- Email: [email protected]
Fourier transform spectroscopy of HCN in the 14-μm region
JOURNAL
OF MOLECULAR
SPECTROSCOPY
138, 54 1-56 1 (1989)
Fourier Transform Spectroscopy of HCN in the 14-pm Region GEOFFREY
DUXBURY
* AND Yu GANG
Department of Physics and Applied Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 ONG, Scotland, United Kingdom
The 710-cm-’ bands of various isotopes of HCN have been measured with a resolution of about 0.005 cm-’ using the National Solar Observatory Fourier transform spectrometer. Six bands of HCN, one band of H’%ZN, and one band of HC15N have been analyzed to obtain accurate band origins and rotational constants. The accuracy of the calculated band origins are better than 0.0003 cm-’ for most bands. Relative integrated intensities have been derived from these spectra by comparison with simulations. and examples of the method used are given. ‘P 1989 Academic Press,Inc. 1. INTRODUCTION
The v2 band of H’2C’4N is secondary calibration standard for the 14-pm region, and is a textbook example of a perpendicular band of a linear molecule. Although this band has been studied many times ( 1)) until the very recent work of Hietanen el al. (2) using a high-resolution Fourier transform spectrometer (FTS), this band had been studied only with high-resolution grating spectrometers (1, 3). The increased resolution and sensitivity of Fourier transform spectrometers has made it possible to make more accurate measurements on many hot bands and isotopic bands which were previously too badly overlapped for accurate measurement. Recently Choe, Tipton, and Kukolich have used the National Solar Observatory (NSO) McMath Solar Fourier transform spectrometer to remeasure the 3300 cm-’ bands with a resolution of 0.0 1 cm-’ (4)) and Choe, Kwak, and Kukolich have studied the 2100 cm-’ bands using the same instrument (5). Our interest in the 14-pm spectrum of HCN arose as a result of current experiments to elucidate the fragmentation routes in secondary amines subject to dc discharges, and of previous experiments to produce methylenimine by pyrolysis and by dc discharge t,6, 7). In all these systems HCN is a stable end product. Diode laser absorption spectra of the HCN produced as the end product in discharges appeared to show a nonequilibrium vibrational excitation (8). In order to test this hypothesis we have analyzed the v2, 2v2-v2, and 3v2-2v2 bands of HCN and the v2 bands of H13CN and HC’*N observed during the original experiments on CH2NH using the National Solar Observatory Fourier transform spectrometer (6, 9, 10). ’ Visiting Scientist, National Solar Observatory Kitt Peak, National Optical Astronomy Observatories operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation.
541
0022-2852189 $3.00 Copyright @ 1989 by Academic Press. Inc. All rightsof reproductionin any form resewed.
DUXBURY
542
AND GANG
II. EXPERIMENTAL
DETAILS
The Fourier transform spectra were obtained with the McMath Fourier transform spectrometer developed by Dr. J. W. Brault at the National Solar Observatory. The HCN was produced as a minor breakdown product of methylamine pyrolysis in a Imm internal diameter quartz S-bend tube at ca. 1000°C. The total pressure of the pyrolysis products in the absorption cell was ca. 500 mTorr. Sixteen traversals of a 60-cm absorption cell were used, and the pyrolyzed gas flowed slowly through the cell. The spectra were recorded with an unapodized resolution of 0.0048 cm-’ using a JPL filter and a liquid-helium-cooled detector. Further details of the data reduction and interpolations are given in Ref. (6). The effective temperature in the cell, deduced from the intensities of the CHzNH spectra, was ca. 300 K, just above the temperature of the laboratory, which was 20°C (293 K). Two spectra were used for the analysis. The first used eight scans of the FTS without purging of the optical path outside the spectrometer, and the second 30 scans with purging. The first spectrum was used for the hot bands since the HCN spectra were stronger, and the second for the fundamental and where interference with water and carbon dioxide lines occurred. The absolute accuracy of the frequency calibration is shown in Table I, where the v2 band lines of CO2 measured as residual impurity in the FTS tank are compared with those tabulated by Kauppinen and Horneman ( I I ) . It can be seen that the McMath results are on average 35 X 10e5 cm-’ higher than those obtained with the Oulu instrument. The simulations were carried out using an Acorn Archimedes microcomputer. In order to facilitate comparison of the simulated with the experimental spectra, the TABLE I A Comparison of CO2 Line Positions with Those in Calibration Tables Q(J) (a) 2 4 6 6 10
12 14 16 18 20 22 24 26 28 30 32 34 36 36 40 42 44 46
667.386963 667.400635 667.423401 667.454173 667.494141 667.541382 667.597534 667.661143 667.773154 667.814697 667.903564 666.000427 668.105713 666.219238 668.341064 668.470947 668.609070 668.754944 668.909241 669.071594 669.241699 669.419922 669.606567
(b) 667.386040 667.400539 667.423321 667.454303 667.493721 667.541330 667.597205 667.661336 667.733721 667.614344 669.903200 666.000275 668.105559 668.219037 666.340695 668.470518 668.606489 668.754593 668.906609 669.071119 669.241503 669.419936 669.606400
a-b X(105) 92 96 6 39 42 5 33 41 -57 35 36 15 15 20 37 43 58 35 43 48 20 -1 17
(a) This work. (b) Tabulated positions, Reference (11). a-c denotes observed - tabulated line positions.
14-pm SPECTRUM
543
OF HCN
Fourier transform spectra were downloaded onto the Archimedes, and were treated to remove as far as was possible the channeling evident in the originals (see Ref. (6)). Both sets of spectra were then plotted using a HP A4 graph plotter. III. ANALYSIS
AND RESULTS
‘a) Observed Spectra
The assigned spectra cover the region from 620 to 820 cm-‘. Lines were assigned to eight different bands (six of HCN, one of H13CN, and one of HC13N) with natural isotopes. The assigned bands are: HCN: 01 ‘O-00’0, 02°0-01 ‘0, 0220-01’0, 0310-0200, 03 ‘0-02’0, 0330-0220. H13CN: 0 1'0-00'0. HC”N: 01 ‘O-00’0. (b) Theoretical Model
Following Maki and Lide ( 22) and Maki (13)) the energy of the vibration-rotation levels in the absence of perturbations can be written as G(u, J) = V, + B,J(J+
1) - D,[J(J+
1) - 1212+ H,[J(J+
1) - f213,
(1)
where v, is the vibrational energy, B, is the rotation constant, D, is the quartic centrifugal distortion constant, and H, is the sextic centrifugal distortion constant. For the ground vibrational state v, = 0 and 1 = 0, so that ( 1) reduces to the usual expression for the ground state of a linear molecule. For all other states we need to consider the effect of the vibrational angular momentum. The operator connecting states differing in 1 by 2 is known as the Z-type doubling operator when the states coupled would otherwise be degenerate, and the l-type resonance operator when they are nondegenerate. The p operator, introduced by Maki and Lide (22), connects states differing in 1 by 4. The Z-type doubling (resonance) parameter, qv, is expanded as a power series in J as follows (13): q”J = q: - qiJ(J
+ 1) + qiJJ2( J + 1)2.
(2)
The (0 1’0) II state exhibits first-order Z-type doubling, since the q vibrational operator can couple a degenerate pair of states having 1 = It 1. The resultant energy levels are given by G(v, J), = G(n, J) - q,J(J
+ 1)
G(v, J)f=
+ 11,
WV, 4 + q,J(J
(3)
where G( 0, J) is given by Eq. ( 1) and qvJ by Eq. (2). For states with I Z 1 the matrix elements of qoJ responsible for the I-type resonance take the form (u.IIH~~),Z+~)=~~{[J(J+
1)-&l+-
l)][J(J+
I)-(I+
l)(Z*2)]
x [(V T Z)(V * 1+ 2)]}“2,
(4)
DUXBURY
544
AND
GANG
and those associated with p may be written as (u,ZINIV.z+4)=~P{[J(J+ X[J(J+
l)-Z(Zk
l)][J(J+
l)-(Z+2)(1+3)][J(J+
l)-(I?
l)(Zk2)]
l)-(Z-t3)(1+4)]
x [(V T Z)(V 1 z + 2)(V F z - 2)(V f z+ 4)]}“2.
(5)
Full expressions for the resultant secular determinants are given in Refs. (4, 5, 12). When the least-squares fitting procedure was carried out for each set of bands, the variables and the constrained constants were chosen in such a way that whenever accurate values were available from earlier microwave and/or other infrared measurements of comparable accuracy to the present ones, the parameters were fixed as constants. In Table II the parameters that have standard deviations given in parentheses TABLE nolecular
state
I
VI
I-
constants
( 0000)
I
a, 0”
1.487221825(40)= 2.90851(5301a 2.72(128)" -
I x10-6
I
Ii" x10-121 q,o x10-3 I
I
qvJ x10-8 qvJJxro-‘2~ Q x10-8
I
state
I
(0220) 1426.530451(12)
I
1.484995(21 3.03265(260) (2.72$
I 1
v,
a,
D"
NV q,o
I
x10-6 x10-121 x10-3 I
Of Ha4 (cm-‘)
-
(-1.2l)f n01ecu1ar
“V
q,o
qvJ
I-
I i.43wd’
constants
, 2.76756(21h
All three
7.709034
I -
1.2
of
HC’ 5N (01'0)
705.9659(l) 1.443157(2) 2.8226(15)
x10-121 1.10 x10-3 I x10-8
qyJJxlo-‘21
(a) (b) (C) (d) lel (fl (41 (h)
(0000)
I
bff Bu D, x10-6
(0330) 2143.7632(5) 2143.759949 1.487854 3.0814 (2.72$'
9.3168
n’3a4
state
(0200) 1411.41376(9) 1411.41380(9)e 1.4858289(20) 3.05321(260) (2.72$ 7.5978g4 lo.o7o7d 4.6sd (-1.2l)f
(01'0) 711.97985(8) 711.97965C 1.481772(2) 2.97467(38) (2.72$ 7.48773d 8.86820d l.1878d (03'0) 2113.4509(3) 2113.450369 1.489570 3.0814 (2.72$'
7.597898 lo.o7o7d 4.6sd
qvJ x10-8 I qvJJxlo-‘21 Q x10-8 I
II
1.10
7.162o(4)h 8.126h
1.0
I
(01'0)
(OOOO)
711.0268(2) I I 1.4xmd’ 1.438653(3) I 2.74773(23)h2.803(6) I 1.72 1.72
I
-
7.o694(94)h
7.w+
I I -
1.2
standard deviations. Ref. (13). Frozen at ground state values. Ref. (2). Fit to microwave l-type doubling Direct fit to 02°0-O040. Frozen at value in Ref. (12). Ref. (51. Ref. (4).
transitions
in
Ref.
(13).
