Far-Infrared Spectrum of S(CN) - American Chemical Society

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Far-Infrared Spectrum of S(CN)2 Measured with Synchrotron Radiation: Global Analysis of the Available High-Resolution Spectroscopic Data Zbigniew Kisiel,*,† Manfred Winnewisser,‡ Brenda P. Winnewisser,‡ Frank C. De Lucia,‡ Dennis W. Tokaryk,§ and Brant E. Billinghurst∥ †

Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland Department of Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, Ohio 43210-1106, United States § Department of Physics and Centre for Laser, Atomic, and Molecular Sciences, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick E3B 5A3, Canada ∥ Canadian Light Source Inc., University of Saskatchewan, 44 Innovation Boulevard, Saskatoon, Saskatchewan, S7N 2 V3, Canada ‡

S Supporting Information *

ABSTRACT: The high resolution Fourier transform spectrum of the chemically challenging sulfur dicyanide, S(CN)2, molecule was recorded at the far-infrared beamline of the synchrotron at the Canadian Light Source. The spectrum covered 50−350 cm−1, and transitions in three fundamentals, ν4, ν7, and ν8, as well as in the hot-band sequence (n + 1)ν4 − nν4, n = 1−4, have been assigned and measured. Global analysis of over 21 300 pure rotation and rotation vibration transitions allowed determination of precise energies for 12 of the lowest vibrationally excited states of S(CN)2, including the five lowest fundamentals. These results constitute an extensive set of benchmarks for ab initio anharmonic force field calculations and the observed and calculated vibration−rotation constants and anharmonic frequencies are compared. The semiexperimental equilibrium, rSE e , geometry of S(CN)2 has also been evaluated. In the course of the measurements, new information concerning the physical chemistry of S(CN)2 has been obtained. S(CN)2 has already been shown to be a firmly bent species, with a nearly harmonic, deep potential for its central bending mode.3 It thus provides one extremum on the scale of bending dynamics of five-atomic chain molecules, compared to the linear limit. Because there was little information about its spectrum in the literature, it was decided to do justice to the rich spectrum that we were experimentally obliged to measure. The two molecules S(CN)2 and NCNCS belong chemically to the group of thiocyanogens also called sulfur cyanides. They polymerize easily at room temperature in solution and rather quickly under dry conditions. The polymerization products

1. INTRODUCTION The study of the rovibrational spectrum of S(CN)2 is actually a stepping-stone in the pursuit of quantum monodromy in the rovibrational energy manifolds of quasi-linear chain-form molecules, which so far include three-, four-, and five-atomic species. The best known of these is H2O,1 whereas the most revealing species has been shown to be NCNCS.2−4 Although the pure rotational (end-over-end) spectrum of NCNCS has allowed us to determine the shape of the central, quasi-linear bending potential function, the vibrational transitions of this mode are weak and lie deep in the far-infrared (FIR) region, at about 80 cm−1. The best synthetic path to NCNCS is a pyrolysis of S(CN)2. The original motivation of the present work, therefore, was to be able to identify the absorption features of S(CN)2 in attempting to detect NCNCS, first in the millimeter-wave region, and then in the FIR. We note that © XXXX American Chemical Society

Special Issue: Terry A. Miller Festschrift Received: August 18, 2013 Revised: October 7, 2013

