Density Functional Theory Functionals Research Articles

Secondary structure determines electron transport in peptides

Proteins play a key role in biological electron transport, but the structure-function relationships governing the electronic properties of peptides are not fully understood. Despite recent progress, understanding the link between peptide conformational flexibility, hierarchical structures, and electron transport pathways has been challenging. Here, we use single-molecule experiments, molecular dynamics (MD) simulations, nonequilibrium Green's function-density functional theory (NEGF-DFT), and unsupervised machine learning to understand the role of secondary structure on electron transport in peptides. Our results reveal a two-state molecular conductance behavior for peptides across several different amino acid sequences. MD simulations and Gaussian mixture modeling are used to show that this two-state molecular conductance behavior arises due to the conformational flexibility of peptide backbones, with a high-conductance state arising due to a more defined secondary structure (beta turn or 310 helices) and a low-conductance state occurring for extended peptide structures. These results highlight the importance of helical conformations on electron transport in peptides. Conformer selection for the peptide structures is rationalized using principal component analysis of intramolecular hydrogen bonding distances along peptide backbones. Molecular conformations from MD simulations are used to model charge transport in NEGF-DFT calculations, and the results are in reasonable qualitative agreement with experiments. Projected density of states calculations and molecular orbital visualizations are further used to understand the role of amino acid side chains on transport. Overall, our results show that secondary structure plays a key role in electron transport in peptides, which provides broad avenues for understanding the electronic properties of proteins.

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Molecular Hydrogen Acts as a Hydrogen Bond Proton Acceptor: From Protonated Betaine Tagging to the Weakest Hydrogen Bond.

In an attempt to gain further insights into the intermolecular interactions implied by Rizzo's group's cautionary tale related to molecular tagging in infrared multiple photon dissociation (IRMPD) spectroscopy with molecular messengers [Masson, A. . J. Chem. Phys. 2015, 143, 104313], in the present study, we provide an in-depth analysis of the noncovalent interaction between the molecular hydrogen and protonated betaine molecule in the gas phase. We aim to shed some new light on the fundamental issues concerning the wide diapason of hydrogen-bonding-type intermolecular interactions, with a wide variety of proton acceptors. We demonstrate that in the course of tagging the protonated betaine with molecular hydrogen from the OH group side, it is the σ bond of molecular hydrogen that plays the role of hydrogen-bonding proton acceptor. The tagging thus induces a small yet significant red shift of the protonated betaine O-H stretching mode. We investigate the performance of a wide range of density functional theory (DFT) functionals for the calculation of anharmonic vibrational frequency shifts of the studied system, which are essential for the correct interpretation of the experimental IRMPD data. For an accurate prediction of the OH stretching frequency shifts, specifically designed functionals such as Handy's group HCTH/407 should be applied. The empirical dispersion correction enhances the systematic overestimation of the anharmonic frequency shift, characteristic of the most widely used DFT functionals. Combining the full-wave function approach with the charge field perturbation and natural bond orbital (NBO) deletion analyses, we demonstrate that the frequency shift in the OH-tagged structure is governed by the σHH → σ*OH intermolecular charge transfer. This interaction stabilizes the OH-tagged dimer as well, in contrast to the dipole-quadrupole electrostatic interaction energy term. Topological analysis of the electron density reveals the presence of an intermolecular bond critical point with a positive value of the density Laplacian very close to the lower limit for hydrogen bonds. NCI analyses demonstrate that the OH···H2 interaction is weaker than the intramolecular CH···O one within the protonated betaine molecule, with the through of reduced density gradient appearing at less negative sign(λ2)·ρ values. Analyzing the O-H stretching vibrational potential with the second-generation absolutely localized molecular orbitals energy decomposition analysis (ALMO-EDA 2) revealed that in the case of betaineH(+) tagged from the OH group side, the permanent electrostatics (ΔEelec), polarization (ΔEpol), and charge-transfer (ΔEct) contributions to the total intermolecular interaction energy contribute favorably to the weak hydrogen bond formation and to the red shift of the fundamental O-H stretching frequency, the ΔEct contribution being the most significant in the last context. The Pauli repulsion term, on the other hand, favors an O-H stretching frequency blue shift as a consequence of the vibrational confinement effects.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions.

