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Using Computational Methods

To Teach Chemical Principles

ACS SYMPOSIUM SERIES 1312

Using Computational Methods

To Teach Chemical Principles

Department of Chemistry, Biochemistry, and Physics

Rider University Lawrenceville, New Jersey, United States

Melissa S Reeves, Editor

Department of Chemistry

Tuskegee University Tuskegee, Alabama, United States

Sponsored by the ACS Division of Chemical Education

American Chemical Society, Washington, DC

Library of Congress Cataloging-in-Publication Data

Names: Grushow, Alexander, editor | Reeves, Melissa Setsuko, 1966- editor |

American Chemical Society Division of Chemical Education | American

Chemical Society Meeting (254th : 2017 : Washington, D.C.)

Title: Using computational methods to teach chemical principles / Alexander

Grushow, editor (Department of Chemistry, Biochemistry, and Physics, Rider

University, Lawrenceville, New Jersey, United States), Melissa S Reeves,

editor (Department of Chemistry, Tuskegee University, Tuskegee, Alabama,

United States) ; sponsored by the ACS Division of Chemical Education.

Description: Washington, DC : American Chemical Society, [2019] | Series: ACS

symposium series ; 1312 | Based on the 254th American Chemical Society

national meeting, held in 2017, in Washington, DC | Includes

bibliographical references and index | Description based on print version

record and CIP data provided by publisher; resource not viewed.

Identifiers: LCCN 2019006545 (print) | LCCN 2019015021 (ebook) | ISBN

9780841234178 (ebook) | ISBN 9780841234208 (alk paper)

Subjects: LCSH: Chemistry Study and teaching Congresses.

Classification: LCC QD40 (ebook) | LCC QD40 U845 2019 (print) | DDC

540.71 dc23

LC record available at https://lccn.loc.gov/2019006545

The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48n1984.

Copyright © 2019 American Chemical Society

All Rights Reserved Reprographic copying beyond that permitted by Sections 107 or 108 of the U.S Copyright Act

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PRINTED IN THE UNITED STATES OF AMERICA

The purpose of the series is to publish timely, comprehensive books developed from the ACSsponsored symposia based on current scientific research Occasionally, books are developed fromsymposia sponsored by other organizations when the topic is of keen interest to the chemistryaudience

Before a book proposal is accepted, the proposed table of contents is reviewed for appropriateand comprehensive coverage and for interest to the audience Some papers may be excluded to betterfocus the book; others may be added to provide comprehensiveness When appropriate, overview

or introductory chapters are added Drafts of chapters are peer-reviewed prior to final acceptance orrejection

As a rule, only original research papers and original review papers are included in the volumes.Verbatim reproductions of previous published papers are not accepted

ACS Books Department

Robert M Whitnell and Melissa S Reeves

Mark J Perri, Mary Akinmurele, and Matthew Haynie

William R Martin and David W Ball

Thomas C DeVore

Arun K Sharma and Lukshmi Asirwatham

Brian J Esselman and Nicholas J Hill

Using Computational Methods To Teach Chemical Principles: Overview . . . 

Integrating Computational Chemistry into an Organic Chemistry Laboratory

Curriculum Using WebMO . . . 

11.

139

vii

Computational Narrative Activities: Combining Computing, Context, and

Communication To Teach Chemical Concepts . . . 

12.

163

Computational Chemistry as a Course for Students Majoring in the Sciences . . . 

Beyond the Analytical Solution: Using Mathematical Software To Enhance

Understanding of Physical Chemistry . . . 

Chapter 1

Using Computational Methods To Teach Chemical Principles : Overview

Alexander Grushow * ,1 and Melissa S Reeves * ,2

1 Department of Chemistry, Biochemistry & Physics, Rider University,

Lawrenceville, New Jersey 08648, United States

2 Department of Chemistry, Tuskegee University, Tuskegee, Alabama 36088, United States

* E-mail: grushow@rider.edu (A.G.).

* E-mail: mreeves@tuskegee.edu (M.S.R.).

While computational chemistry methods are usually a research topic of their own,

even in the undergraduate curriculum, many methods are becoming mainstream

and can be used to appropriately compute chemical parameters that are not easily

measured in the undergraduate laboratory These calculations can be used to help

students explore and understand chemical principles and properties Visualization

and animation of structures and properties are also aids in students’ exploration

of chemistry The ubiquity of personal computing devices capable of running

calculations and the user-friendliness of software to fully optimize small and

medium molecules using graphical interfaces and drop-down control menus has

made it possible to readily use computational chemistry tools in most chemistry

courses in the undergraduate curriculum This book will focus on the use of

computational chemistry as a tool in the classroom and laboratory to teach

chemical principles

Introduction

The chapters in this book are the result of the growing ubiquity of theoretical and computationalmethods in all facets of chemistry education For better or worse, the days of hand calculatingsolutions to Schrödinger equations are long gone The ability to use a computer to solve thousands ofequations in the blink of an eye makes it possible to pursue computations that generate meaningfulresults in a very short time Whether those computations are quantum mechanical, statisticalmechanics or examining molecular dynamics, the even greater power of modern computationalchemistry is the ability to visualize the results of these calculations in ways that provide real chemicalinsight to both experts and novices It is the latter group that the authors within this book serve

© 2019 American Chemical Society

Herein are described many different uses of computers, from high level quantum mechanicalcalculations, through molecular dynamics simulations to the use of mathematical engines to modelchemical systems All of this computing power however is targeted at teaching students aboutchemistry Along the way students will likely learn some other computer-based techniques, but thegoal is to learn about chemistry.

The symposium that resulted in this book was held at the 254thACS National Meeting held inWashington, DC Many of the authors in this book presented talks during that symposium, whichalso was highlighted by an extended afternoon break for participants to go outside and witness thesolar eclipse of 2017 Other chapters represent the work of authors who could not participate in thesymposium, but provide valuable insight into ways computational chemistry can be used to teachchemical principles We are emphasizing the idea that the focus can now be on learning chemistryand not on the theoretical methods themselves While we are not diminishing the importance ofthe theoretical background, we wanted to document the myriad of ways to teach chemistry usingcomputational methods

The objective of this book is to provide the reader with examples of the use of computationalmethods in the classroom and laboratory in various institutional settings While the use ofcomputational methods has been developing for years, we felt that the work of the authors wasimportant to present even though we have not had the opportunity to systematically assess theoutcomes of these innovations We expect that research will be done to explore the effectiveness

of computational methods in the teaching of chemical concepts as computational methods becomemore mainstream Wherever possible we have asked authors to comment on their experiences,challenges, and successes, including student feedback when available, but our primary focus has been

to publicize what various instructors have done to promote the use of computational methods inthe teaching of chemistry In the meantime, we hope that you will find some use in learning aboutthe current innovations and about the successes and challenges that the authors have experienced inbringing computational methods to bear in the teaching of chemistry

