Initial Investigations of the Magnetic Circular Dichroism of

Isobutene using Synchrotron Radiation in the Vacuum

Ultraviolet Region

By

Clifford Sanders

A Thesis Submitted to the Faculty of

The Charles E. Schmidt College of Science

in Partial Fulfillment of the Requirements for the Degree of

Master of Science

Florida Atlantic University

Boca Raton, Florida

August 2009

ii

Acknowledgements

The author wishes to thank the staff of Florida Atlantic University, Committee members

Dr. Snyder, Dr. Perumareddi and Dr. Medina (a grand thanks to Dr. Medina). The author thanks Vonnie Sanders (mother) for always being supportive. The author gives a special thanks to his wife, Keji, for her understanding. The author also wishes to thank Evelyn

Hall, Jennie Soberon, and Cora Woodman for their continued efforts in assisting with his enrollment. Most of all, the author wishes to thank Dr. Narayanan for keeping the author‟s best interest in mind.

iii

Abstract

Author: Clifford Sanders

Title: Initial Investigations of the Magnetic Circular Dichroism of Isobutene using Synchrotron Radiation in the Vacuum Ultraviolet Region

Institution: Florida Atlantic University

Thesis Advisor: Professor Patricia Ann Snyder

Degree: Master of Science

Year: 2009

Ethylene is the simplest alkene. The carbon–carbon double bond is ubiquitous in the field of chemistry. Ethylene serves as the basis for understanding these molecules.

Thus, the assignment of the electronic transitions in ethylene is an important endeavor that many scientists have undertaken, but are yet to decipher theoretically or experimentally.

Synchrotron Radiation in the vacuum ultraviolet region allows for magnetic circular dichroism (MCD) measurements of ethylene and other simple alkenes. Studies of ethylene and propylene revealed that the * (AgB1u ethylene notation) transition is not the lowest energy transition. The 3s(R) (AgB3u ethylene notation) is the lowest energy transition.

iv To further this investigation, MCD and absorption measurement were carried out on isobutene. The isobutene spectra clearly showed four electronic transitions in the 156 to 212 nm wavelength region. These four isobutene transitions have been assigned as

3s, *, 3pσ and 3px proceeding from lower energy to higher energy. The present results support the assignments in ethylene and propylene.

v

Initial Investigations of the Magnetic Circular Dichroism of Isobutene

using Synchrotron Radiation in the Vacuum Ultraviolet Region

List of Figures ...... viii

List of Tables ...... x

List of Equations ...... xi

1. Introduction ...... 1

2. Electromagnetic radiation ...... 5

Polarization ...... 9

Linear polarization ...... 9

Circularly polarization ...... 10

Absorption of radiation ...... 12

Circular dichroism/Magnetic circular dichroism ...... 15

Synchrotron radiation...... 16

3. Theory ...... 19

Molecular orbitals ...... 19

The importance of symmetry ...... 23

Group theory ...... 23

Matrix Representations ...... 26

Character table ...... 27

4. Electronic transitions ...... 31 vi

Spin selection rules ...... 32

Orbital selection rules ...... 33

Valence transitions ...... 34

Rydberg transitions…………………………………………………………………34

Allowed transitions ...... 35

5. Experimental details...... 39

Instrumentation ...... 39

Data reduction ...... 42

6. Experimental Results and Discussion ...... 45

Isobutene spectra ...... 45

Ethylene and propylene spectra ...... 46

Isobutene assignments ...... 48

Vibrational coupling ...... 54

7. Conclusion ...... 61

Appendix ...... 64

References ...... 71

vii

List of Figures

Figure 1.1: Ethylene ...... 1

Figure 1.2: Isobutene ...... 3

Figure 2.1: Electromagnetic wave ...... 5

Figure 2.2: Types of interference ...... 6

Figure 2.3: Common terms and equations ...... 7

Figure 2.4: Electromagnetic spectrum ...... 8

Figure 2.5: Electric field of unpolarized light ...... 9

Figure 2.6: Oscillating electric field for linearly polarized light ...... 10

Figure 2.7: Circularly polarized radiation ...... 11

Figure 2.8: Quarter-wave plate ...... 11

Figure 2.9: Synchrotron radiation ...... 17

Figure 2.10: Energy range of synchrotron radiation ...... 18

Figure 3.1: „s‟, „p‟, and sp2 hybrid orbitals ...... 20

Figure 3.2: Bonding and antibonding molecular orbitals of ethylene ...... 21

Figure 3.3: Molecular orbital structure scheme for molecules containing double bonds . 22

Figure 3.4: Reflection across a plane of symmetry ...... 24

Figure 3.5: Rotation about an axis ...... 25

Figure 3.6: Inversion about an axis ...... 25

Figure 3.7: Improper rotation about an axis ...... 26

viii

Figure 3.8: Proper orientation of isobutene ...... 29

Figure 4.1: Electronic transitions ...... 33

Figure 5.1: Basic experimental setup ...... 40

Figure 5.2: Graph of raw MCD data for isobutene ...... 42

Figure 5.3: Plot of raw MCD data of isobutene and baseline signal ...... 42

Figure 5.4: Corrected MCD graph of isobutene ...... 43

Figure 5.5: Magnetic circular dichroism plot of isobutene ...... 44

Figure 5.6: Isobutene absorption spectrum ...... 44

Figure 6.1: Absorption spectrum of isobutene (wavenumbers) ...... 45

Figure 6.2: Magnetic circular dichroism plot of isobutene (wavenumbers) ...... 46

Figure 6.3: Absorption and MCD spectra of ethylene ...... 47

Figure 6.4: Absorption and MCD spectra of propylene ...... 47

Figure 6.5: Comparison of MCD and absorption spectra of isobutene ...... 51

Figure 6.6: MCD spectrum of π π* transition in isobutene ...... 53

Figure 6.7: MCD spectrum of π→ 3s transition in isobutene ...... 54

ix

List of Tables

Table 3.1: Character Table of the C2v Point Group for Isobutene ...... 30

Table 4.1: Transitions for isobutene ...... 38

Table 6.1: Peak energies for MCD and absorption spectra of isobutene ...... 52

Table 6.2: Vibrational normal modes for isobutene ...... 55

Table 6.3: Allowed vibrational modes for isobutene transitions ...... 58

x

Chapter 1

Figure 1.1: Ethylene

Introduction

Ethylene (C2H4), shown in Figure 1.1, is one of the most important molecules around today. It is extremely important in industry and in biology.1, 2 Ethylene is also the simplest alkene and forms the foundation for all other alkenes.1, 3 Ethylene is quite reactive and can undergo many different reactions to form many useful products.4 Some of the reactions it may undergo include polymerization, oxidation, halogenation, alkylation, and hydration, just to name a few. Ethylene‟s reactiveness stems from the high electron density at its double bond. Ethylene polymerizes to form polyethylene, which is widely used in plastics. In plants, ethylene acts as a hormone and is responsible for the ripening of fruits. Understanding the chemistry of ethylene can lead to increased knowledge about all olefins, since carbon-carbon double bonds are in organic and biological molecules. xi 1 Knowing the electronic structure of a molecule allows scientist to further predict the chemistry of that molecule. The electronic structure of ethylene still eludes scientists when comparing theoretical and experimental results, particularly, for the * transition.3, 5-6 For a long time, this transition was thought to be the lowest energy transition in ethylene3. However, as stated earlier, experimental evidence does not support this claim. Scientists have not been able to thoroughly link theoretical aspects of this transition to experimental results. One scientist states that numerous theoretical studies have been devoted to the assignment of the spectra but their interpretation still remains controversial.5

There are several pathways that a scientist can use to determine the electronic structure of a molecule. There have been multiple attempts to decipher the electronic structure of ethylene by different scientists. One author investigates the   *,   3s, and   3p transitions by way of ab initio calculations of the Franck-Condon factors.5-8

Basically, in this method, the degree of overlap of the wave functions for the excited and ground states of the oscillator is studied. This method relies on the internuclear distance being constant, thus the calculations are independent of nuclear coordinates.5-8 These calculations also found discrepancies between theory and experiment. As the author reports, the first transition is not the   * transition in this region but suggests that the

  3s is the first transition observed.5 In another theoretical calculation, J.Ryu and B.

S. Hudson attempt to decipher the electronic transitions in the region from 6 to 9 eV (the same region for the previous author and this research) through the use of wavepacket calculations1. Wavepacket solutions are merely a sum of multiple waves, which contains

2 a continuum of frequencies. Their research also proved to have discrepancies between theory and experiment.

The controversy discussed above is the impetus for the present research. By analyzing the electronic structure of other simple olefins, there is hope that this will add to the understanding of the electronic structure of ethylene. The immediate goal of this research is to observe and analyze the electronic transitions of 1,1-dimethylethylene

(isobutene), shown in Figure 1.2, in the vacuum ultraviolet region and compare it to that of ethylene. A new technique developed by P. A. Snyder is used to that effect.

Figure 1.2: Isobutene

Snyder designed an instrument that is capable of collecting magnetic circular dichroism (MCD) measurements in the vacuum ultraviolet (VUV) region of the electromagnetic spectrum through the use of synchrotron radiation. Magnetic circular dichroism was chosen in addition to normal absorption spectroscopy because, in the latter, some electronic transitions may not be observed. Synchrotron radiation was employed because of its advantages in carrying out the measurements in the vacuum

3 ultraviolet, such as high polarization and high intensity. In all, it is hoped that this research might be helpful in furthering the understanding of ethylene and showing the potential of this relatively new technique.

4

Chapter 2

Electromagnetic radiation

Electromagnetic radiation has a dual nature; it sometimes behaves as a particle and sometimes as a wave. When electromagnetic radiation is absorbed by molecules, it behaves like a particle with certain energy. The quantum of electromagnetic energy is called the photon. The energy of a photon is related to its frequency or wavelength, quantities associated with the wave nature of electromagnetic radiation.

