The Vibrations of V2O4: Matrix Isolation and Quantum Chemical

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

pubs.acs.org/JPCA

The Vibrations of V2O4: Matrix Isolation and Quantum Chemical Calculations Published as part of The Journal of Physical Chemistry virtual special issue “W. Lester S. Andrews Festschrift”. Olaf Hübner and Hans-Jörg Himmel* Anorganisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 270, D-69120 Heidelberg, Germany S Supporting Information *

ABSTRACT: V2O4 was generated in solid Ne and characterized by infrared spectroscopy and additionally by multireference configuration interaction and density functional calculations. Four vibrational transitions at 1003, 731.7, 640.9, and 309.1 cm−1 (16O2) were observed and, based on the calculations, assigned to bu, au, bu, and bu modes, respectively, of the C2h symmetric structure. The calculated bond distances are in good agreement with the results of previous calculations.

■

INTRODUCTION Vanadium oxides constitute important catalysts. Small metal oxide clusters frequently serve as model systems for the study of the [physical and chemical] properties of metal oxides. Therefore, also vanadium oxide clusters have been the subject of numerous studies. Concerning V2O4, there is a theoretical study of Pykavy, van Wüllen, and Sauer.1 They investigated two different isomers of V2O4 in their two lowest-lying electronic terms by multireference averaged coupled pair functional calculations as well as by density functional calculations. V2O4 is built of a four-membered V2O2 ring, each V atom of which carries an outward standing oxo group, see Scheme 1. In the

agreement with the multireference calculations and relative energies in only qualitative agreement. However, vibrational frequencies neither have been the topic of that study nor of other density functional studies that have been concerned with V2O4.2−6 The experimental knowledge about V2O4 is rather limited. Chertihin, Bare, and Andrews observed two vibrational modes at 624.8 and 752.6 cm−1 for Ar matrices containing vanadium and oxygen and assigned them to V2O4.7 Furthermore, by anion photoelectron spectroscopy a vibrational progression of neutral gas-phase V2O4 was observed with a wavenumber of 1090 ± 30 cm−1,8 likely pertaining to the symmetric combination of the V−O stretching vibrations of the oxo groups. In this work, we report on the observation of four vibrational modes of V2O4 in solid Ne and on accompanying calculations of the vibrational frequencies by multireference configuration interaction (MRCI) calculations based on complete active space self-consistent field (CASSCF) orbitals as well as density functional calculations.

Scheme 1. Structure of V2O4

■

trans isomer the oxo groups point to different sides of the plane of the ring; in the cis isomer they point to the same side. According to the multireference calculations, the trans conformation is the lowest-energy conformation, whereas the cis conformation is calculated to be 4.9 kJ mol−1 higher in energy. Within V2O4, the oxidation state of V is +IV, and each V carries one unpaired electron. The electronic ground term of V2O4 is calculated to be an 1Ag state (C2h) with an antiparallel coupling of the two electrons. For the trans isomer, the 3Bu term with a parallel coupling of the two electrons has a relative energy of 6.9 kJ mol−1. The density functional calculations, relying on the B3LYP functional, yielded structures in good © XXXX American Chemical Society

METHODS Matrix Experiments. Matrices were generated by codeposition of V atoms and mixtures of Ne (l’Air Liquide, 99.999%) and O2 (Messer, 99.999%) onto a Rh-plated Cu surface, cooled to 4.2 K by a pulse-tube refrigerator (Vericold). The O2 content amounted to between 0.12 and 0.50%. Experiments were also Received: September 28, 2017 Revised: November 8, 2017 Published: November 9, 2017 A

DOI: 10.1021/acs.jpca.7b09644 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

are already known for some time,26,27 whereas V2O2 has been identified only recently.28 The signals of VO2(O2), VO2(O2)2, and V2O4 are assigned to these compounds, because their positions are close to absorptions previously assigned to these compounds in solid Ar.7,29 For V2O4 in addition, further new bands are observed for which no counterparts in Ar have been reported. The remainder of the text is concerned with V2O4 only. With 16O2, there are narrower bands at 731.7, 640.9, and 309.1 cm−1, see Figures 1, 2, and 3, and a broader absorption

