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Single-pulse and multiple-pulse femtosecond spectroscopy: Progress toward collective mode-selective chemistry
ELSEVIER
Physica B 219&220 (1996) 734-737
Single-pulse and multiple-pulse femtosecond spectroscopy: Progress toward collective mode-selective chemistry Hitoshi Kawashima, Marc M. Wefers*, Keith A. Nelson Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Abstract Recent efforts in femtosecond pulse-shaping and multiple-pulse femtosecond spectroscopy, with the ultimate aim of coherent optical control over condensed material behavior and structure, are reviewed. Real-time detection methods are also discussed. Experimental demonstrations of coherent control over electronic and vibrational responses are summarized.
1. Introduction "Impulsive" excitation of optic phonons has been demonstrated in a very wide range of materials, with several distinct excitation mechanisms identified and used for spectroscopic observations [-1]. Some recent efforts have been directed toward not only observation of but also control over collective and molecular behavior [-2]. In the case of control over molecular responses, with the ultimate aim of directing chemical reactivity, this represents a revival of interest in "mode-selective chemistry" [3]. By analogy, the area of coherent optical control over condensed material behavior, with the ultimate aim of directing collective structural change, has been called "collective mode-selective chemistry" [-2]. Several discussions of phase transitions and domain switching induced through ultrafast excitation have been presented [4-6]. Our recent attempts to develop the optical tools needed for collective mode-selective chemistry and to
* Corresponding author.
demonstrate some of the possible objectives are briefly reviewed.
2. Optical excitation and detection methods There are two important requirements for almost all attempts at coherent optical manipulation of material behavior and structure. First, the excitation of the sample may require an optical field which is considerably more complex than that of a single ultrashort pulse. As in nuclear magnetic resonance (NMR), multiple-pulse sequences and other complex excitation waveforms with controlled time-dependent amplitude, phase, frequency, and polarization profiles may be necessary for extensive manipulation of the sample response. Second, ultrafast time-resolved detection of any irreversible response in a solid sample may need to be conducted in a single laser shot, i.e. in real time, since the irradiated region of the sample may be permanently changed and replacement with new material after each laser shot is usually impractical. This cannot be accomplished with fast electronic recording devices since even the fastest commercially
0921-4526/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD1 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 8 6 9 - 1
H. Kawashima et al./Physica B 219&220 (1996) 734-737
available streak camera offers time resolution of no better than 1 ps. 2.1. Excitation methods: Jemtosecond pulse shaping
It is now possible to produce, from a single incident femtosecond pulse, complex waveforms whose timedependent amplitude and phase profiles are specified. In addition, control over the time-dependent frequency profile of the waveform (within the frequency bandwidth of the incident pulse) and the polarization profile have been demonstrated. The pulse-shaping method was first developed for applications in ultrafast optical communications [7], but its spectroscopic potential was soon recognized and exploited [8]. The method is based on spectral filtering of the dispersed frequency components of the incident pulse by spatially varying amplitude and phase masks. The masks attenuate or shift the phases of selected frequency components, thereby altering the timedependent amplitude and phase profiles. In the original demonstrations and spectroscopic uses of this method, permanent mask patterns which were etched onto glass substrates were used. Later it was shown that multielement liquid crystal (LC) spatial light modulators (SLMs) could be used, offering computer control over the mask pattern [9]. It is now possible to generate complex waveforms with specified amplitude and phase profiles under computer control, simply specifying to the computer what are the desired waveform features. The required amplitude and phase mask patterns are determined by the computer, the patterns are generated through the computer interface with the SLMs, and the specified waveform is generated [10]. The components needed for this computer-controlled high-fidelity waveform generation are all available commercially. Improvements will continue, but the current capabilities are sufficient for many spectroscopic and control applications. 2.2. Detection methods: reaLtime, single-shot femtosecond optical measurement
As suggested above, one of the ultimate aims of collective mode-selective chemistry are to achieve coherent optical control over material structure. If such an experiment is successful, permanent (or at least long-term) structural change will be induced in the sample after irradiation by just one excitation pulse or pulse sequence. How will the sample's time-dependent response be observed? In general, femtosecond time-resolved measurements are conducted not in real time but with many thousands of excitation-probe repetitions. Recently, a method was demonstrated for single-shot, real-time femtosecond spectroscopy [11]. It is similar to methods for single-shot autocorrelation which are used
735
to characterize an ultrashort laser pulse. Cylindrical lenses are used to focus the excitation and probe beams, with a large angle between them, onto a linear region of the sample. In this manner one part of the probe beam arrives at a particular region of the sample at the same time as the excitation light; another part of the probe beam arrives slightly later; another part arrives later still, and so on. A linear space-to-time correspondence is created at the sample, and this is imaged onto a multielement (CCD) detector. In a single shot, the sample responses at many points along the time axis are recorded. Real-time observations of coherent molecular vibrations were recorded in this manner [11]. Improvements in single-shot detection methodology are possible, including for example the recording of the broadband time-resolved absorption spectrum: However, the techniques developed are already sufficient for time-resolved observations of permanent structural change in condensed materials.
