LOW FIELD STARK MODULATION OF COMPLEX SPECIES
THESIS
Presented in Partial Fulfillment of the Requirements for The Degree Master of Science in the Graduate School of The Ohio State University
By
Kerra Rose Fletcher
*****
The Ohio State University 2008
Dissertation Committee Approved by Professor Frank De Lucia, Advisor
Professor Eric Herbst
Professor Walter Lempert Advisor Chemical Physics Graduate Program ABSTRACT
One of the fundamental problems in the analysis of complex molecules is it dense rotational spectra. Simplifying spectra whose transitions could be accurately predicted would create a powerful analytical tool with useful applications.
Modulation by means of an electric field has proven a useful tool for determining the dipole moment of a molecule. Stark modulation can also be used to simplify the dense spectra of complex molecules at high J values. Modulation makes it possible to separate the absorptions from the otherwise dense background. The distinction between unmodulated and modulated lines is governed by the rotational energy levels of the molecule.
Employing the FASSSTER system, Stark modulation was achieved for various molecules, including acetonitrile and ethyl formate. Acetonitrile, a symmetric rotor, demonstrates first-order effects. Ethyl formate, a prolate asymmetric rotor, exhibits first- and second- order effects, as well as unmodulated transitions.
ii Dedicated to my husband, Jason E. Troutman, without whose
love and support none of this would have been possible.
And it’s subtitled, “A Musical Apology.”
iii ACKNOWLEDGMENTS
I wish to thank my advisor, Frank De Lucia, for his overall support, intellectual guidance, and patience in correcting my scientific errors.
I am grateful Ivan Medvedev for guidance in the lab and answering my innumerable questions.
I thank David Graff for stimulating discussions, scientific and otherwise.
iv VITA
13 October 1980 ...... Born – Lebanon, Virginia
2004 ...... B.S. Chemistry, Emory & Henry College
2004 - Present ...... Graduate Teaching and Research Associate, The Ohio State University
PUBLICATIONS
Research Publication 1. C. J. Wetterer, R. H. Bloomer, E. Carlson, M. S. Dougherty, D. Olive, B. Crawford, S. Cox, K. R. Fletcher, R. Kunkle. “ Preliminary Solutions for the Eclipsing Binaries ROTSEE1 J1806.31+28019.1, V883 Her, V507 Lyr, MQ Peg, and MX Peg.” Information Bulletin on Variable Stars, 554, (2004). http://www.konkoly.hu/
2. J. C. Duchamp, A. Demortier, K. R. Fletcher, D. Dorn, E. B. Iezzi, T. E. Glass, H. C. Dorn. “An Isomer of the Endohedral Metallofullerene Sc3N@C80 with D5h Symmetry.” Chem. Phys. Lett, 375, 655, (2003).
3. E. B. Iezzi, J. C. Duchamp, K. R. Fletcher, T. E. Glass, H. C. Dorn. “Lutetium- based Trimetallic Nitride Endohedral Metallofullerenes: New Contrast Agents.” Nano Letters, 2, 1187, (2002).
FILEDS OF STUDY
Major Field: Chemical Physics
v TABLE OF CONTENTS Page Abstract……………………………………………………………………………………ii Dedication…………………………………………………………..…………………….iv Acknowledgments………………………………..………………………………………..v Vita………………………………………………………………………………………..vi List of Tables……………………………………………………………………………viii List of Figures…………………………………………………………………………….ix
Contents:
Introduction………………………………………………………..………………………1
1. Theory……………………………………………………..……..………………..2
1.1 The Asymmetric Rotor………………………………………………………..2 1.2 Stark Effect for the Symmetric and Asymmetric Rotor……………………….7 1.3 Relative Intensities…………………………………………………………...11
2. Experimental Details……………………………………………..………….…..12
2.1 Introduction…………………………………………………………………..12 2.2 FASSSTER Frequency Calibration Scheme…………………………………16 2.3 FASSST System……………………………………………………………..17 2.4 Lock-in Amplifier……………………………………………………………18
3. Acetonitrile……………………………………………….……………….……..20
3.1 Introduction………………………………………………………………….20 3.2 Experimental Conditions…………………………………………………….20 3.3 Analysis and Discussion……………………………………………………..21
4. Ethyl Formate…………….……………………………………………..……….28
4.1 Introduction…………………………………………………………………..28 4.2 Experimental Conditions…………………………………………………….29 4.3 Analysis and Discussion……………………………………………………..30
Conclusion…………………………………………………………………...…………..43
Bibliography……………………………………………………………………………..45
vi LIST OF TABLES
Table Page
1.1 Character Table for the four group…………………………………………..……5
1.2 Rotational selection rules for asymmetric rotors……….…………….……..…….6
1.3 Ka and Kc can be represented by a numerical change in K…………...…….……..7
3.1 Calculated frequency shifts for the K=6 component………….…………………25
4.1 Rotational constants and dipole moments of ethyl formate conformers……...….29
4.2 Summary for the J=38!38 transition……………………………………………33
4.3 Summary for the J=31!31 transition……………………………………………35
4.4 Summary for the J=37!36 transition……………………………………………36
4.5 The Stark shift for each of the J=37!36 transitions…………………………….40
4.6 Summary for the J=35!34 transition……………………………………..…….41
vii LIST OF FIGURES
Figure Page
1.1 Relation between limiting prolate and limiting oblate asymmetric rotor energy levels………………………………………………………………………………4
