Structure and quadrupole coupling measurements on the NO dimer

JOURNAL OF MOLECULAR SPECTROSCOPY 98, 80-86

(1983)

Structure and Quadrupole Coupling Measurements on the NO Dimer STEPHEN

G. KUKOLICH

*

School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801

Rotational transition frequencies for “NO-‘4N0, “NO-‘5N0, and ‘5NO-‘5N0 were measured using a pulsed-nozzle Fourier transform microwave spectrometer. Rotational constants for the different isotopic combinations allowed an unambiguous structure determination. The molecule is in a cis planar structure with a bond between the nitrogen atoms and an NNO angle 0 = 99.6(2)“. The N-N bond length is 2.236(l) 8, and the NO bond length is 1.161(4) A. Hyperfme structure due to nitrogen quadrupole coupling and spin-rotation interactions was observed and analyzed. Rotation constants, quadrupole coupling tensor, and spin-rotation tensor elements are given. I. INTRODUCTION

The existence of the NO dimer has been supported by many types of experiments but the structure was previously not clearly determined. A communication on this work appeared earlier (I). Further data and analysis of the structure, measured transition frequencies, and hypetfine data are given in the present paper. Since only two independent moments of inertia were obtained from the earlier molecular beam work (2), the structure could not be determined from that data without further information. Hyperhne structure due to nitrogen quadrupole coupling was reported in that work (2). The structure and bonding of many transition metal nitrosyl complexes has been studied and a better understanding of the NO dimer should contribute to that area of research. Three different isotopic forms of the NO dimer were observed in the present study. Measurements of rotational transition frequencies for these different isotopic combinations allow a clear determination of the structure of the complex. The method of isotopic substitution is well known in microwave work and it is required to determine structures for complex molecules. II. EXPERIMENTAL

DETAILS

The microwave spectra were obtained using a pulsed-nozzle Fourier transform spectrometer developed by Balle, Flygare, and coworkers (3, 4). A mixture of 4-6% NO in argon at I-atm pressure was rapidly expanded into the region between two ’ Permanent address: Department of Chemistry, University of Arizona, Tucson, Ariz. 8572 1. 0022-2852183 $3.00 Copyright 0 1983 by Academic Press. Inc. All rights of reproduction in any form reserved.

80

STRUCTURE

81

OF THE NO DIMER

,l,r,,,,,,l,,‘“‘,,

200

500

400

300

KHZ

FIG. 1. Two of the 3,,s - 2,r transitions of “NO-‘4N0. (A) The component at I1 267.37 MHz. (B) The component at I I 266.86 MHz. Both signals appear in this spectrum because component A is above the main oscillator frequency of I1 267.034 MHz and component B is below this frequency. This digitized spectrum has a dispersion of 3.9 kHz/point.

28-cm diameter spherical mirrors using a pulsed solenoid valve operating at 1 pulse/ sec. The 14N0 was C.P. grade obtained from Matheson Gas Products. The 15N0 was 95-at% “N, obtained from Merck Sharp and Dohme of Canada. A a/2 microwave pulse of 2-psec duration was used shortly after the gas pulse to excite the emission signal from the molecules. The molecular emission signal was converted down to 30 MHz using a microwave superhet receiver and then mixed with a 30-MHz sine wave in a balanced mixer to obtain the “free induction decay” signal. The free induction decay signal was digitized at 0.5 qec/point, averaged, and Fourier transformed to obtain the spectrum. The digital spectrum had a point-to-point resolution of 3.9 kHz and a resonance linewidth of about 12 kHz. The nozzle diameter was 0.8 mm.

I -4

A

A

/L -3

I -2

FIG. 2. Calculated hypertine spectrum for the 303 MHz relative to the line center at 11267.292 MHz.

-1

1 0

1 MHz

2r2 transition of “NO-‘4N0

with frequencies in

82

STEPHEN G. KUKOLICH

The 3,,3- 2r2 transitions were measured for “NO-‘4N0, “NO-‘5N0, and “NO15N0. An equal mixture of 14N0 and “NO was used for the “NO-‘5N0 spectra. The 1r0 - loI transitions were measured for “NO-‘5N0 and ‘5NO-‘5N0. The quadrupole hypetfine structure was completely resolved on transitions involving complexes containing 14N0. Most transitions were observed with very high signal to noise ratio. Two of the 303 - 2r2 transitions of “NO-‘4N0 at 11266.86 and 11267.37 MHz are shown in Fig. 1. A calculated spectrum using the “best fit” parameters for the 2r2 3,,3transition at 11267.4 MHz is shown in Fig. 2. The measured transition frequencies are given in Table I. Attempts were made to observe other rotational transitions with higher values of rotational angular momentum. No other lines were seen; this is most likely a result of the highly effective rotational cooling of the gas mixture as it expands through the nozzle. III. ANALYSIS OF DATA

