Infrared diode laser spectroscopy of a high-temperature molecule GeS using spectrum processing by fourier transformation

Journal of

MOLECULAR STRUCTURE Journal of Molecular Structure 352/353 (1995) 395-405

ELSEVIER

Infrared diode laser spectroscopy of a high-temperature molecule GeS using spectrum processing by Fourier transformation Hiromichi

Uehara*,

Koui Horiai, Yasushi Ozaki, Toichi Konno

Department of Chemistry, Faculty of Science, Josai UniversiO,, Keyakidai, Sakado. Saitama 350-02, Japan

Received 10 November 1994

Abstract The vibrational-rotational spectrum of GeS has been observed using a diode laser spectrometer equipped with a heatpipe high-temperature cell of a White cell type. Fringes due to optical reflections inside the high-temperature White cell were inherent in the observation of the spectra. However, they were eliminated, as were high-frequency noises, by Fourier manipulation of the observed diode laser spectrum. About 620 spectral lines for the Av = 1 band sequences of the eight isotopomers, 74Ge32S, 72Ge32S, 7°Ge32S, 73Ge32S, 76Ge32S, 74Ge34S, 72Ge34S and 7°Ge34S have been assigned between 522 and 593 cm 1. These infrared data combined with 91 microwave data from the literature have been analyzed with a leastsquares fit to a Dunham potential function with only 11 parameters which included three Watson type A correction terms. The Dunham Yi~ coefficients have been derived for each of the eight isotopomers. The equilibrium vibrational j • frequencY ~e of 7 4 Ge 3 2 Sls574.269313(271) cm - 1 .

I. Introduction The concept of a high-temperature molecule [1] seldom appeared in the field of high-resolution spectroscopy before we reported [2] in 1989 the infrared diode laser spectrum of NaCI as an example of a high-temperature molecule. Hightemperature molecules, in fact, have themselves long been studied by microwave spectroscopy and by high-resolution infrared spectroscopy under the category of high-temperature spectroscopy. However, it is convenient to classify a group of such chemical species as the NaC1 m o n o m e r into the category of high-temperature molecules [3-5]. q~Dedicated to Professor Yonezo Morino on his 87th birthday. * Corresponding author.

The GeS molecule is a typical high-temperature molecule. Extensive microwave studies by Stieda et al. [6] and by Hoeft et al. [7] have provided rotational and vibrational-rotational D u n h a m Yij coefficients. Stieda et al. [6] have also observed the breakdown of the B o r n - O p p e n h e i m e r approximation for the rotational constant Y0~. Electronic spectra of the A I H - X I E + and E - X band systems [8] of GeS have been observed by D r u m m o n d and Barrow [9] and by Barrow [10]. The band-head analysis has yielded vibrational constants for the X, A and E electronic states. We formerly observed v i b r a t i o n - r o t a t i o n spectral lines of GeS in emission [11]. The analysis has revealed much more accurate vibrational constants for the X state than those given by electronic spectroscopy. However, the spectral resolution of the Fourier transform spectrometer which we used

0022-2860/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-2860(95)08839-3

396

H. Uehara et al./Journal of Molecular Structure 352/353 (1995) 395-405

was moderate, i.e., 0.1 cm -1. It was desirable to observe the vibration-rotation spectral lines more accurately. In the present study, we have observed the Av = 1 vibration-rotation bands of eight isotopomers of GeS with a diode laser spectrometer. Spectral lines, which were obtained using a heat-pipe high-temperature cell of a White cell type [ 12,13], were processed by Fourier transformation [12,13]. It has been found necessary to include in the analysis the effects of breakdown of the Born-Oppenheimer approximation for the vibrational constant Y10(~e) as well as for the rotational constant Y01(Be).

be introduced by the possible time variation of the starting point of the sweep set for each of the four successive scans. GeS tends to sublime at temperatures higher than 420°C. We generated gaseous GeS by charging the White cell with 25 g of GeS and heating the cell to 440°C. Buffer gas (Ar) of 10 Torr was admitted. The White cell was set to 20 traversals giving an optical path length of 20 m. The rather long path length enabled the signals to be observed with a low partial pressure of GeS at a temperature of 440°C. Spectral lines of GeS with narrow line widths owing to the low partial pressure of the sample were observed with good signal to noise ratios in the wavenumber range between 522 and 593 cm -1

2. Experimental Spectra of GeS were observed using a diode laser spectrometer equipped with a heat-pipe hightemperature cell of a White cell type. Since the apparatus is the same as described previously [13] we do not reproduce its description again. Fringes were unavoidably produced by optical reflections inside the high-temperature White cell. Since the fringes and high-frequency noises were removed simultaneously, as was described below, with processing by Fourier transformations, large time constants were no longer required for phasesensitive detection to observe the signals. We used a sweep time of 23 s for a full sweep width, typically of 0.7cm -l, with a time constant of 10ms which is the smallest one available with our spectrometer. We could choose a shorter sweep time for the scale of sweep time setting of our spectrometer but we found that the shortest sweep time was actually 23 s for the full sweep width. The sweep time was limited by the speed of the data conversion of the AD and DA converters used in the data acquisition system of our spectrometer. Wavenumber calibration of the spectrum of GeS was made with the spectrum of SO2 [14]. The procedure of the measurement consisted of four successive scans in each set, i.e., SO2, GeS, GeS plus SO2 and etalon. Therefore, the fact that the scanning speed in this experiment was much faster than usual was very useful to save a lot of time required for the measurements. Moreover, the fast sweep eliminated the uncertainty which may

