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Spectrum of acetylene in the 5-micron region
JOURNAL
OF
MOLECULAR
Spectrum
SPECTROSCOPY
44, 145-164(1972)
of Acetylene
in the 54icron
Region’
JOSEF PLfvA Department of Physics, The Pennsylvania University Park, Pennsylvania
State Uttiversity, 16802
Three II,-&+ bands, 294 + ~6 at 1959.697 and 1940.063 cm-i and 3~s at 2169.166 and l&II “hot” bands occurring cm-r, accompanied by fifteen V-II, X--II, A-II, in the region between 1830 and 2256 cm-i were measured and analyzed. The &+-Z,+ band 3 Y( + ~6 at 2569.666 cm+ was also measured. The upper states of many of the transitions investigated are involved in strong vibrational-rotational interactions causing some effects not previously seen in the vibrationrotation spectra of simple linear molecules. The results obtained were combined with the available information from other regions of the spectrum to calculate an internally consistent set of constants for the ground state, for the II -states OOO1rOO and 606Cl”11as well as for the various higher excited states of the bending vibrations of C2H2. INTRODUCTION
As part of a comprehensive investigation of the vibration-rotation spectrum of acetylene and of its isotopic derivatives (l-5) this paper presents results of highresolution measurements in the 5 P region of the spectrum. Eighteen bands occurring between 1830 and 2250 cm-’ have been measured and analyzed. All of these bands, except those of the IHI transitions v2 + vhl - us1at 1844.372 cm-’ and v2 + us1 - vJ at 2090.213 cm-‘, involve overtones and combinations of the bending modes v4 and vs. The three main bands in this region correspond to the IL-Z,+ transitions ZVJ+ v5 at 1959.697 and 1940.003 cm-’ and 3v~ at 2169.166 cm-‘. The “hot” bands correspond to the various Zf-II, Z--II, and A-II transitions 3vq + v5 - v4 , 2~4 -I- ZVS- US, v4 -I- 3vg - ~4, and 415 - vg . In addition, the Z,+-Z,+ band 3~4+ USat 2560.600 cm-’ was also measured. The bands investigated contain a wealth of information on the strongly interacting states of the bending vibrations and these measurements have made it ultimately possible to obtain a reliable set of spectroscopic constants for the bending stat,es reported in t,he following paper (6). r Presented at the Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1971. This work was supported by the National Science Foundation and by the Office of Naval Research. 145 Copyright
Q 1972 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
146
PLiVA EXPERIMENTAL
The 2.5-m spectrometer (7) equipped with a 30 line/mm S” echellr in doublepass configuration was used for the measurements. ,4 ZrO concentrated arc lamp provided with a sapphire window was employed as the light source and the detector was a liquid Nz-cooled InSb element used in the photovoltaic mode. Excellent signal-to-noise rat,io was attained with t.his experimental set,up and lines separated by 0.030 cm-l were partially resolved. The wavenumber measurements were referred to lines in the 2-O and 1-O bands of CO (8) and the scatter of repeated measurements of unblended lines was less than 0.005 cm-‘. The vacuum tank of the grating monochromator provided an absorption path length of 24 m. Commercial CzHz was used at a pressure of lo-30 mm Hg. OBSERVED
SPECTRUM
The spectrum of C&Hzin the regions 1900-1990 cm-l and 2110-2230 cm-’ with indicated assignments of the individual lines is shown on a compressed wavenumber scale in Figs. 1 and 2. In addition to the prominent Q branches of the main n-2 bands 2~4 + vg and 3~6, numerous Q branches of the “hot” bands can clearly be seen in the spectrum. Due to the strong vibrational-rotational interactions among the upper states, some of these “hot” bands exhibit features not commonly seen in infrared spectra of simple linear molecules. As an illustration, Fig. 3 shows a closeup view of the Q branch of the A,-TI, transition2 000(31)2-OO01’oo at 1945.126 cm-‘: the c and d components of the Au state are split apart to t.he extent t.hat the Qdc component of the Q branch degrades to higher wavenumbers (to t,he right in the picture) while the QEdcomponent, after going only 0.10 cm-l in the same direction, t,urns back and becomes red-degraded (to the left in bhe picture). Another example of a Q branch of somewhat unusual shape can be seen in Fig. 4 showing the 0000°40_OOOOo11 JX,+-II, Q branch at 2151.065 cm-l which forms a band head at 2151.86 cm-l for J = 13 (the returning Q-branch lines cannot be seen). The Q branch of the 000(13)+“~1’oo &+--II, band at 2146.104 cm-l exhibits similar behavior (cf. Fig. 2). Evidence of strong vibrational-rotational interactions in the upper states is also seen in the appearance of the bands 000(22)-“XKIOOo11 (Z,-II,) and 000(22)2-OOOOo11(A,-&). The band centers of these bands are very close, 1932.033 and 1932.289 cm-l, and the Z,--II, band exhibits a strong Q branch (Fig. 5) but its P and R branches are rather weak; on the other hand, the Q branch of the AU-II, band does not show at all whereas the Pad and Rdd branches are fairly strong and the P,, and R,, branches are too weak to be identified with certainty. 2The designation v~Yzv~(v&)~ (with I = / Eq+ ESI) is used for states in which 14 and I:, cease to be good quantum numbers because of vibrational Z-type resonance [cf. Ref. (6)l; a subscript + is added for Z+ states and a subscript - for 2- states.
~~~~ 1. The epectof Cl& between 19tXIand 1990 cm-l recorded in 12th order. Identificationof ban&: A, 2~ + n(I); B, 2~4+ va(I1); C, (3~4+ ~a)*- d(II); D, (3~4+ YS)+’- v4’; H, (2~4i- 2d-o - d; E, (3~4 + a)- 0 - v41; F, (3vr + v6)2 - ~4*(1); G, (2~~ + 2~5)+~ - d(II); I, (%‘4+ %de - Vs’(II). 147
FIG. 2. The spectrum of C2H2 between 2110 and 2230 cm-l recorded in 13th order. Identification of bands: A, 31~5~; B, 41~6~ - VS’; C, 4~6~ - YSI; D, (~4 + 3v5)+” - vr’; E, (~4 + 3~5)~ v,‘(II); F, (~4 + 3&o - ~4~;G, (Y, + 3~5)~ - ~4~0); H, VP+ Y? - ~4~. 148
SPECTRUM OF ACETYLENE
cm-’
I
I I944
4s 20 t 1,111,,
I
I
46
41
149
I
1
48
49
I
14-Q l,lIII Q&b’
,,I ‘lo’
’
,!I
, ‘*o’
,
I ’
2
FIG. 3. The & branches of the Av-l& band (3~4+ V# - yll (Q = 1945.126cm-‘).
2151:oo 0 -
I
2152:OO 5
FIG. 4. The & branch of the &+-II, band 4v? - Y? (YO= 2151.065 cm-*) exhibiting a head at 2151.86 cm-l.
A somewhat unconventional feature of the spectrum is the appearance of bands involving states of 2- symmetry, such as the 8Q--II, band 000(22)_“-OOOOo11at 1932.033 cm-’ (its & branch is shown in Fig. 5)) and the &---II, bands 000(13)-OOOO1’o”at 2171.957 cm-l (Fig. 2) and 000(31)_“-OOOl’Oo at 1972.151 cm-’ (Fig. 1). These are, of course, dipole-allowed transitions (whose P and R branches origi-
PLfVA
150
em4
I
I
I
I
I832
33
34
1933
a
IO
2
,,,,I
FIQ. 5. The &branch
20
I3
I
I
I
I
of the &---II, band (2~4 + 2&O
I
I
32
37
25 I
I
g
I i
- Y& (~0 = 1932.033 cm-l).
nate in the d components and the Q branches go from the c components of the lower II states-opposite to what is true for X+-II transitions), but such bands do not seem to have been reported previously in vibration-rotation spectra. The assignment and analysis of the spectrum in t’he 5-b region was greatly facilitated by predictions based on a preliminary set of molecular constants (9) evaluated from previous measurements (4, 5, 10, 11). Two additional 0002200001 bands were predicted from these constant,s to occur in the region studied, at 1954.87 cm-’ @,+-II,) and 1958.70 cm-’ (AO-II,). The Q branch of the Z,+-II, band can indeed be seen in the predicted position but it is weak and overlapped by lines from other bands to the extent that it defied unambiguous analysis; the Q branch of the A,-& band is very weak and can barely be noticed adjacent to the strong R(7) line of the main 2vq + vg (II) band (Fig. 1). The P and R branches of the two predicted 00022XKlOOl bands could not be identified with certainty in the spectrum. No effort was made to identify the “double-hot” bands or bands due to the isotopic molecules present in natural abundance; the molecule H1‘V3CH is presumably responsible for the two weak nonalternating Q branches observed at 1930 cm-’ and - 2166.5 cm-‘. ROTATIONAL
ANALYSIS
The rotational analysis of the bands observed in the 5-p region was carried out simultaneously with bands from other regions of the spectrum (Q, 5) to obtain internally consistent sets of constants for all the states involved. This was done with the aid of a computer program briefly described in a preceding publication (3). The transitions from the ground vibrational state measured here (the three r&Z,+ bands2vr + ~3 ,3vg , and the 3vq + v5 z ,+-I? @+ band) were combined with the 2,+-Z,+ bands v4 + vj , vt ) v!2+ v4 + v5 ) v3 -I- 2v.1, v?. + 3vq + vs ) Vl -I- v4 +
SPECTRUM OF ACETYLENE
151
v5, vg + 2~5, and with the IL-z,+ band us1(4,5) to obtain the ground state constants listed in Table I. These ground state constants were calculated by the Ieast squares method from combination difference relations (12) rather than from a direct power series fit: this was necessary here since some of the upper states exhibit very strong vibrational-rotational perturbations making the power series fits inadequate for the high-J levels in such states. The available data do not warrant the inclusion of the higher-order distortion constant HO since its use does not significantly improve the fit. The constants listed in Table I for the lower II-states OOO1’o”and OOOO”llinvolved in the “hot” bands are, too, t’he results of simultaneous analyses of twelve bands from each of these states. The constants obtained for the upper states of the bands measured in this investigation are listed in Table II. For the states OOO(21)’ (II) and 000(22)~“, the “hot” transitions to these states observed in the 7.5-p region (4) were also taken into account in obtaining the constants given in this table. The upper state constants quoted in Table II are effective constants obtained by fitting the rotational levels of these states to a conventional power series
vJ = vo + (B’ - Bo + 2Z2Do)[J(J + 1) - Z2] - (D’ - Do + 3Z2Ho)[J(J + 1) - Z212 + (H’ - H,)[J(J
+ 1) - Z2]3.
