Density Functional Study of the Stable Oxidation States and the

ARTICLE pubs.acs.org/JPCA

Density Functional Study of the Stable Oxidation States and the Binding of Oxygen in MO4 Clusters of the 3d Elements Ellie L. Uzunova* Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 11, Sofia 1113, Bulgaria

bS Supporting Information ABSTRACT: The tetraoxide clusters with stoichiometry MO4, and the structural isomers with side-on and end-on bonded dioxygen, are studied by DFT with the B1LYP functional. Diperoxides M(O2)2 are the most stable clusters at the beginning (Sc, Ti) and at the end of the row (CoCu), the latter being planar. For V, Cr, and Mn, the dioxoperoxides O2M(O2) are the most stable isomers. Low-spin states are dominant for the nonplanar diperoxides M(O2)2 and dioxoperoxides O2M(O2), and the local magnetic moment at the metal cations is small. The local charge on the metal cation center is higher in the diperoxides of Sc and Ti; it drops significantly in the dioxoperoxides of V and Cr. The iron dioxosuperoxide in the 3A00 state, which contains end-on bonded dioxygen, OOFeO2, is an exception with higher charge on Fe. In the planar diperoxides of Co, Ni, and Cu, oxygen-to-metal charge transfer is significant, and the local charge on the metal cation is close to 1. In all tetraoxygen clusters of the 3d elements, the cation center remains strongly electrophilic and interacts with Ar atoms from the inertgas matrix, where the clusters are trapped for IR spectral studies. Significant frequency shifts in the matrix are found for the dioxoperoxide of vanadium, O2V(O2), the dioxosuperoxide of iron, OOFeO2, and the nickel diperoxide, Ni(O2)2.

’ INTRODUCTION Transition metal oxides have been extensively studied as bulk materials, while small-sized clusters MnOm with n, m = 15 have attracted attention only in the recent decade.13 The transition metal elements with an incompletely filled d-shell are able to form diverse oxide clusters with reactive functional groups, as molecular oxygen can bind to the metal center in various ways: side-on, end-on, or split to individual atoms, yielding oxide, peroxo-, and superoxo- clusters and mixed compounds such as oxoperoxides or oxosuperoxides.4 The enhanced interest toward nanoscaled materials with applications in catalysis and the design of rechargeable batteries advanced cluster studies as well.15 The proper assignment of the ground states and low-lying excited states, the elucidation of electron distribution, and local magnetic properties rely on theoretical studies. IR spectra are mainly available for matrix-isolated species. Monoxides do not experience significant frequency shifts between the gas phase and solid matrix,6 but already with dioxides the interpretation of spectral features prompted stronger interactions between cluster and matrix: the symmetric stretching vibration of CrO2 in a solid matrix is identified in the range 914960 cm1, while the gasphase value is 895 ( 20 cm1.7 Theoretical and IR spectral studies revealed also that the dioxides of Ti, V, and Cr interact strongly with Ar and Xe atoms of the solid matrices.4,8,9 The presence of low-lying vacant d-levels determines the high electron affinity of these compounds and their ability to participate in further oxidation. Oxygen-rich clusters with higher oxygen content have been isolated among matrix-entrapped oxidation products of laser-ablated metal atoms,4 but the stable oxidation states in mononuclear metaloxygen neutral clusters of the 3d r 2011 American Chemical Society

elements do not exceed MVI.11a The formation of tetraoxides implies a high oxidation state (MVIII) of the metal cation, and though in most clusters the covalent character of the bonds dominates and the local charges on the cation are moderate, such high formal oxidation states are merely stable in anionic species.1012 Discrepancies between cluster model computations at different levels of theory emerge in the assignment of the MO4 global minima of the midrow elements, Mn, Fe, and Co, and for many of the monoanions.4,10 In the present study, the low-energy minima of the tetraoxides MO4 as well as their isomeric clusters with side-on and end-on bonded dioxygen and lower oxidation state of the cation such as dioxoperoxides, dioxosuperoxides, and diperoxides of the 3d elements (ScCu) are examined by DFT with the aim to study their relative stability, bonding scheme, and the ordering of their electronic states with different spin multiplicities. The thermodynamic stability with respect to dioxides and trioxides, vibrational frequencies in the gas phase and in an inert-gas matrix, local magnetic properties, charge density distribution, and electron affinity of the neutral species are also assessed. Molecular electrostatic potential maps are used to estimate the nucleophilic character of the oxygen atoms in the different clusters.

’ METHODS All calculations were performed with the B1LYP method, which includes local and nonlocal terms as implemented in the Received: April 14, 2011 Revised: July 22, 2011 Published: August 29, 2011 10665

dx.doi.org/10.1021/jp2034888 | J. Phys. Chem. A 2011, 115, 10665–10678

The Journal of Physical Chemistry A

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Table 1. Bond Length, Dipole Moment (DM), Dissociation Energy (Dzpe) Corrected for Zero-Point Energy, Spin Contamination Expectation Value ÆS2æ, Vibrational Frequency (ω), and Electron Affinity (EA) for Monoxide Clusters MO in their Ground States, as Calculated by B1LYP and TPSSa cluster

state

RMO, Å

ScO

2 +

Σ

1.658 (1.669) 1.668

Exp. TiO

3

Δ

Exp. VO Exp. CrO

4

Σ

5

Π

Exp. MnO

Σ

6 +

Exp. FeO

NiO

5

Δ

4

Δ

3

Σ

Exp. CuO Exp. a e

ÆS2æ

4.07 (3.56)

6.553 (7.372)

0.751 (0.752)

4.55b

7.01 ( 0.12

1.611 (1.622)

3.80 (3.48)

6.465 (7.580)

1.620

2.96 ( 0.05c

6.87 ( 0.10 d

1.580 (1.590) 1.589

3.80 (3.57) 3.355 ( 0.014e

6.047 (7.363) 6.44 ( 0.20

3.799 (3.796) 6.005 (6.102)

1.620 (1.615)

4.37 (3.83)

4.680 (6.008)

1.615

3.88 ( 0.13f

4.77g

1.642 (1.630)

5.28 (4.52)

3.558 (5.064)

Π

8.843 (8.795)

1.617 (1.608)

5.48 (4.55)

3.840 (5.018)

1.616

4.7 ( 0.2h

4.17 ( 0.08

1.629 (1.634) 1.629

4.86 (4.33)

3.773 (4.458) 3.94 ( 0.14

3.864 (3.766)

1.632 (1.636)

4.95 (4.27)

3.209 (4.417)

6.046 (6.018)

2.043 (2.009)

3.87 ( 0.03

1.627 2

2.012 (2.012)

3.83 ( 0.08

1.646

Exp. CoO Exp.

Dzpe, eV

DM, D

1.777 (1.733)

4.81 (4.49)

2.476 (3.024)

1.724

4.45 ( 0.30i

2.85 ( 0.15

0.769 (0.761)

ω, cm1

EA, eV

1005 (976)

1.145 (1.117)

965

1.35 ( 0.02

1048 (1017)

1.066 (0.976)

1009

1.30 ( 0.03

1043 (1016) 1011

1.205 (0.860) 1.229 ( 0.008

832 (906)

1.085 (1.111)

898

1.221 ( 0.006

845 (900)

1.279 (1.048)

840

1.375 ( 0.01

886 (914)

1.371 (1.207)

880

1.49450 ( 0.00022

885 (867) 853

1.440 (1.322) 1.45 ( 0.01

857 (839)

1.328 (1.204)

838

1.4550 ( 0.0050

586 (660)

1.242 (1.567)

640

1.777 ( 0.006

TPSS calculated values given in brackets. Experimental data for R, DM, D. and ω from ref 61, unless specifically indicated. b Ref 62. c Ref 63. d Ref 64. Ref 65. f Ref 66. g Ref 67. h Ref 68. i Ref 69. Experimental EA from refs 7078.

Gaussian 09 package.1319 The Becke one-parameter functional is closely related to the B3LYP functional,16 the three parameters being substituted by one. In B1LYP, the ratio between Hartree Fock and density functional exchange is determined a priori from purely theoretical considerations, and no further parameters are present. The standard 6-311+G(d) basis set with diffuse and polarization functions was employed, which consists of the WachtersHay all-electron basis set for the first transition row, using the scaling factors of Raghavachari and Trucks.2022 In terms of atomic orbitals, the basis is represented as [10s7p4d1f] for the 3d element, [5s4p1d] for oxygen, and [5s9p5d7f] for Ar. Regarding the optimized geometries of the ground states, the expanded basis set, 6-311+G(2df), produced essentially the same results with maximal deviation in bond lengths of (0.006 Å and 0.3 in bond angles; this basis set, however, is too expensive for CCSD(T) calculations and for optimizations in the Ar cell. B3LYP and B3PW91 calculations have been performed for the low-energy structures of tetraoxygen clusters (Table 2S, Supporting Information), and the results closely matched those of B1LYP calculations. The harmonic vibrations of all the optimized oxide, peroxide, and superoxide clusters were analyzed to reveal the nature of the stationary points obtained. The minima (local and global) on the potential energy surfaces (PES) were identified by the absence of negative eigenvalues in the diagonalized Hessian matrix. Spin contamination was estimated from the ÆS2æ expectation values by treating the DFT orbitals as corresponding to single-determinant HartreeFock wave functions. Coupled-cluster singles and doubles, including noniterative triples (CCSD(T)),2325 single-point calculations have been performed with the B1LYPoptimized geometries for the ground state and the low-lying excited states. Vibrational frequencies were calculated also for oxide clusters encaged in a cell of solid Ar. The calculations were performed with eight Ar atoms from the solid Ar supercell

