THE VIBRATIONAL SPECTRA OF A POLYATOMIC MOLECULE (Revised 3/27/2006)

Size: px
Start display at page:

Download "THE VIBRATIONAL SPECTRA OF A POLYATOMIC MOLECULE (Revised 3/27/2006)"

Transcription

1 THE VIBRATIONAL SPECTRA OF A POLYATOMIC MOLECULE (Revised 3/27/2006) 1) INTRODUCTION The vibrational motion of a molecule is quantized and the resulting energy level spacings give rise to transitions in the mid-ir portion of the electromagnetic spectrum (4000 to ca. 400 cm -1 ). As you know from study of the diatomic harmonic oscillator, the energies (or wavenumber positions, cm -1 ) of these transitions are related to the bond strength (force constant), bond length, and atomic masses (reduced mass). In polyatomic spectra, the positions and relative intensities of the vibrational modes depend on the symmetry (i.e. shape or structure) of the molecule, as well as the bond strengths and masses. For this reason, vibrational spectra (IR and Raman) can provide detailed structural information. This structural information is the objective of this lab, and it is obtained by this analysis, or interpretation, of the infrared and Raman spectra. In this experiment you will obtain infrared and Raman spectra of a polyatomic molecule, predict the selection rules, assign vibrational modes, and then compare these with the vibrational mode positions and intensities predicted for that molecule using HyperChem. Using group theory, we shall predict the spectral selection rules, i.e. predict the spectra for a particular structural model. Assignment of vibrational modes in a spectrum involves relating the experimental spectrum and the predicted spectrum so that each observed vibrational band is identified as to its theoretical origin. A series of empirical rules is provided below to aid in this assignment. Also, a chart defining the well-known positions of group frequencies will be available. (These charts summarize the vast knowledge obtained from the extensive, experimental spectral database that has been collected, literally, over the past 65 years.) Finally, the results of the HyperChem calculation will be compared with the above. Because these calculated normal mode positions will be harmonic frequencies, they must be multiplied by a constant to relate them to the empirical, anharmonic band positions. This constant depends upon the orbital basis set that you use. 2) BACKGROUND For a non-linear polyatomic molecule containing n atoms, there will be 3n-6 vibrational degrees of freedom (3n-5 for a linear molecule) [1]. This number represents the maximum number of vibrational modes for the molecule. However, often the observed number is smaller because of degeneracies and selection rules. Because of the symmetry (i.e. structure), some transitions may be degenerate, and some transitions may be forbidden and not observed; others will be allowed and observed. Allowed or forbidden transitions are also referred to as active or inactive vibrational modes, respectively. Vibrational transitions may also be observed using IR or Raman spectroscopy. For an IR absorption to be allowed between two vibrational levels, a change in dipole moment (µ) must occur as the atoms move, and υ must equal + 1. To be Raman active (i.e. allowed), there must be a change in polarizability (α ij ) during the vibration and υ must equal ± 1. This polarizability can be better understood as an induced dipole. A fundamental vibrational mode will involve a transition from the υ = 0 level to the υ = 1 level. The selection rules for IR and

2 for Raman spectra differ so that the two techniques provide complementary information, not redundant information. Therefore, the Raman spectrum provides significant new structural information, in addition to that provided by the IR spectrum. Group theory is used to predict the characteristic or normal modes of vibration for a molecule. (Normal refers to the fact that these modes of vibration are orthogonal to each other, i.e. independent of each other.) For molecules with many atoms, 3n-6 becomes very large, and this can result in a seemingly complex spectral pattern. However, the presence of symmetry in a molecule often simplifies the vibrational spectrum. Recognition of this symmetry simplifies and allows the interpretation of even complex vibrational spectra, both IR and Raman. The predicted symmetry species define the activity (allowed or forbidden) of each vibrational mode in the IR and in the Raman spectra, and these are referred to as selection rules. Also, the stretching modes can be predicted to distinguish them from the bending and torsional vibrations. The atom masses and force constants determine the precise region of the spectrum at which each normal mode vibrates, i.e., the energy (or frequency or wavenumber) for each. The general region in which various molecular groups will occur can be obtained from group frequency charts, which summarize extensive collections of empirical data. Article II. Empirical Rules Used to Interpret Spectra When we interpret a spectrum, we shall relate (or assign) each band in the spectrum to its origin as predicted by the group theoretical selection rules. The following empirical rules are used in this assignment process for molecular species. The band position (cm -1 ) provides information about the type of vibration. Vibrational modes can be of three basic types, stretching modes (ν), bending modes (δ) or torsional modes (τ). Stretching modes of vibration occur at higher energy, i.e. higher wavenumber, than bending modes. Torsional modes appear at even lower energy. Both the type of vibration and the symmetry species of each vibrational mode influence the relative band intensities. The intensities of asymmetric stretching modes will be greater than asymmetric bending (or torsional) modes in the IR. If one compares asymmetric species with symmetric species of each type (stretch or bend), the asymmetric species will, in general, be stronger in the IR spectrum. For a Raman spectrum, the opposite is true; the symmetric species are stronger. The spectra, both the IR and Raman, will contain some weak bands that are fundamental vibrations and some weak bands that are overtone or combination bands. (Overtone and combination bands are not allowed in the harmonic approximation, and therefore exhibit reduced intensities.) To distinguish the two, compare the IR and Raman spectra. If a band is weak in both the IR and the Raman, it is more likely to be an overtone. A fundamental is expected to be strong in one and weak in the other. However, it is possible, on occasion, to have a mode be weak in both. When comparing IR and Raman band positions, how do you decide if the bands may be ascribed to the "same" vibrational mode, i.e. that these are coincident in the IR and the Raman? This is defined by the experimental error in each spectrum. The maximum precision (for a sharp band) is defined by the spectral resolution used for the scan. For example, if you used 2 cm -1

