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Transitions From Stable to Metastable States in the CrO and CrO Series, N = 1 – 14 2

n

2

n

–

Gennady Lavrenty Gutsev, Konstantin V Bozhenko, Lavrenty G Gutsev, Andrey N Utenyshev, and Sergey M. Aldoshin J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b11036 • Publication Date (Web): 06 Jan 2017 Downloaded from http://pubs.acs.org on January 16, 2017

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The Journal of Physical Chemistry

Transitions from Stable to Metastable States in the Cr2On and Cr2On– Series, n = 1 – 14 G. L. Gutsev,a,* K. V. Bozhenko,b,c L. G. Gutsev,d A. N. Utenyshev,b S. M. Aldoshinb a

Department of Physics, Florida A&M University, Tallahassee, Florida 32307, USA

b

Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka 142432,

Moscow Region, Russia c

Department of Physical and Colloid Chemistry, Peoples’ Friendship University of Russia, Moscow

117198, Russia d

Department of Chemistry and Biochemistry, Florida State University, Tallahassee 32306, USA

Abstract The geometrical and electronic structures of the Cr2On and Cr2On– clusters are computed using density functional theory with the generalized gradient approximation in the range of 1 ≤ n ≤ 14. Local total spin magnetic moments, polarizabilities, binding energies per atom, and energies of abstraction of O and O2 are computed for both series along with electron affinities of the neutrals and vertical detachment energies of the anions. In the lowest total energies states of Cr2O2, Cr2O3, Cr2O4, Cr2O14, Cr2O3–, Cr2O4–, and Cr2O14–, total spin magnetic moments of the Cr atoms are quite large and antiferromagnetically coupled. In the rest of the series, at least one of the Cr atoms has no spin magnetic moment at all. The computed vertical electron detachment energies of the Cr2On– are in good agreement with experimental values obtained in the 1 ≤ n ≤ 7 range. All neutral Cr2On possess electron affinities larger than the electron affinities of halogen atoms when n > 6 and are thus superhalogens. It is found that the neutrals and anions are stable with respect to the abstraction of an O atom in the whole range of n considered whereas both neutrals and anions became unstable toward the O2 loss for n > 7. The polarizability per atom decreases sharply when n moves from one to four and remains nearly constant for larger n values in both series. The largest members in both series, Cr2O14 and Cr2O14– possess the geometrical structures of the Cr2(O2)7 type by analogy with monochromium Cr(O2)4.

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1. INTRODUCTION Transition metal oxides play an important role in various catalytic and biochemical processes and possess a wide range of applications,1 consequently, they are the subject of numerous experimental and theoretical studies. 2,3 Chromium is a member of the 3d-metal series and participates in a number of catalytic and redox reactions as well as in polymerization and photocatalysis reactions.4,5,6 Chromium oxides are used as industrial catalysts, 7 , 8 for polymerization of saturated hydrocarbons, 9 , 10 and as surfacing materials.11,12 A Cr atom has a ([Ar]3d54s1) 7S3 ground state and can exhibit different oxidation numbers in chromium oxide clusters,13 bulk chromium oxides14 such as CrO2, Cr2O3, and Cr5O12, and various salts. 15 Bulk chromium dioxide is widely used as a ferromagnetic carrier in data recording devices.16,17,18 Experimental and theoretical studies19,20,21,22 have proven that the properties of nanoparticles are generally different from those of the corresponding solids. This suggests that nanoparticles may be used 23,24 for synthesizing new compounds with desired properties. Magnetic behavior of chromium oxide clusters is highly sensitive to changes in stoichiometric composition and charge and therefore can be tailored as desired. In particular, small dichromium oxide clusters Cr2On– were found to possess25 ferromagnetic lowest total energy states, whereas the lowest total energy states of neutral Cr2On are antiferromagnetic26 for small n values. Mononuclear CrOn have been the subject of several studies for n values varying from one to four.27,28 Stable and metastable states of CrOn along with their singly positively and negatively charged ions were computed29 for n values up to ten by analogy to the previous study of stable and metastable states of FeOn (n = 1 – 12)30 as well as AlOn and ScOn (n = 1 – 18).31 The existence of stable Fe(O2)n+ cations up to n = 12 has been confirmed experimentally, 32,33,34 whereas Ni(O2)n+ species have been observed for n = 2 – 4.35 Dichromium oxide clusters have received special attention from both experimentalists and theoreticians. Vibrational frequencies of neutral Cr2O2-4 and Cr2O2,4,6 were obtained 36 , 37 from the ACS Paragon Plus Environment

