Exploring the Limits of the XYG3-Type Doubly Hybrid Approximations for the Main-Group Chemistry: The xDH@B3LYP Model

How accurate can Kohn-Sham density functional be for both main-group and transition metal reactions

Achieving chemical accuracy in describing reactions involving both main-group elements and transition metals poses a substantial challenge for density functional approximations (DFAs), primarily due to the significantly different behaviors for electrons moving in the s,p-orbitals or in the d,f-orbitals. MOR41, a representative dataset of transition metal chemistry, has highlighted the PWPB95-D3(BJ) functional, a B2PLYP-type doubly hybrid (bDH) approximation equipped with an empirical dispersion correction, as the leading functional thus far (Dohm et al., J Chem Theory Comput 2018;14: 2596-2608). However, this functional is not among the top bDH methods for main-group chemistry (Goerigk et al., Phys Chem Chem Phys. 2017;19: 32184). Conversely, bDH methods such as DSD-BLYP-D3, proficient in main-group chemistry, often falter for transition metal chemistry. Herein, taking advantage of the home-made Rust-based Electronic-Structure Toolkits, we examine a suite of XYG3-type doubly hybrid (xDH) methods. We confirm that the trade-off in descriptive accuracy between main-group and transition metal systems persists within the realm of perturbation theory (PT2)-based xDH methods. Notably, however, our study ushers in a pivotal advance with the recently proposed renormalized xDH method, R-xDH7-SCC15. This method not only distinguishes itself among the elite methods for main-group chemistry, but also achieves an unprecedented accuracy for the MOR41 dataset, outperforming all other reported DFAs. The efficacy of R-xDH7-SCC15 stems from the successful integration of a renormalized PT2 correlation model (rPT2) and a machine-learning strong-correlation correction (SCC15), marking a significant step forward in the realm of computational chemistry.

Toward Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory

Accurate description of the static correlation poses a persistent challenge in electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development involves a hybrid machine learning strategy that integrates symbolic regression with nonlinear parameter optimization, aiming to achieve a balance between generalization capability, numerical accuracy, and interpretability. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of main-group chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict the whole energy profiles, activation barriers, and reaction pathways within a user-friendly "black-box" framework represents an important advance in the field of electronic structure theory.

Identifying and embedding transferability in data-driven representations of chemical space

Transferability, especially in the context of model generalization, is a paradigm of all scientific disciplines. However, the rapid advancement of machine learned model development threatens this paradigm, as it can be difficult to understand how transferability is embedded (or missed) in complex models developed using large training data sets. Two related open problems are how to identify, without relying on human intuition, what makes training data transferable; and how to embed transferability into training data. To solve both problems for ab initio chemical modelling, an indispensable tool in everyday chemistry research, we introduce a transferability assessment tool (TAT) and demonstrate it on a controllable data-driven model for developing density functional approximations (DFAs). We reveal that human intuition in the curation of training data introduces chemical biases that can hamper the transferability of data-driven DFAs. We use our TAT to motivate three transferability principles; one of which introduces the key concept of transferable diversity. Finally, we propose data curation strategies for general-purpose machine learning models in chemistry that identify and embed the transferability principles.

Regularized and Opposite Spin-Scaled Functionals from Møller-Plesset Adiabatic Connection─Higher Accuracy at Lower Cost

Noncovalent interactions (NCIs) play a crucial role in biology, chemistry, material science, and everything in between. To improve pure quantum-chemical simulations of NCIs, we propose a methodology for constructing approximate correlation energies by combining an interpolation along the Møller-Plesset adiabatic connection (MP AC) with a regularization and spin-scaling strategy applied to MP2 correlation energies. This combination yields cosκos-SPL2, which exhibits superior accuracy for NCIs compared to any of the individual strategies. With the N4 formal scaling, cosκos-SPL2 is competitive or often outperforms more expensive dispersion-corrected double hybrids for NCIs. The accuracy of cosκos-SPL2 particularly shines for anionic halogen bonded complexes, where it surpasses standard dispersion-corrected DFT by a factor of 3 to 5.

QSAR modeling of pyrazoline derivative as carbonic anhydrase inhibitors

The efficacy of 34 pyrazoline derivatives as carbonic anhydrase inhibitors was studied in silico. The quantum descriptors were calculated by the DFT/B3LYP method using the 6-31G(d) basis; the dataset was randomly divided into training and testing. By altering the compounds in the sets, four models were created, and they were then used to determine the predicted pIC50 values for the six chemicals in the test set. According to the OECD guidelines for QSAR model validation and the Golbraikh and Tropsha's criteria for model approval, each created model was independently validated both internally and externally, along with YRandomization. Model 3 is chosen because it has higher R₂, R_2test, and Q_2cv values (R₂ = 0.79, R²_test = 0.95, Q²_cv = 0.64). Only one descriptor has a proportional influence on pIC50 activity, but the other four descriptors have an inverse influence on pIC50 because of the negative contribution coefficient. Given the descriptors of the model, we could propose new molecules with remarkable inhibitory activity.

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23."

