The electron cloud surrounding atoms can act as diffraction gratings and scattering sites for x-rays. This allows determination of solid state structure (i.e., the lattice types and unit cell dimensions) and the structure of molecules.
Diffraction methods are based on Bragg's Law:
n = the order of the diffraction (normally this = 1)
λ = the wavelength of incidence radiation
d = the spacing between lattice planes
θ = the angle between the scattering plane and the incident radiation
When the sample is a powder, this is called powder x-ray diffraction (PXRD) and provides the cell constants for the unit cell of the solid.
When the sample is a single crystal, the intensities of the diffraction peaks is used to identify all atom locations, which gives bond lengths and bond angles.
Neutrons diffract off of nuclei (as compared to electron clouds). This allows accurate structure determination of molecules with light atoms, especially hydrogen. Neutrons also scatter off of spins, so can be used to identify the location and direction of spins in magnetic substances.
Incident radiation can be absorbed by moving electrons from low lying orbitals to higher energy, unoccupied orbitals. This gives a direct measure of the relative energies of the different electronic states in a molecule. In conjunction with computational techniques, orbital energies and electron occupations can be deduced from electronic absorption spectra. This is especially useful for molecules containing transition metals, which we will use later in the course.
Vibrational transitions occur in the IR region of the electromagnetic spectrum. The energy of the IR absorptions are related to the bond strength in molecules and the masses of the connected atoms.
NMR & NQR
NMR = Nuclear Magnetic Resonance
NQR = Nuclear Quadrupole Resonance
Any nucleus with a nonzero spin can be resonance active. NMR is the terminology if I = ½ while NQR refers to resonance from nuclei with I > ½. (I is the spin of the nucleus.)
The resonance condition depends upon the presence of a magnetic field, which removes the degeneracy of the spin levels in the nucleus. Then, application of electromagnetic radiation (typically in the MHz frequency range) allows energy absorption that can be detected. NMR spectroscopy is a powerful technique for structure elucidation, but also gives information about electron distribution.
EPR = Electron Paramagnetic Resonance (also called ESR, Electron Spin Resonance)
EPR is physically similar to NMR but it is the electronic spin (rather than the nuclear) that is the reporting species. EPR is only detectable for molecules or ions with unpaired spins.
Mössbauer Spectroscopy is a specific type of nuclear gamma ray resonance, i.e. gamma rays are absorbed by nuclei. Not many nuclei are Mössbauer active, but 57Fe is one example. Since Fe is so important in many biochemical species, Mössbauer spectroscopy is often used to study these types of molecules. Mössbauer gives chemical shifts, called isomer shifts, that are sensitive to oxidation state and the surrounding environment.
High energy radiation can remove electrons from orbitals in molecules. In photoelectron spectroscopy the kinetic energy of the ejected electrons is measured. This is related to the orbital energy by:
EK = hν – I
EK = electron kinetic energy
hν = energy of the incident radiation
I = Ionization energy
According to Koopman's theorem, I = –orbital energy (this is often, but not always, a reasonable approximation).
If the incident energy is an x-ray, the technique is called XPS (x-ray photoelectron spectroscopy). If the incident energy is in the ultraviolet, the technique is called UPS (ultraviolet photoelectron spectroscopy).
Ionization of gas phase molecules by electron impact or chemical methods can be used to determine mass-to-charge ratios. If the charge of the ion = 1, then the mass of the ion is directly detected. Mass resolution is sufficient to distinguish isotopes. Mass spectrometers with very high resolutions can be used to determine the composition of a molecule simply by the mass of the parent peak.
Measurement of the response of a substance in a magnetic field determines its magnetic susceptibility. There are two types of responses: diamagnetism, where the magnetic field is excluded from the sample and paramagnetism, the the magnetic field is drawn into the sample. Diamagnetism is associated with paired spins and is found in all substances. Paramagnetism is associated with unpaired spins. The paramagnetic susceptibility is complementary to EPR and helps us understand electronic structure of molecules and ions with unpaired spins.
Electrochemical techniques are used to find reduction potentials for molecules. The most commonly used electrochemical technique is cyclic voltammetry (CV). In CV, the potential is changed in a linear fashion from an initial value to a final value and then reversed back to the initial values. The current response is measured at an electrode and the i-V curve is plotted.