When does Hartree-Fock fail?
Normally good for single determinant
Fails at longer bond lengths
What is a configuration interaction?
CI
Interactions between different configurations
eg:
H+ + H-
H* (radical)
What is static correlation?
Electron correlation
when two/more configurations
have similar energies
Correlation equation energy
E(corr) = E(FCI) - E(HF)
What is multi-configuration based on?
HF & DFT use one Slater determinant
Multi use more than one
What is full configurational interaction?
FCI
All possible electron configurations
are taken into account
Captures all dynamic correlation effects
Limited to only small electrons
~10 electrons
What are the spin states for H2?
Some unambiguous eigenstates
two are unclear
What are singlets and triplets?
Triplet:
S = 1, Ms = +1,0,-1
Singlet:
S = 0, Ms = 0
What are configuration state functions?
CSFs
Linear combination of Slater determinants
Eigenfunction of total spin
What is Weyl’s formula?
(Check notes)
What is the couple cluster theory?
(Check notes)
What are common spin states?
Co(3+) usually low spin
3d ions usually high spin
4d/5d ions low spin
∵ stronger crystal field
What are the degeneracy terms?
Non-degenerate = A
Doubly degenerate = E
Triply degenerate = T
What needs to be considered with orbital angular momentum (L)?
When L = 0
consider spin-orbit coupling
Spin & orbital magnetic moments
near each other
will interact
What is important for heavy elements?
Relativistic corrections
Atomic number large
Coulomb attraction v. strong for core electrons
Core electron velocity can approach fraction of speed of light
Effective mass increases
What is the effective core potential?
ECP
Replace nucleus and core electrons
w/ ECP
that mimics effect of valence electrons
What is the unit cell?
Repeat unit of crystals
What is an asymmetric unit?
ASU
Fraction of unit cells
not generated by symmetry operations
What is a space group?
Combined rotational
and translational
set of symmetry operations
What is the Bloch theorem?
(Check notes)
What is the reciprocal space?
Possible wavevectors exist
defined by reciprocal lattice vectors
b1 = 2π/V (bc)
b2 = 2π/V (ca)
B3 = 2π/V (a*b)
(a,b,c all vectors)
What is the Brillouin zone?
Periodic in reciprocal space
Infine possible wavevectors
usually restric k to
lie in first Brillouin zone
centred about origin k=0
(k is vector)
What is an indirect band gap material?
Conduction band
and valence band
don’t cross
eg. Si
What is a conductor?
Conduction band
and valence band
cross
Continuous density of space
eg. Cu
