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Absorption Intensity of Stretching Overtone States of Silane and Germane
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
192, 249 –256 (1998)
MS987673
Absorption Intensity of Stretching Overtone States of Silane and Germane Hai Lin, Dong Wang, Xi-Yi Chen, Xiao-Gang Wang, Zhong-Ping Zhou, and Qing-Shi Zhu1 Open Laboratory of Bond Selective Chemistry and Institute for Advanced Studies, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China Received January 23, 1998; in revised form June 19, 1998
The band absorbance and line absorbance of R branch transitions are obtained from high-resolution Fourier transform measurement of silane and germane local mode overtones (n000), n 5 1–5, under proper sample pressures and absorption lengths. The absorption coefficients of these overtones are derived by linear least-squares fitting. The relative intensities of overtones can be satisfactorily reproduced with the bond dipole model containing two adjustable parameters. © 1998 Academic Press
M i~R i! 5 M 0iR mi exp~2R i/R *i !,
1. INTRODUCTION
The overtone intensities are of great importance in studying the high-lying vibrational states, especially the local mode vibrations of polyatomic molecules. It is known that the intensities of overtone and combination bands arise from three effects (1, 2): (i) the functional dependence of the dipole moment in the electronic ground state on the local mode coordinate R i (“electric anharmonicity”); (ii) the form of basis functions which relates to “potential anharmonicity;” and (iii) the coefficients of these basis functions in the ground and excited eigenstates (“vibration coupling”). It is now well known that the stretching vibrational overtone energy levels of many small polyatomic molecules can be well understood with simple Morse oscillator wavefunctions as local mode basis sets (2). However, the dipole moment function is relatively less known to us. Recently much attention has been devoted to the determination of dipole moment functions and to the study of the effects of electric and potential anharmonicity on intensities. Based on the assumption of bond dipole separability, it is natural to assume that the molecular dipole is a sum of the bond dipole moments (the “bond dipole model”), M~R! 5
O M ~R !e , i
i
i
[1]
i
where R i is the instantaneous bond length of the ith bond and ei is the unit vector along this bond. As for the bond dipole moment, the analysis of vibrational overtones for HI indicated the functional form (3) 1
To whom correspondence should be addressed.
[2]
where m and R *i are empirical parameters. M 0i is required if absolute intensity is concerned. With the bond dipole function of m 5 1, Schek et al. (4) analyzed the C–H vibrational overtone intensities of naphthalene. Halonen (5) successfully reproduced the intensities of (n00000), n 5 1–5 local mode states of benzene. Later Kauppi et al. (6) modeled the intensities of CHX3-type molecules. They found that experimental intensities for CHF3, CHCl3, CHBr3, and CH(CF3)3 can be well reproduced with different m values in Eq. [2]. Therefore, it is not easy to tell which function is best for these molecules. In addition, although the bond dipole function [2] possesses correct asymptotic behavior as R 3 0 and R 3 `, it is an empirical model function without any deeper theoretical justification. Therefore, more experimental data are needed, especially the overtone intensities of those molecules which are close to the local mode limit, to verify the validity of the bond dipole model with the above dipole function. The stretching vibration overtone states of silane and germane have been found to arrive at the local mode limit (7). The intensities of silane fundamental bands, n3 and n4, were measured earlier by Levin et al. (8) and Ball et al. (9). The intensities of v 5 6 –9 states were measured by Bernheim et al. (10). In Ref. (11), the relative intensity of v 5 2–5 of silane and v 5 4 and 5 of germane were reported and tested by an improved dipole model. However, the experiments were done roughly in that the sample pressure was not accurately measured and the estimated data were of low confidence. There were also some unusual assumptions in the theoretical model (11) which we did not use in our work. In the present study, the intensities of v 5 1–5 of silane and germane were remeasured carefully with improved sample preparation technique and pressure measurement method. These data, together with the
249 0022-2852/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.
250
LIN ET AL.
TABLE 1 Experimental Setup of SiH4 Stretching Overtones and Combination States Intensity Measurement
data in Ref. (10), are compared with the calculations using the bond dipole model. 2. EXPERIMENTAL DETAILS AND RESULTS
2.1. SiH4 In our experiment, the SiH4 gas sample with a stated 98% purity was purchased from Dalian Guangming Chemical Com-
pany. The high resolution absorption spectra of SiH4, ranging from 1700 to 13 000 cm21, were recorded on our Bruker IFS120HR Fourier transform spectrometer with different setups listed in Table 1. The focal length of the collimating mirror is 418 mm. A small 15-cm gas cell and a path length up to 105-m adjustable multipass cell equipped with CaF2 windows were used. The former was used in the measurement of the fundamental and low overtone manifolds, while the latter was
FIG. 1. The total vibration–rotational band intensity of the (5000) overtone at 300 K temperature. The absorption coefficient is determined by a least-squares fitting of the integrated absorbance against optic density, the product of PL, where P is the sample pressure and L is the absorption length.