3 resolution, then your precision (or uncertainty) is ±2 cm -1. For broad bands, the precision will be less. The criterion for coincidence is then the sum of the two uncertainties. Article III. Group Theoretical Analysis The first choice of point group used to predict the IR and Raman spectral selection rules should be the ideal structure, the highest symmetry point group possible. Sometimes, more than one structure (and point group) is possible. Do the group theoretical calculation for both and determine which applies to the real spectrum. For example, when calculating the minimum energy geometry, you may find that this geometry has lower symmetry than the ideal and belongs to a lower symmetry point group. You will then need to predict the IR and Raman selection rules for this point group, as well as the ideal, high symmetry point group. When comparing the two sets of predictions with the experimental data, you may then decide which agrees better with the experimental results. There are two "background" pages that will be given to you as handouts in class. These are a) How is Group Theory Used? and b) Applying Group Theory: Representations of Vibrational Motion. Copies of these follow this experiment for your convenient reference. Article IV. HyperChem Output, Anharmonicity Correction, Negative Frequencies, and Degeneracy HyperChem calculates all of the fundamental modes, both IR and Raman, as well as the IR intensities. Thus it outputs two spectra, one with all of the bands plotted, and the second with just the IR active modes. Since it does not calculate Raman intensities, it cannot plot a Raman spectrum. HyperChem also identifies the symmetry species of each mode. Since you know the assignments from your group theoretical results, you can predict the approximate Raman intensity expected for each calculated mode. (The totally symmetric species will be stronger in the Raman.) The frequencies calculated using HyperChem (or any other ab initio calculation) are harmonic frequencies. To correct for anharmonicity the calculated, harmonic frequencies are multiplied by a constant. This constant depends upon the basis set used. Professor Brown recommends use of the HF/6-13G* basis set (select the 6-13G* basis in the setup) to minimize the energy and to calculate the geometry. Multiply your calculated values by , if you use the 6-13G* basis set [2]. This correction will allow you to compare your experimental values with these corrected values. These should agree quite will, but will not give a perfect agreement. Any drastic disagreement here may indicate an error in your group theoretical analysis and empirical assignments. Be sure to describe and discuss this comparison. This correction factor is an empirically determined value which can vary from 0.89 to The precise value needed for each molecule or even for each fundamental vibrational mode may differ slightly. This is especially true for the lower frequency vibrational modes such as bending and torsional modes. After you "assign" each fundamental vibration and compare the experimental and calculated harmonic values, you can calculate the precise coefficient needed for each mode. (These could be placed in another table.) The overall average coefficient for

4 your molecule, as well as the average values for just the stretching modes and for just the bending plus torsional modes will be interesting to calculate and discuss in your report. How much do these differ from the literature value reported above (0.8929)? A negative frequency means that you have not obtained a minimum. A negative frequency indicates an imaginary energy, which occurs if you are at a saddle point. You are not at the minimum energy structure. Go back and recalculate the minimum energy structure. If your molecule exhibits degenerate vibrational modes (E or T species), HyperChem will calculate 2 or 3 essentially identical (i.e. within experimental error) frequencies for doubly or triply degenerate vibrational modes, respectively. Article V. ASSIGNED COMPOUNDS SEE LAB SUPERVISOR Article VI. EXPERIMENTAL PROCEDURE 1. Obtain an IR spectrum of your group s assigned compound using the Mattson FTIR located in room 601B. (Instructions for its operation are also available in 601B.) You will need to schedule the IR with the lab supervisor with at least 1 day s notice. The supervisor will explain how to prepare your sample and operate the instrument, if needed. The strongest absorption bands in your IR spectrum should absorb no more than 1 absorbance unit (A 1); at least 10% transmittance (10-15% is better) is required to insure resolution of multiple peaks within very strong peaks. It s a good idea to record and/or report two IR spectra, one that clearly resolves all bands, even the strongest, and a second (more concentrated or thicker), which provides good definition of the weaker bands in the spectrum. 2. Obtain a Raman spectrum of your group s assigned compound using the Raman spectrometer in the Chemical Engineering Department. Please contact Professor Bahne Cornilsen to set up an appointment for this. He will explain how to prepare a sample and operate the instrument. 3. Predict the infrared and Raman spectra for your molecule (using group theory) and assign the observed vibrational modes (i.e. relate the experimental spectra to the group theoretical predictions). 4. Use HyperChem to draw your molecule, calculate the minimum energy configuration, and generate the vibrational energies for your assigned compound. Often, the point group symmetry of this structure and that used for your group theoretical analysis will be the same; however, the former may be of lower symmetry. You will then need to predict the selection rules using both point groups. Alternatively, but not necessarily, this may indicate you have not reached the global minimum in your calculation. 5. Submit a group report (see below) that presents the above data and results in tables and figures, and includes a comparison of the group theoretical analysis of the experimental

5 spectra and the vibrational modes generated by HyperChem. Evaluate how well the three compare. Article VII. LABORATORY REPORT FORMAT The report should include the following: a) a results section with Figures of your IR and Raman spectra (with the band positions writtenin near each major band). b) the following results from your calculations and experimental IR and Raman spectra i) one or two tables comparing the experimental IR band positions, the experimental Raman band positions, and the calculated band positions (in decreasing order, highest energy on top) for your compound. It is often convenient to include symmetry (species) and band assignment information for each band in your table(s). Use the following symbols: ν, δ, or τ, and the atoms involved; e.g. ν CH or δ CHC. Indicate the intensities of each band in your table(s) by using the following symbols for the IR: vs=very strong, s=strong, m=medium, w=weak, vw=very weak, and for Raman. It is often convenient to compare the calculated results in a second table. ii) a table of calculated bond distances and angles. If there is experimental data in the literature, these can be compared. iii) the calculated total energy (in Kcal/mole and in atomic units) for the optimized geometry. c) a concise discussion to explain how you made your band assignments. d) a discussion relating part c (your empirical band positions and assignments) to your calculated frequencies. e) a table of calculated bond distances and angles. If there is experimental data in the literature, these can be compared. f) a conclusion as to what the actual structure of your molecule is, based on your data. g) Finally, a copy of your HyperChem output should be sent to Professor Cornilsen as an attachment (change first to a *.txt file so it can be ed). NOTE: No preliminary report is required for this experiment. The report must be-submitted (by ) to the lab s faculty advisor, Professor Cornilsen, for grading. Article VIII. REFERENCES 1. Ira N. Levine, Physical Chemistry, 5 th edn., McGraw-Hill Co. Inc., N.Y., 2002, pp J. B. Foresman and A. Frisch, Exploring Chemistry with Electronic Structure Methods, 2 nd edn., Gaussian, Inc., Pittsburgh, PA, 1995, p. 64.

