J . Phys. Chem. 1991,95, 2859-2864
2859
Preliminary Structural Characterisatlon of Complexes of Cyanogen: NHS-NCCN and
Ian I. SUN, Seonghoon Lee, and William Klemperer* Department of Chemistry, Haruard University, Cambridge, Massachusetts 02138 (Received: October 3, 1990)
The complexes of NCCN with itself and with NH3 have been studied by molecular beam electric resonance spectroscopy. In both species a heavy-atom arrangement of C, SyRfmetry is observed. The NH,-NCCN complex appears to exhibit essentially free internal rotation of the NH3 subunit about its internal symmetry axis. The observed rotational constants for the ground internal rotor state are A = 4738.67 (12) MHz, B = 3960.93 (10) MHz, and C = 2145.01 (10) MHz. These constants give a center-of-mass separation of 3.13 (2) A or equivalently an N-C distance of 3.12 (2) A. The electric dipole moment is p = p,, = 1.96 (3) D. From the partially resolved nitrogen quadrupole structure the (vibrational) average tilt of the NH, symmetry axis from the a axis is estimated at 23O. The dimer of NCCN has a T-shaped C, structure. Only a-type transitions have been observed. The rotational constants B and C are well determined as B = 675.77 (15) MHz and C = 586.75 (IO) MHz. A is less well determined as A = 4407 (145) MHz. The bond distance RNCis 3.206 (1) A. The electric dipole moment is p = pa = 0.420 ( 5 ) D. At present we have no observations of tunneling motions such as those observed in (HCCH)2. The observed polar C, structure is different from the nonpolar C2h structure of (C02)2and is taken to indicate the relative subtlety of the stereochemistry of weak interactions.
Introduction Weak intermolecular interactions provided George Pimentel an incentive to extend concepts of bonding from those applied to covalent chemical bonds. His invention of matrix isolation spectroscopy permitted a unique cryogenic environment in which interaction strengths between molecules needed only to exceed those with the host inert gas to allow ready observation of binary complexes. Infrared spectroscopy provided a powerful means for characterization of the funtionalities directly responsible for the interaction. For example, the hydrogen bond is all too readily discernible as a consequence of pronounced intensity enhancement and frequency red shift in the 3000-cm-' region. The study of an increasingly broad range of molecular complexes has predictably grown with the steady increase in spectroscopictechniques. In this report we present the initial rotational spectroscopic results of the structure of two complexes of NCCN, the dimer and the binary complex with NH,. Our initial interest was in the NH3-NCCN system. A previous study of the complex HCNNH,' showed a hydrogen-bonded structure with the atomic arrangement NCH-NH3. The expectations for the NCCN complex were that NCCN would behave like H C N without the H end, thereby binding to NH, through the only other active site, the N lone pair. There is strong incentive to find a strong proton amptor, preferably of simple linear geometry, to which NH3 will form a donor hydrogen bond.2 NCCN appeared an ideal candidate. In the course of the molecular beam electric resonance study of NH,-NCCN it became apparent that (NCCN)2 was polar and readily produced. One of the most interesting classes of van der Waals dimers is dimers made up of two nonpolar species. Complexes involving C02, HCCH, and NCCN are interesting because they are the simplest molecules whose first nonvanishing electrostatic multipole is their quadrupole moment. All three of these molecules have been studied bound to Ar,>' and their complexes are T-shaped. The dipole moments of the three complexes are very different: p = 0.02697.0.06793, and 0.0979 D for Ar-HCCH, A d o 2 , and Ar-NCCN, respectively. The corresponding bond lengths are R,, = 4.04, 3.493, and 3.58 A. In the most (1) Fraser, G. T.; Leopold, K. R.;Klemperer, W. J . Chem. Phys. 1984, 80, 3073. (2) Nelson, D. D., Jr.; Fraser, G. T.; Klemperer, W. Science 1987, 238, 1670. (3) Steed, J. M.; Dixon, T. A.; Klemperer, W. J. Chem. Phys. 1979, 70, 4095. (4) Fraser. G. T.; Pine, A. S.;Suenram, R. D. J . Chem. Phys. 1988.88, 6157. (5) DeLeon, R. L.; Muenter, J. S . J . Chem. Phys. 1980, 72, 6020. (6) Ohshima, Y.;lida. M.; Endo, Y . Chem. Phys. Lett. 1989. 161, 202. (7) Ebenstein, W. L.; Muenter, J. S . J . Chem. Phys. 1984, 80, 1417.
