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Fourier transform emission spectroscopy of the TiF radical in the 407 nm region
Journal of Molecular Spectroscopy 230 (2005) 139–148 www.elsevier.com/locate/jms
Fourier transform emission spectroscopy of the TiF radical in the 407 nm region Takashi Imajo*,1, Yuki Kobayashi, Yoshihiro Nakashima, Keiichi Tanaka, Takehiko Tanaka Department of Chemistry, Faculty of Science, Kyushu University, Hakozaki, Higashiku, Fukuoka 812-8581, Japan Received 1 September 2004; in revised form 21 October 2004 Available online 21 December 2004
Abstract Ultraviolet emission spectra of the TiF radical in the 407 nm region have been observed at a resolution of 0.04 cm1 using a Fourier transform spectrometer. A new electronic assignment of 4C–X4U has been proposed. Rotational analysis has been obtained for the 0–0 and 1–1 vibrational bands of the 4C5/2–X4U3/2, 4C9/2–X4U7/2, and 4C11/2–X4U9/2 subbands and the 0–0 band of 4C7/2–X4U5/2. The lower state rotational and centrifugal distortion constants are consistent with the previous results [J. Mol. Spectrosc. 184 (1997) 186; J. Chem. Phys. 119 (2003) 9496], to the conformation that the lower state of the 407 nm band is the 4U ground electronic state. Rough estimates of the vibrational interval DG(1/2) and the spin–orbit coupling constant A in the 4C state were also obtained. 2004 Elsevier Inc. All rights reserved.
1. Introduction Transition metal atoms with an open d-electron shell have numerous low-lying electronic states with high multiplicities and large orbital angular momenta. As a result electronic spectra of diatomic molecules containing transition metals are very complex, and their characterization has often been the subject of controversy. The electronic spectrum of TiF was first observed in absorption by Diebner and Kay [1] and later in emission by Chatalic et al. [2]. The most prominent group of the bands in the 407 nm region presented in [1,2] was vibrationally analyzed and assigned as belonging to a 4P– X4R transition. These bands were then rotationally analyzed by Shenyavskaya and Dubov [3], who reassigned them to a 2U–2D transition on the basis of the appearance of the rotational structure and theoretical results *
Corresponding author. Fax: +81 3 5981 3656. E-mail address: [email protected] (T. Imajo). 1 Present address: Japan WomenÕs University, Tokyo 112-8681, Japan. 0022-2852/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2004.10.013
[4] which predicted close-lying, low-energy states, 4 R and 2D either of which could be expected to be the ground state. Ram et al. [5] investigated emission bands in the 13 500–16 000 cm1 region using a Fourier transform spectrometer as well as by laser excitation spectroscopy. The observed bands were rotationally analyzed and assigned to a G4U–X4U transition. They proposed that the electronic ground state is X4U, which is supported by ab initio calculation by Boldyrev and Simons [6]. The 4Ur ground state assignment was finally confirmed by the recent observation of the pure rotational spectrum by Sheridan et al. [7]. Ram and Bernath [8] observed similar emission bands of TiCl in the near infrared region and assigned them to a G4U–X4U transition. Theoretical results by Boldyrev and Simons [6] and Sakai et al. [9] support that the electronic ground state of TiCl is 4U. Very recently Maeda et al. [10] measured the pure rotational spectrum of TiCl, which confirmed experimentally the 4U ground state for TiCl. Ram and Bernath [11] suggested that the bands of TiF in the 407 nm region might be due to a 4C–X4U or
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4
U–X4U transition. They also suggested that the band of TiCl in the 420 nm region, which was previously assigned to 2U–2D by Lanini [12] and Phillips and Davis [13], might correspond to a 4C–X4U or 4U–X4U transition. Imajo et al. [14] measured rotationally resolved emission spectrum of TiCl in the 420 nm region by using Fourier transform spectrometer and reassigned the electronic transition to 4C–X4U. The assignment was based on consistency between the lower-state rotational constants derived from the 420 nm band [14] and those from near-infrared bands [8] as well as the argument on the intensity distribution of the rotational structure. In the present work, we have measured emission bands of TiF in the 407 nm region at a resolution of 0.04 cm1 using a Fourier transform spectrometer. As a result, we propose a new electronic assignment of this band as 4C–X4U. Rotational analysis has been obtained for the 0–0 and 1–1 vibrational bands of the 4C5/2–X4U3/ 4 4 4 4 2, C9/2–X U7/2, and C11/2–X U9/2 subbands and the 0–0 4 4 band of C7/2–X U5/2. Intensity pattern of the rotational structure in the 0–0 band of 4C5/2–X4U3/2 was carefully inspected, and the result confirmed that the X value in the upper state is larger than that in the lower state, which provided an evidence for the new electronic assignment.
2. Experimental The experimental setup used for the present emission measurement has been described in detail previously
[14]. Briefly, the TiF radical was produced in an a.c. (60 kHz) discharge of He/TiF4. A mixture of TiF4 powder and sea sand was used for regular vaporization of TiF4 to take place. Emission from a discharge tube was focused onto the entrance aperture of the Fourier transform spectrometer (Bruker IFS120HR) and detected by a photomultiplier (Hamamatsu R-928). The spectral region was limited through an optical interference filter centered at 410 nm with a bandwidth of 10 nm placed in front of the photomultiplier. Total pressure in the discharge tube was maintained at about 1 Torr. The peak discharge current was typically 200 mA. The resolution of the Fourier transform spectrometer was set to 0.04 cm1.
3. Observed spectra and analysis Fig. 1 shows the overview of the observed emission spectrum of TiF in the region 24 480–24 720 cm1, which is the result of a coaddition of several hundred scans with a total effective scanning time of 7 h. Eight Q-branch heads formed by the 0–0 and 1–1 vibrational bands of all four subbands of the 4C–X4U electronic transition of TiF were assigned as shown in Fig. 1. Other features looking like Q-branch heads were left unassigned, although they were probably due to sequence bands with higher vibrational quantum numbers. Attempts to rotationally analyze the corresponding bands were unsuccessful because of line congestion. Fig. 2 shows an expanded spectrum of the
Fig. 1. Overview of the TiF, 4C–X4U emission spectrum.
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
141
Fig. 2. Expanded spectrum of the TiF, 4C5/2 (v = 0)–X4U3/2 (v = 0) band.