Thus light, which is a form of electromagnetic radiation, can also be described in terms of electric and magnetic fields.9 At any point in a light beam, the magnetic field is always perpendicular to the electric field. Both the electric and magnetic fields oscillate in a plane perpendicular to the direction of propagation of the light beam.9 Figure 2.1 shows a schematic of a light wave. The spatial separation between successive crests

5 in the figure is the wavelength. If instead, you plot the intensities of the field as a function of time, you get a similar plot where now the separation between crests is the period. The inverse of the period is the frequency.

Waves traveling in the same medium can interfere with each other constructively or destructively. When two waves with the same amplitude, wavelength, and phase meet, they interfere with each other constructively, as shown in Figure 2.2. The waves reinforce each other and the amplitude doubles. When the same waves, however, meet out of phase by 90o, they interfere with each other destructively, thus canceling each other out. This is also shown in Figure 2.2.

Electromagnetic waves differ in wavelength and frequency, but have the same speed in vacuum, c. A summary of the relationships between wavelength, frequency, and energy of a photon is presented in Figure 2.3. 6

Figure 2.3: Common terms and equations9,10

c= 2.998 x 108 m/s (speed of light)

= wavelength

= frequency

E= energy

h= 6.626 x 10-34 J . s/ particle (Planck‟s constant)

with this, c= 

E= h

E is in J/particle when wavelength is in meters

1 mole = 6.02 x 1023 particles

Thus, energy is directly proportional to frequency and inversely proportional to wavelength. There is a very large range of wavelengths that electromagnetic radiation can have. Electromagnetic radiation ranges from low energy radio waves to high energy gamma rays, with only a minute range that‟s visible to the human eye. The wavelengths of electromagnetic radiation range from radio waves with wavelengths the size of buildings to gamma rays that have wavelengths the size of atomic nuclei or smaller. The visible portion of the electromagnetic spectrum ranges from about 400 to 700 nm. The so-called electromagnetic spectrum is represented in Figure 2.4.

7

Figure 2.4: Electromagnetic spectrum

8

Polarization

Polarization is a property of electromagnetic radiation that is very useful in spectroscopy. For clarity, to describe polarization, only the electric field will be considered. For the single wave depicted in Figure 2.1, the electric field oscillates on a single plane. However, natural sources and most man-made sources produce unpolarized electromagnetic radiation, i.e., radiation that it is made of many single waves each with a different plane of polarization, as depicted in Figure 2.5.

Figure 2.5: Electric field of unpolarized light

Linear polarization

When all the waves have electric fields oscillating on the same plane, the electromagnetic radiation is said to be plane-polarized. Since all the waves are moving in the same direction, this means that the electric fields of all the waves are oscillating along the same line. Thus, plane-polarized light is also referred to as linearly polarized. A linearly polarized wave would resemble the diagram shown in Figure 2.6:

9

Since natural and most man-made sources emit unpolarized waves, a linear polarizer is normally used to achieve linear polarization. The most common method of polarization in the visible region involves the use of a Polaroid filter.11, 12 The filter is made of long-chained molecules that are aligned in the same direction.11, 12 Because the light polarized along the long molecular dimension is preferentially absorbed, the filter is capable of blocking one of the two planes of oscillation of electromagnetic waves. After emerging from the polarizer, the light is at half its intensity.

Circular polarization

Circularly polarized waves result when two linearly polarized waves in two perpendicular planes meet out of phase by 90 degrees. Then the wave resulting from the superposition of the two waves will no longer be linearly polarized.13 Using vector addition, the resultant vector appears to rotate clockwise (when looking back at the source) when the waves are out of phase by 90o. This is known as right circularly polarized light. If the waves are out of phase by –90o, then the resultant vector will appear to rotate counterclockwise. This is known as left circularly polarized light. Figure2.7 illustrates how right circularly polarized light is produced.

10

One way of obtaining circularly polarized light is to use a birefringent crystal.

Such crystals are anisotropic, meaning they don‟t have the same structure in all directions. The crystal has two indices of refraction, for light linearly polarized in the axial direction and light polarized perpendicular to it.10 Calcite is a common birefringent crystal that can be used as a quarter-wave plate, as shown in Figure 2.8.

11

The crystal is cut so that the axial direction is on the plane of the plate and light travels perpendicular to the plate. When the light is polarized at 45˚ to the axial direction, it will split into two components of equal amplitude polarized along the axial direction and perpendicular to it. Given the difference in indices of refraction, the thickness of the plate is made so that the two components have a difference in phase of a quarter wave (or 90º) as they emerge from the crystal.

Circularly polarized waves have many uses in spectroscopy, for many molecules absorb unequal amounts of right and left circularly polarized light. The absorbance difference of left minus right circularly polarized light is known as circular dichroism.

Absorption of radiation

Absorption of electromagnetic radiation involves transitions between energy levels in a system, such as a molecule. The energy levels are quantized, meaning that an electron in its ground state needs to gain a particular energy to reach a certain higher energy level. Here are some things to know about electronic energy:

 form of energy that arises from the motion of electrons about the nucleus, and from the interactions among the electrons and between the electrons and the nucleus.  only certain values of electronic energy are allowed for an atom  said to be quantized  a change of electronic energy level (state) of an atom involves the absorption or emission of a definite amount or quantum, of energy  lowest electronic energy state is called the ground state  any state with energy greater than that of the ground state is an excited state

12

Electrons can be excited to higher energy levels by photons9, 10. A photon can supply the electron with enough energy to move to another level. In other words, the energy that a photon possesses usually correlates with the difference in energy between levels. Thus when atoms or molecules absorb light in moving from one energy state to another, the wavelength  of the light is related to the energies of the two states by the equation:

Efinal - Einitial = hc/ Eq. 2.1

Some things to remember about this relationship are:

 electromagnetic radiation can be considered to consist of photons

 each photon has an energy of hc/

 an atom or molecule can move from one electronic energy state to another by absorbing or emitting a photon

 if it absorbs a photon of energy( hc/, it moves from a lower to a higher energy state, and its energy increases by hc/

Electronic transitions from the ground state are usually seen in the visible, ultraviolet, and vacuum ultraviolet regions of the electromagnetic spectrum. The process of atoms or molecules absorbing energy from photons is usually termed absorption spectroscopy.9, 14 Electromagnetic radiation may also be emitted (emission spectroscopy), or scattered (one example is Raman spectroscopy). Thus all forms of spectroscopy can provide important information about a molecule or atom concerning their electronic structure, which in turn can shed light on their physical and chemical properties.14

The energy that a molecule has is derived from its electronic, vibrational and rotational energies. All these forms of energy are quantized, i.e., only certain values are 13 allowed. Electronic energy, the energy associated with the electrons, represents the biggest energy gap between energy levels. Vibrational energy is the energy associated with the stretching, bending, wagging, and other vibrations of a molecule. The vibrational energy levels are closer together. Rotational energy levels are even closer together than vibrational energy levels. Ultraviolet/visible absorption spectra for most molecules exhibit broad bands. One reason for this is because electronic transitions are accompanied by vibrational and rotational transitions.9 The presence of electronic, vibrational, and rotational transitions usually results in absorption spectra that are broad bands with individual peaks that are difficult to resolve and may in fact, be due to more than one transition with nearly the same energy.

The Beer-Lambert law relates the absorbance A (given by the log10 of the ratio of the initial to the final intensity) of a sample to its concentration C by:

A= ε b C, Eq. 2.2 where the path length b is measured in cm and the molar extinction coefficient ε is given in Lmol-1cm-1. The molar extinction coefficient of a molecule remains the same at a given wavelength regardless of the concentration. Knowing the molar extinction coefficient of a particular chemical species at a given wavelength is very valuable. This is so because the molar extinction coefficient is basically a measure of how strongly a chemical species absorbs light at a given wavelength. Because this is an intrinsic property, unique to a particular chemical species, it can be used as a characterization technique.9-10, 15

14

Circular dichroism/Magnetic circular dichroism

Circular dichroism deals with the different amounts of right or left circularly polarized light absorbed by a molecule.10 Chiral molecules absorb different amounts of left circularly polarized light and right circularly polarized light and thus will exhibit

3 natural circular dichroism spectra. In these spectra, the signal is the difference, Δε = εL -

εR , between the two molar extinction coefficients.

Molecules of ethylene, propylene, and isobutene are not chiral and thus do not exhibit any difference in the absorption of right and left circularly polarized light.

However, when the molecules are placed in a strong magnetic field parallel to the direction of propagation of the radiation, a circular dichroism signal is observed. This effect is called magnetic circular dichroism and the signal is usually given in Δε/T (T stands for Tesla). In both natural circular dichroism and magnetic circular dichroism spectra, peaks may be positive or negative since we are measuring a difference in absorbance. This makes magnetic circular dichroism spectroscopy a valuable tool since closely spaced peaks in absorption spectra can be separated if they have magnetic circular dichroism signals of opposite sign. Magnetic circular dichroism spectroscopy can then give additional information on the electronic structure of molecules.

There are three types of magnetic circular dichroism that a molecule may exhibit.15 They are usually labeled term A, term B, or term C. Term A magnetic circular dichroism requires molecules to have degenerate excited states.15 Term B magnetic circular dichroism arises when there is a mixing between states.3, 15 Term C magnetic circular dichroism requires a molecule to have a degenerate ground state and is temperature dependent.15 Terms A and B are temperature independent. In the case of

15 ethylene, propylene, and isobutene molecules, term B magnetic circular dichroism is observed. Although term B magnetic circular dichroism is difficult to interpret theoretically, it is useful in identifying transitions since the spectra have the same shape as regular absorption spectra but B terms may be positive or negative in sign. However, these terms are generally more difficult to detect than A or C terms and such experiments are only possible when an intense source of electromagnetic radiation, such as synchrotron radiation, is available.

