# Example: Spin-unrestricted Fragments: H2¶

```
#! /bin/sh
# This is a small but important example to illustrate what goes into an accurate
# calculation of the 'true' bond energy of a molecule. The (ADF-specific)
# problem is that in a straightforward molecular calculation, the bond energy is
# computed as the energy difference between at the one hand the molecule, and at
# the other hand the isolated spherically symmetric spin-restricted atoms.
# This spherically symmetric spin-restricted reference (comparison) state is usually
# not the physical ground state of the reference system (isolated atoms) and
# hence the computed energy difference has no direct relation to experimental
# data. To account for the true atomic ground states, one has to add correction
# terms. Study this sample carefully to make sure that you fully understand the
# steps to take and consult the User's Guide for details. See also the this
# document for a discussion of multiplet states.
# See also the example, SD_Cr(NH3)6.
# The H2 case consists of a sequence of simple calculations to demonstrate the
# Unrestricted Fragments options.
# In the first part real spin-unrestricted fragments are used.
# In the second part simulate spin-unrestricted fragments are used.
# Unrestricted fragments
# ======================
# If one uses unrestricted fragments one needs to calculate the unrestricted
# H atom twice, one in which the 1s alpha orbital is occupied, and one in which
# the 1s beta orbital is occupied.
AMS_JOBNAME=H_A $AMSBIN/ams <<eor
System
atoms
H 0.0 0.0 0.0
end
end
Task SinglePoint
Engine ADF
eprint
sfo eig ovl
end
basis
type DZP
end
spinpolarization 1
unrestricted
EndEngine
eor
AMS_JOBNAME=H_B $AMSBIN/ams <<eor
System
atoms
H 0.0 0.0 0.0
end
end
Task SinglePoint
Engine ADF
eprint
sfo eig ovl
end
basis
type DZP
end
spinpolarization -1
unrestricted
EndEngine
eor
AMS_JOBNAME=H2_AB $AMSBIN/ams <<eor
System
atoms
H 0 0 0.375 adf.f=H_A
H 0 0 -0.375 adf.f=H_B
end
end
Task SinglePoint
Engine ADF
title H2 from unrestricted fragments
eprint
sfo eig ovl
end
fragments
H_A H_A.results/adf.rkf
H_B H_B.results/adf.rkf
end
spinpolarization 0
unrestricted
unrestrictedfragments
EndEngine
eor
# In the unrestricted fragment different numbers of spin-alpha and spin-beta electrons usually
# result in different spatial orbitals and different energy eigenvalues for
# spin-alpha and spin-beta when you go to self-consistency.
# For H2 calculated from real unrestricted fragments this will mean that the SFO analysis of
# the H2 molecular orbitals looks a bit unsymmetric.
# However, if one simulates the unrestricted fragments with the key FRAGOCCUPATIONS
# the SFO analysis for H2 will be symmetric.
# Simulated unrestricted fragments with the key FRAGOCCUPATIONS
# =============================================================
# In this approach spin-restricted fragments are used, in which
# one has the same spatial orbitals and energy eigenvalues for
# spin-alpha and spin-beta.
# The energy difference between an unrestricted
# fragment as it is used with the key FRAGOCCUPATIONS and a self-consistent
# unrestricted fragment is computed. This turns out to be quite small,
# confirming that this approach with simulated unrestricted fragments,
# although not formally exact, is also adequate for practical purposes.
$AMSBIN/dirac -n1 < $AMSRESOURCES/Dirac/H
mv TAPE12 t12.rel
AMS_JOBNAME=H_R $AMSBIN/ams <<eor
System
Atoms
H 0.0 0.0 0.0
End
end
Task SinglePoint
Engine ADF
create H file=$AMSRESOURCES/ADF/ZORA/DZP/H
corepotentials t12.rel
H 1
end
EndEngine
eor
AMS_JOBNAME=H_U_noscf $AMSBIN/ams <<eor
System
atoms
H 0 0 0
end
end
Task SinglePoint
Engine ADF
title H unrestr., not self-consistent (as used in unr.frag. calcs)
