Microwave spectrum of the quasilinear molecule, cyanogen isothiocyanate (NCNCS)

IOURNAL

OF MOLECULAR

SPECTROSCOPY

113, l-20 (1985)

Microwave Spectrum of the Quasilinear Molecule, Cyanogen lsothiocyanate (NCNCS) MICHAEL

A. KING, *,I HAROLD

W. KROTO,*

AND

B. M. LANDSBERG,~~

*School of Chemistry and Molecular Sciences, University of Sussex, Falmer, Brighton BNl 9QJ. and tSchoo1 of Physical and Molecular Sciences, University College of North Wales, Bangor, Gwynedd LLS 7 ZUW, U. K.

The R-branch rotational spectrum of cyanogen isothiocyanate, NCNCS, produced by thermal isomerization of sulfur dicyanide, S(CNb, has been measured between 26.5 and 40.0 GHz. The molecule shows archetypal quasilinear dynamic behavior in that the rotational satellite spectroscopic patterns for the low bending vibrational states, which lie below the barrier to linearity, are characteristic of a bent asymmetric top species and as vibrational excitation increases and states lie closer to or above the barrier the patterns gradually correlate with linear characteristic patterns. The spectrum, which consists of four transitions (J = 8 to 1I), has been analyzed by treating the molecule as linear with one large amplitude, bending mode, Y.I;the observed rotational constants were expanded in terms of the expectation values of even powers of the large-amplitude coordinate and various empirical constants determined. The inclusion of a small term in the vibrational Hamiltonian which accounts for the variation of reduced mass with bending coordinate has been found to be important. Relative intensity measurements indicate a barrier to linearity of 308 k 34 cm-’ and a vibrational spacing (in the bent limit) of 97 f I 1 cm-‘. The dipole moment, as determined from the u, = 3, I = 3 state, is 3.163(8) Debye. o 1985 Academic PWSS, IX. INTRODUCTION

During a program of spectroscopic studies investigating pyrolysis reactions (I) it was discovered that sulfur dicyanide, S(CN)I, thermally rearranges to cyanogen isothiocyanate, NCNCS, at a temperature of ca. 850°C (2). A subsequent He(I) photoelectron study of this system (3) gave a more quantitative picture of this and the other processes taking place and, in particular, enabled the optimum conditions for NCNCS production to be determined. Given this information it was possible to obtain excellent microwave spectra of NCNCS which facilitated a detailed analysis of the unusually complex, though tractable rotation-vibration patterns associated with the dynamics of this flexible molecule. The patterns showed distinct qualitative departures from those normally associated with semirigid molecules (4). Furthermore, it was found that the standard (semirigid) asymmetric rotor treatment, including centrifugal distortion corrections up to and including terms in (J6), was inappropriate for describing the observed spectrum quantitatively. These results were not unexpected since both isocyanates and isothiocyanates are known to have rather flexible X-N=C angles. The associated bending mode is usually

’ Present address: I.C.I. New Science Group, P.O. Box 90, Wilton, Middlesborough TS6 8JE, U. K ’ Present address: 24 Larch Grove, Bletchley, Milton Keynes MK2 2LL, U. K. 1

0022-2852185 $3.00 Copyright 0

1985 by Academic Rsss, Inc.

All rights of reproduction in any form reserved.

2

KING, KROTO, AND LANDSBERG

low in frequency and also highly anharmonic. In isocyanates and related compounds the XNC angle has been found to vary over a large range according to the identity of the ligand X, and is generally difficult to determine reliably (4). In fact, the physical significance of the angle cannot be simply defined since even in the ground vibrational state complex motion is involved owing to the complex form of the potential surface associated with this coordinate. EXPERIMENTAL

DETAILS

The photoelectron study of the S(CN)2 - NCNCS isomerization conditions (3) suggested modification of those under which the reaction was originally discovered (2). Subsequently, the best microwave spectra of NCNCS were obtained when S(CNb vapor was flowed at a pressure of lo-50 mTorr through a quartz tube (0.8 cm id) heated to ca. 650°C along 15 cm of its length. The resulting pyrolysis products were passed via a U-tube held at -45°C directly into the cell of the microwave spectrometer. The trap effectively removed parent S(CN)z and other less-volatile constituents, and thus enabled very clean spectra of NCNCS to be obtained. The spectrometer was a Hewlett-Packard HP8460A Stark spectrometer modulated at 33.3 kHz and operating between 26.5 and 40 GHz. Frequency and relative intensity measurements were made at room temperature with sample pressures of ca. 10 mTorr. For the dipole moment determination, the Stark cell was calibrated using OCS, assuming a value of pots = 0.7 15 19 Debye (5). The accuracy of the measurements is considered to be kO.02 MHz for zero-field transitions and kO.05 MHz for Stark lobes. PRELIMINARY

