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Honors Program Theses and Projects Undergraduate Honors Program

5-8-2019

Implementation of Computational Chemistry as part of the Physical Chemistry Curriculum

Erica Hess Bridgewater State University

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Recommended Citation Hess, Erica. (2019). Implementation of Computational Chemistry as part of the Physical Chemistry Curriculum. In BSU Honors Program Theses and Projects. Item 376. Available at: https://vc.bridgew.edu/ honors_proj/376 Copyright © 2019 Erica Hess

This item is available as part of Virtual Commons, the open-access institutional repository of Bridgewater State University, Bridgewater, Massachusetts.

Implementation of Computational Chemistry as part of the Physical Chemistry Curriculum

Erica Hess

Submitted in Partial Completion of the Requirements for Commonwealth Honors in Chemistry

Bridgewater State University

May 8, 2019

Dr. Saritha Nellutla, Thesis Advisor Dr. Steven Haefner, Committee Member Dr. Taryn Palluccio, Committee Member

Acknowledgements

Firstly, I would like to thank my thesis mentor Dr. Saritha Nellutla for her continuous support and assistance throughout this process. Her guidance allowed me to grow as a researcher and to push forward with this work. Thank you for the countless hours around the clock for working with me on this.

I would also like to thank my Dr. Steven Haefner and Dr. Taryn Palluccio for serving on my reading committee and providing invaluable input. Dr. Haefner has been a constant mentor and advisor since the beginning of my undergraduate career. Thank you for all of the support and encouragement over the past four years. Dr. Palluccio always had her door open to me whenever I needed her. Thank you for all of the laughs and constant reassurance in helping me feel confident in my future as a chemist.

I would also like to thank my family- who without them I would be nothing. Every time I was ready to quit, you did not let me, and I will be forever grateful. Thanks mom and dad for continuously believing in me, even when I didn’t believe in myself. Thank you for the late night phone calls, shoulders to cry on, and hugs on my lowest of days. To Mémère, thank you for your unwavering support and faith in me. To my sister, thank you for being my partner in crime, always ready to supply me with laughs.

Lastly, I would like to thank my friends for being with me through it all. To Colleen, you are the best friend I could ever ask for. Thanks for all the late nights, inside jokes, tears, and everything else involved in being roommates. Cam and David, you two have been my soundboard, thanks for constantly inspiring me, the early morning conversations, and steady support over the years. To Eli and Alex, you two have been instrumental in my studies, thanks for the memes, laughs, and shared struggles over the past four years. You two have become the chemistry brothers I’ve always wanted.

1 Table of Contents

Abstract 3

Chapter 1: Introduction 4

Section 1.1. Bachelors of Chemistry Curriculum and accreditation 4 Section 1.2. Physical Chemistry Sub-discipline 5 Section 1.3. Computational Chemistry and its Applications 7 Subsection 1.3.1. Computational Chemistry 7 Subsection 1.3.2. Review of computational chemistry curricula at other institutions 8 Subsection 1.3.3 Work described in this thesis 9

Chapter 2: Theory 10

Section 2.1. Quantum Chemistry and Quantum Mechanics 10 Section 2.2. Schrödinger Equation and Wave Functions 10 Section 2.3. Computational Methods 12 Section 2.4. Basis Sets 14

Chapter 3: Experimental Methodology 16

Section 3.1. Type of calculations done for this thesis 16 Subsection 3.1.1. Natural Bond Orbital analysis 16 Subsection 3.1.2. Geometry Optimization 17 Section 3.2. Types of computational files 17 Subsection 3.2.1. Input Files 17 Subsection 3.2.2. Job Files 18 Subsection 3.2.3. Output Files 19

Chapter 4: The Laboratory Experiments 21

Section 4.1. Photoelectron Spectroscopy (PES) 21 Section 4.2. 1-Dimensional Particle-in-a-Box (1D-PIB) 24

Chapter 5: Summary 27

Appendix A: The Input Files 29

Appendix B: Sample Job Files 40

Appendix C: Sample Output Files 42

References 51

2 ABSTRACT

Physical chemistry is a sub-discipline of chemistry that focuses on the study of matter at the molecular and atomic level. Since physical chemistry provides foundational knowledge necessary to explain concepts ranging from atomic to molecular structure, chemical reactions and dynamics, to spectroscopy properties of chemical and biochemical systems, it has deeper connections to all other sub-fields of chemistry. Therefore, it is imperative for undergraduate students within chemical science baccalaureate degree programs have a comprehensive understanding of physical chemistry concepts. However, many students taking physical chemistry at an undergraduate level often cannot see its inherent connections to other chemistry sub-disciplines. This is because they are overwhelmed not only by the complexity, and often abstractness, of the concepts but also due by the strong mathematics foundations necessary to understand these concepts. Thus, the goal of this project was to exploit the power of computational chemistry to establish connections between the physical chemistry concepts covered in lecture to the chemical systems and their properties that students encountered in other chemistry courses at Bridgewater State University (BSU). More specifically, computational experiments developed as a part of the work presented in this thesis will be incorporated into the Physical Chemistry II (CHEM 382) laboratory curriculum starting in the spring 2020 semester. An added advantage of this work is that the chemistry undergraduates at BSU will gain hands-on experiences in the rapidly growing field of computational chemistry. Work done towards this thesis involved creating computational files for thirteen molecules. Specifically, three types of computational files namely input, job and output files were successfully created for each of the four molecules studied in an experiment on photoelectron spectroscopy, and for each of the nine molecules used for an experiment on one-dimensional particle-in-a-box.

3 CHAPTER 1: Introduction

1. 1. Bachelors of Chemistry Curriculum and Accreditation

The American Chemical Society (ACS), the world’s largest scientific society for chemists and the leading publisher of scientific information1, has created a set of guidelines for promoting excellence in chemistry education at the undergraduate level. Colleges and universities that offer

Bachelor of Science (B.S.) programs in chemistry can go through an ACS approval procedure to certify their programs.2

An ACS approved program provides undergraduate students with an in-depth exposure to five main sub-disciplines of chemistry that are necessary to pursue careers in chemistry and related fields. Students enrolled in these approved programs gain a considerable understanding of chemistry through courses ranging from the introductory level to advanced/specialized topics. In addition, students acquire hands-on experience in a laboratory setting in each sub-discipline. In addition to ensuring students are well prepared for chemistry careers, ACS guidelines also help in establishing a uniform curriculum across all the accredited institutions.3

A B.S. program in Chemistry at Bridgewater State University (BSU) is an ACS approved program offering three concentrations, namely professional chemistry, environmental chemistry, and biochemistry.4 Each of these concentrations has a set of required core courses that include

Physical Chemistry I (CHEM 381) and II (CHEM 382). The physical chemistry courses consist of both a lecture component that meets several times a week and laboratory component that requires students meeting once a week. Physical Chemistry I primarily focuses on thermodynamics and kinetics while Physical Chemistry II covers quantum mechanics and spectroscopy.

4 1. 2. Physical Chemistry Sub-discipline

Traditional sub-disciplines in chemistry are analytical, biochemistry, inorganic, organic, and physical chemistry. Physical chemistry (PChem) is a branch of chemistry that focuses on the study of matter at the molecular and atomic levels and covers foundational concepts encountered in all other branches of chemistry.5 For example, when students learn about thermodynamics, a sub-field in PChem, they learn about evaluating the energies of reactions of chemical (e.g. organic or inorganic molecules) and biological (e.g. proteins and enzymes) systems in order to predict the type of products and the “ideal” experimental conditions that can maximize product yield. Hence, it is essential for undergraduate students enrolled in B.S. program in chemical science to have a good comprehension of the PChem concepts presented in class.

ACS guidelines 3 suggest various PChem concepts and content topics (see Table 1) that should be covered in either a one- or two-semester course sequence. However, topic selection as well as the extent of its coverage is left to the professor’s discretion. In conjunction with lectures,

ACS requires laboratory experience based on physical chemistry topics6 (see Table 2) through hands-on activities. Hands-on laboratory experiments are crucial to understand the theoretical models explored within PChem as many of the models are highly mathematical in nature, but are also essential to understanding various chemical phenomena and analytical techniques often used to characterize chemical compounds. A long-standing belief among undergraduate students is that the content covered in PChem is extremely difficult to understand and holds no important connections to other sub-fields of chemistry. In fact, students at BSU often feel intimidated by

PChem and find it a daunting course to take - a sentiment echoed by undergraduates across other

U.S. institutions.7 Therefore, laboratory experiments offer an excellent opportunity to cement the

5 idea that PChem is a fundamental branch of chemistry that connects to the other chemistry sub- disciplines.

Table 1: The sub-fields of physical chemistry and example coverage concepts suggested by ACS.6

Sub-field of Physical Chemistry Concepts suggested by ACS Thermodynamic functions; Ideal and Non- Thermodynamics and Equilibrium Ideal Systems; Phase Equilibrium and Diagrams Rate Laws and Rate Equations; Relaxation Chemical Kinetics Processes; Rate Theories; Enzyme Kinetics; Photochemistry Postulates of Schrödinger Equation; Operators and Matrix; Particle-in-a-box; Simple Quantum Mechanics Harmonic Oscillator; Hydrogenic Wave Functions Light-matter Interaction; Vibrational Spectra; Spectroscopy Electronic Spectra; Magnetic Spectra; Raman Spectra

Table 2: Example physical chemistry laboratory experiments suggested by ACS.6

Sub-Area of Physical Chemistry Concepts suggested by ACS Heat of Combustion; Thermodynamic Thermodynamics Functions Solid-liquid Phase Diagrams; Liquid-Gas Phase Equilibrium Phase Diagrams Thermal Conductivity of Gases; First-Order Kinetics and Kinetic Theory Kinetic Study; Enzyme Study Isotopic Effects; Vibrational-Rotational Spectroscopy; Electronic –Vibration Spectroscopy Spectroscopy; Atomic Spectroscopy; NMR Spectroscopy Molecular Orbital Theory; Structure, Property Computational and Spectra Calculations

6 Of the two Physical Chemistry I and II courses (CHEM 381 & CHEM 382) offered at BSU, students are often scared or apprehensive about the mathematics involved in CHEM 382 because it primarily focuses on a sub-field known as quantum mechanics, which requires an advanced level of mathematics knowledge to understand its content. Since quantum mechanics describes atomic structure and chemical bonding, and has connections to spectroscopic properties of chemical and biochemical systems, it is crucial for students to not only feel comfortable with

CHEM 382 content, but also to gain a deeper understanding of quantum mechanics and its relation to all other courses in the undergraduate chemistry curriculum at BSU.

1. 3. Computational Chemistry and its Applications

1. 3. 1. Computational Chemistry

While chemists have always been using computational chemistry for calculations on simpler/smaller systems, it was not until recently that computational chemistry has become mainstream. This is due to advances in computer technology such as supercomputers/computing clusters that can process complex multi-step calculations in a matter of seconds or minutes.

Computational chemistry at its core combines classical Newtonian mechanics with quantum mechanics to model chemical systems and chemical phenomena. For example, computational chemistry can be used to predict molecular structure and energy, electron charge distribution and polarity in molecules, reaction rates and rate constants, equilibrium constants, spectroscopic properties, and other properties of chemical systems.8 Therefore, scientific research has been increasingly relying upon computational chemistry to study and/or predict the properties of chemical systems, varying from small organic and inorganic molecular systems to complex proteins and materials in which molecules interact with each other on large length scales.

7 Considering the important role computational chemistry plays in today’s society, it is essential to introduce undergraduate students to computational chemistry during their baccalaureate program. More importantly, computational chemistry has an inherent connection to physical chemistry and therefore can be used as a platform to establish a tangible connection between the theoretical models students learn in classroom to “real world” chemical problems. In fact, faculty across the United States have been attempting to integrate computational chemistry into the physical chemistry curriculum at their respective institutions.

1. 3. 2. Review of computational chemistry curricula at other institutions

As mentioned earlier, a few institutions in other parts of the country have integrated, or are currently working to integrate, computational chemistry into pre-existing physical chemistry courses or introduce it as a new course. For example, at the University of Washington - Seattle, computational chemistry was added to the existing physical chemistry lecture and laboratory courses for undergraduate students during academic years 2007 and 2008.9 At the end of the

2008 academic year, students were given an online survey before final exams and ~92% of the

75 participants replied that computational chemistry helped in their understanding of the material covered in class.9

Another institution that has implemented computational chemistry in their chemistry curriculum is the University of North Carolina at Wilmington (UNCW), where it has been added to laboratory experiments in pre-existing undergraduate chemistry courses.10 Here, computational chemistry was used as a way for students to verify theoretical predictions10 discussed in class and therefore provided them with an opportunity to better understand the mathematical models behind the theoretical predictions. In addition, UNCW has noticed an increase in students conducting undergraduate research, Honors research, and independent

8 studies either in computational chemistry, or using computational work to supplement their synthesis-based projects.10 Assessments based on the PChem topics covered were given to students before and after the introduction of computational chemistry and based on the number of questions answered correctly, the authors suggested that the introduction of computational chemistry helped to improve student understanding of the PChem concepts introduced in class.10

1. 3. 3. Work described in this thesis

As with the aforementioned institutions, incorporating computational chemistry into the existing physical chemistry curriculum at BSU should enable students to make connections between the theoretical models and more traditional chemistry concepts. Therefore, the focus of this thesis is to create a set of computational experiments for students enrolled in the Physical

Chemistry II (CHEM 382) course. CHEM 382 was chosen because of the complexity of the chemistry content covered in this course and its inherent connection to computational chemistry

(vide supra). This project’s goal is to create a library of computational laboratory experiments that can be used as stand-alone “dry” laboratory experiments or that can be used in conjunction with traditional “wet” laboratory experiments focusing on a given topic. For the latter, students will be able to establish the validity of quantum mechanical models while simultaneously collecting and analyzing data through the traditional experimental methods they are familiar with. The experiments described in this work should show the students the usefulness of computational chemistry (and by extension, that of physical chemistry) as well as the connections these sub-fields have to all other fields of chemistry. In fact, these experiments can be implemented in other chemistry courses such as organic chemistry (CHEM 244) and inorganic (CHEM 340 and CHEM 444) at BSU.

9 CHAPTER 2: Theory

2. 1. Quantum Chemistry and Quantum Mechanics

All matter has a hierarchical composition, starting from electrons and nucleons that make up atoms, atoms that make up molecules, and molecules forming macromolecular systems like proteins, DNA, and organic/inorganic polymers. Finally, these large systems make up complex systems ranging from cell walls to plastics.

Quantum chemistry is the study of matter using quantum mechanical principles and models.11 In contrast to Newtonian mechanics (aka classical mechanics), quantum mechanics applies to smallest particles of matter, namely electrons. Quantum mechanics works on two main principles: (i) the wave-particle duality of light and matter and (ii) photons in light and electrons in matter having quantized energies (i.e. matter and light can only have discrete values for their energies). In its essence, quantum mechanics uses the wave nature of matter, more specifically, the wave nature of electrons, to mathematically explain and predict the properties of matter at the macroscopic level.

2. 2. Schrödinger Equation and Wave Functions

The mathematical function that describes the wave nature of electrons is known as a wave function and is denoted by Greek letter Ψ (Psi). According to quantum mechanics,  carries the information about structure and properties of the system it describes. Furthermore,  for a system can be obtained by solving an eigenvalue equation known as the Schrödinger equation, formulated by Erwin Schrödinger in 1926.12 While a time-dependent version is used to describe the evolution of a system as a function of time, a time-independent version is used to describe the

10 “static” behavior of a system. The general form of time-independent Schrödinger equation is given in equation 1.

