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High-Resolution Fourier Transform Emission Spectroscopy of the TiCl Radical in the 420-nm Region
Journal of Molecular Spectroscopy 203, 216 –227 (2000) doi:10.1006/jmsp.2000.8184, available online at http://www.idealibrary.com on
High-Resolution Fourier Transform Emission Spectroscopy of the TiCl Radical in the 420-nm Region Takashi Imajo, DongBing Wang, Keiichi Tanaka, and Takehiko Tanaka Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki, Higashiku, Fukuoka 812-8581, Japan Received April 26, 2000; in revised form June 13, 2000
Emission spectra of the TiCl radical in the 420-nm region have been observed at a resolution of 0.04 cm ⫺1 using a Fourier transform spectrometer. A new electronic assignment of 4 ⌫–X 4 ⌽ has been proposed. Rotational analysis has been provided for the 0 – 0 and 1–1 vibrational bands of the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 and 4 ⌫ 7/ 2 –X 4 ⌽ 5/ 2 spin components and the 0 – 0 band of 4 ⌫ 9/ 2 –X 4 ⌽ 7/ 2 . © 2000 Academic Press 1. INTRODUCTION
Transition metal atoms with open d-electron shells have many low-lying electronic states with high multiplicities and large orbital angular momenta. As a result electronic spectra of diatomic molecules containing transition metals are often very complex. As for titanium-containing diatomic radicals, detailed experimental information has been accumulated for TiN (1– 6) and TiO (7–14), and the electronic states of these radicals have been well established. By contrast, spectroscopic data on titanium halides are much less satisfactory. There have been published a number of spectroscopic studies of TiCl (15–24). The bands of TiCl in the 420-nm region have been interpreted differently by different authors. The strong bands in this region were first assigned to a doublet transition (16). The 4⌸– 4⌺ ⫺ electronic assignment was then proposed by Rao (17) and by Shenyavskaya et al. (18). Later, Lanini (21) interpreted the most prominent bands as due to a 2 ⌽– 2⌬ system on the basis of rotational analysis. Phillips and Davis (23) made a detailed analysis of emission bands in the 410 – 420 nm region measured by a grating spectrometer with a reciprocal dispersion of 0.1 Å mm ⫺1 and assigned these bands to four doublet transitions. Recently Ram and Bernath (24) investigated the emission spectrum of TiCl in the near-infrared region by Fourier transform spectroscopy and observed three new electronic transitions, C 4 ⌬–X 4 ⌽, G 4 ⌽–X 4 ⌽, and G 4 ⌽–C 4 ⌬. Their assignments are supported by ab initio calculations by Boldyrev and Simons (25) and Sakai et al. (26) in which the 4⌽ state is assigned as the electronic ground state of TiCl. Very recently Ram and Bernath (27) reported a new band system of TiCl in the region 11 000 –13 500 cm ⫺1, which was assigned to a 2 ⌽–a 2 ⌽ transition. Ram and Bernath (28) also measured emission spectra of the isovalent ZrCl molecule and observed the C 4 ⌬–X 4 ⌽ transition in the infrared region, which was analogous to the C 4 ⌬–X 4 ⌽ transition of TiCl. They suspected that the emission band of ZrCl in the 420-nm region previously
assigned as 4⌸– 4⌺ by Jordan et al. (29) was a 4 ⌬–X 4 ⌽ or a 4 ⌫–X 4 ⌽ transition. Analogously, Bernath (30) suggested that the emission band of TiCl in the 420-nm region might be a 4 ⌬–X 4 ⌽ or a 4 ⌫–X 4 ⌽ transition. In the present work we have measured emission bands of TiCl in the 420-nm region at a resolution of 0.04 cm ⫺1 using a Fourier transform spectrometer. As a result, we propose a new electronic assignment of this band as 4 ⌫–X 4 ⌽. Rotational analysis has been obtained for the 0 – 0 and 1–1 vibrational bands of the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 and 4 ⌫ 7/ 2 –X 4 ⌽ 5/ 2 spin components and the 0 – 0 band of 4 ⌫ 9/ 2 –X 4 ⌽ 7/ 2 . Intensity pattern of the rotational structure in the 0 – 0 band of 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 was carefully inspected, and the result confirmed that the ⍀ value in the upper state is larger than that in the lower state, which provided evidence for the new electronic assignment. The present work also demonstrates the power of Fourier transform emission spectroscopy for the study of novel radicals which have transitions in the ultraviolet region. 2. EXPERIMENTAL
The emission cell used for the present study is shown in Fig. 1. It was a 30-cm-long, 8-mm inner-diameter Pyrex tube, to which two water-cooled sidearms containing discharge electrodes were attached. CaF 2 windows sealed off both ends of the cell. Helium was fed through the side arms, and a trace amount of the TiCl 4 vapor was introduced through an inlet near an end of the cell. An oil rotary pump (60 m 3/h) evacuated the cell, and the total pressure was maintained at about 1 Torr. A high-voltage ac of 70 kHz generated by a combination of an audio power amplifier (Accuphase P-600, 1 kW) and a step-up transformer (1:30) was applied between the electrodes through a ballast resistor (3 k⍀). The peak current of the discharge was typically 200 mA. The emission cell was placed in front of the entrance aperture (1.2 mm) of the Fourier transform spectrometer (Bruker
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unresolved Q branch which forms a blue-shaded head. Unblended rotational lines have a linewidth of 0.045 cm ⫺1 FWHM. Lines of the two isotopomers Ti 35Cl and Ti 37Cl are well resolved in this part of the spectrum. Figure 5 is an expanded spectrum of the 4 ⌫ 9/ 2 (v ⫽ 0)– 4 X ⌽ 7/ 2 (v ⫽ 0) band. The Q branch of this band has a structure considerably different from that in Fig. 4. This is caused by perturbation in the 4⌫ 9/2 (v ⫽ 0) state, as will be discussed in detail in the following section. 4. ANALYSIS
Five stronger vibronic bands, i.e., the 0 – 0 and 1–1 vibrational bands of the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 and 4 ⌫ 7/ 2 –X 4 ⌽ 5/ 2 spin components and the 0 – 0 band of 4 ⌫ 9/ 2 –X 4 ⌽ 7/ 2 , were subjected to rotational analysis. Wavenumbers of P- and R-branch lines in each band were used in the present analysis. Different spin components were analyzed separately by using a simple expression for the rotational term value: FIG. 1. Schematic diagram of the discharge emission cell. High-voltage ac is applied between the water-cooled electrodes in the side arms. Ultraviolet emission is focused by a CaF 2 lens onto the entrance aperture of the Fourier transform spectrometer.
IFS120HR). The light source module originally attached to the spectrometer had been removed. A CaF 2 lens ( f ⫽ 5 cm) focused emission from the discharge tube onto the aperture. Ultraviolet emission was monitored by a photomultiplier (Hamamatsu R-928), in front of which a 25-cm grating monochromator was placed (Fig. 2). The monochromator worked as an optical band-pass filter, and its slits were adjusted so as to give a typical bandwidth of 200 cm ⫺1. Ultraviolet radiation emerging from the Michelson interferometer was focused onto the entrance slit of the monochromator by a concave mirror (R ⫽ 50 cm). The resolution of the Fourier transform spectrometer was set to 0.04 cm ⫺1. The spectrum was recorded by accumulating 800 interferometer scans, taking 250 min in total. Observed wavenumbers were calibrated against emission lines of the Fe atom, which were obtained in a separate measurement. The standard vacuum wavenumber values were taken from Ref. (31).
F共 J兲 ⫽ B effJ共 J ⫹ 1兲 ⫺ D eff J 2 共 J ⫹ 1兲 2 .
