Progress in time-dependent density-functional theory

DFT and TD-DFT studies to elucidate the configurational isomers of ferric aerobactin, ferric petrobactin, and their ferric photoproducts

Iron-chelating siderophores such as aerobactin and petrobactin are produced by marine bacteria to sequester iron under low iron stress. Those that contain a citrate moiety undergo light-catalyzed ligand-to-metal charge transfer, inducing decarboxylation and formation of photoproducts. In this work, we employed density functional theory to obtain the optimized geometries and determine the relative energies and geometric parameters of different configurations of Fe(III)-coordinated aerobactin, petrobactin, and their photoproducts. Time-dependent density functional theory was then used to compute the UV-Vis absorption spectra of these species, and the comparison against experimental spectra further elucidated the structural configurations most likely to be adopted by these compounds. Frequency calculations provided Fe-O force constants on the same order as other siderophores. The relative energies and predicted spectra support the cis-cis C-fac configuration for ferric aerobactin and the cis-trans C-mer configuration for its photoproduct, while only mild support is found for specific configurations of the ferric petrobactin structures (meta-mer and meta-fac for the precursor, cis-cis para-fac for the photoproduct). The predicted ferric petrobactin spectra are found to be fairly insensitive to the configuration of the ferric complex.

Rank-Reduced Equation-of-Motion Coupled Cluster Triples: an Accurate and Affordable Way of Calculating Electronic Excitation Energies

In the present work, we report an implementation of the rank-reduced equation-of-motion coupled cluster method with approximate triple excitations (RR-EOM-CC3). The proposed variant relies on tensor decomposition techniques in order to alleviate the high cost of computing and manipulating the triply excited amplitudes. In the RR-EOM-CC3 method, both ground-state and excited-state triple-excitation amplitudes are compressed according to the Tucker-3 format. This enables factorization of the working equations such that the formal scaling of the method is reduced to N6, where N is the system size. An additional advantage of our method is the fact that the accuracy can be strictly controlled by proper choice of two parameters defining sizes of triple-excitation subspaces in the Tucker decomposition for the ground and excited states. Optimal strategies of selecting these parameters are discussed. The developed method has been tested in a series of calculations of electronic excitation energies and compared to its canonical EOM-CC3 counterpart. Errors several times smaller than the inherent error of the canonical EOM-CC3 method (in comparison to FCI) are straightforward to achieve. This conclusion holds both for valence states dominated by single excitations and for states with pronounced doubly excited character. Taking advantage of the decreased scaling, we demonstrate substantial computational costs reductions (in comparison with the canonical EOM-CC3) in the case of two large molecules - l-proline and heptazine. This illustrates the usefulness of the RR-EOM-CC3 method for accurate determination of excitation energies of large molecules.

Structure of Multi-State Correlation in Electronic Systems

Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number (N) of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density D(r)─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than N2 determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS. In this study, we report a set of rigorous conditions in the Hamiltonian matrix functional, derived by enforcing the symmetry of a Hilbert subspace, namely the subspace invariance property. We further establish a fundamental theorem on the correlation matrix functional. That is, given the correlation functional for a single state in the N-dimensional subspace, all elements of the correlation matrix functional for the entire subspace are uniquely determined. These findings reveal the intricate structure of electronic correlation within the Hilbert subspace of lowest eigenstates and suggest a promising direction for efficient simulation of excited states.

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

We generalize the definitions of local scalar potentials namedυ kin ${\upsilon _{{\rm{kin}}} }$ andυ N - 1 ${\upsilon _{N - 1} }$ , which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.

Super-resolution techniques to simulate electronic spectra of large molecular systems

An accurate treatment of electronic spectra in large systems with a technique such as time-dependent density functional theory is computationally challenging. Due to the Nyquist sampling theorem, direct real-time simulations must be prohibitively long to achieve suitably sharp resolution in frequency space. Super-resolution techniques such as compressed sensing and MUSIC assume only a small number of excitations contribute to the spectrum, which fails in large molecular systems where the number of excitations is typically very large. We present an approach that combines exact short-time dynamics with approximate frequency space methods to capture large narrow features embedded in a dense manifold of smaller nearby peaks. We show that our approach can accurately capture narrow features and a broad quasi-continuum of states simultaneously, even when the features overlap in frequency. Our approach is able to reduce the required simulation time to achieve reasonable accuracy by a factor of 20-40 with respect to standard Fourier analysis and shows promise for accurately predicting the whole spectrum of large molecules and materials.

Convergence Analysis of the Stochastic Resolution of Identity: Comparing Hutchinson to Hutch++ for the Second-Order Green's Function

Stochastic orbital techniques offer reduced computational scaling and memory requirements to describe ground and excited states at the cost of introducing controlled statistical errors. Such techniques often rely on two basic operations, stochastic trace estimation and stochastic resolution of identity, both of which lead to statistical errors that scale with the number of stochastic realizations (Nξ) as N ξ - 1 . Reducing the statistical errors without significantly increasing Nξ has been challenging and is central to the development of efficient and accurate stochastic algorithms. In this work, we build upon recent progress made to improve stochastic trace estimation based on the ubiquitous Hutchinson's algorithm and propose a two-step approach for the stochastic resolution of identity, in the spirit of the Hutch++ method. Our approach is based on employing a randomized low-rank approximation followed by a residual calculation, resulting in statistical errors that scale much better than N ξ - 1 . We implement the approach within the second-order Born approximation for the self-energy in the computation of neutral excitations and discuss three different low-rank approximations for the two-body Coulomb integrals. Tests on a series of hydrogen dimer chains with varying lengths demonstrate that the Hutch++-like approximations are computationally more efficient than both deterministic and purely stochastic (Hutchinson) approaches for low error thresholds and intermediate system sizes. Notably, for arbitrarily large systems, the Hutchinson-like approximation outperforms both deterministic and Hutch++-like methods.

