- Email: [email protected]
Molecular constants of HCl35
JOURNAL
OF MOLECULAR
SPECTROSCOPY
Molecular
17,
122-130 (19%)
Constants
of HCi3”t
D. H. RANK, B. S. RAO, AND T. A. WIGGINS Department
of Physics,
The Pennsylvania State University, Park, Pennsylvania
University
Additional measurements have been made on the 1-O and 20 bands of HCl”. The spectra were observed using an absorption tube heated to 900” C. Rotational states involving J” values as high as 31 were observed. In addition, lines of the 3-1,4-2, and 5-3 bands have been observed and precisely measured. The newly observed data have been combined with our previously reported measurements on HClas and analyzed. Reliable values have been obtained for the higher order rotational constants, H and L. The Dunham potential constants a, , a2 , aa , and a4 for HClas have been calculated. INTRODUCTION
Since the publication of our previous papers on the HC135 molecule (1, S) we have been able to extend the former measurements to much higher J values by using a heated absorption tube. Twenty-four additional high J lines (J = 15 to J = 30) of the 1-O band have been measured. Eighteen additional lines (J = 18 to J = 26) of the 2-O band have been measured. We were also able to measure twenty-three lines of the 3-l band, twelve lines of t’he 4-2 band, and 3 lines of the 5-3 band. The new data all obtained with t.he echelle spectrograph are very precise. In this paper we will re-examine the analysis of the HC135 moIecular spectrum taking proper cognizance of our extensive new measurements to supplement the previous work. EXPERIMENTAL
DETAILS
Two absorption t,ubes of 1% and 3-meter length were constructed, and could be heated to 900” C and 300” C, respectively. The new measurements were made in the 1.8-p to 5-p region of the spectrum employing our 5-meter echelle spectrograph. The gas pressures used were usually in the region of 1 mm or less to 2 cm of Hg. In a few cases higher gas pressures were used and the small pressure shifts were corrected by an independent determination. t This research was supported by the National Science Foundation. 122
123
MOLECULAR CONSTANTS OF HCl ANALYSIS
GROUND STATE The measurements of the 1-O and 2-O bands of HC13’ yielded forty-seven AzFN values. The new measurements which include very high J value As” ‘s require inclusion of a term in (J + fh)” in order to satisfactorily fit the dat)a. The pertinent expression for A*F”(J) = R(J - 1) - P(J + 1) is AzF’( J)
= [4Bn + 6D” + ( 27/4)HN + (80”
+ (12H” + lOO_f)(J
+ (27/4)L”](
J + +i)
+ 34H” + 75L”)( J + $$)” + x)‘+
16L”(J
+ W)’
+ 20MN(J
(1) + x)“.
TABLE I CALCULATED AND OBSERVED VALUES OF AtF”(J) IN VACIWM WAVE NUMBERS (cm-l) OBTAINED FROM THE 14 AND 2-O BANDS OF HC136 Calc - Obs x 103
J + 4h 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5
62.6222 104.3281 145.9707 187.5246 228.9651 270.2666 311.4045 352.3540 393.0904 433.5895 473.8270 513.7791 553.4221 592.7326 631.6875 670.2641 708.4400 746.1927 783.5015 820.3441 856.6997 892.5477 927.8680 962.6406
25.5 26.5 27.5 28.5 29.5
996.8461 1030.4655 1063.4800 1095.8714 1127.6215
.8735 .6386
f1.3 +1.7 +0.1 -2.7 +1.7 -4.0 +3.1 -4.4 -0.8 -4.5 +2.9 $3.4 -0.9 +3.8 +5.2 $0.6 -8.2 -5.1 -4.8 -4.8 -5.8 $0.6 -4.5 f2.0
.8420
+4.1
.6209
.3264 .9706
.5273 .9634
.2706 .4014 .3584 .0912 .5940
.8241 .7757 .4230 .7288 .6823 .2635 .4482 .1978
.5073 .3489 .7050 .5471
Calc - Obs x 103
.6287 .3237 .9753
.5263 .9650
.2664 .4046 .3542 .0905
.5907 .8282 .7836 .4217 .7302 .6802 .2625 .4460
.8523 .4628 .4706 .8698
.6275
-6.5 +4.4 -4.6 -1.7 +0.1 +0.2 -0.1 -0.2 -0.1 -1.2 -1.2 -4.5 +0.4 +2.4 +7.3 +1.6 -6.0
-6.2 +2.7 f9.4 +1.6 -6.0
124
R,4NK,
RAO,
AND
WIGGINS
The above expression involves 5 degrees of freedom in the least squares fitting process. It’ is well known that the molecular constants are interrelated. The least squares method does not take cognizance of these interrelationships since accurate explicit relationships are not known. It is advisable, however, to reduce the number of degrees of freedom of the above expression if possible to obtain the most realistic molecular constants. We have decided to adopt the following fitting procedure. The measurements TABLE
II
