Journal of Molecular Spectroscopy 290 (2013) 42–47

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Journal of Molecular Spectroscopy

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The pure rotational spectrum of VS (X4R�): A combined Fouriertransform microwave and millimeter-wave study

0022-2852/$ - see front matter � 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.jms.2013.07.002

⇑ Corresponding author. Fax: +1 520 621 5554.E-mail address: lziurys@email.arizona.edu (L.M. Ziurys).

G.R. Adande, L.M. Ziurys ⇑Department of Chemistry and Biochemistry, Department of Astronomy, Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721, United States

a r t i c l e i n f o

Article history:Received 17 May 2013In revised form 29 June 2013Available online 18 July 2013

Keywords:FTMW spectroscopyMillimeter wave spectroscopyVanadium sulfide (VS)Hyperfine structureLaser ablation

a b s t r a c t

The pure rotational spectrum of the vanadium sulfide radical, VS (X4R�), has been measured in the fre-quency range 5–310 GHz using a combination of millimeter-wave direct absorption and Fourier trans-form microwave (FTMW) techniques. In the millimeter-wave region, the radical was produced in anAC discharge from the reaction of VCl4, the vanadium donor, and CS2. In the FTMW instrument, the mol-ecule was created in a supersonic jet, coupled with a laser ablation/DC discharge source (DALAS), from amixture of metal vapor and H2S, heavily diluted in argon. A total of 8 rotational transitions were mea-sured for VS, in which both the quartet fine structure and vanadium hyperfine splittings were resolved.The spectra were analyzed with a Hund’s case (b) Hamiltonian, and rotational, spin–rotation, spin–spin,and hyperfine parameters were determined. The precision of the constants from previous optical studieswas refined and, for the first time, the vanadium quadrupole constant, eQq = �7.6 (4.0) MHz, and thethird order Fermi contact correction, bS = �0.293 (94) MHz, were established. From the fine structureparameters, the nearby 4P and 2R+ states were estimated to lie �6560 cm�1 and �7170 cm�1 abovethe ground state. The hyperfine constants suggest that the bonding in VS is partly ionic, with a significantdegree of covalent character.

� 2013 Elsevier Inc. All rights reserved.

1. Introduction cited state of VS lies about 10,000 cm�1 above the ground state,

Transition metal sulfides are an important class of simple com-pounds from a variety of aspects. They are widely used in the semi-conductor industry, for example, because of their varied opticaland electrical properties [1]. Metal sulfides also play a role in oilrefinement, as they are the byproducts in hydrodesulfurizationprocesses [2]. Analogous to transition metal oxides, these mole-cules are additionally of astrophysical significance; electronic tran-sitions of TiS and YS have been identified in the atmospheres ofAsymptotic Giant Branch (AGB) stars [3]. At a more fundamentallevel, the molecular properties of simple transition metal sulfidespecies have been the subject of numerous theoretical and exper-imental studies [4–6]. These systems typically have a large numberof interacting, low lying electronic states, challenging both spectro-scopic and computational investigations.

One 3d transition-metal monosulfide of interest is VS. Only twospectroscopic studies of this molecule have thus far been con-ducted, both using optical techniques. In 2003, Ran et al. analyzedthe (0,0) and (0,1) rovibrational bands of the C4R� — X4R� elec-tronic transition of VS [8], confirming the ground state rd2 config-uration of the molecule. From interpretation of the spin–orbit andspin–rotation parameters, these authors proposed that the 2R ex-

as has been found for VO. Moreover, their analysis of the vanadiumhyperfine constants suggested that the 4s valence electron contrib-utes only 49% to the 11r orbital, significantly less than the 86% inVO for the analogous 9r orbital. The other study of VS was by Zhu-ang and Steimle [9], who determined the permanent electric dipolemoment of the molecule from the (0,0) band of the same electronictransition studied by Ran et al.

VS has also been the subject of theoretical investigations. In 1986,Bauschlicher and Langhoff [4] used coupled-pair functional (CPF)approaches to examine the bonding in vanadium sulfide. They foundthat the separation between the two vanadium atomic configura-tions 3d34s2 and 3d44s1 was small, about 0.25 eV. As a result, theground state of VS was proposed to be a mixture of these two atomicconfigurations. These authors additionally suggested that VS hadmore covalent character than its VO analog. Bauschlicher and Maitreconducted a further study of VS in 1990 [7], and calculated the Mul-liken populations for VS and VO. They found a slightly larger popula-tion in the 3dr orbital for the sulfide than the oxide.