4
C5/2 (v = 0)–X4U3/2 (v = 0) band, which has P- and Rbranches with well-resolved rotational structure and a blue-shaded Q-branch partially resolved at high J. Unblended rotational lines have a typical line width of 0.048 cm1 FWHM. Observed peak positions of rotational lines for the 4 C5/2–X4U3/2, 4C7/2–X4U5/2, 4C9/2–X4U7/2, and 4C11/2– X4U9/2 subbands are listed in Tables 1–4. Spectral congestion prevented unambiguous assignment of rotational lines for the 1–1 band of the 4C7/2–X4U5/2 subband, although the peak at 24590.6 cm1 was tentatively assigned to the Q-branch head of this band. It was also difficult to assign the Q-branch lines in the 0–0 band of 4C9/2–X4U7/2 as well as 4C11/2–X4U9/2. Wavenumbers with superscript ÔcÕ in Tables 1–4 are those of strongly blended lines, which were excluded from the least squares fitting. Seven vibronic bands, of which line positions are listed in Tables 1–4, were subjected to rotational analysis. Different subbands were analyzed separately by using a simple expression for the rotational term value 2
F ðJ Þ ¼ Beff J ðJ þ 1Þ Deff J 2 ðJ þ 1Þ :
ð1Þ
Since all observed transitions corresponded to DX = +1, the spin–orbit coupling constant A could not be directly determined. Also, no X doubling was resolved. The rotational analysis of each subband was performed in two steps. In the first step, lower state combi-
nation differences were extracted, and they were least squares fitted to determine the rotational and centrifugal distortion constants in the lower state. In the second step, the lower state constants were fixed, and emission line positions were least squares fitted to determine the rotational and centrifugal distortion constants in the upper state as well as the subband origin. The least squares fitting of the combination differences for the v = 0 vibrational state in the X4U3/2 spin component yielded a standard deviation of 0.006 cm1, and the standard deviation in the fitting of the 0–0 band of the 4C5/2–X4U3/2 subband was 0.004 cm1. These values are close to those expected from the typical line width (0.048 cm1) and the fact that this band is relatively unaffected by line congestion. However, the corresponding standard deviations for other bands were greater presumably due to overlapping of lines; 0.017 and 0.022 cm1 for the 4C5/2–X4U3/2, 1–1 band, 0.010 and 0.015 cm1 for the 4C7/2–X4U5/2, 0–0 band, 0.022 and 0.020 cm1 for the 4C9/2–X4U7/2, 0–0 band, 0.023 and 0.016 cm1 for the 4C9/2–X4U7/2, 1–1 band, 0.018 and 0.012 cm1 for the 4C11/2–X4U9/2, 0–0 band, and 0.012 and 0.014 cm1 for the 4C11/2–X4U9/2, 1–1 band. The optimized molecular constants in the lower and upper states are listed in Tables 5 and 6, respectively. It might be misleading that uncertainties for the rotational and centrifugal distortion constants in the upper state (Table 6, in parentheses) are smaller by almost
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Table 1 Transition frequencies in the 4C5/2–4U3/2 subband or TiF J
0–0 R (J)
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 43.5 44.5 45.5 46.5 47.5 48.5 49.5 50.5 51.5 52.5 53.5 54.5 55.5 56.5 57.5 58.5 59.5 60.5 a b c
1–1 a
24530.113 24530.883c 24531.626c 24532.379c 24533.143 24533.913 24534.687 24535.461 24536.243 24537.027 24537.812 24538.605 24539.401 24540.201 24541.005 24541.814 24542.620c 24543.436 24544.255c 24545.081 24545.904 24546.739 24547.562 24548.410 24549.247 24550.097 24550.944c 24551.800 24552.652 24553.514 24554.383 24555.254c 24556.067c 24556.992 24557.870 24558.755 24559.702c 24560.523 24561.428 24562.349c 24563.213 24564.116 24565.021 24565.925 24566.843 24567.784 24568.669 24569.628c 24570.549 24571.467
OC 2 17 4 3 3 1 1 1 1 1 2 0 0 0 1 3 3 2 2 2 2 3 9 2 3 1 1 2 2 0 5 8 50 0 0 3 64 4 9 33 2 2 4 10 5 19 17 19 13 0
b
Q (J)
a
24527.072 24527.130 24527.181 24527.241 24527.308 24527.371 24527.446 24527.521 24527.603 24527.685 24527.773 24527.866 24527.960 24528.062 24528.166 24528.275 24528.383 24528.501 24528.621 24528.744 24528.875 24529.005 24529.143 24529.284 24529.422 24529.573 24529.728 24529.883 24530.043 24530.203 24530.371 24530.546 24530.721 24530.883c 24531.085 24531.274 24531.466 24531.626c 24531.857 24532.058 24532.275 24532.479 24532.699 24532.917 24533.143 24533.364 24533.593
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
OC
4 3 1 1 3 2 2 1 3 2 2 3 1 3 3 4 0 1 1 0 3 1 2 3 3 0 2 1 1 3 3 0 1 19 1 0 1 35 3 6 4 3 2 1 5 1 2
b
P (J)
a
OC
24524.237 24523.524 24522.823 24522.113 24521.412 24520.717c 24520.025 24519.327 24518.636 24517.963 24517.284c 24516.612c 24515.942 24515.275 24514.617 24513.959c 24513.309 24512.661
9 7 2 1 1 4 6 2 7 2 0 2 0 2 1 1 1 1
24511.377 24510.745 24510.112 24509.488 24508.865 24508.246 24507.635 24507.025 24506.418 24505.821 24505.224
1 2 0 2 1 0 2 1 1 2 1
24504.044 24503.460 24502.882 24502.307 24501.737 24501.171 24500.609 24500.056 24499.500 24498.950 24498.405 24497.870 24497.329 24496.802 24496.270 24495.761 24495.232 24494.730 24494.211 24493.722 24493.217 24492.715 24492.232 24491.742 24491.261 24490.781 24490.298
1 0 0 0 0 1 1 2 1 3 4 0 6 2 8 5 7 4 6 9 4 2 6 2 4 2 8
b
R (J)a
O Cb
24548.298c 24549.050 24549.810 24550.575 24551.340 24552.121 24552.858c 24553.684 24554.470 24555.254c 24556.116 24556.858c 24557.668
53 37 26 16 2 1 49 13 22 36 23 41 42
24560.952c 24561.811 24562.656
42 15 7
Q (J)a
24541.924 24542.044 24542.169c 24542.311 24542.436 24542.620c 24542.723c 24542.864 24543.023 24543.188 24543.338c 24543.520 24543.682 24543.851 24544.043 24544.255c 24544.413 24544.620c 24544.817
O Cb
12 8 5 11 5 53 14 8 15 22 9 22 9 3 2 21 20 19 34
P (J)a
O Cb
24532.379c 24531.626c 24530.986 24530.295
74 2 38 19
24526.308 24525.668 24525.026 24524.382 24523.739 24523.130 24522.565 24521.934 24521.328 24520.717c 24520.193c 24519.544 24518.961 24518.374 24517.796 24517.284c 24516.612c 24516.104 24515.545 24515.000 24514.469 24513.959c
22 20 25 36 51 36 17 0 2 5 69 12 17 12 10 68 39 12 5 7 16 40
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Table 2 Transition frequencies in the 4C7/2–4U5/2 subband of TiF J
0–0
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 43.5 44.5 45.5 46.5 47.5 48.5 49.5 50.5 a b c
R (J)a
O Cb
24575.378 24576.124 24576.874 24577.630 24578.382 24579.137 24579.905 24580.667 24581.434 24582.198 24582.969 24583.736 24584.518 24585.294 24586.080 24586.874 24587.653 24588.441 24589.241 24590.016 24590.824 24591.626 24592.425 24593.226 24594.037 24594.846c 24595.651 24596.462 24597.269 24598.077 24598.918 24599.737c 24600.562 24601.389 24602.222 24603.067 24603.890c 24604.733 24605.577 24606.414c 24607.260c 24608.102 24608.972c 24609.879c 24610.662c 24611.528 24612.386 24613.245
6 8 9 6 9 13 5 7 5 9 9 15 9 11 6 5 2 2 8 10 2 6 4 2 8 9 3 1 8 18 3 2 2 4 2 10 3 1 4 3 3 10 8 61 13 7 12 18
Q (J)a
O Cb
24572.509 24572.568 24572.627 24572.679 24572.734 24572.799 24572.867 24572.930 24573.002 24573.080 24573.154 24573.234 24573.318 24573.397 24573.488 24573.577 24573.668 24573.763 24573.864 24573.969 24574.071 24574.169 24574.289 24574.385 24574.515 24574.626c 24574.753 24574.882 24575.008 24575.129c
10 2 3 1 5 2 1 3 2 4 2 3 6 1 5 4 2 1 4 7 5 5 5 13 1 8 3 0 3 14
P (J)a
O Cb
24568.876c 24568.124c 24567.365c 24566.611c 24565.925 24565.212 24564.466 24563.754 24563.059 24562.349c 24561.657 24560.952c 24560.273 24559.586c 24558.908c 24558.219 24557.532 24556.858c 24556.176 24555.509 24554.840 24554.179 24553.514 24552.858c 24552.199 24551.543 24550.944c 24550.249 24549.601 24548.964 24548.298c 24547.694 24547.055 24546.432 24545.799 24545.195 24544.568c 24543.964c 24543.338c 24542.723c 24542.169c 24541.577c 24540.900c
109 79 40 2 31 29 8 14 6 15 9 19 6 4 5 1 7 3 10 5 5 0 2 2 0 3 49 2 2 2 26 5 2 3 5 12 3 14 1 8 42 51 29
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
one order of magnitude than those for the lower state constants (Table 5). This is simply the result of the least squares analysis in which the lower state constants were fixed on determination of the upper state constants. Real uncertainties of the upper state constants are as large as those for the lower state constants, as shown
by the figures in square brackets, as estimated from calculation with slightly varied lower state constants. Q-branch lines could not be assigned for the 0–0 band of 4C9/2–X4U7/2 as well as 4C11/2–X4U9/2. Even in such a case, the J assignment of P - and R-branch lines was uniquely determined by requiring that the resulting molec-
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Table 3 Transition frequencies in the 4C9/2–4U7/2 subband of TiF J
0–0
1–1 a
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 a b c
R (J)
OC
24621.649 24622.390 24623.130 24623.880 24624.627 24625.379 24626.127 24626.875 24627.620 24628.371 24629.121 24629.871 24630.614c 24631.369c 24632.208c 24632.891 24633.648 24634.404 24635.160 24635.918 24636.677 24637.440 24638.197 24638.958 24639.716 24640.477 24641.243 24642.008 24642.788c 24643.543 24644.314 24645.082 24645.848 24646.532 24647.310c 24648.167c 24648.817 24649.566 24650.310 24651.150c
16 13 7 10 9 13 11 8 2 1 3 6 18 18 65 9 9 11 13 13 13 10 12 11 12 11 5 0 20 16 28 37 45 29 9 92 14 20 31 56
b
P (J)
a
24611.954c 24611.359c 24610.662c 24609.879c 24609.100c 24608.421 24607.692 24606.956 24606.244 24605.577 24604.792 24604.131 24603.362 24602.653 24601.931 24601.218c 24600.562 24599.737c 24599.086 24598.377 24597.667 24597.023 24596.258 24595.570 24594.846c 24594.158 24593.464 24592.081 24591.352
OC
100 34 64 8 46 1 7 22 13 40 27 29 23 17 24 24 33 81 21 20 21 43 14 5 13 5 16
b
R (J)a
O Cb
24641.070 24641.945 24642.788c 24643.678c 24644.561 24645.471 24646.390 24647.310c 24648.250c 24649.192 24650.160 24651.150c 24652.135 24653.155 24654.191 24655.255 24656.359
9 12 10 5 1 12 19 14 15 3 2 7 11 11 13 8 18
Q (J)a
O Cb
24629.963 24630.044 24630.126 24630.238 24630.345 24630.453 24630.614c 24630.711 24630.867 24631.021 24631.179 24631.369c 24631.550 24631.760 24631.980 24632.208c 24632.469 24632.735 24633.024 24633.342 24633.740 24634.047
21 15 17 2 7 3 42 6 18 17 7 16 3 4 0 11 6 13 15 7 61 17
P (J)a
O Cb
24617.309 24616.725 24616.162 24615.610 24615.054 24614.526 24614.032 24613.559 24613.063 24612.687c 24612.158 24611.740 24611.359c 24610.985c 24610.662c
16 8 8 6 14 21 9 9 14 66 26 26 9 7 25
42 17
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
ular constants reproduce the position of the unresolved Q-branch head.
