Inversion Doublet in Deuterated Cyanamide - American Chemical

Article pubs.acs.org/JPCA

Rotation and Rotation−Vibration Spectroscopy of the 0+−0− Inversion Doublet in Deuterated Cyanamide Zbigniew Kisiel,*,† Adam Kraśnicki,† Wolfgang Jabs,‡,⊥ Eric Herbst,§ Brenda P. Winnewisser,∥ and Manfred Winnewisser∥ †

Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland Physikalisch-Chemisches Institut, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 58, D-35392 Giessen, Germany § Department of Chemistry, University of Virginia, McCormick Road, Charlottesville, Virginia 22904, United States ∥ Department of Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, Ohio 43210-1106, United States ‡

S Supporting Information *

ABSTRACT: The pure rotation spectrum of deuterated cyanamide was recorded at frequencies from 118 to 649 GHz, which was complemented by measurement of its highresolution rotation-vibration spectrum at 8−350 cm−1. For D2NCN the analysis revealed considerable perturbations between the lowest Ka rotational energy levels in the 0+ and 0− substates of the lowest inversion doublet. The final data set for D2NCN exceeded 3000 measured transitions and was successfully fitted with a Hamiltonian accounting for the 0+ ↔ 0− coupling. A smaller data set, consisting only of pure rotation and rotation-vibration lines observed with microwave techniques was obtained for HDNCN, and additional transitions of this type were also measured for H2NCN. The spectroscopic data for all three isotopic species were fitted with a unified, robust Hamiltonian allowing confident prediction of spectra well into the terahertz frequency region, which is of interest to contemporary radioastronomy. The isotopic dependence of the determined inversion splitting, ΔE = 16.4964789(8), 32.089173(3), and 49.567770(6) cm−1, for D2NCN, HDNCN, and H2NCN, respectively, is found to be in good agreement with estimates from a simple reduced quartic-quadratic double minimum potential. carbodiimide (HNCNH),3−6 which is known for its ability to assemble aminoacids into peptides.2 In a real astrophysical environment of the so-called hot cores the formation of cyanamide is now thought to occur mainly as the gas and dust warm up during the process of star formation.7 In the previous cold core stage, the temperature is 10 K and molecules are detected both in the gas and in ice mantles on dust particles. The gaseous molecules are both exotic by terrestrial standards and strongly unsaturated whereas the molecules in the ice consist mainly of normal hydrogen-rich species such as water, ammonia, and methanol. These icemantle molecules are formed by hydrogenation of precursor heavy atoms and small molecules via successive surface reactions with accreting hydrogen atoms; e.g., CO → HCO → H2CO → H2COH → CH3OH.8 Because in dense cold gas, the ratio of deuterium atoms to hydrogen atoms is near unity despite the fact that the elemental abundance ratio is 10−5, deuterated isotopomers can be produced in a manner and

1. INTRODUCTION Cyanamide (H2NCN, Figure 1) is a small, pentaatomic molecule that is related to some important interstellar

Figure 1. Orientation of the cyanamide molecule in the principal inertial axes and the definition of the NH2 inversion angle ϕ.

molecules, in particular to ammonia. Cyanamide lies on several interesting synthetic paths and may thus be of relevance to prebiotic chemistry. It has been shown that cyanamide can participate in the early stages of a number of biochemical reaction chains. There is, for example, a long-standing finding that in liquid water it can be converted into urea (NH2CONH2).1 Much more recently it was found2 that in low-temperature (10−140 K), water grain-type environments the cyanamide molecule be can be converted into its isomer, © 2013 American Chemical Society

Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: December 31, 2012 Revised: March 20, 2013 Published: March 20, 2013 9889

dx.doi.org/10.1021/jp3128687 | J. Phys. Chem. A 2013, 117, 9889−9898

The Journal of Physical Chemistry A

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cyanamide, mainly because the available laboratory data was insufficient for that purpose. There have been many laboratory studies of the pure rotation17−27 and rotation−vibration28−30 spectrum of cyanamide. Like ammonia, cyanamide has been a prototype molecule for studying large-amplitude inversion motion at the nitrogen atom. In the case of cyanamide the inversion is that of the NH2 group within the framework of a highly prolate asymmetric top and is characterized by a double minimum potential section along the inversion angle ϕ, defined in Figure 1. For the parent H2NCN isotopologue the relative energies of the four lowest inversion substates in this potential, 0+, 0−, 1+, and 1−, are available at better than 0.001 cm−1 precision from the analysis of the far-infrared spectrum.30 The 0−−0+ energy difference has been determined, with even higher precision, to be ΔE = 49.567772(5) cm−1 from a joint fit of all available rotationally resolved data for these two states.29 Most recently, such analyses have been performed for many rare-isotopic species in the H2NCN, HDNCN, and D2NCN series of isotopologues,27 carried out in the process of determining the precise molecular geometry of the cyanamide molecule. Presently, we report extensive spectroscopic results for the two principal deuterated species of cyanamide based on a comprehensive study with millimeter wave techniques and high-resolution far-infrared interferometry. The combined results cover the millimeter to terahertz spectroscopic region of interest to contemporary radioastronomy and allow confident prediction of all pertinent spectroscopic transitions of all three principal species.

