C. R. Brazier et al- Rotational analysis of the 0-0^0 band of the A^3-E-X^3-A2 system of...

8/2/2019 C. R. Brazier et al- Rotational analysis of the 0-0^0 band of the A^3-E-X^3-A2 system of methylnitrene

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Rotational analysis of the 0: band of the a3E-,&42 system of methylnitreneC. R. Brazier and P. G. CarrickPhillips Laboratory/RKFE, Propulsion Directorate, Edwards Air Force Base, California 93523P. F. Bernatha)Department of Chemistry, University of Arizona, Tucson, Arizona 85721(Received 14 May 1991; accepted 2 October 1991)The optical emission spectrum of the methylnitrene radical has been observed at a resolution of0.07 cm .- . Transitions to subbands with K up to 3 in the %!3.42 ground state were observedand a full rotational analysis carried out. Comparison of the structural information with thehighest level theoretical calculations shows agreement to within the estimated error.

INTRODUCTIONThe methylnitrene radical (CH, N) was first observedexperimentally just six years ago by Carrick and Engelking.Using both a flowing afterglow discharge and corona excited

supersonic expansion (CESE) they obtained the electronicemission spectrum with an origin near 3 140 A. By analogywith the isovalent NH radical, for which the,4 311 X 38 -transition is 3360 A, the transition was assigned as2 E - 2 AI. Theoretical calculations2 suggest that thesinglet states analogous to a A, b B +, and c II for NHhave little or no barrier to rearrangement to methyleneimine(CH, NH), and thus only one electronic system is expected.A rotationally resolved spectrum of methylnitrene wasobtained for the first time by Carrick ef aL3 by focusing theemission from a CESE source into the McMath FourierTransform Spectrometer at Kitt Peak National Observa-tory. The resolution obtained, about 0.2 cm-, was suffi-cient toassign thestrongest subband K - K W= 1 - Oin theorigin systems of both CH, N and CD, N. However, even atthis resolution and at a temperature of 12 K, the spectralcongestion was such that none of the other subbands couldbe clearly identified.Other recent experimental studies of methylnitrene in-clude an improved vibrational analysis by Chappell and En-gelking and matrix i solation work by Ferrante.5 In addi-tion, a new theoretical investigation by Xie et al6 using alarge basis set and extensive CI has yielded a ground-statestructure much closer to the experimental one, althoughsome discrepancies still remained. We recently recorded anew spectrum using a slit nozzle. Some lines for all the low Ksubbands 2-3, l-2, O-l, l-0, 2-1, 3-2, and 4-3 were assignedand a full rotational analysis performed. The results of thisanalysis are presented here.EXPERIMENTAL

The spectra used in this analysis were obtained in anidentical fashion to those obtained previously.1r3 The firsthigh-resolution data3 were generated from a pin-hole nozzleand the resolution was limited to 0.2 cm - by the Doppler

) Also at: Department of Chemistry, University of Waterloo, Waterloo,Ontario,CanadaN2L 3Gl.

spread of the jet. A part of this spectrum is shown in Fig.1 (a). The low resolution severely hampered the analysis be-cause many of the features were composed of two or morerotational lines. Following the work of Milkman et al., weconstructed a slot nozzle by drilling a 30 pm by 5 mm chan-nel in the flat end of a glass tube with a pulsed XeCl excimerlaser. A discharge jet expansion using such a nozzle dramati-cally reduces the spread of Doppler velocities of the cooledradicals in the direction of the spectrometer. At the newresolution of 0.07 cm - , most of the features are resolvedinto single rotational lines as can be seen in Fig. 1 (b).The corona jet source tends to remain stable for onlyshort periods of time, so several separate scans were record-ed. Of these scans, two were used in the analysis; the first

A Pinhole0*2cmNLNFIG. 1. Comparison of the methylnitrene emission spectra obtained frompin-hole and slot-type nozzles. The Doppler width of the lines is reduceddramaticall y from 0.2 cm - full width at half maxi mum to 0.07 cm - . Atthe higher resolution most of the lines are well resolved making assignmentof branchesmucheasier.