(1)
The range of validity of these effective constants is indicated by the value of given in the last column for each state. For some of the heavily perturbed states, as, e.g., the 00031 states, the power series fits (1) break down for high-J levels and yield systematic, rather than random, differences in the observed and calculated line positions. For such states the use of the power series (1) was confined to low-J rotational levels (J 5 J,,,). The higher-J levels of these states, J > Jmx up to the J-number quoted in parentheses in the last column of Table II, wherever available experimentally, were fitted to a power series starting with a l/J(J + 1) term,
J,,,
VJ = a-v’J(J
+ 1) + ao + aJ(J
+ 1) + adJ(J + l)]“,
(2)
TABLE I CONSTANTSOF THE LOWER STATES OF W&HI
1.176600
-
oooo"oo
z,+
0001’0~
II, 611.694
f
OOOW1’
II,
f
729.155
f
2 1.175274 & 1.180507 k 2 1.176400 f 1.181090 f
B Error limits given are 90% confidence
16 1.598 f
9
21 21 18 19
16 16 10 11
1.606 1.656 1.606 1.635
intervals
f f f f
(cm-1)a
-
(c) (d) (c) (d)
1.290 f 2.6165f 2.144 f 2.345 f
11 6 8 5
in units of the last decimal.
0.032 f 0.025 f 0.022 f 0.015 f
11 8 5 4
152
PLfVA TABLE
CONSTANTS
state
.g
“0’ -
PO
“0
I
P
-
II
OF THE UPPER ST.%TES OF “Y&Hz OBSERVEII IN THE
ma
(B’ - Bo + 2PDo) X 108
REGION
(IN cm-*)8
D’ - Do)X 10
H’ - Ho)
0.90 f 0.08 1.09 * 0.07 1.85 f 0.28 1.61 * 0.24 1.26 f 0.11 1.49 zt 0.09 0.04 f 0.27 0.10 zt 0.27 0.05 * 0.15 0.08 f. 0.15 -7.44 f 0.25 0.85 z!z 0.25 8.44 f 0.23 -0.10 * 0.55 -2.94 f 0.29 3.07 f 0.49 -6.57 zt 1.02 0.65 f 1.26 7.42 f 1.01 -0.10 f 0.64 3.10 f. 0.89 5.56 f 0.64 (16.89) (-3.13) (24.51) (-13.16) (16.92) 0.97 * 0.35
0.15 -0.23 0.86 0.59 0.18 0.04
x
IC
--
OoOP3’
II”
2169.166 f
0.002
-
OcO(2l)‘(I)
nu
1959.697 zt 0.004
-
Ocm(21)~(11)II”
1940.093 f
0.093
-
OlOlPl~
llu
2701.997 f
0.008
0101’00
=,
2573.528 k 0.013
1844.372 zt (l.012C
oMtoo4*
AC7 2889.363 k 0.066
2160.208 * cl.cQ5c
2090.213 zk ().008b
1.97 11.54 6.04 3.29 1.34 9.08 -6.43 -1.73 -7.57 -2.33 8.77
zk 0.02 f 0.02 zk 0.07 zk 0.06 f 0.04 f. 0.04 zt 0.10 * 0.10 * 0.09 f 0.09 f 0.07
%I+ 2886.220 zk 0.006 2790.794 f 0.010 A,
2151.065 + (1.006’ 2179.100 * ().INQb
9.31 zt 0.07 7.36 zt 0.13
900(13)-O 2; 050(13)*(11) Au
2783.651 f 0.008 2768.486 zt 0.010
2171.957 * (L008b 2156.792 f (LOlOb
7.76 & 0.13 8.10 i 0.29
000(13)P 2%’ 0@0(22)*(11) Ag 000(22)-0 z, oOo(22)+YII) Zo’ 000(31)zfl) Au
2757.798 k 2661.444 zt 2661.188 zt 2648.018 zt 2584.977 f
2146.104 f ( 1932.289 f ( 1932.033 f ( 1918.863 zt ( 1973.283 zk (
8.68 7.50 7.36 7.82 6.38
OOO(31)’ z; 060(31)+0 zu’ OlM(31)~(11) Au
2583.645 z!z 0.012 2560.600 f 0.003 2556.826 f 0.005
1972.151 * ().Ollb 1948.906 f (MO4b 1945.126 f ID.OOSb
6.56 f 0.63 6.61 jz 0.23 6.37 f 0.10
oOO0°40 000(13)*(I)
5.~
0.007 0.012 0.011 0.007 0.022
* * ,. f zt
0.17 0.17 0.20 0.12 0.65
f 0.06 zt 0.05 zt 0.28 f 0.23 zk 0.09 f 0.06
_
-3.37 f 0.25 -0.07 zk 0.25 3.21 f 0.21 -0.12 f 0.69 -0.82 f 0.26 0.80 f 0.52 -2.57 & 1.42 -0.40 f 2.13 2.24 jz 1.70 -0.75 h 0.67 1.86 * 0.95 0.90 * 0.86 (59.25) (4.50) (51.18) (-10.91) (22.17) -0.08 zk 0.46
32 c 35 d 27 e 28 d 38 c 41 d 22 c 19 d 25 e 25 d 27 E 26 d 29 22 c 27 d 25 21 c 19 d 20 26 d 24 23 11 c 12 d 12(23) 12(29) 12(3O)C 25 d
a Referred togroundstate eon&ants (Table I). Th e errs limits given am W% confidence interval. b vc? = 611.694 cm-‘. 0 m’ = 729.155 cm-l. which is the form of an expansion for the eigenvalues of a 2 X 2 matrix in the case of a large interaction constant (off-diagonal matrix element) and nearly degenerate diagonal element,s. The low-J and high-J expansions join smoothly over a range of 2-3 values of J. Except for vo and, to some extent, (B’ - B. + 2Z2Do), the constants in the expansion (1) should not be given much physical significance for the strongly perturbed states since changing the range of J values in making the fits will appreciably change the values of the higher-order constants quoted in parentheses in Table II. For the same reason, the parameters ai of the high-J expansion (2) do not seem to be worth quoting. The sole purpose of these power series fits is to provide, in addition to the wavenumber of the rotationless state v. , smoothed values of the energy levels of the upper states to be used in a subsequent least squares adjustment of spect,roscopic constants capable of representing all the measured energy levels. This forms the subject of the following paper (6). A listing of the observed and calculated line positions of the 5-p bands is given in Table III. vJ
I’0 E’O I’0 1’0 1’0 8’0 2’0 0’1 L-0
Ll9.19 024’19 Lt3.19 bIE’I9 Z22‘19 OZI’I9 CZO’I9 926’09 SE8.09
SQO’O-
0’1 8’0 o-t G’I
o-1
000 lo EOO’O-
ZOO’0 100 ‘0 EOO ‘0 SOO’O 000 ‘0
IOO’O-
o-1
1’0
229’19 81s’19 9tt*19 9IE.19 LIZ-t9 021’19 fZ0’19 626’09 9E8.0961
000’0 000’0000’0 100’0 000’0
ScrL’O9 SS9’09 L95’09 ZB(1.09 66E.09 6IE’09 EtZ’O9 OL1’09 101’09 9E0.0961
100’0 OOO’Q 100’0 000’0
OOO’Oo-1
0’1 0’1 0’1
ZQQ’O-
SL6’6S 026’65 tL8’bS 42t)‘bS bBL’6S
116’6s 226’65 ZLB’5S e28’bs ObL’bS ESL’5S ZEL’6S Zl L-65 6b9’656T
A30
OIvONVlS
8Z L2 92 SZ fZ EZ z2 I2 OZ
NO1 1Vl
fZfi’L6 216’66
L28‘L6 tt6’66EI s 00’2 601-c 2Zz’P EW’B EL%‘01 I I9’ZI LSL’(II61
47200’0
EIT”I 6t2’9 zx-a ELf’OI tt9*2t S9L”lI
f 16’91 *LO’61 47472’12 S2cr’EZ 219’42
61 8t 11 91 SI ‘r1 El
t-w3
(r30’0 2-o E30 lo- z-o 1’3
&30’0200’0
I’0
s-o o-t
910’OE EEZ’ZE 09f0crE L69’9C.61
1’0 ii.0
330’0 000’0 800’0
+16’91 9LO ‘6t 6ll2 ‘It ZZ’I’EZ 809’42 908’L2 1 TO ‘OE 8EZ’ZE 99f’tL EOL’9E
too-o-
‘IOZ’ZE 165 ‘62 186’9Z E6E ‘32 908’12 822’61 959’9 t 160’tI EES’IlOZ