Copyright © 1998 by Academic Press
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TABLE 2 Experimental Setup of GeH4 Stretching Overtones and Combination States Intensity Measurement
used in high overtone manifolds. A turbo-molecular pump was employed to achieve the better than 1024 Pa vacuum of the gas cell. A mechanical pump was applied to the optical compartment of our IFS120HR in order to remove the water and carbon dioxide, and the vacuum of optical compartment remained under 2 Pa during the measurement. The sample gas was frozen by liquid nitrogen at first and then the liquid nitrogen was removed to let the sample slowly vaporize into the multipass gas cell or the small gas cell until the pressure we needed was reached. By doing so, the sample purity was estimated to be better than 99%. The pressures of sample gas were measured by capacitance manometers of 0.5% full-scale accuracy. Altogether three manometers in different applied ranges were used to give the accurate sample pressure. The sample pressure in the multipass cell was monitored during the measurement to check the stability, while the sample pressure in the small cell
could not be monitored since the cell was put inside the evacuated sample compartment of the interferometer during the scanning. However, we can rely on the spectroscopic evidence by comparing lines of different scans during the experiment to check the pressure stability. We observed no substantial decomposition of the sample. In our experiment, the spectra were typically recorded at four to seven different pressures with uncertainties within 2%. The background was recorded with no sample in the gas cell. The laboratory was air conditioned and the temperature of the sample was measured with a small uncertainty and a good stability at 300 6 2 K. In our measurement, the acquisition mode was single-side, fast-return mode. Optical filters were employed to prevent detectors from overload and to eliminate folding. Electronic filters were used to reduce the electronic noises. The scanning velocity of the moving mirror was set to 1.266 cm z s21 for all
Copyright © 1998 by Academic Press
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LIN ET AL.
FIG. 2. The spectrum of the R(3) branch of the (3000) overtone of silane. (A) is the original spectrum, (B) is the deconvoluted spectrum, which demonstrates the components of the original spectrum, and (C) is the simulated spectrum. The absorption lines were fitted simultaneously.
except 0.633 cm z s21 for the (6000) band. A 32-cm21 resolution phase spectrum was recorded for phase correction with the Mertz method. Boxcar apodization function was chosen in most cases except the Norton–Beer Weak function was used for the measurement of the (3100), (2200), and (6000) bands. The spectra were calibrated by residual water lines taken from HITRAN 96. The accuracy was estimated to be 0.001 cm21 for strong lines and 0.005 cm21 for weak lines. The Doppler broadening was greater than the estimated pressure broadening in our experiment. The value of absorbance at wavenumber n, A peak(n), never exceeded 0.50. Based on the Beer–Lambert’s Law (12), we have I~ n ! 5 I 0~ n ! exp~2A~ n ! PL!,
[3]
where A( n ) denotes the absorption coefficient at wavenumber n, P is the sample pressure, and L is the absorption length. The integrated absorption coefficient A is obtained by integrating the A( n ) against the wavenumber of absorption: A5
E
A~n!dn 5
FE
G
ln~I0~n!/I~n!!dn /PL 5 ^Ab&/PL.
[4]
We measured the value of integrated absorbance, ^ Ab& 5 * ln(I 0 ( n )/I( n ))d n , at various sample pressures and absorption lengths, and value A was obtained by a least-squares fitting of the ^ Ab& values to Eq. [4].
The recorded spectra were vibrationally analyzed and assigned in Ref. (13). The local mode notation (n 1 n 2 n 3 n 4 ) used here to label the excited stretching overtone states gives the quantum number of excitation in four individual Si–H bonds. The vibrational–transition moments can be derived from either total vibrational band intensities or individual vibration– rotational line intensities. The results are equivalent if rotation and vibration are separable. However, there are discrepancies between these two results when vibration–rotational interactions are not negligible. Our data were analyzed in both ways. By means of the total vibrational band intensity, the absorbance of overtones or combination bands can be obtained by integrating the absorption lines directly if they are free from overlapping. It works for the (1000), (4000), (5000), and (6000) bands. Of course, the residual water lines were excluded from integration. The value of ^ Ab& of the (5000) band against the optical density, the product of PL is illustrated in Fig. 1 to demonstrate the good linearity. The results are given in Table 2, which shows the observed and calculated values obtained by the theoretical model which will be discussed in the next section. However, due to the poor S/N ratio, the A value for the (6000) band was determined at single sample pressure. For overlapping bands, such as the (2000) and (1100), the (3000) and (2100), and the (3100) and (2200) bands, it is impossible to obtain the band intensity with the method mentioned above. Therefore, the total vibrational band intensities of these bands could be achieved only after the spectrum had been rotationally analyzed and contributions from various
Copyright © 1998 by Academic Press
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TABLE 3 Observed Scaled Intensities of SiH4 Obtained by Individual Line Absorbance
