Example: Bond Energy analysis open-shell fragments: PCCP¶
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, 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 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
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 EPRINT SFO eig ovl END XC GRADIENTS BECKE PERDEW END ATOMS C .0000 .0000 .6681 P .0000 .0000 2.2555 END BASIS Type TZ2P Core Large END NumericalQuality Good END INPUT eor mv TAPE21 t21cp_fpccp $ADFBIN/adf<<eor TITLE cp_fpccp_asu EPRINT SFO eig ovl END 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 NumericalQuality Good END INPUT eor rm TAPE21 logfile $ADFBIN/adf<<eor TITLE pccp_fa1_as EPRINT SFO eig ovl 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 NumericalQuality Good 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