3. Multiple-pulse spectroscopy experiments The first multiple-pulse femtosecond spectroscopy experiments using pulse shaping methods were conducted on optic phonons in organic and inorganic crystals [5, 12]. Sequences of femtosecond pulses were timed to match selected phonon vibrational periods. Each pulse in a sequence exerted a driving force on the selected vibrational mode through impulsive stimulated Raman scattering, leading to successive amplification of the vibrational response. In this manner a degree of control over the coherent vibrational amplitude was demonstrated through the use of temporally shaped excitation waveforms. The possibility for further control over the amplitudes of propagating phonon-polariton modes has been suggested through the use of spatially as well as temporally shaped waveforms, with which phonon amplification at different times and at different locations in the crystal could be achieved [13]. Here we review two recent experiments which illustrate control over electronic as well as vibrational responses and control over the direction as well as amplitude of lattice vibrations. 3.1. Control over a three-level electronic system
Two-pulse and three-pulse sequences were used to control the coherent electronic behavior of potassium atoms in the gas phase [14]. The electronic excited state is split through spin-orbit coupling to yield two levels separated by about 50 cm x. A first femtosecond pulse, whose central frequency is midway between the two resonances and whose spectral bandwidth includes both
736
H. Kawashima et al. /Physica B 219&220 (1996) 734-737
resonances, initiates two coherent electronic responses at the two resonant frequencies. The two coherences begin in phase, then go out of phase, back in phase, and so on due to the small frequency difference. Depending on its delay and optical phase relative to the first pulse, a second pulse may interact constructively or destructively with one or both of the coherences. In general, by varying the relative delay and phase between the two pulses, any desired amplitude ratio and relative phase between the two coherences can be produced. In other words, complete control over the final dual-coherence state may be achieved within the amplitude limitations presented by the total excitation intensity. The results of two-pulse excitation were monitored through measurement of the integrated fluorescence intensity from each of the two levels. This is a two-dimensional coherent optical control experiment, conducted entirely under computer control with the two waveform parameters (relative delay and phase) scanned as the fluorescence is measured. Three-pulse sequences were also used. In this case not only the final dual-coherence state but also the pathway through which it is reached, i.e. the intermediate dualcoherence state formed after the second pulse, is also controlled. This is a four-dimensional experiment, with two relative delay times and two relative optical phases scanned, again conducted in a simple manner under computer control. The results indicated the spectroscopic sophistication possible with current automated pulse shaping methods. They also confirmed the fidelity of the phase and amplitude profiles, which yielded the fluorescence intensities calculated for the potassium three-level system within about 2% for all the waveform parameters used. 3.2. Control over degenerate phonon orientation and amplitude
For a degenerate vibrational mode, different directions of vibrational displacement are possible. In a crystalline solid, this offers the possibility of control over the direction of ionic or molecular motions within the lattice. Control of this sort was suggested for Jahn-Teller molecules, which have degenerate molecular vibrational modes [15]. It was shown theoretically that time-dependent molecular motion along either vibrational coordinate, or along both coordinates with controlled relative vibrational phases, could be induced. In the latter case, molecular pseudorotation and other types of molecular motion are possible. The situation is analogous in crystalline solids. Experiments were conducted on crystalline quartz, which has a two-fold degenerate 128 c m - 1 optic phonon mode. Two excitation pulses with different polarizations were generated with a beamsplitter, and their timing and
