‘b-UUIMI - . wu ~-v-c-—‘. meats itiiliiiilliii This is to certify that the dissertation entitled THREE-LEVEL AND FOUR-LEVEL INFRARED-INFRARED DOUBLE RESONANCE SPECTROSCOPY IN CH3F presented by QUAN SONG has been accepted towards fulfillment of the requirements for Ph. D. degree in CHEMISTRY 1/ ~ ‘ ’ ' A. ‘ \Zr/Laxé(% C-/ /L“RB((’CUU\ Major professor Date /L/€‘"’I 231/772! ] / MSU LS an Affirmative Action/Equal Opportunity Insulation O~12771 F a . r - r j T: :1"? qt: .1‘ 31“ .4 1.. 1 § 1 Va." .2 : L6 ‘5' _-,l. r) ..’; PLACE IN RETURN BOX to remove thie checkout from your record. TO AVOID FINES return on or before one due. DATE DUE DATE DUE DATE DUE II__ I! F—l MSU lo An Affirmetlve Action/Equal Opponunlty lnetltutton cMma-ot THREE-LEVEL AND FOUR-LEVEL INFRARED-INFRARED DOUBLE RESONANCE SPECTROSCOPY IN CH3F Quan Song A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1992 21/ .ngi?’ 066 / ABSTRACT THREE-LEVEL AND FOUR-LEVEL INFRARED-INFRARED DOUBLE RESONANCE SPECTROSCOPY IN CH3F By Quan Song A series of three-level and four-level infrared-infrared (IR-IR) double resonance experiments have been carried out to study saturation spectroscopy, to characterize various features of collisionally-induced transitions, to determine the vibration rotation energies of a highly excited vibrational state, and to measure the precise frequencies of rovibrational transitions in methyl fluoride. In these experiments, either a fundamental rovibrational transition, or a hot band transition in the v3 vibrational mode of CH3F was pumped by a C02 laser coincidence while rovibrational transitions, involving excitation of either the v or 3 the v vibrational mode, were probed by an infrared microwave sideband laser 6 system. Dynamic Stark splitting (Rabi splitting) has been observed in three-level IR-IR double resonance in CH3F. The line shape has been fit to theoretical expressions that were derived from a semi-classical treatment of a three-level system. A very good agreement between theory and experiment has been obtained. Rotation and vibration-rotation transitions in CH3F induced by collision with foreign gases such as H2, He, Ar, Xe or isotopically-labeled CH3F have been studied by the method of four-level IR-IR double resonance. All of the observed transitions obey selection rules. It has been found that Ar or Xe can collisionally- induce direct vibrational transitions in CH3F more readily than CH3F itself. Classical elastic scattering theory has been used to calculate one-dimensional collision kernels with Lennard-Jones and Buckingham-Slater intermolecular potential functions. The results of the calculations demonstrate most of the qualitative features observed in experiments. Initial velocity dependence of? the collisionally-induced rotational energy transfer in CH3F has been studied. It has been found that the r.m.s. velocity change increases as the relative r.m.s. velocity of the colliding molecules increases. Velocity dependence of the rates of rotational energy transfer has also been observed. IR-IR double resonance spectroscopy has been used to observe vibration- rotation transitions in the 3v3 - 2v3 hot band of 12CI-Ifii. Six transitions in this band have been observed and assigned. The Doppler-free feature of IR-IR double resonance line shapes has been employed to obtain precise center frequencies for a number of transitions in CH3F. DEDICATION TO My parents and my family ACKNOWLEDGMENTS I would like to thank Professor Richard H. Schwendeman for his kindly help and encouragement throughout these studies and during the preparation of the thesis. My thanks are extended to the members of this group for their stimulating discussions and friendship. Finally, I would like to thank my parents and my family for their support and encouragement. ii TABLE OF CONTENTS CONTENT LIST OF TABLES LIST OF FIGURES CHAPTER 1. OVERVIEW References CHAPTER 2. OBSERVATION OF THE DYNAMIC STARK SPLI'I'I'ING IN THREE-LEVEL INFRARED-INFRARED DOUBLE RESONANCE I. Introduction 11. Theoretical Part III. Experimental Part IV. Results and Discussion A. Observation of the dynamic Stark splitting B. Determination of Rabi frequency C. The criteria for observing the dynamic Stark splitting D. Precise determination of a laser offset frequency V. Conclusion VI. Appendix: Algebraic Solution For A Three-level System References iii PAGE vi vii 1o 10 12 18' 22 26 28 31 35 CHAPTER 3. COLLISIONALLY INDUCED ROTATIONAL AND VIBRATION AL ENERGY TRANSFER OF METHYL FLUORIDE IN FOREIGN GASES I. Introduction 11. Experimental Details 111. Theoretical Detail IV. Experimental Results A. Foreign gas effects on the double resonance lineshape B. Selection rule for direct rotational energy transfer . C. Vibrational energy transfer from v3=1 to v6=1 vibrational state D. Center frequency shift in double resonance spectra V. Theoretical Collision Kernels A Collision kernel for dipolar-dipolar collision B. Collision kernels for dipolar-nonpolar collision References CHAPTER 4. THE EFFECT OF INITIAL VELOCITY ON 11. III. IV. ROTATIONAL ENERGY TRANSFER IN 13CI-I3F Introduction Theoretical Part . Relative velocity of the colliding molecule Velocity change upon collision Experimental Detail Results and Discussion iv 46 46 50 51 57 57 61 65 72 74 76 78 82 86 86 89 89 90 92 96 A.Three-level double resonance at different pump laser offsets B. Initial velocity dependence of the r.m.s. velocity change upon collision C. Velocity dependence of rates of energy transfer D. Calculation from classical scattering theory References CHAPTER 5. STUDY OF THE 3v3 - 2v3 BAND IN 12CH3F AND DOPPLER-FREE FREQUENCIES 1N 12CH3F AND ”mm 1. Introduction 11. Theoretical Background A. Energy levels in a non-degenerate vibrational mode in 12CH3}? B. Precise measurement of pump laser offset frequency III. Experimental Detail IV. Results and Discussion Observation and assignment of the 3v3 — 2V3 band in 12CH3F Rotational constants in the V3=3 vibrational state of 12CH3F Collisionally induced energy transfer in the V3=2 state GOP”? . Precise frequencies in CH3F V. Conclusion References 96 99 104 107 109 110 110 113 113 114 116 120 120 127 131 134 137 139 LIST OF TABLES TABLE 2.1. Pump and probe transitions used for double resonance in Chapter 2. 3.1. Pump and probe transitions used for double resonance in Chapter 3. 4.1. Pump and probe transitions used for double resonance in Chapter 4. 4.2. Transferred spikes for different pumping offsets in 13CH3F. 4.3. Velocity change during state change upon collision in 13CH3F. 4.4. Relative intensities for collisionally-induced transitions in 13CH3F. 5.1. Pump and probe transitions in the 2v3 — v3 band of 12CH3F. 5.2. Comparison of observed and calculated frequencies in 12CH3F. 5.3. Vibration-rotation parameters for the 3v3 — 2v3 band IIIIZCH3 F. 5.4. Precise frequencies of transitions 'n CH3F. 5.5. Comparison of frequencies of transitions '11 CH3F. vi PAGE 23 52 97 103 105 106 117 123 130 136 138 LIST OF FIGURES FIGURE PAGE 2.1. 2.2. 2.3. 2.4. Four possible energy arrangements for three-level double resonance. In each case the bold arrow represents the pump beam of frequency v1 and the light arrow represents the probe beam of the frequency v2.The 51 and 52 are sign factors used in the equations in the appendix. 14 Block diagram of infrared-infrared double resonance spectrometer. M = mirror; L = lens; PZT = piezoelectric translator; STAB = fluorescence detector and laser stabilization circuitry; B5 = beam splitter; MOD = CdTe electro-optic modulator crystal; POL = polarizer; TWTA = traveling wave tube microwave amplifier; PIN = PIN diode electronically-controlled modulation attenuator; DET = infrared detector; PSD = phase sensitive detector; MOD = 33 kHz square-wave generator; A/ D = analog digital converter 20 Three-level double resonance spectra for 13CH3F recorded at three different sample pressures and 2.2 W infrared power. The QR(4,3) transition in the v3 band was pumped and the QP(5,3) transition in the 2v3 — v3 band was probed. The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3009355309 MHz. The residuals from the least squares fittings of the lineshapes are shown at the bottom of the figure. 25 Three-level double resonance spectra for 13CH3F recorded at two different infrared powers and a sample pressure of 2.5 mTorr. The pump and probe transitions, the lasers and the horizontal axis are the same as in Fig. 2.3. The residuals from the least squares fittings of the lineshapes are shown at the bottom of the figure. 27 vii 2.5. 2.6. 2.7. 2.8. 2.9. Plot of the vibrational contribution to the Rabi frequency xp for the spectra shown in Fig. 2.4. and three additional spectra for the same transition recorded at different powers. The straight line is the least- squares fit of the five points constrained to go through zero. The slope of the line is 5.47 MHz Wm. 29 Three level double resonance spectrum for 12CH3F. The QQ(12, 2) transition in the v3 band was pumped and the QR(12, 2) transition in the 2v3 — v3 band was probed.The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3155602888 MHz. The pump power density was ~ 4 W/cm2 and the sample pressure was 6 mTorr. The residual from the least squares fitting is shown below the spectrum. 30 Three-level double resonance spectrum for 12CH3F. The QR(11,9) transition in the v3 band was pumped and the Q(2(12, 9) transition in the 2V3 - v3 band was probed. The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3091391543 MHz. The pump power density was ~ 3 W/ cm2 and the sample pressure was 2 mTorr. 32‘ Three-level double resonance spectrum for 12CH3F. The QR(11,9) transition in the v3 band was pumped and the QR(12, 9) transition in the 2v3 — v3 band was probed. The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3155802888MI-Iz. The pump power density was ~ 3 W/cm2 and the sample pressure was 2 mTorr. 32 Two-level double resonance spectrum for l3CH3F. The QR(4, 3) transition in the v3 band was both pumped and probed. The pump and probe lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3104300923 MHz. The pump power viii 3.1 3.2 3.3. 3.4. density was ~ 4 W/cm2 and the sample pressure was 3.5 mTorr. The residual from a least squares fitting of the lineshape is shown at the ‘ bottom of the figure. Diagram of the scattering plane for a single scattering event between an active molecule (a) and a perturber (p). The curved path of the active molecule is symmetric about the line that makes an angle 6m with the -z axis. In the figure, 9 = 1r - 29m is the scattering angle; to is the initial separation of a and p; v° is the initial relative velocity; b, which is parallel to the y axis, is the magnitude of the impact parameter; and x is the angle between b and a line (N) that 15 parallel to the line 0f nodes. Spectra of the QP(6,3) transition in the 2v3 - v3 band in 13CH3F taken for a variety of collision partners; the spike and Gaussian components for each lineshape are also shown. Trace (a) is a single resonance spectrum in a pure sample at 7 mTorr; Traces (b) - (f) are double resonance spectra recorded while the QR(4,3) transition in the n3 band was pumped. The samples for the double resonance spectra were 3 mTorr of 13CI-I3F in 50 mTorr of foreign gas, as follows: (b) 12CH3F; (c) H2; (d) He; (e) Ar; (f) Xe. The infrared frequencies for each spectrum are the horizontal axis values shown for (e) plus 30 041 529 MHz. Energy level diagram for 13CH3F for the double resonance transitions shown in Fig. 3.4. Only the levels for 4 S I S 8 and 0 S K S 6 in V3 = 1 are shown. Single resonance (a) and double resonance (b-d) spectra of the QP(7,K) transitions for K S 6 in the 2v — v3 band of 13CH3F. The QR(4,3) transition in the v3 band of 1 CH3F was pumped for the double resonance. The samples were: (a) 13CI~I3F at 30 mTorr; (b) 13CH3F at 17 mTorr; (c) 1 mTorr 13CH3F in 100 mTorr 12CH3F; and (d) 1 mTorr 13CH3F in 100 mTorr Ar. The infrared frequencies for each spectrum ix 33 59 3.5. 3.6. 3.7. 3.8. are the horizontal axis value plus 29 989 650 MHz. 64 Single resonance (a) and double resonance (b) spectra of the QP(14,I<) transitions for K S 5 in the 2v3 - v3 band of 12CH3F. The QQ(12,1) and QQ(12,2) transitions in the v3 band of 12CH3F were simultaneously pumped for the double resonance. The samples were: (a) 30 mTorr 12CH3F; and (b) 1% 12CH3F in Ar at 140 mTorr total pressure. The infrared frequencies for each spectrum are the horizontal axis values plus 30 199 026 MHz. 66 Single resonance (a) and double resonance (b-d) spectra of the QR(9,3,1) and QR(1O, 2,- -1) transitions in the v3 + v 6 -v6 band of 12CH3F. The QQ(12, 1) and QQ(12, 2) transitions in the v3 band of 12CH3}? were simultaneously pumped for the double resonance in (b) and (d), whereas the QR(11,9) transition in the v3 band of 12CH3!" was pumped for (c). The samples were: 12CH3F at 500 mTorr for (a); 1% 12CH3F in 63 mTorr total pressure of Ar for (b) and (c); and 1% 12CH3F in 63 mTorr total pressure of 13CH3F for (d). The infrared frequency for the QR(9,3,1) transition is 31 632 843 MHz minus the horizontal axis value, whereas the infrared frequency for the QR(10,2,-1) transition is 31 660 843 MHz plus the horizontal axis value. 68 Single resonance (a) and double resonance spectra (b) of the transitions shown in Fig. 7. The spectrum in (a) is the same as that in Fig. (7a). The spectrum in (b) was recorded for 60 mTorr of 12CH3}? while the QQ(12,1) and QQ(12,2) transitions in the v3 band of 12CH3F were simultaneously pumped. 70 Single resonance (a) and double resonance (b) spectra of the QR(7,1,- 1) transition in the v3 + v 6 — v band and the QR(12,I<) transitions for K S 9 in the 2v3 - v3 band of 3F. The QQ(12,1) and QQ(12,2) transitions in the v3 band of 12CH3F were simultaneously pumped for (b). The sample pressures were 250 mTorr (a) and 60 mTorr (b). The infrared frequencies for the QR(12,I<) transitions are the horizontal axis x 3.9. 3.10. 3.11. 3.12. values plus 31 556 029 MHz, whereas the infrared frequency for the QR(7,1,-1) transition is 31 532 029 MHz minus the horizontal axis value. 71 Single resonance (a) and double resonance (b) spectra of the QP(5,3) transition in the v3 band of 13CH3F. The QR(4,3) transition in 13CH3F was pumped for the double resonance. The samples were 5 mTorr of 13CH3F in 5 Torr of Ar for both spectra. The infrared frequencies for each spectrum are the horizontal axis value plus 31 089 492 MHz. 73 (a) One-dimensional collision kernel as a function of final velocity calculated as the sum of two Keilson-Storer functions. The 8 values for the two functions are 19.1 m/s and 140.5 m/s and the ratio of the A values is A(broad)/A(narrow) = 0.185. (b) One-dimensional classical collision kernel calculated by the procedure described in the text, The parameters for the calculation are: m =0 35 u for the active molecule and the perturber; e/kB = 300 K; re = 3.5 A ; 0 S b S 10 A ; number of collisions = 20 000. The initial velocity for both kernels was 234 m/ s. The vertical axes have been scaled for convenient plotting and comparison. 77 One-dimensional classical collision kernels as a function of final velocity calculated by the procedure described in the text. The parameters are: 8 /kg = 100 K; re = 4 A ; 0 S b S 4 A ;number of collisions = 40 000; m(active molecule) = 35 u; m(perturber) = 4 u (a) or 131.3 11 (b). The initial velocity for both kernels was 234 m/s. The vertical axes have been scaled for plotting, but are relatively correct for the two plots. 79 One dimensional classical collision kernels as a function of final velocity calculated by the procedure described in the text. The parameters are: 8 /k3 = 100 K; 0 S b S 4 A ;m(active molecule) = 35 u; m(perturber) = 4 u; number of collisions = 40 000; and re = 4A (a) or xi 3.13. 4.1. 4.2. 4.3. 4.4. 3.5 A (b). The initial velocity for both kernels was 234 m / s. The vertical axes have been scaled for plotting, but are relatively correct for the two plots. One-dimensional classical collision kernel as a function of final velocity calculated by the procedureodescribed in the text. The parameters are: 8 /k3 = 100 K; re = 4A ;0 S b S 3; m(active molecule) = 35 u; m(perturber) = 131.3 11; initial velocity = 234 m/s; number of collisions = 30 000. The vertical axis has been scaled. Set up for stabilization of C02 laser to a Stark Lamb dip. M = mirror; PZT = piezoelectric translator and laser output coupling mirror; 85. = beam splitter; FGl, FG2 = function generators; S.M.B. = signal mixing box; HVA = high voltage amplifier; HVP = high voltage power supply; PRM = 90% partially reflecting mirror; DET = detector; PREAMP = preamplifier; OPS = operational power supply; OSC'= oscilloscope. Comparison of three-level double resonance effects observed with three different pump laser offsets. The QR(4,3) transition in the v3 hot band was pumped and the QP(5,3) transition in 2v3 - v3 band was probed. The lasers used are given in Table 4.1. The horizontal axis is the probe laser frequency minus 3009355309 MHz. Comparison of four-level double resonance effects observed with different pump laser offsets (8.6, 23.1 and 37.8 MHz from left to right). The QR(4,3) transition in the v3 band was pumped and the QP(7,3) transition in 2v3 - v3 hot band was probed. The lasers used are given in Table 4.1. The horizontal axis is the probe laser frequency minus 2998865009 MHz. Comparison of the line shape of the transferred spike observed with pump laser offset at 37.8 MHz (upper) to that at 8.6 MHz (lower). The xii 80 81 94 98 100 5.1. 5.2. 5.3. 5.4. 5.5. Gaussion part was removed. The QR(4,3) transition in the v3 band was pumped and the QP(7,3) transition in the 2v3 — v3 hot band was probed. The lasers used are given in Table 4.1. The upper spectrum has been shifted in frequency for comparison. The horizontal axis is the probe laser frequency minus 3004152873 MHz. The geometry for the copropagating double resonance experiment. M = mirror; POL = polarizer; DET = detector. The planes of polarization of the pump and probe lasers were perpendicular to one another. Four level double resonance spectrum for the QR(8,6) transition in the 3V3 - 2v3 band in 12CH3F. The QR(13,6) transition in the 2v3 - v3 band was pumped. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. The pump and probe lasers used are given in Table 5.2. Four level double resonance spectrum for the QR(10,6) transition in the 3V3 — 2v3 band in 12CH3F. The QR(13,6) transition in the 2V3 - v3 band was pumped. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. The pump and probe lasers used are given in Table 5.2. Double resonance spectrum for the QR(8,0), QR(8,3) and QR(8,6) transitions in the 3V3 - 2V3 band in 12CH3F. The QR(7,3) transition in the 2V3 - v3 band was pumped. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. The pump and probe lasers used are given in Table 5.2. The QR(8,6) transition is overlapped with the QR(9,9) transition in the 2v3 - v3 band. Four level double resonance spectrum for the QR(10,0), QR(10,3) and QR(10,6) transitions in the 3V3 - 2v3 band in 12CH3F. The Q12(73) transition in the 2V3 - v3 band was pumped. The horizontal axis is the offset frequency of the probe laser with GHz part removed. The pump xiii 101 119 122 124 125 5.6._ and probe lasers used are given in Table 5.2. 126 Three-level double resonance spectrum for the QR(7,3) pump transition in the 2v3— v3 band and the QR(8, 3) probe In the 3V3 - 2v3 band in 12CH3F. The spectrum was recorded with a setup with which double resonance effects for both counter-propagating and copropagating pump beams could be seen in the same scan. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. The pump and probe lasers used are given in - Table 5.2. 128 5.7. 5.8. Double resonance spectrum for the QQ(9,K) (K=3, 4, 5, 6) transitions in the 2v3 - v3 band in 12CH3F. The QR(7,3) transition in the 2v3 - v3 band was pumped. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. The pump and probe lasers used are given in Table 5.1. 133 Counterpropagating and copropagating three-level double resonance spectra for the QR(12,1) and QR(12,1) transitions in the 2v3 — v3 band when the QQ(12,1) and the QQ(12,2) transitions in the v3 fundamental In 12CH3F are simultaneously pumped by 9P(20) laser. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. 135 xiv Chapter 1 Overview Double resonance involves the simultaneous application to a sample of two radiation sources both resonant or near-resonant with transitions in the molecules of the sample. One of the radiation sources, usually referred to as the pump, has to be sufficiently intense to produce a change in the population distribution between the two levels of the pumped transition. The other radiation source, which may be weak and is known as the probe, is used to monitor the effect of the pump, and the resulting spectrum is called the double resonance spectrum. There are two types of double resonances, one of which is three-level double resonance in which one of the pumped levels is also one of the probed levels. The other is four-level double resonance in which the pumped and probed levels are entirely separated. Three-level double resonance can be used to simplify the assignment of a complicated spectrum. Since the two transitions have a common energy level, knowledge of one transition helps to assign the other. Four-level double resonance in gaseous samples can be used to study collisionally-induced transitions. Since the population has to be transferred from the pumped to the probed levels via intermolecular collision, this type of experiment provides information about the interaction between the colliding molecules. The study of collisionally-induced transitions by the four-level double resonance technique was pioneered by Oka (1-2) in the microwave region. Since that time, double resonance techniques have been used to study various properties of collisionally-induced energy transfer in almost every range of the electromagnetic spectrum. Examples includes studies of selection rules for 2 vibrational energy transfer (3-4), studies of the mechanisms for rotational and vibrational energy transfer (4-10), measurement of rates and channels for rotational energy transfer (7-9, 11-20) and vibrational redistribution (3-5, 21), and studies of velocity changes resulting from both elastic and inelastic collisions (22- 30). Infrared-infrared double resonance has unique advantages for the study of velocity changing collisions. Because the Doppler width in the mid-infrared region is large compared to both the available resolution and the homogeneous width for low-pressure gases, a strong monochromatic infrared laser can prepare molecules in a specific vibration-rotation state with a specific velocity component in the direction of the radiation. A second monochromatic, but continuously tunable infrared laser can then probe states that are collisionally-related to the pumped state and provide detailed information about the correlation between velocity change and state change upon collision. Unfortunately, mainly because of the lack of highly monochromatic tunable sources, studies of this type were very limited until recently. An infrared-infrared double resonance experiment employing the above concept was carried out first by Bischel and Rhodes (27). In their study, the qualitative features of the velocity change during rotationally inelastic collisions in C02 molecules were characterized. However, due to the lack of accuracy of the recorded data, quantitative analysis of the velocity change upon collision was not carried out. Also, because of the limited tunability of their probe source (C02 laser within the laser gain curve), they could not use their system to study molecules other than C02. The first quantitative characterizations of the velocity changes during rotational energy transfer were reported for ISNH3 and 13CH3F by Matsuo et al from this laboratory (28, 29). In these studies, a single transition in a fundamental vibration-rotation band was pumped by radiation from a single-mode C02 laser 3 while a transition in a hot band was probed by a tunable infrared microwave sideband laser source. The achievements of these studies were in providing experimental observations of what we called ”transferred spikes” and in laying a theoretical foundation for analysis of the transferred spikes to extract information about the velocity change during the collisionally-induced transitions. The uniqueness of the experimental strategy was that the pumping power was relatively low (c.w. C02 laser) and the probe source had an extremely high resolution. Low pumping power guaranteed the excitation of molecules with a narrow velocity distribution while a high resolution probe source made it possible to examine the detailed velocity distribution after collision. This was in contrast to the infrared-infrared double resonance experiments employing either a pulsed high-power pump laser, or a relatively lower resolution probe-source (e.g. infrared diode laser), such as the work from Steinfeld’s group at MIT (15-17, 20). In their work, the pumping power density was so high that the power broadening was sufficient to cause pumping of nearly all velocity groups. This thesis is an extension of the infrared-infrared double resonance technique employed by Matsuo et al to broader applications. We concentrate on infrared- infrared double resonance spectroscopy in methyl fluoride. For convenience, we briefly describe here the terminology of the rovibrational transitions in methyl fluoride that are used in this thesis. Methyl fluoride is a symmetric top molecule with six vibrational modes, all of which are infrared active. There are three non-degenerate vibrational modes v1 , v and three degenerate vibrational modes v v and v . We are only ‘2 3 4' 5 6 interested in rovibrational transitions in v3 and v6. The energy levels in the v vibrational mode can be specified with three 3 quantum numbers (in the ground electronic state): v (v=0, 1, 2, 3....), the quantum numbers for vibrational motion; 1 (J =O,1, 2, 3 ..... ), the quantum number for total rotational angular momentum; and K (K=0, 1, 2,...J), the absolute value of the 4 quantum number for the projection of rotational angular momentum in the direction of the molecular axis (C-F bond in CH3F). The selection rules for the vibration-rotation transitions in the v3 mode are Av3 = 1 (only absorption is concerned); AK = 0; and A] = 0, i1 , which corresponds to three different branches: P (AI = -1), Q (AI = 0) and R (AI = 1). We usually call rovibrational transitions from vibrational state v3=0 to v3=1 the v3 fundamental band and from V3=n to V3=m the mv3 - nv hot band. The symbol for a transition is AKAI (I, K) , where I and K are quantumehumbers of the lower state of the transition, A] is P, Q or R depending on whether A] equals -1, 0, or 1, respectively, and AK is always Q since AK = 0. Thus, the QR(4,3) fundamental transition represents a transition from the state with V3=0, 1:4 and K=3 to the state with V3=1, 1:5 and K=3; and the QP(14,2) transition in the 2v3 3 with V3=l, 1:14 and K=2 to the state with V3=2, I=13 and K=2. - v hot band represents a transition from the state A few transitions in the v3 + v 6 - v 6 vibrational band are also used in the thesis. This band contains rovibrational transitions from the vibrational state v6=1 and V3=0 to the vibrational state v6=1 and V3=1. These vibrational states are doubly degenerate and an additional quantum number 1 is necessary to specify a rotational energy level; 1 is the quantum number for the projection of vibrational angular momentum on the molecular axis (1 = 3:1 in either V3=0, v6=1 or V3=1, v6=1). Since only the transitions with selection rule A1 = 0 are used in this thesis, the symbol AKA10, K, 1) is used to represent a transition in this band. For example, the QR(9,3,1) transition in the v3 + v 6 - v 6 band stands for a transition from the rotational level with 1:9, K=3 and 1:1 in the v6=1 vibrational state to the rotational level with 1:10, K=3 and l=1 in the v3=1 and v6=1 vibrational state. Chapter 2 contains studies of three-level double resonance line shapes in methyl fluoride. During the analysis of four-level double resonance spectra, Matsuo (29) found that the three-level double resonance line shape calculated by a semi-classical treatment showed a splitting which was apparent in the observed 5 spectrum, but not resolved. The problem was left unsolved. During our study of effects of initial velocity on the rotational energy transfer in 13CH3F (Chapter 4), we found that some of our three-level double resonance spectra had flat tops. To our surprise, when we reduced or eliminated several possible factors that could wipe out the splitting in the spectra, we started to get spectra that looked like the calculated line shape. In these studies, a rovibrational transition in the v3 fundamental band was pumped by a C02 laser while another rovibrational - v hot band or in the v fundamental band, was 3 3 3 probed by a tunable C02 sideband laser source. Dynamic Stark splitting in transition, either in the 2v infrared-infrared threeolevel double resonance in methyl fluoride was observed. Although dynamic Stark splitting was a well-known phenomenon in the radio- frequency and microwave region, and even a few observations had been reported in the optical region, this work represented the first observation in the infrared region for molecules in thermal equilibrium. By using the method of least squares, we fit the theoretical line shape based on the density matrix formalism to the observed spectrum. The numerical comparison provided a check for the validity of the current theory of three-level double resonance line shapes. The results of the fitting provided information on the sample molecule itself, such as the Rabi frequency and the relaxation rates. Although we were not able to determine reliable relaxation rates in the current studies, mainly because our present apparatus was not good enough, the problems associated with their measurement were extensively studied. Therefore, these studies can be viewed as a promising first step toward such measurements. The topics in Chapter 3 are applications of four-level double resonance to the study of collisionally-induced rotational and vibrational energy transfer in methyl fluoride colliding with different foreign gas molecules, including isotopically- labelled methyl fluoride. For this purpose, a rovibrational transition in the v3 band was pumped by a C02 laser while another rovibrational transition, either in the 6 2v3 — v3 band or in the v3 + v 6 - v 6 band, was probed by our infrared sideband system. The former double resonance combination allowed the study of rotational energy transfer and the latter the study of vibrational energy transfer. While recording double resonance spectra for methyl fluoride in an excess of different foreign gases, the properties of the energy transfer for different colliding pairs could be investigated. The major findings from these experiments included (i) the correlations between translational momentum change and angular momentum change during rotational energy transfer for methyl fluoride colliding with H2, He, Ar, Xe and CH3F; (ii) evidence of direct vibrational energy transfer in methyl fluoride and the corresponding symmetry selection rules; (iii) evidence of a recoil effect when methyl fluoride collides with Ar atoms. For theoretical interpretation of these results, we employed classical elastic scattering theory and the procedures used by Borenstein and Lamb to calculate one-dimensional collision kernels with Lennard-Jones and Buckingham-Slater intermolecular potential functions. The theoretical calculations were able to demonstrate most of the qualitative features for the collisionally-induced rotational transitions observed in experiments. This study indicated the possibility of obtaining quantitative information on the intermolecular interaction potential of the colliding molecules through comparison between more sophisticated calculations (e.g. semi-classical inelastic scattering theory) and experimental observations. Chapter 4 concerns the effect of initial velocity on collisionally-induced rotational energy transfer in methyl fluoride. The velocity component of the pumped molecules in the direction of the pump laser depends on the difference between the frequency of the pump laser and the center frequency of the pump transition. Varying the pump laser frequency changes the relative r.m.s. speed of the colliding molecules. We stabilized a C02 laser to Lamb dips in Stark spectra in a cell outside of the laser cavity. With this stabilization scheme, we were able to lock the laser at different frequencies within the laser gain curve. This technique 7 provided a tunability of about 30 MHz for each laser line. By using the laser stabilized with this scheme as a pumping source, we were able to pump molecules with different relative r.m.s. speed to their colliding partners. This allowed us to study the initial velocity dependence of the collisionally-induced rotational energy transfer. It was found that r.m.s. velocity change increased as the relative r.m.s. velocity of the colliding molecules increased. We used classical elastic scattering theory to calculate the one-dimensional collision kernel at different initial velocities. The results of the calculation failed to represent the qualitative features of the observation. Finally, Chapter 5 contains the applications of double resonance techniques to assign weak transitions in the 3v3 - 2v3 hot band of 12CH3F, to measure precise center frequencies of a few transitions in both 12CH3F and 13CH3F, and to obtain additional information about collisionally-induced transitions. Transitions in the 3v3 - 2v3 band are very weak since the lower vibrational state of the band is a highly excited vibrational state and the population is extremely small. Transitions in this band had not been observed previously. We used strong C02 laser radiation 3 3 hot band of 12CH3F while — 2v3 hot band. This unique technique allowed to pump near—coincident transitions in the 2v — v searching for transitions in the 3v3 us to observe six transitions in the 3v3 — 2v3 band. Molecular constants for the V3=3 vibrational state were determined from the frequencies of the transitions. This work demonstrated the usefulness of the double resonance technique for observing and assigning very weak transitions. In order to obtain precise center frequencies of transitions with infrared-infrared double resonance, we took the advantage of the Doppler-free feature of the double resonance spectra. For this purpose, a series of counterpropagating and copropagating three-level and four- level double resonance spectra were recorded to determine the precise center frequencies for a number of transitions in both 12CH3F and 13CH3F. The absolute accuracy for the transitions determined in this work is ~0.1 MHz which was about 8 one order of magnitude better than the previously measured values. References l. T. Oka, J. Chem. Phys. 45, 754-755 (1966); T. Oka. J. Chem. Phys. 47, 13-26 (1967); T. Oka. J. Chem. Phys. 47, 4852- 4853 (1967); T. Oka, J. Chem. Phys. 48, 4919-4928 (1968); T. Oka, J. Chem. Phys. 49, 3135-3145 (1968). 2. T. Oka, Adv. At. Mol. Phys. 9, 127-206 (1973). 3. F. Menard-Bourcin and L. Doyennette, J. Chem. Phys. 88, 5506-5511 (1988). 4. J. G. Haub and B. J. Orr, J. Chem. Phys. 86, 3380-3409 (1987). 5. C. P. Bewick and B. J. Orr, J. Chem. Phys. 93, 8634-8642 (1990). 6. S. Kano. T. Amano. and T. Shimizu, J. Chem. Phys. 64, 4711-4718 (1976). 7. R. I. McCormick, F. C. De Lucia, and D. D. Skatrud, IEEE J. Quantum Electron. QE-23, 2060-2067 (1987). 8. H. O. Everitt and F. C. De Lucia. J. Chem. Phys. 90, 3520-3527 (1989). 9. H. O. Everitt and F. C. De Lucia, J. Chem. Phys. 92, 6480-6491 (1990). 10. C. P. Bewick, J. F. Martin, and B. J. Orr, J. Chem. Phys. 93, 8643-8657 (1990). 11. N. Morita, S. Kano, Y. Ueda, and T. Shimizu, J. Chem. Phys. 66, 2226-2228 (1977). 12. N. Morita. S. Kano, and T. Shimizu, J. Chem. Phys. 69, 277-280 (1978). 13. W. A. Kreiner, A. Eyer, and H. Jones. J. Mol. Spectrosc. 52, 420-438 (1974). 14. R. M. Lees, C. Young, J. Van der Linde, and B. A. Oliver, J. Mol. Spectrosc. 75. 161- 167 (1979). 15. J. I. Steinfeld, I. Burak, D. G. Sutton, and A. V. Nowak, J. Chem. Phys. 52, 5421-5434 (1970). 16. D. Harradine, B. Foy, L. Laux, M. Dubs, and J. I. Steinfeld, J. Chem. Phys. 81, 4267- 4280 (1984). 9 17. B. Foy, L. Laux, S. Kable and J. I. Steinfeld, Chem. Phys. Lett. 118, 464-467 (1985). 18. Y. Honguh, F. Matsushima, R. Katayama, and T. Shimizu, J. Chem. Phys. 83, 5052- 5059 (1985). 19. K. Veeken, N. Dam, and J. Reuss, Chem. Phys. 100, 171-191 (1985). 20. B. Foy, J. Hetzler, G. Millot, and J. I. Steinfeld, J. Chem. Phys. 88, 6838-6852 (1988). 21. H. K. Haugen, W. H. Pence, and S. R. Leone, J. Chem. Phys. 80, 1839-1852 (1984). 22. E. Arimondo, P. Glorieux, and T. Oka, Phys. Rev. A 17. 1375-1393 (1978); P. Glorieux, E. Arimondo, and T. Oka, J. Phys. Chem. 87, 2133-2141 (1983). 23. R. G. Brewer, R. L. Shoemaker, and S. Stenholm, Phys. Rev. Lett. 33, 63-66 (1974). 24. R. L. Shoemaker, S. Stenholm, and R. G. Brewer, Phys. Rev. A 10, 2037-2050 (1974). 25. J. W. C. Johns, A. R. W. McKellar, T. Oka, and M. Rc'imheld, J. Chem. Phys. 62, 1488- 1496 (1975). 