abundance similar to those of the parent species as both D and H atoms accrete onto grains. Eventually, some instability allows the cold core to begin to collapse to form a star. As the previously cold material collapses inward toward a protostar, or star in the act of formation, it reaches temperatures of 100−300 K and constitutes what is known as a hot core. Hot cores emit rich rotational spectra of terrestrial organic molecules, including internal rotors, which are quite distinct from the exotic species found in the cold core gas.7 The material in the hot core subsequently collapses into either the protostar or a protoplanetary disk that forms in a plane around the protostar. In the first case, the molecules are entirely dissociated at high temperatures, whereas in the second case they can be preserved and add to the molecular inventory of the planets that form out of protoplanetary disks. Cyanamide9 and its newly detected isomer carbodiimide (HNCNH)10 have both been detected under hot-core conditions near the center of our galaxy. The most recent model for the formation of complex molecules such as cyanamide in hot cores suggests that they are formed on the ice mantles of interstellar dust particles as the collapsing material is heated from an initial temperature of 10 K to perhaps 50 K.11 The formation is thought to occur with the aid of photons that dissociate the original ices in the grain mantles. For example, photons can dissociate ammonia and its deuterated isotopomers into radicals such as NH2, NHD, and ND2. Likewise, the radical CN can be produced from HCN or other parent species with a CN group found in the cold ice. At temperatures over 20 K or so, the radicals can begin to diffuse on the cold surface, and recombine to form cyanamide and its deuterated isotopomers:

2. EXPERIMENTAL DETAILS The spectra recorded with microwave techniques and which provided the data analyzed in this work came from two different spectrometers, described in detail in ref 31, and also more briefly in ref 5. The lowest frequency segment, at 118− 179 GHz, was recorded on the backward wave oscillator (BWO)-based spectrometer developed by Analytic & Meßtechnik GmbH of Chemnitz and operated in the Giessen laboratory.32 Two higher frequency segments, covering 202− 221.4 GHz and 570.85−649.65 GHz, were measured with the Cologne millimeter/submillimetre wave/terahertz spectrometer, also using direct generation from high-frequency BWOs. All of these spectra were recorded at room temperature under a continuous flow and at a sample pressure of cyanamide of around 15 mTorr. The estimated frequency accuracy of these measurements was 0.05 MHz. D2NCN was prepared from the parent species by repeated deuteration with D2O. Spectroscopy revealed that in the cells of the microwave spectrometers it was still incompletely deuterated. As measured, the sample contained D2NCN, HDNCN, and H2NCN in approximate ratios of 1:1:0.15, respectively. This turned out to be an advantage because transitions of all three principal isotopic species were available in a single spectrum. The far-infrared absorption spectrum of pure D2NCN was measured in the spectral region between 8 and 360 cm−1, using a Bruker IFS 120 HR Fourier transform interferometer.3,31 The spectrometer employed a 6 m optical path difference and effective resolution of the resulting spectrum was estimated to be 0.0025 cm−1. Wavenumber measurement uncertainty of 0.0002 cm−1 was assumed for the purpose of combining infrared transitions with microwave measurements in weighted fits. The spectra of deuterated cyanamide obtained with microwave techniques and with high-resolution infrared interferom-

H 2N + CN → H 2NCN HDN + CN → HDNCN D2 N + CN → D2 NCN

Such recombination reactions occur readily on icy surfaces, which can be thought of as third bodies that remove sufficient energy from the reaction intermediate to stabilize it.8 As the temperature warms up above 100 K, the molecules produced in the ice, including cyanamide and its isotopomers, evaporate to enrich the gas phase of hot cores.7 Detection of relatively high abundances of deuterated isotopomers at these high temperatures would clearly indicate a nonthermal process and would show instead that their formation started in the cold core stage.12 A similar mechanism can account for the production of carbodiimide and isotopomers from precursor reactive species, although there is strong evidence that isomerization between the two isomeric species occurs readily in ices.10 Cyanamide is regarded as an established interstellar molecule, with the first reported detection9 dating back to 1975. This was on the basis of the 80504.5 and 100629.5 MHz lines of H2NCN observed in the Sgr B2 molecular cloud. Inspection of the current list of reported detections13 reveals 29 transitions, most of which were made in broad-band surveys. The largest numbers of cyanamide lines are reported in the Cummins14 and the Nummelin15 millimeter-wave surveys of Sgr B2, and in the White16 455−507 GHz survey of the Orion KL hot-cloud core. Other reported detections are of similar character, in that they are coincidences noted in the course of other work, so that ref 9 remains the only observational astrophysical study dedicated to cyanamide. In particular, there are no reports of astronomical detection of deuterated 9890



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with the help of the AABS package for “Assignment and Analysis of Broadband Spectra”.33 The package facilitates a synchronized graphical display of the spectrum and of merged predictions for the spectroscopic species of interest and allows rapid transfer of measurements to data files for several fitting programs. Various graphical aids for assignment are available in this package, and it is freely available from the PROSPE Web site.34,35 A summary of the more advanced features of the AABS package and a listing of the examples of its use can be found in ref 36.