2.1 A block diagram of the FASSSTER system……………………………………..14
2.2 The path of radiation from the source, through the tank, and to the detector……15
3.1 A comparison of the Stark field and zero field spectra…………………………..22
3.2 When acetonitrile is exposed to an electric field, the M degeneracy is lifted.…..24
3.3 The Stark spectra of the K=6 component………………………………………..27
4.1 The trans and gauche conformers of ethyl formate……………………………...29
4.2 The ethyl formate spectra from 246 GHz -252 GHz…………………………….31
4.3 The 454,42!444,41 transition does not exhibit any observable Stark effects in the modulated spectra…………………………………………………..……………32
4.4 Transitions that exhibit first-order effects………………………………………..34
4.5 All four transitions exhibit second-order effects………………………………...37
4.6 Diagram of the Stark transitions…………………...…………………………….38
4.7 Transitions are mixed by the Stark effect exhibit one shared lobe………………42
viii INTRODUCTION
One of the fundamental problems in the analysis of complex molecules is it dense rotational spectra. Simplifying spectra whose transitions could be accurately predicted would create a powerful analytical tool with useful applications.
Modulation by means of an electric field has proven a useful tool for determining the dipole moment of a molecule. Stark modulation can also be used to simplify the dense spectra of complex molecules at high J values. The distinction between unmodulated and modulated lines is governed by the rotational energy levels of the molecule.
Employing the FASSSTER system, Stark modulation was achieved for various molecules, including acetonitrile and ethyl formate, both reported here. Acetonitrile, a symmetric rotor, demonstrates first-order effects. Ethyl formate, a prolate asymmetric rotor, exhibits first- and second- order effects, as well as unmodulated transitions.
1 CHAPTER 1
1.1 THE ASYMMETRIC ROTOR
A molecule can be treated as a rigid body rotating freely with each particle comprising the molecule moving relative to each other. The rotational properties of a molecule can be described by the moments of inertia about the three molecular axes. The moment of inertia of a molecule is defined as
2 (1.1) I = !mnrn n where rn is the perpendicular distance of atom n from the principal axis of rotation.
Molecular rotation can be described in terms of motion about the three principal molecular axes Ia, Ib, and Ic where
h h h (1.2) A = 2 B = 2 and C = 2 . 8! Ia 8! Ib 8! Ic
Conventionally, the rotational constants A, B, and C are assigned in decreasing order of size (A>B>C). When two moments of inertia are equal, the molecule is classified as a symmetric rotor. If a molecule’s moments of inertia are all different, it is categorized as an asymmetric rotor. The nature of an asymmetric rotor can be discerned by examining how its behavior deviates from the prolate symmetric rotor (Ia The degree of symmetry of an asymmetric rotor can be described in terms of Ray’s asymmetry parameter [1] (1.3) 2 2B " A " C ! = . A " C The limiting values of ", -1 and +1, correspond to the prolate and oblate symmetric rotor, respectively. The qualitative behavior of an asymmetric rotor is indicated in Figure 1.1. The energy levels are specified using the designation JKaKc, where Ka and Kc represent the limiting prolate and limiting oblate rotors, respectively. By connecting the Ka and Kc levels in sequence, Figure 1.1 demonstrates the relationship between energy levels of the limiting prolate and limiting oblate symmetric rotor. As the prolate symmetric rotor becomes more asymmetric, from the left- toward the right-hand side of the figure, the double degeneracy of all levels with Ka>0 is removed. The same is true for the oblate rotor as it becomes more asymmetric. 3 Fig. 1.1 Relation between limiting prolate and limiting oblate asymmetric rotor energy levels [2]. In order to fully understand the behavior the behavior of the asymmetric rotor energy levels, a quantitative description of the system is necessary. The Hamiltonian for the asymmetric rotor is 2 2 2 (1.4) H= APa + BPb + CPc where A, B, and C are the rotational constants and Pa,b,c are the components of angular momentum. The asymmetric rotor Hamiltonian cannot be solved directly, but, conveniently, the wave functions can be expressed as a linear combination of symmetric rotor functions [13]: ! = a ! J" M # JKM JKM (1.5) JKM where a is a numerical constant and #JKM is the eigenfunction for a symmetric rotor. 