Synchrotron radiation

In a cyclotron, a constant magnetic field bends the trajectory of a moving charged particle into a circle, the particle being accelerated each half-cycle by an electric field.

This electric field has to be switched at the same frequency as the frequency of circulation of the particle since the particle changes direction by 180o during a half-cycle.

In a synchrotron, the frequency at which the electric field is changed is “synchronized” with that of the orbiting charged particles because their mass increases with velocity.

Thus, synchrotron radiation is the name given to light radiated by a charged particle following a curved trajectory influenced by a magnetic field,16 as shown in Figure 2.9.

When charged particles, in particular electrons, are forced to move in a circular orbit by a magnetic field, photons are emitted. At relativistic velocities (when the particles are moving at close to the speed of light) these photons are emitted in a narrow cone in the forward direction, tangential to the orbit.16 These photons are emitted with energies ranging from (long wavelength) infrared to energetic (short wavelength) x-rays.16 The range of wavelengths of this radiation is a function of the energy of the charged particles and the strength of the magnetic field bending the path of the charged particles.

16

Synchrotron radiation is employed because it provides many advantages over other forms of radiation. Synchrotron radiation is intense, collimated, and linearly polarized. Synchrotron radiation is highly linearly polarized in the plane of the storage ring.9 If the optics of the beam line and monochromator optics are appropriate, the radiation entering the experimental chamber will be linearly polarized. Thus a linear polarizer is not needed and the intensity of the synchrotron radiation is not affected. A calcite quarter-wave plate cannot be used with synchrotron radiation since it works only for one wavelength. Instead, the photoelastic effect is used to create a quarter-wave plate of adjustable wavelength. This plate is also used to modulate the circularly polarized radiation it produces and will be described in the experimental section.

Another great asset of synchrotron radiation is that it is highly collimated. The collimated radiation can pass through the superconducting magnet and sample cell without additional optics. Aside from the previous benefits named above, synchrotron radiation covers a wide range of energies ranging from the visible spectrum to gamma rays, as shown in Figure 2.10.

17

Figure 2.10: Energy range of synchrotron radiation

Use of synchrotron radiation makes the measurement of vacuum ultraviolet magnetic circular dichroism possible.

18

Chapter 3

Theory

Molecular orbitals

Quantum chemistry is based on the premise that elementary particles, just like electromagnetic radiation, have a dual nature. Because a wave has extent in space, an electron in an atom cannot be pinpointed and must be represented by a wavefunction ψ that depends on the coordinates of the electron and time. The absolute square of the wavefunction, ψ*ψ, where ψ* is the complex conjugate of ψ, is the probability of finding the electron in a small volume element around a point. This probability can be visualized by an atomic orbital, a cloud with a density given by ψ*ψ.

An atomic orbital is characterized by a set of quantum numbers, n, ℓ and m. The principal quantum number n can take on values n = 1, 2, 3, …, and determines the size of the orbital. The angular momemtum quantum number ℓ determines the shape of the orbital and can take on values ℓ = 0, 1, …, n – 1. The magnetic quantum number m determines the orientation of the orbital and can have 2ℓ + 1 values. The energy of an orbital depends mostly on n (higher n means higher energy) and to a lesser degree on ℓ

(higher ℓ means higher energy).

A carbon atom has four electrons, called valence electrons, that are used to bond to other atoms. Two of the electrons are in the 2s (n = 2, ℓ = 0) orbital and one each in two of three 2p (n = 2, ℓ = 1) orbitals. In molecular orbital theory, when two atoms bond,

19 atomic orbitals form molecular orbitals. These molecular orbitals also represent a probability density. In ethylene, the atomic orbitals become hybridized first. For each carbon atom, a 2s electron is promoted to the empty 2p orbital and the second 2s electron forms hybrid orbitals with two of the sp orbitals. This results in three sp2 hybrid orbitals, which arrange themselves 120° apart on a plane. The s, p, and sp2 hybrid orbitals are shown in Figure 3.1. The p and sp2 hybrid orbitals have lobes with + and – signs to indicate that the wavefunction is positive for one and negative for the other.

Figure 3.1: ‘s’, ‘p’, and sp2 hybrid orbitals

Two of the hybrid orbitals form bonds with the electron of a hydrogen atom. The remaining hybrid bonds to the remaining hybrid from the other carbon atom. Two different molecular orbitals are possible, σ and σ*, shown in Figure 3.2. Likewise, the two remaining 2p orbitals bond to each other. Two different molecular orbitals are possible, π and π*, also shown in Figure 3.2.

20

Figure 3.2: Bonding and antibonding molecular orbitals of ethylene

The σ and π orbitals are called bonding orbitals because the electron density is

concentrated between the carbon atoms. This is not true of the σ* and π* orbitals, called

antibonding orbitals. When the electrons spend more time between the positive carbon

nuclei, their electric potential energy is lowered. Thus, the σ bond has a lower energy

than the σ* bond, while the π bond has lower energy than the π* bond. Likewise, the σ

bond has a lower energy than the π bond because the electron density is concentrated

along the carbon-carbon bond and thus closer to the nuclei. In general, the energy scheme

for the four possible states of the valence electrons associated with any carbon-carbon

double bond is as shown in Figure 3.3.

21

The  molecular orbital has the lowest energy, followed by π, π*, and σ*.

Transitions between these states are of the type called valence transitions. Both the σ and

π molecular orbitals are fully occupied (two electrons of opposite spin) when the molecule is in its ground state. The  molecular orbital is the highest occupied molecular orbital (HOMO), while π* is the lowest unoccupied molecular orbital (LUMO). The σ molecular orbital has lower energy (stronger bond) and is surrounded by the electron density representing the π orbital. Thus, you would expect the absorption of electromagnetic radiation to have the π orbital as the ground state. Theoretically, the absorption could then result from π to π* and π to σ* transitions. This is the case for ethylene, propylene and isobutene molecules.

22 The importance of symmetry

In the application of molecular orbital theory to carbon-carbon bonding, symmetry is very important. It can tell you which atomic orbitals may or may not bond.

For example, in the above discussion, symmetry requires that bonds form only when both participating atomic orbitals have the same inversion symmetry about the internuclear axis.

Symmetry is, in fact, very important in chemistry. It reveals information about the structural, spectral, chiral and other properties of a molecule. Knowing the symmetry of a molecule can tell the chemist the number and kind of energy levels that a molecule may have. Knowing symmetry allows one to know what energy states and what types of transitions are possible. Symmetry can tell the chemist what electronic or vibrational transitions of a molecule are allowed or forbidden.

Group theory

Group theory is a mathematical tool that allows you to determine aspects of the symmetry of a molecule. When a molecule is classified according to its symmetry, it is characterized as having a particular point group. A point group is a complete set of symmetry operations attributed to a molecule. There are four kinds of symmetry operations:17

-reflection in a plane

-one or more rotations about a principal axis

-inversion of all atoms through the center of a molecule

-rotation followed by reflection in a plane perpendicular to the rotational

axis, improper axis

23 Associated with symmetry operations are symmetry elements. A symmetry element is a line, a plane, or a point with respect to which one or more symmetry operations may be carried out. The symmetry elements associated with the symmetry

17 operations previously listed are , Cn, i, and Sn , respectively. There is also an identity operation „E‟, which does not do anything to the molecule. Its purpose is to fulfill the requirements of a group.

 denotes a reflection through a plane. Reflection changes one half of the molecule with the reflection of the other half. Reflection planes may be vertical (v) when they contain the principal axis, horizontal (h) when perpendicular to the principal axis, or dihedral

(d). Two successive reflections are equivalent to the identity operation. Illustrated below in Figure 3.4 is the reflection property of molecules.

Cn is a rotation about a principal axis as shown in Figure 3.5. The principal axis in a molecule is the highest order rotational axis. This principal axis is usually assigned the

“z” axis if Cartesian coordinates are being used. Rotations are considered to be positive when rotated counterclockwise, as we look along the z axis towards the origin.

24

i represents a single point called the inversion center and located at the center of the molecule. Atoms move along a line through the center of the molecule to a point on the other side and equal distance from the inversion center. This is depicted in Figure 3.6.

Sn is an improper rotation that consists of a rotation followed by a reflection through the plane perpendicular to the axis of rotation. This is shown in Figure 3.7.

25 Figure 3.7: Improper rotation about an axis

E is the identity operator. Basically, the molecule is unchanged.

Matrix Representations

Matrices are mathematical representations of the symmetry operations. Each symmetry operation mentioned previously can be represented by a matrix. Below are the matrix representations of the symmetry operations:

Indentity, E

1 0 0 X  X  0 1 0       Y  = Y  0 0 1  Z   Z 

Reflection, 

When a plane of reflection is chosen to coincide with a principal Cartesian plane, reflection of a general point has the effect of changing the sign of the coordinate measured perpendicular to the plane while the other two coordinates that define the plane are left unchanged. Below are the representations for the 3 different planes of reflections:

1 0 0  X  X  1 0 0 X  X  1 0 0 X  X                    0 1 0  Y  = Y  0 1 0 Y  = Y   0 1 0 Y  = Y                    0 0 1  Z   Z  0 0 1  Z   Z   0 0 1  Z   Z 

Reflection in (xy) plane Reflection in (xz) plane Reflection in (yz) plane

26 Inversion, i

1 0 0  X  X  Inversion is simply       a negative unit  0 1 0  Y  = Y        matrix.  0 0 1  Z   Z 

Proper Rotations, Cn

If one defines the principal axis of rotation as the „z‟ axis, the z coordinate will be unchanged by any rotation about the „z‟ axis. However, the x and y coordinates are represented as follows:

 cos x sin x 0 X 1  X 2  Matrix representation of  sin x cos x 0  Y  =  Y  a clockwise rotation    1   2  about the ‘z’ axis.  0 0 1  Z1   Z1 

Improper Rotations, Sn

Similarly to proper rotations, if one defines the principal axis of rotation as the „z‟ axis, the x and y coordinates are the same as the proper rotation. However, since improper rotations also incorporate a horizontal plane of reflection along with the proper rotation, the „z‟ axis changes to its negative counterpart:

 cos x sin x 0   X 2  Remember, an Sn operation is  sin x cos x 0  =  Y     2  a Cn rotation followed by a h  0 0 1  Z1  reflection.