퐻̂Ψ(휏) = 퐸Ψ(휏) (Eq. 1)

The Hamiltonian operator 퐻̂ , or simply the Hamiltonian, in Eq. 1 is the mathematical operator that yields total energy of the system.13 While Eq. 1 can be solved exactly for trivial one

+ electron systems such as the hydrogen atom or H2 molecular ion, it cannot be solved for multi- electron atoms and molecules due to the correlated motion of electrons. Electron correlation is a mechanism in which an electron avoids crossing other electrons’ paths.

A wave function, or state function, Ψtot(휏), for an electron in an atom or molecule is composed of two parts, namely a spatial wave function 휙 (풓⃗ ), and a spin wave function 훼(휔) or

훽(휔).14 The spatial wave function describes the electron’s spatial coordinates (풓⃗ ) with respect to the atomic nucleus. On the other hand, a spin wave function depicts the electron’s intrinsic spin angular momentum (풔⃗ ) where 훼(휔) corresponds to “up spin” orientation and 훽(휔) corresponds to “down spin” orientation.14 Additionally, according to the Pauli principle, the total wave function, tot, of a system should be anti-symmetric with respect to exchange of electrons if it were to accurately describe the system. This restriction implies that electrons can be represented with a unique set of quantum numbers while remaining indistinguishable in tot.

Generally, small to relatively large chemical systems are studied computationally by solving the appropriate form of Eq. 1. Typically this is done by starting with an initial guess for the system’s wave function and solving Eq. 1 in an iterative process until the wave function () and corresponding energy (E) calculated in two successive iterations converge with-in the desired limits. On the other hand, very large biochemical systems like proteins are computationally studied using classical laws of physics.

11 2. 3. Computational Methods

Computational methods that solve Eq. 1 to obtain structure and properties of a molecular system are known as electronic structure methods. Table 3 lists several electronic structure methods with varying sophistication that are currently available for computational chemists.

Some methods like Hartree-Fock are computationally inexpensive but provide a reasonable qualitative description of a molecular system and can also provide reasonable quantitative information about energies and structures depending on the size of the system. Ab initio models, on the other hand, are applicable for a broad range of systems and provide high quality quantitative descriptions of molecular structures and properties. Since these methods treat electron correlations explicitly, they can be computationally very expensive.

Table 3: Commonly used theoretical models, their uses and examples of specific computational methods for each model.18

Theoretical model Uses/Description Examples of computational methods Semi-Empirical • Good for molecules too large for other PM6, AM1 methods • Initial modeling of large molecules Hartree-Fock (HF) • Least expensive ab initio HF • No inclusion of electron correlation effects Coupled Clusters • Add various levels of electron excitation CCSD(T) • Very high accuracy although very expensive Density Functional • Includes effects of electron correlation B3LYP, APFD, PBE Theory (DFT) • Multiple methods exist based on use of either pure or hybrid functionals • Pure functionals have exchange and correlation functionals to describe energy expression • Hybrid functionals contains some contribution from Hartree-Fock

12 Ab initio models based on Density Functional Theory (DFT) were chosen for work described in this thesis because they treat electron-electron correlations quantitatively but at a much lower

15 15 computational cost. DFT solves Eq. 1 for the ground-state electronic energy E0 based on the

Hohenberg-Kohn theorem (1964).16 According to this theorem, a molecule with a non- degenerate ground state can have electronic properties, such as ground-state electronic energy and wave functions, determined by the ground-state electron probability density  17 which in turn is a function of only spatial coordinates.16

According to DFT, the ground-state electronic energy may be written as E0 = E0 [0] where

15 E0 is expressed as a functional of . A functional, in the most simplistic of terms, is a method of mapping out functions over a plane to achieve a numerical value output. Contributions to E0 in terms of pure DFT functionals can be described as shown in Eq. 2.19

퐸0[ρ] = T[ρ] + V[ρ] + U[ρ] + EXC[ρ] (Eq. 2)

Here, T is the kinetic energy functional arising from the motion of electrons, V is electron-nuclei attractive potential energy and nuclei-nuclei repulsion functional, and U is the potential energy functional from electron-electron repulsions. While these contributions are easy to calculate, EXC is difficult to determine as it represents dynamic correlation in the motion of individual electrons and exchange interactions arising from the antisymmetric wave function.17 For practical purposes, EXC is divided into two parts given as:

EXC[] = EX[] + EC[] (Eq. 3)

Here, EX, known as exchange functional, represents interactions between electrons with same spin and EC, known as correlational functional, represents mixed-spin interactions between electrons. Becke20 suggested that the inclusion of Hartree-Fock exchange results in more accurate values for E0. Functionals that mix exchange-correlational functionals with Hartree-

13 Fock exchange are known as hybrid functionals. One of the commonly employed hybrid functionals in DFT calculations is B3LYP, which stands for Becke three-parameter (B3) Lee-

Yang-Parr (LYP).

2. 4. Basis Sets

A Basis set is a set of acceptable trial functions used to construct a tot that describes a chemical system. In molecules they represent mathematical functions of molecular orbitals. A basis set can be thought of as restricting each electron in a system to a particular region of space within a molecule. According to quantum mechanics, there is a finite probability of finding an electron anywhere within a molecule and therefore a larger basis set will impose fewer restrictions on electron position within a molecule. As one would expect a larger basis set provides a more accurate description of its molecular wave function, and therefore results in more accurate calculations of molecular properties. However, since a “true” description of molecular wave function requires an infinite number of functions in a basis set, computations should be carried out using the largest basis set that is practical.

Table 4: Some basis set types and their description.16, 18

Basis Set Type Description • Valence orbitals are described by 2 or more different sized basis Split-Valence functions Polarized • Adds orbitals with angular momentum • Larger versions of s- and p- type functions Diffuse functions • Orbitals can occupy a larger space • Good for systems where electrons are comparatively far from nucleus High Angular • Adds multiple polarized basis sets in the triple zeta basis set Momentum

14 Basis set assigns a group of functions, known as basis functions, to each atom within a molecule and are often classified by the number and types of basis functions (see Table 4). Each basis function is generally composed of a linear combination of several Gaussian functions known as primitives, which serve as approximations for atomic orbitals. For example, NBO analysis on methane (CH4) uses a split-valence basis set which assigns one basis function for each core atomic orbital on each atom and multiple basis functions for each valence atomic orbital on each atom. Explanation of the 6-31+G(d,p) basis set used to perform the NBO analysis on CH4 is as follows. G represents Gaussian functions, ‘6’ represents the number of primitives per core orbital basis function on C and each H. The ‘31’ represents two types of valence orbital basis functions that are made of 3 and 1 primitives, respectively. Finally, ‘+’ indicates addition of a diffuse function to C, ‘d’ indicates an additional polarized function for C, and ‘p’ indicates an additional polarized function for each H.

For a given type of calculation, computational time can vary between a few seconds to a few months depending on the computational method, basis set(s), and computing resources. It is important to balance these factors when approaching any computational work. This delicate balance becomes very important when designing computational laboratory experiments at teaching institutions like BSU. Therefore, for the work described in this thesis, DFT methods were selected to perform computationally inexpensive calculations such as geometry optimization and natural bond orbital analysis on small to medium molecular systems like methane, water, and 1,1-diethyl-2,2-cyanine iodide. As mentioned earlier, DFT methods can provide accuracy similar to some of the high-end methods while using computing resources of low-end methods.

15 CHAPTER 3: Experimental Methodology

The work described in this thesis has been conducted on the C3DDB computing cluster housed at the Massachusetts Green High Performance Computing Center (MGHPCC) in

Holyoke, MA. C3DDB cluster currently has 133 computing nodes consisting of 7,200 cores each with 61 terabytes of memory.21 Computational chemistry software known as Gaussian 09 22 was used to perform all calculations described in this work. Gaussian 09 is capable of predicting many properties of molecules such as molecular geometries and associated energies, electron spin densities, and vibrational frequencies.

Natural Bond Orbital analysis was carried out for a series of diatomic and polyatomic molecules, whereas geometry optimization was performed on a series of -conjugated organic dyes (Table 5 in Chapter 4). While input files for each molecule and example job files are respectively given in Appendices A and B, Appendix C provides example output files for the two

CHEM 382 experiments presented in this work.

3. 1. Type of calculations done for this thesis

3. 1. 1. Natural Bond Orbital analysis

Natural Bond Orbital (NBO) analysis is a multiple step method that establishes the electron density of lone electrons, bonding orbitals, and anti-bonding orbitals on an atom. Core electrons and lone pairs are localized on an atom in atomic orbitals (AOs).16 These AOs are then used to localize the bonding and anti-bonding molecular orbitals (MOs) between the atoms, which are hybridized orbitals.16 The NBO calculation shows the contribution of each atomic orbital to each of the MOs present in the molecule.16

16 3. 1. 2. Geometry Optimization

Each molecular system has a total energy associated with it, and as the atoms in the molecule move, small changes in the total energy occur. This energy is described by a potential energy surface, which is a mathematical way to describe the relationship between the molecular structure and its energy.14 A geometry optimization is a calculation that can be used to determine local minima, maxima, or a transition state in the potential energy surface.14 For the purposes of the work conducted for this thesis, the geometry optimization was used to determine the minima.

3. 2. Types of computational files

3. 2. 1. Input Files

Each computation presented in this work requires an input file, which contains all information needed to start a computation. For example, it contains spatial coordinates of a molecule, computational method and basis set(s) to be used, and properties to be evaluated. An example of an input file is shown in Figure 1 for NBO analysis for methane. The first section contains key words that describe the computational method (B3LYP), the basis set (6-31+G(d,p)) to be utilized, and calculations to execute (optimization (Opt) and NBO analysis). Additionally, it contains some technical information such as the number of cores (8), RAM memory to be used for each core (8 GB), and file name to store intermediate information generated by the software.

The second section has the molecular coordinates for methane along with its charge (0) and spin multiplicity (1). Spin multiplicity is a measure of number of unpaired electrons. For example, if all the electrons in a molecule are spin paired then total spin Stot = 0 and spin multiplicity, defined as 2Stot + 1, will equal to 1. The format in which molecular coordinates are listed is

17 referred to as z-matrix format. Alternately, Cartesian coordinates (x, y, z) for each atom in methane can be listed in the input file.

Section 1 Section 2

Figure 1. The input file created to perform geometry optimization (keyword Opt) and natural bond orbital analysis (keyword NBO) for a methane molecule. While section 1 contains technical information, section 2 contains information about methane. See text for more details.

3. 2. 2. Job Files

The job file contains all of the technical information for the executable command lines to carry out the calculation. An example of a job file is provided in Figure 2 for the analysis of methane. The first section contains information about the number of cores (8), memory allowed

(9000 MB), and time limit (24 hours). The second section indicates the name of the input file to be read (methane) and the file format (gzmat). For gzmat format, the r is the distance between atoms, a is the angle between the atoms, and d is the dihedral angle, which is the angle between the planes. The third and largest section is for the computer to know what directory (i.e. folder) the files are saved in, where the output file should be saved (i.e. storage directory), and other executable system commands.

18

Section 1 Section 2

Section 3

Figure 2. The job file created to perform a calculation for a methane molecule. Section 1 contains technical information, section 2 file name and format, while section 3 contains executive commands. See text for more details.

3. 2. 3. Output Files

The output files are large files which contain all the information about a given type of calculation and can take up multiple pages. The output file shows the data for each iterative step in the process until the calculated wave function and energy between two successive iterations converge within the desired limits. However, the output file format and information varies depending on what type of job was run, as the computer will only write information applicable to the job in the output file. An example output file for the geometry optimization of methane is shown in Figure 3. The first section shown is the final optimized geometry, which can be

19 compared to section 2 of Figure 1. The last section is from the very end of an output file and it remains the same regardless of the type of job. It has a quote, which changes for every output file, as well as the line titled “Normal termination of Gaussian 09,” which includes the date and time it took for the computation. This line indicates that the job was run successfully.

Section 1

Section 2

Figure 3. The output file generated for the geometry optimization of methane. Section 1 contains the file molecular coordinates; section 2 informs that the job ran successfully.

20 CHAPTER 4: The Laboratory Experiments

As part of this thesis, computational data to supplement existing experiments on photoelectron spectroscopy (PES) and one-dimensional particle-in-a-box (1D-PIB) were developed. Table 5 summarizes the results of the computations and files created for this thesis.

As mentioned in Chapter 3, the input, job, and output files are provided as Appendices A, B, and

C, respectively.

Table 5. List of molecules and type of computation done as a part of this work for each of their respective experiments.

Number of Type of Chemical formula of molecules Experiment molecules computation studied studied Natural Bond Photoelectron Orbital (NBO) 4 N2, CO, NH3, CH4 Spectroscopy analysis + + C23H23N2 , C25H25N2 , + + One dimensional Geometry C27H27N2 , C23H23N2 , 9 + + particle-in-a-box optimization C25H25N2 , C27H27N2 , C16H14, C18H16, C20H18

4. 1. 1. Photoelectron spectroscopy (PES)

As stated in section 3. 1. 1, molecular structures are composed of molecular orbitals, with each of these orbitals possessing their own energy. These energies can be obtained from a technique called as photoelectron spectroscopy (PES) which is based on the photoelectric effect.

Photoelectric effect, in simplistic terms, is when a material is exposed to an appropriate energy in the form of light to produce electrical current. Therefore, a laboratory experiment based on PES allows students to develop a deeper understanding of electronic structure of molecules as well as understand the PES in the context of its connection to molecular orbitals and molecular structure,

21 both of which students have previously learned in other chemistry courses at BSU. Since the PES instrument is quite expensive ($200K - $1 million), only few institutions have this facility and unfortunately, BSU does not. However, given the importance of PES, it is currently introduced as a dry lab at BSU using seven molecules that students are very familiar with, namely, N2, CO,

NH3, H2O, CH4, C2H6 and HCHO.

In the current version of the experiment, students are provided with valence molecular orbital

(MO) diagrams and PES spectra for all of the molecules with the exception of HCHO. For

HCHO, computed energies of MOs from literature 23 along with its PES spectrum are given to the students. For each molecule, students are then tasked with: (i) drawing Lewis dot structure,

(ii) filling the valence MO diagram with the appropriate number of electrons and (iii) assigning the peaks in the PES spectrum to a particular MO energy level in the MO diagram. As an example, figure 4 shows the material provided to students and analysis they do.

Figure 4: (a) Valence MO diagram for CH4 formed from valence atomic orbitals on carbon and 23 24 MOs of H4. (b) PES spectral bands of two highest occupied MOs in CH4. (c) Analysis done by the students for currently existing PES experiment.

22

(a) (b) Nitr o g en ( N2) Nitr o g en ( N2) Car b o n Monoxi de Ca (r C b O o n) M onoxide ( C O)

(c) (d)

Figure 5: Lewis dot structures of the four molecules studied for photoelectron spectroscopy Ammonia ( NH ) 25 Methane ( C H ) experiment.A m(a)m dioninitrogena ( N H(b) )carbon monoxide (c)3 ammoniaMet ha(d)ne methane ( C H ) 4 3 4

In this thesis, computational work was carried out for N2, CO, NH3, and CH4 (figure 5) as the computational data for H2O and C2H6 was previously collected by Dr. Nellutla (instructor of

CHEM 382) and her collaborator. To generate the NBO analysis data needed for PES experiment the B3LYP method was selected with a 6-31+G(d,p) basis set. As mentioned in Chapter 3, the

B3LYP method has the ability to produce accurate results at a lower computational cost and was chosen for this work. The 6-31+G(d,p) basis set was chosen because it is large enough to capture the true wavefunction of small molecules chosen for this experiment.

