The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn-Teller effect

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. However, a broad understanding of the configurational inversion of tetrahedral compounds is missing. Here, we report over 250 energies (DLPNO-CCSD(T)) for square planar inversion of third- and fourth-period element species of groups 13, 14, and 15. Surprisingly low inversion barriers are identified for compounds of industrial relevance (e.g., ≈100 kJ mol-1 for Al(OH)4 -). More fundamentally, the second-order Jahn-Teller theorem is disclosed as suitable to rationalize substituent and central element effects. Bond analysis tools give further insights into the preference of eight valence electron systems with four substituents to be tetrahedral. Hence, this study develops a model to understand, memorize, and predict the angular flexibility of tetrahedral species. Perceiving the tetrahedron not as forcingly rigid but as a dynamic structural entity might leverage new approaches and visions for adaptive matter.

The Effect of Particle Size and Composition on the Optical and Electronic Properties of CdO and CdS Rocksalt Nanoparticles

Quantum confinement like behaviour in CdO and CdS nanoparticles is demonstrated through explicit evGW-BSE many-body perturbation theory calculations on 0.6-1.4 nanometre particles of these materials. However, while the lowest optical...

Automated assessment of redox potentials for dyes in dye-sensitized photoelectrochemical cells

Sustainable solutions for hydrogen production, such as dye-sensitized photoelectrochemical cells (DS-PEC), rely on the fundamental properties of its components whose modularity allows for their separate investigation. In this work, we design and execute a high-throughput scheme to tune the ground state oxidation potential (GSOP) of perylene-type dyes by functionalizing them with different ligands. This allows us to identify promising candidates which can then be used to improve the cell's efficiency. First, we investigate the accuracy of different theoretical approaches by benchmarking them against experimentally determined GSOPs. We test different methods to calculate the vertical oxidation potential, including GW with different levels of self-consistency, Kohn-Sham (KS) orbital energies and total energy differences. We find that there is little difference in the performance of these methods. However, we show that it is crucial to take into account solvent effects as well as the structural relaxation of the dye after oxidation. Other thermodynamic contributions are negligible. Based on this benchmark, we decide on an optimal strategy, balancing computational cost and accuracy, to screen more than 1000 dyes and identify promising candidates which could be used to construct more robust DS-PECs.

Generalized Kohn-Sham equations with accurate total energy and single-particle eigenvalue spectrum

We propose a new generalized Kohn-Sham or constrained hybrid method, where the exchange potential is the (equally weighted) average of the nonlocal Fock-exchange term and the self-interaction-corrected exchange potential, as obtained from our constrained minimization method of semi-local approximations. The new method gives an accurate single-particle eigenvalue spectrum with an average deviation between (the negative of) the valence orbital eigenvalues and the experimental ionization potentials of about 0.5 eV, while the deviation of core orbitals is within 2 eV. The improvement in the eigenvalue spectrum is achieved with a minimal increase in the total energy.

The effect of particle size on the optical and electronic properties of magnesium oxide nanoparticles

The quasiparticle states, fundamental gaps, optical gaps, exciton binding energies and UV-vis spectra for a series of cuboidal nanoparticles of the prototypical oxide magnesium oxide (MgO), the largest of which has 216 atoms and edges of 1 nm, were predicted using many-body perturbation theory (evGW-BSE). The evolution of the properties with the particle size was explicitly studied. It was found that, while the highest occupied and lowest unoccupied quasiparticle states and fundamental gap change with the particle size, the optical gap remains essentially fixed for all but the smallest nanoparticles, in line with what was previously observed experimentally. The explanation for these observations is demonstrated to be that, while the optical gap is associated with an exciton that is highly localised around the particle's corner atoms, the highest occupied and lowest unoccupied quasiparticle states, while primarily localised on the oxygen corner atoms (hole) and magnesium corner atoms (electron), show significant delocalisation along the edges. The strong localisation of the exciton associated with the optical gap on the corner atoms is argued to also explain why the nanoparticles have much smaller optical gaps and red-shifted spectra compared to bulk MgO. Finally, it is discussed how this non-quantum confinement behaviour, where the properties of the nanoparticles arise from surface defects rather than differences in localisation of quasiparticle or exciton states, appears typical of alkaline earth oxide nanoparticles, and that the true optical gap of bulk crystals of such materials is also probably the result of surface defects, even if unobservable experimentally.

