Advanced Molecular Orbital Methods Flashcards
Particle correlation
The extent to which the motions of particles depend on the instantaneous (rather than time averaged) positions of other particles
Electron nucleus correlation
Correlation due to charge attraction
What is electron (-electron) correlation subcategorized into
Coulomb correlation
Fermi correlation
Non-dynamical correlation
Coulomb correlation
Correlation due to charge repulsion
In HF-SCF, the orbital depends on the ‘time-average’ field of the other electrons, not on instantaneous positions
Hence HF-SCF does not contain Coulombic correlation
Fermi correlation
Correlations due to Fermion spin
In HF-SCF the Slater determinant incorporates the fermion effects (antisymmetry and Pauli Exclusion Principle)
Same spin electrons have electron ‘clouds’ or densities that are more separated than opposite spin electrons
HF-SCF does have Fermi correlation
Non-dynamical correlation
A correlation that is missing in HF-SCF due to breakdown of the MO approximation
What are advanced ab-initio methods designed to include
Coulomb correlation
Non-dynamical correlation
When is lack of non-dynamical correlation a problem?
If the MO approximations leads to different Slater determinant configurations of similar energy
This can happen if the energy frontier orbitals (HOMO/LUMO) are nearly degenerate
What is incorporating the Coulomb dynamical electron correlation important for
Accuracy
Can be accomplished by ‘post-SCF’ methods
CI, MPn, CC
CI methods
In Yci the orbital optimization (SCF procedure) only induces the first ‘m’ Slater determinants , the other ‘n’ Slater determinants (1000 < n < Million) are used after the SCF iterations are finished
MPn methods
Related to perturbation theory
Yo is Yhf or Ymscf and Ho is a well-defined portion of H so that H1 is also well defined
Normally used for approximating E
(most common is second order MPn)
CC methods
Most accurate approximation known
(see page)
Price vs performance of geometry optimization
MP2 is ideal (bond lengths within 0.015 A)
Although less ideal for transition state geometries
Price vs performance of reaction energies
Cost effective: MP2, CCSD
Cost ineffective: CISD (also not size consistent)