E30’0
3-1 1’0 2’0 0-t 0-t 0-t o-1 E’O 0’1 0’1
699’ZS 866’?Sbl
ESE los
b‘~6’8E EOZ’Icr EL+/‘E’I SSL’SS 0*0-a*
018’12
230’0 530’0 230’0‘r30’0+?30’0too-0 530-o 900’0 900’0
9*16’8E
0’1 1’0 L’O I’0
6 8 L 9 S b E 2 I 0
:: 01
286’8 LE’1.9 86B.E L9E’lQOZ ZW’86 SZE.96 918’f6 ftE’t6 128’88 LEE’9861
3’1
99E’1 0’78’86 SZE’96 EIB’Eb StE’tb 228’89 SEE’98
200’0
0’1
0-t L-0 0-t E’O L-0 L’O S’O
TOO’OZOO’OOOO’OEOO’Otoo.0 tOO’0 ZOO’O-
130’0-
L’O o-t
0-t
230-o 000’0 330’0 ZDO’O230’0-
z-o
2L’r’E’r LSL’S’, eco*e(r ESE ‘OS L99’ZS 966’)s
Z98’EB L6E’tB t’r6’8L 96’1’9L 190’tL 8E9’IL 522’69 ‘7ZB.99 SE’r’VP 840’29bI 0’1 0’1 0’1 L-0 S-O E’O 1-G
198’EB S6E’te 036’8L E6t.91 t90’fL 9E9’1L E22’69 IE8’99 Oft’479 850’29
too-oZoo’otoO’OEOO’OOOO’OZOO.OZOO-OLOO’0 SOD’0 000’0
ur4va
3-O
M
sao
3lV’3(l’)d
r
______ ______ ___- ____ - _____________________ ____ ______ -______ ____ -_ ________ __________
9fL.09 559’09 895’09 Z8?‘09 66t.09 6tE.09 E’12’09 1L1.09 101’09 9E0’09
zoo-oL’O o-1 1’0 S’O
too-oEOO’OIOO’O-
______ --------
*(IZ~OOO
3-O H SRO 3lV’3l r10 3-O M sao 31v’3tr1ki ______---___--__-__--~~~-~------~~~~~~-----~~~~~--~~~~~~~~~~~~~-~~~~~~~~~~~~~~~~~~~~~-~_~~~_~~~~~ 1 OOOOQ-
IT1 3mvcL
000
(continued)
DEVIATION
1869.909 67.544 65.174 62.799 60.417
STANOARO
30 31 32 33 34
8
1893.323 90.995 80.665 86.333 83.99
20 21 22 23 24 25 26 27 28 29
81.659 79.318 76.972 74.623 72.266
16.585 14.256 11.928 9.601 7.274 4.952 2.626 0.302 97.975 95.645
1916.583 14.254 11.926 9.600 7.274 4.949 2.625 1900.300 1897.976 95.650
10 11 12 13 14 15 16 17 18 19
69.910 67.544 65.168
93.320 SC.991 88.659 e6.331 e3.996 81.659 79.313 76.970 74.623 72.265
35.305 32.955 30.599 28.257 25.914 23.578 21.249 18.916
1935.294 32.946 30.601 28.259 25.919 23.582 21.247 18.914
0 1 2 3 4 5 6 7 8 9
-0.oc3 -0.004 -0.006 -0.002 -0.002 -0.000 -0.005 -0.002 o.oco -0.oc3
0.0026
CM-1
0.2 0.001 0.5 -0.000 0.1 -0.OC6
1.0 1.0 0.2 1.0 0.3 1.0 1.c 1.0 0.3 0.5
1.c o.oc2 1.0 0.002 1.c o.oc2 1.0 o.oc1 1.0 -0.000 1.0 o.oc3 1.0 O.OCl 1.c 0.002 1.0 -O.OCl 1.c -0.oc5
0.2 0.011 0.3 o.cc5 0.5 -0.002 1.0 -0.002 1.0 -0.oc5 1.0 -0.oc4 0.2 o.oc.2 0.5 0.002
2013.026 15.317 17.600 19.874 22.139
89.728 92.080 94.430 96.777 99.117 1.451
85.003 87.365
1989.725 92.081 94.432 96.770 99.119 2001.454 3.782 6.104 8.419 10.727
82.640
85.003 87.366
68.404 70.700 73.154 75.527 77.896 80.274
66.032
44.713 47.074 49.439 51.805 54.169 56.540 58.914 61.282 63.654
02.637
77.898 80.269
75.526
1966.030 68.405 70.779 73.153
44.712 47.073 49.436 51.802 54.170 56.539 58.910 61.283 63.656
I.942.353
II
1.0 1.0 1.0 1.0 0.1 1.0
1.0 1.0 0.7 0.5 0.7 1.0 0.8 1.0 0.7 1.0 0.003 -0.001 -0.002 -0.001 -0.002 -0.003
0.002 -0.001 o.ooi 0.001 0.001 -0.002 0.005 0.003 -0.000 -0.001
1.0 0.001 0.5 0.001 0.5 0.003 1.0 0.003 1.0 -0.001 0.8 O.OO! 0.7 0.004 1.0 -0.001 1.0 -0.002
o-c
1947.182 47.574 47.967 48.361 48.754
1943.551 43.878 44.215 44.562 44.917 45.280 45.650 46.026 46.408 46.793
1940.979 41.170 41.378 41.601 41.839 42.092 42.358 42.638 42.930 43.235
40.803
1940.0 16 40.052 40.106 40.179 40.269 40.376 40.501 40.644
P(J)CALC
47.182 47.574 47.962 48.358 48.740
43.552 43.880 44.218 44.564 44.917 45.280 45.651 46.027 46.410 46.791
40.975 41.170 41.375 41.599 41.837 42.088 42.357 42.639 42.930 43.236
40.800
40.642
40.014 40.046 40.106 40.177 40.265 40.373 40.490
OBS
0.3 0.1 0.5 0.7 0.7 1.0 0.7 0.7 0.7
W
____ ____________________~~~~~~~~~~~~-~~~~~_~_~~~_~__
(21)'-00000
III
h R(J)CACC w J P(J)CALC 05s o-c OBS _________________-------~~~~~~~~~--~~--~---~~~__~~~~~~~~~~~~~~~~_~~~~~~~~~~~~~~~~~~~~~~_____-_~__
_____~___________-------~--------~--~~-~~-~~~
RAN0
TABLE
-0.002 -0.006 -0.000 -0.002 -0.004 -0.003 -0.003 -0.002 -0.003
0-c
STANOARD
DEVIATION
2099.970 97.570 95.2R4 92.989 90.693 eB.396
30 31 32 33 34 35
26 27 28 29
2122.715 20.483 la.192 15.902 13.612 11.322 9.033 6.743 4.453 2.162
25.069
27.364
31.959 29.660
34.260
36.563
38.069
2145.805 43.489 41.178
20 21 22 23 24 25
10 11 12 13 14 15 lb 17 16 19
2164.457 62.112 59.771 57.433 55.100 52.771 50.445 48.123
99.065 97.575
2.165
6.744 4.460
22.775 20.404 la.192 15.903 13.613 11.322 9.034
27.364 25.069
45.805 43.490 41.177 30.070 36.563 34.260 31.959 29.459
62.113 59.772 57.433 55.102 52.770 50.444 48.124
64.455
-0.062 0.001 0.001 -0.000 0.002 -0.OCl -0.001 0.001
0.0015
CM-1
0.2 -0.005 0.3 -0.003
1.0 -0.000 1.0 O.OCl 1.c -0.000 1.0 0.001 1.c O.OCl 1.c -0.000 1.0 O.OCl 1.0 0.001 0.3 o.oc7 1.0 o.oc3
1.0 o.ooc 1.0 0.001 I.0 -O.OCl 1.0 O.OCl 1.0 o.ooc 1.0 0.000 1.0 0.000 1.0 -0.001 1.0 0.000 0.7 0.000
0.2 0.3 1.0 0.5 1.c 1.0 1.0 1.0
54.960
2243.136 45.508 47.877 50.242 52.603
2219.252 21.650 24.046 26.441 28.034 31.224 33.612 35.998 38.380 40.760
7.258 9.657 12.056 14.455 16.854
2.463 4.860
2195.282 97.674 2200.068
78.611 80.983 83.359 135.738 88.119 90.504 92.892
76.242
43.134 45.511
40.761
38.378
26.440 28.832 31.222 33.611 35.996
24.046
19.252 21.650
4.860 7.250 9.656 12.054 14.454 16.854
0.068 2.463
95.281 97.674
-0.000 0.000 -0.000 -0.001 -0.002 -0.002 -0.001 -0.002 -0.002 0.001
1.0 1.0 1.0 1.0 1.0 0.7 1.0 1.0 0.3 0.5 0.1 -0.002 0.003 0.1
-0.001 0.000 0.000 -0.000 -0.000 -0.000 -0.001 -0.002 -0.001 -0.000
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.8 0.001 0.5 -0.000 1.0 0.001 1.0 0.002 1.0 0.000 1.0 0.001 0.5 -0.004 1.0 0.002 1.0 0.000
00000
73.879 76.242 78.612 80.985 03.359 85.739 a8.115 90.506 92.892
00003'-
2171.517 73.878
BAND
TABLE III (continued)
79.311 75.859 80.410 80.960 81.507
2178.765
78.224
77.690
77.163
70.646
2173.799 74.237 74,692 75.161 75.643 7b.139
