Dependence of Properties and Exchange Coupling Constants on the

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A: New Tools and Methods in Experiment and Theory

Dependence of Properties and Exchange Coupling Constants on the Charge in the MnO and FeO Series 2

n

2

n

Gennady Lavrenty Gutsev, Konstantin V Bozhenko, Lavrenty Gennady Gutsev, Andrey N Utenyshev, and Sergey M. Aldoshin J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03496 • Publication Date (Web): 05 Jun 2018 Downloaded from http://pubs.acs.org on June 5, 2018

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The Journal of Physical Chemistry

Dependence of Properties and Exchange Coupling Constants on the Charge in the Mn2On and Fe2On Series G. L. Gutsev,*, † K. V. Bozhenko, ‡,§ L. G. Gutsev, ∥ A. N. Utenyshev, ‡ S. M. Aldoshin‡ †

Department of Physics, Florida A&M University, Tallahassee, Florida 32307, United States

‡

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

Moscow Region, Russia §

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

117198, Russia ∥

Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, United States

ABSTRACT The geometrical structure and properties of the neutral and singly charged Mn2Onq and Fe2Onq clusters (q = 0, ±1) are computed using density functional theory with the generalized gradient approximation in the range of 1 ≤ n ≤ 7. The geometrical structures and spin multiplicities of the corresponding species in all six series are similar except for a few exceptions. Antiferromagnetic coupling of total spin magnetic moments of the metal atoms in the lowest total energy states is observed for the majority of species in all six series when n = 1 – 5, correspondingly, the computed magnetic exchange coupling constants are mostly negative. The states of Mn2Onq and Fe2Onq are nonmagnetic or weakly ferromagnetic when n > 5 except for Mn2O7+ where the ground state is antiferromagnetic. The computed adiabatic electron affinities and ionization energies of the neutral species in both series are quite close to one another and increase as n increases. On the other hand, the binding energies of a single oxygen atom and of an O2 dimer decrease as n increases and the Mn2O7+ and Fe2O7+ cations are barely stable with respect to the O2 abstraction. The most stable and least stable species at a given n are the anions and the cations, respectively. The electric dipole polarizability per atom decreases sharply when n moves from one to four and then remains nearly constant for larger n values in the anion series, whereas it is close to the asymptotic value already at n =2 in the neutral series.

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1. INTRODUCTION Transition metal oxides play an important role in various catalytic and biochemical processes, possess a wide range of technological and biomedical applications and were the subject of numerous experimental and theoretical studies.1,2,3,4,5,6,7,8,9,10 Iron oxide nanoparticles play an especially important role as catalysts for a variety of biological and technological processes including those intended for the reduction of global pollution.11 Iron oxide catalysts are also used in the Fisher-Tropsch process of converting a mixture of carbon monoxide and hydrogen into liquid hydrocarbons as well as the Haber process of ammonia production.12,13 Both stoichiometric and non-stoichiometric compositions of iron oxide nanoparticles were observed by many experimental groups using mass spectrometry,14,15,16,17,18,19,20,21 and the nanoparticle electronic structure was probed using photoelectron spectroscopy.22,2324,25,26 Iron oxide nanoparticles were found to be highly effective in CO oxidation at lower temperatures,27 for the conversion of formaldehyde and formic acid to carbon dioxide,28 and oxidation of methane29 and other hydrocarbons.30 These particles possess high catalytic longevity and are resistant to humidity and high concentrations of carbon dioxide which can deactivate catalysts. The interactions of iron oxide clusters with small molecular

species

were

also

the

subject

of

numerous

theoretical

studies

for

both

stoichiometric31,32,33,34,35,36,37 and nonstoichiometric38,39,40,41,42,43,44,45,46,47, 48,49,50 compositions. Currently, there is a revival of interest into oxo chemistry of iron in its highest oxidation states, in particular, Fe2O7.51 Manganese oxides are now highly popular as promising water-oxidizing catalysts,52,53 solar fuel photoanodes, 54 and have potential use in random access memory (RAM) devices. 55 The expected catalytic capability is related with the fact that the natural photosystem II contains CaMn4O5 as an oxygen-evolving complex. Correspondingly, oxidation of water on small manganese oxide cluster was the subject of theoretical simulations where the catalyst was modeled as a cubic (MnO)4 cluster56,57 or non-stoichiometric MnnOn+m+ clusters. 58 Small manganese oxide clusters are also suitable for


