Electronic Spectroscopy of Diatomic VC - The ... - ACS Publications

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Electronic Spectroscopy of Diatomic VC Olha Krechkivska and Michael D. Morse* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, United States S Supporting Information *

ABSTRACT: Resonant two-photon ionization spectroscopy has been applied to diatomic VC, providing the first optical spectrum of this molecule. The ground state is determined to be a 2Δ3/2 state that arises from the 1σ21π42σ21δ1 configuration. The r0″ ground-state bond length is 1.6167(3) Å. The manifold of excited vibronic states in the visible portion of the spectrum is quite dense, but two possible vibrational progressions have been identified. It is noted that VC joins CrC, NbC, and MoC as species in which the metal ns-based 3σ orbital is unoccupied, resulting in large dipole moments in the ground states of these molecules. In the corresponding 5d metal carbides, however, the 3σ orbital is occupied, leading to different ground electronic states of the 5d congeners, TaC and WC.

1. INTRODUCTION The chemical bonding between transition metals and carbon is of high general interest due to the importance of the metal−carbon bond in homogeneous and heterogeneous catalysis, biological chemistry, and organometallic chemistry. In addition, transitionmetal carbides are quite important in materials chemistry due to their hardness, high melting points, excellent resistance to corrosion, and useful electrical properties. As a result, a large amount of work has been performed to characterize the bulk solid phases of these compounds. A number of investigations have also been directed toward understanding the electronic structure and chemical bonding in the smallest organometallic molecules, in which a single metal atom is bonded to a single carbon atom. Spectroscopic studies of diatomic transition-metal carbides began in the 1960s, when spectra of RhC,1−3 RuC,4,5 IrC,6,7 and PtC8−11 were observed emanating from high-temperature furnaces containing the transition metals in graphite vessels. These species have bond energies well in excess of 5.5 eV12−15 and were for many years the only transition-metal monocarbides that were spectroscopically known. In the 1990s, the laser ablation supersonic expansion method was employed for the study of transition-metal carbides, leading to optical studies of many more MC molecules, including CrC,16 FeC,17−22 CoC,23,24 NiC,25 YC,26 ZrC,27 NbC,28 MoC,29,30 PdC,30,31 TaC,32 WC,33−36 and OsC.37 A few studies of matrix isolation ESR spectroscopy of diatomic transition-metal carbides have also been reported, with VC,38,39 CoC,39 NbC,38 and RhC40 known through this technique. More recently, mass-selected anions of MoC−,41 RhC−,42 and WC−41,43 have been used to probe the electronic states of the neutral molecules by photoelectron spectroscopy. In other photoelectron studies, the FeC+,44 CoC+,45 and NiC+46 cations have been probed using rotationally resolved resonant twophoton pulsed field ionization zero electron kinetic energy (PFIZEKE) spectroscopy. Bond energies of VC,47 NbC,47 MoC,47 TcC,48 RuC,14 RhC,12,13 OsC,49 IrC,14,15 and PtC12,15 have been measured by © 2013 American Chemical Society

Knudsen effusion mass spectrometry. Similarly, bond energies of the cations ScC+,50 TiC+,50 VC+,50,51 CoC+,52 YC+,53 ZrC+,53 NbC+,53 MoC+,53 RuC+,54 RhC+,55 HfC+,56 TaC+,56 WC+,56 ReC+,57 IrC+,58 and PtC+59,60 have been measured using guided ion beam mass spectrometry. Bond energies have also been measured for CrC+,61 FeC+,62 CoC+,62 NbC+,63 MoC+,61 and WC+61 by photofragmentation threshold measurements. A simple historical overview of these molecules shows that the monocarbides of transition metals belonging to groups 8−10 (FeC, CoC, NiC, and their 4d and 5d analogues) have typically been investigated prior to the MC molecules belonging to groups 3−5. This is due to several facts: (1) the strength of the MC bond increases for the later members of the transition-metal series, especially in the 4d and 5d series,64,65 making them easier to produce and stabilize, (2) the early members of the transitionmetal series have much stronger bonds to oxygen than to carbon,66 enabling even minor amounts of oxygen to lead to strong metal oxide signals that dominate the spectra, (3) the early members of the transition-metal series are more likely to form highly ionic MC2 adducts, unless the concentration of the carbon source is kept very low, and (4) further clustering to form metallocarbohedrenes (such as Ti8C12)67,68 occurs more readily in the early transition metals than for the metals that occur later in the period. For these reasons, the only 3d transition-metal monocarbides that remain spectroscopically unknown in the gas phase are the early MC species, ScC, TiC, VC, and MnC. In this article, we report the first optical spectroscopic observations on one of these molecules, diatomic VC. The electronic structure of VC has been of interest for some time. In 1986, a matrix isolation ESR study suggested that the ground state is of 2Σ+ symmetry, as is found for the isoelectronic molecules ScO and TiN,69,70 but the spectra exhibited an Special Issue: Terry A. Miller Festschrift Received: May 13, 2013 Revised: June 26, 2013 Published: June 27, 2013 13284

