IR SPECTROSCOPY

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Infrared Spectroscopy

Most Of Us Are Quite Familiar With Infrared Radiation. We Have Seen Infrared Lamps Keep Food Hot And Often Associate Infrared Radiation With Heat. While The Generation Of Heat Is A Probable Event Following The Absorption Of Infrared Radiation, It Is Important To Distinguish Between The Two. Infrared Is A Form Of Radiation That Can Travel Through A Vacuum While Heat Is Associated With The Motion And Kinetic Energy Of Molecules. The Concept Of Heat In A Vacuum Has No Meaning Because Of The Lack Of Molecules And Molecular Motion. Infrared Spectroscopy Is The Study Of How Molecules Absorb Infrared Radiation And Ultimately Convert It To Heat. By Examining How This Occurs, We Will Not Only Learn About How Infrared Radiation Is Absorbed, But We Will Also Learn About Molecular Structure And How The Study Of Infrared Spectroscopy Can Provide Information About The Structure Of Organic Molecules. An Infrared Spectrum Of A Chemical Substance, Is Very Much Like A Photograph Of A Molecule. However, Unlike A Normal Photograph Which Would Reveal The Position Of Nuclei, The Infrared Spectrum Will Only Reveal A Partial Structure. It Is The Purpose Of This Narrative To Provide You With The Tools Necessary To Interpret Infrared Spectra, Successfully. In Some Respects, This Process Is Similar To Reading An X-ray Of The Chest. While Most Of Us Could Easily Identify The Gross Structural Features Of The Chest Such As The Ribs, Most Of Us Would Need Some Guidance In Identifying Those Features On The X-ray Film Associated With Disease.

In Order To Interpret Infrared Spectra, Having Some Idea Or Model Of The Physical Process Involved When A Molecule Interacts With Infrared Radiation Would Be Useful. You May Recall In Introductory Chemistry, The Discussion Of How Atoms Interact With Electromagnetic Radiation Led To The Development Of Quantum Theory And The Introduction Of Quantum Numbers. The Interaction Of Infrared Radiation With Molecules Requires A Similar Treatment. While The Use Of Quantum Theory Is Necessary To Explain This Interaction, Most Of Us Live In A World That Appears Continuous To Us And We Do Not Have Much Experience Discussing Phenomena That Occur In Discrete Steps. The Discussion That Follows Will Attempt To Develop A Model Of How Molecules Interact With Infrared Radiation That Is Based As Much As Possible On Classical Physics. When Necessary, We Will Insert The Modifications Required By Quantum Mechanics. This Model, While Perhaps Oversimplified, Will Contain The Physical Picture That Is Useful To Understand The Phenomena And Will Be Correct From A Quantum Mechanical Standpoint.

Let's Begin First By Considering Two Isolated Atoms, A Hydrogen And A Bromine Atom Moving Toward Each Other From A Great Distance. What Do You Suppose Will Happen Once The Atoms Approach Each Other And Can Feel Each Others Presence? The Potential Energy Curve For The H-Br Molecule Is Shown In Figure 1. As The Two Atoms Approach Each Other Notice That The Potential Energy Drops. If We Recall That Energy Must Be Conserved, What Must Happen To The Kinetic Energy? The Two Atoms Must Attract Each Other And Accelerate Toward Each Other, Thereby Increasing Their Kinetic Energy. The Change In Kinetic Energy Is Illustrated By The Dotted Line In The Figure. At Some Point They Will "collide" As Indicated By The Part Of The Potential Energy Curve That Rises Steeply At Small Interatomic Distances And Then The Atoms Will Begin To Move Away From Each Other. At This Point, We Might Ask, "Will The Molecule Of HBr Survive The Collision"? Unless Some Energy From This System Is Lost, Say By Emission Of A Photon Of Light Or Collision By A Third Body To Remove Some Energy, These Are Two Ships Passing In The Night. The Kinetic Energy Resulting From The Coulombic Attraction Of The Two Atoms Will Exactly Equal The Drop In Potential Energy And The Two Atoms Will

The Potential (solid Line) And Kinetic Energy (dotted Line) Of HBr As A Function Of The Separation Of The Two Nuclei. The Kinetic Energy At Every Point Illustrated By The Dotted Line Is Equal To The Potential Energy Plus The Small Amount Of Kinetic Energy Associated With Initial Motion Of The Two Nuclei When Separated At Large Distances.

