Rotational : A Laboratory for Undergraduate Physical Chemistry

A Thesis Presented to The Honors Academy Missouri University of Science and Technology

In Partial Fulfillment Of the Requirements for Graduating as an Honors Fellow

By Nicole T. Moon

May 2019

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Abstract:

While rotational spectroscopy has become a more prominent field within the past few decades, few laboratory exercises exist that introduce students at the undergraduate level to the concepts and instrumentation used within the field. Here, a physical chemistry laboratory involving the analysis of benzonitrile with a newly renovated Balle-Flygare type, Fourier Transform (FTMW) is introduced as one such exercise. The analysis of benzonitrile is ideally suited for an undergraduate physical chemistry laboratory because it is easily carried out within one laboratory period and involves a comprehensive introduction into the world of rotational spectroscopy. Within this laboratory, students have the opportunity to perform quantum chemical calculations for accurate molecular structure, accrue spectra on a research grade FTMW, and construct an effective Hamiltonian inclusive of nuclear electric quadrupole coupling for transition assignment using analysis software commonly available to the spectroscopic community. Within this thesis, the design, implementation, and the students’ response to this laboratory will be discussed along with all modifications made to the FTMW.

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Table of Contents

Page Abstract……………………………………………………………………………….II Table of Contents…………………………………………………………………….III Table of Figures and Charts……………………………………………………….....IV Acknowledgments…………………………………………………………………….V Chapter: I. Introduction………………………………………………………………..1 II. Experimental Methods…………………………………………………….4 A. Fourier Transform …………………………4 B. Renovations to the FTMW…………..………………………....……...8 C. Development of the Physical Chemistry Laboratory………...………..12 III. Results……………………………………………………………………..15 A. Analysis of Benzonitrile……………………………………………….15 B. Student Response to the Laboratory…………………………………...17 IV. Discussion………………………………………………………………….18 V. Conclusion………………………………………………………………….21 References……………………………………………………………………………...22 Appendix……………………………………………………………………………….[1] Lab 7: Microwave Spectrum of Benzonitrile…………………………………..[1] Survey Questions and Responses………………………………………………[17]

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Table of Figures and Tables

Figure Page Figure 1: Image of FTMW ……………………………………………………………4 Figure 2: Cavity Diagram……………………………………………………………...5 Figure 3: Overview of Microwave Sequence………………………………...………..7 Figure 4: Rebuilding the Diffusion Pump……………...……………………………...9 Figure 5: Original FTMW Circuity…………………………………………………....11 Figure 6: Renovated FTMW Circuity………………………………………………....11 Figure 7: Structure of Benzonitrile…………………………………………………….13 Figure 8: Predicted Spectrum Produced for Benzonitrile…...………………………....14 Figure 9: Intensity File Used within the Preliminary Fit…………………………..…..16 Figure 10: Line File Used within the Preliminary Fit………………………………….16 Figure 11: Parameter File Used within the Preliminary Fit……………………………16 Figure 12: Variable File Used within the Preliminary Fit……………………………..17 Figure 13: Fit File Used within the Preliminary Fit……………………………………17 Figure 14: Results of Student Survey…………………………………………………..18 Figure 15: Undergraduate Students Performing Laboratory…………………………...20

Table Page Table 1: Salvaged FTMW Circuity Components……………………………………….10 Table 2: Potential ……………………………………………………………12 Table 3: Transitions and Ranges Observed..…..……………………………14

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Acknowledgements: I would first like to thank Dr. Grubbs for his guidance and support on this thesis. Without his insight and assistance, this thesis would not have been possible. I especially want to thank him for not only allowing, but encouraging, a shy freshman to join his research group nearly four years ago. Without the wonderful opportunity to work for him and his advice along the way, I would not be where I am today.

I would also like to thank Frank Marshall, Amanda Duerden, Josh Isert, and Bethany Paramathas for their assistance while rebuilding the FTMW and continuous motivation. Without their support and endless jokes, this thesis would not have been nearly as enjoyable. It was a pleasure to work with each and every one of them.

In addition, this project would not have been possible without the CHEM 3459 students, who without a complaint were the first to conduct this laboratory experiment. I could not have asked for a better group of students to work with.

Lastly, I would like to thank the Missouri S&T Honors Academy and Missouri S&T Chemistry Department for allowing me to complete this thesis.

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I. Introduction For a chemist, one of the most powerful tools available to observe molecular behavior is spectroscopy. At its core, spectroscopy is a branch of science concerned with the study and measurement of spectra produced when matter interacts with or emits electromagnetic radiation. While there are many forms of spectroscopy—infrared absorption, Ultraviolet-Visible (UV-Vis), and nuclear magnetic resonance to name a few—this thesis is focused on a form of molecular spectroscopy known as rotational or microwave spectroscopy. Rotational spectroscopy is a powerful tool that utilizes changes in within a in order to arrive at physical constants that can be used to determine the molecular structure of gas phase molecules. Other applications of rotational spectroscopy include determining electronic structures, investigating fundamentals of molecular physics, and establishing barriers to internal . While rotational spectroscopy is a powerful technique, students at the undergraduate level are rarely introduced to the concepts and instrumentation used within the field either due to the shear cost of the instrumentation or lack of quality laboratory exercises on the subject. Within this thesis, a physical chemistry laboratory involving the molecular rotational measurement and analysis of benzonitrile utilizing a newly renovated Balle-Flygare type, Fourier Transform microwave spectrometer (FTMW) is introduced as one such exercise to alleviate this problem.

The field of rotational spectroscopy first emerged shortly after the end of World War II and evolved from the microwave technology developed for radio detection and ranging () equipment used during the war1. As a result, the field is often referred to as microwave spectroscopy in reference to the instrumentation used. The first post war experiments involved studies of the inversion vibration of ammonia and were conducted using a waveguide1. At its core, a waveguide is an instrument that sends a stream of microwave radiation from a source to a detector, measures the light received by the detector, and determines the absorbed by a molecule based on the frequencies of light missing from the data received. While these initial instruments were easy to use, build, and maintain, they also had many problems. These problems included substantial background noise, low sensitivity due to short path lengths, non-constant temperature within the chamber, and line broadening due to molecular collisions.

In the 1980’s, new approaches to remove some of these problems and enhance the sensitively and resolution of the technique culminated with the development of the Fourier P a g e | 2 transform microwave (FTMW) spectrometer by Flygare, and his graduate student at the time, Balle. At the time, Flygare was interested in the magnetic effects that arise from the interaction of nuclear spin coupling in molecules—something that could not be studied precisely with a waveguide instrument due to its short comings. While pondering a solution to this, Flygare came up with the idea that one could use a resonance technique instead of an absorption technique in order couple to the electric dipole of a molecule in the same way nuclear magnetic resonance couples to the magnetic dipole of a molecule. From this idea, the FTMW and modern rotational spectroscopy was developed.

Flygare and Balle’s original FTMW was comprised of three main systems—a source for sample introduction, a cavity, and a circuit2. Samples were injected into the FTMW through a gas mix that entered the system via a pulsed molecular beam nozzle at the top of the cavity2. The cavity consisted of two mirrors situated inside a vacuum chamber2. A circuit—comprised of a pulse generator, amplifier, antenna, detector, and oscilloscope—was then utilized to generate to stimulate the sample’s electric dipole, tune to a desired frequency range, and detect the resulting molecular signal2. This design allowed for a reduction in collision broadening, the molecule to be cooled to a low rotational temperature, and increased sensitivity and resolution that enabled the small rotations of molecules to be precisely observed2. Since its introduction, very few modifications have been made to the original design of the FTMW and it remains to this day a key microwave spectroscopy technique.

Today, there are over fifty active microwave spectroscopy laboratories around the world, comprised not only of principle investigators but also post-doctoral fellows, graduate students, and undergraduate students3. At any given time, these groups can be found conducting research within a wide variety of areas including, but not limited to, , synthetic processes, , pharmaceuticals, and instrument development. Some of the field’s major accomplishments include the determination of molecular dipole moments from spectroscopic data, the identification of molecules in the , determination of atmospheric chemical processes, characterization of amino acid confirmers, and research into the superfluity in helium clusters1. As one can see, microwave spectroscopy has become a prominent field within the past few decades and has the potential to solve some of the toughest questions currently being asked by the scientific community. P a g e | 3

Although microwave spectroscopy has become an ever growing field, students at the undergraduate level are rarely introduced to the theory, research, or instrumentation present within the field. In most academic settings, this means the only opportunity currently available for undergraduate students wanting to gain hands-on experience is to join a microwave spectroscopy research laboratory as an undergraduate researcher. However, for the majority of undergraduate students whose universities do not house one of the fifty research laboratories, this is not an option. As a result, they are unable to gain hands-on experience within the field before graduation, and in some cases are completely unaware of the fact that the field exists.

The two main reasons why undergraduate students are rarely able to gain hands-on experience within microwave spectroscopy is the shear cost of the instrumentation and the lack of quality laboratory exercises on the subject. Since Fourier transform microwave are not commercially available, all FTMWs in operation are custom built by the research group they are housed in. As a result, the research group not only bares the cost of the parts needed to build the instrument, but also the man hours needed to construct it. Taking into consideration all elements of the FTMW’s design, the instrument can cost upwards of $150,000 depending on circuit design, sourcing, and vacuum system. As a result, most universities which do not already house a microwave spectroscopy research laboratory are unable to afford the cost of implementing and maintaining such an instrument.