CALCULATED AND OBSERVED FREQUENCIES IN VXUUM OF THE 14 BAND OF HC1s6
R(J)
J 0 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
Calc - Obs x 103
(Calc)
(Ohs)
2906.2479 2925.8977 2944.9146 2963.2866 2981.0015 2998.0476 3014.4134 3030.0876 3045.0592 3059.3171 3072.8509 3085.6502 3097.7048 3109.0050 3119.5413 3129.3042 3138.2848 3146.4743 3153.8642 3160.4462 3166.2125 3171.1552 3175.2670 3178.5405 3180.9690 3182.5455 3183.2635 3183.1167 3182.0990 3180.2044 3177.4271 3173.7614
.2521 .8950 .9154 .2865 .0013 .0438 .4114 .0862 .0569 .3179 .8490 .6539 .7034 .0026 .5362 .3031 .2869 .4700 .8637 .4418 .2135 .1514 .2644 .5395 .9669 .5403 .2574 .1090 .0857
f3.8 +2.6 +1.0 +2.1 +5.2 +6.1 +7.7 +13.3
.4142 .7417
+12.9 +19.7
a Computed
from A#“(J)
-4.2 $2.7 -0.8 +0.1 +0.2 $3.8 $2.0 +1.4 +2.3 -0.8 +1.9 -3.7 +1.4 +2.4 +5.1 $1.1 -2.1 $4.3 +0.5 $4.4 -1.0
and corresponding
WAVE NUMBERS (cm-l)
P(J) (Calc)
(Ohs)
2865.0991 2843.6254 2821.5691 2798.9433 2775.7609 2752.0353 2727.7797 2703.0074 2677.7320 2651.9668 2625.7255 2599.0216 2571.8686 2544.2801 2516.2696 2487.8507 2459.0367 2429.8412 2400.2774 2370.3585 2340.0976 2309.5078 2278.6019 2247.3926 2215.8926 2184.1142 2152.0696 2119.7709 2087.2299 2054.4583 2021.4673
.0967 .6234 .5713 .9401 .7602 .0363 .7774 ,006s .7320 .9664 .7272 .0208 .8703 .2817 .2724 .8560 .0406 .8409 .2773” .3622a .09778 . 513ga .6037a .3964” . 898ga .1146 .0775 .7868 .2392 .4582
R line.
Calc - Obs x 103
+2.4 +2.0 -2.2 +3.2 +0.7 -1.0 +2.3 $0.6 0.0 +0.4 -1.7 +0.8 -1.7 -1.6 -2.8 -5.3 -3.9 +0.3 +0.1 -3.7 -0.1 -6.0 -1.8 -3.8 -6.3 -0.4 -7.9 +14.1 -9.3 -0.1
MOLECULAR
CONSTANTS
125
OF HCl
reported in 1962 by Rank, Eastman, Rao, and Wiggins (2) which involve lines to J = 16 are somewhat more precise than the newer measurements. We believe that the B” value reported previously (2) is the best that can be obtained from all the data. This BN value was considered to be good to one part in a million and subsequent microwave measurements of Jones and Gordy (3) yield a velocity of light determination in accord with our estimate of the previously quoted error in B”. Thus we have decided to adopt the previous B” determination and thus reduce the number of degrees of freedom in Eq. (1) to four. From preliminary fitting it was noted that the ratios of B”/DN, D”/H”, and H”/L” are approximately equal. To a crude first approximation the theory predicts such a relationship. As the result of the preliminary fitting we have adopted a value of 4.0 X lo-” cm-’ as an approximat’ion for M” and thus have reduced the number of TABLE
III
CALCULATED AND OBSERVED FREQUENCIES IN VMXXM OF THE 2-O BAND OF HC135
(NJ)
1
0 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
Calc -
(Calc)
(OW
5687.6514 5706.0951 5723.3033 5739.2643 5753.9665 5767.3989 5779.5510 5790.4121 5799.9725 5808.2225 5815.1527 5820.7544 5825.0189 5827.9382 5829.5044 5829.7102 5828.5483 5826.0122 5822.0954 5816.7919 5810.0958 5802.0018 5792.5048 5781.5997 5769.2821 5755.5475
.6498 .0932
.3024 .2654 .9673 .3980 .5498 .4147 .9688
.2205 .1481 .7520 .0180 .9320 .5006 .7079
.5458 .OlOl .0984 .7934 .0932 .9966
.5056 .5949
.2725 .5494
x
Obs 103
+1.6 +1.9 +0.9 -1.1 -0.8 $0.9 f1.2 -2.6 +3.7 +2.0 +4.6 +2.4 $0.9 +6.2 +3.8 +2.3 +2.5 $2.1 -3.0 -1.5 +2.6 +5.2 -0.8 f4.8 +9.6 -1.9
WAVE XUMBERS
P(J) (Calc)
(Ohs)
5647.1057 5625.0289 5601.7665 5577.3319 5551.7386 5525.0003 5497.1310 5468.1450
.1075 .0289 .7668 .3318
5438.0565 5406.8801 5374.6309 5341.3234 5306.9728 5271.5942 5235.2028 5197.8139 5159.4427 5120.1048 5079.8153 5038.5897 4996.4433 4953.3911 4909.4485 4864.6304 4818.9518 4772.4273
.7381 .0039
.1274 .1484 .0563 .8776 .6265 .3240 .9763 .5950
.2032 .8183
.4444 .1076 .8123 .5911
.4445 .3882 .4495
.6321 .9563
.4305
(cm-l)
Calc - Obs x 103
-1.8 0.0 -0.3 +0.1 +0.5 -3.6 +3.6 -3.4 $0.2 +2.5 +4.4 -0.6 -3.5 -0.8 -0.4 -4.4 -1.7 -2.8 t3.0 -1.4 -1.2 +2.9 -1.0 -1.7 -4.5 -3.2
RANK,
126
RAO, AND
WIGGINS
degrees of freedom in Eq. (1) to three. All the AzF” data were now treated to least squares and the values obtained for the ground-state constants are given in Table VIII. The results of fitting all the measured A,F” values for the 1-O and 2-O bands are given in Table I. UPPER-STATECONSTANTS u =
1 AND II = 2