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result, determination of a ground-state Ω value of Ω = 3/2 will confirm that the ground electronic state is 2Δ3/2. A ground state with Ω = 1/2 that belongs to Hund’s case (a) will confirm a 4Δ state, and a ground state belonging to Hund’s case (b) with Ω = 1/2 will confirm a 2Σ+ ground state. Although the predicted electronic density of states is certainly formidable, we have recorded optical spectra of diatomic VC using the resonant two-photon ionization technique, with the goal of providing a definitive determination of the ground-state electronic symmetry and bond length. Analysis of our spectroscopic results shows that the molecule does have a ground state of 2Δ3/2 symmetry, with an r0″ bond length of 1.6167(3) Å.

unusually large anisotropy in the g tensor.39 Subsequent ESR experiments led to a revision of this assignment, with the molecule proposed to have a 2Δ3/2 ground state in which the orbital angular momentum has been quenched by strong interactions with the rare gas matrix.38 This unusual quenching behavior, leading to large anisotropy in the g tensor, was also found for the isovalent matrix-isolated molecules NbC, VSi, and NbSi. These molecules were also proposed to have 2Δ3/2 ground states with quenched orbital angular momentum.38 These unusual spectroscopic observations led to a 1993 density functional study of VC by Mattar,71 who considered possible ground states of 2Σ+, 2Π, and 2Δ symmetry. The density functional study predicted a 2Δ ground state deriving from the 1σ21π42σ21δ1 configuration with the 2Σ+ state lying only 2580 cm−1 higher in energy, in agreement with the revised interpretation of the ESR data. The 2Σ+ and 2Δ states, which were found to lie close in energy in the DFT work, were then investigated again using a variety of variational and density functional methods in 1996 by Maclagan and Scuseria.72 This again led to the conclusion that the ground state is of 2Δ symmetry, with the 2Σ+ state lying about 2293 cm−1 higher. The first study to systematically study a large number of electronic states dissociating to the ground separated atom limit of V 3d34s2, 4 F + C 2s 2 2p 2 , 3 P was performed by Majumdar and Balasubramanian in 2003.73 These authors identified the ground state as a 4 Δ state that derives primarily from the 1σ21π42σ11δ13σ1 configuration, although it was found that at higher levels of theory, the 2Δ state was lowered significantly. A comprehensive investigation of all of the 3d carbides and oxides using a variety of density functional methods also predicted VC to have a 2Δ ground state.66 Most recently, an ab initio study of VC using very large basis sets and high-level multireference configuration interaction methods has been performed by Kalemos, Dunning, and Mavridis.74 In this study, 29 electronic states of VC were computed. The 2Δ state was again found to be the ground state, but the 4Δ state was found to lie approximately 1570 cm−1 higher in energy. The 2Σ+ state was found about 2840 cm−1 above the ground state. The electronic density of states was found to be enormous, with all 29 of the calculated Λ−S states (107 different spin−orbit levels, labeled by Ω) lying within 20 000 cm−1 of the ground state. Although the preponderance of theory suggests that the ground state will be of 2Δ symmetry, and this is in agreement with the revised interpretation of the ESR studies, definitive experimental verification is possible using rotationally resolved optical spectroscopy. Using optical spectroscopy, the groundstate Ω value can be unambiguously determined, and this allows the three competing candidates for the ground state (2Δ, 4Δ, and 2 + Σ ) to be readily distinguished. If we consider the molecular orbitals that arise primarily from the valence 3d and 4s orbitals of vanadium and from the 2s and 2p orbitals of carbon, the dominant configurations of these three states are 1σ21π42σ21δ1, 2 Δ; 1σ21π42σ11δ13σ1, 4Δ; and 1σ21π42σ23σ1, 2Σ+. The 2Δ and 4Δ states will exhibit spin−orbit splitting of a magnitude that clearly places the molecules in Hund’s case (a). Further, the orbital responsible for the spin−orbit splitting (1δ) is less than half full; therefore, the lowest Ω value resulting from the term will lie lowest in energy. Thus, the 2Δ state will have Ω = 3/2 for its ground level, while the 4Δ state will have Ω = 1/2 for its ground level. In contrast, the 2Σ+ state is expected to conform to Hund’s case (b), in which Ω = 1/2, but the rotational energy levels are governed primarily by BN(N + 1), rather than by BJ(J + 1). As a

