Introduction to Spectroscopy Flashcards
1
Q
What is spectroscopy?
A
The interaction of electromagnetic radiation and matter concerned with the absorption, emission and scattering of electromagnetic radiation by molecules
2
Q
What can spectroscopy give us information about?
A
Chemical structure
Chemical composition
Kinetics and mechanisms
3
Q
What is electromagnetic radiation?
A
Comprises a combination of oscillating electric and magnetic fields which are in phase with each other
4
Q
What does fields being in phase with each other mean?
A
Oscillating at the same time
5
Q
What is the propagating of light? (to do with energy)
A
A process by which an electromagnetic wave transfers energy between points
6
Q
What does the model of electromagnetic radiation show?
A
Magnetic field goes up and electric field goes sideways
7
Q
What is frequency?
A
Number of oscillations per second (Hz/s^-1)
8
Q
What is wavelength?
A
Distance between two identical peaks in a wave (nm)
9
Q
What do we use to describe light?
A
Waves
10
Q
What does the amplitude affect in light?
A
Higher amplitude = brighter
Lower amplitude = dimmer
11
Q
What else do you increase when you increase frequency of your wave?
A
The energy of your wave
12
Q
How can you plot a wave?
A
Using a sine function as it is periodic with 2π
13
Q
What does the electromagnetic spectrum show?
A
Wavelength, frequency and temperature are all connected with frequency and wavelength being inversely proportional
14
Q
When does classical physics work?
A
For large objects however doesn’t work when describing nature of small objects (atoms)
15
Q
What is the proof of wave properties of light?
A
Young’s double slit experiment (laser fired at optical plate)
- Expectation - two spots on the optical plate behind the slits
- Reality - interference of light producing dark and light spots on the plate (similar patterns to water waves)
Demonstrates wave particle duality
16
Q
What is a challenge to classical physics?
A
Black body radiation
A famous formula (Rayleigh Jeans Law) derived from classical physics is a good approx at high wavelength but completely fails at low wavelength (to do with intensity)
It predicts a continuous increase in frequency which is not observed experimentally
17
Q
How was the problem surrounding black body radiation solved?
A
By discovering the energy quanta
- Max Planck suggested that energy is quantised
Including quantisation in law made for a much much better approximation
18
Q
What is a black body?
A
Can absorb (and emit) all frequencies - perfect absorber
Emits radiation in a continuous spectrum with a maximum that changes with temperature
At room temp - max is in infrared so appears black
At high temp - max is in UV/vis range
19
Q
What is quantum?
A
The smallest possible, and therefore indivisible, units of a given quantity
20
Q
What energies can a particle take in quantum theory?
A
Only certain quantised energy levels
- Not permitted to have an energy that is not one of these levels
Extremely useful in spectroscopy
21
Q
What is the main thing we are interested in for spectroscopy?
A
Transitions between energy levels
22
Q
What is the evidence behind energy quanta?
A
Black body radiation
23
Q
What evidence does the photoelectric effect show?
A
A photon is a particle packet of radiation with energy hv
24
Q
What is the SI unit for energy?
A
Joule/J (kgm^2s^-2)
25
How else can energy be expressed?
As wavenumbers
26
What is an electron volt?
The energy carried by one electron
27
How do you convert energy in joules to energy in wavenumber?
E(cm^-1)=E(J)/hc
28
How do you convert wavelength to energy in wavenumber?
E(cm^-1)=10^7/λ(nm)
29
How do you convert wavelength to energy in electron volts?
E(eV) = 1240/λ(nm)
30
What are the types of molecular energy and what energy is related to each one?
Translational - <10cm^-1
Rotational - <1-100cm^-1
Vibrational - 100-4000cm^-1
Electronic - 10^4-10^5cm^-1
31
What is electronic energy to do with?
What is special about translational energy?
Electronic energy is to do with electrons changing states
Translational energy has no discrete energy levels so is not quantised
32
When does a transition occur?
When electromagnetic radiation is fired at a molecule
33
What do absorption and emission look like in energy levels?
Absorption is increase in energy level when it takes in radiation
Emission is decrease in energy level and releases radiation
34
When can emission occur?
Higher energy level must be more populated for it to happen
Cannot happen to an electron in the ground state
35
What do atomic and molecular spectra give us?
Evidence for quantisation as discrete lines on the spectrum
36
When can a transition occur?
For a transition to occur the frequency of radiation must match exactly with the space between the two levels
37
Can you have a mixture of transitions?
Yes as each vibrational level has lots of rotational levels within it and so on
38
What type of radiation does each spectroscopy need?
Rotational spec needs microwave
Vibrational spec needs infrared
Electronic spec needs ir/visible/UV
39
What determines the peaks on a spectrum?
Transitions between levels
40
What are larger peaks to do with in spectroscopy?
To do with intensity
- involves transitions between further away energy levels
41
What does intensity of spectral peaks depend on?
Transition probabilities (dipoles)
The amount of sample (concentration)
Population of initial energy state
- Higher the population of the initial state the more intense the transition
42
How can you calculate absorbance?
A = εcl = -log(I/I₀)
where ε = molar absorption coefficient, c = conc of sample, l = path length
I = intensity
I₀ = initial intensity
43
What are the units for the molar absorption coefficient?
What are the units for path length?
M^-1cm^-1
cm
44
What does the molar absorption coefficient describe?
Transition probabilities
45
How do you calculate transmittance?
T = I/I₀
46
What is the relationship between absorbance and transmittance?
Higher absorbance = Lower transmittance
However not a linear relationship
47
How do you use an absorption spectrometer to measure absorbance?
Measure intensity with and without sample
48
What are the two parameters involved in emission spectrometry?
Wavelength of excited light
Wavelength of emitted light
49
Are molecules normally in their ground state?
No unless temperature = 0K
50
Why are molecules not normally in their ground state?
Continuous thermal agitation that molecules experience at any temperature above 0K ensures they are distributed over all possible energy levels so they can interact and exchange energy
51
What is the population of a state?
Average number of molecules in a state at any given time
52
What is the key observation surrounding population of states?
States of unequal energy are unequally populated
- there is always a higher population in a lower energy state
- high temp promotes population to higher states
53
What is the formula for Boltzmann distribution and what does it do?
Ni/Nj = e^(ΔE/kt)
where Ni is pop of upper level
and ΔE = Ei-Ej
It provides an estimate of relative populations
54
What does the Boltzmann distribution tell us if T is small or T is large?
T is small it tends to zero so most molecules are in ground state
T is large it tends to one means almost equal number in each state
- Not technically possible to have = 1
55
How does the population of the initial state affect the transition?
Higher the population of initial state the more intense the transition
So the more sensitive the technique will become
56
What else affects populations apart from temperature?
Degeneracy
- Increasing it increases no of permutations for a molecule to be in that level so increases population
57
What is a degenerate state?
An equivalent state of the same energy
- serves to increase the number of states allowing differing populations at each level
58
What does NMR give details about?
