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

Download EDA_meta_gga_hybrid.run

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: Zn₂ . The second example has open shell atomic fragments: Cr₂ , 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 Zn₂ 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
End Input
eor

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
End Input
eor

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
End Input
eor

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
End Input
eor

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
End Input
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
End Input
eor