2. EXPERIMENTAL SECTION In the present study, diatomic VC was investigated using resonant two-photon ionization (R2PI) spectroscopy. The instrument employed has been used in previous studies of the spectroscopy of diatomic TiFe75 and ZrFe76 and is described only briefly here. The source chamber contains a metal sample disk (a 1:1 mol ratio alloy of V/Mn) that is held against a stainless steel block and is rotated and translated using two DC motors (one for rotation and one for translation). Just under the surface of the block lies a channel through which a pulse of helium seeded with 0.1% CH4 is supplied from a pulsed valve. A second channel intersects the gas supply channel at right angles, providing access to the sample disk surface for the focused beam of a pulsed Nd:YAG laser (1064 nm), which ablates the metal sample. The ablated metal atoms travel approximately 1.9 cm down the 2 mm diameter channel prior to expansion into vacuum. During this period, the metal plasma reacts with the small concentration of CH4 seeded in the helium, and the reaction products undergo numerous collisions with helium, cooling their internal degrees of freedom. Final cooling to extremely low temperatures then occurs as the molecules undergo supersonic expansion into vacuum. It was hoped that MnC molecules would be produced along with VC molecules, so that spectra of the two species could be simultaneously recorded; unfortunately, however, MnC was not observed in the mass spectrum and was apparently not produced using this source. Following supersonic expansion into vacuum, the molecular beam is roughly collimated by passage through a 1.3 cm diameter skimmer, after which it enters the Wiley−McLaren ion source of a linear time-of-flight mass spectrometer.77 In the ion source, the molecular beam is exposed to the unfocused output radiation of a Nd:YAG-pumped pulsed dye laser that counterpropagates along the molecular beam path. After a short delay (∼30 ns), the unfocused fifth harmonic output (212.8 nm, 5.83 eV) of a pulsed Nd:YAG laser is directed across the molecular beam at right angles. Neither laser wavelength alone has sufficient energy to ionize the VC molecules in a one-photon process, but the combination of one photon of each wavelength is sufficient to achieve ionization. The ions produced by this process are accelerated up a flight tube to a microchannel plate detector, following which the ion signal is preamplified, digitized, and processed using a personal computer. The entire experimental cycle is repeated at a rate of 10 Hz. To provide the optical spectrum, the ion signals of the masses of interest are monitored as a function of the dye laser wavelength. The dye laser was scanned in low-resolution mode (single grating, 0.14 cm−1 resolution) to obtain vibronically resolved spectra. Low-resolution scans were calibrated using transitions of atomic vanadium, which were recorded simultaneously with the 13285

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The vibronically resolved spectrum displayed in Figure 1 and over the extended range (15 036−18 482 cm−1) shown in the Supporting Information for this article does not lend itself to easy assignment into band systems. A large number of bands are present, and we are unable to make definite vibrational assignments because of the lack of spectra for isotopic modifications other than the predominant 51V12C (98.65%) form. Nevertheless, comparisons to the high-quality ab initio calculations of Kalemos, Dunning, and Mavridis74 suggest that vibrational frequencies in the range of 540−800 cm−1 are to be expected for excited states lying in the probed spectral range. This has permitted us to identify two possible vibrational progressions within the scanned range. These are listed in Table 1, along with the results of fits to the expression82

