CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
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The figure shows the localization length <strong>of</strong> a linear chain <strong>of</strong> antiferromagnetic hydrogen atoms as a<br />
function <strong>of</strong> lattice spacing. The localization length has a maximum at 1.4 Å, indicating that the chain<br />
becomes metallic at around this lattice spacing.<br />
10<br />
Localization length (Bohr^2)<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0 1 2 3 4 5<br />
Lattice spacing (Å)<br />
33.8 Dipole moment (molecules only)<br />
K eyword: dipole moment<br />
The electric dipole moment <strong>of</strong> a finite set <strong>of</strong> point charges <strong>of</strong> charge q i and position vector r i is defined<br />
to be<br />
p = ∑ q i r i . (415)<br />
i<br />
It is easy to show that the value <strong>of</strong> p is independent <strong>of</strong> the origin if the overall system is electrically<br />
neutral.<br />
We may use QMC to estimate the mean dipole moment <strong>of</strong> a molecule by averaging p over the set <strong>of</strong><br />
configurations generated by the VMC or DMC algorithms. The mean value <strong>of</strong> |p| 2 may be determined<br />
in a similar fashion. This will be done if the dipole moment keyword is set to T in the input file.<br />
The raw data will be written to the vmc.hist or dmc.hist file (not the expval.data file!) and the<br />
error bars on components <strong>of</strong> the dipole moment should be evaluated using the reblock utility.<br />
Note that the casino reblock utility reports only the components and not the magnitude <strong>of</strong> the dipole<br />
moment in order to allow the user to decide how to deal with the symmetry. Suppose that symmetry<br />
dictates the dipole moment will point in the x direction. The y and z components should be zero, but<br />
there will be some noise when they are evaluated in QMC. If you work out |p| = √ |p x | 2 + |p y | 2 + |p z | 2<br />
then you will get something larger than |p x<br />
|, tending to |p x | in the limit <strong>of</strong> perfect sampling (i.e., a<br />
biased estimate with finite sampling). You will also get larger error bars on |p| than |p| x<br />
.<br />
For an example application to the water molecule see J. Chem. Phys. 127, 124306 (2007).<br />
34 Atomic forces<br />
The total atomic force is defined as the negative energy gradient with respect to the atomic position<br />
within the Born-Oppenheimer approximation, where the atomic positions are treated as parameters<br />
197