For each molecule a geometry optimization with an NBO analysis was performed. This resulted is an output file containing spatial coordinates of an optimized geometry, energies of each of the MOs, and the percent contribution of each atomic orbital from each atom to a specific

MO. These results will allow the instructor to create a more inquiry-based experiment that will facilitate an in-depth exploration of MO theory and its connection to PES spectroscopy. For example, students will be provided with, in addition to the PES spectrum, the output file for each molecule and may be asked to: (i) construct an MO diagram using orbital energies corresponding

23 to the optimized molecular geometry, (ii) assign the PES spectral peaks to specific MOs and (iii) use the wavefunctions of MOs responsible PES spectra to analyze type and percent contributions of the atomic orbitals, draw contour diagrams of MO wavefunctions, calculate number nodes etc.

4. 2. 1-Dimensional Particle-in-a-Box (1D-PIB)

One of the theoretical models that is extensively covered in CHEM 382 here at BSU is the 1- dimensional particle-in-a-box (1D-PIB). The 1D-PIB model states that a particle of mass (m) is confined to a hypothetical one-dimensional box of length (L) with infinite potential energy walls.

1D-PIB can serve as a semi-quantitative model to analyze the electronic spectra (aka UV-visible spectra) of molecules with conjugated bonds, because the conjugated bonds can be considered as a 1-dimensional box of a fixed length along which -electrons can move from one end of the molecule to the other. The Schrödinger equation of this system can be analytically solved to yield the energies of the particle’s eigenstates and the energies obtained can be used to predict the HOMO – LUMO electronic transitions in the  conjugated molecules.

Currently, students are given stock solutions of selected series of conjugated dyes (cf. figure

6) and are asked to collect UV-visible spectra following the standard operating protocol for the diode array spectrophotometer. From there, students are to analyze the absorbance data to find the wavelength corresponding to the HOMO − LUMO transition for each of the dye in their series and compare those values to the ones predicted from the 1D-PIB model. Students are also asked to determine the effects of structural aspects, such as the length of the box and type of terminating groups, have on HOMO − LUMO transitions in their dye series.

24 (a) (b)

(c)

(f) (d) (e)

(g) (h)

(i)

Figure 6: Molecular structures of the nine dyes studied for one-dimensional particle-in-a-box experiment. (a) 1,1-diethyl-2,2-cyanine (b) 1,1-diethyl-2,2-carbocyanine (c) 1,1-diethyl-2,2- dicarbocyanine (d) 1,1-diethyl-4,4-cyanine (e) 1,1-diethyl-4,4-carbocyanine (f) 1,1-diethyl- 4,4-dicarbocyanine (g) 1,4-diphenyl-1,3-butadiene (h) 1,6-diphenyl-1,3,5-hexatriene (i) 1,8- diphenyl-1,3,5,7-octatetraene 25

25 The work done for this thesis involved running geometry optimization in water using the

B3LYP method. The Los Alamos National Laboratory ECP plus double zeta (LanL2DZ) basis set was selected as it provided the level of accuracy required for the systems studied. The future version of this experiment will include the current experimental protocols of collecting the data and analyzing it in terms of 1D-PIB model. Additionally, students may be asked to, for each of the dye in their series, (i) construct an MO diagram, (ii) confirm that the HOMO – LUMO transition in these dyes is in fact a 휋 → 휋∗ transition and identify the exact nature of MOs involved in the electronic transitions, (iii) compare the computationally predicted HOMO −

LUMO transition wavelength to that of the experimental value and (iv) compare the 1D-PIB model wavefunctions with that of MO wavefunctions.

26

CHAPTER 5: Summary

Geometry optimization or NBO analysis calculation for 13 molecules was performed using

Gaussian 09 at the DFT level with a goal of using the results in the laboratory portion of the

Physical Chemistry II course (CHEM 382) at Bridgewater State University. Specifically, while data on N2, CO, NH3, and CH4 will be used for an existing “dry” laboratory experiment on

+ + + + photoelectron spectroscopy (PES), data on C23H23N2 , C25H25N2 , C27H27N2 , C23H23N2 ,

+ + C25H25N2 , C27H27N2 , C16H14, C18H16, and C20H18 will be used as a supplement for an existing traditional “wet” laboratory experiment designed to illustrate applications of the one dimensional particle-in-a-box model.

The computations developed in this work are carefully designed to be completed in a typical

3 – 4 hours lab period for a class of 16 students in CHEM 382 laboratory. For smaller molecules, like the ones used for PES experiment with very short computational time (few seconds to few minutes), students will be provided with job and input files and they will be asked to submit the calculations and generate the output files themselves. Alternately, students are provided with the job files but may be asked to create their own input files to enhance their computational experience. This will allow the students to learn logistics like preparing an input file, connecting to a cluster, submitting and monitoring a computation, and retrieving the data for analysis. On the other hand, for bigger molecules like the ones used for 1D-PIB experiment that can take 30+ minutes, students will be provided with an output file as it would not be practical for students to generate the output file under the constraint of the scheduled laboratory time.

Finally, as mentioned in Chapter 1, computational chemistry is a tool that can help students understand the complex concepts taught in the physical chemistry courses at BSU. The work

27 done in this thesis will be able to give students at BSU a more concrete understanding of chemical phenomena they encounter in CHEM 382 and other chemistry courses. From this, students will hopefully come to understand computational chemistry and recognize the benefits to implementing it as part of the physical chemistry curriculum at BSU.

28 Appendix A: The Input Files

Input Files for the Molecules used in Photoelectron Spectroscopy Experiment

Nitrogen (N2) Carbon Monoxide (CO)

%nprocshared=8 %nprocshared=8 %mem=8gb %mem=8gb %chk=Nitrogen.chk %chk=methane.chk #n B3LYP/6-31+G(d,p) Opt POP=NBO #n B3LYP/6-31+G(d,p) Opt POP=NBO

Nitrogen CO

0 1 0 1 N C N 1 r2 O 1 r2 Variables: Variables: r2= 1.4200 r2= 1.0570

Ammonia (NH3) Methane (CH4)

%nprocshared=8 %nprocshared=8 %mem=8gb %mem=8gb %chk=methane.chk %chk=methane.chk #n B3LYP/6-31+G(d,p) Opt POP=NBO #n B3LYP/6-31+G(d,p) Opt POP=NBO

Ammonia methane

0 1 0 1 N C H 1 r2 H 1 r2 H 1 r3 2 a3 H 1 r3 2 a3 H 1 r4 2 a4 3 d4 H 1 r4 2 a4 3 d4 Variables: H 1 r5 2 a5 3 d5 r2= 1.0190 Variables: r3= 1.0190 r2= 1.0922 a3= 106.00 r3= 1.0922 r4= 1.0190 a3= 109.47 a4= 106.00 r4= 1.0922 d4= 247.64 a4= 109.47 d4= 240.00 r5= 1.0922 a5= 109.47 d5= 120.00

29 Input Files for the Molecules used in 1-Dimensional Particle-in-a-Box Experiment

1,1-diethyl-2,2-cyanine %nprocshared=8 %mem=8gb %chk=D1.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D1 1 1 C 16 r17 15 a17 14 d17 H 15 r34 14 a34 13 d34 N C 17 r18 16 a18 15 d18 H 17 r35 16 a35 15 d35 C 1 r2 C 18 r19 17 a19 16 d19 H 18 r36 17 a36 16 d36 C 2 r3 1 a3 C 19 r20 18 a20 17 d20 H 19 r37 18 a37 17 d37 C 3 r4 2 a4 1 d4 C 20 r21 19 a21 18 d21 H 20 r38 19 a38 18 d38 C 4 r5 3 a5 2 d5 C 12 r22 11 a22 2 d22 H 22 r39 12 a39 11 d39 C 5 r6 4 a6 3 d6 C 22 r23 12 a23 11 d23 H 22 r40 12 a40 11 d40 C 6 r7 5 a7 4 d7 C 1 r24 2 a24 3 d24 H 23 r41 22 a41 12 d41 C 7 r8 6 a8 5 d8 C 24 r25 1 a25 2 d25 H 23 r42 22 a42 12 d42 C 8 r9 7 a9 6 d9 H 3 r26 2 a26 1 d26 H 23 r43 22 a43 12 d43 C 1 r10 2 a10 3 d10 H 4 r27 3 a27 2 d27 H 24 r44 1 a44 2 d44 C 2 r11 1 a11 3 d11 H 6 r28 5 a28 4 d28 H 24 r45 1 a45 2 d45 N 11 r12 2 a12 1 d12 H 7 r29 6 a29 5 d29 H 25 r46 24 a46 1 d46 C 11 r13 2 a13 1 d13 H 8 r30 7 a30 6 d30 H 25 r47 24 a47 1 d47 C 13 r14 11 a14 2 d14 H 9 r31 8 a31 7 d31 H 25 r48 24 a48 1 d48 C 14 r15 13 a15 11 d15 H 11 r32 2 a32 1 d32 C 15 r16 14 a16 13 d16 H 14 r33 13 a33 11 d33

Variables: r2= 1.3813 a11= 125.71 d19= 359.69 r28= 1.0904 a36= 120.32 r3= 1.4114 d11= 176.89 r20= 1.3987 a28= 120.91 d36= 179.42 a3= 118.73 r12= 2.4674 a20= 120.11 d28= 1.67 r37= 1.0880 r4= 1.3811 a12= 155.81 d20= 359.31 r29= 1.0891 a37= 120.01 a4= 122.01 d12= 142.83 r21= 1.4103 a29= 120.31 d37= 179.56 d4= 353.35 r13= 1.3610 a21= 121.57 d29= 179.91 r38= 1.0857 r5= 1.3804 a13= 128.37 d21= 1.39 r30= 1.0897 a38= 116.58 a5= 119.00 d13= 133.17 r22= 1.4780 a30= 119.83 d38= 181.92 d5= 2.89 r14= 1.4719 a22= 105.80 d30= 179.29 r39= 1.0987 r6= 1.4060 a14= 120.01 d22= 193.32 r31= 1.0864 a39= 109.22 a6= 119.29 d14= 356.11 r23= 1.5129 a31= 114.66 d39= 156.06 d6= 180.98 r15= 1.3376 a23= 116.34 d31= 180.29 r40= 1.0962 r7= 1.3914 a15= 122.35 d23= 39.23 r32= 1.0838 a40= 109.89 a7= 120.97 d15= 153.00 r24= 1.5024 a32= 113.87 d40= 274.21 d7= 181.78 r16= 1.4637 a24= 126.13 d32= 301.48 r41= 1.0932 r8= 1.3844 a16= 119.56 d24= 185.04 r33= 1.0856 a41= 112.30 a8= 119.52 d16= 3.20 r25= 1.4951 a33= 119.75 d41= 39.66 d8= 0.27 r17= 1.4030 a25= 121.63 d33= 334.81 r42= 1.0890 r9= 1.3995 a17= 120.26 d25= 1.86 r34= 1.0854 a42= 110.05 a9= 119.91 d17= 187.62 r26= 1.0916 a34= 121.90 d42= 276.11 d9= 359.11 r18= 1.3936 a26= 120.38 d34= 182.07 r43= 1.0956 r10= 1.3969 a18= 120.36 d26= 175.16 r35= 1.0872 a43= 110.12 a10= 119.68 d18= 183.92 r27= 1.0895 a35= 120.81 d43= 159.80 d10= 5.68 r19= 1.3893 a27= 119.51 d35= 3.38 r44= 1.0976 r11= 1.4929 a19= 119.71 d27= 182.99 r36= 1.0874 a44= 105.40

30 d44= 123.09 d45= 239.54 d46= 64.11 d47= 298.50 d48= 181.18 r45= 1.0966 r46= 1.0917 r47= 1.0891 r48= 1.0962 a45= 105.70 a46= 111.49 a47= 110.70 a48= 109.58

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+ 1,1-diethyl-2,2-carbocyanine (C25H25N2 ) %nprocshared=8 %mem=8gb %chk=D2.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D2 N 16 r17 15 a17 14 d17 H 12 r36 10 a36 6 d36 C 16 r18 15 a18 14 d18 H 13 r37 11 a37 6 d37 1 1 C 17 r19 16 a19 15 d19 H 13 r38 11 a38 6 d38 C C 17 r20 16 a20 15 d20 H 13 r39 11 a39 6 d39 C 1 r2 C 18 r21 16 a21 15 d21 H 14 r40 12 a40 10 d40 C 1 r3 2 a3 C 19 r22 17 a22 16 d22 H 15 r41 14 a41 12 d41 C 1 r4 2 a4 3 d4 C 21 r23 18 a23 16 d23 H 18 r42 16 a42 15 d42 C 2 r5 1 a5 3 d5 C 20 r24 17 a24 16 d24 H 19 r43 17 a43 16 d43 N 2 r6 1 a6 3 d6 C 23 r25 21 a25 18 d25 H 19 r44 17 a44 16 d44 C 3 r7 1 a7 2 d7 C 24 r26 20 a26 17 d26 H 21 r45 18 a45 16 d45 C 4 r8 1 a8 2 d8 C 26 r27 24 a27 20 d27 H 22 r46 19 a46 17 d46 C 7 r9 3 a9 1 d9 H 3 r28 1 a28 2 d28 H 22 r47 19 a47 17 d47 C 6 r10 2 a10 1 d10 H 4 r29 1 a29 2 d29 H 22 r48 19 a48 17 d48 C 6 r11 2 a11 1 d11 H 5 r30 2 a30 1 d30 H 24 r49 20 a49 17 d49 C 10 r12 6 a12 2 d12 H 7 r31 3 a31 1 d31 H 25 r50 23 a50 21 d50 C 11 r13 6 a13 2 d13 H 8 r32 4 a32 1 d32 H 26 r51 24 a51 20 d51 C 12 r14 10 a14 6 d14 H 9 r33 7 a33 3 d33 H 27 r52 26 a52 24 d52 C 14 r15 12 a15 10 d15 H 11 r34 6 a34 2 d34 C 15 r16 14 a16 12 d16 H 11 r35 6 a35 2 d35

Variables: a8= 119.49 r14= 1.4544 d19= 353.27 a25= 119.07 r2= 1.4126 d8= 358.77 a14= 128.64 r20= 1.3905 d25= 178.06 r3= 1.4064 r9= 1.3863 d14= 188.12 a20= 119.38 r26= 1.3999 a3= 121.65 a9= 119.27 r15= 1.3447 d20= 173.20 a26= 121.98 r4= 1.4534 d9= 0.16 a15= 122.66 r21= 1.3793 d26= 181.08 a4= 119.88 r10= 1.4266 d15= 211.90 a21= 121.13 r27= 1.3862 d4= 179.20 a10= 119.60 r16= 1.4680 d21= 183.38 a27= 120.10 r5= 1.4139 d10= 4.85 a16= 123.28 r22= 1.5117 d27= 359.46 a5= 116.02 r11= 1.4875 d16= 185.25 a22= 120.70 r28= 1.0874 d5= 358.58 a11= 110.78 r17= 1.3724 d22= 341.90 a28= 120.63 r6= 1.4614 d11= 176.95 a17= 123.38 r23= 1.3829 d28= 180.61 a6= 119.98 r12= 1.3539 d17= 129.08 a23= 118.97 r29= 1.0838 d6= 178.58 a12= 126.90 r18= 1.4032 d23= 2.13 a29= 119.21 r7= 1.3896 d12= 179.74 a18= 116.20 r24= 1.4139 d29= 178.76 a7= 120.55 r13= 1.5139 d18= 305.70 a24= 123.39 r30= 1.0846 d7= 0.94 a13= 121.08 r19= 1.5099 d24= 184.82 a30= 122.53 r8= 1.3347 d13= 176.41 a19= 124.32 r25= 1.4036