2170.416 70.664 70.933 71.223 71.534 71.864 72.214 72.503 72.971 73.376
69.905 70.189
69.298 69.390 69,505 69.642 69.802
2169.183 69.229
0.5 -0.002
77.164 77.689 78.223 ?a.763
81.518
80.408
76.645
76.140
0.1
0.011
0.5 -0.002
0.7 0.001 1.0 0.001 0.5 0.000 1.0 0.000 0.5 0.001 1.0 0.001 1.0 -0.001 0.5 0.001 1.0 -0.001 1.0 -0.001
73.800 74.23’3 74.692 75.161 75.644
73.376
72.215 72.584 72.973
71.064
-0.002 -0.001 -0.001 0.001 -0.005 -0.000 0.001 0.001 0.002 -0.000
0.000 -0.002 -0.000 -0.002 -0.001 -0.001
0.003 -0.002 -0.002
1.0 1.0 1.0 1.0 0.5 1.0 0.3 1.0 0.7 1.0
1.0 1.0 1.0 0.5 1.0 1.0
0.7 0.3 1.0
70.414 70.663 70.932 71.224 71.529
70.188
69.800 69.984
69.642
69.390 69.503
69.i96
69.186 69.227
53.59, 55.985 58.265’ b0.531 62.7RZ
TABLE III (continued) BLNO 01ocll - OOO,O ________________________________________________________________________________________________________________~____________ 7-c PDD,CILCI,llBS, w I-C SCC,C‘KCI rnss, ” 0-t O”D(CPLCI,015) Y ,OBS, v 0-C J PCCICPLCI
SPECTRUM OF ACETYLENE
TABLE III (continued)
157
PLfVA
TABLE
III
(continued)
0.1 0.5
0.7 0.3
0.1
0.1
0.1
0.1
0.5
TABLE
III
2146.975
2146.544 46.612 46.678 46.143 46.803 46.85, a.903 46.939 46.965 46.9,7
214t.115 46.133 46.16, 46.19, 46.242 46.293 46.349 46.411 46.476
(continued)
160
PLfVA
TABLE
III
(continued)
- OOOOl
TABLE
III
(continued)
69.190
14.154
91.600 e9.41PJ 87.221 e5.032 a*. 860 90.683 78.508 76.336
96.012 43.198
0.416 98.236
-0. ocs -0.011
0.1 0.2 0.1
-0.OOC
O.CObO
0.1
cc-1
O.OOa
0.5 -0.oc3
0.1
0.003 0.1 1.0 -0.004 -0.011 i?: -o.ocs 0.1 -O.OCb 0.5 -0.OC5
13.313 15.109
1910.824
65.821 68.321
63.308
50.719 53.235 55.754 58.273 60.192
1945.702 48.208
-0.002 -o.ooa
0.1 0.1
-0.007
1926.019 24.434 30.864 33.308 35.765 38.233 40.713 43.203
BAND
63.325
55.142 58.282
45.705 48.204 50.124
38.232 40.709
0.1
0.1
2.607
DEVIATION
43.136
0.1
7.109
1.648
4R.140 1q50*3b6 45.428
57.110 54.852 52.604
1966.253 63.$48 61.657 59.378
STANDARD
12 13
:;
1 a 9
j 4 5 6
O.OC52
CM-1
41.610 45.326 43.055
1949.904
56.843 54.522 52.20$
1966.191 63.845 61.505 59.111
3.0bQ
9.916
6.836 4.524
9.lsa
.I PCCICALCl~aeS~ w PDO~CALCIICBS) ___________________________---__--____.
1
1919.351 19.315 19.254
1919.166 19.211 19.254 19.294 19.330 19.360 lg.381 19.394 19.395 19.384
- 00010
0.011
-0.012 0.009
0.003 -0.004 0.005
-0.001 -0.004
0000112
0.1
0.2 0.1
0.1 0.1 0.5
0.1 0.1
1918.885 18.904 18.930 18.960 18.995 19.035 19.077 19.121
0.1
0.1
0.1 0.1
0.1
1999.911 2002.475 5.004 7.569
lcc*Oolf2 lcc+ool I2 L9az.all 85.232 al.663 90.105 92.555 95.016 97.487
9.969
2.551 5.018 1.407
2.802 5.230 i.e.61
0.1
0.2 0.1 0.5
1978.001 80.367 0.2 0.1 0.3
19.03,
1999.609 2002.055 4.514 6.989
9.608 2.054
1.0 0.2
0.3 0.3
0.5
0.1 0.1 0.1
w ______.
19.298
19.166 19.206
19.119
8.006 0.1 0.3a2 0.2 1982.753 2.754 85.139 5.132 87.532 1.516 89.931 9.926 92.338 94.152 4.751 91.176 1.181
w ROOlCALclla0SI RCCICALCIIOBS~ W .__~________________________~_~_~~~~~~_~_
___________________________~~~~~~~__~_~
DEVIATION
69.182
22
STANDARD
1874.151 71.913
20 21
17 18 19
15 lb
1896.021 93.809 91.601
10 11 12 13 14
89.413 87.225 85.043 82.865 80.689 ,*.513 16.336
1.260 4.985 2.725 1900.478 1898.244
1914.116 11.855 9.550
5 6 7 8 9
3 4
*
_1___'!"!4"'_4____99f____l_____OIf_____"____~~~_
________________________________-________________________-__-_____________-___-__________________
84NO000~22~~
0.004
1914.147 74.337 74.549 74.786
13.978
loc+cDl/2 1973.351 13.414 73.492 13.587 73.699 73.830
1973.289
1973.412 13.434 73.464 73.510
1973.287 73.304 13.323 13.342 13.360 13.318 13.395
________________~___~~~~~~__~~~~~~QCOlCALC)iOBSl OOClCALCllOBSl W .-_________________________-_________
0.3
0.1 -0.000 1.0 -0.005
0.2 -0.002
0.2 -0.004
162
PLfVA
TABLE
III
(continued)
RbND 000~311~-00010
ie 19
________________________~~~~~~~_~______________________________________________ 085 Y J PIJlCALC n-c RlJlCALC ORS u 0-C Q,JICp.LC _____________-______~~~~-----------~~~~~~~~______~~-~~~~~________________~~~_____________________ 46.553 1953.656 1948.912 56.044 0.1 -o.o,, 56.055 48.923 58.470 0.1 -0.002 48.94, 58.672
nss
Y
48.928
0.1
O-C
0.005
SPECTRUM
TABLE RPND 000l3i~,;-00000
OF ACETYLENE
III (continued)
163
164
PLfVA
ACKNOWLEDGMENTS The author is greatly indebted to Professor K. Narahari Rao and to Drs. M. E. Mickelson, K. F. Palmer, and S. Ghersetti for communicating their results prior to publication. Thanks are also due to Mr. R. Pulfrey for assistance in the measurements. RECEIVED:
January
15, 1972. REFERENCES
1. S. GHERSETTI AND K. NARAHARIRAO, J. Mol. Spectrosc. 28, 27 and 373 (1968). 8. K. F. PALMER,S. GHERSETTI,ANDK. NARAHARIRAO, J. Mol. Spectrosc. 30, 146 (1969). 3. S. GHERSETTI, J. PLfv.4, ANDK. NAR~HARIRAO, J. Mol. Speclrosc. 38,X3 (1971). 4. K. F. PALMER,M. E. MICKELSON, ANDK. NARAHARIRAO, J. Mol. Spectrosc., in print. 6. S. GHERSETTI ANDK. NARAHARIRAO, private communication. 6. J. PLfVA,J. Mol. Spectrosc. 44, 165 (1972). 7. T. K. MCCUBBIN, R. P. GROSSO, ANDJ. 1). MANGUS, Appl. Optics 1,431 (1962). 8. K. NARAHARIRAO, C. J. HUMPHREYS, ANDD. H. RANK,“Wavelength Standards in the Infrared,” Academic Press, New York 1966. 9. J. PLfva, S. GHERSETTI,M. E. MICKELSON, AND K. NAR.4HaRI RAO, Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1970. 10. T. A. WIGGINS,E. K. PLYLF,R,ANDE. D. TIDWELL,J. Opt. Sot. Amer. 61,1219 (1961). 11. J. F. SCOTTAND K. NARAHaRIRAO,J. Mol. Spectrosc. 18,16 (1966). 18. G. HERZBERG, “Infrared and Raman Spectra of Polyatomic Molecules,” VanNostrand, New York, 1946.