polarizations were controlled with standard delay stages and waveplates. This type of arrangement is practical for two excitation pulses but would be cumbersome with more pulses or if control over the optical phases were also desired. The polarizations of the pulses were adjusted to be 45 ~ apart. In this manner one pulse induced phonon displacements along a specified phonon coordinate Q a and the other along a different coordinate Q2. If the pulses arrived at the sample at the same time, then linear motion along coordinate Q1 + Q2 was induced. On the other hand, if one pulse arrived before the other by one-fourth the vibrational period, then circular (pseudorotational) motion was induced, with the direction (clockwise or counterclockwise) of motion determined by which pulse arrived first. Elliptical motion was also induced, with the degree of ellipticity and the direction of motion determined by the choice of relative delay, With each twopulse excitation sequence, the time-dependent sample birefringence (i.e. optical Kerr effect or OKE) was measured. However, a single O K E measurement is insufficient to uniquely characterize the motion since only a single projection of the two-dimensional polarizability tensor is determined. For example, the incident probe polarization may be adjusted such that only displacements along Q1 are observed. With the incident probe pulse rotated by 45 °, displacements along Q2 can be monitored. For each choice of two-pulse excitation sequence, OKE measurements were conducted with two different incident probe pulse polarizations and the amplitude and phase of the vibrational response was determined. In this manner the time-dependent, two-dimensional vibrational trajectory induced by each excitation pulse sequence was characterized uniquely. Linear, elliptical, and circular motions in controlled directions were all observed, This experiment demonstrates optical control over the time-dependent direction as well as amplitude of vibrational motion in the case of a degenerate vibrational system. Control over several modes with multiple pulses is also possible.
4. Summary A brief review of recent steps toward achieving optical control over condensed matter behavior and structure has been presented. The development of optical tools for controlled excitation and real-time observation of collective mode-selective chemistry and the demonstration of some of the capabilities and possibilities have been discussed. The next challenges will be synthesis of the available tools and their use for driving large-amplitude, farfrom-equilibrium responses which could lead to controlled collective structural rearrangements.
H. Kawashima et al./Physica B 219&220 (1996) 734 737
Acknowledgements This work was s u p p o r t e d in part by O N R grant N00014-92-1503 a n d N S F CHE-9404548. M M W is supported by a g r a d u a t e fellowship from the C a n a d i a n NSERC.
References [ l ] L . Dhar, J. Rogers and K.A. Nelson, Chem. Rev. 94 (1994) 157. [2] H. Kawashima, M.W. Wefers and K.A. Nelson, Ann. Rev. Phys. Chem. 46 (1995) 627. [3] W.S. Warren, H. Rabitz and M. Dahlen, Science 259 (1993) 1581. [4] Y.-X. Yah, E.B. Gamble Jr. and K.A. Nelson, J. Chem. Phys. 83 (1985) 5391.
737
[5] K.A. Nelson, in: Ultrafast Phenomena IX, eds. P. Barbara and W. Knox (Springer, Berlin, 1994). [6] S. Fahy and R. Merlin, Phys. Rev. Lett. 73 (1994) 1122. [7] A.M. Weiner, J.P. Heritage and E.M. Kirschner, J. Opt. Soc. Am. B 5 (1988) 1563. [8] A.M. Weiner, D.E. Leaird, G.P. Wiederrechet and K.A. Nelson, Science 247 (1990) 1317. [9] A.M. Weiner, D.E. Leaird, J.S. Patel and J.R. Wullert, Opt. Lett. 15 (1990) 326. [10] M.M. Wefers and K.A. Nelson, Opt. Lett. 20 (1995) 1047. [11] L. Dhar, J.T. Fourkas and K.A. Nelson, Opt. Lett. 19 (1994) 1. [12] G.P. Wiederrechet, T.P. Dougherty, L. Dhar, K.A. Nelson, D.E. Leaird and A.M. Weiner, Ferroelectrics 150 (1993) 103. [13] L. Dhar and K.A. Nelson, Ferroelectrics 164 (1994) 1. [14] M.M. Wefers, H. Kawashima and K.A. Nelson, J. Chem. Phys. 102 (1995). [15] J.A. Cina and V. Romero-Rochin, J. Chem. Phys. 93 (19901 3844.