Restricted open-shell time-dependent density functional theory with perturbative spin-orbit coupling

When using quantum chemical methods to study electronically excited states of open-shell molecules, it is often beneficial to start with wave functions that are spin eigenfunctions. For excited states of molecules containing heavy elements, spin-orbit coupling (SOC) is important and needs to be included as well. An efficient approach is to include SOC perturbatively on top of a restricted open-shell Kohn-Sham (ROKS) time-dependent density functional theory, which can be combined with the Tamm-Dancoff approximation (TDA) to suppress numerical instabilities. We implemented and assessed the potential of such a ROKS-TDA-SOC method, also featuring the possibility of calculating transition dipole moments between states to allow for full spectrum simulation. Our study shows that the ROKS-TDA-SOC formalism yields a clear and easy-to-use method to obtain electronically excited states of open-shell molecules that are of moderate size and contain heavy elements.

Extended N-centered ensemble density functional theory of double electronic excitations

A recent work (arXiv:2401.04685) has merged N-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended N-centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density-functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn-Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two-electron Hubbard dimer model. A thorough comparison of the true physical ground- and excited-state electronic structures with that of the fictitious ensemble density-functional KS system is also presented. Depending on the choice of the density-functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant.

Nonadiabatic Molecular Dynamics Simulations Provide Evidence for Coexistence of Planar and Nonplanar Intramolecular Charge Transfer Structures in Fluorazene

Fluorazene is a model compound for photoinduced intramolecular charge transfer (ICT) between aromatic moieties. Despite intensive studies, both spectroscopic and theoretical, a complete model of its photophysics is still lacking. Especially controversial is the geometry of its ICT structure, or structures. In order to fill in the gaps in the state of knowledge on this important model system, in the present study I report the results of nonadiabatic molecular dynamics (NAMD) simulations of its photorelaxation process in acetonitrile solution. To afford a direct comparison to spectroscopic data, I use the simulation results as the basis for the calculation of the transient absorption (TA) spectrum. The NAMD simulations provide detailed information on the sequence of events during the excited-state relaxation of the title compound. Following initial photoexcitation into the bright S2 state, the molecule undergoes rapid internal conversion into the S1 state, leading to the locally excited (LE) structure. The LE structure, in turn, undergoes isomerization into a population of ICT structures, with geometries ranging from near-planar to markedly nonplanar. The LE → ICT isomerization reaction is accompanied by the decay of the characteristic excited-state absorption band of the LE structure near 2 eV. The anomalous fluorescence emission band of fluorazene is found to originate mainly from the near-planar ICT structures, in part because they dominate the overall population of ICT structures. Thus, the planar ICT (PICT) model appears to be the most appropriate description of the geometry of the ICT structure of fluorazene.

Absorption Intensities of Organic Molecules from Electronic Structure Calculations versus Experiments: the Effect of Solvation, Method, Basis Set, and Transition Moment Gauge

Recently, we derived experimental oscillator strengths (OSs) from well-defined UV-visible absorption spectral peaks of 100 molecules in solution. Here, we focus on a subset of transitions with the highest reliability to further benchmark the OSs from several wave function methods and density functionals. We consider multiple basis sets, transition moment gauges (length, velocity, and mixed), and solvent corrections. Most transitions in the comparison set come from conjugated molecules and have π → π* character. We use an automated algorithm to assign computed transitions to experimental bands. OSs computed using the Tamm-Dancoff approximation (TDA), CIS, or EOM-CCSD exhibited a strong gauge dependence, which is diminished in linear response theories (TD-DFT, TD-HF, and to a smaller degree LR-CCSD). OSs calculated from TD-DFT with PCM solvent models are systematically larger than apparent OSs derived from experimental spectra. For example, fcomp from hybrid functionals and PCM have mean absolute errors that are ∼10% of n·fexp, where n is a solvent refractive index factor that arises from the energy flux of the radiation field in a dielectric (solvent). Theoretical cavity field corrections considering spherical cavities do not improve the agreement between computed and experimental data. Corrections that account for the molecular shape and the direction of transition dipole moments, or that explicitly account for the effect of solvent molecules on the local field, should be more appropriate.

Toward Modeling the Complexity of the Chemical Mechanism in SERS

Surface-enhanced Raman scattering (SERS) provides detailed information about the binding of molecules at interfaces and their interactions with the local environment due to the large enhancement of Raman scattering. This enhancement arises from a combination of the electromagnetic mechanism (EM) and chemical mechanism (CM). While it is commonly accepted that EM gives rise to most of the enhancement, large spectral changes originate from CM. To elucidate the rich information contained in SERS spectra about molecules at interfaces, a comprehensive understanding of the enhancement mechanisms is necessary. In this Perspective, we discuss the current understanding of the enhancement mechanisms and highlight their interplay in complex local environments. We will also discuss emerging areas where the development of computational and theoretical models is needed with specific attention given to how the CM contributes to the spectral changes. Future efforts in modeling should focus on overcoming the challenges presented in this review in order to capture the complexity of CM in SERS.

Density functional theory from spherically symmetric densities: Ground and excited states of Coulomb systems

Recently, Theophilou [J. Chem. Phys. 149, 074104 (2018)] proposed a peculiar version of the density functional theory by showing that the set of spherical averages of the density around the nuclei determines uniquely the external potential in atoms, molecules, and solids. Here, this novel theory is extended to individual excited states. The generalization is based on the method developed in the series of papers by Ayers, Levy, and Nagy [Phys. Rev. A 85, 042518 (2012)]. Generalized Hohenberg-Kohn theorems are proved to the set of spherically symmetric densities using constrained search. A universal variational functional for the sum of the kinetic and electron-electron repulsion energies is constructed. The functional is appropriate for the ground state and all bound excited states. Euler equations and Kohn-Sham equations for the set are derived. The Euler equations can be rewritten as Schrödinger-like equations for the square root of the radial densities, and the effective potentials in them can be expressed in terms of wave function expectation values. The Hartree plus exchange-correlation potentials can be given by the difference of the interacting and the non-interacting effective potentials.