In order to determine the upper-state constants once the ground-state constants are known the following combination relationship is applicable, namely, Vf( J) = R(J - 1) + P(J), V+(J)
= 2v,, + 2[(B’ - B”) + (D’ - D”)]J” + 2[(0’ - 0”)
+ 3(H’ - W”) + (L’ - L”)]J4
(2)
+ 2([H’ - H”) + 6(L’ - L”)]J6 + 2(L’ - L”)J*. It was found that the term in J” was of no significance. Thus we have LO = L1 = Lz and likewise M. = M1 = M2 . The data were treated to least squares using Eq. (2) and the results obtained for the upper-state constants v = 1 and v = 2 are given in Table VIII. Making use of the upper- and lower-state constants the 1-O and 2-O band lines were computed. The observed line positions and the calculated line positions for the 14 band are given in Table II. Similarly the observed and calculated line positions for the 2-4 band are given in Table III. UPPER-STATECONSTANTS v = 3, v = 4, AND v = 5
The new measurements obtained on the 3-l band lines are considerably more precise than our previous measurements (2) on the 3-O band. Thus it is possible TABLE
IV
CALCULATEDAND OBSERVEDFREQUENCIESIN VACUUM WAVE NUMBERS (cm-l) OF THE 3-O BAND OF HC1a6
J 0 1 2 3 4 5 6 7 8 9 10 11
NJ) (Calc)
(Ohs)
8365.8492 8383.0939 8398.5037 8412.0674 8423.7735 8433.6130 8441.5744 8447.6488 8451.8271 8454.1007 8454.4654 8452.9017
.8442 .0841 .4987 .0712 .7853 .6247 .5718 .6582 .8322 .0995 .4634 .8970
Calc - Obs x 103 +5.0 +9.8 $5.0 -3.8 -11.8 -11.7 $2.6 -9.4 -5.1 +1.2 +2.0 +4.7
R(S)
Calc - Obs x 103
(Calc)
(Ohs)
8325.9032 8303.2267 8278.7653 8252.5323 8224.5418 8194.8078 8163.3451 8130.1685 8195.2932 8158.7348 8120.5091
.9078
-4.6
.7663 .5349 .5436 .8068 .3479 .1714
-1.0 -2.6 -1.8 +1.0 -2.8 -2.9
MOLECULAR
CONSTANTS TABLE
127
OF HCl
V
CALCULATED AND OBSERVED FREQUENCIES IN VACUUM WAVE NUMBERS (cm-11 OF THE 3-l B.*ND OF HC136
R(J)
J
(Calc)
0 1 2 3 4 5 6 7 8 9 10 11 12
(Ohs) 8672
5479.8718 5497.7244 5514.3502 5529.7373 5543.8743 5556.7502 5568.3542 5578.6758 5587.7050 5595.4317 5601.8465 5606.9402 5610.7041 5613.1295 5614.2082 5613.9324 5612.2944
13 14 15 16
Calc - Obs x 103
.7490
+4.6 -0.3 -1.0 +0.6 -1.0 t1.2
6653
+10.5
.7247 .3512 .7367 .8753
.a334 .9381 .6979 .1303 .2054 .9377 .2949
-
+2.1 $6.2 -0.8 t2.8 -5.3 -0.5
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
__
R(J) (Calc) 5273.3255 5290.5861 5306.6253 5321.4314 5334.9934 5347.2997 5358.3395 5368.1023 5376.5778 5383.7558 5389.6266 5394.1808 5397.4090 5399.3025 5399.8525 5399.0508
(Ohs)
Calc - Obs x 103
.9895
+3.9
.3331 .0994
+6.4 +2.9
0205
+6.1
.3044 .8527
-1.9 -0.2 -0.9
.0517
Calc - Obs x 103
.0704
f2.8
.6373
.3723
-4.6 -3.3 +1.0 -0.2
.6202
14.0
.2539
+3.1
.8676
+0.7 -1.3
.6823 .5866
.1749
VI
CALCULATED AND OBSERVED FREQUENCIES IN Vacrr~~ OF THE 4-2 BAND OF HCls
J
(Ohs)
5440.5337 5419.0732 5396.4351 5372.6327 5347 6793 5321.5876 5294.3721 5266.0463 5236 6242 5206.1199 5174.5476 5141.9218 5108.2570 5073.5676 5037.8683 5001.1736
1.7
TABLE
P(s) (Calc)
WI\VE NUMBERS (cm-l)
P(J) (Calc)
5235.1882 5214.3361 5192.3116 5169 1276 5144.7970 5119.3331 5092.7491 5065.0585 5036.2748 5006.4118 4975.4833 4943.5031 4910.4852 4876.4436 4841.3922
(Ohs)
Calc - Obs x 103
.3087 .1350
$2.9 -7.4
.7543 .0610
-5.2 -2.5
.4163
-4.5
128
RANK,
RAO,
AND
TABLE
WIGGINS
VII
CALCULATED AND OBSERVED FREQUENCIES IN VACUUM WAVE NUMBERS (cm-l) OF THE 5-3 BAND OF HCIS
R(J)
J
(Calc)
Calc -
Obs
(Ohs)
5067.376 5084.042 5099.489 5113.706 5126.681 5138.403 5148.861 5158.044
TABLE
P(J)
Calc -
(Calc)
(Ohs)
5030.436 5010.185 4988.765 4966.187 4942.465 4917.610 4891.637
.466 ,609 .637
Obs
-0.001 +0.001 0.000
VIII
OBSERVED AND CALCULATED MOLECULAR ROTATIONAL CONSTANTS (EXPRESSED IN cm-l) Observed Bo =
Calculated a a a
10.440254
D,, = -5.28281 X 1OP H, = 1.7078 X 10-s La = -9.33 X lo-‘3 A!fo = B, = 10.136228 D1 = -5.21572 X lo+ H, = 1.6444 X lo-* BS =
Dz Hz Ba D, Ha
4.0b X 10-17 a a a a a a
9.834665
= -5.15662 X 10-4 = 1.580s X lo-* = 9.534845 = -5.10563 x 1OP =
B4 =
Dq = H4 = B5 =
-5.105; x x 1.51s 9.23605
9.236010 (4-2 band) 9.2363 (44 band)
10-4 lo-*
-5.06243 X lo-’ X 10-a 1.454 8.93755
8.9374, (5-3 band) 8.9395 (5-O band)
Ds = H6 = a Used in fitting data. b Calculated by extrapolating
-5.02734 1.391
ratios
of ground-st.ate
constants.