bands were separated. Then the absorption coefficient of individual line in each band were summed up to yield the total vibrational band absorption coefficients. However, it is quite difficult to assign the lines when J goes high, e.g., higher than nine in the (3000) overtone, owing to the complication of the spectrum. Thus, the band intensities we obtained are just the estimated values. To obtain relative intensities from individual lines, we work out the absorbance of R( J) ( J 5 3, 4, and 5) branches by fitting each absorption line to a Voigt lineshape plus a baseline using a software based on the Levenberg–Marquardt algorithm (14). In our experiment, the effect of the instrumental lineshape is of minor importance and not considered here (12). The lines were assigned according to Ref. (7, 15) and our analysis (17). In the fitting, the lineshape parameters such as linecenter position, height, and width were adjustable and the integrated absorbance was evaluated as the area parameter of the fitting
Voigt function. The blended lines were deconvoluted by fitting them simultaneously. As an example, in Fig. 2 we display the original (A), the deconvoluted (B), and the simulated (C) spectra of the R(3) branch of (3000) overtone. The blended K 5 0 and K 5 1 lines at about 6383.6 cm21 were deconvoluted and the components are shown in (B). The A value obtained by least-squares fitting the ^ Ab& value of each line against the optical density was then summed to yield the absorption coefficients of R( J) branches with J 5 3, 4, and 5. Taking advantage of the method described above, we obtained relative intensities of the R( J) branches, which are displayed in Table 3. It shows that there are a few differences among these experimental values, and the final relative intensities listed in Table 2 are the averaged values over those obtained from three R( J) branches. To estimate the uncertainty of our experimental results, the following sources of error should be considered and upper
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TABLE 4 Observed and Calculated Intensities of SiH4 Stretching Overtones and Combination States
limits for the relative uncertainty they introduce are given as follows: sample purity (1%), gas cell length (2%), isotopic abundance (5%), pressure instability and pressure measurement uncertainty (2%), temperature instability and temperature measurement uncertainty (0.7%), instrumental lineshape function effects (0.5%), residual water weak lines (0.5%), uncertainty in the 100% transmittance level (0.1%), lineshape fitting error (2%), least-squares fitting error (2%), hot band effect and band overlapping effect (varies with individual bands), and the instability of our Bruker IFS120HR spectrometer (0.1%). The uncertainty of the relative intensities was estimated to be less than 7% for those obtained from bands free from overlapping and from individual line intensities, while 15% was estimated for overlapping bands. 2.2 GeH4 The GeH4 gas sample was synthesized and purified by the sample preparing group in our laboratory (16). The purity was about 88%. The most residual substance was CO2. The highresolution absorption spectra of GeH4, ranging from 1700 to 11 000 cm21, were also recorded on our Bruker IFS120HR Fourier Transform spectrometer with different setups listed in Table 4. The sample preparation technique and the experimental configuration are the same as that of SiH4 and will not be repeated here. We point out that with this sample preparation technique, the purity of GeH4 in gas cell is improved to be better than 95%. The acquisition mode was also the single side and fast return. Optical filters were employed to prevent detectors from overload and to avoid folding. Electronic filters were used to eliminate the electronic noises. The scanning velocity of the
moving mirror was 1.266 cm z s21 for all except 0.633 cm z s21 for the (3000) and (2100) bands. Phase correction was performed by the Mertz mode with phase spectrum recorded at a resolution of 32 cm21. The Boxcar apodization function was chosen. The spectra were calibrated by residual water lines taken from HITRAN 96. The accuracy was estimated to be 0.001 cm21 for strong lines and 0.005 cm21 for weak lines. The Doppler broadening was greater than the estimated pressure broadening in our experiment. The recorded spectra were vibrationally analyzed and assigned in Ref. (13). The third stretching overtone manifolds were observed the first time and analyzed (17). We obtained the relative intensities of GeH4 with the method of individual vibration–rotational line integration, which was outlined for SiH4 in the previous section. The lines of R( J), J 5 0, 1, . . . , 6, were used, and only the 74 GeH4 isotopic species were analyzed. The results are listed in Table 5. To estimate the uncertainty of the experimental results of GeH4, we considered the following sources of error and upper limits for the relative uncertainty they introduce: sample purity (8%), gas cell length (2%), pressure instability and pressure measurement uncertainty (2%), temperature instability and temperature measurement uncertainty (0.7%), instrumental lineshape function effects (0.5%), residual water weak lines (0.5%), uncertainty in the 100% transmittance level (0.1%), lineshape fitting error (2%), least-squares fitting error (2%), and the instability of our Bruker IFS120HR spectrometer (0.1%). The overall uncertainty of the relative intensities was estimated to be less than 12%.