4. Discussion In Table 5, the rotational and centrifugal distortion constants in the X4U electronic state obtained in the present study are compared with those previously determined by Ram et al. [5]. They all agree within 2.5r uncertainties. The present ground state constants are also consistent with the millimeter-wave results by Sher-
idan et al. [7], i.e., the effective rotational and centrifugal distortion constants reduced from the constants in [7] are in agreement with the present values within 2.5r. Agreement of the molecular constants provides an evidence for identifying the lower state of the 407 nm band as X4U. Fig. 3 shows an expanded spectrum of the 4C11/ 4 2 (v = 0)–X U9/2 (v = 0) band, where the intensity pattern of R-branch lines is carefully inspected. The sticks inserted in Fig. 3 show their calculated line positions and the numbers are the J00 values. The sequence of R-branch lines is clearly seen and may be traced back
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
145
Table 4 Transition frequencies in the 4C11/2–4U9/2 subband of TiF J
0–0 R (J)
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 a b c
1–1 a
24670.109 24670.840 24671.572 24672.306 24673.041 24673.766 24674.489 24675.226 24675.947 24676.668 24677.395 24678.113 24678.832 24679.552 24680.273 24680.986 24681.701 24682.415 24683.131 24683.844 24684.534 24685.260 24685.968 24686.679 24687.386 24688.089 24688.800 24689.499 24690.156c 24690.918c 24691.605 24692.281 24693.025 24693.712 24694.420 24695.111 24695.821
OC
b
1 2 4 2 3 1 6 4 0 2 2 1 2 0 3 0 0 0 4 5 15 1 0 4 4 1 6 1 46 13 3 29 13 1 5 4 5
a
P (J)
24656.624 24655.917 24655.132 24654.403 24653.635 24652.839 24652.069 24651.297 24650.507 24649.792 24649.019 24648.250c 24647.475 24646.721 24645.946 24645.180 24644.416 24643.678c 24642.863 24642.097 24641.327 24640.556
OC
27 25 1 33 27 6 12 19 43 8 2 0 7 8 2 5 11 43 2 2 2 1
b
R (J)a
O Cb
24687.113 24687.876 24688.636 24689.386 24690.156c 24690.918c 24691.696 24692.474 24693.250 24694.037 24694.819 24695.607 24696.408 24697.212 24698.005 24698.816 24699.635
15 7 4 15 9 13 5 1 2 4 1 1 6 11 0 1 4
Q (J)a
24684.825 24684.996 24685.169 24685.366 24685.576 24685.799 24686.038 24686.298 24686.490
O Cb
P (J)a
O Cb
24675.427 24674.682 24673.952 24673.374c 24672.589 24671.884 24671.198 24670.525 24669.846 24669.169 24668.480 24667.843 24667.175
35 1 26 98 11 1 2 13 12 8 13 11 3
18 13 17 9 1 8 19 37 29
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
to the first line with J00 = 4.5. This is consistent with the electronic assignment of this band to 4C11/2–X4U9/2, because the lowest member in the R-branch of this band is R (4.5). Emission intensities of individual R-, P-, and Qbranch lines are expressed by hcB0 J 0 ðJ 0 þ 1Þ I em / m4 S J exp ; kT
ð2Þ
where the Ho¨nl–London factor SJ is given for the R-, Pand Q-branch lines by S RJ ¼
ðJ 00 þ 2 X00 ÞðJ 00 þ 1 X00 Þ ; 2ðJ 00 þ 1Þ
ð3Þ
S PJ ¼
ðJ 00 1 X00 ÞðJ 00 X00 Þ ; 2J 00
ð4Þ
ðJ 00 þ 1 X00 ÞðJ 00 X00 Þð2J 00 þ 1Þ ; 2J 00 ðJ 00 þ 1Þ
ð5Þ
and S QJ ¼
where the upper and lower signs apply to the bands with DX = +1 and DX = 1, respectively [15]. Calculated intensities indicated by filled circles in Fig. 4 are those corresponding to the X 0 = 5/2 fi X00 = 3/2 transition (DX = +1), where a rotational temperature of 500 K was assumed. The intensity pattern, in which P-branch lines rapidly lose intensity with decreasing J whereas R-branch lines remain rather strong, well reproduces
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Table 5 Effective molecular constantsa of TiF in the X4U State Present work 4
b
Ram et al.
Table 6 Effective molecular constants of TiF in the 4C statea Sheridan et al.
B1 D1
0.36240 (14) 5.05 (72) · 107
0.362226 4.198 · 107
B0 D0
0.364724 (15) 4.179 (36) · 107
0.364752 4.252 · 107
0.364725 4.089 · 107
X4U5/2
B0 D0
0.366975 (41) 4.37 (17) · 107
0.366985 4.462 · 107
0.367040 4.472 · 107
X4U7/2
B1 D1
0.36673 (23) 5.3 (16) · 107
0.366805 4.806 · 107
B0 D0
0.36931 (14) 4.68 (74) · 107
0.369379 4.813 · 107
B1 D1
0.36944 (19) 6.7 (27) · 107
0.369222 5.141 · 107
B0 D0
0.37190 (12) 5.14(78) · 107
0.371828 5.145 · 107
X U3/2
X4U9/2
a
4
C5/2
24526.78146 (79) [10] 0.3667734 (13) [151] 4.2500 (39) [372] · 107
m00 B0 D0
24572.0493 (36) [4] 0.3682692 (74) [391] 4.159 (30) [161] · 107
4
C9/2
m11 B1 D1
24629.641 (11) [2] 0.370037 (48) [231] 7.91 (44) [154] · 107
m00 B0 D0
24618.2950 (66) [9] 0.369880 (19) [136] 5.43 (11) [69] · 107
m11 B1 D1
24683.0202 (60) [8] 0.370645 (25) [195] 0.51 (16) [267] · 107
m00 B0 D0
24666.0414 (40) [9] 0.371215 (12) [112] 4.289 (73) [700] · 107
4
C11/2
b
the observed intensity distribution. Intensity distribution of Q-branch lines is also well reproduced. Calculations with the assumption of DX = 1 result in intensity patterns with stronger P-branch lines and weaker Rbranch lines, which do not match the observed pattern. It is therefore confirmed that the band of current interest is a DX = +1 transition, giving a support to the new electronic assignment of this subband to 4C5/2–X4U3/2. Theoretical calculations by Boldyrev and Simons [6] have not dealt with 4C electronic states. A 4C state may be formed if the 3r electron in the ground configuration 1r21p42r21d13r12p1 is promoted to the 3p orbital. For the TiCl radical, Sakai et al. [9] showed that the 3r orbital mainly consists of the 4s atomic orbital of Ti. Similarly, the 3r molecular orbital of TiF is considered to have a character of the Ti, 4s atomic orbital. The 3p orbital probably corresponds to the Ti, 4pp orbital, and therefore, emission transition from the 4C state thus formed to the ground 4U state is expected to be fully allowed, because it corresponds to a single electron transition in the Ti atom. In the present work, the 4C–X4U transition of TiF was observed around 24 600 cm1. Recently we confirmed the 4C–X4U assignment of the TiCl transition around 23 900 cm1 [14]. It is important to note that the 4C–X4U transitions of these radicals appear in almost the same spectral region. The 4C–X4U transition of TiH was also observed around 19 000 cm1 by Launila and Lindgren [17]. Ram and Bernath [8] discussed
m00 B0 D0 C7/2
1
Determined from combination differences. In cm units. Values in parantheses are uncertainties in units of the last digit corresponding to the standard deviation in the least squares fit. The standard deviations for each fit in cml units are 0.017 (X4U3/2,v = 1), 0.006 (X4U3/2,v = 0), 0.010 (X4U5/2,v = 0), 0.023 (X4U7/2,v = 1), 0.022 (X4U7/2,v = 0), 0.012 (X4U9/2,v = 1), and 0.018 (X4U9/2,v = 0). Also see text.