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dx.doi.org/10.1021/jp408255m | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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2. EXPERIMENTAL DETAILS Chemical Preparation of SCl 2 and S(CN) 2 and Handling of the Samples. Due to chemical safety requirements all chemical preparations had to be carried out in a wet laboratory at the CLS, the facilities of which are considerably more constrained than those of a typical university research laboratory for synthetic chemistry. A significant amount of glassware and other laboratory equipment had to be shipped to the CLS. Sulfur dichloride, SCl2, is necessary in the first step in the most efficient synthesis of S(CN)2, as used in the study of the rotational spectrum.7 Available commercially until April 2011, it must now be synthesized on-site due to safety restrictions. It can be synthesized directly from commercial dichloro-disulfane, S2Cl2, by simply adding gaseous chlorine, Cl2, to 250 mL of the golden yellow liquid in a reaction flask at room temperature.11 The reaction will be catalyzed by ca. 0.1 g of anhydrous FeCl2 or FeCl3. The duration of the gaseous chlorine admission will last approximately 1/2 to 1 h, until the liquid becomes dark red. Now the reaction flask, warmed by the reaction, is cooled to 20 °C and the dark red reaction liquid, which contains besides SCl2 still some S2Cl2 and Cl2, should remain unperturbed for 1 h. After the hour has passed, 2 mL of PCl3 (liquid) is added to stabilize the product SCl2. Now we replace the Cl2 inlet tube with a thermometer for the distillation process. Due to the difference in boiling points (SCl2, +59.6 °C; S2Cl2, +138 °C) the two liquids can easily be separated by distillation. An additional distillation yields a very pure SCl2 sample. Furthermore, it should be mentioned that SCl2 can be stored for up to roughly one year, with a few drops of PCl3 as a stabilizing agent, at about 5 °C. According to Kumar and Shreeve12 the co-condensation of SCl2 and (CH3)3SiCN, trimethylsilyl cyanide, at liquid N2 temperature to produce S(CN)2 produces a pure sample. This makes sense because the reaction to form S(CN)2 is strongly exothermic and we also explored this path. However, in warming the reaction mixture from −186 to −78 °C, the temperature gap is so large that the reaction starts violently. The heat of formation for S(CN)2 cannot be removed fast enough when a large quantity of sample is needed, as in the present case, and thus S(CN)2 polymerizes rapidly. Therefore, after exploring this path, we returned to the method of Long and Steele,9 as in ref 7. According to this protocol, S(CN)2 is synthesized by using 26.5 g of silver cyanide, AgCN, dispersed by vigorous stirring in 200 mL of CS2, in a three-neck flask kept at a temperature of 30 °C. Over a period of 30 min, 10 mL of SCl2 is added using a disposable syringe. After a reaction time of an additional 10 min, reflux of CS2 was observed in the reflux condenser. At this stage the solvent with the reaction product is simply transferred into a Schlenk tube. The lower part of this tube is cooled to dry ice temperature and the product S(CN)2 crystallizes in beautiful, colorless, platelike crystals. The bulk of the cold CS2 solvent is then decanted off. The remaining CS2 is removed by attaching the Schlenk tube to a vacuum line until the vapor pressure of the content [mainly S(CN)2 and unreacted SCl2] reaches less than 2 Torr at 0 °C. The sample is stored by keeping the closed Schlenk tube at dry ice temperature. Far-Infrared Measurements at the Canadian Light Source. The far-infrared beamline at the CLS is equipped with a Bruker IFS 125HR with a maximum optical path difference of

with the general formula [Sy(CN)2]x show colors that range from yellow to red. Cataldo and Keheyan5 pointed out that all polymerization derivatives have very similar FT-IR spectra. Furthermore, they state that sulfur dicyanide is the most stable molecule of the series of thiocyanogens.6 In light of our present investigation, this claim has to be modified. S(CN)2 and NCNCS are linked by thermal isomerization: we have found that S(CN)2 isomerizes with moderate yield to the more stable NCNCS upon heating or spontaneously even at room temperature. Thus, NCNCS, has to be considered the more stable species. High-resolution spectroscopic research on both molecules was started in 2005 and complementing that work with high-resolution FIR spectra of the weak lowest fundamentals required measurements at enhanced sensitivity, such as that provided with synchrotron radiation sources. We have been successful in recording the FIR spectrum of both molecules at the Canadian Light Source (CLS) by using sample illumination provided by the FIR beamline and detection by the installed IFS125HR Bruker Fourier transform spectrometer. The work leading to the successful recording of the spectra also led to new, unambiguous understanding of the chemistry of the isomerization system S(CN)2/NCNCS as well as to the desired spectra. The spectrum of S(CN)2 reported here provides the opportunity for complete understanding of the complex vibration−rotation picture of this molecule. S(CN)2 has five low wavenumber normal modes leading to 11 states with vibrational term values of less than 500 cm−1 above the ground state. Kisiel et al.7 have already presented extensive rotational analyses for the ground state and 12 different vibrationally excited states based on the almost complete 110−375 GHz FASSST rotational spectrum. Those results included precise vibrational energy differences between several states from analysis of extensive perturbations encountered in the spectra. The absolute vibrational energies of the studied states could not, however, be determined without gas-phase, rotationally resolved vibrational spectra. The joint analysis of the present high-resolution FIR data for S(CN)2 and the extensive rotational assignments made in ref 7 is the subject of this paper. It is only the joint analysis of such data that can provide fundamental wavenumbers that are uncontaminated by perturbation contributions delivering, in the process, an extensive benchmarking data set for high level ab initio calculations. The authors of ref 7 observed the fact that S(CN)2 is rather unstable, which makes the observation of its infrared spectrum challenging. Four low-resolution IR studies6,8−10 confirm this fact: their individual results are in some disagreement, partly because they report only solid state KBr pellet and solvent spectra. Our experience concerning the isomerization of S(CN)2 to NCNCS leads to the suspicion that NCNCS and the various polymerization products contained in the S(CN)2 samples used for the low-resolution IR measurements contributed to the inconsistencies. No gas-phase spectroscopy studies of S(CN)2 were found in the literature. We had observed no significant problems concerning sample purity during the measurement of the rotational spectrum. Sample reservoir temperatures were kept low, as only about 10 mTorr of pressure was needed in the cell, and a flow system was used. For the FIR measurements, however, at least an order of magnitude increase in sample pressure and measuring time in the available static cell were needed, so that chemistry in the cell became very important. B



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number of simultaneously treated vibrational states necessitated a switch to the rarely used SPFIT mode of operation involving the use of two digit vibrational state identifiers. For the weighted fits we employed the simple scheme in which uncertainties of 0.1 MHz were assigned to the microwave data and 0.0001 cm−1 for the infrared data.