6 Applying Group Theory: Representations of Vibrational Motion March 24, BCC The following is an introduction to the use of group theory. To apply group theory, we must represent some physical entity that defines the property of interest. For vibrational spectroscopy, we represent the vibrational motion of the molecule in terms of 3 unit Cartesian displacement vectors on each atom. Thus 3n degrees of motion (or degrees-of-freedom) are defined, where n is the number of atoms in the molecule. This is referred to as the basis set. The 3n-6 normal modes of vibration will be combinations of these Cartesian displacement vectors. Six of the 3n degrees of freedom will be rotations (3) and translations (3) of the molecule as a whole. The remaining 3n-6 degrees of freedom represent the normal (i.e. mathematically unique and independent) modes of vibration. After the point group is defined for a molecule, a reducible representation (Γ) is produced by operating on the basis set with each symmetry operation, R. For each atom that is not shifted during the operation (i.e. left invariant) the vectors are summed, with a +1 if the vector is not inverted, and a -1 if the vector is inverted. These sums produce the character for that operation, χ(r). This reducible representation actually represents the chosen basis set, which is the 3n degrees of freedom in the analysis of vibrational motion. For example, see how this representation and the vibrational selection rules are obtained for a tetrahedral molecule (or tetrahedral ion) in Cotton s text, in a section entitled Tetrahedral Molecules, Such as Methane. * A second method of representing molecular motion is to use internal coordinates (bond lengths, bond angles, or torsional angles) as the basis set. Cotton* also obtains reproducible representations (Γ) for the CH stretches and HCH bends of methane, and shows how the reducible representations are reduced. * F. A. Cotton, Chemical Applications of Group Theory, 3 rd edn., Wiley, NY, 1990.

7 HOW IS GROUP THEORY USED? March 24, BCC After we learn to classify molecules in terms of their symmetry, i.e. assign a molecule to the appropriate point group, we wish to apply it to specific examples. This general application process is outlined in the following outline, using vibrational spectroscopy as an example. Other examples are included in parentheses. 1. First, the point group is assigned. 2. Secondly, a basis set is chosen to represent the physical entities that we wish to study, e.g. vibrational modes of a molecule. (Other examples include atomic orbital basis sets to represent and determine hybrid orbitals or molecular orbitals.). For vibrational modes two different basis sets are useful. The first is a Cartesian coordinate basis set, which represents all motions (translation, as well as rotation & vibration about the center-of-mass) of a molecule. The second type of basis set uses internal coordinates, which represent specific inter-atomic motions. In each case our final result will be a group theoretical representation of this basis set which will allow determination of the symmetry of the excited state, vibrational energy levels (and of their corresponding wavefunctions). 3. The symmetry operations of the molecule are applied to the basis set to obtain a reducible representation which represents all of the properties in question. 4. The reducible representation is reduced to form irreducible representations (i.e. it is reduced into "symmetry species") which represent the results of our application. These species represent the excited vibrational states of the molecule, the normal modes of vibration. 5. The irreducible representations (or symmetry species) obtained are then used to determine selection rules for transitions between the energy levels in question, i.e. to predict spectral selection rules for infrared and Raman spectra. The ground state vibrational level is always represented by the totally symmetric symmetry species. (If we represent electronic energy levels or molecular orbitals, selection rules for electronic transitions can be predicted.)

THE VIBRATIONAL SPECTRUM OF A POLYATOMIC MOLECULE (Revised 4/7/2004)

THE VIBRATIONAL SPECTRUM OF A POLYATOMIC MOLECULE (Revised 4/7/2004) INTRODUCTION THE VIBRATIONAL SPECTRUM OF A POLYATOMIC MOLECULE (Revised 4/7/2004) The vibrational motion of a molecule is quantized and the resulting energy level spacings give rise to transitions in the

More information

Chapter 6 Vibrational Spectroscopy

Chapter 6 Vibrational Spectroscopy Chapter 6 Vibrational Spectroscopy As with other applications of symmetry and group theory, these techniques reach their greatest utility when applied to the analysis of relatively small molecules in either

More information

PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 23 (NORMAL MODES AND IRREDUCIBLE REPRESENTATIONS FOR POLYATOMIC MOLECULES)

PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE NO. : 23 (NORMAL MODES AND IRREDUCIBLE REPRESENTATIONS FOR POLYATOMIC MOLECULES) Subject Chemistry Paper No and Title Module No and Title Module Tag 8/ Physical Spectroscopy 23/ Normal modes and irreducible representations for polyatomic molecules CHE_P8_M23 TABLE OF CONTENTS 1. Learning

More information

THEORY OF MOLECULE. A molecule consists of two or more atoms with certain distances between them

THEORY OF MOLECULE. A molecule consists of two or more atoms with certain distances between them THEORY OF MOLECULE A molecule consists of two or more atoms with certain distances between them through interaction of outer electrons. Distances are determined by sum of all forces between the atoms.

More information

16.1 Molecular Vibrations

16.1 Molecular Vibrations 16.1 Molecular Vibrations molecular degrees of freedom are used to predict the number of vibrational modes vibrations occur as coordinated movement among many nuclei the harmonic oscillator approximation

More information

Chemistry 2. Assumed knowledge

Chemistry 2. Assumed knowledge Chemistry 2 Lecture 8 IR Spectroscopy of Polyatomic Molecles Assumed knowledge There are 3N 6 vibrations in a non linear molecule and 3N 5 vibrations in a linear molecule. Only modes that lead to a change

More information

2. Infrared spectroscopy

2. Infrared spectroscopy 2. Infrared spectroscopy 2-1Theoretical principles An important tool of the organic chemist is Infrared Spectroscopy, or IR. IR spectra are acquired on a special instrument, called an IR spectrometer.

More information

USING THE OCEAN OPTICS R-2000 RAMAN SPECTROMETER IN THE UNDERGRADUATE LABORATORY

USING THE OCEAN OPTICS R-2000 RAMAN SPECTROMETER IN THE UNDERGRADUATE LABORATORY Proceedings of the South Dakota Academy of Science, Vol. 79 (2000) 63 USING THE OCEAN OPTICS R-2000 RAMAN SPECTROMETER IN THE UNDERGRADUATE LABORATORY Deanna L. Donohoue, Gary W. Earl and Arlen Viste Department

More information

Lecture 8. Assumed knowledge

Lecture 8. Assumed knowledge Chemistry 2 Lecture 8 IR Spectroscopy of Polyatomic Molecles Assumed knowledge There are 3N 6 vibrations in a non linear molecule and 3N 5 vibrations in a linear molecule. Only modes that lead to a change

More information

CHM Physical Chemistry II Chapter 12 - Supplementary Material. 1. Einstein A and B coefficients

CHM Physical Chemistry II Chapter 12 - Supplementary Material. 1. Einstein A and B coefficients CHM 3411 - Physical Chemistry II Chapter 12 - Supplementary Material 1. Einstein A and B coefficients Consider two singly degenerate states in an atom, molecule, or ion, with wavefunctions 1 (for the lower

More information

Vibrations of Carbon Dioxide and Carbon Disulfide

Vibrations of Carbon Dioxide and Carbon Disulfide Vibrations of Carbon Dioxide and Carbon Disulfide Purpose Vibration frequencies of CO 2 and CS 2 will be measured by Raman and Infrared spectroscopy. The spectra show effects of normal mode symmetries

More information

Types of Molecular Vibrations

Types of Molecular Vibrations Important concepts in IR spectroscopy Vibrations that result in change of dipole moment give rise to IR absorptions. The oscillating electric field of the radiation couples with the molecular vibration

More information

V( x) = V( 0) + dv. V( x) = 1 2

V( x) = V( 0) + dv. V( x) = 1 2 Spectroscopy 1: rotational and vibrational spectra The vibrations of diatomic molecules Molecular vibrations Consider a typical potential energy curve for a diatomic molecule. In regions close to R e (at

More information

Spectroscopic Selection Rules

Spectroscopic Selection Rules E 0 v = 0 v = 1 v = 2 v = 4 v = 3 For a vibrational fundamental (Δv = ±1), the transition will have nonzero intensity in either the infrared or Raman spectrum if the appropriate transition moment is nonzero.