14-rrn SPECTRUM OF HCN
545
were varied, and those without listed standard deviations are from the reference cited. In every band H’ and H” are fixed at 2.72 X lo-l2 cm-’ and qf’ and qf” are fixed at 1.2 X 1O-‘2 cm-’ (from Ref. ( 23)). The vibrational transitions observed are shown schematically in Fig. 1. This is similar to the diagram given by Wang and Overend (3)) but we have used the newer e-f notation ( 14). (c) HCN Ol’O-00’0
at 711.979 84(3)
cm-’
This band has been remeasured very recently using the Oulu high-resolution FIS (2). Our results are given in Table III. We find that there is a small constant frequency shift between the two sets of data which is similar to that found for CO2 (see Section II). The lines reported here extend to much higher values of J than those given in reference (2). The extrapolated position of the high-J lines given in (2) show a Jdependent shift from our measured values. The I-type doubling in the 0 1’0 state has been measured very accurately by microwave spectroscopy ( 12, 15). We have determined qv and qi directly from the l-type doubling transitions, and held them constant during the fitting of the infrared data. (d) HCN 02°0-01 ‘0 and 0220-01 ‘0 First Hot Bands at 699.43405 714.55069 cm-’
cm-’
and at
These bands have previously been reported by Wang and Overend (3). However, the present frequencies are an order of magnitude more accurate, and the standard
3 _____________________--___
(0320)
n v2=
\-------
f0220)
A
/_________________
_____________________-______ __--_
_--_________-___-=.____---_-- i ... _- - ____ . __
v2= 2 (02’0)
c
(0110)
n
\
“a=
1 (
____________________
f (d)
-------_--_____--
._- _-- -_
--____
___ ___-______-___-________----____- f
-----
-- _---__i' _____--__--
__________-_________
(d)
T ._____________-__--_---__ e
(c)
II
(00’0)
v2=
c
0
I I
FIG. 1. The vibrational energy levels of HCN associated with the transitions observed in this work. The new e-fnotation is used, and the older c-d notation is given in brackets to facilitate comparison with earlier papers.
DUXBURY
546
AND
GANG
TABLE III The
01'0
P(J) OS.5
o-c
706.06683 703.10974 700.15265 697.19513 694.23798 691.28082 688.32379 685.36664 682.41003 679.45349 676.49750 673.54187 670.58679 667.63208 664.67810 661.72485 658.77234 655.82050 652.86963 649.91968 646.97070 644.02252 641.07568 638.12982 635.18530 632.24194 629.30005 626.35919 623.42004 620.48218 617.54620 614.61151 611.67828 608.74750 (605.81842) 602.89002
15 3 8 -20 -8 0 10 -9 4 -7 0 2 9 -3 -2 4 9 2 7 11 16 -3 3 -7 -4 -12 -1 -4 -18 -31 -7 -12 -32 25 82 29
J
O-C denotes The
lines
observed in brackets
(a)
band
of HCN
(714.93762) 717.89148 720.84662 723.80115 726.75501 729.70807 732.66040 735.61182 738.56238 741.51184 744.46021 747.40710 750.35309 753.29761 (756.24152) 759.18286 762.12256 765.06146 767.99829 770.93347 773.86621 776.79742 779.72656 702.65332 785.57764 (788.49915) 791.42084 794.33814 797.25372 (800.16516) (803.07465) 805.98254 806.88648 811.78735 814.68500 *1 *2 *3
- calculated are blended
line and
(cm-')
o-c X(105)
R(J) OBS
X(105)
a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
-OO"O
171 -4 0 2 3 -2 0 -1 7 8 9 -19 -12 -20 53 17 -26 15 20 31 6 15 21 1 -42 -136 25 -7 45 -54 -78 -16 13 -3 -34
o-c X(105)
Q(J) OBS
711.99426 712.02368 712.06738 712.12585 712.19861 712.28644 712.38825 712.50482 712.63593 712.78143 712.94159 713.11591 713.30481 713.50806 713.72553 713.95734 714.20331 714.46381 714.73816 715.02661 715.32929 715.64539 715.97601 716.32044 716.67859 717.05048 717.43573 717.83514 718.24768 718.67377 719.11389 719.56610 720.03247 1720.50433) 721.00409 721.50934 722.02728
-19 3 -6 4 -15 17 -7 -7 -5 -11 3 -9 -3 3 -2 -1 -8 18 14 11 26 -18 1 10 11 11 -20 5 -12 -20 7 -27 3 -732 20 24 10
positions. were
omitted
Asterisks denote lines which are so seriously identified. The calculated positions of these *1: 817.58014 R(35) 820.47168 *2: R(36) 823.35988 *3: R(37)
from
the
blended that lines are:
least-square they
CaMOt
fit. be
deviation of the fit (0.0001 cm-‘), is much smaller than that obtained previously (about 0.002 cm-‘). We have also been able to detect the Q branches of the 02*001’0 band, including the branch which was not reported in the earlier study. Our analysis preceded in an iterative fashion. The high-resolution Z-type doubling data of Maki and Lide (12) was used to determine the I-type doubling constants which were held fixed when the infrared spectra were fitted. The revised value of the 02°0-0220 interval was then used to recalculate the l-type doubling constants, and the process cycled until self-consistency was obtained. The observed and calculated lines are given in Table IV.
14-&m SPECTRUM
OF HCN
547
TABLE IV The P(J) OBS
J
‘
3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
696.41191 693.53772 690.61273 687.70355 (684.80835) 681.93060 679.06641 676.21582 673.37915 670.55493 661.14365 664.94257 662.15216 659.37091 656.59772 653.83179 651.07196 648.31641 645.56470 642.81525 640.06702 637.31885 634.57044 631.81927 629.06549 626.30841 623.54840 (620.78381) 618.01270 (615.23907) (612.45905) (609.67236) (606.87933) See
TABLE
OZ"O
- 01'0
band
o-c X(105)
R(J) OBS
11 26 3 10 -116 5 22 -10 0 -27 35 -3 2 -2 -19 -15 9 -11 0
705.39300 708.39490 1711.41333) 714.44287 717.48900 120.54694 723.61798 726.70056 729.79315 732.89661 736.00848 739.12671 742.25153 745.38324 748.51685 751.65295 154.79034 151.92137 761.06213 764.19629 767.32452 770.45000 773.56793 776.67944 (779.78040) 702.87982 785.96576 (709.04010) 792.10944 (795.17523) (79”‘~;;’
2 -6 50 12 -24 -54 20 83 -23 133 175 89 -104
_
of "CN
(cm-')
o-c X(105)
o-c X(105)
Q(J) OS.9
-
37 3 142 -44 42
*1
(699.43671) 6gz3*627' *3 *4 *5
21 32 -27 28 63 -18 -67 12 28 -6 -19 -45 -72 -32 -43 4 -21 -12 -106 14 -38 96 -7 388 172
699.43671 '6 699.42127 699.40851 699.38886 699.36438 699.33099 699.28906 699.23724 699.17438 699.09937 699.01038 698.90662 698.78729 698.65088 690.49646 698.32361 698.13104 697.91870 (697.68610) *I (7g7.15%2' *9 *lo _ *11
'13
102 -43
14 -62 18 -50 40 13 -1 -10 -6 21 10 -3 14 14 0 15 5 27 a4 146
III.
Calculation
of the strongly
blended
lines:
*1: *2: *3: *4:
Q(l) Q(4) Q(5) Q(6)
699.43453 699.43866 699.43988 699.44032
*a: *9: *IO: *ll:
Q(30) Q(31) Q(32) Q(33)
*5: *6: *7:
Q(7) Q(9) Q(28)
699.43943 699.43099 697.43097
*12: *13:
R(32) R(33)
696.85856 696.53973 696.19935 695.83795 801.26177 804.29166
(e) HCN 02°0-O000 Overtone Band These measurements were previously reported by Duxbury and Le Lerre (9) in their paper on the v5 and v6 bands of CHzNH. Their data were fitted using the ldoubling constants determined for the hot bands (see Section (d) above). The resultant position of the 02’0 vibrational level is then consistent with that deduced from the analysis of the 0 1 ‘O-00 ‘0 and the 02 ‘O- 11’0 bands (see Table II). (fl HCN 03’0-0220 and 03’0-02°0 Second Hot Bands These bands are very weak and can only be seen clearly in the spectra in which eight scans were used. Recently, Choe, Kwak, and Kukolich (5) have analyzed the 03 ‘O-00’0 bands recorded using the same Fourier transform spectrometer. Although there is good agreement between the band origins obtained by combining their mea-
DUXBURY
548
AND GANG
TABLE IV-Continued The 0Z20
J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
See
-
Ol’=O
o-c
P(J) OBS
-24 -20 1 -11 -3 14 -6 9 20 7 7 -4 -10 22 14 6 -2 2 -12 -42 16 43 -35 24
of.HCN
X(105)
720.50433 723.50250 726.51563 729.54224 732.58417 735.64124 738.71491 741.80475 744.91223 748.03760 751.18164 754.34607 757.53149 760.73853 763.96942 767.22418 770.50342 773.80975 777.14313 780.50446 783.89551 787.31696 790.76788 (794.24420) 797.76703 (801.31305) (8059if39) _ -
(cm-‘) o-c
R(J) OBS
X(105)
705.72443 702.81110 699.91272 697.02924 694.16168 691.31055 688.47607 685.65975 682.86206 680.08374 677.32617 674.59021 671.87714 669.18848 666.52466 663.88733 661.27771 658.69714 656.14648 653.62689 651.14044 648.68689 646.26636 643.88257 *1 *2 *3 *4 *5
band
-38 -27 -22 19 0 -18 15 4 24 20 -18 -13 -3 -31 20 41 -15 5 -7 -57 -59 -27 -123 -833 -40 -164 1402
*7 *8 *9
Q(J) OBS
(714.58319) 714.63391 714.69000 714.75983 714.84418 (714.93762) 715.05167 715.17847 715.31744 715.47089 (715.64539) 715.81842 716.01300 716.22138 716.44385 716.67859 716.92828 717.19159 717.46790 717.75757 718.06036 (718.37647) 718.70715 719.05209 719.40704 (719.77643) (720.159301 (720.54688) (720.96393) (721.38483)
o-c X(105)
-927 -45 22 -20 -3:: -33 0 -34 -7 745 -30 -26 -16 35 -54 -9 39 34 15 -35 -95 -30 -49 -32 -68 -68 -903 -90 -186
TABLE III. Calculation
of
*1: *2: *3: *4: *5: *6: *7: *8: *9:
= = = = = = = = =
P(27) P(28) P(29) P(30) P(31) R(28) R(29) ~(30) R(31)
the
strongly
blended
lines:
641.53293 639.21945 636.94299 634.70170 632.49785 808.50751 812.15250 815.82999 819.53982
surement with ours of the 02°0-OOo0 band, it has not proved possible to fit data to within the experimental accuracy by using their rotation constants for the 03’0 state. In Table II both sets of parameters are given. The differences probably reflect the problem of checking the absolute frequency calibration of Fourier transform spectroscopy when very high-resolution spectra are recorded. The line positions are given in Table V. (g) H13CN 01 ‘0-OO”O Band This band has previously been analyzed in a fragmentary fashion (3). With the high-resolution FIS the majority of the lines recorded are free for blending, and accurate values of the excited state constants and band origins have been derived. See Table VI.