Character table

The matrices discussed above are 3x3 because they operate on a single vector that represents the position of one atom. If a molecule has 4 atoms, you would need to construct, from the above matrices, a set of 12x12 matrices to represent the symmetry operations of the group. In general, you need 3Nx3N matrices for a molecule with N atoms. This means that two molecules with the same point group will have two different

27 sets of matrices, i.e., two different representations. In fact, mathematically, you can construct an infinite number of representations of a point group.

Fortunately, you can obtain a “unique” representation of a point group if you use appropriate transformations to block diagonalize the matrices of any of the representations. The resulting matrices have non-zero elements only in square blocks along the diagonal from top left to bottom right. Each of the square blocks is called an irreducible representation Γi of the group. The number of different Γi‟s you get is equal to the number of classes of symmetry elements in the group. The set of Γi‟s is unique in that all representations of the group can be described in terms of a linear combination of irreducible representations.

The Γi‟s of a molecular point group are important in many ways. For example, the wavefunction of each electronic or vibrational state in a molecule transforms according to an irreducible representation of the molecular point group. For most point groups, the square blocks in the block-diagonalized matrices can be 1x1, 2x2, or 3x3, i.e., the Γi‟s can have dimension 1, 2, or 3. You then get A, B, E or T species of irreducible representations, where A and B are one-dimensional, E is two-dimensional and T is three-dimensional. The degree of degeneracy of an energy state (barring accidental degeneracy) equals the dimension of the Γi that represents its wavefunction.

In the case of isobutene, the carbon atoms are all on the same plane, as shown in

Figure 3.8. The two hydrogen atoms in the CH2 group are also on the molecular plane.

The same is true of one hydrogen atom from each of the methyl groups. The other two

28 are located symmetrically above and below the molecular plane. Thus, we deduce from

the figure that the molecule has a two-fold rotational axis, C2, along the double bond. By convention, this is chosen to be the z axis. Also by convention, the y axis is chosen to be on the molecular plane, while the x axis is perpendicular to it. In this coordinate system, the molecule is seen to have two vertical mirror planes, σ(zx) and σ(yz). The fourth symmetry element is the identity E. The corresponding point group is C2v.

Since the group has four symmetry classes, it also has four Γi‟s, all of dimension 1 and designated A1, A2, B1, and B2. Thus, without even doing a theoretical calculation, we can assert that all molecular orbitals and all vibrational modes of isobutene are nondegenerate. The designations A and B mean symmetric and antisymmetric, respectively, concerning rotation about the two-fold axis. The 1 and 2 subscripts for A mean symmetric and antisymmetric, respectively, concerning reflection through a mirror plane. All the symmetry properties of the Γi‟s under the operations of the point group are

29 contained in Table 3.1 shown below, the character table for C2v. All the characters of a one-dimensional Γi are 1 or -1, depending on whether it is symmetric or antisymmetric with respect to a symmetry operation.

Table 3.1: Character Table of the C2v Point Group for Isobutene C2v E C2 v(zx) ‟v(yz) 2 2 2 A1 1 1 1 1 z x , y , z A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x, Ry xz B2 1 -1 -1 1 y, Rx yz

The next to last column in the table shows the Γi‟s of the translations Tx, Ty, and

Tz, in the x, y, and z directions, respectively, and the rotations Rx, Ry, and Rz in a right- handed system. The last column shows the Γi‟s for the polarizability tensor elements.

These columns allow us to determine the spectral activities since all Γi‟s that contain a translation will be infrared active while those containing an element of the polarizability tensor will be Raman active. This table is also useful in determining allowed transitions between electronic states and which vibrational states can couple to an electronic transition.

30

Chapter 4

Transitions

Electronic transitions

Absorption of electromagnetic radiation by a molecule involves transitions between its energy levels. Electronic transitions from the ground state are usually seen in the visible, ultraviolet and vacuum ultraviolet regions of the spectrum. For a transition to be allowed, it must involve a change in the electric dipole moment of the molecule. That is to say, if a transition is associated with a time-varying electric dipole moment, the molecule will interact with electromagnetic radiation by absorbing a photon with energy equal to the energy difference between the levels involved in the transition.

Quantum mechanically, the transition is allowed if it has a non-zero probability.

Mathematically, that means that the expectation value of the electric dipole moment operator is not zero for the transition, or

∫e′ee dτ  0, Eq. 4.1 where e′ and e are the wavefunctions for the excited and ground electronic states, e is the electric dipole moment operator, and dτ is a volume element. This condition has to be modified when the quantum mechanical problem is done properly by taking into account that the electrons are moving fast compared to the speed of light in vacuum.

Relativistic quantum mechanic gives the nonintuitive result that electrons must have an

31 intrinsic spin. Then, the total wavefunction that represents the electron is actually given by the product es, where s is the spin wavefunction. It is, thus, the total wavefunction that must satisfy the condition given by Eq. 4.1. The integral can then be written as the product of two integrals, both required to be nonzero. You recover the first condition given by Eq. 4.1 plus a separate condition for the spin wavefunctions,

* ∫s′ s ds ≠ 0, Eq. 4.2 where ds is a volume element in spin space.

Spin selection rules

Spin wavefunctions are orthogonal. This means that, if s′  s, the integral in Eq.

4.2 is zero. For the integral to be nonzero, we must have s′ = s. In other words, only transitions for which S = S′ (ΔS = 0) are allowed. The spin of an electron is “spaced quantized” and characterized by a quantum number s that can take only one of two values s = + ½, - ½. For two electrons, the total spin S = s1 + s2, can then be 0 or 1. Just as in the case of orbital angular momentum, the number of orientations the spin angular momentum can have is given by 2S + 1. There are three orientations for S = 1, but only one for S = 0. The corresponding states are referred to as triplet and singlet, respectively, and the number of orientations is called the multiplicity of the state.

In the case of the σ and π orbitals of ethylene and isobutene, each state is fully occupied by two electrons with opposite spins, i.e., s1 = + ½, and s2 = - ½, so S = 0, making these singlet states. The spin selection rule then requires that the final state also be a singlet for any allowed transition from the σ and π states, i.e., the states involved in an allowed transition must have the same multiplicity.

32

Orbital selection rules

In general, the condition given by Eq. 4.1 results in orbital selection rules:

 The change in angular momentum is ∆ℓ = 0, ± 1.

 For a molecule with inversion symmetry, a change in parity must accompany the

transition, g →u or u→g (Laporte rule).

A nonbonding atomic orbital refers to valence electrons that are not used in bonding to other atoms, such as the lone electron pairs of the oxygen in the Lewis structure of water. The valence electrons of the two carbons involved in a double bond do not have nonbonding orbitals. Thus, in general, the transitions depicted in Figure 4.1 are possible.

33

Valence transitions

* transitions occur in molecules that possess double or triple bonds or aromatic rings. In this transition, a  electron is excited to an antibonding * orbital. These transitions occur in the visible to vacuum ultraviolet range.

* transitions occur in molecules that possess double or triple bonds or aromatic rings. In these transitions, a  electron is excited to an antibonding * orbital. However, the picture of the  and * orbitals presented in Figure 3.2 is too simple. A double bond exists in a molecule and cannot be completely isolated. These orbitals extend over the entire molecule, mixing with other  orbitals. The resulting molecular orbitals in the case of ethylene can be seen in Figure 2 of Reference 18 (Merer and Mulliken). As indicated in that figure, they are assigned as having ag symmetry ( and *). Notice that the higher energy orbital is rather large and is also called a 3s orbital. This is the denomination for the first Rydberg orbital of ethylene.

Rydberg transitions ( R)

In a Rydberg transition, an electron is promoted from a bonding orbital to a

Rydberg orbital, an atomic-like orbital with n greater than that of any occupied molecular orbital. Such orbitals are large compared to the size of the molecule. Similar to atomic transitions, a Rydberg transition is usually part of a series of molecular excitations that occur with systematically narrowing spacing toward the higher energy, terminating at a limit representing the ionization energy of the molecule.10, 19 The transition energy is given by a modified hydrogen-like formula19, 20

2 hv = i – R/(n-) , Eq. 4.3

34 where i is the energy to which the series converges, R is the Rydberg constant, n is an integer, and  is called the quantum defect, which takes into account the fact that the

Rydberg orbital surrounds a molecule rather than a nucleus.

Rydberg transitions are usually sharp, but may be broad sometimes. Thus, lower energy Rydberg transitions may not fit the above formula exactly.18 Allowed valence transitions tend to be broad and it is sometimes hard to separate valence transitions from

Rydberg transitions when they overlap in an absorption spectrum. In the case of ethylene and isobutene, where the HOMO is the  orbital involving 2p electrons, the first lines in the Rydberg series correspond to transitions to atomic-like orbitals with n = 3. Thus, the

 R transitions of interest are  3s and  3p (x, y, or σ).

Allowed transitions

The electric dipole moment operator in Eq. 4.1 has three components, so there are really three integrals, one for each component, and the transition will be allowed if at least one of the integrals is nonzero. This condition can be written in terms of the triple direct product of the irreducible representations of e′, e and e:

Γ(x) Γx

Γ(e′) Γ(y) Γ(e) = Γy , Eq. 4.4

Γ(z) Γz where at least one of the three irreducible representations Γx, Γy or Γz is totally symmetric. The polarization of the allowed transition is given by which irreducible representation is symmetric. For example, if Γx is symmetric, the allowed electronic transition is x-polarized.

