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The Molecular Constants and Potential Energy Curve of the Ground StateX1Σ+in KLi
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
189, 244–248 (1998)
MS987543
The Molecular Constants and Potential Energy Curve of the Ground State X 1S / in KLi V. Bednarska,* I. Jackowska,† W. Jastrze– bski,† and P. Kowalczyk* *Institute of Experimental Physics, Warsaw University, ul. Hozg a 69, 00-681 Warsaw, Poland; and †Institute of Physics, Polish Academy of Sciences, Al. Lotniko´w 32/46, 02-668 Warsaw, Poland Received December 10, 1997
The ground state X 1S / of the diatomic molecule KLi has been studied by analyzing spectra of the B 1P –X 1S / system, simplified by polarization labeling. Rotational and vibrational constants are reported for the X 1S / state covering about 45% of its potential well depth and the potential curve is constructed by the Rydberg–Klein–Rees (RKR) procedure. Comparison with previous experimental and theoretical work is made. q 1998 Academic Press I. INTRODUCTION
Spectroscopic studies of the potassium-lithium dimer under rotational resolution are quite few. Engelke et al. ( 1 ) were the first to achieve such resolution by laser spectroscopy methods. Combining high-resolution excitation spectra in selected spectral regions with more extensive laserinduced fluorescence study, they characterized the ground state X 1S / of KLi up to vibrational level £ Å 33. However, the molecular constants derived in this work were of preliminary character, because the reported differences between observed and calculated line positions exceeded 1 cm01 . The reason for these discrepancies was probably in perturbations of the excited states of KLi involved in the observed transitions, which were neglected in Ref. (1 ) . In our recent experiments ( 2, 3 ) we have investigated the B 1P – X 1S / system by Doppler-free polarization spectroscopy and obtained highly precise molecular constants for the £ Å 0 – 4 levels of the ground state. The aim of the present work is to extend the analysis of the X 1S / state to higher vibrational levels. II. METHOD AND EXPERIMENTAL SETUP
We employ the polarization labeling spectroscopy technique, with the L-type excitation scheme (4) (see Fig. 1). Two laser beams of different frequencies are interacting with a sample of KLi molecules. The fixed wavelength of the first, ‘‘probe’’ laser is resonant with a known transition B 1P( £*b , J *b ) – X 1S / ( £9a , J 9a ) in KLi. The involved rovibrational levels in both states are said to be labeled by the laser light. Note that the probe laser intensity is high enough to transfer considerable part of the molecules to the excited state. The probe beam has to pass a polarizer in front of the sample cell and an analyzer behind it. The polarizer and analyzer are crossed so that the probe beam is extinguished
unless an optical anisotropy is introduced to molecular sample. This can be done by the circularly or linearly polarized light of the second, ‘‘dump’’ laser. The dump laser is tuned across the B 1P –X 1S / band system and orients or aligns the molecules in levels resonant with the laser wavelength. This is achieved mostly by stimulated emission from the upper state levels (excited by the probe laser) down to the ground state. Each time a transition induced by the dump beam involves the upper level ( £*b , J *b ) labeled by the probe laser, the probe beam changes its polarization. Thus the information about the B–X spectrum of KLi is contained in the transmitted intensity of the probe beam. The observed spectrum (called a ‘‘polarization labeling spectrum’’) is simplified by the fact that the observed lines terminate on a single excited state level with fixed ( £*b , J *b ) quantum numbers, whereas a broad range of vibrational levels in the ground state is sampled. In our experimental realization of the described method, a Lumonics EX500 excimer laser pumped simultaneously two dye lasers. The dump dye laser (Lumonics HD500, 2 mJ pulse energy, 0.1 cm01 spectral width) was scanned in the 15 000–17 600 cm01 region. Three dyes, DCM, Rhodamine B, and Rhodamine 6G, were used depending on the frequency required. Residual laser beams were sent into an argon optogalvanic cell and a Fabry–Pe´rot interferometer (FSR Å 1 cm01 ) for frequency calibration. The accuracy in determination of absolute wavenumbers over the whole investigated range was better than 0.1 cm01 . The probe dye laser [home built, Littman-type (5), linewidth below 1 cm01 ], operating on Rhodamine 6G/110 mixture, was set at a fixed wavelength. Because the probe laser line was spectrally rather broad, it was resonant with a few known rovibronic transitions in the B 1P –X 1S / system at the same time. For better control of the probe laser stability during the measurements, we have chosen nine fixed wavelengths coinciding with strong optogalvanic lines of argon. They are
244 0022-2852/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.