In this article we present the first measurements of the purerotational spectrum of VS in its X4R� ground state. The N = 1 ? 0and 2 ? 1 transitions were recorded in the range 5–30 GHz usingFourier transform microwave (FTMW) spectroscopy, while theN = 19 18–N = 24 23 transitions were measured with milli-meter-wave direct absorption methods between 200 and300 GHz. Two different synthesis techniques were employed to

G.R. Adande, L.M. Ziurys / Journal of Molecular Spectroscopy 290 (2013) 42–47 43

generate VS, one using DALAS (Discharge-Assisted Laser AblationSource), and the other via the reaction of CS2 with VCl4 in presenceof an AC discharge. Complex fine/hyperfine patterns were observedin almost every transition, leading to a global fit of a total of 150separate lines. These new data have improved the accuracy ofthe spectroscopic parameters of VS by at least one order of magni-tude, as well as establishing higher order hyperfine terms. Here wepresent our experimental results for VS and interpret them interms of metal-sulfide bonding and periodic trends.

2. Experimental

The two lowest rotational transitions of VS were measuredusing a Balle–Flygare type Fourier transform spectrometer, operat-ing in the range 4–40 GHz, as described in Sun et al. [10]. Thisinstrument consists of a Fabry–Perot cavity containing two alumi-num mirrors in a near confocal arrangement, maintained in a vac-uum chamber at an unloaded pressure of about 10�8 Torr. Reactantgases are introduced into the chamber via a pulsed supersonic noz-zle. Microwave radiation, provided by a synthesizer (AgilentE8257D), is launched into the cavity through an antenna embed-ded near the center of one of the mirrors, and, if a resonance exists,is absorbed by the molecules in the expansion. Molecular emissionis collected by an antenna embedded in the opposite mirror andthen detected by a low-noise amplifier as a function of time, theso-called Free Induction Decay. This signal is digitized and con-verted by a fast Fourier transform (FFT) into a spectrum consistingof two Doppler components. The typical resolution of the instru-ment is 4 kHz. Transition frequencies are taken as the average ofthe two Doppler components.

In order to synthesize the VS radical, DALAS, or Discharge As-sisted Laser Ablation Source [11], was employed. Briefly, vanadiumvapor was generated by ablating a rotating metal rod with aNd:YAG laser beam (200 mJ/pulse). A gas mixture of 0.5% H2S in200 psi of Ar was pulsed from the nozzle, entraining the metal va-por, and the mixture passed through a DC discharge (0.75 kV,20 mA) and expanded into the chamber. Typically, about 3000pulse averages were needed to obtain adequate signal strengths.

In the millimeter wave region, the spectrum was measuredusing one of the direct absorption spectrometers of the Ziurysgroup [12]. The radiation source of the instrument is based onphase-locked Gunn oscillators (84–140 GHz), coupled with fre-quency multipliers to cover the frequency range 130–850 GHz.The radiation is propagated through a glass reaction chamber(�10�3 Torr unloaded pressure) containing the molecules of inter-est, and detected by a helium-cooled InSb bolometer. Phase-sensi-tive detection is employed through modulation of the radiationsource and processing by a lock-in amplifier.

VS was synthesized directly in an AC discharge of VCl4 and CS2 inargon. (Note that VCl4 is an extremely toxic liquid). A mixture of1 mTorr of CS2, 1–2 millitorr of VCl4, and 60 mTorr of Ar, with anAC discharge power of 250 W, gave optimal VS production. H2Swas also tried as a sulfur donor, but only CS2 gave detectable signals.

Transition frequencies were determined from scans 5 MHz inwidth, with an equal number of scans in increasing and decreasingfrequency. Gaussian profiles were then fit to the spectral lines. TheVS spectra were sufficiently strong such that little signal averagingwas necessary. The typical resolution of the spectrometer is 100 kHz.