Implementation of energy and gradient for the TDDFT-approximate auxiliary function (aas) method

In this work, we have implemented the time-dependent density functional theory approximate auxiliary s function (TDDFT-aas) method, which is an approximate TDDFT method. Instead of calculating the exact two-center electron integrals in the K coupling matrix when solving the Casida equation, we approximate the integrals, thereby reducing the computational cost. In contrast to the related TDDFT plus tight-binding (TDDFT+TB) method, a new type of gamma function is used in the coupling matrix that does not depend on the tight-binding parameters. The calculated absorption spectra of silver and gold nanoparticles using TDDFT-aas show good agreement with TDDFT and TDDFT+TB results. In addition, we have implemented the analytical excited-state gradients for the TDDFT-aas method, which makes it possible to calculate the emission energy of molecular systems.

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Toward Consistent Predictions of Core/Valence Ionization Potentials and Valence Excitation Energies by MRSF-TDDFT

Optimizing exchange-correlation functionals for both core/valence ionization potentials (cIPs/vIPs) and valence excitation energies (VEEs) at the same time in the framework of MRSF-TDDFT is self-contradictory. To overcome the challenge, within the previous "adaptive exact exchange" or double-tuning strategy on Coulomb-attenuating XC functionals (CAM), a new XC functional specifically for cIPs and vIPs was first developed by enhancing exact exchange to both short- and long-range regions. The resulting DTCAM-XI functional achieved remarkably high accuracy in its predictions with errors of less than half eV. An additional concept of "valence attenuation", where the amount of exact exchange for the frontier orbital regions is selectively suppressed, was introduced to consistently predict both VEEs and IPs at the same time. The second functional, DTCAM-XIV, exhibits consistent overall prediction accuracy at ∼0.64 eV. By preferentially optimizing VEEs within the same "valence attenuation" concept, a third functional, DTCAM-VAEE, was obtained, which exhibits improved performance as compared to that of the previous DTCAM-VEE and DTCAM-AEE in the prediction of VEEs, making it an attractive alternative to BH&HLYP. As the combination of "adaptive exchange" and "valence attenuation" is operative, it would be exciting to explore its potential with a more tunable framework in the future.

Silver(I) complexes with voriconazole as promising anti-Candida agents

Recognizing that metal ions play an important role in modifying the pharmacological properties of known organic-based drugs, the present manuscript addresses the complexation of the antifungal agent voriconazole (vcz) with the biologically relevant silver(I) ion as a strategy for the development of new antimycotics. The synthesized silver(I) complexes with vcz were characterized by mass spectrometry, IR, UV-Vis and NMR spectroscopy and single-crystal X-ray diffraction analysis. The crystallographic results showed that complexes {[Ag(vcz)(H2O)]CH3SO3}n (1), {[Ag(vcz)2]BF4}n (2) and {[Ag(vcz)2]PF6}n (3) have polymeric structures in the solid state, in which silver(I) ions have a distorted tetrahedral geometry. On the other hand, DFT calculations revealed that the investigated silver(I) complexes 1-3 in DMSO exist as linear [Ag(vcz-N2)(vcz-N19)]+ (1a), [Ag(vcz-N2)(vcz-N4)]+ (2a) and [Ag(vcz-N4)2]+ (3a) species, respectively. The evaluated complexes showed an enhanced anti-Candida activity compared to the parent drug with minimal inhibitory concentration (MIC) values in the range of 0.02-1.05 μM. In comparison with vcz, the corresponding silver(I) complexes showed better activity in prevention hyphae and biofilm formation of C. albicans, indicating that they could be considered as promising agents against Candida that significantly inhibit its virulence. Also, these complexes are much better inhibitors of ergosterol synthesis in the cell membrane of C. albicans at the concentration of 0.5 × MIC. This is also confirmed by a molecular docking, which revealed that complexes 1a - 3a showed better inhibitory activity than vcz against the sterol 14α-demethylase enzyme cytochrome P450 (CYP51B), which plays a crucial role in the formation of ergosterol.

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

The n,π* States of Heteroaromatics: When are They the Lowest Excited States and in What Way Can They Be Aromatic or Antiaromatic?

Heteroaromatic molecules are found in areas ranging from biochemistry to photovoltaics. We analyze the n,π* excited states of 6π-electron heteroaromatics with in-plane lone pairs (nσ, herein n) and use qualitative theory and quantum chemical computations, starting at Mandado's 2n + 1 rule for aromaticity of separate spins. After excitation of an electron from n to π*, a (4n + 2)π-electron species has 2n + 2 πα-electrons and 2n + 1 πβ-electrons (or vice versa) and becomes πα-antiaromatic and πβ-aromatic. Yet, the antiaromatic πα- and aromatic πβ-components seldom cancel, leading to residuals with aromatic or antiaromatic character. We explore vertically excited triplet n,π* states (3n,π*), which are most readily analyzed, but also singlet n,π* states (1n,π*), and explain which compounds have n,π* states with aromatic residuals as their lowest excited states (e.g., pyrazine and the phenyl anion). If the πβ-electron population becomes more (less) uniformly distributed upon excitation, the system will have an (anti)aromatic residual. Among isomers, the one that has the most aromatic residual in 3n,π* is often of the lowest energy in this state. Five-membered ring heteroaromatics with one or two N, O, and/or S atoms never have n,π* states as their first excited states (T1 and S1), while this is nearly always the case for six-membered ring heteroaromatics with electropositive heteroatoms and/or highly symmetric (D2h) diheteroaromatics. For the complete compound set, there is a modest correlation between the (anti)aromatic character of the n,π* state and the energy gap between the lowest n,π* and π,π* states (R2 = 0.42), while it is stronger for monosubstituted pyrazines (R2 = 0.84).

State-Specific Coupled-Cluster Methods for Excited States

We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.

Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

Ultrafast hydrogen production in boron/oxygen-codoped graphitic carbon nitride revealed by nonadiabatic dynamics simulations

Graphitic carbon nitride (g-C3N4 or GCN) shows promise in photocatalytic water splitting, despite facing the challenge of rapid electron-hole recombination. In this study, we investigated the influence of boron/oxygen codoping on the photocatalytic performance of GCN systems for hydrogen generation. First-principles calculations and nonadiabatic molecular dynamics (NAMD) simulations were employed to reveal that the recombination time of photogenerated carriers could be increased by 16% to 64% in the codoped systems compared to the pristine GCN. The time-dependent density functional theory (TDDFT) scheme was utilized to select energy windows and initiate dynamics in cluster models of B/O co-doped heptazine with water molecules. Notably, we observed efficient direct photodissociation of hydrogen atoms from water molecules within 60 fs and proton hops within the hydrogen-bonded network within 80 fs in the co-doped system, diverging from the previously proposed mechanism for pristine heptazine in NAMD simulations. This discovery underscores the significant role of faster proton-coupled electron transfer (PCET) reactions and rapid radiationless relaxation in achieving high photocatalytic efficiency in water splitting. Our work enhances the understanding of the internal mechanism of highly efficient photocatalysts for water splitting and provides a new design strategy for doped GCN.

Inverse Hypercorroles

Ground-state and time-dependent density functional theory (TDDFT) calculations with the long-range-corrected, Coulomb-attenuating CAMY-B3LYP exchange-correlation functional and large, all-electron STO-TZ2P basis sets have been used to examine the potential "inverse hypercorrole" character of meso-p-nitrophenyl-appended dicyanidocobalt(III) corrole dianions. The effect is most dramatic for 5,15-bis(p-nitrophenyl) derivatives, where it manifests itself in intense NIR absorptions. The 10-aryl groups in these complexes play a modulatory role, as evinced by experimental UV-visible spectroscopic and electrochemical data for a series of 5,15-bis(p-nitrophenyl) dicyanidocobalt(III) corroles. TDDFT (CAMY-B3LYP) calculations ascribe these features clearly to a transition from the corrole's a2u-like HOMO (retaining the D4h irrep used for metalloporphyrins) to a nitrophenyl-based LUMO. The outward nature of this transition contrasts with the usual phenyl-to-macrocycle direction of charge transfer transitions in many hyperporphyrins and hypercorroles; thus, the complexes studied are aptly described as inverse hypercorroles.

Leave No Photon Behind: Artificial Intelligence in Multiscale Physics of Photocatalyst and Photoreactor Design

Although solar fuels photocatalysis offers the promise of converting carbon dioxide directly with sunlight as commercially scalable solutions have remained elusive over the past few decades, despite significant advancements in photocatalysis band-gap engineering and atomic site activity. The primary challenge lies not in the discovery of new catalyst materials, which are abundant, but in overcoming the bottlenecks related to material-photoreactor synergy. These factors include achieving photogeneration and charge-carrier recombination at reactive sites, utilizing high mass transfer efficiency supports, maximizing solar collection, and achieving uniform light distribution within a reactor. Addressing this multi-dimensional problem necessitates harnessing machine learning techniques to analyze real-world data from photoreactors and material properties. In this perspective, the challenges are outlined associated with each bottleneck factor, review relevant data analysis studies, and assess the requirements for developing a comprehensive solution that can unlock the full potential of solar fuels photocatalysis technology. Physics-informed machine learning (or Physics Neural Networks) may be the key to advancing this important area from disparate data towards optimal reactor solutions.

Advances in Computational Methods for Modeling Photocatalytic Reactions: A Review of Recent Developments

Photocatalysis is a fascinating process in which a photocatalyst plays a pivotal role in driving a chemical reaction when exposed to light. Its capacity to harness light energy triggers a cascade of reactions that lead to the formation of intermediate compounds, culminating in the desired final product(s). The essence of this process is the interaction between the photocatalyst's excited state and its specific interactions with reactants, resulting in the creation of intermediates. The process's appeal is further enhanced by its cyclic nature-the photocatalyst is rejuvenated after each cycle, ensuring ongoing and sustainable catalytic action. Nevertheless, comprehending the photocatalytic process through the modeling of photoactive materials and molecular devices demands advanced computational techniques founded on effective quantum chemistry methods, multiscale modeling, and machine learning. This review analyzes contemporary theoretical methods, spanning a range of lengths and accuracy scales, and assesses the strengths and limitations of these methods. It also explores the future challenges in modeling complex nano-photocatalysts, underscoring the necessity of integrating various methods hierarchically to optimize resource distribution across different scales. Additionally, the discussion includes the role of excited state chemistry, a crucial element in understanding photocatalysis.

Photochemical formation of the elusive Dewar isomers of aromatic systems: why are substituted azaborines different?

Photochemical reactions enabling efficient transformation of aromatic systems into energetic but stable non-aromatic isomers have a long history in organic chemistry. One recently discovered reaction in this realm is that where derivatives of 1,2-azaborine, a compound isoelectronic with benzene in which two adjacent C atoms are replaced by B and N atoms, form the non-hexagon Dewar isomer. Here, we report quantum-chemical calculations that explain both why 1,2-azaborine is intrinsically more reactive toward Dewar formation than benzene, and how suitable substitutions at the B and N atoms are able to increase the corresponding quantum yield. We find that Dewar formation from 1,2-azaborine is favored by a pronounced driving force that benzene lacks, and that a large improvement in quantum yield arises when the reaction of substituted 1,2-azaborines proceeds without involvement of an intermediary ground-state species. Overall, we report new insights into making photochemical use of the Dewar isomers of aromatic compounds.

Aufbau Suppressed Coupled Cluster Theory for Electronically Excited States

We introduce an approach to improve single-reference coupled cluster theory in settings where the Aufbau determinant is absent from or plays only a small role in the true wave function. Using a de-excitation operator that can be efficiently hidden within a similarity transform, we create a coupled cluster wave function in which de-excitations work to suppress the Aufbau determinant and produce wave functions dominated by other determinants. Thanks to an invertible and fully exponential form, the approach is systematically improvable, size consistent, size extensive, and, interestingly, size intensive in a granular way that should make the adoption of some ground state techniques, such as local correlation, relatively straightforward. In this initial study, we apply the general formalism to create a state-specific method for orbital-relaxed, singly excited states. We find that this approach matches the accuracy of similar-cost equation-of-motion methods in valence excitations while offering improved accuracy for charge transfer states. We also find the approach to be more accurate than excited-state-specific perturbation theory in both types of states.