simplistic picture of bonding the incremental difference in bond strength among the three species is a result of the quadrupoleinduced dipole interaction. The small dipole moment and large bond length of Ar-HCCH indicate that bonding is weakest in this complex, but comparison of the C 0 2 and NCCN complexes is less straightforward. AI-NCCN has a much larger dipole moment but a slightly longer bond length than Ar-HCCH. The structure of dimers of nonpolar linear molecules is a topic of considerable interest.8 The dimer of C02 has a centrosymmetric slipped parallel C, structure,+Ii with a nearest-neighbor C-O distance of 3.15 A, about the same as in the crystal. The dimer of HCCH'2.'3 has a T-shaped C, structure, with tunneling observed through a czh transition state to other equivalent Tshaped configurations. The hydrogen bond distance of 2.743 A is roughly equal to that in the crystal and is much longer than the hydrogen bond length in other HCCH complexes. The long bond length and low anisotropy of the intermolecular potential (as evidenced by the 2.2-GHz tunneling frequency) probably reflect a weak bond. Experimental Section The radio-frequency and microwave spectra of NH,-NCCN and (NCCN)2 were obtained by use of a molecular beam electric resonance ~pectr0meter.I~The Weiss electron impact ionizer has been replaced by a new ionizer that employs a magnetic solenoid that focuses an electron beam along the solenoid axis. This produces coaxial propagation of the electron beam and the molecular beam. The velocity-dependent magnetic force should increase the efficiency of ion extraction from the electron cloud. This ionizer operates with a much longer ionization path length than the Weiss ionizer but a much smaller electron emission current. It will be described in a future publication. NH,-NCCN was formed in a I-atm expansion of a mixture of 3% NH3 and 3% NCCN in Ar. The study of NH,-NCCN was initiated to find a species to which NH, would hydrogen bond, and NCCN seemed an ideal candidate since we thought that its only active sites were the lone pairs on the nitrogen atoms. This hydrogen-bonded species would be a near-symmetric top, so (8) Muenter, J. S. Submitted for publication in J . Chem. Phys. (9) Jucks, K. W.; Huang, Z. S.;Dayton, D.; Miller, R.E. J. Chem. Phys.
1987,86, 4341. (IO) Walsh. M. A.; England, T. H.; Dyke, T. R.;Howard, B. J. Chem. Phys. Lett. 1987, 142, 265 (11) Jucks, K. W.; Juang, Z. S.;Miller, R.E.; Fraser, G. T.; Pine, A. S.; Lafferty, W. J. J. Chem. Phys. 1988, 88, 2185. (12) Prichard. D. G.; Nandi. R. N.; Muenter. J. S . J . Chem. Phvs. 1988, 89,'IlS. (13) Fraser, G. T.; Suenram. R.D.; Lovas, F. J.; Pine, A. S.;Hougen, J. T.; Lafferty, W. J.; Muenter, J. S . J. Chem. Phys. 1988, 89, 6028. (14) Bowen, K. H. Ph.D. Thesis, Harvard University, 1977.
0022-365419 112095-2859%02.50/0 0 1991 American Chemical Societv
2860 The Journal of Physical Chemistry, Vol. 95, No. 7 , 1991
TABLE II: Observed in = 0 Rotatio~lTransitions for NH,-NCCN s -obsd - ~ a i d MHz , JwO JkpKg v, MHz 1239.53 (1201 0.16 1.66 4429.65 (iosj 2.07 5449.85 (140) 0.49 6 106.43 ( 100) 7982.25 (20) 0.1 1 9180.73 (165) 0.68 -1.04 10971.48 (110) 1 1 170.65 (360) -0.12 15129.33 (70) 0.14 -1.13 15162.40 (70) 19348.0 (1.3) 0.15
TABLE I: Fragmentation Pattern of NH,-NCCN probable resonance
a
mle
ionic species
intensity"
15 16 17 26 27 52 53 69
NH' NH2+ NH3' N C+ HNC+ NCCN+ NCCNH' NCCNNH3'
43 2 7 13 15 1
67 0
Relative to mass 52.
microwave searches were conducted from 10 to 20 GHz. Three pairs of lines were discovered, two near 1 1 GHz, two near 15 GHz, and two near 19 GHz, so the hydrogen-bonded species was ruled out as its 2B spacing would have been about 2 GHz. The observed spacing between adjacent microwave lines of 4-6 GHz is only consistent with an asymmetric T-shaped structure. After unsuccessfully trying to fit these as three A J = 1 transitions for two internal rotor states, it was realized that if three of the six transitions were fit as AJ = 1 a-type transitions in the K = 0 stack, two others could be fit as AKp = 2 a-type transitions. This assignment accurately predicts the rest of the spectra. Searches for b-type and C-type transitions were negative. Table 1 shows the relative signal of the 101-202transition on various mass peaks. The NH3+yield in Table I is surprising, since NH3 complexes have unusually been studied on either NH3+ or NH4+. NH3-NCCN transitions are strongest on the NCCNH+ peak, which gives a clear assignment of the spectrum to the NH3-NCCN complex. All reported measurements were obtained on the NCCNH' ion mass peak. The strength of the NCCNH+ peak is surprising since the complex is not hydrogen-bonded. This implies that upon ionization the complex rearranges significantly, essentially undergoing an internal ion-molecule reaction. The strong resonance signals at masses 15 and also at masses 26 and 27 show that there is considerable fragmentation occurring with electron impact ionization. The study of (NCCN)2 was initiated by chance. The electric resonance spectrometer utilizes electrostatic quadrupole fields to focus polar species in the molecular beam. When looking for the best mass peak on which to study NH3-NCCN, we observed focusing on mass 52 but could not detect NH3-NCCN resonances. We guessed correctly that we were observing polar (NCCN),. Spectra for (NCCN)2 were then obtained by expanding a mixture of 3% NCCN in Ar with a stagnation pressure of 3 / 4 atm. Transitions were first seen at 96 and 171 MHz and tentatively assigned to the K P = 2, J = 6, 7 asymmetry doublets. This assignment and the assumption of a T-shaped structure roughly predict the same of the a-type spectra. As will be discussed later, the spectrum does not fit a rigid-rotor model exactly. The resonance intensities are strongest on the NCCN+ ion peak; several transitions were also observed on the parent peak to ascertain the carrier after some initial confusion with Ar-NCCN resonances. Results NH,-NCCN. The spectrum of NH3-NCCN is consistent with a T-shaped oblate asymmetric top with free internal rotation of the NH, subunit. Table 11 lists the observed transitions. Due to the large asymmetry of the complex ( K = +0.40), AJ = 1 , AK, = 1, and AKp = 2 transitions are all observed, so A, B C,and B - Care all well determined and uncorrelated. The m = 0 spectra are expected to fit Watson's semirigid-rotor Hamiltonian,ls but because of the quadrupole hyperfine structure the line widths are too large (hwhm = 0.2-3.6 MHz) to fit the quartic centrifugal distortion constants. If distortion constants are obtained, their uncertainties are larger than 100%. Table 111 shows the rotational constants determined. The microwave spectrum for the first excited internal rotor state of NH3-C02 fits an internal rotor model that assumes no barrier
+
(15) Watson, J.