Structure
Purity
Interaction
Mechanism and reaction rates
59
What does NMR take advantage of?
Takes advantage of the 'nuclear spin' of certain nuclei
60
What is the nuclear spin?
The total angular momentum of the nucleus (I)
It is quantised so only certain spin states and transitions will be permitted
61
What does nuclear spin have?
A nuclear magnetic moment which produces magnetic interactions with the surroundings
62
What does NMR record?
NMR records the absorption of energy between these quantised nuclear energy levels
63
When is a nuclei NMR 'active'?
Only nuclei with spin
Nuclei with an even number of protons and an even number of neutrons do not have spin
64
What nuclear spin will we be studying?
Only I = 1/2 as easy to work with
65
What can we predict in nuclear spin?
Whether there is spin zero, integer or half integer but not actual values
66
What partnerships of protons and neutrons give half integer spin?
Odd protons - Even neutrons
Even protons - Odd neutrons
So therefore only nuclei with an odd number of nucleons we are studying as NMR 'active'
67
What happens if there is no external field or an applied magnetic field to nuclear spin of 1/2?
No external field - spins randomly orientated and therefore degenerate
Applied magnetic field - states no longer degenerate and can align with or against the field
68
If spins are quantised what else is also quantised?
Magnetic moment (m)
69
How many orientations of m are there?
2I+1
Therefore for spin 1/2 nuclei there is two possible orientations
70
What does two possible orientations of the magnetic moment mean?
There is two possible values of mI (magnetic quantum number) - basically means two possible spins ±1/2
71
What is resonance frequency?
Difference in energy which is generated from application of magnetic field
ν=ɣB₀/2π
ν - resonance frequency
ɣ - gyromagnetic frequency (magnetogyric frequency)
B₀ - applied magnetic field strength
72
What happens when we place an NMR sample in a strong applied field?
The spin states of NMR active nuclei are no longer degenerate as they align with or against the applied field
73
What does the spin states in NMR no longer being degenerate create?
Two different states of possible energy, a lower one ɑ (where the spin is aligned) and the higher one β
74
What do we measure in NMR?
The difference in energy between the two spin states
75
What is gyromagnetic frequency?
An intrinsic property of magnetic nucleus
76
What must an NMR experiment be?
Timed based on the isotope and a different spectrum being produced for each NMR active nucleus of interest
77
What does the Boltzmann distribution relate and correspond to?
Relates the relative proportion of the ground and excited states
Corresponds to the probability of a transition occurring
78
What will the energy of the transition be in NMR?
Very small as NMR lies in the radio wave frequency section
79
What does abundancy refer to?
The % of NMR active nuclei present in the sample
80
What does the abundancy impact?
The amount of sample influences the amount of electromagnetic radiation absorbed and hence the intensity of the absorbance
81
What does higher abundance mean?
Easier to measure accurately
So 1H with 99.98% abundance is easier to measure accurately than 13C with 1.11% abundance
82
How are NMR spectra generated?
Short bursts of radio-frequency brings all nuclei into resonance
Successive pulses are applied to a sample (excitation-relaxation cycle)
This intensifies the overall signal with respect to noise (signal to noise ratio) - crucial for nuclei with low abundance
The raw data (Free Induction Domain (FID)) undergoes a Fourier transform
This separates absorptions according to their frequency (energy)
Therefore generating the spectrum
83
What can we do considering ΔE is so small?
Do our measurements several times rather than once
84
What does the pulse of electromagnetic radiation do?
Changes the spin state of the nucleus
85
What do NMR spectrometers allow for?
The sample to constantly spin so observations are equal as surrounded by a magnetic field
86
What does the resonance frequency of the NMR absorptions of a given nucleus depend on?
The chemical environment of the bond
87
How do you calculate a change in energy in NMR?
ΔE = hɣB₀/2π
B₀ is applied magnetic field
ɣ is gyromagnetic frequency
88
How many signals do you expect in a NMR system?
Each NMR active nucleus in a chemically distinct position in a molecule gives rise to a different signal on the spectrum
89
What can nuclei be in NMR?
Chemically equivalent or inequivalent
90
What does chemical equivalent mean and what does identifying it allow you to do?
Chemically equivalent if in same environment so produces one peak on the spectrum
Allows you to predict number of singals
91
What is chemical equivalence directly related to?
Structure and symmetry
92
What is chemical shift?
The variation of resonance frequency with respect to chemical environment?
93
How can you calculate observed frequency?
ν(obs) = ɣBeff/2π
where Beff is the effective magnetic field
94
What is the difference between applied and effective magnetic field?
Applied magnetic field - one we are applying
Effective magnetic field - one a specific chemical environment is experiencing
95
What is the shielding constant (σ) and what is it used for?
The ability of surrounding electrons to alter applied magnetic field
Beff = B₀(1-σ)
96
Why is effective magnetic field smaller than applied magnetic field?
How does the electon density around a nucleus affect the shielding of the nucleus?
Due to electrons around the nucleus
High electron density around nucleus - more shielding - shielded nucleus
Low electron density around nucleus - less shielding - deshielded nucleus
97
What can we use to predict shielding/deshielding?
Electronegativity values and molecular structure
98
What does the direction of the magnetic field cause?
Causes electrons to circulate which induces another magnetic field
Direction of magnetic field means any atom that is found on the outside of the molecule is going to be experiencing a larger magnetic field as two are added together
More deshielded
99
What is magnetic anisotropy?
Electrons in pi systems interact with magnetic field which induces a magnetic field and causes anisotropy
Protons can be strongly shielded or deshielded around pi systems based on position
Effect applies to any nuclei near a pi bond and is magnified by conjugation
100
How do we report chemical shift?
If we reported it as v(obs) it would depend on the machine used which isn't useful
Hence it is reported in ppm
δ(ppm) = v(obs)/v(spec) *10^6
101
How do you calculate observed frequency from other frequencies and what is v(spec)?
v(obs) = v(sample) - v(ref)
v(spec) = spectrometer operating frequency
102
How do shielding and chemical shift relate to each other?
Deshielded -
Less shielding = higher freq/energy/Beff = larger chemical shift
Shielded -
More shielding = lower freq/energy/Beff = smaller chemical shift
103
What happens to the reference chemical in NMR?
it gets set to zero so reported ppm is true for everyone
104
How does equivalency and shielding relate?
Less equivalent protons means more deshielded
- due to electronegative elements as it withdraws electron density away from protons
105
What does the area of each NMR absorption tell you?
The integration tells us the relative number of nuclei responsible for that peak in the spectrum
106
What NMR spectrums can we integrate?
1H,19F,31P but not 13C
107
What NMR active nuclei couple with each other?
NMR active nuclei that are chemically inequivalent - coupling gives evidence of chemical bonding
108
Where does the splitting of peaks come from?
Neighbouring nuclei interact and influence the effective magnetic field experienced at each nucleus as well as electron spins
109
Where can you experience spin-spin coupling?