The Spontaneous Emission Of A Photon Of Light Is Improbable, So This Mechanism Is Unlikely To Drop The HBr Molecule Into The Well. Most Probable From A Physical Perspective, Is The Collision Of Our HBr With A Third Body Which Will Remove Some Energy And Result In The Trapping Of The HBr Molecule In The Well. Though Very Excited, This Molecule Will Now Survive Until Other Collisions With Less Energetic Molecules Leads To An HBr Molecule At The Bottom Of The Well And The Generation Of Heat (kinetic Energy) That Would Be Experienced In The Exothermic Reaction Of Hydrogen And Bromine Atoms To Form Hydrogen Bromide. Let Us Now Consider A Hydrogen Bromide Molecule That Has Lost A Little Kinetic Energy By Collision And Has Been Trapped In The Potential Energy Well Of Figure 1. We Might Ask, "How Would A Molecule That Does Not Have Enough Kinetic Energy To Escape The Well Behave In This Well? A Molecule With Some Kinetic Energy Below This Threshold Value (total Energy Slightly Less Than 0 In Fig. 1) Will Be Able To Move Within This Well. The Internuclear Separation Will Vary Within The Limits Governed By The Available Kinetic Energy. Since This Motion Involves A Stretching Or Compression Of The Internuclear Distance It Is Usually Described As A Vibration. Additional Collisions With Other Molecules Will Eventually Lead To The Dissipation Of The Energy Associated With Formation Of The Hydrogen Bromide Bond. At This Point We Might Ask The Following Question. If We Remove All The Excess Kinetic Energy From HBr, What Will Be Its Kinetic And Potential Energy? Alternatively We Might Ask, "Will The Hydrogen Bromide Molecule Reside At The Very Bottom Of the Well When It Is Cooled Down To Absolute Zero Kelvin?" Before We Answer This Question, Let's Digress For A Little And Discuss The Relative Motions Of The Hydrogen And Bromine Atoms In Terms Of The Physics Of Everyday Objects. Once We Learn How To Describe The Classical Behavior Of Two Objects Trapped In A Potential Energy Well, We Will Return To The Question We Have Just Posed.

One Model We Can Use To Describe Our Hydrogen Bromide Molecule Is To Consider Our HBr Molecule To Be Made Up Of Balls Of Uneven Mass Connected To Each Other By Means Of A Spring. Physicists Found Many Years Ago Some Interesting Properties Of Such A System Which They Referred To As A Harmonic Oscillator. Such A System Repeatedly Interconverts Potential And Kinetic Energy, Depending On Whether The Spring Is Exerting A Force On The Balls Or The Momentum Of The Balls Is Causing The Spring To Be Stretched Or Compressed. The Potential Energy Of This System (PE) Is Given By The Parabola,

PE = K(x-xo)2 -----------1

where X-x_o Is The Displacement Of The Balls From Their Equilibrium Condition When The System Is At Rest And K Is A Measure Of The Stiffness Of The Spring. While This Simple Equation Does Not Apply To Molecules, Please Notice How Similar The Potential Energy Surface Of The Parabola Is To The Bottom Of The Surface Of. The Constant K Is Used To Describe Chemical Bonds And Is Referred To As The force Constant. As You Might Imagine, It Is A Measure Of The Stiffness Of The Chemical Bond.

