Perspective: Fifty years of density-functional theory in chemical physics

PubChemQC B3LYP/6-31G*//PM6 Data Set: The Electronic Structures of 86 Million Molecules Using B3LYP/6-31G* Calculations

The presented "PubChemQC B3LYP/6-31G*//PM6" data set is composed of the electronic properties of 85,938,443 molecules, encompassing a broad spectrum of molecules from essential compounds to biomolecules with a molecular weight up to 1000. These molecules account for 94.0% of the original PubChem Compound catalog as of August 29, 2016. The electronic properties, including orbitals, orbital energies, total energies, dipole moments, and other pertinent properties, were computed by using the B3LYP/6-31G* and PM6 methods. The data set, available in three formats, namely, GAMESS quantum chemistry program files, selected JSON output files, and a PostgreSQL database, provides researchers with the ability to query molecular properties. It is further subdivided into five subdata sets for more specific data. The first two subsets encompass molecules with carbon, hydrogen, oxygen, and nitrogen with molecular weights under 300 and 500, respectively. The third and fourth subsets incorporate molecules with carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur, fluorine, and chlorine, with molecular weights under 300 and 500, respectively. The fifth subset comprises molecules with carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur, fluorine, chlorine, sodium, potassium, magnesium, and calcium, with a molecular weight of under 500. The coefficients of determination for the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap range from 0.892 (for CHON500) to 0.803 (for the whole data set). These comprehensive results pave the way for applications in drug discovery and materials science, among others. The data sets can be accessed under the Creative Commons Attribution 4.0 International license at the following web address: https://nakatamaho.riken.jp/pubchemqc.riken.jp/b3lyp_pm6_datasets.html.

Reproducibility of density functional approximations: How new functionals should be reported

Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations are published every year. To become available in program packages, the novel density functional approximations (DFAs) need to be (re)implemented. However, according to our experience as developers of Libxc [Lehtola et al., SoftwareX 7, 1 (2018)], a constant problem in this task is verification due to the lack of reliable reference data. As we discuss in this work, this lack has led to several non-equivalent implementations of functionals such as Becke-Perdew 1986, Perdew-Wang 1991, Perdew-Burke-Ernzerhof, and Becke's three-parameter hybrid functional with Lee-Yang-Parr correlation across various program packages, yielding different total energies. Through careful verification, we have also found many issues with incorrect functional forms in recent DFAs. The goal of this work is to ensure the reproducibility of DFAs. DFAs must be verifiable in order to prevent the reappearance of the above-mentioned errors and incompatibilities. A common framework for verification and testing is, therefore, needed. We suggest several ways in which reference energies can be produced with free and open source software, either with non-self-consistent calculations with tabulated atomic densities or via self-consistent calculations with various program packages. The employed numerical parameters-especially the quadrature grid-need to be converged to guarantee a ≲0.1 μEh precision in the total energy, which is nowadays routinely achievable in fully numerical calculations. Moreover, as such sub-μEh level agreement can only be achieved when fully equivalent implementations of the DFA are used, the source code of the reference implementation should also be made available in any publication describing a new DFA.

Efficient immobilization and detoxification of gaseous elemental mercury by nanoflower/rod WSe2/halloysite composite: Performance and mechanisms

Gaseous mercury pollution control technologies with low stability and high releasing risks always face with great challenges. Herein, we developed one halloysite nanotubes (HNTs)-supported tungsten diselenide (WSe2) composite (WSe2/HNTs) by one-pot solvothermal approach, curing Hg0 from complicated flue gas (CFG) and reducing second environment risks. WSe2 as a monolayer with nano-flower structure and HNTs with rod shapes in the as-prepared sorbent exhibited outstanding synergy efficiency, resulting in exceptional performance for Hg0 removal with high capture capacity of 30.6 mg·g-1 and rate of 9.09 μg·g-1·min-1, which benefited from the high affinity of selenium and mercury (1 ×1045) and the adequate exposure of Se-terminated. The adsorbent showed beneficial tolerance to high amount of NOx and SOx. An online lab-built thermal decomposition system (TPD-AFS) was employed to explore Hg species on the used-sorbent, finding that the adsorbed-mercury species were principally mercury selenide (HgSe). Density functional theory calculations indicated that the hollow-sites were the major adsorption sites and exhibited excellent selectivity for Hg0, as well as HgSe generation needed to overcome the 0.32 eV energy barrier. The adsorbed mercury displayed high environmental stability after the leaching toxicity test, which significantly decreased its secondary environmental risks. With these advantages, WSe2/HNTs possess enormous potential to achieve the effective and permanent immobilization of gaseous mercury from CFG in the future.

Better performance of Hartree-Fock over DFT: a quantum mechanical investigation on pyridinium benzimidazolate types of zwitterions in the light of localization/delocalization issues

CONTEXT

With the advent of fast computing facilities, combined with rapid emerges of many new and intricate quantum mechanical functionals, computations with pure Hartree-Fock (HF) theory are now-a-days regarded as trivial or obsolete, or even considered as not reliable by many researchers. Consequently, current trends in computational chemistry show extensive use of post-HF theories for smaller molecular systems and various DFT methods for organic and inorganic chemistry related problems (larger molecules/systems). In this contribution, I have tried to show that sometimes, HF might be more suitable over DFT methodologies in addressing structure-property correlations. Molecules studied here were previously synthesized by Boyd in 1966 and important experimental data were produced by Alcalde and co-workers in 1987. Comparison of computed and experimental results clearly shows that HF method was more effective in reproducing the experimental data compared to especially the DFT methodologies. Reliability of HF method was further assured from the very similar results shown by the CCSD, CASSCF, CISD and QCISD methods. Current study also indicates that the localization issue associated with HF proved to be advantageous over delocalization issue of DFT based methodologies, in correctly describing the structure-property correlation for zwitterion systems.