Through chemical bonds
- Can be experienced by nuclei up to 3 bonds apart and more if there is conjugation
110
What are the other names for spin-spin coupling?
J coupling
Scalar coupling
111
In a AX system, for the nucleus A how many possible spin states are there and what does this mean?
Two possible spin states: Aɑ and Aβ
Means the nucleus will therefore resonate at two slightly different frequencies
- Due to different Beff
- If X has a magnetic moment aligned with B₀: Increase in Beff
112
What is true about the difference in energy between spin states?
Very small so both frequencies have basically the same probability - populations very similar
113
What is the selection rule for NMR transitions?
Δml = ±1
Meaning only one transition can occur at a time in a bond with two atoms - changing nuclear spin
114
What is an example of what the selection rule for NMR transitions does?
AɑXɑ can go to AɑXβ but not AβXβ
115
What can happen when scalar coupling occurs to do with nuclear spins?
Antiparallel nuclear spins - e.g. AɑXβ - stabilise so decrease in energy
Paralel nuclear spins - e.g. AɑXɑ - destabilise so increase in energy
116
What does the fact of parallel/antiparallel spins mean?
That transitions have different ΔE which results in splitting of peaks
117
What happens if two transitions are equally/not equally spaced?
If two transitions are equally spaced then they do not split peaks
If two transitions are not equally spaced then they do split peaks
118
What is the coupling constant?
The distance between lines on your split peak is described by it (J) in Hz
119
What is the relationship between nuclei that couple and value of J?
Nuclei which couple have the same J
120
How do you label coupling constants?
1J - nuclei are one bond apart
2J - nuclei are two bonds apart
3J - nuclei are three bonds apart
3J(F,H) - nuclei that are three bonds apart when it is 19F spectrum and is coupling to H
121
What can coupling constants that are the same across spectrums to help with?
Chemical bonding
122
Where is chemical shift taken from?
The middle of the split peak
123
What is the formula for the number of lines (peak multiplicity)?
No of lines = 2nI + 1
where n = coupling nuclei and I = spin quantum numbers
124
How do you calculate J?
J = Δδ * v(spec) (Hz)
125
When calculating J what needs to be remembered?
v(spec) is used in MHz to make J in Hz
126
What does the magnitude of coupling constant depend on?
- Number of bonds separating nuclei
- In general 1J>2J>3J but not always true
- The respective gyromagnetic ratios (often heavier nuclei couple more slowly)
127
What happens when there are two different chemical environment bonds that couple?
Nuclei can couple with more than one environment
We do the largest one first and then continue with the lower ones?
128
How do you get more complex splitting patterns?
e.g. on PF2H in 19F NMR:
- one environment of F
Coupling with P causes a doublet
Coupling with H causes a doublet
So end up with doublet of doublets
129
How do you name complex splitting patterns?
If three lots of two its called triplet of doublets
130
What are the coupling constants in complex splitting patterns?
There are two J values
- One is for the spectra element to the first element 1J
- Second is for the spectra element to the second element 2J
131
What are NMR samples prepared in and why?
Prepared in deuterated solvents
- They do not show peaks on the spectrum
- It avoids the presence of additional hydrogens
132
What are deuterated solvents?
When H has been replaced by D (1H to 2H)
133
What is true about hydrogens on heteroatoms in NMR?
Hydrogens in alcohols, amines, amides, thiols and carboxylic acids are exchangeable and experience hydrogen bonding
134
What happens when an atom is involved in hydrogen bonding in NMR?
It can experience large variations in their chemical shift (deshielding)
135
What do signals of hydrogens in heteroatoms look like?
Often broad and don't evidence J coupling - makes them singlets
136
Why is there large variations in chemical shift with atoms involved in hydrogen bonding?
The bonds are dynamic and the exchange is faster than the time it takes to acquire a 1H NMR spectrum
137
For each exchange in hydrogen bonding what is there an equal chance of?
The new proton having a ±1/2 spin so have a zero spin average
138
What does the zero spin average of hydrogen bonded H do?
Means the environment next to it experiences essentially no spin so no J coupling
139
What is the D2O test?
Add D2O and run the spectrum again - complete disappearance of signals due to exchangeable protons due to H/D exchange
Requires acidic conditions
140
What is important to know about carboxylic acid peaks in NMR?
Hard to see it
If you feel like it is there you can 'go and find it' by integrating the baseline around where you are expecting it
You can also use a hydrogen bond acceptor (e.g. DMSO) as your solvent which produces a visible peak
141
What must you do when assigning an NMR spectrum?
Assign all the peaks even those from impurities
142
Why don't we consider coupling with 13C in 1H or 19F NMR?
The percentage abundance is too low
Coupling will happen but will only represent 1% of the signal so is not observed
143
Why don't we consider coupling in 13C spectrums?
It will be there however J coupling with 1H is surpassed in standard 13C NMR experiments (proton decoupled)
Pulses used are designed to suppress it so avoids the splitting of signals
144
What is the way of reporting NMR?
NMR type (conditions): Chemical shift (multiplicity, coupling constant, Number of H, Assigned hydrogen) ....
e.g. 1H NMR (CDCl3, 400MHz): δ8.54 (d, J=0.21Hz, 1H, H⁴ ....
145
What radiation do molecular rotations occur at?
Microwave radiations
146
What is the simplest (approximate) way to describe a rotating diatomic molecule?
Two atoms of mass m1 and m2 separated by a constant distance r₀ rotating in space
The rigid rotor
147
How do you find the centre of mass for a linear molecule?
r⃗(cm) = 1/m(total) ∑mir⃗i
148
If there is more than one axis of rotation where do they all pass through?
The centre of mass
149
For a diatomic molecule with CoM at the origin of the reference frame what is true?
m1r1 = m2r2
CoM is closer to heavier atom
150
What does the general Hamiltonian for the motion of two atoms in space depend on?
3 coordinates of each atom so very complicated
151
How can you simplify the Hamiltonian for a rotating diatomic?
The rotational energy around the CoM does not depend on where the CoM actually is - energy stays the same
For an isolated molecule the potential term V depends on the interatomic distance but not on position of CoM
152
What happens when you simplify the Hamiltonian of a rotational diatomic?
You now only have to deal with the coordinates of the centre of mass and not each atom
153
What does the interesting term of the Hamiltonian for a rotating diatomic depend on?
The reduced mass of the system
154
What two parts of the Hamiltonian are not considered further?
Potential energy as it is a constant term
Translational kinetic energy as it changes the total energy by a fixed amount which doesn't change the spectrum
155
How can you change the system coordinates of a rotating diatomic?
Placing the origin of the frame at the position of CoM the position of the rotor can now be described by two angles θ and φ - Therefore wavefunction depends on these two variables only
156
What is the simplified Hamiltonian for rotations?