3. Processing of observed diode laser spectra by Fourier transformation We transferred digitized diode laser spectra to a NEC PC-H98 model 100 personal computer, with which we processed all the spectra by Fourier transformation using MS OS/2 F O R T R A N and BASIC [12,13]. Dominant parts of the fringes were the 0.0025 cm -1 spaced ones indicating the presence of the 2 m long etalon. The fringes observed were substantially weaker than most of the signals of GeS. The fringes and the high-frequency noises were eliminated by applying the weighting function to the Fourier space array which was obtained by Fourier transformation of the observed spectrum. The observed spectrum consisted of an original data array of length 2048. We used the rectangular (in some cases, the trapezoidal) truncation functions. The truncation function b(n) was

b(n)=

1 l~
(1)

where n is the data point and k/> 2. In a typical case of the present study the period of the 0.0025 cm -1 spaced fringe was 12 points in the original data array, while the GeS spectral resolution was 14 points, which corresponded to the width of the second derivative line shape at zero-crossings. Therefore, following a criterion [31] for truncating a Fourier space array we selected the boundary k

397

H. Uehara et a l . / J o u r n a l o f M o l e c u l a r Structure 352/353 ( 1 9 9 5 ) 3 9 5 - 4 0 5

Table 1 Vibrational-rotational transition wavenumbers of the Av = 1 bands of GeS Vtta

mb

Obs (cm -1 )

Obs - Calc (10 -3 cm -l)

v "a

mb

Obs (cm -1 )

Obs - Calc (lO -3 cm -I )

V"a

522.98710 532.16130 532.65900 533.15300 536.09970 539.47480 542.78430 578.42430 578.76400 579.43700 581.74430 582.06690 582.39070 582.71070 584.90890 585.21700 585.82860 586.13130 586.43270 589.35980 589.64360 589.92490 592.12430 592.39440 592.65910 522.93080 532.42320 532.90850 536.27360 539.10500 539.57180 542.80290 578.38570 579.02850 579.34670 579.66490 581.84170 582.14590 582.45020 582.75080 585.10600 585.39230 585.96400 586.24480 586.52580 589.24480 589.50760 589.76930 592.04660 592.29160

-0.21 0.02 0.67 -1.04 -0.39 -0.82 -0.05 -0.34 0.38 0.05 -0.56 -1.44 0.44 0.07 -0.37 -0.06 0.68 0.33 0.26 0.34 0.24 -0.74 -1.45 0.94 -0.44 -0.10 0.81 -0.04 -0.I0 0.05 -0.23 -0.03 -0.29 0.11 -0.55 0.36 0.09 -0.42 0.75 -0.19 -0.06 -0.96 1.16 -0.42 -0.19 0.10 -0.03 0.37 -0.10 0.06

1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

81 82 -95 -94 -76 -75 -74 -67 -61 -60 -53 42 43 44 45 46 54 56 66 67 68 69 70 82 83 84 94 95 96 97 -88 -69 -68 -60 -53 -46 -45 53 54 55 57 66 67 68 69 79 80 82 84 97

592.53460 592.77610 522.81280 523.31400 532.12180 532.60000 533.07490 536.36240 539.12700 539.58290 542.73520 578.46920 578.77300 579.07440 579.37380 579.67330 582.00330 582.56950 585.30490 585.57050 585.83280 586.09420 586.35390 589.34300 589.58060 589.81900 592.09280 592.31090 592.52730 592.74150 523.12300 532.22660 532.69190 536.36660 539.50820 542.58175 543.01580 578.33000 578.61470 578.89790 579.45820 581.89930 582.16190 582.42460 582.68330 585.19240 585.43500 585.91360 586.38370 589.28740

-0,13 -0,15 0.57 -0.32 -1.21 0.45 0.17 -0.28 -0.27 -0.29 -0.45 0.04 0.64 0.43 -0.20 0.86 0.67 0.32 -0.19 0.74 0.00 0.00 -0.07 0.04 -0.70 1.03 0.10 -0.04 -0.18 -0.83 -0.42 0.05 -0.14 0.31 -0.16 -0.02 0.61 -0.67 -0.13 0.52 0.52 0.28 -0.26 0.93 -0.25 0.35 1.18 1.20 -0.63 -1.26

3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 6

mb

Obs (cm- l )

Obs - Calc (10 -3 cm -I)

98 99 113 -81 -62 -61 -53 -46 -45 -38 65 66 67 68 69 79 82 95 98 -54 -53 -46 -45 -39 -38 -31 -30

589.50000 589.70900 592.47080 523.35060 532.24470 532.69880 536.28340 539.34680 539.77870 542.76210 578.23280 578.49540 578.75740 579.01750 579.27500 581.76840 582.48490 585.41120 586.04740 532,62010 533.06190 536,11420 536,54480 539,09830 539,51800 542,42185 539,57600

-0.27 -1.19 1.03 -0.29 -0.03 -0.28 -0.34 0.04 0.00 -0.36 0.51 -0.13 0.26 0.38 -0.47 -O.22 0.54 -1.03 0.10 0.24 0.32 -0.03 0.13 0.75 -0.05 0.46 -0.34

72Ge32S 0 -111 0 -110 0 -93 0 -92 0 -91 0 -85 0 -79 0 -78 0 -72 0 -71 0 14 0 15 0 16 0 17 0 24 0 25 0 26 0 34 0 35 0 36 0 37

522.81280 523.34410 532.17040 532.67690 533.18200 536.18860 539.14580 539.63360 542.53365 543.01210 578.42750 578.78050 579.13140 579.48060 581.88310 582.22020 582.55550 585.18170 585.50420 585.82340 586.14060

