Can DLPNO-based embedding method make many-body exapansion pair-wise additive?
Soumen Ghosh
A brief overview:
1. Local coupled cluster method has been combined with many-body expansion to analyze noncovalent interactions in molecular clusters and aggregates.
2. Total interaction energy and cooperativity of different systems have been expressed in terms of fragment and fragment pair-wise contributions
3. A fragment based local coupled cluster embedding approach has been introduced both with Hartree-Fock and point charge environment
4. Energy ordering of isomers of hexamer water clusters and protein-ligand interactions have been examined.
Many-body expansion (MBE) is a fragmentation approach where total energy of a supersystem is expressed as a sum of contributions from all possible monomers (one-body), dimers (two-body), trimers (three-body), etc. MBE is particularly useful to reduce the cost of a calculation if the expansion can be truncated after first few terms. If the expansion can be truncated after second term, it is called pair-wise additive approximation. Many previous calculations have indicated that in correlated calculations, MBE of Hartree-Fock energies converge much slower compared to the correlation energies. Even then, for correlation energies three-body or higher interactions are needed to be considered to achieve desirable accuracy. Point charge embedding has been used in the past to truncate MBE at the two or three –body terms. Quantum embedding approaches have also been useful for such truncations of MBE.
Domain-based local pair natural orbital (DLPNO) coupled cluster method has been particularly useful in reducing the cost of coupled cluster calculations significantly without compromising the accuracy. On top of that, local nature of the orbitals has provided a meaningful way to decompose the total energy or interaction energy of a system. Well-established local energy decomposition (LED) is one approach where this feature of DLPNO method has been utilized in the past. In a work with Dr. Bistoni, Dr. Izsák and Prof Neese, I have used this feature of DLPNO to decompose the total energy of a system in terms of fragment and fragment pair-wise energies and represent them in terms of heat plots. This approach helped us to decompose the many-body part (terms beyond two-body interactions in MBE) of the interaction energies (cooperativity effect) into monomer and fragment pair-wise contributions.
Decomposition of the total interaction (a) and two-body interaction (b) energies in fragment and fragment pair-wise interactions for a water cluster presented in the form of heat plots.
In this work, we have explored the possibility of making MBE pair-wise additive using DLPNO-based embedding approaches. Six isomers of hexamer water clusters have been used as the test systems here. In this embedding approach, only dimers and monomers are treated at the DLPNO coupled cluster level while rest of the system (environment) is treated at a lower level of theory i.e. with point charges or HF method. Point charge embedding with DLPNO coupled cluster method has been found to recover most of the many-body effects for the HF interaction energies but unable to recover the same in the case of the correlation interaction energies. With the HF embedding environment, DLPNO coupled cluster method recovered most of the many-body effects of the correlation interaction energies.
The embedding approach introduced here, falls in the category of large number of wavefunction-in-wavefunction approaches developed over the years. However, use of DLPNO coupled cluster method makes this approach particularly attractive as the highest level wave function method that can be applied on the embedded system is DLPNO-CCSD(T) that can provide accuracy comparable to the “gold standard” canonical CCSD(T) with much less computational cost. This method has also been applied to study protein-ligand interactions.
I find this work particularly exciting not only because of the excellent results that we have reported in the manuscript but also because of the enormous potential applications of these methods in the future for understanding interactions in large biological systems, lattice energy calculations, solvent-solute interactions and many more applications.
This work is funded by a postdoctoral fellowship from the Alexander von Humboldt foundation.
1. Soumen Ghosh, Frank Neese, Róbert Izsák, Giovanni Bistoni. Fragment-Based Local Coupled Cluster Embedding Approach for the Quantification and Analysis of Noncovalent Interactions: Exploring the Many Body Expansion of the Local Coupled Cluster Energy. J. Chem. Theory Comput. 2021, 10.1021/acs.jctc.1c00005.