K. G.J . Chem. Phys. 1967, 46, 1935.
Suni et al.
TABLE III: Spectroscopic Constants for the m = 0 State of NHS-NCCN A = 4738.67 (16) MHz A = 1.365 amu A2 B = 3960.93 (14) MHz fia = 1.96 (3) D C = 2145.01 (14) MHz
to internal rotation.I6 The rotational constants of the excited internal rotor state differ slightly from those of the ground state due to distortion effects. The microwave spectrum of the first excited internal rotor state of NH3-NCCN was calculated by assuming free internal rotation using the ground-state rotational constants. The large asymmetry of the complex causes all the rotational transitions in the excited rotor state except J = 0-1 to be displaced far from those of the ground state. The K = 0, J = 1-2 transition is predicted at 12416.4 MHz, and subsequent scans found a strong transition at 12412.2 MHz, in accord with the assumption of essentially free internal rotation. The dipole moment was measured by recording low-resolution and spectra for the following transitions: Ooo-lol, 101-202r212-211, 322-321. Spectra were recorded for all four transitions at various Stark fields from 700 to loo0 V/cm. Since at high fields the Stark and hyperfine terms in the Hamiltonian are decoupled, the hyperfine pattern will not change appreciably in this range of Stark fields. The dipole moment was calculated by measuring the shift in the various lMJl components of all four transitions as the Stark field was increased from one high field value to another. This produced a consistent value of 1.96 (3) D for the dipole moment. A preliminary attempt was made to obtain a high-resolution spectrum of the Ooo-loltransition at about 996 V/cm. At present this spectrum is only partially resolved, since the transition splits into 1 1 observable components of roughly equal intensity. (NCCN),. For (NCCN), both AKp = 0, AJ = 0 asymmetry doublets and AJ = 1 microwave transitions were observed and are consistent with a C, T-shaped geometry. The observed transitions are listed in Table IV. Due to the four I4N nuclei in the complex, the transition half-widths are large, ranging from 0.4 to 4.0 MHz hwhm for most transitions. The large width observed for the J = 1, Kp = 1 doublet agrees with hyperfine calculations. The spectrum is slightly perturbed from that calculated from a rigid asymmetric rotor model, as might be expected from the spectrum of (HCCH),.13 Fraser et al. found that (HCCH)2 had four tunneling levels due to interconversion of the two subunits between nonequivalent configurations. Two of these tunneling states (E) are degenerate and give rise to a pure rotational spectrum while the other two (Al+ and BI+)give rise to tunneling-rotation spectra." The K p = 1 and Kp = 2 asymmetry doublets could not be simultaneously fit to a Watson rigid-rotor Hamiltonian. Fraser et al. postulated that a vibration-rotation interaction between the K = 0 levels of the first excited bending vibration (0, = I ) and the K p = 2 levels of the ground vibrational state (u, = 0) was pushing down the upper level in the K P = 2 d0ub1ets.l~ The energy difference between the upper K P = 2 level in u, = 0 and the K = 0 level in u, = I was calculated to be about 10.3 cm-'. The K p = 1 levels of u, = 0 will interact with the K P = 3 levels of u, = 1, but the (16) Fraser, G. T.; Leopold, K. R.; Klemperer, W. J . Chem. Phys. 1984, 81, 2577.
Structural Characterization of NH,-NCCN and (NCCN)2 TABLE I
V Observed Rotational Transitions of (NCCN),
JKPKO
JkpKo
322
321 15411 16412 17413
I5412 I6413 17414 524 Ill
523 1 10
625 726 212
624
827
826
928 313
927 312
Oao
101
202 220
303
303
404 43 I 422
330 321
The Journal of Physical Chemistry, Vol. 95, No. 7, 1991 2861
72, 211
321
4M
505
422
523
Y,
MHz
6.895 (3) 12.297 (60) 20.597 (100) 32.682 (60) 47.97 (93) 85.82 (200) 95.66 (50) 171.45 (60) 263.8 (40) 284.01 (138) 442.89 (120) 534.38 (40) 1263.13 (40) 3782.23 (400) 3791.39 (300) 5034.34 (230) 5055.19 (125) 5063.43 (1 10) 6280.48 (190) 6340.83 (160)
obsd - calcd, MHz a
b
-3.20 -3.3 0.28 0.52 0.94 -2.45 -0.06 1.88 -1.17 -0.83 0.36
" K p = 2 asymmetry doublets were omitted from fit due to perturbation. bKP = 4 asymmetry doublets were emitted from fit due to large centrifugal distortion effects.