More information

Symmetry: Translation and Rotation

Symmetry: Translation and Rotation Symmetry: Translation and Rotation The sixth column of the C 2v character table indicates the symmetry species for translation along (T) and rotation about (R) the Cartesian axes. y y y C 2 F v (x) T x

More information

LECTURE 3 DIRECT PRODUCTS AND SPECTROSCOPIC SELECTION RULES

LECTURE 3 DIRECT PRODUCTS AND SPECTROSCOPIC SELECTION RULES SYMMETRY II. J. M. GOICOECHEA. LECTURE 3 1 LECTURE 3 DIRECT PRODUCTS AND SPECTROSCOPIC SELECTION RULES 3.1 Direct products and many electron states Consider the problem of deciding upon the symmetry of

More information

Infrared Spectroscopy: Identification of Unknown Substances

Infrared Spectroscopy: Identification of Unknown Substances Infrared Spectroscopy: Identification of Unknown Substances Suppose a white powder is one of the four following molecules. How can they be differentiated? H N N H H H H Na H H H H H A technique that is

More information

Chemistry 543--Final Exam--Keiderling May 5, pm SES

Chemistry 543--Final Exam--Keiderling May 5, pm SES Chemistry 543--Final Exam--Keiderling May 5,1992 -- 1-5pm -- 174 SES Please answer all questions in the answer book provided. Make sure your name is clearly indicated and that the answers are clearly numbered,

More information

Quote from Eugene Paul Wigner

Quote from Eugene Paul Wigner Quote from Eugene Paul Wigner See also: Current Science, vol. 69, no. 4, 25 August 1995, p. 375 From the preface to his book on group theory: Wigner relates a conversation with von Laue on the use of group

More information

Infrared Spectroscopy

Infrared Spectroscopy Infrared Spectroscopy The Interaction of Light with Matter Electric fields apply forces to charges, according to F = qe In an electric field, a positive charge will experience a force, but a negative charge

More information

Introduction to Molecular Vibrations and Infrared Spectroscopy

Introduction to Molecular Vibrations and Infrared Spectroscopy hemistry 362 Spring 2017 Dr. Jean M. Standard February 15, 2017 Introduction to Molecular Vibrations and Infrared Spectroscopy Vibrational Modes For a molecule with N atoms, the number of vibrational modes

More information

Physical Chemistry II Exam 2 Solutions

Physical Chemistry II Exam 2 Solutions Chemistry 362 Spring 2017 Dr Jean M Standard March 10, 2017 Name KEY Physical Chemistry II Exam 2 Solutions 1) (14 points) Use the potential energy and momentum operators for the harmonic oscillator to

More information

Vibrational Spectroscopy

Vibrational Spectroscopy Vibrational Spectroscopy In this part of the course we will look at the kind of spectroscopy which uses light to excite the motion of atoms. The forces required to move atoms are smaller than those required

More information

Molecular Symmetry. Symmetry is relevant to: spectroscopy, chirality, polarity, Group Theory, Molecular Orbitals

Molecular Symmetry. Symmetry is relevant to: spectroscopy, chirality, polarity, Group Theory, Molecular Orbitals Molecular Symmetry Symmetry is relevant to: spectroscopy, chirality, polarity, Group Theory, Molecular Orbitals - A molecule has a symmetry element if it is unchanged by a particular symmetry operation

More information

Spectroscopy: Tinoco Chapter 10 (but vibration, Ch.9)

Spectroscopy: Tinoco Chapter 10 (but vibration, Ch.9) Spectroscopy: Tinoco Chapter 10 (but vibration, Ch.9) XIV 67 Vibrational Spectroscopy (Typical for IR and Raman) Born-Oppenheimer separate electron-nuclear motion ψ (rr) = χ υ (R) φ el (r,r) -- product

More information

/2Mα 2 α + V n (R)] χ (R) = E υ χ υ (R)

/2Mα 2 α + V n (R)] χ (R) = E υ χ υ (R) Spectroscopy: Engel Chapter 18 XIV 67 Vibrational Spectroscopy (Typically IR and Raman) Born-Oppenheimer approx. separate electron-nuclear Assume elect-nuclear motion separate, full wave fct. ψ (r,r) =

More information

Lecture 4: Polyatomic Spectra

Lecture 4: Polyatomic Spectra Lecture 4: Polyatomic Spectra 1. From diatomic to polyatomic Ammonia molecule A-axis. Classification of polyatomic molecules 3. Rotational spectra of polyatomic molecules N 4. Vibrational bands, vibrational

More information

where, c is the speed of light, ν is the frequency in wave numbers (cm -1 ) and µ is the reduced mass (in amu) of A and B given by the equation: ma

where, c is the speed of light, ν is the frequency in wave numbers (cm -1 ) and µ is the reduced mass (in amu) of A and B given by the equation: ma Vibrational Spectroscopy A rough definition of spectroscopy is the study of the interaction of matter with energy (radiation in the electromagnetic spectrum). A molecular vibration is a periodic distortion

More information

Determining the Normal Modes of Vibration

Determining the Normal Modes of Vibration Determining the ormal Modes of Vibration Introduction vibrational modes of ammonia are shown below! 1 A 1 ) symmetric stretch! A 1 ) symmetric bend! 3a E) degenerate stretch Figure 1 Vibrational modes!