[1]
Since all observed transitions corresponded to ⌬⍀ ⫽ ⫹1, the spin– orbit coupling constant A could not be directly determined. Also, no ⍀ doubling was resolved. 1. The 0 – 0 Band of the 4⌫ 5/2–X 4⌽ 3/2 Spin Component This band is the strongest of the observed bands and relatively isolated from other bands. As a result, an appreciable number of lines of the Ti 37Cl isotopomer were observed separately from those of Ti 35Cl. Line positions of the Ti 35Cl and Ti 37Cl isotopomers belonging to this band are listed in Tables 1 and 2, respectively. These line positions were determined by
3. OBSERVED SPECTRA
The emission spectrum of TiCl was measured in the region 23 820 –24 100 cm ⫺1 with a center wavenumber of the monochromator around 23 860 cm ⫺1. The overview of the spectrum is shown in Fig. 3. Eleven vibronic bands were assigned as belonging to the 4 ⌫–X 4 ⌽ electronic transition of TiCl, as shown in Fig. 3. Figure 4 shows an expanded spectrum of the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band. This band consists of P and R branches well resolved into rotational structure and an
FIG. 2. Schematic diagram of the optical setup used in the present measurement. Ultraviolet emission from the discharge tube was passed through a Michelson interferometer and focused onto a slit of a monochromator used as an optical band-pass filter. A typical spectral bandwidth of the monochromator was 200 cm ⫺1.
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FIG. 3.
Overview of the TiCl, 4 ⌫–X 4 ⌽ emission spectrum.
a deconvolution procedure, in which each line was assumed to have a Gaussian lineshape with a full width at half-maximum of 0.045 cm ⫺1. Several Ti 37Cl lines are overlapped by Ti 35Cl lines. Positions of the Ti 37Cl lines observed as shoulders to the Ti 35Cl peaks are superscripted with “d” in Table 2. Superscripted with “c” in Tables 1 and 2 are positions of the peaks formed by completely overlapping Ti 35Cl and Ti 37Cl lines. The corresponding features were treated as single Gaussian peaks in the deconvolution procedure: note that identical values are listed in Tables 1 and 2. In an early stage of the analysis, peaks of Ti 35Cl and those of 37 Ti Cl were fitted independently by the least-squares method, yielding standard deviations of 0.004 and 0.006 cm ⫺1, respectively. In the final stage, however, they were subjected to a simultaneous least-squares analysis so as to extract as unbiased information as possible from the completely overlapping peaks with superscript “c.” The principle is as follows. We assume that a Ti 35Cl line is located centered at 35 and a Ti 37Cl line at 37 and that they each have a Gaussian lineshape with the same linewidth ⌬ (FWHM). Then, the lineshape function for the overlapping lines will be
FIG. 4.
冋
g共 兲 ⫽ c 35 exp ⫺4 ln 2
冉
冊册 冋 冉
⫺ 35 ⌬
2
⫺ 37 ⫹ c 37 exp ⫺4 ln 2 ⌬
冊册
[2]
2
,
where c 35 and c 37 are relative line intensities. If the difference between the center positions 35 and 37 is sufficiently small compared to the linewidth ⌬, the lineshape g( ) around the peak is approximated by a quadratic function of ,
冋
g共 兲 ⬵ c 35 1 ⫺ 4 ln 2
冉
⫺ 35 ⌬
⫹ c 37
冋
冊册 2
冉
⫺ 37 1 ⫺ 4 ln 2 ⌬
冊册
[3]
2
,
of which the peak position is easily calculated as:
max ⫽
c 35 35 ⫹ c 37 37 . c 35 ⫹ c 37
Expanded spectrum of the TiCl, 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band.
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[4]
FOURIER TRANSFORM EMISSION SPECTROSCOPY OF TiCl
FIG. 5.
219
Expanded spectrum of the TiCl, 4 ⌫ 9/ 2 (v ⫽ 0)–X 4 ⌽ 7/ 2 (v ⫽ 0) band.
In the present analysis, we calculated the 35 and 37 values from the molecular constants of respective isotopomers and took weighted averages as given in Eq. [4]. The resulting wavenumbers were fitted to the observed wavenumbers of the completely overlapping lines. The ratio c 35 :c 37 was simply fixed to 3:1, the isotopic abundance ratio of chlorine, although the overlapping Ti 35Cl and Ti 37Cl transitions have slightly different J values. Table 3 lists the molecular constants thus optimized for the Ti 35Cl and Ti 37Cl isotopomers. Trace (A) of Fig. 6 shows an expanded portion of the observed spectrum for the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band. The Q-branch contour of this band was simulated using the molecular constants listed in Table 3. In the simulation, each line was assumed to have a Gaussian lineshape with a width of 0.05 cm ⫺1 FWHM, and transitions from Q(2.5) to Q(99.5) of Ti 35Cl and Ti 37Cl isotopomers were superposed. The simulated spectrum reproduced the observed Q-branch head very well. However, if we shifted the J assignment of the P- and R-branch lines of either one of the isotopomers or both, the simulated spectrum had a considerably different shape and did not match the observed. The J assignment was thus unambiguously determined for the both isotopomers. 2. The 1–1 Band of 4⌫ 5/2–X 4⌽ 3/2 and 0 – 0 and 1–1 Bands of 4⌫ 7/2–X 4⌽ 5/2 In these bands, stronger features are mostly assigned to Pand R-branch transitions of Ti 35Cl. It was difficult to obtain a sufficient number of definitely assigned Ti 37Cl lines to justify the rotational analysis of this isotopomer. Observed line positions of Ti 35Cl transitions are summarized in Tables 1 and 4. They were subjected to least-squares analysis, and the optimized molecular constants are given in Table 3. 3. The 0 – 0 Band of 4⌫ 9/2–X 4⌽ 7/2 Expanded spectrum of the 4 ⌫ 9/ 2 (v ⫽ 0)–X 4 ⌽ 7/ 2 (v ⫽ 0) band is shown in Fig. 5. P-branch lines of Ti 35Cl with 10.5 ⱕ
J⬙ ⱕ 56.5 and R-branch lines with 4.5 ⱕ J⬙ ⱕ 56.5 were assigned for this band. Observed line positions are listed in Table 5. The line positions fit fairly well to the simple energy formula of Eq. [1] up to J⬙ ⫽ 39.5, above which the observed line positions show systematic deviation from the calculated positions in both P and R branches, presumably due to rotational perturbation. Combination differences corresponding to the energy differences in the lower state provide a satisfactory fit in the range of J⬙ ⫽ 8.5–56.5, which suggests that the rotational perturbation occurs in the upper state, 4⌫ 9/2 (v ⫽ 0). Effective rotational constants for the lower state, X 4 ⌽ 7/ 2 (v ⫽ 0), were determined by a least-squares analysis of the combination differences. Effective rotational constants of the 4 ⌫ 9/2 (v ⫽ 0) state were then derived from the line positions in the range of J⬙ ⫽ 4.5–39.5, where the lower state constants were fixed as determined from the combination differences. Table 3 lists the effective rotational constants thus obtained for the X 4 ⌽ 7/ 2 (v ⫽ 0) and 4⌫ 9/2 (v ⫽ 0) states. As mentioned in the previous section, the Q branch of this band has a strange shape. To clarify the reason for this as well as to verify the J assignment, we performed a simulation of the Q branch. Energy term values in the X 4 ⌽ 7/ 2 (v ⫽ 0) state were calculated using the molecular constants determined by Ram and Bernath (24): these constants are in good agreement with the present results (vide infra). Perturbed term values in the 4 ⌫ 9/2 (v ⫽ 0) state were obtained by adding the observed wavenumbers of P- or R-branch transitions to the calculated term values in the lower state. The term values in the X 4 ⌽ 7/ 2 (v ⫽ 0) and 4⌫ 9/2 (v ⫽ 0) states were then combined to calculate the positions of Q-branch transitions. Transitions from Q(3.5) to Q(56.5) of Ti 35Cl were superposed, where each line was assumed to have a Gaussian lineshape with a width of 0.05 cm ⫺1 FWHM. Line intensities were calculated without taking the effect of the rotational perturbation into account. Trace (B) of Fig. 7 shows the Q-branch contour thus simulated, which is compared with the observed spectrum [Trace (A)]. Sticks
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IMAJO ET AL.