4 Operators such as the asymmetric rotor Hamiltonian are represented by matrices. Their eigenvalues, or energy levels, are found by diagonalizing the matrix. Consequently, the solution of the secular determinant H ! I" = 0 (1.6) yields the energy eigenvalues. Selection Rules For a symmetric rotor, the allowed rotational transitions obey the selection rules $J=0,±1 and $K=0. However, the selection rules are more complex for the asymmetric rotor. The rotational levels of the asymmetric rotor are characterized by the quantum number J and pseudo-quantum numbers Ka and Kc. The selection rules for Ka and Kc involve parity and the direction of the permanent dipole moment. Some restrictions on Ka and Kc result from the symmetry properties of the inertial ellipsoid [2]. For the asymmetric rotor, the symmetry of the inertial ellipsoid is characterized by four group operations. The point group D2 contains the identity element and three C2 operations corresponding to 180° rotation about the principal axes of the inertial ellipsoid. z y x D2 E C2 C2 C2 KaKc A1 1 1 1 1 ee B1 1 1 -1 -1 eo B2 1 -1 1 -1 oo B3 1 -1 -1 1 oe Table 1.1 Character Table of the four group. 5 The component of the electric field is F=X, Y, Z g=a, b, c. (1.7) µF = !cos(Fg)µg g The cos(Fg) represents the angle between the space-fixed and molecule-fixed system [1]. If the dipole moment lies along one principal axis (a, for example), the dipole matrix is (1.8) JKaKc µF J 'K 'a K 'c = µa JKaKc cos(Fa) J 'K 'a K 'c . Generally, successive 180° rotations about each of the principal axes return the molecule to its original orientation [4]. The symmetry about the third principal rotation must counteract the symmetry of the first two rotations. For example, an 180° rotation about the a axis does not change the sign of cos(Fa), but for 180° rotations about b or c axes there is a change in sign. It is readily apparent from the above character table that it transforms according to the B1(eo) representation. In Table 1.2, a, b, and, c indicate the transition moment along the corresponding axis. a-, b-, and c-type selection rules can be derived from this table. For example, the transition moment along the b axis result in eo%oe and oo%ee allowed transitions. A1 B1 B2 B3 ee eo oo oe A1 ee - a b c B1 eo a - c b B2 oo b c - a B3 oe c b a - Table 1.2 Rotational selection rules for asymmetric rotors [2]. 6 Dipole Permitted Transition $Ka $Kc Component µa&0 or a-type ee%eo 0, ±2, . . . ±1, ±3, . . . oe%oo µb&0 or b-type ee%oo ±1, ±3, . . . ±1, ±3, . . . oe%eo µc&0 or c-type ee%oe ±1, ±3, . . . 0, ±2, . . . eo%oo Table 1.3 In principle, Ka and Kc can be represented by a numerical change in K [1]. 1.2 STARK EFFECT FOR THE SYMMETRIC AND ASYMMETRIC ROTOR The splitting of rotational energy states by an electric field is called the Stark effect. The rotational spectrum of a molecule with an electric dipole moment will be modified since the field exerts a torque on the dipole moment. Alternatively, imagine a top spinning on a table. It rotates about its axis, tracing a circular path on the table. This particular top spins at a predictable rate along the same circular path, unless an outside force interferes. Additionally, the top has a positive charge on one end and a negative charge on the other. Now remove the table and replace it with two metal plates, one positively charged plate above and one negatively charged plate below the still spinning top. The positive plate will attract the negative end of the top and vice versa, causing the molecule’s precession to change, and thus, its energy. The Stark effect Hamiltonian can be expressed as H! = "! $ µg#Zg (1.9) g= x,y,z where µ is the dipole moment, ! is the electric field and 'Zg is the direction cosine between the space-fixed axis and the molecule-fixed axis [1]. The applied electric field, (, 7 is constant and has a fixed direction Z in space and µg is constant in the molecule-fixed direction. For linear and symmetric rotors, the dipole moment lies only about the symmetry axis (z) so the Stark effect Hamiltonian operator can be written as (1.10) H! = "µ!#Zz First-order Stark effect can be evaluated using perturbation theory. It is the averaged Stark Hamiltonian over the unperturbed rotational state: (1) µ!KM (1.11) E = JKM H J 'K ' M ' = "µ!# # # = " ! ! JJ JKJK JMJM J(J + 1) The non-vanishing direction cosine matrix elements are given in Table 2.1 of Gordy and (1) Cook. According to the equation, when K=0, E! =0. There is no first-order Stark effect for linear molecules or for the K=0 levels of a symmetric top. The Stark effect causes spectral lines to shift. Depending on the relative orientation of the microwave signal and applied electric field, the Stark frequency displacement is 2µ"KM !v(!M = 0) = (1.12) J(J + 1)(J + 2) and (2M ∓ J)µ"K (1.13) !v(!M = ±1) = J(J + 1)(J + 2) When $M=±1, the microwave radiation is perpendicular to the applied electric field. $M=0 indicates that the signal is parallel to the field. Unlike the symmetric rotor where the dipole moment lies about the axis of symmetry, the asymmetric rotor can have a dipole moment along each of the principal 8 axes of inertia. The Stark effect Hamiltonian for an asymmetric rotor has the form . H! = "! $ µg#Zg g= x,y,z Usually second order Stark effects are observed for the asymmetric rotor. However, for slightly asymmetric rotors and molecules at high J, degenerate or nearly degenerate energy levels are common. In this case, first-order Stark effects are observed and second-order perturbation treatment is not applicable [3]. The matrix element µ12 connects two unperturbed states, E and E . It is JKaKc M J 'KaKc M defined as [4] µ12 = 1 µz! 2 . (1.14) The two possible solutions for the secular equation has the form 1 1 2 2 2 E± = E + E ± (E ! E ) + 4" µ12 . (1.15) 2 ( JKaKc M J 'KaKc M ) 2 JKaKc M J 'KaKc M 2 2 When the electric field becomes larger than energy level separation [( µ12 >>( E - E )2], JKaKc M J 'KaKc M EJ M + EJ ' M (1.16) E = KaKc KaKc ± !