-0.02 0.19 0.80 0.18 -0.49 -0.10 -0.12 -0.40 0.06 0.08 0.04 0.50 0.41 0.16 0.05 0.16 0.04 -0.53 0.73 0.28 -0.59

74Ge32 s 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

-107 -89 -88 -87 -81 -74 -67 21 22 24 31 32 33 34 41 42 44 45 46 56 57 58 66 67 68 -101 -82 -81 -74 -68 -67 -60 31 33 34 35 42 43 44 45 53 54 56 57 58 68 69 70 79 80

398

H. Uehara et al./Journal o f Molecular Structure 352/353 (1995) 395-405

Table 1 Continued Vtta

mb

Obs (cm- 1)

Obs - Calc (10-3 cm -1 )

v "a

38 47 48 49 56 58 59 -104 -86 -85 -79 -78 -72 -71 -65 24 25 26 27 34 36 37 44 45 47 48 49 59 60 69 70 71 -98 -80 -79 -78 -72 -71 -65 -64 -58 -57 34 36 37 38 45 47 48 57 58

586.45770 589.23460 589.53460 589.83450 591.88010 592.45110 592.73170 523.32110 532.48120 532.97640 535.92510 536.41170 539.30200 539.77870 542.61175 578.50650 578.84250 579.17640 579.50840 581.78980 582.42930 582.74540 584.91570 585.21990 585.82340 586.12140 586.41900 589.30190 589.58060 592.02310 592.28640 592.54700 523.23200 532.22010 532.70670 533.19180 536.07320 536.54920 539.37250 539.83850 542.60285 543.05900 578.40140 579.03690 579.35140 579.66490 581.81430 582.41350 582.71070 585.31500 585.59660

0.04 0.52 0.06 1.10 0.01 0.87 -1.15 1.66 0.44 -0.50 -0.02 0.00 -0.27 -0.50 0.14 0.01 0.54 0.54 0.21 -0.62 1.03 0.60 -0.24 0.20 1.00 0.06 0.34 -0.88 -1.64 -0.33 -0.02 -0.76 -0.13 -0.74 -0.60 -0.58 -0.75 -0.17 -0.27 0.04 -0.30 -0.01 -0.27 0.45 -0.06 0.02 0.19 -0.25 -0.45 0.03 0.45

2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5

mb

59 60 72 73 83 84 85 -92 -73 -72 -65 -58 -57 -51 -50 45 47 48 49 57 58 60 69 70 71 72 73 74 75 86 87 88 98 -86 -85 -66 -65 -51 -50 -43 57 61 70 72 84 103 -59 -58 -51 -50 -43

Obs (cm -1 )

585.87540 586.15370 589.35980 589.61640 592.08920 592.32820 592.56390 523.08120 532.37280 532.84830 536.13650 539.35620 539.81010 542.50755 542.95220 578.41130 579.00820 579.30350 579.59820 581.89390 582.17380 582.72850 585.14160 585.40020 585.66050 585.91750 586.17130 586.42400 586.67660 589.33230 589.56350 589.79460 591.99720 522.86630 523.35840 532.44030 532.90320 539.25250 539.69570 542.75720 578.47530 579.57760 581.96260 582.47470 585.40370 589.54560 532.41930 532.87190 536.00130 536.44330 539.49280

Obs - Calc (10-3 cm -~ )

-0.30 0.08 -0.52 -0.39 -0.41 0.54 -0.13 -0.27 -0.35 -0.16 -0.29 -0.47 -0.92 0.08 0.29 -0.10 0.23 -0.33 0.11 0.09 0.35 0.67 0.34 -0.96 1.10 1.51 0.39 -0.17 0.84 -0.32 -0.55 0.83 -0.18 -0.64 -0.21 0.90 -0.28 -0.66 -0.40 0.53 0.01 -0.28 0.07 0.44 -0.59 0.93 0.53 0.36 -0.04 0.52 -0.04

v "a

mb

6 6

Obs (cm -1)

Obs - Calc (10-3 cm -1 )

-51 -35

532.75090 539.61920

-0.85 0.47

-114 -97 -96 -89 -83 -82 7 8 9 10 17 18 19 26 27 28 29 30 39 40 49 50 -108 -90 -89 -83 -76 -70 -69 16 18 19 20 26 27 28 36 37 38 39 40 41 50 51 52 60 61

523.21470 532.22010 532.73620 536.32230 539.34130 539.83850 578.43960 578.80650 579.17140 579.53380 582.03510 582.38490 582.73430 585.13460 585.47200 585.80540 586.14030 586.47110 589.38540 589.70100 592.47080 592.76950 523.23200 532.58240 533.08860 536.09970 539.54730 542.49975 542.92840 578.28700 578.98780 579.34480 579.68240 581.72400 582.05980 582.39430 585.00300 585.32320 585.64080 585.95730 586.26990 586.58280 589.32280 589.61950 589.91390 592.21110 592.49220

-0.20 0.37 -1.10 0.16 -0.11 -1.30 0.20 0.65 0.65 -0.29 1.34 0.31 0.46 0.18 0.99 -0.62 0.86 -0.16 -0.14 -0.30 0.69 -O.lO -0.76 0.14 -0.17 0.78 -0.56 0.02 -0.07 -0.31 0.34 -0.37 1.09 -0.94 -0.20 0.84 -0.65 0.50 0.66 1.33 -0.28 0.03 -0.18 0.22 -0.05 -0.86 0.43