Structural Evolution, Electronic Structures, and Vibrational Properties of Anionic LuGen (n = 5-17) Clusters: From Lu-Linked to Lu-Encapsulated Configurations

The structural evolution pattern and electronic properties of Lu-doped germanium anion clusters, LuGe_n^- (n = 5-17), have been investigated using a global search method combined with a double hybrid density functional theory and by comparing the theoretical PES spectra with the experimental ones. It is found that, for the structural growth patterns, a Lu-linked configuration is preferred for n = 10-14 in which the Lu atom as a linker connects two Ge subclusters and a Lu-encapsulated Ge cage-like motif is preferred for n = 15-17. The simulated PES spectra agree with experimental ones, revealing that the current global minimum structures are the true minima. The properties such as relative stability, charge transfer, highest-energy occupied molecular orbital-lowest-energy unoccupied molecular orbital (HOMO-LUMO) gap, IR, Raman, and ultraviolet-visible (UV-vis) spectra have been evaluated. The results of IR and Raman spectra could provide additional ways to experimentally identify the structure of these clusters. The results of stability, HOMO-LUMO gap, and UV-vis spectra could make the LuGe₁₆^- cluster the most suitable building block for further development as a potential optoelectronic material.

Ab Initio Quantum-Mechanical Predictions of Semiconducting Photocathode Materials

Ab initio Quantum-Mechanical methods are well-established tools for material characterization and discovery in many technological areas. Recently, state-of-the-art approaches based on density-functional theory and many-body perturbation theory were successfully applied to semiconducting alkali antimonides and tellurides, which are currently employed as photocathodes in particle accelerator facilities. The results of these studies have unveiled the potential of ab initio methods to complement experimental and technical efforts for the development of new, more efficient materials for vacuum electron sources. Concomitantly, these findings have revealed the need for theory to go beyond the status quo in order to face the challenges of modeling such complex systems and their properties in operando conditions. In this review, we summarize recent progress in the application of ab initio many-body methods to investigate photocathode materials, analyzing the merits and the limitations of the standard approaches with respect to the confronted scientific questions. In particular, we emphasize the necessary trade-off between computational accuracy and feasibility that is intrinsic to these studies, and propose possible routes to optimize it. We finally discuss novel schemes for computationally-aided material discovery that are suitable for the development of ultra-bright electron sources toward the incoming era of artificial intelligence.

Selfconsistent random phase approximation methods

This Perspective reviews recent efforts toward selfconsistent calculations of ground-state energies within the random phase approximation (RPA) in the (generalized) Kohn-Sham (KS) density functional theory context. Since the RPA correlation energy explicitly depends on the non-interacting KS potential, an additional condition to determine the energy as a functional of the density is necessary. This observation leads to the concept of functional selfconsistency (FSC), which requires that the KS density equals the interacting density defined as the functional derivative of the ground-state energy with respect to the external potential. While all existing selfconsistent RPA schemes violate FSC, the recent generalized KS semicanonical projected RPA (GKS-spRPA) method takes a step toward satisfying it. This leads to systematic improvements in densities, binding energy curves, reference state stability, and molecular properties compared to non-selfconsistent RPA as well as optimized effective potential RPA. GKS-spRPA orbital energies accurately approximate valence and core ionization potentials, and even electron affinities of non-valence bound anions. The computational cost and performance of GKS-spRPA are compared to those of related selfconsistent schemes, including GW and orbital optimization methods, and limitations are discussed. Large differences between KS and interacting densities observed in the absence of FSC and the well-rounded performance of GKS-spRPA suggest that the KS potential as a density functional should be defined via the FSC condition for explicitly potential-dependent density functionals.