3. Results

The initial search for VS was conducted with the FTMW spec-trometer, using predictions based on previous optical constants[8]. VS follows a case bbJ coupling scheme such that the quantumnumber J indicates the fine structure, where J = N + S, and F the

vanadium hyperfine structure (F = J + I). Spin–rotation and spin–spin interactions generate four separate fine structure componentsfor each rotational level, which are further split into octets by thevandium nuclear spin of I = 7/2. In this coupling scheme, selectionrules are DN = ± 1, DJ = 0, ±1 and DF = 0, ±1. However, for the low-est rotational levels, not all these fine and hyperfine componentsexist. Furthermore, the rotational and fine structure splittings areof the same order of magnitude, such that VS is better describedby Hund’s case (a), and N is not a particularly good quantum num-ber. For consistency with millimeter-wave measurements, case (b)notation was still used to specify the low N levels. As shown in Ta-ble 1, hyperfine lines originating in the F1 (J = N + 3/2) fine struc-ture levels in the N = 1 ? 0 and N = 2 ? 1 transitions weremeasured. One transitions is labeled as N = 0 ? �1, such that theF1 (i.e. J = N + 3/2) convention is preserved. This level in fact corre-sponds to the N = 1, J = 1/2 level, belonging to the F3 spin compo-nent. For the millimeter-wave transitions (N = 19 18 toN = 24 23), 190 lines were recorded between 220 and300 GHz; see Table 1. At these frequencies, spectra from all fourspin components were measured, each consisting of hyperfine oc-tets. Some of the octets were partially blended. Overall, 198 indi-vidual lines were recorded for VS.

Fig. 1 presents spectra of the four spin components of theN = 22 21 transition. As the figure shows, the hyperfine structureis well resolved for all four components, but the individual patternsvary. The F2 and F4 components have a Landé-like pattern, with thespacing between hyperfine lines either increasing (F2) or decreas-ing (F4) with F. The hyperfine lines of the F3 and F1 components,on the other hand, merge together to create a ‘‘bandhead’’. The F1

lines reverse in frequency midway through the pattern such thatthe F = 27 26 through F = 25 24 components falls on top ofthe F = 22 21 through F = 24 23 lines. For F3, the lines merelymerge into one bandhead feature at lower F.

These patterns can be explained by the competition betweendiagonal and off-diagonal matrix elements of the effective Hamil-tonian. Simplified diagonal expressions [13], shown below withthe most important terms, generate a bandhead and frequencyreversal in F1 and F4, but Landé-like patterns in F2 and F3:

F1 : þ32

C bþ c2N þ 3

� �� 1ð2N þ 3Þ ð1Þ

F4 : �32

C b� c2N � 1

� �� 1ð2N � 1Þ ð2Þ

F2 : þ12

C bð2N þ 9Þ þ c6

2N þ 3þ 7

� �� �� 1ð2N þ 1Þð2N þ 3Þ ð3Þ

F3 : �12

C bð2N � 7Þ þ c6

2N � 1� 7

� �� �� 1ð2N þ 1Þð2N � 1Þ ð4Þ

In these equations, b = bF � c/3 and C = F(F + 1) � J(J + 1) � I(I + 1).The main off–diagonal elements in the magnetic hyperfine Hamilto-nian are N � 2; J; FjHjN; J; Fih and N; J � 1; FjHjN; J; Fih In the diago-nalization process, on- and off- diagonal elements will be merged,generating terms mixing bF, B and k. VS is far from the ideal case(b), such that the contribution of the off-diagonal elements is signif-icant. Because the off–diagonal terms involving DJ = ± 1 do not di-rectly affect the F4 component, it is the DN = ±2 elements that aremainly responsible for the change to a Landé pattern. At very highN near 50, however, the F4 component will also form a bandhead.The formation of the bandhead in the F3 component arises froman avoided crossing of the F2 and F3 spin levels, which was first ob-served in VO [14], and predicted to occur in VS near N = 30 [8]. Thiscrossing produces a hyperfine perturbation that follows the selec-tion rule DN = 0, DJ = 1, F = 0. The off–diagonal terms

Table 1Observed rotational frequencies of VS (X4R�, v = 0).a

N0 ? N00 F4 F3 F2 F1

J00 = N00 – 3/2 J00 = N00 – 1/2 J00 = N00 + 1/2 J00 = N00 + 3/2

F0 ? F00 m mobs-calc F0 ? F00 m mobs-calc F0 ? F00 m mobs-calc F0 ? F00 m mobs-calc