TABLE 1 Transition Frequencies in the 4⌫ 5/2–X 4⌽ 3/2 Subband of Ti 35Cl
In cm ⫺1 units. In 10 ⫺3 cm ⫺1 units. c Transition frequency was calculated as weighted average of Ti 35Cl and Ti 37Cl frequencies. * Zero weight was given in the fitting. a
b
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TABLE 1—Continued
below Trace (B) represent the calculated positions and intensities of individual Q-branch lines. Numbers below the sticks are the rotational quantum numbers J⬙. The simulated spectrum reproduces the observed shape of the Q branch. Therefore, the strange shape of the Q branch is explained as distorted by the rotational perturbation. The present J assignment was also confirmed. 5. DISCUSSION
The rotational constants in the X 4 ⌽ electronic state obtained in the present study agree within the experimental uncertainty (3) with those previously determined by Ram and Bernath (24). Centrifugal distortion constants are also consistent between the present results and Ram and Bernath’s except for the X 4 ⌽ 5/ 2 (v ⫽ 0) state. Agreement of the molecular constants provides evidence for identifying the lower state of the 420-nm band as X 4 ⌽. Trace (A) of Fig. 6 shows an expanded spectrum of the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band near the Q-branch head. The
Q-branch contour simulated as described in the previous section was subtracted from the observed spectrum and the residual is shown in Trace (B) on an expanded scale, where the intensity pattern of low J P- and R-branch lines was carefully inspected. The stick diagram attached to Trace (C) shows the calculated line positions and intensities for P- and R-branch lines of Ti 35Cl, where the numbers below the sticks designate the J⬙ values. The sequence of R-branch lines of Ti 35Cl is clearly seen in Trace (B), and the sequence may be traced up to J⬙ ⫽ 1.5. This is consistent with the electronic assignment of this band to 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 , because the lowest member in the R branch of this band is R(1.5). Emission intensities of individual R- and P-branch lines are expressed by
冋
I em ⬀ 4 S J exp ⫺
册
hcB⬘J⬘共 J⬘ ⫹ 1兲 , kT
[5]
where the Ho¨nl–London factor S J is given for the R- and P-branch lines by
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TABLE 2 Transition Frequencies in the 4⌫ 5/2 (vv ⴝ 0)–X 4⌽ 3/2 (vv ⴝ 0) Subband of Ti 37Cl
S JR ⫽
共 J⬙ ⫹ 2 ⫾ ⍀⬙兲共 J⬙ ⫹ 1 ⫾ ⍀⬙兲 2共 J⬙ ⫹ 1兲
[6]
共 J⬙ ⫺ 1 ⫿ ⍀⬙兲共 J⬙ ⫿ ⍀⬙兲 , 2J⬙
[7]
and S JP ⫽
respectively, where the upper and lower signs apply to the bands with ⌬⍀ ⫽ ⫹1 and ⌬⍀ ⫽ ⫺1, respectively (32). Calculated intensities shown as the stick diagram in Fig. 6 are those corresponding to the ⍀⬘ ⫽ 5/2 3 ⍀⬙ ⫽ 3/2 transition, where a rotational temperature of 400 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 the observed intensity distribution. Calculations with the assumption of ⌬⍀ ⫽ ⫺1 result in intensity patterns with stronger P-branch lines and weaker R-branch lines, which do not match the observed pattern. It is therefore confirmed that the band of current interest is a ⌬⍀ ⫽ ⫹1 transition, giving support to the new electronic assignment of this subband to 4 ⌫ 5/ 2 – X 4 ⌽ 3/ 2 . Theoretical calculations by Boldyrev and Simons (25) and Sakai et al. (26) have not dealt with 4 ⌫ electronic states. A 4 ⌫ state may be formed if the 3 electron in the ground configuration 1 2 1 4 2 2 1␦ 1 3 1 2 1 is promoted to the 3 orbital. According to Sakai et al. (26), the 3 orbital mainly consists of the 4s orbital of Ti. The 3 orbital probably corresponds to the Ti, 4p orbital. Therefore, emission
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may be extended to higher energy region, a 4⌫ state of TiX may be correlated with the lowest 4 G state of the Ti ⫹ ion, which is located ⬃30 000 cm ⫺1 above the ground state and belongs to the 3d 2 4p configuration (33). Launila and Lindgren (34) have observed a 4⌫ state of TiH at T 0 ⫽ 18 878.10 cm ⫺1. The 4⌫ state of TiF has not been reported so far, but Bernath (30) suspected that an emission band in the 405-nm region may be due to a 4 ⌫–X 4 ⌽ or 4 ⌬–X 4 ⌽ transition. Very recently we confirmed the 4 ⌫–X 4 ⌽ assignment for this band (35) and determined T 0 to be 24 595.18 cm ⫺1. The term values of the 4⌫ states of TiH and TiF are comparable with that of the present 4 ⌫ state of TiCl as well as that of the 4 G state of the Ti ⫹ ion. The ionic picture of Ti ⫹ X ⫺ may give a useful insight for understanding the 4⌫ state of TiCl. Within the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 transition, the origin of the 1–1 vibrational band is higher than that of the 0 – 0 vibrational band by 26.7929 cm ⫺1. This difference, combined with the energy separation ⌬G(1/ 2) ⫽ 404.3663 cm ⫺1 (24) between the v ⫽ 1 and v ⫽ 0 levels of the X 4 ⌽ 3/ 2 spin component, allows us to derive the ⌬G(1/ 2) value for the 4⌫ 5/2 spin component as 431.1592 cm ⫺1. Similarly, the ⌬G(1/ 2) value for the 4⌫ 7/2 spin component is obtained as 435.9795 cm ⫺1. The latter two values disagree by about 5 cm ⫺1, although much closer agreement would be expected without perturbation. For example, the ⌬G(1/ 2) value is 404.3663, 404.3337, 404.3167, and 404.3032 cm ⫺1, respectively, for the ⍀ ⫽ 3/2, 5/2, 7/2, and 9/2 spin components of the ground X 4 ⌽ state (24). Therefore, we must conclude that at least one of the 4⌫ 5/2 (v ⫽ 0), 4⌫ 5/2 (v ⫽ 1), 4⌫ 7/2 (v ⫽ 0), and 4⌫ 7/2 (v ⫽ 1) levels is perturbed. Although the perturbation precludes precise estimation of the vibrational
TABLE 3 Effective Molecular Constants a of TiCl in the 4⌫ and X 4⌽ States
transition from the 4 ⌫ state thus formed to the ground 4 ⌽ state is expected to be fully allowed, because it corresponds to a single electron transition in the Ti atom. Ram and Bernath (24) discussed correlation between the atomic energy levels of the Ti ⫹ ion and lower energy levels of TiX (X ⫽ Cl, F, H). It indicates that the TiX radicals are well described as Ti ⫹ X ⫺ in the lower energy region. If this picture
FIG. 6. Trace (A) shows the observed spectrum for the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band near the Q-branch head. The simulated Q-branch contour was subtracted from Trace (A) and the residual is shown in Trace (B) on an expanded scale. The stick diagram (C) represents the calculated positions and intensities of individual Q-branch lines of Ti 35Cl. The numbers below the sticks are the J⬙ values. See text for details of calculations of the Q-branch contour and line intensities.