More information

PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES)

PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES) Subject Chemistry Paper No and Title Module No and Title Module Tag 8 and Physical Spectroscopy 5 and Transition probabilities and transition dipole moment, Overview of selection rules CHE_P8_M5 TABLE

More information

Introduction to Vibrational Spectroscopy

Introduction to Vibrational Spectroscopy Introduction to Vibrational Spectroscopy Harmonic oscillators The classical harmonic oscillator The uantum mechanical harmonic oscillator Harmonic approximations in molecular vibrations Vibrational spectroscopy

More information

Vibrational Spectra (IR and Raman) update Tinoco has very little, p.576, Engel Ch. 18, House Ch. 6

Vibrational Spectra (IR and Raman) update Tinoco has very little, p.576, Engel Ch. 18, House Ch. 6 Vibrational Spectra (IR and Raman)- 2010 update Tinoco has very little, p.576, Engel Ch. 18, House Ch. 6 Born-Oppenheimer approx. separate electron-nuclear Assume elect-nuclear motion separate, full wave

More information

William H. Brown & Christopher S. Foote

William H. Brown & Christopher S. Foote Requests for permission to make copies of any part of the work should be mailed to:permissions Department, Harcourt Brace & Company, 6277 Sea Harbor Drive, Orlando, Florida 32887-6777 William H. Brown

More information

INFRARED ABSORPTION SPECTROSCOPY. References: See relevant sections in undergraduate text. Learn from your instructor how to use the spectrometer.

INFRARED ABSORPTION SPECTROSCOPY. References: See relevant sections in undergraduate text. Learn from your instructor how to use the spectrometer. INFRARED ABSORPTION SPECTROSCOPY References: See relevant sections in undergraduate text Background: Learn from your instructor how to use the spectrometer. Know definitions of the following and their

More information

Problem Set 5 Solutions

Problem Set 5 Solutions Chemistry 362 Dr Jean M Standard Problem Set 5 Solutions ow many vibrational modes do the following molecules or ions possess? [int: Drawing Lewis structures may be useful in some cases] In all of the

More information

Chemistry 431. NC State University. Lecture 17. Vibrational Spectroscopy

Chemistry 431. NC State University. Lecture 17. Vibrational Spectroscopy Chemistry 43 Lecture 7 Vibrational Spectroscopy NC State University The Dipole Moment Expansion The permanent dipole moment of a molecule oscillates about an equilibrium value as the molecule vibrates.

More information

Lecture 10 Diatomic Vibration Spectra Harmonic Model

Lecture 10 Diatomic Vibration Spectra Harmonic Model Chemistry II: Introduction to Molecular Spectroscopy Prof. Mangala Sunder Department of Chemistry and Biochemistry Indian Institute of Technology, Madras Lecture 10 Diatomic Vibration Spectra Harmonic

More information

Radiant energy is proportional to its frequency (cycles/s = Hz) as a wave (Amplitude is its height) Different types are classified by frequency or

Radiant energy is proportional to its frequency (cycles/s = Hz) as a wave (Amplitude is its height) Different types are classified by frequency or CHEM 241 UNIT 5: PART B INFRA-RED RED SPECTROSCOPY 1 Spectroscopy of the Electromagnetic Spectrum Radiant energy is proportional to its frequency (cycles/s = Hz) as a wave (Amplitude is its height) Different

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Fall, 008

More information

Symmetric Stretch: allows molecule to move through space

Symmetric Stretch: allows molecule to move through space BACKGROUND INFORMATION Infrared Spectroscopy Before introducing the subject of IR spectroscopy, we must first review some aspects of the electromagnetic spectrum. The electromagnetic spectrum is composed

More information

Lecture 11. IR Theory. Next Class: Lecture Problem 4 due Thin-Layer Chromatography

Lecture 11. IR Theory. Next Class: Lecture Problem 4 due Thin-Layer Chromatography Lecture 11 IR Theory Next Class: Lecture Problem 4 due Thin-Layer Chromatography This Week In Lab: Ch 6: Procedures 2 & 3 Procedure 4 (outside of lab) Next Week in Lab: Ch 7: PreLab Due Quiz 4 Ch 5 Final

More information

Spectroscopy in Inorganic Chemistry. Vibration and Rotation Spectroscopy

Spectroscopy in Inorganic Chemistry. Vibration and Rotation Spectroscopy Spectroscopy in Inorganic Chemistry Vibrational energy levels in a diatomic molecule f = k r r V = ½kX 2 Force constant r Displacement from equilibrium point 2 X= r=r-r eq V = ½kX 2 Fundamental Vibrational

More information

Headspace Raman Spectroscopy

Headspace Raman Spectroscopy ELECTRONICALLY REPRINTED FROM SEPTEMBER 2014 Molecular Spectroscopy Workbench Raman Spectroscopy We examine vapor-phase Raman spectroscopy through the acquisition of spectra from gas molecules confined

More information

Raman and stimulated Raman spectroscopy of chlorinated hydrocarbons

Raman and stimulated Raman spectroscopy of chlorinated hydrocarbons Department of Chemistry Physical Chemistry Göteborg University KEN140 Spektroskopi Raman and stimulated Raman spectroscopy of chlorinated hydrocarbons WARNING! The laser gives a pulsed very energetic and

More information

Symmetry. Chemistry 481(01) Spring 2017 Instructor: Dr. Upali Siriwardane Office: CTH 311 Phone Office Hours:

Symmetry. Chemistry 481(01) Spring 2017 Instructor: Dr. Upali Siriwardane   Office: CTH 311 Phone Office Hours: Chemistry 481(01) Spring 2017 Instructor: Dr. Upali Siriwardane e-mail: upali@latech.edu Office: CT 311 Phone 257-4941 Office ours: M,W 8:00-9:00 & 11:00-12:00 am; Tu,Th, F 9:30-11:30 a.m. April 4, 2017:

More information

Chemistry 795T. NC State University. Lecture 4. Vibrational and Rotational Spectroscopy

Chemistry 795T. NC State University. Lecture 4. Vibrational and Rotational Spectroscopy Chemistry 795T Lecture 4 Vibrational and Rotational Spectroscopy NC State University The Dipole Moment Expansion The permanent dipole moment of a molecule oscillates about an equilibrium value as the molecule

More information

Symmetrical: implies the species possesses a number of indistinguishable configurations.

Symmetrical: implies the species possesses a number of indistinguishable configurations. Chapter 3 - Molecular Symmetry Symmetry helps us understand molecular structure, some chemical properties, and characteristics of physical properties (spectroscopy) used with group theory to predict vibrational

More information

MOLECULAR SPECTROSCOPY

MOLECULAR SPECTROSCOPY MOLECULAR SPECTROSCOPY First Edition Jeanne L. McHale University of Idaho PRENTICE HALL, Upper Saddle River, New Jersey 07458 CONTENTS PREFACE xiii 1 INTRODUCTION AND REVIEW 1 1.1 Historical Perspective

More information

Molecular energy levels and spectroscopy

Molecular energy levels and spectroscopy Molecular energy levels and spectroscopy 1. Translational energy levels The translational energy levels of a molecule are usually taken to be those of a particle in a three-dimensional box: n x E(n x,n

More information

Wolfgang Demtroder. Molecular Physics. Theoretical Principles and Experimental Methods WILEY- VCH. WILEY-VCH Verlag GmbH & Co.