METHODS

All computations were performed with Gaussian 09. A wide-range of quantum mechanical methodologies, HF, B3LYP, CAM-B3LYP, BMK, B3PW91, TPSSh, LC-ωPBE, M06-2X, M06-HF, ωB97xD, MP2, CASSCF, CCSD, QCISD, CISD and semi-empirical methods like, Huckel, CNDO, AM1, PM3MM and PM6, were used for investigations.

Applications of the Near Attack Conformation (NAC) approach in the search for Acetylcholinesterase reactivators

The Near Attack Conformation (NAC) approach states that the efficiency of an enzyme-catalyzed reaction depends on the prior attainment of optimal conditions for substrate atom organization and positioning for bond formation. These conditions are prerequisites for the transition state (TS) in which the involved atoms are within the van der Waals range of contact and positioned at an angle similar to that achieved after bond formation. The successful application of this approach to investigate the reactivation mechanism of acetylcholinesterase inhibited by nerve agents has contributed to a better understanding of this mechanism and demonstrated consistent corroboration with experimental data. In this article, we summarize the accomplishments achieved thus far and outline future perspectives.

PiNNwall: Heterogeneous Electrode Models from Integrating Machine Learning and Atomistic Simulation

Electrochemical energy storage always involves the capacitive process. The prevailing electrode model used in the molecular simulation of polarizable electrode-electrolyte systems is the Siepmann-Sprik model developed for perfect metal electrodes. This model has been recently extended to study the metallicity in the electrode by including the Thomas-Fermi screening length. Nevertheless, a further extension to heterogeneous electrode models requires introducing chemical specificity, which does not have any analytical recipes. Here, we address this challenge by integrating the atomistic machine learning code (PiNN) for generating the base charge and response kernel and the classical molecular dynamics code (MetalWalls) dedicated to the modeling of electrochemical systems, and this leads to the development of the PiNNwall interface. Apart from the cases of chemically doped graphene and graphene oxide electrodes as shown in this study, the PiNNwall interface also allows us to probe polarized oxide surfaces in which both the proton charge and the electronic charge can coexist. Therefore, this work opens the door for modeling heterogeneous and complex electrode materials often found in energy storage systems.

High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V^xx operator), and (iii) adaptively compressed exchange (ACE, a low-rank V^xx approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank V^xx approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H₂O)₆₄ configurations (with densities spanning 0.4-1.7 g/cm³), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H₂O)₆₄ configurations. Using an out-of-sample set of (H₂O)₅₁₂ configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

MP2-Based Correction Scheme to Approach the Limit of a Complete Pair Natural Orbitals Space in DLPNO-CCSD(T) Calculations

The domain-based local pair natural orbital (PNO) coupled-cluster DLPNO-CCSD(T) method has been proven to provide accurate single-point energies at a fraction of the cost of canonical CCSD(T) calculations. However, the desired "chemical accuracy" can only be obtained with a large PNO space and extended basis set. We present a simple yet accurate and efficient correction scheme based on a perturbative approach. Here, in addition to DLPNO-CCSD(T) energy, one calculates DLPNO-MP2 correlation energy with the same settings as in the preceding coupled-cluster calculation. In the next step, the canonical MP2 correlation energy is obtained in the same orbital basis. This can be efficiently performed for essentially all molecule sizes accessible with the DLPNO-CCSD(T) method. By taking the difference between the canonical MP2 and DLPNO-MP2 energies, we obtain a correction term that can be added to the DLPNO-CCSD(T) correlation energy. This way, one can obtain the total correlation energy close to the limit of the complete PNO space (cPNO). The presented approach allows us to significantly increase the accuracy of the DLPNO-CCSD(T) method for both closed- and open-shell systems. The latter are known to be especially challenging for locally correlated methods. Unlike the previously developed PNO extrapolation procedure by Altun, Neese, and Bistoni ( J. Chem. Theory Comput. 2020, 16, 6142-6149), this strategy allows us to get the DLPNO-CCSD(T) correlation energy at the cPNO limit in a cost-efficient way, resulting in a minimal overall increase in calculation time as compared to the uncorrected method.

Proposal of spin crossover as a reversible switch of catalytic activity for the oxygen evolution reaction in two dimensional metal-organic frameworks

The development of oxygen evolution reaction (OER) catalysts with high activity and controllability is crucial for clean energy conversion and storage but remains a challenge. Here, based on first-principles calculations, we propose to utilize spin crossover (SCO) in two-dimensional (2D) metal-organic frameworks (MOFs) to achieve reversible control of OER catalytic activity. The theoretical design of a 2D square lattice MOF with Co as nodes and tetrakis-substituted cyanimino squaric acid (TCSA) as ligands, which transforms between the high spin (HS) and the low spin (LS) state by applying an external strain (∼2%), confirms our proposal. In particular, the HS-LS spin state transition of Co(TCSA) considerably regulates the adsorption strength of the key intermediate HO* in the OER process, resulting in a significant reduction of the overpotential from 0.62 V in the HS state to 0.32 V in the LS state, thus realizing a reversible switch for the activity of the OER. Moreover, the high activity of the LS state is confirmed by microkinetic and constant potential method simulations.