Several Other Relationships Were Observed That Do Carry Over In Describing Molecular Systems. For Example, They Found That When A Ball Was Suspended On A Spring From A Horizontal Wall, The Frequency Of Vibration Or Oscillation, n, depended Only On The Mass Of The Ball And The Stiffness Of The Spring. The Term A Is A Constant Of The Proportionality. By Varying The Mass Of The Ball And The Stiffness Of The Spring, They Were Able To Uncover The Following Simple Relationship Between Frequency, Mass And Force Constant:

 ν=A√k/m-----------------2

Suspending A Ball And Spring From A Horizontal Surface Is A Special Case Of The More General Situation When You Have Two More Comparable Masses Attached To Each Other. Under These Circumstances, When Two Similar Masses Are Attached To A Spring, The Relationship Between Frequency Of Vibration, Mass And Force Constant Is Given By:

ν=A√k/μ-----------------3

where m, represents The Product Of The Masses Divided By Their Sum (m1m2)/(m1+m2). This Latter Term Is Found In Other Physical Relationships And Has Been Given The Name, The reduced mass. It Can Easily Be Seen That Equation 2 Is A Special Case Of The More General Relationship Given By Equation 3. If We Consider M1to Be Much Larger Than M2, The Sum Of M1+ M2 m1 and Substituting This Approximation Into (m1m2)/(m1+m2) M2. Substituting M2 into Equation 3 Where M2 Is The Smaller Of The Two Masses Gives Us Exactly The Same Relationship As We Had Above When The Ball Was Suspended From A Horizontal Wall. The Horizontal Wall Is Much More Massive Than The Ball So That The Vibration Of A Smaller Ball Has Very Little Effect On The Wall. Despite Their Simplicity, Equations 2 And 3 Play An Important Role In Explaining The Behavior Of Molecular Systems. However, Before We Discuss The Important Role These Equations Play In Our Understanding Of Infrared Spectroscopy, We Need To Review Some Of The Properties Of Electromagnetic Radiation, Particularly Radiation In The Infrared Range.

On The Extreme Right We Find Radiowaves And Scan From Right To Left We Encounter Terms Which Have Become Familiar To Us; Microwave, Infrared, Visible Ultraviolet And X-rays. All Of These Forms Of Electromagnetic Radiation

 

infrared Spectroscopy, Only The Electric Field Associated With The Electromagnetic Radiation Is Important And We Will Limit Our Present Discussion To How This Field Varies With Time. We Called The Light Wave Associated With A Standing Wave Because This Is How The Electric Field Would

 The Electric Field Of Light Associated With A Standing Wave With A Fixed Wavelength.

vary If We Took A Picture Of The Wave. One Of The Properties Of All Electromagnetic Radiation Is That It Travels In A Vacuum At The Speed Of 3 X 10¹⁰ cm/sec. Therefore, If We Were To Turn This Standing Wave "on" We Would Observe This Oscillating Field Rapidly Passing Us By. If We Examine The Electric Field (or The Magnetic Field Which Is Not Shown), We Observe That The Field Is Repetitive, Varying As A Cos Or Sin Wave. The Length Of The Repeat Unit Along The X Axis Is Called The Wavelength, l, And It Is This Property Which Varies Continuously From 106 Cm (10¹⁰ microns) For Radio Waves Down To 10^-13 Cm (10^-6 microns) For Cosmic Radiation. A Unit Of Length That Is Frequently Used In Infrared Spectroscopy Is The Micron. A Micron Is Equivalent To 10^-4 Cm. If We Were To "stand On The Corner And Watch All The Wavelengths Go By", Since All Electromagnetic Radiation Would Be Traveling At 3 X 10¹⁰ Cm/sec, The Frequency, n, At Which The Shorter Wavelengths Would Have To Pass By Would Have To Increase In Order To Keep Up With The Longer Wavelengths. This Relationship Can Be Described In The Following Mathematical Equation:

ln = C; (c = 3 X 10¹⁰ Cm/sec). ----------- 4

The Frequency Of The Light Times The Wavelength Of The Light Must Equal The Speed At Which The Light Is Traveling.

