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

Download NaCl_pairbonding.run

#! /bin/sh

# This example illustrates advanced usage of the bond energy decomposition

# This example shows the energy decomposition analysis of NaCl with
# neutral fragments: Na and Cl, both open shell atoms

# 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.

$ADFBIN/adf<<eor Atoms Na 0.0 0.0 0.0 End XC GGA BECKE PERDEW End BASIS Type TZ2P Core None End NumericalQuality Good relativistic scalar zora eor rm logfile mv TAPE21 Na_r.t21$ADFBIN/adf<<eor
Atoms
Cl  0.0 0.0 0.0
End
XC
GGA  BECKE PERDEW
End
BASIS
Type TZ2P
Core None
End
Symmetry D(LIN)
IrrepOccupations
SIGMA.g 6
SIGMA.u 2 1
PI.u    8
End
NumericalQuality Good
relativistic scalar zora
eor

rm logfile
mv TAPE21 Cl_r.t21

$ADFBIN/adf<<eor TITLE unrestricted Na XC GGA BECKE PERDEW End Atoms Na 0.0 0.0 0.0 f=Na End NumericalQuality Good relativistic scalar zora unrestricted charge 0 1 Fragments Na Na_r.t21 End IrrepOccupations S 3 // 2 P 3 // 3 End FragOccupations Na S 3 // 2 P 3 // 3 SubEnd End eor rm logfile mv TAPE21 Na_u.t21$ADFBIN/adf<<eor
TITLE unrestricted Cl
XC
GGA  BECKE PERDEW
End
Atoms
Cl  0.0 0.0 0.0 f=Cl
End
NumericalQuality Good
relativistic scalar zora
unrestricted
charge 0 -1
Symmetry D(LIN)
IrrepOccupations
SIGMA.g 3 // 3
SIGMA.u 1 // 2
PI.u    4 // 4
End
Fragments
Cl   Cl_r.t21
End
FragOccupations
Cl
SIGMA.g 3 // 3
SIGMA.u 1 // 2
PI.u    4 // 4
SubEnd
End
eor

rm logfile
mv TAPE21 Cl_u.t21

$ADFBIN/adf<<eor TITLE fragoccupations pair bonding EPRINT SFO eig ovl ORBPOP 20 20 SubEnd End XC GGA BECKE PERDEW End Atoms Na 0.0 0.0 0.0 f=Na Cl 0.0 0.0 2.361 f=Cl End NumericalQuality Good relativistic scalar zora Fragments Na Na_r.t21 Cl Cl_r.t21 End RemoveAllFragVirtuals FragOccupations Na S 3 // 2 P 3 // 3 SubEnd Cl SIGMA.g 3 // 3 SIGMA.u 1 // 2 PI.u 4 // 4 SubEnd End eor rm logfile mv TAPE21 NaClpb.t21$ADFBIN/adf<<eor
TITLE fragoccupations
EPRINT
SFO eig ovl
ORBPOP  20  20
SubEnd
End
XC
GGA  BECKE PERDEW
End
Atoms
Na 0.0 0.0 0.0   f=Na
Cl 0.0 0.0 2.361 f=Cl
End
NumericalQuality Good
relativistic scalar zora
Fragments
Na  Na_r.t21
Cl  Cl_r.t21
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
eor

rm logfile
mv TAPE21 NaCl.t21

$ADFBIN/adf<<eor TITLE unrestricted fragments pair bonding EPRINT SFO eig ovl ORBPOP 20 20 SubEnd End XC GGA BECKE PERDEW End Atoms Na 0.0 0.0 0.0 f=Na Cl 0.0 0.0 2.361 f=Cl End NumericalQuality Good relativistic scalar zora unrestrictedfragments unrestricted charge 0 0 Fragments Na Na_u.t21 Cl Cl_u.t21 End RemoveAllFragVirtuals eor rm logfile mv TAPE21 NaClpb.t21$ADFBIN/adf<<eor
TITLE unrestricted fragments
EPRINT
SFO eig ovl
ORBPOP  20  20
SubEnd
End
XC
GGA  BECKE PERDEW
End
Atoms
Na 0.0 0.0 0.0   f=Na
Cl 0.0 0.0 2.361 f=Cl
End
NumericalQuality Good
relativistic scalar zora
unrestrictedfragments
unrestricted
charge 0 0
Fragments
Na  Na_u.t21
Cl  Cl_u.t21
End
eor

rm logfile
mv TAPE21 NaCl.t21