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

Extending Density-Corrected Density Functional Theory to Large Molecular Systems

Practical density-corrected density functional theory (DC-DFT) calculations rely on Hartree-Fock (HF) densities, which can be computationally expensive for systems with over a hundred atoms. We extend the applicability of HF-DFT using the dual-basis method, where the density matrix from a smaller basis set is used to estimate the HF solution on a larger basis set. Benchmarks on many systems, including the GMTKN55 database for main-group chemistry, and the L7 and S6L data sets for large molecular systems demonstrate the efficacy of our approach. We apply the dual-basis method to both DNA and HIV systems and compare with the literature. The details of a recent reparameterization of HF-r2SCAN-DC4 are explained, showing no loss of performance.

Top-Down versus Bottom-Up Approaches for σ-Functionals Based on the Approximate Exchange Kernel

Recently, we investigated a number of so-called σ- and τ-functionals based on the adiabatic-connection fluctuation-dissipation theorem (ACFDT); particularly, extensions of the random phase approximation (RPA) with inclusion of an exchange kernel in the form of an antisymmetrized Hartree kernel. One of these functionals, based upon the approximate exchange kernel (AXK) of Bates and Furche, leads to a nonlinear contribution of the spline function used within σ-functionals, which we previously avoided through the introduction of a simplified "top-down" approach in which the σ-functional modification is inserted a posteriori following the analytic coupling strength integration within the framework of the ACFDT and which was shown to provide excellent performance for the GMTKN55 database when using hybrid PBE0 reference orbitals. In this work, we examine the analytic "bottom-up" approach in which the spline function is inserted a priori, i.e., before evaluation of the analytic coupling strength integral. The new bottom-up functionals, denoted σ↑AXK, considerably improve upon their top-down counterparts for problems dominated by self-interaction and delocalization errors. Despite a small loss of accuracy for noncovalent interactions, the σ↑AXK@PBE0 functionals comprehensively outperform regular σ-functionals, scaled σ-functionals, and the previously derived σ+SOSEX- and τ-functionals in the WTMAD-1 and WTMAD-2 metrics of the GMTKN55 database.

The Best DFT Functional Is the Ensemble of Functionals

The development of better density functional theory (DFT) methods is one of the most active research areas, given the importance of DFT for ubiquitous molecular and materials simulations. However, this research primarily focuses on improving a specific exchange-correlation Kohn-Sham density functional. Here, a robust procedure is proposed for constructing transferable ensembles of density functionals that perform superior to any constituent individual density functional. It is shown that such ensembles built only with the density functionals predating the GMTKN55 benchmark of 2017 can reach a record-low weighted error of 1.62 kcal mol-1 on this benchmark compared to 3.08 kcal mol-1 of the best constituent density functional. The DENS24 density functional ensembles are also introduced as practical DFT methods with consistently accurate performance for various simulations at affordable cost. DENS24 ensembles are open-source and can be used for simulations online. Additionally, it is shown that the ensembles can be integrated into the SCF procedure by creating mixed DENS24 functionals, which have the same accuracy but are faster than ensembles of independent functionals.

Local Second Order Mo̷ller-Plesset Theory with a Single Threshold Using Orthogonal Virtual Orbitals: A Distributed Memory Implementation

In order to alleviate the computational burden associated with superlinear compute scalings with molecular size in electron correlation methods, researchers have developed local correlation methods that wisely treat relatively small contributions as zeros but still yield accurate energy approximation. Such local correlation techniques can also be combined with parallel computing resources to obtain further efficiency and scalability. This work focuses on the distributed memory parallel implementation of a local correlation method for second order Mo̷ller-Plesset (MP2) theory. This method also only has a single threshold to control the dropping of terms and accuracy of different computing kernels in the algorithm. The process partitioning strategy and distributed parallel implementation with the message passing interface (MPI) are discussed. In particular, the algorithm relies on a fixed sparsity pattern matrix multiplication and a corresponding distributed conjugate gradient solver, which exhibits almost linear scaling in both strong and weak scaling analyses. Numerical experiments on a range of molecules, including linear chains and molecules with 2 and 3-dimensional characters, are reported. For example, with only 32 MPI ranks, this MP2 implementation can calculate the correlation energy of vancomycin in def2-TZVP basis within 0.003% accuracy (10-6.5 threshold) in half an hour, where the same problem is unfeasible to solve with sequential or pure shared memory implementations.

Correcting Dispersion Corrections with Density-Corrected DFT

Almost all empirical parametrizations of dispersion corrections in DFT use only energy errors, thereby mixing functional and density-driven errors. We introduce density and dispersion-corrected DFT (D2C-DFT), a dual-calibration approach that accounts for density delocalization errors when parametrizing dispersion interactions. We simply exclude density-sensitive reactions from the training data. We find a significant reduction in both errors and variation among several semilocal functionals and their global hybrids when tailored dispersion corrections are employed with Hartree-Fock densities.

Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density

ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.

Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian

This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.

Self-Association and Microhydration of Phenol: Identification of Large-Amplitude Hydrogen Bond Librational Modes

The self-association mechanisms of phenol have represented long-standing challenges to quantum chemical methodologies owing to the competition between strongly directional intermolecular hydrogen bonding, weaker non-directional London dispersion forces and C-H⋯π interactions between the aromatic rings. The present work explores these subtle self-association mechanisms of relevance for biological molecular recognition processes via spectroscopic observations of large-amplitude hydrogen bond librational modes of phenol cluster molecules embedded in inert neon "quantum" matrices complemented by domain-based local pair natural orbital-coupled cluster DLPNO-CCSD(T) theory. The spectral signatures confirm a primarily intermolecular O-H⋯H hydrogen-bonded structure of the phenol dimer strengthened further by cooperative contributions from inter-ring London dispersion forces as supported by DLPNO-based local energy decomposition (LED) predictions. In the same way, the hydrogen bond librational bands observed for the trimeric cluster molecule confirm a pseudo-C3 symmetric cyclic cooperative hydrogen-bonded barrel-like potential energy minimum structure. This structure is vastly different from the sterically favored "chair" conformations observed for aliphatic alcohol cluster molecules of the same size owing to the additional stabilizing London dispersion forces and C-H⋯π interactions between the aromatic rings. The hydrogen bond librational transition observed for the phenol monohydrate finally confirms that phenol acts as a hydrogen bond donor to water in contrast to the hydrogen bond acceptor role observed for aliphatic alcohols.

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional

In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, "DH23," whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, "DH24," performs as well as its predecessors.

Doubling down on density-functional theory

In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, "DH23," whose terms are based on good physics. Its 12 coefficients were trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.