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infrared spectra measured in argon matrices. Electron detachment energies were measured for the Cr2On– anions in the range38,39 of n = 1 – 3 and in the range40,41 of n = 1 – 7 using laser photodetachment spectroscopy. Neutral Cr2On (n = 1 – 6) have been studied by Reddy et al.42 and Wang et al.43 using both local spin density approximation (LSDA) and density functional theory with the generalized gradient approximation (DFT-GGA). The geometrical structures of the lowest total energy states found for these chromium oxides were found to be different from those44 of the congener Mo2On and W2On clusters. The Cr2O4-6– anions have been computed45 using the hybrid Hartree-Fock-Density-Functional-Theory (HFDFT) B3LYP method. Polynuclear chromium oxides have also attracted the attention of researches. Bergeron et al.46 have considered the structural motifs in the CrnO2n+2 and CrnO3n series. Janssens et al.47 have determined the ionization energies of Cr3On (n = 0 – 2) using threshold photoionization spectroscopy. Li and Dixon48 have optimized the (MO3)n clusters (M = Cr, Mo, W; n = 1 – 6) and computed their Brönsted basicities and Lewis acidities. Joint theoretical and experimental studies were performed 49,50 for the M3O8 and M3O8– as well as M4O10 and M4O10– pairs (M = Cr, W). Compere et al. 51 computed interactions of small (Cr2O3)n clusters (n = 1 – 3) with ions contained in sea water, while Kumari et al.52 simulated NO oxidation by a (Cr2O3)3 cluster. Peroxochromates with a general formula M3CrO8, where the counterion is the Cr(O2)4– anion and M is an alkali atom, were synthesized 53 long ago, in 1905. These salts were found 54 to possess unusual properties since Cr atoms in the salts are in a Cr(V) state and the salts are expected to be ferroic. This was confirmed by the recent studies done by the Dalal group on M3CrO8 (M = Na, K, Rb), 55 M3CrO8•XH2O (M = Li, Na, Cs),56 and M3-x(NH4)xCrO8 (M = Na, K, Rb, Cs).57 It was shown that the order-disorder transitions in the M3-x(NH4)xCrO8 salts are strongly influenced by directions of hydrogen bonds. It would thus be interesting to synthesize salts with Cr2Ox– counterions which might possess exotic ferroic properties. ACS Paragon Plus Environment

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The purpose of this work is to perform a systematic study of geometrical structures and properties of the dichromium oxide Cr2On and Cr2On– series using a DFT-GGA method. The results obtained for n ranging from 1 to 7 will be used in the interpretation of experimental data obtained from the laser photodetachment spectra of Cr2On–. Since the formal union of two Cr(O2)4– anions via a shared peroxo-group would result into a Cr2O14– anion, we also consider both neutral and anion series in the range of 8 ≤ n ≤ 14. For the lowest total energy states found in the both series, we will compute polarizabilities, binding energies per atom, energies of abstraction of O and O2 from Cr2On and Cr2On–, as well as electron affinities of the neutrals and vertical detachment energies of an extra electron from the anions. In addition, we will compute magnetic exchange coupling constants for both neutrals and anions for n = 1 – 3. 2. DETAILS OF COMPUTATIONS All-electron spin-unrestricted density functional theory with the generalized gradient approximation was used in our computations performed using the GAUSSIAN 0958. We have chosen the BPW91 exchange-correlation functional composed of the Becke exchange59 and the Perdew-Wang correlation60 and the 6-311 + G* basis sets [(15s11p6d1f/10s7p4d1f) for Cr and (12s6p1d/5s4p1d) for O]. 61 This choice is based on our previous studies of species where comparison of the results of computations to experimental data was found to be quite satisfactory; namely, CrO and CrO–,6263,64,65 CrO2 and CrO2–,66 Cr2(CO)2,67 CrO3-5 and CrO3-5–.68,69 The BPW91 functional was found to be the best among many other functionals when reproducing the results of calculations obtained using the couplecluster method with singles, doubles, and non-iterative inclusion of triples [CCSD(T)] 70 for (TiO2)n clusters,71 (CrO3)n clusters,72 and FeO2.73 Computations of binding energies using standard reference sets have shown 74 the BPW91 accuracy to be comparable to that of more recently developed exchangecorrelation functionals. Among HFDFT and DFT functionals, the DFT-GGA functionals showed the best performance in computations75 of Cr2 and Cr3. Jensen76 has recently analyzed the performance of