Wolfgang Demtroder. Molecular Physics. Theoretical Principles and Experimental Methods WILEY- VCH. WILEY-VCH Verlag GmbH & Co. Wolfgang Demtroder Molecular Physics Theoretical Principles and Experimental Methods WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA v Preface xiii 1 Introduction 1 1.1 Short Historical Overview 2 1.2 Molecular

More information

Exercises 16.3a, 16.5a, 16.13a, 16.14a, 16.21a, 16.25a.

Exercises 16.3a, 16.5a, 16.13a, 16.14a, 16.21a, 16.25a. SPECTROSCOPY Readings in Atkins: Justification 13.1, Figure 16.1, Chapter 16: Sections 16.4 (diatomics only), 16.5 (omit a, b, d, e), 16.6, 16.9, 16.10, 16.11 (omit b), 16.14 (omit c). Exercises 16.3a,

More information

B7 Symmetry : Questions

B7 Symmetry : Questions B7 Symmetry 009-10: Questions 1. Using the definition of a group, prove the Rearrangement Theorem, that the set of h products RS obtained for a fixed element S, when R ranges over the h elements of the

More information

CHAPTER 13 LECTURE NOTES

CHAPTER 13 LECTURE NOTES CHAPTER 13 LECTURE NOTES Spectroscopy is concerned with the measurement of (a) the wavelengths (or frequencies) at which molecules absorb/emit energy, and (b) the amount of radiation absorbed at these

More information

Structure Determination. How to determine what compound that you have? One way to determine compound is to get an elemental analysis

Structure Determination. How to determine what compound that you have? One way to determine compound is to get an elemental analysis Structure Determination How to determine what compound that you have? ne way to determine compound is to get an elemental analysis -basically burn the compound to determine %C, %H, %, etc. from these percentages

More information

Literature values: ΔH f, gas = % error Source: ΔH f, solid = % error. For comparison, your experimental value was ΔH f = phase:

Literature values: ΔH f, gas = % error Source: ΔH f, solid = % error. For comparison, your experimental value was ΔH f = phase: 1 Molecular Calculations Lab: Some guideline given at the bottom of page 3. 1. Use the semi-empirical AM1 method to calculate ΔH f for the compound you used in the heat of combustion experiment. Be sure

More information

Chem 442 Review of Spectroscopy

Chem 442 Review of Spectroscopy Chem 44 Review of Spectroscopy General spectroscopy Wavelength (nm), frequency (s -1 ), wavenumber (cm -1 ) Frequency (s -1 ): n= c l Wavenumbers (cm -1 ): n =1 l Chart of photon energies and spectroscopies

More information

Spectroscopy in Inorganic Chemistry. Vibration and Rotation Spectroscopy

Spectroscopy in Inorganic Chemistry. Vibration and Rotation Spectroscopy Spectroscopy in Inorganic Chemistry Symmetry requirement for coupling combination bands and Fermi resonance 2 3 V 3 1505 cm -1 (R, IR) E' stretches v 1 888 cm -1 (R) A 1 ' stretch V 2 718 cm -1 (IR) A

More information

6.2 Polyatomic Molecules

6.2 Polyatomic Molecules 6.2 Polyatomic Molecules 6.2.1 Group Vibrations An N-atom molecule has 3N - 5 normal modes of vibrations if it is linear and 3N 6 if it is non-linear. Lissajous motion A polyatomic molecule undergoes a

More information

Infrared spectroscopy Basic theory

Infrared spectroscopy Basic theory Infrared spectroscopy Basic theory Dr. Davide Ferri Paul Scherrer Institut 056 310 27 81 davide.ferri@psi.ch Importance of IR spectroscopy in catalysis IR Raman NMR XAFS UV-Vis EPR 0 200 400 600 800 1000

More information

Determining the Normal Modes of Vibration

Determining the Normal Modes of Vibration Determining the ormal Modes of Vibration Introduction at the end of last lecture you determined the symmetry and activity of the vibrational modes of ammonia Γ vib 3 ) = A 1 IR, pol) + EIR,depol) the vibrational

More information

Fourier Transform Infrared Spectroscopy of Metal Ligand Complexes *

Fourier Transform Infrared Spectroscopy of Metal Ligand Complexes * OpenStax-CNX module: m34660 1 Fourier Transform Infrared Spectroscopy of Metal Ligand Complexes * Jiebo Li Andrew R. Barron This work is produced by OpenStax-CNX and licensed under the Creative Commons

More information

Chemistry 881 Lecture Topics Fall 2001

Chemistry 881 Lecture Topics Fall 2001 Chemistry 881 Lecture Topics Fall 2001 Texts PHYSICAL CHEMISTRY A Molecular Approach McQuarrie and Simon MATHEMATICS for PHYSICAL CHEMISTRY, Mortimer i. Mathematics Review (M, Chapters 1,2,3 & 4; M&S,

More information

Infrared Spectroscopy

Infrared Spectroscopy Infrared Spectroscopy IR Spectroscopy Used to identify organic compounds IR spectroscopy provides a 100% identification if the spectrum is matched. If not, IR at least provides information about the types

More information

Chapter 3 Introduction to Molecular Symmetry

Chapter 3 Introduction to Molecular Symmetry CHEM 511 Chapter 3 page 1 of 12 Chapter 3 Introduction to Molecular Symmetry This chapter will deal with the symmetry characteristics of individual molecules, i.e., how molecules can be rotated or imaged

More information

13, Applications of molecular symmetry and group theory

13, Applications of molecular symmetry and group theory Subject Paper No and Title Module No and Title Module Tag Chemistry 13, Applications of molecular symmetry and group theory 27, Group theory and vibrational spectroscopy: Part-IV(Selection rules for IR

More information

7a. Structure Elucidation: IR and 13 C-NMR Spectroscopies (text , , 12.10)

7a. Structure Elucidation: IR and 13 C-NMR Spectroscopies (text , , 12.10) 2009, Department of Chemistry, The University of Western Ontario 7a.1 7a. Structure Elucidation: IR and 13 C-NMR Spectroscopies (text 11.1 11.5, 12.1 12.5, 12.10) A. Electromagnetic Radiation Energy is

More information

Ge Homework Problem

Ge Homework Problem Ge 214 - Homework Problem Vibrations of SO 4 units in low symmetry environments Most minerals have structures which are lower symmetry than cubic. As a consequence, symmetrical anions such as SiO 4 2-