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GROUND STATE IN KLi
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FIG. 1. Schematic diagram of the experimental setup and the excitation scheme. A—analyzer, Ar HC—argon hollow-cathode lamp, FP—Fabry– Pe´rot interferometer, l /4—quarter-wave plate, P—polarizer, PD—photodiode, PMT—photomultiplier tube.
listed in Table 1 along with molecular transitions in KLi excited with them. The dump and probe laser pulses were sent in the same direction through the three-section heat pipe oven (6) containing KLi vapor, where they overlapped both spatially and temporally. The transmission of the linearly
polarized probe beam through the molecular sample and the crossed analyzer was monitored by a photomultiplier coupled to the boxcar averager. The polarization labeling spectrum was recorded digitally, together with the optogalvanic spectrum of argon and the interferometer fringes, using an
FIG. 2. Part of the polarization spectrum of KLi observed with circularly polarized dump laser beam. The assigned progression corresponds to ˚. transitions B 1P –X 1S / terminating on the B state level ( £* Å 1, J * Å 36, e-parity), labeled by the probe laser stabilized on the ArI line at l Å 5689.9 A The polarization signal is not corrected for the dump laser intensity.
Copyright q 1998 by Academic Press
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IBM PC computer. A detailed description of our apparatus can be found elsewhere (7).
TABLE 2 The Molecular Constants for the X 1S / State of KLia
III. RESULTS AND DISCUSSION
Figure 2 displays a typical fragment of the polarization labeling spectrum of 39K 7Li. This particular scan contains single £9 progression involving a known B 1P( £*b , J *b ) level.
TABLE 1 Transitions in the B 1P –X 1S / Band System of 39K 7Li Excited by the Labeling Laser (probe laser) Stabilized on Atomic ArI Lines
a All quantities, except when noted, are in cm01 . The quoted error of a constant is one standard deviation. The most important constants are compared with theoretical ones.
In the present work a total of 537 transitions were analyzed for the B 1P –X 1S / band system. We made use only of the labeled levels in the B 1P state from the range £* Å 0–2, studied previously under high resolution (2). Hence, for the ( £9, J 9 ) levels in the X 1S / state we were able to cover the range 0 ° £9 ° 14, 3 ° J 9 ° 64, limited by Franck– Condon factors for the B–X transition. Because the highest £9 vibrational levels observed in the polarization labeling spectrum lie more than 5.5 kT above the bottom of the ground state potential, stimulated emission induced by the dump light was indeed responsible for creating optical anisotropy in the sample, as described in Section 2. The frequency n of any transition was described by n Å T( £*, J * ) 0 T( £9, J 9 ).
[1]
The term values T( £*, J * ) of the excited B 1P state have been accurately measured in the previous Doppler-free study (2 ) with a standard error of 0.002 cm01 . We subtracted from them the measured line positions n and obtained the term values T( £9, J 9 ) of the ground state X 1S / , Copyright q 1998 by Academic Press
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GROUND STATE IN KLi
TABLE 3 Rotationless RKR Potential Energy Curve for the X 1S / State of KLi
according to Eq. [1] . Because the experimental errors of the high-resolution experiment (2 ) were about two orders of magnitude smaller than the uncertainty of the present measurements, no additional errors were introduced to our analysis. We represented the ground state term values by the Dunham expansion T( £9, J 9 ) Å ∑ Ymn ( £ / 12 ) m[J(J / 1)] n .