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TABLE 4 Transition Frequencies in the 4⌫ 7/2–X 4⌽ 5/2 Subband of Ti 35Cl
In cm ⫺1 units. In 10 ⫺3 cm ⫺1 units. * Zero weight was given in the fitting. a
b
interval in the 4⌫ state, it probably has a value similar to but slightly larger than the value ⌬G(1/ 2) ⫽ 404.33 cm ⫺1 in the ground X 4 ⌽ state. Therefore, the stretching force constant
slightly increases on excitation from the X 4 ⌽ state to the present 4⌫ state. The difference between the band origins of the 4 ⌫ 7/ 2 (v ⫽
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TABLE 4—Continued
0)–X 4 ⌽ 5/ 2 (v ⫽ 0) and 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) transitions is 54.9899 cm ⫺1 . Combining this difference with the spin– orbit interval 117 cm ⫺1 between the ⍀ ⫽ 5/2 and 3/2 spin components of the X 4 ⌽ (v ⫽ 0) state, we may calculate the 7/2–5/2 spin– orbit interval in the 4 ⌫ (v ⫽ 0) state as 172 cm ⫺1 . The above value of 117 cm ⫺1 is obtained as three times the spin– orbit coupling constant A ⬙0 ⫽ 39 cm ⫺1 , which was estimated by Ram and Bernath (24) from the effective rotational constants for the different spin components. The value 172 cm ⫺1 divided by four gives an estimate of the spin– orbit coupling constant A ⫽ 43 cm ⫺1 for the 4 ⌫ state. In the same way, the 7/2–5/2 spin– orbit interval in the 4 ⌫ (v ⫽ 1) state is calculated as 176 cm ⫺1 , giving A ⫽ 44 cm ⫺1 . The discrepancy in the two A values is again ascribed to the perturbation described above but these values may be useful as a rough estimate of the spin– orbit coupling constant in the 4 ⌫ electronic state. The method to derive the A constant and the true rotational constant from the effective rotational constants, which worked well in the ground X 4 ⌽ state (24), resulted in unreliable values for the 4 ⌫ state, i.e., the effective rotational constants for the ⍀ ⫽ 5/2 and 7/2 spin components in the v ⫽ 0 level gave A ⫽ 36 cm ⫺1 , whereas A ⫽ 72 cm ⫺1 was obtained from the corresponding constants in the v ⫽ 1 level. For most of the observed bands, the effective rotational constants in the upper and lower states differ very little (less than 0.4%). This means that the bond length is almost the same in the X 4 ⌽ state and the upper 4⌫ state. This and the similarity of the stretching force constant described above indicate that the lower and upper states of the present transition have closely
resembling potential curves, consistent with the absence of ⌬v ⫽ 0 transitions. The effective rotational constants of the Ti 37Cl isotopomer were obtained for the 4⌫ 5/2 (v ⫽ 0) and X 4 ⌽ 3/ 2 (v ⫽ 0) spin components. These constants are compared with the constants of Ti 35Cl for the corresponding states. The constants of Ti 37Cl in the 4⌫ 5/2 (v ⫽ 0) and X 4 ⌽ 3/ 2 (v ⫽ 0) spin components are 0.9689 and 0.9690 times, respectively, those of Ti 35Cl. These ratios are in good agreement with the expected ratio 0.96876 calculated from the reduced masses.
FIG. 7. Trace (A) shows an expanded spectrum of the 4 ⌫ 9/ 2 (v ⫽ 0)–X 4 ⌽ 7/ 2 (v ⫽ 0) band near the Q branch. Trace (B) is a calculated contour of the Q branch. The stick diagram represents the calculated positions and intensities of individual Q-branch lines of Ti 35Cl. The numbers below the sticks are the J⬙ values. See text for details of the calculation of the Q-branch contour and line intensities.
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TABLE 5 Transition Frequencies in the 4⌫ 9/2 (vv ⴝ 0)–X 4⌽ 7/2 (vvv ⴝ 0) Subband of Ti 35Cl
ACKNOWLEDGMENTS The authors thank Dr. S. Civis at Heyrousky Institute of Physical Chemistry, Czech Republic for helpful discussions on the experimental setup. They are also grateful to Professor P. F. Bernath at Waterloo University, Canada for valuable discussions on electronic assignments of the emission spectra of TiCl in the ultraviolet region. Financial support from the Ministry of Education, Science, Sports, and Culture are acknowledged.
REFERENCES 1. T. C. Steimle, J. E. Shirley, K. Y. Jung, L. R. Russon, and C. T. Scurlock, J. Mol. Spectrosc. 144, 27–31 (1990). 2. D. A. Fletcher, C. T. Scurlock, K. Y. Jung, and T. C. Steimle, J. Chem. Phys. 99, 4288 – 4299 (1993). 3. C. Athenour, J.-L. Femenias, and T. M. Dunn, Can. J. Phys. 60, 109 –116 (1980). 4. J. A. Bates, N. L. Ranieri, and T. M. Dunn, Can. J. Phys. 54, 915–916 (1975). 5. T. M. Dunn, L. K. Hanson, and K. A. Rubinson, Can. J. Phys. 48, 1657–1663 (1969).
6. A. E. Douglas and P. M. Veillette, J. Phys. Chem. 72, 5378 –5380 (1980). 7. C. Amiot, E. M. Azaroual, P. Luc, and R. Vetter, J. Phys. Chem. 102, 4375– 4381 (1995). 8. W. H. Hocking, M. C. L. Gerry, and A. J. Merer, Can. J. Phys. 57, 54 – 61 (1979). 9. G. R. Braandes and D. C. Galehouse, J. Mol. Spectrosc. 109, 345–351 (1985). 10. T. C. Steimle and J. E. Shirley, J. Chem. Phys. 91, 8000 – 8002 (1989). 11. C. Linton, J. Mol. Spectrosc. 50, 235–245 (1974). 12. C. Linton, Can. J. Phys. 50, 312–316 (1971). 13. C. M. Pathak and H. B. Palmer, J. Mol. Spectrosc. 33, 137–146 (1970). 14. J. G. Phillips, Astrophys. J. 169, 185–189 (1971). 15. A. Fowler, Proc. R. Soc. London A 79, 509 (1907). 16. K. R. More and A. H. Parker, Phys. Rev. 52, 1150 –1152 (1937). 17. V. R. Rao, Indian J. Phys. 23, 535 (1949). 18. E. A. Shenyavskaya, T. Y. Kuzyakov, and V. M. Tatevskii, Opt. Spectrosc. (SSSR) 12, 197–199 (1962). 19. A. Chatalic, P. Deschamps, and G. Pannetier, C. R. Acad. Sci. Paris 268, 1111–1113 (1969).
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FOURIER TRANSFORM EMISSION SPECTROSCOPY OF TiCl 20. R. L. Diebner and J. K. Kay, J. Chem. Phys. 51, 3547–3554 (1969). 21. K. P. Lanini, Ph.D. dissertation, University of Michigan, Ann Arbor, MI, 1972. 22. T. C. DeVore, High Temp. Sci. 15, 263–273 (1982). 23. J. G. Phillips and S. P. Davis, Astron. Phys. J. Suppl. Ser. 71, 163–172 (1989). 24. R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 186, 113–130 (1997). 25. A. I. Boldyrev and J. Simons, J. Mol. Spectrosc. 188, 138 –141 (1998). 26. Y. Sakai, K. Mogi, and E. Miyoshi, J. Chem. Phys. 111, 3989 –3994 (1999). 27. R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 195, 299 –307 (1999).
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28. R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 186, 335–348 (1997). 29. K. J. Jordan, R. H. Lipson, N. A. McDonald, and D. S. Yang, Chem. Phys. Lett. 193, 499 –506 (1992). 30. P. F. Bernath, private communication. 31. V. Kaufman and B. Edlen, J. Phys. Chem. Ref. Data 3, 825– 843 (1974). 32. I. Kovacs, “Rotational Structure in the Spectra of Diatomic Molecules,” p. 121, American Elsevier, New York, 1969. 33. C. Corliss and J. Sugar, J. Phys. Chem. Ref. Data 8, 1–17 (1979). 34. O. Launila and B. Lindgren, J. Chem. Phys. 104, 6418 – 6422 (1996). 35. T. Imajo, Y. Kobayashi, Y. Nakashima, K. Tanaka, and T. Tanaka, unpublished manuscript.