OF
MOLECULAR
Spectrum
SPECTROSCOPY
44, 145-164(1972)
of Acetylene
in the 54icron
Region’
JOSEF PLfvA Department of Physics, The Pennsylvania University Park, Pennsylvania
State Uttiversity, 16802
Three II,-&+ bands, 294 + ~6 at 1959.697 and 1940.063 cm-i and 3~s at 2169.166 and l&II “hot” bands occurring cm-r, accompanied by fifteen V-II, X--II, A-II, in the region between 1830 and 2256 cm-i were measured and analyzed. The &+-Z,+ band 3 Y( + ~6 at 2569.666 cm+ was also measured. The upper states of many of the transitions investigated are involved in strong vibrational-rotational interactions causing some effects not previously seen in the vibrationrotation spectra of simple linear molecules. The results obtained were combined with the available information from other regions of the spectrum to calculate an internally consistent set of constants for the ground state, for the II -states OOO1rOO and 606Cl”11as well as for the various higher excited states of the bending vibrations of C2H2. INTRODUCTION
As part of a comprehensive investigation of the vibration-rotation spectrum of acetylene and of its isotopic derivatives (l-5) this paper presents results of highresolution measurements in the 5 P region of the spectrum. Eighteen bands occurring between 1830 and 2250 cm-’ have been measured and analyzed. All of these bands, except those of the IHI transitions v2 + vhl - us1at 1844.372 cm-’ and v2 + us1 - vJ at 2090.213 cm-‘, involve overtones and combinations of the bending modes v4 and vs. The three main bands in this region correspond to the IL-Z,+ transitions ZVJ+ v5 at 1959.697 and 1940.003 cm-’ and 3v~ at 2169.166 cm-‘. The “hot” bands correspond to the various Zf-II, Z--II, and A-II transitions 3vq + v5 - v4 , 2~4 -I- ZVS- US, v4 -I- 3vg - ~4, and 415 - vg . In addition, the Z,+-Z,+ band 3~4+ USat 2560.600 cm-’ was also measured. The bands investigated contain a wealth of information on the strongly interacting states of the bending vibrations and these measurements have made it ultimately possible to obtain a reliable set of spectroscopic constants for the bending stat,es reported in t,he following paper (6). r Presented at the Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1971. This work was supported by the National Science Foundation and by the Office of Naval Research. 145 Copyright
Q 1972 by Academic
All rights of reproduction
Press, Inc.
in any form reserved.
146
PLiVA EXPERIMENTAL
The 2.5-m spectrometer (7) equipped with a 30 line/mm S” echellr in doublepass configuration was used for the measurements. ,4 ZrO concentrated arc lamp provided with a sapphire window was employed as the light source and the detector was a liquid Nz-cooled InSb element used in the photovoltaic mode. Excellent signal-to-noise rat,io was attained with t.his experimental set,up and lines separated by 0.030 cm-l were partially resolved. The wavenumber measurements were referred to lines in the 2-O and 1-O bands of CO (8) and the scatter of repeated measurements of unblended lines was less than 0.005 cm-‘. The vacuum tank of the grating monochromator provided an absorption path length of 24 m. Commercial CzHz was used at a pressure of lo-30 mm Hg. OBSERVED
SPECTRUM
The spectrum of C&Hzin the regions 1900-1990 cm-l and 2110-2230 cm-’ with indicated assignments of the individual lines is shown on a compressed wavenumber scale in Figs. 1 and 2. In addition to the prominent Q branches of the main n-2 bands 2~4 + vg and 3~6, numerous Q branches of the “hot” bands can clearly be seen in the spectrum. Due to the strong vibrational-rotational interactions among the upper states, some of these “hot” bands exhibit features not commonly seen in infrared spectra of simple linear molecules. As an illustration, Fig. 3 shows a closeup view of the Q branch of the A,-TI, transition2 000(31)2-OO01’oo at 1945.126 cm-‘: the c and d components of the Au state are split apart to t.he extent t.hat the Qdc component of the Q branch degrades to higher wavenumbers (to t,he right in the picture) while the QEdcomponent, after going only 0.10 cm-l in the same direction, t,urns back and becomes red-degraded (to the left in bhe picture). Another example of a Q branch of somewhat unusual shape can be seen in Fig. 4 showing the 0000°40_OOOOo11 JX,+-II, Q branch at 2151.065 cm-l which forms a band head at 2151.86 cm-l for J = 13 (the returning Q-branch lines cannot be seen). The Q branch of the 000(13)+“~1’oo &+--II, band at 2146.104 cm-l exhibits similar behavior (cf. Fig. 2). Evidence of strong vibrational-rotational interactions in the upper states is also seen in the appearance of the bands 000(22)-“XKIOOo11 (Z,-II,) and 000(22)2-OOOOo11(A,-&). The band centers of these bands are very close, 1932.033 and 1932.289 cm-l, and the Z,--II, band exhibits a strong Q branch (Fig. 5) but its P and R branches are rather weak; on the other hand, the Q branch of the AU-II, band does not show at all whereas the Pad and Rdd branches are fairly strong and the P,, and R,, branches are too weak to be identified with certainty. 2The designation v~Yzv~(v&)~ (with I = / Eq+ ESI) is used for states in which 14 and I:, cease to be good quantum numbers because of vibrational Z-type resonance [cf. Ref. (6)l; a subscript + is added for Z+ states and a subscript - for 2- states.
~~~~ 1. The epectof Cl& between 19tXIand 1990 cm-l recorded in 12th order. Identificationof ban&: A, 2~ + n(I); B, 2~4+ va(I1); C, (3~4+ ~a)*- d(II); D, (3~4+ YS)+’- v4’; H, (2~4i- 2d-o - d; E, (3~4 + a)- 0 - v41; F, (3vr + v6)2 - ~4*(1); G, (2~~ + 2~5)+~ - d(II); I, (%‘4+ %de - Vs’(II). 147
FIG. 2. The spectrum of C2H2 between 2110 and 2230 cm-l recorded in 13th order. Identification of bands: A, 31~5~; B, 41~6~ - VS’; C, 4~6~ - YSI; D, (~4 + 3v5)+” - vr’; E, (~4 + 3~5)~ v,‘(II); F, (~4 + 3&o - ~4~;G, (Y, + 3~5)~ - ~4~0); H, VP+ Y? - ~4~. 148
SPECTRUM OF ACETYLENE
cm-’
I
I I944
4s 20 t 1,111,,
I
I
46
41
149
I
1
48
49
I
14-Q l,lIII Q&b’
,,I ‘lo’
’
,!I
, ‘*o’
,
I ’
2
FIG. 3. The & branches of the Av-l& band (3~4+ V# - yll (Q = 1945.126cm-‘).
2151:oo 0 -
I
2152:OO 5
FIG. 4. The & branch of the &+-II, band 4v? - Y? (YO= 2151.065 cm-*) exhibiting a head at 2151.86 cm-l.
A somewhat unconventional feature of the spectrum is the appearance of bands involving states of 2- symmetry, such as the 8Q--II, band 000(22)_“-OOOOo11at 1932.033 cm-’ (its & branch is shown in Fig. 5)) and the &---II, bands 000(13)-OOOO1’o”at 2171.957 cm-l (Fig. 2) and 000(31)_“-OOOl’Oo at 1972.151 cm-’ (Fig. 1). These are, of course, dipole-allowed transitions (whose P and R branches origi-
PLfVA
150
em4
I
I
I
I
I832
33
34
1933
a
IO
2
,,,,I
FIQ. 5. The &branch
20
I3
I
I
I
I
of the &---II, band (2~4 + 2&O
I
I
32
37
25 I
I
g
I i
- Y& (~0 = 1932.033 cm-l).
nate in the d components and the Q branches go from the c components of the lower II states-opposite to what is true for X+-II transitions), but such bands do not seem to have been reported previously in vibration-rotation spectra. The assignment and analysis of the spectrum in t’he 5-b region was greatly facilitated by predictions based on a preliminary set of molecular constants (9) evaluated from previous measurements (4, 5, 10, 11). Two additional 0002200001 bands were predicted from these constant,s to occur in the region studied, at 1954.87 cm-’ @,+-II,) and 1958.70 cm-’ (AO-II,). The Q branch of the Z,+-II, band can indeed be seen in the predicted position but it is weak and overlapped by lines from other bands to the extent that it defied unambiguous analysis; the Q branch of the A,-& band is very weak and can barely be noticed adjacent to the strong R(7) line of the main 2vq + vg (II) band (Fig. 1). The P and R branches of the two predicted 00022XKlOOl bands could not be identified with certainty in the spectrum. No effort was made to identify the “double-hot” bands or bands due to the isotopic molecules present in natural abundance; the molecule H1‘V3CH is presumably responsible for the two weak nonalternating Q branches observed at 1930 cm-’ and - 2166.5 cm-‘. ROTATIONAL
ANALYSIS
The rotational analysis of the bands observed in the 5-p region was carried out simultaneously with bands from other regions of the spectrum (Q, 5) to obtain internally consistent sets of constants for all the states involved. This was done with the aid of a computer program briefly described in a preceding publication (3). The transitions from the ground vibrational state measured here (the three r&Z,+ bands2vr + ~3 ,3vg , and the 3vq + v5 z ,+-I? @+ band) were combined with the 2,+-Z,+ bands v4 + vj , vt ) v!2+ v4 + v5 ) v3 -I- 2v.1, v?. + 3vq + vs ) Vl -I- v4 +
SPECTRUM OF ACETYLENE
151
v5, vg + 2~5, and with the IL-z,+ band us1(4,5) to obtain the ground state constants listed in Table I. These ground state constants were calculated by the Ieast squares method from combination difference relations (12) rather than from a direct power series fit: this was necessary here since some of the upper states exhibit very strong vibrational-rotational perturbations making the power series fits inadequate for the high-J levels in such states. The available data do not warrant the inclusion of the higher-order distortion constant HO since its use does not significantly improve the fit. The constants listed in Table I for the lower II-states OOO1’o”and OOOO”llinvolved in the “hot” bands are, too, t’he results of simultaneous analyses of twelve bands from each of these states. The constants obtained for the upper states of the bands measured in this investigation are listed in Table II. For the states OOO(21)’ (II) and 000(22)~“, the “hot” transitions to these states observed in the 7.5-p region (4) were also taken into account in obtaining the constants given in this table. The upper state constants quoted in Table II are effective constants obtained by fitting the rotational levels of these states to a conventional power series
vJ = vo + (B’ - Bo + 2Z2Do)[J(J + 1) - Z2] - (D’ - Do + 3Z2Ho)[J(J + 1) - Z212 + (H’ - H,)[J(J
+ 1) - Z2]3.