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hydrocarbon C – H bond activation.59 Manganese oxide clusters are the cores of many molecular magnetic complexes which have extensively been investigated experimentally60,61,62 after Pederson and Khanna 63 careful theoretical study of the experimentally observed 64 S = 10 state in a [Mn12O12( CH3COO)16(H2O)4]⋅2CH3COOH⋅4H2O compound. Manganese oxide clusters were explored65,66,67 using mass spectroscopy and a plethora of both stoichiometric and non-stoichiometric compositions were observed. Recently, it was found68 that the mass spectra obtained by photodissociation of non-stoichiometric MnnOm+ contain intense peaks for stoichiometric fragments. Photoelectron spectra were obtained for the Mn3On– and Mn4On– anions (n = 1, 2)69 and a smaller Mn2O– anion.70 On the theoretical side, stoichiometric clusters (MnO)n (n ≤ 12) were considered by several groups 71,72,73,74,75 while Ganguly et. al. 76 computed non-stoichimetric Mn3O1,2 and Mn4O1-3. The dependence of the structure and total spin magnetic moment on the number of oxygen atoms has been studied for neutral, 77 anionic, 78 and cationic79,80 clusters Fe2On (1≤ n ≤ 6) and the geometries of the cationic species were found to be different in the two studies cited. As for the Mn2On series, geometrical structures and spin multiplicities of the ground states were computed81 only for the neutral series in the range of 1≤ n ≤ 6. Magnetic exchange coupling constants were previously computed82 only for neutral Mn2O2 inside the Mn2O2(NHCHCO2)4 complex. The present work is aimed at a systematic study of the neutral and singly charged species in the Mn2On and Fe2On series in the range of 1≤ n ≤ 7 since both Fe2On– anions 83 and Fe2On+ cations84 were observed in this range in mass-spectroscopic studies. We computed magnetic exchange coupling constants for all species for which antiferromagnetic singlet states exist and explored the dependence of polarizabilities and binding energies on the number of oxygen atoms and charge. Ionization energies and electron affinities computed for neutral Mn2On and Fe2On will also be presented. Special attention was paid to the interpretation of the experimental photodetachment data85 obtained for the Fe2On– anions.


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2. DETAILS OF COMPUTATIONS Our computations are performed using the all-electron spin-polarized density functional theory with the generalized gradient approximation (DFT-GGA) as implemented in the GAUSSIAN 09 program 86 . We have chosen the BPW91 exchange-correlation functional composed of the Becke exchange87 and the Perdew-Wang correlation88 and the 6-311 + G* basis sets 89 of triple-ζ quality. The choice of this functional and basis set is based on our previous assessment of their performance in the case of FeO0,–,90,91 where good agreement with experiment and the results of post-HF studies92,93 was demonstrated. Close agreement between the results of BPW91/6-311+G* computations and experimental data has been found for FenO– (n = 2 – 6),94,95 MnOn– (n = 1 – 4),96,97 Mnn– (n = 2 –16),98 CrCn– (n = 2 – 8),99 Cr3O8,100 and Cr2(CO)2.101 The BPW91 functional was found to reliably reproduce the results of calculations obtained using the couple-cluster method with singles, doubles, and noniterative inclusion of triples [CCSD(T)] 102 for (TiO2)n clusters, 103 (CrO3)n clusters, 104 and FeO2. 105 Computations of binding energies using standard reference sets have shown106 the BPW91 accuracy to be comparable to that of more recently developed exchange-correlation functionals. Our trial geometrical structures had one or two bridging O atoms connecting two metal atoms whereas the rest of oxygen atoms for given n were attached to the metal atoms either dissociatively (oxo or η1) or associatively (peroxo or superoxo = η2 or η3). Since the valence electronic configurations of the ground-state Mn and Fe atoms are (3d54s2) and (3d64s2), respectively, the highest possible spin multiplicities of neutral Mn2 and Fe2 are 11 and 7, respectively, and those of their singly charged ions are 12 and 8, respectively.107 We have optimized states with each trial geometrical structure in the whole span of possible spin multiplicities beginning with the highest spin multiplicity. Each geometry optimization was followed by the calculation of the harmonic vibrational frequencies in order to confirm


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the stationary character of the optimized state. The convergence threshold for total energy was set to 10– 8

eV and the force threshold was set to the default value of 10–3 eV/Å.