0 �1b 5 4 5852.693 �0.017

1 0 6 5 17325.749 0.0245 4 17691.601 0.0114 4 16672.329 0.0293 3 17075.326 0.000

2 1 7 6 28960.854 0.0246 5 29115.390 0.0155 4 29200.279 0.010

19 18 21 20 228814.695 0.037 22 21 230841.029 �0.006 16 15 233804.447 �0.004 17 16 233475.873 �0.00220 19 228823.984 0.028 21 20 230847.858 0.015 17 16 233809.155 �0.004 18 17 233482.260 �0.01319 18 228834.279 �0.022 20 19 230853.472 0.006 18 17 233814.448 �0.032 19 18 233487.256c)

18 17 228845.791 0.049 19 18 230858.101 �0.016 19 18 233820.548 �0.004 24 25 233487.256c)

17 16 228858.311 �0.011 18 17 230861.978 0.028 20 19 233827.527 �0.018 23 22 233490.460c)

16 15 228872.205 0.122 17 16 230865.081 �0.009 21 20 233835.695 0.029 20 19 233490.460c

15 14 228887.058 �0.003 16 15 230867.716 0.076 22 21 233845.167 0.006 21 20 233492.162c)14 13 228903.285 �0.007 15 14 230869.642 �0.047 23 22 233856.332 �0.004 22 21 233492.162c)

20 19 22 21 241240.688 �0.020 23 22 243088.948 0.054 17 16 245836.219 �0.030 18 17 245628.396 0.01421 20 241248.196 0.010 22 21 243095.546 0.087 18 17 245839.857 0.078 19 18 245634.203 �0.00320 19 241256.655 �0.052 21 20 243100.516 �0.167 19 18 245843.990 0.042 20 19 245638.375 �0.24119 18 241266.259 �0.052 20 19 243104.775 �0.025 20 19 245848.919 0.002 25 24 245638.792 �0.02918 17 241276.888 �0.147 19 18 243108.018 0.023 21 20 245854.829 �0.043 21 20 245641.618 0.02117 16 241288.926 0.012 18 17 243110.410 �0.008 22 21 245861.994 �0.051 24 23 245641.618c)

16 15 241301.906 �0.074 17 16 243112.167 �0.022 23 22 245870.731 0.014 22 21 245643.139 0.00915 14 241316.244 �0.020 16 15 243113.505 0.094 24 23 245881.268 0.024 23 22 245643.139c)

21 20 23 22 253630.922 �0.029 24 23 255329.625 0.008 18 17 257888.490 0.014 19 18 257783.286 0.01022 21 253636.966 �0.009 22 21 255341.000 �0.029 19 18 257890.885 �0.013 20 19 257788.560 0.037

� 21 20 253644.038 0.018 21 20 255344.670 �0.010 20 19 257894.010 �0.011 21 20 257792.849c)

20 19 253652.275 0.155 20 19 255347.274 �0.007 21 20 257898.010 �0.009 26 25 257792.849c)

19 18 253661.295 �0.013 19 18 255348.997 �0.013 22 21 257903.101 �0.005 25 24 257795.303c)

18 17 253671.627 0.013 18 17 255350.265c) 23 22 257909.516 �0.028 22 21 257795.303c)

17 16 253683.043 �0.023 17 16 255350.265c) 24 23 257917.675 0.011 24 23 257796.766c)

16 15 253695.648 �0.041 23 24 257927.890 0.003 23 22 257796.766 0.03622 21 24 23 265991.193 0.023 25 24 267563.923 0.009 19 18 269957.371 �0.022 20 19 269940.016 0.036

23 22 265996.041 0.015 24 23 267570.470 0.001 20 19 269958.853 0.101 21 20 269944.852 �0.00822 21 266001.880 0.008 23 22 267575.175 �0.010 21 20 269960.905 0.011 22 21 269948.559 0.01121 20 266008.715 �0.021 22 21 267578.428 0.006 22 21 269964.023 0.005 27 26 269948.559c)

20 19 266016.655 0.007 21 20 267580.384c) 23 22 269968.370 0.002 23 22 269950.976c)

19 18 266025.718 0.085 20 19 267581.492c) 24 23 269974.251 0.000 25 24 269950.976c)

18 17 266035.669 �0.048 19 18 267581.492c) 25 24 269982.056 �0.006 26 25 269952.332c)

17 16 266047.067 0.146 18 17 267581.492c) 26 25 269992.308 �0.010 24 23 269952.332 0.03623 22 25 24 278326.069 0.013 26 25 279792.412 0.037 20 19 282040.053c) 21 20 282097.991 0.001

