Eliminating Systematic Errors in DFT via Connectivity-Based Hierarchy: Accurate Bond Dissociation Energies of Biodiesel Methyl Esters

Abstract

We present a computational study focusing on the determination of accurate bond dissociation energies (BDEs) involved in the combustion of biodiesel methyl esters. We have adapted our previously developed efficient error-cancellation protocols, based on the systematic "connectivity-based hierarchy" (CBH), to derive accurate BDEs of biodiesel molecules at a modest computational cost. Using DFT energies on the full biodiesel molecule in conjunction with accurate G4 energies on the small fragments involved in the CBH reaction schemes, systematic errors in the DFT methods can be cancelled efficiently. Herein, we apply our G4corrected ΔCBH-2 and ΔCBH-3 schemes in conjunction with several popular DFT methods to determine accurate bond dissociation energies of different C−C, C−H, and C−O bonds in biodiesel surrogate molecules. We first evaluate the performance of different DFT methods using a test set of 21 reactions involving various bond dissociations in small to medium biodiesel surrogates (up to methyl decanoate, a C10-methyl ester) by calibration against accurate values calculated with multireference methods (MRACPF2), reported by Carter and co-workers. The CBH-2 corrections for all tested dispersion-corrected functionals yield mean absolute deviations (MADs) in a narrow range of 1.3−1.5 kcal/mol, the best performance being obtained for B97-D3 and ωB97X-D functionals (MAD = 1.3 kcal/mol). Further, significant improvement yielding a MAD of only 0.9 kcal/mol is obtained using the G4-corrected CBH-3 scheme. Finally, the protocol has been applied to derive accurate BDEs of eight different bonds in the larger biodiesel molecule, methyl linolenate, yielding a MAD of only 1.13 kcal/mol using the ΔCBH-3 error correction scheme. The results suggest that our protocol in conjunction with different DFT methods should be broadly applicable to yield accurate BDEs for a variety of large biodiesel molecules.

A Fragmentation-Based Graph Embedding Framework for QM/ML

“…For example, we have developed the Connectivity-Based Hierarchy (CBH) of error cancellation schemes that provides an automated protocol to generate isodesmic-type reactions, which increasingly preserve the chemical environment on both sides of a reaction. , CBH reactions can be used to eliminate certain systematic errors present in approximate levels of theory via a corrective term derived from the reactants and products of the CBH reaction calculated at low and high levels of theory. The CBH approach has been utilized to study a broad range of thermochemical problems with an accuracy comparable to cWFT methods at the cost of low-fidelity DFT calculations, including heat of formation of charged and neutral organic and biomolecules, − redox potentials, p K a s, and bond dissociation energies . Thus, where the direct computation of accurate energies is not possible, the exploitation of systematic error cancellation provides a viable (and often the only) alternative to achieve high accuracies in thermochemistry .…”

“…The CBH approach has been utilized to study a broad range of thermochemical problems with an accuracy comparable to cWFT methods at the cost of low-fidelity DFT calculations, including heat of formation of charged and neutral organic and biomolecules, 16−22 redox potentials, 23 pK a s, 24 and bond dissociation energies. 25 Thus, where the direct computation of accurate energies is not possible, the exploitation of systematic error cancellation provides a viable (and often the only) alternative to achieve high accuracies in thermochemistry. 15 In this context, we note that related ideas using multiple levels of theory have also been developed via the fragmentation-based hybrid QM/QM approach for the study of large molecules to perform electronic structure calculations that would otherwise be computationally prohibitive.…”

Effective Molecular Descriptors for Chemical Accuracy at DFT Cost: Fragmentation, Error-Cancellation, and Machine Learning

“…CBH has been applied to achieve accurate thermochemical values of neutral, , radical, and cationic organic molecules as well as biomolecular , systems. Additionally, the method has been applied to reaction energies, bond dissociation energies, p K a calculations, and redox potentials . The correction method works by first constructing the reaction of a given rung of CBH and then calculating the energy of each of the fragments at a low level baseline (b) and the higher target (t) level of theory.…”

The Corrected Values of ΔrHo(CaHbOd, a≤16) of Atomization of the Aromatic Compounds and Their Uncertainties Determined Using Several Quantum Mechanical Approaches

“…The simplest and most universal way for the increasing accuracy of determination of Δ f H o 298.15 (X) of large compounds is using the thermochemistry of homodesmotic and isodesmic reactions, [1] or other schemes capable to eliminate the systematic errors of their calculations. [2][3][4] However, these approaches are limited by the accuracy of the measured (or literature) values of Δ f H o 298.15 of compounds, used for these reactions or schemes, as well as they are requiring the additional calculations of thermochemical properties of others components of reactions. These schemes are based on the thermochemistry of reactions included several components, thermochemical properties of only one of which are unknown.…”