26. P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668-1688 (1975). 27. W. K. Bischel and C. K. Rhodes, Phys. Rev. A 14, 176-188 (1976). 28. Y. Matsuo, S. K. Lee, and R. H. Schwendeman, J. Chem. Phys. 91, 3948-3965 (1989). 29. Y. Matsuo and R. H. Schwendeman, J. Chem. Phys. 91, 3966-3975 (1989). 30. U. Shin, Q. Song, and R. H. Schwendeman, J. Chem. Phys. 95, 3964-3974 (1991). 10 Chapter 2 Observation of Dynamic Stark Splitting in Three-Level Infrared-Infrared Double Resonance I. Introduction Theoretical and experimental studies of three-level double resonance line shapes have been presented many times (1-18). One of the most interesting phenomena in these studies is dynamic Stark splitting (Rabi splitting; the Autler- Townes effect (1)) which shows a doublet in the probe transition while two of the three energy levels are pumped by fairly strong monochromatic radiation. The phenomenon can easily be observed in the radiofrequency or microwave region of the spectrum (2) in which it is relatively easy to obtain radiant power densities and dipole transition moments large enough to create a Rabi frequency that is greater than either the homogenous or inhomogeneous broadening (3). It is more difficult to see the phenomenon at optical frequencies where the Doppler averaging tends to wash out the effect. Although a few observations of the phenomenon have been reported in the visible region (4-6), the splitting has not, to our knowledge, been reported for infrared-infrared double resonance involving vibration-rotation spectra of gaseous molecules, except in molecular beams in which Doppler effects are greatly suppressed (18). In this chapter studies of dynamic Stark splitting in three-level infrared-infrared double resonance spectra in 12CH3F and 13CH3F are discussed. Our three-level double-resonance experiment was prompted at first by the 11 need to estimate the infrared power density of the output from a C02 laser that was used as the pumping source for a series of infrared-infrared four-level double resonance measurements in methyl fluoride (19-21). We found that dynamic Stark splitting could be observed in 13CH3F at low sample pressure when the QR(4,3) transition in the v3 fundamental was pumped while the QP(5,3) transition in the 2v3 - v3 hot band was probed. Then we investigated three other combinations of pump and probe in 12CH3F. For the combination of the QQ(12,2) pump in the v3 fundamental with theQR(12,2) probe in the 2v3 - v3 hot band, no splitting was observed. By contrast, for the combinations of the QR(11,9) pump in the v3 fundamental with either the QQ(12,9) or the QR(12,9) probe in the 2v3 - v3 hot band, the splitting was clearly seen. Dynamic Stark splitting can be predicted from the semi-classical treatment of a three-level system interacting with two monochromatic electro-magnetic fields. Although both theoretical and experimental studies of three-level double resonance line shapes have been the subject of many papers in the literature, a quantitative numerical comparison between the full semi-classical calculation and the experimental observation has not been found for the case where both spatial degeneracy of the energy levels and Doppler effects of the molecules have to be considered. An interesting question is: How well does the semi-classical double resonance theory predict the line shapes recorded in the laboratory, especially when dynamic Stark splitting is observed? In order to answer the question, we numerically calculated the double-resonance spectra with a computer program that solved the 8x8 linear system of equations that results from a density matrix treatment of the three-level system (13). The program solved these equations for many values of the component of the molecular velocity in the direction of the pump beam, multiplied each of these solutions by the appropriate Boltzmann factor, and summed the result. The spatial degeneracy was treated by calculating 12 the contribution from each component of the spatially degenerate state and then summing the results. In order to improve the speed of the calculation, an algebraic solution of the linear system, valid for all pump and probe powers, was worked out and incorporated into the program (14). Finally, the spectral generation program was incorporated into a full least-squares fitting routine in which the amplitude and center frequency of the probe transition, the Rabi frequency for the pump radiation, and the population and coherence relaxation rates are all adjusted to provide a best fit of the observed spectrum. It was found that the complete semi- classical treatment represents all the observed line shapes very well. As a result of the least squares fitting of the observed line shapes, the Rabi frequency for the pump radiation, and the population and coherence relaxation rates for sample molecules can be obtained. These parameters were found to be much more sensitive to the three-level double resonance spectra that showed a dynamic Stark splitting. We were surprised to find that for nearly all of the double- resonance combinations examined, the dependences on population and coherence relaxation rates are not extremely highly correlated, so that it should be possible to obtain these rates separately from high-quality spectra. As will be seen below, we are not able to determine these rates with our present apparatus. The reason is traced to the fact that a number of effects can broaden the observed line shapes. These effects are analyzed and numerically simulated, and strategies to reduce or eliminate these effects are proposed. Thus, the present work is best regarded as a promising first step toward such measurements. 11. Theoretical Part The density matrix equations for a three-level system have been given many times (e. g., Refs. 4-6, 13-17, and additional references cited in these papers). In the 13 present work we are concerned with energy levels in both a ”stacked" or ”cascade” configuration, in which the levels are arranged such that Ea < Eb < EC, and two ”folded" configurations in which the levels are arranged such that Ea < Eb > EC or Ea > Eb >H «mounts—om "30m .SOA mambo 531608 Emergence—m oHuU n 0023331? Emma H mm 3.23.5 couofiznfim .88— 23 .8833 cosmommuooa u m<30mu§ So I ,_ FEE .38 30a 5 no: 5 3.3% [mi imp 3mm “ 2 / Ml < 1 mm .2 2 a ozFSE 02:58 _. 2 c 1” \\ \.\ (I If \V\ AL \2 Ea ammfi Nou «mm: «8 .5. 21 allows the sidebands to pass through while reflecting the carrier to a fluorescence cell for frequency stabilization. Polarizer POL2, however, lets the pumping laser enter the sample cell while reflecting the probe beam to the detector so that the double resonance signal can be recorded. The probe laser is 100% amplitude modulated at 33 kHz, by chopping the microwaves applied to the modulator crystal, while the pump laser beam is 100% amplitude modulated at 300 Hz by means of a mechanical chopper. In order to stabilize the amplitude of the probe laser, a second detector is used to monitor the laser power in front of the sample cell. The output of the detector drives a feedback circuit which controls the microwave power applied to the modulator crystal so that any change in probe power will be compensated by an appropriate change in microwave power. Typical pump powers at the entrance of the sample cell are ~1-2 W while probe powers are ~20 ttW. The microwave frequency for the IMSL source is provided by a synthesizer (:3 kHz accuracy) and is stepped by the microcomputer that records the spectrum. We use a double modulation scheme to analyze the double resonance signal. The signal detector output is first demodulated by a lock-in amplifier at the chopping frequency of the probe; the output of this amplifier, which contains the sum of the single-resonance and double-resonance effects, is sent to a second lock- in amplifier for an additional demodulation at the chopping frequency of the pump laser. The output of the second amplifier which contains only the double- resonance effect is digitized and recorded by the microcomputer. The detector- preamplifier combination has been shown to provide an essentially linear output by determining that single resonance spectra recorded at low pressure are Gaussian with the expected Doppler width to high accuracy (<0.5%) (26). The sample cell for most of the work was a Pyrex tube, 1 m long and 25 mm 22 in diameter. The 13CH3F sample was obtained from Merck 8: Co., while the 1:ZCH3,F sample was obtained from Peninsular Chemical Research, Inc. Except for the usual freeze-pump-thaw cycling, the samples were used as received. All spectra were recorded at room temperature (~297 K) at pressures in the range 2-20 mTorr; sample pressures were measured by a capacitance manometer. The frequencies for the spectral lines shown in Table 2.1 were calculated from the molecular constants in Refs. (27-28), and the laser frequencies were calculated from the constants in Refs. (29-30). IV. Results and Discussion A. Observation of the dynamic Stark splitting Dynamic Stark splitting in the vibration-rotation spectrum of methyl fluoride was first observed in 13CH3F for the R(4,3) pump in the v3 fundamental and the QP(5,3) probe in the 2v - v hot band. Although the spectra recorded at the beginning showed evidinceif the splitting, the lineshapes did not seem to fit very well with calculation, especially for the lower parts of the trace which seemed to be broadened by some artificial effects. The causes were analyzed and tested experimentally. We found that several factors contributed to the broadening of the experimental line shapes. These factors were frequency modulation of C02 lasers; divergences and misalignment of the pump and probe beams; and four-level double resonance effects. Frequency modulation is necessary for C02 lasers stabilized to the fluorescence Lamb dip in this laboratory. However, decreasing the amplitude of the modulation during the laser locking reduces the effect on the 23 Table 2.1. Pump and probe transitions used for double resonance Sample Transition Band Frequencya Offsetb Laser Pump Transitions 12CH3F QQ(12,2) v3 31 383 940.1 -39.6 126602 9P(20) 12CH3F QR(11,9) v3 31 998 588.1 26.1 12C1302 9P(22) 13CH3F QR(4,3) v3 31 042 692.2 24.26c 126502 9P(20) Probe Transitions 12CH3F QR(12,2) 2v3 - v3 31 557 000.3 -12 971.4 126602 9P(14) 12CH31= QQ(12,9) 2v3 - v3 30 913 528.6 9 386. 8 126602 9P(36) 120131: QR(12,9) 2v3 - v3 31 558 480.5 -14 451.6 126602 9P(14) 13c113,1= QP(5,3) 2v3 - v3 30 092 976.1 14 557.0 136602 9P(16) 13CH3F QR(4.3) 2V3 — v3 31 042 692.2 16 317.0 12c1502 9R(26) aCenter frequency of transition in MHz calculated from the molecular constants in Refs. (27, 28) bLaser frequency - center frequency in MHz. Laser frequencies obtained from Refs. (29, 30) CMeasured offset frequency (see text). Offset from Ref. 27 is 25.8 MHz 24 double resonance line shapes. Divergences and misalignment of the pump and probe beams are effectively reduced by a more careful experiment, although the effects could not be eliminated completely. Finally, the contributions of four-level double resonance effects are reduced by decreasing the sample pressure and increasing the pump modulation frequency. After improving the experimental conditions by taking into account all of the above factors, we were able to obtain spectra that fit theoretical line shapes very well by adjusting the Rabi frequency and the relaxation parameters in calculations. As mentioned above, although the factors which broaden the experimental line shapes can be effectively reduced, it is not easy to eliminate them from our present experimental apparatus. Thus, the relaxation parameters obtained from the least squares fitting of the spectra are not reliable indicators of the rates of collisionally-induced changes in the density matrix elements. Numerical tests have been carried out to see how the above factors affect the relaxation parameters from the fitting (see Theoretical section). However, the quality of the spectra is good enough to test the current theory of ' three-level double resonance line shapes. As will be seen, all of the features of three-level double resonance line shapes can be predicted by theoretical calculation. Figure 2.3 shows a comparison of observed and calculated double resonance line shapes in 13CH3F for the R(4,3) pump in the v3 = 1 (— v3 = 0 fundamental band (v3 band) and the QP(5,3) probe in the v3 = 2 (— v3 = 1 hot band at three different sample pressures. As can be seen from the spectra, the splitting is more clearly resolved at lower pressure as a result of the decrease in the relaxation parameters. As can also be seen from the residuals, very good agreement is obtained between experimental observations and theoretical calculations. 25 111—11 1 14L 1 J L I I Iltlrliltltltlrlt Absorpfion l l A 10.5 mTorr JR 4.5 mTorr 2.5 mTorr M- - fl _ VAVfiflWW 10.5 mTorr _ Wwwflwnmm 2-5 mTorr —. l l l J I 1 i l l Tfi' 11 HI FI ., . r, . A, . ., . —600 —595 —590 —585 Offset Frequency / MHz —605 Fig. 2.3. Three-level double resonance spectra for l3CH3F recorded at three different sample pressures and 2.2 W infrared power. The QR(4,3) transition in the V3 band was pumped and the QP(5.3) transition in the 2V3-V3 band was probed. The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3009355309 MHz. The residuals from the least squares fittings of the lineshapes are shown at the bottom of the figure. 26 B. Determination of Rabi frequency 21:11 E The Vibrational contribution to the Rabi frequency is defined as xp = __hab_ , where “ab is the vibrational transition moment for the pump transition and E is the amplitude of the electric field of the pump radiation. The value of xp is needed in the studies of collisionally-induced transferred spikes in this laboratory. Because of the difficulties in measuring accurate laser power density, we first estimated the Rabi frequency from the Lorentz width that was obtained by least squares fitting of observed and calculated three-level double resonance spectra to a Lorentz function. Since the line shape of three-level double resonance can be very different from a Lorentz function (as in the case where a dynamic Stark splitting is seen), the Rabi frequency obtained by this procedure was not always reliable. The computer program was then modified to fit the observed spectrum to a theoretical equation derived from semi-classical density matrix theory, as shown in the Appendix. This allowed us to obtain the Rabi frequency with much higher reliability. One of the features of the Rabi frequency is its linear dependence on the amplitude of the electric field of the pump radiation, which is proportional to the square root of the pump power. In order to see how well the Rabi frequencies that we obtained obeyed this linear dependence, we recorded the spectra for the R(4,3) pump in the v3 fundamental and the QP(5,3) Probe in the 2v - v hot band in 13CH3F at five different pump powers. In this experiment the Sum: power was controlled by putting an additional polarizer in front of the polarizer (POL2 in Fig. 2.2) that allows the pump beam to enter the sample cell. By rotating the additional polarizer away from the horizontal, the pump power could be reduced. Figure 2.4 shows the spectra and their residuals from the least squares fitting for two different pump 27 I I I F] I I I I [1 I I I I C . ~ 0 _ _ 35 I . O. L -‘ -1 8 . .0 a .8W 1 < -4 J '— 2.2w ‘ i «~me 8w — - WW 22w — r I 1 I I I I I I I I I I ml —603 -598 -593 -588 Offset Frequency / MHZ Fig. 2.4. Three-level double resonance spectra for 13CH3F recorded at two different infrared powers and a sample pressure of 2.5 mTorr. The pump and probe transitions, the lasers and the horizontal axis are the same as in Fig. 2.3. The residuals from the least squares fittings of the lineshapes are shown at the bottom of the figure. 28 powers. The Rabi frequencies obtained at five different pump powers are plotted against the square root of the pump power and shown in Fig. 2.5. The straight line in the figure has been constrained to go through zero and it is apparent that the data agree very well with the expected proportionality of the Rabi frequency to the amplitude of the electric field of the pump laser. C. The criteria for observing dynamic Stark splitting Many years ago, Delsart and Keller (5) listed the criteria for observation of splitting in three-level double resonance in Doppler averaged spectra: the pump frequency should be greater than the probe frequency if the pump and probe beams are in the counterpropagating configuration. The argument was that when the former is true, the relative Doppler effects tend to expand the splitting and if the latter is not true there is uncompensated Doppler broadening in the two- photon contribution to the double resonance. It is very interesting to see how well the criteria describe the spectra in our experiment where both the Doppler effect and the spatial-degeneracy affect the line shapes. For the spectra shown in Fig. 2.3 the criteria are satisfied (Table 2.1), so the splitting is observed. To test the validity of the criteria more examples seemed to be needed, including a case for which the criteria are not satisfied. For this purpose, we examined three other pump and probe combinations in 12CH3F, all in counterpropagating geometry. For the QQ( 12,2) pump in the v3 fundamental band and the QR(12,2) probe in the 2v - v 3 3 hot band the frequency of the pump is less than that of the probe (Table 2.1), so no dynamic Stark splitting should be observed. The recorded spectrum for this pump and probe, shown in Fig. 2.6, shows no splitting and fits the theoretical lineshape 29 80 I I I l I 7.0~ A 6.0— _ 5.0.. — Rabi Frequency / MHz 4S 0 l l 3.04 — 2.0— - 1.0- 4 0-0 I I I I I 0.0 0.3 0.6 0.9 1.2 1.5 1.8 pi/z / W1/2 Fig. 2.5. Plot of the Vibrational contribution to the Rabi frequency xp for the spectra shown in Fig. 2.4. and three additional spectra for the same transition recorded at different powers. The straight line is the least-squares fit of the five points constrained to go through zero. The slope of the line is 5.47 MHz W'l/z. 30 Absorption —4o . , 998 1000 F1602 I 1004 ' 10106 Offset Frequency / MHZ Fig. 2.6.Three level double resonance spectrum for 12CH3F. The QQ(12, 2) transition in the V3 band was pumped and the QR(12, 2) transition in the 2V3-V3 band was probed.The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3155602888 MHz. The pump power density was ~ 4 W/cm2 and the sample pressure was 6 mTorr. The residual from the least-squares fitting is shown below the spectrum. 