Ĥ(rot) = -ħ^2/2μr₀^2 * Λ^2
where μ and r₀ are specific for the molecule being considered
157
What do the solutions to the Schrödinger equation for rotations go by?
Spherical harmonics
158
What QNs do the solutions to the Schrödinger for rotations depend on?
J and MJ - analogous to l and ml in atomic orbitals
J = 0,1,2,...
MJ = 0, ±1, ±2, ....
159
Are the solutions to the Schrödinger of rotations real or complex?
The part that depends on φ is complex except for when MJ = 0
The part that depends on θ is real trig functions
160
How can we turn spherical harmonics into real form?
Sums and differences of wavefunctions with the same J are also valid solutions
By combining wavefunctions with same J and MJ and using Euler's formula we get real wavefunctions to plot
161
What are the different ways to plot the same wavefunction?
We can plot it on the surface of a sphere or we can plot the distance to the origin representing value of the wavefunction
e.g. end up with something that looks like a p orbital
162
How do you calculate rotational energy levels?
E = ħ^2/2μr₀^2 * J(J+1)
163
What QN does energy depend on for rotations?
J but not MJ
164
What are key things that we know about rotational energy levels?
The energy spacing ΔE between energy levels increases with J
The number of degenerate states of each energy level is 2J+1 - corresponds to MJ
165
What is the prerequisite for rotational spectroscopy?
The molecule must have a permanent dipole moment
If does have this then it is microwave active
166
How do you describe the rotation of a polar diatomic?
A polar rotating molecule appears to possess a fluctuating dipole (as dipole rotates)
- produces an oscillating electromagnetic field
- as molecule rotates so does the direction of the dipole
167
What is the interaction of a polar molecule with the EM wave?
If not aligned the molecule will want to rotate
Electric field of an EM wave exerts a torque on an electric dipole
168
What is the transition dipole moment for rotations?
Defines the probability of transition
In a rigid rotor the interatomic distance is fixed meaning the magnitude of μ⃗ is also fixed
If a molecule has no dipole moment the transition dipole moment is zero and no rotational transitions are observed
169
How do you work out if a molecule has a dipole?
Consider dipole as a vector sum and use symmetry and vector sums
170
What is a key idea about molecular dipoles to do with asymmetric vibrations?
If asymmetric vibrations occur then a molecule that didn't have an overall molecular dipole can have one
171
What is the moment of inertia?
I = Σmi*ri^2
where ri is shortest distance from rotating axis
- Analogue of mass
- Analogue in rotational dynamics of mass in linear dynamics
172
What happens with increased moment of inertia?
Increased moment of inertia = harder to rotate
173
How many moments of inertia can a molecule have?
Up to 3 moments of inertia along 3 different rotational axes
174
What does the moment of inertia depend on?
The rotational axis - if mass is concentrated around axis it is easier to rotate and r is smaller - so is moment of inertia
175
What does the rotational classification of molecules depend on?
Shape
____ rotor
Changes solutions to Schrödinger every time
176
What are the rotors that have only one moment of inertia?
Linear rotor - Ia = Ib, Ic = 0
e.g. HCl, CO2
Spherical rotor - Ia = Ib = Ic
e.g. CH4 - no dipole moment but could still have spectrum
177
What are the rotors that have two moments of inertia?
Symmetric rotor - Ia = Ib ≠ Ic, Ic ≠ 0
e.g. Benzene
Can be oblate or prolate
178
What is the difference between oblate or prolate symmetric rotors?
Oblate - 'frisbee'
Ia/Ib < Ic
As distances r are less for A and B
Prolate - 'rugby ball'
Ia/Ib > Ic
As distances r are more for A and B
179
What are the rotors with 3 moments of inertia?
Asymmetric rotor - Ia ≠ Ib ≠ Ic
e.g. H2)
180
Why is the shape of a rotor important?
Solutions to Schrödinger are different for each type
Shapes sometimes determines whether a permanent dipole can be present
181
How do you find moment of inertia for a rigid diatomic?
Find CoM
Use distances from centre of mass to determine moment of inertia
I = m1r1^2 + m2r2^2
182
What can we use instead of CoM for rigid diatomics?
How do you use this to calculate I?
Reduced mass as isn't always easy to determine CoM
I = μr₀^2
where r₀ is distance between atoms
183
What units are used in chemistry for mass?
Atomic mass units (AMU) = Daltons
1 AMU = 1.6605x10^-27 kg
However need to be in kg before doing calculations
184
Where do the integer values of the QN J come from?
Quantised energy levels
185
How do you calculate εJ (cm^-1) for rotational energies of a rigid rotor?
BJ(J+1) where B = h/8π^2Ic and is the rotational constant
186
What are the allowed rotational energy levels for rigid diatomic?
Not equally spaced - faster more rigorous rotation means higher value of J
When J = 0 there is no rotation
εJ values: 0, 2B, 6B, 12B, 20B, 30B etc
187
What do heavier atoms and larger moments of inertia give to do with energy levels?
Closer spaced energy levels
188
What are the selection rules for rotational spec?
1. Molecule must have a permanent dipole - μ≠0
2. Rotational energy can only change by ΔJ = ±1
189
What does the sign of the integrand of transition dipole moments give you in 1D?
If integral is odd, μ=0
If integral is even, μ≠0 in general
If neither odd or even you cannot tell
Even means area under is not zero
190
What type of function is dipole moment?
An odd function
191
What does multiplying by μ convert between for the product of functions?
Converts between odd and even functions
192
Where does the selection rule of ΔJ=±1 come from?
Allowed transitions can only occur between wavefunctions with different symmetry which occur when ΔJ=±1
193
In 3D when are functions symmetric with reference to origin?
When J values are even
194
What does the absorption spectrum for rotational spec look like?
Series of equally spaced lines where the difference between lines is 2B
- As you want ΔεJ = εJ+1- εJ
195
What is the difference between Δε and ε in terms of what they represent?
Δε is the peaks on the spectrum
ε is energy of a certain level
196
What are the different ways to find B in rotational spec?
Either find Δε from spectrum as wavenumbers at certain point - then use 2B(J+1) to find B
Or find distance between two peaks which is equal to 2B
197
What is the intensity of spectral lines determined by in rotational spectroscopy?
Probability of transitions - same for all J so doesn't change anything
Number of molecules at εJ - use Boltzmann distribution
198
How does J affect molecular populations and degenerate levels?
Molecular populations decrease with J but number of degenerate levels increases with J
- So degeneration has a large effect on relative populations
199
What is the final expression for population in rotational levels?
NJ/N0 = (2J+1)e^(-εJ/kT * hc)
Means a non zero energy level has max population
200
What does the function for population of rotational levels have?
A maximum at sqrt(kT/2hcB) - 1/2
However we may not get integer value for Jmax so need to evaluate NJ for two closest integer values to decide if need to round up or down
201
What is the effect of isotopic substitution on microwave spectra?
Change in mass = Change in μ = Change in I = Change in B
202
How does the value of B change for a heavier isotope?
