PCCP: Bond Energy analysis open-shell fragments

Sample directory: adf/PCCP_Unr_BondEnergy/

This example illustrates advanced usage of the bond energy decomposition scheme used in ADF.

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, amongst 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 C-C single bond between two CP radicals in the four-atomic molecule PCCP. The CP fragment calculations used to provide the TAPE21 for the overall PCCP calculation must be done, for technical reasons, in the restricted mode ("cp_fpccp_asr"). The proper spins are then specified in the calculation of the overall molecule using the FragOccupations key ("pccp_fa1_as"). Note that this implies a slight approximation because the bond energy computed in this way refers to the energy difference between closed-shell PCCP and two CP radicals 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 PCCP and two CP radicals 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

a an unrestricted computation of the CP radical ("cp_fpccp_asu") using the restricted CP radical ("cp_fpccp_asr") as a fragment.

$ADFBIN/adf<<eor
TITLE cp_fpccp_asr

XC
GRADIENTS  BECKE PERDEW
END

ATOMS
  C         .0000    .0000    .6681
  P         .0000    .0000   2.2555
END

FRAGMENTS 
C   t21.C
P   t21.P
END

integration 5.0

END INPUT
eor

mv TAPE21 t21cp_fpccp

$ADFBIN/adf<<eor
TITLE cp_fpccp_asu

XC
GRADIENTS  BECKE PERDEW
END

ATOMS
  C         .0000    .0000    .6681  f=CP
  P         .0000    .0000   2.2555  f=CP
END

FRAGMENTS
CP   t21cp_fpccp
END

UNRESTRICTED
CHARGE     0   1

integration 5.0

END INPUT
eor

rm TAPE21 logfile


$ADFBIN/adf<<eor
TITLE pccp_fa1_as

EPRINT
ORBPOP  20  20
SUBEND
END

XC
GRADIENTS  BECKE PERDEW
END

ATOMS
  P         .0000    .0000   2.2555  f=CP_A
  C         .0000    .0000    .6681  f=CP_A
  C         .0000    .0000   -.6681  f=CP_B
  P         .0000    .0000  -2.2555  f=CP_B
END

integration 5.0

FRAGMENTS
CP_A   t21cp_fpccp
CP_B   t21cp_fpccp
END

SYMMETRY   C(LIN)

FRAGOCCUPATIONS
CP_A
  SIGMA 3//2
  PI    2//2
SUBEND
CP_B
  SIGMA 2//3
  PI    2//2
SUBEND
END

END INPUT
eor