Progress in time-dependent density-functional theory

Improving Aufbau Suppressed Coupled Cluster through Perturbative Analysis

Guided by perturbative analysis, we improve the accuracy of Aufbau suppressed coupled cluster theory in simple single excitations, multiconfigurational single excitations, and charge transfer excitations while keeping the cost of its leading-order terms precisely in line with ground-state coupled cluster. Combining these accuracy improvements with a more efficient implementation based on spin adaptation, we observe high accuracy in a large test set of single excitations and, in particular, a mean unsigned error for charge transfer states that outperforms equation-of-motion coupled cluster theory by 0.25 eV. We discuss how these results are achieved via a systematic identification of which amplitudes to prioritize for single- and multiconfigurational excited states, and how this prioritization differs in important ways from the ground-state theory. In particular, our data show that a partial linearization of the theory increases accuracy by mitigating unwanted side effects of Aufbau suppression.

Conical Intersections Studied by the Configuration-Interaction-Corrected Tamm-Dancoff Method

Conical intersections directly mediate the internal energy conversion in photoinduced processes in a wide range of chemical and biological systems. Because of the Brillouin theorem, many conventional electronic structure methods, including configuration interaction with single excitations from a Hartree-Fock reference and time-dependent density functional theory in either the linear response approximation (TDDFT) or Tamm-Dancoff approximation (DFT-TDA), have the wrong dimensionality for conical intersections between the ground state (S0) and the first excited state (S1) of the same multiplicity. This leads to unphysical state crossings. Here, we implement and assess the configuration-interaction-corrected Tamm-Dancoff approximation (CIC-TDA) that restores the correct dimensionality of conical intersections by including the coupling between the reference state and the intersecting excited state. We apply the CIC-TDA method to the S1/S0 conical intersections in ammonia (NH3), ethylene (C2H4), bithiophene (C8H6S2), azobenzene (C12H10N2), and 11-cis retinal protonated Schiff base (PSB11) in vacuo. We show that this black-box approach can produce potential energy surfaces (PESs) of comparable accuracy to multireference wave function methods. The method validated here can allow cost-efficient explorations of photoinduced electronically nonadiabatic dynamics, especially for large molecules and complex systems.

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.

On the Meaning of De-Excitations in Time-Dependent Density Functional Theory Computations

De-excitations play a prominent role within the mathematical formalism of time-dependent density functional theory (TDDFT) and other excited-state response methods. However, their physical meaning remains largely unexplored and poorly understood. It is the purpose of this work to shed new light on this issue. The main thesis developed here is that de-excitations are not a peculiarity of TDDFT but that they are a more fundamental property of the underlying wave functions reflecting how electrons are excited between partially occupied orbitals. The paraquinodimethane (pQDM) molecule is chosen as a convenient model system whose open-shell character can be modulated via twisting of its methylene groups. Using the one-electron transition density matrix as a rigorous basis for our analysis, we highlight qualitative and quantitative parallels in the way that de-excitations are reflected in multireference wave function and TDDFT computations. As a physically observable consequence, we highlight a lowering of the transition dipole moment that derives from destructive interference between the excitation and de-excitation contributions. In summary, we hope that this work will shed new light on formal and practical aspects regarding the application of TDDFT to excited-state computations, especially of diradicaloid systems.

Analytic Gradient for Spin-Flip TDDFT Using Noncollinear Functionals in the Multicollinear Approach

Spin-flip time-dependent density functional theory (TDDFT) is an efficient tool for describing ground and excited states, especially when they exhibit significant multiconfigurational effects. Currently, most implementations and applications rely on collinear functionals. Using noncollinear functionals in spin-flip TDDFT is a more natural and appropriate choice, which preserves energy degeneracy and spin symmetry better. However, its development has been hindered by numerical instabilities in the second-order functional derivatives. We recently proposed a new approach for constructing noncollinear functionals, the multicollinear approach, which provides numerically stable higher-order functional derivatives and has been applied to spin-flip TDDFT calculations. In this study, we apply the multicollinear approach to the spin-flip TDDFT analytic gradient to address its main challenge: calculating the third-order derivatives of noncollinear functionals. Since these derivatives for generalized gradient approximation (GGA) and meta-GGA functionals may have been implemented for the first time, we validated the implementation through benchmark tests, comparing the results with numerical gradients and the analytic gradients of spin-conserving excited states with the same energy. Finally, we demonstrate the application of spin-flip TDDFT analytic gradients in optimizing the geometries of the lower singlet states, including double-excitation states, and calculating the adiabatic excitation energies and dissociation curves. The analytic gradients of spin-flip TDDFT also serve as a reference for studying analytic derivative couplings and provide a new potential option for on-the-fly molecular dynamics simulations. Furthermore, this work provides useful references for the study of other first-order properties and the development of relativistic TDDFT gradients.