X lo+ X 10-E
MOLECULAR
CONSTANTS
OF HCl
t,o obtain better constant’s for the v = 3 state than previously. It can be seen from the previous analysis of the states v = 0, v = 1, and v = 2 that (Ho - H,) = 2(Ho - HI). We will assume for the analysis of the 34 and 3-l bands that (Ho - H3) = 3(H0 - HI) and (271 - Hz) = 2(Ho - HI). In addit’ion it was TABLE
IS
OBSERVED .WD CALCULATED BAND ORIGINS (EXPHESSED IN cm-l) Observed 1-O 2-o 3-o 4-o M) 3-1
2885.9775 5667.9841 8346.7816 10 922.803” 13 396.217h 5460.8041
4-2 5-3
5254.8555 5049.503
a Used in fitting data. b From photographic measurements
Calculated
_.~__.___
a a a 10 922.8396 13 396.336 5460.8040 504k5.54
in Reference TABLE
1.
9
EQUILIBRIUM MOLECULAR CONSTANTS FOR HCls IN cm-l
.ZND DUNH.~M COEFFICIENTS
Calculated
we -
YlO
= 2990.9463
a
N Y?o = -52.81856 0.2243, weye - Y30 = -0.0121s w,z, - Y40 = 10.593416 B. - Yo, = = -0.307181 ac - Y,, 0.0017724 = Ye - YZI ae N Y3, = -0.0001201
a
WJ.
D,Yoz be h Y,? rc N Y,,
= = =
H,Y03 qeNY718 L, ,v Y(14 M.N Yes a, ap a3 a4
= = = = = = = =
a a
a a
-5.31936 x 10-4 0.07510 X 10-a -0.00400 x 10-4 1.748 x 10-a -0.0634 X lo-* -9.93 X IO-13 4.0 X lo-‘7 -2.364519 3.66470 -4.6783 4.944
* Used in fitting
to Dunham
formulas.
-5.315:
X 10-b
0.07230 X 1OW -0.0031* x 10-d 1.695 X lo-* 0.0343 x 10-8 -8.4~ X lo-l3
Dunham
B, = 10.593553
Dunham
wb =’ 2991.0994
RANK,
130
RAO,
AND
WIGGINS
assumed that AL and AM are both equal to zero. fi!Iaking use of the abovementioned assumptions and our previous determinations of the molecular constants for the states v = 0 and v = 1 we have employed least squares methods to obtain the constants for the v = 3 state given in Table VIII. The observed and calculated line positions for the 3-O band and 3-l band are given in Tables IV and V, respectively. hlaking use of procedures similar to those used in determining the molecular const8ants for the v = 3 state we have determined the constant’s for the v = 4 and v = 5 states from the new measurements on the 4-2 and 5-3 bands. The constants obtained for the v = 4 and v = 5 states are given in Table VIII. The observed and calculat,ed line positions for the 4-2 and 5-3 bands are given in Tables VI and VII, respectively. In Table IX we have given the observed band origins of all the HC13’ bands that have been measured. In the column of Table IX designated as calculated we have given the calculated band origins. The bands marked (a) were used to determine w, , w,x, , w,y,, and 0,x,. The agreement between observed and calculated values of the band origins is excellent particularly when one takes into account that t,he 4-O and 5-O bands were obtained photographically and only three lines of t,he 5-3 band were observable. SUMMARY OF RESULTS We have taken the data from Tables VIII and IX and derived the equilibrium values of the various molecular constants. These equilibrium values are given in Table X. niaking use of the equilibrium values of the molecular constants we have made use of Dunham’s (4) theory and calculated the values of the potential constants al, a2 , a3 , and a4 , which are given in Table X. RECEIVED: April 7, 1965 REFERENCES 1. I). H. RANK, W. B. BIRTLEY, D. P. EASTMAN, B. S. Rao, AND T. A. WIGGINS, J. Opt. Sot. Am. 60, 8. D. H. R~NIC, D. 3. GORDON JONES 4. J. L. DUNHAM,
1275 (1960). P. EASTMAN,
B. S. R.40, ANDT. A. WIGGINS, J. Opt. Sot. Am. 62,l Phys.Rev. 136,295 (1964). Phys. Rev. 41, 721 (1932).
AND WALTER
GOHDY,
(1962).