In Addition To Having Wave Properties Such As The Ones We Have Been Discussing, Electromagnetic Radiation Also Has Properties We Would Normally Attribute To Particles. These "particle Like" Properties Are Often Referred To As Characteristics Of photons. We Can Discuss The Wave Properties Of Photons By Referring To The Wavelength (eqn. 4) And Frequency Associated With A Photon. The Energy Of A Single Photon Is A Measure Of A Property We Would Normally Associate With A Particle. The Relationship Which Determines The Energy Associated With A Single Photon Of Light, E, And The Total Energy Incident On A Surface By Monochromatic Light, ET, Is Given By:

E = H n (or Equivalently, E = H C/ l, from Equation 4), ----------- 5

ET = N H n ------- 6

where H Is Planck's Constant And Is Numerically Equal To 6.6 X 10^-27 Erg S And N Is The Number Of Photons. Equations 4 And 5 Tell Us That Photons With Short Wavelengths, In Addition To Having Higher Frequencies Associated With Them, Also Carry More Punch! The Energy Associated With A Photon Of Light Is Directly Proportional To Its Frequency.

At This Point We Are Ready To Return To A Discussion Of How Infrared Radiation Interacts With Molecules. Following Our Discussion Of Balls And Springs, You Have Probably Figured That Infrared Spectroscopy Deals With The Vibration Of Molecules. Actually, Both Rotation And Vibration Of Molecules Is Involved In The Absorption Of Infrared Radiation, But Since Molecular Rotation Is Not Usually Resolved In Most Infrared Spectra Of Large Organic Molecules, We Will Ignore This Additional Consideration. In Order To Derive The Relationship Between Vibrational Energy And Molecular Structure, It Is Necessary To Solve The Schoedinger Equation For Vibrational-rotational Interactions. Since Solution Of This Equation Is Beyond The Scope Of This Treatment, We Will Simply Use The Relationship That Is Derived For A Harmonic Oscillator From This Equation. As You See, The Quantum Mechanical Solution Of A Harmonic Oscillator, Equation 7, Is Remarkably Simple And Very Similar To The Relationship We Obtained From Considering The Classical Model Of Balls And Springs.

E=h/2π√k/μ (n+1/2)-------- 7

Before Discussing The Implications Of Equation 7, Let's Take A Moment To See How Similar It Is To Equations 3 And 5. From Equation 5, We See That Substituting Equation 3 For n results In Equation 7 Except For The (n + 1/2) Term. However We Should Point Out That We Have Substituted The Vibrational Frequency Of Two Masses On A Spring For A Frequency Associated With The Number Of Wave Maxima (or Minima, Null Points. etc.) Passing A Given Point (or Street Corner) Per Unit Time. We Are Able To Do This Because Of The Presence Of The (n +1/2) Term. Let's Discuss The Significance Of The (n + 1/2) Term Before We Returning To Answer This Question. The Previous Time You Encountered The Schroedinger Equation Was Probably When Studying Atomic Spectra In Introductory Chemistry. An Important Consequence Of This Encounter Was The Introduction Of Quantum Numbers, At That Time The Principle Quantum Number, N, The Azimuthal Quantum Number, l, The Magnetic, Ml, And Spin Quantum Number, s. This Time Is No Exception. Meet n, The Vibrational Quantum Number. These Numbers Arise In A Very Similar Manner. The Schroedinger Equation Is A Differential Equation Which Vanishes Unless Certain Terms In It Have Very Discrete Values. For n, The Allowed Values Are 0,1,2,... Let Us Now Consider The Energy Of Vibration Associated With A Molecule In Its Lowest Energy Of Vibration, N = 0. According To Equation 7, The Energy Of Vibration Is Given By 

E=h/4π√k/μ --------8,

when N = 0, The Zero Point Energy. This Equation Allows Us To Answer The Question Posed Earlier About What Would Happen To The Vibrational Energy Of A Molecule At Absolute Zero. According To Quantum Theory The Molecule Would Continue To Vibrate. From The Relationship E = Hn, we Can Evaluate The Vibrational Frequency As

E=h/2π√k/μ --------9

The Same As Found By Classical Physics For Balls And Springs. This Equation States That The Vibrational Frequency Of A Given Bond In A Molecule Depends Only On The Stiffness Of The Chemical 

3

The Potential Energy Surface For A HBr Molecule Illustrating How The Vibrational Energy Levels Vary In Energy With Increasing Vibrational Quantum Number.

bond And The Masses That Are Attached To That Bond. Similarly, According To Equation 7, Once The Structure Of A Molecule Is Defined, The Force Constants And Reduced Mass Are Also Defined By The Structure. This Also Defines The Vibrational Frequencies And Energy Of Absorption. Stated In A Slightly Different Manner, A Molecule Will Not Absorb Vibrational Energy In A Continuous Fashion But Will Do So Only In Discrete Steps As Determined By The Parameters In Equation 7 And Illustrated For The HBr Molecule In Figure 4. We Have Pointed Out That The Vibrational Quantum Number Can Have Positive Integer Values Including A Value Of Zero. Upon Absorption Of Vibration Energy, This Vibrational Quantum Number Can Change By +1 Unit. At Room Temperature, Most Molecules Are In The N = 0 State.