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Pople’s basis sets, to which the 6-311 + G* basis belongs and found it to be competitive with the comparable in size basis sets designed by several other groups. Our trial geometrical structures possessed one, two, and three bridge O atoms connecting two Cr atoms. The rest of oxygen atoms at each particular n value were attached to the Cr atoms in various combinations: dissociatively (oxo, a single O atom), associatevely (peroxo and superoxo, an O2 dimer), or as an ozonide O3 group. Since the valence electronic configuration of a ground-state Cr atom is (3d54s1), the highest possible spin multiplicities of Cr2 and Cr2– are 11 and 12, respectively.77 We have optimized states with each trial geometrical structure in the whole span of possible spin multiplicities in the ranges of 1 ≤ n ≤ 11 and 2 ≤ n ≤ 12 for the neutrals and anions, respectively, beginning with the highest spin multiplicity. In order to obtain low-spin antiferromagnetic states in oxygen-deficient species, one need to use spin-polarized electronic densities as starting guesses. Direct optimizations of symmetric species or optimizations with using non-spin polarized guess electronic densities will result in non-magnetic solutions. This can clearly be seen from the results of optimizations of a Cr2 singlet state either directly or using a guess electronic density from an optimized state of Cr2 with a higher spin multiplicity. The non-magnetic singlet state of Cr2 is higher in total energy than its antiferromagnetic state by 2.21 eV at the BPW91/6-311+G* level. In order to find this antiferromagnetic state, one can first compute a quartet or doublet state of a MnCr dimer and use the computed electronic density as a guess in optimizations of a singlet state of Cr2. Successive oxidation quenches the total spin magnetic moments of the Cr atoms; therefore, we performed optimization beginning with smaller values of 2S + 1 for larger n values. Each geometry optimization was followed by calculations of the harmonic vibrational frequencies, and the geometry was adjusted according to the modes corresponding imaginary frequencies if the optimization led to a transition state. States with adjusted geometries were optimized followed by the vibrational frequencies computations, and the procedure was repeating until a local minimum was found. The convergence threshold for total energy was set to 10–8 eV and the force ACS Paragon Plus Environment

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threshold was set to the default value of 10–3 eV/Å. The total magnetic moment within the Russell-Saunders coupling scheme is defined as µ = (2S + L) µB, where L and S are the total angular and spin moments, respectively, and µB is the Bohr magneton. We will compute the total spin magnetic moment M = 2SµB as [nα – nβ]µB, where nα and nβ are the numbers of the majority spin (spin-up or α) and minority spin (spin-down or β) electrons, respectively, since the spin of an electron is ½. Local total spin magnetic moments on atoms are determined as the differences of natural atomic orbital populations (NAO) in the α- and β-spin representations obtained using the NBO suite.78 The local total spin magnetic moment of an atom A is computed as MA = (NAOAα – NAOAβ)µB. 3. RESULTS AND DISCUSSION We discuss first the geometric structures and spin multiplicities of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 1 – 14 and compute magnetic exchange coupling constants for small species. Next, we consider if the electric dipole polarizability depends on charge and compare our computed adiabatic electron affinities of Cr2On and vertical electron detachment energies of Cr2On– with experimental data. Finally, we discuss the average binding energy per atom in the both series and present the energy of decay channels corresponding to the abstraction of O and O2. 3. 1. Geometrical Structures and Spin Multiplicities The geometrical structures of the lowest total energy states of Cr2On and Cr2On–are presented in Fig. 1 for 1 ≤ n ≤ 6. For comparison, we displayed also the ground-state structures of Cr2 and its anion as obtained in our previous work77 on homonuclear 3d-metal dimers. All optimizations were performed without imposing symmetry constraints, and the structures obtained were reoptimized with proper symmetry constraints in order to assign spectroscopic states. For all species in this range of n, there is at least a plane of symmetry in their nuclear frames, except for the Cr2O2– anion whose geometry is


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presented by a twisted OCrOCr chain. Note that symmetry of the electronic density can be lower than the formal symmetry of a nuclear frame if there is an antiferromagnetic spin coupling between total spin magnetic moments of chromium atoms. Generally, our structures are similar to those obtained in the previous work; however, there are some differences. Veliah et al.79 considered only singlet, triplet, and quintet states of Cr2O, whereas we found the lowest total energy state to have the spin multiplicity of 11 in agreement with the results of Tono et al. 38 It is worth mentioning that the ground-state Mn2O– anion80 has a geometrical shape similar to that of the Cr2O neutral, where as its spin multiplicity of 12 is the same as the spin multiplicity of the ground-state linear Cr2O– anion. We found that the ground state of Cr2O2 is an antiferromagnetic singlet with symmetry distorted from D2h to C2v in agreement with the recent work43, whereas Xiang et al.81 have found 2S + 1 = 9 for the ground state of Cr2O2. We obtained 2S + 1 = 4 for the lowest state of Cr2O5– whereas Lau et al.

45

have obtained 2S + 1 = 2 using the B3LYP method. In our computations,

the doublet is higher in total energy by 0.04 eV. The lowest total energy states of Cr2On and Cr2On– for 7 ≤ n ≤ 9 are shown in Figure 2. Note that the Cr2O7– anion is the largest species in the anion series whose photodetachment spectrum was obtained. Unlike to the case of smaller species presented in Fig. 1, where both neutrals and anions possess the same topology except for the pair with n = 2, the geometries of the neutrals and anions have generally different shapes when n > 6. The Cr2O7– anion has symmetrical Cr2O3 moieties connected via a single O-atom bridge, whereas the Cr atoms in the Cr2O7 neutral are connected with two oxygen bridges, one of which is presented by an O2 dimer. All neutral and anion species possess singlet and doublet lowest total energy states, respectively in the 7 ≤ n ≤ 9 range. The local total spin magnetic moments of the Cr atoms are small and do not exceed 0.2 µB in all lowest total energy states presented in Fig. 2, however, the Cr atoms may possess much larger total spin magnetic moments in singlet and doublet states of the neutrals and anions, respectively. ACS Paragon Plus Environment