24540.412 (10)c [2]d 0.364257 (24) [146] 3.90 (12) [72] · 107
4
0.369413 4.850 · 107
0.371874 5.279 · 107
m11b B1 D1
In cm1 units. m11 and m00, respectively, mean the origins of the 1–1 and 0–0 vibrational bands. c Values in parentheses are uncertainties in units of the last digit corresponding to the standard deviation in the least squares fit, where the lower state constants are fixed as listed in Table 5. The standard deviations for each fit in cm1 units are 0.022 (4C5/2–X4U3/2, v = 1–1), 0.004 (4C5/2–X4U3/2, v = 0–0), 0.015 (4C7/2–X4U5/2, v = 0–0), 0.016 (4C9/2–X4U7/2, v = 1–1), 0.020 (4C9/2–X4U7/2, v = 0–0), 0.014 (4C11/2– X4U9/2, v = 1–1), and 0.012 (4C11/2–X4U9/2, v = 0–0). Also see text. d Values in square brackets are uncertainties in units of the last digit caused by the uncertainties of the lower state constants. a
b
the correspondence between the lower energy levels of TiX (X = Cl, F, H) and the atomic energy levels of the Ti+ ion. It indicates that the TiX radicals are well described as Ti+X in the lower energy region. It is suggested that this picture may be extended to the 4C state of TiX, which is correlated with the lowest 4G state of the Ti+ ion located 30 000 cm1 above the 4F ground state and belonging to the 3d24p configuration [16]. The ionic picture of Ti+X may give a useful insight for understanding the 4C state of TiX. However, the position of the 4C state of TiH is considerably lower than that of the 4G state of the Ti+ ion. It may indicate that there is a subtle difference in the bonding of TiH. Within the 4C5/2–X4U3/2 transition, the origin of the 1–1 vibrational band is higher than that of the 0–0 vibrational band by 13.6 cm1. This difference, combined with the energy separation DG (1/2) = 650.61 cm1 [5] between the v = 1 and v = 0 levels of the X4U3/2 spin component, allows us to derive the DG (1/2) value for the 4C5/2 spin component as 664.2 cm1. Similarly, the
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
147
Fig. 3. Expanded spectrum of the TiF, 4C11/2 (v = 0)–X4U9/2 (v = 0) band. The sticks represent calculated line positions and the numbers are the rotational quantum numbers J00 in the lower state.
Fig. 4. Expanded spectrum of the TiF, 4C5/2 (v = 0)–X4U3/2 (v = 0) band. Filled circles represent the calculated intensities assuming a rotational temperature of 500 K. See text for details of the calculation of line intensities.
DG (1/2) values for the 4C9/2 and 4C11/2 spin components are obtained as 662.1 and 667.8 cm1, respectively. The DG (1/2) values for various spin components of the 4C electronic state disagree by several cm1, although much closer agreement would be expected without perturbation. For example, the DG (1/2) values are 650.61,
650.68, 650.74, and 650.78 cm1, respectively, for the X = 3/2, 5/2, 7/2, and 9/2 spin components of the ground X4U state [5]. Therefore, we must conclude that vibronic levels of the 4C state are perturbed. It is noted that perturbation of the 4C state is also suggested by anomalous negative values of some centrifugal distor-
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tion constants in Table 6. Although the perturbation precludes precise estimation of the vibrational interval in the 4C state, it probably has a value similar to but slightly larger than the value DG (1/2) = 650.70 cm1 in the ground X4U state. Therefore, the stretching force constant slightly increases on excitation from the X4U state to the present 4C state. The difference between the band origins of the 4 C7/2 (v = 0)–X4U5/2 (v = 0) and 4C5/2 (v = 0)–X4U3/ 1 2 (v = 0) transitions is 45.27 cm . Combining this difference with the spin–orbit interval 101.84 cm1 between the X = 5/2 and 3/2 spin components of the X4U (v = 0) state, which Ram et al. [5] determined by laser excitation spectroscopy and corresponds to three times the spin–orbit coupling constant, we may calculate the 7/2–5/2 spin–orbit interval in the 4C (v = 0) state as 147.11 cm1. The value 147.11 cm1 divided by four gives an estimate of the spin–orbit coupling constant A = 36.8 cm1 fot the 4C state. In the same way, the 9/2–7/2 and 11/2–9/2 spin–orbit intervals in the 4 C (v = 0) state are calculated as 148.09 and 149.59 cm1, giving A = 37.0 and 37.4 cm1, respectively. The derived A constants agree within 2%, the average being 37.1 cm1. An alternative method to derive the A constant as well as the true rotational constant from the effective rotational constants, which worked well in the ground X4U state [5], leads to unreliable results for the 4C state, i.e., the effective rotational constants for the X = 5/2 and 11/2 spin components in the v = 0 level for example give A = 45.8 cm1, whereas A = 38.2 cm1 is obtained from the combination of the effective rotational constants for X = 7/2 and 9/2. This shows again that the 4C state is perturbed. For all of the observed bands, the effective rotational constants in the upper and lower states differ very little (less than 1%). This means that the bond length is almost the same in the X4U state and the upper 4C state (The r0 bond length calculated from the average of the effective rotational constants for the four spin compo˚ in the nents of the v = 0 vibrational state is 1.8343 A ˚ in the 4C excited state). This X4U state and 1.8323 A and the similarity of the stretching force constant de-
scribed above indicate that the lower and upper states of the present transition have closely resembling potential curves, consistent with the absence of Dv „ 0 transitions.
Acknowledgments The authors thank Professor P. F. Bernath at Waterloo University, Canada for valuable discussions on electronic assignments of the emission spectra of TiF in the near ultraviolet region. Financial supports from the Ministry of Education, Science, Sports, and Culture are acknowledged.
References [1] R.L. Diebner, J.G. Kay, J. Chem. Phys. 51 (1969) 3547–3554. [2] A. Chatalic, P. Deschamps, C. Pannetier, C.R. Acad. Sci. Paris. Ser. C 270 (1970) 146–149. [3] E.A. Shenyavskaya, V.M. Dubov, J. Mol. Spectrosc. 113 (1985) 85–92. [4] R. Gambi, Gazz. Chim. Ital. 105 (1975) 27–35. [5] R.S. Ram, J.R.D. Peers, Y. Teng, A.G. Adam, A. Muntianu, P.F. Bernath, S.P. Davis, J. Mol. Spectrosc. 184 (1997) 186– 201. [6] A.I. Boldyrev, J. Simons, J. Mol. Spectrosc. 188 (1998) 138–141. [7] P.M. Sheridan, S.K. McLamarrah, L.M. Ziurys, J. Chem. Phys. 119 (2003) 9496–9503. [8] R.S. Ram, P.F. Bernath, J. Mol. Spectrosc. 186 (1997) 113–130. [9] Y. Sakai, K. Mogi, E. Miyoshi, J. Chem. Phys. 111 (1999) 3989– 3994. [10] A. Maeda, T. Hirao, P.F. Bernath, T. Amano, J. Mol. Spectrosc. 210 (2002) 250–258. [11] R.S. Ram, P.F. Bernath, J. Mol. Spectrosc. 186 (1997) 335–348. [12] K.P. Lanini, Ph.D. dissertation, University of Michigan, Ann Arbor, Michigan, 1972. [13] J.G. Phillips, S.P. Davis, Astr. Phys. J. Suppl. Ser. 71 (1989) 163– 172. [14] T. Imajo, D. Wang, K. Tanaka, T. Tanaka, J. Mol. Spectrosc. 203 (2000) 216–227. [15] I. Kovacs, Rotational Structure in the Spectra of Diatomic Molecules, American Elsevier, New York, USA, 1969, p. 121. [16] C. Corliss, J. Sugar, J. Phys. Chem. Ref. Data 8 (1979) 1–19. [17] O. Launila, B. Lindgren, J. Chem. Phys. 104 (1996) 6418–6422.