9.4 m, which allows it to achieve a resolution (fwhh) better than 0.000 96 cm−1 or 28.78 MHz. The spectrometer is equipped with a full range of beamsplitters, detectors, and internal sources that enable it to operate from 12 to 2000 cm−1. Typically, the synchrotron radiation is only used as a radiation source between 12 and 1000 cm−1 as this is where the synchrotron has the greatest radiation power advantage over conventional or thermal sources. The primary sample cell used in this work is a 2 m White type multipass cell with a maximum path length of 72 m using 36 transits. This cell can be cooled to −80 °C using a recirculating chiller. In our first shift (May− June 2011), we were able to meet our goal of recording the high-resolution far-infrared spectrum of S(CN)2 reproducibly in the spectral range from 40 to 350 cm−1, using 100 mTorr of vapor from the synthesis products with the White cell set for 72 m absorption path length. A total of 270 interferograms were accumulated and averaged over 12 h and then transformed to obtain the spectrum analyzed in this work. Significant contamination of S(CN)2 was noted, principally from H2O and isocyanic acid, HNCO, due to residual H2O on the inner surfaces of the transfer tubing and the absorption cell. The degree of contamination varied according to small day-today changes in sample preparation and handling. The high resolution, however, allowed us to determine the carrier molecules of the contaminations, all of which are small molecules, and to obtain dense but almost fully resolved and very assignable spectra for S(CN)2, as shown in this work. Analysis. The precisely known transitions of some of the contaminant molecules were utilized for wavenumber calibration of the recorded far-infrared spectrum. This was first carried out using ground state lines of HNCO13 and, in a second step, by means of far-infrared lines of H2O recently measured with microwave techniques.14 The spectra were then analyzed with the AABS package for Assignment and Analysis of Broadband Spectra.15,16 The package was originally developed for use with broadband pure rotation spectra but is equally applicable to high-resolution infrared spectra, as has recently been shown for deuterated cyanamide.17 A key feature of the package is the use of the Loomis−Wood display method for graphical assignment of high-resolution spectra, as pioneered in the early computer era by the Loomis−Wood program developed in Giessen.18 These techniques are more useful than ever due to challenges posed by the enormous expanses of contemporary highresolution spectra. Any single viewing window upon these spectra may be relatively featureless and uninformative, whereas a suitable correlation of such windows reveals the underlying spectral patterns. The AABS package contains multiple additional tools for navigating and reducing broadband spectra to data sets and is freely available on the PROSPE Web site.19,20 The Hamiltonian for the problem was constructed in block diagonal form, as described in the analysis of the broadband rotational spectrum of S(CN)2.7 Watson’s A-reduced asymmetric rotor Hamiltonian21 was used for the blocks that are diagonal in the vibrational identifier, whereas suitable offdiagonal Coriolis and Fermi resonance blocks were used when it was necessary to connect perturbing vibrational states. The form of such connecting blocks was dependent on the symmetry classification of the pertinent vibrational states in the C2v symmetry point group for S(CN)2, and their selection procedure was described in detail in ref 7. The Hamiltonian was coded and fitted to the spectroscopic measurements with the SPFIT/SPCAT package,22,23 which is integrated with the graphical front-end provided by the AABS package. The large

3. FAR-INFRARED SPECTRUM An overview of the key regions of the far-infrared spectrum of S(CN)2 recorded with synchrotron radiation is given in Figure 1. The spectrum contains three fundamentals, the b-type ν4, a-

Figure 1. Overview of the appearance of the three lowest normal mode bands in the far-infrared spectrum of S(CN)2: the b-type ν4, the a-type ν7, and the c-type ν8. For technical reasons only the P-region part of the ν8 band was recorded.

type ν7, and c-type ν8. The lowest wavenumber ν4 mode gives rise to the strongest band of the three. Prediction of vibration− rotation transitions for this band from the constants from the pure rotation analysis quickly revealed that it contains multiple hot band transitions, as documented in Figure 2. This was very fortunate because such hot bands provide a route to completing the previous analysis7 and precisely placing the measured excited vibrational states on the energy scale. This goal was the primary reason for combining all measurements into a single global fit. The ν4 fundamental and its hot bands were first assigned with the aid of the Loomis−Wood technique, for Pand R-branch sequences for successively higher values of Ka, up to Ka = 27. The exception was v4 = 5 ← 4, which was limited to the lowest Ka transitions, partly due not only to their low intensity but also to the fact that the v4 = 5 state is known to be involved in a perturbation that has not yet been explicitly accounted for. Figure 3 documents the level at which the details in the very complex ν4 band were eventually reproduced. The next stage involved analysis of the bands for the two higher C



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Figure 3. Comparison of a small segment of the high-resolution spectrum of the S(CN)2 ν4 band with its reproduction from the fitted constants. The most intense gray sticks identify transitions in the fundamental band, whereas red highlights transitions in the first hot band, v4 = 2 ← 1. The diamond symbols mark lines actually used in the fit and their selection was made on the basis of clarity of the pertinent transition sequence in the Loomis−Wood display mode.

