Slides

Ab initio MD: CPMD
• How to control adiaba4city?
• Dynamics of Kohn-­‐Sham orbitals as superposi4on of harmonic orbital
classical fields, where ε j and ε i are the eigenvalues of occupied and
unoccupied (virtual) orbitals:
• Lowest frequency:
ω e min ∝
E gap
µ
• The frequency increases like the square root of the energy difference E gap , which is is the
energy difference between HOMO (highest occupied molecular orbital) and LUMO
(lowest unoccupied MO).
• The frequency increases as the inverse of the square root for a decreasing fic44ous mass
parameter μ.
• To ensure adiaba4city, the difference to the highest phonon frequency
should be large: ω min max
e
− ω n
• The only adjustable parameter is μ (thus also called adiaba4city parameter)
• Decreasing μ (lower kine4c energy, closer to BO surface) not only shi‚s the electronic
spectrum upwards on the frequency scale as desired, but also stretches the en4re
spectrum leading to an increase of the maximum frequency according to
ω max e
∝
E cut
µ
where E cut is the largest kine4c energy in an expansion of the wave func4on in terms of a
plane wave basis set.
ω ij
=
( )
µ
2 ε j
− ε i
ω n
max