Physica B 219&220 (1996) 734-737
Single-pulse and multiple-pulse femtosecond spectroscopy: Progress toward collective mode-selective chemistry Hitoshi Kawashima, Marc M. Wefers*, Keith A. Nelson Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Abstract Recent efforts in femtosecond pulse-shaping and multiple-pulse femtosecond spectroscopy, with the ultimate aim of coherent optical control over condensed material behavior and structure, are reviewed. Real-time detection methods are also discussed. Experimental demonstrations of coherent control over electronic and vibrational responses are summarized.
1. Introduction "Impulsive" excitation of optic phonons has been demonstrated in a very wide range of materials, with several distinct excitation mechanisms identified and used for spectroscopic observations [-1]. Some recent efforts have been directed toward not only observation of but also control over collective and molecular behavior [-2]. In the case of control over molecular responses, with the ultimate aim of directing chemical reactivity, this represents a revival of interest in "mode-selective chemistry" [3]. By analogy, the area of coherent optical control over condensed material behavior, with the ultimate aim of directing collective structural change, has been called "collective mode-selective chemistry" [-2]. Several discussions of phase transitions and domain switching induced through ultrafast excitation have been presented [4-6]. Our recent attempts to develop the optical tools needed for collective mode-selective chemistry and to
* Corresponding author.
demonstrate some of the possible objectives are briefly reviewed.
2. Optical excitation and detection methods There are two important requirements for almost all attempts at coherent optical manipulation of material behavior and structure. First, the excitation of the sample may require an optical field which is considerably more complex than that of a single ultrashort pulse. As in nuclear magnetic resonance (NMR), multiple-pulse sequences and other complex excitation waveforms with controlled time-dependent amplitude, phase, frequency, and polarization profiles may be necessary for extensive manipulation of the sample response. Second, ultrafast time-resolved detection of any irreversible response in a solid sample may need to be conducted in a single laser shot, i.e. in real time, since the irradiated region of the sample may be permanently changed and replacement with new material after each laser shot is usually impractical. This cannot be accomplished with fast electronic recording devices since even the fastest commercially
0921-4526/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD1 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 8 6 9 - 1
H. Kawashima et al./Physica B 219&220 (1996) 734-737
available streak camera offers time resolution of no better than 1 ps. 2.1. Excitation methods: Jemtosecond pulse shaping
It is now possible to produce, from a single incident femtosecond pulse, complex waveforms whose timedependent amplitude and phase profiles are specified. In addition, control over the time-dependent frequency profile of the waveform (within the frequency bandwidth of the incident pulse) and the polarization profile have been demonstrated. The pulse-shaping method was first developed for applications in ultrafast optical communications [7], but its spectroscopic potential was soon recognized and exploited [8]. The method is based on spectral filtering of the dispersed frequency components of the incident pulse by spatially varying amplitude and phase masks. The masks attenuate or shift the phases of selected frequency components, thereby altering the timedependent amplitude and phase profiles. In the original demonstrations and spectroscopic uses of this method, permanent mask patterns which were etched onto glass substrates were used. Later it was shown that multielement liquid crystal (LC) spatial light modulators (SLMs) could be used, offering computer control over the mask pattern [9]. It is now possible to generate complex waveforms with specified amplitude and phase profiles under computer control, simply specifying to the computer what are the desired waveform features. The required amplitude and phase mask patterns are determined by the computer, the patterns are generated through the computer interface with the SLMs, and the specified waveform is generated [10]. The components needed for this computer-controlled high-fidelity waveform generation are all available commercially. Improvements will continue, but the current capabilities are sufficient for many spectroscopic and control applications. 2.2. Detection methods: reaLtime, single-shot femtosecond optical measurement
As suggested above, one of the ultimate aims of collective mode-selective chemistry are to achieve coherent optical control over material structure. If such an experiment is successful, permanent (or at least long-term) structural change will be induced in the sample after irradiation by just one excitation pulse or pulse sequence. How will the sample's time-dependent response be observed? In general, femtosecond time-resolved measurements are conducted not in real time but with many thousands of excitation-probe repetitions. Recently, a method was demonstrated for single-shot, real-time femtosecond spectroscopy [11]. It is similar to methods for single-shot autocorrelation which are used
735
to characterize an ultrashort laser pulse. Cylindrical lenses are used to focus the excitation and probe beams, with a large angle between them, onto a linear region of the sample. In this manner one part of the probe beam arrives at a particular region of the sample at the same time as the excitation light; another part of the probe beam arrives slightly later; another part arrives later still, and so on. A linear space-to-time correspondence is created at the sample, and this is imaged onto a multielement (CCD) detector. In a single shot, the sample responses at many points along the time axis are recorded. Real-time observations of coherent molecular vibrations were recorded in this manner [11]. Improvements in single-shot detection methodology are possible, including for example the recording of the broadband time-resolved absorption spectrum: However, the techniques developed are already sufficient for time-resolved observations of permanent structural change in condensed materials.