14-pm SPECTRUM
OF HCN
549
TABLE IV-Continued The
(OZzO)-(Ol'fO) o-c X(105)
P(Jl OBS
J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 20 29 30 31
-21 8 -2 -3 17 -10 -43 137 4 9 -S -6 -2 14 -8 -1 9 -26 -17 18 -39 -4 -30 -59
705.63452 702.66119 699.68677 696.71179 693.73645 690.76013 687.78332 (684.80829) 681.82983 678.85254 675.87488 672.89734 669.91980 666.94244 663.96484 660.98773 658.01093 655.03400 652.05792 649.08258 646.10687 643.13269 640.15857 "'lr'Z'S
-110 -92 -23 -220
(631.24097) (628.27069) 625.30194 (622.33160)
See TABLE
band
of HCN
It(J) OBS
(cm-')
o-c X(105)
720.48975 723.45721 726.42358 729.38916 732.35291 735.31567 738.27649 741.23594 744.19324 747.11935 750.10352 753.05592 756.00641 758.95417 761.90015 764.84473 767.78644 770.72559 773.66242 (776.59607) 779.52924 782.45789 785.38452 788.30847 791.22906 (794.14642) (797.06073) 799.97375 (802.88117) *2 '3
22 -11 -32 -3 -19 11 -3 -22 -34 -18 -16 3 18 -32 -49 13 14 -7 -19 -99 28 -33 -24 -4 -33 -91 -153 -33 -157
Q(J) OSS
o-c X(105)
714.54773 (714.54773) -*4 *5 *6 *7 *8 *9 _ *10
10 275
(714.54773) 714.56299 714.58301 714.61060 714.64563 714.69000 (714.75964) 714.81213 714.89203 714.98608 715.09552 715.22089 715.36360 715.52460 715.70319 715.90216 716.12030 (716.35858) (716.61682)
-168 -33 -21 40 24 1 1445 -6 -14 -17 -4 -20 -55 17 -59 -25 -51 -75 -140 -217
III.
Calculation of the strongly blended *1: l2: *3: *4: *5: *6: *7: *a: *9: *10: *11:
P(27) R(30) R(31) Q(4) Q(5) Q(6) Q(7) Q(S) Q(9) Q(lO, Q(31)
(h) HC15N 01 ‘O-00’0
Band
= = = = = = = = = = =
lines:
634.21273 805.78675 808.68854 714.54187 714.53868 714.53584 714.53392 714.53355 714.53545 714.54044 717.19588
This band is weaker than that of the i3C isotopic form; nevertheless the spectra recorded with the higher HCN concentration have allowed us to derive accurate values for the line frequencies of much of this band. See Table VII. IV. RELATIVE
BAND INTENSITIES
The observation of the high-resolution spectrum of the v2region of HCN has allowed us to determine the relative sizes of the integrated intensities of the sub-bands of HCN and its isotopes. In order to accomplish this we have written a computer program to
DUXBURY
550
AND
GANG
TABLE V The
03'0
J
- OZ"O
o-c
P(J) 0%
-34 -21
690.10510 687.10486 684.09656 681.08319 678.06403 675.03998 672.01093 668.97943 665.94501 (662.90796) (659.86987) (656.83112) (653.79248) (650.75586) (647.721070 (644_6!;5a)
58 -18 4 6 3 -60 -2 58 72 119 154 171 276 368 511
(638.63879)
TABLE
-3 4 -37 -29 -25 -336 -461 31 452 528 151 110
(765.61383) *4
866 1244
635.62213*
See
742.84247 1745.70795) (748.57068) -751.44013. (754.30512) (757.16534) (760.02039) *3
-34 792 a -21 71 3 -20 21 -10
o-c
Q(J) OBS
X(1051
705.00079 (707.96478) 710.90460 713.84393 (716.77649) 719.69959 722.61548 725.52460 728.42590 731.32086 734.20953 737.09192 739.96954
-
(cm-')
o-c
0%
X(105)
*1 693.09912
of HCN
NJ)
0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 la 19 20 21 22
band
X(105)
702.06108 702.10614 702.17499 702.26758 702.38312 702.52234 702.68579 702.87408 703.08667 703.32452 703.58783 703.87720 704.19348 704.93668 704.90729 705.30615 (705.73401) 706.18903
-14 -10 -25 9 -9 -30 -30 15 13 17 3 -la -6 -10 -24 -6 a2 33 -a
706%g7 *6 *7
III.
Calculation *1: *2: *3: *4: *5: *6: *7:
of the = = = = = = =
P(2) P(20) ~(20) R(22) ~~20) Q(21) Q(22)
strongly
blended
lines:
696.08636 641.66535 762.88344 768.61067 707.18826 707.73157 708.30253
TABLE V-Continued The 031e0 - OZzfO band of HCN (cm-')
J
o-c X(105)
Q(J) OBS 686.90179 686.88281 686.85736 686.82544 686.78577 686.74030 686.68738 686.62683
-7 -5 1 ia -58 -15 4 7
J 10 11 12 13 14 15 16 17
o-c
Q(J) OBS
X(105)
686.55841 686.48169 (686.39471) 686.30347 (686.19995) (686.08777) (685.96515) (685.83325)
-4 -42 -270 -56 -166 -204 -310 -331
The 031f0 - OZzeO band of HCN (cm-')
J
Q(J) OBS
2 3
686.99500 (687.06915)
4 5 6 7 a 9
687.16473 687.28436 687.42706 687.59168 (687.77045) 687.98248
See TABLE
III.
o-c X(105) 72 176 45 -6 -a 0 -666 10
J 10 11 12 13 14 15 16 17
Q(J) OBS 688.20599 (688.44605) 668.70520 (688.97430) (689.25714) (689.55072) (689.85358) -
o-c X(1051 -34 -162 24 -238 -406 -606 -800
551
14-pm SPECTRUM OF HCN TABLE VI The 01'0
0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
708.84528 711.72333 (7156J;53)
20 2 997
720.35187 723.22595 726.09845 728.96985 731.83960 734.70831 737.57520 740.4405s (743.30573) 746.16620 749.02673 751.88477 754.74078 757.59479 760.44751 763.29749 766.14563 768.99054 771.83392 774.67432 777.51233 780.34784 (783.17706)
0 17 1 6 -14 7 -1 -3 144 -5 34 10 -19 -47 7 5 44 -8 27 11 12 26 -310 -31
-199
Calculation
of the
simulate the appropriate its application in (b) .
o-c X(105)
-10 -5
(622.30684)
P(28)
(cm-')
R(J) OBS
6 -10 24 -12 -10 1 0 7 10 -12 -8 3 -3 4 -7 -10 67 48 -5 29 5 -102 -95 -243
R(3) R(28) R(29) Q(28) Q(29)
of H')CN
X1105)
700.20514 697.32361 694.44165 691.55878 688.67590 685.79187 682.90784 680.02356 677.13892 674.25415 671.36920 668.48395 665.59894 662.71405 659.82910 656.94446 654.05988 651.17566 (648.29224) 645.40900 642.52551 639.64343 636.76135 (633.87909) (630.99866) (62:1;:43)
*1: *2: *3: *4: *5: *6:
band
o-c
P(J) OBS
J
- OO"O
= = = = = =
786.0zg1 *4
strongly
blended
Q(J) OBS
O-C X(105)
705.97961 706.00610 706.04694 706.10089 706.16791 706.24908 706.34332 706.45105 706.57214 706.70673 706.85453 707.01563 707.19000 707.37787 707.57910 707.79303 708.02026 708.26129 708.51471 708.78155 709.06091 709.35339 (709.65143) 709.97760 (710.30841) 710.65259 (711.00848) *5 *6
19 -29 8 11 -27 6 2 4 2 10 7 -6 -18 -10 11 -21 -39 9 -14 1 -33 -51 -834 -28 -68 -46 -119
lines:
625.24087 717.47617 788.83708 791.66114 711.37898 711.76079
regions of the spectrum.
This is described
below in (a) and
(a) Spectrum Simulation The individual line intensities are calculated using the form for the integrated tensity given by Smith et al. (16) and Johns ( 17),
Si = SiRiFi,
(6)
where Sz is the vibrational band intensity, Ri is the rotational Herman-Wallis factor. The rotational factor is given by Ri=Y’*L+t~p(-~~~~)[l
vo where vi is the line frequency,
in-
factor, and F, is the
-exp(-v,/kT)], r
v. the band origin, Li the Honl-London
factor, Qr the
DUXBURY
552
AND
GANG
TABLE VII The
J 0 1 2 3 4 5 6 I tl 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
(705.28455) 702.41516 699.54395 696.67291 693.79279* 690.93182 688.06146 685.19092 68fi3?:02 676.58283 673.71442 670.84662 (667.97321) 665.11267 662.24683 (659.38324) 656.51782 (653.65375) (650.79157) (647.93048) (645.06930 See
TABLE
R(J) OBS
o-c X(105) -7 91 4 3 11 4 -47 39 26 -13 -51 -13 28 80 -9 31 -20 208 -B
713.89697 (716.76605) 719.63654 722.50562 725.37427 728.24219 731.10901 733.97648 736.84216 739.70672 742.57037 745.43378 748.29614 (751.15747) 754.01617 756.87488 759.73132 (762.56496) 765.44098 768.29291 (771.14331) 773.99280 776.84027 (779.68250)
-110 31 -7 -27 -964 2 7 -33 59 -18 -16 -8 -625 -24 -29 110 -1:: -113 -109 -221
-97 25 -32 -346
Q(J) OBS 711.04071 711.06836 711.11017 711.16547 711.23505 711.31867 (711.41315) 711.52637 711.65100 711.78937 711.94165 (712.10883) 712.28729 712.48145 712.68774 712.90869 713.14246 713.39008 713.65143 713.92651 (714.21558) 714.51666 (714.82983)
o-c X(105) 4 -23 4 -19 -1 36 -225 5 -3 -17 -16 99 -27 52 -25 12 -41 -55 -47 -11 83 42 -121
III.
Calculation *1:
01'0 - OO"O band of HC15N (cm-')
O-C X(105)
P(J) OBS
~(11)
of the
strongly
blended
lines:
= 679.45201
lower state rotational partition function, and E: the lower state rotational energy. In the present work the rotational dependence of the line strengths did not differ from that predicated by the Honl-London formula, and hence F was set equal to unity. In degenerate bands it is common to refer not to the band intensity, but to the vibrational sub-band strength (see Toth (18)). We will denote this by S$. Since the Ho&London formulae are obtained by summing the squares of the direction cosines, a& and Q&, for the degenerate vibration (19), when the line strengths of the three transitions with the same J” are added we obtain the value 2 X (2.7’ + 1) (20). The integrated sub-band intensity will then be approximately twice the vibrational subband strength. There is an ambiguity concerning the definition of the rotational partition function for nearly degenerate states. We have chosen to compute these for each component of the degenerate levels separately, so that there are two for o2 = 1, three for u2 = 2, and five for n2 = 3. The relevant HSnl-London factors for the perpendicular band are then L, = (s’f I
L,= I
I+)(s’+ J”+
(2Y+
1+ 2)
(8)
1
l)(S’rI)(J”*I+ J”(s’ -I- 1)
1)
(9)
553
14-brn SPECTRUM OF HCN
L, = (J”? t
Z)(J” T l-
1)
J”
( 10)
’
respectively, for R, Q, and P branches. S$ takes into account only the rotational partition function. The vibrational sub-band intensity, S~,J, is given by
( 1vofl(P”,,>12,
SE,,= g
(11)
”
where v. is the wavenumber of the band center, Qv the vibrational partition function, and I( p,,,) 1the transition moment of the vibrational sub-band. N is the total number of molecules of the absorbing gas per cm3 per atm and is given by
(12) where IZis Loschmidt’s number, p is the gas pressure in the atmosphere, and C is the isotopic abundance. If ( ( pL,,,)1 is in Debye, S, in cmm2/atm, energies in cm-‘, and Tin Kelvin, sll,
=
v.