3. RESULTS AND DISCUSSIONS First, we consider first the geometric structures and spin multiplicities of the lowest total energy states of the species in the neutral and singly charged Mn2On and Fe2On series for n = 1 – 7. Next we discuss how total spin magnetic moments, magnetic exchange coupling constants, and electric dipole polarizabilities depend on charge and the number of oxygen atoms. Computed adiabatic electron affinities and ionization energies of Mn2On and Fe2On will be compared and the controversy between theoretical estimates and experimental electron detachment energies of the Fe2O2– and Fe2O3– anions will be addressed. Finally, we present the energy of decay channels corresponding to the abstraction of O and O2 in all six series as well as the average binding energy per atom in the neutral series. 3. 1. Geometrical Structures and Spin Multiplicities. The optimized geometries of the lowest total energy states of the Mn2Onq and Fe2Onq clusters (q = 0, ±1, n = 0 – 7) are presented in Figs 1 and 2. The attachment of an O atom to the bare metal dimers, quenches total spin magnetic moments of Mn2O and Fe2O+, and the local total spin magnetic moments on the metal atoms became antiferromagnetically coupled. The states of other monoxide species retain the total spins of the parent dimers except for Mn2O– whose total spin is increased by two with respect to that of bare Mn2. All lowest total energy states are antiferromagnetic (AFM) in the range of 2 ≤ n ≤ 5, except for Fe2O5+ whose lowest total energy states is ferromagnetic (FM). The favorability of antiferromagnetic coupling of total spins on metal atoms can be related to superexchange via double oxo-bridges according to a detailed study34 of superexchange in neutral Fe2O2. In this case the singlet state is stabilized when compared to the septet state due to Pauli repulsion between the iron centers. The fact that the total spin moments on the Fe atoms are coupled ferromagnetically in Fe2O5+ can be related


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to asymmetric geometrical structures of the cluster (see Fig. 2). It is worth noting that the AFM doublet state of Fe2O5+ is higher by 0.23 eV than the lowest total energy FM quartet state.

Figure 1. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Mn2On+, Mn2On and Mn2On– clusters for n = 0 – 7. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton.


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Figure 2. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Fe2On+, Fe2On and Fe2On– clusters for n = 0 – 7. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton.


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Since the highest oxidation states108 of Mn and Fe in oxides are 7 and 6, respectively, the total spin has to be completely or nearly quenched in the states of Mn2Onq and Fe2Onq when n = 6 and 7 because all of the valence electrons of the metal atoms have to participate in the bonding with divalent oxygen atoms. 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. The total spin magnetic moment is computed as M = 2SµB = [nα – nβ]µB, where nα and nβ are the numbers of the spin-up (or α) and spin-down (or β) electrons, respectively. Local total spin magnetic moments (MA) on atoms are the differences between natural atomic orbital populations (NAO) in the αand β-spin representations obtained using the NBO suite,109 that is, MA = (NAOAα – NAOAβ)µB. The values computed in this way are presented in Figs 1 and 2 only if they are larger than 0.2 µB. On the whole, the geometrical structures shown in Figs 1 and 2 are quite similar for each particular n and charge except for two pairs: Mn2O2– – Fe2O2– and Mn2O7 – Fe2O7. While two end-on O atoms in the M2O4 and M2O5 species can sway out of the plane of the central M2O2 unit, the geometrical structures of both Mn2O6, Fe2O6 and their ions have a rigid shape which is typical of other M2O6 where M = 3d-, 4d, or 5d-atom110 and Cr2O6.111 Experimentally, (η2-O2)2Mn(µ-O)2Mn isomers of Mn2O6 where two terminal O2 are peroxo-attached to the central M2O2 unit were observed.112 The lowest total energy state of an isomer with this geometry is an singlet and is above the ground state shown in Fig. 2 by 4.25 eV. The peroxo- and superoxo-type isomers were presumably observed84 during thermal dissociation of the Fe2On+ cations, (n = 4 – 8). It is interesting to compare the behavior of our oxides with 3d-metal species containing sulfur atoms which are valence isoelectronic to oxygen atoms. The local spin magnetic moments of two Fe atoms connected with a double sulfur bridge were found113,114 to be antiferromagnetically coupled and this coupling is independent of various ligands of the Fe atoms. Antiferromagnetic coupling between


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two pairs of iron atoms connected with mono-sulfur bridges was also observed115,116 in the [Fe4S4X4]-2 dianions. It was found recently117 that the magnetic coupling between iron atoms in dibridged [Fe2S2]0,± depends on charge; namely, the local spin magnetic moments of Fe are coupled ferromagnetically in the neutral and anion, but coupled antiferromagnetically in the cation. This behavior is similar to that found for the monobridged Fe2O series (see Figure 2). 3. 2. Magnetic Properties. As can be seen in Fig. 1, the total magnetic spin moments of neutral Mn2On are quenched; the states are antiferromagnetic singlets at n = 1, 2 and 4, antiferromagnetic triplets at n = 3 and 5, and a nonmagnetic singlet at n = 6. The states of corresponding cations and anions are antiferromagnetic at n = 2 – 5 and weakly ferromagnetic at n = 6. At odd n values, oxygen atom are placed non-symmetrically (except n = 7) and the ground states possess larger spin multiplicities at n = 3 and 5. The trends in magnetic properties of the neutral and ionic Fe2On series are qualitatively the same when moving along the series. The quantitative differences can be seen from Fig. 3, where the spin multiplicities of the lowest total energy states of the Mn2Onq and Fe2Onq series (q = 0, ±1) are summarized. One can see that there are substantial differences between the mutual behavior of both neutral and ionic curves in the Mn and Fe panels.