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For the Cr2O8 – Cr2O8– pair, we present four isomers in Fig. 2 which correspond to the lowest total energy states and three nearest in total energy states found in our optimizations. The geometrical structure of the lowest total energy state of Cr2O8 corresponds to the geometry of Cr2O7 with an O atom added to the bridging O2 group thus forming an exotic ozone-type bridge. The geometry of the lowest total energy state of Cr2O8– is formed by adding an O atom to one of dissociatively bound O atoms in the structure of Cr2O7–, which corresponds to the formation of the first peroxo group in the both series. It is worth noting that the states of the Cr2O8 – Cr2O8– pair have been previously optimized82 at the B3LYP/6-311+G* level. The lowest total energy states found were triplet and quartet states for Cr2O8 and Cr2O8–, respectively, with two CrO(O2) moieties connected with two oxygen bridges in both cases. Our optimized singlet 1A (C2 symmetry) state of Cr2O8 which possesses the same topology is higher in total energy by 0.55 eV than the lowest total energy state (see Fig. 2) and corresponds to the third nearest in total energy state. The triplet state with this topology is higher in total energy than the singlet state by 0.06 eV. Even larger gaps of 1.44 eV and 1.94 eV separate our lowest total energy state and the doublet and quartet states with the di-bridged geometrical structures from Ref. [82]. The lowest total energy states of the Cr2On – Cr2On– pairs are shown in Fig. 3 for 10 ≤ n ≤ 14. The states of the neutrals are triplets for n = 10 – 12 and singlets for n = 13 and 14, whereas all anion states are doublets. When moving from n = 10 to n = 14, all dissociatively bonded oxygen atoms are replaced with peroxo- or superoxo-groups. The geometries of the lowest total energy states of Cr2O13 and Cr2O12– also contain single ozonide groups. As might be anticipated, the lowest total energy states of Cr2O14 and Cr2O14– possess the geometries corresponding to the union of two Cr(O2)4 moieties via a dioxygen bridge. The local spin magnetic moments of the Cr atoms in Cr2O14 are antiferromagnetically coupled and their absolute values are close to 1 µB, which corresponds to the presence of a localized spin-orbital.


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3. 2. Magnetic Properties Since the maximal formal valence of a Cr atom is six, and each oxygen atom is divalent, the local spin magnetic moments are completely quenched in Cr2O6. As the dissociatively attached oxygen atoms are replaced with peroxo or superoxo groups, local spin magnetic moments of up to ±0.8 µB appear at some O atoms of the peroxo and superoxo groups. The local spin magnetic moments of the oxygen atoms are coupled antiparallel which results in the singlet lowest total energy states when n > 8 except for n = 10, 11, and 12 where the lowest total energy states are triplets. The spin multiplicities of Cr2On and Cr2On– in the whole range of 1 ≤ n ≤ 14 are presented in Fig. 4 as a function of the number of oxygen atoms. The Cr2O3 and Cr2O5 neutrals possess the triplet lowest total energy state whereas their nearest neighbors have the singlet ground states, which can be related with the asymmetric geometrical structures of these two species. Correspondingly, the Cr2O3– and Cr2O5– anions possess the quartet ground states. As can be seen in Fig. 1, the lowest total energy states of both neutral and anionic Cr2On are antiferromagnetic when 1 ≤ n ≤ 4, except for Cr2O, Cr2O2–, and Cr2O2– whose antiferromagnetic states are somewhat higher in total energy than their high-spin states with the parallel coupling of the local total spin magnetic moments of the Cr atoms. One can evaluate magnetic exchange coupling constants for both neutral and inions in this range of n using the Heisenberg Hamiltonian which can be written as H = -2J12S1S2

(1)

where J12 represents the exchange coupling constant between two magnetic centers with spins S1 and S2. The positive and negative values of J12 indicate that the lowest total energy state is ferromagnetic or antiferromagnetic, respectively. The rigorous construction of a magnetic Hamiltonians is quite complicated; 83 therefore, some approximate expressions are usually used when computing the Heisenberg coupling constants. We chose a simple expression widely used in the literature84,85,86