µ 2 12 demonstrating a linear dependence on the electric field that is typical of first-order Stark 2 2 2 effect. Conversely, if ( µ12 << ( E - E ) , or if the effects of the electric field JKaKc M J 'KaKc M are weak compared to the separation of energy levels, then 2 2 ! µ12 E = EJ M + KaKc (E " E ) J 'KaKc M JKaKc M or (1.17) 9 2 2 " µ12 E = EJ ' M ! . KaKc (E ! E ) J 'KaKc M JKaKc M This demonstrates a quadratic dependence on the electric field that is typical of second- order Stark effect. The above two equations demonstrate that in the presence of an electric field, E increases the energy of state E . Similarly, it decreases the J 'KaKc M JKaKc M energy of E by the same amount so the levels become further separated. J 'KaKc M The second-order approximation takes into account the small changes in the wavefunction due to the electric field [1]: 2 J M " J ' M (2) 2 2 ( Ka Kc Zg Ka Kc ) (1.18) E! = µg! $ J ' E # E KaKc JKaKc J 'KaKc where the denominator indicates the separation of adjacent energy levels. The frequency shift of the Stark lobes can be predicted by the separation of adjacent energy levels when the asymmetric rotor matrix element is assumed to be small in the previous equation. According to the equation, the second-order Stark effect is inversely proportional to the separation of the energy levels. In other words, the smaller the energy separation, the larger the Stark separation. For states at high J for which pairs of K levels are degenerate, the matrix can be approximated using 2 KM JK K M !Zg J ' M . (1.19) ( a c KaKc ) J(J + 1) Two assumptions are made when calculating this approximation. First (because the M levels are often unresolved), the average M value (M/2) will be used. Second, K’a will be used instead of an average K value. 10 1.3 RELATIVE INTENSITIES The degeneracy associated with the quantum number M is removed when an electric field is applied to a polar molecule. The relative intensities of the Stark components determine the type of transition (∆J=+1, ∆J=-1, or ∆J=0). The relative intensities of the M)M±1 Stark components are derived from Table 2.1 in Gordy and 2 Cook. The M dependence of the intensities is proportional to J, M !Fg J ', M ' . For example, when $M=+1 and $J=+1, 2 % 1 ( ∓ !(J ± M + 1)(J ± M + 2)# 2 Q I = ' " $ * = (J ± M + 1)(J ± M + 2) (1.20) ' 1 * 4 4(J + 1)!(2J + 1)(2J + 3)# 2 & " $ ) where J is the lower state. The relative intensities for $M=±1 can be summarized [6]: Q $J=+1 I = (J ± M + 1)(J ± M + 2) 4 P $J=0 I = (J ∓ M )(J ± M + 1) 4 Q $J=-1 I = (J ∓ M )(J ∓ M + 1) 4 11 CHAPTER 2 EXPERIMENTAL DETAILS 2.1 INTRODUCTION A block diagram of the experiment is shown in Figure 2.1. The main components of the system are [5]: • VTO voltage sweeper • Frequency reference synthesizer MLSL-0912 produced by Micro Lambda Wireless, Inc. • Directional coupler C2068-10 produced by MAC Technology, Inc. • Hewlett Packard 33120A function generator • Hewlett Packard 8406A comb generator a solid state frequency multiplier chain • Solid state detector produced by Virginia Diodes • Frequency mixer A produced by M/A-COM and mixer B produced by Mini- Circuits • Stanford Research System Model SR560 amplifier • WR-3.4ZBD detector produced by Virginia Diodes • Data acquisition system with computer • An aluminum gas cell 1 meter in diameter and 0.3 m in height • A HR-8 Precision Lock-In Amplifier manufactured by Princeton Applied Electronics 12 • Model 210-05R High Voltage Power Supply produced by Bertan Associates Incorporated • GRX Pulser produced by Directed Energy Incorporated Inside the cell are two metal plates separated by 2.54 cm. A high voltage feedthrough connects the power supply to the upper plate. The bottom plate is grounded through the tank. When voltage is applied, an electric field is generated between the two plates. This gap between the plates corresponds to the beam diameter of the radiat ion source. In other words, the microwave signal travels between the plates to a copper mirror at the opposite end of the tank. The mirror, which has a radius of curvature of 0.6m, reflects the signal back between the plates to the detector. The detector is the input signal for the lock-in amplifier. Figure 2.2 describes the path of the radiation. 13 Fig. 2.1 A block diagram of the FASSSTER system. 