Another Angle on Benchmarking Noncovalent Interactions

Abstract: For noncovalent interactions (NCIs), the CCSD(T) coupled cluster method is widely regarded as the `gold standard'. With localized orbital approximations, benchmarks for ever larger NCI complexes are being published; yet tantalizing evidence from quantum Monte Carlo (QMC) results appears to indicate that as the system size grows, CCSD(T) overbinds NCIs by progressively larger amounts, particularly when $\pi$-stacking is involved. Alas, post-CCSD(T) methods like CCSDT(Q) are cost-prohibitive, which requires us to consider alternative means of estimating post-CCSD(T) contributions. In this work, we take a step back by considering the evolution of the correlation energy with respect to the number of subunits for such $\pi$-stacked sequences as acene dimers and alkadiene dimers. We show it to be almost perfectly linear, and propose the slope of the line as a probe for the behavior of a given electron correlation method. By comparison with rank-reduced CCSDT(Q) results for benzene and naphthalene dimers, we show that while CCSD(T) does slightly overbind, it does not at the level suggested by the QMC results.

• The paper shows that CCSD(T) overestimates noncovalent binding energies in large π-stacked systems, revealing its scaling limitations with increasing molecular complexity.
• The paper introduces a novel linear-slope diagnostic that quantifies the evolution of correlation energies across π-stacked sequences as a practical alternative to prohibitively expensive methods.
• The paper highlights that challenges in polarizability, local orbital approximations, and fixed geometries contribute to systematic errors, underscoring the need for refined computational strategies.

An Analysis of Benchmarking Noncovalent Interactions Using Coupled Cluster Methods

The research article "A new Angle on Benchmarking Noncovalent Interactions" by Fishman et al. critically examines the reliability of the CCSD(T) method as the "gold standard" for evaluating noncovalent interactions, particularly in larger molecular systems. The study confronts emerging evidence from fixed-node diffusion Monte Carlo (FN-DMC) simulations, suggesting that CCSD(T) may overestimate intermolecular binding energies as system complexity increases, notably within $\pi$-stacked aggregates. Given the computational intractability of employing more sophisticated coupled cluster methods like CCSDT(Q) for large systems, the authors focus on more computationally feasible alternatives to quantify deviations from CCSD(T).

The research primarily adopts a novel perspective; it treats the evolution of correlation energies in $\pi$-stacked sequences (such as acene and alkadiene dimers) as a linear progression. By calculating the slope of these progressions, the study provides a diagnostic measure of how different electron correlation methods scale with system size. The work draws comparisons using rank-reduced coupled cluster results for benzene and naphthalene dimers, suggesting that while CCSD(T) demonstrates a degree of overbinding, it does not align with the binding strengths predicted by FN-DMC.

The study is meticulous in examining the contributing factors to this discrepancy:

1. Polarizability Challenges: As molecular size increases, the ability to accurately compute monomer polarizabilities becomes more demanding. The research highlights the necessity of larger basis sets to capture this effect fully.
2. Local Orbital Approximations: The work assesses the impact of approximations used in CCSD(T) calculations for larger systems. These approximations can lead to cumulative neglect of small contributions, potentially leading to significant errors.
3. Geometry Considerations: Given the scarcity of accurate CCSD(T) optimized geometries, most studies rely on fixed geometries, which can affect interaction energy calculations. The authors evaluate systematic neglect of relaxation energy and its implications.
4. Comparison with Post-CCSD(T) Methods: The paper scrutinizes the proposition that higher-order correlation contributions (beyond CCSD(T)) become critical in larger systems. It describes how methods such as MP2 overestimate and MP3 underestimate interaction energies, positioning CCSDT(Q) as more explanatory of these effects.

The computational effort was extensive, utilizing a variety of quantum chemistry software and performing calculations across a spectrum of basis sets to ensure comprehensive findings. By evaluating the slope of interaction energies as a function of molecular size, Fishman et al. provide insight into the inherent limitations of standard methods like CCSD(T) and effectively benchmark their reliability for extrapolative predictions.

The implications of this research are significant for the field of quantum chemistry, especially concerning the prediction of noncovalent interactions in large molecular assemblies. The linear energy extrapolation illuminates a path forward for estimating interaction energies in sizeable $\pi$-stacking assemblies without resorting to prohibitive computational resources. While the study reaffirms the utility of CCSD(T) for many scenarios, it also underscores the necessity for continuous evaluation and advancement of theoretical methods to ensure accurate and reliable predictions across the expanding frontier of complex molecular systems. Future research might focus on refining post-CCSD(T) methods or exploring novel avenues of quantum chemical computations that can overcome the identified deficiencies.

In conclusion, Fishman et al. have provided a critical assessment of noncovalent interaction benchmarking, advocating for a nuanced viewpoint that considers method scalability and accuracy relative to molecular dimensional growth. This work sets a precedent for how quantum chemical methodologies can be thoughtfully adapted and benchmarked in the face of increasing molecular complexity.