However, this is only half of the problem. Within universities that do possess a FTMW or similar instrumentation, students are still unable to gain hands-on experience due to the lack of quality laboratory exercises. The few microwave spectroscopy laboratory exercises currently in use within undergraduate physical chemistry laboratories often focus on computational calculations to simulate the types of results acquired by a FTMW or to show how to analyze a fake or already acquired data set. As a result, students gain no practical skills within the field and are often left confused as to how this applies to real world applications. This should be considered as a major problem since the American Chemical Society requires that all undergraduates have hands-on laboratory experience with modern instrumentation and data analysis skills in order to graduate with a bachelor’s degree4.

In light of this, this thesis presents a physical chemistry laboratory for the acquisition and analysis of the pure rotational spectrum of benzonitrile as one such exercise to alleviate this P a g e | 4 problem. Within the laboratory, students have the opportunity to make quantum chemical calculations (Using Gaussian09TM software), accrue spectra on a research grade, yet cost- effective, FTMW instrument, and analyze the data they collect. Within the following thesis, the design, implementation, and students’ response to this laboratory will be discussed.

II. Experimental Methods: A. Fourier Transform Microwave Spectroscopy For the purpose of this thesis and corresponding educational laboratory, a Fourier transform microwave spectrometer (FTMW) was utilized to collect the rotational spectrum of benzonitrile5. Traditionally, a FTMW is comprised of three main systems: (i) a source for sample introduction, (ii) a Fabry-Pérot cavity resonator, and (iii) a circuit2. Samples are made into a gas mix consisting of a small (typically <10%) amount of analyte species in an inert (usually Argon) carrier and injected into the FTMW through a pulsed molecular beam nozzle. From here, the sample is introduced into the cavity, which consists of two mirrors situated inside a vacuum chamber2. The circuit—comprised of Figure 1: Image of FTMW utilized in Dr. a pulse generation and amplification side, an antenna that Grubbs Microwave Spectroscopy couples microwaves into the resonator and functions as a Laboratory. detector, a signal detection and manipulation side, and a signal interpretation component (the oscilloscope)—is then utilized by tuning to a desired frequency range, generating microwaves to stimulate the sample, and then detecting the resulting molecular signals2. Pieces of this system will be discussed in detail below and an image of the FTMW used within this thesis can be seen in Figure 1.

When searching for unknown molecular lines, the first step to operating the FTMW consists of stepping the cavity mirror separation in order to adjust its resonance frequency and alignment with the microwave oscillator2. The cavity resonator consists of two mirrors situated inside a vacuum chamber, as seen in Figure 2 below. One of these mirrors is permanently held P a g e | 5 fixed, while the position of the other mirror can be tuned to make small adjustments to the frequencies being observed2. The cavity is inherently a high electric field, narrow bandwidth instrument due to its effective as a bandpass filter. That is, only specific (or small ranges of those wavelengths) can create a standing wave Figure 2: Cavity Diagram within the resonator at a given mirror separation. The amount of times the light passes between the mirrors—a measure of the sensitivity of the instrument—is given by the cavity’s quality factor, Q.2 The resonator’s Q value is calculated from the frequency of light being introduced divided by the bandwidth or range of allowed wavelengths. For a typical resonator, the band width is around 1 MHz at 10 GHZ giving a Q of approximately 10,000. For our resonator, the bandwidth is approximately 500 kHz at 10 GHz producing a Q of approximately 20,000. In order to ensure that there is adequate power of a transition during a transition search, it is a good practice to have step sizes at or lower than these bandwidths. These are determined by the full width, half maximum (FWHM) of the mode utilized to tune the resonator. For most experiments then, the step sizes are generally 500 kHz or less8. This process is generally referred to as “tuning to a mode.”

Once the instrument has been tuned, an experimental acquisition begins with pulsing a gas sample into the vacuum chamber via the molecular beam nozzle. Unlike the original Balle- Flygare design which had its molecular beam nozzle situated at the top of the cavity, the molecular beam nozzle on the FTMW used within this thesis is situated on the back of one of the mirrors and sample enters the cavity through a drilled out hole at the center of that mirror. This design allows for more gas molecules to be stimulated by the microwave pulse contained within the resonator and is known as the beam waist2. When the gas is pulsed, the molecules are forced to expand adiabatically into the vacuum through the small inlet orifice of the nozzle source. Because the molecules are relatively high pressure behind the valve and are being introduced into the vacuum through a small orifice, a bottleneck by which all the molecules exit the nozzle very quickly occurs. The molecular distribution of speeds is very small, due to the bottleneck effect and, according to the kinetic theory of gases, forces the molecules to be translationally P a g e | 6 very cold (<1 K) as this energy is being used to give the molecules their mass flow velocity. However, rotational and, to a lesser extent, vibrational motion are very efficient with mass flow velocity so the molecules achieve very low rotational (<10 K) and vibrational (<100K) temperatures2. The molecules also lose energy through collisions as the collisions between the molecules become less frequent to the point that they are essentially collision free2. This pulse of gas is deliberately kept on a short time scale in order for these equilibrium expansion properties to be rapidly achieved2. Typically, the equilibrium expansion undergoes major changes on a time scale of milliseconds or less7. This is exemplified by the nozzle parameters typically being under 1 millisecond.

There are a few advantages to using a pulsed nozzle source as compared to a continuous source. For example, if N number of particles can be pumped into the cavity during a long-time, t, then the observed signal to noise (S/N) ratio for a period of t would be proportional to 푁/√푃, where P is the number polarizing microwave pulses generated over time t.2 However, if instead all N particles are pulsed into the cavity in a short time such that only one polarizing pulse is generated during time t, the S/N would be proportional to N.2 As a result, the S/N can be greatly increased by simply using a pulsed nozzle set up and can be calculated from the number of molecules, N, that are released in a single pulse of the nozzle. This can be calculated using the formula 푁 = 푐푝푛푣푛퐴푛푡푣, where 푣푛 is the flow velocity at the nozzle, 퐴푛 is the nozzle area, 푡푣 is 7 the pulse valve open time, and 푐푝푛 is the discharge coefficient .

After the molecules are introduced into the cavity, they are then exposed to a microwave pulse introduced into the cavity through an input coupling (antenna) positioned at the center of one mirror. Typically, one microwave pulse interacts with the molecules in the free expansion, and the next microwave pulse passes through an evacuated chamber without interacting with any molecules due to the continuous pulsing of the sample2. Before the microwave pulse (but after the sample introduction), the molecules’ dipole moments are arranged in a random order. However, the microwave pulse polarizes a band frequency that may contain one (or more) of the resonant rotational transitions in the molecules2. Thus, after the pulse, the dipoles of the molecules are aligned in a uniform direction, resulting in a macroscopic polarization of the molecules2. P a g e | 7

A maximum polarization of the gas is achieved following the cavity analog of a π/2 pulse for T2>>Tp, where T2 is the polarization relaxation time related to the lower power steady-state

1 2 transition half width at half height by Δ푣 = 휋푇 and Tp is the microwave pulse length . This is 2 2 because at the cavity analog of a π/2 pulse, the molecular system experiences a population inversion6. The molecules are required to maintain their coherent polarization for a period of time long relative to τc, (the cavity relaxation time constant) where T2 >> τc. This allows the original microwave pulse to die away before the coherent polarization is lost6.

Figure 3: Overview of Microwave Sequence

Once the microwaves disappear, the molecules fall back into their previous relaxed and diverse alignments. This results in the polarized gas coherently emitting at its resonant frequency2. This decay in the polarization over time, or the free induction decay (FID) of the molecules, can be recorded by a detector within the chamber (antenna)2. These signals are then low noise amplified and manipulated to easily collect and digitize on a digital oscilloscope. The resultant signals are collected and average in the time domains. The resultant signals are then Fourier transformed to give the desired spectrum in the frequency domain. Because the FIDs are Fourier transformed, the length of the FID has a direct effect on the resolution of the experiment. Typical FID detection times are on the order of hundreds of microseconds producing linewidths resolvable to <10 kHz9. P a g e | 8

The FTMW instrument is typically utilized to study stable, transient, or short-lived molecular species with transitions within the microwave region of 1 GHz to 40 GHz2. Most rotational measurements are made on gaseous absorption lines having widths ranging from a few kilohertz to a few megahertz2. The natural width of a molecular line may be considered to arise from the Heisenberg uncertainty principle and the probability of spontaneous emission2. FTMW experiments actually do not measure absorption or emission spectra, but rather resonance spectra similar to nuclear magnetic resonance (NMR)2. In fact, FTMW spectroscopy is the electric analogue of NMR and utilizes many of the Bloch equations by leveraging the electric field instead of a magnetic field2. This way of performing the experiment both increases sensitivity and resolution providing parts per trillion sensitivity and 1 kHz resolution2. Thus, the linewidths of FTMW are on the order of 10 kHz. As a result, FTMW is considered to be a high-resolution experiment since the transitions FWHM measurements are on the order of 5 to 10 kHz2.

