Many-body effects are required for an accurate description of both structure and dynamics of large chemical systems. However, there are numerous such interactions to consider, and it is not obvious which ones are significant. We provide a general and fast method for establishing which small set of three- and four-body interactions are important. This is achieved by estimating the maximum many-body effects, ϵmax, that can arise in a given arrangement of bodies. Through careful analysis of ϵmax, we find two overall causes for significant many-body interactions. First, many-body induction propagates in nonbranching paths, that is, in a chain-like manner. Second, linear arrangements of bodies promote the alignment of the dipoles to reinforce the many-body interaction. Consequently, compact and extended linear arrangements are favored. The latter result is not intuitive as these linear arrangements can lead to significant many-body effects extending over large distances. For the first time, this study provides a rigorous explanation as to how cooperative effects provide enhanced stability in helices making them one of the most common structures in biomolecules. Not only do these helices promote linear dipole alignment, but their chain-like structure is consistent with the way many-body induction propagates. Finally, using ϵmax to screen for significant many-body interactions, we are able to reproduce the total three- and four-body interaction energies using a small number of individual many-body interactions.

Using the method of modified Shepard’s interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second–order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard’s interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.

The basis set superposition effect (BSSE) arises in electronic structure calculations of molecular clusters when questions relating to interactions between monomers within the larger cluster are asked. The binding energy, or total energy, of the cluster may be broken down into many smaller subcluster calculations and the energies of these subsystems linearly combined to, hopefully, produce the desired quantity of interest. Unfortunately, BSSE can plague these smaller fragment calculations. In this work, we carefully examine the major sources of error associated with reproducing the binding energy and total energy of a molecular cluster. In order to do so, we decompose these energies in terms of a many-body expansion (MBE), where a “body” here refers to the monomers that make up the cluster. In our analysis, we found it necessary to introduce something we designate here as a many-ghost many-body expansion (MGMBE). The work presented here produces some surprising results, but perhaps the most significant of all is that BSSE effects up to the order of truncation in a MBE of the total energy cancel exactly. In the case of the binding energy, the only BSSE correction terms remaining arise from the removal of the one-body monomer total energies. Nevertheless, our earlier work indicated that BSSE effects continued to remain in the total energy of the cluster up to very high truncation order in the MBE. We show in this work that the vast majority of these high-order many-body effects arise from BSSE associated with the one-body monomer total energies. Also, we found that, remarkably, the complete basis set limit values for the three-body and four-body interactions differed very little from that at the MP2/aug-cc-pVDZ level for the respective subclusters embedded within a larger cluster.

Chemistry, particularly organic chemistry, is mostly concerned with functional groups: amines, amides, alcohols, ketones, and so forth. This is because the reactivity of molecules can be categorized in terms of the reactions of these functional groups, and by the influence of other adjacent groups in the molecule. These simple truths ought to be reflected in the electronic structure and electronic energy of molecules, as reactivity is determined by electronic structure. However, sophisticated ab initio quantum calculations of the molecular electronic energy usually do not make these truths apparent. In recent years, several computational chemistry groups have discovered methods for estimating the electronic energy as a sum of the energies of small molecular fragments, or small sets of groups. By decomposing molecules into such fragments of adjacent functional groups, researchers can estimate the electronic energy to chemical accuracy; not just qualitative trends, but accurate enough to understand reactivity. In addition, this has the benefit of cutting down on both computational time and cost, as the necessary calculation time increases rapidly with an increasing number of electrons. Even with steady advances in computer technology, progress in the study of large molecules is slow.In this Account, we describe two related “fragmentation” methods for treating molecules, the combined fragmentation method (CFM) and systematic molecular fragmentation (SMF). In addition, we show how we can use the SMF approach to estimate the energy and properties of nonconducting crystals, by fragmenting the periodic crystal structure into relatively small pieces. A large part of this Account is devoted to simple overviews of how the methods work.We also discuss the application of these approaches to calculating reactivity and other useful properties, such as the NMR and vibrational spectra of molecules and crystals. These applications rely on the ability of these fragmentation methods to accurately estimate derivatives of the molecular and crystal energies. Finally, to provide some common applications of CFM and SMF, we present some specific examples of energy calculations for moderately large molecules. For computational chemists, this fragmentation approach represents an important practical advance. It reduces the computer time required to estimate the energies of molecules so dramatically, that accurate calculations of the energies and reactivity of very large organic and biological molecules become feasible.

Longstanding conventional wisdom dictates that the widely used Many-Body Expansion (MBE) converges rapidly by the four-body term when applied to large chemical systems. We have found, however, that this is not true for calculations using many common, moderate-sized basis sets such as 6-311++G** and aug-cc-pVDZ. Energy calculations performed on water clusters using these basis sets showed a deceptively small error when the MBE was truncated at the three-body level, while inclusion of four- and five-body contributions drastically increased the error. Moreover, the error per monomer increases with system size, showing that the MBE is unsuitable to apply to large chemical systems when using these basis sets. Through a systematic study, we identified the cause of the poor MBE convergence to be a many-body basis set superposition effect exacerbated by diffuse functions. This was verified by analysis of MO coefficients and the behavior of the MBE with increasing monomer–monomer separation. We also found poor convergence of the MBE when applied to valence-bonded systems, which has implications for molecular fragmentation methods. The findings in this work suggest that calculations involving the MBE must be performed using the full-cluster basis set, using basis sets without diffuse functions, or using a basis set of at least aug-cc-pVTZ quality.