nitrosyl derivatives also containing carbonyl ligands starts with the trinuclear derivative Ru 3 (CO) 10 (µ-NO) 2 , itself obtained from the reaction of Ru 3 (CO) 12 with nitric oxide in boiling benzene (Figure 1) [1].The replacement of two terminal carbonyl groups in Ru 3 (CO) 12 with two bridging nitrosyl groups in Ru 3 (CO) 10 (µ-NO) 2 , donating two "extra" electrons to the central Ru 3 triangle, lengthens one of the three Ru-Ru bonds in the original equilateral triangle Ru 3 (CO) 12 structure to a non-bonding distance of 3.18 Å.As a result, in the Ru 3 (CO) 10 (µ-NO) 2 structure, the two nitrosyl groups, as bridges across the non-bonding Ru• • • Ru distance, contribute to holding together the isosceles Ru 3 triangle.This weaker bonding in the Ru 3 triangle in Ru 3 (CO) 10 (µ-NO) 2 relative to that in the Ru 3 triangle in Ru 3 (CO) 12 makes the former Ru 3 triangle more susceptible to rupture and rearrangement.Thus, the decomposition of Ru 3 (CO) 10 (µ-NO) 2 at 110 • C in an atmosphere of CO leads to the disruption of the Ru 3 triangle with rearrangement to the tetranuclear derivatives Ru 4 (µ 4 -N)(CO) 12 (µ-NO) and Ru 4 (µ 4 -N)(CO) 12 (µ-NCO), as well as the trinuclear derivative Ru 3 (CO) 10 (µ-NO)(µ-NCO) (Figure 2) [2].
The presence of nitride ligands bridging all four ruthenium atoms in the tetranuclear ruthenium carbonyl nitrosyl derivatives formed in the decomposition of Ru 3 (CO) 10 (µ-NO) 2 (Figure 2) suggests that the reduction of an NO group by an adjacent CO group is occurring during the decomposition process.Our density functional theory studies of possible internal such redox processes in trinuclear Ru 3 (CO) 10 (µ-NO) 2 leading to an N 2 O complex Ru 3 (CO) 9 (µ 3 -N 2 O) and finally a dinitrogen complex Ru 3 (CO) 8 (µ 3 -N 2 ) were presented in a previous short communication [3].Here, we present similar density functional theory studies on a wider range of trinuclear and tetranuclear ruthenium carbonyl structures also containing nitrosyl ligands including the reduction of nitrosyl ligands by adjacent CO groups to give, N 2 O and nitride ligands.These include examples of structures with functional theory studies on a wider range of trinuclear and tetranuclear ruthenium carbonyl structures also containing nitrosyl ligands including the reduction of nitrosyl ligands by adjacent CO groups to give, N2O and nitride ligands.These include examples of structures with five-electron donor bridging η 2 -µ3-NO ligands bonded to ruthenium atoms through both their nitrogen and oxygen atoms as well as structures containing the usual three-electron donor NO groups.

Trinuclear Ru3(NO)2(CO)n Derivatives
The optimized geometries are depicted in Figures 3-14 with all bond lengths in Å.All structures are in singlet state.The structures are designated by the labels x-A-y-z or x-A-y, where x is the number of ruthenium atoms, A is the nitrogen-containing group, y is the number of carbonyl groups, and z orders the isomeric structures (if any) by their relative energies.For example, the singlet global minimum of Ru3(CO)10(NO)2 is designated as 3-(NO)2-10-1.

Ru3(CO)10(NO)2
Two low-energy Ru3(CO)10(NO)2 singlet structures were found (Figure 3).The lowest-energy Ru3(CO)10(NO)2 structure, 3-(NO)2-10-1, is the experimental C2v structure with two bridging NO groups leading to coplanar Ru2NO units.The dihedral angles for the bending of the two Ru2N planes in the central Ru2(µ-NO)2 units in 3-(NO)2-10-1 are 156.6°(mPW1PW91) or 157.4° (BP86).The ν(NO) frequencies in 3-(NO)2-10-1 are 1557 and 1572 cm -1 (BP86) (Table S1 in Supporting Information) as compared with the experimental values [1] of 1500 and 1517 cm -1 and consistent with their bridging positions.The Ru-Ru distances of 3.178 Å (mPW1PW91) or 3.226 Å (BP86) indicate no bond between the two ruthenium atoms in the Ru2(µ-NO)2 units, consistent with the low WBI value of 0.12 (Table S42 in the Supporting Information).The other Ru-Ru distances of 2.888 Å (mPW1PW91) or 2.953 Å (BP86), with WBI values of ~0.3 in the typical range for formal single bonds between d-block metals, correspond to the formal single bond required to give each ruthenium atom the favored 18-electron configuration, since the NO ligands each donate three electrons to the central Ru2 unit.functional theory studies on a wider range of trinuclear and tetranuclear ruthenium carbonyl structures also containing nitrosyl ligands including the reduction of nitrosyl ligands by adjacent CO groups to give, N2O and nitride ligands.These include examples of structures with five-electron donor bridging η 2 -µ3-NO ligands bonded to ruthenium atoms through both their nitrogen and oxygen atoms as well as structures containing the usual three-electron donor NO groups.