spectra of VC. To reveal the rotational structure within each vibronic band, the dye laser was scanned in high-resolution mode (dual grating, 0.05 cm−1 resolution). For calibration purposes, partial reflections of the dye laser beam were directed through an I2 absorption cell and a 0.22 cm−1 free spectral range étalon. The transmitted intensities were monitored; étalon fringes were used to linearize the scan, and I2 absorption features were used in conjunction with the I2 atlas78,79 to provide an absolute wavenumber calibration. Because the dye laser is counterpropagated along the molecular beam axis, there is a Doppler shift introduced into the raw spectra because the molecules are moving toward the radiation source at the beam velocity of helium (1.77 × 103 m/s).80 All measured line positions are corrected for this effect, which is less than 0.11 cm−1 for the bands reported here. A correction for the error in the I2 atlas (−0.0056 cm−1) is also made at the same time.81 Survey spectra of 51V12C (mass 63) were recorded over the range of 15 036−18 482 cm−1 (665−541 nm), and approximately 35 vibronic bands were observed over this range. Several of these were investigated at higher resolution, and five were successfully analyzed. A sixth band was determined to consist of two overlapping bands, one of which was also successfully analyzed.

υv ′−0 = T0 + v′ωe′ − (v′2 + v′)ωe′xe′

(3.1)

Table 1. Possible Vibronic Progressions in 51V12C band assignmenta 0−0 1−0 2−0 3−0

3. RESULTS A. Low-Resolution Spectrum. Figure 1 displays a portion of the low-resolution spectrum of VC, as recorded over the 15

T0 (cm−1) ωe′ (cm−1) ωe′xe′ (cm−1) B0′ (cm−1)d B1′ (cm−1)d B0″ (cm−1)d ν0(0−0) (cm−1)d ν0(1−0) (cm−1)d

A0.5-X2Δ3/2 system

B1.5-X2Δ3/2 system

15347.4(1)b 16088.5(−4)b 16811.8(4)c 17514.6(−1) Fitted Spectroscopic Constants

15501.1(0) 16163.6(1)b 16811.8(−1)c 17446.1(0)

15347.2 (0.6) 760.8 (1.3) 9.57 (0.32) 0.48088(52) 0.44989(35) 0.66281(28) 15346.4901(68) 16087.9477(36)

15501.12 (0.09) 676.6 (0.2) 7.08 (0.05) 0.55332(35) 0.66281(28) 16162.9259(78)

a

Vibrational numbering is arbitrary and likely in error. Additional members of these progressions are likely to be found to the red of the scanned region. Numbers provided in parentheses following the band positions are residuals in the vibronic fit, in units of 0.1 cm−1. Error limits (1σ) are provided in parentheses following the fitted spectroscopic constants, in units of the last digit quoted. bThe band was also examined with rotational resolution. The values listed here are from the low-resolution scan. cThe 16811.8 cm−1 band is used in both progressions because bands in both progressions overlap at this wavenumber. dFitted values of ν0, B0′, B1′ , and B0′′ are from a fit of the rotationally resolved data.

Unfortunately, we have no way of determining the vibrational numbering in the upper state and have simply assumed for the tabulation that the first observed band is the 0−0 band. Observation of R2PI spectra using the fifth harmonic (212.8 nm, 5.83 eV) of the Nd:YAG laser as the ionization photon implies that IE(VC) > 5.83 eV. Similarly, the observation of a transition as far to the red as 15 236 cm−1 (1.89 eV) implies that the sum of this energy plus 5.83 eV is sufficient to reach the ionization limit of VC. Together, these results place the ionization energy of VC within the range of 5.83 < IE(VC) < 7.72 eV. B. Rotationally Resolved Spectra. Several of the observed bands were investigated at the higher resolution achieved by operating the dye laser with two diffraction gratings. Many bands were found to overlap with other transitions and were difficult to analyze; these were abandoned. Six bands, however, were readily rotationally resolved and analyzed. The upper states of these transitions are labeled with the notation {xx.xx}Ω′, where Ω′

Figure 1. Vibronically resolved spectrum of VC, recorded over the 15 900−17 000 cm−1 range.