[2]
m ,n
The Dunham coefficients Ymn were calculated using a leastsquares fitting procedure. The series expansion in Eq. [2] was truncated by ascertaining the degree of the polynomial for which the coefficient of the highest term had a standard error lower than 10% of its value. The term values T( £9, J 9 ) were fitted to an rms deviation of 0.03 cm01 , well below the experimental uncertainty. The Dunham coefficients for the X 1S / state resulting from the fit are presented in Table 2. In some cases a rather large number of figures had to be given to avoid any roundoff errors and to reproduce the measured term values. Next, the potential curve for the X 1S / state of KLi was constructed by the Rydberg– Klein – Rees (RKR) method. The results are shown in Table 3, which reports the vibrational energy levels and the corresponding classical turning points for the rotationless potential. It should be noted at this juncture that the experimental Y02 and Y11 constants compare favorably with those calculated using the Kratzer and Pekeris relations (Y02 Å 00.152 1 10 05 cm01 , Y11 Å 00.228 1 10 02 cm01 , respectively ), indicating that the ground state potential curve is close to the Morse potential. The consistency of the obtained constants is also proved by a small value of Y00 , equal to 0.05 cm01 ( note that Y00 is included in the vibrational energies of Table 3) . For comparison, term values calculated from the Dunham coefficients given earlier by Engelke et al. (1) deviate from the experimental ones by up to 1 cm01 in the range of £9 and J 9 quantum numbers investigated here. Hence our data provide an order of magnitude improvement in this range. The experimentally obtained parameters of the X 1S / state potential curve can be confronted with the available results of theoretical calculations. The ground state of KLi has been the subject of various ab initio (8), model potential (9) and pseudopotential (10) calculations. Table 2 contains comparison of the salient experimental and theoretical constants. It can be easily seen that the results of Mu¨ller and Meyer (8) are by far the most accurate, in particular providing the vibrational and rotational constants within 0.5% of the experimental values. From the limited portion of the potential curve sampled by the present measurements it is hazardous to extrapolate toward higher £9 to determine the dissociation energy. Therefore we accept the theoretical value De Å 6138 cm01 (8). The same calculations underestimated dissociation energies
a The first line refers to the bottom of the potential curve: R is the equilibrium distance.
of NaLi and NaK only by 72 and 105 cm01 , respectively [cf. Refs. (11) and (12)]. Thus, our study covers approximately 45% of the ground state potential. However, this investigation should be extended to higher vibrational levels, to obtain more precise experimental information about the potential well depth of the X 1S / state. ACKNOWLEDGMENTS We are grateful to the Polish Committee for Scientific Research for partial funding of this research (Grant KBN 2 P03B 010 10). V.B. is grateful for the ‘‘young researcher’’ Grant KBN 2 P03B 006 13.
REFERENCES 1. F. Engelke, H. Hage, and U. Sprick, Chem. Phys. 88, 443 – 453 ( 1984 ) .
Copyright q 1998 by Academic Press
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2. V. Bednarska, A. Ekers, P., Kowalczyk, and W. Jastrze– bski, J. Chem. Phys. 106, 6332–6337 (1997). 3. W. Jastrze– bski and P. Kowalczyk, Spectrochim. Acta Part A, in print. 4. N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, Phys. Rev. A 24, 822–834 (1981). 5. M. G. Littman and H. J. Metcalf, Appl. Opt. 17, 2224–2227 (1978). 6. V. Bednarska, I. Jackowska, W. Jastrze– bski, and P. Kowalczyk, Meas. Sci. Technol. 7, 1291–1293 (1996).
7. W. Jastrze– bski and P. Kowalczyk, Phys. Rev. A 54, 1046–1051 (1995). 8. W. Mu¨ller and W. Meyer, J. Chem. Phys. 80, 3311–3320 (1984). 9. G. Dotelli, E. Lombardi, and L. Jansen, J. Mol. Struct. 279, 85–91 (1993). 10. R. Ga´spa´r and J. Szabo´, Acta Phys. Acad. Sci. Hung. 74, 391–398 (1994). 11. A. J. Ross, C. Effantin, J. d’Incan, and R. F. Barrow, Mol. Phys. 56, 903–912 (1985). 12. C. E. Fellows, J. Chem. Phys. 94, 5855–5864 (1991).