History of Computational in Chemistry in Our Classes

When we first started our teaching careers, desktop computers were just starting to be regularly

used to perform ab initio or semi-empirical quantum mechanical calculations More often than not

however, the software was limited to a single or small number of available licenses And examination

of anything more than a few heavy atoms took longer than the typical undergraduate studentattention span As a result, these packages were usually used in research situations or on a verylimited basis in the undergraduate curriculum to provide a single example of computational methods.Molecular mechanics and dynamics could also be performed on small systems using a desktopcomputer, but the limitation with this type of computation was that commercial packages were oftencostly and the low cost(and free) applications often did not come with a useful graphical interface.While we are both physical chemists and had used computational resources in our own research,bringing it into the classroom was fraught with many difficulties Most of the time students needed

to learn new computer constructs, such as coding and command-line instructions While we did feelthat these kinds of experiences were important for our undergraduates to engage in, because of thevalue of computational methods used in professional research situations in chemistry, many of theearly exercises expended much more effort in computer programming and less time thinking aboutthe chemistry questions

As indicated by a number of authors in this book, there has been a great development ofcomputational tools to both quickly calculate and easily visualize results of calculations on manytypes of chemical systems These developments have changed our questions from “how do I getstudents to learn how to use computational software?” to “what chemical questions can we exploreusing this relatively easy tool?” Within this book, you will find chapters that explore chemistryquestions that utilize tools such as high-level quantum computational chemistry, moleculardynamics simulations, and computational engines to visualize complex mathematical functions used

in physical chemistry The material, however is not just for the physical chemist, as we havecontributions from organic chemistry and general chemistry as well

Selected Landmarks in Computational Chemistry Education

Computational chemistry has been part of the undergraduate curriculum for decades(1), but

has stubbornly remained in isolated pockets of particular departments Despite the optimistic J

Chem Ed editorial “Computational Chemistry for the Masses (2)” from 1996, computational

chemistry did not spread to the masses As recently as 2015, Fortenberry, et al., argued that

computational chemistry had still not entered the standard undergraduate chemistry curriculum (3) [emphasis added] The same argument has been made by Johnson and Engel (4) Most purveyors of

computational chemistry have made sincere efforts to woo the undergraduate education market withspecialized packages, books (5–7), and even workshops for professors One large barrier has beenthe expense of equipping a computer classroom and purchasing the license to a suite of software; asecond barrier is the regular maintenance and upgrades needed for hardware and software Finally,the professor running the course has to have a plan, curricular materials, and the expertise to use thecomputational tools within the curriculum

A coarse timeline of “landmark” events in the last 25 years of computational chemistryeducation here begins in 1993(see Figure 1) with the publication of the Schwenz and Moore Physical

Chemistry: Developing a Dynamic Curriculum (8) Three of the 31 chapters were computationally

oriented, covering ab initio calculations (9), Hückel calculations (10), and using Monte Carlocalculations to simulate kinetic data(11) That same year, a review by Casanova covered molecular

modeling in education up to that date(1) Coincidentally, 1993 was also the debut of Mosaic, the

first web browser for general users

The 90s saw a rise in the graphical user interface(GUI) and software designed for the desktopcomputer For example, Gaussian was released for the Windows-based PCs in 1994, and Spartan forMac(1994) and Windows (1995) were released Gaussview (the Gaussian GUI) was first available in

1997 Many efforts were made by commercial software companies to produce educational materials

in this period (5–7) Gaussview/Gaussian and Spartan remain highly popular today In 1998, a

paper detailed the“Integration of Computational Chemistry in the Chemistry Curriculum (12)”

at UNC Wilmington; computational chemistry was incorporated in six courses there, includingOrganic 1 and 2 Other papers detailed single courses (13) or single experiments (14–16) utilizingcomputational chemistry

There was a sea change in 2000: the initial release of WebMO (17, 18) and the rise of based computational chemistry Growth was burgeoning in educational use as well in 2001 therewas both an ACS Symposium“Teaching Chemistry in the New Century: Physical Chemistry (19)”

web-which listed 6 computational presentations out of 18, including talks on molecular dynamics andusing symbolic math programs and also a full day symposium at the fall ACS meeting entitled

“Computational Chemistry in the Undergraduate Curriculum.” These were emblematic of the

3

incursions of computational chemistry into education These incursions continued with a number ofsymposia, usually about physical chemistry education, that would include aspects of computationalchemistry While computational chemistry is often used as a synonym for ab initio electronicstructure calculations, many of the symposia included a broader view, as we have done in this book,

to include other types of computation such as molecular mechanics and dynamics, kineticssimulators and the use of symbolic math programs

Figure 1 Timeline of landmark events in computational chemistry education The top row is about technology, the middle row about software, and the bottom row is published works.

The rise of the smartphone, tablet and low cost laptop may have finally broken the cost barrier

We will date this landmark at the advent of the iPhone in 2007 Essentially all college students nowarrive at the classroom with a 1990s supercomputer in their back pocket; they are pre-equipped

to do high level computation and visualization(20) After hardware costs, the next largest barrier

(for the masses) is the purchase and maintenance of software Freely distributed packages have longbeen available, such as PSI4 (21, 22) and GAMESS (23, 24) for electronic structure calculationsand TINKER(25, 26) for molecular dynamics However, the technical issues with downloading

packages, installing them, and maintaining them are nonneglible These barriers, too, may be fallingwith freely available software packages such as WebMO as a web client-based front end to freelydistributed packages such as GAMESS and PSI4(and the WebMO app (27, 28) as the front end to

the front end) There are also freely accessible web servers such as Chem Compute (29)

This brings us to the present time and the final barrier, which is that professors interested inusing the computational tools may be uncertain how to use them in the classroom or lab because

of a lack of training At some point, we envision that there will be a computational experiment inevery lab manual from General Chemistry on up to Physical Chemistry, but that point has not yetbeen reached The chemical education literature now has a number of computational experiments,some of which have already been referenced and others which are described in other chapters in thisbook PSI4 Education (3) is a recent project to build a library of freely available curricular materials.The POGIL-PCL project (30, 31) has developed and tested three guided inquiry computationalexperiments Another recent ACS Symposium Series book (32) also has a couple of examples ofphysical chemistry experiments in computational chemistry or with computational components.Since the American Chemical Society Committee on Professional Training issued the guidelinesallowing advanced courses to replace the traditional two-semester sequences of organic and physicalchemistry(33) it has become possible to have a course entirely about computational chemistry as

part of the undergraduate major There is certainly space in the curriculum to use computationalchemistry.