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TABLE 5 Observed and Calculated Relative Intensities of Stretching Vibrational Bands of GeH4
3. DISCUSSION
There are several points of our experimental data worth discussing. First, the total vibrational band intensities of those overlapping bands could be achieved only after the rotational structure had been analyzed and the contributions from various bands had been separated with the help of the deconvolution method mentioned above. Until now, the lack of necessary detailed knowledge of the vibration–rotational constants prevented us from further progress. However, among the overlapping bands, the intensities of a strong band could be determined with higher accuracy since its overlapping effect could be estimated and actually was rather small. Such is the case in the (2000) and (2100) bands of SiH4. Second, the discrepancies between intensities deduced from the whole band and those from the individual line, together with the differences among the relative intensities deduced from different R( J) branches, indicate vibration–rotational interaction. In the case of SiH4, the intensities deduced from Band is generally smaller than those deduced from Line in our measurement. It is not surprising to realize that the R branches of local mode overtones are usually much stronger than the P branches when compared with the fundamentals. (Although the lines of R( J) are often
free from overlapping when J is low, they must be applied carefully due to the potential vibration–rotation interaction.) The situation of GeH4 is similar to that of SiH4, although we did not deduce the intensities from Band. Finally, it is interesting to note the remarkably unusual behavior of v 5 3 bands of SiH4 and v 5 4 bands of GeH4. In the former, the strikingly weak (3000) overtone and significantly strong (2100) combination band has been observed earlier by McKean et al. (18) and Campargue et al. (19) at medium resolution (0.1– 0.2 cm21) and later by Zhu et al. (7) at higher resolution. Our results reveal that the (2100; 1F2) band is about one order of magnitude stronger than the (3000; F2) band. We also find that, like the (3000) overtone (7), the (2100; 2F2) band located at 6499.77 cm21 is extremely strong in the R branch and weak in the P branch, while the (2100; 1F2) band is equally strong in the P and R branch. In the latter, the (4000) overtone is weaker than the (3100) combination band which was reported in Ref. (11). However, the relative intensities of these bands obtained in this work are quite different from those in reported Ref. (11) for the reason mentioned in the first section. A comparison of our experimental data with those in Ref. (11) can be found in Table 6.
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TABLE 6 Comparison of the Observed Relative Intensities of Stretching Vibrational Bands of GeH4
The intensities of overtone and combination bands of SiH4 and GeH4 reported in this work, together with those measured earlier by Bernheim et al. (10), provide a good test of the dipole model which has been detailed in Ref. (13) and will not be repeated here. Using the bond dipole function [2] with m and R* adjustable, we find that the observed intensities of all overtones and the (1100) combination band of SiH4 obtained by total band intensity can be well reproduced at m 5 5 and R* 5 0.635 Å (see Table 2). The potential energy parameters, De, a, and frr9, are obtained by a global fitting of the stretching band origins with the ACAO model (21), which yields De 5 37 706.9 cm21, a 5 1.394 Å, and frr9 5 1524.7 cm21 Å22. The bond length at the equilibrium nuclear configuration R0 is set to 1.4732 Å. In the case of GeH4, the relative intensities of overtones can be well reproduced with m 5 5 and R* 5 0.585 Å (see Table 5). The potential energy parameters, De, a, and frr9, are also obtained by globally fitting the stretching band origins with the ACAO model (21), which yields De 5 34 956.0 cm21, a 5 1.41422 Å, and frr9 5 594 cm21 Å22. The bond length at the equilibrium nuclear configuration R0 is set to 1.520 Å. In addition, we find that the calculations are quite sensitive to the changes in m and R* values. In this model, although the relative intensities of overtone can be well reproduced, the results of the combination bands are unsatisfied. Furthermore, the bending vibrations are neglected and all intensities are assumed to be carried by the stretching vibrations in our model. This should be taken into account in further studies. ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China and the Chinese Academy of Sciences. We thank Dr. Ze-Yi Zhou and Ms. Ke Deng for help in their GeH4 synthesis.
REFERENCES 1. P. R. Stannard, M. L. Elert, and W. M. Gelbart, J. Chem. Phys. 74, 6050 – 6062 (1981). 2. M. S. Child and L. Halonen, Adv. Chem. Phys. 57, 1–58 (1984). 3. M. S. Burberry and A. C. Albrecht, J. Chem. Phys. 70, 147–152 (1979). 4. I. Schek, J. Jortner, and M. L. Sage, Chem. Phys. Lett. 64, 209 –212 (1979). 5. L. Halonen, Chem. Phys. Lett. 87, 221–225 (1982). 6. E. Kauppi and L. Halenon, J. Chem. Phys. 90, 6980 – 6992 (1989); L. Halonen and E. Kauppi, J. Chem. Phys. 92, 3278 –3282 (1990). 7. Q. S. Zhu, B. S. Zhang, Y. R. Ma, and H. B. Qian, Chem. Phys. Lett. 164, 596 –599 (1989); Spectrochim. Acta A 46, 1223–1229 (1990); Spectrochim. Acta A 46, 1323–1331 (1990); F. G. Sun, X. G. Wang, J. L. Liao, and Q. S. Zhu, J. Mol. Spectrosc. 184, 12–21 (1997); Q. S. Zhu and B. A. Thrush, J. Chem. Phys. 92, 2691–2697 (1989); Q. S. Zhu, H. B. Qian, and B. A. Thrush, Chem. Phys. Lett. 186, 436 – 440 (1991). 8. I. W. Levin and W. T. King, J. Chem. Phys. 37, 1375–1381 (1962). 9. D. F. Ball and D. C. McKean, Spectrochim. Acta A 18, 1019 –1028 (1962). 