accommodating one MO4 cluster, and full relaxation was allowed. The optimizations resulted in distortion of the Ar unit cell which accommodates the TM cluster. The frequencies of the imaginary vibrations, due to the incomplete cluster model and arising from motion of the Ar framework atoms, did not exceed an absolute value of 50 cm1. Smaller models were examined via the double-hybrid density functional B2PLYPD, which includes a second-order perturbation correction for nonlocal correlation effects and dispersion correction,26 by taking into consideration only the Ar atoms positioned close to the transition metal center, having MAr interatomic distances of less than 3 Å after the B1LYP optimization. The bond populations were examined by natural bond orbital (NBO) analysis.27,28 This method yields results that are rather insensitive to basis set enlargement and reveals both covalent and noncovalent effects in molecules. Magnetic moments at the atoms (μ) were calculated following the Mulliken population scheme.29 The calculations of local magnetic moments on metal cation centers and oxygen as the difference between α and β natural orbital populations produced very similar results. The electrostatic potential (ESP) of the clusters was calculated from the B1LYP density, and molecular electrostatic potential (MEP) maps were derived in which areas of enhanced reactivity centers in the various clusters can be discerned. Monoxides and Testing of Methods. The monoxides of the 3d elements have been studied most extensively, and reliable experimental data are available for the dipole moments, dissociation energies, and electron affinities; spectral data are available both from matrix-trapped species and in the gas phase. A large number of theoretical methods have been tested on monoxides, their cations, and anions: DFT (BLYP, B3LYP, BPW91),6 post HartreeFock methods, Multireference Configuration Interaction (MRCI), and coupled-cluster methods.3,59 Table 1 summarizes the results, obtained in the present study by B1LYP and 10666

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Table 2. Bond Lengths, Bond Angles, Spin Contamination Expectation Value ÆS2æ and Energies for Tetraoxides MO4 and Diperoxides M(O2)2a MO4 clusters of Td symmetry and M(O2)2 clusters of D2h and D2d symmetry ΔEtot 102, Hartree,

ΔEtot 102, Hartree, CCSD(T)

RMO, Å

ROO, Å

— OMO, deg

ÆS æ

B1LYP

1

1.823

1.473

46.7

0.000

0.000

0.000

V(O2)2 D2d Cr(O2)2 D2h

2

B2 3 B2u

1.796 1.965

1.441 1.325

47.3 39.4

0.768 3.880

8.487 3.727

10.251 7.245

Mn(O2)2 D2d

4

1.854

1.384

43.9

4.451

1.196

1.883

2

1.844

1.339

42.6

1.788

4.685

6.190

Fe(O2)2 D2d

1

1.751

1.364

45.9

0.000

4.438

5.283

FeO4 Td

1

1.572

0.000

6.043

1.169

Co(O2)2 D2h

4

1.837

1.328

42.4

3.774

0.000

0.000

2

1.870

1.314

41.2

1.796

0.948

1.245

Co(O2)2 D2d

6

B2 2 B1

1.926 1.846

1.336 1.350

40.6 42.9

8.777 1.635

0.704 1.877

2.520 2.642

4

1.951

1.320

39.5

4.672

2.509

2.999

Ni(O2)2 D2h

3

1.853

1.302

41.1

2.021

0.000

0.000

1

1.797

1.323

43.2

0.000

5.685

0.402

Ni(O2)2 D2d

5

1.932

1.320

40.0

6.027

0.391

1.576

Cu(O2)2 D2h

4

1.969

1.310

38.9

3.777

0.000

0.000

2

1.961

1.315

39.2

1.764

1.191

1.187

4

2.034

1.303

37.4

3.776

3.920

cluster model

state

Ti(O2)2 D2d

A1

A2 A1 A1 A1 B3u B3u

A2 B1u Ag B2 B2u B2u

Cu(O2)2 D2d

B1

2

ΔEtot, total energy difference relative to the ground-state Etot (Hartree) for: ScO4 1061.51303 (B1LYP). TiO4 1150.26667 (B1LYP); 1148.77680 by CCSD(T). VO4 1244.83737 (B1LYP); 1243.32404 by CCSD(T). CrO4 1345.23011 (B1LYP); 1343.68352 by CCSD(T). MnO4 1451.70265 (B1LYP); 1450.11966 by CCSD(T). FeO4 1564.38372 (B1LYP); 1562.71815 by CCSD(T). CoO4 1683.42075 (B1LYP); 1681.70906 by CCSD(T). NiO4 1808.96068 (B1LYP); 1807.21218 by CCSD(T). CuO4 1941.13657 (B1LYP); 1939.33908 by CCSD(T). a

the more recent meta-GGA functional TPSS,57 compared with experimental data; in Table 1S (Supporting Information) B3LYP results are included. The vibrational frequencies calculated by TPSS match very well the experimental ones, except for MnO and FeO; the dissociation energies are in most cases overestimated, while electron affinities are systematically underestimated. For the first 3d elements, Sc to Cr, TPSS provides more accurate bond lengths, while B1LYP performs better for the second half of the row, MnO to NiO. The largest discrepancies between experiment and B1LYP calculations are for the dissociation energies of ScO, TiO, and CuO (a difference of 0.40.5 eV) and for NiO (0.65 eV). The electron affinities of ScO, TiO, and CuO are underestimated by B1LYP; B3LYP produces more accurate results, only the electron affinity of VO is underestimated. The largest discrepancies with experiment for the TPSS functional are for the dissociation energies of the midrow elements, and they are overestimated by 0.5 eV for CoO and NiO, by nearly 1 eV for TiO, VO, and FeO, and by more than 1 eV for CrO and MnO. The BPW91 and BLYP functionals tend to overestimate dissociation energies in a similar way.6,9b Regarding the estimation of electron affinities, BPW91 and TPSS provide similar results. The electron affinities of CrO, CoO, NiO, and CuO, though somewhat underestimated, are in fair agreement with experiment; the remaining values are too low. According to the criterion of Lee and Taylor,58 based on the Euclidian norm of the t1 vector of the coupled-cluster singles and doubles wave function, known as T1 diagnostics, a multireference approach is recommended for values of T1 g 0.02. All of the metal monoxide clusters have higher T1 diagnostic values,

ranging from 0.04 to 0.05 for ScO, TiO, and CuO and reaching 0.090.10 for MnO to NiO. Nevertheless, it has been outlined that the multireference methods did not meet the expectations for more accurate treatment of transition-metal compounds,3c and a large number of theoretical studies have successfully applied single-reference methods, most of them based on DFT.3,11b,4244,52,55 The MRCI studies and MRCI(+Q) with Davidson correction included provided less satisfactory results regarding bond lengths and vibrational frequencies of FeO and NiO than the B3LYP studies; the MRCI dissociation of CuO was also significantly underestimated (1.81 eV vs 2.48 eV from B1LYP, vs 2.70 eV by CCSD(T) and 2.85 eV from experiment).3a,59 Recent MRCI and RCCSD(T) studies (restricted coupled-cluster method) of ScO, TiO, CrO, and MnO provided excellent agreement with experimental bond lengths, dissociation energies, and spectroscopic constants at the RCCSD(T) level of theory.60 The adiabatic electron affinities of ScO, TiO, and CrO, calculated by RCCSD(T) with scalar relativistic correction applied, have very good agreement with experiment; the electron affinity of MnO is still slightly underestimated. It is worth noting that the tetraoxygen clusters of the 3d elements have smaller T1 values than the corresponding monoxides, ranging within 0.040.06 for MnO4 and Ni(O2)2, with the largest coupled-cluster amplitudes for the high-spin states within 0.110.16. On the basis of the large data set of theoretical and experimental data available for the monoxides, it can be assumed that the application of DFT with the B1LYP density functional and subsequent B1LYP/CCSD(T) calculations provide a reliable 10667



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approach for studying transition-metal oxides with higher degree of oxidation, MOn. Structure, Bonding, and Stability of Tetraoxides MO4 and Their Isomers: Diperoxides M(O2)2, Dioxoperoxides O2M(O2), Dioxosuperoxides OOMO2, and Peroxosuperoxides OOM(O2). Neutral Clusters. Metal-tetraoxygen clusters with three different types of bonding are considered in the present study, arising from three different oxygen/dioxygen species: O2 (oxide), O22 (peroxide), and O2 (superoxide). The oxides do not contain oxygenoxygen bonds; O22 binds side-on to the transition metal center M(η2-O2); and O2 binds end-on, denoted as M(η1-O2) or MOO. Mixed species with side-on and end-on bonded dioxygen also exist, and the dioxides MO2 also bind dioxygen. Throughout the text and tables, MOn is used to denote oxide-type bonding; M(O2) denotes side-on bonding (peroxides); and MOO denotes end-on bonding of dioxygen (superoxides). The highly symmetric clusters with Td, D2d, and D2h symmetry are summarized in Table 2, and they encompass tetraoxides with equivalent oxygen atoms and the planar (D2h) and nonplanar (D2d) diperoxides. MVIIIO4 clusters are formed by V, Mn, and Fe, among which only FeO4 is a symmetric tetrahedral cluster, but it is endothermic and lies above the dissociation limit to FeO2 + O2. VO4 is a slightly distorted tetrahedron, and together with MnO4, both have C2v symmetry. The tetraoxygen clusters of Ti, Mn, and Fe are much less stable than those

Figure 1. Global minima for the MO4 clusters. The dissociation energies with release of a single oxygen molecule are denoted. (Zeropoint corrections included.)