Balancing Theory and Application

Clearly the tools are available and there is more room in the curriculum to include computationalmethods in a course or a lab The question is, how to implement? As with the utilization of complexinstrumentation, the use of computational methods in chemistry laboratories also raises the question

of how much a student needs to understand about the inner workings of the tools they are using

to learn chemistry In the world of laboratory instrumentation, for example, there is the still openquestion“Does a student need to understand the nuclear relaxation phenomenon to use an NMRinstrument?” Or do students need to know how to shim a magnetic field in an NMR instrument?Does a student need to fully understand population inversions and how lasers work in order use alaser-based spectrometer? There has long been an interest in examining how instruments are used inthe chemistry curriculum(34) but only recently has there been some examination into how use of

instrumentation in the chemistry laboratory impacts student learning(35) However, the definitive

answer of how much students need to understand about those instruments has not appeared inthe educational literature On the other hand, the instrumentation technology and automation hasrendered the question moot, as it is often counterproductive to get “under the hood” for manyinstruments At the undergraduate level, the goal is often to provide students the experience ofusing instrumentation and learning how to interpret the resulting data The advanced work ofunderstanding how instrumentation works and its limitation is often left to advanced courses,independent research or graduate studies

The similar question in computational chemistry is, how much do students need to understandabout the methods they use? In a molecular dynamics simulation do students need to understandthe application of force fields from all the nuclei or molecules in the system? When performing an

ab initio calculation, does a student need to understand how thousands of integrals are evaluated togenerate the matrix elements that will then be manipulated to form a single iteration of a structureminimization? We think, at this point in the technological development, the answer is no (see Figure2) The use of computational tools has permeated the practice of chemistry such that their inclusionshould be as mundane as obtaining an NMR spectrum Students can learn to recognize fromexperience that use of a particular deuterated solvent in NMR spectroscopy might be preferred overanother, without necessarily understanding why Similarly, students can begin to recognize that HF/STO-3G calculations are fast, but MP2/6-31G* and B3LYP/6-311+G** will improve the energyand vibrational frequencies

As stated above, both authors have engaged students in computational methods early in ourteaching careers In those early days, we had students actively coding, developing scripts and creatingtheir own visualizations In large part, we did this because we had to The tools were not available toprovide students the ability to answer even simple chemical questions without some work developingthe computational tools We did have students develop scripts, learn how integrals were calculated,and port output files from a computational program to some sort of graphical output This kind

of activity could take up to an entire 3-hour lab period Now it can be done automatically in afew minutes By using the tools to answer a chemistry question, students can explore their chosendiscipline, and if they become interested in the details of the computational methodology, they canpursue that understanding in advanced coursework or independent research

5

We feel that including computational tools to explore chemical questions should be part of ourgoal to teach students about chemical concepts Yet, it is clear from some of the chapters in thisvolume that there is still room to discuss how to use computational methods in the classroom Itreally does depend on the goals for one’s course or curriculum We could also envision a coursethat is designed to teach chemistry students the tools and techniques of computer programming andcoding This would be very much a course that goes “under the hood” of computational methods.

On the other hand, the amount of material to potentially teach in computational methods isexpansive and would likely take more than even two semesters to do it all justice at the undergraduatelevel

Figure 2 In their undergraduate teaching, the authors are weighing heavily on time for application over time

spent on details of the theory.

In the end, it comes down to the instructor’s preference and course goals As you read thechapters in this book, please take some time to think about how you might implement the ideasthat are described within Some of them require deep exploration of computational methods, whileothers use the computational tools to develop chemical understanding without seeking tounderstand how the tools work Other chapters are found in between these two extremes The reader

is cautioned to make sure they understand the requirements for utilizing the tools and methodsdescribed in each chapter before adopting a particular activity

Overview of the Chapters

The original ACS symposium in Washington, D.C was divided roughly in half between singleexperiments and collections of activities or full courses We have kept a similar division in this book.The authors were encouraged to provide their personal stories as they developed their materials incomputational chemistry As a result, many of the chapters seem conversational because they are adescription the process of development of these activities In so doing the authors also provide insightinto what has worked and what has not

In the first half of this book, the chapters describe one or a couple of computational activities.

In the chapter following this one (Chapter 2), Bruce explains how computational methods can

be used to provide theoretical context and visualization of kinetic molecular theory Chapters 3,

4, and5 provide development of multi-faceted computational experiments that provide chemicalinsight without performing multiple laboratory experiments, many of which would be dangerous ordifficult to set-up in the undergraduate laboratory Stocker describes a series of activities that explorethe energetics for the reaction pathway for the formation of ammonia Phillips has developed a couple

of activities that stem from computations on the insertion of an argon atom into the HF molecule.This experiment has a couple of avenues for additional exploration of chemistry that would not bereadily available in the undergraduate laboratory Reeves, et al., describe an experiment for exploringcomputational thermochemistry on halogenated compounds, showing how useful computationalchemistry can be to examine potentially toxic and hazardous compounds This group is followed byChapter 6 in which Whitnell and Reeves explore the process of developing and testing computationalexperiments within a guided inquiry framework In Chapter 7, Perri, Akinmurele and Hayniedescribe the computational tools that have been made available through a browser-based platform,increasing the accessibility of high-performance computing to educators everywhere Finally, thereare two chapters that explore the use of computational chemistry to extend chemical understandingdeveloped in the physical chemistry laboratory Chapter 8 is a single module by Martin and Ball thatextends the spectroscopic study of acetylene to a computation of tritiated acetylene what is not easilyobtained in an undergraduate laboratory The final chapter (Chapter 9) in this section by DeVoredescribes a couple of different computational extensions to the physical chemistry laboratory frominfrared spectroscopy to the Aufbau principle

In the second half of the book, the chapters cover collections of activities or full courses Chapter

10, by Sharma and Asirwatham, details use of computational activities in an Honors GeneralChemistry course This chapter is significant for its use of computation in multiple applications andtopical settings throughout that foundational semester Several freely accessible software packagesare discussed Esselman and Hill describe in Chapter 11 the integration of ab initio calculations intoOrganic Chemistry lab Their work combining wet labs with insight from computations is aimed atimproving students’ rationalizations of chemical phenomena

In Chapters 12, 13, and 14, different uses of computation in the Physical Chemistry sequence aredescribed Singleton uses Jupyter notebooks to create “computational narratives,” which combinecomplex calculations with written interpretations Tribe emphasizes student programmingassignments to expand student comprehension of the inner workings of computational programs

In Chapter 14, McDonald and Hagan detail using MATLAB assignments throughout PhysicalChemistry to build students’ computational thinking and expertise