J. Chem. Phys. 96 (2), 15 January 1992 0021-9606/92/02091 Q-08$06.00 0 1992 American Institute of Physics 919


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resulted in a strong spectrum with a rotational temperatureof about 12 K. This was used to make initial assignments ofthe line positions. A second spectrum with a rotational tem-perature of 25 K made possible the tracking of branches tohigher rotational quantum number J. As a result, some ofthe centrifugal distortion constants could be determined.ANALYSISInitially the 1-O subband which had previously beenanalyzed using a II - 32 - Hamiltonian was reanalyzedusing a 3E - 3A2 Hamiltonian. As no transition of this typehad been analyzed before, the effective Hamiltonian for a Eelectronic state had to be developed. The starting point wasthe *E Hamiltonian of Endo et ~1.~which we had previouslyused and extended for the analysis of the E - *A1 transitionof CaCH, .9 The only additional terms required are the spin-spin interaction il and the rovibronic interaction terms oiand o, analogous to the lambda doubling parameter o for a311 tate. The effective Hamiltonian and matrix elements fora 3E state are given in the Appendix.The arrangement of the K stacks for CH, N is shown inFig. 2. They are grouped in columns by KR , the rotationalangular momentum about the top axis. This makes it easierto visualize the allowed rotational transitions as they onlyoccur within columns (K k - K V = 0). The rotational an-gular momentum without spin is then K = KR + 1. Strictly

40302010 - --90090 - - -80 - - -70 3E- --60 -50 - -2344030 -- -12331820 :=1 012

CM-l:R= 0

706050 340 3A230 220 110 :=o0

920 Brazier, Carri ck, and Bernath: Rotational analysis of the 0: band

speaking, all of these terms are signed, and in the absence ofro-vibronic coupling, every level except for K = 0 in the% 3A2 ground state is a degenerate pair. For a given value ofKR ( #O) there are 12 possible basis functions as K, and 5can be plus or minus and each of the four resulting K levelscan couple with the spin angular momentum Z ( - 1, 0, or1) to give 12 possible values for the projection of the totalangular momentum P on the top axis. f is the projection ofthe orbital angular momentum on the symmetry axis, anala-gous to the quantum number A of a diatomic molecule. Thequantum number P corresponds to R in the diatomic case.For example, the basis functions for IK:, 1 = 3 are

IJ, c=l, K=4, P=5, 8=1),IJ, c=l, K=4, P=4, X=0),IJ,


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(K = - 3,5, - 4,6) were included and all higher energystates ignored, giving a 24X 24 matrix. For the a, and u2symmetry levels (K = 1, - 2,4) the next set (K = - 5,7)was similarly included giving a 15 X 15 matrix. The (2, - 1)terms can give rise to significant perturbations when differ-ent K levels pass through each other. Such effects are veryuseful in a symmetric top molecule because they determinethe separation of the K stacks. Ordinarily, the spacing of theK stacks cannot be determined and, hence, the absolute val-ue of the A rotational constant is difficult to measure. In afew molecules, such as CH,F perturbations due to lowlying vibrations have allowed the determination of A. For aE or 3E state there is the possibility of different spin-orbitcomponents of separate K levels lying close in energy andinteracting, as can be seen in Fig. 2. A perturbation of thistype was seen for CaCH, ,9 and the value of A determined.Unfortunately, for CH, N, only a few low Jand low K levelshave been seen and no perturbations of this type were ob-served. However, these terms effect the energy levels evenwhen the K levels are not close together, and if the data issufficiently good, A can be determined. This was done forCHJO, where very high precision microwave data wasavailable.In the case of methylnitrene, when both A rotationalconstants were allowed to vary, the absolute value couldonly be determined to 0.4 cm - . When A was constrainedin the least-squares fit and adjusted manually, a gentle mini-mum at A = 5.6 1 cm - was found. The Fourier transform(FT) data for CH, N probes primarily low Jand K levels inthe R = 2 stack of the E state. Some lines from the Sz = 1levels were seen in the higher temperature emission spec-trum allowing the spin-orbit splitting to be determined.Some transitions were also seen in the region of the s1 = 0component, but these were overlapped by a vibrational hotband. The structure of this band is very different from that ofthe origin suggesting that it originates from one of the e vi-brational levels in the excited state. As 61 has already beenassigned,J this leaves 41 and 5; as the most likely assign-ments.It should be noted that the transitions from the R = 1component were incorrectly assigned as being from a = 2to R = & 1 in the ground state by Chappell and Engelk-ing.J The ground state has a very small splitting and followsHunds case (b) coupling where fl has no meaning.