The hyperfme structure on the 2r2 - 303 transition was analyzed along with the data of Western et al. (2) to obtain the rotational constants, the centrifugal distortion constant DJ,the nitrogen quadrupole coupling tensor, and the spin-rotation tensor for the “NO-‘4N0 dimer. Terms were included in the hyperfine Hamiltonian for the nitrogen quadrupole coupling, spin-rotation interaction, and spin-spin interaction. 0Yhypefine = X&q + C(J&jQ)i* j + Z,+n-spine

TABLE I Measured Transition Frequencies for the NO Dimer (Frequencies in MHz)

Complex

14 NO-14NO

Transition

303 +

212

Frequency

(MHZ)

11 264.778(7) 11 266.858(11) II 267.372(l) 11 267.940(21 11 268.866(4)

14

NO-%

I1 202.241(5) 303 + %2 11 202.862(4) 11 203.353(51

110 +

101

20 827.169(g) 20 829.047(3)

15No-15No

11 159.303(3) 303 + 212 cl 110

01

20 444.831(2)

STRUCTURE

OF THE NO DIMER

83

The explicit form of these interactions is given elsewhere (5). The calculated spinspin interaction strength is only 0.056 kHz but it was included in the fit. Only firstorder terms in the rotational energy were included but the errors introduced by this approximation were a few tenths of a kHz or less. A nonlinear least squares fitting routine was used to obtain the best fit of the calculated frequencies to the experimental transition frequencies. The measured and calculated frequencies, along with assigned quantum numbers, are given in Table II. This table includes data obtained in the present experiment and data obtained by Western et al. (2). The spin-rotation interaction tensor elements C,, in the present work are defined by

TABLE II Experimental and Calculated Frequencies for the “NO-‘4N0

Dimer (Frequencies in MHz)

84

STEPHEN G. KUKOLICH

CCJ,,,> = C (J;)C,IJ(J + 1). g This corresponds to the “lab frame” spin-rotation interaction strength and differs in sign from the Mgg spin-rotation tensor elements in the molecule-fixed frame. Both sign conventions often appear in the literature. The values of the adjustable parameters from the least squares fit are given in Table III. Of the possible prolate symmetric top basis distortion constants DJ,D JK,and DK,the present data set is most sensitive to DJ.Since this molecule is a nearly prolate asymmetric top, these parameters should provide a reasonable description of the largest-order centrifugal distortion. The DJ value obtained would correspond to a linear combination of the 7’s. The quadrupole coupling and spin-rotation parameters are in very good agreement with previous values (2). The present rotation constants A, B,and C are each about 0.2 MHz larger than previous values because a centrifugal distortion term is now included in the rotational Hamiltonian. The inertial defect A = Z, - Z, - Zbis 0.15 I amu AZ, which indicates that the complex is planar. The 2,2 - 303 transition of ‘5NO-‘5N0 was observed as a single line. The l,,i 1,0 transition of 15NO-“NO was observed as a doublet with splitting of 54 kHz, but this splitting is larger than expected due to spin-rotation and spin-spin interactions. Since this frequency is higher than normal operating frequencies for this apparatus, the splitting could be due to an instrumental effect. Some hyperhne structure was observed on the ‘5NO-‘4N0 transitions but the interaction constants obtained from the more complete 14NO-14N0 data described the splittings with sufficient accuracy to obtain line centers. If we assume that the distortion constant D_,and the inertial defect A will be the same for the 14NO-‘4N0, 14NO-‘5N0, and “NO-i5N0 dimers, we can calculate rotation constants for all three isotopic combinations using the transition frequencies

TABLE III Values of the Adjustable Parameters Obtained from the Least Squares Fit to the Data Given in Table II (Standard Deviation for the Fit was 0.001 MHz; Indicated Errors are One Standard Deviation) Parameter

Value

(MHZ)

A

25 829.7267(9)

B

5 614.5557(?)

c

4 605.6861(5)

D

.J

eQqaa eQqbb c

aa

%b c

cc

0.03080(l) -4.0657(E) -2.2417(5) -0.01055(16) -0.01375(30) -0.00104~30)

STRUCTURE

85

OF THE NO DIMER TABLE IV

Rotation Constants A, B, and C Obtained by Fitting Observed Transition Frequencies (It Was Assumed that the Distortion Constant and Inertial Defect Would Be the Same for All Three Isotopic Combinations) A(MHZ)

B(MHZ)

C(MHZl

25 829.73

5 614.56

4 605.69

Complex

%o% 14N*

15N0

25

365.44

5 535.57

4 537.76

%I

%o

24 919.63

5 463.13

4 474.811

Note. Transitions numbered 1 through 5 were measured in the present experiment. Transitions numbered 6 through 33 were reported previously (2). The “best fit” adjustable parameters used to obtain the calculated frequencies are given in Table III.