Trinuclear Ru3(NO)2(CO)n Derivatives
The optimized geometries are depicted in Figures 3-14 with all bond lengths in Å.All structures are in singlet state.The structures are designated by the labels x-A-y-z or x-A-y, where x is the number of ruthenium atoms, A is the nitrogen-containing group, y is the number of carbonyl groups, and z orders the isomeric structures (if any) by their relative energies.For example, the singlet global minimum of Ru3(CO)10(NO)2 is designated as 3-(NO)2-10-1.

Trinuclear Ru 3 (NO) 2 (CO) n Derivatives
The optimized geometries are depicted in Figures 3-14 with all bond lengths in Å.All structures are in singlet state.The structures are designated by the labels x-A-y-z or x-A-y, where x is the number of ruthenium atoms, A is the nitrogen-containing group, y is the number of carbonyl groups, and z orders the isomeric structures (if any) by their relative energies.For example, the singlet global minimum of Ru 3 (CO) 10 (NO) 2 is designated as 3-(NO) 2 -10-1.

Ru 3 (CO) 10 (NO) 2
Two low-energy Ru 3 (CO) 10 (NO) 2 singlet structures were found (Figure 3).The lowestenergy Ru 3 (CO) 10 S1 in Supporting Information) as compared with the experimental values [1] of 1500 and 1517 cm −1 and consistent with their bridging positions.The Ru-Ru distances of 3.178 Å (mPW1PW91) or 3.226 Å (BP86) indicate no bond between the two ruthenium atoms in the Ru 2 (µ-NO) 2 units, consistent with the low WBI value of 0.12 (Table S42 in the Supporting Information).The other Ru-Ru distances of 2.888 Å (mPW1PW91) or 2.953 Å (BP86), with WBI values of ~0.3 in the typical range for formal single bonds between d-block metals, correspond to the formal single bond required to give each ruthenium atom the favored 18-electron configuration, since the NO ligands each donate three electrons to the central Ru 2 unit.The single low-energy Ru3(CO)9(NO)2 singlet structure 3-(NO)2-9 is a Cs structure with two bridging NO groups, leading to essentially coplanar Ru2(NO)2 units with dihedral angles for the bending of the two Ru2N2 planes of 175.8° (mPW1PW91) or 176.6° (BP86), close to the 180° indicative of coplanarity (Figure 4).One of the bridging NO groups in 3-(NO)2-9 is a five-electron donor η 2 -µ3-NO group bonding to two ruthenium atoms through its nitrogen atom with Ru-N distances of 2.036 Å (mPW1PW91) or 2.071 Å (BP86) and to the third ruthenium atom through its oxygen atom with a Ru-O distance of 2.216Å (mPW1PW91) or 2.261 Å (BP86).This η 2 -µ3-NO group has a relatively long N-O distance of 1.294 Å (mPW1PW91) or 1.310 Å (BP86), consistent with its very low ν(NO) frequency of 1200 cm -1 .For comparison, the other NO group in 3-(NO)2-9 is a typical threeelectron donor bridging µ-NO group with a more typical nitrosyl N-O distance of 1.204 Å (mPW1PW91) or 1.222 Å (BP86) and a more typical bridging ν(NO) frequency of 1571 cm -1 .The Ru … Ru distance of 3.296 Å (mPW1PW91) or 3.353 Å (BP86) in 3-(NO)2-9 with a low WBI value of 0.08 similar to that in the Ru3(CO)10(µ-NO)2 structure 3-(NO)2-10-1 indicates no direct bond between the two ruthenium atoms in the Ru2(NO)2 unit.The other Ru-Ru distances of 2.780 Å (mPW1PW91) or 2.829 Å (BP86) with WBI values of ~0.35 correspond to formal single bonds.In 3-(NO)2-9, the combination of two rather than three Ru-Ru bonds in the Ru3 triangle, one three-electron donor µ-NO group, one five-electron donor η 2 -µ3-NO group, and the nine terminal CO groups give each of the ruthenium atoms the favored 18-electron configuration.
The single low-energy Ru3(CO)8(NO)2 octacarbonyl structure 3-(NO)2-8 is a singlet C2v structure with two µ3-NO groups bridging all three ruthenium atoms and two µ-CO  3).This leads to a bridging NOCO group well situated for CO 2 elimination. 3The Ru 2 NO units remain coplanar in The single low-energy Ru 3 (CO) 9 (NO) 2 singlet structure 3-(NO) 2 -9 is a C s structure with two bridging NO groups, leading to essentially coplanar Ru 2 (NO) 2 units with dihedral angles for the bending of the two Ru 2 N 2 planes of 175.8 • (mPW1PW91) or 176.6 • (BP86), close to the 180 • indicative of coplanarity (Figure 4).One of the bridging NO groups in 3-(NO) 2 -9 is a five-electron donor η 2 -µ 3 -NO group bonding to two ruthenium atoms through its nitrogen atom with Ru-N distances of 2.036 Å (mPW1PW91) or 2.071 Å (BP86) and to the third ruthenium atom through its oxygen atom with a Ru-O distance of 2.216Å (mPW1PW91) or 2.261 Å (BP86).This η 2 -µ 3 -NO group has a relatively long N-O distance of 1.294 Å (mPW1PW91) or 1.310 Å (BP86), consistent with its very low ν(NO) frequency of 1200 cm −1 .For comparison, the other NO group in 3-(NO) 2 -9 is a typical three-electron donor bridging µ-NO group with a more typical nitrosyl N-O distance of 1.204 Å (mPW1PW91) or 1.222 Å (BP86) and a more typical bridging ν(NO) frequency of 1571 cm −1 .The Ru• • • Ru distance of 3.296 Å (mPW1PW91) or 3.353 Å (BP86) in 3-(NO) 2 -9 with a low WBI value of 0.08 similar to that in the Ru 3 (CO) 10 (µ-NO) 2 structure 3-(NO) 2 -10-1 indicates no direct bond between the two ruthenium atoms in the Ru 2 (NO) 2 unit.The other Ru-Ru distances of 2.780 Å (mPW1PW91) or 2.829 Å (BP86) with WBI values of ~0.35 correspond to formal single bonds.In 3-(NO) 2 -9, the combination of two rather than three Ru-Ru bonds in the Ru 3 triangle, one three-electron donor µ-NO group, one five-electron donor η 2 -µ 3 -NO group, and the nine terminal CO groups give each of the ruthenium atoms the favored 18-electron configuration.
The single low-energy Ru 3 (CO) 8 (NO) 2 octacarbonyl structure 3-(NO) 2 -8 is a singlet C 2v structure with two µ 3 -NO groups bridging all three ruthenium atoms and two µ-CO groups, each bridging an Ru-Ru bonding edge of length 2.681 Å (mPW1PW91) or 2.716 Å (BP86) with a WBI value of 0.21 (Figure 4).The dihedral angles for the bending of the two Ru 2 N planes in the central Ru