performed with 18O2 (Isotec, 99%) and with a 1:2:1 mixture of 16 O2, 16O18O, and 18O2, generated by subjecting a mixture of 16 O2 and 18O2 to a high-frequency discharge. During deposition, the flux of the gas was maintained at 1.0 mL min−1 using a flowcontroller (EL-FLOW, Bronkhorst). The vanadium was evaporated by resistively heating a 0.5 mm vanadium filament (Advent). The deposition rate of V was monitored by a quartz microbalance and approximately held constant by adjusting the electric current. Rates between 0.8 and 0.3 μg cm−1 min−1 were used. The matrices were annealed to 7 and 10 K and irradiated with the light of a tungsten lamp (maximum emission at about 1000 nm). Spectra were recorded with a Bruker Vertex 80v spectrometer. The spectra in the middle infrared range used a Globar source, a KBr beam splitter and a Mercury Cadmium Telluride (MCT) detector, spectra in the far-infrared range used a Hg Lamp, a Mylar multilayer beam splitter and a Bolometer. Quantum Chemical Calculations. The MRCI calculations were performed with the program MOLPRO9,10 in C2h and C1 symmetry. A relativistic ANO basis set was used, namely a [7s6p4d3f2g] contraction at V and a [5s4p3d2f] contraction at O.11,12 Scalar-relativistic contributions were included by means of the Douglas−Kroll−Hess formalism.13 The orbitals for the MRCI calculations were determined by CASSCF calculations.14,15 Two different active spaces were used: a small active space that contained only the two 3d orbitals of V that are occupied by about one electron and a large active space of 10 orbitals that additionally contained 4 nearly doubly occupied V−O bonding orbitals (main contribution 2p of O) and 4 weakly occupied corresponding antibonding orbitals (main contribution 3d of V). The MRCI calculations16−18 correlated the 3d and 4s orbitals of V and the 2s and 2p orbitals of O. Two different reference spaces were used, namely the complete active spaces of the CASSCF calculations of 2 or 10 orbitals. The MRCI calculations with the smaller reference space were performed using the older internally contracted MRCI program.16,17 The calculations with the larger reference space used the newer, more efficient internally contracted MRCI program18 that also contracts the singly external configurations. However, dipole moments are not yet implemented in the new program, and therefore the latter does not allow the calculation of the intensities of the vibrational transitions. Equilibrium distances were determined by a quasi-Newton optimization. Harmonic vibrational frequencies were obtained by numerical differentiation. Density functional calculations were performed with the program Turbomole19−21 using the TPSS functional22 and the def2-TZVP basis set.23 The calculations use the resolution-ofthe-identity approximation for the two-electron integrals24 and the appropriate auxiliary basis set.25 The density functional calculations yield a broken-symmetry state as the lowest-lying state with two unpaired electrons of opposite spin located at the two V atoms, as found earlier.1 The density functional results reported here are those for the broken symmetry state (essentially a mixture between the singlet and triplet terms).

Figure 1. Infrared absorption spectra of matrices obtained from codeposition of V atoms and mixures of Ne and O2 after annealing to 10 K between 680 and 750 cm−1. (a) 16O2, (b) 18O2, (c) 16O2+16O18O +18O2.

Figure 2. Infrared absorption spectra of matrices obtained from codeposition of V atoms and mixures of Ne and O2 after annealing to 10 K between 600 and 650 cm−1. (a) 16O2, (b) 18O2, (c) 16O2+16O18O +18O2.

between 1002 and 1005 cm−1 with maxima at 1003.1 and 1004.2 cm−1, see Figure 4. All these bands are almost absent after deposition, at least when using smaller O2 concentrations, and increase on annealing to 7 K and further increase on annealing to 10 K. On irradiation with visible light the bands decrease, and on a new annealing to 10 K they increase again. With 18O2, the narrower bands shift to 701.9, 611.6, and 295.9 cm−1, and the broader absorption shifts to the range from 961 to 964 cm−1 with maxima at 963.3 and 962.3 cm−1. With an 16 O2+16O18O+18O2 mixture, many additional bands are

■

RESULTS Matrix IR Spectra. On codeposition of V atoms and mixtures of Ne and O2, matrices are obtained that contain VO, VO2, VO2(O2), and VO2(O2)2, as well as V2O2 and V2O4, identified by their IR absorptions. The signals of VO and VO2 B