Figure 4. Illustration of the characteristic features of the P-branch region of the weaker, c-type ν8 band. The perturbation of the ν8 mode with the infrared-inactive ν9 mode has been extensively revealed by the pure rotation data, so that measurement of a relatively small number of infrared transitions allowed precise wavenumber determination for both ν8 and ν9.

Figure 2. Illustration of the good visibility of transitions in the ν4 fundamental of S(CN)2 and in its related (n + 1)ν4 ← nν4 hot band series. The Loomis−Wood display of the figure shows spectral strips centered on the wavenumbers in the fundamental band of successive degenerate rR0,pR1 transition pairs, where the notation is ΔKaΔJKa(J″). Hot band transitions give rise to nearly parallel satellite series regularly spaced to low wavenumber. The prominent top to bottom-left sequence is for the rR1,pR2 transitions in the fundamental.

fundamentals, and the results are illustrated graphically in Figures 4 and 5. In each case the analysis was commenced from a prediction based on pure rotational data and a crude estimate of the band center, which was quickly refined on the basis of unambiguous, Loomis−Wood based assignment of some lowKa transition sequences. The ν7 band turned out to be particularly useful because it provided the route not only to the vibrational wavenumber of the v7 = 1 level but also to that of (v4 = 1, v7 = 1) via the ν7 + ν4 − ν4 hot band. The relevant hot band sequence is clearly evident in the Q-branch region depicted in Figure 5.

Figure 5. Central region of the a-type ν7 band. The visible Q-branches are complicated blends of many individual transitions so that such lines are not useful for determining spectroscopic constants, but their accurate reproduction confirms the results of the fits. The Q-branch series for the ν7 fundamental (black sticks in the top part of the calculated spectrum panel) is interspersed with an analogous series for the ν7 + ν4 − ν4 hot band (red sticks).

4. RESULTS The global fit of the current FIR measurements and the rotational data turned out to consist of 21 306 distinct frequency lines or over 28 000 transitions when the explicitly declared degenerate or near-degenerate blends are considered. A state-by-state breakdown of this fit is provided in Table 1. D



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presently for the three lowest states of S(CN)2 but, as expected, the deviation of fit degrades steadily on proceeding to higher states with successively weaker transitions. The achieved FIR deviations of significantly below 0.0001 cm−1 for the three data subsets with the strongest lines compare favorably with those achieved with the same source and spectrometer. The recent fits for 3-oxetanone,26,27 for example, were at the level of just below 0.0001 cm−1 or higher. The fits for thiophosgene,28 had a deviation of 0.000 085 cm−1 for the parent 35Cl2S, but a higher value, 0.000 110 cm−1 for 35Cl37ClS. The very useful state-bystate breakdown presented here is now an automatic feature built into the PIFORM program available from the PROSPE Web site. The key results concerning the vibrational picture are summarized in Table 2 and Figure 6. The complete results of the fit and the data files necessary for reproducing the fit and the associated predictions are included of the Supporting Information. The availability of all of the studied vibrational states in one global prediction allowed a significant number of small corrections to be made concerning assignments of blended transitions in the rotational spectrum. There were finally only 223 pure rotational transitions that were confidently assigned in the rotational spectrum but rejected from the fit at the 4σ criterion filtering (σ being the measurement uncertainty). A large proportion of these unfitted transitions are in several systematically deviating high-J tails of high-Ka Qbranch sequences for ν7 and ν4 + ν7. Those could now be connected by additional coupling terms with the polyad directly above each of these states (Figure 6). The deviations from the fit are, however, monotonic and devoid of signatures of levelcrossing type behavior so that the improvement in our understanding would be small for the amount of additional effort. The global fit involves a total of 318 fitted parameters. This might at first appear to be an unmanageable number, yet it is put into perspective by the fact that we are accounting for highly resolved vibration and rotation behavior in 13 vibrational states. The average number of parameters per state is 24 and is, therefore, quite reasonable. This number is accidentally identical to the number of constants in the full, octic level, centrifugal distortion Hamiltonian required for just the ground state. That order of the Hamiltonian was necessitated not because of particularly pathological large-amplitude behavior, but due to the very extensive coverage of energy and quantum number values. Furthermore, because the perturbation effects have already been taken care of in the more highly resolved

Table 1. Details of the High-Resolution Microwave and Infrared Data Sets Acquired for S(CN)2 and Incorporated into a Single Global Fit Nlinesa g.s. v4 = v4 = v8 = v9 = v4 = v4 = v4 = v4 = v3 = v4 = v7 = v4 =