Trinuclear Ru 3 (N)(CO) n (NO) Derivatives Arising from CO 2 Loss from Ru 3 (CO) n (NO) 2 Derivatives
The lowest-energy structure 3-NNO-10 of the decacarbonyl is actually an Ru 3 (µ-CO)(CO) 9 (µ-N 2 O) structure with a bent N 2 O ligand bridging the ends of a bent Ru-Ru-Ru chain through Ru-N bonds to its terminal nitrogen atom (Figure 5).One of the

Trinuclear Ru3(N)(CO)n(NO) Derivatives Arising from CO2 Loss from Ru3(CO)n(NO)2 Derivatives
The lowest-energy structure 3-NNO-10 of the decacarbonyl is actually an Ru3(µ-CO)(CO)9(µ-N2O) structure with a bent N2O ligand bridging the ends of a bent Ru-Ru-Ru chain through Ru-N bonds to its terminal nitrogen atom (Figure 5).One of the carbonyl groups in 3-NNO-10 bridges a Ru-Ru bond in the Ru3 chain, exhibiting a ν(CO) frequency of 1929 cm -1 , significantly lower than any of the terminal ν(CO) frequencies.The bridging bent µ-N2O ligand has a single-bond N-N distance of 1.378 Å (mPW1PW91) or 1.407 Å (BP86), a double-bond N=O distance of 1.208 Å (mPW1PW91) or 1.226 Å (BP86), and an N-N-O angle of 116.8°(mPW1PW91) or 117.0° (BP86).This bridging µ-N2O ligand functions as a four-electron donor using two lone pairs of the nitrogen atom in the Ru-N-Ru bridge.This gives the two end ruthenium atoms of the Ru-Ru-Ru chain in 3-NNO-10 the favored 18-electron configuration, but the central ruthenium atom only retains a 16electron configuration.
elimination of another CO2 molecule yielding 3-N2-8, since it has a bent NNO group with its oxygen atom close to the top ruthenium atom.

Trinuclear Dinitrogen Complexes Ru3N2(CO)n (n = 10, 9, 8) Arising Formally by Double CO2 Loss from Ru3(CO)n(NO)2 Trinuclear Derivatives
The lowest-energy Ru3N2(CO)10 structure 3-NN-10 is a Cs structure having a central bent Ru3 unit with Ru-Ru distances of 2.911 Å (mPW1PW91) or 2.950 Å (BP86), corresponding to WBI values of 0.31 and thus a formal single bond and a Ru-Ru-Ru angle of 96.5° (mPW1PW91) or 98.9° (BP86) (Figure 7).Both Ru-Ru bonds are bridged by carbonyl groups exhibiting ν(CO) frequencies of 1864 and 1838 cm -1 , significantly lower than the ν(CO) frequencies of the eight terminal CO groups in the range from 2066 to 1960 cm -1 .The central ruthenium atom bears two terminal CO groups and a terminal dinitrogen ligand with a N≡N distance of 1.117 Å (mPW1PW91) or 1.139 Å (BP86), leading to the favored 18-electron configuration after considering the two Ru-Ru bonds, each bridged by a CO group.The terminal ruthenium atoms of the Ru-Ru-Ru chain each bear three terminal CO groups, thereby leading to 16-electron configurations.The lowest-energy Ru 3 N 2 (CO) 9 structure 3-NN-9 is a C s symmetry structure in which the dinitrogen unit bridges all three ruthenium atoms (Figure 7).The N-N distance in 3-NN-9 of 1.417 Å (mPW1PW91) or 1.446 Å (BP86) suggests a formal single bond using only one valence electron from each nitrogen atom.This makes the other eight valence electrons of the N 2 unit available for donation to the Ru 3 unit, thereby giving each ruthenium atom in 3-NN-9 the favored 18-electron configuration.The lowest-energy Ru 3 N 2 (CO) 8 structure 3-NN-8 is similar to that of 3-NN-9, except for one less CO group on the unique ruthenium atom, thereby giving that ruthenium atom only a 16-electron configuration.

