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

ABSTRACT: 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.

SUBMITTER: Wang Y

PROVIDER: S-EPMC8395692 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Doubly hybrid density functionals that correctly describe both density and energy for atoms.

Project description:Recently, it was argued [Medvedev MG, et al. (2017) Science 355:49-52] that the development of density functional approximations (DFAs) is "straying from the path toward the exact functional." The exact functional should yield both exact energy and density for a system of interest; nevertheless, they found that many heavily fitted functionals for molecular energies actually lead to poor electron densities of atoms. They also observed a trend that, for the nonempirical and few-parameter functionals, densities can be improved as one climbs up the first four rungs of the Jacob's ladder of DFAs. The XYG3 type of doubly hybrid functionals (xDHs) represents a less-empirical and fewer-parameter functional on the top fifth rung, in which both the Hartree-Fock-like exchange and the second-order perturbative (MP2-like) correlation are hybridized with the low rung functionals. Here, we show that xDHs can well describe both density and energy for the same atomic set of Medvedev et al., showing that the latter trend can well be extended to the top fifth rung.

| S-EPMC5878006 | biostudies-literature

A fast doubly hybrid density functional method close to chemical accuracy using a local opposite spin ansatz.

Project description:We develop and validate the XYGJ-OS functional, based on the adiabatic connection formalism and Görling-Levy perturbation theory to second order and using the opposite-spin (OS) ansatz combined with locality of electron correlation. XYGJ-OS with local implementation scales as N(3) with an overall accuracy of 1.28 kcal/mol for thermochemistry, bond dissociation energies, reaction barrier heights, and nonbonded interactions, comparable to that of 1.06 kcal/mol for the accurate coupled-cluster based G3 method (scales as N(7)) and much better than many popular density functional theory methods: B3LYP (4.98), PBE0 (4.36), and PBE (12.10).

| S-EPMC3250148 | biostudies-literature

Accuracy Meets Interpretability for Computational Spectroscopy by Means of Hybrid and Double-Hybrid Functionals.

Project description:Accuracy and interpretability are often seen as the devil and holy grail in computational spectroscopy and their reconciliation remains a primary research goal. In the last few decades, density functional theory has revolutionized the situation, paving the way to reliable yet effective models for medium size molecules, which could also be profitably used by non-specialists. In this contribution we will compare the results of some widely used hybrid and double hybrid functionals with the aim of defining the most suitable recipe for all the spectroscopic parameters of interest in rotational and vibrational spectroscopy, going beyond the rigid rotor/harmonic oscillator model. We will show that last-generation hybrid and double hybrid functionals in conjunction with partially augmented double- and triple-zeta basis sets can offer, in the framework of second order vibrational perturbation theory, a general, robust, and user-friendly tool with unprecedented accuracy for medium-size semi-rigid molecules.

| S-EPMC7645164 | biostudies-literature

Unveiling the Physics Behind Hybrid Functionals.

Project description:We show that accurate exchange-correlation hybrid functionals give very physically optimized effective-correlation potentials, capable of correctly describing the quantum oscillations of atoms and molecules. Based on this analysis and on understanding the error cancellation between semilocal exchange and correlation functionals, we propose a very simple, semilocal correlation potential model compatible with the exact exchange of density functional theory, which performs remarkably well for charge densities and orbital energies.

| S-EPMC7590981 | biostudies-literature

A hybrid single cell demultiplexing strategy that increases both cell recovery rate and calling accuracy

Project description:Recent advances in single cell RNA sequencing allow users to pool multiple samples into one run and demultiplex in downstream analysis, greatly increasing the experimental efficiency and cost-effectiveness. However, the expensive reagents for cell labeling, limited pooling capacity, non-ideal cell recovery rate and calling accuracy remain great challenges for this approach. To date, there are two major demultiplexing methods, antibody-based cell hashing and Single Nucleotide Polymorphism (SNP)-based genomic signature profiling, and each method has advantages and limitations. Here, we propose a hybrid demultiplexing strategy that increases calling accuracy and cell recovery at the same time. We first develop a computational algorithm that significantly increases calling accuracy of cell hashing. Next, we cluster all single cells based on their SNP profiles. Finally, we integrate results from both methods to make corrections and retrieve cells that are only identifiable in one method but not the other. By testing on several real-world datasets, we demonstrate that this hybrid strategy combines advantages of both methods, resulting in increased cell recovery and calling accuracy at lower cost.