σb

σwc

Microwave Data 3439 0.0481 0.502 1792 0.0444 0.444 1784 0.0537 0.537 1473 0.0747 0.747 1386 0.0582 0.582 1620 0.0590 0.590 966 0.0814 0.814 1154 0.0871 0.871 1063 0.0690 0.690 1101 0.0785 0.785 71 0.1148 1.148 1734 0.0685 0.685 1652 0.0789 0.789

1 2 1 1 3 1, v8 = 1 1, v9 = 1 4 1 5 1 1, v7 = 1

total

19235

v4 = 1 ← 0 v4 = 2 ← 1 v4 = 3 ← 2 v4 = 4 ← 3 v4 = 5 ← 4 v7 = 1 ← 0 v4, v7 = 1,1 ← 1,0 v8 = 1 ← 0 total

0.0651 Infrared Data 500 0.0731 461 0.0679 366 0.0725 246 0.0848 20 0.0801 262 0.1017 66 0.1279 150 0.1124

2071

complete fit

0.0831

21306

J range

Ka range

1−100 5−94 6−86 5−84 6−83 6−90 5−83 6−84 6−83 6−84 23−62 5−88 5−89

0−27 0−23 0−23 0−25 0−24 0−24 0−24 0−24 0−24 0−24 0−3 0−25 0−25

15−84 16−87 16−86 17−80 29−61 20−79 12−63 14−60

0−27 0−27 0−27 0−27 0−1 0−27 0−2 13−26

0.654 0.731 0.679 0.725 0.848 0.801 1.017 1.289 1.124 0.831 0.674

a

The number of distinct frequency or wavenumber lines used in the fit. bDeviation of fit in units of MHz for the microwave data and 0.001 cm−1 for the infrared data. cUnitless deviation of the weighted fit assuming 0.1 MHz uncertainties for the microwave measurements and 0.0001 cm−1 for the infrared.

The overall unitless deviation is somewhat less than unity, suggesting that the assumed uncertainties were slightly pessimistic. This is particularly true of the FASSST data, for which it is known from several prior investigations, including those of ClONO224 and HCOOH,25 that its instrumental frequency accuracy is closer to 50 kHz. This is also the case

Table 2. Comparison of the Experimental and the Computed Results for the Normal Modes of S(CN)2 normal mode

νlita (cm−1)

ωcalcb (cm−1)

νcalcc (cm−1)

νobs (cm−1)

νo − νcb (cm−1)

Icalcc (km/mol)

symmetry species

mode description

ν4 ν7 ν8 ν9 ν3

135 329 372 (376)d 378

120 317 357 365 487

121.2 310.9 351.6 358.7 491.3

120.753288(5) 308.782880(6) 351.399591(7) 362.527264(8) 490.243684(11)

−0.4 −2.1 −0.2 3.8 −1.0

7.90 1.71 3.60 0 1.09

A1 B1 B2 A2 A1

∠CSC bend ip ∠SCN bend (asymm) op ∠SCN bend (symm) op ∠SCN bend (asymm) ip ∠SCN bend (symm)

ν2 ν6 ν5 ν1

672 690 2180 2190

672 674 2247 2262

656.2 654.7 2200.1 2210.4

0.01 2.07 0.10 0.22

A1 B1 B1 A1

CS stretch (symm) CS stretch (asymm) CN stretch (asymm) CN stretch (symm)

a ref 8. bScaled calculation at the B3LYP/6-31G(d,p) level, ref 7. cCalculated with CFOUR29 from the CCSD(T)/aug-cc-pVTZ anharmonic force field. dEstimated in ref 8 from the fitted valence force field.

E



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consistent with an even relatively rudimentary ab initio calculation than with fragmentary experimental literature data. In light of the present results the previous harmonic estimate of fundamental waenumbers turns out to be quite satisfactory, although we have now superseded it by fundamental wavenumbers from an anharmonic force field calculation made with the CFOUR package.29 The recommendation for such calculations is to use as high as possible a level of electron correlation correction (CCSD(T), or CCSD in preference to MP2) and a fairly extended correlation consistent basis set from the Dunning series.30 The CCSD(T)/aug-cc-pVTZ level of computation proved to be the highest level that was practicable on a P7-processor based contemporary desktop computer. This level was also found to give the best agreement with experiment, seen in Table 2 to be at the average deviation of 1.5 cm−1 from the experimental values. We point out that we have retained in Table 2 the B1, B2 symmetry labels and mode numbering used previously7,8 but that these labels should, in principle, be reversed, and the mode numbering modified accordingly. This would allow conformance with the IUPAC recommendation on the assignment of these irreproducible representations in the C2v symmetry point group.31 The x axis is thus to be chosen to be perpendicular to the plane of the molecule, such that in the present case the σv(xz) plane becomes the bc inertial plane. There has been some confusion in the literature concerning the assignment of the B1, B2 species because in many older but influential textbooks on vibrational spectroscopy the x axis was implicitly or explicitly chosen to be in the plane of the molecule. The inplane and out-of-plane modes that are antisymmetric with respect to the C2 operation are therefore currently to be assigned to the B2 and B1 species, respectively. The two alternative choices actually have no effect except for the labeling, because the principal inertial axis for a given Coriolis perturbation remains the same. The output of CFOUR follows the more recent convention.