of the remaining 3d elements with respect to release of molecular oxygen (Figure 1). The diperoxides MIV(O2)2 are the dominant chemical formation among the clusters with MO4 stoichiometry. The dioxoperoxides O2MVI(O2), which are abundant among the midrow elements, are summarized in Table 3, together with the low-symmetry tetraoxides MO4, distorted from tetrahedral configuration along a C2 axis, and the asymmetric diperoxides [M(O2)](O2) with two nonequivalent OO bonds. The MO bond lengths in the diperoxides vary in the range 1.75 ( 1.97 Å, and Cu(O2)2 forms the ground state with the longest MO bonds. The MOoxo bonds in dioxoperoxides O2M(O2) are typically short, 1.56 ( 1.58 Å (Table 3), while the MOperoxo bond varies in the same way as for the diperoxides. The OOperoxo bond for most of the diperoxides and dioxoperoxides is within the range 1.30 ( 1.38 Å, and longer OOperoxo bonds are formed by O2Cr(O2), 1.432 Å, and Ti(O2)2, 1.473 Å. All of the superoxides OOMO2 and OOM(O2), which involve end-on bonded dioxygen, appeared as planar clusters of either C2v or Cs symmetry; their data are summarized in Table 4. Tetraoxygen Clusters of Sc, Ti, and V. In its ground state 1A1, Ti(O2)2 has two equivalent OO bonds, while the 3A2 state configuration should be written as [Ti(O2)](O2), as it contains one weakly bound peroxo group (Table 3). Only Sc and Ti form such species with strongly elongated bonds to one peroxo group and nonequivalent OO bond lengths of the side-on bonded oxygen atoms. The structures of [Ti(O2)](O2) in the 3A2 state and [Sc(O2)](O2) in the 2A2 state are rather similar; the MO bond lengths to the more tightly bound dioxygen pair are comparable to the corresponding bonds in the simple peroxides M(O2): in [Sc(O2)](O2), ScO is 1.871 Å vs 1.849 Å in Sc(O2); in [Ti(O2)](O2), TiO is 1.827 Å vs 1.820 Å; the OO bond lengths also match.9 Nevertheless, dissociation of molecular oxygen is an endothermic reaction for [Sc(O2)](O2), requiring 1.37 eV (Figure 1). Ti also forms a superoxo-peroxide OOTi(O2) cluster of C2v symmetry in the 3A1 state, with the superoxo group lying along the C2 axis (Table 4). Though this cluster does not contain strongly elongated bonds, it is less stable than [Ti(O2)](O2) by 0.5 eV. While [Sc(O2)](O2) is thermodynamically stable, [Ti(O2)](O2) and OOTi(O2) would readily dissociate molecular oxygen, the only configuration below the

Table 3. Bond Lengths, Bond Angles, Spin Contamination Expectation Value ÆS2æ, and Energies for Distorted Tetraoxide MO4 Clusters, Diperoxide Clusters [M(O2)](O2) with Nonequivalent Peroxo Bonds, and Dioxoperoxide O2M(O2) Clusters MO4, M(O2)2, and O2M(O2) with C2v symmetry cluster model

a

RMO(1), Å

RMO(2), Å

ROO, Å

— O(1)MO(1), deg

— O(2)MO(2), deg

ÆS2æ

ΔEtot 102, Hartreeb

[Sc(O2)](O2)

2

A2

1.871

2.124

1.4861.331

46.8

36.5

0.758

0.000

[Ti(O2)](O2)

3

A2

1.827

2.059

1.465 1.326

47.3

37.5

2.010

4.330 (4.150)

O2V(O2)

2

A2

1.583

1.974

1.310

113.1

38.8

0.759

0.000

VO4 O2Cr(O2)

4

A1 1 A1

1.711 1.557

1.712 1.774

1.432

104.3 113.2

104.4 47.6

4.039 0.000

6.657 (7.435) 0.000

O2Mn(O2)

2

A1

1.554

1.775

1.397

118.8

46.3

0.813

0.000

MnO4

2

B1

1.555

1.658

2.523

112.4

99.1

1.036

0.709 (0.629)

2

B2

1.555

1.657

2.523

112.4

99.1

1.035

0.709 (0.629)

2

A2

1.596

2.635

111.2

0.919

2.458 (1.039)

1

A1

1.542

1.761

1.377

121.9

46.0

0.000

1.893 (2.576)

3

A2

1.569

1.837

1.374

116.4

43.4

2.316

2.486 (2.265)

B2 2 A2

1.657 1.560

1.848 1.822

1.354 1.366

89.4 119.6

42.9 44.0

4.131 1.004

6.381 7.236

O2Fe(O2) O2Co(O2) a

state

a

4

(1) and (2) refer to the oxygen atoms in the two perpendicular σv planes. b CCSD(T) values given in brackets. 10668



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Table 4. Bond Lengths, Bond Angles, Spin Contamination Expectation Value ÆS2æ, and Energies for Superoxide Clusters OOMO2 and OOM(O2) OOMO2 and OOM(O2) clusters, C2v and Cs symmetry RMO(1), Å

RMO(2), Å

RO(1)O(1), Å

RO(2)O(3), Å

— O(1)MO(1), deg

— MO(2)O(3), deg

ÆS2æ

A1 2 0

1.821

1.892

1.469

1.298

47.6

180.0

2.006

6.153

A

1.827

1.813

1.419

1.287

46.1

155.3

1.777

13.722

3

A1 A2

1.953 1.821

1.788 1.797

1.322 1.418

1.279 1.277

40.2 45.8

180.0 180.0

3.819 4.838

A

1.605

1.982

1.225

115.5

124.0

3.705

0.000

A2

1.808

1.765

1.273

45.8

180.0

3.084

1.303 (6.171)

1.577

1.818

1.257

124.5

3.797

5.261 (3.911)

1.632

1.936

1.209

138.2

131.9

2.645

5.943 (4.379)

1.826

1.618

1.245

42.8

178.5

0.764

6.636

cluster model

state

OOTi(O2)

3

OOV(O2) OOCr(O2) OOMn(O2) OOFeO2 OOFe(O2) OOCoO2

4

3 00 3

4 0

A

2 00

A

OOCo(O2)

2 00

A

a

a

1.401

1.321

ΔEtot 102, Hartree

6.548 (10.651) 2.095 (6.278)

a In clusters of C2v symmetry: (1) and (2) refer to the oxygen atoms in the two perpendicular σv planes; in oxosuperoxides of Cs symmetry: O(1) represents the two equivalent oxygen atoms and O(2) and O(3) represent the nonequivalent oxygen atoms of the superoxofragment, the O(2) atom being bonded to the metal cation: [O(1)]2MO(2)O(3). CCSD(T) values given in brackets.

dissociation limit being the ground-state Ti(O2)2. The [Sc(O2)](O2) in the 2A2 state was detected in the IR spectra of matrixisolated species,30 but neither Ti(O2)2 nor [Ti(O2)](O2) was found.31 The dioxide TiO2 is a very stable cluster; it is by 1.8 eV more stable than ScO2 toward dissociation.9 The abundance of TiO2 relative to Ti(O2)2 or [Ti(O2)](O2) was proposed as an explanation for the failure to detect the latter two clusters among the oxide species trapped in the solid matrices.4 The O2V(O2) cluster in the 2A2 state is of the highest thermodynamic stability among the tetraoxygen species of the 3d elements with respect to either partial dissociation to VO2 + O2, to a release of single oxygen atom, or to complete release of the bonded oxygen, V + 2O2 (Figure 1 and Table 6). The high stability of O2V(O2) toward O2 dissociation was found by BPW91 studies as well.42b Similarly, vanadium trioxide VO3 was the most stable cluster among the MO3 series of the 3d elements, requiring 3.79 eV for the release of molecular oxygen.37 Among the monoxides MO (see Table 1) and the dioxides MO2,9a those of Sc, Ti, and V have higher stability toward fragmentation. For the monoxides, the dissociation energy decreases smoothly from Sc to V, followed by a large drop of stability for CrO and MnO, and again smoothly decreases from FeO to CuO. Such a sharp change of stability between V, Cr, and Mn occurs for the dioxides and trioxides as well. The metaloxygen bonds for the d1d4 elements (Sc to Cr) have a significant contribution of π-component; for Ti and the remaining 3d elements, also a δ-component is added.3a For ScOn and TiOn, the Coulombic stabilization is more significant than the formation of π-dative bonds, as illustrated by the charge distribution (Table 5). In [Sc(O2)](O2) and Ti(O2)2, the local natural charge on the metal cation is 1.771.80, while in the dioxoperoxides of V and Cr the charge on the metal cation centers drops to 1.06 in O2V(O2) and below 0.9 for O2Cr(O2). The absolute electronegativity of the transition metal element increases from Sc to Cr, remains constant for Mn, and then increases further from Fe to Cu.53 The electronegativity also increases with the oxidation state of the element, and between TiIV(O2)2 and O2VVI(O2), a strong increase of electronegativity can be expected. As a 3d3 element, vanadium possesses vacant d-orbitals with favorable orientation to accept electrons from oxygen and to form π and δ bonds. The local charge on the preroxo-type oxygen atoms is very small, and a local magnetic moment is