TABLE V SwctroscoDic Constants for (NCCN), A = 4407 (145) MHz pa = 0.420 (5) D A = -1.49 amu A2 B = 675.77 (1 5) MHz C = 586.75 ( I S ) MHz
energy separation is larger (23.8 cm-l) and both members of the asymmetry doublet should be perturbed nearly equally. The Kp = 1 levels were considered unperturbed enough to extract structural information. The spectrum of (NCCN)2 appears to present a similar problem. If the microwave transitions and the three Kp = 1 asymmetry doublets are fit to a rigid-rotor Hamiltonian, the frequencies of the K P = 2 asymmetry doublets are all overestimated, as is the case for (HCCH)2. A simple vibrational calculation to be discussed later predicts that the Kp = 2 levels of u, = 0 are 12.7 cm-' below the K = 0 levels of u, = 1, and the KP = 1 levels of u, = 0 are 14.2 cm-' below the Kp = 3 levels of u, = 1. Since (NCCN), has much smaller rotational energy level differences than (HCCH)2, the symmetry-allowed perturbations all connect levels with similar energy spacings, and it is difficult to argue that any of the perturbations should be smaller compared to the rest. However, only the Kp = 2 asymmetry doublets have one level that is unperturbed by u, = 1. The other transitions involve two levels that should both be perturbed in the same direction by the same matrix element, so all other transitions should fit a rigid-rotor Hamiltonian. Since the unresolved hyperfine structure produces large line widths, the quartic distortion constants could not be fit. As a result, the K P = 4 asymmetry doublets must also be omitted, since distortion should have an effect of a t least several hundred kilohertz for such high J and K quantum numbers. Table V shows the rotational constants determined by omitting the K p = 2 and KP = 4 doublets from the least-squares fit. The value of A in Table V is determined primarily by the K = 2 and K = 3 microwave lines. High-resolution spectra were obtained for the K P = 2, J = 3 doublet, which has a nearly vanishing hyperfine spectrum due to the small asymmetry of the complex ( K = -0.96). This line was narrowed to about 15 kHz, the ultimate resolution of the instrument. The dipole moment of the complex was measured by Stark shifting the Kp = 2, J = 3 doublet. The frequencies of the MJ = 3-3, 2-2, 3-2, and 2-1 components were measured with a large electric field. The dipole moment was calculated by assuming a two-level system, giving pa = 0.420 (5) D. Structure and Dynamics NH,-NCCN. The observed spectrum of NH3-NCCN is consistent only with a T-shaped structure. The A rotational
Figure 1. Coordinate system used to describe NH3-NCCN. TABLE VI: Possible Structural Constants for NH3-NCCN
R,,. A Iaa, Ibb Iaa, l c c Ibb. Icc
Y,
den
4.885 (94) 4.885 (94) 0.0
3.1124 (6) 3.1294 (5) 3.1294 (5)
constant is close to the B value of free NCCN (4710.9 MHz)," and only a T-shaped structure gives such a large asymmetry ( K = +0.40). Since the sign of the quadrupole moment shows the central C atoms of NCCN to be electron deficient, it is probable that the N H 3 lone pair points toward the two C atoms. Figure 1 shows the equilibrium structure and the coordinates that describe the orientation of the two subunits. The angle x which is not shown is the average angle between the symmetry axis of the NH, subunit and the a axis. This angle describes zero-point vibrational averaging due to the van der Waals bend of the NH3 subunit. The moments of inertia are related to the structural parameters as follows
+ IBsin2 x + Io sin2 y Ibb = I , Sin2 X + 18 COS2 X + 10 COS2 + ICc = Io + Io + M,RCm2 I,, = I , cos2 x
kfS&,z
(1)
where M,is the reduced mass of the complex, I , is the moment of inertia of the NH3 subunit about its symmetry axis, It is the other moment of inertia of NH3, and Io is the moment of inertia of free NCCN. Since x has negligible effects on the rotational constants, it is best obtained from the partially resolved hyperfine fit as x = 23'. Different pairs of rotational constants predict different values of and R,, due to the significant inertial defect (A = 1.365 amu of the complex. Although NH3-NCCN is nonplanar, one can follow Herschbach and Laurie's'* definition of an inertial defect for nonplanar molecules, which measures the contributions of vibrational averaging to the moments of inertia. For a system like NH3-NCCN, whose only nonplanar atoms are part of a freely rotating internal top, the inertial defect takes the following form A = I, - I, -
+ I,
(2)
Since the measured A rotational constant equals h / 8 ~ ~ ( 1-, I,), , the inertial defect takes the usual form (3)
Table VI contains the structural parameters determined from different moments of inertia. The uncertainties in Table VI are probably optimistic, since the distortion terms in the rigid-rotor Hamiltonian were omitted. The best value of y is that obtained from the A rotational constant. To best choose R,, we follow Fraser et al., who found that the C rotational constant of Ar-C02 was less dependent than the other rotational constants on vibrational averaging due to the (17) Edwards, H. G. M.; Mansour, H. R. J . Mol. Sfrucf. 19%7,160,209. (18) Herschbach, D. R.; Laurie, V. W. J . Chem. Phys. 1964,10, 3142.
