B2-PPW91: A promising double-hybrid density functional for the electric response properties

Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach

We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.

Application to nonlinear optical properties of the RSX-QIDH double-hybrid range-separated functional

The effective calculation of static nonlinear optical properties requires a considerably high accuracy at a reasonable computational cost, to tackle challenging organic and inorganic systems acting as precursors and/or active layers of materials in (nano-)devices. That trade-off implies to obtain very accurate electronic energies in the presence of externally applied electric fields to consequently obtain static polarizabilities (α i j ) and hyper-polarizabilities (β i j k andγ i j k l ). Density functional theory is known to provide an excellent compromise between accuracy and computational cost, which is however largely impeded for these properties without introducing range-separation techniques. We thus explore here the ability of a modern (double-hybrid and range-separated) Range-Separated eXchange Quadratic Integrand Double-Hybrid exchange-correlation functional to compete in accuracy with more costly and/or tuned methods, thanks to its robust and parameter-free nature.

Spin-Opposite-Scaled Range-Separated Exchange Double-Hybrid Models (SOS-RSX-DHs): Marriage Between DH and RSX/SOS-RSX Is Not Always a Happy Match

The range-separated version of double-hybrid density functional theory (DH-DFT) with a remarkable efficiency for both ground-state and excited-state characteristics has recently come into spotlight. In this work, based on theoretical arguments, several variants of spin-opposite-scaled range-separated exchange double-hybrid models (SOS-RSX-DHs) have been proposed and validated. More specifically, we first extend the RSX-DHs to design some other related models. Next, the SOS version of the resulting approximations is constructed and thoroughly evaluated using standard benchmark compilations of various properties. It is shown that although there are properties for which the RSX-DH and SOS-RSX-DH frameworks are rival, there are still some problems particularly prone to the self-interaction error issues where our proposed models seem to be beneficial. Furthermore, some of the presented models devoid of any additional corrections can also surpass the recently proposed approximations from different rungs of "Jacob's Ladder". Nonetheless, perusing the results of different methods and detailed comparisons with the predecessors discloses that all things may not necessarily be well with the RSX and SOS-RSX schemes, where the parent DHs as well as their SOS counterparts can still come into play.

Molecular Collision Diameters and Electronic Polarizabilities: Inherent Relationship and Fast Evaluation

The collision diameter σ for a large set of molecular species is related to the static electronic polarizability α_el. A remarkable correlation between these quantities conceptually similar to the analogous one previously identified for atoms is revealed. Our recommended model is the function σ(α_el) = p₁ + p₂α_el^1/3, where p₁ = 0.768 Å and p₂ = 2.168 are the fitting parameters providing the best overall match to the reference data for collision diameter (181 data points). The obtained correlation allows one to easily find the collision diameter of molecules from the known polarizability and vice versa. These findings can be useful for many applications, where there is a need for inexpensive assessments of the collision diameters or electronic polarizabilities, for example, when developing the transport property databases for modeling of chemically reacting flows.

Appraising spin-state energetics in transition metal complexes using double-hybrid models: accountability of SOS0-PBESCAN0-2(a) as a promising paradigm

Through a comprehensive survey, reliable double-hybrid models have been validated and proposed for spin-state energetics in transition metal complexes.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.

Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling

For the first time, we combine time-dependent double-hybrid density functional approximations (TD-DHDFAs) for the calculation of electronic excitation energies with the concepts of spin-component and spin-opposite scaling (SCS/SOS) of electron-pair contributions to their nonlocal correlation components. Different flavors of this idea, ranging from standard SCS parameters to fully fitted parameter sets, are presented and tested on six different parent DHDFAs. For cross-validation, we assess those methods on three benchmark sets that cover small- to medium-sized chromophores (up to 78 atoms) and different excitation types. For this purpose, we also introduce new CC3 reference values for the popular Gordon benchmark set that we recommend using in future studies. Our results confirm that already the (unscaled) parent TD-DHDFAs are accurate and outperform some wave function methods. Further introduction of SCS/SOS eliminates extreme outliers, reduces deviation spans from reference values by up to 0.5 eV, aligns the performance of the Tamm-Dancoff approximation (TDA) to that of full TD calculations, and also enables a more balanced description of different excitation types. The best-performing TD-based methods in our cross validation have mean absolute deviations as low as 0.14 eV compared to the time- and resource-intensive CC3 approach. A very important finding is that we also obtained SOS variants with excellent performance, contrary to wave function based methods. This opens a future pathway to highly efficient methods for the optimization of excited-state geometries, particularly when paired with computing strategies such as the Laplace transform. We recommend our SCS- and SOS-based variants for further testing and subsequent applications.