listed in Table I. The rotation constants obtained by fitting the observed frequencies are listed in Table IV. We do not expect that errors introduced by this assumption will be greater than a few tenths of a megahertz. The inertial defect is nonzero, and we wish to describe the molecule by a planar structure. Depending on which combinations of rotational constants are used, slightly different planar structures will be obtained. The N-N bond length is most accurately determined by comparing the B rotational constants of “NO-‘4N0 and ‘SNO-‘5N0 using the Kraitchman method. Using A and C to determine the planar structure we get 2.3592 A, and using A and B or B and C we get 2.23594 A. These values are in excellent agreement, but since we have not considered vibrational effects or done a complete treatment of the centrifugal distortion, we give the value of 2.236( 1) A for the N-N bond length. The N-O bond length and NNO angle were determined by carrying out least squares fits to the experimental rotational constants. These fits were carried out using B and C, A and B, A and C, and A, B, and C rotational constants. The results are shown in Table V. The lowest standard deviation was obtained using the B and C rotational constants. The N-N bond lengths agree reasonably well with the value of

TABLE V NO Dimer Structure Parameters, N-O Bond Length, N-N Bond Length and NNO Angle Obtained by a Least Squares Fit to Various Combinations of the A, B, and C Rotational Constants Given in Table III Rotational axlstants

B,C

1.1650)

2.236(15)

99.617)

A.B

1.161(4)

2.237(30)

99.6(U)

A.C

1.161(6)

2.234(40)

99.8(17)

A,B,C

1.X1(5)

2.236(36)

99.6(16)

86

STEPHEN G. KUKOLICH

2.236( 1) A obtained using the Kraitchman method. From the results we give the N-O bond length as 1.16 l(4) A and the NNO angle as 99.6(2)“. These error estimates include values obtained from all combinations of rotational constants. Errors due to the finite inertial defect which appears in Table IV are not included in this planar structure. IV. DISCUSSION

The structure for the gas-phase NO dimer is remarkably close to the crystal structure studied by Lipscomb and coworkers (6). The NNO angle of 99.6” is only 5” smaller than the NNO angle of 105” observed for the nitrosyl end of the ONNO complex (7). The N-N bond length of 1.864 A for ONNO* is considerably shorter than the NO dimer value of 2.236 A. The N-O bond length of 1.16 1 8, is only slightly longer than the N-O free molecule bond length of 1.154 A. The calculated equilibrium values of 1.77 (8) and 1.62 A (9) for the N-N bond length are significantly shorter than the observed value. The calculated equilibrium NNO angles of 106 (8) and 112” (9) are reasonably well in line with the observed value. Recent ab initio calculations by Ha (10) yield an N-N bond length of 2.39 A, N-O bond of 1.19 A and NNO angle of 90”. This calculated N-N bond length is very close to the experimental value. The new structure data in combination with measured electric field gradients at nitrogen nuclei should provide useful data for sorting out the various basis sets and correlation effects in molecular orbital calculations. Calculations on complexes of this type appear to be less reliable, at present, than similar calculations on stable molecules. These complexes therefore provide a more stringent test to aid in the refinement of molecular orbital calculations. ACKNOWLEDGMENTS Equipment for this research was funded by the National Science Foundation. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. The author thanks Bob Feltham for helpful discussions on this project. Dick Schwendeman provided helpful suggestions on the structure determination. Hyperfme programs were obtained from Bill Read. RECEIVED:

October 14. 1982 REFERENCES

1. S. G. KUKOLICH,J. Amer. Chem. Sot. 104,4715-4716 (1982). 2. C. M. WESTERN,P. R. R. LANGRIDGE-SMITH,B. J. HOWARD, AND S. E. NOVICK, Mol. Phys. 44, 145-160 (1981). 3. T. J. BALLE AND W. H. FLYGARE,Rev. Sci. Instrum. 52, 33-45 (1981). 4. T. J. BALLE, E. J. CAMPBELL,M. R. KEENAN, AND W. H. FLYGARE,J. Chem. Phys. 72, 922-932 (1980); ibid. 71, 2723-2724 (1979). S. G. KUKOLICH,J. Amer. Chem. Sot. 104, 6927-6929 (1982). W. N. LIPSCOMB,F. E. WANG, AND E. L. LIPPERT,JR.,Acta Crystallog. 14, 1100-I 101 (1961). A. H. BRITTAIN,A. P. Cox, AND R. L. KUCZKOWSKI,Trans. Faraday Sot. 65, 1963-1974 (1969). J. SKAARUP,P. N. SKANCKE,AND J. E. B~GGS, J. Amer. Chem. Sot. 98, 6106-6109 (1976). 9. M. A. BENZEL,C. E. DYKSTRA, AND M. A. VINCENT, Chem. Phys. Lett. 78, 139-142 (1981). 10. T.-K. HA, Theor. Chim. Acta (Berlin) 58, 125-130 (198 1). 5. 6. 7. 8.