In Chapter 15, Grushow details a standalone laboratory course on teaching chemistry withcomputational chemistry intended to follow a course on the fundamentals of Physical Chemistry.The final two chapters have discussions of activities which cover a span of courses Kholod andKosenkov(Chapter 16) discuss using computational chemistry to add research experiences in thecurriculum to a variety of levels of courses Lastly, Price (Chapter 17) has a plan to unify multiplecourses(as well as de-compartmentalize student thinking) with a study of a single unifying chemicalconcept: the hydrogen bond

7

The use of computational chemistry to explore chemistry through visualization andquantification of difficult or impossible to measure properties makes it invaluable as a teaching tool.The chapters in this book provide some interesting ideas and practical insight for the instructor whowants to include more computational and theoretical lessons into their chemistry curriculum Thesmart phone combined with web interfaces have brought us to a time when“bring your own device”

is feasible We have not reached the stage where every lab manual (beginning in General Chemistry)includes a computational experiment, but we are heading in that direction The next key step will

be to make computational methods more accessible for instructors who have not been previouslytrained in using them for chemistry instruction

References

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70, 904

2 JCE staff Computational Chemistry for the Masses J Chem Educ 1996, 73, 104

3 Fortenberry, R C.; McDonald, A R.; Shepherd, T D.; Kennedy, M.; Sherrill, C D.PSI4Education: Computational Chemistry Labs Using Free Software In The Promise of

Chemical Education: Addressing our Students Needs; ACS Symposium Series 1193; American

Chemical Society, 2015; pp 85–98

4 Johnson, L E.; Engel, T Integrating Computational Chemistry into the Physical ChemistryCurriculum J Chem Educ 2011, 88, 569–573

5 Foresman, J B.; Frisch, A Exploring Chemistry With Electronic Structure Methods: A Guide to

Using Gaussian, 2nd ed.; Gaussian: Pittsburgh, PA, 1996

6 Hehre, W J Introducing Molecular Modeling into the Undergraduate Chemistry Curriculum;Wavefunction: Irvine, CA, 1997

7 Viste, A Laboratory Exercises Using HyperChem (Caffery, Mary L.; Dobosh, Paul A.;Richardson, Diane M.) J Chem Educ 1999, 76, 1065

8 Physical Chemistry: Developing a Dynamic Curriculum; Schwenz, R W., Moore, R J., Eds.;American Chemical Society: Washington, DC, 1993

9 Brown, F B Computational Chemistry in the Physical Chemistry Laboratory: Ab InitioMolecular Orbital Calculations In Physical Chemistry: Developing a Dynamic Curriculum;Schwenz, R W., Moore, R J., Eds.; American Chemical Society: Washington, D.C., 1993; pp2–13

10 Moog, R S Hückel Molecular Orbitals In Physical Chemistry: Developing a Dynamic

Curriculum; Schwenz, R W., Moore, R J., Eds.; American Chemical Society: Washington,D.C., 1993; pp 280–291

11 Bluestone, S A Monte Carlo Method for Chemical Kinetics In Physical Chemistry: Developing

a Dynamic Curriculum; Schwenz, R W., Moore, R J., Eds.; American Chemical Society:Washington, D.C., 1993; pp 434–461

12 Martin, N H Integration of Computational Chemistry into the Chemistry Curriculum J

Chem Educ 1998, 75, 241.

13 Holme, T Teaching Computational Chemistry in the Undergraduate and Graduate ChemistryCurriculum J Mol Graph Model 1999, 17, 244–247.

14 Ringan, N S.; Grayson, L Molecular Modelling in the Undergraduate Chemistry Curriculum:The Use of Beta-Lactams as a Case Study J Chem Educ 1994, 71, 856

15 Saiz, E.; Tarazona, M P Molecular Dynamics and the Water Molecule: An Introduction toMolecular Dynamics for Physical Chemistry Students J Chem Educ 1997, 74, 1350–1354

16 Salter, C.; Foresman, J B Naphthalene and Azulene I: Semimicro Bomb Calorimetry andQuantum Mechanical Calculations J Chem Educ 1998, 75, 1341

17 Schmidt, J R.; Polik, W F WebMO; WebMO LLC: Holland, MI, 2018

18 WebMO - Computational Chemistry on the WWW https://www.webmo.net/(accessed Oct 25,2018)

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J Chem Educ 2001, 78, 1173.

20 Williams, A J.; Pence, H E Smart Phones, a Powerful Tool in the Chemistry Classroom J

Chem Educ 2011, 88, 683–686.

21 Parrish, R M.; Burns, L A.; Smith, D G A.; Simmonett, A C.; DePrince, A E.; Hohenstein,

E G.; Bozkaya, U.; Sokolov, A Y.; Di Remigio, R.; Richard, R M.; Gonthier, J F.; James,

A M.; McAlexander, H R.; Kumar, A.; Saitow, M.; Wang, X.; Pritchard, B P.; Verma, P.;Schaefer, H F., III; Patkowski, K.; King, R A.; Valeev, E F.; Evangelista, F A.; Turney, J.M.; Crawford, T D.; Sherrill, C D Psi4 1.1: An Open-Source Electronic Structure ProgramEmphasizing Automation, Advanced Libraries, and Interoperability J Chem Theory Comput

2017, 13, 3185–3197.

22 Psi4: Open-Source Quantum Chemistry; http://www.psicode.org/(accessed Oct 25, 2018)

23 Gordon, M S.; Schmidt, M W Advances in Electronic Structure Theory: GAMESS a DecadeLater In Theory and Applications of Computational Chemistry; Dykstra, C E., Frenking, G., Kim,

K S., Scuseria, G E., Eds.; Elsevier: Amsterdam, 2005; Chapter 41, pp 1167–1189

24 Gordon Group/GAMESS Homepage; https://www.msg.chem.iastate.edu/gamess/(accessedOct 25, 2018)

25 Xie, Q.; Tinker, R Molecular Dynamics Simulations of Chemical Reactions for Use inEducation J Chem Educ 2006, 83, 77

26 Tinker Molecular Modeling Package; https://dasher.wustl.edu/tinker/(accessed Oct 25, 2018)

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Chapter 2

Molecular Dynamics Simulations in First -Semester General Chemistry : Visualizing Gas Particle Motion and Making Connections to Mathematical Gas Law Relationships

C D Bruce *

John Carroll University, 1 John Carroll Blvd., University Heights, Ohio 44118, United States

* E-mail: cbruce@jcu.edu.

