2. Molecular Spectroscopy and Structure Flashcards
What are the two perpendicular components of electromagnetic radiation?
Electric field and magnetic field (these are perpendicular to each other)
B (magnetic field) and E (electric field) are in phase with each other
What are the three key properties of a wave?
Wavelength, frequency, speed
C = v.lambda
What is wavenumber?
The reciprocal of the wavelength in cm^-1
What equation allows you to find the energy of a photon?
E = hv = hc/lambda
What is the equation for the refractive index n(lambda)?
n(lambda) = c/speed of light in material
What does strength refer to in terms of waves?
Amplitude of wave - same for B and E
Which component of the electromagnetic wave dominates? By how much?
The electric field component, 10^5 times stronger than the magnetic field. All light-matter interactions thus stem from electric field interactions.
What axis is the Z axis in an electromagnetic wave?
The direction of travel
What equation represent the electric component of the electromagnetic radiation?
E(t,z) = E0.cos(omega.t - kz.Z)
E(t,z) = electric field vector at position z and time t E0 = amplitude of the wave (electric field strength) omega = angular frequency - 2pi.v t = time kz = wave vector - 2pi/lambda Z = position
What is the units of the electric field strength?
N/C or V/m
How is the energy carried by a classical light wave usually expressed?
As energy density U
What are the equations for energy density and intensity/irradiance of light waves?
Energy Density U (J/m^3) = 0.5(epsilon0)|E0|^2
Intensity I (W/m^2) = 0.5c(epsilon0)|E0|^2
Epsilon0 = permittivity of a vacuum - 8.854x10^-12 F/m E0 = amplitude of the wave c = speed of light
What was Planck’s postulate?
Light energy is quantised into discrete packets called photons with Energy hv.
What is the equation for finding the force of an electrically charged particle?
F = qE
F = force of particle q = electric charge of particle E = electric field
How does a radio antenna work?
Movement of an electron in a transmitter generates an electric field. The filed may then move through space as an EM wave, this hits a receiver and causes an electron to feel the oscillating electric field. This causes the 2nd electron to start moving (electrons raised up an energy level).
What is the ground state of an electron?
A point at which the electron is simultaneously in it’s lowest vibrational, rotational and electronic energy levels. Molecules in levels higher than this are said to be in the excited state.
Can an electron be excited differently and simultaneously?
Yes, a molecule may absorb a photon that excites it both electronically and vibrationally (as long as photons energy = electronic + vibrational excitation energy)
Can the energy of a photon be partially absorbed?
No, once a molecule absorbs a photon all the energy of that photon must be absorbed.
What equation determines the electronic states of hydrogen atoms?
Rydberg equation:
En = -h.c.R/n^2
En = energy of level n n = energy levels - 1, 2, 3 etc
What is the resonance condition?
The ability of an atom/molecule to absorb a photon ONLY when the energy of the photon corresponds precisely to the energy separation between 2 quantum states.
How may an excited molecule lower it’s energy?
- Spontaneous emission of a photon
- stimulated photon emission by absorption of a second photon (LASER)
For a system at equilibrium at room temperature, are all molecules in their ground rotational, vibrational and electronic states?
Nope, at equilibrium the molecules int he system will be spread between different energy levels depending on the amount of thermal energy available to them. Here the lower energy levels will be more populated than the higher energy levels though.
What is the boltzmann distribution equation?
ni/n0 = (gi/g0)exp(-deltaE/Kb.T)
ni = number of molecules in energy level i n0 = number of molecules in the ground state gi = degeneracy of level i g0 = degeneracy of the ground state exp = e to the power ... deltaE = difference in energy between level i and ground state Kb = boltzmann constant (1.38x10^-23 J/K) T = temperature in K
How are the four states populated at varying temperatures?
NMR: almost equally populated
Rotational: excited are well populated
Vibrational: excited state only populated at high temperatures
Electronic: will remain in ground state unless you excited them with something other than heat (although there’ll be a few in excited state as you increase temp)
How does the process of UV/vis absorption spectroscopy work? Why are their broad peaks in the spectra?
Shining a light source through a sample and recording the signal attenuation (how much light drops) as a function of wavelength.
Photons will only be absorbed in their energy is precisely equal to the energy gap between two quantum states (resonance) so peaks occur, defining a footprint.
Saying this, broadening of absorption/emission peaks occurs due to quantum uncertainty, collisions between molecules and instrumentation
How does emission spectroscopy vary form absorbance spectroscopy?
Sample first excited by illumination with short electromagnetic pulse. Then any subsequent luminescence is recorded.
The incident light is monochromatic
How does the incident light of absorbance and emission spectroscopy vary?
Absorbance spectroscopy emits light of multiple wavelengths whereas the incident light of emission spectroscopy is monochromatic.
What is the benefit of emission spectroscopy?
A lack of background signal makes it more accurate
How are absorption and emission spectrum related in simple systems? In what situation does this occur?
They are usually mirror images of each other
molecular must have: similar geometries in ground and excited state, and emission must be from lowest vibrational level
What is the beer-lamber law?
I/I0 = exp(-e.c.l)
OR… log10(I0/I) = A = e.c.l
e = natural molar absorptivity
What observations did Mr. Beer and Mr. Lambert make?
- fraction of light transmitted decreases exponentially w/ increasing distance it travels through the sample
- fraction of light transmitted decreases exponentially w/ increasing concentration of solute
What do we assume for the beer-lambert law?
Thinking of sample in cuvette as series of thin slices width dl.