SPECTROSCOPIC ANALYSIS

The spectrum of NCNCS consists of four equidistantly spaced bunches of lines between 26.5 and 40.0 GHz (Fig. 1) which are readily assignable to R-branch transitions with J = 8 to 11 (28 - 3.2 GHz). A preliminary analysis, assuming that the molecule can be treated as a slightly asymmetric prolate rotor, may be carried out with the aid of the Stark modulation study which is shown for the J = 12 - 11 transition in Figs. 2a-c. This enables the KA = 0 and 1 lines to be identified due to their “slow” secondorder Stark effects. At a field of 500 V/cm (Fig. 2b), the KA = 0 lines are not modulated and the intensities of the KA = 1 lines are reduced by a factor of three, compared with those in the 2000 V/cm spectrum (Fig. 2a). At 100 V/cm (Fig. 2c), these also disappear and the simplified spectrum shows only lines with KA> 1 which are subject to “faster,” predominantly first-order Stark effects. The KA = 2 lines are readily assignable because of their small asymmetry splitting, which is roughly two orders of magnitude less than that of the KA = 1 doublet. As expected, lines with & > 2 show no splitting under the available resolution. A least-squares analysis based on ground-state transition frequencies with J = 81 1 and KA = O-2 (Table I), using a standard semirigid asymmetric rotor Hamiltonian with centrifugal distortion terms up to (J6), yields the constants & = 1628.073( 13) MHz, Co = 1599.353( 13) MHz, A, = 0.400(44) kHz, AJK = -1016.6(71) kHz, and Hm = -28.3( 16) kHz (Table II). A0 was tied at 94.0 GHz and the nine other centrifugal distortion constants were constrained to zero. To show that the observed B. and Co

MICROWAVE SPECTRUM OF NCNCS

$ II

i

4

-

-

-l

L t

4

-

XI%

3

KING, KROTO, AND LANDSBERG

_

3

MICROWAVE

SPECTRUM

OF NCNCS

TABLE I

Ground State Transition Frequencies (MHz) and Rotational Constants for NCNCS Transition

C&C.

ohs.

C-C

909-808

29 044.84

29 044.86

-0.02

919-818

28 933.94

29 934.02

-0.08

918-817

29 192.58

29 192.50

0.08

928-827

29 110.60

0.41

29 111.40

-0.39

29 111.01 927-826

10 010

-

9 0 9

32 271.55

32 271.55

0.00

10 110

-

9 1 9

32 148.51

32 148.55

-0.04

I.019

- 918

32 435.80

32 435.76

0.04

32 345.02

32 344.77

0.25

10 2 9-

9 2 8

-LO 2 8-

9 2 7

32 345.63

32.345.87

-0.24

11 0 11 - 10 0 10

35 498.08

35 498.08

0.00

11 1 11 - 10 1 10

35 362.99

35 362.98

0.01

11 1 10 - 10 1

9

35 678.89

35 678.90

-0.01

11 2 10 - 10 2 9

35 578.98

35.578.84

0.14

11 2 9 -10

35 580.17

35 580.31

-0.14

2 8

12 0 12 - 11 0 11

38 124.45

38 724.43

0.02

12 1 12 - 11 1 11

38 577.35

38 577.27

0.08

12 1 11 - 11 1 10

38 921.84

38 921.92

-0.08

12 2 11 - 11 2 10

38 812.91

38 812.78

0.13

12 2 10 - 11 2 9

38 814.54

38 814.69

-0.15

Notation J' K' K' -

J"

K”

K"

TABLE 11 Derived Constants Ao

94000a

MHZ

Bo

1628.073(13)

MHZ

Co

1599.353(13)

MHZ

0.400(44)

AJ c. JK H

KJ

kHz

-1016.6(71)

kHz

-28.3(16)

kHz

a constrainedvalue.

6

KING, KROTO, AND LANDSBERG

values are consistent with the spectrum being that of NCNCS, rigid rotor constants were calculated for comparison. Transferring the C=N and N-C bond distances from NCNJ (6), the N=C and C=S distances from HNCS (7), and constraining LNCN and LNCS to 180”, with LCNC = 150”, gives B = 1623 MHz and C = 1597 MHz. The good agreement between observed and calculated values essentially confirms that the carrier is NCNCS and was the original means of identification (2). Further analysis of the spectrum using the semirigid rotor approximation is precluded because departures from the expected spectroscopic patterns become serious as KA increases. Predictions based on the derived constants are not reliable and when trial assignments are tested they lead to large variances in the fits. Attempts to analyze the vibrational satellite structure (associated with excitation of the lowest frequency bending vibration, vg) are also very unsatisfactory. The anomalous behavior can be seen semiquantitatively in Figs. 3a-d, where survey scans of the J = 8, 9, 10, and 11 transitions are shown. Two main effects can be identified: (a) Lines with KA > 1 do not bunch close to the KA = 0 transition as they do in general for near-prolate semirigid systems, but march out rapidly to high frequency. This behavior is responsible for the anomalously large values of the derived centrifugal distortion constants, AJK= - 1017 kHz and Hu = -28 kHz, which in this case have little physical significance. (b) For “well behaved” (i.e., semirigid) nearprolate rotors, the vibrational satellites tend to form evenly spaced sequences in vibrational quantum number such that the characteristic ground state pattern is repeated at regular intervals (4). This is not the case for NCNCS, where the satellite sequences show variations in spacing which lead to variations in satellite group pattern (Fig. 3). The deviations from the standard semirigid rotor behavior are due to the highly anharmonic, large amplitude-bending vibration of NCNCS which causes the rotational constants to exhibit anomalous vibrational dependences. In order to explain quantitatively the rotational spectrum it was necessary to consider the form of large-amplitude motion explicity since the usual semirigid perturbation approach breaks down, as discussed above. ANHARMONIC