7OGe32S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H. Uehara et al./Journal of Molecular Structure 352/353 (1995) 395-405

399

Table 1 Continued Vtta

1

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4

mb

62 -84 -83 -76 -70 -69 -63 -62 26 27 28 29 30 37 38 39 48 49 5O 51 52 62 64 72 73 74 75 -96 -77 -76 -70 -63 -62 -56 -55 37 38 4O 48 5O 61 62 63 64 75 76 77 89 -90 -89 -71

Obs (cm -1)

Obs - Calc (10-3 cm-l)

'0tla

592.76950 532.36230 532.85930 536.29750 539.19090 539.66720 542.50165 542.96840 578.31840 578.65160 578.98390 579.31420 579.64280 581.89930 582.21580 582.53000 585.28490 585.58350 585.87940 586.17390 586.46630 589.30690 589.85690 591.98130 592.23950 592.49670 592.75070 523.07720 532.56470 533.05060 535.93400 539.23400 539.69960 542.46545 542.92060 578.47880 578.79380 579.41710 581.84670 582.43980 585.57460 585.84730 586.12150 586.39200 589.27080 589.52290 589.77350 592.63710 522.90290 523.40550 532.20390

-0.42 -0.40 -0.13 -O.24 0.40 -0.51 O.26 -0.32 -0.17 -0.48 -0.10 -0.12 -0.25 0.00 0.60 0.53 -0.10 0.48 -0.01 -0.26 -0.97 -0.76

4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 6

1.06

-0,38 -0.36 0.36 -0.44 -0.58 -0,29 0,11 -0.14 -0.39 -0.60 0.31 -0.36 -0.04 0.63 0.09 -0.74 1.06

1.36 -0.96 -0.12 -1.31 -0.56 0.01 0.77 -0.79

mb

Obs (cm-i)

Obs - Calc (10-3 cm 1)

-63 -62 -56 -55 -48 50 51 52 63 73 77 -55 -48 -41 -40 -56

535.96970 536.43490 539.19090 539.64430 542.78430 579.00080 579.29220 579.58170 582.66290 585.28980 586.29160 536.37050 539.49970 542.55815 542.98990 532.64710

-0.41 0.51 0.68 -0.22 -0.10 0.04 -0.19 -0.68 -0.42 0.59 -0.82 -0.08 -0.12 -0.01 0,66 -0.51

-109 -91 -90 -89 -83 -70 -69 17 18 19 20 21 28 30 37 38 39 40 41 42 52 53 61 62 63 -103 -102 -84 -83 -76 -70 -63 -62

522.89350 532.15780 532.65930 533,15970 536,13650 542,41705 542.89020 578.24940 578.59570 578.94140 579.28390 579.62590 581.97500 582.63240 584.88490 585.19960 585.51360 585.82340 586.13570 586.44440 589.44590 589.73730 592.00930 592.28640 592.56110 522.85860 523.37470 532.44520 532.93560 536.33510 539.19600 542.47085 542.93310

-0.47 -0.63 -1,16 -1.45 -0.48 0.40 0.10 0.10 -0.09 0.67 -0.23 -0.09 -0,50 -0.36 1.14 0.58 0.89 -1.41 0.37 0.14 0.10 0.17 -0.32 0.02 -0.41 0.49 0.05 0.80 0.10 -0.04 0.24 0.47 0.46

73Ge32 s 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

1 1

1 1

- 1.00

1

-0.36 -0.97

1

1

v"a

mb

27 28 29 30 31 38 39 40 49 50 52 53 64 65 66 74 75 76 -96 -78 -77 -76 -70 -69 -63 -62 -56 38 39 40 41 49 52 60 61 62 64 65 77 88 89 90 91 -90 -71 -70 -63 -62 -56 -55 -48

Obs (cm-ll

Obs - Calc

578.27780 578.60700 578.93600 579.26130 579.58620 581.81430 582,12660 582.43980 585.16370 585,45790 586.04090 586.33080 589.41190 589.68270 589.95040 592.04110 592.29620 592.54700 523.26580 532.16490 532.64680 533.12670 535.97790 536.44820 539.24170 539.70260 542.43815 578.43540 578.74570 579.05500 579.36210 581.76400 582.63900 584.90050 585.17490 585.45080 585.99210 586.26060 589.35980 591.98680 592.21550 592.44400 592.66910 523.09680 532.29220 532.76410 536.01620 536.47470 539.20220 539.65110 542.75720

0.04 -0.22 0.88 -0.16 -0.02 -1.28 -1,15 1,47 1~71 1.28 -0,17 -0,08 -0.07 0.39 -0.61 -0.33 0.89 -0.53 -I.03 0.25 0.71 0,53 0.05 -0.11 -0.33 -0.18 0.14 0.24 -0.11 0.12 -0.25 -0.83 -0.34 0.13 -0.80 1.40 0.20 -0.11 1.72 -0.42 -0.67 0.57 0.10 0,86 -0.22 1.33 -0.31 -1.08 0.15 -0.42 -1.15

(10-3 cm 1)

400

H . Uehara et al./Journal o f Molecular Structure 352/353 (1995) 3 9 5 - 4 0 5

Table 1 Continued v ua

mb

3 49 3 50 3 51 3 52 3 61 3 62 3 64 3 77 3 107 4 -64 4 -63 4 -56 4 -55 4 -48 4 64 76Ge32S 0 -85 0 -84 0 -83 0 -77 0 -76 0 -70 0 -69 0 -63 0 -62 0 28 0 29 0 31 0 39 0 40 0 41 0 50 0 52 0 53 0 54 0 55 0 65 0 66 0 67 0 75 0 76 0 77 1 -97 1 -77 1 -70 1 -63 1 -62 l -56 1 -55 1 38 1 39