Dissecting the accountability of parameterized and parameter-free single-hybrid and double-hybrid functionals for photophysical properties of TADF-based OLEDs

Organic light emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) emitters are an attractive category of materials that have witnessed a booming development in recent years. In the present contribution, we scrutinize the accountability of parameterized and parameter-free single-hybrid (SH) and double-hybrid (DH) functionals through the two formalisms, full time-dependent density functional theory (TD-DFT) and Tamm-Dancoff approximation (TDA), for the estimation of photophysical properties like absorption energy, emission energy, zero-zero transition energy, and singlet-triplet energy splitting of TADF molecules. According to our detailed analyses on the performance of SHs based on TD-DFT and TDA, the TDA-based parameter-free SH functionals, PBE0 and TPSS0, with one-third of exact-like exchange turned out to be the best performers in comparison to other functionals from various rungs to reproduce the experimental data of the benchmarked set. Such affordable SH approximations can thus be employed to predict and design the TADF molecules with low singlet-triplet energy gaps for OLED applications. From another perspective, considering this point that both the nonlocal exchange and correlation are essential for a more reliable description of large charge-transfer excited states, applicability of the functionals incorporating these terms, namely, parameterized and parameter-free DHs, has also been evaluated. Perusing the role of exact-like exchange, perturbative-like correlation, solvent effects, and other related factors, we find that the parameterized functionals B2π-PLYP and B2GP-PLYP and the parameter-free models PBE-CIDH and PBE-QIDH have respectable performance with respect to others. Lastly, besides the recommendation of reliable computational protocols for the purpose, hopefully this study can pave the way toward further developments of other SHs and DHs for theoretical explorations in the field of OLEDs technology.

Seeking for Spin-Opposite-Scaled Double-Hybrid Models Free of Fitted Parameters

On the basis of theoretical arguments, a new exchange-correlation energy expression free of any fitted parameter has been proposed for spin-opposite-scaled double-hybrid density functionals (SOS0-DHs). Employing the recently presented DHs, the working expressions for SOS0-DH functionals are obtained and benchmarked numerically against several standard databases. Our test calculations show that for some cases such as interaction energies and barrier heights the SOS0-DHs without dispersion corrections perform better than their non-SOS counterparts. On the other hand, for other properties like atomization energies, the conventional DHs provide reliable results. We hope that the findings of this work can excite further developments of DH functionals in the framework of SOS scheme for a wide variety of applications resolving the failures at a reasonable computational cost. It seems that a bright future lies ahead in this arena.

Relative energies of water nanoclusters (H2O)20: comparison of empirical and nonempirical double-hybrids with generalized energy-based fragmentation approach

The applicability of recently developed parameterized and parameter-free double-hybrids for predicting the relative energies of water nanoclusters has been examined.

Double-hybrid density functionals free of dispersion and counterpoise corrections for non-covalent interactions

We have optimized two double-hybrid density functionals (DHDFs) within the frameworks of B2PLYP and mPW2-PLYP against the S22B database. These two functionals are denoted as B2NC-PLYP and mPW2NC-PLYP, where "NC" represents noncovalent interaction. The DHDFs of B2NC-PLYP and mPW2NC-PLYP are optimized free of dispersion and counterpoise corrections with triple-ζ quality basis sets. Combined with the aug-cc-pVTZ basis set, these two functionals are further assessed with the S66 database. According to our computations, both the B2NC-PLYP and mPW2NC-PLYP functionals seem to be competent for investigating noncovalent interactions. Note that the triple-ζ quality basis sets with adequate polarization and diffuse functions should be employed for practical applications. However, different exchange and correlation functionals may be selected and/or modified to reduce the amount of the Fock-exchange in the future.