Fourier transform emission spectroscopy of the TiF radical in the 407 nm region Takashi Imajo*,1, Yuki Kobayashi, Yoshihiro Nakashima, Keiichi Tanaka, Takehiko Tanaka Department of Chemistry, Faculty of Science, Kyushu University, Hakozaki, Higashiku, Fukuoka 812-8581, Japan Received 1 September 2004; in revised form 21 October 2004 Available online 21 December 2004
Abstract Ultraviolet emission spectra of the TiF radical in the 407 nm region have been observed at a resolution of 0.04 cm1 using a Fourier transform spectrometer. A new electronic assignment of 4C–X4U has been proposed. Rotational analysis has been obtained for the 0–0 and 1–1 vibrational bands of the 4C5/2–X4U3/2, 4C9/2–X4U7/2, and 4C11/2–X4U9/2 subbands and the 0–0 band of 4C7/2–X4U5/2. The lower state rotational and centrifugal distortion constants are consistent with the previous results [J. Mol. Spectrosc. 184 (1997) 186; J. Chem. Phys. 119 (2003) 9496], to the conformation that the lower state of the 407 nm band is the 4U ground electronic state. Rough estimates of the vibrational interval DG(1/2) and the spin–orbit coupling constant A in the 4C state were also obtained. 2004 Elsevier Inc. All rights reserved.
1. Introduction Transition metal atoms with an open d-electron shell have numerous low-lying electronic states with high multiplicities and large orbital angular momenta. As a result electronic spectra of diatomic molecules containing transition metals are very complex, and their characterization has often been the subject of controversy. The electronic spectrum of TiF was first observed in absorption by Diebner and Kay [1] and later in emission by Chatalic et al. [2]. The most prominent group of the bands in the 407 nm region presented in [1,2] was vibrationally analyzed and assigned as belonging to a 4P– X4R transition. These bands were then rotationally analyzed by Shenyavskaya and Dubov [3], who reassigned them to a 2U–2D transition on the basis of the appearance of the rotational structure and theoretical results *
Corresponding author. Fax: +81 3 5981 3656. E-mail address: [email protected] (T. Imajo). 1 Present address: Japan WomenÕs University, Tokyo 112-8681, Japan. 0022-2852/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2004.10.013
[4] which predicted close-lying, low-energy states, 4 R and 2D either of which could be expected to be the ground state. Ram et al. [5] investigated emission bands in the 13 500–16 000 cm1 region using a Fourier transform spectrometer as well as by laser excitation spectroscopy. The observed bands were rotationally analyzed and assigned to a G4U–X4U transition. They proposed that the electronic ground state is X4U, which is supported by ab initio calculation by Boldyrev and Simons [6]. The 4Ur ground state assignment was finally confirmed by the recent observation of the pure rotational spectrum by Sheridan et al. [7]. Ram and Bernath [8] observed similar emission bands of TiCl in the near infrared region and assigned them to a G4U–X4U transition. Theoretical results by Boldyrev and Simons [6] and Sakai et al. [9] support that the electronic ground state of TiCl is 4U. Very recently Maeda et al. [10] measured the pure rotational spectrum of TiCl, which confirmed experimentally the 4U ground state for TiCl. Ram and Bernath [11] suggested that the bands of TiF in the 407 nm region might be due to a 4C–X4U or
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4
U–X4U transition. They also suggested that the band of TiCl in the 420 nm region, which was previously assigned to 2U–2D by Lanini [12] and Phillips and Davis [13], might correspond to a 4C–X4U or 4U–X4U transition. Imajo et al. [14] measured rotationally resolved emission spectrum of TiCl in the 420 nm region by using Fourier transform spectrometer and reassigned the electronic transition to 4C–X4U. The assignment was based on consistency between the lower-state rotational constants derived from the 420 nm band [14] and those from near-infrared bands [8] as well as the argument on the intensity distribution of the rotational structure. In the present work, we have measured emission bands of TiF in the 407 nm region at a resolution of 0.04 cm1 using a Fourier transform spectrometer. As a result, we propose a new electronic assignment of this band as 4C–X4U. Rotational analysis has been obtained for the 0–0 and 1–1 vibrational bands of the 4C5/2–X4U3/ 4 4 4 4 2, C9/2–X U7/2, and C11/2–X U9/2 subbands and the 0–0 4 4 band of C7/2–X U5/2. Intensity pattern of the rotational structure in the 0–0 band of 4C5/2–X4U3/2 was carefully inspected, and the result confirmed that the X value in the upper state is larger than that in the lower state, which provided an evidence for the new electronic assignment.
2. Experimental The experimental setup used for the present emission measurement has been described in detail previously
[14]. Briefly, the TiF radical was produced in an a.c. (60 kHz) discharge of He/TiF4. A mixture of TiF4 powder and sea sand was used for regular vaporization of TiF4 to take place. Emission from a discharge tube was focused onto the entrance aperture of the Fourier transform spectrometer (Bruker IFS120HR) and detected by a photomultiplier (Hamamatsu R-928). The spectral region was limited through an optical interference filter centered at 410 nm with a bandwidth of 10 nm placed in front of the photomultiplier. Total pressure in the discharge tube was maintained at about 1 Torr. The peak discharge current was typically 200 mA. The resolution of the Fourier transform spectrometer was set to 0.04 cm1.
3. Observed spectra and analysis Fig. 1 shows the overview of the observed emission spectrum of TiF in the region 24 480–24 720 cm1, which is the result of a coaddition of several hundred scans with a total effective scanning time of 7 h. Eight Q-branch heads formed by the 0–0 and 1–1 vibrational bands of all four subbands of the 4C–X4U electronic transition of TiF were assigned as shown in Fig. 1. Other features looking like Q-branch heads were left unassigned, although they were probably due to sequence bands with higher vibrational quantum numbers. Attempts to rotationally analyze the corresponding bands were unsuccessful because of line congestion. Fig. 2 shows an expanded spectrum of the
Fig. 1. Overview of the TiF, 4C–X4U emission spectrum.
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
141
Fig. 2. Expanded spectrum of the TiF, 4C5/2 (v = 0)–X4U3/2 (v = 0) band.