Obs (cm -I)

Obs - Calc (10 acre-I)

578.37040 578.66170 578.95260 579.24080 581.76400 582.03510 582.57540 585.92160 592.56390 532.33470 532.79390 535.96970 536.41670 539.51270 579.16000

-0.12 -0.40 0.52 0.35 0.97 -0.10 0.76 0.78 1.04 0.21 0.24 0.93 -0.05 -0.43 0.02

532,19080 532.67790 533.16380 536.05180 536.52940 539.36020 539.82730 542.60285 543.05900 578.42750 578,75310 579.40030 581.92570 582.23480 582.54150 585.23550 585.81750 586.10520 586.39200 586.67660 589.44170 589.70900 589.97480 592.04660 592.29620 592.54700 523.09680 532.88010 536.17630 539.40910 539.86570 542,57435 543.02050 578.27270 578.58150

-0.56 -0.79 -0.89 -0.83 0.13 -0.58 -0.67 0.30 -1.21 0.24 0.12 0.48 0.25 0.62 0.15 -0.03 0,55 -0,09 -0,05 -0.63 0.26 -0.06 -0.27 1.52

-0.34 0.64 -0.21 -0.02 -1.71 -0.40 0.01 0,35 -0.07 -0.06 -0.05

v "a

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 4

mb

40 41 42 50 51 52 53 62 64 65 66 78 79 89 9l 92 -91 -71 -70 -63 -56 -55 -49 -48 49 50 51 53 62 63 64 65 74 77 78 79 92 -84 -65 -64 -63 -56 -49 -48 61 64 65 66 75 111 -57

Obs (cm -1)

578.88930 579.19440 579,49900 581.87510 582.16570 582.45450 582.74100 585.25040 585.78940 586.05790 586.32490 589.39270 589.63710 591.99720 592.45110 592.67340 522.93810 532.53240 532.99810 536.21910 539.37250 539.81780 542,46055 542.89590 578.22770 578.51790 578.80650 579.37830 581.87510 582.14590 582.41350 582.67820 585.00300 585.74610 585.99220 586.23630 589.25190 523.20020 532.12180 532.57780 533.03180 536.17630 539.25250 539.68580 578.23280 579.03690 579.30350 579.56370 581.85960 589.70810 532.53720

Obs - Calc (10-3 cm -~)

0.51 -0.07 0,41 -0.12 0.48 0.85 0.51 -0.27 -1.53 -0.76 0.12 0.47 -0.19 -0.47 1.15 -0.21 -0.30 -0.15 -0.06 -0.29 -1.12 -0.92 0.30 0.26 -0.07 0.05 0.14 -0.33 -0.20 1.16 0.94 -0.59 0.73 -1.49 -0.57 -0.02 - 1.04 -0.27 0.33 0.34 -0,28 0.25 0.09 -0.54 -0.38 -0.06 1.83 -1.08 -0.52 -0.24 -0.37

v 'ta

mb

Obs (cm i)

Obs - Calc (10-3 cm -j )

4 4 4 4 4

-48 -41 78 80 92

536.47920 539.46760 579.20240 579.68240 582.42030

-0.48 -0.15 0.61

74Ge345 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3

-67 -66 -65 -58 -51 -50 -43 -42 61 62 64 65 78 94 -87 -60 -59 -58 -51 -50 74 75 -80 -43 -53 -52 -51 -44 -43 -36 -35 -28 -27 91 -74 -45 -44 -35 -28 -19 -67

532.23680 532.68310 533.12670 536.20580 539.22000 539.64430 542.58605 543.00040 578.24620 578.51280 579.04130 579.30350 582.56950 586.22870 523.04220 532.24070 532.67690 533.11040 536.11420 536.53860 578.31070 578.55620 523.25340 539.46760 532.16490 532.58920 533.01290 535.94280 536.35540 539.21120 539.61270 542.39355 542.78430 578.96540 522.93460 532.41930 532.83380 536.49000 539.26070 542.72390 522.99710

0.25 0.31

72Ge34S 0 -70

533.05650

1.22

0.94

- 1.02

-0.06 0.15 -0.85 0.91 0.59 0.05 0.13 0.14 0.38 0.25 -0.74 -0.02 0.20 0.67 -0.25 -0.65 -0.16 0.12 0.42 -0.41 -1.35 1.18 0.34 0.21 0.41 -0.20 0.57 -0.42 0.82 -0.09 0.54 0.80 -0.70 0.65 -1.29 -0.40 -0.40 0.21

0.36

H. Uehara et al./JournalofMolecular Structure 352/353 (1995) 395-405

401

Table 1 Continued V" a

0 0 0 0 1 1 1 I 3 3

mb

-63 -56 -55 -48 -85 -64 -63 -48 -71 -33

Obs (cm -1)

Obs - Calc (10-3 cm ~)

v" a

mb

536.20990 539.29820 539.73420 542.74900 523.00010 532.65040 533.09510 539.61270 523.29730 539.52260

0.21 -0.49 -0.47 -0.18 0.11 0.70 0.25 -0.40 -0.84 -0.39

7°Ge34S 0 -76 0 -75 0 -61 1 -89 1 -70 1 -68 1 -53 3 -46

Obs (cm -1)

Obs - Calc (10-3 cm -I )

532.55170 533.01770 539.41590 523.25670 532.19940 533.11430 539.79700 536.48560

0.72 -0.21 -0.21 0.49 -0.49 0.57 -0.42 -0.94

a F o r transitions Av = v' - v" = 1. m = J + 1 and m = - J respectively in the R and P branches.

b

larger than 146 (=2048/14). The boundary selected was much smaller than 171 (= 2048/12) points which corresponded to the Fourier domain signal of the 0.0025 cm 1 spaced fringes.