3054ww)~2
5
exp(_E”l,kT)
QU
“,
T'
(13)
The integrated band intensity, SE,,, is then related to Si,, by
SL.l= SZ,,C &Fi,
(14)
where, as we have noted, S’,, m 2S$. In all the calculations the rotational constants and vibrational energies were taken from the current work, and also from Refs. (4, 5, 12, 13). The isotopic abundances were those recommended by de Bievre et al. (21). The partition functions were obtained by direct summation. The absorption spectrum was first calculated with a Gaussian line profile, since at the low pressures used in the experiments the Voigt profile is very close to a Doppler lineshape. However, as the fitting proceeded it proved to be necessary to use a Voigt profile, which was calculated by numerical convolution. The calculated absorbance was converted to transmittance by exponentiation and the result convolved with an instrumental lineshape function. For comparison with the spectra run using the NSO FTS the instrumental function used was the sine function, (sin x/x). (h) Results In our calculations we assumed initially that the transition moments of the Hi3CN and HC”N v2 bands are the same as those of HCN, and that the integrated intensities could be predicted using the relative isotopic fractions. We also assumed that the transition moments of each component of 2v2 - u2 and of 3~2 - 2v2 were identical to v2 -- 0.
a
% TRANS.
709.40
711.55
X TRANS.
b
i
I
709.400
711.557
715.073
713.715
718.031
cm-l
FIG. 2. The Q-branch region of the uz bending fundamental band of HCN. The total pressure of the pyrolysis products of methylamine was ca. 500 mTorr and the partial pressure of HCN ca. 120 mTorr. The observed spectrum is given in (a) and the calculated one in (b) 554
a
698.7
700.04
705.
702. QQ
12
cm-l *ATR ANS.
b
1oov
698.7
--VI
700.040
702.99
705.120
707.26
709.400
cm-l FIG. 3. The Q-branch region of the O2oO-O 1’0 band of HCN and the 0 1‘O-00’0 band of H13Cn with the same conditions as Fig. (2). (a) Observed, (b) calculated.
555
‘/TRANS.
a
m
100
P
II50-
718 cm-l
I 717
I
I
717.2
I
I
717.400
I
I
717.599
I
I
717.
a
cm-l FIG. 4. The Q-branch region of the 0330-0220 band of HCN. The total pressure of the pyrolysis products of methylamine was ca. 500 mTorr and the partial pressure of HCN ca. 420 mTorr. The observed spectrum is given in (a) and the calculated one in (b).
%TRANS.
a loo-
PT
i”
P
50
I
1
I
702
L
-
,
1
703.599
702.9
T”
I
L
I
,
706
705.2
704.400 cm-l
b
r-
1
10
5( 3-
I
702
I
702.9
I
I
1
703.599
I
704.400
,
I
I
705.2
706
cm-l FIG. 5. The Q-branch region of the 03’O-02°0 band of HCN with the same conditions observed spectrum is given in (a) and the calculated one in (b) . 557
as Fig. 4. The
i
1
I
685.90
I
I
686.3
I
L
I
L
687.09
686,7
L
I 687.90
687.5
cm-l
%TRANS.
b
10
I 685.900
1
t
686.300
I
I
686.7
J
I
687.100
I
t
1
687.
S
687.900
cm-l
FIG. 6. The Q-branch region of the 03’0-02*0 band of HCN with the same conditions as Fig. 4, (a) observed, (b) calculated. This Q branch is approximately four times weaker than those shown in Figs. 4 and 5. The broad pressure-broadened lines are due to CO2 in the optical path between the cell and the interferometer.
14-pm SPECTRUM
OF HCN
559
The Q-branch region of the v2 bending fundamental of HCN is illustrated in Fig. 2a and the simulation in Fig. 2b. The Q branch associated with the 15N isotope is clearly seen to the long wavelength side of the main Q branch. Q branches associated with the first and second hot bands are clearly seen within the envelope of the v2 Q branch. This spectrum is much stronger than that recently reported by Hietanen et al. (2). In Fig. 3 Q branches associated with the first hot band, 02°0-01 lfO, and with HC13N are shown. It can be seen that in both examples there is good agreement between the observed and calculated spectra. This suggests that the assumptions made about the transition moments are valid for the fundamental and the first hot band, and that despite the production of the HCN by high-temperature pyrolysis of methylamine, the temperature of the gas in the cell is close to that of the laboratory. However, when Q branches associated with the second hot-band system, 3v2 - 2v2, are examined, we find that the intensities of most of the Q branches are approximately twice those predicted on the basis of the intensities of the fundamental and first hot band. An example is shown in Fig. 4, where the Q branch of the hot band 03 lfO02”O is clearly seen in both the observed and the calculated spectra, and in Fig. 5, where the Q branch of the 03 30-02 ‘0 band is displayed. The 03 ‘O-O22Oband shown in Fig. 6 does not conform to the overall pattern since its intensity is only about a quarter of that of the other bands. This behavior is similar to that found for intensities
TABLE VIII Vibrational Populations, Isotopic Fractions, and Rotational Partition Functions at 300 K Vibrational isotopic
population fraction
and
HCN
HC-N
HCi5N
Total
1
0.0111
0.0037
0000
0.9353
0.0104
0.0034
0110
0.0615
0.0007
0.0002
0290 0220
0.0011 0.0020
Rotational (excluding
partition function, Qr vibrational degeneracy)
HCN
HCi3N
HCiSN
0000
141.46
145.21
145.69
OliO
140.12
0200 0220
140.64 140.79
560
DUXBURY
AND GANG
of the hot bands of the bending vibration of CO? by Reichle and Young (22). The fraction of molecules in the lower vibrational states of all the transitions, the isotopic abundances, and the rotational partition functions are given in Table VIII. The relative values of the integrated intensities used to fit the spectra, together with those of CO*, are given in Table IX.
TABLE IX A Comparison of the Integrated Band Intensities, S:, of HCN at 300 K with Those of CO* Transition
01'0-00'0
S+i-aAtm-i
HCN (al
coa (b)
227
200
7.4 15.3
4.27 15
0310-02'0
0.52
1.0
0310-0220
0.23
0.14
0330-0220
1.01
0.85
01~0-00'0
2.51
OliO-OO@O
0.84
(a) Scaled to 2 X S p,O= 233 cm-’ Atm-’ (see Ref. (16)). This value was obtained from high-pressure measurements, and hence includes all isotopic and hot-band contributions. The values of the integrated intensities of the HCN bands in the table are therefore probably too high, although the relative intensities should be quite accurate. (b) Ref. (22). (c) Isotopes in natural abundance.
14-pm SPECTRUM OF HCN
561
By using the simulation technique we have been able to determine the partial pressures of HCN in the two series of runs. In the low-pressure spectra the partial pressure is estimated to be ca. 120 mTorr out of the total pressure of all constituents of 500 mTorr. The higher-pressure spectra correspond to a partial pressure of ca. 420 mTorr, so that more than half the sample consisted of HCN. ACKNOWLEDGMENTS We are indebtedto SERC for travelfunds and for the supportof one of us (Y.G.). J. W. Braultand Mr. R. Hubbard of NSO for theirhelp in obtaining the spectra. RECEIVED:
We also thank Dr.
August 18, 1989 REFERENCES
I. 2. 3. 4. 5. 6. 7. 8.
P. K. L. YIN AND K. NARAHARIRAO, .I. Mol. Spectrosc. 42, 385-392 (1972), and referencestherein. J. HIETANEN,K. JOLMA,AND V. M. HORNEMAN,J. Mol. Spectrosc. 127,272-274 (1988). V. W. WANG AND J. OVEREND,Spectrochim. Acta Part A 29,687-705 ( 1972). J. I. CHOE,T. TIPTON,AND S. G. KUKOLICH,J. Mol. Spectrosc. 117, 292-307 ( 1986). J. I. CHOE,D. K. KWAK, AND S. G. KUKOLICH,J. Mol. Spectrosc. 121, 75-83 (1987). G. DUXBURY,H. KATO, AND M. L. LE LERRE,Faraday Discuss. Chem. Sot. 71.97-l 10 ( 1981). G. DUXBURY,B. LEMOINE,AND M. L. LE LERRE,J. Mol. Spectrosc. 124, 99-l 17 ( 1987). Y. GANG, M. Phil. Thesis, University of Strathclyde, 1989. 9. G. DUXBURYANDM. L. LE LERRE, J. Mol. Spectrosc. 92,326-348 ( 1982). 10. L. HALONENAND G. DUXBURY,J. Chem. Phys. 83,2078-2090 ( 1985). 11. J. KAUPPINEN AND V. M. HORNEMAN,in “Handbook of Infrared Standards: With Spectral Maps and
Transition Assignments Between 3 and 2600 pm” (G. Guelachvili and K. Narahari Rao, Eds.), Academic Press, New York, 1986. 12. A. G. MAKI AND D. R. LIDE, J. Chem. Phys. 47,3206-3210
( 1967). 13. A. G. MAKI, J. Mol. Spectrosc. 58, 308-315 ( 1975). 14. J. M. BROWN,J. T. HOUGEN,K. P. HUBER,J. W. C. JOHNS,I. KOPP,H. LEFEBRE-BRION, A. J. MERER, D. A. RAMSAY,J. ROSTAS,AND R. N. ZARE, J. Mol. Spectrosc. 55, 500-503 ( 1975). 15. E. FLIEGE,H. DREIZLER, A. P. Cox, AND S. D. HUBBARD,Z Naturforsch. A 39, 1104-l 107, ( 1984). 16. M. A. H. SMITH,C. P. RINSLAND, B. FRIDOVICH, ANDK. NARAHARIRAO, in “Molecular SpectroscopyModem Research” (K. Narahari Rao, Ed.), Vol. 3, pp. 11l-248, Academic Press, New York, 1985. 17. J. W. C. JOHNS,J. Mol. Spectrosc. 125,442-464 ( 1987). 18. R. A. TOTH, J. Mol. Spectrosc. 53, 1-14 (1974). 19. H. C. ALLENAND P. C. CROSS,“Molecular V&-Rotors,” Wiley, New York, 1963. 20. G. HERZBERG “Molecular Spectraand Molecular StructureI. Spectraof Diatomic Molecules”, Van Nostrand, Princeton,NJ, 1950. 21. P. DE BIEVRE,M. GALLET,N. E. HOLDEN,AND I. L. BARNES,J. Phys. Chem. Ref: Data 13,809-891
(1984). 22. H. G. REICHLE AND C. YOUNG, Canad. J. Phys. 50,2662-2673
( 1972).
