A Bond-Energy/Bond-Order and Populations Relationship

Abstract

We report an analytical bond energy from bond orders and populations (BEBOP) model that provides intramolecular bond energy decompositions for chemical insight into the thermochemistry of molecules. The implementation reported here employs a minimum basis set Mulliken population analysis on well-conditioned Hartree–Fock orbitals to decompose total electronic energies into physically interpretable contributions. The model’s parametrization scheme is based on atom-specific parameters for hybridization and atom pair-specific parameters for short-range repulsion and extended Hückel-type bond energy term fitted to reproduce CBS-QB3 thermochemistry data. The current implementation is suitable for molecules involving H, Li, Be, B, C, N, O, and F atoms, and it can be used to analyze intramolecular bond energies of molecular structures at optimized stationary points found from other computational methods. This first-generation model brings the computational cost of a Hartree–Fock calculation using a large triple-ζ basis set, and its atomization energies are comparable to those from widely used hybrid Kohn–Sham density functional theory (DFT, as benchmarked to 109 species from the G2/97 test set and an additional 83 reference species). This model should be useful for the community by interpreting overall ab initio molecular energies in terms of physically insightful bond energy contributions, e.g., bond dissociation energies, resonance energies, molecular strain energies, and qualitative energetic contributions to the activation barrier in chemical reaction mechanisms. This work reports a critical benchmarking of this method as well as discussions of its strengths and weaknesses compared to hybrid DFT (i.e., B3LYP, M062X, PBE0, and APF methods), and other cost-effective approximate Hamiltonian semiempirical quantum methods (i.e., AM1, PM6, PM7, and DFTB3).

Quantum Alchemy Based Bonding Trends and Their Link to Hammett’s Equation and Pauling’s Electronegativity Model

“…Thus, the terms β A Z B and β B Z A in eq 16 can be written as (18) The β-terms account mainly for the large nuclear repulsion term Z A Z B d̅ −1 ≫ E AB in the dependent variable . We note that the linear dependence of β A on Z A is also consistent with the relation (19) between binding energies of elements Q, R, and S with Z Q = Z R − 1 = Z S − 2, which was derived from alchemical enantiomers. 69 Insertion of the definition for electronic binding energies from eq 15 into eq 19 yields (20) which implies a linear relation between the different values for β.…”

“…Partitioning of quantum mechanical observables onto the constituting parts of the quantum many-body system can be done in arbitrarily many ways. Some methods decompose the energy into different physical contributions; − others partition it onto atoms. − These methods have for example been useful to explain differences in interatomic interactions, stability, , or torsional energy profiles across various molecules. Also within the framework of computational alchemical perturbation density functional theory one can meaningfully quantify the effect of different binding partners on the atomic energy of every atom in the system .…”

Initial Decomposition of DATB Induced by an External Electric Field

“…To further understand the characteristics of C−N, we calculated the Mulliken bond orders. 40 The change of the Mulliken value indicates that the original covalent interaction between C and N disappears, which also proves the dissociation of the C−N bond from another aspect. In contrast, the electric field along the [010] direction has little effect on the bonds, indicating that the structural change is weak.…”

“…In particular, the length of the C–N bond violently increases with the increasing strength of the electric field, suggesting the decomposition of this trigger bond. To further understand the characteristics of C–N, we calculated the Mulliken bond orders . The change of the Mulliken value indicates that the original covalent interaction between C and N disappears, which also proves the dissociation of the C–N bond from another aspect.…”

From quantum alchemy to Hammett's equation: Revisiting the covalent bond

“…Less approximate and more recently, energy decomposition methods have been introduced to provide a more detailed understanding of chemical bonding. 11 Some methods decompose the energy into different physical contributions [12][13][14][15][16] while others partition it onto * anatole.vonlilienfeld@utoronto.ca atoms. 17,18 Partitioning of quantum mechanical observables onto the constituting parts of the quantum manybody system can be done in arbitrarily many ways.…”