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– J12 = –

(2)

where ELS and EHS are total energies of the low-spin and high-spin states, respectively, and SLS and SHS are total spins of the states. Generally, low-spin antiferromagnetic states are seriously spincontaminated; therefore, we use in our calculations both formal S values corresponding to the spin multiplicity of the state (pure spin) and the values corresponding to spin-contaminated states obtained in our DFT-GGA computations. The J12 values computed according to Eq. 2 are presented in Table 1 together with the values for Cr2O–, Cr2O2–, and Cr2O3–, computed previously25 using the B3LYP method and same Eq. 2. As can be seen, our values are substantially smaller than the B3LYP values. Experimentally measured exchange coupling constants in hydrogen-bridged chromium dimers of a number of complexes87 are in the range –27.8 cm-1 < J12 < +1.1 cm-1, that is, our value of 19.0 cm-1 obtained for the oxygen-bridged chromium dimer seems to be reasonable. Table 1. Computed Magnetic Exchange Coupling Constants of Cr2On and Cr2On– for 0 ≤ n ≤ 4. a Species Cr2 Cr2– Cr2O Cr2O– Cr2O2 Cr2O2– Cr2O3 Cr2O3– Cr2O4 Cr2O4–

S(S+1)

2S + 1 1 11 2 12 11 1 12 2 1 9 10 2 3 7 8 4 1 5 2 6

0 30 0.75 35.75 30 0 35.75 0.75 0 20 24.75 0.75 2.0 12.0 15.75 3.75 0 6.0 0.75 8.75

BS 2.23 30.01 2.54 35.78 30.05 4.63 35.79 5.24 3.82 20.06 24.83 4.09 3.78 12.07 15.84 5.56 1.73 6.08 2.52 8.85

J S(S+1) -260.7

JBS -281.5

-64.5

-67.9

16.1

19.0

86.0

98.5

-52.2

-64.3

107.7

124.7

-227.6

-274.5

1.3

1.9

-471.9

-650.8

-100.7

-127.2


Theor.b

1347.0

830.7

32.26

10

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a


All values in cm-1. For each species, the first 2S + 1 value corresponds to the lowest total energy state.

BS stands for “broken-symmetry”; that is, the S(S+1) value is obtained from the results of our computations.

b

See Ref. [Error! Bookmark not defined.].

3. 3. Polarizability The components of static dipole electric polarizability tensor correspond to coefficients in the Taylor expansions of total energy perturbed by a weak uniform external static electric field88 E p = E 0 − ∑ µα Fα − α

1 1 ααβ Fa Fβ − ∑ βαβγ Fα Fβ Fγ +.... ∑ 2 α ,β 6 α ,β ,γ

(3)

where Ep is perturbed total energy, F is a static electric field, E0 is total energy in the absence of the field, µα are the components of the permanent dipole moment vector, ααβ are the components of the static dipole electric polarizability tensor (linear polarizability), βαβγ are the components of the first dipole electric hyperpolarizability tensor (second-order nonlinear polarizability). Subscripts run over x, y, and z coordinates. The mean static dipole electric polarizability ( α ), referred to as polarizability, is defined as the trace of the static dipole electric polarizability tensor:

1 3

α = (α xx + α yy + α zz )

(4)

The polarizabilities per atom of the lowest total energy states in the Cr2On and Cr2On– series were computed according to Eq. 4 and presented in Figure 5. As can be seen, the polarizabilities in the both series have the largest difference in the beginning and nearly match each other in the whole range of 4 ≤ n ≤ 14. The largest difference of 22 Å3 is found for the oxygen-free Cr2 – Cr2– pair. The polarizabilities of the Cr and O atoms computed at the BPW91/6-311+ G* level are 10.00 Å3 and 0.43 Å3, respectively. The experimental value89 for the Cr atom polarizability is 8.89±3.35 Å3; that is, our value is in agreement with the experimental value within the experimental uncertainty bars. No experimental value has been reported for the O atom polarizability to the best of our knowledge. The relatively sharp decrease in polarizability of Cr2On and Cr2On– when the number of oxygen atoms ACS Paragon Plus Environment

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exceeds four appears to be due to a small polarizability of oxygen atoms. The nearly linear behaviour of the polarizability curves in Fig. 5 for n > 5 shows a non-additive character of polarizability; namely, the polarizability values for, e.g., Cr2O9 and Cr2O14 in Fig. 5 are 1.48 Å3 and 1.45 Å3, respectively, whereas the sums of atomic polarizabilities of the Cr and O atoms divided by the number of atoms are 2.17 Å3 and 1.62 Å3, respectively. 3. 4. Electron Affinities and Vertical Electron Detachment Energies The adiabatic electron affinity (EAad) of a neutral thermodynamically stable Cr2On species is computed as the difference in total energies of the lowest total energy states of a Cr2On– anion and its neutral parent: EAad(Cr2On) = [Etotel(Cr2On) + E0(Cr2On)] – [Etotel(Cr2On–) + E0(Cr2On–)]

(5)

where Etotel is the total Born-Oppenheimer energy and E0 is the zero-point vibrational energy. Important characteristics of an anion are the vertical detachment energies (VDE) of its extra electron, which can be obtained from experimental photoelectron spectra. If an anion state has the spin multiplicity of 2S + 1, then the instantaneous (geometry not relaxed) neutral states formed after the extra electron detachment may have the spin multiplicity of 2S + 2 or 2S. The corresponding VDE values are computed according to the equation: VDE±( Cr2On–) = Etotel(Cr2On, (2S + 1) ±1) – Etotel(Cr2On–, 2S + 1)