(1)
The range of validity of these effective constants is indicated by the value of given in the last column for each state. For some of the heavily perturbed states, as, e.g., the 00031 states, the power series fits (1) break down for high-J levels and yield systematic, rather than random, differences in the observed and calculated line positions. For such states the use of the power series (1) was confined to low-J rotational levels (J 5 J,,,). The higher-J levels of these states, J > Jmx up to the J-number quoted in parentheses in the last column of Table II, wherever available experimentally, were fitted to a power series starting with a l/J(J + 1) term,
J,,,
VJ = a-v’J(J
+ 1) + ao + aJ(J
+ 1) + adJ(J + l)]“,
(2)
TABLE I CONSTANTSOF THE LOWER STATES OF W&HI
1.176600
-
oooo"oo
z,+
0001’0~
II, 611.694
f
OOOW1’
II,
f
729.155
f
2 1.175274 & 1.180507 k 2 1.176400 f 1.181090 f
B Error limits given are 90% confidence
16 1.598 f
9
21 21 18 19
16 16 10 11
1.606 1.656 1.606 1.635
intervals
f f f f
(cm-1)a
-
(c) (d) (c) (d)
1.290 f 2.6165f 2.144 f 2.345 f
11 6 8 5
in units of the last decimal.
0.032 f 0.025 f 0.022 f 0.015 f
11 8 5 4
152
PLfVA TABLE
CONSTANTS
state
.g
“0’ -
PO
“0
I
P
-
II
OF THE UPPER ST.%TES OF “Y&Hz OBSERVEII IN THE
ma
(B’ - Bo + 2PDo) X 108
REGION
(IN cm-*)8
D’ - Do)X 10
H’ - Ho)
0.90 f 0.08 1.09 * 0.07 1.85 f 0.28 1.61 * 0.24 1.26 f 0.11 1.49 zt 0.09 0.04 f 0.27 0.10 zt 0.27 0.05 * 0.15 0.08 f. 0.15 -7.44 f 0.25 0.85 z!z 0.25 8.44 f 0.23 -0.10 * 0.55 -2.94 f 0.29 3.07 f 0.49 -6.57 zt 1.02 0.65 f 1.26 7.42 f 1.01 -0.10 f 0.64 3.10 f. 0.89 5.56 f 0.64 (16.89) (-3.13) (24.51) (-13.16) (16.92) 0.97 * 0.35
0.15 -0.23 0.86 0.59 0.18 0.04
x
IC
--
OoOP3’
II”
2169.166 f
0.002
-
OcO(2l)‘(I)
nu
1959.697 zt 0.004
-
Ocm(21)~(11)II”
1940.093 f
0.093
-
OlOlPl~
llu
2701.997 f
0.008
0101’00
=,
2573.528 k 0.013
1844.372 zt (l.012C
oMtoo4*
AC7 2889.363 k 0.066
2160.208 * cl.cQ5c
2090.213 zk ().008b
1.97 11.54 6.04 3.29 1.34 9.08 -6.43 -1.73 -7.57 -2.33 8.77
zk 0.02 f 0.02 zk 0.07 zk 0.06 f 0.04 f. 0.04 zt 0.10 * 0.10 * 0.09 f 0.09 f 0.07
%I+ 2886.220 zk 0.006 2790.794 f 0.010 A,
2151.065 + (1.006’ 2179.100 * ().INQb
9.31 zt 0.07 7.36 zt 0.13
900(13)-O 2; 050(13)*(11) Au
2783.651 f 0.008 2768.486 zt 0.010
2171.957 * (L008b 2156.792 f (LOlOb
7.76 & 0.13 8.10 i 0.29
000(13)P 2%’ 0@0(22)*(11) Ag 000(22)-0 z, oOo(22)+YII) Zo’ 000(31)zfl) Au
2757.798 k 2661.444 zt 2661.188 zt 2648.018 zt 2584.977 f
2146.104 f ( 1932.289 f ( 1932.033 f ( 1918.863 zt ( 1973.283 zk (
8.68 7.50 7.36 7.82 6.38
OOO(31)’ z; 060(31)+0 zu’ OlM(31)~(11) Au
2583.645 z!z 0.012 2560.600 f 0.003 2556.826 f 0.005
1972.151 * ().Ollb 1948.906 f (MO4b 1945.126 f ID.OOSb
6.56 f 0.63 6.61 jz 0.23 6.37 f 0.10
oOO0°40 000(13)*(I)
5.~
0.007 0.012 0.011 0.007 0.022
* * ,. f zt
0.17 0.17 0.20 0.12 0.65
f 0.06 zt 0.05 zt 0.28 f 0.23 zk 0.09 f 0.06
_
-3.37 f 0.25 -0.07 zk 0.25 3.21 f 0.21 -0.12 f 0.69 -0.82 f 0.26 0.80 f 0.52 -2.57 & 1.42 -0.40 f 2.13 2.24 jz 1.70 -0.75 h 0.67 1.86 * 0.95 0.90 * 0.86 (59.25) (4.50) (51.18) (-10.91) (22.17) -0.08 zk 0.46
32 c 35 d 27 e 28 d 38 c 41 d 22 c 19 d 25 e 25 d 27 E 26 d 29 22 c 27 d 25 21 c 19 d 20 26 d 24 23 11 c 12 d 12(23) 12(29) 12(3O)C 25 d
a Referred togroundstate eon&ants (Table I). Th e errs limits given am W% confidence interval. b vc? = 611.694 cm-‘. 0 m’ = 729.155 cm-l. which is the form of an expansion for the eigenvalues of a 2 X 2 matrix in the case of a large interaction constant (off-diagonal matrix element) and nearly degenerate diagonal element,s. The low-J and high-J expansions join smoothly over a range of 2-3 values of J. Except for vo and, to some extent, (B’ - B. + 2Z2Do), the constants in the expansion (1) should not be given much physical significance for the strongly perturbed states since changing the range of J values in making the fits will appreciably change the values of the higher-order constants quoted in parentheses in Table II. For the same reason, the parameters ai of the high-J expansion (2) do not seem to be worth quoting. The sole purpose of these power series fits is to provide, in addition to the wavenumber of the rotationless state v. , smoothed values of the energy levels of the upper states to be used in a subsequent least squares adjustment of spect,roscopic constants capable of representing all the measured energy levels. This forms the subject of the following paper (6). A listing of the observed and calculated line positions of the 5-p bands is given in Table III. vJ
I’0 E’O I’0 1’0 1’0 8’0 2’0 0’1 L-0
Ll9.19 024’19 Lt3.19 bIE’I9 Z22‘19 OZI’I9 CZO’I9 926’09 SE8.09
SQO’O-
0’1 8’0 o-t G’I
o-1
000 lo EOO’O-
ZOO’0 100 ‘0 EOO ‘0 SOO’O 000 ‘0
IOO’O-
o-1
1’0
229’19 81s’19 9tt*19 9IE.19 LIZ-t9 021’19 fZ0’19 626’09 9E8.0961
000’0 000’0000’0 100’0 000’0
ScrL’O9 SS9’09 L95’09 ZB(1.09 66E.09 6IE’09 EtZ’O9 OL1’09 101’09 9E0.0961
100’0 OOO’Q 100’0 000’0
OOO’Oo-1
0’1 0’1 0’1
ZQQ’O-
SL6’6S 026’65 tL8’bS 42t)‘bS bBL’6S
116’6s 226’65 ZLB’5S e28’bs ObL’bS ESL’5S ZEL’6S Zl L-65 6b9’656T
A30
OIvONVlS
8Z L2 92 SZ fZ EZ z2 I2 OZ
NO1 1Vl
fZfi’L6 216’66
L28‘L6 tt6’66EI s 00’2 601-c 2Zz’P EW’B EL%‘01 I I9’ZI LSL’(II61
47200’0
EIT”I 6t2’9 zx-a ELf’OI tt9*2t S9L”lI
f 16’91 *LO’61 47472’12 S2cr’EZ 219’42
61 8t 11 91 SI ‘r1 El
t-w3
(r30’0 2-o E30 lo- z-o 1’3
&30’0200’0
I’0
s-o o-t
910’OE EEZ’ZE 09f0crE L69’9C.61
1’0 ii.0
330’0 000’0 800’0
+16’91 9LO ‘6t 6ll2 ‘It ZZ’I’EZ 809’42 908’L2 1 TO ‘OE 8EZ’ZE 99f’tL EOL’9E
too-o-
‘IOZ’ZE 165 ‘62 186’9Z E6E ‘32 908’12 822’61 959’9 t 160’tI EES’IlOZ