Article


are not clearly observed anymore, they are likely contained in the broad basis of the signal at 965.4 cm−1 or obscured by other absorptions at ∼1000 cm−1. The observed spectral positions of the vibrational transitions are listed in Table 1. Quantum Chemical Calculations. The bond distances calculated for V2O4 are shown in Table 2. The MRCI calculations with the small reference space yield a V−V distance of 262.7 pm and V−O distances of 180.9 and 155.3 pm for the oxygen atoms of the ring and for the terminal oxygen atoms. With the larger reference space, a slightly smaller V−V distance of 262.3 pm and somewhat larger V−O distances of 181.8 and 158.4 pm are obtained. For the results with the small reference space, the inclusion of the Davidson correction (+Q) shortens the V−V distance by 0.9 pm and lengthens the V−O distances by 0.5 and 1.1 pm. For the large reference space, the inclusion of the Davidson correction shortens the V− V distance by 0.8 pm and essentially does not affect the V−O distances. The density functional results with the TPSS functional are in good agreement with MRCI results. The values for the V−O distances of 181.7 and 159.7 pm deviate by only 0.1 and 1.3 pm from the Davidson-corrected MRCI values with the large reference space. The calculated harmonic vibrational frequencies are shown in Table 3. For V2O4, there are six allowed vibrational transitions, four of them in the range of the recorded spectra. With the small reference space, for the allowed vibrational transitions, wavenumbers of 1152, 782, 732, 336, 202, and 86 cm−1 are obtained. Changing to the large reference space has a very large impact on the wavenumbers of the two stretching vibrations of the oxo groups; they decrease by 117 and 132 cm−1, whereas the wavenumbers of the other modes decrease by between 2 and 35 cm−1. The inclusion of the Davidson correction affects the results with the small reference space by at most 36 cm−1 and the results with the large reference space by at most 15 cm−1. This yields values of 1049, 768, 696, and 314 cm−1 for the harmonic vibrational frequencies of those transitions that are observed in the IR spectra. An illustration of the nuclear displacements for these modes is given in Scheme 2. The density functional calculations yield values for the vibrational frequencies that deviate from the Davidson-corrected MRCI results by between 7 and 55 cm−1. For all but the two lowestfrequency modes, the density functional values are lower than the MRCI values. For the three highest vibrations involving the motion of the four-membered ring (724, 720, and 641 cm−1), the deviations are relatively large: 44, 31, and 55 cm−1. The large impact of the size of the reference space of the MRCI calculations and also the deviation between the density functional results and the MRCI calculations indicates that a relatively large error (in the order of some 10 cm−1) must be assumed for the calculated vibrational frequencies.

Figure 3. Difference spectra of infrared absorption spectra of matrices obtained from codeposition of V atoms and mixures of Ne and O2 before and after annealing to 10 K between 292 and 312 cm−1. (a) 16 O2, (b) 18O2, (c) 16O2+16O18O+18O2.

Figure 4. Infrared absorption spectra of matrices obtained from codeposition of V atoms and mixures of Ne and O2 after annealing to 10 K between 960 and 970 cm−1 and between 1000 and 1015 cm−1. (a) 16O2, (b) 18O2, (c) 16O2+16O18O+18O2.

observed. Instead of the bands at 640.9 and 611.6 and at 309.1 and 295.9 cm−1, there are triplets of triplets, with wavenumbers at 640.9, 640.3, 639.8, 628.0, 627.4, 626.9, 612.7, 612.3, and 611.7 cm−1 and likewise at 309.2, 308.2, 307.3, 304.0, 303.0, 302.1, 297.9, 296.9, and 296.0 cm−1. Between the bands at 731.7 (16O2) and 701.9 (18O2) cm−1 there is an additional band at 726.0 cm−1 and an other band at 692.7 cm−1. Concerning the absorptions at high wavenumbers, with the 16O2+16O18O+18O2 mixture, there is a new band at 965.4 cm−1 with a companion at 964.5 cm−1, and there are two bands at 1013.1 and 1012.3 cm−1. The broader absorptions (961−964, 1002−1005 cm−1)

Table 1. Vibrational Transitions Observed for V2O4 in Solid Ne Using 16O2, 18O2, and 16O2+16O18O+18O2 vibration