35

All of the transitions being considered in the case of isobutene have the π molecular orbital as the initial state. This is the highest occupied molecular orbital

(HOMO), which has b1 symmetry. Since there are two electrons in this orbital, the state symmetry is the direct product b1 x b1 = A1. Let us now consider each of the transitions:

 => * This is the transition of an electron from the highest occupied molecular orbital

(HOMO) to an unoccupied π* molecular orbital which possesses b1 symmetry also. The final state thus has both electrons with b1 symmetry and the state symmetry is the direct product b1 x b1 = A1. The condition given by Eq. 4.4 for this transition is then

 b   b   1   1  A1 b2 A1  b2   => * Transition is allowed and „z‟ polarized.     a1  a1 allowed

 => 3s This is the transition of an electron from the highest occupied molecular orbital

(HOMO) to an unoccupied molecular orbital which possesses a1 symmetry. The final state thus has one electron of b1 symmetry and one electron of a1 symmetry, while the state symmetry is the direct product a1 x b1 = B1. The condition given by Eq. 4.4 for this transition is then

 b   a allowed  1   1  B1 b2 A1  a2   => 3s Transition is allowed and „x‟ polarized. .     a1   b1 

 => 3pσ This is the transition of an electron from the highest occupied molecular orbital

(HOMO) to an unoccupied molecular orbital which possesses a1 symmetry. The final state thus has one electron of b1 symmetry and one electron of a1 symmetry, while the state symmetry is the direct product a1 x b1 = B1. The condition given by Eq. 4.4 for this transition is then 36

 b   a allowed  1   1   => 3pσ Transition is allowed and „x‟ polarized. B1 b2 A1  a2      a1   b1 

 => 3py This is the transition of an electron from the highest occupied molecular orbital

(HOMO) to an unoccupied molecular orbital which possesses b2 symmetry. The final state thus has one electron of b1 symmetry and one electron of b2 symmetry, while the state symmetry is the direct product b2 x b1 = A2. The condition given by Eq. 4.4 for this transition is then

 b  b   1   2   => 3py Transition is not allowed. A2 b2 A1   b1  not allowed     a1  a2 

 => 3px This is the transition of an electron from the highest occupied molecular orbital

(HOMO) to an unoccupied molecular orbital which possesses b1 symmetry also. The final state thus has two electrons of b1 symmetry and the state symmetry is the direct product b1 x b1 = A1. The condition given by Eq. 4.4 for this transition is then

 b   b   1   1  A1 b2 A1  b2   => 3px Transition is allowed and „z‟ polarized.     a1  a1 allowed

The above results are summarized in Table 4.1. The irreducible representations used for the state notation all have a left superscript of 1 to indicate that these are singlet states, as previously discussed. Also included in Table 4.1 is the orbital notation, which refers to the symmetry of the initial and final orbitals for the electron that is actually making the transition, as discussed above. The first number in the orbital notation is needed because the isobutene molecule has more than one orbital of a particular 37

Table 4.1 Transitions for Isobutene Transition Orbital Notation State Notation Allowed Transitions 1 1  => * 2b1 => 3b1 A1 => A1 z-polarized 1 1  => 3s 2b1 => 9a1 A1=> B1 x-polarized 1 1  => 3p 2b1 => 10a1 A1=> B1 x-polarized 1 1  => 3py 2b1 => 6b2 A1 => A2 Not allowed 1 1  => 3px 2b1 => 4b1 A1=> A1 z-polarized

symmetry species. The numbers are assigned in order of increasing energy and the electronic configuration of the molecule is given by a string of the orbitals (in order of increasing energy) with superscripts that indicate the number of electrons occupying the orbital. The isobutene molecule has 32 electrons and the electronic configuration of the ground state is expected to have 16 fully (doubly) occupied molecular orbitals.

An Ab Initio, Polak-Ribiere Optimization algorithm, HyperChem calculation

(presented in the Appendix) was performed to find the electronic configuration for isobutene. The coordinate system used was the same coordinate system shown in Figure

3.8. The calculation gives 16 fully occupied molecular orbitals, as expected:

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 (1a1) (1b2) (2a1) (3a1) (4a1) (2b2) (5a1) (6a1) (3b2) (7a1) (1b1) (1a2) (4b2) (8a1) (5b2) (2b1) (3b1)

According to the above configuration, both the HOMO and the LUMO for isobutene have b1 symmetry. That is the symmetry of both states of the π to π* transition.

In addition, three other allowed transitions are expected, π to 3s, π to 3pσ and π to 3px. Of the four transitions, the valence transition (π to π*) is expected to be stronger than the other three Rydberg transitions.21

38

Chapter 5

Experimental details

Instrumentation

As previously discussed, molecular absorption spectra are difficult to interpret.

Magnetic circular dichroism spectroscopy is a relatively new technique that can provide a better understanding of absorption spectra. It is a difficult technique since it involves measuring a small difference between large numbers. However, it was made possible by the recent availability of synchrotron radiation sources. Synchrotron radiation is intense and linearly polarized, thus making unnecessary the use of linear polarizers that cut the intensity of unpolarized radiation by half. Even so, the signal to noise ratio needs to be further improved by using modulation techniques.

The heart of the modulation technique used in this experiment is a quarter-wave plate modulator. As a quarter-wave plate, it converts linearly polarized to circularly polarized radiation, as discussed in Chapter 2. Because a continuum of wavelengths is used, the optical thickness of the quarter-wave plate has to be changed continuously. This is done by attaching a piezoelectric transducer to the end of a bar of CaF2, a photoelastic material. When the bar is compressed or stretched, the material becomes birefringent.

The optical thickness of the plate depends on the magnitude of the stress, while compressing or stretching the bar will result in right circularly and left circularly polarized radiation, respectively. The transducer is driven at the natural frequency of 39 vibration of the bar, causing the polarization of the radiation to oscillate between right circular and left circular.

The experiment was performed at the Synchrotron Radiation Center of the

University of Wisconsin-Madison. The instrumentation used was designed and constructed by P. A. Snyder. This unique instrumentation allows circular dichroism, magnetic circular dichroism, and absorption measurements in the vacuum ultraviolet region of the electromagnetic spectrum using synchrotron radiation. Figure 5.1 shows the basic experimental setup.

Figure 5.1: Basic experimental setup

Monochromator

The purpose of the monochromator is to produce a single wavelength from a broadband

(multi-wavelength) source. In this experiment, the source is synchrotron radiation.

LiF Window

The lithium fluoride window is present to filter out stray or scattered radiation (unwanted high energy radiation that might get past the monochromator). The lithium fluoride

40

window also serves to isolate the experimental chamber from the storage ring, beam line, and monochromator.

Quarter-wave plate modulator

The quarter-wave plate modulator was used to transform the linearly polarized radiation from the synchrotron into modulated circularly polarized radiation. The radiation alternates between right circularly polarized light and left circularly polarized radiation at a frequency of 50 kHz.

Superconducting Magnet

The superconducting magnet used in these experiments has a maximum field of 8-10

Tesla.

Photomultiplier Tube

The signal is amplified through photoemission and successive instances of secondary emission.

D.C. Controller

The DC Controller is used to regulate the voltage to the photomultiplier tube so that the

DC output of the photomultiplier tube is constant.

Lock-in Amplifier

The lock-in amplifier is set at 50 kHz, the frequency of the quarter-wave plate modulator.

The lock-in amplifier is thus set to detect the AC signal from the photomultiplier.

Data Acquisition System and Recorder

From the lock-in amplifier, the signal goes to a recorder, giving a hard copy, and to the computerized data acquisition system, where the information can be stored and analyzed at a later time.

41

Data Reduction

The data for isobutene were obtained by P. A. Snyder. The raw data for isobutene is graphed below in Figure 5.2:

Figure 5.2: Graph of raw MCD data for isobutene

Because the data points are taken in a particular environment, a baseline must also be taken at the same corresponding wavelengths under the same conditions. In Figure 5.3 below, the graph of the baseline and the magnetic circular dichroism data are plotted.

42

Next, the baseline data are subtracted from the initial data points to render a corrected graph. Looking at the corrected graph in Figure 5.4, you can see both positive and negative magnetic circular dichroism bands.

The plot is then smoothed to get rid of the high frequency noise. Since it is very time consuming to obtain the magnetic circular dichroism measurements, the data must be taken piecewise and then put together to obtain the whole spectrum. The main reason for taking the data piecewise is that a new electron beam is injected into the storage ring periodically. Another reason is that the concentration used must be changed depending on the absorbance of the sample. The magnetic circular dichroism of isobutene after putting together the pieces is shown next in Figure 5.5:

43

Since the intensity of the synchrotron radiation decreases with time, the absorption data, likewise, must be corrected. The same procedures described for correcting the MCD plots are applied to correct the absorption data. After corrections, the absorption spectrum of isobutene is shown below in Figure 5.6:

44

Chapter 6

Results and discussion

Isobutene spectra

The spectra of isobutene presented in Chapter 5 were plotted as a function of wavelength. However, photon energy is inversely proportional to wavelength λ and directly proportional to frequency υ. It is customary to define wavenumber as k = 1/λ, usually measured in cm-1. Energy is then directly proportional to both k and υ. The three terms are used interchangeably so you may plot either energy or frequency in cm-1. The corrected absorption spectrum of isobutene as a function of energy (wavenumber) is given in Figure 6.1 for the 47,600 to 64,000 cm-1 energy region. The spectrum shows

Figure 6.1: Absorption spectrum of isobutene

45

structure, but no clear indication of separate transitions. On the other hand, the usefulness of MCD spectroscopy is shown in the spectrum of Figure 6.2, covering the same energy

Figure 6.2: Magnetic circular dichroism plot of isobutene

range. The MCD spectrum shows alternating regions of negative and positive signal, indicating the possibility of at least four transitions. However, before a detailed discussion of the isobutene spectra, it is useful to look at the spectra from ethylene and propylene.