More information

Chem 344 Final Exam Tuesday, Dec. 11, 2007, 3-?? PM

Chem 344 Final Exam Tuesday, Dec. 11, 2007, 3-?? PM Chem 344 Final Exam Tuesday, Dec. 11, 2007, 3-?? PM Closed book exam, only pencils and calculators permitted. You may bring and use one 8 1/2 x 11" paper with anything on it. No Computers. Put all of your

More information

Chem Homework = cm -1, HF; cm -1, H 35 Cl; cm -1, H 81 Br; cm -1, H 127 I

Chem Homework = cm -1, HF; cm -1, H 35 Cl; cm -1, H 81 Br; cm -1, H 127 I 1. Chem 344 - Homework 10 2. 3. 4. 0 = 4141.3 cm -1, HF; 2988.9 cm -1, H 35 Cl; 2649.7 cm -1, H 81 Br; 2309.5 cm -1, H 127 I 5. 6. 7. Q16.26,27,28,29) Identify the molecular orbitals for F 2 in the images

More information

Physical Chemistry - Problem Drill 15: Vibrational and Rotational Spectroscopy

Physical Chemistry - Problem Drill 15: Vibrational and Rotational Spectroscopy Physical Chemistry - Problem Drill 15: Vibrational and Rotational Spectroscopy No. 1 of 10 1. Internal vibration modes of a molecule containing N atoms is made up of the superposition of 3N-(5 or 6) simple

More information

Infrared Spectroscopy An Instrumental Method for Detecting Functional Groups

Infrared Spectroscopy An Instrumental Method for Detecting Functional Groups Infrared Spectroscopy An Instrumental Method for Detecting Functional Groups 1 The Electromagnetic Spectrum Infrared Spectroscopy I. Physics Review Frequency, υ (nu), is the number of wave cycles that

More information

Physical Chemistry Lab II CHEM 4644 Spring 2011 Final Exam 5 questions at 3 points each equals 15 total points possible.

Physical Chemistry Lab II CHEM 4644 Spring 2011 Final Exam 5 questions at 3 points each equals 15 total points possible. Physical Chemistry Lab II Name: KEY CHEM 4644 Spring 2011 Final Exam 5 questions at 3 points each equals 15 total points possible. Constants: c = 3.00 10 8 m/s h = 6.63 10-34 J s 1 Hartree = 4.36 10-18

More information

Vibrational Spectra (IR and Raman) update Tinoco has very little, p.576, Engel Ch. 18, House Ch. 6

Vibrational Spectra (IR and Raman) update Tinoco has very little, p.576, Engel Ch. 18, House Ch. 6 Vibrational Spectra (IR and Raman)- 2010 update Tinoco has very little, p.576, Engel Ch. 18, House Ch. 6 XIV 67 Born-Oppenheimer approx. separate electron-nuclear Assume elect-nuclear motion separate,

More information

Appendix D Simulating Spectroscopic Bands Using Gaussian and PGopher

Appendix D Simulating Spectroscopic Bands Using Gaussian and PGopher 429 Appendix D Simulating Spectroscopic Bands Using Gaussian and PGopher This appendix contains methods for using Gaussian 09 121 and PGopher 120 to simulate vibrational and electronic bands of molecules.

More information

Chemistry 483 Lecture Topics Fall 2009

Chemistry 483 Lecture Topics Fall 2009 Chemistry 483 Lecture Topics Fall 2009 Text PHYSICAL CHEMISTRY A Molecular Approach McQuarrie and Simon A. Background (M&S,Chapter 1) Blackbody Radiation Photoelectric effect DeBroglie Wavelength Atomic

More information

Also interested only in internal energies Uel (R) only internal forces, has symmetry of molecule--that is source of potential.

Also interested only in internal energies Uel (R) only internal forces, has symmetry of molecule--that is source of potential. IV. Molecular Vibrations IV-1 As discussed solutions, ψ, of the amiltonian, (Schrödinger Equation) must be representations of the group of the molecule i.e. energy cannot change due to a symmetry operation,

More information

Chemistry 5325/5326. Angelo R. Rossi Department of Chemistry The University of Connecticut. January 17-24, 2012

Chemistry 5325/5326. Angelo R. Rossi Department of Chemistry The University of Connecticut. January 17-24, 2012 Symmetry and Group Theory for Computational Chemistry Applications Chemistry 5325/5326 Angelo R. Rossi Department of Chemistry The University of Connecticut angelo.rossi@uconn.edu January 17-24, 2012 Infrared

More information

Advanced Spectroscopy. Dr. P. Hunt Rm 167 (Chemistry) web-site:

Advanced Spectroscopy. Dr. P. Hunt Rm 167 (Chemistry) web-site: Advanced Spectroscopy Dr. P. Hunt p.hunt@imperial.ac.uk Rm 167 (Chemistry) web-site: http://www.ch.ic.ac.uk/hunt Maths! Coordinate transformations rotations! example 18.1 p501 whole chapter on Matrices

More information

February 8, 2018 Chemistry 328N

February 8, 2018 Chemistry 328N Lecture 7 UV-Vis spectroscopy February 8, 2018 First Midterm Exam When: Wednesday, 2/14 When: 7-9 PM (please do not be late) Where: WEL 2.122 This room!!! What: Covers material through today s lecture

More information

What happens when light falls on a material? Transmission Reflection Absorption Luminescence. Elastic Scattering Inelastic Scattering

What happens when light falls on a material? Transmission Reflection Absorption Luminescence. Elastic Scattering Inelastic Scattering Raman Spectroscopy What happens when light falls on a material? Transmission Reflection Absorption Luminescence Elastic Scattering Inelastic Scattering Raman, Fluorescence and IR Scattering Absorption

More information

(2) Read each statement carefully and pick the one that is incorrect in its information.