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

Accurate machine learning force fields via experimental and simulation data fusion

Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties were affected only mildly and mostly positively. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials.

Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO2.

VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.

Adsorption and evolution of hydrogen molecules on hexagonal boron nitride monolayer: a combined DFT and kinetic monte-carlo simulations study

Density functional theory (DFT) and kinetic Monte-Carlo (kMC) simulation code has been combinedly used to study the adsorption and evolution dynamics of hydrogen molecules over a hexagonal boron nitride (h-BN) monolayer. Maximum adsorption energy from van der Waals curve is predicted to be around 60 to 70 meV using two different DFT functionals. Repulsive lateral interaction between two hydrogen molecules plays a key role in determining the maximum number of adsorptions inside one unit cell of h-BN. Bader charge analysis, electron localization function (ELF), total and partial density of states (DOS) plots have been included to understand the weak interaction going on between the adsorbent and substrate. The input energy parameters from the DFT calculation has been used to perform the kMC simulation for describing the adsorption, desorption and the diffusion pattern of hydrogen molecules with a given time of exposure to an empty h-BN substrate along with the overall surface coverage.

Employing neural density functionals to generate potential energy surfaces.

With the union of machine learning (ML) and quantum chemistry, amid the debate between machine-learned functionals and human-designed functionals in density functional theory (DFT), this paper aims to demonstrate the generation of potential energy surfaces using computations with machine-learned density functional approximation (ML-DFA). A recent research trend is the application of ML in quantum sciences in the design of density functionals such as DeepMind's Deep Learning model (DeepMind21, DM21). Though science reported the state-of-the-art performance of DM21, the opportunity to utilize DeepMind's pretrained DM21 neural networks in computations in quantum chemistry has not yet been tapped. So far in the literature, the Deep Learning density functionals (DM21) have not been applied to generate potential energy surfaces. While the superior accuracy of DM21 has been reported, there is still a scarcity of publications that apply DM21 in calculations in the field. In this context, for the first time in literature, neural density functionals inferring 2D potential energy surfaces (ML-DFA-PES) based on machine-learned DFA-based computational method is contributed in this paper. This paper reports the ML-DFA-generated PES for C4H8, H2O, H2, and H2+ by employing a pretrained DM21m TensorFlow model with cc-pVDZ basis set. In addition, we also analyze the long-range behavior of DM21 based PES to investigate the ability to describe a system at long ranges. Furthermore, we compare PES diagrams from DM21 with popular DFT functionals (b3lyp/ PW6B95) and CCSD(T). In this method, 2D potential energy surfaces are obtained using a method that relies upon the neural network's ability to accurately learn the mapping between 3D electron density and exchange-correlation potential. By inserting Deep Learning inference in DFT with a pretrained neural network, self-consistent field (SCF) energy at different geometries along the coordinates of interest is computed, and then, potential energy surfaces are plotted. In this method, first, the electron density is computed mathematically, and this computed 3D electron density is used as a ML feature vector to predict the exchange correlation potential as a ML inference computed by a forward pass of pre-trained DM21 TensorFlow computational graph, followed by the computation of self-consistent field energy at multiple geometries, and then, SCF energies at different bond lengths/angles are plotted as 2D PES. We implement this in a python source code using frameworks such as PySCF and DM21. This paper contributes this implementation in open source. The source code and DM21-DFA-based PES are contributed at https://sites.google.com/view/MLfunctionals-DeepMind-PES .