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High-Resolution Fourier Transform Emission Spectroscopy of the TiCl Radical in the 420-nm Region Takashi Imajo, DongBing Wang, Keiichi Tanaka, and Takehiko Tanaka Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki, Higashiku, Fukuoka 812-8581, Japan Received April 26, 2000; in revised form June 13, 2000
Emission spectra of the TiCl radical in the 420-nm region have been observed at a resolution of 0.04 cm ⫺1 using a Fourier transform spectrometer. A new electronic assignment of 4 ⌫–X 4 ⌽ has been proposed. Rotational analysis has been provided for the 0 – 0 and 1–1 vibrational bands of the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 and 4 ⌫ 7/ 2 –X 4 ⌽ 5/ 2 spin components and the 0 – 0 band of 4 ⌫ 9/ 2 –X 4 ⌽ 7/ 2 . © 2000 Academic Press 1. INTRODUCTION
Transition metal atoms with open d-electron shells have many low-lying electronic states with high multiplicities and large orbital angular momenta. As a result electronic spectra of diatomic molecules containing transition metals are often very complex. As for titanium-containing diatomic radicals, detailed experimental information has been accumulated for TiN (1– 6) and TiO (7–14), and the electronic states of these radicals have been well established. By contrast, spectroscopic data on titanium halides are much less satisfactory. There have been published a number of spectroscopic studies of TiCl (15–24). The bands of TiCl in the 420-nm region have been interpreted differently by different authors. The strong bands in this region were first assigned to a doublet transition (16). The 4⌸– 4⌺ ⫺ electronic assignment was then proposed by Rao (17) and by Shenyavskaya et al. (18). Later, Lanini (21) interpreted the most prominent bands as due to a 2 ⌽– 2⌬ system on the basis of rotational analysis. Phillips and Davis (23) made a detailed analysis of emission bands in the 410 – 420 nm region measured by a grating spectrometer with a reciprocal dispersion of 0.1 Å mm ⫺1 and assigned these bands to four doublet transitions. Recently Ram and Bernath (24) investigated the emission spectrum of TiCl in the near-infrared region by Fourier transform spectroscopy and observed three new electronic transitions, C 4 ⌬–X 4 ⌽, G 4 ⌽–X 4 ⌽, and G 4 ⌽–C 4 ⌬. Their assignments are supported by ab initio calculations by Boldyrev and Simons (25) and Sakai et al. (26) in which the 4⌽ state is assigned as the electronic ground state of TiCl. Very recently Ram and Bernath (27) reported a new band system of TiCl in the region 11 000 –13 500 cm ⫺1, which was assigned to a 2 ⌽–a 2 ⌽ transition. Ram and Bernath (28) also measured emission spectra of the isovalent ZrCl molecule and observed the C 4 ⌬–X 4 ⌽ transition in the infrared region, which was analogous to the C 4 ⌬–X 4 ⌽ transition of TiCl. They suspected that the emission band of ZrCl in the 420-nm region previously
assigned as 4⌸– 4⌺ by Jordan et al. (29) was a 4 ⌬–X 4 ⌽ or a 4 ⌫–X 4 ⌽ transition. Analogously, Bernath (30) suggested that the emission band of TiCl in the 420-nm region might be a 4 ⌬–X 4 ⌽ or a 4 ⌫–X 4 ⌽ transition. In the present work we have measured emission bands of TiCl in the 420-nm region at a resolution of 0.04 cm ⫺1 using a Fourier transform spectrometer. As a result, we propose a new electronic assignment of this band as 4 ⌫–X 4 ⌽. Rotational analysis has been obtained for the 0 – 0 and 1–1 vibrational bands of the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 and 4 ⌫ 7/ 2 –X 4 ⌽ 5/ 2 spin components and the 0 – 0 band of 4 ⌫ 9/ 2 –X 4 ⌽ 7/ 2 . Intensity pattern of the rotational structure in the 0 – 0 band of 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 was carefully inspected, and the result confirmed that the ⍀ value in the upper state is larger than that in the lower state, which provided evidence for the new electronic assignment. The present work also demonstrates the power of Fourier transform emission spectroscopy for the study of novel radicals which have transitions in the ultraviolet region. 2. EXPERIMENTAL
The emission cell used for the present study is shown in Fig. 1. It was a 30-cm-long, 8-mm inner-diameter Pyrex tube, to which two water-cooled sidearms containing discharge electrodes were attached. CaF 2 windows sealed off both ends of the cell. Helium was fed through the side arms, and a trace amount of the TiCl 4 vapor was introduced through an inlet near an end of the cell. An oil rotary pump (60 m 3/h) evacuated the cell, and the total pressure was maintained at about 1 Torr. A high-voltage ac of 70 kHz generated by a combination of an audio power amplifier (Accuphase P-600, 1 kW) and a step-up transformer (1:30) was applied between the electrodes through a ballast resistor (3 k⍀). The peak current of the discharge was typically 200 mA. The emission cell was placed in front of the entrance aperture (1.2 mm) of the Fourier transform spectrometer (Bruker
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FOURIER TRANSFORM EMISSION SPECTROSCOPY OF TiCl
217
unresolved Q branch which forms a blue-shaded head. Unblended rotational lines have a linewidth of 0.045 cm ⫺1 FWHM. Lines of the two isotopomers Ti 35Cl and Ti 37Cl are well resolved in this part of the spectrum. Figure 5 is an expanded spectrum of the 4 ⌫ 9/ 2 (v ⫽ 0)– 4 X ⌽ 7/ 2 (v ⫽ 0) band. The Q branch of this band has a structure considerably different from that in Fig. 4. This is caused by perturbation in the 4⌫ 9/2 (v ⫽ 0) state, as will be discussed in detail in the following section. 4. ANALYSIS
Five stronger vibronic bands, i.e., the 0 – 0 and 1–1 vibrational bands of the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 and 4 ⌫ 7/ 2 –X 4 ⌽ 5/ 2 spin components and the 0 – 0 band of 4 ⌫ 9/ 2 –X 4 ⌽ 7/ 2 , were subjected to rotational analysis. Wavenumbers of P- and R-branch lines in each band were used in the present analysis. Different spin components were analyzed separately by using a simple expression for the rotational term value: FIG. 1. Schematic diagram of the discharge emission cell. High-voltage ac is applied between the water-cooled electrodes in the side arms. Ultraviolet emission is focused by a CaF 2 lens onto the entrance aperture of the Fourier transform spectrometer.
IFS120HR). The light source module originally attached to the spectrometer had been removed. A CaF 2 lens ( f ⫽ 5 cm) focused emission from the discharge tube onto the aperture. Ultraviolet emission was monitored by a photomultiplier (Hamamatsu R-928), in front of which a 25-cm grating monochromator was placed (Fig. 2). The monochromator worked as an optical band-pass filter, and its slits were adjusted so as to give a typical bandwidth of 200 cm ⫺1. Ultraviolet radiation emerging from the Michelson interferometer was focused onto the entrance slit of the monochromator by a concave mirror (R ⫽ 50 cm). The resolution of the Fourier transform spectrometer was set to 0.04 cm ⫺1. The spectrum was recorded by accumulating 800 interferometer scans, taking 250 min in total. Observed wavenumbers were calibrated against emission lines of the Fe atom, which were obtained in a separate measurement. The standard vacuum wavenumber values were taken from Ref. (31).
F共 J兲 ⫽ B effJ共 J ⫹ 1兲 ⫺ D eff J 2 共 J ⫹ 1兲 2 .