What is the ratio between B and B' equal to?
B is smaller for a heavier isotope
B/B' = I'/I = μ'/μ
203
What happens to energy levels with a heavier isotope?
Decreases all energy levels and reduces ΔεJ
However still equally spaced
204
What does every rotational spectrum show?
Shows the peaks due to isotopes just much smaller peaks
205
What is the problem with a rigid rotor?
Real bonds distort and B is not constant all the time as the bond length is changing
206
What actually happens when a molecule rotates?
Centrifugal force acts on masses
Fcent = mω^2r where ω = angular velocity
Force and distortion is stronger for faster rotations (larger J)
207
If the bond is elastic what do we need to consider?
Hookes law
F = -k(r-re)
where k includes the vibration frequency
The weaker the bond the smaller value of k and the more easily it will distort
208
How do you calculate the energy levels for a non rigid rotor?
Need to include a non rigid rotor correction
εJ = Ej/hc = BJ(J+1) - DJ^2(J+1)^2
where D is the centrifugal distortion constant
209
How do you convert E to ε?
Divide by hc
210
What happens to the correction at higher J?
Correction increases
211
If you are not given D for a non rigid rotor what must you do?
Only look at first few values of J as D term doesn't effect energy as much
212
What does the non rigid rotor cause on the spectrum?
Causes the absorptions to converge
So separation is no longer constant
213
How do we find the rotational spectra of polyatomics?
If not even you cannot use reduced mass so need to find moment of inertia fully
214
Where do vibrational transitions occur?
In the infrared
Wavelength ≈ 1-300μm
Frequency ≈ 10^13 - 10^14 Hz
215
How do you always find E and Ψ?
Set up the Hamiltonian and solve the equation
216
What is the simplest molecular vibration?
That of a diatomic
217
What is the difference in the starting points of the Hamiltonian for rotations and vibrations?
Vibration Hamiltonian has interatomic distance that is allowed to change
218
What is true about the Hamiltonian in rotations and vibrations?
Both need to remove the CoM motion as is not important
219
Which parts of the original Hamiltonian are important for vibrations?
The KE due to change in orientation in r⃗ (rotational energy) and due to change in length of r⃗ (vibrational energy)
Also the potential as it depends on the distance between atoms
220
What is the approximation made when constructing the vibrational Hamiltonian and what does the Hamiltonian end up depending on?
Approximation that molecule is not rotating
Hamiltonian and wavefunction only depend on r⃗ (interatomic distance)
221
How can we further simplify the vibrational wavefunction?
Using Ψ(r) = Χ(r)/r
222
What does the derivative of the potential energy with respect to r in vibrational spec equal?
A function of Force
223
What is the potential energy for vibrations?
V(x) = 1/2kx^2 where x = r-r₀
V(r) = 1/2k(r-r₀)^2
V(θ) = 1/2k(θ-θ₀)^2
224
What does the quadratic equation of potential describe?
Potential energy for small displacements from an equilibrium position
225
Using the potential energy for vibrations what is the model you end up with?
The harmonic oscillator model
Expressing function in terms of displacement and using a parabolic potential we obtain Schrödinger's for a quantum harmonic oscillator
226
What are the wavefunctions of the harmonic oscillator a product of?
A Gaussian and a Hermite polynomial
227
What do the gaussian and hermite polynomial do for the wavefunction of the harmonic oscillator?
Gaussian - makes wavefunction go to zero for large positive/negative values of x
Hermite polynomial - determines the nodal structure
228
What QN are involved in the wavefunction of the harmonic oscillator?
n as only needs one QN as a 1D problem
229
What happens as we increase the QN n for harmonic oscillator?
What can n tell us?
For larger n values, higher probability for the system to be found away from equilibrium position
Number of nodes = n
n=0 most likely to be found at x=0
230
In a quantum system what is possible relating V(x) to Etotal?
It is possible to find a system in a region where V(x) is greater than total energy
231
What are the energies of the Harmonic Oscillator? For diatomic
En = ħ * sqrt(k/μ) * (n+1/2)
ΔE = ħ * sqrt(k/μ)
Therefore change in energy does not depend on n so is constant
Non degenerate
232
What is zero point energy in vibrational spectroscopy?
Due to n+1/2 term in the energy the lowest energy level has a finite KE that cannot be removed
233
What do the values of n have to do with the value of the wavefunction?
If n is even then wavefunction is even
If n is odd then wavefunction is odd
234
At small amplitude what is the potential term well approximated by in vibrations?
A parabola
235
Spectroscopic transitions in IR region are most associated with what transitions?
Transitions between vibrational states
236
What can you use vibrational spectroscopy for?
What is vibrational spectroscopy also called?
A tool for structural identification (functional groups)
IR spectroscopy
237
What wavenumbers are involved in vibrational spec?
What do bond vibration characteristics provide info on?
100-4000cm^-1
Bond strengths
238
What forces are involved in the non rigid rotor?
Both attractive and repulsive forces (e.g. between nuclei or between nuclei and electrons)
239
What do both extensions and compressions of a bond about equivalent r lead to?
Increase in molecular energy
240
What are the solutions to the Schrödinger equation for vibrations?
En = (n+1/2)hv
where v = 1/2π * sqrt(k/meff) (Hz)
241
What is the change in energy equivalent to in vibrations?
ΔE = hv
means there is constant energy separation between vibrational levels
242
What is k in energies of a harmonic oscillator and how are meff and μ related?
k is the spring constant (kgs^-2)
meff is not the same as μ unless it is a diatomic
243
How do the expressions for energy in the harmonic oscillator look in terms of angular frequency?
ω = 2πv
So
En = (n+1/2)ħω where ω = sqrt(k/meff)
ΔE = ħω
244
How do the expressions for energy in the harmonic oscillator look when expressed as wavenumber?
ε = (n+1/2)v̅(osc)
where v̅(osc) = 1/2πc * sqrt(k/meff) and is measured in m^-1
Δε = v̅(osc)
245
As there is constant energy separation in the harmonic oscillator model what does the spectrum look like?
One line in the spectrum in harmonic model
246
What are the selection rules for vibrational spectroscopy?
Vibration must induce a change in dipole moment - Δμ>0
Vibration energy can only change by - Δn = ±1
However second one only true for HO
247
What are the problems with the Harmonic Oscillator?
Only a satisfactory model at low energy levels (Δr is small)
At high compression, nuclear repulsion becomes a factor
At high extension, the bond breaks
So potential energy term is no longer enough to describe behaviour of a particle
Needs something else
248
What helps solve the problems of the Harmonic Oscillator?
A new term: Anharmonicity
249
What kind of potential does the anharmonic oscillator cause?
The morse potential
250
What changes in energy between harmonic and anharmonic oscillator? Looking at the morse potential
In anharmonic oscillator energy increases more sharply under compression and energy levels out to the dissociation energy under extension
251
What is the anharmonic function a good approximation for and what does it include?