Explicitly correlated Fock-space coupled-cluster singles and doubles method for (1,1), (0,2), and (2,0) sectors

A linearly approximated explicitly correlated coupled-cluster singles and doubles model for the Fock-space coupled-cluster method has been formulated and implemented. An extension of the Fock-space wave operators is introduced in order to treat the short-range correlation effects for excited and doubly electron-attached states. We show that an effective reduction in the number of active virtuals can also be obtained by improving how the short-range correlation is treated. Numerical results to gauge the performance for valence and Rydberg excitation energies, double ionization potentials, and double electron attachment energies of several molecules are obtained. Statistical measures of the errors in excitation energies show that the explicitly correlated results are within 0.1 eV from the complete basis set limit already at the double-ζ level unless the excitation energies are too close to the ionization thresholds. Similar accuracy is seen for the double ionization potentials and double electron attachment energies.

Replacing hybrid density functional theory: motivation and recent advances

Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.

Strongly Bound Excitons in Metal-Organic Framework MOF-5: A Many-Body Perturbation Theory Study

During the past years, one of the most iconic metal-organic frameworks (MOFs), MOF-5, has been characterized as a semiconductor by theory and experiments. Here we employ the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation to compute the electronic structure and optical properties of this MOF. The GW calculations show that MOF-5 is a wide-band-gap insulator with a fundamental gap of ∼8 eV. The strong excitonic effects, arising from highly localized states and low screening, result in an optical gap of 4.5 eV and in an optical absorption spectrum in excellent agreement with experiments. The origin of the incorrect conclusion reported by past studies and the implication of this result are also discussed.

Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation

The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase approximation (RPA) has played an important role ever since the conception of the OEP formalism. However, the solution of the OEP equation is computationally fairly expensive and has to be done in a self-consistent way. So far, large scale solid state applications have, therefore, been performed only using the quasiparticle approximation (QPA), neglecting certain dynamical screening effects. We obtain the exact RPA-OEP for 15 semiconductors and insulators by direct solution of the linearized Sham-Schlüter equation. We investigate the accuracy of the QPA on Kohn-Sham bandgaps and dielectric constants, and comment on the issue of self-consistency.

Capturing the Electron-Phonon Renormalization in Molecules from First-Principles

Since the interaction between electrons and atomic nuclei can affect the electronic structure, in recent years, first-principles-based electron-phonon renormalization methods have been applied in the condensed matter physics community to account for the influence of the electron-phonon coupling in solid systems. However, little is yet known about the behavior and trends of the electron-phonon renormalization in the molecules. In this work, the method for the electron-phonon renormalization in molecules has been derived, using which, we exhaustively investigate the zero-point renormalization in 32 molecules with three different density functions. We find that the renormalization of the highest occupied molecular orbital-lowest unoccupied molecular orbital gap due to electron-vibration coupling does not relate to the atomic masses but quite relates to the electronic structure properties of the molecules.

AgBi(SO4)(IO3)2: aliovalent substitution induces structure dimensional upgrade and second harmonic generation enhancement

A new 3D noncentrosymmetric mixed-metal sulfate iodate, AgBi(SO₄)(IO₃)₂, has been designed based on a 2D iodate of AgBi(IO₃)₄via the aliovalent substitution of [IO₃]^- groups by [SO₄]^2- groups. Enhancement of the second harmonic generation response (3.0 × KDP to 3.9 × KDP) has been achieved while retaining a favorable NLO framework. This is a novel strategy to upgrade structural dimensions.

From Kohn-Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Accurately describing excited states within Kohn–Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

Coupling an organic photosensitizer and an inorganic framework into a single-phase material that shows visible-light photocurrent response

A rare hybrid of a 3D Sn–Se type framework and a ruthenium(ii) photosensitizer has been synthesized, and exhibits visible light photocurrent response.

Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach

Molecular quasiparticle and excitation energies determine essentially the spectral characteristics measured in various spectroscopic experiments. Accurate prediction of these energies has been rather challenging for ground-state density functional methods, because the commonly adopted density function approximations suffer from delocalization error. In this work, by presuming a quantitative correspondence between the quasiparticle energies and the generalized Kohn–Sham orbital energies, and employing a previously developed global scaling correction approach, we achieve substantially improved prediction of molecular quasiparticle and excitation energies. In addition, we also extend our previous study on temporary anions in resonant states, which are associated with negative molecular electron affinities. The proposed approach does not require any explicit self-consistent field calculation on the excited-state species, and is thus highly efficient and convenient for practical purposes.

Low-Order Scaling G0W0 by Pair Atomic Density Fitting

We derive a low-scaling G0W0 algorithm for molecules using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO)-based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-ζ (TZ) plus double polarization quality. Also owing to a very small prefactor, a G0W0 calculation for the largest of these clusters takes only 240 CPU hours with these settings. We assess the accuracy of our algorithm for HOMO and LUMO energies in the GW100 database. With errors of 0.24 eV for HOMO energies on the quadruple-ζ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-type basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF approach of accurately representing diffuse atomic orbital (AO) products. We speculate that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented double-ζ (DZ) quality is decreasing with system size. On the augmented DZ level, we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.

Mechanism of absorption wavelength shifts in anion channelrhodopsin-1 mutants

Using a quantum mechanical/molecular mechanical approach, we show the mechanisms of how the protein environment of Guillardia theta anion channelrhodopsin-1 (GtACR1) can shift the absorption wavelength. The calculated absorption wavelengths for GtACR1 mutants, M105A, C133A, and C237A are in agreement with experimentally measured wavelengths. Among 192 mutant structures investigated, mutations at Thr101, Cys133, Pro208, and Cys237 are likely to increase the absorption wavelength. In particular, T101A GtACR1 was expressed in HEK293T cells. The measured absorption wavelength is 10 nm higher than that of wild type, consistent with the calculated wavelength. (i) Removal of a polar residue from the Schiff base moiety, (ii) addition of a polar or acidic residue to the β-ionone ring moiety, and (iii) addition of a bulky residue to increase the planarity of the β-ionone and Schiff base moieties are the basis of increasing the absorption wavelength.

Insights into the Protein Functions and Absorption Wavelengths of Microbial Rhodopsins

Using a quantum mechanical/molecular mechanical approach, the absorption wavelength of the retinal Schiff base was calculated based on 13 microbial rhodopsin crystal structures. The results showed that the protein electrostatic environment decreases the absorption wavelength significantly in the cation-conducting rhodopsin but only slightly in the sensory rhodopsin. Among the microbial rhodopsins with different functions, the differences in the absorption wavelengths are caused by differences in the arrangement of the charged residues at the retinal Schiff base binding moiety, namely, one or two counterions at the three common positions. Among the microbial rhodopsins with similar functions, the differences in the polar residues at the retinal Schiff base binding site are responsible for the differences in the absorption wavelengths. Counterions contribute to an absorption wavelength shift of 50-120 nm, whereas polar groups contribute to a shift of up to ∼10 nm. It seems likely that protein function is directly associated with the absorption wavelength in microbial rhodopsins.

UV-visible absorption spectrum of FAD and its reduced forms embedded in a cryptochrome protein

Cryptochromes are a class of flavoproteins proposed as candidates to explain magnetoreception of animals, plants and bacteria. The main hypothesis is that a biradical is formed upon blue-light absorption by flavin adenine dinucleotide (FAD). In a protein milieu, the oxidized form of FAD can be reduced, leading to four redox derivative forms: anionic and neutral semi-reduced radicals, and anionic and neutral fully reduced forms. All these forms have a characteristic electronic absorption spectrum, with a strong vibrational resolution. Here, we carried out a normal mode analysis at the electrostatic embedding QM/MM level of theory to compute the vibrationally resolved absorption spectra of the five redox forms of FAD embedded in a plant cryptochrome. We show that explicitly accounting for vibrational broadening contributions to electronic transitions is essential to reproduce the experimental spectra. In the case of the neutral radical form of FAD, the absorption spectrum is reproduced only if the presence of a tryptophan radical is considered.