14 a b Fig. 2.2 The path of radiation from the source, through the tank, and to the detector. (a) Side view (b) The view from above 15 2.2 FASSSTER FREQUENCY CALIBRATION SCHEME The experiment was accomplished with the Fast Scan Submillimeter Spectroscopic Technique with Electronic Reference (FASSSTER) system discussed by Medvedev [5]. This technique uses electronically generated reference markers for frequency calibration. The FASSSTER system is complemented by sophisticated calibration software, also developed by Medvedev [5]. The FASSSTER frequency calibration scheme is detailed as follows: The voltage tunable oscillator (VTO) operates in the frequency range of 10.285GHz-10.885GHz. The integrating amplifier chip produces a triangular waveform and a resistor and a capacitor determine the integration time constant. This requires two signals: a reset signal to drain the leftover charge of the capacitor and a computer generated square wave that undergoes integration. The amplitude of the signal that undergoes integration determines the sweep rate of the VTO and the duration of the signal defines the maximum amplitude of the voltage sweep. The integrated signal takes advantage of the high resolution of the integrating amplifier chip, generating a smooth voltage ramp. A directional coupler splits the signal from the VTO. One part is directed to the frequency multiplier chain and one part undergoes frequency calibration. The solid-state multiplier chain creates the desired frequency of the signal. The multiplier chain is comprised of three components: a x8 W-band multiplier chain, a x3 W band amplifier, and a x3 W band multiplier. The final component includes a horn and lens that collimates the radiation. The signal from the VTO and directional coupler is down converted with the signal from the frequency synthesizer at mixer A. The frequency synthesizer produces the 16 frequency reference. It operates near the center of the VTO frequency range, or 10.585 GHz. When the frequency of the VTO is equal to the synthesizer frequency, the resulting frequency at mixer A is zero. A function generator adjusts the mode spacing and driving power applied to the comb generator. The signal from the comb generator is down converted at mixer B with the signal from mixer A. The resulting frequency is passed through an amplifier. At mixer B, zero frequency is achieved when the two signals are equal. When the signal and individual comb modes are equivalent, the resulting frequency is zero. All other markers are calculated with respect to this missing marker. This signal is multiplied by twenty-four to correspond to the output frequency of the multiplier chain. 2.3 FASSST SYSTEM The fast scan submillimeter spectroscopic technique (FASSST) uses backward- wave oscillators to generate radiation in the millimeter and submillimeter region. A gaseous sample is placed in a 6m by 15 cm aluminum cell. The radiation produced by BWOs travel from one end of the cell to the other where a InSb bolometer cooled to liquid helium temperature are used as a detector. A reference gas, usually sulfur dioxide, is contained in a second gas cell. A Fabry-Perot cavity is employed to produce highly predictable inference fringes. A second InSb bolometer is used to detect the fringes. The frequency spacing between adjacent interference fringes and their absolute frequency positions are determined by using known frequencies from the reference gas. Interpolation between positions of adjacent fringes relative to the position of an unknown absorption line yields the calculated line position. 17 2.4 LOCK-IN AMPLIFIER A lock-in amplifier recovers signal in the presence of noise by using a combination of a phase sensitive detector (PSD) and a low pass filter. A PSD multiplies two signals together: the amplified (or input) signal under investigation and the internal reference signal produced by the lock-in amplifier. The detected sinusoidal signal voltage is (2.1) Vsig = Acos(!t). where A is the signal amplitude and * is the angular frequency. The internal reference signal is (2.2) Vref = Bcos(!t + ") . Multiplication of the two signals yields 1 1 V = ABcos! + ABcos(2"t + !) . (2.3) PSD 2 2 If the magnitude of the internal reference amplitude remains constant, the output is proportional to the input signal, proportional to the angle between it and the reference signal, and contains components at twice the reference frequency. The internal reference signal is generated by a phase locked loop (PLL). The PLL locks an internal reference oscillator to an external reference signal provided to the lock- in amplifier. The result is a reference sine wave with a fixed phase shift relative to the external reference signal. The PLL tracks any frequency changes in the external reference signal, so that changes in the external reference frequency will not affect the input signal. The lock–in amplifier only detect signals whose frequency is very close to the internal reference frequency. The low pass filter attenuates noise that has no fixed 18 frequency or phase that differs greatly from the internal signal reference frequency. Noise at frequencies close to the internal reference signal result in low frequency AC output whose attenuation depends on the low pass filter bandwidth and rolloff. Only signal at the internal reference frequency will result in an actual DC output. In other words, the low- pass filter removes the 2*t component. The remaining signal, VPSD = ABcos! , is a DC signal proportional to the signal amplitude. In this experiment, an HR-8 Precision Lock-in Amplifier manufactured by Princeton Applied Research Corporation was used. The HR-8 was chosen for its simplicity and patent operation. 