3. Multiple-pulse spectroscopy experiments The first multiple-pulse femtosecond spectroscopy experiments using pulse shaping methods were conducted on optic phonons in organic and inorganic crystals [5, 12]. Sequences of femtosecond pulses were timed to match selected phonon vibrational periods. Each pulse in a sequence exerted a driving force on the selected vibrational mode through impulsive stimulated Raman scattering, leading to successive amplification of the vibrational response. In this manner a degree of control over the coherent vibrational amplitude was demonstrated through the use of temporally shaped excitation waveforms. The possibility for further control over the amplitudes of propagating phonon-polariton modes has been suggested through the use of spatially as well as temporally shaped waveforms, with which phonon amplification at different times and at different locations in the crystal could be achieved [13]. Here we review two recent experiments which illustrate control over electronic as well as vibrational responses and control over the direction as well as amplitude of lattice vibrations. 3.1. Control over a three-level electronic system
Two-pulse and three-pulse sequences were used to control the coherent electronic behavior of potassium atoms in the gas phase [14]. The electronic excited state is split through spin-orbit coupling to yield two levels separated by about 50 cm x. A first femtosecond pulse, whose central frequency is midway between the two resonances and whose spectral bandwidth includes both
736
H. Kawashima et al. /Physica B 219&220 (1996) 734-737
resonances, initiates two coherent electronic responses at the two resonant frequencies. The two coherences begin in phase, then go out of phase, back in phase, and so on due to the small frequency difference. Depending on its delay and optical phase relative to the first pulse, a second pulse may interact constructively or destructively with one or both of the coherences. In general, by varying the relative delay and phase between the two pulses, any desired amplitude ratio and relative phase between the two coherences can be produced. In other words, complete control over the final dual-coherence state may be achieved within the amplitude limitations presented by the total excitation intensity. The results of two-pulse excitation were monitored through measurement of the integrated fluorescence intensity from each of the two levels. This is a two-dimensional coherent optical control experiment, conducted entirely under computer control with the two waveform parameters (relative delay and phase) scanned as the fluorescence is measured. Three-pulse sequences were also used. In this case not only the final dual-coherence state but also the pathway through which it is reached, i.e. the intermediate dualcoherence state formed after the second pulse, is also controlled. This is a four-dimensional experiment, with two relative delay times and two relative optical phases scanned, again conducted in a simple manner under computer control. The results indicated the spectroscopic sophistication possible with current automated pulse shaping methods. They also confirmed the fidelity of the phase and amplitude profiles, which yielded the fluorescence intensities calculated for the potassium three-level system within about 2% for all the waveform parameters used. 3.2. Control over degenerate phonon orientation and amplitude
For a degenerate vibrational mode, different directions of vibrational displacement are possible. In a crystalline solid, this offers the possibility of control over the direction of ionic or molecular motions within the lattice. Control of this sort was suggested for Jahn-Teller molecules, which have degenerate molecular vibrational modes [15]. It was shown theoretically that time-dependent molecular motion along either vibrational coordinate, or along both coordinates with controlled relative vibrational phases, could be induced. In the latter case, molecular pseudorotation and other types of molecular motion are possible. The situation is analogous in crystalline solids. Experiments were conducted on crystalline quartz, which has a two-fold degenerate 128 c m - 1 optic phonon mode. Two excitation pulses with different polarizations were generated with a beamsplitter, and their timing and