[1]
Since all observed transitions corresponded to ⌬⍀ ⫽ ⫹1, the spin– orbit coupling constant A could not be directly determined. Also, no ⍀ doubling was resolved. 1. The 0 – 0 Band of the 4⌫ 5/2–X 4⌽ 3/2 Spin Component This band is the strongest of the observed bands and relatively isolated from other bands. As a result, an appreciable number of lines of the Ti 37Cl isotopomer were observed separately from those of Ti 35Cl. Line positions of the Ti 35Cl and Ti 37Cl isotopomers belonging to this band are listed in Tables 1 and 2, respectively. These line positions were determined by
3. OBSERVED SPECTRA
The emission spectrum of TiCl was measured in the region 23 820 –24 100 cm ⫺1 with a center wavenumber of the monochromator around 23 860 cm ⫺1. The overview of the spectrum is shown in Fig. 3. Eleven vibronic bands were assigned as belonging to the 4 ⌫–X 4 ⌽ electronic transition of TiCl, as shown in Fig. 3. Figure 4 shows an expanded spectrum of the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band. This band consists of P and R branches well resolved into rotational structure and an
FIG. 2. Schematic diagram of the optical setup used in the present measurement. Ultraviolet emission from the discharge tube was passed through a Michelson interferometer and focused onto a slit of a monochromator used as an optical band-pass filter. A typical spectral bandwidth of the monochromator was 200 cm ⫺1.
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FIG. 3.
Overview of the TiCl, 4 ⌫–X 4 ⌽ emission spectrum.
a deconvolution procedure, in which each line was assumed to have a Gaussian lineshape with a full width at half-maximum of 0.045 cm ⫺1. Several Ti 37Cl lines are overlapped by Ti 35Cl lines. Positions of the Ti 37Cl lines observed as shoulders to the Ti 35Cl peaks are superscripted with “d” in Table 2. Superscripted with “c” in Tables 1 and 2 are positions of the peaks formed by completely overlapping Ti 35Cl and Ti 37Cl lines. The corresponding features were treated as single Gaussian peaks in the deconvolution procedure: note that identical values are listed in Tables 1 and 2. In an early stage of the analysis, peaks of Ti 35Cl and those of 37 Ti Cl were fitted independently by the least-squares method, yielding standard deviations of 0.004 and 0.006 cm ⫺1, respectively. In the final stage, however, they were subjected to a simultaneous least-squares analysis so as to extract as unbiased information as possible from the completely overlapping peaks with superscript “c.” The principle is as follows. We assume that a Ti 35Cl line is located centered at 35 and a Ti 37Cl line at 37 and that they each have a Gaussian lineshape with the same linewidth ⌬ (FWHM). Then, the lineshape function for the overlapping lines will be
FIG. 4.
冋
g共 兲 ⫽ c 35 exp ⫺4 ln 2
冉
冊册 冋 冉
⫺ 35 ⌬
2
⫺ 37 ⫹ c 37 exp ⫺4 ln 2 ⌬
冊册
[2]
2
,
where c 35 and c 37 are relative line intensities. If the difference between the center positions 35 and 37 is sufficiently small compared to the linewidth ⌬, the lineshape g( ) around the peak is approximated by a quadratic function of ,
冋
g共 兲 ⬵ c 35 1 ⫺ 4 ln 2
冉
⫺ 35 ⌬
⫹ c 37
冋
冊册 2
冉
⫺ 37 1 ⫺ 4 ln 2 ⌬
冊册
[3]
2
,
of which the peak position is easily calculated as:
max ⫽
c 35 35 ⫹ c 37 37 . c 35 ⫹ c 37
Expanded spectrum of the TiCl, 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band.
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[4]
FOURIER TRANSFORM EMISSION SPECTROSCOPY OF TiCl
FIG. 5.
219
Expanded spectrum of the TiCl, 4 ⌫ 9/ 2 (v ⫽ 0)–X 4 ⌽ 7/ 2 (v ⫽ 0) band.
In the present analysis, we calculated the 35 and 37 values from the molecular constants of respective isotopomers and took weighted averages as given in Eq. [4]. The resulting wavenumbers were fitted to the observed wavenumbers of the completely overlapping lines. The ratio c 35 :c 37 was simply fixed to 3:1, the isotopic abundance ratio of chlorine, although the overlapping Ti 35Cl and Ti 37Cl transitions have slightly different J values. Table 3 lists the molecular constants thus optimized for the Ti 35Cl and Ti 37Cl isotopomers. Trace (A) of Fig. 6 shows an expanded portion of the observed spectrum for the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band. The Q-branch contour of this band was simulated using the molecular constants listed in Table 3. In the simulation, each line was assumed to have a Gaussian lineshape with a width of 0.05 cm ⫺1 FWHM, and transitions from Q(2.5) to Q(99.5) of Ti 35Cl and Ti 37Cl isotopomers were superposed. The simulated spectrum reproduced the observed Q-branch head very well. However, if we shifted the J assignment of the P- and R-branch lines of either one of the isotopomers or both, the simulated spectrum had a considerably different shape and did not match the observed. The J assignment was thus unambiguously determined for the both isotopomers. 2. The 1–1 Band of 4⌫ 5/2–X 4⌽ 3/2 and 0 – 0 and 1–1 Bands of 4⌫ 7/2–X 4⌽ 5/2 In these bands, stronger features are mostly assigned to Pand R-branch transitions of Ti 35Cl. It was difficult to obtain a sufficient number of definitely assigned Ti 37Cl lines to justify the rotational analysis of this isotopomer. Observed line positions of Ti 35Cl transitions are summarized in Tables 1 and 4. They were subjected to least-squares analysis, and the optimized molecular constants are given in Table 3. 3. The 0 – 0 Band of 4⌫ 9/2–X 4⌽ 7/2 Expanded spectrum of the 4 ⌫ 9/ 2 (v ⫽ 0)–X 4 ⌽ 7/ 2 (v ⫽ 0) band is shown in Fig. 5. P-branch lines of Ti 35Cl with 10.5 ⱕ
J⬙ ⱕ 56.5 and R-branch lines with 4.5 ⱕ J⬙ ⱕ 56.5 were assigned for this band. Observed line positions are listed in Table 5. The line positions fit fairly well to the simple energy formula of Eq. [1] up to J⬙ ⫽ 39.5, above which the observed line positions show systematic deviation from the calculated positions in both P and R branches, presumably due to rotational perturbation. Combination differences corresponding to the energy differences in the lower state provide a satisfactory fit in the range of J⬙ ⫽ 8.5–56.5, which suggests that the rotational perturbation occurs in the upper state, 4⌫ 9/2 (v ⫽ 0). Effective rotational constants for the lower state, X 4 ⌽ 7/ 2 (v ⫽ 0), were determined by a least-squares analysis of the combination differences. Effective rotational constants of the 4 ⌫ 9/2 (v ⫽ 0) state were then derived from the line positions in the range of J⬙ ⫽ 4.5–39.5, where the lower state constants were fixed as determined from the combination differences. Table 3 lists the effective rotational constants thus obtained for the X 4 ⌽ 7/ 2 (v ⫽ 0) and 4⌫ 9/2 (v ⫽ 0) states. As mentioned in the previous section, the Q branch of this band has a strange shape. To clarify the reason for this as well as to verify the J assignment, we performed a simulation of the Q branch. Energy term values in the X 4 ⌽ 7/ 2 (v ⫽ 0) state were calculated using the molecular constants determined by Ram and Bernath (24): these constants are in good agreement with the present results (vide infra). Perturbed term values in the 4 ⌫ 9/2 (v ⫽ 0) state were obtained by adding the observed wavenumbers of P- or R-branch transitions to the calculated term values in the lower state. The term values in the X 4 ⌽ 7/ 2 (v ⫽ 0) and 4⌫ 9/2 (v ⫽ 0) states were then combined to calculate the positions of Q-branch transitions. Transitions from Q(3.5) to Q(56.5) of Ti 35Cl were superposed, where each line was assumed to have a Gaussian lineshape with a width of 0.05 cm ⫺1 FWHM. Line intensities were calculated without taking the effect of the rotational perturbation into account. Trace (B) of Fig. 7 shows the Q-branch contour thus simulated, which is compared with the observed spectrum [Trace (A)]. Sticks
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IMAJO ET AL.