Equation 7 Predicts That The Energy Level Spacings Should All Be Equal. Notice According To The Spacings Actually Converge To A Continuum For Large Values Of N. For Small Values Of N, N = 0, 1, 2, Equation 7 Gives A Good Approximation Of The Vibrational Energy Levels For HBr. Equation 7 Was Derived From The Approximation That The Potential Energy Surface Is Like A Parabola. Near The Minimum Of This Surface, Around The Zero Point Energy, This Is A Good Approximation. As You Go Up From The Minimum, The Resemblance Decreases And The Assumptions Made In Solving The Schroedinger Equation No Longer Are Valid.

Let Us Now Return And Question The Wisdom Of Substituting The Vibrational Frequency Of A Molecule For The Frequency Of Electromagnetic Radiation In Equation 5. I Hope At This Point Of The Discussion This Does Not Seem So Absurd. If The Vibrational Frequency Of The Molecule, As Determined By The Force Constant And Reduced Mass, Equals The Frequency Of The Electromagnetic Radiation, Then This Substitution Makes Good Sense. In Fact, This Gives Us A Mechanism By Which We Can Envision Why A Molecule Will Absorb Only Distinct Frequencies Of Electromagnetic Radiation. It Is Known That Symmetrical Diatomic Molecules Like Nitrogen, Oxygen And Hydrogen, Do Not Absorb Infrared Radiation, Even Though Their Vibrational Frequencies Are In The Infrared Region. These Homonuclear Diatomic Molecules Have No Permanent Dipole Moment And Lack A Mechanism By Which They Can Interact With The Electric Field Of The Light. Molecules Like HBr And HCl Which Have A Permanent Dipole, Resulting From An Unequal Sharing Of The Bonding Electrons, Have A Dipole Which Oscillates As The Bond Distance Between The Atoms Oscillate. As The Frequency Of The Electric Field Of The Infrared Radiation Approaches The Frequency Of The Oscillating Bond Dipole And The Two Oscillate At The Same Frequency And Phase, The Chemical Bond Can Absorb The Infrared Photon And Increase Its Vibrational Quantum Number By +1. This Is Illustrated In Figure 5. Of Course, Some HBr Molecules May Not Be Correctly Oriented Toward The Light To Interact And These Molecules Will Not Absorb Light. Other Factors Will Also Influence The Intensity And Shape Of The Absorption. However, When The Frequency Of The Electromagnetic Radiation Equals The Vibrational Frequency Of A Molecule, Absorption Of Light Does Occur And This Leads To An Infrared Spectrum That Is Characteristic Of The Structure Of A Molecule.

Up To Now We Have Discussed Molecules Changing Their Vibrational Quantum Number By +1. A Change Of -1 Is Also Equally Possible Under The Influence Of Infrared Radiation. This Would Lead To Emission Of Infrared Radiation. The Reason Why We Have Not Discussed This Possibility Is That Most Molecules At Room Temperature Are In The Ground Vibrational Level (n=0) And Cannot Go Any Lower. If We Could Get A Lot Of Molecules, Let's Say With N = 1, Use Of Infrared Could Be Used To Stimulate Emission. This Is How An Infrared Laser Works.

An HBr Molecule Interacting With Electromagnetic Radiation. In Order For This Interaction To Occur Successfully, The Frequency Of The Light Must Equal The Natural Vibrational Frequency Of The HBr And The Electric Field Must Be Properly Orientated.