Once a spectrum has been collected by the FTMW, an effective Hamiltonian fit can be determined for the molecular system by assigning quantum numbers to the system using analysis software. Within the following experiment, the software utilized was Pickett’s SPCAT/SPFIT program10. It is through these fits that the rotational constants, along with other small energy effects (centrifugal distortion, nuclear electric quadrupole coupling constants, ect.) for a particular molecule can be determined. Since the rotational constants A, B, and C are inversely proportional to the moments of inertia averaged over a vibrational state, the distribution of mass for the molecule can be found and used to determine the overall structure of the molecule12.

B. Renovations to the FTMW

As mentioned previously, one of the main reasons why undergraduate students are rarely able to gain hands-on experience within microwave spectroscopy is due to the shear cost of the instrumentation. Since Fourier transform microwave spectrometers are not commercially available, most FTMWs in operation are custom built by the research group for which they are housed. The same is true for the FTMW housed in Dr. Grubbs’s microwave spectroscopy research laboratory on the campus of the Missouri University of Science and Technology. This particular FTMW was acquired by Dr. Grubbs back in 2013 when it was decommissioned from a P a g e | 9 microwave spectroscopy laboratory at Oxford University (Brian Howard). After being reassembled on the campus of Missouri S&T, the FTMW was in operation with only minor repairs and modifications for nearly five years. However, in the summer of 2018, a power surge resulted in the loss of the main oscilloscope, pulse generator, attached computer, and heating coil on the diffusion pump of the FTMW. With only the cavity, vacuum pump, minor circuitry components, and Helmholtz coils in working condition, this misfortune was taken as an opportunity to see how cost effectively the FTMW could be rebuilt for the dual purpose of being both a research grade instrument and an educational tool.

The first step to rebuilding the FTMW was to rewire and reassemble the diffusion pump in order to bring the cavity back down to vacuum. This was a relatively simple process and only took a few days to complete. Since the heating coil had malfunctioned, all of the oil within the diffusion pump had A congealed to the inner components. Thus, the process began by detaching the diffusion pump from the chamber and disassembling its inner components for cleaning. As the parts were drying, the heating mantel was disconnected, rewired, and soldered back into place. Once everything was tested, new oil was B C Figure 4: Rebuilding the Diffusion Pump: placed within the diffusion pump and it was reattached to the a.) Reattaching the Diffusion Pump to the chamber. This allowed for the cavity to be brought back down to Chamber b.) Heating Coil c.) Diffusion Pump vacuum and for circuitry tests to commence.

The second step to rebuilding the FTMW was by far the most difficult and time consuming for it involved the rebuilding and testing of all circuitry components. The main circuity components that needed to be replaced were the main oscilloscope and pulse generator. Within the old FTMW design, the main computer served as a graphical user interface and controlled the microwave pulse sequence, stepper motor used for tuning, and acted as the main oscilloscope. Therefore, when it was lost in the power surge, it crippled all operation of the FTMW. Due to this, it was decided that the main oscilloscope and pulse generator would no longer be housed in one component as a precautionary measure to ensure that there would be no other critical failures in the future. A replacement scope and pulse generator were obtained in P a g e | 10 refurbished form from EbayTM in order to keep the cost of the instrument down. The pulse generator obtained is a Quantum Composers 9520TM series pulse generator while the oscilloscope obtained is a Tektronix TDS5054B Digital Phosphor OscilloscopeTM. Both instruments were obtained for around $2,600. Cheaper options for these components were found and would probably work if chosen and obtained, but since the FTMW was also to be used as a research instrument, the quality of the instrumentation had to also be considered.

Once all components arrived, a series of diagnostic tests were ran before they were integrated into the existing circuity setup. These included basic electronic checks and compatibility with other components. The most difficult part of the integration process was establishing the 30 MHz reference frequency with the new components, which took many hours and tests to get right. Once this was established, the entire circuit could be reassumed, and included both the main scope, pulse generator, and salvaged components seen in Table 1. In order to improve the performance of the circuit by minimizing cable loses, some circuit components were rearranged in order to cut down on the amount of dead space. A before and after diagram of the FTMW circuit can be seen below in Figures 5 and 6. Table 1: Salvaged FTMW Circuitry Components

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Figure 5: Original FTMW Circuitry Design

Figure 6: Renovated FTMW Circuitry Design

After the circuit was rebuilt, the FTMW was ready to be tested with OCS—a common molecule used in the calibration and parameterization of microwave spectrometers due to its very intense signal and multiple isotopologues. At first, OCS was difficult to observe due to the pulse generator parameters needing to be perfected and oscilloscope trigger levels not being properly set for phase stability, but once OCS was observed it signaled the completion of the FTMW renovations and allowed for the development of the laboratory exercise. P a g e | 12

C. Development of the Physical Chemistry Laboratory Once the FTMW was again operational, the opportunity arose for the second problem— the lack of quality laboratory exercises—to be addressed. It was around this time that an idea was proposed for a microwave spectroscopy laboratory to be implemented during the spring semester within the CHEM 3459: Accelerated Physical Chemistry Laboratory class. The goal was that through this laboratory students would have the opportunity to make Gaussian® calculations, accrue spectra on a research grade FTMW, and perform an effective Hamiltonian fit inclusive of nuclear electric quadrupole coupling using analysis software commonly available to the spectroscopic community. Through these three exercises, students would be able to experience for themselves the process professional microwave spectroscopists use to accrue and analyze data while gaining hands-on experience. In addition, through the corresponding lecture and supplemental readings, it was also a goal that the students become familiar with the theory and concepts present within microwave spectroscopy such as the concept of rigid rotors, momentum operators, selection rules, and quadrupole coupling.

During the development of this laboratory exercise, the first decision to be made was in regards to what molecule the students should observe. For a molecule to be considered, it had to be volatile, possess a strong dipole moment, be inexpensive to purchase and relatively safe for students to handle. After preliminary research, it was also decided that the molecule should not possess spin-spin or spin- interactions as this would complicate the analysis and prevent novice students from being able to complete the Hamiltonian fit on their own. With these requirements as guidelines, the potential molecule was originally narrowed down to the selection seen in Table 2. From this selection, it was ultimately decided that benzonitrile was the molecule of choice for it had a high vapor pressure, large dipole moment (4.3 D 12), was readily available, and safe for students to use. The benzonitrile used within this laboratory was acquired from Sigma-Aldrich®.

Table 2: Potential Molecules

Molecule Volatility Dipole Moment Cost Safety

H2O Yes Yes $0 Health: 0

Benzonitrile Yes Yes $25-$66 Health: 2 P a g e | 13

As a gas: $215 NH Yes Yes Health: 3 3 As a liquid: $20+

Acetone Yes Yes Depends on grade Health: 2

HCl (DCl) Yes Yes $352 Health:3

Benzonitrile was first observed using rotational spectroscopy in 1954, in which approximately twenty absorption lines were observed and fitted to a rigid asymmetric rotor14. During this initial study, it was determined that the A, B, and C rotational constants for benzonitrile were 5.654, 1.546, and 1.2145 GHz respectively14 and that the principle moments of inertial for benzonitrile were 89.370, 326.740, and 416.1863 amu respectively13. From this information, it was determined that benzonitrile possessed a planar structure with ring Figure 7: Structure of Benzonitrile dimensions essentially the same as in benzene13. The rotational spectrum of benzonitrile is thus expected to be characteristic of a near-prolate symmetric rotor with dipole moment in the small inertial axis13.

While the pure rotational spectrum of benzonitrile has been known for some time, there is still much to learn about the molecule. Within the last decade, cyano-benzenes—including benzonitrile—have been found in the interstellar medium within the proto-planetary nebula CRL61813. Research is currently being performed to determine if benzonitrile is present in any other regions of interstellar space and how this might apply to the formation of life. Therefore, in addition to meeting all the requirements above, benzonitrile’s rich history and continuing relevance to academic research makes it a great candidate for a potential microwave spectroscopy laboratory.

Once the molecule had been chosen, a predicted spectrum of benzonitrile was produced using previous effective Hamiltonian literature values in order to determine what frequency ranges and absorption lines the students should observe12. From the predicted spectrum, as seen in Figure 8, it was determined that the frequency range of 8 to 10 GHz provided an abundance of transitions for the students to observe and characterize. From this range, 21 transitions within 16 separate frequency ranges—containing a wide range of strong and weak transitions—were selected for observation. It was decided during the development of this lab that 21 transitions P a g e | 14 were ideal for they provided students with enough data to produce a Hamiltonian fit while also allowing the laboratory to be conducted within one scheduled class period. The 21 transitions selected can be seen below in Tale 3. For each transition measurement event, it was determined that students would set up the instrument, tune to the desired frequency, collect the spectra, and calculate the line center for each doublet observed. Each transition measurement event took on average 5-7 minutes to complete. With 16 separate transition measurements being required, it was estimated that students would take approximately 1.5 hours to complete the in-class potion of the lab, allowing for two groups of students to easily conduct the laboratory exercise per four hour laboratory period.