10. R. A. Bernheim, F. W. Lampe, J. F. O’Keefe, and J. R. Qualey, III, J. Chem. Phys. 80, 5906 –5908 (1984). 11. J. L. Liao and Q. S. Zhu, Chem. Phys. Lett. 274, 328 –334 (1997). 12. P. R. Griffiths and J. A. de Haseth, in “Fourier Transform Infrared Spectrometry,” pp. 338 –341, Wiley, New York, 1986. 13. L. Halenon and M. S. Child, Comput. Phys. Commun. 51, 173–193 (1988). 14. D. W. Marquardt, J. Soc. Ind. Appl. Math. 11, 431– 441 (1963). 15. Q. S. Zhu, H. B. Qian, H. Ma, and L. Halonen, Chem. Phys. Lett. 177, 261–264 (1991); F. G. Sun, X. G. Wang, Q. S. Zhu, C. Pierre, and G. Pierre, Chem. Phys. Lett. 239, 373–379 (1994); Q. S. Zhu, A. Campargue, and F. Stoeckel, Spectrochim. Acta A 50, 663– 670 (1994). 16. F. G. Sun, Ph.D. thesis, University of Science and Technology of China, Hefei, China, pp. 13–15, 1996. [See references therein]. 17. X. Y. Chen, H. Lin, X. G. Wang, D. Wang, and Q. S. Zhu, unpublished manuscript. 18. D. C. McKean, A. R. Morrision, and M. I. Kelly, Chem. Phys. Lett. 109, 347–351 (1984). 19. A. Campargue, F. Stoeckel, and M. C. Terrile, Chem. Phys. 110, 145–152 (1986). 20. M. Chevalier and A. De Matino, J. Chem. Phys. 90, 2077–2089 (1989). 21. X. G. Wang, Ph.D. thesis, University of Science and Technology of China, Hefei, China, pp. 1–20, 1997.
Copyright © 1998 by Academic Press
192, 249 –256 (1998)
MS987673
Absorption Intensity of Stretching Overtone States of Silane and Germane Hai Lin, Dong Wang, Xi-Yi Chen, Xiao-Gang Wang, Zhong-Ping Zhou, and Qing-Shi Zhu1 Open Laboratory of Bond Selective Chemistry and Institute for Advanced Studies, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China Received January 23, 1998; in revised form June 19, 1998
The band absorbance and line absorbance of R branch transitions are obtained from high-resolution Fourier transform measurement of silane and germane local mode overtones (n000), n 5 1–5, under proper sample pressures and absorption lengths. The absorption coefficients of these overtones are derived by linear least-squares fitting. The relative intensities of overtones can be satisfactorily reproduced with the bond dipole model containing two adjustable parameters. © 1998 Academic Press
M i~R i! 5 M 0iR mi exp~2R i/R *i !,
1. INTRODUCTION
The overtone intensities are of great importance in studying the high-lying vibrational states, especially the local mode vibrations of polyatomic molecules. It is known that the intensities of overtone and combination bands arise from three effects (1, 2): (i) the functional dependence of the dipole moment in the electronic ground state on the local mode coordinate R i (“electric anharmonicity”); (ii) the form of basis functions which relates to “potential anharmonicity;” and (iii) the coefficients of these basis functions in the ground and excited eigenstates (“vibration coupling”). It is now well known that the stretching vibrational overtone energy levels of many small polyatomic molecules can be well understood with simple Morse oscillator wavefunctions as local mode basis sets (2). However, the dipole moment function is relatively less known to us. Recently much attention has been devoted to the determination of dipole moment functions and to the study of the effects of electric and potential anharmonicity on intensities. Based on the assumption of bond dipole separability, it is natural to assume that the molecular dipole is a sum of the bond dipole moments (the “bond dipole model”), M~R! 5
O M ~R !e , i
i
i
[1]
i
where R i is the instantaneous bond length of the ith bond and ei is the unit vector along this bond. As for the bond dipole moment, the analysis of vibrational overtones for HI indicated the functional form (3) 1
To whom correspondence should be addressed.
[2]
where m and R *i are empirical parameters. M 0i is required if absolute intensity is concerned. With the bond dipole function of m 5 1, Schek et al. (4) analyzed the C–H vibrational overtone intensities of naphthalene. Halonen (5) successfully reproduced the intensities of (n00000), n 5 1–5 local mode states of benzene. Later Kauppi et al. (6) modeled the intensities of CHX3-type molecules. They found that experimental intensities for CHF3, CHCl3, CHBr3, and CH(CF3)3 can be well reproduced with different m values in Eq. [2]. Therefore, it is not easy to tell which function is best for these molecules. In addition, although the bond dipole function [2] possesses correct asymptotic behavior as R 3 0 and R 3 `, it is an empirical model function without any deeper theoretical justification. Therefore, more experimental data are needed, especially the overtone intensities of those molecules which are close to the local mode limit, to verify the validity of the bond dipole model with the above dipole function. The stretching vibration overtone states of silane and germane have been found to arrive at the local mode limit (7). The intensities of silane fundamental bands, n3 and n4, were measured earlier by Levin et al. (8) and Ball et al. (9). The intensities of v 5 6 –9 states were measured by Bernheim et al. (10). In Ref. (11), the relative intensity of v 5 2–5 of silane and v 5 4 and 5 of germane were reported and tested by an improved dipole model. However, the experiments were done roughly in that the sample pressure was not accurately measured and the estimated data were of low confidence. There were also some unusual assumptions in the theoretical model (11) which we did not use in our work. In the present study, the intensities of v 5 1–5 of silane and germane were remeasured carefully with improved sample preparation technique and pressure measurement method. These data, together with the
249 0022-2852/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.