31 exceptionally well. The other two systems examined use the QR(11,9) pump in the v3 fundamental, and either the QQ(12,9) or the QR(12,9) probe in the 2v - v hot band. Although the criteria for observing the splitting are satisfied for bith 3 systems, the frequency of the QR( 12,9) probe is closer to the pump transition than that of the QQ(12,9) probe (Table 2.1). This predicts a larger splitting in the QQ(12,9) probe than in the QR(12,9) probe when all the other conditions are the same. Figure 2.7 and Fig. 2.8 show the spectra recorded for these two systems at the same pump power and sample pressure. As can be seen, the spectra show exactly what is expected. D. Precise determination of a laser offset frequency It turns out that the QR(4,3) transition in the v3 fundamental of 13’CH3F can not only be pumped with the 9P(32) 12C1602 laser, but can also be probed with the IMSL system driven by the 9R(26) 13C1602 laser. Figure 2.9 shows the spectrum for this double resonance combination. This is an example of a ”two-level” double resonance. In fact, it should be viewed as a three-state double resonance in terms of the degenerate m states, since the planes of polarization of the pump and probe beams are orthogonal so that if the selection rule for the pump beam is A m = 0, the corresponding selection rule for the probe is A m = :1. One of the applications of the two-level double resonance configuration is to determine a precise offset frequency of the pump laser from the center frequency of the pump transition. As will be seen below, accurate knowledge of the pump offset is essential for studying velocity changing collisions (Chapter 4). In the least squares fitting procedure for three-level double-resonance spectra we assume a value for the offset of the pump 32 .1 40-4 Absorption -20 f T v I ' T W t e I ' —415 —41:5 —41 1 —409 —407 —405 —403 Offset Frequency / MHz Fig. 2.7. Three-level double resonance spectrum for 12CH3F. The QR(11,9) transition in the V3 band was pumped and the QQ(12, 9) transition in the 2V3-V3 band was probed. The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 30913915.43 MHz. The pump power density was ~ 3 W/cm2 and the sample pressure was 2 mTorr. Absorption 4 cl .23 ' 4&5 ' 4&7 ' 4&9 i 4351 ' 453 ' 435 Offset Frequency / MHz Figure. 2.8. Three-level double resonance spectrum for 12CH3F. The QR(1 1,9) transition in the V3 band was pumped and the QR(12, 9) transition in the 2V3-V3 band was probed. The lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 31558028.88MHz. The pump power density was ~ 3 W/cm2 and the sample pressure was 2 mTorr. 33 Absorpbon _204 .i -30- ‘ 'i ‘40 I I I T I 325 330 335 340 345 350 355 Offset Frequency / MHZ Fig. 2.9. Two-level double resonance spectrum for 13‘CI‘13F. The QR(4, 3) transition in the V3 band was both pumped and probed. The pump and probe lasers used are given in Table 2.1. The horizontal axis is the probe laser frequency minus 3104300923 MHz. The pump power density was ~ 4 W/cm2 and the sample pressure was 3.5 mTorr. The residual from a least squares fitting of the lineshape is shown at the bottom of the figure. 34 laser frequency from the center frequency of the pump transition and fit the center frequency of the probe transition. In two-level double resonance the two center frequencies are the same, so that it is a simple matter to adjust the assumed offset until the fitted center frequency is consistent with the assumed value. The accuracy of the offset obtained in this way is mainly determined by the three-level double resonance line shape, which is Doppler free. If the laser frequencies are taken from Ref. (29-30), the resulting offset of the 9P(32) 12C1602 laser from the center frequency of the QR(4,3) transition in the v3 band of 13CH3F is 24.26 MHz. The overall accuracy of the value is estimated to be better than 0.1 MHz. Compared with the previously measured value the accuracy is increased by more than one order of magnitude. A more systematic method for measurement of accurate pump laser offsets will be discussed in Chapter 4 where counterpropagating and copropagating three-level double resonance techniques are used. V. Conclusion We have observed dynamic Stark splitting in three-level infrared-infrared double-resonance spectra for vibration rotation transitions of gas phase molecules. The line shapes have been found to be very well represented by calculation by means of a semi-classical density matrix treatment of a three level system including spatial degeneracy and Doppler effects interacting with two monochromatic radiations. The criteria for observation of dynamic Stark splitting in Doppler-averaged spectra have been tested and found to agree with our observations very well. It has been shown that population and coherence relaxation rates can probably be obtained independently by least squares fitting 35 the observed line shapes of high quality spectra. We have also pointed out the problems associated with frequency modulation of the lasers, such as that used for frequency stabilization, as well as the problems that result from beam misalignment or beam divergence and from four-level double resonance effects. These problems have to be solved in order to get reliable relaxation rates. Frequency modulation effects can be reduced by using the stabilization scheme of Schupita gt a_l_ (31), or by using a Lamb dip in a laser Stark spectrum for stabilization as described in Chapter 4. Beam misalignment and divergence effects can be reduced significantly by using samples at higher pressure (>15 mTorr). Four-level double-resonance effects may be more difficult to eliminate. It may be possible to reduce or eliminate four-level effects by increasing the chopping frequency of the pump radiation or by using some form of polarization modulation. VI. Appendix Algebraic solution for a three-level system The purpose of this appendix is to present our algebraic solution of the density matrix equations for a three-level system under the influence of two sources of radiation. The equations differ from those given by Takami (15) by including different relaxation rates for the two population differences and for the three coherences and by including factors to make them useful for the four possible energy-level configurations numbered arbitrarily in Fig. 2.1. The method of 36 solution has been described in a previous paper from this laboratory and will not be repeated here (14). The derivation begins by writing H = H”) +Hm +H‘” » (AI) in which H”) is the Hamiltonian for an individual molecule in the absence of any fields, Hmis the interaction that results from the applied radiation, and Hm is the effective Hamiltonian for molecular collision; the effect of Hm is included as empirical relaxation terms in the density matrix equations. As shown in Fig. 2.1, we assume a 3—level system with energy levels Ea’ Eb’ and Ec that are eigenval- ues of H”); the corresponding eigenfunctions are used as the basis functions for expansion of the density matrix. The matrix elements of. Hm are Hill: = -p.jk(81c0521tvlt+82c0521w2t) , (A2) where 81, v1 and 22, v2 are the electric fields and frequencies of the two radiation sources. We assume that "ab = “ba and ubc = ucb are the only non-zero ele- ments of the transition dipole moment it, that 51V1” vba = (Eb - EaJ/h (A3) and that 52v2 ~ vc Ec - Eb l/h . (M) b = i The sign factors 51 and 52 are :1 , as in Fig. 2.1. The equation of motion for the den- sity matrix p is taken to be p = -3§[H(0) +Hm, p ] —l“p(p-p‘°’) (A5) 37 in which [Hm + Hm, p J is the commutator of H”) + Hm with p, I“D is a super- matrix of relaxation coefficients, and p ‘0’ is the thermal equilibrium value of p. Eq. (AS) is solved in the steady—state limit by application of the rotating-wave approximation. First, we substitute _ d e--21I:is,v,t s pba ' ba ' u" _ cl e.2rtiszv2t pCb ‘ Cb 1 (A7) and -2ni[s,v‘+szvzjt pca = dca W” into the expanded form of Eq.(A5) and then write the resulting equation as a time derivative of paa’ pbb’ pcc’ dba’ c1Cb or d c a on the left-hand side of the equals sign On the right-hand side all terms that oscillate at frequency v1 - v2 or higher are eliminated. The resulting equations are then set to zero to obtain the steady- state solutions. When the procedure just described is carried out, it is found that the terms proportional to e, or 82 contain only two linear combinations of the diagonal den- srty matrix elements, paa - pbb and pbb - pcc' It rs therefore useful to transform the diagonal elements as follows: d=Sp (A9) 38 where p here is a column vector containing the diagonal elements of the density matrix, ( ) d1 paa¢pbb d = d2 = p bb—pcc d 3 (paa+pbb+pcc, and Then, if the relaxation dependence of p is written '=_1" _ (0), P p“) P ) after transformation d =-l‘d(d-d‘°’) where _ -1 Fd—SFPS. (A10) (All) (A12) (A13) (All) For our system, in which levels a, b, and c are in different vibrational states, we assume that l‘ p is an ordinary diagonal matrix with elements 73, 7h, and 1". Then, 39 r \ {276wa Yb-Ya yb-‘Ya 1 rd = -5 yb—yc -(yb+2yc) yC-yb . (A15) C278+yb+yc -Ya-Yb+27c -(Ya+yb+yc] If Ya = Yb = 7c = 7p, which should be approximately true for methyl fluoride, I“ d is diagonal with diagonal elements 7p. In this case, d3 is decoupled from (11 and d2. This is the approximation that was employed here, though for slightly greater generality, (11 and d2 are allowed to have different relaxation parameters, 71 and 72. As a final point concerning the relaxation matrix, we assume that collisions cause only loss of coherence; i.e., there is no collisional coherence transfer. There- fore, db a’ dcb’ and clC a decay with collisional relaxation parameters Yba’ ch’ and Yca respectively. The result of all this is to produce a system of 8 linear equations for the densi- ty matrix elements, as follows: Ad = rd“ we) in which the transposes of d and d0 are d=(d d'a "ad (1, d'cb dgb), «m and ‘0 d =(d‘l’ooood‘2’oo); we) the matrix A is 0 7ba 81 o 7 o o 0 x1 x2 -7 -617ba-—2— o o o 0 x2 x1 0 o 7 Yca 83 o o —7 X X o ~72 o -83Yca o 31 o l o o o o-ZovaS2 1 X2 0 0 “70‘7527cb (AW) and F is a diagonal matrix whose non-zero values are equal to the diagonal val- ues of A. Also, and djk = dj'l< +i 1i , l-lbaer h I X1: (A21) (A23) 41 v 52 = $2v2(1-p—C—z)-vcb. $24) In these equations V2 is the component of the molecular velocity in the direction of beam 1, c is the speed of light, and p = :1 for copropagating or counterpropa- gating beams, respectively. If we assume that beam 2 is the probe beam that is detected and analyzed, then the absorption coefficient is proportional to the velocity average of dé'b or to 52 0° {ill/u): .. f = 7.1; I e dcb dvz (A25) in which u2 = szT/ m where k3 is the Boltzmann constant, T is the temperature, and m is the molecular mass. For our work, the integration in eq. (A25) is per- formed numerically. Normally, the summation is carried out to V2 = tau with (V/ C) sz smaller than the smallest of the relaxation parameters. The linear system in eq. (A16) may be solved for déb algebraically by a tech- nique previously described (14). The result is to give déb as a ratio of determi- nants, 311 C1 a21 C2 311 an an a22 d" cb / (A26) in which 2 x1 a11 = Ga+—Y—+Dn[Aa(BbDa-GaAa ) —Da(GbDa-Ab )] , (A27) 1 42 xrxz 812 = -Bb——2—Y—+Dn[Aa(Gan-Ab J—Da(BbDb-GbAa )3 , l xrxz a2] = —Bb-2——+Dn[Aa(GbDa-AbJ—Db(B D 43a».a J], 72 a22 = Gb In these equations, 2 2 ba x2 + T + unpra (BbDb - GbAa )- Db [<3an - Ab )] . b A — axlxz, Bb = BXIXZI Ab = AaBb’ (A28) (A30) (A31) (A32) . (A33) (A34) (A35) (A36) (A37) (A38) (A39) 43 a _ _ (81+82) we) 4[(5,+sz)2+y‘ca] ’ Yca B: 4[(81+52)2+YZC3] . (A41) Although not needed for the work described here, the absorption coefficient for beam 1 is proportional to w 2 s] -(vz/u) f1 = _ e %a de W2) JEu .00 for which dliia = C1312 / arrarz , (A43) C2 a22 azr a22 The lineshape functions f1 and f2 contain the sum of single resonance and double resonance contributions. The single resonance contribution for detection of beam 2 may be computed from the usual two-level lineshape, which follows from the three-level equations by setting x1=0. The result is 529ch fés’ = (M4) 5: + Yzcb + ch (xi/72) . The corresponding result for fl‘s’ is 44 SrCrYba {:9 = 2 2 -, 81+YiJa+Ybaix1/Yli (A45) The pure double-resonance lineshape is then obtained by subtracting the appro- priate f is) from fi' If the calculation includes a summation over m states, it is nec- essary to recall that the formula for the absorption coefficient for beam 2 is aabs = lénszcbp‘cb (fz— SSJ/cez. we) Therefore, the f2 - fés) for each m state must be multiplied by the appropriate val- ue of “Cb before performing the summation. REFERENCES 1. S. H. Autler and C. H. Townes, Phys. Rev. 100, 703-722 (1955). 2. A. P. Cox, G. W. Flynn, and E. B.Wilson, Jr., J. Chem. Phys. 42, 3094 (1965). 3. H. Jones, in Modern Aspects of Microwave Spectroscopy, edited by G. Chantry (Academic, New York, 1979), pp. 123—216. 4. Th. Hansch and P. Toschek, Z. Physik 236, 213-244 (1970). 5. C. Delsart and J.-C. Keller, J. Phys. (Paris) 9, 350-360 (1978). 6. C. Delsart and J.-C. Keller, J. Phys. 13.9, 2769-2775 (1976). 7. M. S. Feld and A. Javan, Phys. Rev. 177, 540 (1969). 8. N. Skribanowitz, M. J. Kelly, and M. S. Feld, Phys. Rev. A 6, 2302-2311 (1976). 9. R. M. Whitley and C. R. Stroud, Phys. Rev. A 14 1498-1513 (1976). 10. P. R. Berman, P. F. Liao, and J. E. Bjorkholm, Phys. Rev. A 20, 2389-2404 (1979). 11. V. P. Kaftandjian, C. Delsart, and J. C. Keller, Phys. Rev. A 23, 1365-1374 (1979). .12. P. R. Berman and R. Salomaa, Phys. Rev. A 25 2667-2692 (1982). 45 13. C. Feuillade, J. G. Baker, and C. Bottcher, Chem. Phys. Lett. 40, 121-125 (1976). 14. S. T. Sandholm and R. H. Schwendeman, J. Chem. Phys. 78, 3476-3482 (1983). 15. M. Takami, Japan J. Appl. Phys. 15, 1063-1071 (1976); 15, 1889-1897 (1976); 17, 125- 133 (1978). 16. H. W. Galbraith, M. Dubs, and J. I. Steinfeld, Phys. Rev. A 26, 1528-1538 (1982). 17. C. Feuillade and P. R. Berman, Phys. Rev. A 29, 1236-1257 (1984). 18. N. Dam, L. Oudejans, and J. Reuss, Chem. Phys. 140, 217-231 (1990). 19. Y. Matsuo, S. K. Lee, and R. H. Schwendeman, J. Chem. Phys. 91, 3948-3965 (1989). 20. Y. Matsuo and R. H. Schwendeman, J. Chem. Phys. 91, 3966-3975 (1989). 21. U. Shin, Q. Song, and R. H. Schwendeman, J. Chem. Phys. 95, 3964-3974 (1991). 22. C. J. Borde’, J. L. Hall, C. V. Kunasz and D. G. Hummer, Phys. Rev. A14, 236-263 (1976). 23. J. Keilson and J. E. Storer, Q. Appl. Math. 10, 243-253 (1952). 24. C. Freed and A. Javan, Appl. Phys. Lett. 17, 53-56 (1970). 25. G. Magerl, W. Schupita, and E. Bonek, IEEE J. Quantum Electron. QE- 18, 1214-1220 (1982). 26. H.-G. Cho and R. H. Schwendeman, unpublished work. 27. S. K. Lee, R. H. Schwendeman, and G. Magerl, J. Mol. Spectrosc. 117, 416-434 (1986). 28. S. K. Lee, R. H. Schwendeman, R. L. Crownover, D. D. Skatrud, and F. C. DeLucia, J. Mol. Spectrosc. 123. 145-160 (1987). 29. F. R. Petersen, E. C. Beaty, and C. R. Pollock, J. Mol. Spectrosc. 102, 112-122 (1983). 30. C. Freed, L. C. Bradley, and R. G. O’Donnell, IEEE J. Quantum Electron. QE-16, 1195-1206 (1980). 31. W. Schupita, A. Ullrich, and G. Magerl, IEEE J. Quantum Electron. QE-25, 2154-2160 ( 1989). 46 Chapter 3 Collisionally Induced Rotational and Vibrational Energy Transfer of Methyl Fluoride in Foreign Gases I. Introduction Knowledge of the properties of state-to-state collisionally-induced transitions among molecular energy levels is of fundamental importance for understanding the nature of the collisional process and of the intermolecular potentials. Because of the experimental difficulty and the theoretical complexity, much less is known about the principles and mechanisms for collisionally-induced transitions than for radiation-induced transitions. However, recent advances in experimental techniques and the rapid increase in the available speed of numerical computation have opened up new prospects for study in this field. Among the various methods that have been used for the study of collisionally-induced transitions is the technique of four-level double resonance that was pioneered in the microwave region by Oka (1-2) and that has been used since in almost every range of the electromagnetic spectrum. Examples include four-level double resonance experiments that have been performed by combining infrared techniques with techniques in the radiofrequency region (3-5), through the microwave (6-12), millimeter-wave (13-15), and infrared (16-38) regions to the visible and ultraviolet regions (39-44). 47 A very important advantage of infrared-infrared double resonance is related to the fact that the Doppler width at the infrared frequencies is large compared to both the available resolution and the inhomogeneous width for low-pressure gases. This makes it possible to monitor double resonance effects as a function of the component of the velocity of the molecules in the direction of the beam and therefore provide information about changes in velocity upon collision. Recently, infrared-infrared double resonance experiments of the type just described were reported for 15NI-13 (35), 13CH3F (36) and 12CH3}: (38) from this laboratory. In these experiments, a rovibrational transition in a fundamental band was pumped while a rovibrational transition in a hot band was probed. The lineshape of the probing transition was found to be a superposition of a broad Gaussian and a sharp spike. TheiGaussian component was interpreted to be the result of the near resonant vibration-vibration (V-V) energy transfer, in which the pumped molecule swapped vibrational energy with a molecule in the ground vibrational state. In this process, the molecules transferred to the probed level were not the molecules that were pumped. These molecules came from a near thermal equilibrium distribution and the resulting contribution to the probe transition was a Gaussian function with the expected Doppler width. The spike component was assumed to be the result of the direct collisionally-induced transition, where the pumped molecules find themselves at the lower state of the probe as a result of collisions. Since the pumped molecules had a very narrow distribution of the velocity component in the direction of the beam and the collisionally-induced transitions occur without much change in velocity for the system investigated, the resulting contribution to the line shape of the probe transition was a sharp spike. In the experiments just described the spike components were observed only when the K quantum numbers of the lower level of the probe transition and the 48 upper level of the pump transition satisfied the selection rule K (probe) - K (pump) = 3n, where n is a positive or negative integer or zero. This is the selection rule found by Oka many years ago (1,2) for collisionally-induced rotational transitions in C3,, molecules. It was found that a phenomenological collision kernel that was a sum of two Keilson- Storer kernels (Ref.