Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties

The Quality of Embedding Charges Is Critical for Convergence of Many-Body Expansions When BSSE Is Absent

There is conflicting evidence in the literature concerning the benefits of charge embedding on the convergence of many-body expansions (MBEs). Using a systematic series of water and ion-water clusters of varying size, this study indicates that the effects of charge embedding can be masked by basis set superposition error (BSSE). When BSSE is removed, this study demonstrates that charge embedding can significantly accelerate MBE convergence, where the electrostatically embedded two-body method, EE-MBE(2), can often yield accuracy close to the four-body method, MBE(4). Contrary to previous studies on smaller systems, this work shows that the performance of EE-MBE is highly sensitive to the charge model, with the best performance obtained when the natural population analysis (NPA) charge model is used and generated at the same level of theory used in the subsystem and supersystem calculations. It was demonstrated that the "3c" composite method, PBEh-3c, yields NPA atomic charges that are in excellent agreement with those obtained from supersystem density functional theory calculations. The linear-scaling X-Polarization method provides a more general approach to estimating these supersystem QM atomic charges, but its performance depends on how the fragments are defined.

On the origin of optical rotation changes during the κ-carrageenan disorder-to-order transition

It is well established that solutions of both polymeric and oligomeric κ-carrageenan exhibit a clear change in optical rotation (OR), in concert with gel-formation for polymeric samples, as the solution is cooled in the presence of certain ions. The canonical interpretation - that this OR change reflects a 'coil-to-helix transition' in single chains - has seemed unambiguous; the solution- or 'disordered'-state structure has ubiquitously been assumed to be a 'random coil', and the helical nature of carrageenan in the solid-state was settled in the 1970s. However, recent work has found that κ-carrageenan contains substantial helical secondary structure elements in the disordered-state, raising doubts over the validity of this interpretation. To investigate the origins of the OR, density-functional theory calculations were conducted using atomic models of κ-carrageenan oligomers. Changes were found to occur in the predicted OR owing purely to dimerization of chains, and - together with the additional effects of slight changes in conformation that occur when separated helical chains form double-helices - the predicted OR changes are qualitatively consistent with experimental results. These findings contribute to a growing body of evidence that the carrageenan 'disorder-to-order' transition is a cooperative process, and have further implications for the interpretation of OR changes demonstrated by macromolecules in general.

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application ("Fragme∩t"), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Cluster many-body expansion: A many-body expansion of the electron correlation energy about a cluster mean field reference

The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized nth order Bethe-Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the MBE. This method, named cluster MBE (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from a RHF reference. We present numerical results for strongly correlated systems, such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended π space of several large π-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 10⁶⁶ determinants for the exact FCI solution.

Modeling Complex Solvent Effects on the Optical Rotation of Chiral Molecules: A Combined Molecular Dynamics and Density Functional Theory Study

The challenge of assigning the absolute stereochemical configuration to a chiral compound can be overcome via accurate ab initio predictions of optical rotation, a sensitive molecular property that is further complicated by solvent effects. The solvent's "chiral imprint"-the transfer of the chirality from the solute to the surrounding achiral solvent-is explored here using conformational averaging and time-dependent density-functional theory. These complex solvent effects are taken into account via simple averaging over a molecular dynamics trajectory together with the explicit quantum mechanical consideration of the solvent molecules within the solute's cybotactic region and implicit modeling of the bulk solvent. We consider several axes along which the system's optical rotation varies, including the sampling of the dynamical trajectory, the quality of the one-electron basis set, and the use of continuum solvent models to account for bulk effects.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH₄···(H₂O)₂₀, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.