etry have a small overlap offering a rare opportunity for direct comparison of the two techniques (Figure 2). It is possible to

3. ANALYSIS The measured frequencies of transitions in and between the 0+ and 0− inversion substates were fitted simultaneously in a twostate coupled fit based on Pickett’s reduced axis Hamiltonian.37 This has already been used for H2NCN,25,29 for D2NCN,25 and for the rare isotopic species of cyanamide.27 The Hamiltonian is in 2 × 2 block-diagonal form

Figure 2. Comparison of the same spectral segment of the spectrum of D2NCN measured with an FTIR spectrometer at a resolution of 0.0025 cm−1 (top) and a submillimeter spectrometer employing microwave techniques with a resolution of 0.5 MHz or 0.000017 cm−1 (bottom). In the FTIR spectrum the spectral line width is spectrometer limited, whereas in the submillimeter spectrum the line width is sample pressure limited.

+ − ⎛ (0+) ⎞ Hrot Hc(0 ,0 ) ⎜ ⎟ H=⎜ + − ⎟ (0 ,0 ) (0−) Hrot + ΔE ⎠ ⎝ Hc +

(1) −

) (0 ) where the diagonal H(0 rot and Hrot blocks correspond to singlestate Watson’s reduced asymmetric rotor Hamiltonian for the two inversion substates, in representation Ir and the Areduction.38 ΔE is the vibrational energy difference, E(0−) − E(0+), between the two substates. The off-diagonal interstate + − ,0 ) coupling blocks H(0 are equivalent to a second-order c Coriolis coupling term.37 Because in the cyanamide molecule inversion of the NH2 group takes place through a motion about the b-principal axis, this term is given by

follow how the decrease in resolution affects spectral appearance, as the otherwise highly resolved FTIR spectrum is still 2 orders of magnitude poorer in resolution than the submillimetre spectrum. For this reason a relatively small number of measured microwave lines usually has a greater effect on the determination of most of the spectroscopic parameters than a much larger number of infrared lines that can typically be measured. The microwave spectra of the deuterated cyanamide sample were combined into a single spectrum and subjected to analysis

+ −

Hc(0

,0 )

= (Fac + FacJP 2 + FacK Pz 2 + ...)(PaPc + PP c a)

(2)

Figure 3. Comparison between the measured J = 8 ← 7, aR-branch rotational transitions of D2NCN and HDNCN. The values of Ka are indicated, and transitions for Ka ≥ 3 are doubly degenerate. Intensities in D2NCN reflect the 2:1 nuclear spin statistical weights for Ka = even:odd in the 0+ substate and 1:2 weights for Ka = even:odd in the 0− substate. The lack of symmetry makes the HDNCN molecule devoid of statistical weights so that relative intensities of transitions in the two inversion substates reflect mainly the Boltzmann factor due to their energy difference. 9891



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J K The Fac and Fac adjustable parameters in the empirical centrifugal distortion expansion of the Fac coupling constant were found to be necessary for H2NCN.25 Presently, terms of even higher order in this expansion were also found to be advantageous for fitting the large data sets acquired for the three main isotopic species, because their inclusion allowed the use of shorter centrifugal distortion expansions in Hrot. In addition, cyanamide is a rather prolate molecule (κ < −0.99) so that S-reduction of the asymmetric rotor Hamiltonian would normally be used as the method of choice.29 We have, nonetheless, preferred to use the A-reduction because, in our previous work on perturbations in isotopic cyanamide,27 and in acrylonitrile,36,39 and ClONO240 it was found that this reduction offered significantly greater numerical stability. All fits and predictions were carried out with the SPFIT/SPCAT package of Pickett.41,42

4. D2NCN The data for this isotopic species adopted from the literature20,22,26 consists of only 12 pure rotational transitions for the 0+ substate, 9 transitions for the 0− substate, and two 0+ ← 0− rotation−vibration transitions. The frequencies do not exceed 58 GHz, and the values of quantum numbers were limited to J ≤ 4 and Ka ≤ 2, except for three qQ1-branch transitions for J = 10−12.20 Starting from predictions based on the most recent fit using eqs 1 and 2,25 we have been able to extend this data set very considerably. Figure 3 illustrates some of the principal characteristics of the pure rotation spectra of deuterated cyanamide. Cyanamide is a highly prolate molecule with only one nonzero permanent dipole moment component, μa. This has the consequence that the pure rotational spectrum has the form of broadly separated bands of aR-branch transitions for a common value of J + 1 ← J. The central region of each band contains all but the two Ka = 1 lines, which are split apart by the factor approximatly equal to (J + 1)(B − C). A prominent feature affecting the intensities of transitions in rotational spectra of cyanamide is the presence of nuclear spin statistical weights, as summarized in Table 1. The

Figure 4. Illustration of perturbations between some of the lowest rotational levels in the 0+ and 0− inversion substates of D2NCN as manifested in wavenumbers of the aR-branch pure rotation transitions. The plotted quantity is simply the transition wavenumber scaled by (J″ + 1) to make the plots roughly horizontal. At low J and for Ka ≠ 1 the plots are expected to converge to the value B + C = 0.597 cm−1, indicated on the diagrams by the horizontal dashed lines. The circle markers denote measured transitions and continuous lines are for calculation based on the final fit. The smaller, black markers and corresponding lines denote unperturbed line sequences; see text.