24 23 278329.961 �0.009 25 24 279799.199 0.044 21 20 282040.053c) 22 21 282102.502 0.02323 22 278334.834 �0.002 24 23 279803.767 0.019 22 21 282041.508 0.089 23 22 282105.805c)

22 21 278340.646 �0.035 23 22 279806.413c) 23 22 282043.712 �0.016 28 27 282105.805c)

21 20 278347.518 �0.009 19 18 279806.413c) 24 23 282047.433 �0.007 24 23 282108.051c)

20 19 278355.378 �0.022 22 21 279808.115c) 25 24 282052.896 �0.028 27 26 282108.051c)

19 18 278364.306 �0.014 21 20 279808.115c) 26 25 282060.644 �0.017 25 26 282109.328c)

18 17 278374.403 0.097 20 19 279808.115c) 27 26 282071.289 �0.014 26 25 282109.328 0.01224 23 26 25 290639.414 0.001 27 26 292015.537 0.016 23 22 294132.965c) 22 21 294256.874 0.012

25 24 290642.574 0.009 26 25 292022.709 0.003 22 21 294132.965c) 23 22 294261.008 0.00424 23 290646.599 �0.029 20 19 292026.055 �0.068 21 20 294134.611c) 24 23 294264.062c)

23 22 290651.595 �0.031 25 24 292027.240 �0.016 24 23 294134.611c) 29 28 294264.062c)

22 21 290657.553 �0.027 21 20 292028.497 �0.077 26 25 294142.817 �0.031 25 24 294266.106c)

21 20 290664.466 �0.044 22 21 292030.160c) 27 26 294150.764 0.012 28 27 294266.106c)

19 18 290681.376 0.002 24 23 292030.160c) 28 27 294162.174 �0.008 27 26 294267.329 0.043

a In MHz.b Correlated with the N = 1, J = 1/2 level in the case (b) limit.c Blended line, not included in the fit.

44G

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olecularSpectroscopy

290(2013)

42–47

Fig. 1. Representative millimeter-wave spectra of VS (X4R�) arising from theN = 22 21 transition, showing the vanadium hyperfine structure, labeled byquantum number F, in all four spin components. In the top panel, the F1 (J = N + 3/2)and F2 (J = N + 1/2) components near 269.9 GHz are displayed. For F2, the completehyperfine octet is readily discernible, showing a classic Lande-like pattern, while F1

octet exhibits a bandhead as the hyperfine components reverse in frequency, with 3sets of blended lines. The middle panel displays the F3 (J = N – 1/2) component near267 GHz; in this case, four blended hyperfine lines form a bandhead. The lowestpanel shows the F4 component near 266 GHz, where a regular Lande-like octet isclearly present. An asterisk indicates an unidentified line. Each spectrum wascreated from a 110 MHz wide scan, 70 s in duration. The scan was cropped to about65 MHz for display.

Fig. 2. Millimeter-wave spectrum of the F2 spin component of VS (X4R�) in theN = 24 23 transition near 294 GHz. Unlike the N = 22 21 transition, thebandhead structure begins to appear in the hyperfine octet at this higher N, asthe off-diagonal DJ = 1 elements begin to dominate. This spectrum was createdfrom a 110 MHz wide scan, 70 s. in duration, then cropped to 45 MHz.

Table 2Spectroscopic constants for VS (X4R�).

Parameter VS VS (optical)b

B 6104.7271(20) 6106.24(75)D 0.0034286(20) 0.00962(393)c 658.64(12) 658.0(4.2)cD 0.000988(46) 0.01(3)cs 0.106(28) 0.84(81)k 63425.3(2.5) 63407.9(6.0)kD 0.0387(10) 0.5(1)bF 454.30(55) 448.6(3.3)c �70.0(1.3) �77(12)CI 0.1567(62) –bs �0.293(94) –bFD �0.00021(13) –eQq �7.6(4.0) –rms of fit 0.046 35.7r0 (Å) 2.05288(3) 2.0526

a Constants in MHz unlesss specified. Errors quoted are 3r.b From Ran et al. 2003. Errors are 3r.

G.R. Adande, L.M. Ziurys / Journal of Molecular Spectroscopy 290 (2013) 42–47 45

N; J � 1; FjHjN; J; Fih become increasingly important as N approaches30 and alter the Landé pattern, creating a bandhead-type structurefor the F3 component starting at the N = 21 22 transition, as thefigure shows. These off-diagonal elements begin to influence theF2 octet near the N = 24 23 transition and a bandhead is formedhere also, as shown in Fig. 2, towards lower F. Note that the patternis almost a mirror image of the F3 level in Fig. 1.