250
LIN ET AL.
TABLE 1 Experimental Setup of SiH4 Stretching Overtones and Combination States Intensity Measurement
data in Ref. (10), are compared with the calculations using the bond dipole model. 2. EXPERIMENTAL DETAILS AND RESULTS
2.1. SiH4 In our experiment, the SiH4 gas sample with a stated 98% purity was purchased from Dalian Guangming Chemical Com-
pany. The high resolution absorption spectra of SiH4, ranging from 1700 to 13 000 cm21, were recorded on our Bruker IFS120HR Fourier transform spectrometer with different setups listed in Table 1. The focal length of the collimating mirror is 418 mm. A small 15-cm gas cell and a path length up to 105-m adjustable multipass cell equipped with CaF2 windows were used. The former was used in the measurement of the fundamental and low overtone manifolds, while the latter was
FIG. 1. The total vibration–rotational band intensity of the (5000) overtone at 300 K temperature. The absorption coefficient is determined by a least-squares fitting of the integrated absorbance against optic density, the product of PL, where P is the sample pressure and L is the absorption length.
Copyright © 1998 by Academic Press
ABSORPTION INTENSITY OF SILANE AND GERMANE
251
TABLE 2 Experimental Setup of GeH4 Stretching Overtones and Combination States Intensity Measurement
used in high overtone manifolds. A turbo-molecular pump was employed to achieve the better than 1024 Pa vacuum of the gas cell. A mechanical pump was applied to the optical compartment of our IFS120HR in order to remove the water and carbon dioxide, and the vacuum of optical compartment remained under 2 Pa during the measurement. The sample gas was frozen by liquid nitrogen at first and then the liquid nitrogen was removed to let the sample slowly vaporize into the multipass gas cell or the small gas cell until the pressure we needed was reached. By doing so, the sample purity was estimated to be better than 99%. The pressures of sample gas were measured by capacitance manometers of 0.5% full-scale accuracy. Altogether three manometers in different applied ranges were used to give the accurate sample pressure. The sample pressure in the multipass cell was monitored during the measurement to check the stability, while the sample pressure in the small cell
could not be monitored since the cell was put inside the evacuated sample compartment of the interferometer during the scanning. However, we can rely on the spectroscopic evidence by comparing lines of different scans during the experiment to check the pressure stability. We observed no substantial decomposition of the sample. In our experiment, the spectra were typically recorded at four to seven different pressures with uncertainties within 2%. The background was recorded with no sample in the gas cell. The laboratory was air conditioned and the temperature of the sample was measured with a small uncertainty and a good stability at 300 6 2 K. In our measurement, the acquisition mode was single-side, fast-return mode. Optical filters were employed to prevent detectors from overload and to eliminate folding. Electronic filters were used to reduce the electronic noises. The scanning velocity of the moving mirror was set to 1.266 cm z s21 for all
Copyright © 1998 by Academic Press
252
LIN ET AL.
FIG. 2. The spectrum of the R(3) branch of the (3000) overtone of silane. (A) is the original spectrum, (B) is the deconvoluted spectrum, which demonstrates the components of the original spectrum, and (C) is the simulated spectrum. The absorption lines were fitted simultaneously.
except 0.633 cm z s21 for the (6000) band. A 32-cm21 resolution phase spectrum was recorded for phase correction with the Mertz method. Boxcar apodization function was chosen in most cases except the Norton–Beer Weak function was used for the measurement of the (3100), (2200), and (6000) bands. The spectra were calibrated by residual water lines taken from HITRAN 96. The accuracy was estimated to be 0.001 cm21 for strong lines and 0.005 cm21 for weak lines. The Doppler broadening was greater than the estimated pressure broadening in our experiment. The value of absorbance at wavenumber n, A peak(n), never exceeded 0.50. Based on the Beer–Lambert’s Law (12), we have I~ n ! 5 I 0~ n ! exp~2A~ n ! PL!,
[3]
where A( n ) denotes the absorption coefficient at wavenumber n, P is the sample pressure, and L is the absorption length. The integrated absorption coefficient A is obtained by integrating the A( n ) against the wavenumber of absorption: A5
E
A~n!dn 5
FE
G
ln~I0~n!/I~n!!dn /PL 5 ^Ab&/PL.
[4]
We measured the value of integrated absorbance, ^ Ab& 5 * ln(I 0 ( n )/I( n ))d n , at various sample pressures and absorption lengths, and value A was obtained by a least-squares fitting of the ^ Ab& values to Eq. [4].