Implementation of a freely available molecular dynamics(MD) software program

in a general chemistry class to assist students in learning the relationship among

particle motion, macroscopic properties, and mathematical gas laws is described

In this activity, students acquire skills in data analysis while developing a deeper

understanding of the origin of macroscopic physical properties of gases The

activity is easy to implement and does not require significant expertise in

computational chemistry on the part of the instructor

Introduction

The transition from novice to professional chemist requires not only acquisition of contentknowledge but also development of chemical intuition grounded in that content knowledge.Visualization of atomic and molecular level processes is a valuable tool in a instructor’s toolbox forhelping students at all levels acquire content knowledge and use that knowledge to develop accuratechemical intuition (1) Many types of visualizations exist, ranging from interactive laboratory

simulations to mathematically accurate computational techniques(2–6) The former are traditionally

used in introductory level courses while the latter are often reserved for higher-level courses afterstudents have additional subject-specific content knowledge This chapter will argue that students

at the General Chemistry level can benefit from introduction to and use of mathematically accuratemodels of chemical behavior to develop a better understanding of molecular-level behavior via bothvisualization of particle motion and confirmation of mathematical relationships typically taught inthe General Chemistry curriculum

Readers of this book are likely already aware of the value of using computational techniques inthe curriculum, but for some instructors, the barrier to introducing a new technology, particularlyone not in their area of expertise, is too great The activity described in this chapter is accessiblefor students and instructors at all knowledge levels At the introductory level, the addition ofcomputational tools to the course provides another mechanism for students to learn the required

© 2019 American Chemical Society

content in a way that appeals to visual learners and to those who are ready for more advancedunderstanding of molecular-level behavior Many students, even those at the upper-level, considermolecules to be stationary images of Lewis structures they learn to draw in general chemistry Earlyintroduction to molecular motion helps students with topics such as kinetics and reactionmechanisms in a way that stationary images cannot.

Visualization Activities

In each semester of my general chemistry lecture course of approximately thirty students, I assignstudents five“Visualization” activities, one of which is described in this chapter The Visualizationassignments are independent of each other, vary in complexity and technique, and often make use

of PhET(7) or Jmol (8) resources The primary objective is to help students understand

molecular-level phenomena, so I select activities that allow students to visualize concepts such as dissociation(comparing electrolytes and nonelectrolytes as well as building skills for understanding spectatorions) (9), molecular geometry (10), and crystal structures (11) Many students report that theVisualization activities are the most helpful assignments for learning chemistry (more thanhomework, weekly quizzes, daily on-the-fly clicker questions, or daily warm-up questions) I use the

freeware Virtual Substance molecular dynamics simulation software (12) as one of the Visualization

assignment to teach gas laws, data analysis, and relationships between kinetic energy andtemperature Other software programs can be used to accomplish the same goals depending onaccess (purchased from companies such as Wavefunction (13)) or instructor familiarity (other

freeware such as NAMD(14)).

Using Molecular Dynamics Software To Aid Student Learning

With the complementary goals of improving content knowledge and assisting students in thetransition from novice to professional chemists, I have implemented assignments using the moleculardynamics(MD) software package Virtual Substance (12) in both my General Chemistry and Physical

Chemistry courses I have written about using the software in the Physical Chemistry curriculum

on the first day of the lecture course (15) and in a lab situation (16) where students develop

mathematical relationships that describe the physical behavior of real and ideal gases

In this chapter, I describe how I have used an activity in the General Chemistry course wherestudents conduct MD simulations on ideal gases, collect data on the physical properties(Temperature, Pressure, Volume, Kinetic Energy, and Potential Energy) of the system during thesimulation, and use spreadsheet software (Excel, for example) to understand the relationships amongthese properties by plotting their data and using the trendline feature to determine physical constants.This activity addresses a number of course learning goals including understanding mathematicalrelationships among physical properties of ideal gases, representing and interpreting data graphically,and relating kinetic energy to temperature and particle motion These learning goals are three of themost difficult for novice students They can easily memorize and grind through the ideal gas law, butthey do not really understand the origin of these physical properties at the atomic or molecular level.They also struggle with interpreting data graphically as well as using a spreadsheet program to clearlyrepresent the data they have collected, particularly if this is the first time they are asked to do so.There are a number of places in the general chemistry curriculum where data analysis skills can

be developed, particularly in the laboratory component of the course Students frequently collect,plot, and analyze data Performing a similar activity in the lecture course further cements theimportance of graphical analysis and interpretation of data, skills students need on their path from

novice to professional chemist This connection may be particularly valuable when students havedifferent instructors for the lecture and lab components of the course As students are somewhatfamiliar with the application of these skills, and explicit instructions for constructing plots can beprovided, it is somewhat more challenging for students to understand that particle interactionsdetermine macroscopic physical properties and the mathematical relationships between thoseproperties Molecular dynamics simulations provide a perfect opportunity for students to learn each

of these content topics and skills

Implementation and Results

Keeping in mind that the purpose of the activity is student learning, students at the generalchemistry level do not need to understand how an MD simulation works beyond knowing that theparticles are following the laws of physics that govern their motion These topics can be adequatelyexplained at the instructor’s discretion as the Virtual Substance (16) MD software program isintroduced and the activity to be completed is distributed The first steps in using the software requireselecting the substance to use(He, Ne, Ar, Kr, Xe, or user defined), the type of boundary conditions(Fixed Walls or Periodic Boundary Conditions), and the Potential Model (No potential = ideal gas,soft sphere, Lennard-Jones, and options for adding finite extensible nonlinear elastic models fortreating polymers) as seen in Figure 1

Figure 1 Screenshot of Virtual Substance initial set up for 128 Argon atoms treated as an ideal gas and

using periodic boundary conditions.

Depending on the goals of the instructor for use of this activity, these selections can be explainedfully or minimally My preference is that the students understand that periodic boundary conditionsare a mechanism for replicating the box in all dimensions, therefore mimicking bulk-like behavior

by allowing particles to pass through one edge of the box and reappear on the other side as if theboundary did not exist I also explain that the other Potential Models in the software allow modeling

of real gas behavior and how real gases differ from ideal gases on a general chemistry level, i.e realgases have volume and experience intermolecular forces Beyond that, I do not discuss in detail thedifferent options for real gas potential models

Once the Virtual Substance is built using the process outlined in the previous paragraph, the nextstep is to run the simulation Once again, the instructor can choose how much or how little detail isnecessary for the student to understand the simulation The user must select the type of simulation(constant energy, constant volume and temperature, or constant temperature and pressure), targetsfor that selected simulation type, time step (0.5, 1.0, 2.0, 5.0, or 10.0 fs), number of steps (500, 1000,

2000, 5000, 10000, 20000), and how frequently the calculations should be reported to the user.After building the Virtual Substance and selecting the simulation settings, the user selects RunSimulation, and the data appears in an output screen (Figure 2a) while the movement of thesubstance is observed in another part of the screen(Figure 2b) A typical simulation of an ideal gas on

a personal computer will take under a minute

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Figure 2 Screenshot of Virtual Substance a) simulation parameters for 128 Argon gas particles treated as

an ideal gas with periodic boundary conditions after 120 ps of Molecular Dynamics Simulation under conditions of constant volume (1.0 L/mol) and temperature (298 K) and b) static image at the conclusion

of the simulation Instantaneous and average values of the temperature, pressure, volume, and total, kinetic,

and potential energy are reported.