4. Analysis We have revealed before [11,15] that infrared and far-infrared emission spectroscopy using a Fourier transform spectrometer is very useful to observe with ease the v i b r a t i o n - r o t a t i o n spectra of high-temperature molecules. It would also be easy to measure very m a n y spectral lines using a high-resolution Fourier transform spectrometer. In this study, we observed the spectra of GeS with a diode laser spectrometer. However, a rather large number, i.e. 616, of the spectral lines could be collected and measured with comparative ease with the aid of a high-performance personal computer (PC-H98 model 100), which we also used for the calculation of the least-squares fits. In total 616 lines were assigned to the Av = 1 band sequences of eight isotopomers, 127 lines to n = 1-0 to 7 - 6 bands of 74Ge32S, 125 lines to n = 1-0 to 7 - 6 bands of 72Ge32S, 114 lines to v = 1-0 to 7 - 6 bands of 7°Ge32S, 99 lines to v = 1-0 to 5 - 4 bands of 73Ge32S, 91 lines to n = 1-0 to 5 - 4 bands of 76Ge32S, 41 lines to v = 1-0 to 4 - 3 bands of 74G34S, 11 lines to v = 1-0 to 4 - 3 bands of 72Ge345 and 8 lines to v = 1-0 to 4 - 3 bands of 7°Ge34S.

We followed the method of analysis reported previously [16]. The method was to fit the observed transitions to a set of the D u n h a m potential constants, by the method of least-squares. The D u n h a m potential function can be expressed as

g(r)/hc = -eve ~2 ~e

1 q-

+BeJ(J+l)[

ai~ i

+~(-1)i(i+l)~ili=l (2)

where ~ = (r - re)/r e. The energy levels are related to the D u n h a m

Y/j

Table 2 D u n h a m potential constants for GeS ~e(74Ge32S) (cm-l ) A~ UB(cm z u) AGe

574.269313(271)a 0.729(383) 4.16410925(139) - 1.452(111)

~xs

-1.8844(500)

al az

-3.0599215(411) 5.777357(538) -8.51517(805) 10.2238(880) -8.676(767) -3.49(294)

a3

a4 a5 a6

a The uncertainty (twice the standard errors) in the last digits is given in parentheses.

H. Uehara et al./Journal of Molecular Structure 352/353 (1995) 395-405

402

Table 3 Dunham coefficients for GeS Coefficients (cm -1)

74Ge328

From potential function (this work)

7°Ge328

73G32S

576.673748 (299) a -1.672456 (151) 5.491 (293) -2.78 (244) -2.90 (146)

579.203478 (309) a -1.687161 (153) 5.563 (301) -2.82 (249) -2.96 (150)

575.453950 (297) a -1.665389 (151) 5.456 (295) -2.75 (243) -2.87 (145)

72Ge32S

Other sources

From potential function (this work)

Yl0 Y2o 104 x Y3o 106 × ]I4o 107 × Yso

574.269015 (297) a -1.658538 (150) 5.423 (294) -2.73 (240) -2.84 (143)

574.267 (27) b'c -1.639 (17) - 3 8 (30)

Yol 104 × Yll 108 x Y21 109 × ]I31 1011 × Y41 108 × Yo2 1011 × Yl2 1012 × Y22 1014 x ]I32 l015 x Y03 1016 × Y13 1018 × Y23 102° × Yo4 1022 × YI4 1027 × ]I05

0.1865657607 (625) 0.186565757 (13) b'd -7.491182 (151) -7.49103 (15) -4.094 (439) -4.37 (63) -2.490 (808) -2.84 (80) -9.13 (565) -7.8763612 (113) -7.8828 (87) -7.5645 (156) -10.0 (37) -1.0764 (671) -1.001 (744) -1.99252 (140) -1.6797 (159) -1.980 (529) -1.053381 (720 -2.839 (120) -8.7312 (432) -

0.1881313963 (631) -7.585674 (153) -4.163 (443) -2.543 (825) -9.37 (580) -8.0091061 (116) -7.7242 (160) -1.1037 (688) -1.031 (766) _2.04311 (143) -1.7295 (164) -2.047 (547) -1.089186 (754) -2.948 (124) -9.1038 (450)

0.1897854730 (636) -7.685932 (155) -4.237 (455) -2.599 (844) -9.62 (595) -8.1505545 (120) -7.8951 (163) -1.1331 (707) - 1.063 (790) -2.09747 (147) -1.7834 (169) -2.120 (566) -1.127997 (781) -3.066 (129) -9.5111 (470)

0.1873364120 (628) -7.537644 (152) -4.128 (443) -2.516 (817) -9.25 (572) -7.9415635 (114) -7.6428 (158) -1.0898 (680) -1.016 (755) -2.01732 (141) -1.7041 (162) -2.013 (538) - 1.070893 (741) -2.892 (122) -8.9131 (441)

we Be

574.269313 (271) 0.1865657950 (624)

576.674049 (273) 0.1881314312 (629)

579.203783 (283) 0.1897855085 (635)