Table 1. Nuclear Spin Statistical Weights for Rotational Levels in Cyanamide 0−

0+ H2NCN D2NCN

even Ka

odd Ka

even Ka

odd Ka

1 2

3 1

3 1

1 2

weights arise from the effective C 2v symmetry group classification of the fully protonated or fully deuterated species of cyanamide and, for a given J, result in intensity alternations between transitions for successive values of the Ka quantum number. In addition, the same J,Ka transition alternates in intensity between the 0+ to the 0− substates. These effects are visible in the D2NCN spectrum in Figure 3, but they are not present in the corresponding spectrum of the asymmetric HDNCN species in the lower part of that figure. The known problems of fitting the rotationally resolved spectrum of cyanamide25,29 have been ascribed to perturbations between the two lowest inversion states. In D2NCN the abundant frequency coverage provided by the far-infrared spectrum allowed us to identify regions of avoided crossings due to these perturbations explicitly, as shown in Figure 4. This was facilitated by the use of graphical Loomis−Wood

techniques, which were pioneered in a computer version in Giessen43 and are also available in the AABS package.36 Graphical analysis allowed the initial microwave based assignment of pure rotational transitions for the lowest values of Ka to be extended to a much broader range of J values covered by the infrared spectrum. Perturbations between rotational levels in two interacting vibrational substates take place within a single J-matrix of the Hamiltonian, and the result is symmetric repulsive behavior of members of the interacting pair of levels. The J-dependence and the anticipated mirror image nature of this behavior give an immediate handle on the assignment, which relies on matching the J-dependent profiles for transition sequences in the perturbing vibrational states. This has been done in Figure 4. These plots are based on straightforward scaled line frequencies and are not as yet dependent on any fits. 9892



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The superscripts u and l on the values of Ka identified in Figure 4 are shorthand notation used to distinguish the upper and lower frequency aR-branch transitions for a given value of J, respectively. The u index also corresponds to the summation Ka + Kc = J for quantum numbers of the pertinent rotational levels, and l corresponds to Ka + Kc = J + 1. It turns out that a given Ka series of transitions is only perturbed in one of the two inversion substates. The same series in the second substate has thus been drawn in Figure 4 in black and provides a useful reference of unperturbed behavior. Thus in the top left pane the unperturbed series is for 0+, Ka = 0, whereas in the lower left pane this is for the state 0−, with Ka = 2u. Once satisfactory perturbation fits are available the observed perturbations can be identified in a more precise way, as shown in Figure 5. This plot makes it easy to assess the magnitude of the perturbation contribution. In the regions close to perturbation maxima, the perturbation contributions for

assigned lines exceed 5, 2.2, and 6.5 GHz, respectively, from top to bottom of Figure 5. The transitions at each perturbation maximum are too perturbed to allow unambiguous assignment, because their perturbation contributions are 34.8, 16.5, and 62.7 GHz for the three plots in Figure 5. The resulting values of spectroscopic constants for the diagonal blocks in the Hamiltonian are reported in Table 2, whereas those for the off-diagonal, coupling blocks are summarized in Table 3. Table 4 also allows inspection of the coverage of quantum number values and of transition types by the microwave and the infrared subsets. The infrared spectrum provided access to transitions with J ≤ 83 and Ka ≤ 15 for both inversion substates. The success with which the FTIR spectrum of D2NCN is reproduced by the final fit is illustrated in Figure 6. Interestingly, the numbers of aR-branch pure rotation transitions and of the c-type rotation−vibration transitions measured in the infrared spectrum are almost identical at close to 1300 each. The extensive quantum number coverage, the moderate number of adjustable parameters, and the overall rms deviation of the weighted fit of close to unity are all indicators of a successful fit of the combined microwave and infrared data. The input files for the SPFIT program and the reformatted results of fit for D2NCN and for the other isotopic species studied in this work are included in the Supporting Information. It is noted that the present values of ΔE and F are somewhat different from ΔE = 15.781(30) cm−1 and F = 261.28(71) MHz reported in ref 25. This is, however, readily rationalizable. The very small data set used previously25 was crucially dependent on six interstate transitions from ref 21, only three of which were used in a later work by the same authors.22 It turns out that half of the originally reported interstate transitions are 1 to 2 MHz away from the prediction based on the current fit and that small difference is sufficient to significantly distort the results obtained with a very small data set. The current F = 267.5995(18) MHz is, however, in excellent agreement with F = 267 MHz estimated in ref 25 on the basis of the results for H2NCN. These problems are similar to those resulting from some misassignment issues identified for the rare isotopic species of cyanamide.27