induced to the side-on bonded dioxygen fragment, which equals one electron (Table 5). Thus, the side-on bonded dioxygen donates an electron to V, and though the VOperoxo bonds are lengthened, the overall stability of the molecule is increased, as it is also stabilized by a Coulomb component. In the IR spectra of Ar matrix isolated species, the ground-state O2V(O2) cluster interacts with atoms from the matrix, and a VAr bond is formed.4,8,32 The diperoxide V(O2)2 and a peroxosuperoxide OOV(O2) lie at more than 2.7 eV above the global minimum. A C2v symmetry tetraoxide VO4 with close to tetrahedral structure in the 4A1 state is separated from the global minimum by 1.81 eV (Table 3 and Figure 2). The strictly tetrahedral VO4 has nondegenerate electronic state with orbital occupancy 6a211e46t621t31 and thus is also in the 4A1 state, but an imaginary E symmetry vibration classifies it as a saddle point. Spin-pairing, which leads to a degenerate state 2 T1, requires energy of 1.4 eV. The C2v symmetry cluster in the 4 A1 state, which is a local minimum, is formed by minor elongation of two VO bonds of the tetrahedral cluster by 0.001 Å; the — OVO angle deformation is also small, nearly 5. The t1 orbital is split into a2 + b1 + b2 MOs, and the electron configuration reads as 13a212a127b117b12. In the latter case, a second-order JahnTeller distortion is accomplished with a symmetry descent Td f C2v but with minor structural change. The D2d symmetry diperoxide in the 2B2 state as well as the C2v symmetry 2A2 ground state are a result of first-order JahnTeller distortion of a hypothetical VO4 in the 2T1 state. Tetraoxygen Clusters of Cr, Mn, and Fe. The dioxoperoxide O2Cr(O2) in the 1A1 ground state is thermodynamically much less stable than O2V(O2) (Figure 1). Both of the triplet configurations are planar—a diperoxide with side-on bonded dioxygen, Cr(O2)2 in the 3B2u state, and a superoxo-peroxide with both side-on and end-on bonded dioxygen, (O2)CrOO in the 3A1 state (Figure 3)—and they are found at higher energies than the dissociation limit to CrO2 + O2. The local positive charge on the Cr atom in O2Cr(O2) is small, as compared to the other groundstate clusters, and the HOMOLUMO gap is small too (Table 5); thus, further coordination would stabilize the cluster. A number of polymeric species have been predicted by theoretical studies and observed experimentally.3335 Compared to O2V(O2), in O2Cr(O2) all CrO bond lengths are shorter, while the OO bond is elongated (Table 3). A sharp decrease in 10669



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Table 5. Vibrational Frequencies, Magnetic Moments on Atoms (μ, Bohr Magnetons), HOMO(SOMO)LUMO gaps (H/S/L, eV) Net Natural Charges on Atoms, and Natural Atomic Orbital Occupancies on Metal Cations for MO4 in States at the Global Minimum state ω, cm1 μM

[Sc(O2)](O2); C2v; 2A2

Ti(O2)2; D2d; 1A1

O2V(O2); C2v; 2A2

68b2; 78b1; 150a2; 419a1; 458b2; 616b1;

108e; 129b1; 527a1; 677e;

133b2; 183b1; 221a2; 336a1; 523b2;

657a1; 888a1; 1183a1

704b2; 897a1; 953b2

546a1; 1081b1; 1087a1; 1214a1

0.06

0.10

0.00

μO(oxo)

0.02

μO(perox)

0.52; 0.01

0.00

0.53

qM qO(oxo)

1.80

1.77

1.06 0.39

0.44

0.14

H/S/L

3.19

4.41

4.24

M 3d

1.05

2.05

3.40

M 4s

0.10

0.14

0.12

qO(perox)

state 1

ω, cm

0.34; 0.56

O2Cr(O2); C2v; 1A1

OOFeO2; Cs; 3A00

O2Mn(O2); C2v; 2A1

109a2; 209b2; 271b1; 336a1; 594a1;

237b2; 267a2; 268b1; 350a1;

56a00 ; 85a00 ; 89a0 ; 140a0 ; 286a0 ;

663b2; 964a1; 1099a1; 1115b1

574a1; 626b2; 997a1; 1042a1; 1069b1

310a0 ; 906a0 ; 948a0 ; 1329a0

μM μO(oxo)

0.00 0.00

1.40 0.13

3.00 0.38

μO(perox)

0.00

0.07

0.77 (FeOsuperox); 0.99 (Oend-superox)

qM

0.87

1.29

qO(oxo)

0.23

0.39

1.44 0.65

qO(perox)

0.21

0.26

H/S/L

3.03

3.17

2.90

M 3d

4.46

5.47

6.26

M 4s

0.16

0.21

0.25

state ω, cm1

Co(O2)2; D2h; 4B3u

0.18 (FeOsuperox); 0.05 (Oend-superox)

Ni(O2)2; D2h; 3B1u

Cu(O2)2; D2h; 4B2u

152b3u; 173b2u; 175au; 428ag; 446b3g;

154b2u; 183b3u; 268au; 421ag; 429b3g;

118b3u; 125b2u; 150au; 199b3g; 332ag;

469b1u; 666b2u; 1133b1u; 1167ag

583b1u; 588b2u; 1198b1u; 1247ag

355b2u; 489b1u; 1143b1u; 1234ag

μM

1.19

0.09

0.22

μO

0.45

0.52

0.69

qM

1.03

0.93

1.11

qO

0.26

0.23

0.28

H/S/L

3.46

4.21

3.67

M 3d

7.61

8.71

9.57

M 4s

0.31

0.31

0.26

thermodynamic stability of the tetraoxo species is observed between V and Cr with respect to all possible fragmentation reactions, and the midrow elements Cr, Mn, and Fe form much less stable clusters than the remaining elements (Table 6). The tetrahedral MnO4 would have a degenerate electronic state: either 2T1 or 2T2. According to the experimental orbital occupancies and energy gaps, deduced from the photoelectron spectrum of MnO4, the 1t61 HOMO and the 6t62 MO (next below the HOMO) are separated by 1.36 eV.12 The removal of an electron from either the HOMO or the next lower-energy orbital would yield a degenerate state 2T1 or 2T2 for the hypothetically tetrahedral MnO4; these two degenerate states are closely spaced by energy, and each would undergo structural change to lift degeneration. JahnTeller distortion yields the C2v symmetry dioxoperoxide O2Mn(O2) in the 2A1 state, which is

the most stable cluster according to the B1LYP results of the present study, and two iso-energetic and iso-structural tetraoxides MnO4 in 2B1 and 2B2 states, with two shorter and two longer MnO bonds (Figure 4). At higher energy, another tetraoxide with equivalent MnO bonds and minor distortion from Td symmetry is found in the 2A2 state. The 2A1 state could be regarded as originating from the 2T2 configuration and the 2A2 state from 2T1, while the 2B1 and 2B2 states may result from either the 2T1 or the 2T2 degenerate state. Both the present study and previous theoretical studies find that the 2A1 state of O2Mn(O2) and the 2B1; 2B2 states of MnO4 are closely spaced by energy (see Table 3), and the predicted energy gap is small (0.180.19 eV); however, BPW91 calculations assign the distorted oxide as the global minimum.12 CCSD(T) calculations agree with the B1LYP ordering of the 2A1 and 2B1,2 states and predict a similar energy 10670



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Table 6. Dissociation Energies (Dzpe, eV)a of MO4 in States at the Global Minimum with Reduction to Either Trioxide or to the Metal Atom MO4 w MO3 + O

a

MO4 w M + 2O2

Sc

2.674

6.945

Ti

2.600

7.760

V

3.394

8.446

Cr

2.216

4.819

Mn Fe

2.161 2.180

2.877 2.556

Co

2.403

2.573

Ni

3.114

2.489

Cu

2.973

2.309

Zero-point correction included.

Figure 2. Global minimum, ground states corresponding to the different isomeric VO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. V atoms are small dark-yellow circles amd O atoms large blue circles. The arrows (not to scale) denote the energy difference ΔEtot, corresponding to adiabatic transitions (zero-point corrections included).

gap; however, the 2A2 state of the tetraoxide MnO4 is assigned as the global minimum (Table 3). The dioxoperoxide O2Mn(O2) was detected in the IR spectra of matrix-isolated species.36 The geometry of this cluster is very similar to that of O2Cr(O2), but the manganese atom bears a higher local charge and also a higher magnetic moment than the expected value for a doublet state. Antiferromagnetic coupling with both the oxo- and side-onbonded oxygen atoms occurs and is responsible for the overall low-spin state. Diperoxides Mn(O2)2 with D2d symmetry were found in 4A2 and 2A1 states, the former lying close to the dissociation limit and the latter being of even much lower stability. In the peroxosuperoxide with C2v symmetry OOMn(O2) in the 4A2 state, the side-on bonded dioxygen forms similar bonds as the side-on bonded dioxygen in the diperoxides Mn(O2)2 with D2d symmetry, while the end-on bonded OO group connects to the metal cation center with a relatively short MnO bond (Table 4). The breaking of one MnOperoxo bond in the 4 A2 state of Mn(O2)2 requires only 0.21 eV (Figure 4). Iron forms all types of isomers with FeO4 stoichiometry: dioxoperoxides O2Fe(O2) in the 1A1 and 3A2 states, a planar dioxosuperoxide OOFeO2 in the 3A00 state, which is the global minimum, according to B1LYP calculations, a peroxosuperoxide

Figure 3. Global minimum, ground states corresponding to the different isomeric CrO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. Cr atoms are small dark-green circles and O atoms large blue circles. See also the Figure 2 caption for details.

Figure 4. Global minimum, ground states corresponding to the different isomeric MnO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. Mn atoms are small violet circles and O atoms large blue circles. See also Figure 2 caption for details.