Figure 6. Summary of the vibrational term values determined for the lowest excited vibrational states of S(CN)2 from the global fit of combined microwave and infrared data. The two boxes identify the triad and the tetrad of states, each of which is connected by multiple internal perturbation terms in a picture unravelled in the analysis of the rotational spectrum. The arrows identify the observed vibrational transitions that facilitate the term value determination. Red bars identify the five lowest fundamentals.

microwave data, addition of the current infrared data to the fit only required expansion of the parameters of fit by the very desirable vibrational energies. Suitable construction of the vibrational parameters of the fit allowed derivation of precise vibrational wavenumbers for all excited states for which transitions had been previously assigned in the rotational spectrum. Figure 6 summarizes both the values of the vibrational terms and the connections used for their derivation. The vibrational terms in the nν4 sequence result from measurement of the (n + 1)ν4 ← nν4 hot bands, those for ν7 and ν8 are derived from their fundamental bands, whereas ν4ν7 results from the ν7 + ν4 − ν4 hot band. On the other hand, the vibrational terms for the remaining four states, in particular for the infrared-inactive ν9 (A2 symmetry), are the consequence of the presence in the global fit of the rotational analysis of strong perturbations within the two polyads marked in Figure 6. That analysis allowed relative wavenumber differences within each polyad to be determined at sub-megahertz precision, as summarized in Figure 17 of ref 7. The present vibrational spectra deliver the complete vibrational term for at least one state in each polyad. The values for the remaining polyad states then result as a matter of course with precision corresponding to that for the state involved in the measured vibrational transition. Inspection of Table 2 shows that uncertainties concerning the wavenumbers of the lowest normal modes of S(CN)2 have finally been resolved. The study in ref 7 showed that relative intensities in the broadband rotational spectrum were more

5. VIBRATIONAL ANHARMONICITY The plethora of precise wavenumbers now available for the vibrational states of S(CN)2 allow several additional checks. One concerns the evaluation of the anharmonicity constants in the relationship32 Eυ =

⎛

∑ ⎝υi + ⎜

i

1 ⎞⎟ ωi + 2⎠

⎛

∑ ⎝υi + ⎜

i,j≥i

⎞⎛ 1 ⎟⎜ 1⎞ υj + ⎟xij ⎠ ⎝ 2 2⎠

(1)

describing the departures of vibrational energies from the harmonic picture on multiple vibrational excitation. For a long sequence of excited states of a given mode, this relationship leads to the series of useful formulas shown in Figure 7, which enable several different evaluations of the x4,4 anharmonicity constant for the ν4 mode. These values are highly consistent, averaging to x4,4 = 0.1399(3) cm−1, in support of the validity of the vibrational term value determinations. The small magnitude of this constant and its barely discernible monotonic trend are indicative of the harmonic behavior of the ν4 mode, contrasting with its low wavenumber. For the case of a one-to-one mixed excitation of two modes, eq 1 simply leads to xa,b = νaνb − νa − νb where νaνb, νa, and νb are used as shorthand for anharmonic wavenumbers (vibrational term values) relative to the ground state. We thus derive x4,7 = 0.1785, x4,8 = 0.0286, and x4,9 = 0.1542 cm−1 from the experimental wavenumber values in Figure 6. It is intriguing to find that although the improvement F



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Table 3. Comparison of the Experimental and Calculated Vibration−Rotation Constants (MHz) for the Five Lowest Normal Modes of S(CN)2 obs

Figure 7. Evidence for the consistency in the evaluation of the anharmonicity constant x44 from the present results by using a convenient reformulation based on differences in vibrational term values of adjacent excited states of the ν4 mode.

Gc 2 3ω82 + ω9 2 2ω8 ω82 − ω9 2

(2)

δ(C9−C0) =

Gc 2 3ω9 2 + ω82 2ω9 ω9 2 − ω82

(3)

|(o − c)/o | (%)

ν4

A4 − A0 B4 − B0 C4 − C0

92.92485 10.33781 1.80901

ν7

A7 − A0 B7 − B0 C7 − C0

−143.08349 −3.87961 3.39196

ν8

A8 − A0 B8 − B0 C8 − C0

20.46244 4.0687 3.16379

13.85 6.39 3.48b

32.3 57.1 10.0

ν9

A9 − A0 B9 − B0 C9 − C0

138.88903 6.7883 3.57399

156.24 7.22 3.64b

12.5 6.3 1.8

ν3

A3 − A0 B3 − B0 C3 − C0

135.78454 −10.2635 −4.50752

120.80 −10.01 −4.47

11.0 2.5 0.8

84.93 10.29 1.741 −167.17 −3.67 3.60

8.6 4.8 0.4 16.8 5.4 6.2

a

Calculated with CFOUR29 from the CCSD(T)/aug-cc-pVTZ anharmonic force field. bCorrected for the perturbation contribution (see text) to compare with the deperturbed experimental values. The calculated effective values were 1.57 MHz for ν8 and 5.54 MHz for ν9.