4. Analysis

The VS spectra were analyzed using the non-linear least squareprogram SPFIT [15], employing the following case (b) effectiveHamiltonian:

Heff ¼ Hrot þHss þHsr þHmhf þHeOq þHnsr ð5Þ

The resulting spectroscopic parameters are given in Table 2,alongside previous values from the study of Ran et al. [8]. Distor-tion constants to the spin–spin, spin–rotation and Fermi contactparameters were found to be essential in the fit. Similar to otherquartet sigma molecules [16,17], it was additionally necessary to

include third order spin–orbit corrections to the Fermi contactand spin–rotation parameters, bs, and cs, respectively. The globalfit, including 150 unblended lines in the microwave and millimeterwave range, has an rms of 46 kHz.

The fitted constants are in good agreement with previous opti-cal work, as shown in Table 2, but improve their accuracy by atleast one order of magnitude. The present study has also allowedthe first determination of the quadrupole coupling constant eQqand the third order Fermi contact term bS for the X4R� state of VS.

5. Discussion

The electron configuration for VS is [core] 11r1 3d2 [5]. Thelowest energy electron configurations of atomic vanadium are[Ar] 4s23d3 and [Ar] 4s13d4. As suggested by theory, the groundstate of vanadium sulfide likely correlates with a mixture of these

46 G.R. Adande, L.M. Ziurys / Journal of Molecular Spectroscopy 290 (2013) 42–47

two atomic states. Therefore, the r electron in VS should have boths and d character.

Because the Fermi contact parameter for VS is relatively large atbF = 454.30 MHz, the r electron must contain significant s contri-bution to its orbital makeup. The percent s character can be calcu-lated from the following equation:

%ð4sÞ ¼ bFðmolecularÞ1

2S bFðatomicÞð6Þ

The Fermi contact term for atomic vanadium is 3105 MHz [18].Thus, the r electron in VS is 44% 4s in composition, similar to thevalue of 49% derived from the optical work [8]. In VO, on the otherhand, the electron in the r orbital is estimated to be 85.6% 4s incharacter [19]. There is consequently more hybridization of the rvalence orbital in VS as compared to VO, most likely sdr. Theoret-ical calculations of Bauschlinger and Maitre [7] suggest that the3dr population is larger in VS than VO, although the Mulliken pop-ulation in the pr orbital does not vary between the two species.The smaller s contribution to the 11r orbital in VS also indicatesless ionic bonding.

From the dipolar hyperfine constant c, the radial expectationvalue of the unpaired electrons wavefunction can be estimated[20]:

c ¼ 32

gslBgNlN1n

Xn

i¼1

ð3 cos2 hi � 1Þr3

i

� �; ð7Þ

where n is the number of unpaired electrons. The expectation val-ues for the angular factor hcos2h � 1i are �4/7, 4/7 and 4/5 for dd,dr and pr orbitals, respectively [20]. Assuming a d2 r1 configura-tion for VS with the r orbital being 50% s and 50% d in character (dcan only be dd), the expectation value of the radial electron densityis calculated to be h1/r3i = 1.162 a.u�3. The corresponding value forVO is h1/r3i = 1.617 a.u�3. The smaller value of h1/r3i in VS com-pared to VO indicates that the unpaired electrons on average are lo-cated further away from the metal atom, consistent with the greaterd contribution to the r molecular orbital.

The nuclear quadrupole coupling constant eQq has been deter-mined in VS for the first time in the present study. Applying a sim-ple Townes–Daily analysis, eQq can be expressed as [21]:

eQq ¼ eQq320 ndr þ12

ndp � ndd

� �: ð8Þ

Here ni are the molecular orbital populations and eQq320 is thequadrupole coupling constant of a vanadium atom containing asingly occupied 3d orbital. Note that the contribution to the nucle-ar quadrupole constant of VS from the 4s orbital is zero. An approx-imate value of eQq320 can be evaluated with the formula fromGordy and Cook [22]:

eQq320 ¼ �2:3532lðlþ 1Þ

ð2lþ 3Þð2l� 1ÞQa0

r

� �3� �

: ð9Þ

Here Q is the electric quadrupole of the vanadium nucleus,Q = �5 fm2 [23]. Using h1/r3i = 1.162 a.u�3 calculated from the cparameter, then eQq320 = 7.81 MHz. For a r1 d2 configuration with50% dr character, ndd = 2 and ndr = 0.5 and ndp = 0; substitutingthese values into equation (8), the quadrupole coupling constantof vanadium sulfide is calculated to be eQq = �11.7 MHz. This valueis in good agreement with the measured value of �7.6 MHz.