OOFe(O2) in the 3A2 state, a diperoxide Fe(O2)2 in the 1A1 state, and a tetraoxide FeO4 with Td symmetry, in the 1A1 state (Figure 5). The nonplanar dioxoperoxides of C2v symmetry in the 1A1 and 3A2 states are separated by 0.16 eV, and the interconversion requires a minor change of geometry—elongation of the FeO peroxo bonds (Table 3). Subsequent breaking of one FeOperoxo bond, further lengthening of the FeO bonds, and rotation of the end-on bonded dioxygen to reach planar structure would bring the cluster to the 3A00 ground state of OOFeO2 (Figure 5, Table 4). In the latter configuration, the local magnetic moment on the iron cation is high, as for a quartet state; electron density is delocalized over the oxygen atoms; and antiferromagnetic ordering of electrons on oxide-type oxygens and superoxide-type oxygen atoms is observed (Table 5). It is typical for superoxides that the terminal oxygen atom of the superoxo group bears practically no charge, and an unpaired electron remains located on this atom.9 The superoxo bond length, OOsuperoxo, takes values within 1.23 ( 1.30 Å, the shortest bond being found in O2FeOO and the longest one in (O2)TiOO (Table 4). The global minimum on the Fe + 2O2 potential energy surface has been a subject of controversy: BPW91 studies46 and TPSS calculations, performed in the present study, denote the tetrahedral FeO4 as the global minimum; B1LYP and B3LYP studies denote the 3A00 state of OOFeO2 as the most stable configuration; and according to 10671



Figure 5. Global minimum, ground states corresponding to the different isomeric FeO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. Fe atoms are small red circles and O atoms large blue circles. See also Figure 2 caption for details.

CCSD(T) calculations, the dioxoperoxide O2Fe(O2) in the 1A1 state is the most stable one. The energy gap between O2Fe(O2) in the 1A1 state and OOFeO2 the 3A00 state, resulting from B3LYP calculations (0.23 eV), is smaller than the B1LYP calculated one, while the CCSD(T) gap is larger, 0.7 eV. With larger basis set, 6-311+G(2df), B3LYP places these two states as nearly isoenergetic. It has been argued42a that CCSD(T) calculations could depend on the preoptimization method and the chosen density functional; therefore, CCSD(T) calculations were repeated with TPSS-optimized geometries, and the result was the same: O2Fe(O2) in the 1A1 state was confirmed as the lowest-energy cluster, separated from the OOFeO2 3A00 state by an even larger energy gap of 1.26 eV. Photochemically induced reversible interconversion between the OOFeO2 and O2Fe(O2) isomers was detected in an inert-gas solid matrix.10 The conversion OOFeO2 f O2Fe(O2) occurs upon red light excitation, while the reverse reaction is achieved by near-IR light excitation. The low-energy reversible transition indicates that the B1LYP and B3LYP results correctly assign these configurations as separated by a small-tomoderate energy gap of 0.20.5 eV, while TPSS predicts 0.79 eV. At the B1LYP level, the two configurations lie close to the dissociation limit to FeO2 + O2, and thus the OOFeO2 cluster is highly reactive: it would also release either an oxygen atom or undergo total fragmentation, requiring energy of 2.02.5 eV (Table 6). The planar peroxosuperoxide of C2v symmetry was not reported so far in experimental studies, possibly because it has overlapping IR bands with the other interconvertible isomers. Tetraoxygen Clusters of Co, Ni, and Cu. The three last elements (Co, Ni, Cu) of the 3d row form planar diperoxide clusters with side-on bonded dioxygen, M(O2)2, as the most stable configurations. In the 4B3u ground state of Co(O2)2, the four equivalent CoO bonds are elongated compared to the D2d symmetry diperoxides, while the OO bond lengths are shorter than a typical peroxo bond. The 6B2 state of a D2d symmetry cluster lies very close in energy to the planar ground state, and with slightly higher energy the 2B3u planar cluster of Co(O2)2 is

ARTICLE

Figure 6. Global minimum, ground states corresponding to the different isomeric CoO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. Co atoms are small dark-blue circles and O atoms large blue circles. See also Figure 2 caption for details.

Figure 7. Global minimum, ground states corresponding to the different isomeric NiO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. Ni atoms are small green circles and O atoms large blue circles. See also Figure 2 caption for details.

found (Table 2 and Figure 6). Thus, two alternative ways of interconversion exist—one slightly higher in energy, but with minor change in geometry, and the other with smaller energy change, requiring elongation of the CoO bonds and rotation of the peroxo bonds to occupy two perpendicular planes. The zeropoint energy is higher than the energy required for the transformation, but the path to the sextet state would certainly have a higher activation barrier. A similar behavior is predicted for Ni(O2)2 in its 3B1u ground state; however, the interconversion path is unidirectional to the 5B2 state (Figure 7). The required bond length change is smaller than for Co(O2)2. LSDA calculations also assign the D2h symmetry Ni(O2)2 in a triplet state as the global minimum.38 Natural orbital analysis reveals that in all planar diperoxide clusters the charge on the metal cation is close to 1, and the 4s orbital is significantly populated (Table 5). The high 3d and 4s occupancies indicate significant ligand-to-metal charge transfer in these clusters. The diperoxide Co(O2)2 with D2d symmetry in the 4A2 state lies close to the dissociation limit; this applies to Ni(O2)2 in the singlet state as well. The spectroscopic studies of Chertihin et al.39 have identified OOCo(O2), OOCoO2, and O2Co(O2) in the Ar matrix but not diperoxides, and they were neglected in nearly all previous theoretical studies.9,3941 A quartet ground state of Co(O2)2 was assigned 10672



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by PW91 computations of Johnson et al., with bond lengths similar to those of the planar 4B3u ground state of the present study.42a Both PW91 and BPW9142b predict a minor deviation of Co(O2)2 from planarity, adopting thus D2 symmetry in the global minimum, with oxygen atoms rotated by 6.5 around the C2 axis which crosses the OO bonds. In the BPW91 optimized geometry, the oxygen atoms are displaced by 0.206 Å from the molecular plane of the B1LYP predicted 4B3u ground state. In the solid matrix IR study of the CoO2 + O2 reaction, the number of isomers was limited to only two, OOCoO2 and O2Co(O2), and a BPW91-calculated 2A2 state of O2Co(O2) was suggested as the global minimum.40 According to the present study, all of the cobalt superoxo-isomers, as well as the dioxoperoxides, are thermodynamically unstable. The tetraoxygen clusters of the second half of the row elements do not coordinate inert gas atoms (Table 10). No species with CoO4 stoichiometry were detected in a solid nitrogen matrix.39

Figure 8. Global minimum, ground states corresponding to the different isomeric CuO4 clusters, and low-lying local minima ordered as to their relative energies and grouped according to spin multiplicity. Cu atoms are small dark-red circles and O atoms large blue circles. See also Figure 2 caption for details.

Copper forms diperoxide clusters with side-on bonded oxygen atoms, Cu(O2)2, in doublet and quartet states, the planar ones being more stable. The global minimum corresponds to Cu(O2)2 in the 4B2u state. The 2B2u state of Cu(O2)2 is separated by 0.32 eV from the ground state (Figure 8). The bond lengths and angles of the planar Cu(O2)2 in 4B2u and 2B2u states are very similar (Table 2). The 4B1 isomer with D2d symmetry has strongly elongated CuO bonds; it lies above the dissociation limit. Though Cu(O2)2 is stable with respect to losing one oxygen molecule, it is the least stable cluster in the MO4 series of the 3d elements with respect to complete dissociation Cu + 2O2 (Table 6). Superoxo isomers with end-on bonded dioxygen are particularly stable with the CuO2 stoichiometry9 and less stable in the CuO3 stoichiometry,4,37 while for CuO4 they are found at much higher energies, more than 2 eV above the dissociation limit. Monoanions of the Tetraoxides and Their Isomers. The monoanions M(O2)2 of Sc and Ti are of D2d symmetry with equivalent MO bonds to the side-on bonded dioxygen. In Sc(O2)2 with the 1A1 ground state, the ScO bonds are elongated, as compared with the two more tightly bound oxygen atoms in the neutral parent, and the OO bonds are elongated as well (Table 7). In the 2A1 state of Ti(O2)2, the TiO bonds are elongated by 0.066 Å; the OO bonds undergo minor lengthening by 0.01 Å, compared with the neutral parent. The next three elements, V, Cr, and Mn, form highly stable monoanions O2V(O2), CrO4, and MnO4, and the energy gain is in the range typical for superhalogens: 3.65.0 eV. Vanadium forms stable monoanions of the diperoxide and the dioxoperoxide clusters, both of them in the singlet state. The D2d symmetry V(O2)2 monoanion in the 1A1 state is less stable than the neutral dioxoperoxide; it originates from the 2B2 parent cluster but with all VO and OO bonds being significantly elongated (Tables 2 and 7). The O2V(O2) cluster in

Table 7. Bond Lengths, Bond Angles, Spin Contamination Expectation Value ÆS2æ, and Energies for Tetraoxide MO4 and Diperoxide M(O2)2 Monoanionsa MO4; M(O2)2 cluster model

state

ROO, Å

— OMO, deg

ÆS2æ

ΔEtot 102, Hartree

Sc(O2)2 (D2d)

1

1.959

1.519

45.6

0.000

9.861

Ti(O2)2 (D2d) V(O2)2 (D2d)

2

A1 1 A1

1.889 1.862

1.483 1.476

46.2 46.7

0.758 0.000

5.788 3.483

Cr(O2)2 (D2d)

4

1.856

1.474

46.8

3.818

6.409

2

1.828

1.438

46.3

0.795

MnO4 (Td)

1

1.597

Mn(O2)2 (D2d)

3

1.829

1.456

46.9

2.065

1

1.805

1.432

46.8

0.000

FeO4 (D2d)

2

1.608

109.3

0.789

10.486 (13.249)

Fe(O2)2 (D2h) FeO4 (D2d)

4

1.829 1.697

1.470

47.4 86.9

3.817 8.797

11.216 (10.658) 10.917

Fe(O2)2 (D2d)

2

1.808

1.436

46.8

0.821

Fe(O2)2 (D2h) Co(O2)2 (D2h) CoO4 (Td) Ni(O2)2 (D2h) Cu(O2)2 (D2h)