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Assessment of advanced xDH@B3LYP methods in describing various potential energy curves driven by π-π, CH/π, and SH/π non-bonded interactions

Accurate description of potential energy curves driven by non-bonded interactions remains a great challenge for pure density functional approximations (DFAs). It is because the R−6 decay behavior of dispersion cannot be intrinsically captured by the (semi)-local ingredients and the exact-exchange used in the popular hybrid DFAs. Overemphasizing the accuracy on the equilibrium region for the functional construction would likely deteriorate the overall performance on the other regions of potential energy surfaces. In consequence, the empirical dispersion correction becomes the standard component in DFAs to treat the non-bonded interactions. In this Letter, we demonstrate that without the use of empirical dispersion correction, doubly hybrid approximations, in particular two recently proposed revXYG3 and XYG7 functionals, hold the promise to have a balanced description of non-bonded interactions on the whole potential energy curves for several prototypes of π- π, CH/ π, and SH/ π interactions. The error of revXYG3 and XYG7 for non-bonded interactions is around 0.1 kcal/mol, and their potential energy curves almost coincide with the accurate CCSD(T)/CBS curves.

Analytic Gradients for the Long-Range-Corrected XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Assessment

An analytic gradient algorithm for the long-range-corrected (lrc-) XYG3 type of doubly hybrid functionals has been derived and implemented. Due to the introduction of a long-range second-order perturbation (lrPT2) as the correction, the Z-vector equations need to be modified, where the construction of a unique total Lagrangian of the method is required. Geometry optimizations using lrc-XYG3 and lrc-XYGJ-OS have then been applied to the A21 data set that consists of 21 noncovalently interacting systems with CCSD(T) reference data for structures, in order to testify the idea of introducing lrPT2 for a better description of intermolecular interactions. While lrc-XYG3 was observed to offer a better description in dispersion-dominant systems as compared to the XYG3 functional, lrc-XYGJ-OS stands out with an overall better balanced performance in reproducing intermolecular geometries.

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for ¹³C, ¹⁵N, ¹⁷O, ¹⁹F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for ¹H and ¹³C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental ¹³C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.

DeepNCI: DFT Noncovalent Interaction Correction with Transferable Multimodal Three-Dimensional Convolutional Neural Networks

A multimodal deep learning model, DeepNCI, is proposed for improving noncovalent interactions (NCIs) calculated via density functional theory (DFT). DeepNCI is composed of a three-dimensional convolutional neural network (3D CNN) for abstracting critical and comprehensive features from 3D electron density, and a neural network for modeling one-dimensional quantum chemical properties. By merging features from two networks, DeepNCI is able to reduce the root-mean-square error of DFT-calculated NCI from 1.19 kcal/mol to ∼0.2 kcal/mol for a NCI molecular database (>1000 molecules). The representativeness of the joint features can be visualized by t-distributed stochastic neighbor embedding (t-SNE), where they can distinguish categorized NCI systems quite well. Therefore, the fused model performs better than its component networks. In addition, the 3D CNN takes electron density as inputs that are in the same range, despite the size of molecular systems, so it can promote model applicability and transferability. To clarify the applicability of DeepNCI, an application domain (AD) has been defined with merged features using the K-nearest-neighbor method. The calculations for external test sets are shown that AD can properly monitor the reliability for a prediction. The model transferability is tested with a small database of homolysis bond dissociation energy including only dozens of samples. With NCI database pretrained parameters, the same or better performance than the reported results is achieved by transfer learning. This suggests that the DeepNCI model is transferable and it may transfer to other relative tasks, which possibly can resolve some small sampling problems. The source code of DeepNCI can be freely accessed at https://github.com/wenzelee/DeepNCI.

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E₃ to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wave function ab initio approaches. Intriguingly, (a) the introduction of E₃ makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (LDA) in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.

Noncovalent Interactions from Models for the Møller-Plesset Adiabatic Connection

Given the omnipresence of noncovalent interactions (NCIs), their accurate simulations are of crucial importance across various scientific disciplines. Here we construct accurate models for the description of NCIs by an interpolation along the Møller-Plesset adiabatic connection (MP AC). Our interpolation approximates the correlation energy, by recovering MP2 at small coupling strengths and the correct large-coupling strength expansion of the MP AC, recently shown to be a functional of the Hartree-Fock density. Our models are size consistent for fragments with nondegenerate ground states, have the same cost as double hybrids, and require no dispersion corrections to capture NCIs accurately. These interpolations greatly reduce large MP2 errors for typical π-stacking complexes (e.g., benzene-pyridine dimers) and for the L7 data set. They are also competitive with state-of-the-art dispersion enhanced functionals and can even significantly outperform them for a variety of data sets, such as CT7 and L7.

Doubly Hybrid Functionals Close to Chemical Accuracy for Both Finite and Extended Systems: Implementation and Test of XYG3 and XYGJ-OS

While being widely used to understand the chemical reactions in heterogeneous catalysis or other multidisciplinary systems, a great challenge that semilocal and hybrid density functional approximations (DFAs) are facing is to deliver a uniformly accurate description for both finite and extended systems. Herein, we perform reliable and well-converged periodic calculations of two doubly hybrid approximations (DHAs), XYG3 and XYGJ-OS, and demonstrate that the good accuracy of DHAs achieved for molecules is transferable to the semiconductors and insulators. Such an accuracy is not only for energetic properties but also for the first- and second-order response properties, which is general for different kinds of chemical environments, including simple cubic bulks, perovskite-type transition metal oxides like TiO2, and heterogeneous systems like CO adsorption on the NaCl(100) surface. The present finding has strengthened the predictive power of DFT, which not only will inspire the future development of the top-rung DFAs but also will boost their applications in multidisciplinary studies with high accuracy and efficiency.