OF MOLECULAR
SPECTROSCOPY
Molecular
17,
122-130 (19%)
Constants
of HCi3”t
D. H. RANK, B. S. RAO, AND T. A. WIGGINS Department
of Physics,
The Pennsylvania State University, Park, Pennsylvania
University
Additional measurements have been made on the 1-O and 20 bands of HCl”. The spectra were observed using an absorption tube heated to 900” C. Rotational states involving J” values as high as 31 were observed. In addition, lines of the 3-1,4-2, and 5-3 bands have been observed and precisely measured. The newly observed data have been combined with our previously reported measurements on HClas and analyzed. Reliable values have been obtained for the higher order rotational constants, H and L. The Dunham potential constants a, , a2 , aa , and a4 for HClas have been calculated. INTRODUCTION
Since the publication of our previous papers on the HC135 molecule (1, S) we have been able to extend the former measurements to much higher J values by using a heated absorption tube. Twenty-four additional high J lines (J = 15 to J = 30) of the 1-O band have been measured. Eighteen additional lines (J = 18 to J = 26) of the 2-O band have been measured. We were also able to measure twenty-three lines of the 3-l band, twelve lines of t’he 4-2 band, and 3 lines of the 5-3 band. The new data all obtained with t.he echelle spectrograph are very precise. In this paper we will re-examine the analysis of the HC135 moIecular spectrum taking proper cognizance of our extensive new measurements to supplement the previous work. EXPERIMENTAL
DETAILS
Two absorption t,ubes of 1% and 3-meter length were constructed, and could be heated to 900” C and 300” C, respectively. The new measurements were made in the 1.8-p to 5-p region of the spectrum employing our 5-meter echelle spectrograph. The gas pressures used were usually in the region of 1 mm or less to 2 cm of Hg. In a few cases higher gas pressures were used and the small pressure shifts were corrected by an independent determination. t This research was supported by the National Science Foundation. 122
123
MOLECULAR CONSTANTS OF HCl ANALYSIS
GROUND STATE The measurements of the 1-O and 2-O bands of HC13’ yielded forty-seven AzFN values. The new measurements which include very high J value As” ‘s require inclusion of a term in (J + fh)” in order to satisfactorily fit the dat)a. The pertinent expression for A*F”(J) = R(J - 1) - P(J + 1) is AzF’( J)
= [4Bn + 6D” + ( 27/4)HN + (80”
+ (12H” + lOO_f)(J
+ (27/4)L”](
J + +i)
+ 34H” + 75L”)( J + $$)” + x)‘+
16L”(J
+ W)’
+ 20MN(J
(1) + x)“.
TABLE I CALCULATED AND OBSERVED VALUES OF AtF”(J) IN VACIWM WAVE NUMBERS (cm-l) OBTAINED FROM THE 14 AND 2-O BANDS OF HC136 Calc - Obs x 103
J + 4h 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5
62.6222 104.3281 145.9707 187.5246 228.9651 270.2666 311.4045 352.3540 393.0904 433.5895 473.8270 513.7791 553.4221 592.7326 631.6875 670.2641 708.4400 746.1927 783.5015 820.3441 856.6997 892.5477 927.8680 962.6406
25.5 26.5 27.5 28.5 29.5
996.8461 1030.4655 1063.4800 1095.8714 1127.6215
.8735 .6386
f1.3 +1.7 +0.1 -2.7 +1.7 -4.0 +3.1 -4.4 -0.8 -4.5 +2.9 $3.4 -0.9 +3.8 +5.2 $0.6 -8.2 -5.1 -4.8 -4.8 -5.8 $0.6 -4.5 f2.0
.8420
+4.1
.6209
.3264 .9706
.5273 .9634
.2706 .4014 .3584 .0912 .5940
.8241 .7757 .4230 .7288 .6823 .2635 .4482 .1978
.5073 .3489 .7050 .5471
Calc - Obs x 103
.6287 .3237 .9753
.5263 .9650
.2664 .4046 .3542 .0905
.5907 .8282 .7836 .4217 .7302 .6802 .2625 .4460
.8523 .4628 .4706 .8698
.6275
-6.5 +4.4 -4.6 -1.7 +0.1 +0.2 -0.1 -0.2 -0.1 -1.2 -1.2 -4.5 +0.4 +2.4 +7.3 +1.6 -6.0
-6.2 +2.7 f9.4 +1.6 -6.0
124
R,4NK,
RAO,
AND
WIGGINS
The above expression involves 5 degrees of freedom in the least squares fitting process. It’ is well known that the molecular constants are interrelated. The least squares method does not take cognizance of these interrelationships since accurate explicit relationships are not known. It is advisable, however, to reduce the number of degrees of freedom of the above expression if possible to obtain the most realistic molecular constants. We have decided to adopt the following fitting procedure. The measurements TABLE
II
CALCULATED AND OBSERVED FREQUENCIES IN VXUUM OF THE 14 BAND OF HC1s6