2862 The Journal of Physical Chemistry, Vol. 95, No. 7, 1991
Suni et al. TABLE VIII: Vibrationally Averaged Structural Constants of (NCCN)2 Ground State
N
I
= 90' O2 = 13.9 ( 5 ) O R,, = 4.987 (1) A
I
?J
Hi,,= Fp2 + V ( a )
Figure 2. Coordinate system used to describe (NCCN),.
V ( a ) = V4(1 -COS 4 a ) / 2
van der Waals bend! This should hold for any planar complex whose largest amplitude van der Waals modes are in-plane motions. The four heavy atoms of NH3-NCCN are coplanar, and one expects that the in-plane rocking motion of the NH, subunit against the NCCN subunit should be the largest amplitude van der Waals bend, so the R,, value obtained from the C rotational constant is probably least affected by vibrational averaging. Table VI1 summarizes the structural parameters obtained from I,,, I,,, and the quadrupole coupling constant. The uncertainties .in Table VI1 are based on the choice of different pairs of rotational constants. The likely equilibrium structure has x = 0' and y = 0'. ( N C C w 2 . The structure of (NCCN)2 is the C, T-shaped geometry of (HCCH)2,12J3not the C2, slipped parallel structure of (C02)2e11 and (N2O),.I9 The large dipole moment and the absence of C-type transitions indicate the complex is nearly planar, although the inertial defect of -1.49 amu A2 is problematic. Perhaps the complex is slightly nonplanar or the out-of-plane van der Waals bend is a very large amplitude motion'* or the consequences of centrifugal distortion have been underestimated. Figure 2 shows the coordinates of the subunits in the complex. The angle O2 which is not shown arises from zempoint vibrations and is the angle between the NCCN subunit bonded through its N atom and the a axis. Clearly two angles and a distance cannot be fit with two moments of inertia. However, a nearly centrosymmetric structure can be ruled out by the large dipole moment observed. Assuming the negative inertial defect results from vibrational motion of a planar system, the moments of inertia of the dimer can be related to that of the monomer as follows: I,, = Io sin2 O1 + Io sin2 e2
+ IO COS2 02 + WRcm2 = 210 + pR,,'
= IO COS2 81
(4)
where Io is the moment of inertia of NCCN. The third of these equations allows an R,, of 4.987 (1) A to be extracted directly from the C rotational constant, while the first gives one polar angle as a function of the second. The negative inertial defect suggests that the NCCN subunit that is bonded through its N atom has larger amplitude motions than the other subunit, a surprising passibility in light of the tunneling motion observed in (HCCH),.13 We suggest an equilibrium structure where the subunit bonded (19) Huang, Z. S.;Miller,
~
R. E. J . Chem. Phys. 1988.89. 5408.
+ Vg(l -COS
8a)/2
+ ...
(6)
where p is the angular momentum conjugate to the internal coordinate a, and F = h2/(410) is inversely proportional to the reduced moment of inertia for the internal rotation. Here the potential expansion was truncated after the first term, and the basis functions used were those for free internal rotation (e""). For high barriers terms up to m = 55 had to be included. As a first approximation, assume that the potential between the two subunits is spherical, as has been pastulated for HCCH." The best measurement of the NCCN quadrupole moment to date is -6.2 (4) D derived from the spectral moments of collision-induced far-infrared and microwave spectra. The only high-level calculations on the ground electronic state are by McLean and Yoshimine (Hartree-Fock method), who calculate a quadrupole moment of -9.1 D A.21 Since quadrupole moments derived from collision-induced spectra can be unreliable, the value of Yoshimine and McLean will be used throughout this communication. An electrostatic model of the barrier for two point quadrupoles predicts V, = 9Q2/ 16RS,giving a potential barrier of 76.1 cm-'. Diagonalizing eq 5 one obtains an inversion frequency of 1.66 kHz and calculates the lowest excited bending vibration of E symmetry to be about 13.17 cm-I above the ground state. An inversion frequency this low would not be observable. The same calculation with the measured quadrupole moment cited above gives an inversion frequency 600 times larger, demonstrating the tremendous sensitivity of the tunneling frequency to the barrier height. Considering both the validity of the one-dimensional tunneling model and of the point-quadrupole interaction, the inversion frequency is not expected to be accurately predicted. If the inversion frequency is big enough to be resolved, we should see rotation-inversion transitions in the K p = 1 stack split from the pure rotation transitions by the inversion frequency plus the difference in A constants between the AI+and BI+tunneling states. The difference in A values will become vanishingly small for slow tunneling. If the nuclear quadrupole coupling is larger than the inversion splitting, the effects on the spectrum are interesting. The inversion motion will interchange the two pairs of nitrogen quadrupoles, so that for some nuclear spin states the energies of the two adjacent tunneling minima will be different. In this case the 2 X 2 matrix for the tunneling motion will have diagonal matrix elements resulting from the quadrupole exchange that are larger than the off-diagonal elements resulting from inversion. This would result in partial quenching of the tunneling motion. We have neither direct spectroscopic evidence of tunneling nor indirect evidence through narrowing of spectral lines. (20) Dagg, I. R.; Anderson, A.;
~~
(5)
Here
TABLE VII: Best Vibrationally Averaged Structural Constants of NH3-NCCN Ground State x = 23 (2)" RNX 3.1 17 (17) A 4 = 4.9 ( 1 0 ) O pid 0.61 (3) D Rcm= 3.129 (17) A
I,,
3.084 (1) A 0.420 (5) D
through its C atoms is relatively fixed and the subunit bonded through its N atom vibrates in a wide amplitude motion. If one uses I,, this corresponds to Ol = 90' and O2 = 13.9' in Figure 2. Table VI11 summaries the best structural parameters. In actuality both NCCN subunits are undergoing zero-point oscillations, so the angles given in Table VIII are only an estimate consistent with both the rotational constants and the dipole moment. The study of wide amplitude motions in van der Waals complexes is a subject of particular importance. We have searched unsuccessfully for evidence of tunneling between different equivalent T-shaped configurations such as that observed by Fraser et al. in (HCCH)2.13Following Fraser the usual Hamiltonian for 4-fold one-dimensional internal rotation is