2024-05-29 | GSE230810 | GEO

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms.

Project description:Connections between the Görling-Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew-Burke-Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.

| S-EPMC7735712 | biostudies-literature

Efficient implementation of the pair atomic resolution of the identity approximation for exact exchange for hybrid and range- separated density functionals.

Project description:An efficient new molecular orbital (MO) basis algorithm is reported implementing the pair atomic resolution of the identity approximation (PARI) to evaluate the exact exchange contribution (K) to self-consistent field methods, such as hybrid and range-separated hybrid density functionals. The PARI approximation, in which atomic orbital (AO) basis function pairs are expanded using auxiliary basis functions centered only on their two respective atoms, was recently investigated by Merlot et al. [J. Comput. Chem. 2013, 34, 1486]. Our algorithm is significantly faster than quartic scaling RI-K, with an asymptotic exchange speedup for hybrid functionals of (1 + X/N), where N and X are the AO and auxiliary basis dimensions. The asymptotic speedup is 2 + 2X/N for range separated hybrids such as CAM-B3LYP, ωB97X-D, and ωB97X-V which include short- and long-range exact exchange. The observed speedup for exchange in ωB97X-V for a C68 graphene fragment in the cc-pVTZ basis is 3.4 relative to RI-K. Like conventional RI-K, our method greatly outperforms conventional integral evaluation in large basis sets; a speedup of 19 is obtained in the cc-pVQZ basis on a C54 graphene fragment. Negligible loss of accuracy relative to exact integral evaluation is demonstrated on databases of bonded and nonbonded interactions. We also demonstrate both analytically and numerically that the PARI-K approximation is variationally stable.

| S-EPMC4325599 | biostudies-other

Quantifying the Accuracy of Density Functionals on Transition Metal Bulk and Surface Properties.

Project description:Density functional theory would be exact when the exact exchange-correlation (xc) functional would be known, but since it is regretfully not known, dozens of xc functionals have been developed in the past decades, with some of them better suited for describing certain systems and/or properties. For transition metals (TMs), recent systematic studies assessing bulk properties─shortest interatomic bond distance, δ, cohesive energy, Ecoh, and bulk modulus, B0─and surface features─surface energy, γ, work function, ϕ, and interlayer distances, δij─of 27 TM bulks and 81 TM surfaces, highlighted that generalized gradient approximation (GGA) based xc functionals are, overall, better suited than other types of xc functionals for the TMs bulk and surfaces description, such as Perdew-Burke-Ernzerhof (PBE) or Vega-Viñes (VV). Still, some basic local density approximation xc functionals were not assessed, such as the Hedin-Lundqvist (HL) and Perdew-Zunger (PZ), or GGAs such as the revised Perdew-Burke-Ernzerhof (revPBE) or the Armiento-Mattsson (AM05). Here, we expand the analysis by not only including them but also the recent meta-GGA strongly constrained appropriately normed (SCAN) xc functional, characterized by fulfilling all 17 mathematical conditions an xc must comply, plus the Bayesian error estimation functional (BEEF) xc, a functional parametrized over a large and diverse set of experimental results using machine learning. The present results reveal that none of the xc studied excel neither PBE nor VV, yet AM05 and SCAN performance is quite acceptable, while BEEF xc probably needs more shells of parametrization to reach competitive accuracy levels.

| S-EPMC10688177 | biostudies-literature

Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights.

Project description:To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies.

| S-EPMC9393870 | biostudies-literature

Spatially extended hybrid methods: a review.

Project description:Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.

| S-EPMC5832735 | biostudies-literature

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