R(J)
J 0 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
Calc - Obs x 103
(Calc)
(Ohs)
2906.2479 2925.8977 2944.9146 2963.2866 2981.0015 2998.0476 3014.4134 3030.0876 3045.0592 3059.3171 3072.8509 3085.6502 3097.7048 3109.0050 3119.5413 3129.3042 3138.2848 3146.4743 3153.8642 3160.4462 3166.2125 3171.1552 3175.2670 3178.5405 3180.9690 3182.5455 3183.2635 3183.1167 3182.0990 3180.2044 3177.4271 3173.7614
.2521 .8950 .9154 .2865 .0013 .0438 .4114 .0862 .0569 .3179 .8490 .6539 .7034 .0026 .5362 .3031 .2869 .4700 .8637 .4418 .2135 .1514 .2644 .5395 .9669 .5403 .2574 .1090 .0857
f3.8 +2.6 +1.0 +2.1 +5.2 +6.1 +7.7 +13.3
.4142 .7417
+12.9 +19.7
a Computed
from A#“(J)
-4.2 $2.7 -0.8 +0.1 +0.2 $3.8 $2.0 +1.4 +2.3 -0.8 +1.9 -3.7 +1.4 +2.4 +5.1 $1.1 -2.1 $4.3 +0.5 $4.4 -1.0
and corresponding
WAVE NUMBERS (cm-l)
P(J) (Calc)
(Ohs)
2865.0991 2843.6254 2821.5691 2798.9433 2775.7609 2752.0353 2727.7797 2703.0074 2677.7320 2651.9668 2625.7255 2599.0216 2571.8686 2544.2801 2516.2696 2487.8507 2459.0367 2429.8412 2400.2774 2370.3585 2340.0976 2309.5078 2278.6019 2247.3926 2215.8926 2184.1142 2152.0696 2119.7709 2087.2299 2054.4583 2021.4673
.0967 .6234 .5713 .9401 .7602 .0363 .7774 ,006s .7320 .9664 .7272 .0208 .8703 .2817 .2724 .8560 .0406 .8409 .2773” .3622a .09778 . 513ga .6037a .3964” . 898ga .1146 .0775 .7868 .2392 .4582
R line.
Calc - Obs x 103
+2.4 +2.0 -2.2 +3.2 +0.7 -1.0 +2.3 $0.6 0.0 +0.4 -1.7 +0.8 -1.7 -1.6 -2.8 -5.3 -3.9 +0.3 +0.1 -3.7 -0.1 -6.0 -1.8 -3.8 -6.3 -0.4 -7.9 +14.1 -9.3 -0.1
MOLECULAR
CONSTANTS
125
OF HCl
reported in 1962 by Rank, Eastman, Rao, and Wiggins (2) which involve lines to J = 16 are somewhat more precise than the newer measurements. We believe that the B” value reported previously (2) is the best that can be obtained from all the data. This BN value was considered to be good to one part in a million and subsequent microwave measurements of Jones and Gordy (3) yield a velocity of light determination in accord with our estimate of the previously quoted error in B”. Thus we have decided to adopt the previous B” determination and thus reduce the number of degrees of freedom in Eq. (1) to four. From preliminary fitting it was noted that the ratios of B”/DN, D”/H”, and H”/L” are approximately equal. To a crude first approximation the theory predicts such a relationship. As the result of the preliminary fitting we have adopted a value of 4.0 X lo-” cm-’ as an approximat’ion for M” and thus have reduced the number of TABLE
III
CALCULATED AND OBSERVED FREQUENCIES IN VMXXM OF THE 2-O BAND OF HC135
(NJ)
1
0 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
Calc -
(Calc)
(OW
5687.6514 5706.0951 5723.3033 5739.2643 5753.9665 5767.3989 5779.5510 5790.4121 5799.9725 5808.2225 5815.1527 5820.7544 5825.0189 5827.9382 5829.5044 5829.7102 5828.5483 5826.0122 5822.0954 5816.7919 5810.0958 5802.0018 5792.5048 5781.5997 5769.2821 5755.5475
.6498 .0932
.3024 .2654 .9673 .3980 .5498 .4147 .9688
.2205 .1481 .7520 .0180 .9320 .5006 .7079
.5458 .OlOl .0984 .7934 .0932 .9966
.5056 .5949
.2725 .5494
x
Obs 103
+1.6 +1.9 +0.9 -1.1 -0.8 $0.9 f1.2 -2.6 +3.7 +2.0 +4.6 +2.4 $0.9 +6.2 +3.8 +2.3 +2.5 $2.1 -3.0 -1.5 +2.6 +5.2 -0.8 f4.8 +9.6 -1.9
WAVE XUMBERS
P(J) (Calc)
(Ohs)
5647.1057 5625.0289 5601.7665 5577.3319 5551.7386 5525.0003 5497.1310 5468.1450
.1075 .0289 .7668 .3318
5438.0565 5406.8801 5374.6309 5341.3234 5306.9728 5271.5942 5235.2028 5197.8139 5159.4427 5120.1048 5079.8153 5038.5897 4996.4433 4953.3911 4909.4485 4864.6304 4818.9518 4772.4273
.7381 .0039
.1274 .1484 .0563 .8776 .6265 .3240 .9763 .5950
.2032 .8183
.4444 .1076 .8123 .5911
.4445 .3882 .4495
.6321 .9563
.4305
(cm-l)
Calc - Obs x 103
-1.8 0.0 -0.3 +0.1 +0.5 -3.6 +3.6 -3.4 $0.2 +2.5 +4.4 -0.6 -3.5 -0.8 -0.4 -4.4 -1.7 -2.8 t3.0 -1.4 -1.2 +2.9 -1.0 -1.7 -4.5 -3.2
RANK,
126
RAO, AND
WIGGINS
degrees of freedom in Eq. (1) to three. All the AzF” data were now treated to least squares and the values obtained for the ground-state constants are given in Table VIII. The results of fitting all the measured A,F” values for the 1-O and 2-O bands are given in Table I. UPPER-STATECONSTANTS u =
1 AND II = 2