THEORY

The model used to make a detailed analysis of the microwave spectrum of NCNCS is based on the two-dimensional anharmonic oscillator method of Duckett et al., first applied to the rotation and rotation-vibration data of HCNO (8). In this approach, molecules are treated as linear with one large amplitude bending vibration (v7 in the case of NCNCS). For HCNO (8), the bending motion was modeled by the Hamiltonian Hvib = Pi/2ms + A02 + B84,

(1)

where 8 = [19:+ 0:]“2 is the displacement from the linear configuration (in radians); Pi = Pix + P&with Ps, = -ih(d/tM,) etc.; me is a reduced mass (assumed independent of 0); and A and B are potential constants. After dealing with the vibrational problem, the dimensionless coordinate q = [qz -t q:]“2 = [mo-y(@+ O;)]“‘, with y = 27~0, was chosen to reduce the Hamiltonian, which becomes Hvib/hc = flop’ + aq2 + bq4.

(2)

MlCROWAVE

OF NCNCS

$I

7 m 0

z

C

Z

-3

SPECTRUM

-

G

-i

_

a ::

:

%! C C m

-

II

8

KING,

KROTO,

AND

LANDSBERG

The constant v. is a scale factor taken to be equal to the first interval in the largeamplitude vibration, G( 1, 1) - G(0, 0),3 and pX = -i(d/dq,), etc. The Hamiltonian Equation (2) was diagonalized using a truncated basis of two-dimensional harmonic oscillator functions ]vZ) and the expectation values of q* calculated from the anharmanic wavefunctions ]iY,) = C c&Z). The observed rotational constants were then expanded as Bar = Bt - a(511q21i$ (3) where B$ is the rotational constant of the hypothetical linear configuration corrected for the contribution of the large-amplitude motion, but averaged over the other vibrations. The form of the Hamiltonian, Equation (2), is not particularly appropriate for dealing with the NCNCS rotational data since the parameter (Yin Equation (3) is dependent upon the value of v. chosen for the reduction and may only be determined accurately if vibrational data is available. In order to overcome the influence of the scale factor on the results, the reduction described by Malloy (9) was chosen for this work. It was also found desirable to include a small correction term to take account of the variation of reduced mass with bending coordinate. The modified Hamiltonian used is Hvib

=

$g(p)Pg

+

v2P2

+

(4)

v4P4,

where p = [pz + pi]“* is a generalized bending coordinate; P, = [P& + P$]“2, with Pox = -ih (tJ/dp,) and Ppy= - ih @/dp,); and g(p) is the G-matrix element corresponding to the large-amplitude motion. The latter may be expanded as g(p) = go +

82P2

+ 84P4

+ * * - *

(5)

Substituting the first two terms into Equation (4) yields Hvib = IgOP, + fg2P,p2Pp + v@* +

v4p4.

(6)

On transforming to the dimensionless coordinate q = (2V4/goh2)1’6p, the Hamiltonian becomes Hvib = hCl’o[p* + bpq2p + Uq* + q4], (7) where q = [qz + qz] ‘I2 and p = rp’ + pz] ‘I*, with px = -i(d@q,) and py = -i(d/dq,J. The constant a = V2(2/goh2)1/3( V4)-*j3 determines the shape of the potential curve, and b = g2(h/go)2’3(2V4)-“3 represents the variation of the reciprocal reduced mass with q2. v. = (goh2/2)2/3( V4)‘j3 is a scale parameter which may only be determined if vibrational energy level spacings are known. Note that the eigenvectors of Equation (7) do not depend on the value of v. [cf. Eq. (2)]. The Hamiltonian matrix for each value of 1 was set up in a truncated basis set of harmonic oscillator functions and diagonalized. The basis functions are defined by (p’ + yq2)ln) = (2n + l)y”21n).

(8)

The size of basis set required depends critically on the value of the parameter y. For NCNCS, a value of 16 ensures that only 35 functions are needed to adequately represent 3 Notation G(v, I).

1

NCNCS

11

10

J = 1241

9

39 8

fJ

6

7

8

FIG. 4. Survey scan of the J =

10 __

and u-, - 6.

LO 0

9

7

39 6

6

I

8

12- 1I transition

9

5

I

of NCNCS

39 ‘

6

5

L

I

39 2

5

I

I

3

at 2000 V/cm showing

6

L

5

‘

3

I

3

I

I

0

0

I

386

le

of the four sets of transitions

38.6

2

2

1'

II

II

1'

II

2

If 3

1'

assignments

39 0

L

I

2

I

1e

II

le

0

I

38 L

with 1 = UT, UT-

le

GHz

I/l= Y

l/l= v-2

I/l= v-L

11,=v-6

2, VT~ 4,

0

W

10

KING, KROTO, AND LANDSBERG TABLE III Line Frequencies, Assignments, and Effective Rotational Constants for NCNCS (MHz) 1

v7

J=8

J=9

J = 10

J = 11

B

D X103

0

0

1

le 28933.94 32148.51 35362.99 38577.35 1607.5073(3) 0.408(l)