4
C5/2 (v = 0)–X4U3/2 (v = 0) band, which has P- and Rbranches with well-resolved rotational structure and a blue-shaded Q-branch partially resolved at high J. Unblended rotational lines have a typical line width of 0.048 cm1 FWHM. Observed peak positions of rotational lines for the 4 C5/2–X4U3/2, 4C7/2–X4U5/2, 4C9/2–X4U7/2, and 4C11/2– X4U9/2 subbands are listed in Tables 1–4. Spectral congestion prevented unambiguous assignment of rotational lines for the 1–1 band of the 4C7/2–X4U5/2 subband, although the peak at 24590.6 cm1 was tentatively assigned to the Q-branch head of this band. It was also difficult to assign the Q-branch lines in the 0–0 band of 4C9/2–X4U7/2 as well as 4C11/2–X4U9/2. Wavenumbers with superscript ÔcÕ in Tables 1–4 are those of strongly blended lines, which were excluded from the least squares fitting. Seven vibronic bands, of which line positions are listed in Tables 1–4, were subjected to rotational analysis. Different subbands were analyzed separately by using a simple expression for the rotational term value 2
F ðJ Þ ¼ Beff J ðJ þ 1Þ Deff J 2 ðJ þ 1Þ :
ð1Þ
Since all observed transitions corresponded to DX = +1, the spin–orbit coupling constant A could not be directly determined. Also, no X doubling was resolved. The rotational analysis of each subband was performed in two steps. In the first step, lower state combi-
nation differences were extracted, and they were least squares fitted to determine the rotational and centrifugal distortion constants in the lower state. In the second step, the lower state constants were fixed, and emission line positions were least squares fitted to determine the rotational and centrifugal distortion constants in the upper state as well as the subband origin. The least squares fitting of the combination differences for the v = 0 vibrational state in the X4U3/2 spin component yielded a standard deviation of 0.006 cm1, and the standard deviation in the fitting of the 0–0 band of the 4C5/2–X4U3/2 subband was 0.004 cm1. These values are close to those expected from the typical line width (0.048 cm1) and the fact that this band is relatively unaffected by line congestion. However, the corresponding standard deviations for other bands were greater presumably due to overlapping of lines; 0.017 and 0.022 cm1 for the 4C5/2–X4U3/2, 1–1 band, 0.010 and 0.015 cm1 for the 4C7/2–X4U5/2, 0–0 band, 0.022 and 0.020 cm1 for the 4C9/2–X4U7/2, 0–0 band, 0.023 and 0.016 cm1 for the 4C9/2–X4U7/2, 1–1 band, 0.018 and 0.012 cm1 for the 4C11/2–X4U9/2, 0–0 band, and 0.012 and 0.014 cm1 for the 4C11/2–X4U9/2, 1–1 band. The optimized molecular constants in the lower and upper states are listed in Tables 5 and 6, respectively. It might be misleading that uncertainties for the rotational and centrifugal distortion constants in the upper state (Table 6, in parentheses) are smaller by almost
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Table 1 Transition frequencies in the 4C5/2–4U3/2 subband or TiF J
0–0 R (J)
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 43.5 44.5 45.5 46.5 47.5 48.5 49.5 50.5 51.5 52.5 53.5 54.5 55.5 56.5 57.5 58.5 59.5 60.5 a b c
1–1 a
24530.113 24530.883c 24531.626c 24532.379c 24533.143 24533.913 24534.687 24535.461 24536.243 24537.027 24537.812 24538.605 24539.401 24540.201 24541.005 24541.814 24542.620c 24543.436 24544.255c 24545.081 24545.904 24546.739 24547.562 24548.410 24549.247 24550.097 24550.944c 24551.800 24552.652 24553.514 24554.383 24555.254c 24556.067c 24556.992 24557.870 24558.755 24559.702c 24560.523 24561.428 24562.349c 24563.213 24564.116 24565.021 24565.925 24566.843 24567.784 24568.669 24569.628c 24570.549 24571.467
OC 2 17 4 3 3 1 1 1 1 1 2 0 0 0 1 3 3 2 2 2 2 3 9 2 3 1 1 2 2 0 5 8 50 0 0 3 64 4 9 33 2 2 4 10 5 19 17 19 13 0
b
Q (J)
a
24527.072 24527.130 24527.181 24527.241 24527.308 24527.371 24527.446 24527.521 24527.603 24527.685 24527.773 24527.866 24527.960 24528.062 24528.166 24528.275 24528.383 24528.501 24528.621 24528.744 24528.875 24529.005 24529.143 24529.284 24529.422 24529.573 24529.728 24529.883 24530.043 24530.203 24530.371 24530.546 24530.721 24530.883c 24531.085 24531.274 24531.466 24531.626c 24531.857 24532.058 24532.275 24532.479 24532.699 24532.917 24533.143 24533.364 24533.593
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
OC
4 3 1 1 3 2 2 1 3 2 2 3 1 3 3 4 0 1 1 0 3 1 2 3 3 0 2 1 1 3 3 0 1 19 1 0 1 35 3 6 4 3 2 1 5 1 2
b
P (J)
a
OC
24524.237 24523.524 24522.823 24522.113 24521.412 24520.717c 24520.025 24519.327 24518.636 24517.963 24517.284c 24516.612c 24515.942 24515.275 24514.617 24513.959c 24513.309 24512.661
9 7 2 1 1 4 6 2 7 2 0 2 0 2 1 1 1 1
24511.377 24510.745 24510.112 24509.488 24508.865 24508.246 24507.635 24507.025 24506.418 24505.821 24505.224
1 2 0 2 1 0 2 1 1 2 1
24504.044 24503.460 24502.882 24502.307 24501.737 24501.171 24500.609 24500.056 24499.500 24498.950 24498.405 24497.870 24497.329 24496.802 24496.270 24495.761 24495.232 24494.730 24494.211 24493.722 24493.217 24492.715 24492.232 24491.742 24491.261 24490.781 24490.298
1 0 0 0 0 1 1 2 1 3 4 0 6 2 8 5 7 4 6 9 4 2 6 2 4 2 8
b
R (J)a
O Cb
24548.298c 24549.050 24549.810 24550.575 24551.340 24552.121 24552.858c 24553.684 24554.470 24555.254c 24556.116 24556.858c 24557.668
53 37 26 16 2 1 49 13 22 36 23 41 42
24560.952c 24561.811 24562.656
42 15 7
Q (J)a
24541.924 24542.044 24542.169c 24542.311 24542.436 24542.620c 24542.723c 24542.864 24543.023 24543.188 24543.338c 24543.520 24543.682 24543.851 24544.043 24544.255c 24544.413 24544.620c 24544.817
O Cb
12 8 5 11 5 53 14 8 15 22 9 22 9 3 2 21 20 19 34
P (J)a
O Cb
24532.379c 24531.626c 24530.986 24530.295
74 2 38 19
24526.308 24525.668 24525.026 24524.382 24523.739 24523.130 24522.565 24521.934 24521.328 24520.717c 24520.193c 24519.544 24518.961 24518.374 24517.796 24517.284c 24516.612c 24516.104 24515.545 24515.000 24514.469 24513.959c
22 20 25 36 51 36 17 0 2 5 69 12 17 12 10 68 39 12 5 7 16 40
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143
Table 2 Transition frequencies in the 4C7/2–4U5/2 subband of TiF J
0–0
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 43.5 44.5 45.5 46.5 47.5 48.5 49.5 50.5 a b c
R (J)a
O Cb
24575.378 24576.124 24576.874 24577.630 24578.382 24579.137 24579.905 24580.667 24581.434 24582.198 24582.969 24583.736 24584.518 24585.294 24586.080 24586.874 24587.653 24588.441 24589.241 24590.016 24590.824 24591.626 24592.425 24593.226 24594.037 24594.846c 24595.651 24596.462 24597.269 24598.077 24598.918 24599.737c 24600.562 24601.389 24602.222 24603.067 24603.890c 24604.733 24605.577 24606.414c 24607.260c 24608.102 24608.972c 24609.879c 24610.662c 24611.528 24612.386 24613.245
6 8 9 6 9 13 5 7 5 9 9 15 9 11 6 5 2 2 8 10 2 6 4 2 8 9 3 1 8 18 3 2 2 4 2 10 3 1 4 3 3 10 8 61 13 7 12 18
Q (J)a
O Cb
24572.509 24572.568 24572.627 24572.679 24572.734 24572.799 24572.867 24572.930 24573.002 24573.080 24573.154 24573.234 24573.318 24573.397 24573.488 24573.577 24573.668 24573.763 24573.864 24573.969 24574.071 24574.169 24574.289 24574.385 24574.515 24574.626c 24574.753 24574.882 24575.008 24575.129c