16

18

O2

O2

VOr out-of-plane (bu)

309.1

295.9

VOr stretching (bu)

640.9

611.6

VOr stretching (au) VOt stretching (bu)

731.7 1003.1/1004.2

701.9 963.3/962.3 C

16

O2+16O18O+18O2

309.2, 308.2, 307.3 304.0, 303.0, 302.1 297.9, 296.9, 296.0 640.9, 640.3, 639.8 628.0, 627.4, 626.9 612.7, 612.3, 611.7 731.5, 726.0, 702.1, 692.7 1013.1/1012.3, 965.4/964.5 DOI: 10.1021/acs.jpca.7b09644 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article


Table 2. Structural Parameters of the 1Ag Ground Term of V2O4 by MRCI Calculations with an ANO Basis Set and by Density Functional Calculations with the TPSS Functional calculation

reference

E, Hartree

rV−V e , pm

MRCI MRCI+Q MRCI MRCI+Q TPSS

CAS2 CAS2 CAS10 CAS10

−2197.230 448 −2197.466 427 −2197.326 407 −2197.519 858 −2189.410 307

262.7 261.8 262.3 261.5 260.3

V−Oi

re

V−Ot

re

, pm

180.9 181.4 181.8 181.8 181.7

, pm

155.3 156.4 158.4 158.4 159.7

VVOt

αe

, deg

142.9 140.7 149.2 145.4 134.4

Table 3. Harmonic Vibrational Frequencies (cm−1) and in Parentheses Corresponding Intensities (km mol−1) of the 1Ag Ground Term of V2O4 by MRCI Calculations with an ANO Basis Set and by Density Functional Calculations with the TPSS Functional and the TZVP Basis Set MRCI(2)a

a

vibr

sym

ν12 ν4 ν8 ν6 ν11 ν3 ν5 ν10 ν2 ν7 ν9 ν1

bu ag au bg bu ag bg bu ag au bu ag

− 86 157 202 304 336 386 529 732 775 782 1152 1193

MRCI(10)a +Q

(111) (0) (16) (0) (49) (0) (0) (81) (0) (119) (1282) (0)

86 159 198 297 328 377 521 711 758 768 1123 1157

(113) (0) (16) (0) (51) (0) (0) (72) (0) (120) (1229) (0)

−

+Q

67 122 195 287 318 365 527 708 760 778 1035 1061

71 134 194 285 314 364 518 696 751 768 1049 1076

TPSS 84 167 187 278 304 348 506 641 720 724 1031 1053

exp (23) (0) (14) (0) (36) (0) (0) (419) (0) (128) (540) (0)

309.1b

640.9b 731.7b 1003.1b 1090 ± 30c

The number in parentheses denotes the size of the reference space (two or ten orbitals). bPresent work. cReference 8.

Formerly, bands at 624.8 and 752.6 cm−1 (using 16O2) have been assigned to V2O4 in solid Ar, close to the bands observed here at 640.9 and 731.7 cm−1 for V2O4 in Ne. Also the 18 O−16O isotopic shifts for these bands of 28.9 and 30.9 cm−1 for the Ar matrix favorably agree with the shifts of 29.3 and 29.8 cm−1 for the Ne matrix. Additionally, the isotopic shift of 12.8 cm−1 for the band at 611.7 cm−1 observed with 16O18O in Ar is very close to the shift of 12.9 cm−1 for the Ne counterpart at 627.4 cm−1. However, the positions of the three bands at 752.5, 738.8, and 721.8 cm−1 reported for the Ar matrix using 16O18O show a rather symmetric alignment (differences of 13.7 and 17.0 cm−1), whereas the positions observed for the Ne matrix at 731.5, 726.0, and 702.1 cm−1 show a pronounced asymmetric pattern (differences of 5.5 and 23.9 cm−1). It is also possible that the Ar matrix bands erroneously have been assigned to V2O4. The Ar study reports also unassigned bands at 720.3 and 691.5 cm−1 using 16O2 and 18O2, respectively, with an isotopic shift of 28.8 cm−1 almost the same as that of the 752.5 cm−1 band. For these band positions, the difference from our Ne matrix values is even somewhat smaller. For these bands, no additional bands using 16O18O are reported. But assuming the same asymmetric alignment as observed for the Ne matrix, the additional band can be inferred to appear at ∼715 cm−1, and it might be that it remained undetected because of overlap with another unassigned band at 716.3 cm−1. Hence, it is possible that the bands belonging to V2O4 in Ar are those at 720.3 and 691.5 cm−1. The MRCI calculations yield values of 1049, 768, 696, and 314 cm−1 for the allowed transitions in the range of the Ne matrix spectra. They deviate from the observed transitions at ∼1003, 732, 641, and 309 cm−1 by up to 55 cm−1, whereas the density functional results of 1031, 724, 641, and 304 cm−1 deviate by up to only 28 cm−1. It was already noted that a