900−17 000 cm−1 range. A number of vibronic bands are easily visible, despite the fact that the VC signal intensity was quite weak compared to other species that were observed in the mass spectrum. To put this in perspective, spectra of VO (mass 67) were recorded simultaneously with those of VC (mass 63), even though we provided no intentional source of oxygen. The most intense features observed in the spectrum of VC were approximately a factor of 10 weaker than the 0−0 band of the C4Σ− ← X4Σ− band system of VO, reflecting the small amount of VC present in the molecular beam. Despite the low intensity of the VC peak in the mass spectrum, the signal-to-noise ratio was quite good. The bands in the 15 900−17 000 cm−1 range that were rotationally resolved and analyzed are labeled in Figure 1. 13286

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Table 2. Rotationally Resolved and Fitted Bands of VCa,b band {15.35}0.5 ← X Δ3/2 {16.09}0.5 ← X 2Δ3/2 {16.16}1.5 ← X 2Δ3/2 {16.47}0.5 ← X 2Δ3/2 {17.57}2.5 ← X 2Δ3/2 {18.38}2.5 ← X 2Δ3/2 2

Ω′

ν0 (cm−1)

B′ (cm−1)

r′ (Å)

B″ (cm−1)

0.5 0.5 1.5 0.5 2.5 2.5

15346.4901(68) 16087.9477(36) 16162.9259(78) 16470.5697(70) 17568.2432(125) 18384.4471(118)

0.48088(52) 0.44989(35) 0.55332(35) 0.50738(35) 0.53506(66) 0.53736(47)

1.8998(10) 1.9642(8) 1.7711(6) 1.8496(6) 1.8011(11) 1.7972(8)

0.66281(28) 0.66281(28) 0.66281(28) 0.66281(28) 0.66281(28) 0.66281(28)

a

Error limits (1σ) are provided in parentheses following the listed value, in units of the last digit quoted. The internuclear distances, r′, are not necessarily representative of the true bond length of the state, owing to interactions with other neighboring states. These are only provided for general reference. bThe {15.35}0.5 ← X 2Δ3/2 band is assigned as the 0−0 band of the A0.5-X2Δ3/2 system in Table 1; the {16.09}0.5 ← X 2Δ3/2 band is assigned as the 1−0 band of the A0.5-X2Δ3/2 system in Table 1; and the {16.16}1.5 ← X 2Δ3/2 band is assigned as the 1−0 band of the B1.5X2Δ3/2 system in Table 1. The remaining three bands are unclassified at present.

confirmed by the first lines of R(1.5), Q(2.5), and P(3.5). This identifies the band as an Ω′ = 2.5 ← Ω″ = 1.5 transition. The lower traces in Figures 2 and 3 display a simulated spectrum that is plotted using the PGopher program.83 All rotational fits, however, were performed using the simplified expression in eq 3.2.

denotes the Ω value of the upper state and xx.xx is the band origin wavenumber divided by 1000. We choose this notation, rather than the more common notation using square brackets, to emphasize that for most of these bands, we have not been able to associate the bands with a particular excited electronic state. The notation {xx.xx}Ω′ identifies the energy of the vibronic level and its Ω value without identifying the vibrational quantum number or the T0 value of the 0−0 band. In other publications, we use the [xx.xx]Ω′v′-v″ notation to indicate that the band’s vibrational numbering, Ω value, and the location of the 0−0 band are known, with [xx.xx] giving the T0 value of the 0−0 band, divided by 1000. All of the rotationally resolved bands were found to originate from a lower level with Ω = 1.5. Further, all bands could be adequately fitted with the same lower-state rotational constant, implying that they originate from the same lower level, which is presumably the ground state. Accordingly, the six bands were included in a combined fit in which they were fitted to the formula ν = ν0 + B′J ′(J ′ + 1) − B″J ″(J ″ + 1)

(3.2)

with B″ constrained to the same value for all bands. Fitted values of the parameters ν0, B′, and B″ are provided in Table 2. The 18 384 cm−1 band displayed in Figure 2 exhibits a rotational structure that is similar to the 17 568 cm−1 band. The band shows an intense R branch that quickly forms a band head, a Q branch of moderate intensity, and a weak P branch. This intensity pattern suggests a ΔΩ = +1 transition, which is

Figure 3. Rotationally resolved spectrum of the {16.09}0.5 ← X 2Δ3/2 band of VC. The simulated spectrum, in blue, was calculated for a rotational temperature of 15 K.