in the level of anharmonic calculation was advantageous for the fundamental wavenumbers, this was not so for the anharmonicity constants. The relatively modest MP2/aug-ccpVDZ calculation delivered x4,4 = 0.131, x4,7 = 0.174, x4,8 = −0.002, and x4,9 = 0.117 cm−1, which are in considerably better agreement with experiment than for the CCSD(T)/aug-ccpVTZ level (x4,4 = 0.039, x4,7 = −0.406, x4,8 = 0.110, and x4,9 = 0.357 cm−1). A similar result was previously found for the x11,11 anharmonicity constant in acrylonitrile.16 Finally, the experimental vibration−rotational constants for the five normal modes can also be compared with results from the anharmonic calculation. In this case, the finding is the same as that for the vibrational wavenumbers, in that the higher the level of calculation, the better. The comparison made in Table 3 shows that, with the exception of the ν8 mode, the agreement of computation with experiment is at the level of better or considerably better than 17%. It should be remembered that in the case of explicitly fitted interstate perturbations the experimental values are deperturbed whereas those resulting from the computation are effective values, inclusive of all perturbations. The most significant such difference is for the C rotational constants of ν8 and ν9 modes, which are Coriolis coupled around the c-principal axis. To facilitate the comparison, we used a correction similar to that employed for the much larger effect of this type found for phenylacetylene.33 Adaptation of the relationships used therein to the present case leads to the perturbation increments δ(C8−C0) =

calca

of the Coriolis interaction constant Gc = 797 MHz for this purpose. As discussed in ref 7, the origin of Gc turns out to be purely anharmonic, as the symmetry-allowed ζ(c) 8,9 Coriolis coefficient is exactly zero, due to the form of the normal mode vectors for the two modes.

6. MOLECULAR STRUCTURE Availability of the anharmonic force field calculations for S(CN)2 allows the evaluation of its molecular geometry to be updated to the currently preferred semiexperimental equili30,34 brium, rSE This geometry is evaluated from the e , geometry. ground state constants for the measured isotopic species and the calculated (Be − B0) corrections to equilibrium, and we have recently also found it to be the optimum structure for acrylonitrile35 and cyanamide.36 For S(CN)2 we used the same CCSD(T)/aug-cc-pVTZ anharmonic calculation as for the normal mode wavenumbers, the isotopic rotational constants from ref 7 and the STRFIT program for least-squares structure determination.37 The preferred rSE e geometry is drawn in Figure 8, and it is also compared in Table 4 with other geometry types

Figure 8. Orientation of the S(CN)2 molecule in the principal inertial axes and values of the semiexperimental equilibrium, rSE e , geometry determined in this work.

that need to be subtracted from the computed values, as has been done in Table 3. We needed to use the experimental value G



Article

Table 4. Summary of the structural parameters (Å and degree) determined for S(CN)2 r(SC) ∠(CSC) r(CN) ∠(SCN) a b

rs

r0

r(1) m , ref 7

a (rSE e )

calcb

1.701(5) 98.2(3) 1.158(6) 175.0(6)

1.698(6) 98.6(5) 1.160(9) 175.4(11)

1.6985(13) 98.48(8) 1.1587(10) 175.19(12)

1.6972(4) 98.36(3) 1.1602(4) 175.14(5)

1.7059 97.77 1.1617 175.37

Semiexperimental equilibrium geometry determined by using the (Be − B0) corrections computed at the CCSD(T)/aug-cc-pVTZ level Equilibrium structure calculated at the CCSD(T)/aug-cc-pVTZ level.

