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1. Embedded, graph‐theoretically defined many‐body approximations for wavefunction‐in‐DFT and DFT‐in‐DFT : Applications to gas‐ and condensed‐phase ab initio molecular dynamics, and potential surfaces for quantum nuclear effects

   https://doi.org/10.1002/qua.26244  

   Ricard, Timothy C.; Kumar, Anup; Iyengar, Srinivasan S. (May 2020, International Journal of Quantum Chemistry)

   Abstract We present a graph‐theoretic approach to adaptively compute many‐body approximations in an efficient manner to perform (a) accurate post‐Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium‐ to large‐sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed‐phase simulations at the cost of pure density functionals, (c) reduced‐cost on‐the‐fly basis extrapolation for gas‐phase AIMD and condensed phase studies, and (d) accurate post‐HF‐level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM‐like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many‐body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph‐theoretic methods. Specifically, a region of chemical interest is coarse‐grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many‐body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one‐dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two‐dimensional periodic boundary conditions. 

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2. Implementation of symmetry-adapted perturbation theory based on density functional theory and using hybrid exchange–correlation kernels for dispersion terms

   https://doi.org/10.1063/5.0090688  

   Xie, Yi; Smith, Daniel G.; Sherrill, C. David (July 2022, The Journal of Chemical Physics)

   We report the implementation of a symmetry-adapted perturbation theory algorithm based on a density functional theory [SAPT(DFT)] description of monomers. The implementation adopts a density-fitting treatment of hybrid exchange–correlation kernels to enable the description of monomers with hybrid functionals, as in the algorithm by Bukowski, Podeszwa, and Szalewicz [Chem. Phys. Lett. 414, 111 (2005)]. We have improved the algorithm by increasing numerical stability with QR factorization and optimized the computation of the exchange–correlation kernel with its 2-index density-fitted representation. The algorithm scales as O( N 5 ) formally and is usable for systems with up to ∼3000 basis functions, as demonstrated for the C 60 –buckycatcher complex with the aug-cc-pVDZ basis set. The hybrid-kernel-based SAPT(DFT) algorithm is shown to be as accurate as SAPT(DFT) implementations based on local effective exact exchange potentials obtained from the local Hartree–Fock (LHF) method while avoiding the lower-scaling [ O( N 4 )] but iterative and sometimes hard-to-converge LHF process. The hybrid-kernel algorithm outperforms Hartree–Fock-based SAPT (SAPT0) for the S66 test set, and its accuracy is comparable to the many-body perturbation theory based SAPT2+ approach, which scales as O( N 7 ), although SAPT2+ exhibits a more narrow distribution of errors. 

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3. Measuring Density-Driven Errors Using Kohn–Sham Inversion

   https://doi.org/doi.org/10.1021/acs.jctc.0c00391  

   Nam, Seungsoo; Song, Suhwan; Sim, Eunji; and Burke, Kieron (July 2020, Journal of chemical theory and computation)

   Kohn–Sham (KS) inversion, that is, the finding of the exact KS potential for a given density, is difficult in localized basis sets. We study the precision and reliability of several inversion schemes, finding estimates of density-driven errors at a useful level of accuracy. In typical cases of substantial density-driven errors, Hartree–Fock density functional theory (HF-DFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HF-DFT also makes errors much smaller than the density-driven errors being calculated. Two paradigm examples, stretched NaCl and the HO·Cl– radical, illustrate just how accurate HF-DFT is. 

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4. Density Sensitivity of Empirical Functionals

   https://doi.org/doi.10.1021/acs.jpclett.0c03545  

   Song, Suhwan; Vuckovic, Stefan; Sim, Eunji; and Burke, Kieron (January 2021, The journal of physical chemistry letters)

   Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We illustrate with catastrophic failures of a toy functional applied to H2+ at varying bond lengths, where the standard fitting procedure misses the exact functional; Grimme’s D3 fit to noncovalent interactions, which can be contaminated by large density errors such as in the WATER27 and B30 data sets; and double-hybrids trained on self-consistent densities, which can perform poorly on systems with density-driven errors. In these cases, more accurate results are found at no additional cost by using Hartree–Fock (HF) densities instead of self-consistent densities. For binding energies of small water clusters, errors are greatly reduced. Range-separated hybrids with 100% HF at large distances suffer much less from this effect. 

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5. Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics

   https://doi.org/10.1021/acs.jpca.3c07385  

   Iyengar, Srinivasan S; Schlegel, H Bernhard; Sumner, Isaiah; Li, Junjie (July 2024, The Journal of Physical Chemistry A)

   We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events. 

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