# Example: Multiplet States: [Cr(NH3)6]3+¶

```
#! /bin/sh
# The computation of multiplet states corresponding to an open-shell system can
# be carried out with ADF by first computing the 'Average-of-Configuration'
# (aoc) state, where all orbitals in the open shell are degenerate and equally
# occupied. This computation is spin-restricted and serves as a fragment file
# for the multiplet run, where then different occupation numbers are assigned to
# the various orbitals in the open shell. The corresponding energies are
# computed in the field of the aoc, which is achieved by not iterating the self-
# consistency equations to convergence but only computing the orbitals in the
# initial field.
# Since ADF requires that all symmetry-partners in an irreducible representation
# (irrep) have equal occupations, the multiplet calculation, where such orbitals
# are not equally occupied, must be carried out in a formally lower point group
# symmetry. The point group to select and the appropriate occupation numbers to
# apply must be worked out by the user 'on paper' in advance.
# See the discussion of Multiplet energies in ADF manual.
# The script starts with the 'creation' of the required basic atoms, N, H, Cr
# using a fair basis set quality.
# The next step is the computation of the ammonia fragment NH3. This is not a
# crucial step here: the multiplet state computation can equally well be carried
# out by not using any intermediate compound fragments. However, it illustrates
# once more how a bigger molecule can be built up from smaller, but not trivial
# fragments.
$AMSBIN/dirac -n1 < $AMSRESOURCES/Dirac/Cr.2p
mv TAPE12 t12.rel
AMS_JOBNAME=Cr $AMSBIN/ams <<eor
System
Atoms
Cr 0.0 0.0 0.0
End
End
Task SinglePoint
Engine ADF
create Cr file=$AMSRESOURCES/ADF/ZORA/TZP/Cr.2p
corepotentials t12.rel
Cr 1
end
EndEngine
eor
AMS_JOBNAME=NH3 $AMSBIN/ams <<eor
System
symmetrize
atoms
N 0 0 0
H -0.95522523 0 0.3711068
H 0.477612615 -0.8272493155158333 0.3711068
H 0.477612615 0.8272493155158333 0.3711068
end
end
Task SinglePoint
Engine ADF
title AMMONIA
basis
core Small
type TZP
CreateOutput No
end
noprint sfo,frag,functions
symmetry C(3V)
EndEngine
eor
# The input of the atomic coordinates does not use expressions. In this case to
# enforce exact symmetry relations 14-digit input values are required.
# The symmetrization key is used to enforce the symmetry to machine precision,
# and to put the molecule in the right orientation for the symmetry.
# The symmetry specification is redundant: the program would
# also find it by itself.
# == Average-of-Configuration ==
# The next step is to compute the reference state, with respect to which we will
# later compute the multiplet states. The reference state is the so-called
# 'Average-of-configuration' (aoc) state. The result file (TAPE21) of this
# calculation will be used as a fragment file.
AMS_JOBNAME=AOC $AMSBIN/ams <<eor
System
symmetrize
atoms
Cr 0.00000000 0.00000000 0.00000000
N 0.00000000 1.71464325 1.21243632 adf.f=NH3|1
H 0.00000000 1.46615142 2.20663314 adf.f=NH3|1
H -0.82724932 2.29340040 1.03672570 adf.f=NH3|1
H 0.82724932 2.29340040 1.03672570 adf.f=NH3|1
N -1.48492461 -0.85732162 1.21243632 adf.f=NH3|2
H -1.26972438 -0.73307571 2.20663314 adf.f=NH3|2
H -1.57251835 -1.86311912 1.03672570 adf.f=NH3|2
H -2.39976767 -0.43028128 1.03672570 adf.f=NH3|2
N 1.48492461 -0.85732162 1.21243632 adf.f=NH3|3
H 1.26972438 -0.73307571 2.20663314 adf.f=NH3|3
H 2.39976767 -0.43028128 1.03672570 adf.f=NH3|3
H 1.57251835 -1.86311912 1.03672570 adf.f=NH3|3
N 0.00000000 -1.71464325 -1.21243632 adf.f=NH3|4
H 0.00000000 -1.46615142 -2.20663314 adf.f=NH3|4
H 0.82724932 -2.29340040 -1.03672570 adf.f=NH3|4
H -0.82724932 -2.29340040 -1.03672570 adf.f=NH3|4
N 1.48492461 0.85732162 -1.21243632 adf.f=NH3|5
H 1.26972438 0.73307571 -2.20663314 adf.f=NH3|5
H 1.57251835 1.86311912 -1.03672570 adf.f=NH3|5
H 2.39976767 0.43028128 -1.03672570 adf.f=NH3|5
N -1.48492461 0.85732162 -1.21243632 adf.f=NH3|6
H -1.26972438 0.73307571 -2.20663314 adf.f=NH3|6
H -2.39976767 0.43028128 -1.03672570 adf.f=NH3|6
H -1.57251835 1.86311912 -1.03672570 adf.f=NH3|6
end
end
Task SinglePoint
Engine ADF
title Cr(NH3)6 : Average-of-Configuration run
comment
using NH3-fragments
end
fragments
Cr Cr.results/adf.rkf
NH3 NH3.results/adf.rkf
end
Basis CreateOutput=No
irrepoccupations
A1.G 8.75
A2.G 2
E1.G 16 1.5 0.75
A1.U 2
A2.U 8
E1.U 20
end
scf
iterations 25
mixing 0.15
end
symmetry D(3d)