- All photons travelling perpendicular to large face of ‘slice’
- If a molecule within this slice lies in the path of a photon then it will absorb the photon
- Each molecule has an effective cross section: rho
- No cooperative absorption between molecules
- Absorbing species forms single homogenous phase and doesn’t scatter light
What fraction of the area of the ‘slice’ is opaque to photons?
Equal to the ratio of the total cross sectional area of all the absorbing molecules compared to the total area of the large face of the slice
–> number of photons absorbed in slice is proportional to the concentration
How are the many very small slices combined together?
An integral is used,
this is because the slices are very thin and the intensity of the light entering the slice depends on the light leaving the previous slice
What is another name for the decade molar absorptivity?
The extinction coefficient
What is the transmittance T?
The ratio I/I0 (%)
What is the relationship between T and A?
A = -log10(T)
What is the units of the extinction coefficient?
dm3.mol-1.cm-1
Describe a typical beer-lambert plot of A against c
The gradient of the line would be linear initially, but at higher concentrations the gradient would become less steep
Why does the deviation from linear behaviour occur in the beer-lambert plot?
- Refractive index changes with conc.
- Absorbance saturates
- Association/Dissociation of the solute
- Solute may fluoresce, contributing to I
How do we use absorption spectroscopy to determine the concentrations of two distinct solute species in a solution? What assumptions are made? When is this method most effective?
The measured absorbance at a given wavelength is the sum of the contributions from each solute. So, measure the absorbance of the solution at two separate wavelengths (lambda 1 and 2), knowing the two molar absorptivity’s, we can put solve this using simultaneous equations.
Assume that: solutes do not react and both obey the Beer-Lambert law
Most effective when one solution absorbs more strongly at one wavelength and vice versa
How may you calculate concentrations of two solutes which REACT using absorption spectroscopy (e.g. a weak acid)?
Vary the degree of dissociation by varying pH of the solution. Carry out 3 experiments, at low, med and high pH. At low pH can assume all HA, at high pH all A- and in the middle it’ll be a mixture of both.
Low pH: Eha = A1/c’
High pH: Ea- = A2/c’
Med pH: A3 = Eha[HA] + Ea-[A-]
Rearrange to find [A-] or [HA]
[HA] = c’.((A2-A3)/(A2-A1))
If you choose med pH as the pH of the solution you are testing then can find out the concentration of HA and A- in it.
pKa = pH - log({A3-A1}/{A2-A1})
What is the Henderson-Hasselbach equation?
pH = pKa + log([A-]/[HA])
What wavelength should a spectroscopy involved solutes which react be undertaken at?
A wavelength at which the absorbance of the products are very different form one another
What is the isobestic point?
A point on a (absorbance/ wavelength) plot where all absorbance curves converge - the absorbance is independent of pH At this point. So literally the worst for testing but shows there is true equilibrium between the solutes
What broad categories can we separate molecular orbitals into (2)?
Valence - bonding orbitals of the atoms - change significantly in reactions/ionisation etc
Core - core orbitals of the atoms - don’t change
What 6 categories can molecular orbitals be split into? Describe each category briefly
- sigma bonding orbitals - constructive overlapping along line joining centre of atoms - no modal planes between nuclei - single bonds - form molecular backbone but not often involved in chemical reactions
- sigma* anti-bonding orbitals - destructive overlapping - one perpendicular modal plane - much higher energy than sigma
- pi bonding orbitals - constructive p atomic orbital overlap above & below atom bonding centres - double bonds - one nodal plane in plane of nuclei
- pi* anti-bonding orbitals - two nodal planes, in plane and perpendicular to plane of nuclei - pi-pi* orbitals have much less energy separation than sigma (UV vis)
- n non-bonding (not bonding/anti-bonding) - no restriction on nodal planes - lone pairs - least tightly bound
- d electrons - colourful
What is a chromophore? How do they fluoresce?
The chromophore is a region in the molecule where the energy difference between two different molecular orbitals falls within the range of the visible spectrum.
Visible light that hits the chromophore can thus be absorbed by exciting an electron from its ground state into an excited state
Two categories
How would you label the molecular orbitals of methanal?
1sO
What is the shorthand for the n to pi* transition?
pi*
What is the electronic state of a molecule?
The electronic configuration and arrangement of electrons’ spins in a molecule
What would the ground state of a closed shell molecule look like?
All electrons paired up in molecular orbitals so their spins cancel to give a total angular spin angular momentum of 0.
e.g. 2 Electrons in the sigma MO (one spin up and one spin down)
If you excite a closed shell species, what two possible spin states may occur?
Singlet excite state - electrons in ground and excited states have opposite spin (S = 0)
Triplet excited state - electrons in ground and excited state have the same spin (S = 1)
What does S stand for in electronic configuration stuff?
Total spin angular momentum
What is the name of states with S=0 and S=1? How does the energy of these states vary?
S = 0 = Singlet = S S = 1 = triplet = T
S0 = ground state S1/T1...S3/T3 = excited states
There is no T0 state - at the ground state all stuff is singlet as most molecules have closed shell ground state configurations
If they have the same electronic configuration, would the triplet or singlet state typically be lower in energy?
Triplet state is typically lower in energy than the singlet state
What is the electronic configurations notation including electronic states?
If: (pi up)(n)(pi* down) then 1(pi, pi*)
Why does electronic excitation not occur with thermal energy?
Because the electronic states are separate day large energy gaps - too large for thermal excitation to broach. So electronic excitation occurs with absorption of photon of correct frequency.
What is the equation for excitation due to photon absorption?
S1 = S0 + hv