(45); equation given below on P. 57) represented the velocity changes during the collisionally-induced transition very well. One of the parameters in the K-5 kernel can be interpreted to be the r.m.s. change in speed upon collision. By numerical fitting of the theoretical lineshape obtained from the phenomenological kernel to the observed spectrum, values of the r.m.s. speed change for several transitions were determined. The previous studies from this laboratory of velocity change during collisionally-induced transitions were the results of self-collisions between dipolar molecules (35-38). In the present study, we describe the results of energy transfer in CH3F when colliding with different foreign gases. There were three motivations for undertaking this work. First, we wanted to learn more about the correlations of velocity change and state change for collisions in which the dipole-dipole interaction was not the dominant effect. We also wanted to find out how the mass of the perturber would affect the velocity change of the active molecule during the collision. Both of these questions could be answered by studying samples of dilute methyl fluoride in different monatomic gases or nonpolar molecules. Second, unlike the self-collisions of methyl fluoride, where the V-V process plays an important role in transferring population to the probed level, for methyl fluoride- foreign gas collisions, only the direct energy transfer process dominates the contribution to the spectra. This is because the V-V process is either completely absent (as when the foreign gas is an atomic species) or it involves excitation of foreign gas molecules whose spectra are not probed. This allows us to distinguish 49 the direct energy transfer process from the V-V process. The advantage of this is to observe the effect of the direct transfer without the complication of the V-V transfer. This advantage can be employed in the study of rotationally-resolved direct vibrational energy transfer from the V3=1 to v6=1 vibrational state in 12CH3F, which was made possible by the recent assignment of high resolution + v spectra in the v - v 6 hot band for the molecule (46). In pure methyl fluoride 3 6 these effects are dominated by the V-V processes. The final motivation of the study was concerned with the phenomenological collision kernel that is a sum of two K-S kernels and that has been used to describe the velocity change during the collisionally-induced transition (35-38). The K-8 collision kernel was originally introduced to describe Brownian motion (45) and then applied to other collisional problems because of its simplicity (47, 48). One of the most important reasons we used this kernel, in addition to its simplicity, was that the theoretical line shape derived from the kernel described the experimental observations very well, but we wanted further evidence to justify the use of the ' phenomenological collision kernel in our study. For this purpose, we used the method of Borenstein and Lamb (47) to calculate one-dimensional collision kernels from the classical elastic scattering theory using Lennard-Jones or Buckingham- Slater intermolecular potential functions (49). It turned out that the calculated kernel and a sum of the two K-S kernels had in general the same shape. The classical calculation of elastic collision kernels also helped explain the line shapes of the observed spectra. Although the collision process in our experiment is not elastic, and probably not classical, the change in internal energy and angular momentum for collisionally-induced rotational transitions is small compared to the energy and angular momentum of the collision, and classical scattering calculations often give a a view of the collision process that is at least qualitatively 50 correct. In spite of the simplicity of the model and the crudeness of the potential function, it turns out that by adding consideration of the collision diameter, as obtained for example from lineshape measurements, the calculated collision kernels provide a useful and instructive view of the experimental lineshapes. 11. Experimental Details The double resonance spectrometer used for this work was identical to that used for the study described in Chapter 2 except that a 2 meter sample cell was used and the chopping frequency for the pump was 150 Hz. We needed a longer optical path because the densities of sample molecules used in this study were lower and the absorptions were much weaker. A slower pump chopping frequency was used because we were studying the energy transfer process and we wanted the period of the pump on or the pump off to be substantially longer than the time required for the molecules to reach the steady state. By contrast, for the three-level double resonance spectra described in Chapter 2, the four-level double resonance effects should be eliminated as much as possible. All of the gases were commercial samples used without further purification. Sample mixtures were prepared by adding gases to the sample cell at the appropriate pressures, which were measured by means of a capacitance manometer. Typical pump powers at the entrance of the sample cell were ~1 W while probe powers were ~20 uW. All spectra were recorded at room temperature, ~ 297 K. The lasers and microwave frequency offsets for the transitions studied in this work were taken from previous reports from this laboratory (46,50,51) and are 51 shown in Table 3.1. The laser frequencies for the various C02 isotopic species were calculated from the molecular constants reported in Refs. (52,53). III. Theoretical Detail For calculation of the one-dimensional collisional kernel by the procedure of Borenstein and Lamb (47), we consider the interaction of an active molecule and a 0 perturber which, at time -t, are at r a = ra and r p = r3, respectively, defined in a space-fixed coordinate system; the initial unperturbed velocities of these molecules are v2 and v0, respectively, in the same space-fixed frame. It is well D known that the motion of the active molecule is in the plane defined by the initial vector connecting the two particles, to = r2 - ti}, and the initial relative velocity vector, v0 = V? — v3 (49). Borenstein and Lamb have shown that if va’ is the asymptotic velocity of the active molecule long after the interaction, then in the space-fixed frame (47), v = vO+Av a a a where m _ p 0 . _ _ Ava————ma+mpv [sran (1 cosG)p] (A1) in which mal and mP are the masses of the active and perturber molecules, respectively; v0 is the magnitude of v0, the initial relative velocity; 9 is the angle between the extension of v0 and v’, the asymptotic relative velocity long after the collision; and p and q are unit vectors in the scattering plane defined such that p is in the original direction of v0 and q is perpendicular to p. The unit vector q is in the direction of b, whose length and direction are defined to be the length and 52 Table 3.1. Pump and Probe Transitions Used for Double Resonance Sample Transition Band Symmetry Frequency“a Offsetg'c Laser Pump Transitions 13CH3F 912(43) v, A 31 042 693. 8 -24. 26 12C1602 9P(32) 12c14312 QQ(12,1) v3 E 31 383 841. 7 -58. 71 ”€160, 9P(20) 12CH3F °Q(12,2) v, E 31 383 940.1 39. 70 12C1602 9P(20) ”CI-13F QR(11,9) v3 A 31998 588.1 -26. 10 ”€130, 9P(22) Probe Transitions 13CH3F QR(5,3) v, A 31 088 539. 2 -12 952. 96 12c1602 9P(30) 13CH3F QP(6,3) 2v3 — 93 A 30 040 816. 7 -12 712. 01 136602 9P(18) 13CH3F Q13(7,0) 2v3 — 93 A 29 987 762. 1 -10 888. 01 136602 9P(20) 13CH3F QP(7,1) 293 — 93 E 29 987 793. 1 -10 856. 95 13C1602 9P(20) 13CH3F Q130,2) 2v3 - v3 1: 29 987 886. 9 -10 763. 20 130602 9P(20) 13CH3F QP(7,3) zv3 - v, A 29 988 045. 1 -10 605. 03 136602 9P(20) 13CH3F QP(7,4) 293 - v3 E 29 988 270. 6 -10 379. 44 130602 9P(20) 13CH3F QP(7,5)' 293 — 93 E 29 988 568. 1 -10 081. 95 136502 9P(20) 130131: QP(7,6) 2v3 - v3 A 29 988 943. 6 -9 706. 49 136602 9P(20) 12CH3F Q1>(14,0) 2v3 - v3 A 30 197 402. 9 -15 623. 25 130602 9P(12) 12CH3I= QP(14,1) 2v3 — 93 E 30197 444. 7 -15 581. 38 136602 9P(12) 120435 QP(14,2) 293 - v, E 30 197 571. 0 -15 455.13 136602 9P(12) 12C11313 QP(14,3) 2v3 — v3 A 30 197 783. 9 -15 242. 28 130602 9P(12) “Cl-13F Qr>(14,4) 293 — v3 E 30 198 087. 0 -14 939.16 13c1602 9P(12) 120135 QP(14,S) 293 - v, E 30 198 485. 7 -14 540. 44 130602 9P(12) “Cl-13F QR(7,1,-1) v, + v6 - v6 E 31 531 894.1 -12 134. 83 12C1602 9P(14) 12C1138 QR(9,3,1) 93 + v,5 - v,5 E 31 632 525. 7 -14 317. 71 ”(21502 9P(10) ”CI-13F QR(10,2,-l) v3 + v6 - v6 A 31 661 334. 5 14 491. 07 120602 9P(10) 120131: 91102.0) 293 - 93 A 31556 943. 0 12 914.16 "(21602 9P(14) 12CH3F QR(12,1) 2v3 — v3 1-: 31 556 957. 2 12 928. 33 12c1602 9P(14) 12crrgr 911022) 293 - v, F. 31 557 000. 4 12 971. 51 12c1602 9P(14) 120435 014023) 293 - 93 A 31 557 074. 6 13 045. 71 12c1602 9P(14) 12c1431: 012024) 2v3 - v3 E 31 557 183. 2 13 154. 33 “€150, 9P(14) ”can: Q1102.5) 293 -— v, E 31 557 331. 2 13 302. 29 ”€160, 9P(14) ”CI-13F QR(12,6) 2v3 — 93 A 31 557 525.1 13 496.18 ”cub, 9P(l4) ”CI-13F 9R(12,7) 2v3 - v, E 31 557 773. 3 13 744. 43 “€160, 9P(14) 120131: QR(12,8) 293 - v3 13 31 558 086. 4 14 057. 55 12(:1‘502 9P(14) 1201313 QR(12,9) 203 — v, A 31 558 477. 2 14 448. 36 120602 9P(14) aCenter frequency of the transition in MHz. bCenter frequency of the transition minus the C02 laser frequency in MHz. cLaser frequencies calculated from the constants in References (52) and (53). 53 direction, respectively, of ra-r-p at the point of closest approach for the condition of no interacting potential. The one-dimensional collision kernel that is of interest in this work is the quantity W(vz, vz’) dvz’ which is defined to be the probability per unit time that an active molecule with initial space-fixed Z-component of velocity VZ has its final Z-component of velocity between VZ' and vz’ +dvz’. To compute W(vz, vz’) we follow Borenstein and Lamb (47) and calculate vz’ = Vaz' for a large number of randomly-chosen scattering events for a single active molecule with initial Z- component of velocity equal to vz =v22. We set up inside the computer a number of bins of width dvz and increment the count in the appropriate bin for each calculated value of V'az~ In order to make a random selectionof scattering events, we set up a new particle-fixed coordinate system centered at the perturber, but rotated from the space-fixed frame so that the new 2 axis is in the direction of v° (Fig. 3.1). The new y axis is in the direction of b and therefore in the plane of to and v°; the y axis is assumed to make an angle x with the line of nodes, the intersection of the space-fixed XY and the new particle-fixed xy planes, as defined by Wilson, Decius, and Cross (W DC) (54). The new x axis completes a right-handed coordinate system and is in the direction of the collisional angular momentum, O x v0. The initial space-fixed Z component of the velocity of the active L = ur molecules is fixed for all scattering events, while for each event the initial space- fixed X and Y components of this velocity as well as all three components of the initial space-fixed velocity of the perturber are randomly chosen from the appropriate Boltzmann distributions defined by the assumed particle masses and the temperature. To take into account all of the possible relative positions of the active molecules and perturber at time -t, we assume that the tip of r0 in the center of mass frame 54 144111111111111] ® ‘ 0 Z Figure 3.1 Diagram of the scattering plane for a single scattering event between an active molecule (a) and a perturber (p). The curved path of the active molecule is symmetric about the line that makes an angle 9m with the -z axis. In the figure, 9 = 1r: - 2 9m is the scattering angle; to is the initial separation of a and p; v0 is the initial relative velocity; b, which is parallel to the y axis, is the magnitude of the impact parameter; and x is the angle between b and a line (N) that is parallel to the line of nodes. 55 lies in an element of volume of magnitude dV = v0 dt db b dx that is located by cylindrical coordinates (b, x, z=v0t) in the center-of-mass frame (Fig. 3.1); t is the time that would be required for the active molecule to reach the position of closest approach to the scattering center for the case of no interacting potential. The final value of Val is independent of t, so that if the probability of an encounter for v=v0 with r0 in the range defined by t, t+dt, b, b+db, x, and x + dx is P v0 b dt db dx then the probability per unit time for such an encounter is P v0 b db dx. ‘ To calculate v’az , we write I _ 0 vaZ " VaZii'AvaZ where Avaz = WV [SlflGg’k‘ (1—C039)p.k] in which k is a unit vector in the space-fixed Z direction. According to WDC (54), the direction cosines are pOk = c050 and q 0 k = sin0sinx, where 0 is the angle between the Z and z axes. In our case, __ 0 0 cost) - vZ/v and 56 l 2 2 2 sine = (v0 -VZ) /v0. Therefore, 1 m 2 2 2 _ p (0 0) . . 0 Av - v -v srnxsrnG-v (l-cosO) . aZ ma+mp Z Z Finally, to complete the integration, the impact parameter b is randomly selected from the range 0 to b (max) and the angle x is randomly selected from the range 0 to 21:. Then, after calculation of v' aZ’ the appropriate vZ’ bin is identified and incremented by va. If the number of events is made very large, the result should be proportional to the classical collision kernel for the assumed masses, temperature, and interaction potential. Normalization can be achieved by multiplying the contents of each bin by the number of molecules per unit volume and dividing each result by the sum of the va values for all of the events. For these initial calculations, two potential functions were chosen: the Lennard-Jones 6-7 function (49), and the Buckingham-Slater potential (49), 62 'Y le 6 I' V‘” ‘ v—-6i“"i“i“§ii‘6(?) i In these equations, a is the well depth at the equilibrium value of r = re. Unfortunately, we have no specific information about the value of e and re to use for this purpose. Consequently, a number of calculations were performed with e / 57 k3 (k3 is the Boltzmann constant) in the range 100-500 K and re in the range of 3.5- 4.5 A. These ranges were selected on the basis of examination of Table I-A in Ref. (55). Most of the calculations were performed with the Lennard-Jones 6-12 potential, but a few Buckingham-Slater calculations were performed to test the dependence of the shape of the collision kernel on the repulsive part of the potential curve. Since the results for the two potentials were not qualitatively different, the Lennard-Jones 6-12 potential was used exclusively after these tests were completed. For comparison with the lineshapes of the transferred spikes that were measured and analyzed in our previous work, some of the calculated collision kernels were fit by least squares to a sum of Keilson-Storer collision kernels (45), A. . _ 1 _ . _ 2 2 W (vz, v Z) - 2 513 exp[ (v Z aivz) /Bi:i 1 in which or? = 1 - [iii/u2 where u2 = 2 kBT / m, with T the temperature and m the molecular mass; the A, are expansion coefficients and the Bi may be interpreted as J2 times the r.m.s. change in the Z component of the velocity as a result of collision for the molecules that contribute to the ith component of the expansion. IV. Experimental Results A. Foreign gas effects on the double-resonance lineshape The effects of five different foreign gases (12CH3F, H2, He, Ar, and Xe) on the 58 lineshapes of infrared-infrared four-level double resonance in 13CH3F have been investigated. In Figure 2, the spectra of 3 mTorr 13CH3F in 50 mTorr of different foreign gases were each compared to the spectrum of 7 mTorr pure 13CH3F sample for the QP(6,3) probe transition in the 2v hot band while the QR(4,3) 3‘V3 transition in the v3 fundamental band was pumped. The dotted traces are the spike and Gaussian components in the observed spectrum separated by the least squares fitting program used in Ref. 35. It is apparent that for collisions with 120131: (Fig. 3.2b), H2 (Fig. 3.2c), and He (Fig. 3.2d), a transferred spike with substantial intensity is seen, whereas for Ar (Fig. 3.2e) and Xe (Fig. 3.2f) the lineshape is mostly a broad Gaussian shape. The same experiments were repeated with different ratios of the partial pressures of the sample and- foreign gas and the qualitative pattern of the line shapes did not change. i In contrast to methyl fluoride self collisions, where the spike components were attributed to direct rotational energy transfer and the Gaussian component to the near resonant V-V transfer, for methyl fluoride - foreign gas collisions, both spike and Gaussian components are results of the direct rotational energy transfer processes. The reason has already been mentioned for this: that for perturbers that do not have vibrational energy levels (e. g. He, Ar and Xe), the V-V process simply does not exist, while for perturbers that have vibrational levels, for which the V-V process can occur (e.g. 13CH3F-12CH3F collision), the result of the V-V process is to increase the population of a vibrationally excited state of the perturber, which is not probed. ‘ The spike component of the lineshapes includes a contribution from pumped molecules whose velocity underwent little change during the rotationally inelastic collision. This is an indication of a weak collision, where conversion from rotational energy to translational energy is small and the molecular path is not 59 —785 Figure 3.2 Spectra of the QP(6,3) transition in the 2v3-v3 band in l3CH3F taken for a’ variety of collision partners; the spike and Gaussian components for each lineshape are also shown. Trace (a) is a single resonance spectrum in a pure sample at 7 mTorr; Traces (b) - (f) are double resonance spectra recorded while the QR(4,3) transition in the v3 band was pumped. The samples for the double resonance spectra were 3 mTorr of 13CH3F in -7'55 —7'25 —e'95 Offset Frequency / MHz —665 -635 50 mTorr of foreign gas, as follows: (b) 12CH3F; (c) H2; ((1) He; (e) Ar; (0 Xe. The infrared frequencies for each spectrum are the horizontal axis values shown for (e) plus 30 041 529 MHz. 60 deflected significantly. The weak collision may be due to the effect of a long range intermolecular force at a large collisional impact parameter, or a light perturber. The broad Gaussian components in Fig. 3.2 have widths that are comparable to the Doppler width (31 MHz) of the probe transition. This component results from pumped molecules whose velocity is completely scrambled during collision. These molecules lose all ”memory” of the initial velocity during collision, which is characteristic of a strong