5. HDNCN This isotopologue is different from D2NCN and H2NCN in two respects. The single deuterium substitution eliminates the nuclear spin statistical weights that are characteristic of the other two species. Thus the transition intensities reflect only the relative populations and dipole moments in the two inversion substates. This results in the disappearance of intensity alternation with the value of Ka, as can be seen in the bottom pane of Figure 3. Second, the inversion axis in HDNCN is rotated slightly in the ab-inertial plane, so that the Hamiltonian coupling term now consists of two terms, + −

Hc(0

,0 )

= (Fac + FacJP 2 + FacK Pz 2 + ...)(PaPc + PP c a) + (Fbc + FbcJP 2 + FbcK Pz 2 + ...)(PbPc + PP c b)

Figure 5. Perturbation plot for aR-branch transitions in D2NCN based on a frequency difference between the actual frequency and an unperturbed frequency, ν0, derived by zeroing the terms responsible for coupling between the 0+ and 0− inversion substates. This plot is complementary to Figure 4 but provides a much more direct measure of the involved perturbations, which for the most perturbed measured transitions exceed 6 GHz in magnitude. The mirror image nature of the plots unambiguously identifies the involved transition series.

(3)

20,26

Previous measurements on HDNCN were limited to seven transitions for each substate, for Ka = 0 and 1, and up to J = 3 ← 2. We have been able to extend this data set to a total of 334 measured transitions, with further details as specified in Table 4. Useful initial conditions for the perturbation fits were set up by taking the average values of the key coupling parameters F and ΔE from those for H2NCN and D2NCN. 9893



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Table 2. Spectroscopic Constants in the Pure Rotation Part of the Hamiltonian Determined from the Global Fit of Transitions in and between the 0+ and 0− Inversion Substates for the Three Main Isotopologues of Cyanamide H2NCN 0+ a

A/MHz B/MHz C/MHz

312141.992(69) 10130.35604(35) 9865.32454(35)

HDNCN 0−

0+

304453.63(10) 10113.07668(30) 9866.23663(30)

214257.080(35) 9605.4591(39) 9256.4123(39)

D2NCN 0−

210531.83(14) 9597.89063(76) 9263.28752(72)

0+

0−

157660.4088(55) 9156.53450(39) 8742.99646(36)

156091.326(12) 9153.40678(52) 8751.59313(61)

ΔJ/kHz ΔJK/kHz ΔK/kHz δJ/kHz δK/kHz

3.80627(26) 395.665(60) 44150.9(45) 0.140754(33) 299.562(57)

3.82216(24) 359.408(77) 27930.6(83) 0.119763(38) 211.569(85)

3.4522(11) 256.947(63) 23996.2(91) 0.15697(15) 247.8(19)

3.4652(10) 255.305(90) 17090(14) 0.15142(10) 173.59(22)

3.09286(19) 218.486(10) 9114.06(30) 0.120643(52) 202.80(11)

ΦJ/Hz ΦJK/Hz ΦKJ/Hz ΦK/Hz ϕJK/Hz ϕK/Hz

−0.001079(99) 1.681(19) −339.7(38) 18616.(98) [0.] [0.]

−0.00071(10) 1.027(27) −191.4(41) 4273.(174) [0.] [0.]

0.00100(41) 1.418(36) −139.9(12) [10436.]b [0.] [0.]

0.00099(38) 1.645(68) 78.9(28) [2426.]b [0.] [0.]

0.001222(46) 3.477(21) −69.27(24) 2256.3(33) 1.574(38) 1067.(10)

LKJ/mHz LKKJ/mHz LK/mHz

13.73(64) −4071.(72) [0.]

2.70(41) −1423.9(63) [0.]

[0.] −130.9(14) −337.(10)

12.08(63) −3241.(87) [0.]

6.33(37) −679.(12) [0.]

3.08250(20) 221.634(20) 6932.06(40) 0.12917(12) 159.58(26) 0.000646(86) 1.866(56) −4.11(77) 578.8(40) 1.02(11) 243.(31) [0.] −278.2(27) 362.(11)

a

The quantities in parentheses are standard errors in units of the least significant digit of the value of the constant. bAssumed value, set equal to the average of the values of HK for the same substate in H2NCN and D2NCN.

Table 3. Spectroscopic Constants in the Off-Diagonal Hamiltonian Blocks Coupling the Two Inversion States in Cyanamide H2NCN ΔE/MHz ΔE/cm−1 Fca/MHz FJca/MHz FKca/MHz FJJca/kHz FJK ca /kHz FKK ca /kHz FKKK ca /kHz Fbc/MHz FJbc/MHz FKbc/MHz σwa Nmwb Nirc

HDNCN

1486004.36(18) 49.567770(6)

D2NCN

962009.210(94) 32.089173(3)

346.870(33) 0.001397(12) −1.5150(55) 0.00001177(61) −0.0559(21) [0.] [0.]

281.972(44) 0.0007325(42) −1.7945(95) [0.] [0.] 9.32(38) [0.]

[0.] [0.] [0.]