Close Stacking of Antiaromatic Ni(II) Norcorrole Originating from a Four-Electron Multicentered Bonding Interaction

A π-conjugated molecule with one electronic spin often forms a π-stacked dimer through molecular orbital interactions between two unpaired electrons. The bonding is recognized as a multicentered two-electron interaction between the two π-conjugated molecules. Here, we disclose a multicentered bonding interaction between two antiaromatic molecules involving four electrons. We have synthesized an antiaromatic porphyrin analogue, Ni(II) bis(pentafluorophenyl)norcorrole. Its dimer adopts a face-to-face stacked structure with an extremely short stacking distance of 2.97 Å. The close stacking originates from a multicenter four-electron bonding interaction between the two molecules. The bonding electrons were experimentally observed via synchrotron X-ray diffraction analysis and corroborated by theoretical calculations. The intermolecular interaction of the molecular orbitals imparts the stacked dimer with aromatic character that is distinctly different from that of its monomer.

Ultrafast Computational Screening of Molecules with Inverted Singlet-Triplet Energy Gaps Using the Pariser-Parr-Pople Semiempirical Quantum Chemistry Method

Molecules with an inverted energy gap between their first singlet and triplet excited states have promising applications in the next generation of organic light-emitting diode (OLED) materials. Unfortunately, such molecules are rare, and only a handful of examples are currently known. High-throughput virtual screening could assist in finding novel classes of these molecules, but current efforts are hampered by the high computational cost of the required quantum chemical methods. We present a method based on the semiempirical Pariser-Parr-Pople theory augmented by perturbation theory and show that it reproduces inverted gaps at a fraction of the cost of currently employed excited-state calculations. Our study paves the way for ultrahigh-throughput virtual screening and inverse design to accelerate the discovery and development of this new generation of OLED materials.

DELFI: a computer oracle for recommending density functionals for excited states calculations

Density functional theory (DFT) is the workhorse of computational quantum chemistry. One of its main limitations is that choosing the right functional is a non-trivial task left for human experts. The choice is particularly hard for excited state calculations when using its time-dependent formulation (TD-DFT). This is due to the approximations of the method, but also because the photophysical properties of a molecule are defined by a manifold of states that all need to be properly described. This includes not only the relative energy of the states, but also capturing the correct character, order, and intensity of the transitions. In this work, we developed a neural network to recommend functionals to be used on molecules for TD-DFT calculations, by simultaneously considering all these properties for a manifold of states. This was possible by developing a scoring system to define the accuracy of an excited state's calculation against a higher-accuracy reference. The scoring system is generalizable to any level of theory; we here applied it to evaluate the performance of common functionals of different rungs against a higher accuracy method on a large set of organic molecules. The results are collected in a database that we released and made open, providing four million data points to the community for future applications. The scoring system assigns a value between zero and one hundred to each functional for each molecule, transforming the complicated task of learning photophysical properties into a simpler regression task. We used the dataset to train a graph attention neural network to predict the scores for unseen molecules. We call this oracle DELFI (Data-driven EvaLuation of Functionals by Inference), which can be used to quickly screen and predict the ranking of functionals to calculate the optical properties of organic molecules. We validated DELFI in two in silico experiments: choosing a common functional for a series of spiropyran-merocyanine isomers and a unique functional to screen a large dataset of over 50 000 organic photovoltaic molecules, for which an extensive benchmark would be unfeasible. A corresponding web application allows DELFI to be easily run and the results to be analyzed, alleviating the hurdle of choosing the right functional for TD-DFT calculations.

Understanding of complex spin up-conversion processes in charge-transfer-type organic molecules

Despite significant progress made over the past decade in thermally activated delayed fluorescence (TADF) molecules as a material paradigm for enhancing the performance of organic light-emitting diodes, the underlying spin-flip mechanism in these charge-transfer (CT)-type molecular systems remains an enigma, even since its initial report in 2012. While the initial and final electronic states involved in spin-flip between the lowest singlet and lowest triplet excited states are well understood, the exact dynamic processes and the role of intermediate high-lying triplet (T) states are still not fully comprehended. In this context, we propose a comprehensive model to describe the spin-flip processes applicable for a typical CT-type molecule, revealing the origin of the high-lying T state in a partial molecular framework in CT-type molecules. This work provides experimental and theoretical insights into the understanding of intersystem crossing for CT-type molecules, facilitating more precise control over spin-flip rates and thus advancing toward developing the next-generation platform for purely organic luminescent candidates.

Evaluating the Impact of the Tamm-Dancoff Approximation on X-ray Spectrum Calculations

The impact of the Tamm-Dancoff approximation (TDA) for time-dependent density functional theory (TDDFT) calculations of X-ray absorption and X-ray emission spectra (XAS and XES) is investigated, showing small discrepancies in the excitation energies and intensities. Through explicit diagonalization of the TDDFT Hessian, XES was considered by using full TDDFT with a core-hole reference state. This has previously not been possible with most TDDFT implementations as a result of the presence of negative eigenvalues. Furthermore, a core-valence separation (CVS) scheme for XES is presented, in which only elements including the core-hole are considered, resulting in a small Hessian with the dimension of the number of remaining occupied orbitals of the same spin as the core-hole (CH). The resulting spectra are in surprisingly good agreement with the full-space counterpart, illustrating the weak coupling between the valence-valence and valence-CH transitions. Complications resulting from contributions from the discretized continuum are discussed, which can occur for TDDFT calculations of XAS and XES and for TDA calculations of XAS. In conclusion, we recommend that TDA be used when calculating X-ray emission spectra, and either CVS-TDA or CVS-TDDFT can be used for X-ray absorption spectra.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Mitochondria-Associated Transcriptome Profiling via Localizable Aggregation-Induced Emission Photosensitizers in Live Cells

In recent decades, there has been increasing interest in studying mitochondria through transcriptomic research. Various exogenous fusion protein-based proximity labeling methods have been reported that focus on the site of one particular protein/peptide and might also influence the corresponding localization or interactome. To enable unbiased and high spatial-resolution profiling of mitochondria-associated transcriptomes in live cells, a flexible RNA proximity labeling approach was developed using aggregation-induced emission (AIE) type photosensitizers (PSs) that possess great mitochondria-targeting capabilities. Their accumulation in an enclosed mitochondrial environment tends to enhance the fluorescence emission and reactive oxygen species generation. By comparing the in vitro optical properties, photosensitization processes, as well as the in cellulo mitochondrial specificity and RNA labeling performance of four AIE PSs, high-throughput sequencing analysis was conducted using TFPy-mediated RNA proximity labeling in live HeLa cells. This approach successfully captured a comprehensive list of transcripts, including mitochondria-encoded RNAs, as well as some nuclear-derived RNAs located at the outer mitochondrial membrane and interacting organelles. This small molecule-based proximity labeling method bypasses complex genetic manipulation and transfection steps, making it readily applicable for diverse research purposes.