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Figure 3. Spin multiplicities of the lowest total energy states of the Mn2On+,0, – and Fe2On+,0, – clusters as a function of n. Since all of the species in the Mn2Onq and Fe2Onq series (q = 0, ±1) have antiferromagnetic states when n = 1 – 5, one can evaluate magnetic exchange coupling constants using the Heisenberg Hamiltonian which, for two spin centers, 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 or negative value of J12 indicates that the lowest total energy state is ferromagnetic or antiferromagnetic, respectively. The rigorous construction of a magnetic Hamiltonians is quite complicated;118 therefore, approximate expressions are usually used when computing the Heisenberg exchange coupling constants. We chose a simple expression widely used in the literature119,120,121,122


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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 non-projected total spins of the states. The values obtained using Eq. 2 will be denoted in Table 1 as JBS. Generally, low-spin AFM states are significantly more spin-contaminated than the high-spin FM states. One can also use spin multiplicities of the LS and HS states; in this case one uses SHS2 – SLS2 = S(S+1)HS – S(S+1)LS as the denominator in Eq. 2. The values computed in this way are denoted in Table 1 as JS(S+1). Both JS(S+1 and JBS values computed for the Mn2Onq and Fe2Onq species (n = 2 – 5, q = 0, ±1) are presented in Table 1. In the Mn2-based series, the constants of neutral and ionic clusters generally increase in the absolute value when n grows. The exchange coupling constant of the Mn2O2 core in the Mn2O2(NHCHCO2)4 complex was previously computed123 using several methods, and it was found that the computed values strongly depend on the method used. Note that their Jab(2) and Jab(3) definitions correspond to our JS(S+1 and JBS, respectively. The J12(2) and J12(3) constants computed at the B3LYP/6311G** level are –94.7 and –124 cm-1, respectively, and are in a qualitative agreement with our values of –146.9 cm-1 and -188.1 cm-1, respectively, obtained for the free-standing Mn2O2 cluster. The trend of increasing absolute values of J12 is also observed in the Fe2-based series (see Table 1) as well in the Cr2On and Cr2On– series considered previously.124 The experimental values125 of µ-oxobridged iron dimers –Fe–O–Fe– measured for 32 compounds are within the range from 160 cm-1 to 265 cm-1 and our constants (absolute values) for free-standing Fe2O1-4 are in qualitative concordance with the experimental data. For visual comparison, the computed JS(S+1) constants are presented in Figure 4. As can be seen there is no strict ordering in the whole n range. Only in the Fe2-series, there is the order JS(S+1)(neutral) > JS(S+1)(cation) > JS(S+1)(anion) when 2≤ n ≤ 4. Especially noticeable is the fact that the constants of the Mn2O3 and Fe2O3 series are substantially smaller than the constants of their nearest neighbors.


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Table 1. Computed Magnetic Exchange Coupling Constants J12 of Mn2On+,0, – and Fe2On+,0, – clusters for 1 ≤ n ≤ 5. Mn2Onq cation

neutral

anion

n

JS(S+1)

JBS

JS(S+1)

JBS

JS(S+1)

JBS

1

35.7

41.2

-60.0

-69.5

8.7

10.1

2

-18.01

-21.4

-146.9

-188.1

-59.6

-71.6

3

-115.9

-141.5

-70.2

-81.6

-10.5

-12.0

4

-221.7

-264.3

-317.5

-494.6

-61.3

-72.8

5

-493.8

-629.5

-390.1

-411.2

-617.2

-636.9

Fe2On cation

q

neutral

anion

n

JS(S+1)

JBS

JS(S+1)

JBS

JS(S+1)

JBS

1

-63.7

-98.7

76.4

104.4

75.5

71.2

2

-19.5

-25.6

-173.0

-231.0

-102.4

-129.7

3

-14.1

-18.1

-119.2

-161.4

-41.8

-53.0

4

-143.2

-177.6

-218.3

-373.1

-133.8

-175.2

5

614.5

900.9

-388.9

-494.7

-80.6

-95.7

In order to make sure that this is not related to the basis size effects, we performed additional computations of Mn2O30,±1 and Fe2O30,±1 using the Def2TZVPP basis set from Alricht’s group,126; the 6311+G(3df) basis set developed by the Pople’s group89, and the Dunning’s aug-cc-pVQZ basis sets127 of quadruple-ζ quality. The basis extension led generally to increased values of JS(S+1) and JBS by 5-12 cm-1 (see Table S1) but such an increase do not affect the trend observed for the values computed with the 6311+G* basis. One can assume that the reduced magnetic exchange in the Mn2O3 and Fe2O3 neutrals and ions with respect to their neighbors is related to asymmetry of the Mn and Fe atomic environments. Generally, the exchange coupling constants of ions are smaller in the absolute value than the constants


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of the corresponding neutral parents. The largest in the absolute value constants correspond to Mn2O5+ and Fe2O5–.