In the assigned activity, all students are required to run five separate simulations at a fixedtemperature and a series of molar volumes They are then required to prepare Pressure versus molarVolume, Vm , (see Figure 3) and Pressure vs V m-1plots and determine the value of the gas constant,

R I do not tell them how to numerically determine R, which results in guided discussion in class as

students ask about that part of the assignment How to proceed after making plots is not immediatelyobvious to many students After our in-class discussion, students typically choose to use a linear fit of

their Pressure vs V m-1plot to determine R (the slope of the trendline is RT), but some students will perform a fit to the curve from their Pressure vs V m-1plot and determine R from the equation of that

fit For example, in Figure 3, the fit yields P = (24.375) Vm(-1.003)for simulations conducted at 298 K

Using P = RT/V m , the calculated value of R would be 0.0818 L atm mol-1K-1, an error of less than1% from the accepted value of 0.0821 L atm mol-1K-1 This level agreement is the norm, which doesgive students some comfort that they are on the right track

Students are subsequently asked to perform additional simulations of argon gas at either a fixedvolume and a series of temperatures(still using a constant volume and temperature simulation) or afixed pressure and a series of temperatures(using a constant pressure and temperature simulation)

In both cases, students are again asked to determine the gas constant, R In addition, students arerequired to plot the average kinetic energy as a function of temperature See Figure 4 If appropriate

to the class, instructors could point out that the slope of the energy vs temperature plot is 3/2 Rand discuss the equipartition theorem demonstrating the three translation degrees of freedom each

Figure 3 Student-submitted plot for Virtual Substance simulation of Argon at 298 K and a series of molar volumes The line, which is the best fit by least squares regression, is y = 24.375x -1.003 , where y is pressure in

atmospheres and x is volume in L/mol, with correlation coefficient 0.9999.

Figure 4 Student-submitted plot for Virtual Substance simulation of Argon at fixed pressure and a series of temperatures The line, which is the best fit by least squares regression, is y = 12.372x + 12.535, where y is average kinetic energy in J mol -1 and x is temperature in Kelvin, with correlation coefficient 0.9999.

Conclusions

Impact on Student Learning

Student learning was evaluated using three measures: 1) the submitted assignments, 2) a pre/post set of 6 clicker questions(see Table 1), and 3) relevant questions on the final exam The resultsshowed distinct improvements in students’ understanding of gas motion and the connectionbetween that motion and the physical properties of pressure, temperature, volume, and kinetic

15

energy There were clearly areas where student misconceptions were still evident even after thevisualization activity, however.

In the submitted assignments, students were able to collect the appropriate data and generatethe requested plots(representative plots shown in Figures 3 and 4) They were able to follow theinstructions in the assignment sheet easily In their summary paragraph, many students stated thatthey were able to understand and make connections more clearly as a result of visualizing gas particlebehavior and the relationship between physical properties Representative statements from studentsinclude the following

• “Being able to watch the simulations enhanced my ability to understand the conceptsbehind the math associated with the ideal gas law.”

• “It was helpful to me because I am a visual learner and when I see things it makes meunderstand them more thoroughly.”

• “The visualization of the movement of gasses showed the random nature of the movement

of the gases in a way that describing it does not.”

• “I could see the relationships in the gas law physically in action which helped me to formmore realistic connections in understanding the material.”

In the post-activity clicker questions, most students were able to identify the correct staticimage of gas particles distributed throughout a container, select the correct relationships betweenvolume and pressure(inversely proportional) and volume and temperature (directly proportional),and relate pressure to macroscopic and molecular-level relationships In the 2017 class, 65% ofstudents showed improved scores on the clicker questions after completing the MD activity Asshown in Table 1, improved scores were primarily due to increased understanding of relationshipsbetween gas properties

Parts of their paragraphs describing their observations along with the questions they answeredincorrectly on the post-activity clicker questions highlighted their continued misunderstandings onsome of the important physical relationships, particularly among kinetic energy, average velocity, andtemperature While they were able to make a plot showing that kinetic energy and temperature aredirectly proportional(Figure 4), they did not understand that kinetic energy was related to particlevelocity We had not yet studied the Maxwell-Boltzmann distribution relating particle velocity totemperature, and some students made incorrect statements that the particles were moving faster orslower when pressure or volume changed while temperature was held constant These statement are,

of course, incorrect Perhaps the computer was refreshing less frequently or they felt that they wereseeing the particles move more slowly, but the average kinetic energy at constant temperature wasconstant, so their perceptions were incorrect This misconception was very enlightening to me as aninstructor When we arrived at kinetic-molecular theory and the Maxwell-Boltzmann distribution, Iopened the Virtual Substance program and ran a simulation for the entire class We talked about thedistribution of particle speeds and how that depended solely on temperature for an ideal gas Theyhad a context for understanding the new material, which is always helpful for learning and retainingknowledge

Table 1 Clicker Question Summary Note that this clicker set allows multiple selections per

question.

Extensions and Challenges

While my classes are relatively small, this activity can easily be used with larger classes Most

of the work is performed independently The instructor will need to review student submissions,but there is no additional equipment or preparation required Variations on data collected and plotsprepared are endless depending on the goals of the instructor As mentioned earlier, other topics atthe general chemistry level can be clarified by use of Virtual Substance simulations, for example, hownon-zero volume and intermolecular forces (i.e those in real gases) impact physical properties ofpressure and internal energy, or a more explicit understanding of internal energy as the sum of kineticand potential energy, just to name two If more insight into how the least squares fit is used to create

a trendline, activities such as the Multi-Function Data Flyer (17) could be used

The challenges associated with this activity are the same as those associated with teaching ingeneral: students arrive with preconceived ideas about a topic Some students are resistant toactivities that challenge their preconceived ideas and will continue to cling to those instead Technicaldifficulties have been relatively minimal Access to a PC is required, but the software works on avariety of machines and operating systems, including Windows 10 Installing and running several

17

simulations of ideal gases should take less than 30 minutes Simulations using a Lennard-Jonespotential will take longer, and may be better suited to homework assignments or lab activities (16).The activity itself is usually one students enjoy When I ask what component of the course wasmost helpful for their learning, the visualization activities are consistently rated very highly As Ihope is clear from the collection of chapters in this book, computational chemistry is just one tool

in the arsenal to improve student learning It is not a magic bullet It is another way to aid learners

in developing a molecular-level understanding of chemical behavior that will serve them well as theymove from novice to professional chemist

References

1 Mahaffy, P G.; Holme, T A.; Martin-Visscher, L.; Martin, B E.; Versprille, A.; Kirchhoff,M.; McKenzie, L.; Towns, M Beyond “Inert” Ideas to Teaching General Chemistry from RichContexts: Visualizing the Chemistry of Climate Change (VC3) Journal of Chemical Education

Journal of Chemical Education 2016 , 93 (6), 1160–1161.