10 2 3 1 5 2 1 3 2 4 2 3 6 1 5 4 2 1 4 7 5 5 5 13 1 8 3 0 3 14
P (J)a
O Cb
24568.876c 24568.124c 24567.365c 24566.611c 24565.925 24565.212 24564.466 24563.754 24563.059 24562.349c 24561.657 24560.952c 24560.273 24559.586c 24558.908c 24558.219 24557.532 24556.858c 24556.176 24555.509 24554.840 24554.179 24553.514 24552.858c 24552.199 24551.543 24550.944c 24550.249 24549.601 24548.964 24548.298c 24547.694 24547.055 24546.432 24545.799 24545.195 24544.568c 24543.964c 24543.338c 24542.723c 24542.169c 24541.577c 24540.900c
109 79 40 2 31 29 8 14 6 15 9 19 6 4 5 1 7 3 10 5 5 0 2 2 0 3 49 2 2 2 26 5 2 3 5 12 3 14 1 8 42 51 29
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
one order of magnitude than those for the lower state constants (Table 5). This is simply the result of the least squares analysis in which the lower state constants were fixed on determination of the upper state constants. Real uncertainties of the upper state constants are as large as those for the lower state constants, as shown
by the figures in square brackets, as estimated from calculation with slightly varied lower state constants. Q-branch lines could not be assigned for the 0–0 band of 4C9/2–X4U7/2 as well as 4C11/2–X4U9/2. Even in such a case, the J assignment of P - and R-branch lines was uniquely determined by requiring that the resulting molec-
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Table 3 Transition frequencies in the 4C9/2–4U7/2 subband of TiF J
0–0
1–1 a
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 a b c
R (J)
OC
24621.649 24622.390 24623.130 24623.880 24624.627 24625.379 24626.127 24626.875 24627.620 24628.371 24629.121 24629.871 24630.614c 24631.369c 24632.208c 24632.891 24633.648 24634.404 24635.160 24635.918 24636.677 24637.440 24638.197 24638.958 24639.716 24640.477 24641.243 24642.008 24642.788c 24643.543 24644.314 24645.082 24645.848 24646.532 24647.310c 24648.167c 24648.817 24649.566 24650.310 24651.150c
16 13 7 10 9 13 11 8 2 1 3 6 18 18 65 9 9 11 13 13 13 10 12 11 12 11 5 0 20 16 28 37 45 29 9 92 14 20 31 56
b
P (J)
a
24611.954c 24611.359c 24610.662c 24609.879c 24609.100c 24608.421 24607.692 24606.956 24606.244 24605.577 24604.792 24604.131 24603.362 24602.653 24601.931 24601.218c 24600.562 24599.737c 24599.086 24598.377 24597.667 24597.023 24596.258 24595.570 24594.846c 24594.158 24593.464 24592.081 24591.352
OC
100 34 64 8 46 1 7 22 13 40 27 29 23 17 24 24 33 81 21 20 21 43 14 5 13 5 16
b
R (J)a
O Cb
24641.070 24641.945 24642.788c 24643.678c 24644.561 24645.471 24646.390 24647.310c 24648.250c 24649.192 24650.160 24651.150c 24652.135 24653.155 24654.191 24655.255 24656.359
9 12 10 5 1 12 19 14 15 3 2 7 11 11 13 8 18
Q (J)a
O Cb
24629.963 24630.044 24630.126 24630.238 24630.345 24630.453 24630.614c 24630.711 24630.867 24631.021 24631.179 24631.369c 24631.550 24631.760 24631.980 24632.208c 24632.469 24632.735 24633.024 24633.342 24633.740 24634.047
21 15 17 2 7 3 42 6 18 17 7 16 3 4 0 11 6 13 15 7 61 17
P (J)a
O Cb
24617.309 24616.725 24616.162 24615.610 24615.054 24614.526 24614.032 24613.559 24613.063 24612.687c 24612.158 24611.740 24611.359c 24610.985c 24610.662c
16 8 8 6 14 21 9 9 14 66 26 26 9 7 25
42 17
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
ular constants reproduce the position of the unresolved Q-branch head.
4. Discussion In Table 5, the rotational and centrifugal distortion constants in the X4U electronic state obtained in the present study are compared with those previously determined by Ram et al. [5]. They all agree within 2.5r uncertainties. The present ground state constants are also consistent with the millimeter-wave results by Sher-
idan et al. [7], i.e., the effective rotational and centrifugal distortion constants reduced from the constants in [7] are in agreement with the present values within 2.5r. Agreement of the molecular constants provides an evidence for identifying the lower state of the 407 nm band as X4U. Fig. 3 shows an expanded spectrum of the 4C11/ 4 2 (v = 0)–X U9/2 (v = 0) band, where the intensity pattern of R-branch lines is carefully inspected. The sticks inserted in Fig. 3 show their calculated line positions and the numbers are the J00 values. The sequence of R-branch lines is clearly seen and may be traced back
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
145
Table 4 Transition frequencies in the 4C11/2–4U9/2 subband of TiF J
0–0 R (J)
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 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 40.5 a b c
1–1 a
24670.109 24670.840 24671.572 24672.306 24673.041 24673.766 24674.489 24675.226 24675.947 24676.668 24677.395 24678.113 24678.832 24679.552 24680.273 24680.986 24681.701 24682.415 24683.131 24683.844 24684.534 24685.260 24685.968 24686.679 24687.386 24688.089 24688.800 24689.499 24690.156c 24690.918c 24691.605 24692.281 24693.025 24693.712 24694.420 24695.111 24695.821
OC
b
1 2 4 2 3 1 6 4 0 2 2 1 2 0 3 0 0 0 4 5 15 1 0 4 4 1 6 1 46 13 3 29 13 1 5 4 5
a
P (J)
24656.624 24655.917 24655.132 24654.403 24653.635 24652.839 24652.069 24651.297 24650.507 24649.792 24649.019 24648.250c 24647.475 24646.721 24645.946 24645.180 24644.416 24643.678c 24642.863 24642.097 24641.327 24640.556
OC
27 25 1 33 27 6 12 19 43 8 2 0 7 8 2 5 11 43 2 2 2 1
b
R (J)a
O Cb
24687.113 24687.876 24688.636 24689.386 24690.156c 24690.918c 24691.696 24692.474 24693.250 24694.037 24694.819 24695.607 24696.408 24697.212 24698.005 24698.816 24699.635
15 7 4 15 9 13 5 1 2 4 1 1 6 11 0 1 4
Q (J)a
24684.825 24684.996 24685.169 24685.366 24685.576 24685.799 24686.038 24686.298 24686.490
O Cb
P (J)a
O Cb
24675.427 24674.682 24673.952 24673.374c 24672.589 24671.884 24671.198 24670.525 24669.846 24669.169 24668.480 24667.843 24667.175
35 1 26 98 11 1 2 13 12 8 13 11 3
18 13 17 9 1 8 19 37 29
In cm1 units. In 103 cm1 units. Zero weight was given in the fitting.
to the first line with J00 = 4.5. This is consistent with the electronic assignment of this band to 4C11/2–X4U9/2, because the lowest member in the R-branch of this band is R (4.5). Emission intensities of individual R-, P-, and Qbranch lines are expressed by hcB0 J 0 ðJ 0 þ 1Þ I em / m4 S J exp ; kT
ð2Þ
where the Ho¨nl–London factor SJ is given for the R-, Pand Q-branch lines by S RJ ¼
ðJ 00 þ 2 X00 ÞðJ 00 þ 1 X00 Þ ; 2ðJ 00 þ 1Þ
ð3Þ
S PJ ¼
ðJ 00 1 X00 ÞðJ 00 X00 Þ ; 2J 00
ð4Þ
ðJ 00 þ 1 X00 ÞðJ 00 X00 Þð2J 00 þ 1Þ ; 2J 00 ðJ 00 þ 1Þ
ð5Þ
and S QJ ¼
where the upper and lower signs apply to the bands with DX = +1 and DX = 1, respectively [15]. Calculated intensities indicated by filled circles in Fig. 4 are those corresponding to the X 0 = 5/2 fi X00 = 3/2 transition (DX = +1), where a rotational temperature of 500 K was assumed. The intensity pattern, in which P-branch lines rapidly lose intensity with decreasing J whereas R-branch lines remain rather strong, well reproduces
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T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
Table 5 Effective molecular constantsa of TiF in the X4U State Present work 4
b
Ram et al.
Table 6 Effective molecular constants of TiF in the 4C statea Sheridan et al.
