Energy-Corrected MFCC

EC-MFCC was introduced by Li et al.⁵¹ as a follow-up to the Divide and Conquer Local Correlation (DCLC) fragment-based method. EC-MFCC differs from DCLC in that it also inclues two-body interactions. The higher-body interactions are computed among the pseudoatoms not the fragments (our terminology; the original manuscript refers to them as fragments) and rely on the EC-MFCC Screening method to avoid computing negligible two-body interactions.

At the one-body level EC-MFCC is the same as DCLC. Since it uses essentially two fragmentation methods, from our perspective, EC-MFCC is a multi-layer fragment- based method. The first layer is a traditional MBE using pseudoatoms as fragments and the DCLC Capping Method. The second layer is the DCLC calculation. Hence the energy for the two-body EC-MFCC method is given by:

\[\begin{split}E \approx& \left(\sum_{I} E_I +\sum_{I<J}\Delta E_{IJ}\right) + \left(E^{DCLC} - \sum_{I}E_I\right)\\ \approx& E^{DCLC} + \sum_{I<J}\Delta E_{IJ}\end{split}\]

where summation indices are pseudoatoms and \(E^{DCLC}\) is the energy of the fragments computed using a 1-body GMBE (fragments/pseudoatoms again adhereing to our terminology). EC-MFCC was applied to a series of medium to large systems. Energies and geometries were computed with EC-MFCC and compared to small basis MP2 supersystem results.

Name		Fragments	Embedding	Caps	Screening
EC-MFCC	Layer 0	Divide and Conquer Local Correlation Fragmentation Method	N/A	DCLC Capping Method	N/A
	Layer 1	N/A	N/A	DCLC Capping Method	EC-MFCC Screening