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 Sz -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