We Have Previously Discussed The Infrared Region Of The Electromagnetic Spectrum In Terms Of The Wavelength Of The Light That Is Involved, 2.5-15 m ((4000-650 Cm^-1). According To Equation 4, We Can Also Express This Region Of The Electromagnetic Spectrum In Terms Of The Frequency Of The Light. There Is An Advantage To Discussing The Absorption Of Infrared Radiation In Frequency Units. According To Equation 5, Energy Is Directly Proportional To Frequency. The Energy Associated With An Absorption Occurring At Twice The Frequency Of Another Can Be Said To Require Twice The Energy. Occasionally, Weak Bands Occur At Twice The Frequency Of More Intense Bands. These Are Called overtones and They Result When The Vibrational Quantum Number Changes By +2. While These Transitions Are Weak And Are Theoretically Forbidden (i.e. They Occur With An Intensity Of Less Than 5 % Of The Same Transition That Involves A Change Of +1 In The Vibrational Quantum Number) They Are Easy To Identify When Units Of Frequency Are Used. Sometimes Absorption Bands Involving A Combination Of Frequencies Occur. There Is No Physical Significance To Adding Together Wavelengths - There Is A Physical Significance To The Addition Of Frequencies Since They Are Directly Proportional To Energy. To Convert Wavelength To Frequency According To Equation 4, We Need To Multiply The Speed Of Light By The Reciprocal Of Wavelength. Since The Speed Of Light Is A Universal Constant, The Curious Convention Of Simply Using The Reciprocal Of Wavelength Has Evolved. Thus A Peak At 5 m would Be Expressed As 1/(5x10-4 cm) Or 2000 Cm-1. You Will Note That 2000 Cm-1 is Not A True Frequency. A True Frequency Would Have Units Of Cycles/sec. To Convert 2000 Cm-1 to A True Frequency One Would Need To Multiply By The Speed Of Light (cm/sec). However, 2000 Cm-1 is Proportional To Frequency And This Is How Frequency Units In Infrared Spectroscopy Are Expressed. What Would Be The Frequency Of Light With A Wavelength Of 10 m?

Analysis Of IR Spectra

At This Point We Are Ready To Leave Diatomic Molecules And Start Talking About Complex Organic Molecules. Before Doing So, It Should Be Pointed Out That The Discussion That Follows Is An Oversimplification Of The True Vibrational Behavior Of Molecules. Many Vibrational Motions Of Molecules Are Motions That Involve The Entire Molecule. Analysis Of Such Motions Can Be Very Difficult If You Are Dealing With Substances Of Unknown Structure. Fortunately, The Infrared Spectrum Can Be Divided Into Two Regions, One Called The Functional Group Region And The Other The Fingerprint Region. The Functional Group Region Is Generally Considered To Range From 4000 To Approximately 1500 Cm-1 and All Frequencies Below 1500 Cm-1 are Considered Characteristic Of The Fingerprint Region. The Fingerprint Region Involves Molecular Vibrations, Usually Bending Motions, That Are Characteristic Of The Entire Molecule Or Large Fragments Of The Molecule. Hence The Origin Of The Term. Used Together, Both Regions Are Very Useful For Confirming The Identity Of A Chemical Substance. This Is Generally Accomplished By A Comparison Of The Spectrum Of An Authentic Sample. As You Become More Proficient In Analyzing Infrared Spectra, You May Begin To Assign Bands In This Region. However, If You Are Just Beginning To Interpret Spectra Of Organic Molecules, It Is Best To Focus On Identifying The Characteristic Features In The Functional Group Region. The Functional Group Region Tends To Include Motions, Generally Stretching Vibrations, That Are More Localized And Characteristic Of The Typical Functional Groups Found In Organic Molecules. While These Bands Are Not Very Useful In Confirming Identity, They Do Provide Some Very Useful Information About The Nature Of The Components That Make Up The Molecule. Perhaps Most Importantly, The Frequency Of These Bands Are Reliable And Their Presence Or Absence Can Be Used Confidently By Both The Novice And Expert Interpreter Of Infrared Spectra. The Discussion Which Follows Focuses Primarily On The Functional Group Region Of The Spectrum. Some Functional Groups Are Discussed In More Detail Than Others. You Will Find That All This Information Is Summarized In Table 1 Which Should Prove Useful To You When You Try To Interpret An Unknown Spectrum. Finally, You Should Bear In Mind That Although We Have Developed A Model That Can Help Us Understand The Fundamental Processes Taking Place In Infrared Spectroscopy, Interpretation Of Spectra Is To A Large Extent An Empirical Science. Information About The Nature Of A Compound Can Be Extracted Not Only From The Frequencies That Are Present But Also By Peak Shape And Intensity. It Is Very Difficult To Convey This Information In Table Form. Only By Examining Real Spectra Will You Develop The Expertise To Accurately Interpret The Information Contained Within. Be Sure To Examine The Spectra Contained In This Handout Carefully. Whenever You Interpret A Spectrum And Extract Structural Information, Check Your Assignments By Examining The Spectrum Of A Known Substance That Has Similar Structural Features.