OF MOLECULAR
SPECTROSCOPY
138, 54 1-56 1 (1989)
Fourier Transform Spectroscopy of HCN in the 14-pm Region GEOFFREY
DUXBURY
* AND Yu GANG
Department of Physics and Applied Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 ONG, Scotland, United Kingdom
The 710-cm-’ bands of various isotopes of HCN have been measured with a resolution of about 0.005 cm-’ using the National Solar Observatory Fourier transform spectrometer. Six bands of HCN, one band of H’%ZN, and one band of HC15N have been analyzed to obtain accurate band origins and rotational constants. The accuracy of the calculated band origins are better than 0.0003 cm-’ for most bands. Relative integrated intensities have been derived from these spectra by comparison with simulations. and examples of the method used are given. ‘P 1989 Academic Press,Inc. 1. INTRODUCTION
The v2 band of H’2C’4N is secondary calibration standard for the 14-pm region, and is a textbook example of a perpendicular band of a linear molecule. Although this band has been studied many times ( 1)) until the very recent work of Hietanen el al. (2) using a high-resolution Fourier transform spectrometer (FTS), this band had been studied only with high-resolution grating spectrometers (1, 3). The increased resolution and sensitivity of Fourier transform spectrometers has made it possible to make more accurate measurements on many hot bands and isotopic bands which were previously too badly overlapped for accurate measurement. Recently Choe, Tipton, and Kukolich have used the National Solar Observatory (NSO) McMath Solar Fourier transform spectrometer to remeasure the 3300 cm-’ bands with a resolution of 0.0 1 cm-’ (4)) and Choe, Kwak, and Kukolich have studied the 2100 cm-’ bands using the same instrument (5). Our interest in the 14-pm spectrum of HCN arose as a result of current experiments to elucidate the fragmentation routes in secondary amines subject to dc discharges, and of previous experiments to produce methylenimine by pyrolysis and by dc discharge t,6, 7). In all these systems HCN is a stable end product. Diode laser absorption spectra of the HCN produced as the end product in discharges appeared to show a nonequilibrium vibrational excitation (8). In order to test this hypothesis we have analyzed the v2, 2v2-v2, and 3v2-2v2 bands of HCN and the v2 bands of H13CN and HC’*N observed during the original experiments on CH2NH using the National Solar Observatory Fourier transform spectrometer (6, 9, 10). ’ Visiting Scientist, National Solar Observatory Kitt Peak, National Optical Astronomy Observatories operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation.
541
0022-2852189 $3.00 Copyright @ 1989 by Academic Press. Inc. All rightsof reproductionin any form resewed.
DUXBURY
542
AND GANG
II. EXPERIMENTAL
DETAILS
The Fourier transform spectra were obtained with the McMath Fourier transform spectrometer developed by Dr. J. W. Brault at the National Solar Observatory. The HCN was produced as a minor breakdown product of methylamine pyrolysis in a Imm internal diameter quartz S-bend tube at ca. 1000°C. The total pressure of the pyrolysis products in the absorption cell was ca. 500 mTorr. Sixteen traversals of a 60-cm absorption cell were used, and the pyrolyzed gas flowed slowly through the cell. The spectra were recorded with an unapodized resolution of 0.0048 cm-’ using a JPL filter and a liquid-helium-cooled detector. Further details of the data reduction and interpolations are given in Ref. (6). The effective temperature in the cell, deduced from the intensities of the CHzNH spectra, was ca. 300 K, just above the temperature of the laboratory, which was 20°C (293 K). Two spectra were used for the analysis. The first used eight scans of the FTS without purging of the optical path outside the spectrometer, and the second 30 scans with purging. The first spectrum was used for the hot bands since the HCN spectra were stronger, and the second for the fundamental and where interference with water and carbon dioxide lines occurred. The absolute accuracy of the frequency calibration is shown in Table I, where the v2 band lines of CO2 measured as residual impurity in the FTS tank are compared with those tabulated by Kauppinen and Horneman ( I I ) . It can be seen that the McMath results are on average 35 X 10e5 cm-’ higher than those obtained with the Oulu instrument. The simulations were carried out using an Acorn Archimedes microcomputer. In order to facilitate comparison of the simulated with the experimental spectra, the TABLE I A Comparison of CO2 Line Positions with Those in Calibration Tables Q(J) (a) 2 4 6 6 10
12 14 16 18 20 22 24 26 28 30 32 34 36 36 40 42 44 46
667.386963 667.400635 667.423401 667.454173 667.494141 667.541382 667.597534 667.661143 667.773154 667.814697 667.903564 666.000427 668.105713 666.219238 668.341064 668.470947 668.609070 668.754944 668.909241 669.071594 669.241699 669.419922 669.606567
(b) 667.386040 667.400539 667.423321 667.454303 667.493721 667.541330 667.597205 667.661336 667.733721 667.614344 669.903200 666.000275 668.105559 668.219037 666.340695 668.470518 668.606489 668.754593 668.906609 669.071119 669.241503 669.419936 669.606400
a-b X(105) 92 96 6 39 42 5 33 41 -57 35 36 15 15 20 37 43 58 35 43 48 20 -1 17
(a) This work. (b) Tabulated positions, Reference (11). a-c denotes observed - tabulated line positions.
14-pm SPECTRUM
543
OF HCN
Fourier transform spectra were downloaded onto the Archimedes, and were treated to remove as far as was possible the channeling evident in the originals (see Ref. (6)). Both sets of spectra were then plotted using a HP A4 graph plotter. III. ANALYSIS
AND RESULTS
‘a) Observed Spectra
The assigned spectra cover the region from 620 to 820 cm-‘. Lines were assigned to eight different bands (six of HCN, one of H13CN, and one of HC13N) with natural isotopes. The assigned bands are: HCN: 01 ‘O-00’0, 02°0-01 ‘0, 0220-01’0, 0310-0200, 03 ‘0-02’0, 0330-0220. H13CN: 0 1'0-00'0. HC”N: 01 ‘O-00’0. (b) Theoretical Model
Following Maki and Lide ( 22) and Maki (13)) the energy of the vibration-rotation levels in the absence of perturbations can be written as G(u, J) = V, + B,J(J+
1) - D,[J(J+
1) - 1212+ H,[J(J+
1) - f213,
(1)
where v, is the vibrational energy, B, is the rotation constant, D, is the quartic centrifugal distortion constant, and H, is the sextic centrifugal distortion constant. For the ground vibrational state v, = 0 and 1 = 0, so that ( 1) reduces to the usual expression for the ground state of a linear molecule. For all other states we need to consider the effect of the vibrational angular momentum. The operator connecting states differing in 1 by 2 is known as the Z-type doubling operator when the states coupled would otherwise be degenerate, and the l-type resonance operator when they are nondegenerate. The p operator, introduced by Maki and Lide (22), connects states differing in 1 by 4. The Z-type doubling (resonance) parameter, qv, is expanded as a power series in J as follows (13): q”J = q: - qiJ(J
+ 1) + qiJJ2( J + 1)2.
(2)
The (0 1’0) II state exhibits first-order Z-type doubling, since the q vibrational operator can couple a degenerate pair of states having 1 = It 1. The resultant energy levels are given by G(v, J), = G(n, J) - q,J(J
+ 1)
G(v, J)f=
+ 11,
WV, 4 + q,J(J
(3)
where G( 0, J) is given by Eq. ( 1) and qvJ by Eq. (2). For states with I Z 1 the matrix elements of qoJ responsible for the I-type resonance take the form (u.IIH~~),Z+~)=~~{[J(J+
1)-&l+-
l)][J(J+
I)-(I+
l)(Z*2)]
x [(V T Z)(V * 1+ 2)]}“2,
(4)
DUXBURY
544
AND
GANG
and those associated with p may be written as (u,ZINIV.z+4)=~P{[J(J+ X[J(J+
l)-Z(Zk
l)][J(J+
l)-(Z+2)(1+3)][J(J+
l)-(I?
l)(Zk2)]
l)-(Z-t3)(1+4)]
x [(V T Z)(V 1 z + 2)(V F z - 2)(V f z+ 4)]}“2.
(5)
Full expressions for the resultant secular determinants are given in Refs. (4, 5, 12). When the least-squares fitting procedure was carried out for each set of bands, the variables and the constrained constants were chosen in such a way that whenever accurate values were available from earlier microwave and/or other infrared measurements of comparable accuracy to the present ones, the parameters were fixed as constants. In Table II the parameters that have standard deviations given in parentheses TABLE nolecular
state
I
VI
I-
constants
( 0000)
I
a, 0”
1.487221825(40)= 2.90851(5301a 2.72(128)" -
I x10-6
I
Ii" x10-121 q,o x10-3 I
I
qvJ x10-8 qvJJxro-‘2~ Q x10-8
I
state
I
(0220) 1426.530451(12)
I
1.484995(21 3.03265(260) (2.72$
I 1
v,
a,
D"
NV q,o
I
x10-6 x10-121 x10-3 I
Of Ha4 (cm-‘)
-
(-1.2l)f n01ecu1ar
“V
q,o
qvJ
I-
I i.43wd’
constants
, 2.76756(21h
All three
7.709034
I -
1.2
of
HC’ 5N (01'0)
705.9659(l) 1.443157(2) 2.8226(15)
x10-121 1.10 x10-3 I x10-8
qyJJxlo-‘21
(a) (b) (C) (d) lel (fl (41 (h)
(0000)
I
bff Bu D, x10-6
(0330) 2143.7632(5) 2143.759949 1.487854 3.0814 (2.72$'
9.3168
n’3a4
state
(0200) 1411.41376(9) 1411.41380(9)e 1.4858289(20) 3.05321(260) (2.72$ 7.5978g4 lo.o7o7d 4.6sd (-1.2l)f
(01'0) 711.97985(8) 711.97965C 1.481772(2) 2.97467(38) (2.72$ 7.48773d 8.86820d l.1878d (03'0) 2113.4509(3) 2113.450369 1.489570 3.0814 (2.72$'
7.597898 lo.o7o7d 4.6sd
qvJ x10-8 I qvJJxlo-‘21 Q x10-8 I
II
1.10
7.162o(4)h 8.126h
1.0
I
(01'0)
(OOOO)
711.0268(2) I I 1.4xmd’ 1.438653(3) I 2.74773(23)h2.803(6) I 1.72 1.72
I
-
7.o694(94)h
7.w+
I I -
1.2
standard deviations. Ref. (13). Frozen at ground state values. Ref. (2). Fit to microwave l-type doubling Direct fit to 02°0-O040. Frozen at value in Ref. (12). Ref. (51. Ref. (4).
transitions
in
Ref.
(13).
