Spectroscopy
Analysis of the Vibrational Spectrum of a Linear Molecule JCE
Richard W. Schwenz, University of Northern Colorado
William F. Polik, Hope College
Sidney H. Young, University of South Alabama
This document provides a moderately interactive tutorial describing the analysis of vibrational frequencies obtained from the infrared spectrum of hydrogen chloride.
An Introduction to NMR Concepts JCE
Scott Van Bramer, Widener University
Mathcad introduction to NMR concepts. Acquisition parameters of the instrument, the basis of quadrature detection, apodization, and zero filling are discussed.
Circular Birefringence and Circular Dichroism Simulation JCE
Zachary Brown, University of Wisconsin-Green Bay
Ronald Starkey, University of Wisconsin-Green Bay
Fundamental principles of circular dichroism and circular birefringence are examined, including interactive graphs which permit the user to alter the phase difference or absorption between the circular components to simulate both phenomena. Advanced graphing and matrix manipulation are also used to show both the 2D and 3D perspectives, and how to create animations which can be used by various media players. This document can be used by an undergraduate audience in either an instrumental or physical chemistry, or the animations could be used as a visual aid to accompany a lecture.
Exploring Digital Signals and Noise in Instrumental Analysis JCE
Augustus W. Fountain III, United States Military Academy
Mathcad document to allow the student to gain a familiarity with the concepts of signal-to-noise ratios and to explore the advantages of ensemble averaging and digital filtering analytical signals.
Exploring Light Amplification by Stimulated Emission in Lasers JCE
Michael A. Waxman, University of Wisconsin-Superior
This document allows the students to use a simple approach to study the time evolution of the power output of a laser and its dependence upon the amplification coefficient, the length of the active medium, and the reflectivity of the cavity mirrors.
Exploring the Morse Potential JCE
Theresa Julia Zielinski, Monmouth University
The goal of the 'Exploring the Morse Potential' document is to provide hands on practice with the Morse potential energy function and the units used for calculating this potential. In the document is a step-by-step description of how to create the Morse potential function for HCl.
Femtochemistry JCE
Mark David Ellison, Wittenberg University
Students explore a simple solution to the time-dependent Schrödinger equation in the context of understanding femtochemistryl. After a review of the time-independent harmonic oscillator model studentsstudy the process of exciting molecules with an ultrafast laser pulse and in a superposition that has time-dependent behavior.
Finding Molecular Vibrational Frequencies from HCl to SO2 JCE
Franklin M.C. Chen, University of Wisconsin-Green Bay
Theresa Julia Zielinski, Monmouth University
Students learn about finding molecular vibrational frequencies through normal mode analysis and numerical solutions for simple molecule such as HCl and more complicate molecules such as CO2 and SO2. Topics such as displacement coordinates, internal coordinates, symmetry coordinates, and their relationship are developed.
Introduction to Franck-Condon Factors JCE
Theresa Julia Zielinski, Monmouth University
George M. Shalhoub, La Salle University
The background document contains a very brief introduction to Franck-Condon factors through a sequence of guided inquiry type exercises. Students use potential energy diagrams for a diatomic molecule to examine a transition from a ground electronic state to an excited electronic state including consideration of the vibrational levels of each state. The overlap of vibrational wave functions introduces Franck-Condon factors. All of the exercises in this document are done with pencil and paper as preparation for more detailed work to be done in the companion computational document The Franck-Condon Factors.
Rotational States of Carbon Monoxide JCE
Theresa Julia Zielinski, Monmouth University
David M. Hanson, State University of New York at Stony Brook
This Mathcad document develops the components that contribute to the observed rotational absorption spectrum of CO.
The Iodine Spectrum JCE
George Long, Indiana University of Pennsylvania
Theresa Julia Zielinski, Monmouth University
The goal of this document is to present a systematic development of the relationship between spectroscopic experiments and the determination of molecular bond lengths in the excited state of diatomic molecules for which a high resolution vibronic spectrum is available. This document can serve as a template for students to use for data analysis of the UV-vis spectrum of I2 or other diatomic gases.
The Morse Oscillator
Kevin Lehmann, Princeton University
In this worksheet, we find a presentation of the vibrational motion of a diatomic molecule held together with a potential function of a special form known as the Morse Potential. Both the classical and quantum motion of the oscillator will be studied, and explicit expressions for eigenenergies and wavefunctions are given The effect of rotation is also discusses. The document contains embedded 20 exercises and 4 advanced problems for users to test their mastery of the topic.
Using a Computer to Help Understand How Symmetry Principles Reduce Calculations JCE
Louis Kijewski, Monmouth University
This Mathcad document uses symmetry to simplify the evaluation of an eigenvalue problem by reducing a matrix to sparse form. The sparse matrix is then transformed to block diagonal form. Group theory is used to set up the calculations without going through the proofs of the methods. The ability to use symmetry principles to get the vibrational frequencies and other information about molecules with symmetry is an important asset to any chemist.
Vibronic Spectra of Diatomic Molecules and the Birge-Sponer Extrapolation JCE
Theresa Julia Zielinski, Monmouth University
George M. Shalhoub, La Salle University
The goal of this document is to examine the potential energy curve for both the ground and excited state of an electronic transition in order to set the stage for a Birge-Sponer determination of the Do and De dissociation energies of the excited state of a diatomic molecule from experimental UV-vis spectral data. After using this document students will be able to: explain the relationship between the potential energy curves for excited and ground states in a molecule; explain the significance of each parameter in a Morse potential energy function; and use a Birge-Sponer plot to determine dissociation energy of an electronic excited state of a diatomic molecule. IodineSpectrum.mcd, is the companion template for the analysis of the UV-vis spectrum of a diatomic molecule.