collision For a strong collision, the conversion from rotational energy to translational energy can be large and the molecular path is deflected substantially. A strong collision may result from a small collisional impact parameter, or from a heavy pertuber. The lineshapes in Fig. 3.2 show that collisionally-induced rotational energy transfer without much change of the translational momentum can readily occur between species with substantial dipole moments or between species in which the mass of the perturber is relatively small compared to the mass of the active molecule. Thus, we attribute the existence of the transferred spike in the l3CH3F/ 12CH3F colliding pair (Fig. 3.2b) to the long-range dipole-dipole interaction for which collisions of large impact parameter can induce rotational transitions. The existence of transferred spikes for the 13CH3F/H2 (Fig. 3.2c) and 13CH3,F/ He (Fig. 3.2d) colliding pairs is attributed to the low mass of the perturber, which is insufficient to cause a substantial change in the velocity of the 13CH3F active molecule, even for collisions of relatively low impact parameter. For 13CH3F/ Ar (Fig. 3.2e) and 13CH3F/ Xe (Fig. 3.2f) colliding pairs, most of the collisionally- induced rotational transitions randomize the velocity. The hard collisions are presumably the result of small impact parameter and/ or relatively heavy perturbers. It is interesting to note that the spike for the 13CH3F/ H2 colliding pair (Fig. 61 3.2e) is broader than the spike for the 13CH3F / He (Fig. 3.2d) colliding pair in spite of the greater mass for He than for Hz. This may indicate that the form of the intermolecular potential function may be more sensitive in determining the correlation of the velocity change and the state change during the collisionally induced transition. The qualitative features of the collision kernels that result from different masses of the perturbers, collisional impact parameters and parameters in the potential functions are discussed in Section V. The results from calculations demonstrate most of the tendencies observed above. B. Selection rule for direct rotational energy transfer The most important selection rule for collision-induced direct rotational energy transfer in molecules with C3,, symmetry is Mr = 3n (1-2), where n is a positive or negative integer or zero. Thus, methyl fluoride molecules in an initial state (Lk) find themselves only in the final states (J ’,k’) after collision, where k’-k=3n. Since the selection rule connects rotational states with the same nuclear spin state, we can interpret the selection rule to be the result of the difficulty in changing the nuclear spin state by collisions. In the previous work from this laboratory, where pure methyl fluoride samples were studied (36, 38), double resonance effects were observed for all values of k. This was because collisionally-induced rotational energy transfer occurs by two mechanisms for methyl fluoride self-collision - direct transfer, and V-V transfer. The direct transfer process obeys the selection rule while the V-V process does not. In the CH3F-foreign gas sample studied here, because only the direct transfer process is responsible for the double resonance 62 effects, the selection rule for the collisionally-induced rotational transfer should be clearly seen. Figure 3.3 shows the energy levels of a four-level system used for observation of the selection rule. The (J ,K) = (5,3) level in the V3=1 vibrational state in 13CI-I3F was pumped by absorption of radiation by the QR(4,3) transition in the v3 band, while the (7,K) (K = | k l = 0 - 6) levels in the same vibrational state were probed by absorption of the QP(7,K) transitions in the 2V3 - v3 band. Figure 3.4 shows a comparison of the observed spectra for the QP(7,K) transitions in the 2V3 - v3 hot band in different experimental conditions. Fig. 3.4 (a) is a regular single resonance spectrum which gives a view of the relative intensities of the probe transition at thermal equilibrium. Fig. 3.4 (b) is a double resonance spectrum for 17 m torr of pure l3CH3,F sample, in which the transferred spike is obvious only for the QP(7,3) transition, but double-resonance effects are seen for all of the transitions. Fig. 3.4 (c) and Fig. 3.4 (d) are double resonance spectra recorded for 1% of 13CH3F, by volume, in 12CH3F and in Ar, respectively, at a total pressure of 100 mTorr. As can be seen in Fig. 3.4 (c) and Fig. 3.4 (d), only the Q130,0), 01303), and QP(7,6) transitions have appreciable intensity. This is a very good graphic illustration of the Alt = 3n selection rule. This selection rule holds for CH3F-Ar collision as well as for CH3F- CH3F collision even though the former is expected to be a much harder collision than latter. In Fig. 3.4 (b) substantial intensities are also seen for the probe transitions with K=1,2 and 4,5. Upon comparison with Figs. 3.4 (c) and 3.4 (d), it is clear that these transitions are the results of the V-V process. In Figure 3.4, the selection rule was illustrated in ortho methyl fluoride molecules. In order to demonstrate the same selection rule in para methyl fluoride molecules, we simultaneously pumped the QQ( 12,2) and QQ(12,1) transitions (different velocity groups) in the v3 band of 12CI-I3F and probed QP(14,K) Probe P(7,K) (K=O, 1, 2, 3, 4, 5, 6) in 2v3 - v3 hot band __8 __7 J 8 7 __8 7 _6 __8 __7 _6 _5 __7 __7 _ 5 6 _6 g 5 __4 K=6 V3=1 _5 — 4 K: 5 4 _4 K=4 —4 _- =2 K=3 l K=0 Pump R(4,3) in v3 fundamental Figure 3.3 Energy level diagram for 13CH3F for the double resonance transi- tions shown in Fig. 3.4. Only the levels for 4 s I s 8 and 0 s K s 6 in V3 = 1 are shown. P(7,K) 4 K 01 2 3 4 5 6 ‘ (a) S -i a t B .. (b) _C) < i _ (C) — W 7 (d) ' J V J T J ' l ' -2ooo — 1 700 — 1 400 -1 100 -800 -500 Offset Frequency / MHz Figure 3.4. Single resonance (a) and double resonance (b-d) spectra of the QP(7,K) transitions for K S 6 in the 2V3-V3 band of 13CH3F. The QR(4,3) transition in the V3 band of l3CH3F was pumped for the double resonance. The samples were: (a) 13CH3F at 30 mTorr; (b) l3CH3F at 17 mTorr; (c) 1 mTorr 13CH3F in 100 mTorr 12CH3F; and (d) 1 mTorr 13CH3F in 100 mTorr Ar. The infrared frequencies for each spectrum are the horizontal axis value plus 29 989 650 MHz. 65 transitions with K = 0-5 in the 2V3 - V3 band in the same molecule. Figure 3.5 shows a comparison of the double resonance spectrum recorded for 1% 12CH3F in argon at a total pressure of 140 mTorr to the single resonance spectrum for 30 mTorr of purelzCH3F. It is clear in Fig. 3.5 (b) that the intensities are substantially increased for the transitions with K = 1, 2, 4, and 5 and suppressed for transitions with K = 0 and 3. C. Vibrational energy transfer from v3 = 1 to v6 = 1 Rotationally selective vibrational energy transfer is a subject of several recent publications. Orr and his coworkers observed selection rules for rotationally specific mode-to-mode vibrational energy transfer from the v6 = 1 to the v4 = 1 vibrational state in DzCO self collisions in their infrared-ultraviolet double resonance experiments (41-44). In DZCO the v4 = 1 vibrational level is about 51 cm'1 lower than the v6 = 1 level. In 12CI-I3F the closest vibrational level to v3 = 1 is the v6=1 level, which is approximately 134 cm'1 above the v3 = 1 level. Although evidence for the energy flow between the v3 = 1 and v6 = 1 vibrational states in methyl fluoride was reported many years ago (56-57), the existence of direct energy transfer between the two vibrational states was not clear. The assignment + v hot band in 12crr3r= (46) of the high resolution spectrum of the V - V 3 6 6 provides a convenient way to probe the population in a specific rotational level in the v6 = 1 vibrational state. By probing the spectra in the V3 + V 6 — V 6 hot band while pumping a transition in the V3 fundamental for a 12CH3F sample in excess of foreign gas, the collisionally-induced rotationally specific direct vibrational energy transfer from v3 =1 to v6 = 1 vibrational levels can be studied. 66 P(14,K) K: 01 2 3 4 5 Absorption (b) I T j I — 1800 -1500 -1200 -900 -600 -300 Offset frequency / MHz Figure 3.5. Single resonance (a) and double resonance (b) spectra of the QP(14,K) transitions for K S 5 in the 2V3-V3 band of 12CH3F. The QQ(12,1) and QQ(12,2) transitions in the V3 band of 12CH3F were simultaneously pumped for the double resonance. The samples were: (a) 30 mTorr 12CH3F; and (b) 1% 12CH3F in Ar at 140 mTorr total pressure. The infrared frequencies for each spectrum are the horizontal axis values plus 30 199 026 MHz. 67 Figure 3.6 is a comparison of single resonance (Fig. 3.6 a) and double resonance spectra (Fig. 3.6 b-d) of the QRO =9, K=3, l=1) transition in the V + V - V 6 band in para 12CH3F and the QR(10,2,-1) transition in the same band 3 6 in ortho 12CH3F. The single resonance spectrum was taken with the sample at 500 mTorr pressure while the double resonance spectra were taken at 63 mTorr total pressure with 1% 12CH3F in Ar for Figs. 3.6b and 3.6c and in 13CH3F for Fig. 3.6d. For Fig. 3.6 b, the QQ(12,1) and QQ(12,2) transitions in the v3 band of 12CH3F (para levels) were pumped and there is a clear intensity enhancement of the E level (para) transition. By contrast, for Fig. 3.6 c, the QR(11,9) transition in the V3 band (ortho levels) was pumped and there is a corresponding intensity enhancement of the A level (ortho) transition. In each of these spectra there is a weak double resonance effect at the transition that would result from collisionally-induced ortho-para or para-ortho transitions. We have not yet performed the very careful intensity measurements that would be required to tell whether these are the result of V-V transfer from the relatively small number of 12CH3F - 12CI-I;:,F collisions in the sample or whether there is a small probability of direct ortho-para transition as a result of 12CH3F-Ar collisions. It is clear in Fig. 3.6b and 3.6c that the ortho-ortho (E-E) and para-para (A-A) selection rule, which here must be generalized to A (k-l) = 3n, is strongly preferred in the observed double resonance effects. This indicates that the CH3F-Ar collisions are strong enough to induce direct vibrational energy transfer in CH3F and the energy transfer process is governed by the symmetry selection rule A (k-l) = 3n. Figure 3.6d shows the double resonance spectrum of 1% 12CH3F in 13CH3F at 63 mTorr total pressure, recorded for the QQ(12,2)-QQ(12,1) pump. In this spectrum, almost no double resonance effects are seen. The corresponding spectrum for the QR(11,9) pump is almost the same. This indicates that 12CH3F- 68 _ a(9.3.1) r R(10.2.-1) A i (a) C .4 .9 9 i (b) o —i (I) .D < , (c) - (a) ,., _ Am r I T I f I r I r 150 260 350 450 560 660 Offset Frequency / MHz Figure 3.6. Single resonance (a) and double resonance (b-d) spectra of the QR(9,3,1) and QR(10,2,-1) transitions in the V3+V6-V6 band of 12CH3F. The QQ(12,1) and QQ(12,2) transitions in the V3 band of 12CH3F were simultaneously pumped for the double resonance in (b) and ((1), whereas the QR(11,9) transition in the V3 band of 12CH3F was pumped for (c). The samples were: 12CH3F at 500 mTorr for (a); 1% 12CH3F in 63 mTorr total pressure of Ar for (b) and (c); and 1% 12CH3F in 63‘ mTorr total pressure of 13CH3F for (d). The infrared frequency for the QR(9,3,1) transition is 31 632 843 MHz minus the horizontal axis value, whereas the infrared frequency for the QR(10,2,-1) transition is 31 660 843 MHz plus the horizontal axis value. 69 13CH3F collisions can hardly induce direct vibrational energy transfer from V3 = 1 to v6 = 1. The above observations are understandable. Because of the large energy gap between the V3=1 and v6=1 vibrational states (134 cm'l) in 12CH3F, a large energy conversion is required during the energy transfer. This can only occur for a fairly strong collision. A CH3F-Ar collision is a much harder collision than a CH3F- CH3F collision, therefore the former can induce the direct vibrational energy transfer in methyl fluoride while the latter cannot. Although CH3F-CH3F collisions do not induce direct vibrational energy transfer, they appear to induce V-V energy transfer quite readily. This can be seen in Fig. 3.7. Figure 3.7a is the single resonance spectrum shown in Fig. 3.6a, while Fig. 3.7b is a double resonance spectrum recorded for 60 mTorr of pure 12CH3F while the QQ(12,1) and QQ(12,2) transitions in the V3 band were pumped. Strong double resonance effects are seen in the probe transitions (Fig. 3.7b). Since the ratio of the intensities of the two transitions in the V3 + V 6 - V 6 band is essentially the. same for the single resonance (Fig. 3.7a) and the double resonance spectra (Fig. 3.7b), showing no evidence for selection rules, the vibrational energy transfer in pure CH3F must be the result of the V-V process. Figure 3.8 shows a comparison of the single and double resonance spectra for — v6 hot band and the QP(12,k) band when the QQ(12,1) and the R(7,1,-1) probe transition in the V 3 + V 6 3‘V3 QQ(12,2) in the V3 fundamental band was pumped. Two spikes are seen in the (k=0,1,2,3...9) probe transitions in the 2V spectrum which correspond to the three level double resonance effects for the QP(12,1) and QP(12,2) transitions, respectively. The double resonance effects for the QR(7,1,-1), QP(12,6) and QP(12,9) transitions are all the result of the V-V process. Thus, by comparing the relative intensities of the QR(7,1,-1) transition in 70 1 R(9,3.1) E R(10.2.-1) A (0) Absorption 1 (b) t ‘ V T ' T 150 250 350 460 560 660 Offset Frequency / MHZ Figure 3.7. Single resonance (a) and double resonance spectra (b) of the transitions shown in Fig. 7. The spectrum in (a) is the same as that in Fig. (7a). The spectrum in (b) was recorded for 60 mTorr of 12CH3F while the QQ(12,1) and QQ(12,2) transitions in the V3 band of 12CH3F were simultaneously pumped. _ (0) SR C _. .9 75. 1 L. O —i U) .0 '4 <1: —( .R(7.1.-1) R(12.K) (b) DR 1 K- 0123 4 5 e 7 a 9 . , . , . , . , . 0 520 1040 1560 2080 2600 Offset Frequency / MHZ Figure 3.8. Single resonance (a) and double resonance (b) spectra of the QR(7,1,-1) transition in the V3+V6-V6 band and the QR(12,K) transitions for K S 9 in the 2V3-V3 band of 12CH3F . The QQ(12,1) and QQ(12,2) transitions in the V3 band of 12CH3F were simultaneously pumped for (b). The sample pressures were 250 mTorr (a) and 60 mTorr (b). The infrared frequencies for the QR(12,K) transitions are the horizontal axis values plus 31 556 029 MHz, whereas the infrared frequency for the QR(7,l,-l) transition is 31 532 029 MHz minus the horizontal axis value. 72 the V + V band to the relative intensities of the QR(12,6) and the QR(12,9) 3 6 6 transitions in the 2V3 - V3 band in single resonance and double resonance spectra, -V the relative efficiency of V-V transfer for the two processes: (a) CH3F (V3=1) + CH3F (V3=0) = CH3F (V3=0) + CH3F (V3=1), (b) CH3F (V3=1) + CH3F (v6=0) = CH3F (V3=0) + CH3F (v6=1), can be obtained. Our results showed that the V-V transfer for process (b) is 50-60% as efficient as the V-V transfer for process (a). The difference is almost certainly the result of the larger vibrational energy for v6 = 1 than for V3 =1. D. Center frequency shift in double resonance spectra While recording four-level double resonance effects for dilute mixtures of 13CH3F in the rare gases Ar and Xe, we found substantial evidence for a shift in the center frequency in the double resonance spectrum. Figure 3.9 shows a comparison of a single resonance spectrum for the QR(5,3) transition in the V 3 band of 13CH3F to the corresponding double resonance spectrum when the QR(4,3) transition in the V3 band was pumped. The sample used was a mixture of 5 m Torr of 13CH3F in 5 Torr of Ar. A clear shift in the center frequency of the double resonance compared to the single resonance is seen. This shift was roughly proportional to the partial pressure of the foreign gas within the pressure range we examined (<10 Torr). The shift only occurs in the double resonance spectrum. The frequency shift in the single resonance spectrum is very small. An interesting point is that the shift in frequency for the several cases studied is always toward the direction that would occur if the velocity component of the pumped molecule in the direction of the pump laser changed sign during collision, as if a recoil effect is being seen. In the following section, we show from calculations of classical 73 ‘ R(5.3) (b) Double Resonance Absorption (0) Single Resonance f T T I , . . . , e , . . . , -985 -945 -905 -865 Offset frequency / MHz Figure 3.9. Single resonance (a) and double resonance (b) spectra of the QP(5,3) transition in the V3 band of 13CH3F . The QR(4,3) transition in 13CH3F was pumped for the double resonance. The samples were 5 mTorr of 13CH3F in 5 Torr of Ar for both spectra. The infrared frequencies for each spectrum are the horizontal axis value plus 31 089 492 MHz. 74 a- collision kernels that a recoil effect is expected for under certain collisional conditions, although the pressure dependence of shift can not be explained. V. Theoretical collision kernels We used the procedure described in the Theory section to calculate a number of classical collision kernels. The purposes of these calculations were (i) to deter- mine the shape of the classical collision kernels when an appropriate Lennard- ]ones 6-y function was assumed to be the intermolecular potential, so that the ra- tionale for using the phenomenological collision kernel (the sum of the two K-S kernel) in the previous studies from this laboratory could be justified; and (ii) to ascertain whether the qualitative features of the observed line shapes for different perturbers in this study could be predicted from the classical calculation. Consid- ering the known inadequacy of classical calculations and the uncertainty about the potential function, we did not attempt any quantitative comparison of ob- served and calculated results. In addition, the calculations were performed for elastic collisions, whereas the observations were for inelastic collisions. However, since the internal energy change (rotational energy) is so small compared with the kinetic energy of the molecules, it seemed reasonable to assume an elastic process for a rough initial calculation. The procedure for our calculation can be summarized as follow: 1. Pick appropriate values of e and re for Lennard-Jones potential. 2. Select the z-component of the velocity of the active molecule in a space-fixed coordinate system. 75 3. Randomly choose the impact parameter and the initial values of velocity components from appropriate Maxwell distributions. 