(6)

Experimental VDEs of the Cr2On– anions were obtained in the range of 0 ≤ n ≤ 7. The anions in this range are thermodynamically stable whereas the larger anions are metastable, as we will see below. Comparison of our computed values and the values obtained from photoelectron spectra is done in Table 2. Our computed VDE values are in good agreement with experiment within the experimental uncertainty bars, and the largest difference of 0.24 eV is obtained for the Cr2O5– anion. Adiabatic electron affinities (EAad) deduced from the experimental spectra and the EAad computed in this work are within 0.2 eV of each other, except for Cr2O7 where the difference is 0.67 eV. This discrepancy is


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related with the different geometrical structures of Cr2O7 and Cr2O7– (see Fig. 2) and the difference between total energies of Cr2O7 computed at the equilibrium and anion geometries is 0.92 eV. This relaxation energy was only partly accounted for in an experimental estimate based on an assumption of similar geometrical topologies of the Cr2O7 and Cr2O7– species. Experimental VDE values of the Cr2On– anions obtained by Tono et al. 39 are 1.3 eV, 1.8 eV, and 2.0 eV for n = 1, 2, and 3, respectively, and are somewhat larger than the experimental VDEs presented in Table 2 which were obtained from the better resolved electron photodetachment spectra. The VDE values of Cr2O4– , Cr2O5–, and Cr2O6– have been previously computed 45 at the B3LYP/6-31G* level of theory. Their values which are presented in the footnotes to Table 2 are in slightly worse agreement with experiment than our BPW91/6-311+G* values. Vertical electron detachment energies computed in the whole range of n from 0 to 14 are presented in Figure 6. The maximal VDE value of 6.17 eV belongs to Cr2O7– and the VDE values gradually decrease to 4.41 eV as n grows to 14 and to 0.43 eV as n decreases to zero. Quite remarkably, the VDE– and VDE+ values corresponding to an extra electron detachment from the doublet anion states to the singlet and triplet neutral states nearly match each other. Despite the fact that both Cr2On neutrals and Cr2On– anions are unstable toward the O2 loss for n > 7, one can still compute the adiabatic electron affinity according to Eq. 5 because O2 loss energies do not appreciably depend on charge for a given n > 7 value. One can also use a thermodynamic cycle for the EAad evaluation. As an example, we consider the Cr2O14 case. The EAad value of Cr2O14 computed using Eq. 5 is 4.11 eV and matches within roundoff errors the value of 4.12 eV obtained from the cycle:


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Note that the anion is stable toward the abstraction of a O2– anion. Beginning with n = 5, the EAad values of Cr2On are higher than the electron affinity of a Cl atom (3.62 eV)90; therefore, these Cr2On species belong to the class of compounds known as superhalogens.91,92 A special case is presented by Cr2O7 which possess the largest EAad in the series. The sum of the maximal formal valencies of two Cr atom is 12 and the sun of normal valencies of the O atoms is 14; that is, one may consider the Cr2O7 as possessing two holes and thus capable of forming a stable Cr2O7–2 dianion by analogy with SO4 which accepts two electrons from hydrogen atom and forms the strong acid H2SO4. Our optimizations of a singlet state of the Cr2O7–2 dianion resulted in a state which is lower in total energy than the lowest total energy state of the Cr2O7– anion by 0.78 eV; that is, the anion is stable with respect to the second electron detachment. Therefore, the existence of dichromic acid H2Cr2O7 or dichromate salts such as Na2Cr2O7 is not surprising.

Table 2. Comparison of Computational and Experimental Data.

2S + 1 VDE– VDE+ Exp

2S + 1 tw exp

Cr2– 2

Cr2O– 12

0.43

1.27

Cr2O2– Cr2O3– Cr2O4– 10 4 2 Vertical electron detachment energy 2.70 b 1.70 1.70

Cr2O5– 4

Cr2O6– 2

Cr2O7– 2

3.53 c

4.38 d

6.17

b

1.64 5.16 4.69 2.70 3.10 5.48 5.72 5.69 a 0.505±0.005 1.17±0.03 1.69±0.03 1.83±0.05 2.84±0.05 3.82±0.05 4.45±0.05 5.90±0.03 Adiabatic electron affinity Cr2 Cr2O Cr2O2 Cr2O3 Cr2O4 Cr2O5 Cr2O6 Cr2O7 1 11 1 3 2 4 2 1 0.43 1.02 1.40 1.58 2.40 3.37 4.21 4.85 0.505±0.005 0.9±0.1 1.65±0.03 1.68±0.02 2.55±0.03 3.49±0.02 4.28±0.02 5.57±0.05


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a

Experimental value for Cr2 is from Ref. [93], all other experimental values are from Ref. [40].