8.134(87) −0.0000688(41) −0.309(34)

1.573 377 2059

1.316 334

494551.996(25) 16.4964789(8) 267.5995(18) [0.] −0.97587(71) [0.] 0.00188(32) 1.675(74) 0.01158(25) [0.] [0.] [0.] 1.189 477 2616

The root-mean-square, unitless deviation of the weighted fit. bThe number of transitions measured with microwave techniques. cThe number of transitions measured with the infrared interferometer.

a

found from the current experimental geometry27 to be by an angle of 1.77°. The magnitude of this rotation might be expected to be reflected in the relative values of the fitted leading interaction constants Fca and Fbc. In fact, the empirical estimate from tan−1(Fca/Fbc) gives 1.65°, which confirms the validity of the interstate perturbation fit. It is also possible to determine from this fit that for HDNCN the 0+ ↔ 0− interaction will exhibit avoided crossing-type perturbation behavior similar to those shown in Figures 4 and 5. This will, however, be maximized at frequencies of pure rotational transitions falling well outside the range covered by the present

Even though the spectrum at our disposal was only that up to 649 GHz, obtained with microwave techniques, it was eventually possible to assign over 111 c-type interstate transitions, including both 0+ ← 0− and 0− ← 0+ transitions. These data could be satisfactorily fitted with the Hamiltonian used for D2NCN, with the modification as in eq 3. The resulting values of spectroscopic constants are reported in Tables 2−3 and it can be seen that the precision of the determination of the inversion splitting is only a factor of 4 poorer than for D2NCN. The rotation in the ab inertial plane of the inertial axes from the parent isotopic species to HDNCN is 9894



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Table 4. Details of the Microwave and the Infrared Data Sets Acquired for the Three Cyanamide Isotopologues H2NCN 0+ Jmax Kmax a Ntrans(Δv=0) Ntrans(Δv≠0) σfit/MHz

51 6 155 32 0.107

Jmax Kmax a Ntrans(Δv=0) Ntrans(Δv≠0) σfit/cm−1

70 6 275 1280 0.00030

HDNCN 0− 65 6 140 50 0.116

0+ Microwave 43 10 113 58 0.091 Infrared

70 6 294 210 0.00038

D2NCN 0− 47 10 110 53 0.083

0+

0−

53 12 173 99 0.147

50 12 148 57 0.116

84 15 714 837 0.00021

83 15 590 475 0.00032

Figure 6. Illustration of the nature of the far-infrared spectrum of D2NCN, which consists of compact rotation−vibration Q-branches, among diffuse combs of R-branch transitions. These are all interstate c-type transitions and can be either for 0− ← 0+ or 0+ ← 0−.

far-infrared transitions from the fit. The observed systematic deviations can be attributed to interactions with vibrationally excited states,29 whereas it is unavoidable that they will be poorly accounted for by the two-state model in eq 1. It turns out that if we apply in the fitting process the relatively generous rejection criterion of ν(obs−calc) > 10σ then all assigned lines can be fitted with the present parameter suite, provided that the fit is limited to transitions with Ka ≤ 6. Incomplete deuteration of the sample measured in the millimeter- and submillimeterwave spectra allowed 115 new transitions to be added to the Ka ≤ 6 data set for H2NCN and the results of the new fit are compared with those for the deuterated species in Tables 2 and 3. Even though the rms deviation of this fit is higher than for the deuterated species, its stability is excellent and the resulting parameters should enable confident prediction of all transitions of H2NCN of relevance to radioastronomy. Also, although the values of many of the fitted parameters are different from those previously tabulated,29 the value of the inversion splitting ΔE remains practically unchanged.

spectra. For the 0+ inversion substate, for example, the perturbation maxima will fall at frequencies from 1.5 to 1 THz for Ka = 3 to Ka = 1, respectively.

6. H2NCN The most recent tabulation of spectroscopic constants for the parent isotopic species of cyanamide is available in Table 1 of ref 29. It is the corresponding data set and the fit that are the source of the linelist for H2NCN in the jpl spectral line catalog.44 The original file of spectroscopic parameters is not available therein and in the course of this work we were unable to reproduce the published fit. This is largely due to its considerable numerical instability arising from the use of numerous adjustable parameters including some very highorder angular momentum terms up to P14. We identified several typing mistakes in the published constants, whereas reproduction of an unstable fit is crucially dependent on the starting conditions. It was, therefore, decided to redo the fit from scratch by using the suite of adjustable parameters that was found successful for the two deuterated species. The previous need to use high-order parameters arose out of the attempt to encompass a rather limited number of higher Ka transitions in the fit. Even with the upper limit of Ka ≤ 9 adopted in ref 29, the authors were forced to drop as many as 277 of the assigned

7. CONCLUSIONS The present work provides a unified treatment of rotation and rotation−vibration spectra of the lowest inversion doublet in the three principal isotopic species of cyanamide. It can be seen 9895