4. Calculate the classical scattering angle in the center-of-mass coordinate sys- tem. 5. Randomly choose x, the orientation angle of the scattering plane relative to the space-fixed frame. 6. Calculate the z-component of final velocity of the active molecule in the space-fixed frame. 7. Multiply by the normalizing factor and add to the population of an appro- priate velocity box. 8. Repeat the Steps 3 to 7 many times. One of the problems associated with the calculation was how to choose the maximum impact parameter (Step 2). In our calculation all encounters, even those with very large impact parameters, for which there is essentially no change in velocity, are considered to be ”collisions". Even worse, the number of encounters per unit time within a range of impact parameter db increases with b. Thus if very large b values are allowed in the calculation, the one-dimensional collision kernel shows a strong spike within a very small range about the initial vz value. Since the collisions we are concerned with should be hard enough to induce rotational transitions, collisions with very large impact parameter should be excluded. Our solution to this problem was to set the maximum impact parameter to a collision diameter near that calculated from the estimated linewidth parameter for an appropriate rotational transition. Unfortunately, there are not many linewidth measurements for CH3F in foreign gases. A few values of linewidth parameters are given in Refs. (58-63) and these show that the halfwidth at halfheight for self broadening is about 15 Nfl-Iz / Torr (collision diameter ~ 15 A ) for low I and 76 decreases with increasing 1. For CH3F -Ar, the width is about 3 MHz / Torr (collision diameter ~ 5.5 A ). Since this is all the information available, the best that we could do was to calculate the collision kernel for a variety of values of the maximum impact parameter and note the differences. A. Collision kernel for dipolar-dipolar collision One-dimensional collision kernels were calculated for CH3F-CH3F collisions. The purpose of these calculations was to see how close the calculated kernel was to the sum of two K-S collision kernels. Figure 3.10 shows a comparison of a theoretically-calculated kernel to the sum of two K-S kernels. For the theoretically- calculated kernel, the Lennard-Jones potential function of the form of Eq. (12) with rs/kb = 300K and re = 3.5 A was used. The impact parameter b was constrained within 0 < b < 10 A and 20 000 events were counted in the calculation. The selection of the values for e and re was on the basis of examination of the potential constants reported in Table I-A of Ref. (55). The B values for the two K-S collision kernels are 19. 1 m/s and 140. 5 m/s and the ratio of the A values A(broad)/ A(narrow) = 0.185, which are close to those obtained experimentally (36,38). As shown in Fig. 3.10, the two collision kernels have in general a similar shape. Although adjustment of the form of the potential function may bring the calculated kernel even closer to the sum of the two K-S kernels, we did not intend to do that due to the reasons mentioned above. However, the qualitative agreement between the two kernels to some extent justified the phenomenological collision kernel we have used to describe the velocity change upon collision in the previous experiments from this laboratory. 77 I I I I —100. O. 100. 200. 300. 400. 500. V2 / (m/S) Figure 3.10. (a) One-dimensional collision kernel as a function of final velocity calculated as the sum of two Keilson-Storer functions. The [3 values for the two functions are 19.1 m/s and 140.5 m/s and the ratio of the A values is A(broad)/A(narrow) = 0.185. (b) One-dimensional classical collision kernel calculated by the procedure described in the text, The parameters for the calculation are: m = 35 u for the active molecule and the perturber; 21kg = 300 K; rc = 3.5 A; 0 S b S 10 A; number of collisions = 20 000. The initial velocity for both kernels was 234 m/s. The vertical axes have been scaled for convenient plotting and comparison. 78 B. Collision kernels for dipolar-nonpolar collision In dipolar-nonpolar collisions, the impact parameter is supposed to be smaller than in dipolar-dipolar collisions. The well depth of the intermolecular potential (8 in the Lennard-Jones potential function) is also smaller for the former than for the latter. Figure 3.11 shows the effect of the mass of the perturber on the collision kernel. The parameters used in the calculations are: r»:/kb = 100K ; re = 3.5; 0 < b < 4 A ; number of collisions = 40 000; m (active) = 35 u; m (perturber) = 4 u (Fig 3.11 a); or m (perturber) = 131.3 u (Fig. 3.11b). The collision kernel in Fig. 3.11a is for the methyl fluoride - helium reduced mass and shows a substantial spike, whereas the kernel in Fig. 3.11b is for the methyl fluoride - xenon reduced mass and is much broader. This tendency agrees with the observed experimental data shown in Fig. 3.2. The width of the spike in the calculated collision kernel increases with increased value of E/kb in the potential function and especially with decreased ' value of the ratio b (max) / re; the latter comparison is shown in Fig. 3.12. The parameters used in calculations are: e/kb = 100K ; 0 < b < 4 A ; number of collisions = 40 000; m (active) = 35 u; re = 4 A (Fig 3.12 a); re = 3.5 A (Fig. 3.12b). The four-level spectra for methyl fluoride - hydrogen show a broader spike than for methyl fluoride - helium (Figs. 3.2c and 3.2d). We therefore conclude that the intermolecular potential function for CH3F - H2 either has a well that is deeper or has a ratio of collision diameter to equilibrium distance that is smaller than the potential function for CH3F - He. According to Table I-A in Ref. (55), the equilibrium distance in the potential for Hz-HZ collisions is ~ 0.5 A , greater than the corresponding value for He-He collisions. 79 - <0) 5 :0 _ i ‘60 i: ‘ s ,6 ._¢ _ 7 I I I I I xix—’1 -800 -400 O 400 800 vZ / m/s Figure 3.11. One-dimensional classical collision kemels as a function of final velocity calculated by the procedure described in the text. The parameters are: elkB = 100 K; re = 4 A; 0 S b S 4 A; number of collisions = 40 000; m(active molecule) = 35 u; m(perturber) = 4 u (a) or 131.3 u (b). The initial velocity for both kernels was 234 mls. The vertical axes have been scaled for plotting, but are relatively correct for the two plots. 80 l l l l l —( -— «—( —I 4 —q 4 + -1 4+ * 4 4 4 4 q ‘4, ‘5‘ 4,4}+ *4 '— + ++++ ‘44 4 44 4+4+**‘*++ ++*++4 <+*++** ‘+++++4 4 —1 # T 4 —1 — + 4 (b) * -« 4 —« 4. § 43- 4 4 -—( +0 6 —‘ +* ++ ‘+++ +‘ + 4 ‘9 44* + ‘ ‘+*+ ++44** +4+§ s44++**‘+ +**++ 11111 l i l —100. O. 100. 200. 300. 400. 500. V2 / (m/S) Figure 3.12. One -dimensional classical collision kernels as a function of final velocity calculated by the procedure described in the text. The parameters are: E/kB = 100 K; 0 S b S 4 A; m(active molecule) = 35 u; m(perturber) = 4 11; number of collisions = 40 000; and r6 = 4 A (a) or 3.5 A (b). The initial velocity for both kernels was 234 mls. The vertical axes have been scaled for plotting, but are relatively correct for the two plots. 81 ' ' I I T I I I f I J I I r r l +*+ ' —t +4 L -4 *I ‘94 + _ 4 :7} ++ * 44 - f 4 + 4*4“ #- 4 | 4 —-< N ++ — 4 : 4 "’ + 4 "‘9 4* I *4 “g +; I 4. + 4 | + _ j t _, 4 “- I 9' *4‘ l *- 4. —l * + : {- W —I + 4+ | + + + _, w i “‘4’ ‘1 " I 4 V 4* I *4 ‘T + I *4"t ‘ * 4 3‘ i ‘4' . 4. + at * _. ‘1 {’4’ I ** + *4 g 44 ”4" I + 4 4 I 1"" r I J I T I J I F J T T J l T Figure 3.13. One-dimensional classical collision kernel as a function of final velocity calculated by the procedure described in the text. The parameters are: 81k]; = 100 K; r6 = 4 A; 0 s b s 3 A; m(active molecule) = 35 u; m(perturber) = 131.3 11; initial velocity = 234 m/s; number of collisions = 30 000. The vertical axis has been scaled. 82 The collision kernels calculated for the methyl-fluoride - argon and methyl fluoride - xenon reduced mass show a significant ”recoil effect" if the maximum impact parameter is limited to a small value (<3 A ). This effect is especially dramatic for methyl fluoride -xenon, as shown in Fig. 3.13. We have not, however, been able to interpret the fact that the experimental data show a recoil effect that increases with increasing pressure. It appears that more sophisticated calculations are required to demonstrate this feature of these spectra. References l. T. Oka, J. Chem. Phys. 45, 754-755 (1966); T. Oka, J. Chem. Phys. 47, 13-26 (1967); T. Oka, J. Chem. Phys. 47, 4852- 4853 (1967); 'r. Oka, J. Chem. Phys. 48, 4919-4928 (1968); T. Oka, J. Chem. Phys. 49, 3135-3145 (1968). 2. T. Oka, Adv. At. Mol. Phys. 9, 127-206 (1973). 3. E. Arimondo, P. Glorieux, and T. Oka, Phys. Rev. A 17, 1375-1393 (1978); P. Glorieux, E. Arimondo, and T. Oka, J. Phys. 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Bernstein, ed.), pp 111-199, Plenum Press, New York, 1979. 50. S. K. Lee, R. H. Schwendeman, and G. Magerl, J. Mol. Spectrosc. 117, 416-433 (1986). 85 51. S. K. Lee, R. H. Schwendeman, R. L. Crownover, D. D. Skatrud, and F. C. De Lucia, J. Mol. Spectrosc. 123, 145-160 ( 1987). 52. F. R. Petersen, E. C. Beaty, and C. R. Pollock, J. Mol. Spectrosc. 102, 112-1122 (1983). 53. C. Freed, L. C. Bradley, and R. G. O’Donnell, IEEE J. Quantum Electron. QE- 16, 1195- 1206 (1980). 54. E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, “Molecular Vibrations”, Appendix I, Mcguire-Hill, New York, 1955. 55. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids”, Wiley, London, 1964. 56. E. Weitz and G. W. Flynn, J. Chem. Phys. 58, 2679-2683 (1973). 57. E. Weitz and G. W. Flynn, J. Chem. Phys. 58, 2781-2793 (1973). 58. O. R Gilliam, R. D. Edwards, and W. Gordy, Phys. Rev. 75, 1014-1016 (1949). 59. G. Birnbaum, E. R. Cohen, and J. R. Rusk, J. Chem. Phys. 49, 5150-5156 (1968). 60. R G. Brewer and R. L. Schoemaker, Phys. Rev. Lett. 27, 631-634 (1971). 61. H. Jetter, E. F. Pearson, C. L. Norris, J. C. McGurk, and W. H. Flygare, J. Chem. Phys. 59, 1796-1804 (1973). 62. P. Glorieux, J. Legrand, and B. Macke, Chem. Phys. Lett. 40, 287-291 (1976). 63. S. T. Sandholm and R. H. Schwendeman, J. Chem. Phys. 78, 3476-3482 (1983). 86 Chapter 4 The Effect of Initial Velocity on Rotational Energy Transfer in 13CH3F I. Introduction As has been demonstrated in Chapter 3 and in the previous papers from this laboratory, pumping a near-coincident molecular transition with a very monochromatic infrared laser was able to prepare molecules in an excited state with a specific velocity component in the direction of the pump laser (1-3). This velocity component is determined by the Doppler effect and can be varied by changing the pump laser frequency (or pump laser offset). Smith et al have used this concept to carry out a series of measurements of velocity dependences of rates for rotational energy transfer in N32 and 7Liz colliding with rare gas atoms (4-6). In these experiments, the pump transitions were in the visible region and the well- developed continuously-tunable dye laser can change the pump laser frequency easily. In this study we use a similar technique in the infrared region to investigate the velocity dependence of collisionally-induced rotational transitions in 13CH3F. Study of the velocity dependence of a collisional process using velocity selection by Doppler shift is probably more difficult in the infrared region than in the visible region. Besides the fact that a strong and continuously tunable infrared 87 laser is hard to find, the absolute frequency stability of the pump laser required for the same velocity resolution is much more rigorous in the infrared region than in the visible region. This is because the Doppler shift in frequency for a molecule with a given velocity is proportional to the frequency of the transition. Thus, a change in the frequency of the radiation has a smaller effect on the velocity when the frequency is larger. Nevertheless, A. T. Mattick et al. investigated the velocity dependence of collisional broadening in an infrared transition in NH3 (7). In order to study the velocity dependence of rotational energy transfer in CH3F by infrared- infrared double resonance, we had to have a pump source that was both tunable and very monochromatic. In the previous double resonance experiments from this laboratory (1-3), a conventional C02 laser stabilized to a fluorescence Lamb dip of C02 (8) was used as the pump source. A C02 laser operated with this stabilization scheme emits very monochromatic radiation at the center frequency of each laser transition. Since velocity selection by Doppler shift does not require a large tunability in order to change the velocity component substantially, typically a Doppler half width of the pump transition, the tunability of a C02 laser line within its laser gain profile should be large enough as long as the frequency of the laser is stabilized properly. For this purpose, Weber and Terhune used a Lamb dip in a laser Stark spectrum for frequency stabilization of a C0 laser (9). The advantage of this stabilization scheme, in addition to the extremely high frequency stability (at least as good as fluorescence Lamb dip stabilization), was to be able to stabilize the laser line at any frequency within the laser gain curve. For the work described here, we used the same technique to stabilize a C02 laser to a Stark Lamb dip of CH3F. The technique allowed us to lock the laser to any frequency within 21:15 MHz of the center frequency of the laser transition, which provided a tunability of about 30 MHz for each C02 laser line. 88 For our experiment, the Lamb dip of a Stark spectrum in 13CH3F (10) was used to stabilize the 9P(32) C02 laser which pumps the QR(4,3) transition in the V3 fundamental band in 13CH3F. With this pumping, the velocity dependence of the double resonance effects was investigated for a number of probe transitions in the 2V3 — V 3 characteristics of the collisionally-induced rotational energy transfer (e.g. r.m.s. band. The questions we wanted to answer were whether the velocity change, relative rates) were velocity dependent, and if so, what were the dependences. One of the motivations of this experiment can be attributed to the Keilson and Storer (K-S) collision kernel (11) that we have used to obtain the root- mean-square (r.m.s.) velocity change upon collision from four-level infrared- infrared double resonance line shapes. The K-S kernel has been used in various collisional problems (1-3, 12-16). The parameter representing the r.m.s. velocity change in the kernel is now assumed to be a constant, which is equivalent to the assumption that the r.m.s. velocity change is independent of the initial velocity of the colliding molecules. Since the K-S collision kernel has been used so many times we would like to know if this assumption is true. In addition, from a practical point of view, knowledge of the velocity dependence of the parameter is essential in order to simulate the collision process (i.e., determine the final velocity distribution) with the kernel for molecules that have an initial velocity distribution instead of a single velocity. In fact, as will be seen, our experimental results show a linear dependence of the parameter on the r.m.s. relative velocity of the colliding molecules. In order to see how the classical elastic scattering theory describes the velocity dependence of the r.m.s. velocity change during collision for a Lennard-Jones molecular potential function, we used the Monte Carlo calculation discussed in Chapter 3 to simulate collisional processes with two different initial velocities of 89 active molecules. Although the simulation also showed a velocity dependence of the r.m.s. velocity change during collision, the calculated variation was opposite to that observed in experiment. The disagreement between the observed and calculated results will be discussed. II. Theoretical Part A. Relative velocity of the colliding molecule In our experiment, the active molecules (the molecules pumped) have a fixed velocity component in the direction of the pump laser. All of the other velocity components of both the active molecules and the perturbers are assumed to be in an equilibrium distribution. If we choose a coordinate system so that the pump beam travels in the space-fixed z direction, the velocity component in the z direction for the active molecules can be calculated from the Doppler equation (17) v = -C— (V - VO ), (4.1) 2 v0 1 p where c is the speed of light, V1 is the frequency of the pump laser and V: is the center frequency of the pump transition. If only molecules with vaz equal to V2 given by Eq. (3.1) are pumped, then the probability of finding an excited active molecule with velocity va = vaxi + Vayj + vazk, and a perturber with velocity v =v i+v j+v k, P PX PY z P 90 can be expressed as deaxdvaydvazdvpxdvPydvpz, where 8(vaz—vz) (V:x+v:y) (v:x+v:y+v:z) w = — - . . n5/2u2u3 “p u2 - u2 “2’ a P a P where u,I and up are the most probable speeds in thermal equilibrium for the active molecules and perturbers respectively. In this study, only self collisions of l3CH3F molecules were studied, so “a = 1113 = m , where m is the mass of a 13CH3F molecule, R is the gas constant and T is the temperature. The root mean square (r.m.s.) speed of the colliding molecules can be calculated by ./ (6, 3) 83.1 599.5 8.61 0.014 50.46 0.08 223.1 634.3 9.53 0.015 62.52 0.10 365.1 697.0 10.73 0.015 77.13 0.11 (5, 3) —> (7, 3) 83.1 599.5 12.87 0.021 73.83 0.12 223.1 634.3 14.07 0.022 86.24 0.14 365. 1 697.0 15.62 0.022 112.96 0.16 (5, 3) —) (8, 3) 83.1 599.5 17.35 0.029 99.14 0.17 223.1 634.3 18.77 0.030 1118.55 0.19 365. 1 697.0 21. 17 0.030 134.20 0.19 aRotational state change from (J,K) to (J ’,K’) upon collision in the v3=2 vibrational state. 1The z-component of the initial velocity of active molecule before collision. cInitial root mean square relative speed of the colliding molecules (vzz+5u u=(2RT/M)1’2=375.5 mls. “The same as in Table 4.2 °ri=(Avms)i / vp (i=l,2) 2,2)1/2, 106 TABLE 4.4 Relative intensities for collisionally-induced transitions in l3CH3F State changea v,b A1/A2c AllAGd 142/116'3 111‘ R23 (5, 3) 4 (6, 3) 599.5 1.98 0.59 0.30 1.00 1.00 697.0 1.94 0.60 0.33 1.06 1.15 (5, 3) .3 (7, 3) 599.5 1.21 0.26 0.21 1.00 1.00 697.0 1.18 0.38 0.34 1.23 1.32 (5, 3) —. (8. 