A Summary Of The Principle Infrared Bands And Their Assignments.

R Is An Aliphatic Group.

Factors Influencing The Location And Number Of Peaks

Before Beginning A Detailed Analysis Of The Various Peaks Observed In The Functional Group Region, It Might Be Useful To Mentioned Some Of The Factors That Can Influence The Location And Number Of Peaks We Observe In Infrared Spectroscopy. Theoretically, The Number Of Fundamental Vibrations Or normal Modes available To A Polyatomic Molecule Made Up Of N Atoms Is Given By 3N-5 For A Totally Linear Molecule And 3N-6 For All Others. By A Normal Mode Or Fundamental Vibration, We Mean The Simple Independent Bending Or Stretching Motions Of Two Or More Atoms, Which When Combined With All Of Normal Modes Associated With The Remainder Of The Molecule Will Reproduce The Complex Vibrational Dynamics Associated With The Real Molecules. Normal Modes Are Determined By A Normal Coordinate Analysis (which Will Not Be Discussed In This Presentation). If Each Of These Fundamental Vibrations Were To Be Observed, We Would Expect Either 3N-5 Or 3N-6 Infrared Bands. There Are Some Factors Which Decrease The Number Of Bands Observed And Others That Cause An Increase In This Number. Let's Discuss The Latter First.

We Have Already Mentioned overtones, Which Are Absorption Of Energy Caused By A Change Of 2 Rather Than 1 In The Vibrational Quantum Number. While Overtones Are Usually Forbidden Transitions And Therefore Are Weakly Absorbing, They Do Give Rise To More Bands Than Expected. Overtones Are Easily Identified By The Presence Of A Strongly Absorbing Fundamental Transition At Slightly More Than Half The Frequency Of The Overtone. On Occasion, combination Bands are Also Observed In The Infrared. These Bands, As Their Name Implies, Are Absorption Bands Observed At Frequencies Such As ₁ + ₂ or ₁ - ₂, Where ₁ and ₂ refer To Fundamental Frequencies. Other Combinations Of Frequencies Are Possible. The Symmetry Properties Of The Fundamentals Play A Role In Determining Which Combinations Are Observed. Fortunately, Combination Bands Are Seldom Observed In The Functional Group Region Of Most Polyatomic Molecules And The Presence Of These Bands Seldom Cause A Problem In Identification. Another Cause Of Splitting Of Bands In Infrared Is Due To A Phenomena Called Fermi Resonance. While A Discussion Of Fermi Resonance Is Beyond The Scope Of This Presentation, This Splitting Can Be Observed Whenever Two Fundamental Motions Or A Fundamental And Combination Band Have Nearly The Same Energy (i.e. ₁ and 2₂ or ₁ and ₂ + ₃). In This Case, The Two Levels Split Each Other. One Level Increases While The Other Decreases In Energy. In Order To Observe Fermi Resonance, In Addition To The Requirement That A Near Coincidence Of Energy Levels Occurs, Other Symmetry Properties Of These Vibrations Must Also Be Satisfied. As A Consequence, Fermi Resonance Bands Are Not Frequently Encountered.

