A Molecular "Thermometer" for Measuring Effective Non-Local Exchange

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate density functional calculations require accurate treatment of non-local exchange (NLX).
• Quantifying the effective strength of NLX in various computational methods is challenging, especially beyond simple global hybrids.
• Existing methods often struggle to provide a reliable measure of NLX's contribution to electronic structure.

Purpose of the Study:

• To introduce a novel molecular probe for quantifying the effective non-local exchange (NLX) strength in computational methods.
• To establish a relative scale ($t_X$) for evaluating NLX, ranging from 0 (local density approximation) to 100 (Hartree-Fock).
• To benchmark a wide array of density functional approximations and other computational methods based on their NLX description.

Main Methods:

• Utilized the isomerization of hexaethynylbenzene to carbo-benzene as a molecular probe due to its high sensitivity to exchange effects.
• Defined a relative measure, $t_X$, based on the isomerization energy to quantify effective NLX.
• Evaluated various density functional approximations (GGAs, meta-GGAs, global hybrids, range-separated hybrids, double hybrids), semiempirical methods, and machine-learned potentials.

Main Results:

• The $t_X$ scale effectively tracks the Hartree-Fock exchange content in global hybrids.
• Most common GGAs, meta-GGAs, and global hybrids were found to provide insufficient effective NLX.
• Range-separated hybrids, double hybrids, and some local hybrids demonstrated improved performance, approaching the coupled-cluster reference value ($t_X=60$).
• Semiempirical and machine-learned methods showed varying degrees of empirical NLX accounting.

Conclusions:

• The proposed hexaethynylbenzene isomerization reaction provides a valuable and compact thermochemical benchmark for assessing NLX in computational methods.
• The $t_X$ measure highlights deficiencies in NLX treatment for many standard electronic structure methods.
• This benchmark facilitates the development and refinement of computational models aiming for more accurate descriptions of non-local exchange effects.