Ethylene and propylene spectra

Figure 6.3 shows the absorption and MCD spectra of ethylene for the 54,000 to

64,000 cm-1 energy region, with both ε and Δε measured in Lmol-1cm-1. Figure 6.4 shows the absorption and MCD spectra of propylene for the 52,000 to 65,500 cm-1 energy region, with MCD in Lmol-1cm-1T-1. The spectra were taken from Reference 3 (Snyder et al.). The spectra of ethylene and propylene have generally the same shape, but the spectra for ethylene have sharper features. There also seems to be a shift of the whole spectrum to lower energy for propylene. Neither absorption spectrum gives any indication that

46

Figure 6.3: Absorption and MCD spectra of ethylene

Figure 6.4: Absorption and MCD spectra of propylene

47 there is more than one electronic transition, while both MCD spectra show three distinct transitions, with positive, negative and positive signals. The first transition (lowest energy) has a vibrational progression of 800 cm-1 for ethylene and 400 cm-1 for propylene. The second transition has a vibrational progression of 1350 cm-1 in propylene in the absorption spectrum. The third transition shows a doublet structure in both spectra for both molecules. In ethylene, the doublets are separated from each other by 1300 cm-1, while the two peaks of each doublet are separated by 500 cm-1. In propylene, the separations are 1300 and 460 cm-1, respectively.

The authors of Reference 3 made the following assignments for both ethylene and propylene. The first transition was assigned to π  3s, the second to π π*, and the last to π→ 3p (3pσ and/or 3py) for propylene. The same three transitions are observed in ethylene, where the π  3s is the lowest energy transition, and the π π* and the π→ 3p

(3pσ and/or 3py) are very close in energy, with the π→ 3p (3pσ and/or 3py) occurring first in the MCD spectra. The progression of 800 cm-1 in the π  3s transition of ethylene was

-1 assigned to a CH2 wagging vibration with a frequency of 943 cm in the electronic ground state. Since the π→ 3p transitions are not orbitally allowed in ethylene, the authors argued that two vibrational modes (CH2 scissors and CH2 twisting), separated by

420 cm-1 in the electronic ground state, serve as two separate vibronic origins for progressions of the C=C stretching mode, thus resulting in the doublet structure.

Although the frequency of this stretching mode is much larger in the electronic ground state of ethylene, it is expected to be about 1350 cm-1 in the excited states.21

48

Isobutene assignments

In comparing the spectra of isobutene in Figures 6.1 and 6.2 to those of ethylene and propylene in Figures 6.3 and 6.4, there are some differences. In terms of the features in the spectra, the order of sharpness is ethylene, isobutene and propylene. This could be related to molecular symmetry, with sharper features for the higher symmetry, since the number of allowed rotational modes increases with decreasing molecular symmetry. The larger the number of rotational modes coupling to a vibrational mode, the broader the vibrational line is in the spectrum. In addition, all the π→ 3p transitions are forbidden in ethylene and therefore are vibronically allowed, which tends to give sharper peaks.

In terms of the overall energy shift of the spectra, the trend to lower energies for larger molecules is now more obvious. This shift seems to be mostly due to the energy shift of the π π* transition, and is more easily seen in the MCD spectra. The start of this transition in the MCD spectrum shifts from 58,000 to 55,000 to 50,000 cm-1 as molecular size increases. This could be due to a shift to lower energy for the π* molecular orbital. Since a C-C bond is nearly 50% longer than a C-H bond, replacing the hydrogen with a methyl group would reduce the overlap between the π* orbital and orbitals belonging to the groups attached to the carbons in the double bond.

However, the main difference is that the MCD spectrum of isobutene has at least seven regions of alternating negative and positive signal. The first transition is negative and ranges from 47,600 to 49,600 cm-1. This region has a peak molar extinction coefficient of 867 L mol-1cm-1 in the absorption spectrum and is assigned to the π  3s transition, as in the case of ethylene and propylene.3 The second transition is positive and ranges from 49,600 to 55,170 cm-1. This transition has a peak molar extinction coefficient 49 of 9064 L mol-1cm-1, the highest in the absorption spectrum, which is consistent with the assignment to the valence transition, π π*. The third transition is a negative transition

-1 and ranges from 55,170 to 59,740 cm . This transition has been assigned to a π→ 3pσ

3 and/or π  3py transition in ethylene and propylene. However, in those molecules, the transition has a longer energy range. That seems to be the case in isobutene, but the transition is overlapped by another with an opposite MCD signal. The overlap starts at

59,400 cm-1, where an unusually sharp change in slope is observed in the MCD spectrum of Figure 6.2. This overlap seems to continue up to the high energy limit of the figure, as three regions of positive signal are observed. Since the π  3py transition is not allowed for isobutene, it is reasonable to assign the overlapping transition with negative MCD signal to π→ 3pσ. It would also seem reasonable for the third transition in ethylene and propylene with a negative MCD signal to be assigned to π→ 3pσ. The other overlapping transition in isobutene with a positive MCD signal is then assigned to π  3px, which is allowed for isobutene. Interestingly, the π π* and π  3px transitions assigned to the

1 1 regions of the MCD spectrum with negative signal are both z-polarized A1 => A1 transitions. Moreover, the π→ 3pσ and π→ 3s transitions assigned to the regions of the

1 1 MCD spectrum with positive signal are both x-polarized A1 => B1 transitions.

However, the sign of the MCD signal (B term) is not easily predicted as it is given by a sum over states involving the electric and magnetic transition moments.

In isobutene, the first transition does not seem to have any structure in either spectrum. The second and third transitions do show structure in both spectra, although the structure for the second transition is not as pronounced in the MCD spectrum. To further

50 compare the structures, the two spectra are plotted together on the same scale in Figure

6.5. The units for the molar extinction coefficient and the relative MCD signal are the

Figure 6.5: Comparison of MCD and absorption spectra

Wavenumber (cm-1) same as those in Figures 6.1 and 6.2. Clearly, there is a correspondence between the observed peak energies in the MCD and absorption spectra of isobutene. For both the second and third transitions, most of the peak energies seem to be equally spaced, indicating vibrational progressions. Moreover, for the third transition, there is a doublet

51 structure, consisting of a well-defined peak and a shoulder (sh), that repeats with equal energy spacing and is visible in both spectra. In order to determine the energy spacing between adjacent peaks, the peak energies (wavenumbers) are listed for both spectra in

Table 6.1 below.

Table 6.1: Peak energies for MCD and absorption spectra of isobutene (Lmol-1cm-1) Peak # MCD energy (103 cm-1) Absorption energy (103 cm-1) 1 48.97 49.04 867 2 51.36 5644 3 51.85 4 52.74 8927 5 52.85 6 53.95 9064 7 53.85 8 54.40 9 55.48 55.45 8606 10 55.97 (sh) 55.95 (sh) 5932 11 56.86 56.82 5953 12 57.37 (sh) 57.34 (sh) 3867 13 58.23 58.22 3616 14 58.72 (sh)

Peak 1 corresponds to the first transition and has nearly the same energy in the two spectra. The second transition shows vibrational structure in both spectra, although the peaks in the MCD spectrum are not as pronounced and occur at different energies from those in the absorption spectrum. Thus, two vibrational spacings are observed for the second transition. The first is 1290 cm-1, corresponding to the energy difference between peaks 2 and 4, and 4 and 6. The second is 1000 cm-1, corresponding to the energy difference between peaks 3 and 5, and 5 and 7. Peak 8, seen at 54,400 cm-1 for the second transition of the MCD spectrum, does not seem to correlate to any other peak in either spectrum. The doublets in the third transition have a vibrational spacing of about

1370 cm-1, which corresponds to the energy difference between peaks 9 and 11, and

52 peaks 11 and 13. The spacing between the first peak of the doublet and the second peak of the same doublet (the shoulder) is about 500 cm-1 for the three doublets listed, peaks 9 and 10, peaks 11 and 12, and peaks 13 and 14. There are seven doublets in Figures 6.1 and 6.2, but beyond the third, the peaks seem to be shifted by the overlapping transitions.

Finally, the features in the overlapping transition with a positive MCD signal do not seem to fall in a progression, again possibly because of the overlap between transitions.

Some additional structure is observed upon closer examination of the π π* transition of the MCD spectrum of isobutene. Figure 6.6 reveals four additional peaks around 54,270, 54,430, 54,580, and 54,720 cm-1.

Figure 6.6: MCD spectrum of π π* transition in isobutene

Similarly, the π→ 3s transition of the MCD spectrum of isobutene reveals additional structure. Figure 6.7 shows, in addition to the main peak at 48,970 cm-1, a shoulder at 48,110 cm-1, giving a separation of 760 cm-1.

53

Figure 6.7: MCD spectrum of π→ 3s transition in isobutene

Vibrational coupling To determine which vibrational modes are responsible for the structure observed in the isobutene spectra, it is necessary to know the symmetry and frequency in cm-1 of all vibrational normal modes. A complete list of all 30 modes is given in Table 6.2. The data, obtained from Reference 22, was modified to agree with the Cartesian coordinate system shown in Figure 3.8 of the present work. In reference 22, the x and z axes are

54

Table 6.2: Ground state vibrational normal modes for isobutene22

interchanged. This has the effect of interchanging the mode symmetries b1 and b2. To

determine the symmetry species of vibrations that can couple to an electronic transition,

Eq. 4.4 must again be applied, but slightly modified. The initial and final states are now

55 products of an electronic and a vibrational wavefunction, so the irreducible representation of each state is now the product of the irreducible representations of the electronic and vibrational states. Since all of the vibrational states are totally symmetric in the ground

1 state, the initial A1 electronic state (π state) is always multiplied by the a1 irreducible representation of the ground vibrational state. The irreducible representation of the final electronic state will be multiplied by the irreducible representation of an excited vibrational state, which can have symmetry a1, a2, b1, or b2, as indicated in Table 6.2.