Scheme 2. Selected Vibrational Modes of V2O4

■

DISCUSSION Assignment of the Observed Bands. The observed bands are assigned to V2O4 for the following reasons: (a) With increasing V content, the signals more strongly increase than those of compounds with one V atom only (VO, VO2, VO2(O2), VO2(O2)2). (b) The behavior of the signals (on annealing and irradiation) is similar to that of the signals of V2O2.28 However, directly after deposition of the matrices the signals are weaker than those of V2O2 and, in particular, they are almost absent at low oxygen concentrations and appear only after annealing to 7 K. (c) With the 16O2+16O18O+18O2 mixture for two of the signals (309 and 641 cm−1), triplets of triplets are observed, indicating the presence of four oxygen atoms in a symmetric environment with two sets of two symmetryequivalent oxygen sites. The Supporting Information contains a comparison of the observed and calculated isotopic splitting patterns. (d) Two of the bands observed here are close to the two bands previously assigned to V2O4 in solid Ar.7 (e) The observed vibrational transitions favorably agree with the results of the quantum chemical calculations on V2O4. D


Article

The Journal of Physical Chemistry A relatively large error must be assigned to the calculated frequencies. Taking into account such an error margin of some 10 cm−1, there is agreement between the experimental and calculated values. Furthermore, concerning the isotopic shifts, there is excellent agreement between the calculated and experimental values for the different isotopologues. Although the main feature of the electronic wave function, namely, the two unpaired electrons at the V sites, is described by the small active space of two orbitals, the increase of the size of the active space from 2 to 10 orbitals has a pronounced effect on the vibrational frequencies. But even this 10-orbital active space is still far from an all-valence orbital active space, and therefore it is likey that the further enlargement of the active space will still markedly improve the frequencies. Calculated Structure and Bonding Situation. The MRCI calculations yield a structure for the 1Ag ground term with V−O distances of 181.8 and 158.4 pm for the ring oxygen and terminal oxygen atoms, respectively, and a V−V distance of 261.5 pm. These values are in good agreement with the values obtained by the former multireference averaged coupled pair functional (MRACPF) study1 of 186 and 159 pm for the V−O distances and of 263 pm for the V−V distance. Also the V−V− O angle for the terminal oxygens of 145.4° is close to the former MRACPF result of 141.1°. This supports the assumption that the description of the V2O4 ground term by the MRCI calculations in principle is correct. The former MRACPF calculations1 already indicate that there is essentially no bonding between the V atoms, because the two leading configurations in the expansion of the wave function are those that either occupy the symmetric or the antisymmetric combination of the 3d orbitals that take the two remaining 3d electrons, and the two configurations contribute with similar weight to the wave function. The absence of a V−V bond in V2O4 is in clear contrast to the situation in V2O2, where there is V−V bonding.28 To obtain a quantitative description, a natural bond orbital (NBO) analysis30 and an “atoms in molecules” (AIM) analysis31 is performed. The NBO analysis yields a V−V bonding orbital occupied by 1.118 electrons, and a corresponding V−V antibonding orbital occupied by 0.847 electrons. This leads to a value of only 0.136 for the bond order, hence, essentially no bonding. The AIM analysis yields six bond critical points for the V−O bonds but no bond critical point between the V atoms. Instead, there is a ring critical point between the V atoms in the middle of the V2O2 ring, see Figure 5, confirming the absence of a direct V−V bond. The V−V distance calculated for V2O4 of 261.5 pm is close to the V−V distance of 261.9 pm found for solid VO2.32 However, the present results indicate that there is no V−V bonding in V2O4, whereas for (the most stable polymorph of) solid VO2 calculations argue for a V−V bond,33 and it is concluded that the breaking of this bond is responsible for the observed insulator−metal phase transition.33 Intensities of Vibrational Transitions. The former Ar matrix study7 did not report a frequency for (the asymmetric combination of) the V−O stretching motion of the terminal VO groups of V2O4. In this context it is noteworthy that the calculations indicate that the transition of this mode should have the largest intensity. The TPSS calculations yield for this transition (1031 cm−1) an intensity of 540 km mol−1, and for the most intense transition of the ring deformation modes (640 cm−1) they yield an intensity of 419 km mol−1. According to the MRCI calculations with the small two-orbital reference