EndEngine
eor
# Occupation numbers are specified, to make certain what the reference state is
# that we will start from in the subsequent calculations. The result file TAPE21
# is saved to serve as fragment file in the subsequent calculations.
# == One-determinant states ==
# Now, we proceed with the multiplet calculations. In the example they are
# combined in one single run, but they could also be evaluated in separate runs.
# For each calculation it is required to:
# a) Use the aoc TAPE21 file as fragment file
# b) Choose which molecular orbitals in the open shell to occupy: select the
# appropriate point group symmetry and the UnRestricted key if necessary and
# specify the occupation numbers, using the irreducible representations of the
# selected point group.
# The results are one-determinant calculations, which must then, later, be
# combined analytically to obtain the required multiplet energy values.
AMS_JOBNAME=SD $AMSBIN/ams <<eor
System
symmetrize
atoms
Cr 0.00000000 0.00000000 0.00000000 adf.f=CrA6
N 0.00000000 1.71464325 1.21243632 adf.f=CrA6
H 0.00000000 1.46615142 2.20663314 adf.f=CrA6
H -0.82724932 2.29340040 1.03672570 adf.f=CrA6
H 0.82724932 2.29340040 1.03672570 adf.f=CrA6
N -1.48492461 -0.85732162 1.21243632 adf.f=CrA6
H -1.26972438 -0.73307571 2.20663314 adf.f=CrA6
H -1.57251835 -1.86311912 1.03672570 adf.f=CrA6
H -2.39976767 -0.43028128 1.03672570 adf.f=CrA6
N 1.48492461 -0.85732162 1.21243632 adf.f=CrA6
H 1.26972438 -0.73307571 2.20663314 adf.f=CrA6
H 2.39976767 -0.43028128 1.03672570 adf.f=CrA6
H 1.57251835 -1.86311912 1.03672570 adf.f=CrA6
N 0.00000000 -1.71464325 -1.21243632 adf.f=CrA6
H 0.00000000 -1.46615142 -2.20663314 adf.f=CrA6
H 0.82724932 -2.29340040 -1.03672570 adf.f=CrA6
H -0.82724932 -2.29340040 -1.03672570 adf.f=CrA6
N 1.48492461 0.85732162 -1.21243632 adf.f=CrA6
H 1.26972438 0.73307571 -2.20663314 adf.f=CrA6
H 1.57251835 1.86311912 -1.03672570 adf.f=CrA6
H 2.39976767 0.43028128 -1.03672570 adf.f=CrA6
N -1.48492461 0.85732162 -1.21243632 adf.f=CrA6
H -1.26972438 0.73307571 -2.20663314 adf.f=CrA6
H -2.39976767 0.43028128 -1.03672570 adf.f=CrA6
H -1.57251835 1.86311912 -1.03672570 adf.f=CrA6
end
end
Task SinglePoint
Engine ADF
title Cr(NH3)6 : SlaterDeterminants run
fragments
CrA6 AOC.results/adf.rkf
end
noprint frag
scf
iterations 0
end
slaterdeterminants
Check AOC
A1.g 4 0.375 // 4 0.375
A2.g 1 // 1
E1.g:1 4 0.375 0.1875 // 4 0.375 0.1875
E1.g:2 4 0.375 0.1875 // 4 0.375 0.1875
A1.u 1//1
A2.u 4//4
E1.u:1 5//5
E1.u:2 5//5
SUBEND
State1
A1.g 4 1 // 4 1
A2.g 1 // 1
E1.g:1 4 0 0 // 4 0 1
E1.g:2 4 0 0 // 4 0 0
A1.u 1//1
A2.u 4//4
E1.u:1 5//5
E1.u:2 5//5
SUBEND
State2
A1.g 4 1 // 4 1
A2.g 1 // 1
E1.g:1 4 0 0 // 4 1 0
E1.g:2 4 0 0 // 4 0 0
A1.u 1//1
A2.u 4//4
E1.u:1 5//5
E1.u:2 5//5
SUBEND
State3
A1.g 4 1 // 4 1
A2.g 1 // 1
E1.g:1 4 0 1 // 4 0 0
E1.g:2 4 0 0 // 4 0 0
A1.u 1//1
A2.u 4//4
E1.u:1 5//5
E1.u:2 5//5
SUBEND
end
symmetry C(I)
unrestricted
EndEngine
eor
# The SlaterDeterminants block may contain any number of sub blocks, each
# starting with an (arbitrary) title record, followed by a set of occupation
# numbers and closed by a SubEnd record. Each such subkey block specifies a
# single one-determinant-state calculation. All occupation numbers must
# reference the irreps of the specified point group symmetry, C(I) in the
# example, and must be just a reassignment of the electrons that are equally
# distributed over the corresponding degenerate irreps in the reference aoc
# calculation.
# The so-obtained energies of the one-determinant states can now be combined to
# calculate the desired multiplet energies. See the ADF manual.
# Note carefully that in the calculation of the SingleDeterminants, the scf
# procedure is prevented to cycle to convergence by setting the subkey
# Iterations to zero in the SCF data block.
```