Deq - the dissociation energy - cannot go above this at high extension else will break bond
Good approximation for actual potential
252
What happens to energy levels in the anharmonic oscillator?
Need to 'correct' the energy at each level with an 'anharmonicity constant' , xa
Increasing effect at higher vibrational levels
So the energies converge to Deq
253
How do you calculate energy levels for an anharmonic oscillator?
En = (n+1/2)hv - (n+1/2)^2 * hv * xa
254
What is true about the lowest energy level in the anharmonic oscillator?
It is still non zero however smaller than for harmonic oscillator
255
What do we expect to see on the anharmonic oscillator spectra?
Multiple lines given states with n ≥ 1 are populated as spacing between levels is not equal
256
What is the Birge-Spooner Plot?
A plot that allows you to calculate dissociation energy
257
What are the practical issues with the Birge-Spooner plot?
Dissociation energy is measured from lowest state 0 not from bottom of potential well (misses zero point energy)
Triangular shape is an approximation - will overestimate Deq
Only lowest transitions are easy to measure so need linear extrapolation
258
What are important things to know about Birge-Spooner plot?
Area = Dissociation energy
Each bar in the diagram represents a vibrational transition
259
What are the consequences of anharmonicity?
Dissociation limit and breaking of selection rules
260
What information can you gain from a vibrational spectra?
Oscillation frequency depends on bond force constant and reduced mass
261
How does the zero point energy shift for anharmonicity?
E₀ = 1/2hv - 1/4hv * anharmonicity constant
262
What are the key observations from the anharmonic oscillator?
- Energy levels converge
- Dissimilar energy spacing between levels
- Allow bonds to dissociate
- Allows for breaking of selection rule
263
How does the selection rule change when considering the anharmonic oscillator?
Δn = ±1 → Δn = ±1, ±2, ±3,....
where + is absorption and - is emission
264
What does the new selection rule for anharmonic oscillators lead to?
Appearance of 'overtones'
265
How do you name overtones and hot bands in the anharmonic oscillator model?
0→1 'Fundamental absorption'
0→2 'First overtone of the fundamental absorption'
0→3 'Second overtone ....
1→2 'First hot band'
1→3 'First overtone of the first hot hand'
2→3 'Second hot band
266
What are overtones?
Jumps of more than n=1 in a anharmonic oscillator that result from Δn > 1
267
What are important things about overtones?
In an anharmonic regime we expect to see bands at:
- ΔE₀₋₁ = hv(1-2xa)
- ΔE₀₋₂ = 2hv(1-3xa)
- ΔE₀₋₃ = 3hv(1-4xa)
where xa is small so 1-bxa is close to 1
Roughly located at the multiplies of fundamental vibrational frequencies
268
How do the amplitude of transitions change for higher overtones?
Amplitude of transitions (transition dipole) is lower for higher overtones
Intensity of peak is less
269
What can we use the equations of overtone energy to calculate?
Given we know position of spectral lines we can solve equations simultaneously to find xa and hv which can be used to find k
270
What is the Boltzmann distribution for vibrational energy levels?
Ni/Nj = e^-ΔE/kT
no degenerate energy levels
where Ni is population of upper level
271
What is true about the population of state n=1 for vibrational levels?
Population of one is around 1% of ground state population using ΔE = 1000cm^-1
However heating the sample promotes molecules to excited vibrational states
272
What does heating the sample to promote molecules to excited vibrational states cause?
Causes transitions to happen from energy levels other than n=0 and are called hot bands
273
What is the difference between harmonic and anharmonic oscillators when referring to hot bands?
Harmonic - all transitions have same energy so peaks are coincident - nothing happens to spectrum if you populate higher levels so no hot bands
Anharmonic - each successive transition will have less energy - can see hot bands causing multiple lines on spectrum
274
What does the presence of overtones and hot bands do to the spectrum?
Overtones - cause extra peaks towards higher energy
Hot bands - cause extra peaks towards lower energy but are within each 'fundamental' peak - at lower energy due to anharmonicity
275
What controls the intensity of hot bands and overtones?
Intensity of hot bands - controlled by Boltzmann distribution (initial state population)
Intensity of overtones - controlled by transition probabilities
276
How many DoF do atoms and molecules have?
Atoms - 3 DoF that are all translational
Molecules - 3N DoF - each atom brings 3
277
Are all DoF translational?
No due to bonds not all motions are translational - rotations and vibrations occur
278
What happens when atoms in a molecule all move in the same direction?
If move in same direction - translates - always 3 of these
If move in different directions - rotations and vibrations
279
What is the general formula for no of vibrations DoF in linear molecules?
3N-5
280
What is the general formula for no of vibrations DoF in non linear molecules?
3N-6
281
How do you find number of bend/stretch DoF?
Find total DoF and rotational DoF
Use that to find vibrational DoF
Use that to find bend/stretch
282
What is true about general stretching/bending modes?
If vector sum stays zero - stretch/bend will not be seen
If vector sum doesn't - stretch/bend will be seen
283
When are vibrations IR active?
When they cause a change in dipole
284
What does isotopic substitution do to a IR spec?
What do actual vibrational spectrums look like?
Changes it
Stretching vibrations are broad and overlap
285
What is true about molecules and types of excitation?
Every molecule doesn't undergo a single type of excitation at any one time - so can have simultaneous transitions
286
What is the Born-Oppenheimer approximation?
Energy transitions can be considered separately; a molecule may execute vibrations, rotations and electronic transitions without any one effecting the other
287
What does the Born-Oppenheimer approximation mean for total energy of a molecule?
It can be split up
Etot = Erot + Evib + Eelec
288
What is true about energies of different motions?
They spread and overlap each other
- Can share energy
Many states where energy is shared between motions
- Can be coupled
289
What can electronic states and vibrational states have?
Electronic states can have vibrational and rotational states between them
Vibrational states can have rotational states between them
290
What do all energy levels exist as?
A 'ladder'
291
When can a single photon excite multiple transitions simultaneously?
Provided:
1. Motions are coupled (influence each other)
2. Core selection rules are satisfied
- while all changing together e.g. J still cannot jump more than one rotational energy level
292
When are motions coupled?
Motions are coupled when one motion (e.g. vibrations) affects another motion (e.g. rotations)
- can only share energy if coupled
293
What couples vibrations and rotations?
1. Same force constant (k)
- Allows for transfer of energy
2. As you rotate vibrations occur and vice versa
294
How do you calculate rough energy level spacing?
Ignore the corrections for non rigid rotor and anharmonic oscillator
ε = BJ(J+1) + (n+1/2)v̅
Δε = ṽ + 2Bm where m = ±1, ±2 etc and ṽ is band origin
295
What is true on the spectrum when ΔJ = +1 or ΔJ = -1?
ΔJ = +1 → R branch to the right
ΔJ = -1 → P branch to the left
296
What happens to energy spacing/levels in the vibrational/rotational spectrum?