14-rrn SPECTRUM OF HCN
545
were varied, and those without listed standard deviations are from the reference cited. In every band H’ and H” are fixed at 2.72 X lo-l2 cm-’ and qf’ and qf” are fixed at 1.2 X 1O-‘2 cm-’ (from Ref. ( 23)). The vibrational transitions observed are shown schematically in Fig. 1. This is similar to the diagram given by Wang and Overend (3)) but we have used the newer e-f notation ( 14). (c) HCN Ol’O-00’0
at 711.979 84(3)
cm-’
This band has been remeasured very recently using the Oulu high-resolution FIS (2). Our results are given in Table III. We find that there is a small constant frequency shift between the two sets of data which is similar to that found for CO2 (see Section II). The lines reported here extend to much higher values of J than those given in reference (2). The extrapolated position of the high-J lines given in (2) show a Jdependent shift from our measured values. The I-type doubling in the 0 1’0 state has been measured very accurately by microwave spectroscopy ( 12, 15). We have determined qv and qi directly from the l-type doubling transitions, and held them constant during the fitting of the infrared data. (d) HCN 02°0-01 ‘0 and 0220-01 ‘0 First Hot Bands at 699.43405 714.55069 cm-’
cm-’
and at
These bands have previously been reported by Wang and Overend (3). However, the present frequencies are an order of magnitude more accurate, and the standard
3 _____________________--___
(0320)
n v2=
\-------
f0220)
A
/_________________
_____________________-______ __--_
_--_________-___-=.____---_-- i ... _- - ____ . __
v2= 2 (02’0)
c
(0110)
n
\
“a=
1 (
____________________
f (d)
-------_--_____--
._- _-- -_
--____
___ ___-______-___-________----____- f
-----
-- _---__i' _____--__--
__________-_________
(d)
T ._____________-__--_---__ e
(c)
II
(00’0)
v2=
c
0
I I
FIG. 1. The vibrational energy levels of HCN associated with the transitions observed in this work. The new e-fnotation is used, and the older c-d notation is given in brackets to facilitate comparison with earlier papers.
DUXBURY
546
AND
GANG
TABLE III The
01'0
P(J) OS.5
o-c
706.06683 703.10974 700.15265 697.19513 694.23798 691.28082 688.32379 685.36664 682.41003 679.45349 676.49750 673.54187 670.58679 667.63208 664.67810 661.72485 658.77234 655.82050 652.86963 649.91968 646.97070 644.02252 641.07568 638.12982 635.18530 632.24194 629.30005 626.35919 623.42004 620.48218 617.54620 614.61151 611.67828 608.74750 (605.81842) 602.89002
15 3 8 -20 -8 0 10 -9 4 -7 0 2 9 -3 -2 4 9 2 7 11 16 -3 3 -7 -4 -12 -1 -4 -18 -31 -7 -12 -32 25 82 29
J
O-C denotes The
lines
observed in brackets
(a)
band
of HCN
(714.93762) 717.89148 720.84662 723.80115 726.75501 729.70807 732.66040 735.61182 738.56238 741.51184 744.46021 747.40710 750.35309 753.29761 (756.24152) 759.18286 762.12256 765.06146 767.99829 770.93347 773.86621 776.79742 779.72656 702.65332 785.57764 (788.49915) 791.42084 794.33814 797.25372 (800.16516) (803.07465) 805.98254 806.88648 811.78735 814.68500 *1 *2 *3
- calculated are blended
line and
(cm-')
o-c X(105)
R(J) OBS
X(105)
a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
-OO"O
171 -4 0 2 3 -2 0 -1 7 8 9 -19 -12 -20 53 17 -26 15 20 31 6 15 21 1 -42 -136 25 -7 45 -54 -78 -16 13 -3 -34
o-c X(105)
Q(J) OBS
711.99426 712.02368 712.06738 712.12585 712.19861 712.28644 712.38825 712.50482 712.63593 712.78143 712.94159 713.11591 713.30481 713.50806 713.72553 713.95734 714.20331 714.46381 714.73816 715.02661 715.32929 715.64539 715.97601 716.32044 716.67859 717.05048 717.43573 717.83514 718.24768 718.67377 719.11389 719.56610 720.03247 1720.50433) 721.00409 721.50934 722.02728
-19 3 -6 4 -15 17 -7 -7 -5 -11 3 -9 -3 3 -2 -1 -8 18 14 11 26 -18 1 10 11 11 -20 5 -12 -20 7 -27 3 -732 20 24 10
positions. were
omitted
Asterisks denote lines which are so seriously identified. The calculated positions of these *1: 817.58014 R(35) 820.47168 *2: R(36) 823.35988 *3: R(37)
from
the
blended that lines are:
least-square they
CaMOt
fit. be
deviation of the fit (0.0001 cm-‘), is much smaller than that obtained previously (about 0.002 cm-‘). We have also been able to detect the Q branches of the 02*001’0 band, including the branch which was not reported in the earlier study. Our analysis preceded in an iterative fashion. The high-resolution Z-type doubling data of Maki and Lide (12) was used to determine the I-type doubling constants which were held fixed when the infrared spectra were fitted. The revised value of the 02°0-0220 interval was then used to recalculate the l-type doubling constants, and the process cycled until self-consistency was obtained. The observed and calculated lines are given in Table IV.
14-&m SPECTRUM
OF HCN
547
TABLE IV The P(J) OBS
J
‘
3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
696.41191 693.53772 690.61273 687.70355 (684.80835) 681.93060 679.06641 676.21582 673.37915 670.55493 661.14365 664.94257 662.15216 659.37091 656.59772 653.83179 651.07196 648.31641 645.56470 642.81525 640.06702 637.31885 634.57044 631.81927 629.06549 626.30841 623.54840 (620.78381) 618.01270 (615.23907) (612.45905) (609.67236) (606.87933) See
TABLE
OZ"O
- 01'0
band
o-c X(105)
R(J) OBS
11 26 3 10 -116 5 22 -10 0 -27 35 -3 2 -2 -19 -15 9 -11 0
705.39300 708.39490 1711.41333) 714.44287 717.48900 120.54694 723.61798 726.70056 729.79315 732.89661 736.00848 739.12671 742.25153 745.38324 748.51685 751.65295 154.79034 151.92137 761.06213 764.19629 767.32452 770.45000 773.56793 776.67944 (779.78040) 702.87982 785.96576 (709.04010) 792.10944 (795.17523) (79”‘~;;’
2 -6 50 12 -24 -54 20 83 -23 133 175 89 -104
_
of "CN
(cm-')
o-c X(105)
o-c X(105)
Q(J) OS.9
-
37 3 142 -44 42
*1
(699.43671) 6gz3*627' *3 *4 *5
21 32 -27 28 63 -18 -67 12 28 -6 -19 -45 -72 -32 -43 4 -21 -12 -106 14 -38 96 -7 388 172
699.43671 '6 699.42127 699.40851 699.38886 699.36438 699.33099 699.28906 699.23724 699.17438 699.09937 699.01038 698.90662 698.78729 698.65088 690.49646 698.32361 698.13104 697.91870 (697.68610) *I (7g7.15%2' *9 *lo _ *11
'13
102 -43
14 -62 18 -50 40 13 -1 -10 -6 21 10 -3 14 14 0 15 5 27 a4 146
III.
Calculation
of the strongly
blended
lines:
*1: *2: *3: *4:
Q(l) Q(4) Q(5) Q(6)
699.43453 699.43866 699.43988 699.44032
*a: *9: *IO: *ll:
Q(30) Q(31) Q(32) Q(33)
*5: *6: *7:
Q(7) Q(9) Q(28)
699.43943 699.43099 697.43097
*12: *13:
R(32) R(33)
696.85856 696.53973 696.19935 695.83795 801.26177 804.29166
(e) HCN 02°0-O000 Overtone Band These measurements were previously reported by Duxbury and Le Lerre (9) in their paper on the v5 and v6 bands of CHzNH. Their data were fitted using the ldoubling constants determined for the hot bands (see Section (d) above). The resultant position of the 02’0 vibrational level is then consistent with that deduced from the analysis of the 0 1 ‘O-00 ‘0 and the 02 ‘O- 11’0 bands (see Table II). (fl HCN 03’0-0220 and 03’0-02°0 Second Hot Bands These bands are very weak and can only be seen clearly in the spectra in which eight scans were used. Recently, Choe, Kwak, and Kukolich (5) have analyzed the 03 ‘O-00’0 bands recorded using the same Fourier transform spectrometer. Although there is good agreement between the band origins obtained by combining their mea-
DUXBURY
548
AND GANG
TABLE IV-Continued The 0Z20
J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
See
-
Ol’=O
o-c
P(J) OBS
-24 -20 1 -11 -3 14 -6 9 20 7 7 -4 -10 22 14 6 -2 2 -12 -42 16 43 -35 24
of.HCN
X(105)
720.50433 723.50250 726.51563 729.54224 732.58417 735.64124 738.71491 741.80475 744.91223 748.03760 751.18164 754.34607 757.53149 760.73853 763.96942 767.22418 770.50342 773.80975 777.14313 780.50446 783.89551 787.31696 790.76788 (794.24420) 797.76703 (801.31305) (8059if39) _ -
(cm-‘) o-c
R(J) OBS
X(105)
705.72443 702.81110 699.91272 697.02924 694.16168 691.31055 688.47607 685.65975 682.86206 680.08374 677.32617 674.59021 671.87714 669.18848 666.52466 663.88733 661.27771 658.69714 656.14648 653.62689 651.14044 648.68689 646.26636 643.88257 *1 *2 *3 *4 *5
band
-38 -27 -22 19 0 -18 15 4 24 20 -18 -13 -3 -31 20 41 -15 5 -7 -57 -59 -27 -123 -833 -40 -164 1402
*7 *8 *9
Q(J) OBS
(714.58319) 714.63391 714.69000 714.75983 714.84418 (714.93762) 715.05167 715.17847 715.31744 715.47089 (715.64539) 715.81842 716.01300 716.22138 716.44385 716.67859 716.92828 717.19159 717.46790 717.75757 718.06036 (718.37647) 718.70715 719.05209 719.40704 (719.77643) (720.159301 (720.54688) (720.96393) (721.38483)
o-c X(105)
-927 -45 22 -20 -3:: -33 0 -34 -7 745 -30 -26 -16 35 -54 -9 39 34 15 -35 -95 -30 -49 -32 -68 -68 -903 -90 -186
TABLE III. Calculation
of
*1: *2: *3: *4: *5: *6: *7: *8: *9:
= = = = = = = = =
P(27) P(28) P(29) P(30) P(31) R(28) R(29) ~(30) R(31)
the
strongly
blended
lines:
641.53293 639.21945 636.94299 634.70170 632.49785 808.50751 812.15250 815.82999 819.53982
surement with ours of the 02°0-OOo0 band, it has not proved possible to fit data to within the experimental accuracy by using their rotation constants for the 03’0 state. In Table II both sets of parameters are given. The differences probably reflect the problem of checking the absolute frequency calibration of Fourier transform spectroscopy when very high-resolution spectra are recorded. The line positions are given in Table V. (g) H13CN 01 ‘0-OO”O Band This band has previously been analyzed in a fragmentary fashion (3). With the high-resolution FIS the majority of the lines recorded are free for blending, and accurate values of the excited state constants and band origins have been derived. See Table VI.