4 Smith, G C.; Hossain, M M Visualization of Buffer Capacity with 3-D “Topo” Surfaces:Buffer Ridges, Equivalence Point Canyons and Dilution Ramps Journal of Chemical Education

2016, 93 (1), 122–130.

5 Wichmann, A.; Timpe, S Can Dynamic Visualizations with Variable Control Enhance theAcquisition of Intuitive Knowledge? Journal of Science Education and Technology 2015, 24 (5),709–720

6 Tay, G C.; Edwards, K D DanceChemistry: Helping Students Visualize Chemistry Conceptsthrough Dance Videos Journal of Chemical Education 2015, 92 (11), 1956–1959

7 Perkins, K.; Adams, W.; Dubson, M.; Finkelstein, N.; Reid, S.; Wieman, C.; LeMaster, R.PhET: Interactive Simulations for Teaching and Learning Physics The Physics Teacher 2006, 44,18–23

8 Jmol: An Open-Source Java Viewer for Chemical Structures in 3D http://www.jmol.org/

9 Lancaster, K.; Reid, S.; Moore, E.; Chamberlain, J.; Loeblein, T.; Parson, R.; Perkins, K Sugar

and Salt Solutions https://phet.colorado.edu/en/simulation/sugar-and-salt-solutions

10 Moore, E B.; Olson, J.; Lancaster, K.; Chamberlain, J.; Lancaster, K.; Paul, A.; Perkins, K

Molecule Shapes https://phet.colorado.edu/en/simulation/molecule-shapes

11 Chaplin, M Water Structure and Science http://www1.lsbu.ac.uk/water/ice1hsc.html

12 Papanikolas, J Virtual Substance https://www.unc.edu/~jpapanik/VirtualSubstance/VGMain.htm

13 Odyssey, Wavefunction, Inc., Irvine, CA

14 Phillips, J C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel,

R D.; Kale, L.; Schulten, K Scalable molecular dynamics with NAMD J Comput Chem 2005,

26(16), 1781–802

15 Bruce, C D Beyond the Syllabus: Using the First Day of Class in Physical Chemistry as anIntroduction to the Development of Macroscopic, Molecular-Level, and Mathematical Models.

Journal of Chemical Education 2013 , 90 (9), 1180–1185.

16 Bruce, C D.; Bliem, C L.; Papanikolas, J M., “Partial Derivatives: Are You Kidding?”:

Teaching Thermodynamics Using Virtual Substance In Advances in Teaching Physical Chemistry;

Ellison, M D., Schoolcraft, T A.; , Eds.; ACS Symposium Series 973; American ChemicalSociety, 2007; pp 194−206

17 Shodor http://www.shodor.org/interactivate/activities/MultiFunctionDataFly/

19

Chapter 3

Using Electronic Structure Calculations To Investigate the

Kinetics of Gas -Phase Ammonia Synthesis

Kelsey M Stocker *

Department of Chemistry and Biochemistry, Suffolk University,

8 Ashburton Place, Boston, Massachusetts 02108, United States

* E-mail: kstocker2@suffolk.edu.

Computational chemistry techniques are valuable tools for teaching concepts in

thermodynamics and chemical kinetics In this experiment, undergraduate

physical chemistry students gain valuable, authentic experience with the tools of

computational chemistry and a more “hands-on” interaction with the energy

landscape of a chemical reaction Students use electronic structure calculations

to determine the geometry, vibrational frequencies, and energy of the reactants,

products, intermediates, and transition states in a four-step gas-phase ammonia

synthesis reaction Using transition state theory, they construct the reaction

coordinate diagram and calculate activation energies, rate constants, and

I developed this lab to fit into the Advanced Theories of Reaction Rates module of my

second-semester 400-level physical chemistry course At this point in the course, my students have learnedabout the laws of thermodynamics, physical and chemical equilibria, reaction mechanisms, ratelaws, and potential energy surfaces I wrote this lab to give my students the experience of studyingthe kinetics of a realistic, multi-step reaction mechanism using reaction coordinate diagrams andtransition state theory There are five primary learning goals associated with this experiment:

© 2019 American Chemical Society

• Perform authentic electronic structure calculations

• Construct a reaction coordinate diagram for a multi-step reaction

• Apply the thermodynamic formulation of transition state theory

• Calculate activation energies, rate constants, and equilibrium constants

• Use kinetics data to evaluate plausibility of reaction mechanism

Throughout this chapter I have noted possible adaptations and extensions that can be used

to make the experiment appropriate for a variety of courses I have also attempted to make thedescription of the procedure general enough that it can be used with various electronic structureprograms and interface packages I teach a “quantum first” approach, so by the time we conductthis experiment my students have been exposed to partition functions, statistical mechanics, andcomputational chemistry techniques However, the experiment utilizes the thermodynamicformulation of transition state theory so it could easily be used in a“thermo first” course design (12).

Why Ammonia Synthesis?

The formation of ammonia is a vitally important process made up of structurally simple species,which makes it an ideal reaction for a computational kinetics experiment(13) After investigating

the kinetics of the multi-step gas-phase mechanism, students have a deeper appreciation for theimportance of heterogeneous catalysis in industrial processes The reaction may look harmlessenough on paper, but it turns out to be so devilishly difficult to carry out that the first industriallyviable process yielded two separate Nobel Prizes in Chemistry: Fritz Haber in 1918 and Carl Bosch

in 1931(14, 15) I typically can’t resist including a brief synopsis of Fritz Haber’s story in the rest of

my pre-lab lecture (16) The synthesis of ammonia has history

But it’s not old news by a longshot considering that new, more efficient catalysts remain anarea of active research(17) Even the gas-phase reaction, while not industrially viable, was still being

investigated nearly a century after the Haber-Bosch process was developed The energetics of the phase mechanism used in this lab weren’t fully mapped until 2003 (18)

gas-Reaction Mechanism

In their computational study of several potential gas-phase mechanisms, Hwang and Mebelidentified the following four-step pathway as the most favorable (18):

The overall reaction is

Conveniently, this mechanism does not include any ions or radical species The reactioncoordinate diagram includes nine distinct stages: five minima (reactants, intermediates, or products)and four maxima (transition states)

Experimental Procedure

The calculations for this lab follow the general procedure shown in Figure 1 and are completedwithin a single four-hour laboratory period

Figure 1 Simplified workflow for calculations.

