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Car-Parrinello Lagrangian<br />

L = T −V<br />

L CP<br />

=<br />

T<br />

I<br />

EKINC (T e )<br />

<br />

1<br />

2 M ˙<br />

I<br />

R 2 I<br />

+ ∑ µ ˙ φ ˙<br />

i<br />

φ i<br />

<br />

i<br />

<br />

∑<br />

I<br />

kinetic energy (nuclei + electrons/orbitals)<br />

EKS (V e )<br />

<br />

− Ψ ˆ<br />

0<br />

H e<br />

Ψ<br />

<br />

+ constraints<br />

0 <br />

potential energy<br />

orthonormality<br />

• EKINC = T e <br />

• TEMPP = 2 / (n degrees of freedom k) with k=1.38×10 -­‐23 J/K, Boltzman const. <br />

• EKS = V e (Kohn-­‐Sham energy = E pot ) <br />

• ECLASSIC = E phys = T I + V e = E conserved – T e = EHAM – EKINC <br />

• EHAM = T I + T e + V e = E conserved = EHAM = ECLASSIC + EKINC <br />

(constant of mo4on)

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