31 d30= 181.28 a35= 108.53 r40= 1.0900 d44= 108.16 a49= 122.76 r31= 1.0867 d35= 299.24 a40= 115.86 r45= 1.0895 d49= 1.87 a31= 120.38 r36= 1.0757 d40= 36.70 a45= 119.48 r50= 1.0905 d31= 179.77 a36= 120.44 r41= 1.0862 d45= 180.26 a50= 120.95 r32= 1.0838 d36= 4.79 a41= 120.25 r46= 1.0926 d50= 1.08 a32= 116.21 r37= 1.0939 d41= 7.34 a46= 112.60 r51= 1.0896 d32= 178.72 a37= 111.86 r42= 1.0905 d46= 313.59 a51= 120.25 r33= 1.0876 d37= 301.87 a42= 120.58 r47= 1.0967 d51= 179.68 a33= 119.92 r38= 1.0965 d42= 2.46 a47= 109.07 r52= 1.0891 d33= 179.35 a38= 109.31 r43= 1.0964 d47= 194.76 a52= 120.22 r34= 1.0980 d38= 184.22 a43= 105.32 r48= 1.0927 d52= 180.06 a34= 108.14 r39= 1.0939 d43= 224.29 a48= 112.06 d34= 56.74 a39= 111.82 r44= 1.0959 d48= 78.83 r35= 1.0984 d39= 66.99 a44= 106.08 r49= 1.0861

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+ 1,1-diethyl-2,2-dicarbocyanine (C27H27N2 ) %nprocshared=8 %mem=8gb %chk=D3.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D3 C 17 r18 15 a18 14 d18 H 13 r38 12 a38 11 d38 C 18 r19 17 a19 15 d19 H 14 r39 13 a39 12 d39 1 1 C 19 r20 18 a20 17 d20 H 15 r40 14 a40 13 d40 N C 20 r21 19 a21 18 d21 H 18 r41 17 a41 15 d41 C 1 r2 C 21 r22 20 a22 19 d22 H 19 r42 18 a42 17 d42 C 2 r3 1 a3 C 22 r23 21 a23 20 d23 H 21 r43 20 a43 19 d43 C 3 r4 2 a4 1 d4 C 23 r24 22 a24 21 d24 H 22 r44 21 a44 20 d44 C 4 r5 3 a5 2 d5 C 20 r25 19 a25 18 d25 H 23 r45 22 a45 21 d45 C 5 r6 4 a6 3 d6 C 16 r26 15 a26 14 d26 H 24 r46 23 a46 22 d46 C 6 r7 5 a7 4 d7 C 26 r27 16 a27 15 d27 H 26 r47 16 a47 15 d47 C 7 r8 6 a8 5 d8 C 1 r28 2 a28 3 d28 H 26 r48 16 a48 15 d48 C 8 r9 7 a9 6 d9 C 28 r29 1 a29 2 d29 H 27 r49 26 a49 16 d49 C 1 r10 2 a10 3 d10 H 3 r30 2 a30 1 d30 H 27 r50 26 a50 16 d50 C 2 r11 1 a11 3 d11 H 4 r31 3 a31 2 d31 H 27 r51 26 a51 16 d51 C 11 r12 2 a12 1 d12 H 6 r32 5 a32 4 d32 H 28 r52 1 a52 2 d52 C 12 r13 11 a13 2 d13 H 7 r33 6 a33 5 d33 H 28 r53 1 a53 2 d53 C 13 r14 12 a14 11 d14 H 8 r34 7 a34 6 d34 H 29 r54 28 a54 1 d54 C 14 r15 13 a15 12 d15 H 9 r35 8 a35 7 d35 H 29 r55 28 a55 1 d55 N 15 r16 14 a16 13 d16 H 11 r36 2 a36 1 d36 H 29 r56 28 a56 1 d56 C 15 r17 14 a17 13 d17 H 12 r37 11 a37 2 d37

Variables: r5= 1.3781 a7= 120.84 d9= 359.65 r12= 1.3483 r2= 1.3810 a5= 118.87 d7= 181.09 r10= 1.3984 a12= 125.98 r3= 1.4106 d5= 1.80 r8= 1.3849 a10= 119.36 d12= 152.12 a3= 119.18 r6= 1.4044 a8= 119.47 d10= 0.42 r13= 1.4511 r4= 1.3791 a6= 118.76 d8= 0.12 r11= 1.4810 a13= 122.79 a4= 122.10 d6= 179.23 r9= 1.4009 a11= 124.78 d13= 180.54 d4= 358.07 r7= 1.3899 a9= 120.07 d11= 176.34 r14= 1.3455

32 a14= 123.42 r23= 1.3863 d31= 180.74 a40= 110.36 r49= 1.0935 d14= 194.62 a23= 119.25 r32= 1.0906 d40= 2.53 a49= 112.20 r15= 1.4614 d23= 0.26 a32= 120.96 r41= 1.0812 d49= 57.56 a15= 122.32 r24= 1.4021 d32= 0.82 a41= 120.13 r50= 1.0941 d15= 184.02 a24= 120.24 r33= 1.0890 d41= 355.59 a50= 111.59 r16= 2.4914 d24= 359.31 a33= 120.22 r42= 1.0835 d50= 292.33 a16= 158.32 r25= 1.4118 d33= 179.82 a42= 121.17 r51= 1.0967 d16= 178.73 a25= 119.81 r34= 1.0896 d42= 180.91 a51= 109.24 r17= 1.3584 d25= 2.48 a34= 119.66 r43= 1.0873 d51= 175.68 a17= 130.91 r26= 1.4870 d34= 179.59 a43= 120.57 r52= 1.0975 d17= 182.41 a26= 103.65 r35= 1.0862 d43= 1.54 a52= 105.28 r18= 1.4711 d26= 193.16 a35= 114.77 r44= 1.0866 d52= 119.80 a18= 116.99 r27= 1.5136 d35= 179.69 a44= 120.38 r53= 1.0974 d18= 4.28 a27= 121.48 r36= 1.0787 d44= 179.99 a53= 104.91 r19= 1.3361 d27= 3.47 a36= 117.31 r45= 1.0875 d53= 235.48 a19= 124.12 r28= 1.5105 d36= 326.59 a45= 119.93 r54= 1.0931 d19= 174.21 a28= 126.19 r37= 1.0892 d45= 179.48 a54= 111.79 r20= 1.4527 d28= 179.43 a37= 122.05 r46= 1.0846 d54= 73.18 a20= 119.59 r29= 1.5053 d37= 359.78 a46= 115.30 r55= 1.0919 d20= 1.15 a29= 123.16 r38= 1.0887 d46= 180.25 a55= 112.87 r21= 1.4067 d29= 356.39 a38= 117.04 r47= 1.0988 d55= 306.90 a21= 118.52 r30= 1.0897 d38= 16.70 a47= 108.12 r56= 1.0976 d21= 181.52 a30= 121.07 r39= 1.0844 d47= 124.45 a56= 108.70 r22= 1.3897 d30= 177.32 a39= 119.05 r48= 1.0982 d56= 188.58 a22= 120.58 r31= 1.0895 d39= 2.96 a48= 108.35 d22= 181.67 a31= 119.49 r40= 1.0751 d48= 241.72

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+ 1,1-diethyl-4,4-cyanine (C23H23N2 ) %nprocshared=8 %mem=8gb %chk=D4.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D4 C 11 r15 4 a15 3 d15 H 11 r32 4 a32 3 d32 C 15 r16 11 a16 4 d16 H 13 r33 12 a33 11 d33 1 1 C 16 r17 15 a17 11 d17 H 14 r34 13 a34 12 d34 N C 17 r18 16 a18 15 d18 H 17 r35 16 a35 15 d35 C 1 r2 C 18 r19 17 a19 16 d19 H 18 r36 17 a36 16 d36 C 2 r3 1 a3 C 19 r20 18 a20 17 d20 H 19 r37 18 a37 17 d37 C 3 r4 2 a4 1 d4 C 20 r21 19 a21 18 d21 H 20 r38 19 a38 18 d38 C 4 r5 3 a5 2 d5 C 12 r22 11 a22 4 d22 H 22 r39 12 a39 11 d39 C 5 r6 4 a6 3 d6 C 22 r23 12 a23 11 d23 H 22 r40 12 a40 11 d40 C 6 r7 5 a7 4 d7 C 1 r24 2 a24 3 d24 H 23 r41 22 a41 12 d41 C 7 r8 6 a8 5 d8 C 24 r25 1 a25 2 d25 H 23 r42 22 a42 12 d42 C 8 r9 7 a9 6 d9 H 2 r26 1 a26 3 d26 H 23 r43 22 a43 12 d43 C 1 r10 2 a10 3 d10 H 3 r27 2 a27 1 d27 H 24 r44 1 a44 2 d44 C 4 r11 3 a11 2 d11 H 6 r28 5 a28 4 d28 H 24 r45 1 a45 2 d45 N 11 r12 4 a12 3 d12 H 7 r29 6 a29 5 d29 H 25 r46 24 a46 1 d46 C 12 r13 11 a13 4 d13 H 8 r30 7 a30 6 d30 H 25 r47 24 a47 1 d47 C 13 r14 12 a14 11 d14 H 9 r31 8 a31 7 d31 H 25 r48 24 a48 1 d48

33 Variables: r2= 1.3535 d8= 0.42 a14= 124.64 r20= 1.3983 d25= 26.07 r3= 1.3818 r9= 1.3959 d14= 351.17 a20= 120.25 r26= 1.0852 a3= 122.04 a9= 119.78 r15= 1.3519 d20= 359.22 a26= 118.75 r4= 1.3890 d9= 1.21 a15= 129.12 r21= 1.4071 d26= 180.09 a4= 120.08 r10= 1.3769 d15= 309.71 a21= 121.45 r27= 1.0894 d4= 0.92 a10= 120.05 r16= 1.5025 d21= 0.66 a27= 119.07 r5= 1.4139 d10= 5.84 a16= 120.34 r22= 1.4756 d27= 180.84 a5= 118.55 r11= 1.4812 d16= 178.27 a22= 166.22 r28= 1.0899 d5= 354.54 a11= 119.15 r17= 1.4071 d22= 82.03 a28= 121.07 r6= 1.4164 d11= 180.42 a17= 122.62 r23= 1.5255 d28= 357.10 a6= 122.52 r12= 4.1063 d17= 29.09 a23= 113.39 r29= 1.0893 d6= 184.29 a12= 127.91 r18= 1.3933 d23= 297.47 a29= 120.02 r7= 1.3938 d12= 328.25 a18= 120.74 r24= 1.5007 d29= 181.20 a7= 121.99 r13= 1.3922 d18= 178.63 a24= 119.86 r30= 1.0892 d7= 176.38 a13= 60.01 r19= 1.3886 d24= 184.29 a30= 119.80 r8= 1.3839 d13= 332.86 a19= 119.82 r25= 1.5187 d30= 181.26 a8= 119.76 r14= 1.3411 d19= 359.38 a25= 115.02 r31= 1.0861 d34= 180.06 a38= 116.77 r42= 1.0939 d45= 261.91 a31= 115.77 r35= 1.0853 d38= 183.17 a42= 111.83 r46= 1.0947 d31= 181.10 a35= 121.37 r39= 1.0965 d42= 289.64 a46= 111.49 r32= 1.0891 d35= 0.52 a39= 110.28 r43= 1.0953 d46= 49.96 a32= 112.20 r36= 1.0872 d39= 55.00 a43= 109.92 r47= 1.0940 d32= 126.64 a36= 120.19 r40= 1.0962 d43= 170.73 a47= 111.80 r33= 1.0851 d36= 180.46 a40= 109.88 r44= 1.0944 d47= 287.89 a33= 115.10 r37= 1.0877 d40= 174.17 a44= 107.22 r48= 1.0953 d33= 170.99 a37= 119.94 r41= 1.0951 d44= 144.00 a48= 109.76 r34= 1.0815 d37= 180.87 a41= 111.27 r45= 1.0947 d48= 169.51 a34= 120.69 r38= 1.0851 d41= 51.08 a45= 106.69

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+ 1,1-diethyl-4,4-carbocyanine (C25H25N2 ) %nprocshared=8 %mem=8gb %chk=D5.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D5 C 4 r11 3 a11 2 d11 C 2 r24 1 a24 3 d24 C 11 r12 4 a12 3 d12 C 24 r25 14 a25 13 d25 1 1 C 12 r13 11 a13 4 d13 C 1 r26 2 a26 3 d26 N N 13 r14 12 a14 11 d14 C 26 r27 1 a27 2 d27 C 1 r2 C 14 r15 13 a15 12 d15 H 2 r28 1 a28 3 d28 C 2 r3 1 a3 C 15 r16 14 a16 13 d16 H 3 r29 2 a29 1 d29 C 3 r4 2 a4 1 d4 C 16 r17 15 a17 14 d17 H 6 r30 5 a30 4 d30 C 4 r5 3 a5 2 d5 C 17 r18 16 a18 15 d18 H 7 r31 6 a31 5 d31 C 5 r6 4 a6 3 d6 C 18 r19 17 a19 16 d19 H 8 r32 7 a32 6 d32 C 6 r7 5 a7 4 d7 C 19 r20 18 a20 17 d20 H 9 r33 8 a33 7 d33 C 7 r8 6 a8 5 d8 C 20 r21 19 a21 18 d21 H 11 r34 4 a34 3 d34 C 8 r9 7 a9 6 d9 C 21 r22 20 a22 19 d22 H 12 r35 11 a35 4 d35 C 9 r10 8 a10 7 d10 C 14 r23 13 a23 12 d23 H 13 r36 12 a36 11 d36