C
Ibb
RNX pind =
Yan, S.;Smith, W.; J o s h , C. G.; Read,
L.A. A. Con. J. Phys. 1986, 64, 1475. (21) McLean,
A. D.: Yoshimine, M. IBM J . Res. Den, Suppl. 1%7.
Structural Characterization of NH3-NCCN and (NCCN),
The Journal of Physical Chemistry, Vol. 95, No. 7, 1991 2863
an angle of 57.43O between the subunits and the line connecting the centers of mass. The separation taken for the C, geometry will be the (HCCH), bond length plus the difference in van der Waals radii between hydrogen and nitrogen. This yields a value of R,, = 5.031 A. If we use eq 7 and the theoretical value of the quadrupole moment, the C , structure is stabilized 1025.3 cm-I and the C , structure, 388.0 cm-’. The point quadrupole model predicts that the c2h structure is 637.3 cm-* more stable than the TABLE X Comparison of the Structural Parameters of C , one. Homomolecular Dimers A simple improvement on this model is to take NCCN as an extended quadrupole and posit an equal amount of charge concentrated on each atom. Using the theoretical quadrupole mo- .. (NCCN); RNx = 3.20 3.2 0.42 ment, one obtains a stabilization of 406.3 cm-l for the T-shaped (CO,), R C =~3.15 3.1 0.00 structure. The slipped parallel structure now has its energy minimum when the two subunits overlap about 0.50 A less than Discussion the overlap that forms a rectangle between two C and two N The complexes of NCCN are interesting to compare with atoms. The stabilization at that point is 449.7 cm-I, so this simple complexes of CO, and HCCH, since all three have a quadrupole model predicts that the Cu structure is only 43.4 cm-’more stable moment as their first nonvanishing electrostatic multipole. All than the C , structure. The difference between this result and three molecules have been studied in complexes with NH3,16.22 that employing point quadrupoles is that extended quadrupoles all form T-shaped complexes, and the NCCN and CO, complexes include repulsive interactions that are bigger in the c2h structure exhibit nearly free internal rotation of the NH3 subunit. N, structure. This simple model of NCCN already than in the C H,-N,O has a 3-fold rather than a 6-fold barrier, so one would suggests that the question of which orientation is stablest is a subtle not expect free internal rotation. Table IX summarizes the one. Indeed, some preliminary calculations done in collaboration comparisons between the three complexes. Following Buckingham with Dr. Brian Howard indicate that the full multipole moment and Fowler, the van der Waals radii are taken from P a ~ l i n g . ~ ’ - ~ ~expansion predicts the C , structure to be slightly lower in energy Bond strength trends are consistent only for NH3-N20, which than the C,,. As discussed by Muenter* for CO, and HCCH the has the lowest induced dipole moment and a bond length longer structure of dimers of linear nonpolar molecules is delicately than the sum of the van der Waals radii. The bond length in balanced by electrostatic plus semiempirical dispersion models. NH3-CO2 is shorter than NH3-NCCN and is difficult to raThe barrier height between the nonpolar C,, and the polar C, tionalize given the much larger dipole moment of the NH3-NCCN form of (NCCN)2 is not known and is unlikely to be observable complex. Both NH3-NCCN and NH3-C02 have bond lengths unless it is lower than in (HCCH),. shorter than the sum of the van der Waals radii. The contradictory The crystal structure of NCCNZ6 is orthorhombic with a trends in dipole moments, bond lengths, and bending amplitudes nearest-neighbor N-C distance of 3.181 A and an angle of 80.8’ illustrated in Table IX demonstrate that simple ideas about the between these two molecules. If one uses the structure suggested relationships of these quantities with bond strengths fail. in Table VIII, the gas-phase dimer of NCCN has a nearestThe bond lengths and dipole moments of (HCCH)2,12,13 (Cneighbor N - C distance of 3.206 A and an angle of 86.1O between 02)2,11 and (NCCN)2 are tabulated in Table X. All three the two subunits. Since the two NCCN molecules in the crystal complexes have bond lengths about equal to the sum of their van do not lie in the same plane, comparison of the angles in the der Waals radii. Interestingly, in two other series (Ar and NH3) gas-phase dimer and crystal is not valid, but the nearest-neighbor where C , complexes have been studied with HCCH, NCCN, and N-C separations agree to within 0.025 A. Due to the near C02, the CO, complex has the shortest bond length relative to certainty of large-amplitude motions in the gas-phase dimer and the van der Waals radii. This does not hold for the dimers of the possibility of large-amplitude motions in the crystal, this HCCH, NCCN, and CO,. agreement may be fortuitous. Both (HCCH), and (CO,), have been studied