Example: Bond Energy analysis meta-GGA, (meta-)hybrids: Zn2, Cr2, CrH¶

#! /bin/sh

# This example illustrates the bond energy decomposition scheme using metaGGA or
# metahybrid or hybrid functionals in ADF.

# The first example is straightforward with closed shell atomic fragments: Zn_2.
# The second example has open shell atomic fragments: Cr_2, and the extra
# complication that spin symmetry breaking lowers the energy of the molecule,
# although the total S_z-value is zero. The third example has open shell atomic
# fragments, and the molecule is open shell: CrH.

# == Zn2 ==

# In the first example for Zn_2 the metahybrid TPSSh is used. In the bond energy
# analysis, the bond energy is split in a Pauli repulsion term, a steric
# interaction, and an orbital interaction.

$ADFBIN/adf <<eor
   Atoms
      Zn 0.0 0.0 0.0
      Zn 0.0 0.0 3.2
   End
   XC
    metahybrid TPSSh
   end
   Basis
    Type TZ2P
    Core None
   End
   dependency bas=1e-4
   BeckeGrid
      Quality good
   End
eor

rm TAPE21 logfile


# == Cr2 ==

# In the second example for Cr2 the metaGGA TPSS is used. Since the fragments
# are open shell, one may want to use unrestricted fragments, however, this is
# not possible in ADF. A fair approximation to a computation with unrestricted
# fragments can be achieved with the key FRAGOCCUPATIONS. You tell ADF that you
# want to treat the fragments as if they were unrestricted; this causes the
# program to duplicate the one-electron orbitals of the fragment: one set for
# spin-alpha and one set for spin-beta. You can then specify occupation numbers
# for these spin-unrestricted fragments, and occupy spin-alpha orbitals
# differently from spin-beta orbitals. Especially for the Pauli-repulsion it is
# important that one chooses the spin-occupations on the different fragments
# such that they are 'prepared for bonding'.

# Of course, the unrestricted fragments that you use in this way, are not self-
# consistent: 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, while here you have
# spatially identical fragment orbitals. Nevertheless it is often a fair
# approximation which gives you a considerable extension of analysis
# possibilities.

# Spin-symmetry breaking is enforced by the use of the key ModifyStartPotential
# in combination with the key key UNRESTRICTED. In the ADF output one can find
# that there is spin-density on both of the atoms.



$ADFBIN/adf <<eor
   Atoms
      Cr.1 0.0 0.0 0.0
      Cr.2 0.0 0.0 1.8
   End
   XC
      metagga TPSS
   end
   Basis
      Type TZ2P
      Core None
   End
   dependency bas=1e-4
   BeckeGrid
      Quality good
   End
   unrestricted
   charge 0 0
   ModifyStartPotential
      Cr.1 1 // 0
      Cr.2 0 // 1
   End 
   FragOccupations
      Cr.1
         S 4 // 3
         P 6 // 6
         D 5 // 0
      SubEnd
      Cr.2
         S 3 // 4
         P 6 // 6
         D 0 // 5
      SubEnd
   End
eor

rm TAPE21 logfile


# In order to calculate the effect of self-consistency one should calculate the
# Cr atom spin-unrestrictedly.


$ADFBIN/adf <<eor
   Atoms
      Cr 0.0 0.0 0.0
   End
   XC
      metagga TPSS
   end
   Basis
      Type TZ2P
      Core None
   End
   BeckeGrid
      Quality good
   End
   unrestricted
   charge 0 6
   FragOccupations
      Cr
         S 4 // 3
         P 6 // 6
         D 5 // 0
    SubEnd
   End
eor

rm TAPE21 logfile


# == CrH ==

# In the third example for CrH the hybrid B3LYP is used.


$ADFBIN/adf <<eor
   Atoms
      Cr 0.0 0.0 0.0
      H  0.0 0.0 1.65
   End
   XC
      hybrid B3LYP
   end

   Basis
      Type TZ2P
      Core None
   End
   dependency bas=1e-4
   BeckeGrid
      Quality good
   End
   unrestricted
   charge 0 5
   FragOccupations
      Cr
         S 4 // 3
         P 6 // 6
         D 5 // 0
    SubEnd
      H
         S 0 // 1
    SubEnd
   End
eor

rm TAPE21 logfile


# In order to calculate the effect of self-consistency of spin-polarization on
# the atoms one should calculate the Cr and H atom spin-unrestrictedly.


$ADFBIN/adf <<eor
   Atoms
      Cr 0.0 0.0 0.0
   End
   XC
      hybrid B3LYP
   end
   Basis
      Type TZ2P
      Core None
   End
   dependency bas=1e-4
   BeckeGrid
      Quality good
   End
   unrestricted
   charge 0 6
   FragOccupations
      Cr
         S 4 // 3
         P 6 // 6
         D 5 // 0
      SubEnd
   End
eor

rm TAPE21 logfile

$ADFBIN/adf <<eor
   Atoms
      H 0.0 0.0 0.0
   End
   XC
      hybrid B3LYP
   end
   Basis
      Type TZ2P
      Core None
   End
   dependency bas=1e-4
   BeckeGrid
      Quality good
   End
   unrestricted
   charge 0 1
   FragOccupations
      H
         S 1 // 0
      SubEnd
   End
eor

rm TAPE21 logfile