Trinuclear Ruthenium Carbonyl Isocyanates Ru 3 (N)(CO) n (NCO) and Ru 3 (CO) n (NCO)(NO)
A terminal isocyanate group NCO, considered artificially as a neutral pseudohalogen ligand, is a one-electron donor like the halogens themselves.However, a neutral isocyanate group bridging a pair of metal atoms through its nitrogen atom is a three-electron donor similar to a bridging nitrosyl group.Such bridging isocyanate ligands are predicted consistently in polynuclear ruthenium carbonyl derivatives to exhibit a low ν(CO) frequency in the narrow range of 1310 ± 4 cm −1 (BP86).In the chemistry of trinuclear and tetranuclear ruthenium carbonyl isocyanate derivatives, an isocyanate ligand can arise by the carbonylation of a nitride ligand.
ruthenium atom in 3-NN-9 the favored 18-electron configuration.The lowest-energy Ru3N2(CO)8 structure 3-NN-8 is similar to that of 3-NN-9, except for one less CO group on the unique ruthenium atom, thereby giving that ruthenium atom only a 16-electron configuration.

Trinuclear Ruthenium Carbonyl Isocyanates Ru3(N)(CO)n(NCO) and Ru3(CO)n(NCO)(NO)
A terminal isocyanate group NCO, considered artificially as a neutral pseudohalogen ligand, is a one-electron donor like the halogens themselves.However, a neutral isocyanate group bridging a pair of metal atoms through its nitrogen atom is a threeelectron donor similar to a bridging nitrosyl group.Such bridging isocyanate ligands are predicted consistently in polynuclear ruthenium carbonyl derivatives to exhibit a low ν(CO) frequency in the narrow range of 1310 ± 4 cm -1 (BP86).In the chemistry of trinuclear and tetranuclear ruthenium carbonyl isocyanate derivatives, an isocyanate ligand can arise by the carbonylation of a nitride ligand.
The lowest-energy Ru3(N)(CO)8(NCO) structure, namely the Cs symmetry structure 3-NNCO-8, has the isocyanate ligand bridging two ruthenium atoms and the nitride ligand bridging all three ruthenium atoms (Figure 9).Structure 3-NNCO-8 can be derived The other structure, 3-NNCO-9-2, of similar energy to 3-NNCO-9-1, has two isocyanate ligands.It may be regarded as Ru 3 (CO) 8 (µ-NCO)(η 3 -µ 3 -NCO), in which the nitride ligand in 3-NNCO-9-1 has been carbonylated to form a second isocyanate ligand that uses all three of its atoms to bond to all three ruthenium atoms in the cluster (Figure 8).This latter isocyanate group, formally considered as neutral, is a five-electron donor to the Ru 3 system.
The lowest-energy Ru 3 (N)(CO) 7 (NCO) structure 3-NNCO-7 has a central bent Ru-Ru-Ru chain with the nitride ligand bridging all three ruthenium atoms (Figure 9).One of the edges of the Ru-Ru-Ru chain is bridged by the isocyanate group and the other edge by a CO group.its three-electron donor bridging NO group with a bridging three-electron donor NCO group.
its three-electron donor bridging NO group with a bridging three-electron donor NCO group.
The lowest-energy Ru3(N)(CO)7(NCO) structure 3-NNCO-7 has a central bent Ru-Ru-Ru chain with the nitride ligand bridging all three ruthenium atoms (Figure 9).One of the edges of the Ru-Ru-Ru chain is bridged by the isocyanate group and the other edge by a CO group.The lowest-energy Ru3(NO)(CO)10(NCO) structure 3-NONCO-10 is closely related to the experimental Ru3(CO)10(µ-NO)2 structure [1] by the replacement of one of the bridging µ-NO groups with a bridging µ-NCO group (Figure 10).The bridging ν(NO) frequency of 1564 cm -1 in 3-NONCO-10 is essentially the mean of the bridging ν(NO) frequencies of 1572 and 1557 cm -1 in the experimental Ru3(µ-NO)2(CO)10 structure 3-(NO)2-10-1.A Ru3(CO)10(NCO)(NO) derivative exhibiting a bridging µ(NO) frequency of 1507 cm -1 has been observed experimentally as a minor product from the decomposition of Ru3(CO)10(µ-NO)2 at 110 °C under 1 atm CO, but has not been structurally characterized [2].The lowest-energy Ru3(CO)9(NCO)(NO) structure 3-NONCO-9 can be derived from the Ru3(CO)10(µ-NCO)(µ-NO) structure 3-NONCO-10 by the removal of one CO group from the Ru(CO)4 unit (Figure 10).The NO group in 3-NONCO-9 remains a three-electron donor, as reflected by its ν(NO) frequency of 1525 cm -1 , but it bridges all three ruthenium atoms, thereby becoming a five-electron donor through two N→Ru dative bonds and one N-Ru single bond.In this way, each ruthenium atom in 3-NONCO-9 can retain the favored 18-electron configuration.The lowest-energy Ru 3 (CO) 9 (NCO)(NO) structure 3-NONCO-9 can be derived from the Ru 3 (CO) 10 (µ-NCO)(µ-NO) structure 3-NONCO-10 by the removal of one CO group from the Ru(CO) 4 unit (Figure 10).The NO group in 3-NONCO-9 remains a three-electron donor, as reflected by its ν(NO) frequency of 1525 cm −1 , but it bridges all three ruthenium atoms, thereby becoming a five-electron donor through two N→Ru dative bonds and one N-Ru single bond.In this way, each ruthenium atom in 3-NONCO-9 can retain the favored 18-electron configuration.