Figure 5. Contour diagram of the electron density within the plane of the V2O2 ring. (■) Bond critical points. (●) Ring critical point. At the bond critical points of the V−O bonds of the ring, the electron density amounts to 0.150 bohr−3; at the bond critical points of the exo V−O units (not shown in the figure), it amounts to 0.305 bohr−3.

space, these two transitions have intensities of 1229 km mol−1 and of only 72 km mol−1. Thus, by the small MRCI calculations, the intensity of the asymmetric vibration of the terminal VO group even is considerably larger than by the TPSS functional. The evaluation of the observed spectra yields relative intensities of the bands at 1003, 732, 641, and 309 cm−1 of 0.15, 0.23, 1.00, and 0.10. Except for the high-frequency mode, they are in good agreement with the values of 1.29, 0.30, 1.00, 0.09 obtained for these modes with the TPSS functional. Obviously, the intensity observed for the asymmetric stretching mode of the terminal VO groups in V2O4 is remarkably weak. This is likely to be the reason for the fact that the band has not been observed in the former Ar matrix experiments. Apparently the calculations considerably overestimate the intensity of this transition. However, the large difference between the TPSS result and the MRCI result with the small reference space indicates that these intensities strongly depend on the description of the electronic structure, and a more advanced computational treatment is likely to improve the results. Formation in the Matrix. Concerning the formation of V2O4, two pathways are likely: (a) the reaction of V2O228 (built from V234 and O2) with another O2 molecule or (b) the combination of two VO2 molecules (built from V atoms and O2). In the first case, assuming that the V2O2 ring is unlikely to be broken by the reaction with a O2 molecule, when using a 16 O2+18O2 mixture, only isotopologues with the same oxygen isotope in both of the ring positions and also in both of the external positions should appear ( 1 6 OV 1 6 O 2 V 1 6 O, 16 OV18O2V16O, 18OV16O2V18O, 18OV18O2V18O). In the second case either only the pure isotopologues or the isotopologue with both the two ring positions and the two external positions occupied by different oxygen isotopes should appear (16OV16O2V16O, 16OV16O18OV18O, 18OV18O2V18O). In experiments using 18O2+16O2 mainly the 16OV16O18OV18O isotopologue and pure 16O and 18O isotopologues are observed. This indicates that the formation of V2O4 mainly proceeds via the combination of two VO2 molecules. Comparison with Other M2O4 Transition-Metal Clusters. The V2O4 molecule in several aspects is similar to the Co2O4 molecule that has been characterized in detail.35 Both have a centrosymmetric structure composed of a fourmembered M2O2 ring and two oxo groups pointing outward. Accordingly, as in the case of V2O4, also for Co2O4, IR E