34 H 15 r37 14 a37 13 d37 H 24 r43 14 a43 13 d43 H 26 r49 1 a49 2 d49 H 16 r38 15 a38 14 d38 H 24 r44 14 a44 13 d44 H 27 r50 26 a50 1 d50 H 19 r39 18 a39 17 d39 H 25 r45 24 a45 14 d45 H 27 r51 26 a51 1 d51 H 20 r40 19 a40 18 d40 H 25 r46 24 a46 14 d46 H 27 r52 26 a52 1 d52 H 21 r41 20 a41 19 d41 H 25 r47 24 a47 14 d47 H 22 r42 21 a42 20 d42 H 26 r48 1 a48 2 d48 Variables: r2= 1.3831 r13= 1.3422 r23= 1.3782 r33= 1.0851 r43= 1.0962 r3= 1.3371 a13= 123.61 a23= 62.69 a33= 116.46 a43= 106.26 a3= 125.61 d13= 225.27 d23= 305.03 d33= 180.58 d43= 87.63 r4= 1.4598 r14= 4.2697 r24= 9.9463 r34= 1.0855 r44= 1.0955 a4= 119.97 a14= 123.81 a24= 153.67 a34= 121.09 a44= 106.40 d4= 1.22 d14= 179.15 d24= 14.30 d34= 185.62 d44= 205.00 r5= 1.5097 r15= 1.3543 r25= 1.5158 r35= 1.0889 r45= 1.0946 a5= 117.05 a15= 57.48 a25= 116.38 a35= 115.70 a45= 111.62 d5= 356.20 d15= 124.29 d25= 327.36 d35= 43.21 d45= 57.60 r6= 1.4099 r16= 1.3838 r26= 1.4794 r36= 1.0884 r46= 1.0943 a6= 122.56 a16= 122.12 a26= 124.33 a36= 120.78 a46= 111.56 d6= 184.98 d16= 0.09 d26= 178.14 d36= 357.37 d46= 295.36 r7= 1.3952 r17= 1.3877 r27= 1.5240 r37= 1.0851 r47= 1.0953 a7= 121.38 a17= 119.95 a27= 115.63 a37= 118.99 a47= 109.67 d7= 178.69 d17= 0.40 d27= 5.22 d37= 180.28 d47= 176.66 r8= 1.3857 r18= 1.4147 r28= 1.0837 r38= 1.0894 r48= 1.0972 a8= 119.89 a18= 118.86 a28= 115.98 a38= 119.33 a48= 109.27 d8= 359.85 d18= 0.73 d28= 179.51 d38= 180.76 d48= 125.75 r9= 1.3959 r19= 1.4161 r29= 1.0804 r39= 1.0890 r49= 1.0972 a9= 119.95 a19= 122.82 a29= 118.66 a39= 120.87 a49= 109.25 d9= 359.83 d19= 176.71 d29= 179.14 d39= 355.68 d49= 244.22 r10= 1.4114 r20= 1.3930 r30= 1.0843 r40= 1.0891 r50= 1.0950 a10= 121.85 a20= 122.26 a30= 121.81 a40= 119.98 a50= 111.46 d10= 359.94 d20= 176.03 d30= 359.61 d40= 181.41 d50= 59.96 r11= 1.3546 r21= 1.3828 r31= 1.0871 r41= 1.0890 r51= 1.0950 a11= 120.43 a21= 119.64 a31= 120.13 a41= 119.80 a51= 111.51 d11= 173.88 d21= 1.23 d31= 180.29 d41= 180.78 d51= 298.18 r12= 1.4514 r22= 1.3959 r32= 1.0873 r42= 1.0861 r52= 1.0951 a12= 125.36 a22= 119.69 a32= 120.16 a42= 115.76 a52= 109.92 d12= 5.98 d22= 1.59 d32= 180.35 d42= 179.20 d52= 179.24

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+ 1,1-diethyl-4,4-dicarbocyanine (C27H27N2 ) %nprocshared=8 %mem=8gb %chk=D6.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D6 C 1 r3 2 a3 C 3 r8 1 a8 2 d8 C 1 r4 2 a4 3 d4 C 4 r9 1 a9 2 d9 1 1 N 2 r5 1 a5 3 d5 C 7 r10 3 a10 1 d10 C C 2 r6 1 a6 3 d6 C 5 r11 2 a11 1 d11 C 1 r2 C 3 r7 1 a7 2 d7 C 9 r12 4 a12 1 d12

35 C 8 r13 3 a13 1 d13 C 26 r28 22 a28 19 d28 H 15 r43 13 a43 8 d43 C 11 r14 5 a14 2 d14 C 27 r29 24 a29 23 d29 H 16 r44 15 a44 13 d44 C 13 r15 8 a15 3 d15 H 4 r30 1 a30 2 d30 H 17 r45 16 a45 15 d45 C 15 r16 13 a16 8 d16 H 6 r31 2 a31 1 d31 H 20 r46 18 a46 17 d46 C 16 r17 15 a17 13 d17 H 7 r32 3 a32 1 d32 H 22 r47 19 a47 18 d47 C 17 r18 16 a18 15 d18 H 8 r33 3 a33 1 d33 H 23 r48 20 a48 18 d48 C 18 r19 17 a19 16 d19 H 9 r34 4 a34 1 d34 H 25 r49 21 a49 19 d49 C 18 r20 17 a20 16 d20 H 10 r35 7 a35 3 d35 H 26 r50 22 a50 19 d50 C 19 r21 18 a21 17 d21 H 11 r36 5 a36 2 d36 H 27 r51 24 a51 23 d51 C 19 r22 18 a22 17 d22 H 11 r37 5 a37 2 d37 H 27 r52 24 a52 23 d52 C 20 r23 18 a23 17 d23 H 12 r38 9 a38 4 d38 H 28 r53 26 a53 22 d53 N 23 r24 20 a24 18 d24 H 13 r39 8 a39 3 d39 H 29 r54 27 a54 24 d54 C 21 r25 19 a25 18 d25 H 14 r40 11 a40 5 d40 H 29 r55 27 a55 24 d55 C 22 r26 19 a26 18 d26 H 14 r41 11 a41 5 d41 H 29 r56 27 a56 24 d56 C 24 r27 23 a27 20 d27 H 14 r42 11 a42 5 d42

Variables: r2= 1.4335 r14= 1.5237 r25= 1.4158 r36= 1.0973 r47= 1.0892 r3= 1.5118 a14= 115.71 a25= 118.61 a36= 109.34 a47= 121.15 a3= 118.34 d14= 180.66 d25= 176.08 d36= 59.52 d47= 3.90 r4= 1.4103 r15= 1.3424 r26= 1.3937 r37= 1.0973 r48= 1.0851 a4= 118.93 a15= 124.35 a26= 122.38 a37= 109.17 a48= 118.89 d4= 181.53 d15= 161.93 d26= 183.78 d37= 301.10 d48= 179.67 r5= 1.4370 r16= 1.4463 r27= 1.5024 r38= 1.0871 r49= 1.0861 a5= 120.20 a16= 120.69 a27= 120.72 a38= 120.15 a49= 122.35 d5= 357.07 d16= 178.55 d27= 177.35 d38= 179.51 d49= 182.29 r6= 1.4118 r17= 1.3414 r28= 1.3822 r39= 1.0870 r50= 1.0892 a6= 117.91 a17= 123.58 a28= 119.69 a39= 116.66 a50= 119.96 d6= 177.12 d17= 149.35 d28= 358.72 d39= 340.54 d50= 178.47 r7= 1.4599 r18= 1.4773 r29= 1.5160 r40= 1.0949 r51= 1.0963 a7= 116.91 a18= 123.60 a29= 116.36 a40= 111.47 a51= 106.23 d7= 5.95 d18= 185.05 d29= 353.38 d40= 297.37 d51= 233.26 r8= 1.3542 r19= 1.4171 r30= 1.0840 r41= 1.0952 r52= 1.0954 a8= 122.10 a19= 125.20 a30= 121.89 a41= 109.89 a52= 106.45 d8= 185.98 d19= 49.26 d30= 180.92 d41= 178.40 d52= 115.85 r9= 1.3951 r20= 1.3888 r31= 1.0849 r42= 1.0949 r53= 1.0889 a9= 121.47 a20= 116.03 a31= 121.67 a42= 111.51 a53= 119.83 d9= 1.22 d20= 227.64 d31= 180.66 d42= 59.18 d53= 179.25 r10= 1.3362 r21= 1.4260 r32= 1.0819 r43= 1.0876 r54= 1.0946 a10= 120.04 a21= 119.20 a32= 121.16 a43= 120.89 a54= 111.63 d10= 355.55 d21= 180.83 d32= 173.77 d43= 356.36 d54= 302.84 r11= 1.4788 r22= 1.4178 r33= 1.0852 r44= 1.0893 r55= 1.0953 a11= 116.88 a22= 123.20 a33= 120.49 a44= 115.72 a55= 109.68 d11= 180.99 d22= 1.27 d33= 356.06 d44= 332.60 d55= 183.77 r12= 1.3852 r23= 1.3832 r34= 1.0870 r45= 1.0891 r56= 1.0943 a12= 119.88 a23= 120.09 a34= 120.08 a45= 120.19 a56= 111.55 d12= 359.79 d23= 181.18 d34= 179.44 d45= 3.57 d56= 65.08 r13= 1.4526 r24= 1.3535 r35= 1.0842 r46= 1.0896 a13= 126.65 a24= 122.09 a35= 118.48 a46= 120.75 d13= 172.06 d24= 359.81 d35= 179.39 d46= 1.21

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36 1,4-diphenyl-1,3-butadiene (C16H14) %nprocshared=8 %mem=8gb %chk=D7.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water) D7 C 16 r17 15 a17 14 d17 H 13 r36 12 a36 11 d36 C 17 r18 16 a18 15 d18 H 15 r37 14 a37 13 d37 1 1 C 18 r19 17 a19 16 d19 H 16 r38 15 a38 14 d38 N C 19 r20 18 a20 17 d20 H 19 r39 18 a39 17 d39 C 1 r2 C 20 r21 19 a21 18 d21 H 20 r40 19 a40 18 d40 C 2 r3 1 a3 C 21 r22 20 a22 19 d22 H 21 r41 20 a41 19 d41 C 3 r4 2 a4 1 d4 C 14 r23 13 a23 12 d23 H 22 r42 21 a42 20 d42 C 4 r5 3 a5 2 d5 C 2 r24 1 a24 3 d24 H 24 r43 14 a43 13 d43 C 5 r6 4 a6 3 d6 C 24 r25 14 a25 13 d25 H 24 r44 14 a44 13 d44 C 6 r7 5 a7 4 d7 C 1 r26 2 a26 3 d26 H 25 r45 24 a45 14 d45 C 7 r8 6 a8 5 d8 C 26 r27 1 a27 2 d27 H 25 r46 24 a46 14 d46 C 8 r9 7 a9 6 d9 H 2 r28 1 a28 3 d28 H 25 r47 24 a47 14 d47 C 9 r10 8 a10 7 d10 H 3 r29 2 a29 1 d29 H 26 r48 1 a48 2 d48 C 4 r11 3 a11 2 d11 H 6 r30 5 a30 4 d30 H 26 r49 1 a49 2 d49 C 11 r12 4 a12 3 d12 H 7 r31 6 a31 5 d31 H 27 r50 26 a50 1 d50 C 12 r13 11 a13 4 d13 H 8 r32 7 a32 6 d32 H 27 r51 26 a51 1 d51 N 13 r14 12 a14 11 d14 H 9 r33 8 a33 7 d33 H 27 r52 26 a52 1 d52 C 14 r15 13 a15 12 d15 H 11 r34 4 a34 3 d34 C 15 r16 14 a16 13 d16 H 12 r35 11 a35 4 d35 Variables: r2= 1.3831 r13= 1.3422 r23= 1.3782 r33= 1.0851 r43= 1.0962 r3= 1.3371 a13= 123.61 a23= 62.69 a33= 116.46 a43= 106.26 a3= 125.61 d13= 225.27 d23= 305.03 d33= 180.58 d43= 87.63 r4= 1.4598 r14= 4.2697 r24= 9.9463 r34= 1.0855 r44= 1.0955 a4= 119.97 a14= 123.81 a24= 153.67 a34= 121.09 a44= 106.40 d4= 1.22 d14= 179.15 d24= 14.30 d34= 185.62 d44= 205.00 r5= 1.5097 r15= 1.3543 r25= 1.5158 r35= 1.0889 r45= 1.0946 a5= 117.05 a15= 57.48 a25= 116.38 a35= 115.70 a45= 111.62 d5= 356.20 d15= 124.29 d25= 327.36 d35= 43.21 d45= 57.60 r6= 1.4099 r16= 1.3838 r26= 1.4794 r36= 1.0884 r46= 1.0943 a6= 122.56 a16= 122.12 a26= 124.33 a36= 120.78 a46= 111.56 d6= 184.98 d16= 0.09 d26= 178.14 d36= 357.37 d46= 295.36 r7= 1.3952 r17= 1.3877 r27= 1.5240 r37= 1.0851 r47= 1.0953 a7= 121.38 a17= 119.95 a27= 115.63 a37= 118.99 a47= 109.67 d7= 178.69 d17= 0.40 d27= 5.22 d37= 180.28 d47= 176.66 r8= 1.3857 r18= 1.4147 r28= 1.0837 r38= 1.0894 r48= 1.0972 a8= 119.89 a18= 118.86 a28= 115.98 a38= 119.33 a48= 109.27 d8= 359.85 d18= 0.73 d28= 179.51 d38= 180.76 d48= 125.75 r9= 1.3959 r19= 1.4161 r29= 1.0804 r39= 1.0890 r49= 1.0972 a9= 119.95 a19= 122.82 a29= 118.66 a39= 120.87 a49= 109.25 d9= 359.83 d19= 176.71 d29= 179.14 d39= 355.68 d49= 244.22 r10= 1.4114 r20= 1.3930 r30= 1.0843 r40= 1.0891 r50= 1.0950 a10= 121.85 a20= 122.26 a30= 121.81 a40= 119.98 a50= 111.46 d10= 359.94 d20= 176.03 d30= 359.61 d40= 181.41 d50= 59.96 r11= 1.3546 r21= 1.3828 r31= 1.0871 r41= 1.0890 r51= 1.0950 a11= 120.43 a21= 119.64 a31= 120.13 a41= 119.80 a51= 111.51 d11= 173.88 d21= 1.23 d31= 180.29 d41= 180.78 d51= 298.18 r12= 1.4514 r22= 1.3959 r32= 1.0873 r42= 1.0861 r52= 1.0951 a12= 125.36 a22= 119.69 a32= 120.16 a42= 115.76 a52= 109.92 d12= 5.98 d22= 1.59 d32= 180.35 d42= 179.20 d52= 179.24

37 1,6-diphenyl-1,3,5-hexatriene (C18H16) #%nprocshared=8 %mem=8gb %chk=D8.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water) D8 C 10 r11 9 a11 8 d11 H 6 r24 5 a24 4 d24 C 11 r12 10 a12 9 d12 H 8 r25 7 a25 1 d25 0 1 C 6 r13 5 a13 4 d13 H 9 r26 8 a26 7 d26 C C 13 r14 6 a14 5 d14 H 10 r27 9 a27 8 d27 C 1 r2 C 14 r15 13 a15 6 d15 H 11 r28 10 a28 9 d28 C 2 r3 1 a3 C 15 r16 14 a16 13 d16 H 12 r29 11 a29 10 d29 C 3 r4 2 a4 1 d4 C 16 r17 15 a17 14 d17 H 14 r30 13 a30 6 d30 C 4 r5 3 a5 2 d5 C 17 r18 16 a18 15 d18 H 15 r31 14 a31 13 d31 C 5 r6 4 a6 3 d6 H 1 r19 2 a19 3 d19 H 16 r32 15 a32 14 d32 C 1 r7 2 a7 3 d7 H 2 r20 1 a20 3 d20 H 17 r33 16 a33 15 d33 C 7 r8 1 a8 2 d8 H 3 r21 2 a21 1 d21 H 18 r34 17 a34 16 d34 C 8 r9 7 a9 1 d9 H 4 r22 3 a22 2 d22 C 9 r10 8 a10 7 d10 H 5 r23 4 a23 3 d23

