Approaching Coupled Cluster Accuracy with Density Functional Theory Using the Generalized Connectivity-Based Hierarchy

This Perspective reviews connectivity-based hierarchy(CBH), asystematic hierarchy of error-cancellation schemes developed in ourgroup with the goal of achieving chemical accuracy using inexpensivecomputational techniques ("coupled cluster accuracy with DFT").The hierarchy is a generalization of Pople's isodesmic bondseparation scheme that is based only on the structure and connectivityand is applicable to any organic and biomolecule consisting of covalentbonds. It is formulated as a series of rungs involving increasinglevels of error cancellation on progressively larger fragments ofthe parent molecule. The method and our implementation are discussedbriefly. Examples are given for the applications of CBH involving(1) energies of complex organic rearrangement reactions, (2) bondenergies of biofuel molecules, (3) redox potentials in solution, (4)pK (a) predictions in the aqueous medium,and (5) theoretical thermochemistry combining CBH with machine learning.They clearly show that near-chemical accuracy (1-2 kcal/mol)is achieved for a variety of applications with DFT methods irrespective of the underlying density functional used.They demonstrate conclusively that seemingly disparate results, oftenseen with different density functionals in many chemical applications,are due to an accumulation of systematic errors inthe smaller local molecular fragments that can be easily correctedwith higher-level calculations on those small units. This enablesthe method to achieve the accuracy of the high level of theory (e.g.,coupled cluster) while the cost remains that of DFT. The advantagesand limitations of the method are discussed along with areas of ongoingdevelopments.