Can one use the electronic absorption spectra of metalloporphyrins to benchmark electronic structure methods? A case study on the cobalt porphyrin

In this article, we describe calculations on the absorption spectrum of cobalt(ii) porphyrin, using density functional (DFT) and multireference n-electron valence perturbation (NEVPT) theories. With these calculations, we describe the lowest-energy states of doublet and quartet spin multiplicities, the excited states that originate the Q and B bands of porphyrins, some higher-energy π-π* excitations and charge-transfer states, HOMO-LUMO gaps, and ionisation potentials. Results undoubtedly show that the position of B band is essentially independent on the DFT functional, while the Q band is better described by pure functionals, and these bands do not depend on the initial state of the transition (whether doublet or quartet) as well. However, other excitation energies, orbital energies, and ionisation potentials strongly depend on the functional, in some cases varying more than 2 eV. Based on these results we conclude that one should not use the UV-Vis spectrum of metalloporphyrins to benchmark density functionals, mainly those properties related to coordination with the metallic ion. Furthermore, the results show that functionals that yield correct spectra may be based on an incorrect ground state description. Moreover, we reinforce that one must be skeptical about the reference chosen to benchmark electronic structure calculations, such as DFT functionals and active spaces for multireference calculations.

Final-State Simulations of Core-Level Binding Energies at Metal-Organic Hybrid Interfaces: Artifacts Caused by Spurious Collective Electrostatic Effects

Core-level energies are frequently calculated to explain the X-ray photoelectron spectra of metal-organic hybrid interfaces. The current paper describes how such simulations can be flawed when modeling interfaces between physisorbed organic molecules and metals. The problem occurs when applying periodic boundary conditions to correctly describe extended interfaces and simultaneously considering core hole excitations in the framework of a final-state approach to account for screening effects. Since the core hole is generated in every unit cell, an artificial dipole layer is formed. In this work, we study methane on an Al(100) surface as a deliberately chosen model system for hybrid interfaces to evaluate the impact of this computational artifact. We show that changing the supercell size leads to artificial shifts in the calculated core-level energies that can be well beyond 1 eV for small cells. The same applies to atoms at comparably large distances from the substrate, encountered, for example, in extended, upright-standing adsorbate molecules. We also argue that the calculated work function change due to a core-level excitation can serve as an indication for the occurrence of such an artifact and discuss possible remedies for the problem.

Diradicalar Character and Ring Stability of Mesoionic Heterocyclic Oxazoles and Thiazoles by Ab Initio Mono and Multi-Reference Methods

Mesoionics are neutral compounds that cannot be represented by a fully covalent or purely ionic structure. Among the possible mesomeric structures of these compounds are the diradical electronic configurations. Theoretical and experimental studies indicate that some mesoionic rings are unstable, which may be related to a significant diradical character, that until then is not quantified. In this work, we investigated the diradical character of four heterocycles: 1,3-oxazol-5-one, 1,3-oxazol-5-thione, 1,3-thiazole-5-one, and 1,3-thiazole-5-thione. The oxazoles are known to be significatively less stable than thiazoles. DFT and ab initio single (B3LYP, MP2, CCSD, and QCISD) and ab initio multi-reference (MR-CISD) methods with three basis sets (6-311+G(d), aug-cc-pVDZ, and aug-cc-pVTZ) were employed to assess the diradical character of the investigated systems, in gas phase and DMSO solvent, from three criteria: (i) HOMO-LUMO energy gap, (ii) determination of energy difference between singlet and triplet wave functions, and (iii) quantification of the most significant diradical character (y₀, determined in the unrestricted formalism). All of the results showed that the diradical character of the investigated systems is very small. However, the calculated electronic structures made it possible to identify the possible origin of the oxazoles instability, which can help the design of mesoionic systems with the desired properties.