14-pm SPECTRUM
OF HCN
549
TABLE IV-Continued The
(OZzO)-(Ol'fO) o-c X(105)
P(Jl OBS
J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 20 29 30 31
-21 8 -2 -3 17 -10 -43 137 4 9 -S -6 -2 14 -8 -1 9 -26 -17 18 -39 -4 -30 -59
705.63452 702.66119 699.68677 696.71179 693.73645 690.76013 687.78332 (684.80829) 681.82983 678.85254 675.87488 672.89734 669.91980 666.94244 663.96484 660.98773 658.01093 655.03400 652.05792 649.08258 646.10687 643.13269 640.15857 "'lr'Z'S
-110 -92 -23 -220
(631.24097) (628.27069) 625.30194 (622.33160)
See TABLE
band
of HCN
It(J) OBS
(cm-')
o-c X(105)
720.48975 723.45721 726.42358 729.38916 732.35291 735.31567 738.27649 741.23594 744.19324 747.11935 750.10352 753.05592 756.00641 758.95417 761.90015 764.84473 767.78644 770.72559 773.66242 (776.59607) 779.52924 782.45789 785.38452 788.30847 791.22906 (794.14642) (797.06073) 799.97375 (802.88117) *2 '3
22 -11 -32 -3 -19 11 -3 -22 -34 -18 -16 3 18 -32 -49 13 14 -7 -19 -99 28 -33 -24 -4 -33 -91 -153 -33 -157
Q(J) OSS
o-c X(105)
714.54773 (714.54773) -*4 *5 *6 *7 *8 *9 _ *10
10 275
(714.54773) 714.56299 714.58301 714.61060 714.64563 714.69000 (714.75964) 714.81213 714.89203 714.98608 715.09552 715.22089 715.36360 715.52460 715.70319 715.90216 716.12030 (716.35858) (716.61682)
-168 -33 -21 40 24 1 1445 -6 -14 -17 -4 -20 -55 17 -59 -25 -51 -75 -140 -217
III.
Calculation of the strongly blended *1: l2: *3: *4: *5: *6: *7: *a: *9: *10: *11:
P(27) R(30) R(31) Q(4) Q(5) Q(6) Q(7) Q(S) Q(9) Q(lO, Q(31)
(h) HC15N 01 ‘O-00’0
Band
= = = = = = = = = = =
lines:
634.21273 805.78675 808.68854 714.54187 714.53868 714.53584 714.53392 714.53355 714.53545 714.54044 717.19588
This band is weaker than that of the i3C isotopic form; nevertheless the spectra recorded with the higher HCN concentration have allowed us to derive accurate values for the line frequencies of much of this band. See Table VII. IV. RELATIVE
BAND INTENSITIES
The observation of the high-resolution spectrum of the v2region of HCN has allowed us to determine the relative sizes of the integrated intensities of the sub-bands of HCN and its isotopes. In order to accomplish this we have written a computer program to
DUXBURY
550
AND
GANG
TABLE V The
03'0
J
- OZ"O
o-c
P(J) 0%
-34 -21
690.10510 687.10486 684.09656 681.08319 678.06403 675.03998 672.01093 668.97943 665.94501 (662.90796) (659.86987) (656.83112) (653.79248) (650.75586) (647.721070 (644_6!;5a)
58 -18 4 6 3 -60 -2 58 72 119 154 171 276 368 511
(638.63879)
TABLE
-3 4 -37 -29 -25 -336 -461 31 452 528 151 110
(765.61383) *4
866 1244
635.62213*
See
742.84247 1745.70795) (748.57068) -751.44013. (754.30512) (757.16534) (760.02039) *3
-34 792 a -21 71 3 -20 21 -10
o-c
Q(J) OBS
X(1051
705.00079 (707.96478) 710.90460 713.84393 (716.77649) 719.69959 722.61548 725.52460 728.42590 731.32086 734.20953 737.09192 739.96954
-
(cm-')
o-c
0%
X(105)
*1 693.09912
of HCN
NJ)
0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 la 19 20 21 22
band
X(105)
702.06108 702.10614 702.17499 702.26758 702.38312 702.52234 702.68579 702.87408 703.08667 703.32452 703.58783 703.87720 704.19348 704.93668 704.90729 705.30615 (705.73401) 706.18903
-14 -10 -25 9 -9 -30 -30 15 13 17 3 -la -6 -10 -24 -6 a2 33 -a
706%g7 *6 *7
III.
Calculation *1: *2: *3: *4: *5: *6: *7:
of the = = = = = = =
P(2) P(20) ~(20) R(22) ~~20) Q(21) Q(22)
strongly
blended
lines:
696.08636 641.66535 762.88344 768.61067 707.18826 707.73157 708.30253
TABLE V-Continued The 031e0 - OZzfO band of HCN (cm-')
J
o-c X(105)
Q(J) OBS 686.90179 686.88281 686.85736 686.82544 686.78577 686.74030 686.68738 686.62683
-7 -5 1 ia -58 -15 4 7
J 10 11 12 13 14 15 16 17
o-c
Q(J) OBS
X(105)
686.55841 686.48169 (686.39471) 686.30347 (686.19995) (686.08777) (685.96515) (685.83325)
-4 -42 -270 -56 -166 -204 -310 -331
The 031f0 - OZzeO band of HCN (cm-')
J
Q(J) OBS
2 3
686.99500 (687.06915)
4 5 6 7 a 9
687.16473 687.28436 687.42706 687.59168 (687.77045) 687.98248
See TABLE
III.
o-c X(105) 72 176 45 -6 -a 0 -666 10
J 10 11 12 13 14 15 16 17
Q(J) OBS 688.20599 (688.44605) 668.70520 (688.97430) (689.25714) (689.55072) (689.85358) -
o-c X(1051 -34 -162 24 -238 -406 -606 -800
551
14-pm SPECTRUM OF HCN TABLE VI The 01'0
0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
708.84528 711.72333 (7156J;53)
20 2 997
720.35187 723.22595 726.09845 728.96985 731.83960 734.70831 737.57520 740.4405s (743.30573) 746.16620 749.02673 751.88477 754.74078 757.59479 760.44751 763.29749 766.14563 768.99054 771.83392 774.67432 777.51233 780.34784 (783.17706)
0 17 1 6 -14 7 -1 -3 144 -5 34 10 -19 -47 7 5 44 -8 27 11 12 26 -310 -31
-199
Calculation
of the
simulate the appropriate its application in (b) .
o-c X(105)
-10 -5
(622.30684)
P(28)
(cm-')
R(J) OBS
6 -10 24 -12 -10 1 0 7 10 -12 -8 3 -3 4 -7 -10 67 48 -5 29 5 -102 -95 -243
R(3) R(28) R(29) Q(28) Q(29)
of H')CN
X1105)
700.20514 697.32361 694.44165 691.55878 688.67590 685.79187 682.90784 680.02356 677.13892 674.25415 671.36920 668.48395 665.59894 662.71405 659.82910 656.94446 654.05988 651.17566 (648.29224) 645.40900 642.52551 639.64343 636.76135 (633.87909) (630.99866) (62:1;:43)
*1: *2: *3: *4: *5: *6:
band
o-c
P(J) OBS
J
- OO"O
= = = = = =
786.0zg1 *4
strongly
blended
Q(J) OBS
O-C X(105)
705.97961 706.00610 706.04694 706.10089 706.16791 706.24908 706.34332 706.45105 706.57214 706.70673 706.85453 707.01563 707.19000 707.37787 707.57910 707.79303 708.02026 708.26129 708.51471 708.78155 709.06091 709.35339 (709.65143) 709.97760 (710.30841) 710.65259 (711.00848) *5 *6
19 -29 8 11 -27 6 2 4 2 10 7 -6 -18 -10 11 -21 -39 9 -14 1 -33 -51 -834 -28 -68 -46 -119
lines:
625.24087 717.47617 788.83708 791.66114 711.37898 711.76079
regions of the spectrum.
This is described
below in (a) and
(a) Spectrum Simulation The individual line intensities are calculated using the form for the integrated tensity given by Smith et al. (16) and Johns ( 17),
Si = SiRiFi,
(6)
where Sz is the vibrational band intensity, Ri is the rotational Herman-Wallis factor. The rotational factor is given by Ri=Y’*L+t~p(-~~~~)[l
vo where vi is the line frequency,
in-
factor, and F, is the
-exp(-v,/kT)], r
v. the band origin, Li the Honl-London
factor, Qr the
DUXBURY
552
AND
GANG
TABLE VII The
J 0 1 2 3 4 5 6 I tl 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
(705.28455) 702.41516 699.54395 696.67291 693.79279* 690.93182 688.06146 685.19092 68fi3?:02 676.58283 673.71442 670.84662 (667.97321) 665.11267 662.24683 (659.38324) 656.51782 (653.65375) (650.79157) (647.93048) (645.06930 See
TABLE
R(J) OBS
o-c X(105) -7 91 4 3 11 4 -47 39 26 -13 -51 -13 28 80 -9 31 -20 208 -B
713.89697 (716.76605) 719.63654 722.50562 725.37427 728.24219 731.10901 733.97648 736.84216 739.70672 742.57037 745.43378 748.29614 (751.15747) 754.01617 756.87488 759.73132 (762.56496) 765.44098 768.29291 (771.14331) 773.99280 776.84027 (779.68250)
-110 31 -7 -27 -964 2 7 -33 59 -18 -16 -8 -625 -24 -29 110 -1:: -113 -109 -221
-97 25 -32 -346
Q(J) OBS 711.04071 711.06836 711.11017 711.16547 711.23505 711.31867 (711.41315) 711.52637 711.65100 711.78937 711.94165 (712.10883) 712.28729 712.48145 712.68774 712.90869 713.14246 713.39008 713.65143 713.92651 (714.21558) 714.51666 (714.82983)
o-c X(105) 4 -23 4 -19 -1 36 -225 5 -3 -17 -16 99 -27 52 -25 12 -41 -55 -47 -11 83 42 -121
III.
Calculation *1:
01'0 - OO"O band of HC15N (cm-')
O-C X(105)
P(J) OBS
~(11)
of the
strongly
blended
lines:
= 679.45201
lower state rotational partition function, and E: the lower state rotational energy. In the present work the rotational dependence of the line strengths did not differ from that predicated by the Honl-London formula, and hence F was set equal to unity. In degenerate bands it is common to refer not to the band intensity, but to the vibrational sub-band strength (see Toth (18)). We will denote this by S$. Since the Ho&London formulae are obtained by summing the squares of the direction cosines, a& and Q&, for the degenerate vibration (19), when the line strengths of the three transitions with the same J” are added we obtain the value 2 X (2.7’ + 1) (20). The integrated sub-band intensity will then be approximately twice the vibrational subband strength. There is an ambiguity concerning the definition of the rotational partition function for nearly degenerate states. We have chosen to compute these for each component of the degenerate levels separately, so that there are two for o2 = 1, three for u2 = 2, and five for n2 = 3. The relevant HSnl-London factors for the perpendicular band are then L, = (s’f I
L,= I
I+)(s’+ J”+
(2Y+
1+ 2)
(8)
1
l)(S’rI)(J”*I+ J”(s’ -I- 1)
1)
(9)
553
14-brn SPECTRUM OF HCN
L, = (J”? t
Z)(J” T l-
1)
J”
( 10)
’
respectively, for R, Q, and P branches. S$ takes into account only the rotational partition function. The vibrational sub-band intensity, S~,J, is given by
( 1vofl(P”,,>12,
SE,,= g
(11)
”
where v. is the wavenumber of the band center, Qv the vibrational partition function, and I( p,,,) 1the transition moment of the vibrational sub-band. N is the total number of molecules of the absorbing gas per cm3 per atm and is given by
(12) where IZis Loschmidt’s number, p is the gas pressure in the atmosphere, and C is the isotopic abundance. If ( ( pL,,,)1 is in Debye, S, in cmm2/atm, energies in cm-‘, and Tin Kelvin, sll,
=
v.