E30’0
3-1 1’0 2’0 0-t 0-t 0-t o-1 E’O 0’1 0’1
699’ZS 866’?Sbl
ESE los
b‘~6’8E EOZ’Icr EL+/‘E’I SSL’SS 0*0-a*
018’12
230’0 530’0 230’0‘r30’0+?30’0too-0 530-o 900’0 900’0
9*16’8E
0’1 1’0 L’O I’0
6 8 L 9 S b E 2 I 0
:: 01
286’8 LE’1.9 86B.E L9E’lQOZ ZW’86 SZE.96 918’f6 ftE’t6 128’88 LEE’9861
3’1
99E’1 0’78’86 SZE’96 EIB’Eb StE’tb 228’89 SEE’98
200’0
0’1
0-t L-0 0-t E’O L-0 L’O S’O
TOO’OZOO’OOOO’OEOO’Otoo.0 tOO’0 ZOO’O-
130’0-
L’O o-t
0-t
230-o 000’0 330’0 ZDO’O230’0-
z-o
2L’r’E’r LSL’S’, eco*e(r ESE ‘OS L99’ZS 966’)s
Z98’EB L6E’tB t’r6’8L 96’1’9L 190’tL 8E9’IL 522’69 ‘7ZB.99 SE’r’VP 840’29bI 0’1 0’1 0’1 L-0 S-O E’O 1-G
198’EB S6E’te 036’8L E6t.91 t90’fL 9E9’1L E22’69 IE8’99 Oft’479 850’29
too-oZoo’otoO’OEOO’OOOO’OZOO.OZOO-OLOO’0 SOD’0 000’0
ur4va
3-O
M
sao
3lV’3(l’)d
r
______ ______ ___- ____ - _____________________ ____ ______ -______ ____ -_ ________ __________
9fL.09 559’09 895’09 Z8?‘09 66t.09 6tE.09 E’12’09 1L1.09 101’09 9E0’09
zoo-oL’O o-1 1’0 S’O
too-oEOO’OIOO’O-
______ --------
*(IZ~OOO
3-O H SRO 3lV’3l r10 3-O M sao 31v’3tr1ki ______---___--__-__--~~~-~------~~~~~~-----~~~~~--~~~~~~~~~~~~~-~~~~~~~~~~~~~~~~~~~~~-~_~~~_~~~~~ 1 OOOOQ-
IT1 3mvcL
000
(continued)
DEVIATION
1869.909 67.544 65.174 62.799 60.417
STANOARO
30 31 32 33 34
8
1893.323 90.995 80.665 86.333 83.99
20 21 22 23 24 25 26 27 28 29
81.659 79.318 76.972 74.623 72.266
16.585 14.256 11.928 9.601 7.274 4.952 2.626 0.302 97.975 95.645
1916.583 14.254 11.926 9.600 7.274 4.949 2.625 1900.300 1897.976 95.650
10 11 12 13 14 15 16 17 18 19
69.910 67.544 65.168
93.320 SC.991 88.659 e6.331 e3.996 81.659 79.313 76.970 74.623 72.265
35.305 32.955 30.599 28.257 25.914 23.578 21.249 18.916
1935.294 32.946 30.601 28.259 25.919 23.582 21.247 18.914
0 1 2 3 4 5 6 7 8 9
-0.oc3 -0.004 -0.006 -0.002 -0.002 -0.000 -0.005 -0.002 o.oco -0.oc3
0.0026
CM-1
0.2 0.001 0.5 -0.000 0.1 -0.OC6
1.0 1.0 0.2 1.0 0.3 1.0 1.c 1.0 0.3 0.5
1.c o.oc2 1.0 0.002 1.c o.oc2 1.0 o.oc1 1.0 -0.000 1.0 o.oc3 1.0 O.OCl 1.c 0.002 1.0 -O.OCl 1.c -0.oc5
0.2 0.011 0.3 o.cc5 0.5 -0.002 1.0 -0.002 1.0 -0.oc5 1.0 -0.oc4 0.2 o.oc.2 0.5 0.002
2013.026 15.317 17.600 19.874 22.139
89.728 92.080 94.430 96.777 99.117 1.451
85.003 87.365
1989.725 92.081 94.432 96.770 99.119 2001.454 3.782 6.104 8.419 10.727
82.640
85.003 87.366
68.404 70.700 73.154 75.527 77.896 80.274
66.032
44.713 47.074 49.439 51.805 54.169 56.540 58.914 61.282 63.654
02.637
77.898 80.269
75.526
1966.030 68.405 70.779 73.153
44.712 47.073 49.436 51.802 54.170 56.539 58.910 61.283 63.656
I.942.353
II
1.0 1.0 1.0 1.0 0.1 1.0
1.0 1.0 0.7 0.5 0.7 1.0 0.8 1.0 0.7 1.0 0.003 -0.001 -0.002 -0.001 -0.002 -0.003
0.002 -0.001 o.ooi 0.001 0.001 -0.002 0.005 0.003 -0.000 -0.001
1.0 0.001 0.5 0.001 0.5 0.003 1.0 0.003 1.0 -0.001 0.8 O.OO! 0.7 0.004 1.0 -0.001 1.0 -0.002
o-c
1947.182 47.574 47.967 48.361 48.754
1943.551 43.878 44.215 44.562 44.917 45.280 45.650 46.026 46.408 46.793
1940.979 41.170 41.378 41.601 41.839 42.092 42.358 42.638 42.930 43.235
40.803
1940.0 16 40.052 40.106 40.179 40.269 40.376 40.501 40.644
P(J)CALC
47.182 47.574 47.962 48.358 48.740
43.552 43.880 44.218 44.564 44.917 45.280 45.651 46.027 46.410 46.791
40.975 41.170 41.375 41.599 41.837 42.088 42.357 42.639 42.930 43.236
40.800
40.642
40.014 40.046 40.106 40.177 40.265 40.373 40.490
OBS
0.3 0.1 0.5 0.7 0.7 1.0 0.7 0.7 0.7
W
____ ____________________~~~~~~~~~~~~-~~~~~_~_~~~_~__
(21)'-00000
III
h R(J)CACC w J P(J)CALC 05s o-c OBS _________________-------~~~~~~~~~--~~--~---~~~__~~~~~~~~~~~~~~~~_~~~~~~~~~~~~~~~~~~~~~~_____-_~__
_____~___________-------~--------~--~~-~~-~~~
RAN0
TABLE
-0.002 -0.006 -0.000 -0.002 -0.004 -0.003 -0.003 -0.002 -0.003
0-c
STANOARD
DEVIATION
2099.970 97.570 95.2R4 92.989 90.693 eB.396
30 31 32 33 34 35
26 27 28 29
2122.715 20.483 la.192 15.902 13.612 11.322 9.033 6.743 4.453 2.162
25.069
27.364
31.959 29.660
34.260
36.563
38.069
2145.805 43.489 41.178
20 21 22 23 24 25
10 11 12 13 14 15 lb 17 16 19
2164.457 62.112 59.771 57.433 55.100 52.771 50.445 48.123
99.065 97.575
2.165
6.744 4.460
22.775 20.404 la.192 15.903 13.613 11.322 9.034
27.364 25.069
45.805 43.490 41.177 30.070 36.563 34.260 31.959 29.459
62.113 59.772 57.433 55.102 52.770 50.444 48.124
64.455
-0.062 0.001 0.001 -0.000 0.002 -0.OCl -0.001 0.001
0.0015
CM-1
0.2 -0.005 0.3 -0.003
1.0 -0.000 1.0 O.OCl 1.c -0.000 1.0 0.001 1.c O.OCl 1.c -0.000 1.0 O.OCl 1.0 0.001 0.3 o.oc7 1.0 o.oc3
1.0 o.ooc 1.0 0.001 I.0 -O.OCl 1.0 O.OCl 1.0 o.ooc 1.0 0.000 1.0 0.000 1.0 -0.001 1.0 0.000 0.7 0.000
0.2 0.3 1.0 0.5 1.c 1.0 1.0 1.0
54.960
2243.136 45.508 47.877 50.242 52.603
2219.252 21.650 24.046 26.441 28.034 31.224 33.612 35.998 38.380 40.760
7.258 9.657 12.056 14.455 16.854
2.463 4.860
2195.282 97.674 2200.068
78.611 80.983 83.359 135.738 88.119 90.504 92.892
76.242
43.134 45.511
40.761
38.378
26.440 28.832 31.222 33.611 35.996
24.046
19.252 21.650
4.860 7.250 9.656 12.054 14.454 16.854
0.068 2.463
95.281 97.674
-0.000 0.000 -0.000 -0.001 -0.002 -0.002 -0.001 -0.002 -0.002 0.001
1.0 1.0 1.0 1.0 1.0 0.7 1.0 1.0 0.3 0.5 0.1 -0.002 0.003 0.1
-0.001 0.000 0.000 -0.000 -0.000 -0.000 -0.001 -0.002 -0.001 -0.000
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.8 0.001 0.5 -0.000 1.0 0.001 1.0 0.002 1.0 0.000 1.0 0.001 0.5 -0.004 1.0 0.002 1.0 0.000
00000
73.879 76.242 78.612 80.985 03.359 85.739 a8.115 90.506 92.892
00003'-
2171.517 73.878
BAND
TABLE III (continued)
79.311 75.859 80.410 80.960 81.507
2178.765
78.224
77.690
77.163
70.646
2173.799 74.237 74,692 75.161 75.643 7b.139