Optical gap and fundamental gap of oligoynes and carbyne

The optoelectronic properties of various carbon allotropes and nanomaterials have been well established, while the purely sp-hybridized carbyne remains synthetically inaccessible. Its properties have therefore frequently been extrapolated from those of defined oligomers. Most analyses have, however, focused on the main optical transitions in UV-Vis spectroscopy, neglecting the frequently observed weaker optical bands at significantly lower energies. Here, we report a systematic photophysical analysis as well as computations on two homologous series of oligoynes that allow us to elucidate the nature of these weaker transitions and the intrinsic photophysical properties of oligoynes. Based on these results, we reassess the estimates for both the optical and fundamental gap of carbyne to below 1.6 eV, significantly lower than previously suggested by experimental studies of oligoynes.

Carbyne, a linear sp-hybridized carbon allotrope, is synthetically inaccessible and its properties are extrapolated from those of defined oligomers. Here the authors analyze weak optical bands in two series of oligoynes and reassess the optical and fundamental gap of carbyne to lower values than previously suggested.

Rapid Prediction of Ultraviolet-Visible Spectra from Conventional (Non-Time-Dependent) Density Functional Theory Calculations

We present an approximate approach for the simulation of UV/vis spectra using conventional [non-time-dependent (non-TD)] DFT computations. It uses Kohn-Sham orbitals and orbital energies to estimate both the excitation energies and the associated oscillator strengths. For a wide range of systems from small molecules to large molecular dyes used in electrochromic and solar-cell applications, reasonable UV/vis spectra are generated, each with just two conventional DFT computations. The accuracy is generally comparable to what one would expect from TD-DFT calculations. In comparison to TD-DFT, the protocol of the present study provides an intuitive and notably more rapid means for simulating electronic absorption properties. It enables efficient screening of materials for a wide range of relevant applications.

Synthesis and Properties of Perylene-Bridge-Anchor Chromophoric Compounds

The quest to control chromophore/semiconductor properties to enable new technologies in energy and information science requires detailed understanding of charge carrier dynamics at the atomistic level, which can often be attained through the use of model systems. Perylene-bridge-anchor compounds are successful models for studying fundamental charge transfer processes on TiO₂, which remains among the most commonly investigated and technologically important interfaces, mostly because of perylene's advantageous electronic and optical properties. Nonetheless, the ability to fully exploit synthetically the substitution pattern of perylene with linker (= bridge-anchor) units remains little explored. Here we developed 2,5-di-tert-butylperylene (DtBuPe)-bridge-anchor compounds with t-Bu group substituents to prevent π-stacking and one or two linker units in both the peri and ortho positions, by employing a combination of Friedel-Crafts alkylations, bromination, iridium-catalyzed borylation, and palladium-catalyzed cross-coupling reactions. Photophysical characterization and computational analysis by density functional theory (DFT) and time-dependent DFT (TD-DFT) were carried out on four DtBuPe acrylic acid derivatives with a single or a double linker in peri (12b), ortho (15b), peri,peri (18b), and ortho,ortho (21b). The energies of the unoccupied orbitals {LUMO, LUMO + 1, LUMO + 2} are strongly affected by the presence of a π-conjugated linker, resulting in a stabilization of these states and a red shift of their absorption and emission spectra, as well as the loss of vibronic structure in the spectrum of the peri,peri compound, consistent with the strong bonding character of this substitution pattern.

Hole-hole Tamm-Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ^* and nπ^* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

Relationships between Orbital Energies, Optical and Fundamental Gaps, and Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory

The relationships between Kohn-Sham (KS) and generalized KS (GKS) density functional orbital energies and fundamental gaps or optical gaps raise many interesting questions including the physical meanings of KS and GKS orbital energies when computed with currently available approximate density functionals (ADFs). In this work, by examining three diverse databases with various ADFs, we examine such relations from the point of view of the exciton shift of quasiparticle theory. We start by calculating a large number of excitation energies by time-dependent density functional theory (TDDFT) with a large number of ADFs. To relate the exciton shift implicit in TDDFT to the exciton shift that is explicit in Green's function theory, we define the exciton shift in TDDFT as the difference of the response shift and the quasiparticle shift. We found a strong correlation between the response shift and the amount of Hartree-Fock exchange included in the density functional, with the response shift varying between -1 and 5 eV. This range is an order of magnitude larger than the mean errors of the TDDFT excitation energies. This result suggests that, with currently available functionals, the KS or GKS orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.