While the magnetic hyperfine parameters give insight into theelectronic structure of VS in the ground state, the spin–rotationand spin–spin constants c and k can contain information pertainingto the excited electronic states. The spin–spin constant of the effec-tive Hamiltonian consists of the true first order spin–spin interac-tion and a second order spin–orbit contribution, arising fromcoupling between ground and excited electronic states. Heavier

molecules containing a transition metal typically have largespin–orbit interactions and low lying electronic states, such thatthe second order term is dominant [21,24]. The second orderspin–orbit contribution to k can be written as [25]:

kð2Þn ¼30ð2S� 2Þ!ð2Sþ 3Þ!

XR;n0

XK0 ;R0½3R2 � SðSþ 1Þ�

�j n0K0S0R0�

jHSOjnKSRij2

ðEn � En0 Þð10Þ

Similarly, c is a combination of the first order spin–rotationinteraction and a dominant second order contribution arising froma cross term between the Coriolis coupling �B(N+L� + N�L+) andHSO. The spin–rotation parameter can be expressed as [25]:

cð2Þn ¼ �2BX

n0

nKSRh jL� n0Kþ 1SRj i n0Kþ 1SRh jHSO nKSRþ 1j iðEn � En0 Þ SRh jS� SRþ 1j i

ð11Þ

The ground state can interact with excited electronic states throughthe spin–orbit operator according to the selection rules DS ¼ 0;�1;DR ¼ �DK ¼ 0;�1; DX ¼ 0 [26]. The electronic energy level struc-ture in VS should mimic that of VO, which has been explored byHopkins et al. [27]. Therefore, the likely interacting excited statesare 2R+, 2P and 4P terms. If DK = 0, the microscopic spin–orbitoperator of interest is aliz.siz.; if the interaction follows DK = +1,the important operators are ½ al+s� and ½ al�s+. In the rather crudeapproximation that the dominant electron configuration for VS isdr1dd2 (it is clear that the r orbital is sd hybridized), then the ma-trix elements connecting the ground and relevant exited states are:

4P3=2� HSO

4R3=2

¼ affiffiffi

2p

4P1=2� HSO

4R1=2

¼ a

ffiffiffi2pffiffiffi3p

4P�1=2� HSO

4R�1=2

¼ affiffiffi

2p

2P3=2� HSO

4R3=2

¼ a

2P1=2� HSO

4R1=2

¼ 2affiffiffi

3p

2Rþ1=2

D HSO4R1=2

¼ 4affiffiffi

6p

2Rþ�1=2

D HSO4R�1=2

¼ 4affiffiffi

6p ð12Þ

Assuming that the qualitative ordering of states is similar tothat in VO, the 2P state in VS must lie much higher in energy thanboth 4P and 2R+ states [27]; therefore, its effect can be neglected.Furthermore, the fine structure energy splittings in the groundstate in VS are typically no larger than �5 cm�1. Similarly, the en-ergy differences between the X ladders of the B4P state are�200 cm�1 [19]. Consequently, one can neglect the fine structureenergy differences relative to those separating the respective elec-tronic states, and assume E(4R3/2)–E(4P3/2)�E(4R1/2)–E(4P1/2). Tak-ing into account K-doubling in P states, Eqs. (10) and (11) thenreduce to the following expressions:

8k � �2j 4P1=2�

jHSOj4R1=2j2

Eð4R1=2Þ � Eð4P1=2Þ�

2j 2Rþ1=2

DjHSOj4R1=2

j2

Eð4R1=2Þ � Eð2R1=2Þð13Þ

c � 4ffiffiffi3p B

4R1=2�

jL�j4P3=2

4P3=2� HSO

4R3=2

Eð4R1=2Þ � Eð4P1=2Þ

ð14Þ

Evaluating the matrix element involving the L� operator as-sumes the pure precession approximation, namely, that the inter-acting 4R and 4P states are well described by single configurations

Fig. 3. Experimentally determined ground state r0 bond lengths for 3d transitionmetal sulfides and oxides. The molecular electron configurations are given beneatheach 3d metal across the series. The sulfur and oxygen series both show clearminima at vanadium, which corresponds to the addition of an electron into the non-bonding d orbital.