2170.416 70.664 70.933 71.223 71.534 71.864 72.214 72.503 72.971 73.376
69.905 70.189
69.298 69.390 69,505 69.642 69.802
2169.183 69.229
0.5 -0.002
77.164 77.689 78.223 ?a.763
81.518
80.408
76.645
76.140
0.1
0.011
0.5 -0.002
0.7 0.001 1.0 0.001 0.5 0.000 1.0 0.000 0.5 0.001 1.0 0.001 1.0 -0.001 0.5 0.001 1.0 -0.001 1.0 -0.001
73.800 74.23’3 74.692 75.161 75.644
73.376
72.215 72.584 72.973
71.064
-0.002 -0.001 -0.001 0.001 -0.005 -0.000 0.001 0.001 0.002 -0.000
0.000 -0.002 -0.000 -0.002 -0.001 -0.001
0.003 -0.002 -0.002
1.0 1.0 1.0 1.0 0.5 1.0 0.3 1.0 0.7 1.0
1.0 1.0 1.0 0.5 1.0 1.0
0.7 0.3 1.0
70.414 70.663 70.932 71.224 71.529
70.188
69.800 69.984
69.642
69.390 69.503
69.i96
69.186 69.227
53.59, 55.985 58.265’ b0.531 62.7RZ
TABLE III (continued) BLNO 01ocll - OOO,O ________________________________________________________________________________________________________________~____________ 7-c PDD,CILCI,llBS, w I-C SCC,C‘KCI rnss, ” 0-t O”D(CPLCI,015) Y ,OBS, v 0-C J PCCICPLCI
SPECTRUM OF ACETYLENE
TABLE III (continued)
157
PLfVA
TABLE
III
(continued)
0.1 0.5
0.7 0.3
0.1
0.1
0.1
0.1
0.5
TABLE
III
2146.975
2146.544 46.612 46.678 46.143 46.803 46.85, a.903 46.939 46.965 46.9,7
214t.115 46.133 46.16, 46.19, 46.242 46.293 46.349 46.411 46.476
(continued)
160
PLfVA
TABLE
III
(continued)
- OOOOl
TABLE
III
(continued)
69.190
14.154
91.600 e9.41PJ 87.221 e5.032 a*. 860 90.683 78.508 76.336
96.012 43.198
0.416 98.236
-0. ocs -0.011
0.1 0.2 0.1
-0.OOC
O.CObO
0.1
cc-1
O.OOa
0.5 -0.oc3
0.1
0.003 0.1 1.0 -0.004 -0.011 i?: -o.ocs 0.1 -O.OCb 0.5 -0.OC5
13.313 15.109
1910.824
65.821 68.321
63.308
50.719 53.235 55.754 58.273 60.192
1945.702 48.208
-0.002 -o.ooa
0.1 0.1
-0.007
1926.019 24.434 30.864 33.308 35.765 38.233 40.713 43.203
BAND
63.325
55.142 58.282
45.705 48.204 50.124
38.232 40.709
0.1
0.1
2.607
DEVIATION
43.136
0.1
7.109
1.648
4R.140 1q50*3b6 45.428
57.110 54.852 52.604
1966.253 63.$48 61.657 59.378
STANDARD
12 13
:;
1 a 9
j 4 5 6
O.OC52
CM-1
41.610 45.326 43.055
1949.904
56.843 54.522 52.20$
1966.191 63.845 61.505 59.111
3.0bQ
9.916
6.836 4.524
9.lsa
.I PCCICALCl~aeS~ w PDO~CALCIICBS) ___________________________---__--____.
1
1919.351 19.315 19.254
1919.166 19.211 19.254 19.294 19.330 19.360 lg.381 19.394 19.395 19.384
- 00010
0.011
-0.012 0.009
0.003 -0.004 0.005
-0.001 -0.004
0000112
0.1
0.2 0.1
0.1 0.1 0.5
0.1 0.1
1918.885 18.904 18.930 18.960 18.995 19.035 19.077 19.121
0.1
0.1
0.1 0.1
0.1
1999.911 2002.475 5.004 7.569
lcc*Oolf2 lcc+ool I2 L9az.all 85.232 al.663 90.105 92.555 95.016 97.487
9.969
2.551 5.018 1.407
2.802 5.230 i.e.61
0.1
0.2 0.1 0.5
1978.001 80.367 0.2 0.1 0.3
19.03,
1999.609 2002.055 4.514 6.989
9.608 2.054
1.0 0.2
0.3 0.3
0.5
0.1 0.1 0.1
w ______.
19.298
19.166 19.206
19.119
8.006 0.1 0.3a2 0.2 1982.753 2.754 85.139 5.132 87.532 1.516 89.931 9.926 92.338 94.152 4.751 91.176 1.181
w ROOlCALclla0SI RCCICALCIIOBS~ W .__~________________________~_~_~~~~~~_~_
___________________________~~~~~~~__~_~
DEVIATION
69.182
22
STANDARD
1874.151 71.913
20 21
17 18 19
15 lb
1896.021 93.809 91.601
10 11 12 13 14
89.413 87.225 85.043 82.865 80.689 ,*.513 16.336
1.260 4.985 2.725 1900.478 1898.244
1914.116 11.855 9.550
5 6 7 8 9
3 4
*
_1___'!"!4"'_4____99f____l_____OIf_____"____~~~_
________________________________-________________________-__-_____________-___-__________________
84NO000~22~~
0.004
1914.147 74.337 74.549 74.786
13.978
loc+cDl/2 1973.351 13.414 73.492 13.587 73.699 73.830
1973.289
1973.412 13.434 73.464 73.510
1973.287 73.304 13.323 13.342 13.360 13.318 13.395
________________~___~~~~~~__~~~~~~QCOlCALC)iOBSl OOClCALCllOBSl W .-_________________________-_________
0.3
0.1 -0.000 1.0 -0.005
0.2 -0.002
0.2 -0.004
162
PLfVA
TABLE
III
(continued)
RbND 000~311~-00010
ie 19
________________________~~~~~~~_~______________________________________________ 085 Y J PIJlCALC n-c RlJlCALC ORS u 0-C Q,JICp.LC _____________-______~~~~-----------~~~~~~~~______~~-~~~~~________________~~~_____________________ 46.553 1953.656 1948.912 56.044 0.1 -o.o,, 56.055 48.923 58.470 0.1 -0.002 48.94, 58.672
nss
Y
48.928
0.1
O-C
0.005
SPECTRUM
TABLE RPND 000l3i~,;-00000
OF ACETYLENE
III (continued)
163
164
PLfVA
ACKNOWLEDGMENTS The author is greatly indebted to Professor K. Narahari Rao and to Drs. M. E. Mickelson, K. F. Palmer, and S. Ghersetti for communicating their results prior to publication. Thanks are also due to Mr. R. Pulfrey for assistance in the measurements. RECEIVED:
January
15, 1972. REFERENCES
1. S. GHERSETTI AND K. NARAHARIRAO, J. Mol. Spectrosc. 28, 27 and 373 (1968). 8. K. F. PALMER,S. GHERSETTI,ANDK. NARAHARIRAO, J. Mol. Spectrosc. 30, 146 (1969). 3. S. GHERSETTI, J. PLfv.4, ANDK. NAR~HARIRAO, J. Mol. Speclrosc. 38,X3 (1971). 4. K. F. PALMER,M. E. MICKELSON, ANDK. NARAHARIRAO, J. Mol. Spectrosc., in print. 6. S. GHERSETTI ANDK. NARAHARIRAO, private communication. 6. J. PLfVA,J. Mol. Spectrosc. 44, 165 (1972). 7. T. K. MCCUBBIN, R. P. GROSSO, ANDJ. 1). MANGUS, Appl. Optics 1,431 (1962). 8. K. NARAHARIRAO, C. J. HUMPHREYS, ANDD. H. RANK,“Wavelength Standards in the Infrared,” Academic Press, New York 1966. 9. J. PLfva, S. GHERSETTI,M. E. MICKELSON, AND K. NAR.4HaRI RAO, Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1970. 10. T. A. WIGGINS,E. K. PLYLF,R,ANDE. D. TIDWELL,J. Opt. Sot. Amer. 61,1219 (1961). 11. J. F. SCOTTAND K. NARAHaRIRAO,J. Mol. Spectrosc. 18,16 (1966). 18. G. HERZBERG, “Infrared and Raman Spectra of Polyatomic Molecules,” VanNostrand, New York, 1946.