Variables: r2= 1.3431 d9= 181.55 a16= 120.21 r23= 1.0860 d29= 179.79 r3= 1.4481 r10= 1.3921 d16= 359.58 a23= 116.35 r30= 1.0858 a3= 122.43 a10= 120.21 r17= 1.3916 d23= 358.90 a30= 121.21 r4= 1.3418 d10= 0.28 a17= 119.72 r24= 1.0886 d30= 0.12 a4= 122.94 r11= 1.3915 d17= 359.88 a24= 118.86 r31= 1.0870 d4= 181.74 a11= 119.72 r18= 1.3980 d24= 359.58 a31= 119.82 r5= 1.4480 d11= 359.91 a18= 120.03 r25= 1.0858 d31= 179.70 a5= 122.74 r12= 1.3980 d18= 0.26 a25= 121.23 r32= 1.0867 d5= 178.17 a12= 120.03 r19= 1.0887 d25= 0.98 a32= 120.13 r6= 1.3431 d12= 359.98 a19= 118.78 r26= 1.0870 d32= 180.03 a6= 122.64 r13= 1.4758 d19= 358.85 a26= 119.82 r33= 1.0868 d6= 180.07 a13= 126.22 r20= 1.0858 d26= 179.93 a33= 120.05 r7= 1.4759 d13= 178.55 a20= 121.14 r27= 1.0867 d33= 180.22 a7= 126.43 r14= 1.4017 d20= 180.77 a27= 120.13 r34= 1.0879 d7= 178.26 a14= 123.63 r21= 1.0882 d27= 179.69 a34= 118.44 r8= 1.4017 d14= 11.32 a21= 117.10 r28= 1.0868 d34= 179.87 a8= 123.64 r15= 1.3990 d21= 0.79 a28= 120.05 d8= 350.94 a15= 120.87 r22= 1.0880 d28= 179.76 r9= 1.3990 d15= 179.88 a22= 120.05 r29= 1.0879 a9= 120.88 r16= 1.3921 d22= 359.21 a29= 118.42

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38 1,8-diphenyl-1,3,5,7-octatetraene (C20H18) %nprocshared=8 %mem=8gb %chk=D9.chk #n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water)

D9 C 11 r12 10 a12 9 d12 H 7 r26 1 a26 2 d26 C 12 r13 11 a13 10 d13 H 8 r27 7 a27 1 d27 0 1 C 13 r14 12 a14 11 d14 H 9 r28 8 a28 7 d28 C C 14 r15 13 a15 12 d15 H 10 r29 9 a29 8 d29 C 1 r2 C 15 r16 14 a16 13 d16 H 11 r30 10 a30 9 d30 C 2 r3 1 a3 C 16 r17 15 a17 14 d17 H 12 r31 11 a31 10 d31 C 3 r4 2 a4 1 d4 C 17 r18 16 a18 15 d18 H 13 r32 12 a32 11 d32 C 4 r5 3 a5 2 d5 C 18 r19 17 a19 16 d19 H 14 r33 13 a33 12 d33 C 5 r6 4 a6 3 d6 C 19 r20 18 a20 17 d20 H 16 r34 15 a34 14 d34 C 1 r7 2 a7 3 d7 H 2 r21 1 a21 3 d21 H 17 r35 16 a35 15 d35 C 7 r8 1 a8 2 d8 H 3 r22 2 a22 1 d22 H 18 r36 17 a36 16 d36 C 8 r9 7 a9 1 d9 H 4 r23 3 a23 2 d23 H 19 r37 18 a37 17 d37 C 9 r10 8 a10 7 d10 H 5 r24 4 a24 3 d24 H 20 r38 19 a38 18 d38 C 10 r11 9 a11 8 d11 H 6 r25 5 a25 4 d25 Variables: a14= 122.95 r26= 1.0887 d37= 180.27 r2= 1.4021 d14= 178.39 a26= 114.99 r38= 1.0879 r3= 1.3987 r15= 1.4759 d26= 174.38 a38= 118.46 a3= 120.95 a15= 125.86 r27= 1.0857 d38= 179.87 r4= 1.3917 d15= 178.82 a27= 121.06 a4= 120.18 r16= 1.4020 d27= 359.22 d4= 0.17 a16= 123.50 r28= 1.0882 r5= 1.3917 d16= 11.58 a28= 117.28 a5= 119.71 r17= 1.3985 d28= 0.26 d5= 359.92 a17= 120.92 r29= 1.0882 r6= 1.3983 d17= 179.97 a29= 120.06 a6= 120.06 r18= 1.3918 d29= 359.26 d6= 360.00 a18= 120.17 r30= 1.0883 r7= 1.4765 d18= 359.51 a30= 117.02 a7= 123.59 r19= 1.3918 d30= 358.96 d7= 181.07 a19= 119.72 r31= 1.0881 r8= 1.3427 d19= 359.84 a31= 120.20 a8= 126.12 r20= 1.3982 d31= 359.14 d8= 354.92 a20= 120.06 r32= 1.0860 r9= 1.4475 d20= 0.32 a32= 116.11 a9= 122.85 r21= 1.0856 d32= 357.37 d9= 178.46 a21= 121.30 r33= 1.0886 r10= 1.3415 d21= 179.62 a33= 119.04 a10= 122.56 r22= 1.0870 d33= 359.66 d10= 181.10 a22= 119.79 r34= 1.0858 r11= 1.4457 d22= 179.94 a34= 121.23 a11= 122.89 r23= 1.0866 d34= 0.21 d11= 178.29 a23= 120.10 r35= 1.0869 r12= 1.3415 d23= 179.78 a35= 119.80 a12= 122.95 r24= 1.0868 d35= 179.63 d12= 179.64 a24= 120.01 r36= 1.0866 r13= 1.4474 d24= 179.85 a36= 120.10 a13= 122.49 r25= 1.0879 d36= 180.01 d13= 178.46 a25= 118.41 r37= 1.0868 r14= 1.3428 d25= 179.84 a37= 120.01

39 Appendix B: Sample Job Files

Example of a job file for the Photoelectron Spectroscopy experiment

Nitrogen (N2) #!/bin/bash #SBATCH -n 8 #SBATCH --mem=9000 #SBATCH -p defq #SBATCH -t 24:00:00 set -x # This is a Job Script for Running Gaussian 09 filename=Nitrogen filetype=gzmat module add c3ddb/gaussian unset PGI_TERM prgname=g09 ## Setting up scratch ## STORAGE_DIR="/scratch/users/ehess/${SLURM_JOB_ID}.${filename}" GAUSS_SCRDIR=$STORAGE_DIR export GAUSS_SCRDIR STORAGE_DIR mkdir -pv $STORAGE_DIR cd $STORAGE_DIR ## Copying relavent files ## cp $SLURM_SUBMIT_DIR/${filename}.${filetype} $STORAGE_DIR for a in $extrafiles ; do cp -r $SLURM_SUBMIT_DIR/$a $STORAGE_DIR/ ; done cat ${filename}.${filetype} ## Executing Gaussian 09 ## $prgname < ${filename}.${filetype} > ${filename}.out ## These files will be copied back to your directory ## cp -a $STORAGE_DIR $SLURM_SUBMIT_DIR

40 Example of a job file for the one-dimensional Particle-in-a-Box (1D-PIB) experiment

1,1-diethyl-2,2-cyanine #!/bin/bash #SBATCH -n 8 #SBATCH --mem=9000 #SBATCH -p defq #SBATCH -t 24:00:00 set -x # This is a Job Script for Running Gaussian 09 filename=D1 filetype=gzmat module add c3ddb/gaussian unset PGI_TERM prgname=g09 ## Setting up scratch ## STORAGE_DIR="/scratch/users/ehess/${SLURM_JOB_ID}.${filename}" GAUSS_SCRDIR=$STORAGE_DIR export GAUSS_SCRDIR STORAGE_DIR mkdir -pv $STORAGE_DIR cd $STORAGE_DIR ## Copying relavent files ## cp $SLURM_SUBMIT_DIR/${filename}.${filetype} $STORAGE_DIR for a in $extrafiles ; do cp -r $SLURM_SUBMIT_DIR/$a $STORAGE_DIR/ ; done cat ${filename}.${filetype} ## Executing Gaussian 09 ## $prgname < ${filename}.${filetype} > ${filename}.out ## These files will be copied back to your directory ## cp -a $STORAGE_DIR $SLURM_SUBMIT_DIR

41 Appendix C: Sample Output Files

Example of an output file for the Photoelectron Spectroscopy experiment

Nitrogen (N2) ------! Optimized Parameters ! ! (Angstroms and Degrees) ! ------! Name Definition Value Derivative Info. ! ------! R1 R(1,2) 1.1051 -DE/DX = 0.0 ! ------GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

*********************************************************************** Stoichiometry N2 Framework group D*H[C*(N.N)] Deg. of freedom 1 Full point group D*H NOp 8 Largest Abelian subgroup D2H NOp 8 Largest concise Abelian subgroup C2 NOp 2

*********************************************************************** Rotational constants (GHZ): 0.0000000 59.1017813 59.1017813

**********************************************************************

Population analysis using the SCF density.

**********************************************************************

Orbital symmetries: Occupied (SGG) (SGU) (SGG) (SGU) (PIU) (PIU) (SGG) Virtual (PIG) (PIG) (SGG) (SGU) (PIU) (PIU) (SGG) (PIG) (PIG) (SGU) (SGU) (SGG) (PIU) (PIU) (PIG) (PIG) (SGU) (SGG) (SGU) (DLTG) (DLTG) (PIU) (PIU) (DLTU) (DLTU) (SGG) (PIG) (PIG) (SGU) (SGG) (SGU) The electronic state is 1-SGG. Alpha occ. eigenvalues -- -14.45962 -14.45796 -1.13573 -0.56411 -0.47301 -0.47301 -0.43916 Alpha virt. eigenvalues -- -0.04140 -0.04140 0.06376 0.07946 0.09250 Alpha virt. eigenvalues -- 0.09250 0.14090 0.17365 0.17365 0.25929 Alpha virt. eigenvalues -- 0.51440 0.75050 0.80328 0.80328 0.89369 Alpha virt. eigenvalues -- 0.89369 0.92989 0.97934 1.40029 1.43978 Alpha virt. eigenvalues -- 1.43978 1.53741 1.53741 1.92913 1.92913 Alpha virt. eigenvalues -- 2.51272 2.61139 2.61139 2.87193 3.58222 Alpha virt. eigenvalues -- 3.88785

*********************************************************************** Mulliken charges: 1 N 0.000000 2 N 0.000000 Sum of Mulliken charges = 0.00000 Charge = 0.0000 electrons Dipole moment (field-independent basis, Debye): X= 0.0000 Y= 0.0000 Z= 0.0000 Tot= 0.0000

******************************Gaussian NBO Version 3.1****************************** N A T U R A L A T O M I C O R B I T A L A N D N A T U R A L B O N D O R B I T A L A N A L Y S I S ******************************Gaussian NBO Version 3.1****************************** 42

Summary of Natural Population Analysis:

Natural Population Natural ------Atom No Charge Core Valence Rydberg Total ------N 1 0.00000 1.99974 4.94997 0.05028 7.00000 N 2 0.00000 1.99974 4.94997 0.05028 7.00000 ======* Total * 0.00000 3.99948 9.89995 0.10057 14.00000

Natural Population ------Core 3.99948 ( 99.9871% of 4) Valence 9.89995 ( 98.9995% of 10) Natural Minimal Basis 13.89943 ( 99.2816% of 14) Natural Rydberg Basis 0.10057 ( 0.7184% of 14) ------

Atom No Natural Electron Configuration ------N 1 [core]2S( 1.62)2p( 3.33)3S( 0.03)3d( 0.01)4p( 0.01) N 2 [core]2S( 1.62)2p( 3.33)3S( 0.03)3d( 0.01)4p( 0.01)

******************************************************************************************** NATURAL BOND ORBITAL ANALYSIS:

Occupancies Lewis Structure Low High Occ. ------occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ======1(1) 1.90 13.98312 0.01688 2 3 0 2 0 0 0.03 ------

Structure accepted: No low occupancy Lewis orbitals

------Core 3.99948 ( 99.987% of 4) Valence Lewis 9.98364 ( 99.836% of 10) ======Total Lewis 13.98312 ( 99.879% of 14) ------Valence non-Lewis 0.00000 ( 0.000% of 14) Rydberg non-Lewis 0.01688 ( 0.121% of 14) ======Total non-Lewis 0.01688 ( 0.121% of 14) ------

*********************************************************************************************

(Occupancy) Bond orbital/ Coefficients/ Hybrids ------1. (2.00000) BD ( 1) N 1 - N 2 ( 50.00%) 0.7071* N 1 s( 38.33%)p 1.60( 61.29%)d 0.01( 0.38%) 0.0000 -0.6034 0.1384 -0.0053 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7812 0.0506 -0.0042 0.0000 0.0000 0.0000 0.0000 -0.0614 ( 50.00%) 0.7071* N 2 s( 38.33%)p 1.60( 61.29%)d 0.01( 0.38%) 0.0000 -0.6034 0.1384 -0.0053 0.0001 43 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.7812 -0.0506 0.0042 0.0000 0.0000 0.0000 0.0000 -0.0614 2. (2.00000) BD ( 2) N 1 - N 2 ( 50.00%) 0.7071* N 1 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.9977 -0.0064 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0671 0.0000 0.0000 0.0000 ( 50.00%) 0.7071* N 2 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.9977 -0.0064 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0671 0.0000 0.0000 0.0000 3. (2.00000) BD ( 3) N 1 - N 2 ( 50.00%) 0.7071* N 1 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9977 -0.0064 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0671 0.0000 0.0000 ( 50.00%) 0.7071* N 2 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9977 -0.0064 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0671 0.0000 0.0000 4. (1.99974) CR ( 1) N 1 s(100.00%)p 0.00( 0.00%) 1.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5. (1.99974) CR ( 1) N 2 s(100.00%)p 0.00( 0.00%) 1.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 6. (1.99182) LP ( 1) N 1 s( 63.41%)p 0.58( 36.54%)d 0.00( 0.05%) -0.0003 0.7946 0.0525 -0.0021 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6041 -0.0216 0.0002 0.0000 0.0000 0.0000 0.0000 -0.0221 7. (1.99182) LP ( 1) N 2 s( 63.41%)p 0.58( 36.54%)d 0.00( 0.05%) -0.0003 0.7946 0.0525 -0.0021 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.6041 0.0216 -0.0002 0.0000 0.0000 0.0000 0.0000 -0.0221 8. (0.00836) RY*( 1) N 1 s( 59.53%)p 0.65( 38.66%)d 0.03( 1.81%) 0.0000 0.0641 0.7547 0.1470 -0.0025 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1327 0.6057 0.0460 0.0000 0.0000 0.0000 0.0000 -0.1344 9. (0.00007) RY*( 2) N 1 s( 44.69%)p 0.85( 38.19%)d 0.38( 17.13%) 10. (0.00000) RY*( 3) N 1 s( 99.47%)p 0.00( 0.36%)d 0.00( 0.16%) 11. (0.00000) RY*( 4) N 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 12. (0.00000) RY*( 5) N 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 13. (0.00000) RY*( 6) N 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 14. (0.00000) RY*( 7) N 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 15. (0.00000) RY*( 8) N 1 s( 55.51%)p 0.01( 0.47%)d 0.79( 44.03%) 16. (0.00000) RY*( 9) N 1 s( 0.33%)p99.99( 99.40%)d 0.80( 0.27%) 17. (0.00000) RY*(10) N 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 18. (0.00000) RY*(11) N 1 s( 0.00%)p 1.00( 0.45%)d99.99( 99.55%) 19. (0.00000) RY*(12) N 1 s( 0.00%)p 1.00( 0.45%)d99.99( 99.55%) 44 20. (0.00000) RY*(13) N 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 21. (0.00000) RY*(14) N 1 s( 38.72%)p 0.65( 25.09%)d 0.93( 36.18%) 22. (0.00836) RY*( 1) N 2 s( 59.53%)p 0.65( 38.66%)d 0.03( 1.81%) 0.0000 0.0641 0.7547 0.1470 -0.0025 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1327 -0.6057 -0.0460 0.0000 0.0000 0.0000 0.0000 -0.1344 23. (0.00007) RY*( 2) N 2 s( 44.69%)p 0.85( 38.19%)d 0.38( 17.13%) 24. (0.00000) RY*( 3) N 2 s( 99.47%)p 0.00( 0.36%)d 0.00( 0.16%) 25. (0.00000) RY*( 4) N 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 26. (0.00000) RY*( 5) N 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 27. (0.00000) RY*( 6) N 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 28. (0.00000) RY*( 7) N 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 29. (0.00000) RY*( 8) N 2 s( 55.51%)p 0.01( 0.47%)d 0.79( 44.03%) 30. (0.00000) RY*( 9) N 2 s( 0.33%)p99.99( 99.40%)d 0.80( 0.27%) 31. (0.00000) RY*(10) N 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 32. (0.00000) RY*(11) N 2 s( 0.00%)p 1.00( 0.45%)d99.99( 99.55%) 33. (0.00000) RY*(12) N 2 s( 0.00%)p 1.00( 0.45%)d99.99( 99.55%) 34. (0.00000) RY*(13) N 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 35. (0.00000) RY*(14) N 2 s( 38.72%)p 0.65( 25.09%)d 0.93( 36.18%) 36. (0.00000) BD*( 1) N 1 - N 2 ( 50.00%) 0.7071* N 1 s( 38.33%)p 1.60( 61.29%)d 0.01( 0.38%) ( 50.00%) -0.7071* N 2 s( 38.33%)p 1.60( 61.29%)d 0.01( 0.38%) 37. (0.00000) BD*( 2) N 1 - N 2 ( 50.00%) 0.7071* N 1 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) ( 50.00%) -0.7071* N 2 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) 38. (0.00000) BD*( 3) N 1 - N 2 ( 50.00%) 0.7071* N 1 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%) ( 50.00%) -0.7071* N 2 s( 0.00%)p 1.00( 99.55%)d 0.00( 0.45%)