Tetranuclear Derivatives with Central Ru 4 N Units
The decomposition of Ru 3 (CO) 10 (µ-NO) 2 at 110 • C under a CO atmosphere yields two tetranuclear products, Ru 4 (µ 4 -N)(CO) 12 (µ-NO) and Ru 4 (µ 4 -N)(CO) 12 (µ-NCO), that have been structurally characterized by X-ray crystallography (Figures 11 and 12) [2].Both species are found to have a central Ru 4 butterfly unit capped by the nitrogen atom bridging all four ruthenium atoms.The nitrosyl or isocyanate ligand bridges the body of the butterfly and each ruthenium atom bears three CO terminal groups.Considering the bridging µ 4 -N nitride ligand as a donor of all five of its valence electrons and the bridging η 2 -NO or η 2 -NCO group as a three-electron donor, all four ruthenium atoms have the favored 18-electron configuration in these Ru 4 (µ 4 -N)(CO) 12 (µ-X) derivatives (X = NO, NCO).
The decarbonylation of the Ru4(µ4-N)(CO)12(µ-X) (X = NO, NCO) derivatives preserves the central capped butterfly Ru4(µ4-N) unit as well as the bridging X group in the low-energy structures (Figures 11 and 12).The electronic configurations of the

Thermochemistry
Table 1 shows the carbonyl dissociation energies of the Ru 3 (CO) n (NO) 2 (n = 10, 9, 8) derivatives.The dissociation of a carbonyl ligand is highly endothermic for Ru 3 (CO) n (NO) 2 (n = 10, 9) but only mildly endothermic for Ru 2 (CO) 8 (NO) 2 .This suggests the viability of the Ru 3 (CO) n (µ-NO) 2 (n = 10, 9) structures for CO dissociation and the possibility of easy CO dissociation from the Ru 3 (µ-CO) 2 (CO) 6 (µ 3 -NO) 2 structure.Table 2 shows the energies for other types of reactions involving the trinuclear ruthenium carbonyl nitrosyls, including their dissociation into smaller fragments.In general, such processes appear to be highly endothermic, suggesting the viability of the indicated trinuclear species.The one exception is possibly the same Ru 3 (CO) 8 (NO) 2 (3-(NO) 2 -8), being only slightly endothermic toward CO dissociation (Table 1) and also nearly being thermoneutral for dissociation into Ru 2 (CO) 6 and Ru 2 (CO) 2 (NO) 2 fragments, with the ruthenium atom in the latter species having the favored 18-electron configuration.