extensively. The The large dipole moments of both NH3-NCCN and (NCCN), theoretical calculations published on these two systems prior to may result from the large polarizability of NCCN,,’ all = 7.76 definitive structural determination were not in agreement on which cm3 and aI = 3.64 cm3. Barton and co-workers2*calculated the form was stablest; indeed some suggested that the two forms had first-order dipole moment of hypothetical T-shaped (CO,), using similar energies. We are aware of no theoretical calculations to purely quadrupolar interactions in order to explain their inability date on (NCCN), but are presently collaborating with Dr. B. J. to deflect (CO,), in a molecular beam. They usedz9 Howard to model the system electrostatically. The lowest order (8) Pind = 3 Q W . L + )l l..!! term in the multipole expansion of the electrostatic energy of (NCCN)2 is the quadrupole-quadrupole energy. The following This formalism gave a first-order dipole moment of 0.18 D, which simple relationship has been given for the energy between two point was subsequently refined to about 0.32 D by SCF calculations quadrupoles at various orientationsz5 to include HOMO-LUMO charge transfer. Equation 8 predicts a value of 0.34 D for NCCN, using the best theoretical value for va = Y~Q~R-S(I- 5 COS^ e, - 5 COS^ e, + 17 COS, e, COS, el + the quadrupole moment of -9.1 D A. The dipole moment of 2 sin2 8 , sin2 8, - 16 sin 8 , cos 0, sin e2 cos e,) (7) NH3-NCCN also appears likely to be accounted for in terms of It is interesting to compare the relative energy of the Czhand C , the moment induced in NCCN by the dipole moment of NH, and structures predicted by this simple model. The separation taken the moment induced in NH3 by the quadruple moment of for the C,, geometry will be that observed in (C02),10*11 plus the NCCN. [Note that the polarizability of NH3 is 50%greater than difference in van der Waals radii between nitrogen and oxygen. that of Ar while the separation in the NH3-NCCN complex is This yields a parallel distance of 3.24 A between the two NCCN 25% shorter than that in Ar-NCCN, which would produce an units. The quadrupole energy is minimized when the two subunits induced moment near 0.3 D on the NH3 subunit.] We are heoverlap by 0.47 A more than the overlap that puts two C and two sistant to indicate a numerical estimate based on point multipole N atoms in a rectangle. This corresponds to R,, = 3.845 A and interactions in view of the poor energy predictions seen in (NCTABLE I X Comparison of the Structural Parameters of T-Shaped NH3 Complexes fiindr D RN-B,A Rw~wA x 3.0 N H3-N20 0.21 3.09 NHI-COI 0.41 2.99 3.2 22.1 0.61 3.12 3.2 23 NHrNCCN
(22) Fraser, G. T.; Nelson, D. D., Jr.; Gerfen, G. J.; Klemperer, W. J . Chem. Phys. 1985,83, 5442. (23) Buckingham, A. D.; Fowler, P. W. J . Chem. Phys. 1983, 79,6426. (24) Pauling, L. The Nature of rhe Chemical Bond, 3rd ed.; Cornel1 University Press: Ithaca, NY, 1960; pp 256-264. (25) Buckingham, A. D. Adu. Chem. Phys. 1967, 12, 107.
(26) Parkes, A. S.; Hughes, R. E. Acta Crystallogr. 1963, 16, 734. (27) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory oj Gasses and Liquids; John Wiley and Sons: New York, 1964. ( 2 8 ) Barton, A. E.; Chablo, A.: Howard, B. J. Chem. Phys. Lett. 1979,60, 414. (29) Buckingham, A. D.; Pople, J. A. T r a m Faraday Soc. 1955,51, 1029.
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CN)z. It does not appear necessary to postulate an appreciable geometric distortion of the NCCN molecule to reasonably account for the large induced moment. It is noteworthy that NCCN possesses a very low lying ru* orbital and suggests that a molecular orbital picture of NCCN complexes may be insightful. The lowest lying A-r* electronic transition in NCCN involves an excited state 33 290 cm-l above The lowest lying electronic states in H C N the ground and CH,CN are at 52 260 and 55 000 cm-I, respectively.32 The overlap of the two neighboring C N .rr* orbitals apparently produces a much lower energy molecular orbital, 2ru*. This orbital is of the proper symmetry to interact with the lone pair on the N atom of either NH, or NCCN. This picture is consistent with the molecular orbital picture that emerges from the calculations of McLean and Yoshimine.zl We hope in the near future to examine the geometry of the H20-NCCN complex to compare the structure and internal rotation to that of the H20-C02 system. The weak complexes of NCCN belie our original idea that NCCN chemistry would be analogous to that of HCN without (30) Woo, S.C.; Liu, T. K. J . Chem. Phys. 1937, 5, 161. (31) Callomon, J. H.; Davey, A. B. Proc. Phys. SOC.,London 1963, 82, 335. (32) Herzberg, G. Molecular Spectra and Molecular Structure; D. Van Nostrand: New York, 1966; Vol. Ill, pp 588, 631.