Figure 8: Predicted Spectrum Produced for Benzonitrile

Table 3: Transitions and Frequency Ranges Observed

Frequency Range (MHz) Lines to be Observed (MHz) 8205.43560 8205.43560 8206.56430 8206.56430 8206.82920 8282.75330 8282.75330 8284.11480 8284.11480 8284.87170 8359.82310 8359.82310 8361.17070 8361.17070 8361.93010 8361.93010 8769.78900 8769.78900 10343.8168 10343.8168 10344.8171 10344.8171 11029.5776 11030.3016 11030.3016 11080.7921 11080.7921 11082.0553 11082.0553 11085.0234 11085.0234 11219.4020 11219.4207 11219.4207 11220.0116 11220.0116 11220.01617 P a g e | 15

In addition to the in-class portion of the lab, it was decided that students would also be tasked with performing a quantum chemical calculation using the Gaussian09® software available via the intensive computational cluster known as the Forge. These quantum chemical calculations produced theoretical starting points inclusive of nuclear electric quadrupole coupling in order to provide a starting point for the students to construct an effective Hamiltonian fit of the benzonitrile molecule. To achieve this, the software was employed to optimize the geometry and of benzonitrile utilizing a modest level of theory and basis set (B3LYP/6-311G++(d,p). The front-end program of Gaussian09®, Gauss View 5.0TM, was employed to build the molecule and set up these calculations to ensure easy transference to the Forge while also providing the students with another type of experience with a familiar program employing quantum chemical calculations since they use the software in multiple previous laboratory experiments. Once the calculations were complete, students would export the findings of the calculations into Pickett’s SPCAT/SPFIT programs10 suite to analyze the spectra collected during the in-class portion of the lab and develop a proper effective Hamiltonian for their molecular assignment. Step by step directions were developed and provided to the students for both the quantum chemical calculations and transition measurement exercise portions of the lab. The entire laboratory write- up can be found within the appendix and example spectra, calculations, and fits can be seen within the following results section.

III. Results: A. Analysis of Benzonitrile: Before the laboratory exercise could be used within the physical chemistry laboratory, benzonitrile had to first be observed on the FTMW and fit using Pickett’s SPCAT/SPFIT program as a proof of concept. In order to run benzonitrile on the FTMW, a loop was created in the gas line to house the solution and was attached to an argon tank which served as the backing gas. The argon gas pulsing through the solution carried the benzonitrile vapor into the FTMW for sampling. The gas pressure was kept at a constant 17 psi for the duration of the analysis while the power attenuation was kept at 10. Using these parameters, all 21 lines were observed. The spectra were collected at a rate of 3 FIDs per second with 163 FIDS per averaging cycle. P a g e | 16

Once the spectra had been collected, a preliminary fit was created using Pickett’s SPCAT/SPFIT program10. A successful fit of the Hamiltonian was achieved, which indicated that the analysis of benzonitrile could be a viable physical chemistry laboratory. Below the intensity, line, parameter, and variable files that were used for the Hamiltonian fit are shown below as well as the resulting fit file. Within Pickett’s program, the intensity file is used to denote the molecule dipole moments, the line file is used to input measured spectral lines, and the parameter and variable files are used indicate the desired parameters to be used within the Hamiltonian fit or variables to be used for a prediction. The output file produced through the analysis is the fit file which shows the determined Hamiltonian fit and RMS values.

Figure 9: Intensity File Used Within the Preliminary Fit

Figure 10: Line File Used Within the Preliminary Fit

Figure 11: Parameter File Used Within the Preliminary Fit P a g e | 17

Figure 12: Variable File Used Within the Preliminary Fit

Figure 13: Fit File Produced Within the Preliminary Fit

B. Student Response to the Laboratory: Once the proof of concept was deemed a success, the rotational spectroscopy laboratory exercise was approved for use within the spring CHEM 3459: Accelerated Physical Chemistry Laboratory course. The exercise was run as the course’s lab 7 during the weeks of March 14th through April 10th, 2019. In total, eighteen students broken up into eight groups performed the laboratory exercise during the four week rotation. At the end of each laboratory, the students were required to turn in a written report which included the data collected in lab, their quantum chemical calculations, and Hamiltonian fits to be graded. At the end of the four weeks, the students were also asked to fill out a brief anonymous survey about their opinion on the lab and any changes they would make. As of April 17th, 2019, six of the eighteen students had filled out the survey. An overview of the results can be seen below in Figure 14. Within the survey, a ‘1’ P a g e | 18

was used to indicate a response of ‘great’ and ‘5’ was used to indicate a response of ‘poor’. The entire survey and responses can also be found within the appendix.

Figure 14: Results from Student Survey

IV. Discussion: During the spring 2019 Chem 3459 laboratory course, eighteen students had the opportunity to perform the rotational spectroscopy laboratory presented within this thesis. This group of students was predominantly made up of third and fourth year undergraduates, whom had a diverse chemistry background with emphasis ranging from biochemistry to analytical chemistry. While this was not planned, the diversity in chemistry backgrounds gave us the opportunity to compare how students with different fields of interest responded to the exercise. As a result, this provided a way to determine if the laboratory exercise was suitable for all chemistry undergraduates and not just those already interested in physical chemistry. From the P a g e | 19 feedback generated from the student survey, the overall response to the laboratory was positive. In fact, all students who participated within the survey indicated that they believe this laboratory exercise should continue to be offered in the future. In addition, no overall trends based on emphasis area—such as the ability to grasp the concepts presented in the lab or interest in the topic—can be seen. Thus, it was determined that while there are some improvements to be made, the laboratory exercise as a whole was suitable for all chemistry undergraduates.

Overall, the number one thing the students enjoyed most about the laboratory was the hands-on experience they were able to obtain. From the responses received, it appears that before this laboratory, many students had not had the opportunity to gain hands-on experience with either microwave spectroscopy or large scale benchtop instrumentation. While many chemistry courses offer students the opportunity to learn about various instrumentation, students rarely have the chance to operate such instrumentation beyond simply inserting the sample into the instrument and watching as the teaching assistant performs the rest of the analysis. However, in this laboratory, the students were the ones responsible for tuning and operating the instrument with help from the teaching assistant only when needed. This made the students feel as if they were learning practical skills instead of simply following instructions. As a result, this laboratory helped fill an important void they deemed currently missing within their undergraduate education.

However, while the overall attitude towards the laboratory was positive, there were also a few areas the students indicated needed improvement. The main area in need of improvement was the analysis section in which the students were tasked with constructing an effective Hamiltonian inclusive of nuclear electric quadrupole coupling for transition assignment using Pickett’s SPCAT/SPFIT programs10. The biggest complaint the students had with this was the learning curve associated with the programs. Since the vast majority of students had never used these programs prior to this course, many struggled to understand how to operate the programs in order to generate the results needed, even with instructions provided to them. In order to help curb this problem in the future, they requested clearer instructions be written for the students to follow and possibly an example analysis during the laboratory lecture. Another option proposed was to exchange Pickett’s SPCAT/SPFIT programs out for a simpler program. However, this would go against the purpose of this laboratory exercise which was to expose the students to P a g e | 20 instrumentation and programs used within actual rotational spectroscopy research. A conversation regarding this problem was had prior to the development of this exercise and it was determined that while there is a learning curve associated with SPCAT/SPFIT, the experience the students would receive by working with these programs was too great to replace it with a simpler program.

Another area in need of improvement is the disconnect between the main concepts presented in the laboratory and the students’ ability to grasp them. According to the survey, only a few students felt that they were able to grasp the concepts presented in the laboratory well with the majority of students feeling lost or neutral on the subject. Some factors that potentially played into this could be the learning curve associated with the programs and the fact that the majority of the students were currently in the process of taking the quantum chemistry course from which many of the concepts are derived. One possible solution to this is to extend the laboratory exercise over two class periods in order to provide more lecture Figure 15: Undergraduate Students Performing time to cover the background material. However, with a Laboratory limited number of class periods per semester, this most likely would not be possible. Instead, the more likely solution would be to provide the students with additional reading material on the subject in order to prepare them better for the laboratory.

As mentioned in the beginning of this thesis, the main goal of this project was to create a laboratory exercise that solved the two problems currently facing undergraduates from being able to obtain hands-on experience within the field of rotational spectroscopy. These two problems were the shear cost of the instrumentation and the lack of quality laboratory exercises on the subject. From the students’ responses and the success of the laboratory exercise over the four week period, it appears that the laboratory exercise was at least partially successful in creating a quality experience for learning and performing experiments pertaining to the subject of rotational spectroscopy. However, in regards to the cost of the instrumentation, it has yet to be determined if this project has had any effect on that particular problem. While the renovation to the FTMW P a g e | 21 was able to be completed for roughly $3,000, the majority of the instrumentation—such as the main cavity, vacuum pump, and space to house the instrument—was already available to us. As a result, any academic institution currently without a FTMW that would be interested in performing this exercise would encounter a substantially higher cost than what was presented here. Therefore, the next great challenge to be tackled in order to provide all undergraduates with an opportunity to gain experience within rotational spectroscopy would be to develop a more cost effect FTMW for teaching purposes utilizing equipment and/or platforms that (a) available on-hand at most university sites or (b) can be purchased at minimum cost due to the continual drop in pricing of common microwave and radiofrequency components. An example of this being to incorporate the GPS signal as a clock reference instead of our 10 MHz clock as that is free for everyone to use.