Let us first look at the   * and 3px transitions, both having state notation

1 1 A1  A1. Thus the allowed vibronic transitions are as follows:

 b   b   1   1  A1a1 b2 A1a1  b2  All vibrations with a1 symmetry are     allowed and are „z‟ polarized. a1  a1  allowed  b   a  allowed  1   1  All vibrations with b1 symmetry A1b1 b2 A1a1  a2      are allowed and are „x‟ polarized. a1   b1   b  b   1   2  Transitions with a symmetry do not A a b A a  b 2 1 2  2  1 1  1  couple with these transitios     a1  a2   b  a   1   2  All vibrations with b2 symmetry A1b2 b2 A1a1   a1  allowed     are allowed and are „y‟ polarized. a1  b2 

The allowed vibronic transitions associated with the   3s and 3p (both are of state

1 1 notation A1 B1) are as follows:

 b   a  allowed  1   1  B1a1 b2 A1a1  a2  All vibrations with a1 symmetry are     allowed and are „x‟ polarized. a1   b1 

56

 b  b   1   1  All vibrations with b1 symmetry are B1b1 b2 A1a1  b2      allowed and are „z‟ polarized. a1  a1  allowed  b  a   1   2  B1a2 b2 A1a1   a1  allowed All vibrations with a2 symmetry are     allowed and are „y‟ polarized. a1  b2   b  b   1   2  Transitions with b2 symmetry are not B1b2 b2 A1a1   b1      allowed with these electronic transitions. a1  a2 

1 1 For the 3py transition (state notation A1  B2), the following results are obtained:

 b  b   1   2  A2 a1 b2 A1a1   b1  Transitions with a1 symmetry do not couple     with orbitally allowed transitions. a1  a2   b  a   1   2  All vibrations with b1 symmetry are A2b1 b2 A1a1   a1  allowed     allowed and are „y‟ polarized. a1  b2   b   b   1   1  A2a2 b2 A1a1  b2  All vibrations with a2 symmetry     are allowed and are „z‟ polarized. a1  a1  allowed  b   a  allowed  1   1  All vibrations with b2 symmetry A2b2 b2 A1a1  a2      are allowed and are „x‟ polarized. a1   b1 

The results are summarized in Table 6.3 below for the four allowed transitions in isobutene. The common and state notations are shown in the first two columns. The third column indicates the energy range of each transition. The fourth column shows the vibrational mode symmetries that are allowed to couple to each electronic transition. The last column indicates the frequencies obtained from the vibrational progressions in the observed spectra.

57

Table 6.3: Allowed vibrational modes for isobutene transitions Allowed State Energy range Allowed Observed frequencies Transitions Notation (cm-1) Vibrations from spectra (cm-1) 1 1  => 3s A1=> B1 47,600-49,600 a1, a2, b1 760 1 1  => * A1 => A1 49,600-55,170 a1, b1, b2 1000, 1290 1 1  => 3p A1=> B1 55,170-64,000 a1, a2, b1 500, 1370 1 1  => 3px A1=> A1 59,400-64,000 a1, b1, b2

The  => 3s transition is orbitally allowed in isobutene and can couple to vibrational modes of a1, a2, and b1 symmetry. In ethylene, a vibrational progression of

-1 800 cm was assigned to a CH2 wagging mode. According to Table 6.2, there is only one

-1 CH2 wagging mode in isobutene, with a frequency of 890 cm in the electronic ground state. It has b1 symmetry and is expected to have a lower frequency in an excited state.

The progression observed at 760 cm-1 in isobutene is then assigned to this mode.

The  => * transition is orbitally allowed and can couple to vibrational modes of a1, b1, and b2 symmetry. When an electron is promoted from the  to the * orbital, there is a shift in electron density from the region between the two carbons in the double bond to the regions between the two H atoms and between the two CH3 groups. One would expect that symmetrical vibrations (a1 modes) would more strongly couple to this transition since the * orbital, shown in Figure 3.2, has four lobes symmetrically placed above and below the molecular plane. What can the extra electron density do to the two

58

H atoms and the two CH3 groups? Inserting something between the two H atoms can force them to move in a symmetrical scissors mode. In the case of the CH3 groups, it can cause the groups to rock (symmetrical rocking mode) or to deform (symmetrical deformation mode). According to Table 6.2, the CH2 scissors mode and the CH3 symmetrical deformation mode have frequencies of 1416 and 1366 cm-1, respectively, in the electronic ground state. These modes are expected to have lower frequencies in electronic excited states, so the vibration at 1290 cm-1 is assigned to one or both of these

-1 modes. The vibration at 1000 cm is assigned to the CH3 symmetrical rocking mode, which, according to Table 6.2, has a frequency of 1076 cm-1 in the electronic ground state.

For the  => 3px transition, no vibrational progression was observed. For the  =>

3ptransition, the doublet structure cannot be explained as was done in the case of ethylene3 since it implicitly assumes that the transition is not orbitally allowed, which is not the case in isobutene. One possible explanation is that there is only one transition, the orbitally allowed  => 3pσ transition. The purely electronic transition then provides one vibronic origin. The second vibronic origin (for the second peak in the doublet structure) could then be from 2 quanta of the CH2 twisting vibration with ground state frequency of

981 cm-1, according to Table 6.2. A more likely explanation is that we have two overlapping transitions with positive MCD signal giving rise to two progressions from the C=C stretching mode. One of the transitions is obviously  => 3pσ, since it is orbitally allowed for isobutene. The likely candidate for the other transition is  => 3py, which is not orbitally allowed. If that is the case, it is reasonable to conclude that  => 3py gives rise to the progression of the shoulder, which is by far the weaker of the two peaks in the 59 doublet structure. This explanation is consistent with the suggested assignment for ethylene and propylene from Reference 3.

60

Chapter 7

Conclusion

Knowing the chemistry of ethylene can be very valuable to science. Ethylene is important in many aspects of society. From its importance in industry concerning the production of plastics to its critical role in biology where its behavior as a hormone is responsible for the ripening of fruits, ethylene is a molecule worthy of further investigation. The enigma that has always plagued theorist concerning ethylene is the absorption spectrum. The π→π* transition has always been assumed to be the lowest energy transition in ethylene. However, experimental evidence never supported the claim.

The absorption spectrum of ethylene just doesn‟t reveal enough information to back this claim. On the other hand; magnetic circular dichroism measurements on ethylene does give more information about the transitions in ethylene and can further aid in relating theory and experiment.

In previous research, magnetic circular dichroism (MCD) measurements were taken on ethylene and propylene. Both MCD spectra clearly exhibited three electronic transitions. The transitions, in order of increasing energy, were identified as a π→3s transition, the π→π* transition, and a π→3p transition. The π→3s transition was assigned to the region from 50,000 to 57,000 cm-1 in ethylene and 52,000 to 55,080 cm-1 in propylene. The π→π* transition was assigned to the region from 57,000 to 62,500 cm-1 in ethylene and 55,080 to 58,760 cm-1 in propylene. The ranges for the π→3p transition 61 were 57,000 to 62,500 cm-1 and 58,760 to 65,550cm-1, respectively. Thus the MCD measurements revealed three similar electronic transitions in ethylene and propylene.

Results obtained from the MCD measurements in isobutene also followed a similar pattern confirming that the π→3s transition may indeed be the lowest energy transition in ethylene. In isobutene, the π→3s transition has a negative MCD signal in the region ranging from 47,600 to 49,600 cm-1. The positive π→π* transition is assigned

-1 to the region from 49,600 to 55,170 cm . The negative π→3pσ transition is assigned to the 55,170 – 64,000 cm-1 region. However, there is a 4th transition revealed in the MCD spectrum of isobutene. This is in agreement with a group theoretical analysis that shows

th four allowed transitions. The 4 electronic transition is assigned as the π→3px transition and it ranges from 59,400 – 64,000 cm-1. There appears to be some overlapping between the two electronic transitions in the region from 55,170 to 64,000cm-1.

All transitions in the MCD spectrum of isobutene appear to couple to some vibrational mode. The π→3s electronic transition (lowest energy) appears to couple to a wagging mode with a measured frequency of 760cm-1. For the π→π* electronic transition, several vibrations are identified as coupling with this transition. The CH2

-1 scissors and/or the CH3 symmetric deformation are assigned to the vibration at 1290 cm ,

-1 while the CH3 symmetric rocking mode is assigned to the frequency at 1000 cm . Most noticeable in the third transition, π→3pσ, are the doublets that progress through this region. The spacing between the main peaks of the doublets is 1370 cm-1 with the spacing between the two peaks of a doublet being about 500 cm-1. The doublet structure is explained by assuming two overlapping transitions each with a vibrational progression

-1 of 1370 cm assigned to the C=C stretching mode. The transition overlapping the π→3pσ

62 th transition is postulated to be π→3py. In the π→3px transition (4 transition), there appears to be vibronic coupling that is difficult to decipher because of the overlapping of the two transitions.

P. A. Snyder‟s technique of taking magnetic circular dichroism measurements in the vacuum ultraviolet region using an experimental end station designed by herself proves useful in shedding more information on the electronic structure of ethylene. In the three studies performed on the three olefins (ethylene, propylene, and isobutene), the results obtained show similar features that strongly suggest that the π→π* transition is not the lowest energy transition.