Mechanism of biomolecular recognition of trimethyllysine by the fluorinated aromatic cage of KDM5A PHD3 finger

The understanding of biomolecular recognition of posttranslationally modified histone proteins is centrally important to the histone code hypothesis. Despite extensive binding and structural studies on the readout of histones, the molecular language by which posttranslational modifications on histone proteins are read remains poorly understood. Here we report physical-organic chemistry studies on the recognition of the positively charged trimethyllysine by the electron-rich aromatic cage containing PHD3 finger of KDM5A. The aromatic character of two tryptophan residues that solely constitute the aromatic cage of KDM5A was fine-tuned by the incorporation of fluorine substituents. Our thermodynamic analyses reveal that the wild-type and fluorinated KDM5A PHD3 fingers associate equally well with trimethyllysine. This work demonstrates that the biomolecular recognition of trimethyllysine by fluorinated aromatic cages is associated with weaker cation-π interactions that are compensated by the energetically more favourable trimethyllysine-mediated release of high-energy water molecules that occupy the aromatic cage.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

Structural and electronic properties of nanosize semiconductor HfSin0/-/2- (n = 6-16) material: a double-hybrid density functional theory investigation

Equilibrium geometries, thermodynamic stabilities, chemical reactivities, and electronic properties of neutral, mono-, and di-anionic Hf-doped silicon nanoclusters HfSi_n^0/-2- (n = 6-16) are calculated by employing an ABCluster global search technique combined with mPW2PLYP scheme. Based on the concordance between simulated and experimental PES, the true global minima are confirmed for n = 6, 9, and 12-16. Optimized geometries for neutral HfSi_n nanoclusters can be divided into three stages: first, Hf atom prefers locating on the surface site of the cluster for n = 6-9, which can be obtained by adding one, two, three, and four Si atoms to HfSi₅ tetragonal bipyramid, respectively (denoted as additive type); then, Hf atom is surrounded by Si atoms with half-cage configuration for n = 10-13; finally, Hf atom is encapsulated into Si cage pattern for n = 14-16. For mono-anions, it is from additive type (n = 6-11) to the cagelike configuration with Hf atom resided in silicon clusters (n = 12-16). For di-anions, it is additive type (n = 6-9) to the Hf-linked configuration (n = 10-11), and in the end to the Hf-encapsulated cagelike motif (n = 12-16). The thorough analysis of stability and chemical bonding revealed that the neutral HfSi₁₆ and di-anionic HfSi₁₅^2- are magic nanoclusters with good thermodynamic and chemical stability, which may make them as the most suitable building block for new functional materials. We suggest that the experimental PES of HfSi_n^- with n = 7, 8, 10, and 11 should be further examined due to the lack of comparably low electron binding energy peaks.

Mechanistic Chromatographic Column Characterization for the Analysis of Flavonoids Using Quantitative Structure-Retention Relationships Based on Density Functional Theory

This work aimed to unravel the retention mechanisms of 30 structurally different flavonoids separated on three chromatographic columns: conventional Kinetex C18 (K-C18), Kinetex F5 (K-F5), and IAM.PC.DD2. Interactions between analytes and chromatographic phases governing the retention were analyzed and mechanistically interpreted via quantum chemical descriptors as compared to the typical 'black box' approach. Statistically significant consensus genetic algorithm-partial least squares (GA-PLS) quantitative structure retention relationship (QSRR) models were built and comprehensively validated. Results showed that for the K-C18 column, hydrophobicity and solvent effects were dominating, whereas electrostatic interactions were less pronounced. Similarly, for the K-F5 column, hydrophobicity, dispersion effects, and electrostatic interactions were found to be governing the retention of flavonoids. Conversely, besides hydrophobic forces and dispersion effects, electrostatic interactions were found to be dominating the IAM.PC.DD2 retention mechanism. As such, the developed approach has a great potential for gaining insights into biological activity upon analysis of interactions between analytes and stationary phases imitating molecular targets, giving rise to an exceptional alternative to existing methods lacking exhaustive interpretations.