V. Conclusion: The aim of this project was to develop a solution to the problems currently preventing undergraduates from obtaining hands-on experience within rotational spectroscopy. In response to this, a laboratory exercise involving the analysis of benzonitrile with a newly renovated Balle- Flygare type, Fourier Transform microwave spectrometer (FTMW) was introduced as one such solution. Within this laboratory exercise, students had the opportunity to perform quantum chemical calculations for accurate molecular structure, accrue spectra on a research grade FTMW, and construct an effective Hamiltonian inclusive of nuclear electric quadrupole coupling for transition assignment using analysis software commonly available to the spectroscopic community. While the renovations to the FTMW did not completely solve the problem of the instrumentation’s cost, but, rather, mitigated it, the laboratory itself provided a quality exercise for students to experience all aspects of rotational spectroscopy research. In addition, based on the student responses, it can be determined that more laboratory exercises like the one presented are currently needed. However, in order to provide equal opportunities for undergraduates across all institutions, the next challenge to be faced is the development of a more cost-effective FTMW for teaching purposes. The hope is that one day undergraduate students at any university would be able to gain hands-on experience within rotational spectroscopy and discover their passion for physical chemistry. P a g e | 22

References:

1. Walker, N. R. 2007, Phil. Trans. R. Soc., 365. 2813 2. Balle, T.J.; Flygare, W. H. 1981, Rev. Sci. Instrum., 52(1). 33 3. (2019). Research Groups in Rotational Spectroscopy. Retrieved from: http:// www.ifpan.edu.pl/~kisiel/rotlinks.htm 4. (2015) ACS Guidelines and Evaluation Procedures for Bachelor’s Degree Program. Washington, D.C.: American Chemical Society 5. Duerden, A. J.; Moon, N.; Grubbs, G. S. J. Chem Ed. (in prep) 6. Campbell, E. J.; Buxton, L. W.; Balle, T. J.; Keenan, M. R.; Flygare, W. H. 1981, J. Chem. Phys., 74(2). 829 7. Balle, T. J.; Campbell, E. J.; Kennnan, M. R.; Flygare, W. H. 1979, J. Chem. Phys., 71(6). 2723 8. Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. 1980, J. Chem. Phys., 72(2). 922 9. Ekkers, J.; Flygare, W. H. 1976, Rev. Sci. Instrum., 47(4). 448 10. Novick, S.E. 2016, J. Mol. Spec., 329. 1 11. Campbell, E. J.; Buxton, L. W.; Balle, T. J.; Flygare, W. H. 1981, J Chem. Phys., 74(2). 813 12. Wohlfart, K.; Schnell, M.; Grabow, J. U.; Küpper, J. 2008. J. Mol. Spec., 247. 119 13. Lide, D. R. 1954, J. Chem. Phys., 22. 1577 14. Eriandsson, G. 1954, J. Chem. Phys., 22. 1152

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Appendix:

Laboratory Experiment #7: The Microwave Spectroscopy of Benzonitrile This laboratory procedure was written by Nicole Moon in partial fulfillment of graduation requirements for the Missouri S&T Honors Academy.

INTRODUCTION For a chemist, one of the most powerful tools available to observe molecular behavior is spectroscopy. As many students have probably learned before, spectroscopy is a branch of science concerned with the study and measurement of spectra produced when matter interacts with or emits electromagnetic radiation. There are many forms of spectroscopy: infrared absorption, UV-Vis, and nuclear magnetic resonance to name a few. Within this laboratory, a form of molecular spectroscopy—rotational spectroscopy—will be explored. Rotational spectroscopy is a powerful tool that utilizes changes in rotational energy in order to arrive at physical constants that can be used to determine the molecular structure of gas phase molecules. Other applications of rotational spectroscopy include determining electronic structures, investigating fundamentals of molecular physics, and establishing barriers to internal rotations. In this lab, you will be taking the rotational spectrum of benzonitrile. The molecule will be introduced into a Fourier transform microwave (FTMW) spectrometer using a gas mix of the sample’s vapor and a carrier gas. The corresponding spectra gathered will then be analyzed to obtain molecular information about benzonitrile. A. Rotation of Rigid Rotors In order to grasp the fundamentals of rotational spectroscopy, one must first understand the basic principles of molecular rotation. This begins with the classical expressions for the and rotational energy of molecular rotors. All molecules have three nuclear degrees of freedom: translational, rotational, and vibrational. The simplest molecular system which possesses rotational motion is a , which can be thought of as a . A rigid rotor can be visualized as two spheres connected by a solid rod. The axis of rotation for the rigid rotor is perpendicular to the plane of rotation and passes through the rotor’s center of mass. In a sense, the rigid rotor can be said to be equivalent to a single mass moving on a ring with a fixed radius, which is equal to the bond length between the atoms. The single mass can be expressed by using the reduced mass formula where m1 and m2 are the respective masses of the two atoms

(푚 푚 ) 휇 = 1 2 . (1) (푚1+푚2) [2]

The origin of the coordinate system is chosen as the center of mass so that the total kinetic energy can be written as the sum of the kinetic energy of translational motion and the kinetic energy of the motion relative to the center of mass. Thus, the translational and rotational motions can be treated separately. Before the rotational kinetic energy can be derived, the classical angular momentum of a rigid systems must first be defined, which can be written as: 푃 = 퐼 ∙ 휔 (2) where ω is the angular velocity and I is the . When the rotation on x, y, and z-axis represent the principal axes system (referred to as a, b, and c), the components of angular moment then become:

푃푥 = 퐼푥휔푥 (3)

푃푦 = 퐼푦휔푦 (4)

푃푧 = 퐼푧휔푧 (5) From this information, the rotational kinetic energy can now be derived as:

2 2 2 1 1 2 1 2 1 2 1 푃푥 1 푃푦 1 푃푧 퐸푟 = 휔 ∙ 퐼 ∙ 휔 = 퐼푥휔푥 + 퐼푦휔푦 + 퐼푧휔푧 = ( ) + ( ) + ( ) (6) 2 2 2 2 2 퐼푥 2 퐼푦 2 퐼푧 The kinetic energy has a similar form to that of linear motion with the moment of inertia and the angular velocity taking on the roles of mass and linear velocity. When no torque is applied to the 2 2 2 system, the kinetic energy of rotation remains constant, or, in other words, 푃푥 + 푃푦 + 푃푧 = 푐표푛푠푡푎푛푡 = 푃2. In addition, with no forces opposing the rotation, only kinetic energy can be stored within the rigid rotor system. The centripetal acceleration of the system can thus be expressed as

|푣(푡)|2 훼 (푡) = (7) 푐푒푛푡푟𝑖푝푒푡푎푙 푟 where v(t) is the system’s velocity and r is the distance between the two atoms, or bond length. In the discussion thus far, molecules have been treated as rigid rotors, consisting of two or more atoms connected to opposite ends of a solid rod. Within this model, the distance between the atoms does not change while the molecule rotates. However, a more accurate representation could be visualized as two atoms connected to opposite ends of a spring. Thus, the will distort as the molecule rotates, which in turns effects the molecule’s moment of inertia. This distortion of the molecule is known as centrifugal distortion and results in the lengthening of molecular bonds and an increase in the moment of inertia. This ultimately contributes to a reduction in the rotational constant of the molecule and causes the rotational energy levels to be slightly closer together than the rigid rotor model would predict. To account for centrifugal distortion, a constant known as the centrifugal distortion constant (D) is used within the calculation of rotational energy levels. The centrifugal distortion constant is defined as [3]

ℎ3 퐷 = (8) 32휋4퐼2푟2푘푐 where h is Plank’s constant, I is the moment of inertia tensor, r is the bond length, k is the Boltzmann constant, and c is the . B. Angular Momentum Operators Now that the fundamentals of rotation have been discussed, it is time to introduce the concept of angular momentum operators. In order to describe the characteristic energy levels of a system required for finding microwave spectral frequencies, the eigenvalues of the Hamiltonian operator for rotational motion must be known. Hamiltonian operators are mathematical expressions used to describe the total energy of a system. The eigenvalues of the Hamiltonian operator can usually be expressed in terms of the angular momentum operators, which will be derived here. In this case, the classical angular momentum of a system of particles can also be expressed as:

푷 = ∑푛 풓푛 × 풑푛 (9) th where pn is the instantaneous linear momentum of the n particle and rn is its radius vector from the center of rotation, which is assumed to be fixed in space. To derive the corresponding quantum mechanical angular momentum operators, one ℏ 휕 substitutes the relations X → X and px→ ( )( ), and repeats the process for both y and z. Thus, 𝑖 휕푥 the components of the angular momentum operator can be expressed as:

ℏ 휕 휕 푃 = ∑ ( ) [푌 ( ) − 푍 ( )] (10) 푥 푛 𝑖 휕푧 휕푦

ℏ 휕 휕 푃 = ∑ ( ) [푍 ( ) − 푋 ( )] (11) 푦 푛 𝑖 휕푥 휕푧

ℏ 휕 휕 푃 = ∑ ( ) [푋 ( ) − 푌 ( )] (12) 푧 푛 𝑖 휕푦 휕푥 The Hamiltonian operator for angular momentum can then be obtained from the classical Hamiltonian when the momenta are replaced by their conjugate operators. When no torque is applied, the classical Hamiltonian of the rigid rotor consists only of kinetic energy which can be expressed in terms of the angular momentum operators in the principal axes. Thus, the Hamiltonian can be expressed as:

2 2 2 ℋ = 푃푥 + 푃푦 + 푃푧 (13) C. Rotation and Angular Moment Operators for Asymmetric Molecules While rigid rotors are useful to explain the fundamental principles of rotation, molecules are not rigid. In addition, most molecules are not linear. Instead, most molecules—including benzonitrile—fall into the category of asymmetric top molecules. For a molecule to be considered an asymmetric top, all three of its principal moments of inertia must not be equal to zero and no two moments of inertia may be equal. For an asymmetric rotor there is also no internal component of the angular momentum that is a constant throughout the motion. As a [4] result, considerable complexity is encountered in analyzing the pure rotational spectrum of these molecules. However, the discussion here will be kept as simple as possible. To begin, one can describe the behavior of the asymmetric rotor in terms of Ray’s asymmetry parameter, 휅, defined as:

2퐵−퐴−퐶 휅 = . (14) 퐴−퐶 휅 is a measure of the molecule’s asymmetry and where A, B, and C are the rotational constants with respect to the a, b, and c axes. In asymmetric molecules, the a-axis corresponds to the axis running through the most amount of mass within the molecule while the c-axis corresponds to the axis running through the least amount of mass. As a result, it is typically noted that A>B>C. The limiting values of 휅 are -1 and +1, which correspond to prolate symmetric tops (which are shaped like footballs) and oblate symmetric tops (which are shaped like disks). For a purely asymmetric top, 휅 = 0. In general, the problem of rotation for an asymmetric rotor is treated in terms of a Cartesian axis system tied to the molecule such that its origin is located at the center of mass. When the axis system is constructed in this way, it is referred to as the principal axis system, defined by the principal axes of inertia a, b, and c mentioned above, and these correspond to the rotational constants A, B, and C as detailed in the following paragraph. Following the same principles as those outlined for the symmetric rigid rotor, the quantum mechanical Hamiltonian describing the rotation of a rigid asymmetric body can thus be defined as:

2 2 2 ℋ = 퐴푃푎 + 퐵푃푏 + 퐶푃푐 (15)

ℎ2 ℎ2 ℎ2 where 퐴 = 2 , 퐵 = 2 , and 퐶 = 2 . It is often a common practice to express rotational 8휋 퐼푎 8휋 퐼푏 8휋 퐼푐 spectroscopic constants in units of megahertz (MHz). Thus, A would be expressed as 퐴 = 5.05376∗105 2 , and likewise for B and C. 퐼푎 (푎푚푢−Å ) Unlike the symmetric rotor Hamiltonian, the Hamiltonian for an asymmetric rotor is such that the Schrödinger wave equation cannot be solved directly. Thus, a closed general expression for the asymmetric rotor wave function is not possible. However, the wave functions can be represented by a linear combination of symmetric rotor functions. Though, for simplicity’s sake, the discussion regarding asymmetric rotors will stop here. For students wanting a more complete explanation than what is provided here, it is suggested that you refer to any physical chemistry or quantum chemistry textbook. D. Selection Rules A vital part of spectroscopy is the concept of selection rules, which dictate how the spectra is 푚푛 produced. For most , the for the transition dipole moment (휇푥 ) can be derived from the equation [5]

푚푛 ∗ 휇푥 = ∫ 휓푚 (푥)휇푥(푥푒 + 푥)휓푛(푥)푑푥 (16)

where x is the vibrational amplitude, µx is the dipole moment along the electric field direction, and Ψm /Ψn are the respective wavefunctions of the molecule in question. Within rotational spectroscopy, for a molecule to absorb microwave radiation and have a , the molecule must have a permanent . Thus, it can be 푚푛 concluded that an allowed transition must have 휇푥 ≠ 0 and, therefore, selection rules rendering a nonzero value can be established. For simplicity sake, this will not be derived here, but can be found in many physical chemistry text books. The permanent electric dipole moment is a vector quantity that can be broken into components along the principal axes and these components are referred to as µa, µb, and µc. The transitions due to a change in µa are known as “a-type” transitions, those due to a change in µb are known as “b-type” transitions, and likewise, those due to a change in µc are “c-type” transitions. The presence of different types of transition for asymmetric rotors, although at times can be complex, can also be advantageous. For example, this information can be of great aid in distinguishing the conformational isomers of a molecule and in the assignment of the spectrum. This will be demonstrated further within this lab. As for selection rules specific to rotational spectroscopy, the rotational transitions observed will follow the selection rule of ∆J = Jfinal - Jinitial = -1,0, +1 for asymmetric rotors, where J is the rotational molecular angular momentum quantum number in the initial and final rotational states of the molecule. The dependence of a given rotational on the quantum number J is given by:

ℏ2 ℎ2 퐸 = 2 퐽(퐽 + 1) = 2 2 퐽(퐽 + 1) = ℎ푐퐵퐽(퐽 + 1) (17) 2휇푟표 8휋 휇푟0 In this equation, the constants specific to a molecule are combined into the rotational constant B. The energy corresponding to a rotational transition is thus:

∆퐸 = 퐸퐽(푓𝑖푛푎푙) − 퐸퐽(𝑖푛𝑖푡𝑖푎푙) (18) It is also important to note that due to the of ∆J = -1,0,+1 selection rule the R-branch and corresponds to a ∆J = +1 transitions, the P-branch and corresponds to ∆J = -1 transitions, and the Q-branch corresponds to ∆J=0. Each of these corresponds to specific types of relationships of A, B, and C which is beyond the scope of this lab and will be provided to you.

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E. Fourier Transform Microwave Spectroscopy For this lab, a Fourier transform microwave spectrometer (FTMW) will be utilized to collect the rotational spectrum of benzonitrile. Traditionally, an FTMW is comprised of three main systems, which include a source for sample introduction, a cavity, and a circuit. Samples are injected into the FTMW through a gas mix that enters the system via a pulsed molecular beam nozzle. From here, the sample is introduced into the cavity, which consists of two mirrors situated inside a vacuum chamber. A circuit—comprised of a pulse generator, amplifier, antenna, detector, and a scope—is then utilized to generate microwaves to stimulate the sample, tune to a desired frequency range, and detect the resulting molecular signals. Pieces of this system will be discussed in detail below and an image of the FTMW that will used within this lab is presented in Figure 1. Figure 7: FTMW utilized in Dr. Grubbs's Research Lab Within this experiment, benzonitrile will be introduced to the FTMW using a gas mix of the sample’s vapor and a carrier gas. In general, the sequence of operations performed by the FTMW to obtain a desired spectrum begins with pulsing the gas sample into a vacuum chamber via a molecular beam nozzle. This pulse of gas allows a large number of molecules to adiabatically expand into the vacuum thereby achieving very low rotational temperatures. Through this process, the molecules lose energy and collisions between molecules become less frequent to the point that they are essentially collision free. In addition, the pulse of gas is deliberately kept on a short time scale in order for equilibrium expansion properties to be rapidly achieved. There are a few advantages of using a pulsed nozzle source as compared to a continuous source. For example, if N number of particles can be pumped into the cavity during a long-time t, then the observed signal to noise ratio (S/N) for period of time t would be proportional to 푁/√푃, where P is the number polarizing microwave pulses generated over time t. However, if instead all N particles are pulsed into the cavity in a short time such that only one polarizing pulse is generated during time t, the S/N would be proportional to N. As a result, the signal to noise ratio can be greatly increased by simply using a pulsed nozzle set up. After entering the vacuum, the particles are directed between two mirrors, which make up the cavity. One of these mirrors is permanently held fixed, while the position of the other mirror can be tuned to make small adjustments to the frequencies being observed. When searching for unknown molecular lines, an additional step consisting of stepping the cavity mirror separation must be performed in order to adjust its resonance frequency and alignment with the microwave oscillator. Since the cavity band width is around 1 MHz, the step sizes are generally 500 kHz or less. This process is generally referred to as “tuning to a mode” and will be demonstrated within this laboratory. [7]