Each time n and J are changing by one
As go to right - ΔE should get bigger
As go to left - ΔE should get smaller
297
What populations do we need to account for in vib/rot spec?
Only rotational populations as all vibrational transitions are taking place from ground state
298
Why do we need to account for rotational populations in vib/rot spectrums?
As there is a non zero max population energy level
So intensity of bands in spectrum will not be equal
- Instead they will be proportional to the population of levels
299
What is the difference between peaks in vib/rot spectrum?
2B
300
What happens to the value of J as you go outwards from the centre in vib/rot spectrum?
Increases as it goes outwards
301
What can you determine from vib/rot spectrum?
Bond lengths
Bond strengths
Isotopic substitution
302
What does the subscript of each peak indicate in vib/rot spectrum?
Indicates value of J'' for which the transition takes place - always refers to the bottom transition in ground state vibrational level - denotes initial rotational level
303
When a molecule vibrates what is different between the P branch and R branch?
Molecule has rotational relaxation in P branch and rotational excitation in R branch
- For P branch molecule was rotating more before the condition
304
What are several things to note about the vib/rot spectrum of CO?
ΔJ = 0 (origin) is called Q branch and for diatomic it is forbidden (due to selection rule) but sometimes visible
P branch is complicated by isotope effect of 13CO which is centred to the left of the origin
- Overlap of lines from 13CO and 12CO serves to increase intensity of some peaks
305
What is the isotope effect?
Another spectrum centred at a slightly different place so confuses lines - spacing between lines also changes which complicates it more
306
Why do we ignore emission transitions in vib/rot spec?
Just introduces extra complication
307
What can we tell about rotations from the vib/rot spectrum?
We can assume a rigid rotor so assume 2B energy spacing
- Use low J values to find B and then can determine atomic masses/bond lengths
Can compare J's for P and R branching
- B constant will be slightly different as vibrations cause different bond lengths
Using higher order peaks we can determine nature of non rigid rotor and determine D
308
How can you test rigid rotor model in vib/rot spec?
Compare low J values with high J values to test rigid rotor
309
What can you tell about vibrations from a vib/rot spectrum?
Using fundamental frequency (middle of spectrum) we can determine spring constant k or effective mass
310
What happens to overtones in vib/rot spec?
Still there but just exist at a different wavenumber so different part of spectrum
- occurs at around x2 the wavenumber
311
What does temperature affect in vib/rot spectrum?
Spread of rotational bands increase as more states being populated so more transitions can occur
Changing temperature changing population of states
312
Where do the wavelengths of electronic transitions lie?
Lie in the UV/vis range
313
What couples electronic and vibrational motions?
The shift in potential when you excite an electron - causes the molecule to want to be a different bond length
314
When do transitions occur for elec/vib spec?
When photon of visible light is absorbed
- from most populated ground state up to any excited state
- corresponds to peaks in spectra
315
What is the range of absorbed light in vibrational spectroscopy?
2-50 kJmol^-1
316
What are the main trends in IR spectroscopy?
Higher wavenumber = higher energy
Bond order ↔ Bond strength ↔ Force constant ↔ Vibrational E
Bond order ↔ Bond strength ↔ Reduced mass ↔ Vibrational E
317
What is special about an IR spectrum?
It is unique and can be used to find FGs regardless of complexity
318
What are some more trends in IR spectroscopy?
Stretching and bending vibrations in single bonds occur together at below ⁓ 1700cm^-1
Stretching frequencies follow: triple bonds>double bonds>single bonds
Stretching frequencies are higher than bending frequencies
Bonds to H atoms have higher stretching force than those to heavier atoms
- more energy
319
What is the fingerprint region in IR spectroscopy?
A unique region to every molecule below 1500cm^-1
Contains a complex set of absorptions that can be compared to known fingerprint regions to identify compounds
320
When can you tell if something is a C-H stretch?
If it is a sharp peak starting before 3000cm^-1
321
Why is different about the OH and NH stretching vibrations in IR spectroscopy?
Presence of hydrogen bonds make absorption bands broad and shifts then to lower wavenumber due to weaker bonds
Particularly strong for carboxylic acids - very broad
Appearance of signals will depend on how the spectrum is measured
- neat or in diluted solution
322
How does the appearance of OH and NH vibrations in IR spectroscopy change based on how spectrum is measured?
If neat - Strong H bonding so broad signal
If diluted - No intermolecular interactions so sharp signal
323
What does the IR spectra of carbonyl metal compounds contain?
When bound to metal centres CO shows intermediate freq of double and triple bond
- Position of CO band indicates strength of CO bond
324
How do we report IR spectra?
Highest frequency first (neat or diluted) wavenumber (bond), wavenumber (bond),...., wavenumber, wavenumber - fingerprint region
e.g.
vmax (neat) 3120 (=CH2), 2973 (C-H), ...., 1593, 1460, 999, 902 cm^-1
325
What are the wavelengths of transitions for electronic spectroscopy?
200-700nm
UV/Vis range
326
What is the absorption of radiation in UV/Vis region usually associated with?
Valence electronic transitions in atoms and molecules
327
What are the selection rules in electronic spectroscopy?
Transitions between any energy level can be observed: Δn = any
Only transitions for which Δl = ±1 are allowed
Only transitions where ΔS = 0 are allowed
328
What are the other names for NMR, vibrational, rotational and electronic spectroscopy?
Vibrational Spectroscopy = IR spectroscopy
Rotational Spectroscopy = Microwave spectroscopy
Electronic Spectroscopy = UV/Vis spectroscopy
NMR Spectroscopy = Radiowave spectroscopy
329
Is there a universal model for electronic spec?
No there isn't - not like rigid rotor or harmonic oscillator
- spectra depends on specific characteristics of each molecule
330
What can be used to explain some electronic spec trends?
Simple models
- There are also general rules that apply to light induced electronic transitions
331
What is light absorption in elec spec mostly due to?
Interaction of lights electric field with charges (notably electrons) in molecules
332
What does light absorption require in electronic spec?
Requires formation, in the final wavefunction, of one extra (or one less) nodal surface perpendicular to polarisation of electric field
333
If dipole moment is not zero what is true about Ψf(x) and Ψi(x)?
They have different parity along the E direction - symmetric/antisymmetric inversions (g or u)
334
What changes the parity of a wavefunction?
Introducing one nodal surface
335
What happens when you have interaction of light with an s orbital?
You get a p orbital as one extra nodal surface is produced
336
In polyelectron atoms are orbitals degenerate?
No they are not degenerate
- Electron now also depends on QN l
337
Can you predict exact energies of transitions in electronic spec?
No they are hard to predict but can still interpret spectra
338
When are light induced transitions not allowed? (Orbitals)
When it is occurring between d orbitals in isolated atoms - can only occur if they combine to form MOs
339
Due to the selection rule what is absorption of light?