TABLE 1 Transition Frequencies in the 4⌫ 5/2–X 4⌽ 3/2 Subband of Ti 35Cl
In cm ⫺1 units. In 10 ⫺3 cm ⫺1 units. c Transition frequency was calculated as weighted average of Ti 35Cl and Ti 37Cl frequencies. * Zero weight was given in the fitting. a
b
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FOURIER TRANSFORM EMISSION SPECTROSCOPY OF TiCl
TABLE 1—Continued
below Trace (B) represent the calculated positions and intensities of individual Q-branch lines. Numbers below the sticks are the rotational quantum numbers J⬙. The simulated spectrum reproduces the observed shape of the Q branch. Therefore, the strange shape of the Q branch is explained as distorted by the rotational perturbation. The present J assignment was also confirmed. 5. DISCUSSION
The rotational constants in the X 4 ⌽ electronic state obtained in the present study agree within the experimental uncertainty (3) with those previously determined by Ram and Bernath (24). Centrifugal distortion constants are also consistent between the present results and Ram and Bernath’s except for the X 4 ⌽ 5/ 2 (v ⫽ 0) state. Agreement of the molecular constants provides evidence for identifying the lower state of the 420-nm band as X 4 ⌽. Trace (A) of Fig. 6 shows an expanded spectrum of the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band near the Q-branch head. The
Q-branch contour simulated as described in the previous section was subtracted from the observed spectrum and the residual is shown in Trace (B) on an expanded scale, where the intensity pattern of low J P- and R-branch lines was carefully inspected. The stick diagram attached to Trace (C) shows the calculated line positions and intensities for P- and R-branch lines of Ti 35Cl, where the numbers below the sticks designate the J⬙ values. The sequence of R-branch lines of Ti 35Cl is clearly seen in Trace (B), and the sequence may be traced up to J⬙ ⫽ 1.5. This is consistent with the electronic assignment of this band to 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 , because the lowest member in the R branch of this band is R(1.5). Emission intensities of individual R- and P-branch lines are expressed by
冋
I em ⬀ 4 S J exp ⫺
册
hcB⬘J⬘共 J⬘ ⫹ 1兲 , kT
[5]
where the Ho¨nl–London factor S J is given for the R- and P-branch lines by
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IMAJO ET AL.
TABLE 2 Transition Frequencies in the 4⌫ 5/2 (vv ⴝ 0)–X 4⌽ 3/2 (vv ⴝ 0) Subband of Ti 37Cl
S JR ⫽
共 J⬙ ⫹ 2 ⫾ ⍀⬙兲共 J⬙ ⫹ 1 ⫾ ⍀⬙兲 2共 J⬙ ⫹ 1兲
[6]
共 J⬙ ⫺ 1 ⫿ ⍀⬙兲共 J⬙ ⫿ ⍀⬙兲 , 2J⬙
[7]
and S JP ⫽
respectively, where the upper and lower signs apply to the bands with ⌬⍀ ⫽ ⫹1 and ⌬⍀ ⫽ ⫺1, respectively (32). Calculated intensities shown as the stick diagram in Fig. 6 are those corresponding to the ⍀⬘ ⫽ 5/2 3 ⍀⬙ ⫽ 3/2 transition, where a rotational temperature of 400 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 the observed intensity distribution. Calculations with the assumption of ⌬⍀ ⫽ ⫺1 result in intensity patterns with stronger P-branch lines and weaker R-branch lines, which do not match the observed pattern. It is therefore confirmed that the band of current interest is a ⌬⍀ ⫽ ⫹1 transition, giving support to the new electronic assignment of this subband to 4 ⌫ 5/ 2 – X 4 ⌽ 3/ 2 . Theoretical calculations by Boldyrev and Simons (25) and Sakai et al. (26) have not dealt with 4 ⌫ electronic states. A 4 ⌫ state may be formed if the 3 electron in the ground configuration 1 2 1 4 2 2 1␦ 1 3 1 2 1 is promoted to the 3 orbital. According to Sakai et al. (26), the 3 orbital mainly consists of the 4s orbital of Ti. The 3 orbital probably corresponds to the Ti, 4p orbital. Therefore, emission
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223
may be extended to higher energy region, a 4⌫ state of TiX may be correlated with the lowest 4 G state of the Ti ⫹ ion, which is located ⬃30 000 cm ⫺1 above the ground state and belongs to the 3d 2 4p configuration (33). Launila and Lindgren (34) have observed a 4⌫ state of TiH at T 0 ⫽ 18 878.10 cm ⫺1. The 4⌫ state of TiF has not been reported so far, but Bernath (30) suspected that an emission band in the 405-nm region may be due to a 4 ⌫–X 4 ⌽ or 4 ⌬–X 4 ⌽ transition. Very recently we confirmed the 4 ⌫–X 4 ⌽ assignment for this band (35) and determined T 0 to be 24 595.18 cm ⫺1. The term values of the 4⌫ states of TiH and TiF are comparable with that of the present 4 ⌫ state of TiCl as well as that of the 4 G state of the Ti ⫹ ion. The ionic picture of Ti ⫹ X ⫺ may give a useful insight for understanding the 4⌫ state of TiCl. Within the 4 ⌫ 5/ 2 –X 4 ⌽ 3/ 2 transition, the origin of the 1–1 vibrational band is higher than that of the 0 – 0 vibrational band by 26.7929 cm ⫺1. This difference, combined with the energy separation ⌬G(1/ 2) ⫽ 404.3663 cm ⫺1 (24) between the v ⫽ 1 and v ⫽ 0 levels of the X 4 ⌽ 3/ 2 spin component, allows us to derive the ⌬G(1/ 2) value for the 4⌫ 5/2 spin component as 431.1592 cm ⫺1. Similarly, the ⌬G(1/ 2) value for the 4⌫ 7/2 spin component is obtained as 435.9795 cm ⫺1. The latter two values disagree by about 5 cm ⫺1, although much closer agreement would be expected without perturbation. For example, the ⌬G(1/ 2) value is 404.3663, 404.3337, 404.3167, and 404.3032 cm ⫺1, respectively, for the ⍀ ⫽ 3/2, 5/2, 7/2, and 9/2 spin components of the ground X 4 ⌽ state (24). Therefore, we must conclude that at least one of the 4⌫ 5/2 (v ⫽ 0), 4⌫ 5/2 (v ⫽ 1), 4⌫ 7/2 (v ⫽ 0), and 4⌫ 7/2 (v ⫽ 1) levels is perturbed. Although the perturbation precludes precise estimation of the vibrational
TABLE 3 Effective Molecular Constants a of TiCl in the 4⌫ and X 4⌽ States
transition from the 4 ⌫ state thus formed to the ground 4 ⌽ state is expected to be fully allowed, because it corresponds to a single electron transition in the Ti atom. Ram and Bernath (24) discussed correlation between the atomic energy levels of the Ti ⫹ ion and lower energy levels of TiX (X ⫽ Cl, F, H). It indicates that the TiX radicals are well described as Ti ⫹ X ⫺ in the lower energy region. If this picture
FIG. 6. Trace (A) shows the observed spectrum for the 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) band near the Q-branch head. The simulated Q-branch contour was subtracted from Trace (A) and the residual is shown in Trace (B) on an expanded scale. The stick diagram (C) represents the calculated positions and intensities of individual Q-branch lines of Ti 35Cl. The numbers below the sticks are the J⬙ values. See text for details of calculations of the Q-branch contour and line intensities.
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IMAJO ET AL.