Using Density Functional Theory for Testing the Robustness of Mobile-Proton Molecular Dynamics Simulations on Electrosprayed Ions: Structural Implications for Gaseous Proteins

Current experiments only provide low-resolution information on gaseous protein ions generated by electrospray ionization (ESI). Molecular dynamics (MD) simulations can yield complementary insights. Unfortunately, conventional MD does not capture the mobile nature of protons in gaseous proteins. Mobile-proton MD (MPMD) overcomes this limitation. Earlier MPMD data at 300 K indicated that protein ions generated by "native" ESI retain solution-like structures with a hydrophobic core and zwitterionic exterior [Bakhtiari, M.; Konermann, L. J. Phys. Chem. B 2019, 123, 1784-1796]. MPMD redistributes protons using electrostatic and proton affinity calculations. The robustness of this approach has never been scrutinized. Here, we close this gap by benchmarking MPMD against density functional theory (DFT) at the B3LYP/6-31G* level, which is well suited for predicting proton affinities. The computational cost of DFT necessitated the use of small peptides. The MPMD energetic ranking of proton configurations was found to be consistent with DFT single-point energies, implying that MPMD can reliably identify favorable protonation sites. Peptide MPMD runs converged to DFT-optimized structures only when applying 300-500 K temperature cycling, which was necessary to prevent trapping in local minima. Temperature cycling MPMD was then applied to gaseous protein ions. Native ubiquitin converted to slightly expanded structures with a zwitterionic core and a nonpolar exterior. Our data suggest that such inside-out protein structures are intrinsically preferred in the gas phase, and that they form in ESI experiments after moderate collisional excitation. This is in contrast to native ESI (with minimal collisional excitation, simulated by MPMD at 300 K), where kinetic trapping promotes the survival of solution-like structures. In summary, this work validates the MPMD approach for simulations on gaseous peptides and proteins.

Existence of La-site antisite defects in [Formula: see text] ([Formula: see text], Fe, and Co) predicted with many-body diffusion quantum Monte Carlo

The properties of [Formula: see text] (M: 3d transition metal) perovskite crystals are significantly dependent on point defects, whether introduced accidentally or intentionally. The most studied defects in La-based perovskites are the oxygen vacancies and doping impurities on the La and M sites. Here, we identify that intrinsic antisite defects, the replacement of La by the transition metal, M, can be formed under M-rich and O-poor growth conditions, based on results of an accurate many-body ab initio approach. Our fixed-node diffusion Monte Carlo (FNDMC) calculations of [Formula: see text] ([Formula: see text], Fe, and Co) find that such antisite defects can have low formation energies and are magnetized. Complementary density functional theory (DFT)-based calculations show that Mn antisite defects in [Formula: see text] may cause the p-type electronic conductivity. These features could affect spintronics, redox catalysis, and other broad applications. Our bulk validation studies establish that FNDMC reproduces the antiferromagnetic state of [Formula: see text], whereas DFT with PBE (Perdew-Burke-Ernzerhof), SCAN (strongly constrained and appropriately normed), and the LDA+U (local density approximation with Coulomb U) functionals all favor ferromagnetic states, at variance with experiment.

Benchmarking First-Principles Reaction Equilibrium Composition Prediction

The availability of thermochemical properties allows for the prediction of the equilibrium compositions of chemical reactions. The accurate prediction of these can be crucial for the design of new chemical synthesis routes. However, for new processes, these data are generally not completely available. A solution is the use of thermochemistry calculated from first-principles methods such as Density Functional Theory (DFT). Before this can be used reliably, it needs to be systematically benchmarked. Although various studies have examined the accuracy of DFT from an energetic point of view, few studies have considered its accuracy in predicting the temperature-dependent equilibrium composition. In this work, we collected 117 molecules for which experimental thermochemical data were available. From these, we constructed 2648 reactions. These experimentally constructed reactions were then benchmarked against DFT for 6 exchange-correlation functionals and 3 quality of basis sets. We show that, in reactions that do not show temperature dependence in the equilibrium composition below 1000 K, over 90% are predicted correctly. Temperature-dependent equilibrium compositions typically demonstrate correct qualitative behavior. Lastly, we show that the errors are equally caused by errors in the vibrational spectrum and the DFT electronic ground state energy.

How Do Surface Polar Molecules Contribute to High Open-Circuit Voltage in Perovskite Solar Cells?

To date, the improvement of open-circuit voltage (V_OC ) offers a breakthrough for the performance of perovskite solar cells (PSCs) toward their theoretical limit. Surface modification through organic ammonium halide salts (e.g., phenethylammonium ions PEA⁺ and phenmethylammonium ions PMA⁺ ) is one of the most straightforward strategies to suppress defect density, thereby leading to improved V_OC . However, the mechanism underlying the high voltage remains unclear. Here, polar molecular PMA⁺ is applied at the interface between perovskite and hole transporting layer and a remarkably high V_OC of 1.175 V is obtained which corresponds to an increase of over 100 mV in comparison to the control device. It is revealed that the equivalent passivation effect of surface dipole effectively improves the splitting of the hole quasi-Fermi level. Ultimately the combined effect of defect suppression and surface dipole equivalent passivation effect leads to an overall increase in significantly enhanced V_OC . The resulted PSCs device reaches an efficiency of up to 24.10%. Contributions are identified here by the surface polar molecules to the high V_OC in PSCs. A fundamental mechanism is suggested by use of polar molecules which enables further high voltage, leading ways to highly efficient perovskite-based solar cells.