Figure 4. Magnetic exchange coupling constants (in cm-1) of the Mn2On+,0, – and Fe2On+,0, – clusters (n = 1 – 5) as a function of n. 3. 3. Polarizability. Polarizability is an important characteristic of a chemical compound and it is interesting to explore how it depends on charge. 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 field128 E p = E 0 ! ! µ! F! ! !

1 1 !!" Fa F! " ! !"!# F! F! F! + .... ! 2 " ,! 6 " ,# ,! ACS Paragon Plus Environment

(3)

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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 α, β, γ run over x, y, and z coordinates. The mean static dipole electric polarizability ( α ), referred to as isotropic polarizability, is defined as the trace of the static dipole electric polarizability tensor:

1 3

(4)

α = (α xx + α yy + α zz )

The polarizabilities per atom of the lowest total energy states in the Mn2On+,0, – and Fe2On+,0, – series computed according to Eq. 4 are presented in Figure 5. As one can see, the polarizabilities in all M2On+,0, – series have the largest values at n = 1 and converge to the value of 1.5 – 1.6 Å3 independent of charge. Polarizabilities of the cations converge to asymptotic values at n = 2, the neutrals converge at n = 3, and the anions converge at n = 4. This result is quite surprising because it shows that the polarizabilities do not dependent either on charge or at the metal atom type despite the atomic polarizabilities of the Mn and Fe atoms are quite different. The computed BPW91/6-311+G* values for these atoms are 11.03 Å3 and 8.49 Å3, respectively, are in fair agreement with the values129 of 11.19 Å3 and 9.47 Å3, respectively, computed using modified coupled-pair functional (MCPF) method. The polarizability behavior in the Cr2On and Cr2On– series124 is quite similar, and the decrease in the polarizability when n increases was related to the small polarizability of an O atom which is 0.43 Å3 at the BPW91/6-311+ G* level.


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Figure 5. Polarizability per atom (in Å3) of the the Mn2On+,0, – and Fe2On+,0, – clusters as a function of n.

3. 4. Electron Affinities and Electron Detachment Energies The adiabatic electron affinity (EAad) of a neutral M2On species is computed as the difference in total energies of the lowest total energy states of the neutral species and its anion: EAad(M2On) = [Etotel(M2On) + E0(M2On)] – [Etotel(M2On–) + E0(M2On–)]

(5)

The adiabatic ionization energy (IEad) of a neutral M2On species is defined in a similar way: IEad(M2On) = [Etotel(M2On+) + E0(M2On+)] – [Etotel(M2On) + E0(M2On)]


(6) 15


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where Etotel is the total Born-Oppenheimer energy and E0 is the zero-point vibrational energy. The EAad and IEad values of neutral Mn2On and Fe2On computed according to Eqs (5) and (6) are displayed in Figure 6. As can be seen, there is a relatively small difference between the EAad values in two series for a given n value, and the largest difference of 0.68 eV corresponds to the values at n = 4. The difference in the IEad values is somewhat larger and reaches 1.02 eV for the values at n = 7. One may note that both EAad and IEad values increase when n grows. However, there is a difference between the trends in the Mn2On and Fe2On series; namely, both EAad and IEad values of Mn2O7 are larger than those of Mn2O6 whereas it is not so for the analogous members in the Fe2On series.

Figure 6. Adiabatic electron affinities (EAad) and ionization energies (IE) of the Mn2On and Fe2On clusters as a function of n. All values are in eV.