There Are Also Several Factors Which Decrease The Number Of Infrared Bands Observed. Symmetry Is One Of The Factors That Can Significantly Reduce The Number Of Bands Observed In The Infrared. If Stretching A Bond Does Not Cause A Change In The Dipole Moment, The Vibration Will Not Be Able To Interact With The Infrared Radiation And The Vibration Will Be Infrared Inactive. Other Factors Include The Near Coincidence Of Peaks That Are Not Resolved By The Spectrometer And The Fact That Only A Portion Of The Infrared Spectrum Is Usually Accessed By Most Commercial Infrared Spectrometers.

This Concludes The General Discussion Of Infrared Spectroscopy. At This Point We Are Ready To Start Discussing Some Real Spectra.

Carbon-Hydrogen Stretching Frequencies

Let's Take One More Look At Equation 7 And Consider The Carbon-hydrogen Stretching Frequencies. Since K And MH Are The Only Two Variables In This Equation, If We Assume That All C-H

stretching Force Constants Are Similar In Magnitude, We Would Expect The Stretching Frequencies Of All C-H Bonds To Be Similar. This Expectation Is Based On The Fact That The Mass Of A Carbon Atom And Whatever Else Is Attached To The Carbon Is Much Larger The Mass Of A Hydrogen. The Reduced Mass For Vibration Of A Hydrogen Atom Would Be Approximately The Mass Of The Hydrogen Atom Which Is Independent Of Structure. All C-H Stretching Frequencies Are Observed At Approximately 3000 Cm-1, Exactly As Expected. Fortunately, Force Constants Do Vary Some With Structure In A Fairly Predictable Manner And Therefor It Is Possible To Differentiate Between Different Types Of C-H Bonds. You May Recall In Your Study Of Organic Chemistry, That The C-H Bond Strength Increased As The S Character Of The C-H Bond Increased. Some Typical Values Are Given Below In Table 2 For Various Hydridization States Of Carbon. Bond Strength And Bond Stiffness Measure Different Properties. Bond Strength Measures The Depth Of The Potential Energy Well Associated With A C-H. Bond Stiffness Is A Measure Of How Much Energy It Takes To Compress Or Stretch A Bond. While These Are Different Properties, The Stiffer Bond Is Usually Associated With A Deeper Potential Energy Surface. You Will Note In Table 2 That Increasing The Bond Strength Also Increases The C-H Bond Stretching Frequency.

Carbon Hydrogen Bond Strengths As A Function Of Hybridization

Type Of C-H Bond Bond Strength IR Frequency

kcal/mol Cm-1

sp3 hybridized C-H	CH3CH2CH2-H	99	<3000
sp2 hybridized C-H	CH2=CH-H	108	>3000
sp Hybridized C-H	HCC-H	128	3300

 

The Effect Of Ring Strain On The Carbonyl Frequencies Of Some Cyclic Molecules

Ring Size	ketone: Cm-1	lactones: Cm-1	lactams: Cm-1
3	cyclopropanone: 1800
4	cyclobutanone: 1775	b-propiolactone: 1840
5	cyclopentanone: 1751	g-butyrolactone: 1750	g-butyrolactam: 1690
6	cyclohexanone: 1715	d-valerolactone: 1740	d-valerolactam: 1668
7	cycloheptanone: 1702	e-caprolactone: 1730	e-caprolactam: 1658

 

The Effect Of Conjugation On Carbonyl Frequencies.

Non-conjugated Compound	Frequency cm-1	Conjugated Compound	Frequency cm-1		Frequency cm-1
butanal	1725	2-butenal	1691	benzaldehyde	1702
2-butanone	1717	methyl Vinyl Ketone	1700, 1681	acetophenone	1685
propanoic Acid	1715	propenoic Acid	1702	benzoic Acid	1688
ethyl Propionate	1740	ethyl Acrylate	1727	ethyl Benzoate	1718
butanoic Anhydride	1819, 1750	2-butenoic anhydride	1782, 1722	benzoic anhydride	1786, 1726
cis-cyclohexane-1,2- dicarboxylic anhydride	1857, 1786	1-cyclohexene-1,2- dicarboxylic anhydride	1844, 1767	phthalic anhydride	1852, 1762

 

 

 

 

 

 

 

 

 

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