Analysis of Bonding by Quantum Chemistry─Resolving Delocalization Stabilization in a Mechanistic Basis and New Hückel Model

No general and unique understanding of the mechanism of covalent bonding in physical terms is provided by current computational methods or by a consensus among experts. Bonding is studied by energy decomposition analysis but may also be related to the interatomic motion of valence electrons within the molecule. This dynamical view of the mechanism of bonding is not widely appreciated. The aim here is to make it accessible by translation into a corresponding form of quantum chemical energy analysis. The interatomic electron motion is directly related to the delocalization taking place when atomic basis functions are combined into molecular orbitals. A "tribasis method" is introduced, allowing an atomic basis set to form subsets of (1) strictly localized atomic functions and (2) interatomic bridge functions which allow delocalization. Calculations can then identify ground states without (no bridge functions) and with delocalization. The scheme is based on exact quantum mechanics but demonstrated by a minimal basis treatment of H₂⁺ and H₂ in Hartree-Fock and valence bond approximations which show that the bond energy is a sum of repulsive localization and more strongly attractive delocalization energies. The tribasis method is used to reconstruct the Hückel theory of π-electron delocalization in planar hydrocarbon molecules to account for the "overlap problem". In its empirically fitted form, the new theory can accurately resolve both π → π* transition energy and aromatic stabilization energy. The picture of covalent bonding emerging from both hydrogenic and Hückel calculations is that there is a presence of a Pauli repulsion of localization which is overcome by a roughly twice as strong delocalization stabilization to form the bond.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Five-membered N-heterocyclic beryllium(I) compounds: fluctuating electronic structures with ambiphilic reactivity

The structure, bonding, and reactivity of the five-membered N-heterocyclic beryllium compounds (NHBe), BeN₂C₂H₄ (1) and BeN₂(CH₃)₂C₂H₂ (2) were studied at the M06/def2-TZVPP//BP86/def2-TZVPP level of theory. The molecular orbital analysis indicates that NHBe is an aromatic 6π-electron system with an unoccupied σ-type spⁿ-hybrid orbital on Be. Energy decomposition analysis combined with natural orbitals for chemical valence has been carried out with Be and L (L = N₂C₂H₄ (1), N₂(CH₃)₂C₂H₂ (2)) in their different electronic states as fragments at the BP86/TZ2P level of theory. The results indicate that the best bonding representation can be considered as an interaction between Be⁺ having the 2s⁰2p_x¹2p_y⁰2p_z⁰ electronic configuration and L^-. Accordingly, L^- forms two donor-acceptor σ-bonds and one electron sharing π-bond with Be⁺. Compounds 1 and 2 show high proton and hydride affinity at beryllium, indicating its ambiphilic reactivity. The protonated structure results from adding a proton on the lone pair of electrons in the doubly excited state. On the other hand, the hydride adduct is formed by donating electrons from the hydride to an unoccupied σ-type spⁿ-hybrid orbital on Be. These compounds show very high exothermic reaction energy for adduct formation with two electron donor ligands such as cAAC, CO, NHC, and PMe₃.

DFT and TD-DFT study of hydrogen bonded complexes of aspartic acid and n water (n = 1 and 2)

CONTEXT

Hydrogen bonds (HB) influence the conformational preferences of biomolecules and their optical and electronic properties. The directional interaction of molecules of water can be a prototype to understand the effects of HBs on biomolecules. Among the neurotransmitters (NT), L-aspartic acid (ASP) stands out due to its importance in health and as a precursor of several biomolecules. As it presents different functional groups and readily forms inter- and intramolecular HBs, ASP can be considered a prototype for understanding the behavior of NTs when interacting by HB with other substances. Although several theoretical studies have been performed in the past on isolated ASP and its formed complexes with water, both in gas and liquid phases, using DFT and TD-DFT formalisms, these works did not perform large basis set calculations or study electronic transitions of ASP-water complexes. We investigated the HB interactions in complexes of ASP and water molecules. The results show that the interactions between the carboxylic groups of ASP with water molecules, forming cyclic structures with two HBs, lead to more stable and less polar complexes than other conformers formed between water and the NH₂ group. It was observed that there is a relationship between the deviation in the UV-Vis absorption band of the ASP and the interactions of water with the HOMO and LUMO orbitals with the stabilization/destabilization of the S₁ state to the S₀ of the complexes. However, in some cases, such as 1:1 complex ASP-W2, this analysis may be inaccurate due to small changes in ΔE.

METHODS

We studied the landscapes of the ground state surface of different conformers of isolated L-ASP and the L-ASP-(H₂O)_n complexes (n = 1 and 2) using the DFT formalism, with the B3LYP functional, and six different basis sets: 6-31 +  + G(d,p), 6-311 +  + G(d,p), D95 +  + (d,p), D95V +  + (d,p), cc-pVDZ, and, cc-pVTZ basis sets. The cc-pVTZ basis set provides the minimum energy of all conformers, and therefore, we performed the analysis with this basis set. We evaluated the stabilization of the ASP and complexes using the minimum ground state energy, corrected by the zero point energy and the interaction energy between the ASP and the water molecules. We also calculated the vertical electronic transitions S₁ ← S₀, and their properties using the TD-DFT formalism at B3LYP/cc-pVTZ level with the optimized geometries for S₀ state with the same basis set. For the analysis of the vertical transitions of isolated ASP and the ASP-(H₂O)_n complexes, we calculated the electrostatic energy in the S₀ and S₁ states. We performed the calculations with the Gaussian 09 software package. We used the VMD software package to visualize the geometries and shapes of the molecule and complexes.