The 16 088 cm−1 band displayed in Figure 3 shows rotational structure that is similar to that of the 15 346 and 16 471 cm−1 bands. All three bands show a comparatively weak R branch beginning with R(1.5), a stronger Q branch beginning with Q(1.5), and an intense P branch beginning with P(1.5). These first lines identify the band as an Ω′ = 0.5 ← Ω″ = 1.5 transition, which is consistent with the pattern of branch intensities. One additional band, near 16 163 cm−1, was successfully analyzed as an Ω′ = 1.5 ← Ω″ = 1.5 transition. This feature, however, was overlapped by at least one other band and is displayed in the supporting data. It will not be discussed further here.

4. DISCUSSION The observation that all six rotationally resolved bands have Ω″ = 1.5 and the same value of B″ identifies the ground state as the 1σ21π42σ21δ1, 2Δ3/2 state that has been obtained in most of the computational studies71,72,74 and in the revised interpretation of the ESR data.38 Neither of the other possibilities, 4Δ and 2Σ+, would have Ω″ = 1.5. The measured value of B0″ for the ground

Figure 2. Rotationally resolved spectrum of the {18.38}2.5 ← X 2Δ3/2 band of VC. The simulated spectrum, in blue, was calculated for a rotational temperature of 20 K. 13287

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state, 0.66281(28) cm−1, would give a bond length of 1.6182(3) Å if it were simply converted in the usual way.82 In this case, however, we can estimate the spin−orbit splitting in the 2Δ state and make a correction for the spin-uncoupling operator, which couples the 2Δ3/2 and 2Δ5/2 levels. The spin-uncoupling operator leads to effective B values for the 2Δ3/2 and 2Δ5/2 states that are different from the true B value, which is related to the bond length.84 The unpaired electron in the X2Δ state resides in the 1δ orbital, which is purely of vanadium 3d character. For such a case, the spin−orbit constant, A, may be estimated as A = ζ3d(V), where ζ3d(V) is the spin−orbit parameter for the 3d orbital in atomic vanadium, 177 cm−1.84 The spin-uncoupling operator causes the rotational levels of the 2Δ3/2 and 2Δ5/2 levels to have different effective B values, given as82 ⎛ B ⎞⎟ Beff (2Δ3/2 ) = B⎜1 − ⎝ 2A ⎠ ⎛ B ⎞⎟ Beff (2Δ5/2 ) = B⎜1 + ⎝ 2A ⎠

orbitals, and the pair of nonbonding 1δ orbitals, which are purely 3dδ(V) in character. The ground state is primarily composed of the 1σ21π42σ21δ1, 2 Δ configuration.74 This state has a triple bond due to the complete occupancy of the 2σ and 1π bonding orbitals and the lack of electrons in the antibonding 2π and 4σ orbitals.66,74 The 4 Δ state that has been considered as a candidate for the ground state transfers one electron from the 2σ to the 3σ orbital. The low-lying 2Σ+ state is generated from the 2Δ ground state by moving the 1δ electron to the 3σ orbital. These states are similar in energy because the 2σ, 1δ, and 3σ orbitals all lie close in energy. The 3σ orbital places much of its electron density on the side of the molecule opposite to the negatively charged carbon atom. As a result, an interesting consequence of having an empty 3σ orbital is that the VC ground state is calculated to have an exceptionally large dipole moment of 7.36 D (in the sense of V+C−) in the calculation with the most extensive basis set.74 Transfer of an electron from the 2σ bonding orbital to the 3σ orbital to form the 4Δ state reduces the dipole moment significantly, to 2.42 D.74 Similarly, transfer of the metal-based 1δ electron to the 3σ orbital to form the low-lying 2Σ+ state also reduces the dipole moment quite significantly, to 2.88 D.74 These results are consistent with those of other transition-metal carbides, where the lack of electrons in the metal-based 3σ orbital leads to high calculated dipole moments of 6.76 D for the 1σ21π42σ21δ2, 3Σ− ground state of CrC;16,87 6.77 D for the 1σ21π42σ21δ1, 2Δ ground state of NbC;88 and 5.87 D for the 1σ21π42σ21δ2, 3Σ− ground state of MoC.89 Experimental measurement in the case of MoC provides confirmation that the dipole moment is indeed quite large, 6.07(18) D.90 These results suggest that the VC, CrC, NbC, and MoC molecules will function quite effectively as Lewis acids, readily accepting the donation of an electron pair into the empty 3σ orbital. With the completion of this study, the ground terms of the isovalent molecules VC, NbC, 28 and TaC 32 are now experimentally known. The 3d and 4d carbides, VC and NbC, share a 1σ21π42σ21δ1, X2Δ3/2 ground state, while the 5d carbide, TaC, has a 1σ21π42σ23σ1, X2Σ+ ground state. This is an example of the well-known relativistic stabilization of the 6s orbital, which is the dominant contributor to the 3σ orbital in TaC.32 Other examples in which the ground term of the 5d carbide differs from that of its 3d and 4d congeners are CrC, MoC (1σ21π42σ21δ2, 3 − Σ (Ω = 0+))16,29 versus WC (1σ21π42σ21δ13σ1, 3Δ1)33 and CoC, RhC (1σ 2 1π 4 2σ 2 1δ 4 3σ 1 , 2 Σ + ) 2 , 2 3 versus IrC (1σ21π42σ21δ33σ2, 2Δ5/2).7 The relative stabilization of the 6s orbital, as compared to the 5d orbitals, may be quantified by comparing the orbital energies in the atoms, as calculated relativistically using numerical Dirac−Fock theory, to the nonrelativistic orbital energies, as calculated using numerical Hartree−Fock methods. These calculations have been reported by Desclaux for the ground configurations of the atoms.91 Using the data of Desclaux, the relativistic effects on the nd and (n+1)s orbital energies are illustrated in Figure 5 for V, Nb, and Ta. Relativistic stabilization occurs for all of the s orbitals because these penetrate close to the nucleus, where the electron velocity approaches the speed of light. The d orbitals, however, suffer a relativistic destabilization because the contraction of the s orbitals causes the nonpenetrating d orbitals to be more effectively shielded from the nuclear charge. As a result, relativistic effects both stabilize the s orbital and destabilize the d orbital, magnifying the relative stabilization of the s orbital. This effect is greatest in the 5d series due to the large nuclear charge,