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As can be seen from Figure 6, both EAad and IE values in the Mn2On and Fe2On series grow as n increases. This trend can be interpreted as follows. As the number of oxygen atoms increases, more and more oxygen AOs are involved into the formation of molecular orbitals which an electron detaches from (neutrals) or attaches to (anions). This pattern is clearly seen in Figures 1-7 of the ESI for the Mn2On and Mn2On– species. The HOMOs and LUMOs of the Fe2On species are quite similar. In the case of the largest Mn2O7 and Mn2O7– species, the frontier molecular orbitals are composed entirely from oxygen AOs. The EA and IE values of the oxygen atom computed at the BPW91/6-311+G* level are 14.03 eV and 1.63 eV which explains the EAad and IE growth in the Mn2On and Fe2On series as n increases. The important characteristics of an anion are the vertical detachment energies (VDE) of an extra electron which can be measured experimentally and be used for the EAad determination. If the ground state of an anion is not a singlet, then an electron detachment results into the formation of two final neutral states corresponding to the electron detachment from the α- and β-spin representations. The VDE values of an M2On– anion can be computed as VDE±( M2On–) = Etotel(M2On, (2S + 1) ±1) – Etotel(M2On–, 2S + 1)

(7)

where Etotel is the total Born-Oppenheimer energy. To the best of our knowledge, the experimental VDEs were obtained from the laser photodetachment spectra25 only for the Fe2On– anions in the range of 1 ≤ n ≤ 5 and the Mn2O– anion.130 To compare of our results with experimental values we use the smallest value from each pair of the computed VDEs if the anion state is not a singlet. The computed VDE values of the Mn2On– and Fe2On– anions are presented in Fig. 7 together with the EAad values of the Mn2On and Fe2On neutrals and the experimental VDEs of Fe2On–. One can notice that the VDE values are close to the EAad values, except for n = 7, and both of them nearly match the experimental values in the Fe2On– series. The largest difference of 1.08 eV between the VDE and EAad values in the Mn2On series is attained at n = 2. Such a large discrepancy has


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to be related to different geometrical topologies of Mn2O2 and Mn2O2– (see Fig. 1). The experimental VDE obtained130 from the photoelectron spectrum of Mn2O – is 1.37 eV which nearly matches our VDE value of 1.39 eV. It should be underlined that we used our own estimates for the feature positions in the experimental spectra of the Fe2O2– and Fe2O3– anions marked with question marks and considered them as the experimental values when compiling Figure 7. The experimental spectra of these anions contain fingerprints of two isomers which caused ambiguities in the experimental assignment and was indicated by the authors 131. The isomer structures of Fe2O2– and Fe2O3– are shown in Fig. 8 together with the computed VDE values and experimental values derived from the photoelectron spectra. As can be seen in Fig. 8, the experimental values of 2.36 eV (Fe2O2–) and 3.06 eV (Fe2O3–) correspond to the anion states whose geometrical structures are “open”.

Figure 7. Comparison of the VDEs of the anions with the adiabatic electron affinities (AEA) of the Mn2On – Mn2On– pair (the top panel) and the Fe2On – Fe2On– pair (the bottom panel). Experimental VDEs of Fe2On– ( n = 1– 5) are also shown in the bottom panel. All values are in eV.


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Figure 8. A scheme of the vertical detachment of an electron from the lowest total energy states of two closely spaced isomers of the Fe2O2– and Fe2O3– anions. The energies of “~ 1.4 eV” and “~ 2.7 eV” for the Fe2O2– and Fe2O3– anions, respectively, are roughly estimated from positions of the experimental peaks marked with “?” in the photoelectron spectra in Ref. [22]. In order to check the dependence of the computed VDE values for the both states of the Fe2O2– and Fe2O3– anions on basis sets, we repeated computations using the Def2TZVPP, 6-311+G(3df), and augcc-pVQZ basis sets. No significant changes with resect to the values computed using the 6-311+G* basis set were observed (see Table S3). 3. 5. Binding Energies of O and O2 in M2On+,0, –. Based on the results of our computations, one can evaluate the binding energies of O and O2 in the M2On q (q = +, 0, – ) series according to the equations


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el el el Eb(M2On-1q – O) = Etot ( M2On-1 q) + E0(M2On-1 q) + Etot (O) – [Etot (M2On q) + E0(M2On q)]

(8)

el el el Eb(M2On-2 q – O2) = Etot ( M2On-2 q) + E0(M2On-2 q) + Etot (O2) + E0(O2) – [Etot ( M2On q) +E0(M 2On q)]

(9)

where Etotel is the total Born-Oppenheimer energy and E0 is the zero-point vibrational energy. Our computed energies of abstractions of an oxygen atom and an oxygen dimer (in its ground triplet state) are presented in Figures 9 and 10, respectively. As can be seen in Figure 9, the binding energies in all series decrease as n increases with several exclusions, especially notable in the Mn2On+ curve. Note that the cations are less stable and the anions are somewhat more stable than their neutral parents. Curiously, the binding energies of both the neutrals and their ions are quite close to each other at n = 1 and 7, in agreement with the experimental mass-spectroscopy data presented in Table 2. There is quite a striking disagreement between theoretical and experimental values for the energy of O2 abstraction for the even-n cations Fe2O4+ and Fe2O6+. Таble 2. Comparison of our Computed Binding Energies of O in Fe2On and Fe2On+ with Experiment. Decay Channel Fe2O → Fe2 + O Fe2O2 → Fe2O + O