Intramolecular rate-constant calculations based on the correlation function using temperature dependent quantum Green's functions

A theoretical method for calculating rate constants for internal conversion (IC), intersystem crossing (ISC) and radiative (R) electronic transitions is presented. The employed method uses temperature-dependent quantum Green's functions, which give the opportunity to consider almost any nth-order polynomial perturbation operator and the influence of external electromagnetic fields on the rate constants. The rate constants of the IC, ISC and R processes are calculated for two important indocyanine molecules namely indocyanine green (ICG) and heptamethine cyanine (IR808) at the Franck-Condon level using the temperature-dependent quantum Green's function approach. Calculations at the time-dependent density functional theory level with the MN15 functional show that ICG and IR808 have only one triplet state below the S1 state. The main deactivation channel of the S1 state is the IC process with a large (kIC(S1 → S0)) rate constant of ∼109-1011 s-1. The estimated quantum yield of fluorescence (φfl) is ∼0.001-0.24 for the two studied molecules, which agrees rather well with experimental values. Thus, the present approach enables calculations of the three kinds of rate constants and the quantum yield of fluorescence using the same computational methodology.

Internal conversion induced by external electric and magnetic fields

We have developed a new methodology for calculating contributions to the rate constants (kIC) of internal conversion that are induced by external electric (kIC-E) or magnetic (kIC-M) fields. The influence of the external electric and magnetic fields on the kIC was estimated for seven representative molecules. We show that the kIC-E contribution calculated at a field strength of 1011 V m-1 is generally as large as the kIC rate constant in the absence of the external field. For indocyanine green, azaoxa[8]circulene, and pyromitene 567, the kIC-E contribution is as large as kIC already at a field strength of 109 V m-1. Such electric-field strengths occur for example in plasmonic studies and in strong laser-field experiments. The induced effect on the kIC rate constant should be accounted for in calculations of photophysical properties of molecules involved in such experiments. The induced effect of an external magnetic field on kIC can be neglected in experiments on Earth because the magnetic contribution becomes significant only at very strong magnetic fields of 104-105 T that cannot be achieved on Earth. However, the magnetic effect on the rate constant of internal conversion can be important in astrophysical studies, where extremely strong magnetic fields occur near neutron stars and white dwarfs.

Metallaantiaromaticity of 10-Platinacorrole Complexes

The aromaticity of cyclic π-conjugated organometallic compounds is known as metallaaromaticity. π-Conjugated metallacycles, such as metallabenzenes and metallapentalenes, have been investigated in order to understand the involvement of the d electrons from the metal center in the π-conjugated systems of the organic ligands. Here, we report the synthesis of Pd(II) 10-platinacorrole complexes with cyclooctadiene (COD) and norbornadiene (NBD) ligands. While the Pd(II) 10-platinacorrole COD complex adopts a distorted structure without showing appreciable antiaromaticity, the corresponding NBD complex exhibits a distinct antiaromatic character due to its highly planar conformation. Detailed density functional theory (DFT) calculations revealed that two d orbitals are involved in macrocyclic π-conjugation. We furthermore demonstrated that Craig-Möbius antiaromaticity is not present in the studied system. The synthesis of 10-platinacorroles enables a systematic comparison of the antiaromaticity and aromaticity of closely related porphyrin analogues, providing a better understanding of π-conjugation that involves d orbitals.

A Proof-of-Principle Design for Through-Space Transmission of Unidirectional Rotary Motion by Molecular Photogears

The construction of molecular photogears that can achieve through-space transmission of the unidirectional double-bond rotary motion of light-driven molecular motors onto a remote single-bond axis is a formidable challenge in the field of artificial molecular machines. Here, we present a proof-of-principle design of such photogears that is based on the possibility of using stereogenic substituents to control both the relative stabilities of two helical forms of the photogear and the double-bond photoisomerization reaction that connects them. The potential of the design was verified by quantum-chemical modeling through which photogearing was found to be a favorable process compared to free-standing single-bond rotation ("slippage"). Overall, our study unveils a surprisingly simple approach to realizing unidirectional photogearing.

Activating two-dimensional semiconductors for photocatalysis: a cross-dimensional strategy

The emerging two-dimensional (2D) semiconductors substantially extend materials bases for versatile applications such as semiconductor photocatalysis demanding semiconductive matrices and large surface areas. The dimensionality, while endowing 2D semiconductors the unique properties to host photocatalytic functionality of pollutant removal and hydrogen evolution, hurdles the activation paths to form heterogenous photocatalysts where the photochemical processes are normally superior over these on the mono-compositional counterparts. In this perspective, we present a cross-dimensional strategy to employ thenD (n= 0-2) clusters or nanomaterials as activation partners to boost the photocatalytic activities of the 2D semiconductors. The formation principles of heterogenous photocatalysts are illustrated specifically for the 2D matrices, followed by selection criteria of them among the vast 2D database. The computer investigations are illustrated in the density functional theory route and machine learning benefitted from the vast samples in the 2D library. Synthetic realizations and characterizations of the 2D heterogenous systems are introduced with an emphasis on chemical methods and advanced techniques to understand materials and mechanistic studies. The perspective outlooks cross-dimensional activation strategies of the 2D materials for other applications such as CO2removal, and materials matrices in other dimensions which may inspire incoming research within these fields.