Once the molecules are positioned within the chamber, they are then exposed to a microwave pulse applied to the cavity through an input coupling (antenna) position at the center of one mirror. Typically, one microwave pulse interacts with the molecules in the free expansion, and the next microwave pulse interacts with the evacuated chamber due to the continuous pulsing of the sample. Before the microwave pulse, the molecule’s dipole moments are arranged in a random order. However, the microwave pulse polarizes a band frequency that may contain one of the resonant transitions in the molecules. Thus, after the pulse, the dipoles of the molecules are then aligned in a uniform direction, resulting in a macroscopic polarization of the molecules. Once the microwave disappears, the molecules fall back into their previous relaxed and diverse alignments. This results in the polarized gas coherently emitting at its resonant frequency. This decay in the polarization over time, or the free induction decay (FID) of the molecules, can be recorded by a detector within the chamber (antenna). These signals are then Fourier transformed to give the desired spectrum. An FTMW is typically utilized to study stable, transient, or short-lived molecular species with transitions within the microwave region of 1 GHz to 40 GHz. Most rotational measurements are made on gaseous absorption lines having widths ranging from a few kilohertz to a few megahertz. The natural width of a molecular line may be considered to arise from the Heisenberg Uncertainty principle and the probability of spontaneous emission. FTMW experiments actually do NOT measure absorption or emission spectra, but rather resonance spectra similar to nuclear magnetic resonance (NMR). In fact, FTMW spectroscopy is the electric analogue of NMR and utilizes many of the same equations by leveraging the electric field instead of a magnetic field. This way of performing the experiment both increases sensitivity AND resolution providing ppt sensitivity and 1 kHz resolution. Thus, the linewidths of FTMW are on the order of 10 kHz. This concepts will be demonstrated further within the following lab. EXPERIMENTAL PART 1: QUANTUM CHEMICAL CALCULATIONS This part can be performed before or after the experimental section, but make sure Part 2 is finished before you leave the scheduled laboratory time as that part takes precedence. For this section you will set up calculations to determine the geometric and thermodynamic properties of benzonitrile. You will need to refer to your handouts and training on setting up Gaussian calculations in order to submit to the cluster and carry out the calculations as desired. In this experiment, you will perform only one quantum chemical calculation. For this calculation, you will be using the basis set B3LYP and the sub-basis set 6-311G++ (d,p). The B3LYP basis set is referred to as DFT or density functional theory because it assumes a functional form and makes a calculation based on that. The details of these calculations aren’t important here, it is just useful to note that different methodologies will produce different results and utilize different computational time costs. Use GaussView 5.0TM to construct the benzonitrile molecule. An example is shown below: [8]

Benzonitrile

Once constructed, in GaussView you will go to Calculate → Gaussian Calculation Setup. This should open up a window with many tabs with the “Job Type” tab preselected. In the dropdown menu under that tab, select Optimization. When this is selected the “Keyword” line will change to show the addition of “opt.” Leave the default settings as is and move on to the next tab, “Method.” B3LYP method and Basis Set Example Select “DFT” from the second dropdown menu to the right of the word “Method.” Make sure that B3LYP is the selected DFT type. After that, change the Basis Set to 6-311G++ (d,p) using the first dropdown menu to the right of “Basis Set”. In addition, select “++” in the drop down menu directly to the right of the” 6-311G” setting. In the parenthesis’s dropdowns select “d” for the first one and “p” for the second. Leave everything else in the default and move to the tab “Title.” Under the “Job Title” field, name the job “Benzonitrile B3LYP 6-311G++ (d,p).” In the “Additional Keywords” toward the bottom of the window, type “output=pickett” and click “Update.” After the title and additional keywords are added, click the “Submit…” button at the bottom of the window. A window will pop up asking you to save the job, click “Save.” Place the file in a calculations folder and name it “lab7_benzonitrile_B3LYP_6311G.gjf”. Make sure the “Write Cartesians” box is checked. After this, click “Save”. After clicking “Save”, the program will prompt you to submit the following file to Gaussian. This would normally connect you to a windows version of Gaussian which we do not have. Click cancel and follow the next few steps to prep your file and run it on the cluster. Close the GaussView 5 program. Open the putty window on your computer to log onto forge.mst.edu. Enter name and password. Make sure you have a folder on the cluster named Gaussian, calculations, etc. You can check this by sending the command ls and hitting enter at the prompt. Type cd foldername and press ENTER to access the file. Move your file into the folder using WinSCP and logging in the same way as you do to the putty window (this was done at the beginning of the semester). Replace the first line of the file to the following:

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%mem=2GB %RWF=/state/partition1/tmp/ %Int=/state/partition1/tmp/ %D2E=/state/partition1/tmp/ %Scr=/state/partition1/tmp/ %chk=benzonitrileb3lyp6311g.chk Save the file and we are ready to run the job. Use the information below for the scripting. Just change the input and output names at the bottom to the desired filename and click the disk (Save) at the top left-hand corner. The file should look something like this: #SBATCH --job-name=benzonit #SBATCH --ntasks=4 #SBATCH --mem=4000 #SBATCH --nodes=1 #SBATCH --time=1-10:10:00 #SBATCH --export=all #SBATCH --out=Forge-%j.out module load gaussian g09 < lab_benzonitrile_b3lyp_6311g.gjf > lab_benzonitrile_b3lyp_6311g.out To submit the job, make sure you are still in your file on the cluster in the putty window. At the command prompt type sbatch batchguassian.sub and hit ENTER. The cluster will look nonresponsive for a short period and then return with your job number as part of the descriptor. To check if you are running type qstat and hit ENTER in the command prompt (use qstat –u username to limit it to only you). You should also get an e-mail when your job starts and finishes. When you are done with the putty window, log out by typing “exit” in the command line and pressing ENTER.

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PART 2: MICROWAVE SPECTROSCOPY EXPERIMENT Step 1: Tuning to a Mode Use the figures found below as a guide for the laboratory procedure. The items of importance are labeled.

Tuning Scope

Power Box (Big Blue Box)

Ion Gauge Main Scope

Anritsu

Microwave Generator

Figure 2: Overview of FTMW Setup As you begin the lab, you will first need to setup the FTMW to be able to tune to a mode, or a resonance frequency where all tangential electric fields in the cavity are zero. When viewed with the tuning scope, these will look like Gaussian peaks. First, you will turn on the two scopes. The main scope should already be on, while the tuning scope will be turned on by pressing the square button on top of the instrument. From here, you will turn on the ion gauge—which measures the vacuum pressure—by flipping the bottom switch on the ion gauge box. Next, you will turn on the three power supplies, making sure the supply labeled ‘LNA’ is set to 15 V, the

Power Power Switch Buttons

Figure 3: Power Supplies Figure 4: HP Microwave Generator [11]

one labeled ‘Cooler’ is set to 12 V, and the one labeled ‘Power’ is set to 12 V as well. This should already be done for you but is easy to check. Next, you will need to switch on the HP Microwave generator (underneath the big blue box). To do this, simply flip the switch in the bottom left-hand corner from standby to on. Verify that it reads 30 MHz of continuous wave at the top right-hand corner. If it is set to continuous wave, it will show “CW” before the frequency. Additionally, check that the power cord in the front of the large power box (the big blue box) is firmly plugged in. After this, the pulse generator will need to be set up for tuning, which is the top black box near the refrigerator (See figure 5 below) First, turn on the pulse generator by pressing the power button on the top right-hand corner. Once it is on, you will recall the settings used for tuning. To do this, press the function button (yellow button) and look for the music note in the top left brackets on the display screen. Once it appears, press the recall button (#9 on the key pad). Using round knob, scroll until ‘7’ is the function to be recalled and hit the recall button again. If this was successful, you should see ‘Configured Recall’ on the bottom of the screen. After this, check to make sure the music note has disappeared. If it has not, press the function button again. The pulse generator has now been set up for tuning.

Channel A Power Button

Music Note (if activated) Round knob

Next (move between settings) Recall Button

Run/Stop

Function Button

Figure 5: Pulse Generator Set-up Once the pulse generator is ready, the last instrument that needs to be set up is the Anritsu Microwave Generator. Turn on the Anritsu by pushing the button in the bottom left-hand corner. Verify that the green light next to the word ‘operate’ has come on. To look for modes, the Anritsu needs to be set to analog sweep mode. Do this by pressing the second dark grey button from the left along the horizontal button row. The words ‘Analog Sweep’ should appear indented when activated. From here, you will need to input the frequency to be examined. This can be done by first selecting ‘Edit F5’ by pressing the first dark grey button from the top along the vertical button row. The frequency entered needs to be the target frequency minus 30 MHz due to the fact that a 30 MHz signal is used as a reference frequency by the FTMW. (Please see list at [12] the end of this procedure for the full set of frequencies your group will be examining.) For example, if the target frequency is 8205.4356 MHz, you will use the number pad to enter 8.175453 GHz, which is the target frequency minus 30 MHz and converted to GHz. Next, you will need to change dF to 100 MHz (0.1 GHz as seen on the screen). This can be done by selecting ‘Edit dF’ by pressing the second dark grey button from the top along the vertical button row. Then, use the key pad or round knob to enter 100 MHz if it isn’t already the set value. While tuning, you may need to change the dF value either higher or lower to zoom in or out on respectively on the modes in order to perfectly center them. To continue, set the level to -10 dBm by pressing the button labeled ‘Level’ and entering the desired value. Finally, make sure the trigger value is set to auto by pressing the fourth dark grey button from the top along the vertical button row.

Edit F5

Edit dF

Level Button Analog Sweep Button

CW Button Trigger

Figure 6: Anritsu Microwave Generator After this is completed, you are ready to tune the cavity to a proper mode. To generate the modes, switch the Anritsu to output (button on the top right-hand corner; the light should turn green when engaged) and press Run/Stop on the pulse generator (bottom right-hand corner). You should now see something resembling ‘peaks’ on the tuning scope’s screen. With help from the TA, tune to the right most mode in the group by centering it in the middle of the screen. You can do this by having one person slightly turn the rod at the back of the instrument while another watches the scope (See Figure 7). By turning the rod, you are moving the position of the mirrors within the FTMW. Be sure to turn the rod slowly and gently since even the slightest movement can have a large impact on the position of the modes. To move the modes right, turn the rod clockwise. To move the modes left, turn the rod counterclockwise. Once it is centered, zoom in by changing the dF value to 50 MHz (0.05 GHz) then 10 MHz (0.01 GHz) then 1 MHz (0.001 GHz) to make sure it is truly centered. If the peak becomes off centered, turn the rod at the back of the instrument to correct the change.