Article


(5) Jakubikova, E.; Rappé, A. K.; Bernstein, E. R. Density Functional Theory Study of Small Vanadium Oxide Clusters. J. Phys. Chem. A 2007, 111, 12938−12943. (6) Wang, Y.; Gong, X.; Wang, J. Comparative DFT Study of Structure and Magnetism of TMnOm (TM = Sc−Mn, n = 1 − 2,m = 1 − 6) Clusters. Phys. Chem. Chem. Phys. 2010, 12, 2471−2477. (7) Chertihin, G. V.; Bare, W. D.; Andrews, L. Reactions of LaserAblated Vanadium Atoms with Dioxygen. Infrared Spectra of VO, VO2, OOVO2, and V2O2 in Solid Argon. J. Phys. Chem. A 1997, 101, 5090−5096. (8) Zhai, H.-J.; Wang, L.-S. Electronic Structure and Chemical Bonding of Divanadium-Oxide Clusters (V2Ox, x = 3 − 7) from Anion Photoelectron Spectroscopy. J. Chem. Phys. 2002, 117, 7882−7888. (9) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; et al. MOLPRO, Version 2012.1, a Package of ab initio Programs; TTI GmbH: Stuttgart, Germany, 2012. (10) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: a General-Purpose Quantum Chemistry Program Package. WIREs Comput. Mol. Sci. 2012, 2, 242−253. (11) Roos, B. O.; Lindh, R.; Malmqvist, P.-A.; Veryazov, V.; Widmark, P.-O. New Relativistic ANO Basis Sets for Transition Metal Atoms. J. Phys. Chem. A 2005, 109, 6575−6579. (12) Roos, B. O.; Lindh, R.; Malmqvist, P.-A.; Veryazov, V.; Widmark, P.-O. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set. J. Phys. Chem. A 2004, 108, 2851−2858. (13) Wolf, A.; Reiher, M.; Hess, B. A. The Generalized Douglas-Kroll Transformation. J. Chem. Phys. 2002, 117, 9215−9226. (14) Knowles, P. J.; Werner, H.-J. An Efficient Second-Order MC SCF Method for Long Configuration Expansions. Chem. Phys. Lett. 1985, 115, 259−267. (15) Werner, H.-J.; Knowles, P. J. A Second Order Multiconfiguration SCF Procedure with Optimum Convergence. J. Chem. Phys. 1985, 82, 5053−5063. (16) Knowles, P. J.; Werner, H.-J. An Efficient Method for the Evaluation of Coupling Coefficients in Configuration Interaction Calculations. Chem. Phys. Lett. 1988, 145, 514−522. (17) Werner, H.-J.; Knowles, P. J. An Efficient Internally Contracted Multiconfiguration-Reference Configuration Interaction Method. J. Chem. Phys. 1988, 89, 5803−5814. (18) Shamasundar, K. R.; Knizia, G.; Werner, H.-J. A New Internally Contracted Multi-Reference Configuration Interaction Method. J. Chem. Phys. 2011, 135, 054101−17. (19) TURBOMOLE V6.6 2014, a Development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989−2007, TURBOMOLE GmbH, 2007. Online at http://www.turbomole.com. (20) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Electronic Structure Calculations on Workstation Computers: The Program System TURBOMOLE. Chem. Phys. Lett. 1989, 162, 165− 169. (21) Treutler, O.; Ahlrichs, R. Efficient Molecular Numerical Integration Schemes. J. Chem. Phys. 1995, 102, 346−354. (22) Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Nonempirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401−4. (23) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297−3305. (24) Eichkorn, K.; Treutler, O.; Ö hm, H.; Häser, M.; Ahlrichs, R. Auxiliary Basis Sets to Approximate Coulomb Potentials. Chem. Phys. Lett. 1995, 242, 652−660. (25) Weigend, F. Accurate Coulomb-Fitting Basis Sets for H to Rn. Phys. Chem. Chem. Phys. 2006, 8, 1057−1065. (26) Gong, Y.; Zhou, M.; Andrews, L. Spectroscopic and Theoretical Studies of Transition Metal Oxides and Dioxygen Complexes. Chem. Rev. 2009, 109, 6765−6808.

absorptions with a structure of a triplet of triplets have been observed when using a mixture of 16O2, 16O18O, and 18O2. Both clusters have a singlet 1Ag ground state, and it seems that also for Co2O4 there is no metal−metal bond. However, Co2O4 has a planar structure (D2h), whereas V2O4 is nonplanar (C2h). Souvi et al.35 explain this difference in terms of different characters of the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of the MO 2 monomers and, hence, different favorable overlaps when forming the dimers. A simple explanation could also be the following. For V2O4, the remaining 3d electron on each V atom (an early transition metal with a more diffuse 3d shell) is avoiding the electrons of the V−O bonds and therefore is taking the position of a corner of a tetrahedral environment of the V atoms. For Co2O4 by contrast, because of the larger nuclear charge of Co the remaining five 3d electrons are located closer to the nucleus and thus interfere less with the Co−O bonds that then adopt a triangular arrangement. To obtain more insight, it would be interesting to investigate the electronic structure of Co2O4 by multireference methods as has been done for V2O4.1 The same holds for other systems like Ti2O4, Zr2O4, Hf2O4, and Cr2O4 for which density functional calculations predict either nonplanar C2h (Ti, Zr, Hf) or planar D2h (Cr) structures.36,37

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b09644. • Calculated vibrational frequencies of the isotopologues, natural bonding orbital analysis PDF

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 (0)6221 54 8446. Fax: +49 (0)6221 54 5707. ORCID

Hans-Jörg Himmel: 0000-0001-8111-3047 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Fincancial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. The authors also acknowledge support by the state of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) through Grant No. INST 40/467-1 FUGG.