b

VDE– = 3.44 eV (singlet) VDE+ = 3.22 eV (triplet), see Ref. [45];

c

the ground state of Cr2O5– was found to be a doublet in Ref. [45], the VDE+ is 3.90 eV;

d

VDE– = 4.71 eV, see Ref. [45];

3. 5. Binding Energies of O and O2 in Cr2On and Cr2On–. The results of our computations can be used for evaluating the binding energies of O and O2 in the Cr2On and Cr2On– series according to the equations el el el Eb(Cr2On-1 – O) = Etot ( Cr2On-1) + E0(Cr2On-1) + Etot (O) – [Etot (Cr2On) + E0(Cr2On)]

(7)

el el el Eb(Cr2On-2 – O2)=Etot ( Cr2On-2) + E0(Cr2On-2) + Etot (O2) + E0(O2) – [Etot (Cr2On) +E0(Cr2On)]

(8)

where Etotel is the total Born-Oppenheimer energy and E0 is the zero-point vibrational energy. Binding energies per atom can be computed according to the equation el el el Eatom(Cr2On) = [mEtot (Cr) + nEtot (O)] – Etot ( Cr2On) – E0(Cr2On)]/(m + n)

(9)

Binding energies of the Cr2On– anions were computed according to Eqs (7) – (9) after the proper replacement of the neutrals by their anions. In order to gain insight into the basis set superposition errors (BSSE), we performed computations using the COUNTERPOISE keyword for the Cr2O8 (singlet) → Cr2O6 (singlet) + O2 (triplet) and Cr2O8 (singlet) → Cr2O7 (singlet) + O (triplet) channels. The BSSE energies found are practically the same for the both channels and are equal to 0.0865 eV (2 kcal/mol). One can assume that the BSSE energies are not significantly larger in other dichromium oxides considered in this work. The binding energies per atom computed for the neutral Cr2On and anionic Cr2On– clusters are presented in Fig. 7 as a function of the number of oxygen atoms. In the whole n range, the values corresponding to the anions are somewhat larger than the values of the corresponding neutrals. The maximum in both series corresponds to n = 6 and the binding energies decrease when moving to smaller and larger n values. The absolute minima in the binding energies per atom of 0.53 eV and 0.74 eV ACS Paragon Plus Environment

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belong to Cr2 and Cr2–, respectively. Adding an O atom results in the binding energy jumping to 2.33 eV and 2.66 eV for Cr2O and Cr2O– , respectively. Binding energies per atom of the Cr2O7 and anionic Cr2O7–, 4.21 eV and 4.75 eV, are smaller by ~0.2 eV than the binding energies per atom of Cr2O6 and Cr2O6–, 4.45 eV and 4.98 eV, respectively. The smallest binding energies per atom at n > 7 belong to the Cr2O14 and Cr2O14– pair, 4.36 eV and 4.62 eV, respectively. The decrease in the binding energies per atom in both series is related to the loss of stability with respect to an O2 dimer abstraction when n > 7 (see Fig. 8), and the most exothermic in both series are Cr2O11 (–1.54 eV) and Cr2O14– (–1.81 eV). As can be noted, the O2 abstraction energy is nearly independent of the number of oxygen atoms when n > 10. It is worth noting that the Cr2On– anions are stable toward the decay via the Cr2On– → Cr2On + O2– channel. This is because the EAad value of O2 is much smaller than the EAad of Cr2On–. The EAad(O2) computed according to Eq. (5) at the BPW91/6311+G* level is 0.47 eV. This value is in excellent agreement with the experimental value94 of 0.448 ± 0.006 eV and the best CCSD(T) value95 of 0.452±0.01 eV. All species in both Cr2On and Cr2On– series are stable with respect to an oxygen atom abstraction. 4. CONCLUDING REMARKS This work presents the results of computations on geometrical structures and properties in the Cr2On and Cr2On– series using density functional theory with the generalized gradient approximation in the range of 1 ≤ n ≤ 14. The largest n value of 14 corresponds to the number of oxygen atoms in the union of two Cr(O2)4 moieties via a shared O2. It is found that the lowest total energy states of Cr2On and Cr2On– are ferromagnetic or antiferromagnetic for n = 1 – 4, and we computed magnetic exchange coupling constants J12 in this n range. The Cr atoms in Cr2On and Cr2On– for larger n carry no or small local spin magnetic moments except for Cr2O14 and Cr2O14–. In the case of the lowest total energy state of Cr2O14, the local spin magnetic moments are ±0.9 µB, i.e., the moments are coupled