It may also be asked, why have we observed only the bending normal modes ν4, ν7, ν8, ν9, and ν3 and not completed the picture with the four higher stretching modes? The incompleteness of the study at this time is partly due to low intensity of the stretching bands (Table 2) but is also implicated in an interesting chemical puzzle. In fact, we began our measurements in the ν1, ν5 stretching region. We admitted S(CN)2 into the 72 m absorption cell to record its spectrum, and at around 185 mTorr of pressure we saw and recorded two bands near 2017 and 2261 cm−1. Then we pyrolyzed the S(CN)2, froze the products in liquid nitrogen, and admitted them into the cell. Surprisingly, we saw only the same two bands, but much stronger: only 7 mTorr of gas was required. At this point, our first measuring campaign (May/ June 2011) at the CLS ended. We believed that the trapping and subliming had purified the sample. When the experiment resumed in May 2012, we again attempted to record the stretching modes of S(CN)2 to start with, and again we observed the same two bands reappear at roughly the pressure we used a year before, 185 mTorr. However, we made another surprising discovery: overnight (after 12 h running time), the intensity of these two bands had dramatically increased! We then realized that contrary to past belief, NCNCS is a more stable isomer than S(CN)2, and we were observing the spontaneous conversion of S(CN)2 as it relaxed to the more stable form. This was confirmed by a preliminary rotational analysis of the 2017 cm−1 band, which showed conclusively that it belonged to NCNCS. This experimentally established relative stability is confirmed by ab initio computations, because at the CCSD(T)/aug-cc-pVTZ level NCNCS is estimated to be more stable than S(CN)2 by 50 kJ mol−1. Further work showed that pyrolysis of S(CN)2 provided enough energy to push the molecule more rapidly over a barrier, allowing it to relax to its lower energy form, NCNCS. Now, to our further surprise, NCNCS has in the stretching region unexpectedly strong absorptions which mask each of the S(CN)2 absorptions. Therefore, we concluded that the stretching bands of S(CN)2 can only be measured in a flow system and not in a static cell, where the isomerization reaction inevitably occurs during the 12 h necessary for data collection with the interferometer.

evaluated in a systematic manner from the same data. We note that all of these types of geometry are very similar, which is not surprising because S(CN)2 consists entirely of heavy atoms. Nevertheless, the rs and r0 parameters are considerably less precise than the r(1) m ones, which are in turn of poorer quality than for rSE . There is an overall improvement in precision by an e order of magnitude from left to right in Table 4, obtained by application of successively more refined methods of structure determination. On the other hand, the rs geometry is essentially unchanged since its first evaluation in ref 8, except for the present use of the Costain criterion38 for a realistic uncertainty estimate associated with small inertial coordinates. It should be added that S(CN)2 is endowed with a considerable vibrationally induced inertial defect, Δ = Ic − Ia − Ib. For a planar molecule the equilibrium value of this quantity should be zero so that only two out of the three moments of inertia are independent parameters. For S(CN)2 the ground state inertial defect is Δ0 = 0.49041(1) u Å2 and is well calculable, also for the excited vibrational states.7 This significant nonzero value interferes with planar geometry evaluation so that we turned to the stratagem previously employed for the water molecule39 of evaluating and averaging three geometries, each determined by using only two out of the three available rotational constants. The cited uncertainty results, in this case, from a combination of the statistical uncertainty of the two-parameter reduced-constant fit with the spread of values over three such fits. The procedure was not necessary for the r(1) m geometry because the adjustable parameters of this method account for the inertial defect completely. It was, however, required for the rSE e evaluation because the anharmonic calculation reduces the inertial defect, incompletely, to 0.0189 u Å2.

7. CONCLUSIONS The combination of measurements made with two powerful methods of current broadband high-resolution molecular spectroscopy in the millimeter wave and far-infrared regions enabled us to provide with this work a unified treatment of pure rotation and vibration−rotation data of the S(CN)2 molecule. The results obtained for the ground vibrational state and the multitude of low-lying excited vibrational states displayed in Figure 6 finally clarify the low-wavenumber normal mode picture of this molecule. These results also constitute an extensive set of data for calibration of anharmonic force field calculations, and we have tested those against the level of calculation that is currently accessible for routine use by a spectroscopist. Anharmonic force field calculations are becoming a desirable complement to high-resolution spectroscopic measurements so that it is crucial to provide unambiguous experimental data to extend calibrations to a broader range of molecules and symmetry types, which will allow the computational specialists to further refine the method.

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ASSOCIATED CONTENT

S Supporting Information *

The results of the global SPFIT fit for S(CN)2 and the input files required for reproducing this fit are available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Z. Kisiel: e-mail, [email protected]; fax, 048-22-8430926. Notes

The authors declare no competing financial interest. H



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ACKNOWLEDGMENTS This work is dedicated to Terry Miller in recognition of his outstanding contributions to science, the OSU International Symposium on Molecular Spectroscopy, and the Journal of Molecular Spectroscopy on the occasion of his 70th birthday. The OSU team thanks the Army Research Office, NSF, and NASA for their support of this work. ZK thanks Adam Kraśnicki and Filip Pawłowski for tutelage in anharmonic force field calculations and acknowledges financial support from a grant from the Polish National Science Centre, decision number DEC/2011/02/A/ST2/00298. Damien Forthomme is thanked for the initial analysis of the ν4 sequence and the ν7 band, and DWK acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC). The experimental part of the research described in this paper was performed at the Canadian Light Source, which is funded by the Canada Foundation for Innovation, the Natural Sciences and Engineering Research Council of Canada, the National Research Council Canada, the Canadian Institutes of Health Research, the Government of Saskatchewan, Western Economic Diversification Canada, and the University of Saskatchewan.

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Far-Infrared Spectrum of S(CN) - American Chemical Society

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