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1. Benchmark coupled-cluster lattice energy of crystalline benzene and assessment of multi-level approximations in the many-body expansion

   https://doi.org/10.1063/5.0159410  

   Borca, Carlos H. ; Glick, Zachary L. ; Metcalf, Derek P. ; Burns, Lori A. ; Sherrill, C. David ( June 2023 , The Journal of Chemical Physics)

   The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller–Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod–Teller–Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol−1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol−1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is −54.01 kJ mol−1, compared to an estimated experimental value of −55.3 ± 2.2 kJ mol−1. 

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2. Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach

   https://doi.org/10.1063/1.5125802  

   Veccham, Srimukh Prasad ; Lee, Joonho ; Head-Gordon, Martin ( November 2019 , The Journal of Chemical Physics)
3. Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs

   https://doi.org/10.1063/1.4986110  

   Liu, Kuan-Yu ; Herbert, John M. ( October 2017 , The Journal of Chemical Physics)
4. Convergence of the Many-Body Expansion for Energy and Forces for Classical Polarizable Models in the Condensed Phase

   https://doi.org/10.1021/acs.jctc.6b00335  

   Demerdash, Omar ; Head-Gordon, Teresa ( August 2016 , Journal of Chemical Theory and Computation)
5. Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties

   https://doi.org/https://doi.org/10.1021/acs.jpca.9b03864  

   Peyton, Benjamin G. Crawford ( January 2019 , Journal of physical chemistry)

   The underlying reasons for the poor convergence of the venerated many-body expansion (MBE) for higher-order response properties are investigated, with a particular focus on the impact of basis set superposition errors. Interaction energies, dipole moments, dynamic polarizabilities, and specific rotations are computed for three chiral solutes in explicit water cages of varying sizes using the MBE including corrections based on the site–site function counterpoise (or “full-cluster” basis) approach. In addition, we consider other possible causes for the observed oscillatory behavior of the MBE, including numerical precision, basis set size, choice of density functional, and snapshot geometry. Our results indicate that counterpoise corrections are necessary for damping oscillations and achieving reasonable convergence of the MBE for higher order properties. However, oscillations in the expansion cannot be completely eliminated for chiroptical properties such as specific rotations due to their inherently nonadditive nature, thus limiting the efficacy of the MBE for studying solvated chiral compounds. 

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