Copyright q 1998 by Academic Press
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189, 244–248 (1998)
MS987543
The Molecular Constants and Potential Energy Curve of the Ground State X 1S / in KLi V. Bednarska,* I. Jackowska,† W. Jastrze– bski,† and P. Kowalczyk* *Institute of Experimental Physics, Warsaw University, ul. Hozg a 69, 00-681 Warsaw, Poland; and †Institute of Physics, Polish Academy of Sciences, Al. Lotniko´w 32/46, 02-668 Warsaw, Poland Received December 10, 1997
The ground state X 1S / of the diatomic molecule KLi has been studied by analyzing spectra of the B 1P –X 1S / system, simplified by polarization labeling. Rotational and vibrational constants are reported for the X 1S / state covering about 45% of its potential well depth and the potential curve is constructed by the Rydberg–Klein–Rees (RKR) procedure. Comparison with previous experimental and theoretical work is made. q 1998 Academic Press I. INTRODUCTION
Spectroscopic studies of the potassium-lithium dimer under rotational resolution are quite few. Engelke et al. ( 1 ) were the first to achieve such resolution by laser spectroscopy methods. Combining high-resolution excitation spectra in selected spectral regions with more extensive laserinduced fluorescence study, they characterized the ground state X 1S / of KLi up to vibrational level £ Å 33. However, the molecular constants derived in this work were of preliminary character, because the reported differences between observed and calculated line positions exceeded 1 cm01 . The reason for these discrepancies was probably in perturbations of the excited states of KLi involved in the observed transitions, which were neglected in Ref. (1 ) . In our recent experiments ( 2, 3 ) we have investigated the B 1P – X 1S / system by Doppler-free polarization spectroscopy and obtained highly precise molecular constants for the £ Å 0 – 4 levels of the ground state. The aim of the present work is to extend the analysis of the X 1S / state to higher vibrational levels. II. METHOD AND EXPERIMENTAL SETUP
We employ the polarization labeling spectroscopy technique, with the L-type excitation scheme (4) (see Fig. 1). Two laser beams of different frequencies are interacting with a sample of KLi molecules. The fixed wavelength of the first, ‘‘probe’’ laser is resonant with a known transition B 1P( £*b , J *b ) – X 1S / ( £9a , J 9a ) in KLi. The involved rovibrational levels in both states are said to be labeled by the laser light. Note that the probe laser intensity is high enough to transfer considerable part of the molecules to the excited state. The probe beam has to pass a polarizer in front of the sample cell and an analyzer behind it. The polarizer and analyzer are crossed so that the probe beam is extinguished
unless an optical anisotropy is introduced to molecular sample. This can be done by the circularly or linearly polarized light of the second, ‘‘dump’’ laser. The dump laser is tuned across the B 1P –X 1S / band system and orients or aligns the molecules in levels resonant with the laser wavelength. This is achieved mostly by stimulated emission from the upper state levels (excited by the probe laser) down to the ground state. Each time a transition induced by the dump beam involves the upper level ( £*b , J *b ) labeled by the probe laser, the probe beam changes its polarization. Thus the information about the B–X spectrum of KLi is contained in the transmitted intensity of the probe beam. The observed spectrum (called a ‘‘polarization labeling spectrum’’) is simplified by the fact that the observed lines terminate on a single excited state level with fixed ( £*b , J *b ) quantum numbers, whereas a broad range of vibrational levels in the ground state is sampled. In our experimental realization of the described method, a Lumonics EX500 excimer laser pumped simultaneously two dye lasers. The dump dye laser (Lumonics HD500, 2 mJ pulse energy, 0.1 cm01 spectral width) was scanned in the 15 000–17 600 cm01 region. Three dyes, DCM, Rhodamine B, and Rhodamine 6G, were used depending on the frequency required. Residual laser beams were sent into an argon optogalvanic cell and a Fabry–Pe´rot interferometer (FSR Å 1 cm01 ) for frequency calibration. The accuracy in determination of absolute wavenumbers over the whole investigated range was better than 0.1 cm01 . The probe dye laser [home built, Littman-type (5), linewidth below 1 cm01 ], operating on Rhodamine 6G/110 mixture, was set at a fixed wavelength. Because the probe laser line was spectrally rather broad, it was resonant with a few known rovibronic transitions in the B 1P –X 1S / system at the same time. For better control of the probe laser stability during the measurements, we have chosen nine fixed wavelengths coinciding with strong optogalvanic lines of argon. They are
244 0022-2852/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.