19 CHAPTER 3 ACETONITRILE 3.1 INTRODUCTION Acetonitrile (methyl cyanide or CH3CN), a common organic solvent, is an abundant species detected in massive star forming regions. Spectral line surveys of these regions can provide information about physical and chemical properties during the evolution of stars. Chang et al. [6] observed spectral lines from acetonitrile, among other large organic molecules, at 138.3 GHz to 150.7 GHz in the Orion-KL hot core. Nummelin et al. [7] observed acetonitrile, among other molecular species, in Sagittarius B2 between 218 GHz and 263 GHz. Araya et al. [8] also detected acetonitrile in several hot molecular cores. Radiative association reactions can proceed rapidly in the interstellar medium. A possible mechanism for the production of acetonitrile is + + CH3 + HCN ) CH3CNH followed by recombination to give CH3CN [9]. 3.2 EXPERIMENTAL CONDITIONS A commercial sample of acetonitrile (99% pure) without additional purification was used. The spectrum was taken with 6.8 mtorr of sample at room temperature. Approximately 850V was applied to the Stark plates creating an inhomogeneous electric 20 field of 3.3+104V/m between the plates. The spectrum was taken using the setup discussed in Chapter 2, producing transitions in the frequency range 246 GHz to 257 GHz. 3.3 ANALYSIS AND DISCUSSION Figure 3.1 is a spectra of the J=14!13 transition of acetonitrile. When rotational selection rules are applied to energy levels of a symmetric rotor, it follows that the allowed transitions for J+1!J absorptions are v = 2B(J + 1) . However, the lines separate according to different K values when centrifugal distortion is taken into consideration. The corresponding expression is (3.1) 3 2 v = 2B(J+1)-4DJ(J+1) -2DJK(J+1)K where B=9198.899299 MHz, DJ=3.8048 kHz, and DJK=177.417 kHz for acetonitrile [10]. 21 Fig. 3.1 A comparison of the Stark field (red spectra) and the zero field (blue spectra) of acetonitrile. 22 The red spectra in Figure 3.2 is the J=14!13 transition of acetonitrile with approximately 850V applied to the Stark plates. As expected, the spectrum indicates first- order Stark effects. The displacement of the Stark lobes can be determined by equation (1.13) (2M ∓ J )µ#K !v(!M = ±1) = " J(J 1) J 2 + ( + ) where µ=3.913D [10] and (=3.0+104V/m. $M=±1 indicates that the microwave radiation is perpendicular to the applied field. The calculated frequency shifts are summarized in Table 3.1. The negative sign indicates a shift to the left of the unmodulated line and a positive sign indicates a shift to the right. 23 Fig. 3.2 When acetonitrile is exposed to an electric field, the M degeneracy is lifted. 24 $M = ±1 Calculated frequency shift, MHz 0, -13 -15.508 1, -12 -13.122 2, -11 -10.736 3, -10 -8.351 4, -9 -5.965 5, -8 -3.579 6, -7 -1.193 7, -6 1.193 8, -5 3.579 9, -4 5.965 10, -3 8.351 11, -2 10.736 12, -1 13.122 13, 0 15.508 Table 3.1 Calculated frequency shifts for the K=6 component. 25 Figure 3.3 is a close view of the K=6 component of the transition. The largest fourteen Stark lobes are degenerate, causing the relative intensities to be much stronger than the remaining dispersed lobes. These remaining lobes overlap with the K=5 and K=7 and therefore not completely resolved. 26 Fig. 3.3 The Stark spectra of the K=6 component. 27 CHAPTER 4 ETHYL FORMATE 4.1 INTRODUCTION Ethyl formate is a likely candidate for interstellar detection. A similar molecule, methyl formate, has been identified as an abundant species in hot cores of molecular clouds. Theoretically, ethyl formate is produced in the interstellar medium by a gas-phase reaction followed by a dissociative reaction [11, 12]: + + [C2H5OH2] + H2CO2 ) [HC(OH)OC2H5] + H2 + - [HC(OH)OC2H5] + e ) HCOOC2H5 + H Two isomers of ethyl formate (Figure 4.1) exist due to the rotations around the carbon-oxygen bond: the trans conformer and the gauche conformer. Trans ethyl formate comprises 61% of the sample at room temperature and gauche ethyl formate constitutes the remainder. The dipole moments and rotational constants for each conformer are summarized in the following table. With a " value of –0.9571 and –0.8149 for the trans and gauche conformer, respectively, ethyl formate shows the spectrum of a prolate asymmetric rotor. 