G.R. Adande, L.M. Ziurys / Journal of Molecular Spectroscopy 290 (2013) 42–47 47

differing only by a single spin–orbital, in this case drd2 and dpd2,respectively. This assumption is partly true, as theory predicts thatthe 4P state arises from promotion of the r electron to the dp orbi-tal [4]. Assuming that the molecular spin–orbit parameter in VS isapproximately the same as the atomic spin–orbit constant ofvanadium, a(V3d) = 177 cm�1 [26], the above equations yieldDE(4P � 4R�) � 6560 cm�1 and DE(2R+ � 4R�) � 7170 cm�1. The4P � 4R� energy difference is in relatively good agreement withthe calculated value of Bauschlicher and Langhoff [4], who foundDE(4P � 4R�) � 5872 cm�1 using CPF methods. There are noknown calculations of the 2R+ � 4R� energy in VS for comparison.

The inclusion of the third order terms, cs and bs, was necessaryto fit the data with sufficient accuracy. Without these parameters,the fit degraded with an rms of 90 kHz. These terms arise from thespin–orbit distortion of the spin–rotation and Fermi contact inter-actions with nearby excited electronic states. Theoretical consider-ations initially prompted Hougen [28] to conclude that R states ofeven multiplicities required S + 1/2 spin rotation parameters toaccurately reproduce the energy level structure, while S suchparameters were necessary for odd multiplicities. Using perturba-tion theory, Brown and Milton [29] subsequently identified anadditional third order spin–rotation parameter arising from Hsr -� Hso. Similarly, Cheung and Merer [16] introduced the third orderterm bs to interpret the energy level structure of the electronicstates of VO. This high resolution study is additional evidence thatmodeling of R states of quartet multiplicity requires such higherorder terms.

From the VS rotational constant measured here, the r0 bondlength was determined to be 2.05288 Å. The theoretical re valueis 2.07 Å, obtained by DFT methods [5]. The study by Ran et al.yielded r0 = 2.0526 Å. The bond length of VS represents a local min-imum in the 3d transition metal monosulfides series, as both TiSand CrS have longer bond lengths of 2.0851 Å and 2.0781 Å, respec-tively. A similar minimum is seen in the 3d oxide series at VO.Other common bond length trends are apparent in the 3d oxideand sulfide series, as shown in Fig. 3.

As seen in the figure, a ‘‘double hump’’ structure is evident nearchromium and then near copper, as predicted by theory [5]. How-ever, the ‘‘double hump’’ is more striking in the sulfides than theoxides. Through the series, it is postulated that there is competitionbetween the increased nuclear charge, which causes the contrac-tion of the d orbitals and shortens the bond lengths, and theanti-bonding character of the molecular orbitals, which increases

bond distances [6]. For both the sulfides and oxides, the dp orbitalsare strongly anti-bonding; adding electrons to these orbitals in-creases the bond length despite the increased nuclear charge, asobserved at chromium and copper, where p1 and p3 configurationsare created. The r orbital seems to be slightly anti-bonding for theoxides series, as well, because the bond lengths also increase fromFeO (r1) to CoO (r2). On the other hand, they decrease from FeS toCoS. This difference may be due to the greater overlap between themetal 3dr and the sulfur 3pr orbitals, as compared to that be-tween the metal and the 2pr orbital of the oxygen.

6. Conclusion

The pure rotational spectrum of VS has been measured in themicrowave and millimeter wave regions across eight rotationaltransitions. The vanadium hyperfine structure was found to exhibitvarying patterns in the four fine structure components, illustratingthe contribution of off-diagonal terms in the hyperfine Hamilto-nian. In the spectroscopic analysis, the need for higher order fineand hyperfine parameters in this 4R� state is made evident. Inter-pretation of the hyperfine parameters confirms the hybrid charac-ter of the bonding in transition metal sulfides, as partly ionic,partly covalent. However, comparison with VO clearly indicatesthat VS is less ionic than its oxide counterpart.

Acknowledgment

This work was supported by NSF Grant CHE-1057924.

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