1

If 29192.58 32435.80 35678.89 389i1.84 1621.8958U)

2

2f

29044.84 32271.55 35498.08 38724.45 1613.7100(5) 0.664(2)

0.529(4)

32345.02 35578.98 38812.91 29111.01

1617.3295(4) 0.316(2)

2

2e

3

3

29177.76

32419.47 35661.08 38902.62 1621.0436(6) 0.352(2)

4

4

29256.65

32507.16 35757.55 39007.85 1625.4253(13) 0.340(S)

5

5

29342.89

32602.93 35862.90 39122.78 1630.2175(6) 0.353(2)

6

6

29433.48

32703.59 35973.64 39243.59 1635.2489(6) 0.345(3)

7

7

29526.72

32807.19 36087.60 39367.89 1640.4299(15) 0.351(6)

8

8

29621.58 32912.53 36203.45 39494.29 1645.7025(25) 0.374UO)

9

9

32345.63 35580.17 38814.54

33019.42 36320.67 39621.89 1651.1024(78) 0.664(31)

10 10

36437.93 39750.06 1656.35

0.35

11 11

39878.50 1661.71

0.35

2

0

28981.99 32201.72 35421.31 38640.75 1610.2119(8) 0.628(3)

3

le 28900.37

3

If 29159.01 32398.51 35637.87 3887'7.08 1620.0313(7) 0.531(3)

4

2f

32111.21 35321.97 38532.60 1605.6416(6) 0.404(2)

35588.27 38823.08 29118.44 32353.58

1617.7449(g) 0.332(4)

4

2e

35588.95 38824.10

5

3

29219.84 32466.20 35712.51 38958.71 1623.3812(g) 0.353(4)

6

4

29324.87

7

5

29430.50 32700.29 35969.99 39239.62 1635.0837(6) O-346(2)

32582.94 35840.93 39098.83 1629.2129(l) 0.330(l)

8

6

29535.62 32817.09 36098.49 39379.79 1640.9231(3) 0.34211)

9

7

29639.93 32932.96 36225.93 39518.85 16%.7179(20) 0.346(8)

10

8

33047.84 36352.28 39656.62 1652.4667(l) 0.373(O)

11

9

36477.53 39793.23 1658.15

o.3sa

12 10

39928.66 1663.79

0.35*

4

0

5

le 28872.00 32079.74 35287.38 38494.94 1604.0571(4) 0.352(2)

5

If 29131.35 32367.80 35604.16 38840.37 1618.4846(7) 0.471(3)

6

2f

6

2e

28843.92

32048.35 35252.63 38456.73 1602.5386(8) 0.606(3)

29154.16 32393.25 35632.25 38871.19 1619.7302(8) 0.339(3)

a

Constrainedvalue.

MICROWAVE

SPECTRUM

11

OF NCNCS

TABLE III-Continued

J=E

J=9

J = 10

J = 11

v7

1

7

3

29291.80 32546.20 35800.50 39054.72 1627.3770(5) 0.337(2)

8

4

29419.23 32687.82 35956.29 39224.67 1634.4552(15) 0.325(6)

B

D

X103

9

5

29539.85 32821.76 36103.64 39385.44 1641.1559(19) 0.334(8)

10

6

29655.54 32950.36 36245.09 39539.74 1647.5828(3) 0.325(l)

11

7

33074.93 36382.12 39689.22 1653.8125(2) 0.330(l)

12

8

13

9

6

0

36515.81 39835.07

1659.90

0.35

39977.97 1665.85

0.35

28155.78 31950.67 35145.46 38340.22 1597.5877(11) 0.274(4)

7

le 28916.37

7

If 29189.53 32432.59 35615.54 38918.42 1621.6926(g) 0.318(4)

32129.12 35341.83 38554.41 1606.5016(4) 0.227(2)

8

2f

35744.37

38994.14

29246.13 32495.44

1624.793(22) 0.099(94)

8

2e

35744.90 38994.90

9

3

29403.09 32669.84 35936.51 39203.09 1633.5601(l) 0.340(O)

10

4

29542.11

11

5

29670.59 32967.05 36263.43 39559.77 1648.4197(16) 0.335(7)

32824.32 36106.46 39388.49 1641.2815(6) 0.327(3)

12

6

33102.06 36411.94 39721.73 1655.1732(2) 0.351(6)

13

7

36554.45 39877.20 1661.65

0.35

anharmonic states up to v7 = 13. The eigenfunctions of Equation (7) 1%) were then used to calculate the expectation values of even powers of q and the rotational constants expanded as &I = B8 - “,(q2) + y,(q4) + +‘), (9) where B8 is an effective equilibrium rotational constant, corrected for the effects of the large-amplitude motion but averaged over the other modes. The constants, (Ye. 77, and t7 are empirical rotation-vibration interaction terms. In order to account for l-doubling, which occurs for rotational levels with 1= 1, the following expansion was used: B,,; = B,, 5

q,(q2) + b(q4)>

where q7 and r7 are empirical Z-doubling-type constants. The I-doubled components are labeled by the value of I/( and a parity label e or f (10). ANALYSIS