28 µa µb µc A B C Debye MHz trans 1.85 0.69 - 17746.60 2904.73 2579.14 gauche 1.44 1.05 0.25 9985.34 3839.48 3212.94 Table 4.1 Rotational constants and dipole moments of ethyl formate conformers [13]. Fig. 4.1 The trans (left) and gauche (right) conformers of ethyl formate [13]. 4.2 EXPERIMENTAL CONDITIONS A commercial sample of ethyl formate (98% pure) without additional purification was used. The spectrum was taken at room temperature with 10 mtorr of sample. Approximately 500V were applied to the Stark plates, creating an electric field of 2.0x104 V/m. The spectrum was taken using the lock-in amplifier setup discussed in previous chapter, producing transitions in the frequency range 246-252 GHz as seen in Figure 4.2. The known frequency range of the rotational spectrum for ethyl formate was extended to encompass the range 106 GHz-337 GHz using the FASSST system. Using 29 SPFIT, over 1500 new spectral lines were assigned to the ground state of ethyl formate [5]. The spectrum produced by the FASSSTER system was compared to the FASSST spectrum for analysis. 4.3 ANALYSIS AND DISCUSSION All ethyl formate transitions revealed in the modulated spectra can be classified into one of three categories: unmodulated, first-order effects, or second-order effects. These distinctions are governed by the energy levels of ethyl formate. No modulation Widely separated nondegenerate rotational energies of the unperturbed molecule will not be modulated at the low fields in this experiment. The 454,42!444,41 transition at 246.681832 GHz ( Figure 4.3) disappears in the modulated spectrum. When using the approximation discussed in Chapter 1 Section 2, the Stark shift is 8.3+10-3 MHz, a small contribution of the Stark effect to the transition frequency. This contribution is so small- smaller than a linewidth- that there is no Stark modulation. 30 Fig. 4.2 The ethyl formate spectra from 246 GHz – 252 GHz. 31 Fig. 4.3 The 454,42!444,41 transition does not exhibit any observable Stark effects in the modulated spectra. 32 Degenerate Energy Levels: First-order Effects Degenerate rotational energy levels of ethyl formate produce first-order Stark effects and will be modulated at low fields. This is the most commonly observed effect in the modulated ethyl formate spectrum. The transitions 3820,18!3819,20, 3820,18!3819,19, 3820,19!3819,19, and 3820,19!3819,20 all occur at 250.146329 GHz as seen in Figure 4.4. The frequency shifts of the Stark lobes are calculated using the equation (1.13) (2M ∓ J)µ"K !v(!M = ±1) = . J(J + 1)(J + 2) When $J=0 and $M=±1, a completely resolved Stark pattern will have (2J+1) components. For instance, the largest frequency shift (55MHz) and weakest relative intensity occurs for M=38. In other words, the Stark components are so spread out and weak that they are not observed, leaving only the zero field line in the modulated spectrum. Observed Transition Transition Lower Energy Upper Energy Conformation Transition Frequency, GHz Level, GHz Level, GHz Type 3820,18!3819,20 250.146329 7556.21023 7816.35656 gauche b-type 3820,18!3819,19 250.146329 7556.21023 7816.35656 gauche b-type 3820,19!3819,19 250.146329 7556.21023 7816.35656 gauche b-type 3820,19!3819,20 250.146329 7556.21023 7816.35656 gauche b-type Table 4.2 Summary for the J=38!38 transition. 33 Fig. 4.4 Transitions that exhibit first-order effects. 34 The same argument can be applied to the transitions 3120,11!3119,12, 3120,13!3119,13, 3120,11!3119,12, and 3120,12!3119,12, also seen in Figure 4.5 and summarized in Table 4.3. Observed Transition Transition Lower Energy Upper Energy Conformation Transition Frequency, GHz Level, GHz Level, GHz Type 3120,11!3119,12 250.150045 5832.04243 6082.19247 gauche b-type 3120,13!3119,13 250.150045 5832.04243 6082.19247 gauche b-type 3120,11!3119,12 250.150045 5832.04243 6082.19247 gauche b-type 3120,12!3119,12 250.150045 5832.04243 6082.19247 gauche b-type Table 4.3 Summary for the J=31!31 transition. Nondegenerate, Closely Spaced Energy Levels: Second-order Effects An interesting case occurs when two nearby energy levels lie close together as discussed in Chapter 1 Section 2. The nearly degenerate energy levels of ethyl formate will produce observable second-order effects. 35 The frequency transitions 373,34!364,33, 374,34!364,33, 373,34!363,33, and 374,34!363,33 appear in the frequency range 251.6 GHz- 251.7 GHz (Figure 4.5). Table 4.4 summarizes the rotational transitions, and the upper and lower state energy levels. Observed Transition Transition Lower Energy Upper Energy Conformation Transition Frequency, GHz Level, GHz Level, GHz Type 373,34!364,33 251.655742 4749.3509 5001.0067 gauche b-type 374,34!364,33 251.670729 4749.3509 5001.0217 gauche a-type 373,34!363,33 251.679508 4749.3271 5001.0067 gauche a-type 374,34!363,33 251.694495 4749.3271 5001.0217 gauche b-type Table 4.4 Summary for the J=37!36 transition. 36 Fig. 4.5 All four transitions exhibit second-order effects. 