Hydration of p-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p-$$\\end{document}aminobenzoic acid: structures and non-covalent bondings of aminobenzoic acid-water clusters

ContextMicro-hydration of the aminobenzoic acid is essential to understand its interaction with surrounding water molecules. Understanding the micro-hydration of the aminobenzoic acid is also essential to study its remediation from wastewater. Therefore, we explored the potential energy surfaces (PESs) of the para-aminobenzoic acid-water clusters, ABWn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_n$$\\end{document}, n=1-10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=1-10$$\\end{document}, to study the microsolvation of the aminobenzoic acid in water. In addition, we performed a quantum theory of atoms in molecules (QTAIM) analysis to identify the nature of non-covalent bondings in the aminobenzoic acid-water clusters. Furthermore, temperature effects on the stability of the located isomers have been examined. The located structures have been used to calculate the hydration free energy and the hydration enthalpy of the aminobenzoic acid using the cluster continuum solvation model. The hydration free energy and the hydration enthalpy of the aminobenzoic acid at room temperature are evaluated to be −7.0 kcal/mol and −18.1 kcal/mol, respectively. The hydration enthalpy is in perfect agreement with a previous experimental estimate. Besides, temperature effects on the calculated hydration enthalpy and free energy are reported. Finally, we calculated the gas phase binding energies of the most stable structures of the ABWn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_n$$\\end{document} clusters using twelve functionals of density functional theory (DFT), including empirical dispersion. The DFT functionals are benchmarked against the DLPNO-CCSD(T)/CBS. We have found that the three most suitable DFT functionals are classified in the following order: PW6B95D3 > MN15 > ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}B97XD. Therefore, the PW6B95D3 functional is recommended for further study of the aminobenzoic acid-water clusters and similar systems.MethodsThe exploration started with classical molecular dynamics simulations followed by complete optimization at the PW6B95D3/def2-TZVP level of theory. Optimizations are performed using Gaussian 16 suite of codes. QTAIM analysis is performed using the AIMAll program.

An antibacterial lead identification of novel 1,3,4-oxadiazole derivatives based on molecular computer aided design approaches

Merging Density Functional Theory (DFT) with the Quantitative Structure-Activity Relationship (2D/3D-QSAR) modeling represents a promising avenue for exploring antibacterial activity and discovering potential drugs effective against both gram-positive and gram-negative microorganisms. In this study, we employed this integrated approach to investigate a newly synthesized and promising class of 1,3,4-oxadiazole derivatives renowned for their high performance as antibacterial agents. To ensure an accurate characterization and thorough description of the targeted biological activity, we systematically evaluated various DFT functionals to precisely predict the geometrical and electronic descriptors of the investigated compounds. These descriptors were crucial for developing and validating the proposed 2D/3D-QSAR models. Our results reveal that the introduction of a donor group enhances the antibacterial activity of the derivatives. The analysis of molecular descriptors underscores the positive impact of this modification on the compounds' efficacy against bacteria. Additionally, our experimental compounds exhibit favorable characteristics concerning oral bioavailability, a crucial aspect in drug development. The identification of robust correlations between antibacterial activity and specific descriptors was achieved by conducting an extensive analysis that encompassed multiple linear regression (MLR), Random Forest (RF), and Artificial Neural Networks (ANN). Subsequently, a partial least squares (PLS) model was employed to construct 3D-QSAR models based on the Comparative Molecular Field Analysis (CoMFA) and Comparative Similarity Indices Analysis (CoMSIA) descriptors. Validation of the output models was performed using leave-one-out and bootstrapping strategies. The resultant 2D/3D-QSAR models demonstrated a high correlation between experimental and predicted activity values. Leveraging these models, the developed MLR model, expressed as pMIC = -12.704 + 0.260 logP – 6.104 10-03 SAG – 51.385 qN33, serves as a valuable tool for predicting antibacterial activity. we indicate that the machine learning methods, Artificial Neural Networks (ANN) and Random Forest (RF), outperform traditional models in accurately predicting antibacterial activity. We designed ten novel molecules, subjecting them to molecular docking and molecular dynamics simulations to predict their optimal postures when docked in the target and gain insights into the formed interactions. Additionally, Absorption, Distribution, Metabolism, Excretion, and Toxicity (ADMET) analysis was applied to discern the potential behavior of these novel compounds in the human body. As a result, the newly suggested chemical, X4, X10, exhibited robust inhibitory potential against gram-negative microbes.

Invariant Molecular Representations for Heterogeneous Catalysis.