and

(3.3) −1

−1

Employing Beff = 0.66281(28) cm and A = 177 cm and solving for B gives B0″ = 0.66405(28) cm−1, which may be inverted to give r0″ = 1.6167(3) Å. This is our best estimate of the r0 bond length in the X2Δ state of VC and compares to computed values of the re bond lengths of 1.577,71 1.645,72 1.690,73 and 1.636 Å.74 It is very similar to the bond length of CrC, which is 1.6188(6) Å.16 A qualitative understanding of the chemical bonding in VC may be obtained by considering a simplified molecular orbital picture based on the calculations of Kalemos, Dunning, and Mavridis,74 as amplified in personal communications with Prof. Kalemos.85 This is illustrated schematically in Figure 4, where the orbital images were generated from a B3LYP calculation using the

Figure 4. Qualitative molecular orbital diagram for VC.

LANL2DZ basis set in Gaussian 09.86 The 2s(C) orbital is rather uninvolved in the chemical bonding and is the main contributor to the 1σ lone pair orbital in the molecule. The 2σ bonding orbital is primarily the bonding combination of the 3dσ(V) orbital and the 2pσ(C) orbital; the 4σ orbital is the corresponding antibonding combination. The 3σ orbital is a nonbonding orbital localized mainly on vanadium; it is dominated by 4s(V) character that is shifted off-axis by an admixture of 3dσ(V) character and polarized away from the negatively charged carbon by an admixture of 3pσ(V) character. This picture is completed by the 1π pair of 3dπ(V)−2pπ(C) bonding orbitals, the corresponding 2π pair of antibonding 13288

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Figure 5. Relativistic effects on atomic orbital energies in V, Nb, and Ta.

giving a net relative stabilization of the 6s orbital of 2.62 eV for Ta.

5. CONCLUSION The optical spectrum of VC has been investigated for the first time, allowing the ground state to be identified as a 2Δ3/2 state arising from the 1σ21π42σ21δ1 configuration. The rotationally resolved spectra have determined the r0″ ground-state bond length to be 1.6167(3) Å.

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ASSOCIATED CONTENT

S Supporting Information *

Low-resolution and high-resolution spectra, a list of observed vibronic bands, and lists of assigned lines and rotational fits. This material 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]. Fax: (801)-581-8433. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy under Grant No. DE-FG0301ER15176. We greatly appreciate helpful conversations with Apostolos Kalemos regarding the molecular orbitals in the VC molecule.

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REFERENCES

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