Two labeling schemes may be envisaged for designating the bending-rotation levels of NCNCS. In the bent limit, the four quantum numbers vg , J, Ka, and Kc, may be used, but a more convenient scheme for the purposes of the analysis is the linear

12

KING,

KROTO,

AND LANDSBERG

molecule designation u7, J, 1, and the parity labels, e or f. Note that the quantum number I as used here is always positive and correlates with the value of 111in truly linear systems. The parity labels e and f are only needed for I = 1 or 2 for which splittings are observed. The linear and bent limit quantum numbers are related according to J-J l++K/, 217- I ++ ;vg. Note that, in particular, the linear molecule quantum number v7 is rather poor owing to the effects of anharmonicity, but it still serves as a convenient label. The transitions of NCNCS were assigned according to their Stark effects and relative intensities. The assignment was also aided by the recognition of simple patterns formed by lines with the same value of v7 - I (i.e., same vg). In all, four sets of transitions with v7 - 1 = 0, 2, 4, and 6 have been assigned. These are shown for the J = 12 11 transition in Fig. 4. The assignments of lines with 1 3 9 could be checked by the absence of analogous lines in lower-J transitions since I < J. In addition, although all the measured lines are rather broad (typically 0.75 MHz at 10 mTorr), broadening was particularly evident at higher values of 1.This is probably due to unresolved quadrupole hyperfine structure. Effective rotational constants for each v$ level were obtained by a least-squares method using the relation AE = 2B,,(J+

1) - 4D,,(J+

l)3.

(11)

In cases where only one or two frequencies were available (e.g., for the 11 ‘I J = 11 line) the value of Bvl was extracted by assuming D,, = 0.35 kHz. For pairs of transitions TABLE IV

Matrix Elements of the Operators q*, q4,q6,p’, and pq’p (nlq%l>

= (n + 1) Y -’

akpin+z>

=



= f(6n2 + 1211- 2Z2+ COY-’

* Joa-la.

Y-*

cnlq41n+2> = t2n + 4)*lq21n+2>Y -* = tJ~ullq2ln+2>Y-~ Ullqsln>

f

t[lOn’ + 30$ + 44n + 24 - 6(n + 1)Z21Y-s

ullq61n+2>

-

t(15n2 + 6On + 72 - 3Z2)ullq21n+2>Y-’

cnlq61n+4>

= 3(n + 3)ullq41n+4> Y-*

011q61n+6> = fJGTiFT.cnlq4ln+4>u-t cnlp21n>

= (II + l,Y*

cnlp2ln+2>

= -6JLTTCiG*

Ullp$pln>

= i(2n2 + 4n + 8 + 2Z2)Yo

UIIp9p ln+2> = 0 u1 lps2pln+4> =

MICROWAVE

SPECTRUM OF NCNCS

13

with I= 2, which are split as a result of second-order l-doubling, the average frequency was used. The derived effective constants are listed in Table III together with the measured transition frequencies and assignments. In order to carry out a quantitative analysis of the data, a computer program was written which simultaneously fits the parameters a, b, B8, a7, y7, c7, q7, and r7 to the observed rotational constants. The various matrix elements used in the program are listed in Table IV. The best fit to the experimental data was obtained when all eight parameters were varied (Fit 1). The derived parameters are given in Table V. These results were obtained using the 45B,, values listed in Table VI which were assigned equal weights in the fitting procedure. To illustrate the importance of the extra kinetic energy term, which allows for the variation of reduced mass with bending coordinate, the results of a fit in which the parameter b was constrained to zero are also given (Fit 2). The neglect of this small term causes the standard deviation of the fit to increase by a factor of 4.5 and several of the fitted parameters to be only poorly determined (Table V). The largest residual occurs for the & value, which yields a J = 11 frequency 59 MHz too low. In contrast, when the extra kinetic energy term is included (Fit I), the quality of

TABLE V Spectroscopic Constants of NCNC9 Fit2

Fit1

*

1528.7(11)

BO

1549.3(14) -0.8(19)

-10.26(40)

9 y7 El q7"

2.69(11)

2.91(41)

-0.145(10)

-0.055(23)

4.32(60)

-0.36(308)

0.118(26)

0.32(13)

a

-8.923(29)

-9.81(12)

b

-0.0809(22)

r7

0.211

od IId f WO

a)

o.oc 0.960

45

45

15.4t1.7

15.4t1.7

Standarddeviations in

an-1

parentheses.

b) Note that the cceff. of

is

+q, by conventian.

See also qns.(lO) and (17) in text. c) Valuz constrained to zero. d) Standard deviation of the fit. e) No. of B values included in the fit. f) v. value derivedfmintensitynm.5uremnts.

14

KING, KROTO, AND LANDSBERG TABLE VI Observed and Calculated Rotational Constants of NCNCS (MHz) Fit 1

v7

1

CbS.

CdC.

Fit 2 C-C

CdC.