To cover all species included in the reaction mechanism, students must perform six geometryoptimizations(N2, H2, NNH2, H2NNH2, HNNH3, and NH3), four transition state optimizations(TS1, TS2, TS3, and TS4), and ten vibrational frequency analyses (all species)

Computational Details

Our lab computers are equipped with Gaussian 09, which is linked to an installation of WebMOversion 16.1 (19, 20) All calculations were done using the PBE0 level of theory and the “Routine:6-31G(d)” basis set I selected the combination of theory and basis set that gave results for ΔH°rxn(-90.35 kJ mol-1), ΔS°rxn(-197.77 J mol-1K-1), and ΔG°rxn(-31.40 kJ mol-1) that were closest tothe values computed from standard back-of-the-textbook thermodynamic tables (-91.88 kJ mol-1, -198.11 J mol-1K-1, and -32.80 kJ mol-1, respectively) (21).

A thorough discussion of the shortcomings of density functional theory is beyond the scope

of my course so I prioritized matching experimental data when choosing a level of theory I find

it also has the added benefit of increasing students’ confidence in computational methods, whichcan be helpful if you plan to do additional computational labs later in the course However, the vastmajority of other levels of theory and basis sets will still produce reaction coordinate diagrams thatare qualitatively similar to the results shown here, so you can use whatever works best for your class

Optimization of Reactants, Products, and Intermediate Species

Students build all stable species(non-transition states) in the WebMO molecule editor I assignpre-lab work that includes drawing Lewis structures of all reactants, products, and intermediates.Students are then equipped to determine the total charge and spin multiplicity of all species whensetting up their WebMO jobs They all turn out to be neutral molecules in the singlet state, which are

23

the default settings for WebMO jobs, so you could omit any discussion of charge or spin multiplicityand have students ignore those options when submitting jobs.

WebMO has the option to perform a geometry optimization and frequency analysis in a singlejob However, there is not an option for a combined transition state optimization and frequencyanalysis For ease of instruction and to avoid confusion, I have students do all structure optimizationsseparately from frequency analyses Once the structure optimization completes successfully,students can view the results from the Job Manager and select“New Job Using This Geometry” tocontinue on to the frequency analysis

Optimization of Transition States

There are several options for obtaining the transition state structures You can adapt thetransition state optimizations to suit available computational resources, length of lab period, andcourse level

Import Coordinates

Importing coordinates is the fastest and most frustration-free option for students You canprovide the transition state coordinates in XYZ format or as a Gaussian input file The XYZcoordinates of all four transition states are provided in Tables 1-4 To avoid a “plug and chug” effect,consider asking students to predict the general structure of the transition state based on the reactantsand products; this could be assigned as pre-lab work or as part of an in-class discussion A transitionstate optimization should still be performed on each structure(which should finish very quickly)before moving on

Table 1 Transition state 1 XYZ coordinates

Table 3 Transition state 3 XYZ coordinates

if students have a moderate amount of experience with the WebMO interface The optimization ofTS4 in particular is very sensitive to dihedral angles, so ideally students are comfortable manipulatingmolecular structures in three dimensions

Transition State Search

The most authentic method for locating the transition states is performing a transition statesearch, or saddle calculation This calculation requires two structures on either side of the saddlepoint to be specified and interpolates between them to produce a structure that is close to thetransition state The resulting structure should then be used as input for a transition state optimizationbefore continuing I have not yet implemented this procedure in my class, primarily due to concernsabout time constraints Additional considerations to keep in mind are that the two input structuresmust have the same atomic numbering scheme, so students must be especially careful when creatingthe inputs

25

Figure 2 Transition state structures with interatomic distances in Angstrom.

For some transition states, you can approximate a saddle calculation by performing a coordinatescan To reach TS1, start with the NNH2structure and perform a coordinate scan over one of the H-N-N bond angles, with a maximum angle of 179.9° (extending to 180° will cause the Gaussian job tofail) Optimize the highest energy structure along the coordinate scan as a transition state

Verifying Transition States

Regardless of the method chosen to locate and optimize a transition state, the structures should

be verified as such This can be accomplished by a vibrational frequency analysis or an intrinsicreaction coordinate calculation Aside from verifying a transition state, the results of the vibrationalfrequency analyses are the source of all thermodynamic data that students record and use later in theircalculations

Vibrational Frequencies

For each transition state, I have students perform a vibrational analysis to confirm that thestructure represents a saddle point on the potential energy surface The simplest analysis is to recordany imaginary(negative) frequencies in the results There should not be any such frequencies forreactants, products, or intermediates, but there should be exactly one for a transition state Inparticular, TS3 and TS4 can be tricky to locate and my students appreciate the straightforwardvalidation that they “got it right”

WebMO also has the ability to animate each vibrational mode Animation of the transitionstate imaginary frequency is a helpful tool for demonstrating the simultaneous bond formation anddissociation that occurs along the reaction coordinate Students also find it fairly entertaining,especially if the structure resembles a stick figure human in any way

Intrinsic Reaction Coordinate

An intrinsic reaction coordinate(IRC calculation in WebMO) takes the input transition statestructure and moves along the reaction coordinate The IRC is calculated in both the forward andreverse directions by default If the transition state structure is correct, the IRC should arrive at thestructure of the expected products when moving in one direction, and should arrive at the structure

of the expected reactants when moving in the opposite direction

The reaction coordinate path can be animated in WebMO and very clearly demonstratesreactants progressing through the transition state to become products Students can optimize thestructures that result from the forward and reverse IRC calculation and compare their geometries tothe expected reactant and product species that they have already optimized individually.

Data Analysis and Results

The internal energy, enthalpy, and entropy of each species should be recorded from thevibrational frequencies calculation I structure the data analysis prompts in the lab handout to guidethem through a sensible spreadsheet design; it also happens to make it much easier to track downerrors when the intermediate values are tabulated and turned in

While I provide the four-step mechanism shown in Reactions 1-4, I ask students to re-writeeach reaction stage to be stoichiometrically balanced with the end product (2 NH3) Thestoichiometrically balanced mechanism steps are

I ask students to get at least this far in their analysis and check in with me before leaving lab.The most common error is adding too many H2molecules to the transition state stages, essentiallyforgetting that one has been “used up” to form the transition state

Once all reaction stages have been balanced correctly, they use their data for the individualspecies to create a table of calculated thermodynamic quantities, as shown in Table 5 The convention

of reporting values relative to the first stage is not mandatory, but can make it easier to get an initialsense of the energy landscape

Table 5 Calculated thermodynamic quantities relative to first reaction stage

(kJ mol -1 )

Entropy (J mol -1 K -1 )

Internal Energy (kJ mol -1 )