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observatory and offers a significant number of relatively closely spaced transitions for detection. The present results also deliver precise values of the inversion splitting in cyanamide. It is now possible to follow the considerable effect of the deuteration on the location of the energy levels in the double minimum inversion potential, illustrated in Figure 8. In the first approximation, the shape of

from Table 4 that the treatment based on the reduced axis Hamiltonian is able to deal with successively higher values of the Ka quantum number that are not involved in additional vibrational perturbation and become accessible in the process of deuterium substitution. This is in inverse proportion to the pertinent values of the A rotational constant, because the lower the A the larger the value of Ka before levels of the lowest inversion doublet reach energy levels of higher vibrational states. Interactions between apparently distant vibrational states are unavoidable in molecules with large A rotational constant and transition measurements in the terahertz region, as has been studied in detail for acrylonitrile.36,39 Nevertheless, providing that predictions are limited to the ranges of the quantum numbers J and Ka listed in Table 4, the spectroscopic constants from the robust fits reported in Tables 2 and 3 are expected to provide confident spectral predictions for frequencies well into the terahertz region. Line list tables produced under these constraints are included in the Supporting Information. It is of interest to explore which parts of the rotationally resolved spectrum of D2NCN might be of relevance in astrophysical observations. The temperature dependence of the intensity envelope of this spectrum is illustrated in Figure 7.

Figure 8. Comparison of the experimentally determined splitting between the 0+ and 0− inversion substates for the studied species of cyanamide (black) and the values calculated from the double minimum quartic-quadratic potential (red).

this potential is expected to remain invariant on deuteration, whereas the reduced mass for the inversion motion20 increases by 70% from H2NCN to D2NCN. The eigenvalues in this potential approximation can be calculated with the reduced quartic-quadratic potential45 V (z) = A(z4 + Bz 2)

(4)

where z is a dimensionless displacement coordinate for the motion, and A and B are adjustable parameters. The energy levels in this potential can be estimated either from suitable tabulations45 or calculated with program ANHARM46 available from the PROSPE Web site.35 The experimentally determined30 relative energies of the 0+, 0−, 1+, and 1− levels for H2NCN, are described within 0.3 cm−1 by the reduced quarticquadratic potential with A = 113.57 cm−1 and B = −4.0634. The isotopic dependence of these parameters is given by47

Figure 7. Calculated intensity profiles of the high-resolution spectrum due to transitions involving the 0+ and 0− substates of D2NCN. The spectrum is made up of pure rotation a-type transitions in each substate (blue), and rotation−vibration c-type transitions between the two substates (black). Decreasing temperature reduces the domination of the pure rotation transitions in the spectrum and makes some of the rotation−vibration transitions, in particular the relatively dense 0− ← 0+, rQ0 branch near 630 GHz, an attractive observational target.

The intensities were calculated by using the 0+ and 0− state dipole moments as well as the interstate transition moment determined for H2NCN.25 The maximum of the rotational envelope displays a steady shift to low frequency with decreasing temperature, whereas some of the more prominent rotation−vibration features show a significant increase in intensity in relation to the pure rotation transitions. The most interesting of such features is the c-type, interstate rQ0 branch near 630 GHz, which falls into band 9 of the ALMA

AD

⎛ μ ⎞2/3 =⎜⎜ H ⎟⎟ AH ⎝ μD ⎠

BD

⎛ μ ⎞−1/3 =⎜⎜ H ⎟⎟ BH ⎝ μD ⎠

(5)

where the subscript H refers to the parent isotopic species and D refers to either one of the two deuterated species. μ is the reduced mass for the motion as defined in ref 20. The conversion between the reduced coordinate z and the inversion angle ϕ of Figure 1 is given in eq A12 of ref 47. Inspection of 9896