575.454249 (271) O. 1873364466 (627)

a The uncertainty (two standard errors) in the last digits is given in parentheses. b The uncertainty (on standard error) in the last digits is given in parentheses. c Ref. [11]. d Ref. [6].

coefficients by the equation

F(v, J) = Z YiJ (v "}- ½)i[j(j _.}_1)]j i)

(3)

The Yij coefficients can then be related to the potential constants by equations given by Bouanich [17], who expanded the Yij coefficients up to eighth-order contributions. Stieda et al. [6] have reported 34, 18, 19, 14, 2, 2 and 2 rotational transition frequencies for v = 0 - 5 states of

Simultaneous analysis of all the 616 vibrationalrotational and the 91 rotational transitions revealed that it was necessary to include, for Ylo and Y0~, correction terms to the Dunham treatment such as those due to the breakdown of the Born-Oppenheimer approximation. thompson et al. [18] introduced for we and B e terms similar to Watson's [19] A terms for Yl0 and Y01 i.e.

74Ge32S, v = 0 - 4 states o f 7°Ge32S, v = 0 - 4 states o f 7 2 G e 3 2 S , v = 0 - 2 s t a t e s o f Y 6 G e 3 2 S , v -~ 0 - 1 state o f 72Ge34S, v = 0 - 1 states o f 74Ge34S a n d v = 0 - 1

states of 7°Ge34S, respectively. These microwave transitions in the frequency range from 11 to 111 GHz were also included in the present fit.

B e = UB

AB+ I i")a l+

ma

mbb

"'

H. Uehara et al./Journal of Molecular Structure 352/353 (1995) 395-405

403

76Ge32s

74Ge34S

571.980343 (30 l)a -1.654.345 (149) 5.358 (290) -2.69 (237) -2.78 (140)

562.368748 (290) a -1.590515 (144) 5.093 (276) -2.51 (222) -2.56 (129)

564.824144 (292)a -1.604433 (145) 5.160 (279) -2.55 (225) -2.61 (132)

567.406704 (302) -1.619138 (147) 5.231 (283) -2.60 (230) -2.67 (135)

0.1850817623 (621) -7.401981 (149) -4.029 (432) -2.441 (792) -8.92 (552) -7.7515621 (111) -7.4149 (153) -1.0509 (655) -0.974 (723) - 1.94535 (136) -1.6334 (155) -1.918 (512) -1.020264 (706) -2.739 (115) -8.3895 (415)

0.1789140059 (600) -7.035084 (142) -3.764 (404) -2.243 (728) -8.06 (499) -7.2435457 (103) -6.8125 (141) -0.9493 (592) -0.865 (643) - 1.75728 (123) -1.4507 (138) -1.674 (447) -0.890917 (617) -2.352 (990) -7.0818 (331)

0.1804796468 (605) -7.127628 (143) -3.830 (411) -2.292 (744) -8.27 (512) -7.3708698 (106) -6.9626 (144) -0.9744 (608) -0.892 (662) - 1.80382 (126) -1.4956 (142) -1.734 (463) -0.922512 (638) -2.446 (103) -7.3971 (346)

0.1821337290 (611) -7.225836 (145) -3.901 (418) -2.345 (761) -8.50 (526) -7.5065912 (111) -7.1232 (147) -1.0015 (625) -0.921 (684) - 1.85387 (130) -1.5441 (147) -1.798 (480) -0.956797 (662) -2.548 (107) -7.7423 (383)

571.980637 (276) 0.1850817960 (619)

562.369027 (266) 0.1789140374 (599)

564.824427 (267) 0.1804796788 (604)

567.406991 (277) 0.1821337617 (609)

where, U~, UB, Aa, A b, A~ and A b are isotopically invariant constants, m e is the mass of the electron, m a and mb are the atomic masses of atoms a and b and # is the reduced mass. To a good approximation the A and A B terms are the same as Watson's A terms. The D u n h a m correction which is included in Watson's A terms but not in A and AR is usually much smaller than Watson's A terms [18,20]. At first, retaining 12 adjustable parameters, U~, Ub, AGe AS, AGe, A S , a l , a2, a3, a4, a5 and a6, we fitted a total of 707 vibrational-rotational and rotational transitions to the D u n h a m potential constants. However, a value for the parameter A s was not determined due to an insufficient number of vibrational-rotational spectral lines observed

72Ge34S

70Ge34s

for the isotopomers which included 345. Although the value of A s was not determined with the mass difference between 32S and 34S, the correclion term (meAS/ms)itself is by no means small enoa~gh to be neglected, where m s stands for m32S or m34s. Therefore, we c h o s e We(74Ge32S) instead of U~ as an adjustable parameter and used the relation

/

,1~

we#2 1 +

A~+

(6)

We#- =

I+

+ \mbj

instead of Eq. (4) for the calculation of the least-squares fit since the parameter we was affected only by the uncertainty of a n amount

404

H. Ueharaet al./Journal of Molecular Structure 352/353 (1995) 395-405

me (m32S --m34s)Aw/m32sm34s. s Primes denote the isotopic species. Actually, the parameter A~s was neglected, i.e. set equal to zero, in the fit and all transitions were simultaneously fitted to the Dunham potential by using the resultant 11 parameters, w~(74Ge32S), UB, AGew, AGe, A S, al, a2, a3, a4, a 5 and a 6. Atomic masses required in this analysis were taken from Mills et al. [21]. The weights for the observed data were set to be proportional to (1/6obs) 2, where the errors of the measurements, 6obs, were estimated to be 0.0010cm -1 for the infrared transitions and were 9 - 5 0 k H z following Ref. [6] for the microwave transitions. The resultant as of the least-squares fit were 0.00057cm -1 and 10kHz for the infrared and the microwave transitions, respectively. The 616 vibrational-rotational transitions, together with the differences obs - calc are listed in Table 1.