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Tuning Rod

Figure 7: Rod for Adjusting potion of Mirror Step 2: Collecting the Spectra Once the instrument is tuned, it will need to be set up to run. First, the Anritsu will need to be switched to continuous source. To do this, ‘Run/Stop’ and Anritsu’s output needs to be turned off for safety. Once that is done, you will change the level value on the Anritsu to +10 dBm by following the steps above. Next, on the pulse generator, you will recall the run function by pushing function → recall #9 → setting 3. Remember to check to make sure that the music note has disappeared before moving on. Afterwards, open the Argon tank next to the FTMW and verify the regulator is set to roughly 17 psi. Also, check that there is a decent amount of benzonitrile in the coiled loop between the Argon tank and the nozzle (this should already be done for you but should be checked). The instrument is now ready to collect spectra. Once this is completed, you should turn back on the Anritu’s output and ‘Run/Stop’. When these are turned on, gas will start pulsing into the chamber, which can be verified by watching the pressure value change on the ion gauge reading. One person should check to make sure no benzonitrile is being pushed out of the loop and entering the chamber when the gas first begins to pulse. To do this, simply watch the benzonitrile for a few moments after the gas begins to pulse. If it is escaping the loop, turn down the pressure on the argon tank regulator. Once this is completed, it is time to officially collect the spectra. On the main scope, click on the ‘single sequence’ button on the right side of the screen to begin collecting data. The scope will then collect 163 acquisitions, or snap shots, of the data. When it is done running, it will display an average of the data on the main screen. If all goes as planned, you should see at least two peaks on the screen similar to what is shown Figure 8. Each line observed should have two corresponding peaks due to splitting. If you see something similar to Figure Figure 8: Example Spectra [14]

7, use the vertical cursors to determine the center of the line you just measured. Do this by placing the vertical cursors over the peaks you acquired by simply clicking and dragging them. Make sure they are centered by zooming into the spectra until you can see the peaks clearly. This can be done by right clicking on the mouse and dragging over the desired area to be zoomed in on. A series of options should appear when you let go of the mouse. Click on ‘zoom 1’ → ‘resize’. Once you have the vertical cursors centered on top of the two peaks (one on each), add together f1 and f2 seen in the top right corner of the screen. Now divide this number by two and add it to the frequency inputted into the Anritsu. This will give you the frequency of the line you are observing. If there are more than one set of peaks in the spectra, take the line center of all and record them in your notebook. If you do not see any peaks, please consult the TA to determine what may be the problem. After determining the line center for each set of peaks, make sure to save your data so that you can assign the spectra later. This can be done on the main scope by going to File → Save As → Waveform → Options. At this point, verify that the source is Channel 1, data destination is Spreadsheet CSV, the waveform data range is All, and Frames is 164 to 164. Press OK once this has been verified. Then name the file with your group number and frequency, place it in the appropriate class folder, and press save. Before you save, verify that your file is being saved as a CSV file. If it is not set as a CSV file, ask your TA for assistance. You have now completed the steps for acquiring one frequency range. Repeat the steps for tuning and collecting spectra for all frequency ranges assigned below.

Frequencies to be Measured (MHz) 8205.4356 8206.56430 8282.75330 8284.11480 8359.82310 8361.17070 8361.93010 8769.78900 10343.8168 10344.8171 11030.3016 11080.7921 [15]

11082.0553 11085.0234 11219.4207 11220.0116 CALCULATIONS AND ANALYSIS We will be using Pickett’s SPFIT/SPCAT program suite1 in order to make transition assignments and develop a proper effective Hamiltonian for our molecular assignment. You will need a Windows machine in order to do this part of the lab. This will take some time, so please budget time in your lab report preparation for these analyses!!! To prepare for this, copy the starting input files benzostart.par, benzostart.var, benzostart.lin, benzostart.int, and the programs spfit.exe and spcat.exe from the electronic course program into a singular folder on your computer. Now we will move on to our calculation of benzonitrile. Once the calculation is finished, open up your output file text (you can use WinSCP or Wordpad® or GaussView® under Results→View File) and go to the very bottom. There should be a section denoted by dashed lines that was generated from your output=pickett keyword. Copy the space in between the dashed lines - NOT the dashed lines – and paste it into your .par and .var files. You can open these files with a text editor like Notepad®. Change the fifth value on the third line from 0 to 30. Then save these files and close them. Now scroll up your file slightly above the top dashed line and look for the “Dipole moment” heading. What is reported on this line is the vector components, µa, µb, and µc, along with the total vector. Open your .int file and type in the first calculated value after 1, second after 2, and third after 3 going to the hundredths digit. Save the file and close it. You will now need to run the .var file in SPCAT to generate the .cat file. This is done simply by dragging your .var file over the SPCAT.exe executable. This will generate a few files, but the one we are concerned with is the .cat file. Open the .cat file with Notepad. You will notice that the information is separated into effective columns. The first column is the predicted transition measurements in MHz according to our current Hamiltonian input (right now we only have our predicted rotational constants and quadrupole coupling constants in the prediction). The third column is the predicted intensity of the transition, and, finally, the two columns after the number “304” is the Pickett quantum numbers associated with this transition (these are the same as the “true” quantum numbers for our system). The intensity is reported such that the more positive the value, the stronger the transition. Furthermore, this number is exponential so an increase in 1 is a large jump in intensity. Now, you are ready to assign transitions. To do this, open up the .lin file. We have provided a couple of transition assignments for you to start making comparisons between your prediction and the actual assignment. Use this as a guide for both your analysis and formatting as these are correct assignments to two previously measured transitions. The relative position, [16] intensity, and predicted quantum numbers of other transitions in your earlier prediction can now be used to get the correct quantum number assignment. A note about assigning quantum numbers, though. This is probably the most difficult thing spectroscopists do and it isn’t always trivial. Although we have tried to make it as easy as possible on the student with these directions and starting points, this will still be somewhat challenging to the novice so please come get help if you need it. Remember, you cannot go on until you have a sizeable amount of transitions assigned as you have 5 unknowns in your Hamiltonian from the beginning. Save the .lin and close when finished. Once the transitions have been assigned, open your .par file with Notepad. You will need to again change the fifth value on the 3rd row to 30. Next, you need to change every value beyond the 3rd row in the 3rd column to 1.00000000E+02 (there should be 5 values that need changing). Also change the value in the 2nd row, 2nd column to 99 and the 5th value in the 2nd row to 0.0000E+00 and the 6th value in the 2nd row to 1.0000E+11. Save the .par file and close it. Now run the .par file by dragging it over SPFIT.exe executable, tabulate the values and Microwave RMS and NEW RMS error. Your fit now has only rotational constants and quadrupole coupling constants in it. However, as a molecule rotates, it also vibrates, distorting the rotor and thus deviating from the rigid rotor. In order to accommodate this and correctly match our uncertainty, we need to add quartic centrifugal constants until we are close to the uncertainty of the measurement—making sure the values we add are well defined. By “well defined”, we mean that the value uncertainty is approximately 1/3 or less of the fitted value. To add centrifugal distortion constants, go to Kisiel’s Pickett Crib Sheet Page at http://www.ifpan.edu.pl/~kisiel/asym/pickett/crib.htm and scroll down to Appendix I. Add the parameters -DeltaJ, -DeltaJK, etc. to the .par file until these criterion are met. You should not have to go past –deltaK. The numbers are the parameter codes that go next to the value in the .par file. Add the parameter directly below all the others and make the 2nd column value 1.000000000000000E-03 and the 3rd column 1.00000000E+02. Each time you add a parameter, make sure you change the 1st value in the 2nd row of the .par file to the number of rows you have past the 3rd row. Each time you add a value and run the .par file (by dragging it over SPFIT.exe), look at the new .fit file and make sure your RMS values are going down and that the uncertainty of the new parameter is not too large as described earlier. When you reach a point where you have used all five of the centrifugal distortion terms or they no longer are well defined as described earlier, you are finished. Afterwards, tabulate and report your constants, errors, and RMS values as before. CONGRATULATIONS! Now, you are finished and have successfully used the SPFIT/SPCAT program suite, the gold standard of rotational spectroscopy for effective Hamiltonian construction. DISCUSSION QUESTIONS AND COMMENTS 1. Describe the differences between your fit and the reported values in Ref. 2. As you can tell, many of your transition measurements are spot on with theirs. What, then is the source of the differences between your value and theirs? [17]

2. What type of transitions did we observe in the spectra? What gives this away? 3. Again, use Ref. 2. What do they report as the experimental dipole moment and what dipole moment did you calculate? Can you identify where the sources of any differences may be? 4. The possesses a quadrupolar nucleus. Discuss what is meant by the nuclear electric quadrupole coupling constant(s) and how can this be used to understand the bond environment around the nitrogen in benzonitrile. REFERENCES 1. H. M. Pickett, J. Mol. Spectrosc. 148 (1991) 371-377. K. Wohlfart, M. Schnell, J.-U. Grabow, J. Küpper, J. Mol. Spectrosc. 247 (2008) 119- 121.

Student Survey:

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Students’ Responses:

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