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(9) Turner, B. E.; Kislyakov, A. G.; Liszt, H. S.; Kaifu, N. Microwave Detection of Interstellar Cyanamide. Astrophys. J. 1975, 201, L149− L152. (10) McGuire, B. A.; Loomis, R. A.; Charness, C. M.; Corby, J. F.; Blake, G. A.; Hollis, J. M.; Lovas, F. J.; Jewell, P. R.; Remijan, A. J. Interstellar Carbodiimide (HNCNH): A New Astronomical Detection From the GBT PRIMOS Survey via Maser Emission Features. Astrophys. J. 2012, 758 (L33), 1−6. (11) Garrod, R. T.; Widicus Weaver, S. L.; Herbst, E. Complex Chemistry in Star-forming Regions: an Expanded Gas-grain Warm-up Chemical Model. Astrophys. J. 2008, 682, 283−302. (12) Aikawa, Y.; Wakelam, V.; Hersant, F.; Garrod, R. T.; Herbst, E. From Prestellar to Protostellar Cores. II. Time Dependence and Deuterium Fractionation. Astrophys. J. 2012, 760, i.d. 40 (1-19). (13) Lovas, F. J.; Bass E. J.; Dragoset R. A.; Olsen, K. J. NIST Recommended Rest Frequencies for Observed Interstellar Molecular Microwave Transitions, 2009 Revision, URL http://www.nist.gov/ pml/data/micro/index.cfm (14) Cummins, S. E.; Linke, R. A.; Thaddeus, P. A Survey of the Millimeter-wave Spectrum of Sagittarius B2. Astrophys. J. Suppl. Ser. 1986, 60, 819−878. (15) Nummelin, A.; Bergman, P.; Hjalmarson, Å.; Friberg, P.; Irvine, W. M.; Millar, T. J.; Ohishi, M.; Saito, S. A Three-position Spectral Line Survey of Sagittarius B2 Between 218 and 263 GHz. I. The Observational Data. Astrophys. J. Suppl. Ser. 1998, 117, 427−529. (16) White, G. J.; Araki, M.; Greaves, J. S.; Ohishi, M.; Higginbottom, N. S. A Spectral Survey of the Orion Nebula from 455 - 507 GHz. Astron. Astrophys. 2003, 407, 589−607. (17) Tyler, J. K.; Thomas, L. F.; Sheridan, J. Microwave Spectrum and Structure of Cyanamide. Proc. Chem. Soc. 1959, 155−156. (18) Millen, D. J.; Topping, G.; Lide, D. R. Microwave Spectrum and Nonplanarity of Cyanamide. J. Mol. Spectrosc. 1962, 8, 153−163. (19) Macdonald, J. N.; Taylor, D.; Tyler, J. K.; Sheridan, J. 14NQuadrupole Coupling in the Microwave Spectrum of Cyanamide, NH2CN. J. Mol. Spectrosc. 1968, 26, 285−293. (20) Tyler, J. K.; Sheridan, J.; Costain, C. C. The Microwave Spectra of Cyanamide Conclusions from μa Transitions. J. Mol. Spectrosc. 1972, 43, 248−261. (21) Attanasio, A.; Bauder, A.; Günthard, H. H. Analysis of the Microwave Spectrum of Cyanamide by Rotation-inversion Theory. Mol. Phys. 1972, 24, 889−891. (22) Attanasio, A.; Bauder, A.; Günthard, H. H. Analysis of Infrared and Microwave Spectra of Cyanamide and Cyanamide-d2 by Rotationinversion Theory. Chem. Phys. 1974, 6, 373−381. (23) Johnson, D. R.; Suenram, R. D.; Lafferty, W. J. Laboratory Microwave Spectrum of Cyanamide. Astrophys. J. 1976, 208, 245−252. (24) Brown, R. D.; Godfrey, P. D.; Kleibömer, B. Microwave Spectrum and Structure of Cyanamide: Semirigid Bender Treatment. J. Mol. Spectrosc. 1985, 114, 257−273. (25) Read, W. G.; Cohen, E. A.; Pickett, H. M. The RotationInversion Spectrum of Cyanamide. J. Mol. Spectrosc. 1986, 115, 316− 332. (26) Brown, R. D.; Godfrey, P. D.; Head-Gordon, M.; Wiedenmann, K.; Kleibömer, B. The Vibrational Dependence of the Electric Field Gradient in Cyanamide. J. Mol. Spectrosc. 1988, 130, 213−220. (27) Krasnicki, A.; Kisiel, Z.; Jabs, W.; Winnewisser, B. P.; Winnewisser, M. Analysis of the Mm- and Submm-wave Rotational Spectra of Isotopic Cyanamide: New Isotopologues and Molecular Geometry. J. Mol. Spectrosc. 2011, 267, 144−149. (28) Birk, M.; Winnewisser, M. The Rotation-vibration Spectrum of Gaseous Cyanamide (H2NCN). Chem. Phys. Lett. 1986, 123, 382− 385. (29) Birk, M.; Winnewisser, M.; Cohen, E. A. The High Resolution Fourier-transform Far Infrared Spectrum of Cyanamide, H2NCN. J. Mol. Spectrosc. 1993, 159, 69−78. (30) Moruzzi, G.; Jabs, W.; Winnewisser, B. P.; Winnewisser, M. Assignment and Power Series Analysis of the FIR Fourier Transform Spectrum of Cyanamide Using a Multimolecule Ritz Program. J. Mol. Spectrosc. 1998, 190, 353−364.

Figure 8 reveals that estimates from this simple potential account for the experimental inversion splitting in the two deuterated species at the 1 cm−1 level. We have also found that the accuracy of this prediction cannot be improved further by adding a sextic term in eq 4 but only by fine-tuning the expression for the reduced mass of the motion (by reducing the participation of the nitrile group nitrogen). Nevertheless, the number of accurate energy data other than those for the lowest inversion doublet is still too small to embark on such modifications.

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ASSOCIATED CONTENT

S Supporting Information *

Input files, results of fits, and calculated line lists for D2NCN, HDNCN, and H2NCN. 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: 048-22-8430926. Present Address ⊥

Bruker Daltonik GmbH, Fahrenheitstrasse 4, D-28359 Bremen, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from a grant from the Polish National Science Centre, decision number DEC/2011/02/A/ST2/ 00298, is gratefully acknowledged. The work in Giessen was supported in part by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie and the Max-Planck research award. The Cologne work was supported in part by the Deutsche Forschungsgemeinschaft and funds from the Science Ministry of the Land Nordrhein-Westfalen. The authors also enjoyed the support rendered by the Microwave Laboratory of The Ohio State University and E.H. wishes to thank NASA for support of his spectroscopic program while he was at The Ohio State University.

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REFERENCES

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Inversion Doublet in Deuterated Cyanamide - American Chemical

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