Generating Exchange-Correlation Functionals with a Simplified, Self-Consistent Correlation Factor Model

We focus on the spherically averaged exchange-correlation hole ρ_XC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρ_X^model(r, u) is multiplied by a CF (f_C(r, u)) to yield an approximation to the exchange-correlation hole ρ_XC(r, u) = f_C(r, u) ρ_X^model(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.

A DFT/TDDFT Investigation on Fluorescence and Electronic Properties of Chromone Derivatives

The development of quick and precise detection technologies for active compounds in vivo is critical for disease prevention, diagnosis and pathological investigation. The fluorescence signal of the fluorophore usually defines the probe's sensitivity to the chemical being examined. Many natural compounds containing flavone and isoflavone scaffolds exhibit a certain amount fluorescence, albeit with poor fluorescence quantum yields. Therefore, we used density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations to investigate the fluorescence characteristics of chromium-derived fluorophores in more depth. Different substituents are introduced at different positions of the chromone. As weak electron donor groups, alkyl and aromatic groups were discovered to have varying quantum yields on the fluorophore scaffold, and longer alkyl chains are favorable to enhance fluorescence quantum yield. In comparison to the amino group, substituted amino group can avoid group rotation, and the introduction of cyclic amines such as pyrrolidine and heterocyclic amines can improve optical characteristics. The electron-donating methoxy group at position 6 helps to increase the fluorescence quantum yield.

A density functional theory for ecology across scales

Ecology lacks a holistic approach that can model phenomena across temporal and spatial scales, largely because of the challenges in modelling systems with a large number of interacting constituents. This hampers our understanding of complex ecosystems and the impact that human interventions (e.g., deforestation, wildlife harvesting and climate change) have on them. Here we use density functional theory, a computational method for many-body problems in physics, to develop a computational framework for ecosystem modelling. Our methods accurately fit experimental and synthetic data of interacting multi-species communities across spatial scales and can project to unseen data. As the key concept we establish and validate a cost function that encodes the trade-offs between the various ecosystem components. We show how this single general modelling framework delivers predictions on par with established, but specialised, approaches for systems from predatory microbes to territorial flies to tropical tree communities. Our density functional framework thus provides a promising avenue for advancing our understanding of ecological systems.

Data-Driven Machine Learning for Understanding Surface Structures of Heterogeneous Catalysts

The design of heterogeneous catalysts is necessarily surface-focused, generally achieved via optimization of adsorption energy and microkinetic modelling. A prerequisite is to ensure the adsorption energy is physically meaningful is the stable existence of the conceived active-site structure on the surface. The development of improved understanding of the catalyst surface, however, is challenging practically because of the complex nature of dynamic surface formation and evolution under in-situ reactions. We propose therefore data-driven machine-learning (ML) approaches as a solution. In this Minireview we summarize recent progress in using machine-learning to search and predict (meta)stable structures, assist operando simulation under reaction conditions and micro-environments, and critically analyze experimental characterization data. We conclude that ML will become the new norm to lower costs associated with discovery and design of optimal heterogeneous catalysts.

Synthesis and Biological Evaluation of Octahydroquinazolinones as Phospholipase A2, and Protease Inhibitors: Experimental and Theoretical Exploration

Phospholipase A2 (PLA2) promotes inflammation via lipid mediators and releases arachidonic acid (AA), and these enzymes have been found to be elevated in a variety of diseases, including rheumatoid arthritis, sepsis, and atherosclerosis. The mobilization of AA by PLA2 and subsequent synthesis of prostaglandins are regarded as critical events in inflammation. Inflammatory processes may be treated with drugs that inhibit PLA2, thereby blocking the COX and LOX pathways in the AA cascade. To address this issue, we report herein an efficient method for the synthesis of a series of octahydroquinazolinone compounds (4a-h) in the presence of the catalyst Pd-HPW/SiO₂ and their phospholipase A2, as well as protease inhibitory activities. Among eight compounds, two of them exhibited overwhelming results against PLA2 and protease. By using FT-IR, Raman, NMR, and mass spectroscopy, two novel compounds were thoroughly studied. After carefully examining the SAR of the investigated compounds against these enzymes, it was found that compounds (4a, 4b) containing both electron-donating and electron-withdrawing groups on the phenyl ring exhibited higher activity than compounds with only one of these groups. DFT studies were employed to study the electronic nature and reactivity properties of the molecules by optimizing at the BLYP/cc-pVDZ. Natural bond orbitals helped to study the various electron delocalizations in the molecules, and the frontier molecular orbitals helped with the reactivity and stability parameters. The nature and extent of the expressed biological activity of the molecule were studied using molecular docking with human non-pancreatic secretory phospholipase A2 (hnps-PLA2) (PDB ID: 1DB4) and protease K (PDB ID: 2PWB). The drug-ability of the molecule has been tested using ADMET, and pharmacodynamics data have been extracted. Both the compounds qualify for ADME properties and follow Lipinski's rule of five.

Interplay between Facets and Defects during the Dissociative and Molecular Adsorption of Water on Metal Oxide Surfaces

Surface terminations and defects play a central role in determining how water interacts with metal oxides, thereby setting important properties of the interface that govern reactivity such as the type and distribution of hydroxyl groups. However, the interconnections between facets and defects remain poorly understood. This limits the usefulness of conventional notions such as that hydroxylation is controlled by metal cation exposure at the surface. Here, using hematite (α-Fe₂O₃) as a model system, we show how oxygen vacancies overwhelm surface cation-dependent hydroxylation behavior. Synchrotron-based ambient-pressure X-ray photoelectron spectroscopy was used to monitor the adsorption of molecular water and its dissociation to form hydroxyl groups in situ on (001), (012), or (104) facet-engineered hematite nanoparticles. Supported by density functional theory calculations of the respective surface energies and oxygen vacancy formation energies, the findings show how oxygen vacancies are more prone to form on higher energy facets and induce surface hydroxylation at extremely low relative humidity values of 5 × 10^-5%. When these vacancies are eliminated, the extent of surface hydroxylation across the facets is as expected from the areal density of exposed iron cations at the surface. These findings help answer fundamental questions about the nature of reducible metal oxide-water interfaces in natural and technological settings and lay the groundwork for rational design of improved oxide-based catalysts.