Catalyst screening is a critical step in the discovery and development of heterogeneous catalysts, which are vital for a wide range of chemical processes. In recent years, computational catalyst screening, primarily through density functional theory (DFT), has gained significant attention as a method for identifying promising catalysts. However, the computation of adsorption energies for all likely chemical intermediates present in complex surface chemistries is computationally intensive and costly due to the expensive nature of these calculations and the intrinsic idiosyncrasies of the methods or data sets used. This study introduces a novel machine learning (ML) method to learn adsorption energies from multiple DFT functionals by using invariant molecular representations (IMRs). To do this, we first extract molecular fingerprints for the reaction intermediates and later use a Siamese-neural-network-based training strategy to learn invariant molecular representations or the IMR across all available functionals. Our Siamese network-based representations demonstrate superior performance in predicting adsorption energies compared with other molecular representations. Notably, when considering mean absolute values of adsorption energies as 0.43 eV (PBE-D3), 0.46 eV (BEEF-vdW), 0.81 eV (RPBE), and 0.37 eV (scan+rVV10), our IMR method has achieved the lowest mean absolute errors (MAEs) of 0.18 0.10, 0.16, and 0.18 eV, respectively. These results emphasize the superior predictive capacity of our Siamese network-based representations. The empirical findings in this study illuminate the efficacy, robustness, and dependability of our proposed ML paradigm in predicting adsorption energies, specifically for propane dehydrogenation on a platinum catalyst surface.

Influence of Steric and Dispersion Interactions on the Thermochemistry of Crowded (Fluoro)alkyl Compounds.

ConspectusAlkanes play a pivotal role in industrial, environmental, and biological processes. They are characterized by their carbon-carbon single-bond structure, remarkable stability, and conformational diversity. Fluorination of such compounds imparts unique physicochemical properties that often enhance pharmacokinetic profiles, metabolic stability, and receptor interactions while keeping beneficial properties. However, such per- and polyfluoroalkyl substances (PFAS) show a persistent presence in the environment and potential adverse health effects, which propelled them to the forefront of global environmental and health discussions. Alkyl compounds are also prototypical for stereoelectronic (SE) effects that are widely applied in chemistry. Substituents are typically described as electron-density-donating/withdrawing and/or responsible for sterically interacting with reagents or strategic groups in the molecule. That alkane branching can result in higher stability compared to less-branched isomers has been investigated in detail also by testing quantum chemical methods, in particular density functional theory (DFT). Alkane branching results in spatially compact structures with close intramolecular contacts so that at a specific size the detailed balance of attractive London dispersion and covalent versus repulsive Pauli exchange interactions shifts to new, chemically unfragile situations. This may lead to dissociation at room temperature and opens the central question: what is the smallest crowed alkane that cannot be made synthetically? In this Account, we try to shed light on the interplay among the various (free) energy components for crowded (fluoro)alkane dissociation. In this context, homolytic cleavage of the central C-C bond in a series of model alkanes of increasing size with tert-butyl (tBu), adamantyl (Ad), and [1.1.1]propellanyl (Prop) substituents is investigated. Reference energies are calculated at the PNO-LCCSD(T)-F12b level and used to benchmark the performance of contemporary DFT functionals. In line with previous conclusions, the application of dispersion corrections to density functionals is mandatory. For crowed structures, the accurate description of the midrange correlation effects, specifically repulsive van der Waals interactions, is crucial, and we observed that the density-dependent VV10 correction is superior to D4 in this context, although the asymptotic region is better described by the latter. The best available dispersion-inclusive functionals show systematic and reasonably small residual errors and can be safely applied to large systems (>100 atoms), for which coupled cluster methods with large basis sets are not computationally feasible anymore. For qualitatively correct predictions of synthetic accessibility under equilibrium conditions (free energy), the inclusion of thermostatistical (entropy) contributions is also essential. According to our results, tetra-tert-butylmethane (C17tBu) is the largest and most crowded system with a positive dissociation free energy and should be synthesizable. The difference between hydrogenated and perfluorinated systems originates from the increase in the steric repulsion of spatially close substituents, which is not compensated to the same extent by attractive orbital and dispersion interactions. A sometimes-assumed similar steric demand for fluorine and hydrogen atoms is not corroborated by our investigations on crowded systems. Perfluorination is found to substantially decrease thermal stability, rendering perfluorinated hexamethylethane (C8tBuF) the last potentially stable representative.

Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density Functional Theory.

Exact simulations of quantum circuits (QCs) are currently limited to ∼50 qubits because the memory and computational cost required to store the QC wave function scale exponentially with qubit number. Therefore, developing efficient schemes for approximate QC simulations is a current research focus. Here, we show simulations of QCs with a method inspired by density functional theory (DFT), a widely used approach for studying many-electron systems. Our calculations can predict marginal single-qubit probabilities (SQPs) with over 90% accuracy in several classes of QCs with universal gate sets, using memory and computational resources linear in qubit number despite the formal exponential cost of the SQPs. This is achieved by developing a mean-field description of QCs and formulating optimal single- and two-qubit gate functionals─analogues of exchange-correlation functionals in DFT─to evolve the SQPs without computing the QC wave function. Current limitations and future extensions of this formalism are discussed.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat.

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

Jahn–Teller distortion in Sr2FeO4: group-theoretical analysis and hybrid DFT calculations

We present theoretical justification for distorted Ruddlesden–Popper (RP) phases of the first-order by using hybrid density functional theory (DFT) calculations and group-theoretical analysis. We, thus, demonstrate the existence of the Jahn–Teller effect around an Fe^{4texttt {+}} ion in Sr_{2}FeO_{4}. On the calculation side, we have established a combination of Wu–Cohen (WC) exchange and Perdew-Wang (PW) correlation in a three-parameter functional WC3PW, giving the most accurate description of Sr_{2}FeO_{4} from the comparison of three hybrid DFT functionals. Self-consistently obtained Hartree–Fock exact exchange of 0.16 demonstrates consistent results with the experimental literature data. Importantly, we explain conditions for co-existing proper and pseudo-Jahn–Teller effects from the crystalline orbitals, symmetry-mode analysis and irreps products. Moreover, phonon frequency calculations support and confirm the results of symmetry-mode analysis. In particular, the symmetry-mode analysis identifies a dominating irreducible representation of the Jahn-Teller mode (X2+) and corresponding space group (SG) of ground state structure (SG Cmce model). Therefore, the usually suggested high-symmetry tetragonal crystal structure (SG I4/mmm model) is higher in energy by 121 meV/f.u. (equivalent to the Jahn-Teller stabilization energy) compared with the distorted low-symmetry structure (SG Cmce model). We also present diffraction patterns for the two crystal symmetries to discuss the differences. Therefore, our results shed light on the existence of low-symmetry RP phases and make possible direct comparisons with future experiments.

The Best Models of Bodipy's Electronic Excited State: Comparing Predictions from Various DFT Functionals with Measurements from Femtosecond Stimulated Raman Spectroscopy.

Density functional theory (DFT) and time-dependent DFT (TD-DFT) are pivotal approaches for modeling electronically excited states of molecules. However, choosing a DFT exchange-correlation functional (XCF) among the myriad of alternatives is an overwhelming task that can affect the interpretation of results and lead to erroneous conclusions. The performance of these XCFs to describe the excited-state properties is often addressed by comparing them with high-level wave function methods or experimentally available vertical excitation energies; however, this is a limited analysis that relies on evaluation of a single point in the excited-state potential energy surface (PES). Different strategies have been proposed but are limited by the difficulty of experimentally accessing the electronic excited-state properties. In this work, we have tested the performance of 12 different XCFs and TD-DFT to describe the excited-state potential energy surface of Bodipy (2,6-diethyl-1,3,5,7-tetramethyl-8-phenyldipyrromethene difluoroborate). We compare those results with resonance Raman spectra collected by using femtosecond stimulated Raman spectroscopy (FSRS). By simultaneously fitting the absorption spectrum, fluorescence spectrum, and all of the resonance Raman excitation profiles within the independent mode displaced harmonic oscillator (IMDHO) formalism, we can describe the PES at the Franck-Condon (FC) region and determine the solvent and intramolecular reorganization energy after relaxation. This allows a direct comparison of the TD-DFT output with experimental observables. Our analysis reveals that using vertical absorption energies might not be a good criterion to determine the best XCF for a given molecular system and that FSRS opens up a new way to benchmark the excited-state performance of XCFs of fluorescent dyes.