The recorded spectra were vibrationally analyzed and assigned in Ref. (13). The local mode notation (n 1 n 2 n 3 n 4 ) used here to label the excited stretching overtone states gives the quantum number of excitation in four individual Si–H bonds. The vibrational–transition moments can be derived from either total vibrational band intensities or individual vibration– rotational line intensities. The results are equivalent if rotation and vibration are separable. However, there are discrepancies between these two results when vibration–rotational interactions are not negligible. Our data were analyzed in both ways. By means of the total vibrational band intensity, the absorbance of overtones or combination bands can be obtained by integrating the absorption lines directly if they are free from overlapping. It works for the (1000), (4000), (5000), and (6000) bands. Of course, the residual water lines were excluded from integration. The value of ^ Ab& of the (5000) band against the optical density, the product of PL is illustrated in Fig. 1 to demonstrate the good linearity. The results are given in Table 2, which shows the observed and calculated values obtained by the theoretical model which will be discussed in the next section. However, due to the poor S/N ratio, the A value for the (6000) band was determined at single sample pressure. For overlapping bands, such as the (2000) and (1100), the (3000) and (2100), and the (3100) and (2200) bands, it is impossible to obtain the band intensity with the method mentioned above. Therefore, the total vibrational band intensities of these bands could be achieved only after the spectrum had been rotationally analyzed and contributions from various
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TABLE 3 Observed Scaled Intensities of SiH4 Obtained by Individual Line Absorbance
bands were separated. Then the absorption coefficient of individual line in each band were summed up to yield the total vibrational band absorption coefficients. However, it is quite difficult to assign the lines when J goes high, e.g., higher than nine in the (3000) overtone, owing to the complication of the spectrum. Thus, the band intensities we obtained are just the estimated values. To obtain relative intensities from individual lines, we work out the absorbance of R( J) ( J 5 3, 4, and 5) branches by fitting each absorption line to a Voigt lineshape plus a baseline using a software based on the Levenberg–Marquardt algorithm (14). In our experiment, the effect of the instrumental lineshape is of minor importance and not considered here (12). The lines were assigned according to Ref. (7, 15) and our analysis (17). In the fitting, the lineshape parameters such as linecenter position, height, and width were adjustable and the integrated absorbance was evaluated as the area parameter of the fitting
Voigt function. The blended lines were deconvoluted by fitting them simultaneously. As an example, in Fig. 2 we display the original (A), the deconvoluted (B), and the simulated (C) spectra of the R(3) branch of (3000) overtone. The blended K 5 0 and K 5 1 lines at about 6383.6 cm21 were deconvoluted and the components are shown in (B). The A value obtained by least-squares fitting the ^ Ab& value of each line against the optical density was then summed to yield the absorption coefficients of R( J) branches with J 5 3, 4, and 5. Taking advantage of the method described above, we obtained relative intensities of the R( J) branches, which are displayed in Table 3. It shows that there are a few differences among these experimental values, and the final relative intensities listed in Table 2 are the averaged values over those obtained from three R( J) branches. To estimate the uncertainty of our experimental results, the following sources of error should be considered and upper
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TABLE 4 Observed and Calculated Intensities of SiH4 Stretching Overtones and Combination States
limits for the relative uncertainty they introduce are given as follows: sample purity (1%), gas cell length (2%), isotopic abundance (5%), pressure instability and pressure measurement uncertainty (2%), temperature instability and temperature measurement uncertainty (0.7%), instrumental lineshape function effects (0.5%), residual water weak lines (0.5%), uncertainty in the 100% transmittance level (0.1%), lineshape fitting error (2%), least-squares fitting error (2%), hot band effect and band overlapping effect (varies with individual bands), and the instability of our Bruker IFS120HR spectrometer (0.1%). The uncertainty of the relative intensities was estimated to be less than 7% for those obtained from bands free from overlapping and from individual line intensities, while 15% was estimated for overlapping bands. 2.2 GeH4 The GeH4 gas sample was synthesized and purified by the sample preparing group in our laboratory (16). The purity was about 88%. The most residual substance was CO2. The highresolution absorption spectra of GeH4, ranging from 1700 to 11 000 cm21, were also recorded on our Bruker IFS120HR Fourier Transform spectrometer with different setups listed in Table 4. The sample preparation technique and the experimental configuration are the same as that of SiH4 and will not be repeated here. We point out that with this sample preparation technique, the purity of GeH4 in gas cell is improved to be better than 95%. The acquisition mode was also the single side and fast return. Optical filters were employed to prevent detectors from overload and to avoid folding. Electronic filters were used to eliminate the electronic noises. The scanning velocity of the
moving mirror was 1.266 cm z s21 for all except 0.633 cm z s21 for the (3000) and (2100) bands. Phase correction was performed by the Mertz mode with phase spectrum recorded at a resolution of 32 cm21. The Boxcar apodization function was chosen. The spectra were calibrated by residual water lines taken from HITRAN 96. The accuracy was estimated to be 0.001 cm21 for strong lines and 0.005 cm21 for weak lines. The Doppler broadening was greater than the estimated pressure broadening in our experiment. The recorded spectra were vibrationally analyzed and assigned in Ref. (13). The third stretching overtone manifolds were observed the first time and analyzed (17). We obtained the relative intensities of GeH4 with the method of individual vibration–rotational line integration, which was outlined for SiH4 in the previous section. The lines of R( J), J 5 0, 1, . . . , 6, were used, and only the 74 GeH4 isotopic species were analyzed. The results are listed in Table 5. To estimate the uncertainty of the experimental results of GeH4, we considered the following sources of error and upper limits for the relative uncertainty they introduce: sample purity (8%), gas cell length (2%), pressure instability and pressure measurement uncertainty (2%), temperature instability and temperature measurement uncertainty (0.7%), instrumental lineshape function effects (0.5%), residual water weak lines (0.5%), uncertainty in the 100% transmittance level (0.1%), lineshape fitting error (2%), least-squares fitting error (2%), and the instability of our Bruker IFS120HR spectrometer (0.1%). The overall uncertainty of the relative intensities was estimated to be less than 12%.