Theoretical Methods
This study uses two different DFT methods.The first DFT method is the BP86 method, which combines Becke's 1988 exchange functional (B) with Perdew's 1986 gradientcorrected correlation functional method (BP86) [4,5].The second method uses a newer generation functional, mPW1PW91, which combines the modified Perdew-Wang exchange functional with Perdew-Wang's 91 gradient correlation functional [6].This functional has been shown to be better for second-and third-row transition-metal compounds [7].
The geometries of all structures considered were fully optimized using both the MPW1PW91 and BP86 methods.The vibrational frequencies and the corresponding infrared intensities were determined analytically at the same levels.All of the predicted ν(CO) and ν(NO) frequencies discussed in this paper were obtained from the BP86 method, which were found to be close to the experimental results without scaling factors for the compounds containing transition metals [8].This concurrence may be accidental, since the theoretical vibrational frequencies predicted by BP86 are harmonic frequencies, whereas the experimental fundamental frequencies are anharmonic.All vibrational frequencies are given in the Supporting Information.The NBO analysis used the same DFT methods to provide information on the WBI values for the Ru-Ru interactions discussed in the manuscript (Table S42 of the Supporting Information) [9].
The Stuttgart-Dresden double-ζ (SDD) basis set with an effective core potential (ECP) was used for the ruthenium atoms [10,11].In this basis set, the 28 core electrons for the ruthenium atoms are replaced by ECP.Such an effective core approximation includes scalar relativistic contributions, which become significant for the heavy transition metal atoms.For the ruthenium atoms, our loosely contracted DZP basis set (14s11p6d/10s8p3d) uses the Wachters primitive set augmented by two sets of p functions and one set of d functions contracted following Hood et al. [12,13].
The all-electron double-ζ plus polarization (DZP) basis sets, namely, (9s5p1d/4s2p1d), are used for the carbon, oxygen, and nitrogen atoms.The basis sets are Huzinaga and Dunning's contracted double-ζ contraction sets [14,15] plus a set of spherical harmonic d polarization functions with the orbital exponents α d (C) = 0.75, α d (O) = 0.85, and α d (N) = 0.80.All of the computations were carried out with the Gaussian 09 program [16], in which the fine grid (75, 302) is the default for the numerical evaluation of the integrals.