C-C

0

0

1613.710 1613.982 -0.272

1615.347 -1.637

1

le

1607.507

1607.716 -0.209

1608.839 -1.332

1

If

1621.896

1622.126 -0.230

1623.368 -1.472

2

2

1617.329 1617.453 -0.124

1618.214 -0.885

3

3

1621.044 1621.097

-0.053

1621.374 -0.330

4

4

1625.425 1625.455

-0.030

1625.304

0.121

5

5

1630.217 1630.259 -0.042

1629.795

0.422

6

6

1635.249 1635.333

-0.084

1634.699

0.550

7

7

1640.430 1640.564 -0.134

1639.915

0.515

8

8

1645.702 1645.879 -0.177

1645.374

0.328

9

9

1651.102 1651.229

-0.127

1651.023

10

10

1656.35

1656.58

-0.23

1656.83

-0.48

0.079

11

11

1661.71

1661.90

-0.19

1662.76

-1.05

2

0

1610.212 1610.304 -0.092

1611.018 -0.806

3

le

1605.642 1605.543

0.099

1605.887 -0.245

3

If

1620.031 1619.920

0.111

1620.201 -0.170

4

2

1617.745 1617.490

0.255

1617.247

0.498

5

3

1623.381 1623.078

0.303

1622.406

0.975

6

4

1629.213

1628.934

0.279

1628.015

1.198

7

5

1635.084

1634.851

0.233

1633.865

1.219

8

6

1640.923 1640.747

0.176

1639.864

1.059

9

7

1646.718 1646.585

0.133

1645.968

0.750

10

8

1652.467

1652.350

0.117

1652.152

0.315

11

9

1658.15

1658.03

0.12

1658.40

-0.25

12

10

1663.79

1663.63

0.16

1664.70

-0.91

-0.221

1602.538

0.001

1603.850

0.207

1603.444

0.613

1618.485 1618.236

0.249

1617.570

0.915

1619.730 1619.412

0.318

1618.497

1.233

1602.539 1602.760 1604.057

9

5

1627.377 1627.089

0.288

1625.994

1.383

1634.455 1634.232

0.223

1633.152

1.303

1641.156 1640.993

0.163

1640.100

1.056

MICROWAVE

15

SPECTRUM OF NCNCS

TABLE VI-Continued V7

obs.

talc.

G-c

c&c.

O-C

10

6

1647.583

1647.469

0.114

1646.921

0.662

11

7

1653.812 1653.720

0.092

1653.662

0.150

12

8

1659.90

1659.79

0.11

1660.36

-0.46

13

9

1665.85

1665.70

0.15

1667.02

-1.17

6

0

1597.588 1597.887 -0.299

1600.030 -2.442

7

le

1606.502

1606.552 -0.050

1606.774 -0.272

7

If

1621.693

1621.774 -0.081

8

2

1624.793 1624.914 -0.121

1622.179 -0.486 1624.566

0.227

9

3

1633.560 1633.693 -0.133

1633.156

0.404

10

4

1641.281

1641.031

0.250

11

5

1648.420 1648.670 -0.250

1648.510 -0.090

12

6

1655.173 1655.457 -0.284

1655.747 -0.574

13

7

1661.65

1662.83

1641.480 -0.199

1661.95

-0.30

-1.18

fit obtained is remarkably good and, in the worst case, leads to an (o-c) value of only 7.6 MHz for the 62, J = 11 transition frequency. In order to estimate the scale parameter v. in the vibrational Hamiltonian, Equation (7), relative intensity measurements were made for the 33, 53 and 73, J = 11 lines. At 23°C these were found to be in the ratio 1:0.60:0.36, respectively. Assuming a relative accuracy of +5%, these values yield energy level spacings of 105 +- 10 cm-’ for G(5, 3) - G(3,3) and G(7,3) - G(5,3). By comparing these frequencies with those calculated using an assumed value of the scale parameter, v. was fixed at I 5.4 + 1.7 cm-‘. DIPOLE MOMENT DETERMINATION

The frequencies of Stark lobes of the 33 J = 11 line were measured at three different field strengths (1055, 855, and 655 V/cm) and the Stark shifts were analyzed using the first-order expression AE = 0.50344E,p,[2ZM/J(J

+ l)(J + 2)],

(12)

where AE is in MHz, E, in V/cm, and pUain Debye. The measured frequencies and assignments are given in Table VII. A plot of AE against E&f was found to be more or less linear and, from the slope, pa was determined to be 3.1626(79) Debye. RESULTS AND DISCUSSION

The modified two-dimensional anharmonic oscillator model has been quite successful in accounting for the anomalous structure of the R-branch rotational spectrum of NCNCS. The results indicate that the large-amplitude motion may be described by the effective Hamiltonian

16

KING, KROTO, AND LANDSBERG TABLE VII Stark Lobe Frequencies and Assignments for the 33 J = I1 Transition of NCNCS (MHz) M

(1055V/an)

(855v/ad

(655V/cm)

-6

38881.06

-5

38884.86

-4

38883.73

38888.29

-3

38884.85

38888.33

-2

38890.67

38893.08

38895.31

-1

38896.39

38897.83

38898.85

1

38908.34

38907.26

38906.17

2

38914.26

38912.04

38909.68

3

38920.45

38916.95

4

38926.25

5

38932.20

6

38938.22

38913.42 38917.11

38926.25

a u(O) = 38902.62MHz. Estimatedaccuracyf 0.05 MHz.