Deciphering the origin of the first steps in the degradation of azo dyes: a computational study

Azo dyes find applications across various sectors including food, pharmaceuticals, cosmetics, printing, and textiles. The contaminating effects of dyes on aquatic environments arise from toxic effects caused by their long-term presence in the environment, buildup in sediments, particularly in aquatic species, degradation of pollutants into mutagenic or mutagenic compounds, and low aerobic biodegradability. Therefore, we theoretically propose the first steps of the degradation of azo dyes based on the interaction of hydroperoxyl radical (•OOH) with the dye. This interaction is studied by the OC and ON mechanisms in three azo dyes: azobenzene (AB), disperse orange 3 (DO3), and disperse red 1 (DR1). Rate constants calculated at several temperatures show a preference for the OC mechanism in all the dyes with lower activation energies than the ON mechanism. The optical properties were calculated and because the dye-•OOH systems are open shell, to verify the validity of the results, a study of the spin contamination of the ground [Formula: see text] and excited states [Formula: see text] was previously performed. Most of the excited states calculated are acceptable as doublet states. The absorption spectra of the dye-•OOH systems show a decrease in the intensity of the bands compared to the isolated dyes and the appearance of a new band of the type π → π* at a longer wavelength in the visible region, achieving up to 868 nm. This demonstrates that the reaction with the •OOH radical could be a good alternative for the degradation of the azo dyes.

Boosting Photocatalytic Water Splitting of Polymeric C60 by Reduced Dimensionality from Two-Dimensional Monolayer to One-Dimensional Chain

The recent synthesis of monolayer fullerene networks (Hou, L., et al. Nature 2022, 606, 507) provides new opportunities for photovoltaics and photocatalysis because of their versatile crystal structures for further tailoring of electronic, optical, and chemical function. To shed light on the structural aspects of the photocatalytic water splitting performance of fullerene nanomaterials, we compare the photocatalytic properties of individual polymeric fullerene chains and monolayer fullerene networks from first-principles calculations. We find that the photocatalytic efficiency can be further optimized by reducing the dimensionality from two-dimensional (2D) to one-dimensional (1D). The conduction band edge of the polymeric C60 chain provides an external potential for the hydrogen reduction reaction much higher than that of its monolayer counterparts over a wider range of pH values, and there are 2 times more surface active sites in the 1D chain than in the 2D networks from a thermodynamic perspective. These observations identify the 1D fullerene polymer as a more promising candidate as a photocatalyst for the hydrogen evolution reaction in comparison to monolayer fullerene networks.

Diagrammatic multiplet sum method (MSM) density functional theory (DFT): Investigation of the transferability of integrals in "simple" DFT-based approaches to multideterminantal problems

Kohn-Sham density functional theory (DFT) typically works well for describing dynamic correlation. Two other types of correlation, arising in the cases of degenerate (static) or quasidegenerate (nondynamic) zero-order states, represent a difficult problem for DFT. When symmetry is present, multiplet sum method (MSM) DFT [Ziegler et al., Theor. Chim. Acta 4, 877 (1977)] provides one of the earliest and simplest ways to include static correlation in DFT. MSM-DFT assumes that DFT provides a good description of single-determinant energies and uses symmetry and simple ansätze to include the effects of static correlation. This is equivalent to determining the off-diagonal matrix elements in a small configuration interaction (CI) eigenvalue problem. Our ultimate goal, however, is nondynamic correlation in cases where symmetry is inadequate for fixing the dynamic-correlation limitation of DFT. To this end, we have developed a diagrammatic approach to MSM-DFT, which does not, by itself, solve the nondynamic correlation problem in DFT but which facilitates comparison with wave function CI and so allows educated guesses of off-diagonal CI matrix elements even in the absence of symmetry. In every case, an additional exchange-only ansatz (EXAN) allows the MSM-DFT formulas to be transformed into wave function formulas. This EXAN also works for transforming time-dependent DFT into time-dependent Hartree-Fock. Although not enough to uniquely guess DFT formulas from wave function formulas, the diagrammatic approach and the EXAN provide important constraints on any guesses that might be used. We illustrate how diagrammatic MSM-DFT may be used to guess a nondynamic correlation correction for the dissociation of H2 and how diagrammatic MSM-DFT may be used to guess a nonsymmetry-based coupling element in the O2 multiplet problem, which is reasonably close to a previous symmetry-derived result.

Theoretical characterization and biological activity investigation of indirubins, cyclin dependent kinases inhibitors

Up to now, significant research efforts have been directed towards investigating indirubin and its derivatives as potential candidates for developing new compounds with multiple biological activities. In the present work, natural indirubin and numerous of its chemical derivatives referred to as indirubins have been investigated computationally using DFT method with the B3LYP/6-311 + G(d,p) level of theory, in order to reveal structure- biological activity relationship. We started with a structural properties description. Results analysis indicated that extra interaction sites were provided through the set of substitutions in compounds (1): Indirubin-3'-monoxime, (2): Indirubin-5-sulfonic acid, (3): 5-Nitro-indirubinoxime, (4): 5'-OH-5-nitro-indirubinoxime (AGM130), (5): 7-Bromo-5'-carboxyindirubin-3'-oxime, and (6): 7 BIO and consequently, extra hydrogen bonds may be formed with the active sites of molecular targets, such as GSK-3, CDKs, and Aurora kinases, as well as the aryl hydrocarbon receptor. Subsequently, to get more information on the electronic properties of indirubin and its analogues, HOMO, LUMO, Egap, and further electronic parameters were carried out. The indirubin derivatives showed an easier interaction with its environment than indirubin, the parent compound. The UV-Visible spectra of indirubin and compounds 1-6 were also produced using TD-DFT with B3LYP functional and 6-311 + G(2d,p) basis set. The relationship between absorption and chemical structure is discussed. Two phototoxic brominated compounds showed important absorption spectra modifications. It was also found that the main absorption bands of all compounds derived from π→π*(HOMO→LUMO) transitions.Communicated by Ramaswamy H. Sarma.