*******************************************************************************************

Final structure in terms of initial Z-matrix: N N,1,r2 Variables: r2=1.10512555 1\1\GINC-NODE020\FOpt\RB3LYP\6-31+G(d,p)\N2\EHESS\14-Mar-2019\0\\#n B3LYP/6-31+G(d,p) Opt POP=NBO\\Nitrogen\\0,1\N,0.,0.,0.1574372264\N,0.,0.,1.2625627736\\Version=AS64L-G09RevD.01\State=1-SGG\HF=- 109.5297794\RMSD=1.462e-09\RMSF=4.467e-09\Dipole=0.,0.,0.\Quadrupole=0.3914903,0.39, 14903,-0.7829806,0.,0.,0.\PG=D*H [C*(N1.N1)]\\@

Democracy is the recurrent suspicion that more than half of the people are right more than half of the time. -- E. B. White Job cpu time: 0 days 0 hours 6 minutes 24.5 seconds. File lengths (MBytes): RWF= 5 Int= 0 D2E= 0 Chk= 1 Scr= 1 Normal termination of Gaussian 09 at Thu Mar 14 10:04:02 2019.

45 Example of an output file for the one-dimensional Particle-in-a-Box (1D-PIB) experiment

1,1-diethyl-2,2-cyanine ------! Optimized Parameters ! ! (Angstroms and Degrees) ! ------! Name Definition Value ! Name Definition Value ------

! R1 R(1,2) 1.399 ! R51 R(25,48) 1.0963 ! R2 R(1,10) 1.4169 ! A1 A(2,1,10) 122.0799 ! R3 R(1,24) 1.4959 ! A2 A(2,1,24) 119.6998 ! R4 R(2,3) 1.4489 ! A3 A(10,1,24) 118.1886 ! R5 R(2,11) 1.4176 ! A4 A(1,2,3) 116.998 ! R6 R(3,4) 1.3682 ! A5 A(1,2,11) 120.9155 ! R7 R(3,26) 1.0811 ! A6 A(3,2,11) 121.9565 ! R8 R(4,5) 1.4371 ! A7 A(2,3,4) 122.029 ! R9 R(4,27) 1.0864 ! A8 A(2,3,26) 117.8919 ! R10 R(5,6) 1.4195 ! A9 A(4,3,26) 119.9684 ! R11 R(5,10) 1.431 ! A10 A(3,4,5) 120.5903 ! R12 R(6,7) 1.3945 ! A11 A(3,4,27) 120.2952 ! R13 R(6,28) 1.0869 ! A12 A(5,4,27) 119.1116 ! R14 R(7,8) 1.4165 ! A13 A(4,5,6) 121.4821 ! R15 R(7,29) 1.0855 ! A14 A(4,5,10) 118.3822 ! R16 R(8,9) 1.399 ! A15 A(6,5,10) 120.1324 ! R17 R(8,30) 1.0864 ! A16 A(5,6,7) 120.8099 ! R18 R(9,10) 1.4214 ! A17 A(5,6,28) 118.5488 ! R19 R(9,31) 1.0817 ! A18 A(7,6,28) 120.6408 ! R20 R(11,13) 1.427 ! A19 A(6,7,8) 119.0342 ! R21 R(11,32) 1.0784 ! A20 A(6,7,29) 120.711 ! R22 R(12,13) 1.3947 ! A21 A(8,7,29) 120.2533 ! R23 R(12,21) 1.4142 ! A22 A(7,8,9) 121.2706 ! R24 R(12,22) 1.4966 ! A23 A(7,8,30) 119.7931 ! R25 R(13,14) 1.4438 ! A24 A(9,8,30) 118.9352 ! R26 R(14,15) 1.3712 ! A25 A(8,9,10) 120.3452 ! R27 R(14,33) 1.0811 ! A26 A(8,9,31) 117.9719 ! R28 R(15,16) 1.4355 ! A27 A(10,9,31) 121.6706 ! R29 R(15,34) 1.0863 ! A28 A(1,10,5) 119.5146 ! R30 R(16,17) 1.4206 ! A29 A(1,10,9) 122.091 ! R31 R(16,21) 1.4311 ! A30 A(5,10,9) 118.3905 ! R32 R(17,18) 1.3938 ! A31 A(2,11,13) 126.5359 ! R33 R(17,35) 1.0869 ! A32 A(2,11,32) 117.658 ! R34 R(18,19) 1.4178 ! A33 A(13,11,32) 115.7534 ! R35 R(18,36) 1.0856 ! A34 A(13,12,21) 122.3229 ! R36 R(19,20) 1.3982 ! A35 A(13,12,22) 119.3277 ! R37 R(19,37) 1.0863 ! A36 A(21,12,22) 118.3272 ! R38 R(20,21) 1.4209 ! A37 A(11,13,12) 119.7576 ! R39 R(20,38) 1.0818 ! A38 A(11,13,14) 122.721 ! R40 R(22,23) 1.5411 ! A39 A(12,13,14) 117.3586 ! R41 R(22,39) 1.0919 ! A40 A(13,14,15) 121.7939 ! R42 R(22,40) 1.092 ! A41 A(13,14,33) 118.0803 ! R43 R(23,41) 1.0953 ! A42 A(15,14,33) 119.978 ! R44 R(23,42) 1.0957 ! A43 A(14,15,16) 120.6309 ! R45 R(23,43) 1.0963 ! A44 A(14,15,34) 120.2211 ! R46 R(24,25) 1.54 ! A45 A(16,15,34) 119.1047 ! R47 R(24,44) 1.091 ! A46 A(15,16,17) 121.5839 ! R48 R(24,45) 1.0899 ! A47 A(15,16,21) 118.4353 ! R49 R(25,46) 1.0953 ! A48 A(17,16,21) 119.9663 ! R50 R(25,47) 1.0958 ! A49 A(16,17,18) 120.7306 46 ! A50 A(16,17,35) 118.5974 ! A57 A(20,19,37) 119.0242 ! A51 A(18,17,35) 120.672 ! A58 A(19,20,21) 120.1976 ! A52 A(17,18,19) 119.1919 ! A59 A(19,20,38) 118.2891 ! A53 A(17,18,36) 120.6444 ! A60 A(21,20,38) 121.5108 ! A54 A(19,18,36) 120.1625 ! A61 A(12,21,16) 119.3373 ! A55 A(18,19,20) 121.2299 ! A62 A(12,21,20) 121.9848 ! A56 A(18,19,37) 119.745 ! A63 A(16,21,20) 118.6759

! A64 A(12,22,23) 113.4889 ! D30 D(27,4,5,10) -176.2752 ! A65 A(12,22,39) 107.8879 ! D31 D(4,5,6,7) 179.8047 ! A66 A(12,22,40) 107.3783 ! D32 D(4,5,6,28) 0.0378 ! A67 A(23,22,39) 110.6675 ! D33 D(10,5,6,7) -0.8702 ! A68 A(23,22,40) 110.7334 ! D34 D(10,5,6,28) 179.363 ! A69 A(39,22,40) 106.3656 ! D35 D(4,5,10,1) 0.1714 ! A70 A(22,23,41) 111.6093 ! D36 D(4,5,10,9) -179.1258 ! A71 A(22,23,42) 111.8312 ! D37 D(6,5,10,1) -179.1744 ! A72 A(22,23,43) 109.0986 ! D38 D(6,5,10,9) 1.5284 ! A73 A(41,23,42) 107.8974 ! D39 D(5,6,7,8) -0.2548 ! A74 A(41,23,43) 108.1738 ! D40 D(5,6,7,29) -179.8052 ! A75 A(42,23,43) 108.1032 ! D41 D(28,6,7,8) 179.5071 ! A76 A(1,24,25) 112.7328 ! D42 D(28,6,7,29) -0.0432 ! A77 A(1,24,44) 108.6042 ! D43 D(6,7,8,9) 0.7077 ! A78 A(1,24,45) 108.1081 ! D44 D(6,7,8,30) -178.9116 ! A79 A(25,24,44) 110.9251 ! D45 D(29,7,8,9) -179.7398 ! A80 A(25,24,45) 110.9523 ! D46 D(29,7,8,30) 0.6408 ! A81 A(44,24,45) 105.192 ! D47 D(7,8,9,10) -0.0202 ! A82 A(24,25,46) 111.3121 ! D48 D(7,8,9,31) -178.7646 ! A83 A(24,25,47) 111.2195 ! D49 D(30,8,9,10) 179.6023 ! A84 A(24,25,48) 109.3663 ! D50 D(30,8,9,31) 0.8579 ! A85 A(46,25,47) 108.3446 ! D51 D(8,9,10,1) 179.6326 ! A86 A(46,25,48) 108.2511 ! D52 D(8,9,10,5) -1.0893 ! A87 A(47,25,48) 108.2501 ! D53 D(31,9,10,1) -1.6704 ! D1 D(10,1,2,3) 7.5367 ! D54 D(31,9,10,5) 177.6077 ! D2 D(10,1,2,11) -176.5288 ! D55 D(2,11,13,12) 157.1429 ! D3 D(24,1,2,3) -174.5474 ! D56 D(2,11,13,14) -27.6195 ! D4 D(24,1,2,11) 1.3871 ! D57 D(32,11,13,12) -25.5776 ! D5 D(2,1,10,5) -5.6774 ! D58 D(32,11,13,14) 149.6599 ! D6 D(2,1,10,9) 173.5928 ! D59 D(21,12,13,11) 172.1778 ! D7 D(24,1,10,5) 176.3765 ! D60 D(21,12,13,14) -3.3114 ! D8 D(24,1,10,9) -4.3533 ! D61 D(22,12,13,11) -9.5655 ! D9 D(2,1,24,25) -86.0023 ! D62 D(22,12,13,14) 174.9452 ! D10 D(2,1,24,44) 37.3383 ! D63 D(13,12,21,16) 4.3576 ! D11 D(2,1,24,45) 150.9783 ! D64 D(13,12,21,20) -176.1592 ! D12 D(10,1,24,25) 91.9942 ! D65 D(22,12,21,16) -173.9158 ! D13 D(10,1,24,44) -144.6651 ! D66 D(22,12,21,20) 5.5675 ! D14 D(10,1,24,45) -31.0252 ! D67 D(13,12,22,23) 94.7465 ! D15 D(1,2,3,4) -4.1471 ! D68 D(13,12,22,39) -142.2531 ! D16 D(1,2,3,26) 172.0229 ! D69 D(13,12,22,40) -27.9697 ! D17 D(11,2,3,4) 179.9639 ! D70 D(21,12,22,23) -86.9271 ! D18 D(11,2,3,26) -3.8661 ! D71 D(21,12,22,39) 36.0733 ! D19 D(1,2,11,13) 163.6449 ! D72 D(21,12,22,40) 150.3567 ! D20 D(1,2,11,32) -13.5886 ! D73 D(11,13,14,15) -174.6996 ! D21 D(3,2,11,13) -20.625 ! D74 D(11,13,14,33) 0.8788 ! D22 D(3,2,11,32) 162.1415 ! D75 D(12,13,14,15) 0.6455 ! D23 D(2,3,4,5) -1.1074 ! D76 D(12,13,14,33) 176.2239 ! D24 D(2,3,4,27) 178.2685 ! D77 D(13,14,15,16) 0.9084 ! D25 D(26,3,4,5) -177.1998 ! D78 D(13,14,15,34) 178.4925 ! D26 D(26,3,4,27) 2.1761 ! D79 D(33,14,15,16) -174.5878 ! D27 D(3,4,5,6) -177.5553 ! D80 D(33,14,15,34) 2.9963 ! D28 D(3,4,5,10) 3.1081 ! D81 D(14,15,16,17) 178.7181 ! D29 D(27,4,5,6) 3.0614 ! D82 D(14,15,16,21) 0.1041 47 ! D83 D(34,15,16,17) 1.1074 ! D105 D(19,20,21,12) -178.5172 ! D84 D(34,15,16,21) -177.5067 ! D106 D(19,20,21,16) 0.9693 ! D85 D(15,16,17,18) -178.5575 ! D107 D(38,20,21,12) 2.0681 ! D86 D(15,16,17,35) 1.3722 ! D108 D(38,20,21,16) -178.4454 ! D87 D(21,16,17,18) 0.0357 ! D109 D(12,22,23,41) 60.2621 ! D88 D(21,16,17,35) 179.9654 ! D110 D(12,22,23,42) -60.7198 ! D89 D(15,16,21,12) -2.643 ! D111 D(12,22,23,43) 179.7459 ! D90 D(15,16,21,20) 177.8566 ! D112 D(39,22,23,41) -61.1961 ! D91 D(17,16,21,12) 178.7198 ! D113 D(39,22,23,42) 177.822 ! D92 D(17,16,21,20) -0.7806 ! D114 D(39,22,23,43) 58.2878 ! D93 D(16,17,18,19) 0.5247 ! D115 D(40,22,23,41) -178.8927 ! D94 D(16,17,18,36) -179.8672 ! D116 D(40,22,23,42) 60.1254 ! D95 D(35,17,18,19) -179.4035 ! D117 D(40,22,23,43) -59.4088 ! D96 D(35,17,18,36) 0.2045 ! D118 D(1,24,25,46) 60.1437 ! D97 D(17,18,19,20) -0.3362 ! D119 D(1,24,25,47) -60.7788 ! D98 D(17,18,19,37) 179.3067 ! D120 D(1,24,25,48) 179.712 ! D99 D(36,18,19,20) -179.9462 ! D121 D(44,24,25,46) -61.8974 ! D100 D(36,18,19,37) -0.3033 ! D122 D(44,24,25,47) 177.1801 ! D101 D(18,19,20,21) -0.422 ! D123 D(44,24,25,48) 57.6709 ! D102 D(18,19,20,38) 179.0113 ! D124 D(45,24,25,46) -178.4381 ! D103 D(37,19,20,21) 179.9325 ! D125 D(45,24,25,47) 60.6394 ! D104 D(37,19,20,38) -0.6342 ! D126 D(45,24,25,48) -58.8698