H(cm-‘) = [15.4 f 1.7][$ - 0.0809(22)pq2p - 8.923(29)q2 + q4].

(13)

The effective bending potential function consists of a circular valley with a minimum at 141= 2.112(4). There is a hump at the linear configuration, 141= 0, which lies 308 f 34 cm-’ above the valley. The calculated energy eigenvalues of Equation (13) are shown diagramatically in Fig. 5. Only levels within which rotational transitions have been observed are included. The levels form four distinct but overlapping manifolds with u7 - 1 = 0, 2, 4, and 6. This is in contrast with the energy level pattern of the two-dimensional harmonic oscillator where levels with the same values of u are degenerate. The calculated pattern has more in common with the bent model where each (nondegenerate) vibrational state, ug = 0, 1, 2, and 3, has an associated stack of prolate-top K levels. If the A constant is defined as the separation of the 0’ and 1I levels, then A0 = 8 1 + 9 GHz. Similarly, the bending vibrational frequency in the bent limit may be defined as the separation of the 0’ and 2’ levels, giving u9 = 97 f 11 cm-‘. The zero-point energy is 48 f 5 cm-‘, which is roughly half the estimated value of v9, in agreement with the nondegenerate harmonic oscillator formula E(V) = W(V+ 4).

(14)

Yamada and Winnewisser (II) have defined a correlation parameter which gives an empirical measure of quasilinearity, YO= 1 - 4[G(l, 1) - G(O, O)l/[W,

0) - W4 011.

(15)

MICROWAVE SPECTRUM OF NCNCS

17

160 -

I20 -

80 -

____

12'0

LO-

O-

-LO -

~

11"

~

10'0

86 -80 -

99 -120

___

6‘

~

53

~

3'

~

20

-

L2 -160 -

~

77 6

-6

v=/+2 -2oo-

~

55

___ -2LO

LL 33

-

22 -

1' 00

-280

-

-300

-

v=/

FIG. 5. Energy-level diagram for the 07 bending vibrational levels of NCNCS as obtained from Equation (13). The estimated relative error in the energies is + 11%. Levels are labeled using the designation u$.

In the bent limit, this parameter has a value of +l and in the linear limit -1. It thus traces the change of a rotational degree of freedom into a vibrational one. For NCNCS, y. = +0.89, which may be compared with the values +0.93 for NCNCO (22) and +0.72 for HNCS (13).

KING, KROTO, AND LANDSBERG

18

The effective B values obtained from the spectrum are quite well reproduced by the empirical expression B,, = 1528.7( 11) + 10.26(49)(q2)

+ 2.69( 1 l)(q4) + 0.145( 10)(q6),

(16)

and for the 1 = 1 states by B,,: = B,, + l.08(15)(q2)

+ 0.1 18(26)(q4),

(17)

where the expectation values are obtained from the anharmonic wavefunctions, i.e., the eigenfunctions of Equation (13). The pq2p kinetic energy term in the vibrational Hamiltonian appears to be particularly important for obtaining good agreement between theory and experiment. Indeed, it seems unlikely that such a full analysis would have been possible without its inclusion. In the case of HCNO, a similar model has led to a much improved fit of rotation and vibration-rotation data (14) compared with that originally reported by Duckett et al. (8). It should be noted in Table V that fit 1, which includes the b (kinetic) term, has a standard deviation over 4X lower than that for fit 2, where this term is not present. Perhaps most interesting are the differences in cz7and q7 between the two fits. It can be seen that the o-c values for fit 2 show a quite systematic and characteristic trend for the n7 - I = 0 stack; starting off negative, gradually becoming positive, and then becoming negative again as n7 and 1 increase. This trend, which is repeated for the higher values of v7 - 1(=2,4,6), is not observed in fit 1. It was found that the original problems in assignment and fitting were always present even for lines of low v if the b term was not included. It is evident that b will affect levels of low v or 1 as its terms off-diagonal by two in v are zero. It is therefore the low-order terms in q” like B8 and cz7and q7 that are most likely to be affected by the KE term. The constants given in fit 1 are thus much more realistic. It is also worth noting that q7 in a case like this is not readily compared with the standard l-type doubling q for a well-behaved linear molecule. First, we note that it is the coefficient of (q2) and in a quasilinear situation the q2 potential term has the opposite sign to that for a closely harmonic potential. Due to this, major contributions to (q2) arise from higher-order terms such as q4, q6, etc. Consequently, it is not at all meaningful to consider that q7 has the same simple physical significance that it has for a well-behaved linear system where it is given essentially by a term of the form B2/u. Perhaps the most rewarding aspect of the analysis is the way in which the observed spectroscopic patterns manifest the dynamic behavior associated with a molecule with ambivalent linear/nonlinear character. This can be shown most clearly by disentangling the transitions shown in Fig. 4 and collating them as separated sequences for different v9 (=O, 1, 2, and 3) as has been done in Fig. 6. When KA is low, i.e., less than 3, and v9 = 0 we see that the sequence in KA has the pattern close to that of a typical slightly asymmetric rotor in that the KA = 0 and 2 lines lie close to each other and are flanked, roughly symmetrically, by the KA = 1 lines [(4), p. 1011. As v9 increases the KA = 0 line in particular shifts and the pattern gradually changes (Fig. 6) to correlate at vg = 3 with a pattern more typical of a linear molecule, in that the sequence begins with a Ka = I = 0 line which is followed to the high-frequency side by the KA = 1 = 1