polarizations were controlled with standard delay stages and waveplates. This type of arrangement is practical for two excitation pulses but would be cumbersome with more pulses or if control over the optical phases were also desired. The polarizations of the pulses were adjusted to be 45 ~ apart. In this manner one pulse induced phonon displacements along a specified phonon coordinate Q a and the other along a different coordinate Q2. If the pulses arrived at the sample at the same time, then linear motion along coordinate Q1 + Q2 was induced. On the other hand, if one pulse arrived before the other by one-fourth the vibrational period, then circular (pseudorotational) motion was induced, with the direction (clockwise or counterclockwise) of motion determined by which pulse arrived first. Elliptical motion was also induced, with the degree of ellipticity and the direction of motion determined by the choice of relative delay, With each twopulse excitation sequence, the time-dependent sample birefringence (i.e. optical Kerr effect or OKE) was measured. However, a single O K E measurement is insufficient to uniquely characterize the motion since only a single projection of the two-dimensional polarizability tensor is determined. For example, the incident probe polarization may be adjusted such that only displacements along Q1 are observed. With the incident probe pulse rotated by 45 °, displacements along Q2 can be monitored. For each choice of two-pulse excitation sequence, OKE measurements were conducted with two different incident probe pulse polarizations and the amplitude and phase of the vibrational response was determined. In this manner the time-dependent, two-dimensional vibrational trajectory induced by each excitation pulse sequence was characterized uniquely. Linear, elliptical, and circular motions in controlled directions were all observed, This experiment demonstrates optical control over the time-dependent direction as well as amplitude of vibrational motion in the case of a degenerate vibrational system. Control over several modes with multiple pulses is also possible.
4. Summary A brief review of recent steps toward achieving optical control over condensed matter behavior and structure has been presented. The development of optical tools for controlled excitation and real-time observation of collective mode-selective chemistry and the demonstration of some of the capabilities and possibilities have been discussed. The next challenges will be synthesis of the available tools and their use for driving large-amplitude, farfrom-equilibrium responses which could lead to controlled collective structural rearrangements.
H. Kawashima et al./Physica B 219&220 (1996) 734 737
Acknowledgements This work was s u p p o r t e d in part by O N R grant N00014-92-1503 a n d N S F CHE-9404548. M M W is supported by a g r a d u a t e fellowship from the C a n a d i a n NSERC.
References [ l ] L . Dhar, J. Rogers and K.A. Nelson, Chem. Rev. 94 (1994) 157. [2] H. Kawashima, M.W. Wefers and K.A. Nelson, Ann. Rev. Phys. Chem. 46 (1995) 627. [3] W.S. Warren, H. Rabitz and M. Dahlen, Science 259 (1993) 1581. [4] Y.-X. Yah, E.B. Gamble Jr. and K.A. Nelson, J. Chem. Phys. 83 (1985) 5391.
737
[5] K.A. Nelson, in: Ultrafast Phenomena IX, eds. P. Barbara and W. Knox (Springer, Berlin, 1994). [6] S. Fahy and R. Merlin, Phys. Rev. Lett. 73 (1994) 1122. [7] A.M. Weiner, J.P. Heritage and E.M. Kirschner, J. Opt. Soc. Am. B 5 (1988) 1563. [8] A.M. Weiner, D.E. Leaird, G.P. Wiederrechet and K.A. Nelson, Science 247 (1990) 1317. [9] A.M. Weiner, D.E. Leaird, J.S. Patel and J.R. Wullert, Opt. Lett. 15 (1990) 326. [10] M.M. Wefers and K.A. Nelson, Opt. Lett. 20 (1995) 1047. [11] L. Dhar, J.T. Fourkas and K.A. Nelson, Opt. Lett. 19 (1994) 1. [12] G.P. Wiederrechet, T.P. Dougherty, L. Dhar, K.A. Nelson, D.E. Leaird and A.M. Weiner, Ferroelectrics 150 (1993) 103. [13] L. Dhar and K.A. Nelson, Ferroelectrics 164 (1994) 1. [14] M.M. Wefers, H. Kawashima and K.A. Nelson, J. Chem. Phys. 102 (1995). [15] J.A. Cina and V. Romero-Rochin, J. Chem. Phys. 93 (19901 3844.