3054ww)~2
5
exp(_E”l,kT)
QU
“,
T'
(13)
The integrated band intensity, SE,,, is then related to Si,, by
SL.l= SZ,,C &Fi,
(14)
where, as we have noted, S’,, m 2S$. In all the calculations the rotational constants and vibrational energies were taken from the current work, and also from Refs. (4, 5, 12, 13). The isotopic abundances were those recommended by de Bievre et al. (21). The partition functions were obtained by direct summation. The absorption spectrum was first calculated with a Gaussian line profile, since at the low pressures used in the experiments the Voigt profile is very close to a Doppler lineshape. However, as the fitting proceeded it proved to be necessary to use a Voigt profile, which was calculated by numerical convolution. The calculated absorbance was converted to transmittance by exponentiation and the result convolved with an instrumental lineshape function. For comparison with the spectra run using the NSO FTS the instrumental function used was the sine function, (sin x/x). (h) Results In our calculations we assumed initially that the transition moments of the Hi3CN and HC”N v2 bands are the same as those of HCN, and that the integrated intensities could be predicted using the relative isotopic fractions. We also assumed that the transition moments of each component of 2v2 - u2 and of 3~2 - 2v2 were identical to v2 -- 0.
a
% TRANS.
709.40
711.55
X TRANS.
b
i
I
709.400
711.557
715.073
713.715
718.031
cm-l
FIG. 2. The Q-branch region of the uz bending fundamental band of HCN. The total pressure of the pyrolysis products of methylamine was ca. 500 mTorr and the partial pressure of HCN ca. 120 mTorr. The observed spectrum is given in (a) and the calculated one in (b) 554
a
698.7
700.04
705.
702. QQ
12
cm-l *ATR ANS.
b
1oov
698.7
--VI
700.040
702.99
705.120
707.26
709.400
cm-l FIG. 3. The Q-branch region of the O2oO-O 1’0 band of HCN and the 0 1‘O-00’0 band of H13Cn with the same conditions as Fig. (2). (a) Observed, (b) calculated.
555
‘/TRANS.
a
m
100
P
II50-
718 cm-l
I 717
I
I
717.2
I
I
717.400
I
I
717.599
I
I
717.
a
cm-l FIG. 4. The Q-branch region of the 0330-0220 band of HCN. The total pressure of the pyrolysis products of methylamine was ca. 500 mTorr and the partial pressure of HCN ca. 420 mTorr. The observed spectrum is given in (a) and the calculated one in (b).
%TRANS.
a loo-
PT
i”
P
50
I
1
I
702
L
-
,
1
703.599
702.9
T”
I
L
I
,
706
705.2
704.400 cm-l
b
r-
1
10
5( 3-
I
702
I
702.9
I
I
1
703.599
I
704.400
,
I
I
705.2
706
cm-l FIG. 5. The Q-branch region of the 03’O-02°0 band of HCN with the same conditions observed spectrum is given in (a) and the calculated one in (b) . 557
as Fig. 4. The
i
1
I
685.90
I
I
686.3
I
L
I
L
687.09
686,7
L
I 687.90
687.5
cm-l
%TRANS.
b
10
I 685.900
1
t
686.300
I
I
686.7
J
I
687.100
I
t
1
687.
S
687.900
cm-l
FIG. 6. The Q-branch region of the 03’0-02*0 band of HCN with the same conditions as Fig. 4, (a) observed, (b) calculated. This Q branch is approximately four times weaker than those shown in Figs. 4 and 5. The broad pressure-broadened lines are due to CO2 in the optical path between the cell and the interferometer.
14-pm SPECTRUM
OF HCN
559
The Q-branch region of the v2 bending fundamental of HCN is illustrated in Fig. 2a and the simulation in Fig. 2b. The Q branch associated with the 15N isotope is clearly seen to the long wavelength side of the main Q branch. Q branches associated with the first and second hot bands are clearly seen within the envelope of the v2 Q branch. This spectrum is much stronger than that recently reported by Hietanen et al. (2). In Fig. 3 Q branches associated with the first hot band, 02°0-01 lfO, and with HC13N are shown. It can be seen that in both examples there is good agreement between the observed and calculated spectra. This suggests that the assumptions made about the transition moments are valid for the fundamental and the first hot band, and that despite the production of the HCN by high-temperature pyrolysis of methylamine, the temperature of the gas in the cell is close to that of the laboratory. However, when Q branches associated with the second hot-band system, 3v2 - 2v2, are examined, we find that the intensities of most of the Q branches are approximately twice those predicted on the basis of the intensities of the fundamental and first hot band. An example is shown in Fig. 4, where the Q branch of the hot band 03 lfO02”O is clearly seen in both the observed and the calculated spectra, and in Fig. 5, where the Q branch of the 03 30-02 ‘0 band is displayed. The 03 ‘O-O22Oband shown in Fig. 6 does not conform to the overall pattern since its intensity is only about a quarter of that of the other bands. This behavior is similar to that found for intensities
TABLE VIII Vibrational Populations, Isotopic Fractions, and Rotational Partition Functions at 300 K Vibrational isotopic
population fraction
and
HCN
HC-N
HCi5N
Total
1
0.0111
0.0037
0000
0.9353
0.0104
0.0034
0110
0.0615
0.0007
0.0002
0290 0220
0.0011 0.0020
Rotational (excluding
partition function, Qr vibrational degeneracy)
HCN
HCi3N
HCiSN
0000
141.46
145.21
145.69
OliO
140.12
0200 0220
140.64 140.79
560
DUXBURY
AND GANG
of the hot bands of the bending vibration of CO? by Reichle and Young (22). The fraction of molecules in the lower vibrational states of all the transitions, the isotopic abundances, and the rotational partition functions are given in Table VIII. The relative values of the integrated intensities used to fit the spectra, together with those of CO*, are given in Table IX.
TABLE IX A Comparison of the Integrated Band Intensities, S:, of HCN at 300 K with Those of CO* Transition
01'0-00'0
S+i-aAtm-i
HCN (al
coa (b)
227
200
7.4 15.3
4.27 15
0310-02'0
0.52
1.0
0310-0220
0.23
0.14
0330-0220
1.01
0.85
01~0-00'0
2.51
OliO-OO@O
0.84
(a) Scaled to 2 X S p,O= 233 cm-’ Atm-’ (see Ref. (16)). This value was obtained from high-pressure measurements, and hence includes all isotopic and hot-band contributions. The values of the integrated intensities of the HCN bands in the table are therefore probably too high, although the relative intensities should be quite accurate. (b) Ref. (22). (c) Isotopes in natural abundance.
14-pm SPECTRUM OF HCN
561
By using the simulation technique we have been able to determine the partial pressures of HCN in the two series of runs. In the low-pressure spectra the partial pressure is estimated to be ca. 120 mTorr out of the total pressure of all constituents of 500 mTorr. The higher-pressure spectra correspond to a partial pressure of ca. 420 mTorr, so that more than half the sample consisted of HCN. ACKNOWLEDGMENTS We are indebtedto SERC for travelfunds and for the supportof one of us (Y.G.). J. W. Braultand Mr. R. Hubbard of NSO for theirhelp in obtaining the spectra. RECEIVED:
We also thank Dr.
August 18, 1989 REFERENCES
I. 2. 3. 4. 5. 6. 7. 8.
P. K. L. YIN AND K. NARAHARIRAO, .I. Mol. Spectrosc. 42, 385-392 (1972), and referencestherein. J. HIETANEN,K. JOLMA,AND V. M. HORNEMAN,J. Mol. Spectrosc. 127,272-274 (1988). V. W. WANG AND J. OVEREND,Spectrochim. Acta Part A 29,687-705 ( 1972). J. I. CHOE,T. TIPTON,AND S. G. KUKOLICH,J. Mol. Spectrosc. 117, 292-307 ( 1986). J. I. CHOE,D. K. KWAK, AND S. G. KUKOLICH,J. Mol. Spectrosc. 121, 75-83 (1987). G. DUXBURY,H. KATO, AND M. L. LE LERRE,Faraday Discuss. Chem. Sot. 71.97-l 10 ( 1981). G. DUXBURY,B. LEMOINE,AND M. L. LE LERRE,J. Mol. Spectrosc. 124, 99-l 17 ( 1987). Y. GANG, M. Phil. Thesis, University of Strathclyde, 1989. 9. G. DUXBURYANDM. L. LE LERRE, J. Mol. Spectrosc. 92,326-348 ( 1982). 10. L. HALONENAND G. DUXBURY,J. Chem. Phys. 83,2078-2090 ( 1985). 11. J. KAUPPINEN AND V. M. HORNEMAN,in “Handbook of Infrared Standards: With Spectral Maps and
Transition Assignments Between 3 and 2600 pm” (G. Guelachvili and K. Narahari Rao, Eds.), Academic Press, New York, 1986. 12. A. G. MAKI AND D. R. LIDE, J. Chem. Phys. 47,3206-3210
( 1967). 13. A. G. MAKI, J. Mol. Spectrosc. 58, 308-315 ( 1975). 14. J. M. BROWN,J. T. HOUGEN,K. P. HUBER,J. W. C. JOHNS,I. KOPP,H. LEFEBRE-BRION, A. J. MERER, D. A. RAMSAY,J. ROSTAS,AND R. N. ZARE, J. Mol. Spectrosc. 55, 500-503 ( 1975). 15. E. FLIEGE,H. DREIZLER, A. P. Cox, AND S. D. HUBBARD,Z Naturforsch. A 39, 1104-l 107, ( 1984). 16. M. A. H. SMITH,C. P. RINSLAND, B. FRIDOVICH, ANDK. NARAHARIRAO, in “Molecular SpectroscopyModem Research” (K. Narahari Rao, Ed.), Vol. 3, pp. 11l-248, Academic Press, New York, 1985. 17. J. W. C. JOHNS,J. Mol. Spectrosc. 125,442-464 ( 1987). 18. R. A. TOTH, J. Mol. Spectrosc. 53, 1-14 (1974). 19. H. C. ALLENAND P. C. CROSS,“Molecular V&-Rotors,” Wiley, New York, 1963. 20. G. HERZBERG “Molecular Spectraand Molecular StructureI. Spectraof Diatomic Molecules”, Van Nostrand, Princeton,NJ, 1950. 21. P. DE BIEVRE,M. GALLET,N. E. HOLDEN,AND I. L. BARNES,J. Phys. Chem. Ref: Data 13,809-891
(1984). 22. H. G. REICHLE AND C. YOUNG, Canad. J. Phys. 50,2662-2673
( 1972).