The only data for fi = 0 in the E state are from laser-induced fluorescence (LIF) measurements reported pre-viously. Comparison of the emission spectra and LIF spec-tra for the fi = 2 and 1 components shows that the LIF dataare subject to random errors of up to 0.05 cm - . Such errorswere expected because the scan to scan reproducibility of theLIF signals was typically of this size. The shifts were pro-duced by variations in the direction of flow of the nozzleresulting in different Doppler shifts. This could be overcomeif the experiments were repeated using a slot nozzle.For the final fit, 247 FT li nes and 8 LIF transitions wereincluded; these are listed in Table I together with residuals.The transitions observed spanned rotational levels up toJ = 13 for K = 0, 1, 2, and 3. The ground state could befitted adequately with just four adjustable parameters: B,

D,, il, and (ebb + E,, )/2 as can be seen in Table II. For theexcited state, many more parameters were required to obtaina satisfactory fit. Inclusion of the (2, - 1) terms connectingthe K stacks improved the variance from 0.95 to 0.90. Sever-al other higher-order terms such as D,, and qe were alsorequired. The values for these parameters are poorly deter-mined and subject to significant variation depending on theparticular group of parameters selected to fit the data.DISCUSSION

The ground-state rotational constant B = 0.9296 cm- found from fitting the electronic emission data to a E - A2Hamiltonian, is changed little from the earlier fit of the 1-Osubband to a 311 Z - Hamiltonian (0.9308 cm - ). Asthe value of the A rotational constant could not be reliablydetermined, calculation of the geometry depends on fixingthe structure of the methyl group. Using the new theoreticalvalues of Xie et ~1.~ (see Table III) gives r,_,, = 1.420 A ingood agreement with the theoretical value of 1.424 A. Usingthe experimental bond angle3 determined from B rotationalconstants for CH, N and CD, N gives rc-N = 1.412 A; essen-tially the same as the earlier experi mental value. The CD, Nmolecule has not yet been reanalyzed using a E - A2 Ham-iltonian, so it is not possible to make a reliable comparisonbetween isotopomers using the new data.In view of the fact that the theoretical calculations give abond angle near 109 at all levels of theory, it is likely that thevalue for the H-C-H bond angle, estimated earlier3 is toolow. This is most likely due to zero-point vibrational contri-butions to the rotational constants of CD, N and CH,Nwhich affect the precision of structure estimates based onisotopic substitution. An accurate determination of the Arotational constant is required to definitively solve this prob-lem. This could be obtained either from microwave observa-tions or further LIF experiments to probe the levels whichare predicted to exhibit internal perturbations due to thecrossing of levels of different R and K.

The x A2 ground state of CH, N could be fitted ade-quately with just four adjustable parameters, while a total ofsixteen were required for the excited state. In addition, thecentrifugal distortion constant D, was at least a factor of 5smaller in the2 E state than in the ground state, although areliable D, value could not be determined. This suggests thepresence of either some internal or external perturbation in-teraction which makes the energy levels hard to describe by aconventional effective Hamiltonian. In the relatively smallnumber of levels probed at high precision, no obvious localperturbations were seen. The majority of the lines observedwere very weak and, hence, not determined precisely enoughto spot small perturbations.Some information on the Jahn-Teller interaction in the2 3E state can be extracted from the experimental param-eters. From the values of A and A


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TABLE I. Observed lines of methylnitrene (in cm- ).J 1-O ubband

P, (J)123 31 803.7585 O.cMl4 31 802.9568 - 0.00495 31 801.9003 - OH056 31 800.5796 0.00357 31 798.9929 - 0.0006891011 31190.1947 - 0.03681213 31 784.4050 - o.m90P,,(J)1234 31 186.3052 - 0x03456 31 776.4486 o.ooo3789

pa cn12 31 821.5782 0.00753 31 817.4278 - 0.00884 31 813.1382 0.00665 31 808.6586 0.01036I89