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GROUND STATE IN KLi
245
FIG. 1. Schematic diagram of the experimental setup and the excitation scheme. A—analyzer, Ar HC—argon hollow-cathode lamp, FP—Fabry– Pe´rot interferometer, l /4—quarter-wave plate, P—polarizer, PD—photodiode, PMT—photomultiplier tube.
listed in Table 1 along with molecular transitions in KLi excited with them. The dump and probe laser pulses were sent in the same direction through the three-section heat pipe oven (6) containing KLi vapor, where they overlapped both spatially and temporally. The transmission of the linearly
polarized probe beam through the molecular sample and the crossed analyzer was monitored by a photomultiplier coupled to the boxcar averager. The polarization labeling spectrum was recorded digitally, together with the optogalvanic spectrum of argon and the interferometer fringes, using an
FIG. 2. Part of the polarization spectrum of KLi observed with circularly polarized dump laser beam. The assigned progression corresponds to ˚. transitions B 1P –X 1S / terminating on the B state level ( £* Å 1, J * Å 36, e-parity), labeled by the probe laser stabilized on the ArI line at l Å 5689.9 A The polarization signal is not corrected for the dump laser intensity.
Copyright q 1998 by Academic Press
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BEDNARSKA ET AL.
IBM PC computer. A detailed description of our apparatus can be found elsewhere (7).
TABLE 2 The Molecular Constants for the X 1S / State of KLia
III. RESULTS AND DISCUSSION
Figure 2 displays a typical fragment of the polarization labeling spectrum of 39K 7Li. This particular scan contains single £9 progression involving a known B 1P( £*b , J *b ) level.
TABLE 1 Transitions in the B 1P –X 1S / Band System of 39K 7Li Excited by the Labeling Laser (probe laser) Stabilized on Atomic ArI Lines
a All quantities, except when noted, are in cm01 . The quoted error of a constant is one standard deviation. The most important constants are compared with theoretical ones.
In the present work a total of 537 transitions were analyzed for the B 1P –X 1S / band system. We made use only of the labeled levels in the B 1P state from the range £* Å 0–2, studied previously under high resolution (2). Hence, for the ( £9, J 9 ) levels in the X 1S / state we were able to cover the range 0 ° £9 ° 14, 3 ° J 9 ° 64, limited by Franck– Condon factors for the B–X transition. Because the highest £9 vibrational levels observed in the polarization labeling spectrum lie more than 5.5 kT above the bottom of the ground state potential, stimulated emission induced by the dump light was indeed responsible for creating optical anisotropy in the sample, as described in Section 2. The frequency n of any transition was described by n Å T( £*, J * ) 0 T( £9, J 9 ).
[1]
The term values T( £*, J * ) of the excited B 1P state have been accurately measured in the previous Doppler-free study (2 ) with a standard error of 0.002 cm01 . We subtracted from them the measured line positions n and obtained the term values T( £9, J 9 ) of the ground state X 1S / , Copyright q 1998 by Academic Press
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GROUND STATE IN KLi
TABLE 3 Rotationless RKR Potential Energy Curve for the X 1S / State of KLi
according to Eq. [1] . Because the experimental errors of the high-resolution experiment (2 ) were about two orders of magnitude smaller than the uncertainty of the present measurements, no additional errors were introduced to our analysis. We represented the ground state term values by the Dunham expansion T( £9, J 9 ) Å ∑ Ymn ( £ / 12 ) m[J(J / 1)] n .