Performance of TDDFT Vertical Excitation Energies of Core-Substituted Naphthalene Diimides

We have evaluated the performance of various density functionals, covering generalized gradient approximation (GGA), global hybrid (GH) and range‐separated hybrid (RSH), using time dependent density functional theory (TDDFT) for computing vertical excitation energies against experimental absorption maximum (λ_max) for a set of 10 different core‐substituted naphthalene diimides (cNDI) recorded in dichloromethane. The computed excitation in case of GH PBE0 is most accurate while the trend is most systematic with RSH LCY‐BLYP compared to λ_max. We highlight the importance of including solvent effects for optimal agreement with the λ_max. Increasing the basis set size from TZ2P to QZ4P has a negligible influence on the computed excitation energies. Notably, RSH CAMY‐B3LYP gave the least error for charge‐transfer excitation. The poorest agreement with λ_max is obtained with semi‐local GGA functionals. Use of the optimally‐tuned RSH LCY‐BLYP* is not recommended because of the high computational cost and marginal improvement in results.

The Electron Affinity as the Highest Occupied Anion Orbital Energy with a Sufficiently Accurate Approximation of the Exact Kohn-Sham Potential

Negative ions are not accurately represented in density functional approximations (DFAs) such as (semi)local density functionals (LDA or GGA or meta-GGA). This is caused by the much too high orbital energies (not negative enough) with these DFAs compared to the exact Kohn–Sham values. Negative ions very often have positive DFA HOMO energies, hence they are unstable. These problems do not occur with the exact Kohn–Sham potential, the anion HOMO energy then being equal to minus the electron affinity. It is therefore desirable to develop sufficiently accurate approximations to the exact Kohn–Sham potential. There are further beneficial effects on the orbital shapes and the density of using a good approximation to the exact KS potential. Notably the unoccupied orbitals are not unduly diffuse, as they are in the Hartree–Fock model, with hybrid functionals, and even with (semi)local density functional approximations (LDFAs). We show that the recently developed B-GLLB-VWN approximation [Gritsenko et al. J. Chem. Phys.2016, 144, 204114] to the exact KS potential affords stable negative ions with HOMO orbital energy close to minus the electron affinity.

Variational calculations of excited states via direct optimization of the orbitals in DFT

A direct optimization method for obtaining excited electronic states using density functionals is presented.

Photoelectrochemistry of Ferrites: Theoretical Predictions vs. Experimental Results

This paper gives an overview about recent theoretical and experimental work on electronic and optical properties of spinel ferrites MFe2O4. These compounds have come into focus of research due to their possible application as photocatalyst material for photoelectrochemical water splitting. The theoretical background of state-of-the-art quantum-chemical approaches applied for predicting electronic and optical band gaps, absolute band positions, optical absorption spectra, dielectric functions and Raman spectra, is briefly reviewed. Recent applications of first-principles methods on magnetic and electronic properties of ferrites with M = Mg and the first row of subgroup elements Sc to Zn are presented, where it is shown that the fundamental band gap is strongly dependent on the spin state and the degree of inversion of the spinel structure. The observed variation of electronic properties may serve as an explanation for the large scattering of experimental results. The exchange of M and Fe cations has also a pronounced effect on the Raman spectra of ferrites, which is analyzed at atomic scale from first principles. Calculated optical absorption spectra of ferrites are compared to experimental spectra. The electronic nature of the first excitations and the role of oxygen vacancies are discussed. For the calculation of absolute band positions, which have a significant impact on the photoelectrochemical activity of the ferrites, models of the most stable ferrite surfaces are developed that take into account their polar nature and the interaction with the solvent. Theoretically predicted valence and conduction band edges are compared to results from electrochemical measurements. The role of cation exchange on the surface electronic structure is investigated both theoretically and experimentally.