Q, tJl31 807.4442 0.004431 808.5198 - 0.000831 809.3197 - 0.005731 809.8677 0.0025

31 808.8519 0.010531 807.9353 - 0.003131 806.8139 - 0.003631 805.4839 - 0.0007Qu (JI

31 798.3175 O.OfX931 795.6190 - 0.001031 792.6708 - 0.001531 789.4749 0.00363 1 782.3347 0.01183 1 778.3923 0.006531 774.2244 0.0096

Q,,(J)31 827.2385 0.010831 824.9546 0.017131 822.5049 - o.cQ6731 819.9272 0.006431 817.1624 0.002931 814.2256 - 0.001031 811.1184 - 0.003631 804.4039 0.0053

R,(J)3 1 809.2279 - 0.002031 812.2077 0.@30931 814.8808 O.ooO531 817.2801 - o.ooal31 819.4195 0.002031 821.3035 0.00363 1 822.9422 0.00823 1 824.3401 0.0141

RI, (JI31 803.9615 o.cal531 803.0746 - o.oo9031 801.9697 - 0.010031800.6156 - 0.01153 1799.0339 0.0102

Rx (J)31 830.5637 0.017931 829.9015 - 0.005031 829.1102 - 0.0108

P,,(J)

31797.3731 - 0.004831 794.7129 0.001331 791.7858 0.003831 785.1627 0.010631781.4711 0.007931 777.5296 - 0.003431 713.3795 0.0113

pa (Jl

31 830.3467 0.009531 829.7847 O.ooOl31 829.0394 - 0.0027

Q,I (J)31 857.014 0.04131858.798 0.00231 860.520 - 0.00131 862.130 - 0.041

Qu (J)31 802.9568 0.00331 802.1442 - o.cxxl731 801.0730 0.00173 1799.7364 - o.ooo431 798.1380 - 0.00813 1796.3037 - 0.000631 794.2182 0.001031 791.8958 0.005431 789.3214 - 0.008831 786.5418 - O.WO631 783.5303 - 0.00293 1 780.3009 - 0.0072

Q,,(J)31 832.4949 - 0.00173 1 834.0701 0.009431 835.4019 - 0.010331 836.5660 - 0.007831 837.5460 - 0.007331 838.3544 O.OOCG31 838.9721 - 0.007031 839.4339 0.0052Qx (J)

31 850.800 0.02131 850.700 O.CQ931 850.511 - 0.03931 850.344 - 0.00431 850.077 0.00031 849.727 - 0.00131 849.298 0.007

R,,(J)31 806.6719 O.OCO431 807.7217 - o.ooo231 808.5092 0.000731 809.0359 o.OcxJ331 809.1149 0.000631 808.6586 - 0.0012

31 805.9361 - 0.0052

R,,(J)31 835.8147 - o.oooo31 839.0438 0.014131 842.0227 O.coll31 844.8306 0.010431 847.4266 - 0.009431 849.8629 - 0.0121

R,,(J)31 858.010 - 0.01731 859.726 0.003

Qu (J)

$Ir:ii7957Ia


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TABLE I. (Continued.)O-1 ubband

P, tn Q,(J)12 31 806.4230 0.00773 31 807.5579 0.00514 31 808.3503 - 0.00745 31 800.9654 0.0145 31 808.8722 - 0.00376 31799.5924 - 0.00947891011

P,,(J) Q,,(J)1 31 799.58792 31 794.1376 - 0.0142 31 797.31973 31789.9206 0.0076 31794.6670

R,(J) P,,(J)31 811.1775 0.017031 813.8855 - O.cwl31 816.2863 0.003631 818.3898 - O.CQ87

R,,(J)0.0021 31 802.74000.0066 31 802.05120.0088 31 799.6281

3 1 799.2049 - o.a)353 1 796.6572 0.007631 793.9033 - o.ooo131 790.9128 - 0.002731 787.6649 - 0.009631784.1783 - 0.002131 780.4363 - o.ooo431 776.4499 0.000831 772.2345 0.010831 767.7745 0.0074- 0.0071- 0.00710.00454 31 785.3831 0.0083 31791.7029 - 0.0047 31 798.0081 0.00165 31 780.5537 - 0.0052 31788.4812 - 0.00276 31 775.4564 - 0.0190 31784.9778 - 0.02027 31 781.2497 - 0.008389