Rational design of iron catalysts for C-X bond activation

We have quantum chemically studied the iron-mediated CX bond activation (X = H, Cl, CH₃ ) by d⁸ -FeL₄ complexes using relativistic density functional theory at ZORA-OPBE/TZ2P. We find that by either modulating the electronic effects of a generic iron-catalyst by a set of ligands, that is, CO, BF, PH₃ , BN(CH₃ )₂ , or by manipulating structural effects through the introduction of bidentate ligands, that is, PH₂ (CH₂ )_n PH₂ with n = 6-1, one can significantly decrease the reaction barrier for the CX bond activation. The combination of both tuning handles causes a decrease of the CH activation barrier from 10.4 to 4.6 kcal mol^-1 . Our activation strain and Kohn-Sham molecular orbital analyses reveal that the electronic tuning works via optimizing the catalyst-substrate interaction by introducing a strong second backdonation interaction (i.e., "ligand-assisted" interaction), while the mechanism for structural tuning is mainly caused by the reduction of the required activation strain because of the pre-distortion of the catalyst. In all, we present design principles for iron-based catalysts that mimic the favorable behavior of their well-known palladium analogs in the bond-activation step of cross-coupling reactions.

First-principles calculations of hematite (α-Fe2O3) by self-consistent DFT+U+V

Owing to the confined Fe-3d orbitals and self-interaction error of exchange-correlation functionals, approximate DFT fails to describe iron oxides electronic structure and magnetic properties accurately. Hybrid DFT or DFT + U can solve these problems, but the former is expensive, and the latter only considers on-site interactions. Here, we used DFT + U + V, a DFT + U extension including inter-site interactions, to simulate the structural, magnetic, and electronic properties, along with Fe and O K-edge XAS spectra of α-Fe₂O₃. Two types of atomic orbital projectors were studied, orthogonalized and non-orthogonalized. DFT + U + V improves the description of the structural, magnetic, and electronic properties of α-Fe₂O₃ compared to approximate DFT. The accuracy of the correction depends on the orbital projector used. DFT + U + V with orthogonalized projectors achieves the best experimental agreement at a fraction of hybrid DFT cost. This work emphasizes the importance of inter-site interactions and the type of atomic orbital projectors used in the theoretical research of α-Fe₂O₃.

Molecular engineering on D-π-A organic dyes with flavone-based different acceptors for highly efficient dye-sensitized solar cells using experimental and computational study

CONTEXT

The improvement of new organic flavone-based donor-spacer-acceptor (D-π-A) type dye molecules of the 3-(4-hydroxypiperidin-2-yloxy)-7-hydroxy-2-(3,4-dihydroxyphenyl)-4H-chromen-4-one (D1), 7-hydroxy-2-(3,4-dihydroxyphenyl)-3-(piperidin-4-yloxy)-4H-chromen-4-one (D2), and 3-((2-aminopyridin-4-yloxy)methoxy)-7-hydroxy-2-(3,4-dihydroxyphenyl)-4H-chromen-4-one (D3) were successfully designed and synthesized for dye-sensitized solar cells (DSSCs).

METHODS

Here, we discuss the synthesis of flavone compounds as well as their photophysical and electrochemical characterization. Using the Gaussian 09w software, the electronic structures and apsorption spectra have been calculated at the B3LYP, B3PW91, CAM-B3LYP, MPW1PW91, PBEPBE, and ωB97XD theory with the 6-311G(d,p) basis sets.

RESULTS

The computed values of the D2 molecule ground state optimized HOMOs-LUMOs energy is well positioned for advantageous charge transfer (CT) into the semiconducting material (TiO₂) as well as the electron injection process. With a high power conversion efficiency (PCE) of 3.46% (V_OC = 0.718 V, J_SC = 7.07 mA cm^-2, and FF = 0.68), the D2 compound also demonstrated good photovoltaic (PV) properties.

CONCLUSION

These findings unequivocally demonstrate that altering the D-π-A metal-free organic material electron-withdrawing capacity is a useful strategy for enhancing the optical and electrical characteristics of the organic PV system.

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

Comparison of Conformational Analyses of Naturally Occurring Flavonoid-O-Glycosides with Unnatural Flavonoid-CF2-Glycosides Using Molecular Modeling

Many glycosylated natural products display biological activity and are deglycosylated by the metabolic processes of the body. Although unnatural CF2-glycosides have been proposed as nonhydrolyzable analogues, CF2-derivatives of natural products are exceedingly challenging to synthesize and few examples exist. These difluorinated molecules may have unique conformational behavior as a consequence of changing the glycosidic linkage. In this study, we performed conformational searches using MacroModel followed by molecular dynamics simulations to investigate the conformational behavior of the glycosidic bonds in flavonoid-O-glycosides and in corresponding CF2-glycosylated derivatives. Compared to their O-glycosylated analogues, flavonoid-3-CF2-glycosides and flavonoid-5-CF2-glycosides showed conformational bias, whereas flavonoid-7-CF2-glycosides showed more flexibility. Flavonoid-5-CF2-glycosides were the least flexible compared to all others. Our results show that the site of the glycosylation and the substitution pattern on the flavonoid determine the conformational properties of these molecules. These two factors influence the steric destabilization and/or stereoelectronic stabilization which govern the conformational behavior of the flavonoid glycosides. Moreover, a docking study of quercitrin and its CF2-analogue into murine ribosomal kinase RSK2 demonstrated the potential for flavonoid-CF2-glycosides to retain a similar binding pose as the parent O-glycoside. These findings will assist in designing stable flavonoid-CF2-glycosides for carbohydrate research.