TW 5.61 5.85

Experim. a 5.60±0.14 4.50 ±0.30

Decay Channel

TW

Fe2O+ → Fe2+ + O +

Fe2O2 → Fe2O +

+

Theor. a

5.34

5.11±0.14

5.64

5.02

4.25±0.19

5.47

+O

3.87

3.86±0.19

4.22

+O

+

Experim. a

Fe2O3 → Fe2O2 + O

4.71

4.94±0.36

Fe2O4 → Fe2O3 + O

4.82

...

Fe2O4+ → Fe2O3+ + O

3.91

1.98±0.21

4.22

Fe2O5 → Fe2O4 + O

3.86

...

Fe2O5+ → Fe2O4+ + O

3.47

3.85±0.27

3.76

Fe2O6 → Fe2O5 + O

3.75

...

Fe2O6+ → Fe2O5 ++ O

3.40

1.95±0.27

3.69

Fe2O7 → Fe2O6 + O

0.73

...

Fe2O7+ → Fe2O6 ++ O

0.46

...

...

a

Fe2O3 → Fe2O2

132

All values are in eV. Experimental and theoretical data are from Ref. [ ]. The binding energies of an oxygen atom in the Mn2On+,0, – series are generally larger than those

of the corresponding species in the Fe2On+,0, – series, especially at the beginning where Eb(Fe2 – O) = 5.61 eV and Eb(Mn2 – O) = 6.39 eV. On the whole, our computed binding energies presented in Table 2 are in satisfactory agreement with experiment except for Fe2O2, Fe2O4+ and Fe2O6+ where the discrepancy exceeds 1.2 eV. The reasons for such a large difference are unclear. The high stability of the


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M2O species was indirectly confirmed also by the results133 of photodissociation of Mn2O+ since this cation did not dissociate even at the highest photon energy used.

Figure 9. The energies of abstraction of an O atom from the Mn2On+,0, – and Fe2On+,0, – clusters. All values are in eV.

Figure 10. The energies of abstraction of an O2 dimer from the Mn2On+,0, – and Fe2On+,0, – clusters. All values are in eV.


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The energies required to detach an O2 dimer in the M2On q series (2 ≤ n ≤ 7) are presented in Figure 10. As can be seen from comparison of Figs 9 and 10, the general trend in decreasing binding energies when n increases is preserved. However, the dependence on charge is more expressed and curves are better separated except at the beginning and the end of the series. The order of the binding energies is the same: Eb(anion) > Eb(neutral) > Eb(cation). The binding energy of O2 approaches to zero at the Mn2O7+ and Fe2O7+ cations (0.52 eV and 0.46 eV, respectively), whereas it is relatively high for the corresponding anions (2.73 eV and 1.18 eV, respectively). We have also estimated the averaged binding capability of atoms in the neutral M2On series by computing the binding energies per atom Eatom according to the equation el el el Eatom(M2On) = [2Etot ( M) + nEtot (O)] – Etot ( M2On) – E0(M2On)]/(n + 2)

(10)

where Etotel is the total Born-Oppenheimer energy and E0 is the zero-point vibrational energy. The Eatom values are presented as functions of the number of oxygen atoms in Figure 11. Both curves have a parabolic character and show a decreasing pattern at n = 4 (Fe2On) and n = 6 (Mn2On).

Figure 11. Average binding energies (in eV) per atom in the Fe2On and Fe2On series.