[2]
m ,n
The Dunham coefficients Ymn were calculated using a leastsquares fitting procedure. The series expansion in Eq. [2] was truncated by ascertaining the degree of the polynomial for which the coefficient of the highest term had a standard error lower than 10% of its value. The term values T( £9, J 9 ) were fitted to an rms deviation of 0.03 cm01 , well below the experimental uncertainty. The Dunham coefficients for the X 1S / state resulting from the fit are presented in Table 2. In some cases a rather large number of figures had to be given to avoid any roundoff errors and to reproduce the measured term values. Next, the potential curve for the X 1S / state of KLi was constructed by the Rydberg– Klein – Rees (RKR) method. The results are shown in Table 3, which reports the vibrational energy levels and the corresponding classical turning points for the rotationless potential. It should be noted at this juncture that the experimental Y02 and Y11 constants compare favorably with those calculated using the Kratzer and Pekeris relations (Y02 Å 00.152 1 10 05 cm01 , Y11 Å 00.228 1 10 02 cm01 , respectively ), indicating that the ground state potential curve is close to the Morse potential. The consistency of the obtained constants is also proved by a small value of Y00 , equal to 0.05 cm01 ( note that Y00 is included in the vibrational energies of Table 3) . For comparison, term values calculated from the Dunham coefficients given earlier by Engelke et al. (1) deviate from the experimental ones by up to 1 cm01 in the range of £9 and J 9 quantum numbers investigated here. Hence our data provide an order of magnitude improvement in this range. The experimentally obtained parameters of the X 1S / state potential curve can be confronted with the available results of theoretical calculations. The ground state of KLi has been the subject of various ab initio (8), model potential (9) and pseudopotential (10) calculations. Table 2 contains comparison of the salient experimental and theoretical constants. It can be easily seen that the results of Mu¨ller and Meyer (8) are by far the most accurate, in particular providing the vibrational and rotational constants within 0.5% of the experimental values. From the limited portion of the potential curve sampled by the present measurements it is hazardous to extrapolate toward higher £9 to determine the dissociation energy. Therefore we accept the theoretical value De Å 6138 cm01 (8). The same calculations underestimated dissociation energies
a The first line refers to the bottom of the potential curve: R is the equilibrium distance.
of NaLi and NaK only by 72 and 105 cm01 , respectively [cf. Refs. (11) and (12)]. Thus, our study covers approximately 45% of the ground state potential. However, this investigation should be extended to higher vibrational levels, to obtain more precise experimental information about the potential well depth of the X 1S / state. ACKNOWLEDGMENTS We are grateful to the Polish Committee for Scientific Research for partial funding of this research (Grant KBN 2 P03B 010 10). V.B. is grateful for the ‘‘young researcher’’ Grant KBN 2 P03B 006 13.
REFERENCES 1. F. Engelke, H. Hage, and U. Sprick, Chem. Phys. 88, 443 – 453 ( 1984 ) .
Copyright q 1998 by Academic Press
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2. V. Bednarska, A. Ekers, P., Kowalczyk, and W. Jastrze– bski, J. Chem. Phys. 106, 6332–6337 (1997). 3. W. Jastrze– bski and P. Kowalczyk, Spectrochim. Acta Part A, in print. 4. N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, Phys. Rev. A 24, 822–834 (1981). 5. M. G. Littman and H. J. Metcalf, Appl. Opt. 17, 2224–2227 (1978). 6. V. Bednarska, I. Jackowska, W. Jastrze– bski, and P. Kowalczyk, Meas. Sci. Technol. 7, 1291–1293 (1996).
7. W. Jastrze– bski and P. Kowalczyk, Phys. Rev. A 54, 1046–1051 (1995). 8. W. Mu¨ller and W. Meyer, J. Chem. Phys. 80, 3311–3320 (1984). 9. G. Dotelli, E. Lombardi, and L. Jansen, J. Mol. Struct. 279, 85–91 (1993). 10. R. Ga´spa´r and J. Szabo´, Acta Phys. Acad. Sci. Hung. 74, 391–398 (1994). 11. A. J. Ross, C. Effantin, J. d’Incan, and R. F. Barrow, Mol. Phys. 56, 903–912 (1985). 12. C. E. Fellows, J. Chem. Phys. 94, 5855–5864 (1991).
Copyright q 1998 by Academic Press
AID
JMS 7543
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6t2b$$$$83
04-20-98 14:40:39
mspa