Rational modification of hydroxy-functionalized covalent organic frameworks for enhanced photocatalytic hydrogen peroxide evolution

Covalent organic frameworks (COFs), a class of flexibly tunable crystalline materials, have fascinating potential in photocatalytic hydrogen peroxide (H2O2) evolution under visible light irradiation. However, achieving efficient catalytic activity by tuning the composition of COFs and the linkages of building blocks is still a challenge. Herein, four imine-linked COFs with different numbers of hydroxy-functionalized are constructed to unveil the latent structure-activity relationship between the reversibility of bonding in supramolecular chemistry and the photocatalytic H2O2 performance. As the optimized material, TAPT-HTA-COF (1H-COF) containing single hydroxy group in aldehyde node exhibits a highest ordered structure and conjugation degree along and across the plane in the extended frameworks originating from the flexibly reversible iminol-to-ketoenamine tautomerism than others, which broadens the visible light absorption and accelerates the dissociation of photogenerated carriers in 1H-COF. These merits ensure that 1H-COF has the highest H2O2 yield (44.5 μmol L-1) and O2 two-electron reduction pathway among the four COFs under visible light irradiation (λ > 420 nm, 10 vol% isopropanol aqueous solution). At the same time, the long-range ordered framework of 1H-COF is well preserved during the photocatalytic H2O2 evolution process assisted by the proton-induced tautomerization. This work facilitates the design and development of COF-based photocatalysts in the evolution of H2O2.

Comparative antibacterial analysis of the anthraquinone compounds based on the AIM theory, molecular docking, and dynamics simulation analysis

BACKGROUND

Hydroxyanthraquinones and anthraquinone glucoside derivatives are always considered as the active antibacterial components.

METHODS

Comparison of structure characteristics and antibacterial effect of these compounds was performed by applying quantum chemical calculations, atoms in molecules theory, molecular docking, and dynamics simulation procedure. Density functional theory calculation with B3LYP using 6-31G (d, p) basis set has been used to determine ground state molecular geometries.

RESULTS

The molecular geometric stability, electrostatic potential, frontier orbital energies, and topological properties were analyzed at the active site. Once glucose ring is introduced into the hydroxyanthraquinone rings, almost all of the positive molecular potentials are distributed among the hydroxyl hydrogen atoms of the glucose rings. In addition, low electron density ρ (r) and positive Laplacian value of the O-H bond of the anthraquinone glucoside are the evidences of the highly polarized and covalently decreased bonding interactions. The anthraquinone glucoside compounds have generally higher intermolecular binding energies than the corresponding aglycones due to the strong interaction between the glucose rings and the surrounding amino acids. Molecular dynamics simulations further explored the stability and dynamic behavior of the anthraquinone compound and protein complexes through RMSD, RMSF, SASA, and Rg.

CONCLUSION

The type of carboxyl, hydroxyl, and hydroxymethyl groups on phenyl ring and the substituent glucose rings is important to the interactions with the topoisomerase type II enzyme DNA gyrase B.

Thermochemical evaluation of adaptive and fixed density functional theory quadrature schemes

A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn-Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0-3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work.

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

Fundamental Variable and Density Representation in Multistate DFT for Excited States

Complementary to the theorems of Hohenberg and Kohn for the ground state, Theophilou's subspace theory establishes a one-to-one relationship between the total eigenstate energy and density ρ_V(r) of the subspace spanned by the lowest N eigenstates. However, the individual eigenstate energies are not directly available from such a subspace density functional theory. Lu and Gao (J. Phys. Chem. Lett. 2022, 13, 7762) recently proved that the Hamiltonian projected on to this subspace is a matrix functional H[D] of the multistate matrix density D(r) and that variational optimization of the trace of the Hamiltonian matrix functional yields exactly the individual eigenstates and densities. This study shows that the matrix density D(r) is the necessary fundamental variable in order to determine the exact energies and densities of the individual eigenstates. Furthermore, two ways of representing the matrix density are introduced, making use of nonorthogonal and orthogonal orbitals. In both representations, a multistate active space of auxiliary states can be constructed to exactly represent D(r) with which an explicit formulation of the Hamiltonian matrix functional H[D] is presented. Importantly, the use of a common set of orthonormal orbitals makes it possible to carry out multistate self-consistent-field optimization of the auxiliary states with singly and doubly excited configurations (MS-SDSCF).

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

The fourth-order expansion of the exchange hole and neural networks to construct exchange–correlation functionals

The curvature Q σ of spherically averaged exchange (X) holes ρX, σ(r, u) is one of the crucial variables for the construction of approximations to the exchange–correlation energy of Kohn–Sham theory, the most prominent example being the Becke–Roussel model [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)]. Here, we consider the next higher nonzero derivative of the spherically averaged X hole, the fourth-order term T σ. This variable contains information about the nonlocality of the X hole and we employ it to approximate hybrid functionals, eliminating the sometimes demanding calculation of the exact X energy. The new functional is constructed using machine learning; having identified a physical correlation between T σ and the nonlocality of the X hole, we employ a neural network to express this relation. While we only modify the X functional of the Perdew–Burke–Ernzerhof functional [Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], a significant improvement over this method is achieved.

