Two complementary molecular energy decomposition schemes: The Mayer and Ziegler–Rauk methods in comparison

Abstract

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions ͓Chem. Phys. Lett. 382, 265 ͑2003͔͒, and the Ziegler-Rauk dissociation energy decomposition ͓Inorg. Chem. 18, 1558 ͑1979͔͒. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density A has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities.

Ferrocene Orientation Determined Intramolecular Interactions Using Energy Decomposition Analysis

“…Although in principle one cannot go wrong when choosing a particular decomposition scheme in EDA [45] the interaction energies of the same complex can significantly depend on the fragmentation channels [20,21,22,23,24,36,38,46,74] within the same EDA scheme. Table 1 summarizes the previous EDA studies of ferrocene using different models in the ETS scheme.…”

“…The decomposed energy terms of a molecule also depends on the theory employed [74]. Table 3 compares the EDA energies using different level of theory combining with the TZ2P+ basis set.…”

Electronic structure and bonding of lanthanoid(iii) carbonates

“…[54][55][56][57][58] The bonding energy (DE) between two fragments is defined as the sum of three terms: DE = DE Pauli + DE electrostatic + DE orbitalic . The first two terms are computed by considering the unperturbed fragments and account for the Pauli (steric) repulsion (DE Pauli ) and electrostatic interaction (DE electrostatic ), while the third term (DE orbitalic ) is the energy released when the densities are allowed to relax.…”

The theory of surface-enhanced Raman scattering

“…The effect of insertion of an atom into a molecule creates a perturbation to the energy which has also been termed the deformation energy. 31 A deformation in the crystal lattice can also be induced by an adsorbate. 32 The deformation potential is usually defined 33 as the effective electric potential experienced by free electrons in a semiconductor or metal resulting from a local deformation in the crystal lattice.…”