Summary
The experimental Ru 3 (CO) 10 (µ-NO) 2 structure is shown to be a low-energy structure.The decarbonylation of Ru 3 (CO) 10 (µ-NO) is predicted to convert one of the three-electron donor µ-NO groups into a five-electron donor η 2 -µ 3 -NO group bridging all three ruthenium atoms.Further decarbonylation leads to a low-energy Ru 3 (µ-CO) 2 (CO) 6 (µ 3 -NO) 2 structure with two three-electron donor µ 3 -NO groups bridging all three ruthenium atoms and two µ-CO groups bridging the two Ru-Ru bonds.
The lowest-energy Ru 3 (N)(CO) 9 (NO) structure obtained by the loss of CO 2 from Ru 3 (µ-NO) 2 (CO) 10 has a bridging η 3 -µ 3 -N 2 O ligand but with an elongated N-N bond.A higher-energy Ru 3 (µ 3 -N)(CO) 9 (η 2 -µ-NO) isomer has a nitride ligand bridging all three ruthenium atoms and a five-electron donor η 2 -µ-NO group.The decarbonylation of these structures leads to low-energy Ru 3 (µ 3 N)(CO) n (µ-NO) (n = 8, 7) structures in which the nitride ligand bridges all three ruthenium atoms and the three-electron donor µ-NO ligand bridges only two of the ruthenium atoms.
The loss of two CO 2 units from Ru 3 (CO) 10 (µ-NO) 2 leads to a low-energy Ru 3 (CO) 8 (η 2 -µ 3 -N 2 ) species in which a dinitrogen ligand with an elongated N-N distance bridges all three ruthenium atoms.This type of bridging dinitrogen ligand is also found in the low-energy carbonyl-richer structure Ru 3 (CO) 9 (η 2 -µ 3 -N 2 ).
The carbonylation of a nitride ligand leads to an isocyanate ligand.An isocyanate ligand bridging two metal atoms through its nitrogen atom is a three-electron donor similar to an NO ligand bridging two metal atoms.The experimentally observed Ru 3 (CO) 10 (µ-NCO)(µ-NO), as a minor product from the decomposition of Ru 3 (µ-NO) 2 (CO) 10 , is found to be a low-energy structure.The decarbonylation of Ru 3 (CO) 10 (µ-NCO)(µ-NO) to give Ru 3 (CO) 9 (µ-NCO)(µ-NO) is predicted to preserve the central Ru 2 (µ-NCO)(µ-NO) unit.
3-(NO) 2 -10-2.In addition, the entire Ru 2 (µ-NO) 2 unit in 3-(NO) 2 -10-2 is nearly coplanar as indicated by their dihedral angles of 177.3 • (mPW1PW91) or 178.4 • (BP86), close to the 180 • for ideal planarity.The Ru• • • Ru distances of 3.306 Å (mPW1PW91) or 3.356 Å (BP86), with a low WBI value of 0.08, indicate no direct bond between the two ruthenium atoms in the Ru 2 (µ-NO) 2 unit.The other Ru-Ru distances of 2.806 Å (mPW1PW91) or 2.853 Å (BP86), with WBI values of ~0.3, correspond to formal single bonds, thereby giving each ruthenium atom the favored 18-electron configuration.The low ν(NO) frequency of 974 cm −1 in the NOCO group of 3-(NO) 2 -10-2 is consistent with a single N-O bond rather than the multiple bonds in separate NO ligands.The other ν(NO) frequency in 3-(NO) 2 -10-2 of 1581 cm −1 is close to the ν(NO) frequencies of 3-(NO) 2 -10-1 and in a typical region for bridging ν(NO) groups.2.1.2.Ru 3 (CO) n (NO) 2 (n = 9, 8, 7) 2 (µ 3 -NO) 2 units in 3-(NO) 2 -8 of 161.2 • (mPW1PW91) or 160.8 • (BP86) indicate significant deviations from non-planarity.The ν(NO) frequencies of 1435 and 1413 cm −1 for the two µ 3 -NO groups bridging all three ruthenium atoms in 3-(NO) 2 -8 are significantly lower than the ν(NO) frequencies of 1572 and 1557 cm −1 for the two µ-NO groups bridging Ru-Ru edges in the Ru 3 (CO) 10 (µ-NO) 2 structure 3-(NO) 2 -10-1.The two edge-bridging µ-CO groups in 3-(NO) 2 -8 exhibit ν(CO) frequencies of 1907 and 1858 cm −1 , which are significantly lower than the ν(CO) frequencies of the six terminal CO groups ranging from 2069 to 1983 cm −1 .The Ru• • • Ru distance of 3.383 Å (mPW1PW91) or 3.490 Å (BP86) in 3-(NO) 2 -8 with a low WBI value of 0.07 indicates no bond between the two ruthenium atoms in the Ru 2 (µ 3 -NO) 2 units.The other Ru-Ru distances of 2.681 Å (mPW1PW91) or 2.716 Å (BP86) in 3-(NO) 2 -8, with WBI values of 0.21, correspond to its formal single bonds.This configuration of the Ru-Ru bonds and the bonding of the CO and NO groups to the central Ru 3 unit in 3-(NO) 2 -8 leads to the favored 18-electron configuration for the two ruthenium atoms in the Ru 2 (µ 3 -NO) 2 unit, but only a 14-electron configuration for the unique third ruthenium atom.The latter ruthenium atom has a large vacancy in its coordination sphere consistent with its electronic configuration of four electrons less than the favorable 18-electron configuration.Molecules 2024, 29, x FOR PEER REVIEW 4 of 14 groups, each bridging an Ru-Ru bonding edge of length 2.681 Å (mPW1PW91) or 2.716 Å (BP86) with a WBI value of 0.21 (Figure 4).The dihedral angles for the bending of the two Ru2N planes in the central Ru2(µ3-NO)2 units in 3-(NO)2-8 of 161.2° (mPW1PW91) or 160.8° (BP86) indicate significant deviations from non-planarity.The ν(NO) frequencies of 1435 and 1413 cm -1 for the two µ3-NO groups bridging all three ruthenium atoms in 3-(NO)2-8 are significantly lower than the ν(NO) frequencies of 1572 and 1557 cm -1 for the two µ-NO groups bridging Ru-Ru edges in the Ru3(CO)10(µ-NO)2 structure 3-(NO)2-10-1.The two edge-bridging µ-CO groups in 3-(NO)2-8 exhibit ν(CO) frequencies of 1907 and 1858 cm -1 , which are significantly lower than the ν(CO) frequencies of the six terminal CO groups ranging from 2069 to 1983 cm -1 .The Ru … Ru distance of 3.383 Å (mPW1PW91) or 3.490 Å (BP86) in 3-(NO)2-8 with a low WBI value of 0.07 indicates no bond between the two ruthenium atoms in the Ru2(µ3-NO)2 units.The other Ru-Ru distances of 2.681 Å (mPW1PW91) or 2.716 Å (BP86) in 3-(NO)2-8, with WBI values of 0.21, correspond to its formal single bonds.This configuration of the Ru-Ru bonds and the bonding of the CO and NO groups to the central Ru3 unit in 3-(NO)2-8 leads to the favored 18-electron configuration for the two ruthenium atoms in the Ru2(µ3-NO)2unit, but only a 14-electron configuration for the unique third ruthenium atom.The latter ruthenium atom has a large vacancy in its coordination sphere consistent with its electronic configuration of four electrons less than the favorable 18-electron configuration.
carbonyl groups in 3-NNO-10 bridges a Ru-Ru bond in the Ru 3 chain, exhibiting a ν(CO) frequency of 1929 cm −1 , significantly lower than any of the terminal ν(CO) frequencies.The bridging bent µ-N 2 O ligand has a single-bond N-N distance of 1.378 Å (mPW1PW91) or 1.407 Å (BP86), a double-bond N=O distance of 1.208 Å (mPW1PW91) or 1.226 Å (BP86), and an N-N-O angle of 116.8 • (mPW1PW91) or 117.0 • (BP86).This bridging µ-N 2 O ligand functions as a four-electron donor using two lone pairs of the nitrogen atom in the Ru-N-Ru bridge.This gives the two end ruthenium atoms of the Ru-Ru-Ru chain in 3-NNO-10 the favored 18-electron configuration, but the central ruthenium atom only retains a 16-electron configuration.The lowest-energy Ru 3 (N)(CO) 9 (NO) structure 3-NNO-9-1 of the nonacarbonyl, like that of the decacarbonyl, is a C s symmetry structure with a bridging N 2 O group of a different type than that in 3-NNO-10 (Figure 5).Each nitrogen atom in the linear bridging η 2 -µ 3 -N 2 O group of 3-NNO-9-1 forms Ru-N bonds with all three ruthenium atoms.This linear bridging η 2 -µ 3 -N 2 O group has an elongated N-N distance of 2.417 Å (mPW1PW91) or 2.428 Å (BP86) and a double-bond N=O distance of 1.202 Å (mPW1PW91) or 1.220 Å (BP86), and exhibits a ν(NO) frequency of 1579 cm −1 .The total of six Ru-N bonds formed by the η 2 -µ 3 -NO group allows it to become an 8-electron donor to the Ru 3 chain, thereby giving each ruthenium atom in 3-NNO-9-1 the favored 18-electron configuration.