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4. CONCLUDING REMARKS Our systematic study of the structure and properties of the oxides of the dimers Mn2 and Fe2 formed by 3d-metal atoms was performed using all-electron density functional theory with the generalized gradient approximation (DFT-GGA) and a relatively large basis set of triple-ζ quality. The Mn2On and Fe2On oxides and their singly charged ions were computed in the range of 1 ≤ n ≤ 7 in which all oxygen atoms can all be attached dissociatively (oxo- or η1). According to the results of our computations, there are more similarities between the behavior in the Mn2Onq and Fe2Onq series (q = 0, ±1) than differences. A number of interesting peculiarities were revealed by analyzing the results of calculations It was found that nearly all lowest total energy states are antiferromagnetic when 2 ≤ n ≤ 5. When n > 5, the lowest total energy states in all six series are nonmagnetic or weekly ferromagnetic except for Mn2O7 which is antiferromagnetic. There is also the difference for n =1, where neutral Mn2O has an antiferromagnetic singlet state but the state of Fe2O is ferromagnetic. The opposite behavior was found for the corresponding cation states: Fe2O+ has an antiferromagnetic doublet whereas Mn2O+ has ferromagnetic state whose spin multiplicity is 12. Correspondingly, the magnetic exchange coupling constants of these pairs have opposite signs which is also the case for the Mn2O5+ and Fe2O5+ pair. It is quite surprising that isotropic polarizabilities of the neutral Mn2On and Fe2On oxides converge to the asymptotic value already at n = 2. The trend toward an increase of electron affinities and ionization energies as n increases is similar in both Mn2On and Fe2On series, although the difference in the corresponding values can be as large as 1 eV, e.g., ionization energies of Mn2O7 and Fe2O7 are 11.22 eV and 10.24 eV, respectively. One more confirmation of the reliability of our computational approach can be obtained from comparison of the computed vertical electron detachment energies with experimental data where we see very good agreement. Moreover, we explained the ambiguities in the experimental assignment by finding isomers responsible for unidentified features in the photoelectron of the Fe2O2– and Fe2O3–


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anions. The binding energies of O and O2 in both neutral and ionic Mn2On and Fe2On series decrease as n increases and approach nearly zero value for neutral Fe2O7 and its cation and anion. This is another interesting peculiarity of the series that the binding energies are nearly independent on charge at n = 1 and 7. The order of the binding energies of both O and O2 is the same: Eb(anion) > Eb(neutral) > Eb(cation), although the differences are more pronounced for the O2 binding energies. ACKNOWLEDGEMENT The research was carried out within the state assignment of FASO of Russia (State registration № 01201361863). The work has been performed with the financial support from the fundamental research program of the Presidium RAS № 32 "Nanostructures: physics, chemistry, biology, fundamentals of technology" (State registration № АААА-А18-118030290068-6). KVB acknowledges support by the Ministry of Education and Science of the Russian Federation for the program to improve the competitiveness of People′ s Friendship University of Russia (RUDN University) among the World′ s leading research and education centers in the 2016 – 2020. ANU acknowledges support by I.M. Sechenov First Moscow State Medical University of the Russian Ministry of Health (Sechenov University), Оrganic Сhemistry Department, 8/2 Trubetskaya str., Moscow, Russia 119991. ASSOCIATED CONTENT Supporting Information The numerical data Figures 4-10 are based on are provided as tables in the Supporting Information, which also contains Cartesian coordinates of the species shown in Figs 1-2 as well as excerpts of the G09 output files. The Supporting Information is available free of charge on the ACS Publications website at DOI: AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ORCID G. L. Gutsev: 0000-0001-7752-5567


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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 Mn2On+, Mn2On and Mn2On– clusters for n = 0 – 7. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton. Figure 2. Geometrical structures, bond lengths, and local total spin magnetic moments of the lowest total energy states of the Fe2On+, Fe2On and Fe2On– clusters for n = 0 – 7. Bond lengths are in Å and local total spin magnetic moments are in Bohr magneton. Figure 3. Spin multiplicities of the lowest total energy states of the Mn2On+,0, – and Fe2On+,0, – clusters as a function of n. Figure 4. Magnetic exchange coupling constants (in cm-1) of the Mn2On+,0, – and Fe2On+,0, – clusters (n = 1 – 5) as a function of n. Figure 5. Polarizability per atom (in Å3) of the the Mn2On+,0, – and Fe2On+,0, – clusters as a function of n. Figure 6. Adiabatic electron affinities (EA) and ionization energies (IE) of the Mn2On and Fe2On clusters as a function of n. All values are in eV. Figure 7. Comparison of the VDEs of the anions with the adiabatic electron affinities (AEA) of the Mn2On – Mn2On– pair (the top panel) and the Fe2On – Fe2On– pair (the bottom panel). Experimental VDEs of Fe2On– ( n = 1– 5) are also shown in the bottom panel. All values are in eV. Figure 8. A scheme of the vertical detachment of an electron from the lowest total energy states of two closely spaced isomers of the Fe2O2– and Fe2O3– anions. The energies of “~ 1.4 eV” and “~ 2.7 eV” for the Fe2O2– and Fe2O3– anions, respectively, are roughly estimated from positions of the experimental peaks marked with “?” in the photoelectron spectra in Ref. [22]. Figure 9. The energies of abstraction of an O atom from the Mn2On+,0, – and Fe2On+,0, – clusters. All values are in eV. Figure 10. The energies of abstraction of an O2 dimer from the Mn2On+,0, – and Fe2On+,0, – clusters. All values are in eV. Figure 11. Average binding energies (in eV) per atom in the Fe2On and Fe2On series.


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TOC Graphic


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