Combining real-space and local range separation-The MH24 locally range-separated local hybrid functional.

In this work, the development of a new general-purpose exchange-correlation hybrid functional based on the recent locally range-separated local hybrid approach is presented. In particular, the new functional, denoted as MH24, combines a non-empirical treatment of the admixture of locally range-separated long-range exact exchange with a new real-space separation approach for the real-space exact-exchange admixture governed by the local mixing function (LMF) and a new empirical LYP-based approach for the correlation functional to enable a flexible description of same- and opposite-spin correlation effects. The nine empirical parameters of the MH24 model have been optimized using a state-of-the-art super-self-consistent-field approach, which exploits the sensitivity of specific properties, such as core ionization potentials, electron affinities, and atomization energies, to the exact-exchange admixture in specific regions in real space and the separation of the LMF into a core, valence, and asymptotic part.

Toward a correct treatment of core properties with local hybrid functionals.

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region.

Assessing locally range-separated hybrid functionals from a gradient expansion of the exchange energy density.

Locally range-separated hybrid (LRSH) functionals feature a real-space-dependent range separation function (RSF) instead of a system-independent range-separation parameter, which thus enables a more flexible admixture of exact exchange than conventional range-separated hybrid functionals. In particular, the development of suitable RSF models and exploring the capabilities of the LRSH approach, in general, are tasks that require further investigations and will be addressed in this work. We propose a non-empirical scheme based on a detailed scaling analysis with respect to a uniform coordinate scaling and on a short-range expansion of the range-separated exchange energy density to derive new RSF models from a gradient expansion of the exchange energy density.

A Local Hybrid Functional with Wide Applicability and Good Balance between (De)Localization and Left-Right Correlation.

A new local hybrid functional, LH20t, with a position-dependent exact-exchange admixture governed by a simple local mixing function (() = ·τ()/τ()), combined with gradient-corrected (PBE) exchange and meta-GGA (B95) correlation, as well as a second-order GGA-based pig2 calibration function to address the ambiguity of exchange-energy densities, has been constructed. The adjustable parameters of LH20t have been optimized in a multistep procedure based on thermochemical kinetics data and measures of spurious nondynamical correlation. LH20t has subsequently been evaluated for the full GMTKN55 main-group energetics test suite, with and without an added DFT-D4 dispersion correction.

Relativistic local hybrid functionals and their impact on 1s core orbital energies.

In this work, we report the first relativistic density functional theory calculations using relativistic local hybrid functionals. Besides outlining the construction of relativistic local hybrid exchange within a two-component-relativistic framework based on the picture-change transformation of the density matrix and a recently developed relativistic iso-orbital indicator, we investigate the influence of two-electron-relativistic effects, using relativistic functional ingredients in local hybrid functionals, and the choice of the exchange-correlation functional on atomic 1s core orbital energies of light and heavier elements. Finally, we discuss the applicability of relativistic 1s core orbital shifts for the relativistic correction of non-relativistic 1s core excitation energies.

Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory.

In contrast to nonrelativistic density functional theory, the ratio between the von Weizsäcker and the Kohn-Sham kinetic energy density, commonly used as iso-orbital indicator t within exchange-correlation functionals beyond the generalized-gradient level, violates the exact iso-orbital limit and the appropriate parameter range, 0 ≤ t ≤ 1, in relativistic density functional theory. Based on the exact decoupling procedure within the infinite-order two-component method and the Cauchy-Schwarz inequality, we present corrections to the relativistic and the picture-change-transformed nonrelativistic kinetic energy density that restores these exact constraints. We discuss the origin of the new correction terms and illustrate the effectiveness of the current approach for several representative cases.

Efficient Semi-Numerical Implementation of Relativistic Exact Exchange within the Infinite-Order Two-Component Method Using a Modified Chain-of-Spheres Method.

We present an efficient implementation of relativistic exact exchange within the infinite-order two-component method (IOTC) by employing a state-of-the-art seminumerical integration technique. For accurate consideration of the picture change, inherent to two-component methods, we propose a new scheme based on a relativistic or picture-change transformation of the density matrix, which provides a simple and efficient formulation of relativistically transformed quantities such as the electron density or exact exchange and thus avoids expensive integral transformations. We show that the new scheme does not introduce additional numerical or theoretical errors beyond the approximations of the IOTC method.

Lessons from the Spin-Polarization/Spin-Contamination Dilemma of Transition-Metal Hyperfine Couplings for the Construction of Exchange-Correlation Functionals.

Hyperfine couplings (HFCs) of open-shell transition-metal centers are known to often depend crucially on core-shell spin polarization (CSSP). The latter is typically underestimated by semilocal density functionals, while admixture of exact exchange (EXX) in (global) hybrid functionals enhances CSSP. Unfortunately, a metal-ligand antibonding character of one or more of the singly occupied molecular orbitals of the complex will cause substantial valence-shell spin polarization (VSSP), which for global hybrids with higher EXX admixtures may lead to substantial spin contamination, thereby deteriorating the overall electronic structure and the dipolar couplings.

Development of a TDDFT-Based Protocol with Local Hybrid Functionals for the Screening of Potential Singlet Fission Chromophores.

Chromophores suitable for singlet fission need to meet specific requirements regarding the relative energies of their S, S, and T (and T) electronic states. Accurate quantum-chemical computations of the corresponding energy differences are thus highly desirable for materials design. Methods based on density functional theory (DFT) have the advantage of being applicable to larger, often more relevant systems compared to more sophisticated post-Hartree-Fock methods.

New approaches for the calibration of exchange-energy densities in local hybrid functionals.

The ambiguity of exchange-energy densities is a fundamental challenge for the development of local hybrid functionals, or of other functionals based on a local mixing of exchange-energy densities. In this work, a systematic construction of semi-local calibration functions (CFs) for adjusting the exchange-energy densities in local hybrid functionals is provided, which directly links a given CF to an underlying semi-local exchange functional, as well as to the second-order gradient expansion of the exchange hole. Using successive steps of integration by parts allows the derivation of correction terms of increasing order, resulting in more and more complicated but also more flexible CFs.

Validation of local hybrid functionals for TDDFT calculations of electronic excitation energies.

The first systematic evaluation of local hybrid functionals for the calculation of electronic excitation energies within linear-response time-dependent density functional theory (TDDFT) is reported. Using our recent efficient semi-numerical TDDFT implementation [T. M.

Efficient Semi-numerical Implementation of Global and Local Hybrid Functionals for Time-Dependent Density Functional Theory.

Local hybrid functionals with position-dependent exact-exchange admixture offer increased flexibility compared to global hybrids. For sufficiently advanced functionals of this type, this is expected to hold also for a wide range of electronic excitations within time-dependent density functional theory (TDDFT). Following a recent semi-numerical implementation of local hybrid functionals for ground-state self-consistent-field calculations (Bahmann, H.

The vibrational spectrum of FeO2(+) isomers--theoretical benchmark and experiment.

Infrared photodissociation is used to record the vibrational spectrum of FeO2 (+)(He)2-4 which shows three bands at 1035, 980, and 506 cm(-1). Quantum chemical multi-reference configuration interaction calculations (MRCISD) of structures and harmonic frequencies show that these bands are due to two different isomers, an inserted dioxo complex with Fe in the +V oxidation state and a side-on superoxo complex with Fe in the +II oxidation state. These two are separated by a substantial barrier, 53 kJ/mol, whereas the third isomer, an end-on complex between Fe(+) and an O2 molecule, is easily converted into the side-on complex.