the H end. The central carbons are active, and NCCN complexes that do interact on the nitrogen end are much less tightly bound than the corresponding HCN and NH3 complexes. The N-F bond distance in HF-NH3, HF-NCH, and HF-NCCN are 2.70,2.805, and 2.863 A, re~pectively.~~ Clearly the nitrogen lone pair is much less active on a nitrogen atom that is sp hybridized than one that is sp3 hybridized. What is surprising is that the bond distance is so much longer (0.06 A) in HF-NCCN than in HF-NCH. One might argue that the short HF-NCH bond length results from strong dipole-dipole coupling absent in HF-NCCN. However, electrostatic models consistently show that one cannot make bonding arguments from only the lowest order multipole. The molecular orbital picture developed by McLean and Yoshimine may hold a clue to the comparatively weak bond in HF-NCCN. One of the nonbonding lone pairs occupies a Q orbital that is composed mainly of s and p orbitals from the two interior carbons. Thus, the lone pairs may be less accessible in NCCN than in HCN. Acknowledgment. This work was supported by the National Science Foundation. (33) Novick, S. E.;Leopold, K. R.; Klemperer, W. In Atomic and Molecular Clusters; Bernstein, E. R., Ed.; Elsevier: New York, 1990 pp 359-391.
State-Resolved Vibrational-Energy-Transfer Channels from S, 0' p-Dlfluorobenzene in Collision with He and Ar David L. Catlett, Jr.? and Charles S. Parmenter* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: October 8, 1990) State-testate vibrational energy transfer (VET) from the zero-point level of SIp-difluorobenzene (pDFB) vapor at 300 K has been studied for single collisions with He and Ar. As Seen in other polyatomic VET studies, high selectivity occurs among possible channels in this 30-mode molecule. The competition among VET channels has a marked dependence on collision partner. Large absolute rate constants are measured for total VET from the Oo level and for the dominant state-to-state channels. The total VET rate constant is 1.6 X IO6 Torr-l s-I for He and 1.8 X IO6 T o w 1s-' for Ar, roughly one-fifth hard 0 119 cm-I sphere for each. The transfer channels involve quantum changes in only the two lowest frequency modes, ~ 3 = and us = 173 cm-l. The channel Oo 30' dominates VET for each gas. With Ar collisions, for which five channels have been measured, it accounts for about 90% of the transfer. With He, it is 60% of the transfer, competing with the Oo 8l channel that has about 30%. The absolute rate constants for the two He + pDFB channels are within a factor of 2 of values calculated by Clary using three-dimensional quantal scattering theory. A treatment of the SSH-T model accounts well for the competition between VET channels as well as for the differences between collision partners. The account is in the familiar form of propensity rules, similar to those developed earlier for VET in SI benzene, aniline, and pyrazine.
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Introduction Collisional vibrational energy transfer (VET) in polyatomics remains along the central problems of chemical physics. The fact that one of the earliest applications of lasers to chemical physics involved state-resolved VET studies attests to its venerable nature.l Recent applications of new laser techniques underscore the persistent interest.2 One of the most productive routes to the study of VET is based on the optical pump-dispersed fluorescence approach so long used for diatomics in 300 K thermal systems? When practical tunable UV pumps were developed,4 the method became suitable also for polyatomics. Its first application, involving the 30-mode molecule b e n ~ e n e showed ,~ immediately the advance in VET resolution provided by the method. From an initial level selected among several possibilities, one could obtain absolute state-testate cross sections for every important VET channel. The VET flow pattern *To whom correspondence should be addressed. 'Present address: Texas Instruments, Inc., 13353 Floyd Road, P.O. Box 655012. Mail Stop 374, Dallas, TX 75265.
0022-365419112095-2864$02.50/0
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is defined by this set of rate constants. If the constants are normalized among themselves, one obtains the branching ratios (1) (a) Yardley, J. T.; Moore, C. B. J . Chem. Phys. 1966,45, 1066. (b) Hocker, L.0.;Kovan, M. A.; Rhodes, C. K.; Flynn, G. W.; Javan, A. Phys. Rev. Lett. 1966, 17, 233. (2) (a) Hetzler, J.; Millot, G.; Steinfeld, J. I. J . Chem. Phys. 1989, 90, 5434. (b) Zhu, L.; Hershberger. J. F.; Flynn, G. W . J. Chem. Phys. 1990, 92, 1687. (3) The method had its genesis with I,: Wood, R. W. Philos. Mag. (Ser. 6) 1911,21, 309. Franck, J.; Wood,R. W. Philos. Mag. (Ser. 6 ) 1911,21, 314; Yerh. Dtsch. Phys. Ges. 1911, 13, 78. I2 has also played a prominent role in the continuing evolution of the technique: Steinfeld, J. I. J. Phys. Chem. Ref. Data 1984, 13, 445. Krajnovich, D. J.; Butz, K. W.; Du, H.; Parmenter, C. S.J . Chem. Phys. 1989, 92, 7705. (4) Two types of pump capable of exciting SI single vibronic levels (SVL) were required. Tunable CW sources led to SVL fluorescence spectra containing the level population information needed for VET: Parmenter, C. s.; Schuyler, M. W. Transiiions Non Radiar. Mol., Reun. Soc. Chim. Phys., 2Orh, 1969 1970.29 ( J . Chim. Phys. Suppl. 1%9-70). Tunable nanosecond sources provided the SVL fluorescence lifetimes needed for conversion of relative to absolute rate constants: Gelbart, W. M.; Freed, K.F.; Jortner, J.; Rice, S.A. Chem. Phys. Lett. 1970, 6, 345. Ware, W. R. In Creation and Electron of the Excited Stare; Lamola, A. A., Ed.; Marcel Dekker: New York, 1971.
0 1991 American Chemical Society