2

1.896

1.393

43.1

1.806

3

1.812

1.450

47.2

2.052

10.613 (10.298)

3

1.624

2.070

4.316 (7.084)

2

1.811

1.410

45.8

0.759

8.502

1

1.841

1.426

45.5

0.000

7.972

3

1.935

1.402

42.4

2.020

6.353

A1

B1 B2 A1 B1 A1 A1 B3g A2

6

B1 B3u B3g A1 B1g Ag B2g

a

RMO, Å

0.674 16.563 5.558 3.137

8.722 5.795

CCSD(T) values given in brackets. 10673



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Table 8. Bond Lengths, Bond Angles, Spin Contamination Expectation Value ÆS2æ, and Energies for Monoanions of Distorted Tetraoxide Clusters MO4, Diperoxide Clusters with Nonequivalent Peroxo Bonds M(O2)2, and of Dioxoperoxide Clusters O2M(O2) MO4, C2v/Cs symmetry cluster model O2V(O2)

state

RMO(2),a Å

ROO, Å 1.482

0.000

13.120

0.880

17.759

1.452

118.6

47.0

0.774

15.668

1.840

1.454

85.6

46.5

3.790

122.1

45.9 122.0

0.800 1.752

11.917 (12.034) 11.615 (11.417) 10.200

O2Cr(O2)

2

1.605

1.821

4

1.721

B1

ΔEtot 102, Hartreeb

47.5

1.693

A1

ÆS2æ

98.0

1.840

1.601

B2

— O(2)MO(2), deg

114.0

1.625

2

A1

— O(1)MO(1), deg

111.6

1

CrO4

6.619

O2Fe(O2) O2FeOO

2

A2 2 00 A

1.579 1.607

1.785 1.873

1.443 1.309

O2Fe(O2)

4

1.693

1.829

1.425

45.9

3.873

O2Co(O2)

3

1.627

1.961

1.360

109.2

40.6

2.589

9.796 (9.922)

1

1.612

1.798

1.420

114.7

46.5

0.000

7.070 (7.230)

3

1.714

1.858

1.391

71.3

44.0

2.306

4.912 (4.906)

B2 A2 A1 B2

a

RMO(1),a Å

(1) and (2) refer to the oxygen atoms in the two perpendicular σv planes. b CCSD(T) values given in brackets.

the 1A1 state is the global minimum. Compared with the parent cluster in the 2A2 state, the monoanion has shortened VOperoxo bond lengths to the two side-on bonded oxygen atoms and an elongated peroxo bond OO; the two VOoxo bonds undergo minor lengthening (Tables 3 and 8). The B1LYP calculated adiabatic electron affinity of 3.57 eV coincides with the B3LYP calculated one;43 it is smaller than the experimentally determined value of 4.0 eV45 but still sufficiently high to classify O2V(O2) as a highly electrophilic cluster. Chromium forms three types of monoanion clusters: Cr(O2)2, O2Cr(O2), and CrO4. The latter, with C2v symmetry and in 2B2 state, is the global minimum, and the calculated adiabatic electron affinity of 4.83 eV is close to the experimental value of 4.98 eV.46 Compared to its neutral parent, the CrO4 cluster has no OO bond, two CrO bonds elongated by 0.044 Å, and two CrO bonds shortened by 0.081 Å. More species of anionic type are formed than neutral clusters, and O2Cr(O2) in the 2A1 state lies 0.57 eV above CrO4 in the 2B2 state (Tables 7 and 8). The diperoxide monoanion Cr(O2)2 in the 4B1 state is also more stable than the lowest energy neutral cluster. The MnO4 monoanion is the only one with strictly tetrahedral symmetry as a global minimum among the monoanions of the 3d elements. The calculated MnO bond length is smaller than the one determined in solution, 1.649 Å; in crystal salts the MnO distance varies considerably (1.6051.759 Å).47,48 The B1LYP calculated adiabatic electron affinity of 4.70 eV for MnO4 agrees with previous studies and the experimental value of 4.8 ( 0.1 eV.12 The other monoanionic species, diperoxides in the 3B1 and 1A1 states, are much less stable than the tetrahedral configuration (Table 7). The compounds LiMnO4 and LiFeO4 are promising components for Li-ion batteries; therefore, the structure and stability of the anions is of significant interest.4951 While the dianion FeO42 is tetrahedral, with an FeO bond length of 1.656 Å calculated at the B1LYP level, the monoanion FeO4 would have a degenerate state in Td symmetry with a singly occupied orbital 2e1. Attempts to simulate a Madelung field and to counterbalance the excess negative charges in a study with pure density functionals also resulted in a degenerate state of FeO4.52 The present study reveals a monoanion FeO4 in the 2 A1 state with four equivalent FeO bonds and minor distortion from Td to D2d symmetry (Table 7). Compared to the neutral

Table 9. Calculated Absolute Electronegativitiesa (χ, eV) and Hardness (η, eV), HOMO(SOMO)LUMO Gaps (H/S/L, eV), and Adiabatic Electron Affinities (EA, eV) for Low-Lying States of FeO4 cluster, symmetry, state 1

χ

η

H/S/L

FeO4, Td, A1

8.47

3.89

3.18

O2Fe(O2), C2v, 1A1 OOFeO2, Cs, 3A00

7.31 7.20

3.55 4.40

3.12 2.90

MnO4, C2v, 2B1

9.19

4.75

3.75

Cla

8.30

4.68

Bra

7.59

4.22 EA

O2Fe(O2), C2v, 1A1 + e f O2Fe(O2), C2v, 2A2

3.29

FeO4, Td, 1A1 + e f FeO4, D2d, 2A1

4.08

O2Fe(O2), C2v, 3A2 + e f O2Fe(O2), C2v, 2A2 O2Fe(O2), C2v, 1A1 + e f FeO4, D2d, 2A1

3.45 4.28

O2Fe(O2), C2v, 3A2 + e f Fe(O2)2, D2h, 4B3g

3.73

OOFeO2, Cs, 3A00 + e f O2Fe(O2), C2v, 2A2

3.24

OOFeO2, Cs, 3A00 + e f OOFeO2, Cs, 2A00

3.59

χ = (I + A)/2; η = (I A)/2; ref 53. I is ionization potential, and A is vertical electron affinity.

a

tetrahedral cluster FeO4 in the 1A1 state, the FeO bonds in the monoanion are elongated. The monoanions FeO4 in the 2A1 state and O2Fe(O2) in the 2A2 state and the planar Fe(O2)2 in the 4B3g state and O2FeOO in the 2A00 state are closely spaced by energy at either the B3LYP or B1LYP level of theory. BPW91 calculations denoted FeO4 in the 2A1 state as the global minimum; according to B1LYP and B3LYP calculations, O2Fe(O2) in the 2A2 state is the global minimum; CCSD(T) calculations are in favor of FeO4. The electron attachment to the dioxosuperoxide leads to weakening of the bond OO and strengthening of the FeOsuperoxo bond. Iron forms also planar diperoxide monoanion Fe(O2)2 in the 2B3u state, the oxide FeO4 with D2d symmetry in the 6A2 state, the diperoxide monoanion Fe(O2)2 in the 2B1 state, and the dioxoperoxide monoanion O2Fe(O2) in the 4B2 state (Tables 7 and 8). The high values of the calculated absolute electronegativity of the tetrahedral cluster FeVIIIO4 and the distorted-tetrahedral 10674



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Table 10. Harmonic Vibrational Frequencies (> 250 cm1, IR-Active) for MO4 Clusters in Solid Ar and Nearest MAr Interatomic Distances, Calculated by B1LYP/(B2PLYPD)a ω (in Ar), cm1

cluster 2

R(MAr), Å 30

adsorption complex

[Sc(O2)](O2); A2

1185; 885; 654; 612; 460; 404

1102; 836; 632; 613

2.994 (2.963)

Sc(O2)2Ar

Ti(O2)2; 1A1 O2V(O2); 2A2

949; 903; 710; 670; 667; 526 1222; 1077; 1068; 547; 501; 334

1122; 975; 974; 55632

2.996 (2.904) 2.742 (2.686)

Ti(O2)2Ar O2V(OO)Ar

O2Mn(O2); 2A1

1069; 1043; 998; 625; 574; 351; 268

975; 95136

1222; 1002; 686; 351

1204, 975, 87210

1081; 1041; 1034; 614; 603; 341; 326

969; 956; 558; 54810

3 00

OOFeO2; A 1

O2Fe(O2); A1 4

Co(O2)2; B3u

1132; 667; 463

Ni(O2)2; 3B1u

1047

5

a

ω (exptl), cm1

Ni(O2)2; B2

1168; 522

Cu(O2)2; 4B2u

1143; 490

106438 11104,56

B2PLYPD results listed in brackets.