law of errors. However, a 6 and Y40 are not significantly evaluated and values of Y41 and I15o suffer from the truncation errors. Previous Yij coefficients obtained from an infrared emission study [11] and those from a microwave study [6] are also listed in Table 3. The Dunham coefficients determined in the present study are all in excellent agreement within cr with those given by microwave spectroscopy [6] and infrared emission spectroscopy [l l] with the exception of the Y30 value, which the former emission spectroscopy could hardly determine. Table 3 also lists equilibrium molecular constants we and Be. Values of we were obtained using Eq. (6) with We (74Ge32S) and A~ listed in Table 2. Similarly, values of Be were obtained using Eq. (5) with the Ub and the Aas in Table 2. If the isotopically invariant constant UB is related to the rotational constant BeB° by the equation Bea ° = Us~#

5. Results and discussion With only 11 parameters we succeeded in reproducing the 616 vibrational-rotational transitions of eight isotopomers of GeS and 91 rotational transitions of seven isotopomers of GeS, with the relative uncertainties of A u / u ~ 1.0 x 1 0 - 6 and A u / v ~ 1.5 × 10-7, respectively. Dunham potential constants obtained from the fit are given in Table 2. These constants can be used with confidence to calculate the potential curve in the region covered by the data. A~ e of GeS was determined for the first time in this experiment. The present values of AGc and A s were essentially determined by the microwave transitions included in the fit and are compared with the previous values [6] of -1.472(36) and -1.894(20) for A0~c and AS~, respectively. The agreement between the present values of AB and the values of A01 of Ref. [6] is quite good. Therefore the Dunham correction is smaller than the error limits indicated. The 20 rovibrational Dunham Y~i coefficients, calculated using the constants in Table 2, are given in Table 3 for the eight isotopomers. The uncertainties were estimated from the error matrix of the least-squares fit by use of the propagation

(7)

this can be used to determine the internuclear distance r eBO as a model parameter within the Born-Oppenheimer approximation [20]. The value of r~ ° was found to be 2.012042 79(34) A, In conclusion, the present study greatly improved the accuracy of the vibrational Y,.j coefficients of GeS over previous studies and also revealed higher-order vibrational-rotational Yij coefficients. A total of 11 potential constants including three Watson type A constants, A~ e, Ag e and As , have been determined. Since the Yij coefficients have been determined from the potential function they provide a set of the molecular constants of GeS which have theoretical consistency.

Acknowledgement We wish to thank Dr. J.F. Ogilvie for helpful discussions.

References [1] Professor Maurizio Spoliti of Rome visited Professor Yonezo Morino at the Institute of Sagami in 1979 and gave us a talk on high-temperaturemolecules.

H. Uehara et al./Journal of Molecular Structure 352/353 (1995) 395 405

[2] H. Uehara, K. Horiai, K. Nakagawa and T. Fujimoto, J. Mol. Spectrosc., 134 (1989) 98. [3] P.F. Bernath, in H.L. Strauss (Ed.), Annu. Rev. Phys. Chem., (1990) 91. [4] M.J. Almond, Short-lived Molecules, Ellis Horwood, England, 1990. [5] H. Uehara, in J. Menon (Ed.), Trends in Physical Chemistry, Vol. 2, Council of Scientific Research Integration, India, 1991, p. 99. [6] W.U, Stieda, E. Tiemann, T. T6rring and J. Hoeft, Z. Naturforsch. 31a (1976) 374. [7] J. Hoeft, F.J. Lovas, E. Tiemann, R. Tischer and T. T6rring, Z. Naturforsch., Teil A, 24 (1969) 1217. [8] K.P. Huber and G. Herzberg, Constants of diatomic molecules, Van Nostrand Reinhold, New York, 1979. [9] G. Drummond and R.F. Barrow, Proc. Phys. Soc. (London), A65 (1952) 277. [10] R.F. Barrow, Proc. Phys. Soc. (London), 53 (1941) 116. [11] H. Uehara, K. Horiai. K. Sueoka and K. Nakagawa, Chem. Phys. Lett., 160 (1989) 149.

405

[12] H. Uehara, K. Horiai, Y. Ozaki and T. Konno, Chem. Phys. Lett., 215 (1993) 505. [13] H. Uehara, K. Horiai, Y. Ozaki and T. Konno, Spectrochim. Acta, Part A, 50 (1994) 1389. [14] J.W.C. Johns, personal communication, 1987. [15] H. Uehara, K. Horiai, T. Konno and K. Miura, Chem. Phys. Lett., 169 (1990) 599. [16] H. Uehara, T. Konno, Y. Ozaki, K. Horiai, K. Nakagawa and J.W.C. Johns, Can. J. Phys., 72 (1994) 1145. [17] J.P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer, 19 (1978) 381. [18] G. Thompson, A.G. Maki and W. Weber, J. Mol. Spectrosc., 118 (1986) 540. [19] J.K.G. Watson, J. Mol. Spectrosc., 80 (1980) 411. [20] E. Tiemann, A. Arnst, W.U. Stieda, T. T6rring and H.J. Hoeft, Chem. Phys., 67 (1982) 133. [21] I. Mills, T. Cvitas, K. Homann, N. Kallay and K. Kuchitsu, Quantities, Units and Symbols in Physical Chemistry, Blackwell, Oxford, 1988.