■

REFERENCES

(1) Pykavy, M.; van Wüllen, C.; Sauer, J. Electronic Ground States of the V2O4 +/0/− Species from Multireference Correlation and Density Functional Studies. J. Chem. Phys. 2004, 120, 4207−4215. (2) Vyboishchikov, S. F.; Sauer, J. Gas-Phase Vanadium Oxide Anions: Structure and Detachment Energies from Density Functional Calculations. J. Phys. Chem. A 2000, 104, 10913−10922. (3) Calatayud, M.; Andrés, J.; Beltrán, A. A Systematic Density Functional Theory Study of VxOy+ and VxOy (x = 2 − 4, y = 2 − 10) Systems. J. Phys. Chem. A 2001, 105, 9760−9775. (4) Matsuda, Y.; Bernstein, E. R. Identification, Structure, and Spectroscopy of Neutral Vanadium Oxide Clusters. J. Phys. Chem. A 2005, 109, 3803−3811. F


Article

The Journal of Physical Chemistry A (27) Hübner, O.; Hornung, J.; Himmel, H.-J. The Electronic Structure of VO in its Ground and Electronically Excited States: A Combined Matrix Isolation and Quantum Chemical (MRCI) Study. J. Chem. Phys. 2015, 143, 024309−11. (28) Hübner, O.; Himmel, H.-J. Multiple Metal−Metal Bond or No Bond? The Electronic Structure of V2O2. Angew. Chem., Int. Ed. 2017, 56, 12340−12343. (29) Zhao, Y.; Gong, Y.; Chen, M.; Zhou, M. Noble Gas−TransitionMetal Complexes: Coordination of VO2 and VO4 by Ar and Xe Atoms in Solid Noble Gas Matrixes. J. Phys. Chem. A 2006, 110, 1845−1849. (30) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Landis, C. R.; Weinhold, F. NBO 6.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2013; http://nbo6.chem.wisc.edu/. (31) Biegler-König, F.; Schönbohm, J.; Bayles, D. AIM2000−A Program to Analyze and Visualize Atoms in Molecules. J. Comput. Chem. 2001, 22, 545−559. (32) Longo, J. M.; Kierkegaard, P.; et al. A Refinement of the Structure of VO2. Acta Chem. Scand. 1970, 24, 420−426. (33) Yuan, X.; Zhang, W.; Zhang, P. Hole-Lattice Coupling and Photoinduced Insulator-Metal Transition in VO2. Inorg. Chem. 1992, 31, 567−576. (34) Hübner, O.; Himmel, H.-J. Low-Energy Excited States of Divanadium: A Matrix Isolation and MRCI Study. Phys. Chem. Chem. Phys. 2016, 18, 14667−14677. (35) Souvi, S. O.; Danset, D.; Alikhani, M. E.; Manceron, L. Formation and Structure of Co2O4: A Combined IR Matrix Isolation and Theoretical Study. J. Phys. Chem. A 2010, 114, 11399−11407. (36) Gong, Y.; Zhang, Q.; Zhou, M. Matrix Isolation Infrared Spectroscopic and Theoretical Study of Group IV Metal Oxide Clusters: M2O2 and M2O4. J. Phys. Chem. A 2007, 111, 3534−3539. (37) Zhang, Q.; Zhao, Y.; Gong, Y.; Zhou, M. Matrix Isolation Infrared Spectroscopic and Theoretical Study of Dinuclear Chromium Oxide Clusters: Cr2On (n = 2,4,6) in Solid Argon. J. Phys. Chem. A 2007, 111, 9775−9780.

G


The Vibrations of V2O4: Matrix Isolation and Quantum Chemical

Recommend Documents