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antiferromagnetically,

In

the Cr2O14– anion the local

spin magnetic moments

are

also

antiferromagnetically coupled but with different absolute values (–1.1 µB and +0.4 µB. respectively). The results of our computations on the vertical electron detachment energies and adiabatic electron affinities (EAad) are in good agreement with the experimental data obtained from laser photodetachment spectra except for the EAad of Cr2O7, where our value are smaller by ~0.7 eV. This disagreement is related with the different geometric topologies for the lowest total energy states of the neutral Cr2O7 and its anion Cr2O7–. Beginning with n = 6, the EAad values of Cr2On exceed the EA of halogen atoms and these dichromium oxides are therefore superhalogens. The Cr2O7–2 dianion was found to be lower in total energy than the Cr2O7– anion which might be expected from the existence of dichromate salts. The second EAad of Cr2O7 is 0.78 eV as computed at the BPW91/6-311+G* level. The Cr(O2)4– anion serves as a counterion in various [M3]+[Cr(O2)4]– salts which are ferroic. According to the results of our calculations performed at the BPW91/6-311+G* level, the EAad of Cr(O2)4 is 3.50 eV and the decay channel Cr(O2)4– → CrO4– + 2O2 is exothermic by –1.40 eV. The EAad of Cr2(O2)7 is 4.12 eV and the decay channel Cr(O2)7– → Cr2O7– + 3O2 + O is exothermic by –1.42 eV. Both Cr(O2)4–2 and Cr(O2)7–2 dianions are unstable with respect to an electron detachment by –1.80 eV and –0.24 eV, respectively, and can be stabilized by external fields of positively charged counterions. By analogy with the existence of [M3]+[CrO8]– salts, one can expect the existence of [Mx]+[Cr2O14]– salts, which may have an interesting ferroic behavior. ASSOCIATED CONTENT SUPPORTING INFORMATION Cartesian coordinates of the clusters shown in Figs 1-3 together with the excerpts of G09 output files of the lowest total energy and some excited states are provided as the supporting information.This information is available free of charge via the Internet at http://pubs.acs.org.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. NOTES The authors declare no competing financial interest.


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FIGURE CAPTIONS Figure 1. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 2 – 7. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton. Different colors are used for the chromium atoms with spin-up and spin-down local total magnetic moments. Figure 2. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 7 – 9 along with those of three low-lying isomers of Cr2O8 and Cr2O8–. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton. Figure 3. Geometrical structures along with selected bond lengths, and local total spin magnetic moments of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 10 – 14. Bond lengths are in Å and local spin magnetic moments are in Bohr magneton. Different colors are used for the chromium atoms with spin-up and spin-down local total magnetic moments. Figure 4. Spin multiplicities of the lowest total energy states of the Cr2On and Cr2On– clusters as a function of n. Figure 5. Polarizability per atom (in Å3) of the Cr2On and Cr2On– clusters as a function of n. Out-of-thescale value of polarizability per atom of Cr2– is 30.26 Å3. Figure 6. Adiabatic electron affinities (EA) of the neutral Cr2On clusters along with the vertical detachment energies of an extra electron from the states of the Cr2On– clusters (n = 0 – 14) to the neutral states with the spin multiplicities less by one (VDE–) or larger by one (VDE+) than the spin multiplicity of the given anion state. All values are in eV. Figure 7. Average binding energies (in eV) per atom in the Cr2On and Cr2On– series. Figure 8. The energies (in eV) of abstraction of O and O2 from the Cr2On and Cr2On– clusters. All values are in eV. TOC Graphic


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Figure 1. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 2 – 7. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton. Different colors are used for the chromium atoms with spin-up and spin-down local total magnetic moments. 249x598mm (300 x 300 DPI)


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Figure 2. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 7 – 9 along with those of three low-lying isomers of Cr2O8 and Cr2O8–. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton. 256x610mm (300 x 300 DPI)



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Figure 3. Geometrical structures along with selected bond lengths, and local total spin magnetic moments of the lowest total energy states of the Cr2On and Cr2On– clusters for n = 10 – 14. Bond lengths are in Å and local spin magnetic moments are in Bohr magneton. Different colors are used for the chromium atoms with spin-up and spin-down local total magnetic moments. 242x432mm (300 x 300 DPI)


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Figure 4. Spin multiplicities of the lowest total energy states of the Cr2On and Cr2On– clusters as a function of n. 127x76mm (150 x 150 DPI)



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Figure 5. Polarizability per atom (in Å3) of the Cr2On and Cr2On– clusters as a function of n. Out-of-thescale value of polarizability per atom of Cr2– is 30.26 Å3. 141x86mm (150 x 150 DPI)


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Figure 6. Adiabatic electron affinities (EA) of the neutral Cr2On clusters along with the vertical detachment energies of an extra electron from the states of the Cr2On– clusters (n = 0 – 14) to the neutral states with the spin multiplicities less by one (VDE–) or larger by one (VDE+) than the spin multiplicity of the given anion state. All values are in eV. 138x86mm (150 x 150 DPI)



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Figure 7. Average binding energies (in eV) per atom in the Cr2On and Cr2On– series. 127x76mm (150 x 150 DPI)


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Figure 8. The energies (in eV) of abstraction of O and O2 from the Cr2On and Cr2On– clusters. All values are in eV. 145x107mm (150 x 150 DPI)


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