Synthesis and Spectroscopic Characterization of Selected Phenothiazines and Phenazines Rationalized Based on DFT Calculation

Two unique structures were isolated from the phosphorylation reaction of 10H-phenothiazine. The 5,5-dimethyl-2-(10H-phenothiazin-10-yl)-1,3,2-dioxaphosphinane 2-oxide (2a) illustrates the product of N-phosphorylation of phenothiazine. Moreover, a potential product of 2a instability, a thiophosphoric acid 2b, was successfully isolated and structurally characterized. Molecule 2a, similarly to sulfoxide derivative 3, possesses interesting phosphorescence properties due to the presence of d-pπ bonds. The X-ray, NMR, and DFT computational studies indicate that compound 2a exhibits an anomeric effect. Additionally, the syntheses of selected symmetrical and unsymmetrical pyridine-embedded phenazines were elaborated. To compare the influence of phosphorus and sulfur atoms on the structural characteristics of 10H-phenothiazine derivatives, the high-quality crystals of (4a,12a-dihydro-12H-benzo[5,6][1,4]thiazino[2,3-b]quinoxalin-12-yl)(phenyl)methanone (1) and selected phenazines 5,12-diisopropyl-3,10-dimethyldipyrido[3,2-a:3′,2′-h]phenazine (5) and 5-isopropyl-N,N,3-trimethylpyrido[3,2-a]phenazin-10-amine (6a) were obtained. The structures of molecules 1, 2a, 2-mercapto-5,5-dimethyl-1,3,2-dioxaphosphinane 2-oxide (2b), 3,7-dinitro-10H-phenothiazine 5-oxide (3), 5 and 6a were determined by single-crystal X-ray diffraction measurements.

A structural optimization algorithm with stochastic forces and stresses

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such as quantum Monte Carlo or neural network states, or are performed on quantum devices that have intrinsic noise. Our proposed algorithm is based on the combination of two ingredients: an update rule derived from the steepest-descent method, and a staged scheduling of the targeted statistical error and step size, with position averaging. We compare it with commonly applied algorithms, including some of the latest machine learning optimization methods, and show that the algorithm consistently performs efficiently and robustly under realistic conditions. Applying this algorithm, we achieve full-degree optimizations in solids using ab initio many-body computations, by auxiliary-field quantum Monte Carlo with plane waves and pseudopotentials. A potential metastable structure in Si is discovered using density-functional calculations with synthetic noisy forces.

Intramolecular Interactions in Derivatives of Uracil Tautomers

The influence of solvents on intramolecular interactions in 5- or 6-substituted nitro and amino derivatives of six tautomeric forms of uracil was investigated. For this purpose, the density functional theory (B97-D3/aug-cc-pVDZ) calculations were performed in ten environments (1 > ε > 109) using the polarizable continuum model (PCM) of solvation. The substituents were characterized by electronic (charge of the substituent active region, cSAR) and geometric parameters. Intramolecular interactions between non-covalently bonded atoms were investigated using the theory of atoms in molecules (AIM) and the non-covalent interaction index (NCI) method, which allowed discussion of possible interactions between the substituents and N/NH endocyclic as well as =O/−OH exocyclic groups. The nitro group was more electron-withdrawing in the 5 than in the 6 position, while the opposite effect was observed in the case of electron donation of the amino group. These properties of both groups were enhanced in polar solvents; the enhancement depended on the ortho interactions. Substitution or solvation did not change tautomeric preferences of uracil significantly. However, the formation of a strong NO∙∙∙HO intramolecular hydrogen bond in the 5-NO2 derivative stabilized the dienol tautomer from +17.9 (unsubstituted) to +5.4 kcal/mol (substituted, energy relative to the most stable diketo tautomer).

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

Computational Investigation of Substituent Effects on the Fluorescence Wavelengths of Oxyluciferin Analogs

Oxyluciferin, which is the light emitter for firefly bioluminescence, has been subjected to extensive chemical modifications to tune its emission wavelength and quantum yield. However, the exact mechanisms for various electron-donating and withdrawing groups to perturb the photophysical properties of oxyluciferin analogs are still not fully understood. To elucidate the substituent effects on the fluorescence wavelength of oxyluciferin analogs, we applied the absolutely localized molecular orbitals (ALMO)-based frontier orbital analysis to assess various types of interactions (i.e. permanent electrostatics/exchange repulsion, polarization, occupied-occupied orbital mixing, virtual-virtual orbital mixing, and charge-transfer) between the oxyluciferin and substituent orbitals. We suggested two distinct mechanisms that can lead to red-shifted oxyluciferin emission wavelength, a design objective that can help increase the tissue penetration of bioluminescence emission. Within the first mechanism, an electron-donating group (such as an amino or dimethylamino group) can contribute its highest occupied molecular orbital (HOMO) to an out-of-phase combination with oxyluciferin's HOMO, thus raising the HOMO energy of the substituted analog and narrowing its HOMO-LUMO gap. Alternatively, an electron-withdrawing group (such as a nitro or cyano group) can participate in an in-phase virtual-virtual orbital mixing of fragment LUMOs, thus lowering the LUMO energy of the substituted analog. Such an ALMO-based frontier orbital analysis is expected to lead to intuitive principles for designing analogs of not only the oxyluciferin molecule, but also many other functional dyes.