CASINO manual - Theory of Condensed Matter

• ‘DET 1 2 PL 6 3’ means ‘add an electron of spin 2 (down) to determinant 1, band 6, k-point 3’.
• ‘DET 1 2 MI 6 3’ means ‘remove an electron of spin 2 (down) in determinant 1 from band 6,
k-point 3’.
• For nonperiodic systems, the k-point indices should just be set to 1.
• If one subtracts a spin-up electron then the value of the input parameter neu should be decreased
accordingly. Likewise for spin-down electrons. Similarly if one adds an electron.
A multideterminant expansion is specified by the keyword ‘MD’:
START MDET
Title
MDET example: use a multideterminant expansion.
Multideterminant/excitation specification (see manual)
MD
3
1.d0 1 0
0.5d0 2 1
0.5d0 2 1
DET 2 1 PR 4 5 6 7
DET 3 2 PR 4 5 6 7
END MDET
Notes:
• The ‘3’ in the line after ‘MD’ specifies that there are three determinants in the expansion.
• The next three lines contain the determinant expansion coefficients for the three determinants
(1, 0.5 and 0.5). Each expansion coefficient is followed by a ‘label’ and then an ‘optimizable’
flag.
• The ‘optimizable’ flag must be 0 or 1, specifying that the expansion coefficient is fixed or free
to be optimized.
• All coefficients with the same label must have the same ‘optimizable’ flag. The ratios of these
coefficients will be fixed during the optimization. There is therefore only one optimizable parameter
in the example above, since the coefficients of the second and third determinants are
constrained to be equal.
• At least one determinant expansion coefficient must be fixed.
• The excitation specifications are of the same form as for the ‘SD’ case. For example, ‘DET 2 1
PR 4 5 6 7’ means ‘in determinant 2 promote an electron of spin 1 (up) from band 4, k-point 5
to band 6, k-point 7’.
Multideterminant expansions and excitations as described above are fully functional for Gaussian
(gwfn.data), plane-wave (pwfn.data) and blip (bwfn.data) orbitals. They may also be used with
numerical atomic (awfn.data) orbitals, although the excitation information must also be supplied in
the awfn.data file (see Sec. 7.8.4).
If blip or plane-wave orbitals are used then the user may specify a phase angle for a particular band
and k point and a particular determinant and spin using
ORB_PHASE
where the phase angle is given in radians. The phase angle is used in the construction of a real orbital
when the band is occupied at k but not −k, as described in Sec. 15. Specifying a phase has no effect
when the band is occupied at both k and −k, or when the band is unoccupied at k.
If one is studying a HEG and a complex wave function is used (i.e., complex wf = T) then the
orbitals in the Slater determinants are of the form exp(ik · r), where the {k} are simulation-cell
reciprocal-lattice points offset by the constant k offset vector specified in the free particles block in
the input file. Before the occupancy of the plane-wave orbitals is worked out, the k vectors are
sorted into increasing order of azimuthal angle φ k (innermost), then polar angle θ k , then magnitude
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