MnVIIIO4 with C2v symmetry classify these tetraoxides as very strong oxidants (Table 9).53 The individual clusters with Mn and Fe in oxidation state VIII could be obtained by electrochemical methods; FeO4 is more reactive due to the smaller HOMO LUMO gap and the lower absolute hardness. For the dioxoperoxide O2Fe(O2) in the 1A1 state and the dioxosuperoxide O2FeOO in the 3A00 state, the absolute electronegativity drops by more than 1 eV. The photoelectron spectrum of FeO4 is in a much narrower range than the spectrum of FeO2, and the transitions are within the range 3.24.2 eV, similarly to the spectrum of FeO3, but with a more pronounced fine structure.54 Gutsev et al. performed detailed studies on the possible transitions.55 The calculations of the present study also favor the Td w D2d singletdoublet transition as responsible for the high-energy spectral band, while for the mid- and low-energy bands tripletquartet and tripletdoublet transitions have a significant contribution. In the planar monoanion of Co(O2)2 with the 3B3g ground state, the peroxo bonds are elongated by 0.122 Å, while the shortening of the CoO bonds is minor, as compared with the neutral parent in the 4B3u ground state. Similarly to the parent cluster, the monoanion can also experience conversion to the 3A2 state of O2Co(O2) with C2v symmetry, as it lies very close in energy. The conversion requires major structural changes: rotation of side-on bonded dioxygen to reach orientation perpendicular to the σh plane; breaking of one OO bond and significant shortening of the two bonds to the separated oxygen atoms of oxide type CoOoxo; and the two CoOperoxo bonds to the sideon bonded oxygen atoms are lengthened. The global minimum assignment differs according to the used density functional: PW91 calculations42a denoted the O2Co(O2) monoanion with C2v symmetry in the triplet state as the lowest-energy configuration, and BPW91 calculations42b favored a tetrahedral configuration. The B1LYP and CCSD(T) calculations of the present study assign the planar diperoxide Co(O2)2 in the 3B3g state as the most stable monoanion, followed by the 3A2 state of O2Co(O2), while the tetrahedral CoO4 monoanion in the 3A1 state is of considerably lower stability and placed close in energy to the singlet state of O2Co(O2). It should be noted, however, that the B1LYP-calculated triplet states of O2Co(O2) are significantly spin-contaminated. Ni(O2)2 in the 2B1g state is related to the neutral parent Ni(O2)2 in the 3B1u state, and the structural changes upon electron attachment are similar to those observed with Co(O2)2. The monoanion Cu(O2)2 is planar

and appears in either the 3B2g state or the 1Ag state, which are separated by 0.44 eV, a gap similar to the one found between the neutral species in 4B2u and 2B2u states (Tables 2 and 7). The electron affinities of the tetraoxygen species gradually decrease from Fe to Cu. Vibrational Frequencies and Cluster Reactivity. The lowlying by energy MO4 clusters encompass diperoxides M(O2)2 of D2h and D2d symmetry and dioxoperoxides O2M(O2) of C2v symmetry; most superoxo-species OOM(O2) and OOMO2 are of Cs symmetry. Ti(O2)2 is a typical example of a D2d symmetry cluster, but it was not detected spectrally, due to its inferior stability. The b2 symmetry vibration in Ti(O2)2 is the one of highest frequency, and it also has high intensity; it is attributed to the counter-phase stretching vibration of the OO bonds (Table 5). Coordination of a single Ar atom to Ti was confirmed at both the B1LYP and B2PLYPD levels of theory; the geometry of Ti(O2)2 experienced a minor change, and no significant frequency shifts are predicted. The planar diperoxides span the irreducible representation Γ[M(O2)2, D2h] = 2ag(R) + au + b3g(R) + 2b1u(IR) + 2b2u(IR) + b3u(IR); the most intense IR band is detected in the high-frequency range 10001200 cm1, and it originates from the b1u vibration, which is again a counterphase stretching of the two equivalent OO bonds. More significant frequency shifts between calculated frequencies of isolated and matrix-entrapped species were found for the planar diperoxides, especially Ni(O2)2, though direct bonds with noble gas atoms were not formed (Table 10). Among the matrixisolated species with CoO4 stoichiometry, dioxosuperoxides and dioxoperoxides were detected,40 despite their lower thermodymamic stability predicted by the calculations. The planar Co(O2)2 has a strong IR band, calculated at 1132 cm1, which corresponds to the b1u vibration. It is not shifted by interactions with the matrix. The dioxoperoxides span the irreducible representation Γ[O2M(O2), C2v] = 4a1(IR,R) + 2b1(IR,R) + 2b2(IR,R) + a2(R); according to the calculations, the most intense bands in the IR spectra of O2M(O2) [M = V, Cr, Mn, Fe] are in the region 9501250 cm1 (Table 5). The diperoxide of Sc also falls in this symmetry group because of the nonequivalent type of side-on bonded dioxygen, [Sc(O2)](O2). Coordination of Ar atoms was revealed for Sc and V (Table 10), but similarly to Ti(O2)2, the [Sc(O2)](O2) cluster does not undergo deformation. The structural changes experienced by the O2M(O2) clusters upon coordination of Ar are more significant than with other configurations, and the frequency shifts increase accordingly. This is in 10675



Figure 9. MO4 cluster, entrapped in the cubic unit cell of solid Ar. Ar atoms from the matrix are dark blue, oxygen atoms light blue, and the transition metal center light green. (a) Cluster model before optimization. (b) B1LYP optimized structure.

Figure 10. Molecular electrostatic potential maps (au) of MO4 clusters. Areas of positive EP are yellow, and the negative EPs are displayed in blue. (a) FeO4, 1A1; (b) Mn(O2)2,4A2; (c) (O2)FeOO, 3 A2; (d) O2FeOO, 3A00 ; (e) O2Mn(O2), 2A1; (f) O2Cr(O2), 1A1; (g) Co(O2)2, 4B3u.

difference to the MO3 species, for which minor frequency shifts in the solid matrix have been predicted by B1LYP calculations.37 Strong distortion of the Ar cell accommodating the clusters O2M(O2) was observed (Figure 9). After the coordination of an Ar atom to V, the O2V(O2)Ar cluster is formed.4 The symmetry is lowered to Cs, and the state becomes 2A00 ; the structure is substantially changed from that of O2V(O2). The peroxo-bonded oxygen atoms become nonequivalent, with one VOperoxo bond being shortened to 1.956 Å and the other elongated to 2.004 Å, which yields a structure intermediate between dioxoperoxide and dioxosuperoxide. Another cluster which strongly interacts with the matrix is the planar dioxosuperoxide O2FeOO. The cation center does not bind atoms from the matrix (the shortest FeAr distance is 3.45 Å) and retains its planar structure; however, the vibrational spectrum is significantly altered. The highest-frequency vibration, which corresponds to the OOsuperoxo stretching mode,

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undergoes a downward shift by more than 100 cm1 in the solid matrix. The vibration, which corresponds to OFeO antisymmetric stretching and comes next in both frequency and intensity after the OOsuperoxo mode, undergoes a positive frequency shift by 54 cm1 (Tables 5 and 10). The symmetric stretching vibration OFeO which is also IR active is shifted significantly downward. The calculated IR frequencies of the O2FeOO cluster encaged in the Ar cell are in better agreement with experiment than those of isolated O2FeOO. The molecular electrostatic potential (MEP) maps indicate a broad electrophilic area in the region of the cation centers, which for planar clusters like Co(O2)2 and Ni(O2)2 has a maximum in direction perpendicular to the plane of the atoms (Figure 10). Nucleophilic regions are formed in the vicinity of the oxygen atoms. The oxide-type oxygen atoms are more strongly nucleophilic than the side-on bonded atoms from dioxygen, which, in their turn, are more nucleophilic than end-on bonded oxygen atoms. In dioxosuperoxides, the electron density in the vicinity of the oxo-type atoms forms a broad area, while the nucleophilic activity of the superoxo- oxygen atoms is small. In the O2Cr(O2) MEP map, the peroxo atoms form a singular area of increased electron density around both atoms, which is a typical feature of peroxides. A different picture is observed in the MEP map of O2Mn(O2), which is representative for the dioxoperoxides of Mn and Fe: the oxide-type oxygen atoms and each of the peroxo atoms bear distinct areas of increased electron density.

’ CONCLUSIONS The tetraoxygen clusters of the 3d elements appear in the form of diperoxides, dioxoperoxides, and dioxosuperoxides, among which the diperoxides MIV(O2)2 are the most stable species for the first (Sc, Ti) and the last (Co, Ni, Cu) members of the row. Dioxoperoxides O2MVI(O2) are the global minima for V, Cr, and Mn. Iron forms a dioxosuperoxide, OOFeVO2, which has low stability toward fragmentation; it is metastable in the inert-gas matrix, and interconversion to O2FeVI(O2) in the singlet state is feasible via the triplet state of O2FeVI(O2). O2V(O2) is the most stable tetraoxygen cluster among the 3d-row elements with respect to any fragmentation reaction: release of an oxygen atom, molecular oxygen, or reduction to metallic V. In the M(O2)2 and O2M(O2) ground-state clusters, the metal cation is in a low-spin state, and Sc, Ti, V, and Cr bear a negligible local magnetic moment. The clusters interact with Ar atoms from the inert-gas matrix, and those of Sc, Ti, and V form MAr bonds; significant frequency shifts are observed for O2V(O2), OOFeO2, and Ni(O2)2. ’ ASSOCIATED CONTENT

bS

Supporting Information. Tables with calculated molecular properties of monoxides using B3LYP and calculated geometries of the ground-state tetraoxides using B3LYP and B3PW91. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. 10676