MICROWAVE

19

SPECTRUM OF NCNCS

1

8

9

I

I

v=2

I

3

4

K 8

7

I

I

6

5

I

I

2 1

10

!I=3 K

6

5

I

I

4

3

2

I

II

1

1

I

0 I

FIG. 6. Diagram in which the vibrational satellite branches of Fig. 4 have been collated separately to show how the characteristic spectroscopic patterns vary with increasing excitation of the bending vibration. What is elegantly depicted by NCNCS is the way in which KA = I asymmetry splitting for v = 0 changes into ltype doubling (for I = 1) as u increases to 3.

/-doublet [(4), p. 1521. Thus, we see that NCNCS displays essentially archetypal quasilinear dynamic behavior, showing a spectroscopic pattern characterizing a bent molecule for states deep in the double-minimum well (~9 low) where the barrier is relatively high but changing, as v9 increases and the barrier becomes less significant, to display a pattern more consistent with that of a linear system. What we see is that the Kdoubling splitting of an asymmetric rotor given by f(B - C)J(J + 1) for KA = 1 does indeed correlate with I-type doubling in a linear molecule given by fqJ(J + 1) for 1 = 1. This situation, which is implicit in the discussion by Herzberg (15), has been proven by Watson (16). Unfortunately, an accurate geometric structure for NCNCS cannot be obtained from the present analysis. In particular, the nature of the coordinate q cannot be determined without knowledge of the G-matrix element associated with the largeamplitude motion. Thus, the CNC angle corresponding to the potential minimum is unknown. The parameter B$ = 1528.7( 11) MHz represents the rotational constant of a hypothetical linear configuration, corrected for the contribution of the bending motion. If Bij’ constants are obtained for other isotopic species it will be possible to estimate the r,-type structure for this configuration. Finally, it is relevant to discuss briefly the origin of the quasilinearity. The three most feasible canonical structures for NCNCS and the related molecule, NCN3, are

KING,

20

KROTO,

AND LANDSBERG

/N\ NC“\\s N I

II

III

IV

V

VI

In the case of NCNCS, the bent form (I) makes the most significant contribution to the overall structure, with smaller contributions from the linear forms, II and III. On the other hand, all three NCN, structures are bent, IV-VI, since it is not possible to construct linear forms without placing like charges on adjacent atoms; such structures are expected to be of very minor importance. Thus, it is observed experimentally that whereas NCNCS shows some tendency toward linearity (LCNC - 1.50”) NCNj is a well-behaved bent molecule (LCNN = 120”) (6). ACKNOWLEDGMENT We are grateful to the SERC for the award of a research studentship to M.A.K. RECEIVED:

June

2 1, 1984 REFERENCES

1. H. W. KROTO, Chem. Sot. Rev. 11,435-49 1 (1982). M. A. KING AND H. W. KROTO, J. Chem. Sot. Chem. Commun.,

2. 3. 4. 5.

606 (1980). M. A. KING AND H. W. KROTO, Unpublished work. H. W. KROTO, “Molecular Rotation Spectra,” Wiley, London, 1975. J. M. L. J. REINARTZAND A. DYMANLJS,Chem. Phys. Lett. 24,346-351 (1974).

6. C. C. COSTAINAND H. W. KROTO, Canad. J. Phys. SO, 1453-1457 (1972). 7. K. YAMADA, M. WINNEWISSER,G. WINNEWISSER,L. B. SZALANSKI,AND M. C. L. GERRY, J. Mol. Spectrosc. 79,295-3 13 ( 1980). 8. J. A. DUCKETT, A. G. ROBIETTE,AND I. M. MILLS, J. Mol. Spectrosc.62, 19-33 (1976). 9. J. B. MALLOY, JR., J. Mol. Spectrosc. 44, 504-535 (1972). 10. J. M. BROWN,J. T. HOUGEN,K.-P HUBER,J. W. C. JOHNS,I. KOPP, H. LEFEBVRE-BRION, A. J. MERER, D. A. RAMSEY, J. ROSTAS, AND R. N. ZARE, J. Mol. Spectrosc. 55, 500-503 (1975). II. K. YAMADA AND M. WINNEWISSER,Z. Naturforsch.a 31, 139-144 (1975). 12. W. H. HOCKINGAND M. C. L. GERRY, J. Mol. Spectrosc. 59, 338-354 (1976). 13. K. YAMADA, M. WINNEWISSER,G. WINNEWISSER,L. B. SZALANSKI,AND M. C. L. GERRY, J. Mol.

Spectrosc. 64,401-414 (1977). 14. B. M. LANDSBERG,Unpublished work. IS. G. HERZBERG,“Infra Red and Raman Spectra of Polyatomic Molecules,” pp. 377-378, Van Nostrand, Princeton, New Jersey, 1945. 16. J. K. G. WATSON, Unpublished work.