Accurate Diels-Alder reaction energies from efficient density functional calculations

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Density Functional Theory (DFT)

Background:

• Accurate prediction of reaction energies is crucial in computational chemistry.
• Semilocal functionals often exhibit significant errors, particularly endothermic energy errors.
• Various advanced functionals and correction methods have been developed to improve accuracy.

Purpose of the Study:

• To comprehensively assess the performance of diverse DFT functionals and methods for reaction energy calculations.
• To evaluate the impact of dispersion corrections and different reference orbitals on accuracy.
• To identify robust methods for benchmarking chemical reactions, including Diels-Alder reactions and self-interaction error-sensitive cases.

Main Methods:

• Benchmarking of semilocal, global hybrid, empirical, range-separated, and double-hybrid functionals.
• Assessment of dispersion corrections (e.g., D3, Vydrov-Van Voorhis 10).
• Evaluation of direct random phase approximation (dRPA) and RPAX2 methods with various reference orbitals.
• Use of large, augmented correlation-consistent valence basis sets and extrapolation to the complete basis set limit.
• Comparison against coupled cluster singles, doubles, and perturbative triples (CCSD(T))/complete basis set (CBS) reference energies.

Main Results:

• Global hybrid functionals generally improve accuracy over semilocal functionals but primarily shift energies exothermically.
• Dispersion corrections yield mixed results; Vydrov-Van Voorhis 10 correction outperforms the D3 correction for Diels-Alder reactions.
• Empirical functionals like M08-SO perform reasonably without explicit dispersion correction.
• The dRPA method, when using appropriate reference orbitals, provides excellent results for Diels-Alder reactions.
• dRPA methods exhibit delocalization errors, as evidenced by SIE11 test sets and H2(+) dissociation.
• RPAX2 demonstrates good performance across Diels-Alder, SIE11 test sets, and H2(+)/H2 potential energy curves, indicating no self-interaction error and reduced static correlation errors.

Conclusions:

• No single method is universally superior; the choice depends on the specific chemical system and desired accuracy.
• The direct random phase approximation (dRPA) shows significant promise but requires careful selection of reference orbitals to mitigate delocalization errors.
• The RPAX2 method emerges as a highly accurate and robust approach, effectively addressing self-interaction and static correlation errors.
• Simplified test sets (DARC6, SIE9) are proposed for future benchmarking efforts.