3) 599.5 0.88 0.23 0.25 1.00 1.00 697.0 0.81 0.33 0.53 1.32 1.86 aRotational state change from (I,K) to (J’,I(’) upon collision in the v3=l vibrational state. bInitial root mean square relative velocity (m/s) of colliding molecules (v22+5u2/2)m, u=(2RT/M)1/2=375.5 mls. °I'he ratio of intensity for the narrow spike to that for the broad spike. dThe relative intensity of the narrow spike to the Gaussian in the observed spectrum. °I‘he relative intensity of the broad spike to the Gaussian in the observed spectrum fThe ratio of the intensity of the narrow spike to that at vr=599.5 mls. 8The ratio of the intensity of the broad spike to that at v,=599.5 mls. 107 increases. If the broad component is interpreted as resulting from collisions with small impact parameter, this is an indication that a greater proportion of hard collisions is required for rotational energy transfer with larger A]. For the same A], the ratio decreases slightly as the initial relative r.m.s. velocity increases. This indicates that a collision with a larger relative velocity is harder than that with a smaller velocity. For the same initial relative r.m.s velocity, the ratios of the areas of both the narrow and the broad components of the transferred spikes to the Gaussian component decrease as A] increases while for the same A], the ratios increase as the relative r.m.s. velocity increases. This indicates that the time required for rotational energy transfer increases as A] increases and that for a larger initial relative velocity a shorter time is required for a rotational energy transfer. Finally, for the same A], the intensity of either the narrow or the broad component of the spike is larger at larger relative r.m.s. velocity than that at smaller relative r.m.s. velocity. The difference is greater as A] increases. The former is understandable since the larger the relative velocity of the colliding molecules, the larger the collisional rate. The latter indicates again that a collision with a larger relative velocity is harder so that it favors a collisionally-induced transition with a large A]. D. Calculation from classical scattering theory In Chapter 2, we described an application of classical elastic scattering theory and a Monte Carlo calculation to simulate the collisional processes concerned in our experiment. In that chapter, most of the features observed in the experiments 108 agreed qualitatively with calculations. We had expected that the calculation would be able to predict the qualitative feature of dependence of r.m.s. velocity change on initial relative velocity discussed in this chapter. However, the results of the calculation indicate that the r.m.s. velocity change should decrease as the relative r.m.s. initial velocity of the colliding molecules increases, which is just opposite to the results from experiment. This contradiction may not be surprising considering the crudeness of the model we used in our simulation. For the simulation, the collision process was assumed to be classical and elastic, and the result is understandable upon realization that the larger the relative velocity, the less time the molecules interact during collision, which leads to a smaller deflection and therefore a smaller change in the 2 component of the velocity. By contrast, the collisional process we studied in our experiment was neither classical nor elastic. In order for a collision to induce a state-to-state transition, the collision must be hard enough. For larger relative velocity for a colliding pair, the smaller interaction time can be compensated by a larger interaction potential, i.e., a smaller impact ' parameter, which may cause a larger deflection angle during collision. In order to interpret our experimental result correctly, it appears that a full quantum mechanical treatment of the rotationally inelastic collision process may be required. Although a quantum mechanical calculation for an inelastic scattering process is typically very complicated and time consuming, our experimental results provide considerable data for comparison, which may lead to additional understanding of the fundamental nature of intramolecular collisional interaction. 109 References 1. Y. Matsuo, S. K. Lee, and R. H. Schwendeman, J. Chem. Phys. 91, 3948-3965 (1989). 2. Y. Matsuo and R. H. Schwendeman, J. Chem. Phys. 91, 3966-3975 (1989). 3. U. Shin, Q. Song, and R. H. Schwendeman, J. Chem. Phys. 95, 3964-3974 (1991). 4. N. Smith, T. A. Brunner, R. D. Driver, and D. E. Pritchard, J. Chem. Phys. 69, 1498- 1503 (1978). 5. N. Smith, T. A. Brunner, and D. E. Pritchard, J. Chem. Phys. 74, 467-482 (1982). 6. N. Smith, T. P. Scott, D. E. Pritchard, J. Chem. Phys. 81, 1229-1247 (1978). 7. A. T. Mattick, A. Sanchez, N. A. Kumit, and A. J avan, Appl. Phys. Lett. Vol. 23 (12), 675-678 (1973). 8. C. Freed and A Javan, Appl. Phys. Lett. 17, 53-56 (1970). 9. W. H. Weber and R. W. Terhune, Opt. Lett. 6, 455-457 (1981). 10. S. M. Freund, G. Duxbury, M. Romheld, J. T. Tredje, and T. Oka, J. Mol. Spectrosc. 52, 38-57 (1974). 11. J. Keilson and J. E. Storer, Q. Appl. Math. 10, 243-253 (1952). 12. M. Borenstein and W. E. Lamb, Phys. Rev. A5, 1311-1322 (1972). 13. J. Schmidt, P. R. Berman, and R. G. Brewer, Phys. Rev. Lett., 31, 1103-1106 (1973). 14. C. Brechignac, R. Vetter, and P. R. Berman, Phys. Rev. A17, 1609(1978). 15. C. G. Aminoff, J. Javanainen, and M. Kaivola, Phys. Rev. A28, 722(1983). 16. J. E. M. Haverkort, J. P. Woerdman, and P. R. Berman, Phys. Rev. A36, 5251-5264 (1987). ' 17. W. Demtroder, Laser Specu'oscopy, edited by F. P. Schafer (Springer Series in Chemical Physics 5, 1982), pp. 86. 18. Q. Song and R. H. Schwendeman, J. Mol. Spectrosc. 149, 356.374 (1991). 110 Chapter 5 Study of the 3v3 - 2V3 Band in 12CH3F' and Doppler-Free Frequencies in 12CH3F and 13CH3F I. Introduction Methyl fluoride has been considered as an ideal compound for a number of spectroscopic applications with lasers. In addition to its stability and strong absorption near the 10 um region the molecule has many near coincidences of vibration-rotation transitions with C02 laser lines (1,2). Because of this, various experiments have been carried out in methyl fluoride with C02 lasers as excitation sources. Examples include studies of rotational and vibrational energy transfer (3- 5), relaxation processes in the optically-pumped far-infrared laser (6-8), observation of dynamic Stark splitting (9), measurement of light-induced drift (10,11), and studies of the correlation of change in velocity with collisionally- induced rotational energy transfer (12-14). These applications stimulated a considerable number of spectroscopic investigations for this molecule. Vibration-rotation transitions of 12CH3F in the 10 um region have been studied extensively several times. High resolution spectra (Doppler limited) for the v3 fundamental, the 2V3 - v3 hot band and the v3 + v 6 - v 6 hot band have been measured with the infrared sideband laser system in this laboratory (2,15), and with FI'IR spectrometers by D. Papousek et a1 (16). The molecular constants for the relevant vibrational levels have been determined to an accuracy that allows a lll frequency of a rovibrational transition to be calculated within several MHz. However, in spite of these spectroscopic studies, there has been no report of frequencies of transitions in the 3v3 — 2v3 hot band. In addition, only a few transitions in CH3F have been measured with Doppler-free resolution (9,17-19). The major purposes of this study were to investigate rovibrational transitions in the 3v3 - 2v3 band of 12CH3F and to carry out precise frequency measurements fundamental and the 2v - v hot band for some important transitions in the v3 3 3 of CH3F. The rovibrational transitions in the 3v3 — 2v3 hot band of methyl fluoride are expected to be difficult to observe with conventional single modulation spectrosc0py. Since the V3=2 vibrational state is about 2000 cm'1 above the ground vibrational state, the population in thermal equilibrium at room temperature is extremely small (N2v3 /N0 ~6x10 '5) which leads to very weak absorptions for transitions in this hot band. Besides, there are several unassigned weak hot bands - v band which makes it 3 3 even harder to assign the spectrum even if transitions can be observed. High in the region that have larger intensities than the 2v resolution infrared spectroscopy of methyl fluoride showed many near coincidences of the vibration rotation transitions in the 2v3 — v3 hot band with C02 lasers (2). These near coincidences can be employed to pump molecules from the V3=1 to the V3=2 vibrational state with strong C02 laser radiation. By searching for transitions in the 3v3 — 2v3 band while a transition in the 2v3 - v3 band is pumped - i.e., by using infrared-infrared double resonance - the chances of observing transitions in this band increase dramatically. First, the intensities of transitions in the 3v3 — 2v band will increase as a result of the pumping effect on 3 the population. Second, which may be more important, our knowledge of double resonance lineshapes in this molecule (12,13) can help us to make a correct assignment for the transitions in the 3v - 2v3 band. In the present study, the 3 transitions in the 3v3 - 2v3 band were searched with a probe laser while either the 112 QR(7,3) or the QR(13,6) transition in the 2V3 - v:3 band was pumped. Six 3 band of 12CH3F were observed and assigned. The frequencies obtained have been fit to equations for the rotational levels in the V3=3 transitions in the 3v3 - 2v vibrational state by the least squares method and molecular constants for this vibrational state have been obtained. The Doppler—free feature of the spikes in infrared-infrared double resonance spectra can be used to determine the precise center frequencies of both pump and probe transitions. Knowledge of precise center frequencies of the pump transitions is found to be desirable in this laboratory for the study of the r.m.s. velocity change during collisionally-induced rotational energy transfer (Chapter 4). Recently, we found that Doppler free frequencies for the pump and probe transitions could be obtained from three-level or four-level double resonance spectra recorded separately with copropagating and counter-propagating configurations for the pump and probe beams. In this work, we used the technique to obtain Doppler- free frequencies for several important transitions in both 12CH3F and l3CH3F. Some of these frequencies have been used to deduce the precise pump laser offsets in Chapter 4. We also carried out infrared-infrared four-level double resonance within the 2v - v hot band. As will be discussed below, the four-level double resonance 3 3 effect in the 3v3 — 2v3 band observed by pumping a 2V3 - v3 transition shows only the direct rotational energy transfer, while that in the 2V3 - v3 band with the same pumping shows the direct rotational energy transfer and near vibration- vibration transfer in opposite phases. The information about the relative rates of these two energy transfer processes obtained from the experimental line shapes will be discussed. 113 II. Theoretical background A. Energy levels in a non-degenerate vibrational mode in 12CH3F The v3 vibration in 12CH3F is a non-degenerate vibration rotation mode whose energy levels can be calculated by means of the equations (20), E(v,],l<) -..- EV+BV](]+1)+(Av—BV)K2—DJ(V)]2(J+1)2 -DI(I‘<’)J(J+1)1(2-DI(<")I<4+H](")]"3(1+1)3+HJ(I‘<’)12(J+1)21<2 (v) 4 (v) 6 (v) 4 4 (v) 3 3 2 +HK] ](]+1)I< +HK K +LJ 1 (1+1) +LIJII0) is slower than the Vibrational swapping process. 133 . 0(9.5) - Q(9.3) Q(9,4) Q(9,5) Absorpfion I I I 560 860 1160 1460 1760 Offset Frequency / MHZ Figure 5 .7. Double resonance spectrum for the QQ(9,K) (K=3, 4, 5, 6) transitions in the 2v3-v3 band in 12CH3F. The QR(7,3) transition in the 2v3-v3 band was pumped. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. The pump and probe lasers used are given in Table 5.1. 134 D. Precise frequencies in CH3F The QQ(12, 1) and QQ(12, 2) transitions in the v3 band of 12CH3F, and the QR(4,3) transition the v3 band of 13CH3F are the most commonly used transitions for optical pumping in the study of laser induced phenomena in methyl fluoride. Prior to the present study, the best values for the frequencies of the QQ(12, 1) and QQ(12, 2) transitions in the v3 band of 12CH3F were measured by a wave guide laser Lamb dip technique and the reported accuracy was 10.5 MHz (17). In the work described in Chapter 4, we found it desirable to know pump laser offset frequencies to within $0.1 MHz. This can be achieved by measuring the frequency of the pump transition to within :01 MHz if the pump laser has been precisely calibrated. If the pump laser frequency is not precisely calibrated, the frequencies of both pump and probe transitions need to be measured to within that accuracy. By using counterpropagating and copropagating three-level infrared-infrared double resonance techniques, the frequencies of both pump and probe transitions can be easily determined to within an accuracy of 10.1 MHz. Figure 5.8 shows the copropagating and counterpropagating three-level double resonance spectra for theQR(12,1) andQR(12, 2) probe transitions in the 2v3 - v3 hot band when theQQ(12,1) and C2Q(12,2) transitions in the v3 fundamental of 12CH3F are simultaneously pumped by the 9P(20) 12C02 laser. The spikes for the QQ(12, 1) transition are much weaker than for QQ(12, 2) transition because the pump offset for QQ(12,1) is much larger than that for QQ(12, 2). As a result, a substantially smaller number of molecules can be pumped into the probed level in the former case than in the latter. Each of the four spikes in Fig. 5.8 was recorded 5 times with a narrow band scan and the line shape was fit to a Lorentz function. The center frequencies from the fitting were averaged to obtain the final frequency of the spike. The values obtained in this way were used to determine the center frequencies of the pump and probe transitions and the pump laser offsets. 135 1(a) Capropagating . R(12.2) R(12,1) C _. '43 4 0- m-NL -~A-+. 3"“? 1.3-1..“ L _ W. O U) -1 _O < -— ‘ (b) Counterpropagating R(12,1) R(12.2)J +W L: Anh‘ W#;Lv“:——.v #:m AV 61% M' I I I I I I I I r I I I fi—j— I I I I 830 880 930 980 Offset Frequency / MHZ 10:50 Figure 5.8. Counterpropagating and copropagating three-level double resonance spectra for the QR(12,1) and QR(12,1) transitions in the 2v3-v3 band when the QQ(12,1) and the QQ(12,2) transitions in the v3 foundamental in 12CH3F are simultaneously pumped by 9P(20) 12C02 laser. The horizontal axis is the offset frequency of the probe laser with the GHz part removed. 136 TABLE 5.4 Precise Frequencies of Transitions in CH3F _ Transition Band Frequencya Offsetb Laser 12CH31= QQ(12,1) v3 31 383 841. 69 -58. 72 120602 9P(20) QQ(12,2) v3 31 383 940. 19 39. 78 12c1602 9P(20) 01202.1) 2v3 - v3 31 556 947. 84 12 918. 96 120602 91:04) Q1202.2) 2v3 — v3 31 556 991. 49 12 962. 61 12c1602 91>t14) 13CH3F - QR(4,3)) 43 31 042 693. 80 -24. 26 126602 9P(32) Qp(5,3) 2v3 - v3 30 092 980. 48 -14 572. 61 ”@602 9P(16) 0905.3) 2v3 - v3 30 040 821. 28 -12 707. 45 136602 9mg) Q120,3) 2V3 - v3 29 988 049. 41 -10 600. 68 l3c1602 9P(20) aCenter frequency of the transition in MHz determined in this work. Estimated absolute accuracy is $0.1 MHz. t’Center frequency of the transition minus the C02 laser frequency in MHz. Laser frequen- cies calculated from the constants in References (24) and (25). 137 Similar measurements were also carried out in 13CH3F for the QR(4,3) pump in the 3 band and the Ores), QP(6,3), QP(7,3) and 013033) probes in the 3v band. The obtained Doppler-free frequencies are shown in Table 5.4. - 2v hot V 3 3 Since the halfwidths at half height for the spikes observed in the experiments are less than 1 MHz, the center frequencies of the spikes can be determined to within ~0.02 MHz. However, a slight misalignment between the pump and probe beams can result in a discrepancy of the velocity components between the molecules pumped and molecules probed. This discrepancy can cause a shift in frequency for the spike in the three level double resonance spectra. Careful alignment can reduce the uncertainty to within $0.05 MHz. In fact, the frequencies of the spikes recorded in the same day are reproducible to within $0.02 MHz and on different days with different alignments are reproducible to within $0.05 MHz. The overall uncertainty in the absolute frequencies determined in this work is estimated to be ~$0.1 MHz, which is approximately one order of magnitude smaller than the values obtained from the previous experiment. A comparison of the frequencies determined from this work to that of previous work is shown in Table 5.5. V. Conclusion We have observed and assigned six transitions in the 3v3 - 2v3 hot band of ”CI-I317 by infrared-infrared double resonance. The molecular constants for the V3=3 vibrational state of 12CH3F have been obtained for the first time. These constants can provide frequencies for transitions in the 3v3 — 2v3 hot band of 12CH3F with sufficient accuracy for reliable assignment. We have also measured laser pump frequency offsets for the QQ(12,1) and C2Q(12,2) transitions in the v fundamental of 12CIr-I3F to $0.1 MHz, which is one order of magnitude higher accuracy than the previously-reported values. The center frequencies for the 3 138 TABLE 5.5 Comparison of Frequencies of Transitions in CH3F 12CH3F Method QQ(12,1) a QQ(12,2) 3‘ Q1202.1) b QR(12,2) b This work 3138384169 3138394019 3155694784 3155699149 Waveguide laser Lamb tiipC 313838414 313839385 IR-MW sideband laserd 313838417 313839401 315569572 315570004 FI'IR“ 313838434 313839420 315569497 315569936 13CH3F Method QR(4,3) a Q1>(5,3) b QP(6,3) b 090.3) b This work 31 042 693. 80 30 092 980. 48 30 040 821. 28 29 988 049. 41 IR-MW sideband laserr 31 042 692. 24 30 092 976.1 30 040 816. 7 29 988 045. 1 “Center frequency of transition in the v3 band in MHz bCenter frequency of transition in the 2v - v band in MHz cRef. (17). dRef. (2). “Ref. (15). fRef. (1) 3 3 139 QR(12,1) andQR(12, 2) transitions in the 2v3 — v3 hot band have also been determined to this accuracy. This work demonstrated further the usefulness and extremely high sensitivity of the double resonance technique for observation and assignment of very weak transitions, even though in a highly excited vibrational state. References 1. S. K. Lee, R. H. Schwendeman, and G. Magerl, J. Mol. Spectrosc. 117, 416434 (1986). 2. S. K. Lee, R. H. Schwendeman, R. L. Crownover, D. D. Skatrud, and F. C. DeLucia, J. Mol. Spectrosc. 123, 145-160 (1987). 3. J. M. Preses and G. W. Flynn, J. Chem. Phys. 66, 3112-3116 (1977). 4. R. S. Shearey and G. W. Flynn, J. Chem. Phys. 72, 1175-1186 (1980). 5. Q. Song and R. H. Schwendeman, J. Mol. Spectrosc. 153 (1992). 6. W. H. Matteson and F. C. De Lucia, IEEE J. Quantum Electron. QE-l9, 1284 (1983). 7. R. I. McCormick, F. C. De Lucia, and D. D. Skatrud, IEEE J. Quantum Electron. QB- 23, 2060 (1987). 8. R I. McCormick, H. O. Everitt, F. C. 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