Directional - depends on how much the molecule is orientated with respect to the electric field
340
What can π electrons in polyene molecules with conjugation be reasonably described as?
Particle in a 1D box or particle in a ring
1D box for straight chain
Ring for benzene
As the π electron is not localised so is free to move around the bounds of the structure
341
Why can linear polyenes be approximated to a 1D box system?
As they are free to move along the molecule length (V=0) but can't jump off it (V=infinity)
342
How good are approximations of π electrons in conjugated molecules using models?
Level of agreement works surprisingly well for some molecules but should not be expected for all molecules
343
How do you work out path length in an approximated pi molecule?
L = k*r(bond) + b
where k is number of conjugated bonds, r is average bond length and b is extra distance either side of molecule (usually considered to be one extra bond in total)
344
When do you include the + b in approximation of path length in electronic spec?
You test with it and without it to see which one is more accurate then use that
345
How do you find value of n in approximation of conjugated molecules?
It is the quantum number of the highest occupied state
Remember that there is no degeneracy for particle in a 1D box but there is some for particle on a ring
346
How do you find transition energy for approximated conjugated molecules?
What is the effect of transition energy as chain length increases?
E = h^2/8mL^2 * (2n+1)
Size of the box increases with chain length which reduces energy gap
QN increases with chain length so increases energy gap
Effect of the box size prevails as it is squared so transition energy should decrease as chain length increases
347
What does UV/Vis spectroscopy do?
Provides info on electronic structure so can be used to identify new compounds
Allows us to quantify the concentration of chromophores (Coloured chemical compounds that are both inorganic and organic) using Beer-lambert law
Can monitor course of reaction
348
How do you calculate absorption and transmission in UV/Vis?
T = I/I₀ *100
A = log(I₀/I)
At A = 1 90% of light absorbed
At A = 2 99% of light absorbed
349
What is the beer-lambert rule?
A = εcl
ε = molar absorption coefficient (M^-1 cm^-1)
c = conc of sample
l = path length
350
What does the molar absorption coefficient give us information on?
Probability of that electronic transition - it is an intrinsic property of molecule
351
When is the beer-lambert law valid?
For dilute solutions as all molecules/atoms experience the same irradiation
352
What are chromophores?
Organic molecules that absorb UV/Vis light containing one of the following FGs
C=C
C triple bond
C=O
N=O
353
How are transitions described? In electronic spectroscopy
By the MOs involved:
n = non bonding orbital
σ/σ* = bonding orbitals
π/π* = anti bonding orbitals
354
Which two transitions are the only ones observed in UV/Vis spec?
n→π* and π→π*
355
What does conjugation do to π→π* transitions?
Increased conjugation lowers energy of the transitions
- shifting absorptions to longer wavelength
- termed red shift
356
What does extended aromaticity do to π→π* transitions?
Similar behaviour with λmax shifting to higher values as conjugation
357
What are the origins of colour?
Colour arises due to absorption of visible light whenever it is of the right magnitude to excite e- from ground state to excited state (electronic transition)
358
How do you know what colour will be observed?
The colour observed is the complimentary of the colour absorbed
359
What colours are complimentary?
Red and green
Orange and blue
Yellow and purple
360
What is the order of wavelength of absorbance of different colours? from high to low
Red
Orange
Yellow
Green
Blue
Indigo/Violet
361
What are the values of wavelengths for absorbance of different colours?
Red - 800-620
Orange - 620-580
Yellow - 580-560
Green - 560-490
Blue - 490-430
Indigo - 430-380
362
What is the origin of colour in TM complexes?
d orbitals are not degenerate in TM complexes
- hence d-d transitions are possible between electronic states
- typically weak transitions but absorb in visible region so they appear coloured
363
What is charge transfer and what does it do? (In TM complexes)
Charge transfer occurs when electrons are transferred from ligand to metal or metal to ligand
- Results in strong absorbance and more intense colour than d-d transitions
364
What is mass spectrometry?
Enables ID of molecules based on mass/fragmentation patterns and isotopic distribution
Not a spectroscopic technique as no interaction of light with matter
Highly sensitive
365
What is the mass to charge ratio in MS and what is it used for?
m/z = B^2r^2 / 2V
B = Applied magnetic field
r = radius of curved path
V = applied voltage
Used as the comparison tool
366
What is the whole system for MS under?
High vacuum (<10^-9 atm)
367
What is the process of MS?
Sample introduction
Ionisation
Acceleration
Deflection - light ions travel less distance
Detection
368
What is the ionisation technique of electron impact ionisation (EI)?
Sample of gas phase bombarded with high energy electrons (70 eV)
These will ionise the molecule and cause significant fragmentation
However molecular ion peak may not be present
369
What are the ionisation and fragmentation equations for EI ionisation?
Ionisation: M + e- → M+· + 2e-
Fragmentation: M+· → A+ + B· or → C+· + D
Formation of positive ions and radicals or positive radial ion and atom
370
Are formations of anion radicals possible in EI ionisation?
Yes but far less likely
371
What is an electron impact mass spectrometer generally set up to do?
EI-MS normally set up to detect positive ions
372
What is the ionisation technique of electrospray ionisation (ESI)?
Solution of sample is passed through a small capillary with high applied voltage
- Produces charged droplets from which solvent rapidly evaporates to leave naked ions
373
What is important to know about Electospray ionisation?
Relatively mild form of ionisation that often leads to observation of molecular ion peaks as [MH]+
- normally leads to less fragmentation
Particularly suitable for large compounds as don't need to vaporise sample
374
What is key to know about MS?
Only charged species will be detected
375
What is there to know about fragmentation in MS?
Any species may fragment in different ways
- spectrum will consist of a plot of detected m/z values against relative intensity
Strongest peak is termed the 'base peak' and is assigned relative intensity of 100%
376
What is the spectrum in MS plotted with?
m/z values against relative intensity
377
Why does fragmentation occur in MS?
Molecular ions normally highly energetic
- usually break apart into fragments which then can also break down
378
What can fragmentation be used for?
Pattern/Intensity of fragments are characteristic of each compound (molecular fingerprint)
- also depends on ionisation technique
379
What are isotope distribution patterns in MS?
Elements with different stable isotopes give rise to characteristic lines in spectrum
- Relative intensities of those reflect isotopic abundancy
380
How do you use isotope distribution patterns to find probability and therefore peak % of molecular ion peaks where the compound can have different values due to isotopes?
Find every possible mass of compound
Multiply decimal abundance of all atoms involved to find probability
e.g. if Br2 is 79Br-79Br then probability = 0.507*0.507 as have 50.7% abundance
Find largest probability and set that to 100% then find all other based on this
381
What is high resolution mass spectrometry (HRMS)?
It measures m/z values of ions to several decimal places
Exact masses rather than nominal measures (integer values) can be determined thanks to HRMS
382
What is the difference between exact mass and molecular weight?
Exact mass is mass of sample being measured
Molecular weight is mass of one mole of sample