Q,(J) P2J a12345 31 806.0216 31 823.622 - 0.0107 31 822.343 - 0.004 31796.6008 31791.6039 31786.433

-

Qu (J) R,,(J)31 806.8456 0.001731 802.3667 - 0.0030 31 807.1140 - o.ooo931 801.3886 - 0.00623 1 800.2391 0.0029 31 808.1459 - 0.015331 798.8371 - 0.003431795.3105 0.004231 793.1697 - 0.002531 790.8177 0.017431788.1999 0.0032

Pz, J) Qx tn

02, (JI R,,(J)31 827.624 0.022

0.010

0.0330.0260.013

31 819.761 - 0.017 31 826.461 - 0.00231 817.162 - 0.01831 814.391 - o.co4 31824.424 - 0.01731 811.458 0.025

2-l subband

31831.280 0.009 31 836.27131 832.660 - 0.013 31 839.35431 827.128 - 0.017 31833.817 - 0.013 31 842.18131 826.416 - 0.007 31834.780 - 0.00731 825.503 - 0.010 31 835.576 0.01731 824.424 0.001 31 836.166 0.011

Q, (J) R, (J) R,,(J) 4, (J)2 31 812.8164 - o.coO2 31 808.7743 0.0033 31 841.352 - 0.0043 31 815.5944 o.coO3 31 809.4363 0.00034 31 810.0623 - 0.0039 31 818.0506 - 0.00345 31 810.6449 - 0.0022 31820.2427 0.00146 31 810.9376 - 0.0297 31822.1670 - 0.00527 31 811.0296 - 0.00628 31 810.8579 - 0.0020


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924 Brazier, Carrick, and Bernath: Rotational analysis of the 0: band

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J. Chem. Phys., Vol. 96, No. 2,15 January 1992


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Brazier, Carrick, and Bernath: Rotational analysis of the 0: band 925TABLE II. Molecular constants for the 0: band of the2 E - ;i A, systemofCH,N (incm-).

ConstantT

4da4-t

10 %5,AB10 D,10 D,,IO&

Cd,,(6, +&l/20161h0260e2bh,

31 830.913( 12)- 22.517( 16)0.855 21(66) - 0.2133(78)3.2716(63)4.3( 15)5.61b 5.422 90(55)0.929 410(48) 0.844 65( 17)7.03b

7.2( 14)3.76(30)

- 0.2707(33)- 0.003 29( 14) 0.0656(63)

0.8925(40)- 0.017 43(75)

0.001 278(58)- 0.49( 17)

0.210(87)- 0.099( 20)- 0.0226(93)

One standard deviation error in parentheses.bHeld fixed.

Methylnitrene has three Jahn-Teller active modes, butin their vibrational analysis Chappell and Engelking4 foundthat one I*~ exhibits the strongest interaction. They deter-mined a Jahn-Teller coupling constant k 2 = 0.19 for thismode with k < 0.02 for V~ and Ye. Even the v6 value ofk 2 = 0.19 is considered a weak Jahn-Teller effect. Child andLonguet-HigginsI use the parameter D = k 2/2 to describethe Jahn-Teller effect. In the Appendix of Ref. 13, they givea table relating D to the quenching parameter d, and interpo-lating the quoted values gives d = 0.71 for D = 0.095. Theprojection of the orbital angular momentum, gee, s thusfound to be 0.9 15.The total projection of the angular momentum for amolecule with a single degenerate mode is given by 70 000 cm - *. 6 Hence,E,, for the B 3,42state is expected to be very small and indeedthis term was too small to determine experimentally.