A theoretical protocol for the rational design of the bioinspired multifunctional hybrid material MIP@cercosporin.

Rational design of polymeric materials prepared with the molecular imprinting technology is gaining even more space, as it can provide the optimal conditions to direct the laboratory molecularly imprinting polymer (MIP) preparation, maximizing their efficiency while reducing costs and preparation time, when compared to try-and-error approaches. We perform a rational design of an MIP with specific cavities for cercosporin accommodation by means of computational tools. The main steps of an MIP preparation were simulated and it was found that the most appropriated functional monomer to be used in the MIP preparation for cercosporin is the acrylamide, while the most suitable crosslinking agent is found to be p-divinylbenzene. Also, the most suitable solvents to remove cercosporin from the cavity are those with low dielectric constant, such as chloroform. This kind of solvent can then be used in washing step, in the case of use the MIP for sensing destinations. On the other hand, solvents like water, which has high dielectric constants, can efficiently improve the interactions between cercosporin and the functional monomer acrylamide, being indicated when the objective is to attract or maintain the cercosporin inside the MIP cavity. Thus, a MIP@cercosporin hybrid material can be used in aqueous solutions more reliably, or even the cercosporin detection in this media can be favoured. In the selectivity analysis of the material prepared in this specific condition, the results point that this MIP can also detect elsinochrome A with high efficiency, and could be more selective for hypericin, altertoxin, hypocrelin A, and phleichrome mycotoxins. The main steps of a MIP synthesis were theoretically simulated trough density functional theory (DFT) calculations aiming to direct and optimize the synthesis and applications of the material before the bench tests. Initially, in order to choose the most suitable functional to be employed for cercosporin calculations, eight of the DFT functionals that had been previously used for cercosporin calculations in literature were tested, which were the LCWPBE, B3LYP, CAM-B3LYP, M062-X, mPW1PW91, PBE0, TPSSh, and ωb97Xd. The theoretical 1H NMR chemical shifts for cercosporin molecule were calculated and compared with experimental results to analyze the performance of the functionals. Of all these, the best results were obtained with the TPSSh functional, employing the 6-31G(d,p) basis set, and this level of theory was then used for all the following steps. All the simulations were performed by means of geometry optimizations and frequency calculations. Additionally, AIM calculations were employed for further analysis of the interactions between the chosen functional monomer and cercosporin template in step 1, which was functional monomer selection. In washing step, the calculations were done using implicit solvation model, and finally, in selectivity tests, the putative "solid" MIP was simulated by freezing the positions of the monomers after the template remotion, and then other structurally similar toxins were placed in its cavity for the geometry optimizations and frequency calculations.

Total and orbital density-based analyses of molecules revealing long-range interaction regions.

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

Bond dissociation energies of the fifth‐row elements (InI): A quantum theoretical benchmark study

AbstractThe bond dissociation energies (BDE) of most main‐group elements have been accurately measured. However, the BDE values for heavy elements, particularly those from the fifth period (InI), are still missing or poorly validated. This study aims to identify the most accurate computational methods for calculating BDE values of compounds containing fifth‐row elements, including In, Sn, Sb, Te, and I, with a focus on readily accessible methods in software packages. The investigation involved a benchmark study using density functional theory (DFT), in addition to the 2nd order Møller–Plesset perturbation theory (MP2) and the coupled cluster with single, double, and perturbative triple excitations CCSD(T). The DFT functionals used in the study include APFD, B3LYP, B3LYP‐D3, B3P86, B97‐D3, BHandH, HSEH1PBE, M06‐2X, MN12‐SX, MN15‐L, and TPSSH. The functionals were carefully selected to cover some popular functionals as well as to cover all levels of the Jacob's ladder of DFT accuracy. The computed BDE values were compared with experimental values, and the results were filtered to remove any possible outliers. The statistical errors (MAPE, RMSE, and Pearson's) were then calculated and used to assess the performance of the methods.