In vivo three-dimensional brain imaging with chemiluminescence probes in Alzheimer's disease models

Optical three-dimensional (3D) molecular imaging is highly desirable for providing precise distribution of the target-of-interest in disease models. However, such 3D imaging is still far from wide applications in biomedical research; 3D brain optical molecular imaging, in particular, has rarely been reported. In this report, we designed chemiluminescence probes with high quantum yields, relatively long emission wavelengths, and high signal-to-noise ratios to fulfill the requirements for 3D brain imaging in vivo. With assistance from density-function theory (DFT) computation, we designed ADLumin-Xs by locking up the rotation of the double bond via fusing the furan ring to the phenyl ring. Our results showed that ADLumin-5 had a high quantum yield of chemiluminescence and could bind to amyloid beta (Aβ). Remarkably, ADLumin-5's radiance intensity in brain areas could reach 4 × 107 photon/s/cm2/sr, which is probably 100-fold higher than most chemiluminescence probes for in vivo imaging. Because of its strong emission, we demonstrated that ADLumin-5 could be used for in vivo 3D brain imaging in transgenic mouse models of Alzheimer's disease.

Solvent Effects and pH Dependence of the X-ray Absorption Spectra of Proline from Electrostatic Embedding Quantum Mechanics/Molecular Mechanics and Mixed-Reference Spin-Flip Time-dependent Density-Functional Theory

The accurate description of solvent effects on X-ray absorption spectra (XAS) is fundamental for comparing the simulated spectra with experiments in solution. Currently, few protocols exist that can efficiently reproduce the effects of the solute/solvent interactions on XAS. Here, we develop an efficient and accurate theoretical protocol for simulating the solvent effects on XAS. The protocol combines electrostatic embedding QM/MM based on electrostatic potential fitted operators for describing the solute/solvent interactions and mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) for simulating accurate XAS spectra. To demonstrate the capabilities of our protocol, we compute the X-ray absorption of neutral proline in the gas phase and ionic proline in water in all relevant K-edges, showing excellent agreement with experiments. We show that states represented by core to π* transitions are almost unaffected by the interaction with water, whereas the core to σ* transitions are more impacted by the fluctuation of proline structure and the electrostatic interaction with the solvent. Finally, we reconstruct the pH-dependent XAS of proline in solution, determining that the N K-edge can be used to distinguish its three protonation states.

Theory and modeling of light-matter interactions in chemistry: current and future

Light-matter interaction not only plays an instrumental role in characterizing materials' properties via various spectroscopic techniques but also provides a general strategy to manipulate material properties via the design of novel nanostructures. This perspective summarizes recent theoretical advances in modeling light-matter interactions in chemistry, mainly focusing on plasmon and polariton chemistry. The former utilizes the highly localized photon, plasmonic hot electrons, and local heat to drive chemical reactions. In contrast, polariton chemistry modifies the potential energy curvatures of bare electronic systems, and hence their chemistry, via forming light-matter hybrid states, so-called polaritons. The perspective starts with the basic background of light-matter interactions, molecular quantum electrodynamics theory, and the challenges of modeling light-matter interactions in chemistry. Then, the recent advances in modeling plasmon and polariton chemistry are described, and future directions toward multiscale simulations of light-matter interaction-mediated chemistry are discussed.

The search for a maximum of the D-π-A paradigm for second order nonlinear optical molecular materials

Push-pull π-conjugated molecules are one of the paradigms of second order nonlinear optical (NLO) materials and have been extensively explored. However, high-performance second order NLO materials with an optimum electron donor (D), π-bridge (π) and acceptor (A) under this paradigm are still the most sought-after. In the present work, D-π-A molecules with optimal D, π and A combination for strong second order NLO properties are proposed based on molecular orbital theories. The optimal D-π-A push-pull molecule achieves an unprecedentedly strong NLO response under the D-π-A paradigm, i.e., the static first hyperpolarizability reaches -453.92 × 10-30 esu per heavy atom using azulene as part of the π-bridge and acceptor to synergistically reinforce the strength of the acceptor. The protocols of D-π-A NLO molecule design through frontier molecular orbital matching of D, π and A with optimal combination of electron donating and accepting strengths shed light on future molecular NLO materials exploration. The simulated two-dimensional second order spectra provide useful information (e.g., sum frequency generation) on the applications of those D-π-A push-pull molecules in nonlinear optics.

Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

Learning from the 4-(dimethylamino)benzonitrile twist: Two-parameter range-separated local hybrid functional with high accuracy for triplet and charge-transfer excitations

The recent ωLH22t range-separated local hybrid (RSLH) is shown to provide outstanding accuracy for the notorious benchmark problem of the two lowest excited-state potential energy curves for the amino group twist in 4-(dimethylamino)benzonitrile (DMABN). However, the design of ωLH22t as a general-purpose functional resulted in less convincing performance for triplet excitations, which is an important advantage of previous LHs. Furthermore, ωLH22t uses 8 empirical parameters to achieve broad accuracy. In this work, the RSLH ωLH23ct-sir is constructed with minimal empiricism by optimizing its local mixing function prefactor and range-separation parameter for only 8 excitation energies. ωLH23ct-sir maintains the excellent performance of ωLH22t for the DMABN twist and charge-transfer benchmarks but significantly improves the errors for triplet excitation energies (0.17 vs 0.24 eV). Additional test calculations for the AE6BH6 thermochemistry test set and large dipole moment and static polarizability test sets confirm that the focus on excitation energies in the optimization of ωLH23ct-sir has not caused any dramatic errors for ground-state properties. Although ωLH23ct-sir cannot replace ωLH22t as a general-purpose functional, it is preferable for problems requiring a universally good description of localized and charge-transfer excitations of both singlet and triplet multiplicity. Current limitations on the application of ωLH23ct-sir and other RSLHs to the study of singlet-triplet gaps of emitters for thermally activated delayed fluorescence are discussed. This work also includes the first systematic analysis of the influence of the local mixing function prefactor and the range-separation parameter in an RSLH on different types of excitations.