In order to determine the upper-state constants once the ground-state constants are known the following combination relationship is applicable, namely, Vf( J) = R(J - 1) + P(J), V+(J)
= 2v,, + 2[(B’ - B”) + (D’ - D”)]J” + 2[(0’ - 0”)
+ 3(H’ - W”) + (L’ - L”)]J4
(2)
+ 2([H’ - H”) + 6(L’ - L”)]J6 + 2(L’ - L”)J*. It was found that the term in J” was of no significance. Thus we have LO = L1 = Lz and likewise M. = M1 = M2 . The data were treated to least squares using Eq. (2) and the results obtained for the upper-state constants v = 1 and v = 2 are given in Table VIII. Making use of the upper- and lower-state constants the 1-O and 2-O band lines were computed. The observed line positions and the calculated line positions for the 14 band are given in Table II. Similarly the observed and calculated line positions for the 2-4 band are given in Table III. UPPER-STATECONSTANTS v = 3, v = 4, AND v = 5
The new measurements obtained on the 3-l band lines are considerably more precise than our previous measurements (2) on the 3-O band. Thus it is possible TABLE
IV
CALCULATEDAND OBSERVEDFREQUENCIESIN VACUUM WAVE NUMBERS (cm-l) OF THE 3-O BAND OF HC1a6
J 0 1 2 3 4 5 6 7 8 9 10 11
NJ) (Calc)
(Ohs)
8365.8492 8383.0939 8398.5037 8412.0674 8423.7735 8433.6130 8441.5744 8447.6488 8451.8271 8454.1007 8454.4654 8452.9017
.8442 .0841 .4987 .0712 .7853 .6247 .5718 .6582 .8322 .0995 .4634 .8970
Calc - Obs x 103 +5.0 +9.8 $5.0 -3.8 -11.8 -11.7 $2.6 -9.4 -5.1 +1.2 +2.0 +4.7
R(S)
Calc - Obs x 103
(Calc)
(Ohs)
8325.9032 8303.2267 8278.7653 8252.5323 8224.5418 8194.8078 8163.3451 8130.1685 8195.2932 8158.7348 8120.5091
.9078
-4.6
.7663 .5349 .5436 .8068 .3479 .1714
-1.0 -2.6 -1.8 +1.0 -2.8 -2.9
MOLECULAR
CONSTANTS TABLE
127
OF HCl
V
CALCULATED AND OBSERVED FREQUENCIES IN VACUUM WAVE NUMBERS (cm-11 OF THE 3-l B.*ND OF HC136
R(J)
J
(Calc)
0 1 2 3 4 5 6 7 8 9 10 11 12
(Ohs) 8672
5479.8718 5497.7244 5514.3502 5529.7373 5543.8743 5556.7502 5568.3542 5578.6758 5587.7050 5595.4317 5601.8465 5606.9402 5610.7041 5613.1295 5614.2082 5613.9324 5612.2944
13 14 15 16
Calc - Obs x 103
.7490
+4.6 -0.3 -1.0 +0.6 -1.0 t1.2
6653
+10.5
.7247 .3512 .7367 .8753
.a334 .9381 .6979 .1303 .2054 .9377 .2949
-
+2.1 $6.2 -0.8 t2.8 -5.3 -0.5
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
__
R(J) (Calc) 5273.3255 5290.5861 5306.6253 5321.4314 5334.9934 5347.2997 5358.3395 5368.1023 5376.5778 5383.7558 5389.6266 5394.1808 5397.4090 5399.3025 5399.8525 5399.0508
(Ohs)
Calc - Obs x 103
.9895
+3.9
.3331 .0994
+6.4 +2.9
0205
+6.1
.3044 .8527
-1.9 -0.2 -0.9
.0517
Calc - Obs x 103
.0704
f2.8
.6373
.3723
-4.6 -3.3 +1.0 -0.2
.6202
14.0
.2539
+3.1
.8676
+0.7 -1.3
.6823 .5866
.1749
VI
CALCULATED AND OBSERVED FREQUENCIES IN Vacrr~~ OF THE 4-2 BAND OF HCls
J
(Ohs)
5440.5337 5419.0732 5396.4351 5372.6327 5347 6793 5321.5876 5294.3721 5266.0463 5236 6242 5206.1199 5174.5476 5141.9218 5108.2570 5073.5676 5037.8683 5001.1736
1.7
TABLE
P(s) (Calc)
WI\VE NUMBERS (cm-l)
P(J) (Calc)
5235.1882 5214.3361 5192.3116 5169 1276 5144.7970 5119.3331 5092.7491 5065.0585 5036.2748 5006.4118 4975.4833 4943.5031 4910.4852 4876.4436 4841.3922
(Ohs)
Calc - Obs x 103
.3087 .1350
$2.9 -7.4
.7543 .0610
-5.2 -2.5
.4163
-4.5
128
RANK,
RAO,
AND
TABLE
WIGGINS
VII
CALCULATED AND OBSERVED FREQUENCIES IN VACUUM WAVE NUMBERS (cm-l) OF THE 5-3 BAND OF HCIS
R(J)
J
(Calc)
Calc -
Obs
(Ohs)
5067.376 5084.042 5099.489 5113.706 5126.681 5138.403 5148.861 5158.044
TABLE
P(J)
Calc -
(Calc)
(Ohs)
5030.436 5010.185 4988.765 4966.187 4942.465 4917.610 4891.637
.466 ,609 .637
Obs
-0.001 +0.001 0.000
VIII
OBSERVED AND CALCULATED MOLECULAR ROTATIONAL CONSTANTS (EXPRESSED IN cm-l) Observed Bo =
Calculated a a a
10.440254
D,, = -5.28281 X 1OP H, = 1.7078 X 10-s La = -9.33 X lo-‘3 A!fo = B, = 10.136228 D1 = -5.21572 X lo+ H, = 1.6444 X lo-* BS =
Dz Hz Ba D, Ha
4.0b X 10-17 a a a a a a
9.834665
= -5.15662 X 10-4 = 1.580s X lo-* = 9.534845 = -5.10563 x 1OP =
B4 =
Dq = H4 = B5 =
-5.105; x x 1.51s 9.23605
9.236010 (4-2 band) 9.2363 (44 band)
10-4 lo-*
-5.06243 X lo-’ X 10-a 1.454 8.93755
8.9374, (5-3 band) 8.9395 (5-O band)
Ds = H6 = a Used in fitting data. b Calculated by extrapolating
-5.02734 1.391
ratios
of ground-st.ate
constants.