eprint
sfo eig ovl
end
fragments
H H_R.results/adf.rkf
end
scf
iterations 0
end
spinpolarization 1
unrestricted
EndEngine
eor
# By setting the scf iterations to zero (a value of one (1) would give the same
# result) we prevent cycling to self-consistency. The energy of the 'final' one-
# electron orbitals is consequently computed in the start-up potential, i.e. the
# field of the restricted (basic) atom, where spin-alpha and spin-beta are equally
# occupied, in this case by 0.5 electron each. The not-self-consistent,
# unrestricted H atom is precisely the 'unrestricted' fragment as it can be used
# in an adf calculation with the FRAGOCCUPATIONS key. The fragment file must be
# the TAPE21 result file from a restricted run, but at start-up you can specify
# that the Fragment Orbitals are, for purposes of reference and comparison,
# occupied in an unrestricted way in the final molecule.
# A calculation that uses restricted fragments right away computes the bonding
# energy relative to the restricted fragments. The difference between using
# restricted and unrestricted fragments is the 'bonding' energy computed in the
# run above.
AMS_JOBNAME=H_U_scf $AMSBIN/ams <<eor
System
atoms
H 0 0 0
end
end
Task SinglePoint
Engine ADF
title H unr. self-consistent from unr.0
eprint
sfo eig ovl
end
fragments
H H_R.results/adf.rkf
end
fragoccupations
H
s 1 // 0
subend
end
spinpolarization 1
unrestricted
EndEngine
eor
# Here we start with the unrestricted fragment and relax to self-consistency.
# The 'bonding energy', i.e. the relaxation energy, is very small, demonstrating
# that using non-self-consistent unrestricted fragments involves only a small
# error (which, moreover, can be computed as shown here).
# The key UnRestricted sets the spin-unrestricted mode. The key Charge is used
# to specify a net total charge of zero and a net total spin polarization by an
# excess of 1.0 spin-alpha electrons over spin-beta.
AMS_JOBNAME=H2_R $AMSBIN/ams <<eor
System
atoms
H 0 0 0.375
H 0 0 -0.375
end
end
Task SinglePoint
Engine ADF
title H2 restricted, from restricted fragments
eprint
sfo eig ovl
end
fragments
H H_R.results/adf.rkf
end
EndEngine
eor
# This is the simplest approach, using restricted fragments. The bonding energy
# must be corrected because the reference (restricted H atoms, with 0.5
# electrons in spin-alpha and 0.5 in spin-beta) is far from the true H-atom
# ground state: see the previous runs on the single H atom.
AMS_JOBNAME=H2_U $AMSBIN/ams <<eor
System
atoms
H.1 0 0 0.375
H.2 0 0 -0.375
end
end
Task SinglePoint
Engine ADF
title H2 from simulated unrestricted fragments using the FRAGOCCUPATIONS key
eprint
sfo eig ovl
end
fragments
H.1 H_R.results/adf.rkf
H.2 H_R.results/adf.rkf
end
fragoccupations
H.1
s 1 // 0
subend
H.2
s 0 // 1
subend
end
irrepoccupations
sigma 2
end
modifystartpotential
H.1 1 // 0
H.2 0 // 1
end
EndEngine
eor
# This should be a fair approximation (in the LDA model) to the bonding energy
# of H2 with respect to the unrestricted H atoms. The difference between the
# bonding energies of this and the previous run should be very close to the
# energy of the not-self-consistent unrestricted H-atom with respect to the
# restricted basic atom.
# == Excited state ==
AMS_JOBNAME=H2_excited $AMSBIN/ams <<eor
System
atoms
H 0 .0 0.375
H 0 .0 -0.375
end
end
Task SinglePoint
Engine ADF
title H2 excited
eprint
sfo eig ovl
end
fragments
H H_R.results/adf.rkf
end
fragoccupations
H
s 1 // 0
subend
end
irrepoccupations
sigma.g 1 // 0
sigma.u 1 // 0
end
spinpolarization 2
unrestricted
EndEngine
eor
# Finally the calculation of an excited state, with respect to unrestricted
# fragments. The excitation energy is obtained by comparing the energy with the
# energy of the ground state calculation. This difference compares reasonably,
# but not accurately, to the difference in one-electron ground state energies of
# the involved orbitals (Koopman's theorem).
# Note that excitation energies can also be calculated with Time-Dependent DFT,
# using the EXCITATIONS key of ADF. See related sample runs.
```