For the2 3E state, ebb should be equal in magnitude butopposite in sign to l bb or the ground state assuming no othercontributions. However, ebb or the 2 E state is much larg-er, suggesting interactions with other unknown excitedstates. For E,, in the 1 E state contributions due to theJahn-Teller interaction can occur. Following the same pro-cedure as Liu et aLi4*15 gives E,, = - 0.47 cm - in reason-able accord, considering the approximations required, withthe measured value of eaa = - 0.27 cm - .CONCLUSION

The 2 3E - x A2 transition of methylnitrene has beenfully analyzed for the first time. Unfortunately, little extrastructural information could be determined, although it isclear that experiment and the highest level theory now agreeto within the error of the measurements. Further analysis ofdeuterated methylnitrene remains to be done. In addition,emission spectra to several excited vibrational levels of theground state are available.ACKNOWLEDGMENTS

We appreciate the expert technical assistance of J. Wag-ner and G. Ladd in obtaining the spectra at Kitt Peak. TheNational Solar Observatory is operated by the Association ofUniversities for Research in Astronomy Inc., under contractwith the National Science Foundation. This research wassupported by the Astronautics Laboratory (now PhillipsLaboratory, Propulsion Directorate), Edwards Air ForceBase, California.APPENDIX: HAMILTONIAN AND MATRIX ELEMENTSFOR A 3E ELECTRONIC STATE

Hamiltonian terms diagonal in KH = H,, + &ax + Hm- + Hc, + HSR + f&mHso + &OR = aL,S, - ZaN, CL, + G, 1,H ROT= AN: + RN; + N; 1,H,, = - D,N4 - D,N2N; - D,N:,HsR = E,,N,S, + (ebb + E,,)(N+ S- + N- S+ l/4,Hss = 2/l(S; - S2/3).

Interaction terms between levels differing in KJ. Chem. Phys., Vol. 96, No. 2, 15 January 1992


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926 Brazier, Carrick, and Bernath: Rotational analysis of the 0: band

H = h, [A- Iv: + A, N2- ] + h, [A- (N*N- + N- Iv,) + A: w&v+ + N, N,)]+o,[A-S+ +AZ,S*-]+o,[A-bS,S- +S-SJ+A2+GzS+ +S+SJ]+ el [AN, S, + A: N-S- ] + ~27A- (NJ- +% N,) + A: W,S+ +S+ Nz)]+ E2bA2- (&N-w + N- s,) + A: (SzN+ + N+ s, I].

Diagonal matrix elements(JKPX;+ IHjJKPX;k) =u~~,~C-~AK~, +2/2(X2-22/3) +e,,KI: f 1/2(~,, +eC,)(2-X2)

+ (A-B)K+B[J(J+ 1) -2(K+8)8+2]-DD,K4-DD,[J(J+ 1) -2(K+2)8+2]K2-DN[ (J(Jf 1))2 - 4I;KJ(J+ 1) + (8 - 6X2)J(J+ 1)- (4-6Z2)K2-2EK+4(1 - X2)1,

where!3= (5 IL I!z )

andL=((sL +GzlC)-

Spin-uncoupling(JK,P + 12 + 1; + IH IJKPE; rt >

= - [B-2D,[J(J+ 1) +K- l-221 -DD,K2- (ebb + Ecc)/~]x[W(J+ 1) -2(K+I:)(K+Z+ l)l,

(JK,P + 2,H + 2; + (H (JKPE; + )= -2D,[J(J+ 1) - K(K- 1)]2[J(J+ 1)- K(K + l)]12.

Elements off-diagonal in K(J,-K+~,-PP+~,-Z;*IIH(JKPZ;&)

= +(-l)J-K+h,[J(J+l)-(K+I:-l)(K+ B - 2)]2[J(J+ 1)- (K+Z)(K+Z-l)]2,

(J,-K+2,-P+l,-E-l;~~IHIJKP~;f)= f ( - l)J--K+l(E, - 2h,)

x[W(J+ 1) -2(K+S)(K+Z- 1)]2,(J, -K + 2, -P, - Z - 2; f IHIJKPZ; +. )

= + ( - l)J-Kf2(01 + h, -E, ),

(J,-K-1,-P-1,-E;~IHIJKPZ;*)= f (- 1)J-K[h2(2K+ 1) +~E,,I:]

x[J(J+ 1) - (K+2)(K+Z+ 1>12,(J, - K - 1, - P, - Z + 1; f (HIJKPX; + )

= + (- 1)J-K[(~2, -h2)(2K+ 1)+ (02 -&,)(2x - 111 (2)2.

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C. R. Brazier et al- Rotational analysis of the 0-0^0 band of the A^3-E-X^3-A2 system of...

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