2. 3 .
Trinuclear Dinitrogen Complexes Ru3N2(CO)n (n = 10, 9, 8) Arising Formally by Double CO2 Loss from Ru3(CO)n(NO)2 Trinuclear Derivatives The lowest-energy Ru3N2(CO)10 structure 3-NN-10 is a Cs structure having a central bent Ru3 unit with Ru-Ru distances of 2.911 Å (mPW1PW91) or 2.950 Å (BP86), corresponding to WBI values of 0.31 and thus a formal single bond and a Ru-Ru-Ru angle of 96.5° (mPW1PW91) or 98.9° (BP86) (Figure 7).Both Ru-Ru bonds are bridged by carbonyl groups exhibiting ν(CO) frequencies of 1864 and 1838 cm -1 , significantly lower than the ν(CO) frequencies of the eight terminal CO groups in the range from 2066 to 1960 cm -1 .The central ruthenium atom bears two terminal CO groups and a terminal dinitrogen ligand with a N≡N distance of 1.117 Å (mPW1PW91) or 1.139 Å (BP86), leading to the favored 18-electron configuration after considering the two Ru-Ru bonds, each bridged by a CO group.The terminal ruthenium atoms of the Ru-Ru-Ru chain each bear three terminal CO groups, thereby leading to 16-electron configurations.

2. 3 .
Trinuclear Dinitrogen Complexes Ru 3 N 2 (CO) n (n = 10, 9, 8) Arising Formally by Double CO 2 Loss from Ru 3 (CO) n (NO) 2 Trinuclear Derivatives The lowest-energy Ru 3 N 2 (CO) 10 structure 3-NN-10 is a C s structure having a central bent Ru 3 unit with Ru-Ru distances of 2.911 Å (mPW1PW91) or 2.950 Å (BP86), corresponding to WBI values of 0.31 and thus a formal single bond and a Ru-Ru-Ru angle of 96.5 • (mPW1PW91) or 98.9 • (BP86) (Figure 7).Both Ru-Ru bonds are bridged by carbonyl groups exhibiting ν(CO) frequencies of 1864 and 1838 cm −1 , significantly lower than the ν(CO) frequencies of the eight terminal CO groups in the range from 2066 to 1960 cm −1 .The central ruthenium atom bears two terminal CO groups and a terminal dinitrogen ligand with a N≡N distance of 1.117 Å (mPW1PW91) or 1.139 Å (BP86), leading to the favored 18-electron configuration after considering the two Ru-Ru bonds, each bridged by a CO group.The terminal ruthenium atoms of the Ru-Ru-Ru chain each bear three terminal CO groups, thereby leading to 16-electron configurations.elimination of another CO2 molecule yielding 3-N2-8, since it has a bent NNO group with its oxygen atom close to the top ruthenium atom.

Figure 13 .
Figure 13.The optimized Ru 4 (N) 2 (CO) n (n = 12, 11) structures with bond distances in Å.Further decarbonylation of Ru 4 (N) 2 (CO) 11 gives two isomeric decacarbonyls Ru 4 (N) 2 (CO) 10 having essentially the same energy within the error limits of the calculations (Figure 14).Structure 4-NN-10-1 retains the Ru 4 N 2 distorted octahedron of 4-NN-11 with both nitride ligands bridging the entire Ru 4 tetragon.Structure 4-NN-10-2 is a bicapped tetrahedral Ru 4 N 2 structure with a central Ru 3 N tetrahedron having a Ru 2 N face capped by the fourth ruthenium atom and a Ru 3 face capped by the second nitrogen atom.Thus, 4-NN-10-2 has five Ru-Ru bonds, one nitrogen atom bonded to four ruthenium atoms, and the other nitrogen atom bonded to only three ruthenium atoms, whereas 4-NN-10-1 has only four Ru-Ru bonds and both nitrogens bonded to all four ruthenium atoms.

Table 1 .
Energies (∆E) and free energies (∆G, at 298 K) in kcal/mol for carbonyl dissociation of Ru 3 (CO) n (NO) 2 structures.Both ∆E and ∆G include the zero-point vibrational energy (ZPVE) corrections.

Table 2 .
Energies (∆E) and free energies (∆G, at 298K) in kcal/mol for disproportionation and fragmentation processes of the trinuclear ruthenium carbonyl nitrosyls.Both ∆E and ∆G include zero-point vibrational energy (ZPVE) corrections.The Ru 3 (CO) n (NO) 2 structures considered in Table2are the same as those in Table1.