Bond energy details
In the framework of Kohn-Sham MO theory and in conjunction with the fragment approach, one can decompose the bond energy between the fragments of a molecular system - say, a base and a substrate for E2 elimination - into contributions associated with the various orbital and electrostatic interactions. In ADF, we follow a Morokuma-type energy decomposition method. The overall bond energy ΔE is divided into two major components. In the first place, the preparation energy ΔEprep corresponding to the amount of energy required to deform the separated fragments, A and B say, from their equilibrium structure to the geometry they acquire in the overall molecule (ΔEprep,geo), and to excite them to their valence electronic configuration (ΔEprep,el). In the second place, the interaction energy ΔEint between the prepared fragments.
ΔE = ΔEprep + ΔEint = ΔEprep,geo + ΔEprep,el + ΔEint
In the following step, the interaction energy ΔEint is further decomposed into three physically meaningful terms, which are printed in the ADF output file.
ΔEint = ΔVelst + ΔEPauli + ΔEoi = ΔE0 + ΔEoi
The term ΔVelst corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the prepared fragments as they are brought together at their final positions, giving rise to an overall density that is simply a superposition of fragment densities ρA+ρB. (Note that we use the convention that energy terms containing potential energy only, kinetic energy only, or both kinetic and potential energy are indicated by V, T, and E, respectively.) For neutral fragments, ΔVelst is usually attractive. The Pauli repulsion ΔEPauli arises as the energy change associated with going from ρA+ρB the wave function Ψ0=NA[ΨAΨB] that properly obeys the Pauli principle through explicit antisymmetrization (A operator) and renormalization (N constant) of the product of fragment wave functions. It comprises the destabilizing interactions between occupied orbitals, and is responsible for any steric repulsion. In case of neutral fragments, it can be useful to combine ΔVelst and ΔEPauli in a term ΔE0 which, in the past, has been conceived as the steric interaction. However, we prefer to reserve the designation steric interaction or repulsion for ΔEPauli because that is, as already mentioned, the only source of net repulsive interactions between molecular fragments. Finally, the wavefunction is allowed to relax from Ψ0 to the fully converged wave function Ψ. The associated orbital interaction energy ΔEoi accounts for electron pair bonding, charge transfer (e.g., HOMO-LUMO interactions) and polarization (empty/occupied orbital mixing on one fragment due to the presence of another fragment). This can be further decomposed into the contributions from the distinct irreducible representations Γ of the interacting system using the extended transition state method. In systems with a clear σ/π separation, this symmetry partitioning proves to be very informative.
ΔEoi = ∑Γ ΔEoi,Γ
An extensive discussion of the physical meaning of all the terms in the energy decomposition is given in
F.M. Bickelhaupt and E.J. Baerends,
Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry,
In: Rev. Comput. Chem.; Lipkowitz, K. B. and Boyd, D. B., Eds.;
Wiley-VCH: New York, 2000, Vol. 15, 1-86.
Text is mostly taken from: Chemistry with ADF, G. te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen, J.G. Snijders, T. Ziegler J. Comp. Chem. 22 (2001) 931.
Links
ADF User Documentation: bond energy analysis
ADF-GUI: analysis
Examples: analysis options: fragment orbitals and bond energy decomposition
References: bond energy analysis
Related: molecule built from fragments, the Kohn-Sham MO model,
bond energy analysis