Future work needed to further the understanding of the electronic transitions in ethylene would consist of a better fitting to define maximums and peak separations in the spectra. This would also aid in distinguishing vibronic frequencies and assignments. A calculation of the mixing of transition states (Rydberg and valence) would help to define electronic transition assignments. This would involve a calculation of magnetic and electronic transition moments. Also needed is an analysis of the oscillator strengths for the transitions in the absorption spectrum of isobutene. Finally, perhaps research on another simple olefin would give a better understanding of the electronic structure of ethylene.

63

Appendix

Hyperchem Calculation

Single Point, AbInitio, molecule = (untitled).

Convergence limit = 0.0000100 Iteration limit = 50

Accelerate convergence = YES

The initial guess of the MO coefficients is from eigenvectors of the core Hamiltonian.

Starting HyperGauss calculation with 76 basis functions and 144 primitive Gaussians.

MOLECULAR POINT GROUP C2V

Vibrational Analysis, AbInitio, molecule = (untitled).

AbInitio

Convergence limit = 0.0000100 Iteration limit = 50

Accelerate convergence = YES

The initial guess of the MO coefficients is from eigenvectors of the core Hamiltonian.

Shell Types: S, S=P, 6D.

RHF Calculation:

Singlet state calculation

Number of electrons = 32

Number of Doubly-Occupied Levels = 16

Charge on the System = 0

Total Orbitals (Basis Functions) = 76

64 Primitive Gaussians = 144

Starting HyperGauss calculation with 76 basis functions and 144 primitive Gaussians.

2-electron Integral buffers will be 32000 words (double precision) long.

Two electron integrals will use a cutoff of 1.00000e-010

Regular integral format is used.

2877209 integrals have been produced.

Iteration = 1 Difference = 302.5249464622

Iteration = 2 Difference = 414.6444908246

Iteration = 3 Difference = 44.1835526720

Iteration = 4 Difference = 10.3983974450

Iteration = 5 Difference = 1.9846103875

Iteration = 6 Difference = 0.0508521271

Iteration = 7 Difference = 0.0043561798

Iteration = 8 Difference = 0.0007384452

Iteration = 9 Difference = 0.0000987431

Iteration = 10 Difference = 0.0000064927

ENERGIES AND GRADIENT

Total Energy = -97954.3998537 (kcal/mol)

Total Energy = -156.100253148 (a.u.)

Electronic Kinetic Energy = 97840.0938614 (kcal/mol)

Electronic Kinetic Energy = 155.918094976 (a.u.)

65 The Virial (-V/T) = 2.0012 eK, ee and eN Energy = -172845.3246009 (kcal/mol)

Nuclear Repulsion Energy = 74890.9247471 (kcal/mol)

RMS Gradient = 9.4767146 (kcal/mol/Ang)

MOLECULAR POINT GROUP C2V

EIGENVALUES(eV)

Symmetry: 1 A1 1 B2 2 A1 3 A1 4 A1

Eigenvalue: -305.693516 -305.246728 -305.245959 -304.800244 -29.386348

Symmetry: 2 B2 5 A1 6 A1 3 B2 7 A1

Eigenvalue: -25.606695 -24.954325 -19.257475 -16.625851 -16.512515

Symmetry: 1 B1 1 A2 4 B2 8 A1 5 B2

Eigenvalue: -15.917473 -14.967536 -14.165357 -13.802120 -12.803805

Symmetry: 2 B1 3 B1 9 A1 10 A1 6 B2

Eigenvalue: -9.069729 4.753387 6.454849 7.705320 8.019944

Symmetry: 11 A1 7 B2 2 A2 4 B1 8 B2

Eigenvalue: 8.711176 8.726365 9.279620 9.684245 10.217381

Symmetry: 12 A1 9 B2 13 A1 10 B2 5 B1

Eigenvalue: 10.946252 13.437693 13.672922 19.836828 19.870553

Symmetry: 14 A1 15 A1 6 B1 3 A2 11 B2

Eigenvalue: 19.973621 21.471390 22.896750 23.187929 24.318930

Symmetry: 16 A1 17 A1 7 B1 12 B2 18 A1

Eigenvalue: 24.605998 25.493708 26.627535 28.645697 29.302071

Symmetry: 13 B2 4 A2 8 B1 19 A1 14 B2

66

Eigenvalue: 31.239099 31.602437 32.109367 32.419792 32.527790

Symmetry: 20 A1 21 A1 15 B2 22 A1 23 A1

Eigenvalue: 32.985171 33.849251 34.058638 37.858381 41.516674

Symmetry: 16 B2 17 B2 5 A2 9 B1 6 A2

Eigenvalue: 41.869631 44.348562 45.181402 46.775420 54.086158

Symmetry: 18 B2 19 B2 10 B1 24 A1 25 A1

Eigenvalue: 57.649783 59.473814 59.567614 60.222401 60.999763

Symmetry: 26 A1 7 A2 11 B1 27 A1 20 B2

Eigenvalue: 67.721172 68.494142 68.747236 68.851270 71.058547

Symmetry: 8 A2 28 A1 21 B2 12 B1 29 A1

Eigenvalue: 72.178499 72.555848 73.653474 77.333332 80.074527

Symmetry: 30 A1 22 B2 31 A1 32 A1 23 B2

Eigenvalue: 86.805620 88.985049 123.561889 125.134815 128.419815

Symmetry: 33 A1

Eigenvalue: 133.584428

ATOMIC ORBITAL ELECTRON POPULATIONS

C 1 S C 1 S C 1 Px C 1 Py C 1 Pz

1.996473 0.650560 0.550969 0.701762 0.741238

C 1 S C 1 Px C 1 Py C 1 Pz C 1 Dx2

0.590087 0.528826 0.375029 0.227401 -0.019705

C 1 Dy2 C 1 Dz2 C 1 Dxy C 1 Dxz C 1 Dyz

0.032751 0.022675 0.000036 0.007238 0.017043

C 2 S C 2 S C 2 Px C 2 Py C 2 Pz

67

1.996726 0.667923 0.492718 0.687010 0.756250

C 2 S C 2 Px C 2 Py C 2 Pz C 2 Dx2

0.483956 0.428049 0.206120 0.168877 -0.018148

C 2 Dy2 C 2 Dz2 C 2 Dxy C 2 Dxz C 2 Dyz

0.020084 0.022685 0.003782 0.010440 0.017786

C 3 S C 3 S C 3 Px C 3 Py C 3 Pz

1.996632 0.628788 0.698964 0.678576 0.687726

C 3 S C 3 Px C 3 Py C 3 Pz C 3 Dx2

0.651823 0.402663 0.314878 0.366527 0.021602

C 3 Dy2 C 3 Dz2 C 3 Dxy C 3 Dxz C 3 Dyz

0.012446 0.021775 0.013926 0.003129 0.008049

C 4 S C 4 S C 4 Px C 4 Py C 4 Pz

1.996632 0.628788 0.698964 0.678576 0.687726

C 4 S C 4 Px C 4 Py C 4 Pz C 4 Dx2

0.651828 0.402665 0.314877 0.366525 0.021602

C 4 Dy2 C 4 Dz2 C 4 Dxy C 4 Dxz C 4 Dyz

0.012446 0.021774 0.013926 0.003129 0.008049

H 5 S H 5 S H 6 S H 6 S H 7 S

0.525997 0.308151 0.525997 0.308155 0.526902

H 7 S H 8 S H 8 S H 9 S H 9 S

0.310712 0.522057 0.296650 0.522057 0.296650

H 10 S H 10 S H 11 S H 11 S H 12 S

68

0.526902 0.310712 0.522057 0.296651 0.522057

H 12 S

0.296647

NET CHARGES AND COORDINATES

Atom Z Charge Coordinates(Angstrom) Mass

(Mulliken) x y z

1 6 -0.422382 0.00000000 -0.12063953 -1.39431849 12.01100

2 6 0.055742 -0.00000000 -0.12063953 -0.05431849 12.01100

3 6 -0.507501 -0.00000000 -1.43699815 0.70568151 12.01100

4 6 -0.507506 0.00000000 1.19571908 0.70568151 12.01100

5 1 0.165852 0.00000000 0.81466790 -1.93431849 1.00800

6 1 0.165848 0.00000000 -1.05594697 -1.93431849 1.00800

7 1 0.162386 -0.00000000 -1.23781899 1.77732869 1.00800

8 1 0.181293 -0.88998733 -2.00856223 0.44236223 1.00800

9 1 0.181293 0.88997764 -2.00857469 0.44235649 1.00800

10 1 0.162387 -0.00000000 0.99653992 1.77732869 1.00800

11 1 0.181292 0.88998733 1.76728316 0.44236223 1.00800

12 1 0.181295 -0.88997764 1.76729562 0.44235649 1.00800

Net Charge (Electrons):

-0.0000

Dipole Moment (Debye):

X: -0.0000 Y: 0.0000 Z: 0.5026 Ttl: 0.5026

Quadrupole Moment (Debye-Ang):

69

XX: -27.9635 YY: -25.6936 ZZ: -26.5204

XY: -0.0000 XZ: 0.0000 YZ: -0.0606

Octapole Moment (Debye-Ang^2):

XXX: -0.0000 YYY: 9.2991 ZZZ: -2.4201

XYY: -0.0000 XXY: 3.3735 XXZ: 0.5937

XZZ: -0.0000 YZZ: 3.1994 YYZ: -3.3493 XYZ: 0.0000

Hexadecapole Moment (Debye-Ang^3):

XXXX: -42.5180 YYYY: -223.7444 ZZZZ: -181.3195

XXXY: -0.0000 XXXZ: -0.0000 YYYX: -0.0002

YYYZ: 1.2139 ZZZX: 0.0000 ZZZY: 0.2919

XXYY: -40.5063 XXZZ: -41.9422 YYZZ: -68.0619

XXYZ: -0.0716 YYXZ: -0.0000 ZZXY: 0.0000

70

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