TABLE 4 Transition Frequencies in the 4⌫ 7/2–X 4⌽ 5/2 Subband of Ti 35Cl
In cm ⫺1 units. In 10 ⫺3 cm ⫺1 units. * Zero weight was given in the fitting. a
b
interval in the 4⌫ state, it probably has a value similar to but slightly larger than the value ⌬G(1/ 2) ⫽ 404.33 cm ⫺1 in the ground X 4 ⌽ state. Therefore, the stretching force constant
slightly increases on excitation from the X 4 ⌽ state to the present 4⌫ state. The difference between the band origins of the 4 ⌫ 7/ 2 (v ⫽
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TABLE 4—Continued
0)–X 4 ⌽ 5/ 2 (v ⫽ 0) and 4 ⌫ 5/ 2 (v ⫽ 0)–X 4 ⌽ 3/ 2 (v ⫽ 0) transitions is 54.9899 cm ⫺1 . Combining this difference with the spin– orbit interval 117 cm ⫺1 between the ⍀ ⫽ 5/2 and 3/2 spin components of the X 4 ⌽ (v ⫽ 0) state, we may calculate the 7/2–5/2 spin– orbit interval in the 4 ⌫ (v ⫽ 0) state as 172 cm ⫺1 . The above value of 117 cm ⫺1 is obtained as three times the spin– orbit coupling constant A ⬙0 ⫽ 39 cm ⫺1 , which was estimated by Ram and Bernath (24) from the effective rotational constants for the different spin components. The value 172 cm ⫺1 divided by four gives an estimate of the spin– orbit coupling constant A ⫽ 43 cm ⫺1 for the 4 ⌫ state. In the same way, the 7/2–5/2 spin– orbit interval in the 4 ⌫ (v ⫽ 1) state is calculated as 176 cm ⫺1 , giving A ⫽ 44 cm ⫺1 . The discrepancy in the two A values is again ascribed to the perturbation described above but these values may be useful as a rough estimate of the spin– orbit coupling constant in the 4 ⌫ electronic state. The method to derive the A constant and the true rotational constant from the effective rotational constants, which worked well in the ground X 4 ⌽ state (24), resulted in unreliable values for the 4 ⌫ state, i.e., the effective rotational constants for the ⍀ ⫽ 5/2 and 7/2 spin components in the v ⫽ 0 level gave A ⫽ 36 cm ⫺1 , whereas A ⫽ 72 cm ⫺1 was obtained from the corresponding constants in the v ⫽ 1 level. For most of the observed bands, the effective rotational constants in the upper and lower states differ very little (less than 0.4%). This means that the bond length is almost the same in the X 4 ⌽ state and the upper 4⌫ state. This and the similarity of the stretching force constant described above indicate that the lower and upper states of the present transition have closely
resembling potential curves, consistent with the absence of ⌬v ⫽ 0 transitions. The effective rotational constants of the Ti 37Cl isotopomer were obtained for the 4⌫ 5/2 (v ⫽ 0) and X 4 ⌽ 3/ 2 (v ⫽ 0) spin components. These constants are compared with the constants of Ti 35Cl for the corresponding states. The constants of Ti 37Cl in the 4⌫ 5/2 (v ⫽ 0) and X 4 ⌽ 3/ 2 (v ⫽ 0) spin components are 0.9689 and 0.9690 times, respectively, those of Ti 35Cl. These ratios are in good agreement with the expected ratio 0.96876 calculated from the reduced masses.
FIG. 7. Trace (A) shows an expanded spectrum of the 4 ⌫ 9/ 2 (v ⫽ 0)–X 4 ⌽ 7/ 2 (v ⫽ 0) band near the Q branch. Trace (B) is a calculated contour of the Q branch. The stick diagram represents the calculated positions and intensities of individual Q-branch lines of Ti 35Cl. The numbers below the sticks are the J⬙ values. See text for details of the calculation of the Q-branch contour and line intensities.
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IMAJO ET AL.
TABLE 5 Transition Frequencies in the 4⌫ 9/2 (vv ⴝ 0)–X 4⌽ 7/2 (vvv ⴝ 0) Subband of Ti 35Cl
ACKNOWLEDGMENTS The authors thank Dr. S. Civis at Heyrousky Institute of Physical Chemistry, Czech Republic for helpful discussions on the experimental setup. They are also grateful to Professor P. F. Bernath at Waterloo University, Canada for valuable discussions on electronic assignments of the emission spectra of TiCl in the ultraviolet region. Financial support from the Ministry of Education, Science, Sports, and Culture are acknowledged.
REFERENCES 1. T. C. Steimle, J. E. Shirley, K. Y. Jung, L. R. Russon, and C. T. Scurlock, J. Mol. Spectrosc. 144, 27–31 (1990). 2. D. A. Fletcher, C. T. Scurlock, K. Y. Jung, and T. C. Steimle, J. Chem. Phys. 99, 4288 – 4299 (1993). 3. C. Athenour, J.-L. Femenias, and T. M. Dunn, Can. J. Phys. 60, 109 –116 (1980). 4. J. A. Bates, N. L. Ranieri, and T. M. Dunn, Can. J. Phys. 54, 915–916 (1975). 5. T. M. Dunn, L. K. Hanson, and K. A. Rubinson, Can. J. Phys. 48, 1657–1663 (1969).
6. A. E. Douglas and P. M. Veillette, J. Phys. Chem. 72, 5378 –5380 (1980). 7. C. Amiot, E. M. Azaroual, P. Luc, and R. Vetter, J. Phys. Chem. 102, 4375– 4381 (1995). 8. W. H. Hocking, M. C. L. Gerry, and A. J. Merer, Can. J. Phys. 57, 54 – 61 (1979). 9. G. R. Braandes and D. C. Galehouse, J. Mol. Spectrosc. 109, 345–351 (1985). 10. T. C. Steimle and J. E. Shirley, J. Chem. Phys. 91, 8000 – 8002 (1989). 11. C. Linton, J. Mol. Spectrosc. 50, 235–245 (1974). 12. C. Linton, Can. J. Phys. 50, 312–316 (1971). 13. C. M. Pathak and H. B. Palmer, J. Mol. Spectrosc. 33, 137–146 (1970). 14. J. G. Phillips, Astrophys. J. 169, 185–189 (1971). 15. A. Fowler, Proc. R. Soc. London A 79, 509 (1907). 16. K. R. More and A. H. Parker, Phys. Rev. 52, 1150 –1152 (1937). 17. V. R. Rao, Indian J. Phys. 23, 535 (1949). 18. E. A. Shenyavskaya, T. Y. Kuzyakov, and V. M. Tatevskii, Opt. Spectrosc. (SSSR) 12, 197–199 (1962). 19. A. Chatalic, P. Deschamps, and G. Pannetier, C. R. Acad. Sci. Paris 268, 1111–1113 (1969).
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FOURIER TRANSFORM EMISSION SPECTROSCOPY OF TiCl 20. R. L. Diebner and J. K. Kay, J. Chem. Phys. 51, 3547–3554 (1969). 21. K. P. Lanini, Ph.D. dissertation, University of Michigan, Ann Arbor, MI, 1972. 22. T. C. DeVore, High Temp. Sci. 15, 263–273 (1982). 23. J. G. Phillips and S. P. Davis, Astron. Phys. J. Suppl. Ser. 71, 163–172 (1989). 24. R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 186, 113–130 (1997). 25. A. I. Boldyrev and J. Simons, J. Mol. Spectrosc. 188, 138 –141 (1998). 26. Y. Sakai, K. Mogi, and E. Miyoshi, J. Chem. Phys. 111, 3989 –3994 (1999). 27. R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 195, 299 –307 (1999).
227
28. R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 186, 335–348 (1997). 29. K. J. Jordan, R. H. Lipson, N. A. McDonald, and D. S. Yang, Chem. Phys. Lett. 193, 499 –506 (1992). 30. P. F. Bernath, private communication. 31. V. Kaufman and B. Edlen, J. Phys. Chem. Ref. Data 3, 825– 843 (1974). 32. I. Kovacs, “Rotational Structure in the Spectra of Diatomic Molecules,” p. 121, American Elsevier, New York, 1969. 33. C. Corliss and J. Sugar, J. Phys. Chem. Ref. Data 8, 1–17 (1979). 34. O. Launila and B. Lindgren, J. Chem. Phys. 104, 6418 – 6422 (1996). 35. T. Imajo, Y. Kobayashi, Y. Nakashima, K. Tanaka, and T. Tanaka, unpublished manuscript.
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