37 The separation of the upper interacting energy levels (374,34 and 373,34) is 5001.00217 GHz- 5001.0067 GHz=15.01 MHz. Similarly for the lower states (364,33 and 363,33) 4749.3509 GHz – 4749.32712 GHz = 23.78 MHz. Fig. 4.6 Diagram (not drawn to scale) of the Stark effect for the J=37!36 transitions of ethyl formate. The second-order approximation takes into account the small changes in the wavefunction due to the electric field (eqn. 1.18): 2 J M " J ' M (2) 2 2 ( Ka Kc Zg Ka Kc ) E! = µg! $ J ' E # E KaKc JKaKc J 'KaKc where the denominator indicates the separation of adjacent energy levels. The matrix can be approximated using eqn. 1.19 38 2 KM JK K M !Zg J ' M ( a c KaKc ) J(J + 1) For the upper and lower state, the approximation gives 37 36 KM ( ! 4) KM ( ! 4) = 2 = 0.05263 and = 2 = 0.05405 , (4.1) J(J + 1) 37 ! 38 J(J + 1) 36 ! 37 respectively. Conveniently, the conversion factor [13] MHz (4.2) µ! = 0.50348 V D " cm makes the second-order Stark shift calculation very simple. The dipole moment for this calculation reflects the type of interaction between the levels, not the observed transition type. For this case, the interaction between the upper and lower states is c-type. For the 373,34!364,33 transition (4.3) MHz V 0.05263 0.05405 !v(2) = (0.50348 )2 (0.25D)2 (200 )2[# # ] = #3.6MHz . V cm 15.01MHz 23.78MHz D " cm (2) Similarly, for the 374,34!363,33 transition, $v =3.6 MHz. For the 374,34!364,33 transition (4.4) MHz V 0.05263 0.05405 !v(2) = (0.50348 )2 (0.25D)2 (200 )2[ # ] = 0.7815MHz V cm 15.01MHz 23.78MHz D " MHz V 0.05263 0.05405 !v(2) = (0.50348 )2 (0.25D)2 (200 )2[ # ] = 0.7815MHz V cm 15.01MHz 23.78MHz D " cm cm (2) Similarly, for the 373,34!363,33 transition, $v = -0.7815 MHz. Inspection of Figure 4.5 reveals a discrepancy between the calculated and observed shifts due to the assumptions mentioned in the Chapter 1 Section 2. 39 Transition Calculated Stark shift Observed Stark shift MHz MHz 373,34!364,33 -3.6 Broadened and not observed 374,34!364,33 0.7815 1.5 373,34!363,33 -0.7815 -1.5 374,34!363,33 3.6 Broadened and not observed Table 4.5 The Stark shift for each transition. Because of the weak transitions and the large frequency shift, the Stark lobes for the 373,34!364,33 and 374,34!363,33 transitions are not observed. In contrast, the 374,34!364,33 and the 373,34!363,33 transitions exhibit stronger Stark lobes at a small frequency displacement because they are not so widely dispersed. A similar argument can be applied to the 3511,25!3411,24 and 3511,24!3411,23 transitions at 248.999251GHz and 249.003408GHz, respectively. (The adjacent transitions, 3510,25!3410,24 and 3512,24!3412,23, are not nearly degenerate with the transitions shown in Figure 4.7; these levels do not interact with 3511,25!3411,24 and 3511,24!3411,23). In this instance, the Stark frequency shift for 3511,25!3411,24 and 3511,24!3411,23 is approximately 2 MHz, causing the Stark lobes to significantly overlap. Unlike the 374,34!364,33 and 373,34!363,33 transitions which exhibit two distinct Stark lobes, the 40 3511,25!3411,24 and 3511,24!3411,23 transitions are mixed by the Stark effect and exhibit only one shared lobe. Observed Transition Transition Lower energy level Upper energy level Conformation Transition Frequency, GHz GHz GHz Type 3512,24!3412,23 248.601141 5143.80291 5392.40405 gauche a-type 3511,25!3411,24 248.999252 4998.58958 5247.58883 gauche a-type 3511,24!3411,23 249.003408 4998.59551 5247.59892 gauche a-type 3510,25!3410,24 249.608882 4867.55342 5117.16230 gauche a-type Table 4.6 Summary of the frequency transitions and energy levels for J=35!34 transitions. 41 Fig. 4.7 The transitions that are mixed by the Stark effect exhibit only one shared lobe. 42 CONCLUSION The modulated spectrum of ethyl formate has demonstrated that dense spectra of a complicated molecule can be simplified. Modulation makes it possible to separate the absorptions from the otherwise dense background. The type of modulation each transition exhibits can be accurately predicted if the rotational energies are known. Generally, the rules governing modulation can be summarized: If rotational energy levels are nondegenerate and widely spaced, then the corresponding transition will not be modulated by an observable amount in an electric field. If rotational energy levels are degenerate, then the corresponding transitions will exhibit first-order Stark effects. If rotational energy levels are nondegenerate and closely spaced, then the corresponding transitions will exhibit observable second-order Stark effects. In order for Stark modulation to be a useful analytical tool, only a fraction of transitions in the dense spectra should be modulated. Determining the minimum applied voltage that would result in a Stark frequency shift would improve the applicability of this experiment in future studies. For example, modulating all transitions that exhibit 43 first-order Stark effects in the ethyl formate spectrum would only require approximately 20V applied to the metal Stark plate. 44 BIBLIOGRAPHY 1. 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