X lo+ X 10-E
MOLECULAR
CONSTANTS
OF HCl
t,o obtain better constant’s for the v = 3 state than previously. It can be seen from the previous analysis of the states v = 0, v = 1, and v = 2 that (Ho - H,) = 2(Ho - HI). We will assume for the analysis of the 34 and 3-l bands that (Ho - H3) = 3(H0 - HI) and (271 - Hz) = 2(Ho - HI). In addit’ion it was TABLE
IS
OBSERVED .WD CALCULATED BAND ORIGINS (EXPHESSED IN cm-l) Observed 1-O 2-o 3-o 4-o M) 3-1
2885.9775 5667.9841 8346.7816 10 922.803” 13 396.217h 5460.8041
4-2 5-3
5254.8555 5049.503
a Used in fitting data. b From photographic measurements
Calculated
_.~__.___
a a a 10 922.8396 13 396.336 5460.8040 504k5.54
in Reference TABLE
1.
9
EQUILIBRIUM MOLECULAR CONSTANTS FOR HCls IN cm-l
.ZND DUNH.~M COEFFICIENTS
Calculated
we -
YlO
= 2990.9463
a
N Y?o = -52.81856 0.2243, weye - Y30 = -0.0121s w,z, - Y40 = 10.593416 B. - Yo, = = -0.307181 ac - Y,, 0.0017724 = Ye - YZI ae N Y3, = -0.0001201
a
WJ.
D,Yoz be h Y,? rc N Y,,
= = =
H,Y03 qeNY718 L, ,v Y(14 M.N Yes a, ap a3 a4
= = = = = = = =
a a
a a
-5.31936 x 10-4 0.07510 X 10-a -0.00400 x 10-4 1.748 x 10-a -0.0634 X lo-* -9.93 X IO-13 4.0 X lo-‘7 -2.364519 3.66470 -4.6783 4.944
* Used in fitting
to Dunham
formulas.
-5.315:
X 10-b
0.07230 X 1OW -0.0031* x 10-d 1.695 X lo-* 0.0343 x 10-8 -8.4~ X lo-l3
Dunham
B, = 10.593553
Dunham
wb =’ 2991.0994
RANK,
130
RAO,
AND
WIGGINS
assumed that AL and AM are both equal to zero. fi!Iaking use of the abovementioned assumptions and our previous determinations of the molecular constants for the states v = 0 and v = 1 we have employed least squares methods to obtain the constants for the v = 3 state given in Table VIII. The observed and calculated line positions for the 3-O band and 3-l band are given in Tables IV and V, respectively. hlaking use of procedures similar to those used in determining the molecular const8ants for the v = 3 state we have determined the constant’s for the v = 4 and v = 5 states from the new measurements on the 4-2 and 5-3 bands. The constants obtained for the v = 4 and v = 5 states are given in Table VIII. The observed and calculat,ed line positions for the 4-2 and 5-3 bands are given in Tables VI and VII, respectively. In Table IX we have given the observed band origins of all the HC13’ bands that have been measured. In the column of Table IX designated as calculated we have given the calculated band origins. The bands marked (a) were used to determine w, , w,x, , w,y,, and 0,x,. The agreement between observed and calculated values of the band origins is excellent particularly when one takes into account that t,he 4-O and 5-O bands were obtained photographically and only three lines of t,he 5-3 band were observable. SUMMARY OF RESULTS We have taken the data from Tables VIII and IX and derived the equilibrium values of the various molecular constants. These equilibrium values are given in Table X. niaking use of the equilibrium values of the molecular constants we have made use of Dunham’s (4) theory and calculated the values of the potential constants al, a2 , a3 , and a4 , which are given in Table X. RECEIVED: April 7, 1965 REFERENCES 1. I). H. RANK, W. B. BIRTLEY, D. P. EASTMAN, B. S. Rao, AND T. A. WIGGINS, J. Opt. Sot. Am. 60, 8. D. H. R~NIC, D. 3. GORDON JONES 4. J. L. DUNHAM,
1275 (1960). P. EASTMAN,
B. S. R.40, ANDT. A. WIGGINS, J. Opt. Sot. Am. 62,l Phys.Rev. 136,295 (1964). Phys. Rev. 41, 721 (1932).
AND WALTER
GOHDY,
(1962).