CASINO manual - Theory of Condensed Matter

• The modification functions are of the form
w nl (r) = ( c 0nl + c 1nl r + . . . + c Nnl r N ) (
−Anl r 2 )
exp
r l , (2)
1 + B nl r
where A nl , B nl and {c 0nl , . . . , c Nnl } are optimizable parameters. n and l are the principal and
orbital-angular-momentum quantum numbers of the orbitals that are modified using w nl .
• Each modification function w nl is added to the corresponding HF radial function, which is
found by interpolation from the data in awfn.data. The resulting radial function can then be
multiplied by the spherical harmonic Y lm (θ, φ) to give the corresponding orbitals for each of
the 2l + 1 possible values of the magnetic quantum number m. (In fact the radial function is
multiplied by appropriate linear combinations of spherical harmonics to give real-valued orbitals.)
• For s orbitals, the value of c 1n0 is determined by the electron–nucleus Kato cusp condition:
c 1n0 = −Zc 0n0 , where Z is the atomic number of the atom in an all-electron calculation and Z
is zero in a pseudopotential calculation.
• If the spin-dependence flag is set to 1 then different parameters are used for spin-up and spindown
electrons; if it is set to zero then the same parameters are used for spin-up and spin-down
electrons.
• If an orbital with quantum numbers n and l occurs in any determinant in the wave function,
but no corresponding modification function is given in correlation.data, then a warning is
printed and the unmodified orbital is used.
• The ‘expansion order’ specifies the value of N in Eq. (2). For s orbitals, the number of free c
parameters is N multiplied by the number of independent spin types; for orbitals with higher
angular momenta the number of c parameters is N + 1 multiplied by the number of independent
spin types. The expansion order must be at least 1.
• If parameter values are not supplied (as is the case in the example above) then default values
are used: by default A nl = 1, B nl = 0 and c inl = 0. If too many parameters are given then the
extra ones are ignored.
• Note that we must have A nl > 0 and B nl ≥ 0, otherwise the corresponding orbital is unnormalizable.
7.4.6 Molecular orbital modifications
The format of the data set used to specify molecular orbital modifications in correlation.data is as
follows:
START MOLORBMODS
Title
Molecular orbital modifications for the XXX molecule
START GAUSSIAN MO COEFFICIENTS
Parameter values ; Optimizable (0=NO; 1=YES)
END GAUSSIAN MO COEFFICIENTS
START GAUSSIAN EXPONENTS
Parameter values ; Optimizable (0=NO; 1=YES)
END GAUSSIAN EXPONENTS
START GAUSSIAN PRIMITIVE CORRECTIONS
Parameter values ; Optimizable (0=NO; 1=YES)
END GAUSSIAN PRIMITIVE CORRECTIONS
END MOLORBMODS
Each of the three blocks for coefficients, exponents and primitives can be present or absent independently.
Notes:
• The success of molorbmod optimization is likely to vary from system to system (it is perhaps
best for small molecules, since the algorithm was designed with such systems in mind). One
of the main problems is that regions of the configuration space where the potential energy is
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