’ ACKNOWLEDGMENT CPU time at the BG08-MADARA computer cluster, financially supported by project RNF01/0110 of the Bulgarian national science fund, is gratefully acknowledged. Thanks are due to Prof. G. S. Nikolov for helpful discussions and recommendations. ’ REFERENCES (1) Somorjai, G. A.; Contreras, A. M.; Montano, M.; Rioux, R. M. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 10557. (2) Modrow, H. Appl. Spectrosc. Rev. 2004, 39, 183. (3) (a) Harrison, J. F. Chem. Rev. 2000, 100, 679. (b) Niu, S.; Hall, M. B. Chem. Rev. 2000, 100, 353.(c) Siegbahn, P. E. M. In Adv. in Chem. Phys.; Prigogine, I., Rice, S., Eds.; John Wiley & Sons Inc.: New York, 1996; Vol. XCIII, p 333. (4) Gong, Y.; Zhou, M.; Andrews, L. Chem. Rev. 2009, 109, 6765. (5) Matsui, T; Iwasaki, M.; Sugiyama, R.; Unno, M.; Ikeda-Saito, M. Inorg. Chem. 2010, 49, 3602. (6) Gutsev, G. L.; Rao, B. K.; Jena, P. J. Phys. Chem. A 2000, 104, 5374. (7) Wenthold, P. G.; Jonas, K.-L.; Lineberger, W. C. J. Chem. Phys. 1997, 106, 9961. (8) Zhao, Y.; Gong, Y.; Chen, M.; Zhou, M. J. Phys. Chem. A 2006, 110, 1845. (9) (a) Uzunova, E. L.; Mikosch, H.; Nikolov, G. J. Chem. Phys. 2008, 128, 094307. (b) Uzunova, E. L.; Nikolov, G.; Mikosch, H. ChemPhysChem 2004, 5, 192. (10) Gong, Y.; Zhou, M. F.; Andrews, L. J. Phys. Chem. A 2007, 111, 12001. (11) (a) Riedel, S.; Kaupp, M. Coord. Chem. Rev. 2009, 253, 606. (b) Cremer, D. Mol. Phys. 2001, 99, 1899. (12) Gutsev, G. L.; Rao, B. K.; Jena, P.; Wang, X. B.; Wang, L. S. Chem. Phys. Lett. 1999, 312, 598. (13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, € Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; S.; Daniels, A. D.; Farkas, O.; Fox, D. J. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (14) Becke, A. D. J. Chem. Phys. 1996, 104, 1040. (15) Adamo, C.; Barone, V. Chem. Phys. Lett. 1997, 274, 242. (16) Adamo, C.; Di Matteo, A; Barone, V.; di Matteo, A. In Adv. Quantum Chem.; Sabin, J., L€owdin, P.-O., Lami, A., Br€andas, E. J., Barone, V., Sabin, J. R., Zerner, M. C., Eds.; Academic Press: New York, 1999; Vols. 3536, p 45. (17) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785–789. (18) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200. (19) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (20) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (21) Hay, P. J. J. Chem. Phys. 1977, 66, 4377. (22) Raghavachari, K.; Trucks, G. W. J. Chem. Phys. 1989, 91, 1062. (23) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem. 1978, XIV, 545. (24) (a) Cizek, J. Adv. Chem. Phys. 1969, 14, 35. (b) Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910.

ARTICLE

(25) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (26) (a) Schwabe, T.; Grimme, S. Phys. Chem. Chem. Phys. 2006, 8, 4398. (b) Schwabe, T.; Grimme, S. Phys. Chem. Chem. Phys. 2007, 9, 3397. (27) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (28) Weinhold, F.; Carpenter, J. E. The Structure of Small Molecules and Ions; Plenum: New York, 1988. (29) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (30) Gong, Y.; Ding, C. F.; Zhou, M. F. J. Phys. Chem. A 2007, 111, 11572. (31) Chertihin, G. V.; Andrews, L. J. Phys. Chem. 1995, 99, 6356. (32) Chertihin, G. V.; Bare, W. D.; Andrews, L. J. Phys. Chem. A 1997, 101, 5090. (33) Veliah, S.; Xiang, K.; Pandey, R.; Recio, J. M.; Newsam, J. M. J. Phys. Chem. B 1998, 102, 1126. (34) Xiang, K.; Pandey, R.; Recio, J. M.; Francisco, E.; Newsam, J. M. J. Phys. Chem. A 2000, 104, 990. (35) Chertihin, G. V.; Bare, W. D.; Andrews, L. J. Chem. Phys. 1997, 107, 2798. (36) Chertihin, G. V.; Andrews, L. J. Phys. Chem. 1997, 101, 8547. (37) Uzunova, E. L. J. Phys. Chem. A 2011, 115, 1320. (38) Citra, A.; Chertihin, G. V.; Andrews, L.; Neurock, M. J. Phys. Chem. A 1997, 101, 3109. (39) Chertihin, G. V.; Citra, A.; Andrews, L.; Bauschlicher, C. W., Jr. J. Phys. Chem. A 1997, 101, 8793. (40) Danset, D.; Alikhani, M. E.; Manceron, L. J. Phys. Chem. A 2005, 109, 105. (41) Uzunova, E. L.; Nikolov, G., St.; Mikosch, H. J. Phys. Chem. A 2002, 106, 4104. (42) (a) Johnson, G. E.; Reveles, J. U.; Reilly, N. M.; Tyo, E. C.; Khanna, S. N.; Castleman, A. W., Jr. J. Phys. Chem. A 2008, 112, 11330. (b) Pradhan, K.; Gutsev, G. L.; Weatherford, C. A.; Jena, P. J. Chem. Phys. 2011, 134, 144305. (43) Vyboishchikov, S. F.; Sauer, J. J. Phys. Chem. A 2000, 104, 10913. (44) Calatayud, M.; Berski, S.; Beltran, A.; Andres, J. Theor. Chem. Acc. 2002, 108, 12. (45) Wu, H. B.; Wang, L. S. J. Chem. Phys. 1998, 108, 5310. (46) Gutsev, G. L.; Jena, P.; Zhai, H.-J.; Wang, L. S. J. Chem. Phys. 2001, 115, 7935. (47) Rabe, P.; Tolkiehn, G.; Werner, A. J. Phys. C: Solid State Phys. 1979, 12, 1173. (48) Seferiadis, N.; Dubler, E.; Oswald, H. R. Acta Crystallogr. 1986, C42, 942. (49) Bruce, P. G.; Armstrong, A. R.; Gitzendanner, R. J. Mater. Chem. 1999, 9, 193. (50) Armstrong, A. R.; Robertson, A. D.; Bruce, P. G. J. Power Sources 2005, 146, 275. (51) Notter, D. A.; Gauch, M.; Widmer, R.; W€ager, P.; Stamp, A.; Zah, R.; Althaus, H.-J. Environ. Sci. Technol. 2010, 44, 6550. (52) Atanasov, M. Inorg. Chem. 1999, 38, 4942. (53) Pearson, R. G. Inorg. Chem. 1988, 27, 734. (54) (a) Wu, H. B.; Desai, S. R.; Wang, L. S. J. Am. Chem. Soc. 1996, 118, 5296. (b) Wu, H. B.; Desai, S. R.; Wang, L. S. J. Am. Chem. Soc. 1996, 118, 7434. (55) Gutsev, G. L.; Weatherford, C. A.; Pradhan, K.; Jena, P. J. Phys. Chem. A 2010, 114, 9014. (56) Darling, J. H.; Garton-Sprenger, M. B.; Ogden, J. S. Faraday Symp. Chem. Soc. 1973, 7, 75. (57) Tao, J. M.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Phys. Rev. Lett. 2003, 91, 146401. (58) (a) Lee, T.; Taylor, P. Int. J. Quantum Chem. 1989, 23, 199. (b) Lee, T. Chem. Phys. Lett. 2003, 372, 362. (59) Basch, H.; Osman, R. Chem. Phys. Lett. 1982, 93, 51. (60) Miliordos, E.; Mavridis, A. J. Phys. Chem. A 2010, 114, 8536. (61) Merer, A. J. Annu. Rev. Phys. Chem. 1989, 40, 407. 10677



ARTICLE

(62) Shirley, J.; Sculrock, C.; Steimle, T. J. Chem. Phys. 1990, 93, 1568. (63) Steimle, T. C.; Shirley, J. E. J. Chem. Phys. 1989, 91, 8000. (64) Loock, H.; Simard, B.; Wallen, S.; Linton, C. J. Chem. Phys. 1998, 109, 8980. (65) Suenram, R. D.; Fraser, G. T.; Lovas, F. J.; Gillies, C. V. J. Mol. Spectrosc. 1991, 148, 114. (66) Steimle, T. C.; Nachman, D. F.; Shirley, J. E.; Bauschlicher, C. W., Jr.; Langhoff, S. R. J. Chem. Phys. 1989, 91, 2049. (67) Kang, H.; Beauchamp, J. L. J. Am. Chem. Soc. 1986, 108, 5663. (68) Steimle, T. C.; Nachman, D. F.; Shirley, J. E.; Merer, A. J. Chem. Phys. 1989, 90, 5360. (69) Steimle, T. C.; Nachman, D. F.; Fletcher, D. A. J. Chem. Phys. 1987, 87, 5670. (70) Wu, H.; Wang, L. S. J. Phys. Chem. A 1998, 102, 9129. (71) Wu, H.; Wang, L. S. J. Chem. Phys. 1997, 107, 8221. (72) Wu, H.; Wang, L. S. J. Chem. Phys. 1998, 108, 5310. (73) Wenthold, P. G.; Gunion, R. F.; Lineberger, W. C. Chem. Phys. Lett. 1996, 258, 101. (74) Gutsev, G. L.; Rao, B. K.; Jena, P.; Li, X.; Wang, L. S. J. Chem. Phys. 2000, 113, 1473. (75) Drechsler, G.; Boesl, U.; Bassmann, C.; Schlag, E. W. J. Chem. Phys. 1997, 107, 2284. (76) Li, X.; Wang, L. S. J. Chem. Phys. 1999, 111, 8389. (77) Ramond, T. M.; Davico, G. E.; Hellberg, F.; Svedberg, F.; Salen, P.; Soderqvist, P.; Lineberger, W. C. J. Mol. Spectrosc. 2002, 216, 1. (78) Polak, M. L.; Gilles, M. K.; Ho, J.; Lineberger, W. C. J. Phys. Chem. 1991, 95, 3460.

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Density Functional Study of the Stable Oxidation States and the

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