# Example: Electron Pair bonding in NaCl: open shell fragments¶

```
#! /bin/sh
# This example illustrates advanced usage of the bond energy decomposition
# scheme used in ADF.
# This example shows the energy decomposition analysis of NaCl with
# neutral fragments: Na and Cl, both open shell atoms
# See also the example with ionic fragments: Na+ and Cl-.
# A proper decomposition of an electron-pair bond energy requires specifying
# opposite spins for the unpaired electrons of the respective radical fragments,
# which can be done with the input key FragOccupations. The specified alpha- and
# beta-spin configurations of the radical fragments are shown in the output
# section B U I L D.
# Please note that if one neglects explicitly specifying opposite spins for the
# unpaired electrons of the fragments, each of them is treated as being half an
# alpha and half a beta electron and consequently, they enter into a spurious
# Pauli repulsive interaction. This results, among others, into the Pauli
# repulsion term being too repulsive and the orbital interaction term being too
# much stabilizing.
# The example consists of an analysis of the Na-Cl single bond between two
# open shell atoms. Two methods are described here.
# The first method uses spin-restricted fragments but simulates unrestricted fragments
# with the use of the FRAGOCCUPATIONS key.
# The second method uses real unrestricted atoms.
# Unrestricted fragments with fragoccuaptions
# -------------------------------------------
# The proper spins in this method are specified in the calculation of the overall
# molecule using the FragOccupations key. Note that this implies a slight
# approximation because the bond energy computed in this way refers to the
# energy difference between closed-shell NaCl and two open shell atoms that are
# described by orbitals from a spin-restricted SCF calculation, which have been
# given an unrestricted occupation. In other words, the set of alpha- and beta-
# spin orbitals are identical and the effect of spin polarization is missing. In
# practice, this leads to minor energy differences with respect to the correct
# bond energy, that is, the energy difference between closed-shell NaCl and the two
# open shell atoms treated in the unrestricted mode, i.e., for which the set of
# alpha- and beta-spin orbitals are allowed to relax toward different solutions
# in the SCF procedure. This correction term can be computed directly by
# carrying out an unrestricted computation of the Na and Cl atom using the spin
# restricted atoms as a fragment.
# Real unrestricted fragments
# ---------------------------
# The unrestricted calculated Na and Cl atom are used as fragments.
# Prepared for bonding
# --------------------
# Note that the Cl atom that is used as fragment is given an electron
# configuration that is so called 'prepared for bonding' in order to minimize
# the Pauli repulsion in the electron pair bond.
# In this case it means that there is a hole in the valence Cl p_z orbital,
# that will later form an electron pair bond with the valence s orbital of Na.
# Pair bonding
# ------------
# The pure orbital interaction effect of forming the electron bonding combination
# of the two radicals can be isolated from the full orbital interaction by carrying out a
# separate calculation. In this calculation the bond energy analysis is performed in
# the absence of (almost) all virtual fragment orbitals, using the key REMOVEALLFRAGVIRTUALS.
# Note that in the calculation there is a slight orbital relaxation term in addition to the
# pure orbital interaction, because not only the bonding combination of the singly occupied
# orbitals of the fragments are included, but also the anti-bonding combination.
AMS_JOBNAME=Na_r $AMSBIN/ams <<eor
System
atoms
Na 0.0 0.0 0.0
end
end
Task SinglePoint
Engine ADF
basis
core None
type TZ2P
CreateOutput Yes
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=Cl_r $AMSBIN/ams <<eor
System
atoms
Cl 0.0 0.0 0.0
end
end
Task SinglePoint
Engine ADF
irrepoccupations
SIGMA.g 6
SIGMA.u 2 1
PI.u 8
end
basis
core None
type TZ2P
CreateOutput Yes
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
symmetry D(LIN)
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=Na_u $AMSBIN/ams <<eor
System
atoms
Na 0.0 0.0 0.0 adf.f=Na
end
end
Task SinglePoint
Engine ADF
fragments
Na Na_r.results/adf.rkf
end
fragoccupations
Na
S 3 // 2
P 3 // 3
SubEnd
end
irrepoccupations
S 3 // 2
P 3 // 3
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
spinpolarization 1
title unrestricted Na
unrestricted
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=Cl_u $AMSBIN/ams <<eor
System
atoms
Cl 0.0 0.0 0.0 adf.f=Cl
end
end
Task SinglePoint
Engine ADF
fragments
Cl Cl_r.results/adf.rkf
end
fragoccupations
Cl
SIGMA.g 3 // 3
SIGMA.u 1 // 2
PI.u 4 // 4
SubEnd
end
irrepoccupations
SIGMA.g 3 // 3
SIGMA.u 1 // 2
PI.u 4 // 4
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
spinpolarization -1
symmetry D(LIN)
title unrestricted Cl
unrestricted
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=NaCl_pb $AMSBIN/ams <<eor
System
atoms
Na 0.0 0.0 0.0 adf.f=Na
Cl 0.0 0.0 2.361 adf.f=Cl
end
end
Task SinglePoint
Engine ADF
eprint
orbpop 20 20
end
sfo eig ovl
end
fragments
Na Na_r.results/adf.rkf
Cl Cl_r.results/adf.rkf
end
fragoccupations
Na
S 3 // 2
P 3 // 3
SubEnd
Cl
SIGMA.g 3 // 3
SIGMA.u 1 // 2
PI.u 4 // 4
SubEnd
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
removeallfragvirtuals
title fragoccupations pair bonding
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=NaCl $AMSBIN/ams <<eor
System
atoms
Na 0.0 0.0 0.0 adf.f=Na
Cl 0.0 0.0 2.361 adf.f=Cl
end
end
Task SinglePoint
Engine ADF
eprint
orbpop 20 20
end
sfo eig ovl
end
fragments
Na Na_r.results/adf.rkf
Cl Cl_r.results/adf.rkf
end
fragoccupations
Na
S 3 // 2
P 3 // 3
SubEnd
Cl
SIGMA.g 3 // 3
SIGMA.u 1 // 2
PI.u 4 // 4
SubEnd
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
title fragoccupations
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=NaCl_unrfrag_pb $AMSBIN/ams <<eor
System
atoms
Na 0.0 0.0 0.0 adf.f=Na
Cl 0.0 0.0 2.361 adf.f=Cl
end
end
Task SinglePoint
Engine ADF
eprint
orbpop 20 20
end
sfo eig ovl
end
fragments
Na Na_u.results/adf.rkf
Cl Cl_u.results/adf.rkf
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
removeallfragvirtuals
spinpolarization 0
title unrestricted fragments pair bonding
unrestricted
unrestrictedfragments
xc
gga BECKE PERDEW
end
EndEngine
eor
AMS_JOBNAME=NaCl_unrfrag $AMSBIN/ams <<eor
System
atoms
Na 0.0 0.0 0.0 adf.f=Na
Cl 0.0 0.0 2.361 adf.f=Cl
end
end
Task SinglePoint
Engine ADF
eprint
orbpop 20 20
end
sfo eig ovl
end
fragments
Na Na_u.results/adf.rkf
Cl Cl_u.results/adf.rkf
end
numericalquality Good
relativity
level scalar
formalism ZORA
end
spinpolarization 0
title unrestricted fragments
unrestricted
unrestrictedfragments
xc
gga BECKE PERDEW
end
EndEngine
eor
```