************************************************************************************************** Stoichiometry C23H23N2(1+) Framework group C1[X(C23H23N2)] Deg. of freedom 138 Full point group C1 NOp 1 Rotational constants (GHZ): 0.5750082 0.1024208 0.0910627

********************************************************************** Population analysis using the SCF density. **********************************************************************

Alpha occ. eigenvalues -- -14.42132 -14.41823 -10.29316 -10.29155 -10.27757 Alpha occ. eigenvalues -- -10.27654 -10.24571 -10.24531 -10.23651 -10.23563 Alpha occ. eigenvalues -- -10.23414 -10.23323 -10.22702 -10.22510 -10.22169 Alpha occ. eigenvalues -- -10.22016 -10.22010 -10.21970 -10.21864 -10.21821 Alpha occ. eigenvalues -- -10.21495 -10.21313 -10.20848 -10.19150 -10.18937 Alpha occ. eigenvalues -- -1.01372 -1.00870 -0.88560 -0.88281 -0.86028 Alpha occ. eigenvalues -- -0.84506 -0.81663 -0.78796 -0.78423 -0.78201 Alpha occ. eigenvalues -- -0.76543 -0.76243 -0.73779 -0.68799 -0.67771 Alpha occ. eigenvalues -- -0.66889 -0.66433 -0.65402 -0.62890 -0.61541 Alpha occ. eigenvalues -- -0.61177 -0.57368 -0.56674 -0.55182 -0.54765 Alpha occ. eigenvalues -- -0.53231 -0.52005 -0.49513 -0.49426 -0.48780 Alpha occ. eigenvalues -- -0.48583 -0.47241 -0.46887 -0.46732 -0.46509 Alpha occ. eigenvalues -- -0.46163 -0.45814 -0.45342 -0.44629 -0.43328 Alpha occ. eigenvalues -- -0.42640 -0.41536 -0.40927 -0.40315 -0.40050 Alpha occ. eigenvalues -- -0.39412 -0.38931 -0.38412 -0.38084 -0.37793 Alpha occ. eigenvalues -- -0.37006 -0.36467 -0.36246 -0.36113 -0.35686 Alpha occ. eigenvalues -- -0.33039 -0.32852 -0.30535 -0.28028 -0.26125 Alpha occ. eigenvalues -- -0.25971 -0.21096 Alpha virt. eigenvalues -- -0.10238 -0.06847 -0.04813 -0.02458 -0.01825 Alpha virt. eigenvalues -- -0.00200 0.04541 0.07130 0.08103 0.09635 Alpha virt. eigenvalues -- 0.10806 0.11088 0.11682 0.12389 0.12688 Alpha virt. eigenvalues -- 0.13058 0.13360 0.13631 0.14014 0.14383 Alpha virt. eigenvalues -- 0.14865 0.15006 0.15241 0.15786 0.15895 Alpha virt. eigenvalues -- 0.16032 0.16233 0.16820 0.17152 0.17513 Alpha virt. eigenvalues -- 0.17905 0.18339 0.18900 0.20246 0.21048 48 Alpha virt. eigenvalues -- 0.21199 0.21635 0.21967 0.22663 0.22843 Alpha virt. eigenvalues -- 0.23566 0.24279 0.24413 0.24576 0.25057 Alpha virt. eigenvalues -- 0.25573 0.25823 0.26213 0.26459 0.26843 Alpha virt. eigenvalues -- 0.27527 0.28474 0.28516 0.29146 0.29688 Alpha virt. eigenvalues -- 0.29887 0.30676 0.30822 0.31529 0.31899 Alpha virt. eigenvalues -- 0.32420 0.32999 0.33358 0.33535 0.34532 Alpha virt. eigenvalues -- 0.35007 0.36154 0.36506 0.36647 0.37052 Alpha virt. eigenvalues -- 0.37528 0.37743 0.37898 0.38181 0.38669 Alpha virt. eigenvalues -- 0.39007 0.39327 0.39735 0.40136 0.40517 Alpha virt. eigenvalues -- 0.40849 0.41201 0.41272 0.41656 0.42063 Alpha virt. eigenvalues -- 0.42616 0.42900 0.44056 0.44406 0.44749 Alpha virt. eigenvalues -- 0.44857 0.45610 0.45947 0.46319 0.47127 Alpha virt. eigenvalues -- 0.47733 0.49141 0.49795 0.50790 0.50855 Alpha virt. eigenvalues -- 0.51769 0.52642 0.53580 0.54367 0.55721 Alpha virt. eigenvalues -- 0.56269 0.57206 0.58135 0.58787 0.59308 Alpha virt. eigenvalues -- 0.60413 0.61087 0.61599 0.63760 0.64709 Alpha virt. eigenvalues -- 0.65853 0.66535 0.67708 0.67809 0.68191 Alpha virt. eigenvalues -- 0.68804 0.70087 0.72548 0.73300 0.74193 Alpha virt. eigenvalues -- 0.76022 0.76893 0.77700 0.78038 0.79150 Alpha virt. eigenvalues -- 0.80135 0.81368 0.85273 0.98044 0.99918 Alpha virt. eigenvalues -- 1.00803 1.01956 1.06001 1.06996 1.07949 Alpha virt. eigenvalues -- 1.08662 1.09756 1.10587 1.11026 1.11328 Alpha virt. eigenvalues -- 1.11568 1.12592 1.13286 1.14143 1.15104 Alpha virt. eigenvalues -- 1.15512 1.15580 1.16216 1.16906 1.17653 Alpha virt. eigenvalues -- 1.17943 1.18387 1.20080 1.20393 1.21232 Alpha virt. eigenvalues -- 1.22823 1.23634 1.24613 1.26949 1.29006 Alpha virt. eigenvalues -- 1.29307 1.31646 1.33801 1.37537 1.38952 Alpha virt. eigenvalues -- 1.40761 1.43510 1.44169 1.47852 1.48335 Alpha virt. eigenvalues -- 1.55300 1.55794 1.60426 1.61513 1.63329 Alpha virt. eigenvalues -- 1.64792 1.66857 1.82441 1.93011

**************************************************************************************************** Mulliken charges:

1 N -0.227586 27 H 0.272902 2 C 0.349259 28 H 0.260925 3 C -0.334288 29 H 0.256558 4 C -0.303762 30 H 0.254276 5 C 0.371956 31 H 0.258291 6 C -0.381637 32 H 0.241613 7 C -0.261441 33 H 0.290177 8 C -0.251380 34 H 0.273858 9 C -0.324527 35 H 0.262031 10 C 0.158285 36 H 0.257360 11 C -0.401399 37 H 0.255569 12 N -0.218335 38 H 0.265557 13 C 0.321515 39 H 0.242437 14 C -0.319531 40 H 0.256562 15 C -0.300182 41 H 0.227776 16 C 0.372426 42 H 0.221463 17 C -0.381304 43 H 0.228131 18 C -0.257174 44 H 0.234285 19 C -0.250487 45 H 0.237415 20 C -0.324014 46 H 0.230102 21 C 0.159401 47 H 0.224579 22 C -0.366147 48 H 0.224683 23 C -0.626155 24 C -0.344269 25 C -0.624688 26 H 0.288915 49 Sum of Mulliken charges = 1.00000 Charge= 1.0000 electrons Dipole moment (field-independent basis, Debye): X= -4.5965 Y= -1.5471 Z= 11.7100 Tot= 12.6746

********************************************************************************************* *****

N-N= 2.021053258948D+03 E-N=-6.336523496667D+03 KE= 9.933963612179D+02 1\1\GINC- NODE052\FOpt\RB3LYP\LANL2DZ\C23H23N2(1+)\EHESS\14-Mar-2019\0\ \#n B3LYP/LANL2DZ GFinput opt=(verytight) nosymm scf=(qc,verytight) integral=ultrafine SCRF=(Solvent=Water) \\D1\\1,1\N,0.0174276216,0.0360775016,0.0554304124\C,0.0901188357,-0.1516541686,1.4398957645 \C,1.4135666933,-0.2361758171,2.0236199074\C,2.546898921,-0.221784683,1.257283012 6\C,2.4602360008,- 0.144689028,-.1750976217\C,3.6212919534,-0.18005008 55,-0.9909808266\C,3.5206421545,-0.1082962662,- 2.3800264641\C,2.237884 6782,-0.0044886403,-2.9719246155\ C,1.0787870708,0.0417315242,- 2.1898248969\C,1.1662337732,-0.0155357311,-0.7723138885\C,-1.0831583063,-0.1674564089,2.2353328645\N,- 2.2294631063,-0.2035437461,4.3898260704\C,-1.1985358973,-0.6608709216, 3.5693601015\C,-0.3461061957,- 1.7020213441,4.0928762057\C,-0.5415301808,-2.2366237971,5.3403570274\C,-1.6245994411,- 1.7860258461,6.1677094101\C,-1.8619073003,-2.3445678221,7.4522004249\C,-2.9367448492,- 1.9144903902,8.2283590632\C,-3.8034294386,-0.9159754106,7.7166282871\C,-3.5947591703,- 0.3526027499,6.4541233593\C,-2.4938621857,-0.7696488436, 5.6585096409 \C,- 3.0678675285,0.9511886732,3.938769281\C,-4.3673660598,0.5260157718,3.2276788445\C,-1.3122941578, 0.2541313706,-0.594114054\C,-2.025845148,-1.0643058491,-0.9464580994\H,1.4908867701,- .2486586553,3.10192138 \H,3.5261785636,-0.2584453025,1.7263603909 \H,4.5918876735,-0.2682472513,- 0.5097077813\H,4.4094162239,-0.13864196 46,-3.0025830867\H,2.1440277548,0.0343405993,-4.0535800937\H,0.1257715824,0.1006790808,-2.6981263546 \H,-1.9971052195,0.1878697117,1.7864636991\H,0.4172925775,-2.1087653861,3.4444017497\H,0.100288389,- 3.03623759 83,5.6992522872\H,-1.1881273041,-3.1155354123,7.8168145634\H,-3.1155238431,- 2.340733887,9.2105902078\H,-4.6505072189, -0.5822161173,8.3092611987\H,-4.2947526943,0.3940937049,6.1038691464\H,- 3.2905046625,1.5658520041,4.8133621858\H, -2.4499933792,1.5653175601,3.2802942961\H,-5.0074274564,-0.0749622906,3.8824969363\H,-4.1645607538,- 0.0603339697, 2.3245510205\H,-4.9251793288,1.4227388034,2.9335057782\H,- 1.9272647045,0.8650419186,0.0683535962\H,-1.158568611, 0.8640167931,-1.4841811303\H,-2.2080284971,- 1.6697424636,-0.0520076931\H,-1.4342201683,-1.6594432762,-1.6511380201 \H,-2.9926130316,-0.84110184,-1.4127483739\\ Version=AS64L-G09 RevD.01\HF=-999.5159294\RMSD=0.000e+00\RMSF=4.428e-07\Dipole=- 0.5534346,0.3610365,-0.0086912\Quadrupole=-1.9624855,-32.1648387,34.1273242,-5.9326088,-24.9937364,- 11.9625015\PG=C01 [X(C23H23N2)]\\@

I DO NOT KNOW WHAT I MAY APPEAR TO THE WORLD; BUT TO MYSELF I SEEM TO HAVE BEEN ONLY LIKE A BOY PLAYING ON THE SEASHORE, AND DIVERTING MYSELF IN NOW AND THEN FINDING A SMOOTHER PEBBLE OR A PRETTIER SHELL THAN ORDINARY, WHILST THE GREAT OCEAN OF TRUTH LAY ALL UNDISCOVERED BEFORE ME. -- NEWTON (1642-1726) Job cpu time: 1 days 17 hours 10 minutes 46.5 seconds. File lengths (MBytes): RWF= 382 Int= 0 D2E= 0 Chk= 12 Scr= 1 Normal termination of Gaussian 09 at Thu Mar 14 17:34:57 2019.

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REFERENCES

1. About ACS: Who We Are and What We Do. https://www.acs.org/content/acs/en/about.html (accessed Jan 4, 2019). 2. Handbook containing 2015 ACS Guidelines for B.S. Programs in Chemical Sciences published by ACS at: https://www.acs.org/content/dam/acsorg/about/governance/committees/training/2015-acs- guidelines-for-bachelors-degree-programs.pdf 3. Handout describing Importance of ACS Certification of B.S. Programs at U.S. Institutions can be accessed from: https://www.acs.org/content/dam/acsorg/about/governance/committees/training/acsapproved/ degreeprogram/why-acs-approval-matters-for-a-chemistry-program.pdf 4. List of the available academic programs in Department of Chemical Sciences at Bridgewater State University can be found at https://www.bridgew.edu/department/chemical- sciences/academic-programs (accessed Apr 29, 2019). 5. Physical Chemistry. https://www.acs.org/content/acs/en/careers/college-to-career/areas-of- chemistry/physical-chemistry.html (accessed Jan 4, 2019). 6. Supplemental handbook, published by ACS, containing Guidelines for Physical Chemistry Content for B.S. programs in U.S. can be accessed from: https://www.acs.org/content/dam/acsorg/about/governance/committees/training/acsapproved/ degreeprogram/physical-chemistry-supplement.pdf 7. Lewars, E. G. Computational chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics, Third ed.; Springer: 2016. 8. Johnson, L. E.; Engel, T. Journal of Chemical Education2011, 88(5), 569–573. 9. Martin, N. H. Journal of Chemical Education1998, 75(2), 241–243. 10. Lagowski, J. J.; Bosma, W. B. Chemistry: Foundations and Applications; Macmillan Reference USA: New York, 2004; Vol. 4. 11. Levine, I. N. Quantum chemistry, Fifth ed.; Prentice Hall of India: New Delhi, 2006. 12. Pilar, F. L. Elementary quantum chemistry, Second ed.; Dover Publications: Mineola, 2011. 13. Szabo, A.; Ostlund, N. S. Modern quantum chemistry: introduction to advanced electronic structure theory; Dover Publications: Mineola, NY, 2006. 14. Cramer, C. J. Essentials of computational chemistry theories and models, Second ed.; Wiley: Chichester, 2014. 15. Foresman, J. B.; Frisch, Æ. Exploring chemistry with electronic structure methods, Second ed.; Gaussian: Pittsburgh, PA, 1996. 16. Levine, I. N. Quantum chemistry, Fifth ed.; Prentice Hall of India: New Delhi, 2006. 17. Foresman, J. B. Exploring chemistry with electronic structure methods, Third ed.; Gaussian: Wallingford, 2015. 18. Sukumar, N. A matter of density: exploring the electron density concept in the chemical, biological, and materials sciences; Wiley: Hoboken, NJ, 2013. 19. Becke, A. D., Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98, 5648-5652. 20. Resources http://www.mghpcc.org/resources/computer-systems-at-the- mghpcc/c3ddb/resources/ (accessed Aug 28, 2018). 21. Gaussian 09, Rev. D.01, Frisch, M. J. et.al., Gaussian, Inc., Wallingford CT, 2013.

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22. Simon and McQuarrie Physical Chemistry: A Molecular Approach textbook, 1st edition, pg 439 23. Picture adapted from www.educator.com 24. Data is taken from Simon and McQuarrie Physical Chemistry: A Molecular Approach 1st edition. 25. All structures drawn using ChemDraw Professional PerkinElmer Informatics, Inc.

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