(2) Read each statement carefully and pick the one that is incorrect in its information. Organic Chemistry - Problem Drill 17: IR and Mass Spectra No. 1 of 10 1. Which statement about infrared spectroscopy is incorrect? (A) IR spectroscopy is a method of structure determination based on the

More information

Química Orgânica I. Ciências Farmacêuticas Bioquímica Química. IR spectroscopy AFB QO I 2007/08 1 AFB QO I 2007/08 2

Química Orgânica I. Ciências Farmacêuticas Bioquímica Química. IR spectroscopy AFB QO I 2007/08 1 AFB QO I 2007/08 2 Química Orgânica I Ciências Farmacêuticas Bioquímica Química AFB QO I 2007/08 1 IR spectroscopy AFB QO I 2007/08 2 1 Adaptado de: Organic Chemistry, 6th Edition; L. G. Wade, Jr. Organic Chemistry, William

More information

Infrared Spectroscopy

Infrared Spectroscopy Infrared Spectroscopy Introduction Spectroscopy is an analytical technique which helps determine structure. It destroys little or no sample. The amount of light absorbed by the sample is measured as wavelength

More information

Abstract. The vibrational properties of pentane, neopentane, polyethylene and polyvinylchloride are

Abstract. The vibrational properties of pentane, neopentane, polyethylene and polyvinylchloride are Computational Infrared Spectroscopy: Pentane, Neopentane, Polyethylene and Polyvinylchloride Eman Mousa Alhajji North Carolina State University Department of Materials Science and Engineering MSE 255 Lab

More information

Degrees of Freedom and Vibrational Modes

Degrees of Freedom and Vibrational Modes Degrees of Freedom and Vibrational Modes 1. Every atom in a molecule can move in three possible directions relative to a Cartesian coordinate, so for a molecule of n atoms there are 3n degrees of freedom.

More information

Experiment 3: The Rovibrational Spectrum of HCl (was Experiment 4 in the syllabus, but the original Experiment 3 was canceled)

Experiment 3: The Rovibrational Spectrum of HCl (was Experiment 4 in the syllabus, but the original Experiment 3 was canceled) Varberg and Kuwata Chemistry 312 Spring 28 Experiment 3: The Rovibrational Spectrum of HCl (was Experiment 4 in the syllabus, but the original Experiment 3 was canceled) Meet for lab on Thursday, April

More information

Effect of mass attached to the spring: 1. Replace the small stopper with the large stopper. Repeat steps 3-9 for each spring set.

Effect of mass attached to the spring: 1. Replace the small stopper with the large stopper. Repeat steps 3-9 for each spring set. EXERCISE 1: Representing molecular vibrations with spring oscillations A spring is a common model for covalent chemical bonds. One of the interesting interpretations of quantum mechanics is that bonds

More information

CHAPTER-IV. FT-IR and FT-Raman investigation on m-xylol using ab-initio HF and DFT calculations

CHAPTER-IV. FT-IR and FT-Raman investigation on m-xylol using ab-initio HF and DFT calculations 4.1. Introduction CHAPTER-IV FT-IR and FT-Raman investigation on m-xylol using ab-initio HF and DFT calculations m-xylol is a material for thermally stable aramid fibers or alkyd resins [1]. In recent

More information

ChemWiki BioWiki GeoWiki StatWiki PhysWiki MathWiki SolarWiki

ChemWiki BioWiki GeoWiki StatWiki PhysWiki MathWiki SolarWiki Ashley Robison My Preferences Site Tools FAQ Sign Out If you like us, please share us on social media. The latest UCD Hyperlibrary newsletter is now complete, check it out. ChemWiki BioWiki GeoWiki StatWiki

More information

VIBRATION-ROTATION SPECTRUM OF CO

VIBRATION-ROTATION SPECTRUM OF CO Rice University Physics 332 VIBRATION-ROTATION SPECTRUM OF CO I. INTRODUCTION...2 II. THEORETICAL CONSIDERATIONS...3 III. MEASUREMENTS...8 IV. ANALYSIS...9 April 2011 I. Introduction Optical spectroscopy

More information

Brief introduction to molecular symmetry

Brief introduction to molecular symmetry Chapter 1 Brief introduction to molecular symmetry It is possible to understand the electronic structure of diatomic molecules and their interaction with light without the theory of molecular symmetry.

More information

Asymmetry of Peaks in the XPS of Polymers

Asymmetry of Peaks in the XPS of Polymers Asymmetry of Peaks in the XPS of Polymers When a photon is absorbed by a material, the energy transferred may cause the excitation of both the electronic and atomic structure of the compounds on the surface.

More information

Chemistry 21b Final Examination

Chemistry 21b Final Examination Chemistry 21b Final Examination Out: 11 March 2011 Due: 16 March 2011, 5 pm This is an open book examination, and so you may use McQuarrie or Harris and Bertolucci along with the posted Lecture Notes and

More information

Study of vibrational spectra of 4-methyl-3-nitrobenzaldehyde

Study of vibrational spectra of 4-methyl-3-nitrobenzaldehyde Indian Journal of Pure & Applied Physics Vol. 44, September 2006, pp. 644-648 Study of vibrational spectra of 4-methyl-3-nitrobenzaldehyde B S Yadav, S K Tyagi* & Seema** Molecular Spectroscopy and Biophysics

More information

QUANTUM CHEMISTRY PROJECT 3: PARTS B AND C

QUANTUM CHEMISTRY PROJECT 3: PARTS B AND C Chemistry 460 Fall 2017 Dr. Jean M. Standard November 6, 2017 QUANTUM CHEMISTRY PROJECT 3: PARTS B AND C PART B: POTENTIAL CURVE, SPECTROSCOPIC CONSTANTS, AND DISSOCIATION ENERGY OF DIATOMIC HYDROGEN (20

More information

A56. Raman Spektroscopy. Jan Publisher: Institute of Physical Chemistry

A56. Raman Spektroscopy. Jan Publisher: Institute of Physical Chemistry Physikalische-Chemisches Praktikum für Anfänger A56 Raman Spektroscopy Jan. 2017 Publisher: Institute of Physical Chemistry 1 Objectives 1. Take the Raman spectra of CO 2 (s), CS 2 (l), C 6 H 6 (l) and

More information

If you like us, please share us on social media. The latest UCD Hyperlibrary newsletter is now complete, check it out.

If you like us, please share us on social media. The latest UCD Hyperlibrary newsletter is now complete, check it out. Sign In Forgot Password Register username username password password Sign In If you like us, please share us on social media. The latest UCD Hyperlibrary newsletter is now complete, check it out. ChemWiki

More information

WEBSITE DATA FOR CHAPTER 6

WEBSITE DATA FOR CHAPTER 6 66 WEBSITE DATA FOR CHAPTER 6 Spectroscopic Identification of Organic Compounds by Infared Spectroscopy I. INTRODUCTION NOTE. It should be pointed out that a reciprocal centimeter is not a unit of frequency.

More information

( )( s 1

( )( s 1 Chemistry 362 Dr Jean M Standard Homework Problem Set 6 Solutions l Calculate the reduced mass in kg for the OH radical The reduced mass for OH is m O m H m O + m H To properly calculate the reduced mass

More information

Tables for Group Theory

Tables for Group Theory Tables for Group Theory By P. W. ATKINS, M. S. CHILD, and C. S. G. PHILLIPS This provides the essential tables (character tables, direct products, descent in symmetry and subgroups) required for those

More information