B1 D1
0.36240 (14) 5.05 (72) · 107
0.362226 4.198 · 107
B0 D0
0.364724 (15) 4.179 (36) · 107
0.364752 4.252 · 107
0.364725 4.089 · 107
X4U5/2
B0 D0
0.366975 (41) 4.37 (17) · 107
0.366985 4.462 · 107
0.367040 4.472 · 107
X4U7/2
B1 D1
0.36673 (23) 5.3 (16) · 107
0.366805 4.806 · 107
B0 D0
0.36931 (14) 4.68 (74) · 107
0.369379 4.813 · 107
B1 D1
0.36944 (19) 6.7 (27) · 107
0.369222 5.141 · 107
B0 D0
0.37190 (12) 5.14(78) · 107
0.371828 5.145 · 107
X U3/2
X4U9/2
a
4
C5/2
24526.78146 (79) [10] 0.3667734 (13) [151] 4.2500 (39) [372] · 107
m00 B0 D0
24572.0493 (36) [4] 0.3682692 (74) [391] 4.159 (30) [161] · 107
4
C9/2
m11 B1 D1
24629.641 (11) [2] 0.370037 (48) [231] 7.91 (44) [154] · 107
m00 B0 D0
24618.2950 (66) [9] 0.369880 (19) [136] 5.43 (11) [69] · 107
m11 B1 D1
24683.0202 (60) [8] 0.370645 (25) [195] 0.51 (16) [267] · 107
m00 B0 D0
24666.0414 (40) [9] 0.371215 (12) [112] 4.289 (73) [700] · 107
4
C11/2
b
the observed intensity distribution. Intensity distribution of Q-branch lines is also well reproduced. Calculations with the assumption of DX = 1 result in intensity patterns with stronger P-branch lines and weaker Rbranch lines, which do not match the observed pattern. It is therefore confirmed that the band of current interest is a DX = +1 transition, giving a support to the new electronic assignment of this subband to 4C5/2–X4U3/2. Theoretical calculations by Boldyrev and Simons [6] have not dealt with 4C electronic states. A 4C state may be formed if the 3r electron in the ground configuration 1r21p42r21d13r12p1 is promoted to the 3p orbital. For the TiCl radical, Sakai et al. [9] showed that the 3r orbital mainly consists of the 4s atomic orbital of Ti. Similarly, the 3r molecular orbital of TiF is considered to have a character of the Ti, 4s atomic orbital. The 3p orbital probably corresponds to the Ti, 4pp orbital, and therefore, emission transition from the 4C state thus formed to the ground 4U state is expected to be fully allowed, because it corresponds to a single electron transition in the Ti atom. In the present work, the 4C–X4U transition of TiF was observed around 24 600 cm1. Recently we confirmed the 4C–X4U assignment of the TiCl transition around 23 900 cm1 [14]. It is important to note that the 4C–X4U transitions of these radicals appear in almost the same spectral region. The 4C–X4U transition of TiH was also observed around 19 000 cm1 by Launila and Lindgren [17]. Ram and Bernath [8] discussed
m00 B0 D0 C7/2
1
Determined from combination differences. In cm units. Values in parantheses are uncertainties in units of the last digit corresponding to the standard deviation in the least squares fit. The standard deviations for each fit in cml units are 0.017 (X4U3/2,v = 1), 0.006 (X4U3/2,v = 0), 0.010 (X4U5/2,v = 0), 0.023 (X4U7/2,v = 1), 0.022 (X4U7/2,v = 0), 0.012 (X4U9/2,v = 1), and 0.018 (X4U9/2,v = 0). Also see text.
24540.412 (10)c [2]d 0.364257 (24) [146] 3.90 (12) [72] · 107
4
0.369413 4.850 · 107
0.371874 5.279 · 107
m11b B1 D1
In cm1 units. m11 and m00, respectively, mean the origins of the 1–1 and 0–0 vibrational bands. c Values in parentheses are uncertainties in units of the last digit corresponding to the standard deviation in the least squares fit, where the lower state constants are fixed as listed in Table 5. The standard deviations for each fit in cm1 units are 0.022 (4C5/2–X4U3/2, v = 1–1), 0.004 (4C5/2–X4U3/2, v = 0–0), 0.015 (4C7/2–X4U5/2, v = 0–0), 0.016 (4C9/2–X4U7/2, v = 1–1), 0.020 (4C9/2–X4U7/2, v = 0–0), 0.014 (4C11/2– X4U9/2, v = 1–1), and 0.012 (4C11/2–X4U9/2, v = 0–0). Also see text. d Values in square brackets are uncertainties in units of the last digit caused by the uncertainties of the lower state constants. a
b
the correspondence between the lower energy levels of TiX (X = Cl, F, H) and the atomic energy levels of the Ti+ ion. It indicates that the TiX radicals are well described as Ti+X in the lower energy region. It is suggested that this picture may be extended to the 4C state of TiX, which is correlated with the lowest 4G state of the Ti+ ion located 30 000 cm1 above the 4F ground state and belonging to the 3d24p configuration [16]. The ionic picture of Ti+X may give a useful insight for understanding the 4C state of TiX. However, the position of the 4C state of TiH is considerably lower than that of the 4G state of the Ti+ ion. It may indicate that there is a subtle difference in the bonding of TiH. Within the 4C5/2–X4U3/2 transition, the origin of the 1–1 vibrational band is higher than that of the 0–0 vibrational band by 13.6 cm1. This difference, combined with the energy separation DG (1/2) = 650.61 cm1 [5] between the v = 1 and v = 0 levels of the X4U3/2 spin component, allows us to derive the DG (1/2) value for the 4C5/2 spin component as 664.2 cm1. Similarly, the
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
147
Fig. 3. Expanded spectrum of the TiF, 4C11/2 (v = 0)–X4U9/2 (v = 0) band. The sticks represent calculated line positions and the numbers are the rotational quantum numbers J00 in the lower state.
Fig. 4. Expanded spectrum of the TiF, 4C5/2 (v = 0)–X4U3/2 (v = 0) band. Filled circles represent the calculated intensities assuming a rotational temperature of 500 K. See text for details of the calculation of line intensities.
DG (1/2) values for the 4C9/2 and 4C11/2 spin components are obtained as 662.1 and 667.8 cm1, respectively. The DG (1/2) values for various spin components of the 4C electronic state disagree by several cm1, although much closer agreement would be expected without perturbation. For example, the DG (1/2) values are 650.61,
650.68, 650.74, and 650.78 cm1, respectively, for the X = 3/2, 5/2, 7/2, and 9/2 spin components of the ground X4U state [5]. Therefore, we must conclude that vibronic levels of the 4C state are perturbed. It is noted that perturbation of the 4C state is also suggested by anomalous negative values of some centrifugal distor-
148
T. Imajo et al. / Journal of Molecular Spectroscopy 230 (2005) 139–148
tion constants in Table 6. Although the perturbation precludes precise estimation of the vibrational interval in the 4C state, it probably has a value similar to but slightly larger than the value DG (1/2) = 650.70 cm1 in the ground X4U state. Therefore, the stretching force constant slightly increases on excitation from the X4U state to the present 4C state. The difference between the band origins of the 4 C7/2 (v = 0)–X4U5/2 (v = 0) and 4C5/2 (v = 0)–X4U3/ 1 2 (v = 0) transitions is 45.27 cm . Combining this difference with the spin–orbit interval 101.84 cm1 between the X = 5/2 and 3/2 spin components of the X4U (v = 0) state, which Ram et al. [5] determined by laser excitation spectroscopy and corresponds to three times the spin–orbit coupling constant, we may calculate the 7/2–5/2 spin–orbit interval in the 4C (v = 0) state as 147.11 cm1. The value 147.11 cm1 divided by four gives an estimate of the spin–orbit coupling constant A = 36.8 cm1 fot the 4C state. In the same way, the 9/2–7/2 and 11/2–9/2 spin–orbit intervals in the 4 C (v = 0) state are calculated as 148.09 and 149.59 cm1, giving A = 37.0 and 37.4 cm1, respectively. The derived A constants agree within 2%, the average being 37.1 cm1. An alternative method to derive the A constant as well as the true rotational constant from the effective rotational constants, which worked well in the ground X4U state [5], leads to unreliable results for the 4C state, i.e., the effective rotational constants for the X = 5/2 and 11/2 spin components in the v = 0 level for example give A = 45.8 cm1, whereas A = 38.2 cm1 is obtained from the combination of the effective rotational constants for X = 7/2 and 9/2. This shows again that the 4C state is perturbed. For all of the observed bands, the effective rotational constants in the upper and lower states differ very little (less than 1%). This means that the bond length is almost the same in the X4U state and the upper 4C state (The r0 bond length calculated from the average of the effective rotational constants for the four spin compo˚ in the nents of the v = 0 vibrational state is 1.8343 A ˚ in the 4C excited state). This X4U state and 1.8323 A and the similarity of the stretching force constant de-
scribed above indicate that the lower and upper states of the present transition have closely resembling potential curves, consistent with the absence of Dv „ 0 transitions.
Acknowledgments The authors thank Professor P. F. Bernath at Waterloo University, Canada for valuable discussions on electronic assignments of the emission spectra of TiF in the near ultraviolet region. Financial supports from the Ministry of Education, Science, Sports, and Culture are acknowledged.
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