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TABLE 5 Observed and Calculated Relative Intensities of Stretching Vibrational Bands of GeH4
3. DISCUSSION
There are several points of our experimental data worth discussing. First, the total vibrational band intensities of those overlapping bands could be achieved only after the rotational structure had been analyzed and the contributions from various bands had been separated with the help of the deconvolution method mentioned above. Until now, the lack of necessary detailed knowledge of the vibration–rotational constants prevented us from further progress. However, among the overlapping bands, the intensities of a strong band could be determined with higher accuracy since its overlapping effect could be estimated and actually was rather small. Such is the case in the (2000) and (2100) bands of SiH4. Second, the discrepancies between intensities deduced from the whole band and those from the individual line, together with the differences among the relative intensities deduced from different R( J) branches, indicate vibration–rotational interaction. In the case of SiH4, the intensities deduced from Band is generally smaller than those deduced from Line in our measurement. It is not surprising to realize that the R branches of local mode overtones are usually much stronger than the P branches when compared with the fundamentals. (Although the lines of R( J) are often
free from overlapping when J is low, they must be applied carefully due to the potential vibration–rotation interaction.) The situation of GeH4 is similar to that of SiH4, although we did not deduce the intensities from Band. Finally, it is interesting to note the remarkably unusual behavior of v 5 3 bands of SiH4 and v 5 4 bands of GeH4. In the former, the strikingly weak (3000) overtone and significantly strong (2100) combination band has been observed earlier by McKean et al. (18) and Campargue et al. (19) at medium resolution (0.1– 0.2 cm21) and later by Zhu et al. (7) at higher resolution. Our results reveal that the (2100; 1F2) band is about one order of magnitude stronger than the (3000; F2) band. We also find that, like the (3000) overtone (7), the (2100; 2F2) band located at 6499.77 cm21 is extremely strong in the R branch and weak in the P branch, while the (2100; 1F2) band is equally strong in the P and R branch. In the latter, the (4000) overtone is weaker than the (3100) combination band which was reported in Ref. (11). However, the relative intensities of these bands obtained in this work are quite different from those in reported Ref. (11) for the reason mentioned in the first section. A comparison of our experimental data with those in Ref. (11) can be found in Table 6.
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TABLE 6 Comparison of the Observed Relative Intensities of Stretching Vibrational Bands of GeH4
The intensities of overtone and combination bands of SiH4 and GeH4 reported in this work, together with those measured earlier by Bernheim et al. (10), provide a good test of the dipole model which has been detailed in Ref. (13) and will not be repeated here. Using the bond dipole function [2] with m and R* adjustable, we find that the observed intensities of all overtones and the (1100) combination band of SiH4 obtained by total band intensity can be well reproduced at m 5 5 and R* 5 0.635 Å (see Table 2). The potential energy parameters, De, a, and frr9, are obtained by a global fitting of the stretching band origins with the ACAO model (21), which yields De 5 37 706.9 cm21, a 5 1.394 Å, and frr9 5 1524.7 cm21 Å22. The bond length at the equilibrium nuclear configuration R0 is set to 1.4732 Å. In the case of GeH4, the relative intensities of overtones can be well reproduced with m 5 5 and R* 5 0.585 Å (see Table 5). The potential energy parameters, De, a, and frr9, are also obtained by globally fitting the stretching band origins with the ACAO model (21), which yields De 5 34 956.0 cm21, a 5 1.41422 Å, and frr9 5 594 cm21 Å22. The bond length at the equilibrium nuclear configuration R0 is set to 1.520 Å. In addition, we find that the calculations are quite sensitive to the changes in m and R* values. In this model, although the relative intensities of overtone can be well reproduced, the results of the combination bands are unsatisfied. Furthermore, the bending vibrations are neglected and all intensities are assumed to be carried by the stretching vibrations in our model. This should be taken into account in further studies. ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China and the Chinese Academy of Sciences. We thank Dr. Ze-Yi Zhou and Ms. Ke Deng for help in their GeH4 synthesis.
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