A TDDFT exploration on the excited-state intramolecular proton transfer in 2-(2'-hydroxyphenyl)-benzimidazole derivatives

Excited-state intramolecular proton transfer (ESIPT) reactions are one of the fundamental energy transformation reactions in catalysis and biological process. The combining ESIPT with the twisted intramolecular charge transfer (TICT) brings the richness of optical, photoelectronic performances to certain functional compounds. Delineating the mechanism of ESIPT + TICT reactions and further understanding why a specific functional group dominates are fundamentally crucial for the design and application of the functionally photoelectric materials. In this paper, six 2-(2'-hydroxyphenyl) benzimidazole (HBIgens) derivatives involved in ESIPT + TICT were investigated by density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations to have an insight into the photophysical and photochemical process in acetonitrile. The optimized geometries indicated that the intramolecular hydrogen bonds (-O-H···N-) were enhanced in the corresponding first singlet, which provided the fundamentally outstanding prerequisites of the ESIPT reactions. By further charge analysis, it is indicated that the introduction of substitutes to the different positions would determine the Stokes' shifts, and the electron-adopting p-cyanophenyl group mainly contributed to the TICT structure. Constraint scanning the potential energy curves of both ground and first singlet excited states, the electron-adopting N,N-diethylamino group on the meta position could enhance the barrier and inhibit the ESIPT reaction. Furthermore, the nucleus independent chemical shift (NICS(1)_ZZ) values of phenol groups indicate the relationship between the reversal aromaticity and the barrier of ESIPT, both of which were proved to be negatively correlated in the ESIPT reaction. It is concluded that not only both types and positions of substituents can tune the excited-state proton transfer behaviors in HBIgen derivatives, but also the aromatic rule can easily be applied to elaborate the ESIPT reaction.

Ultra-fast prediction of D-π-A organic dye absorption maximum with advanced ensemble deep learning models

The quick and precise estimation of D-π-A Organic Dye absorption maxima in different solvents is an important challenge for the efficient design of novel chemical structures that could improve the performance of dye-sensitized solar cells (DSSCs) and related technologies. Time-Dependent Density Functional Theory (TD-DFT) has often been employed for these predictions, but it has limitations, including high computing costs and functional dependence, particularly for solvent interactions. In this study, we introduce a high-accuracy and rapid deep-learning ensemble method using daylight fingerprints as chemical descriptors to predict the absorption maxima (λmax) of D-π-A organic dyes in 18 different solvent environments. This study introduces a novel approach leveraging advanced ensemble deep learning of 10 models of multiple neural architectures including convolutional networks to demonstrate exceptional predictive power in capturing complex relationships between molecular structures with solvent interaction and absorption maximum. Leveraging a comprehensive range of molecular descriptors from organic dye fingerprints, we developed a highly accurate ensemble model with an R2 of 0.94 and a mean absolute error (MAE) of 8.6 nm, which enhances predictive accuracy and significantly reduces computational time. Additionally, we developed a user-friendly web-based platform that allows for quick prediction of absorption maxima including solvent effect. This tool, which directly uses SMILES representations and advanced deep learning techniques, offers significant potential for accelerating the discovery of efficient dye candidates for various applications, including solar energy, environmental solutions, and medical research. This research opens the door to more effective next-generation dye design, which will facilitate rapid testing in a variety of fields and design an efficient new material.

Excited-state configuration of nitroarenes enables oxidative cleavage of aromatics over alkenes

The ozonolytic deconstruction of aromatics remains a challenge in organic chemistry. Ozone preferentially reacts with alkenes over arenes, meaning that once the initial aromatic cleavage occurs, the dearomatized products are inherently more reactive than the starting materials. Consequently, the process cannot be halted, resulting in full oxidation. Addressing this challenge requires subverting intrinsic rules of chemoselectivity to transform a less reactive substrate in the presence of a more reactive one. We demonstrate that this concept can be achieved by using photoexcited nitroarenes. Crucial to the success of this chemoselective process is the use of a nitroarene that is preferentially excitable to a triplet π,π* state over the n,π* state. This switch in excited-state configuration provides an otherwise inaccessible manifold, in which oxidative cleavage is diverted toward aromatics in the presence of alkenes.

Theoretical study of solvent effects on the white light emission mechanism of single molecule 4-OH-naphthalimide

Organic white light materials fabricated on the basis of single molecules have applied to manufacture the white light-emitting diodes due to their good photostability and relatively simple material preparation. In this work, the different fluorescence emission mechanisms of the NapH1 in n,n-dimethylformamide (DMF) and toluene are investigated to elucidate the process for generating single-molecule near-white-light. From the analysis of bond lengths and electrostatic potential analysis, the intermolecular hydrogen bond can form in DMF instead of in toluene. From the potential energy curves, it is clear that intermolecular proton transfer is not feasible in either DMF or toluene. Frontier molecular orbitals analysis, the dissociation constants and the vertical excitation energies are used to confirm that NapH1 can undergo the deprotonation process in DMF rather than in toluene. Combined with the calculations of the fluorescence values, only the original structure exists stably in toluene which emits blue fluorescence. And the dual fluorescence peaks of NapH1 in DMF are originated from the enol form and the deprotonated form, interacting jointly to emit near-white light. This work contributes to the investigation and advancement for single-molecule organic white luminescent materials.

Overview of Developments in the MRCC Program System

mrcc is a versatile suite of quantum chemistry programs designed for accurate ab initio and density functional theory (DFT) calculations. This contribution outlines the general features and recent developments of the package. The most popular features include the open-ended coupled-cluster (CC) code, state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)], second-order algebraic-diagrammatic construction, and combined wave function theory-DFT approaches. Cost-reduction techniques are implemented, such as natural orbital (NO), local NO (LNO), and natural auxiliary function approximations, which significantly decrease the computational demands of these methods. This paper also details the method developments made over the past five years, including efficient schemes to approach the complete basis set limit for CCSD(T) and the extension of our LNO-CCSD(T) method to open-shell systems. Additionally, we discuss the new approximations introduced to accelerate the self-consistent field procedure and the cost-reduction techniques elaborated for analytic gradient calculations at various levels. Furthermore, embedding techniques and novel range-separated double-hybrid functionals are presented for excited-state calculations, while the extension of the theories established to describe core excitations and ionized states is also discussed. For academic purposes, the program and its source code are available free of charge, and its commercial use is also facilitated.

Energy decomposition analysis for excited states: an extension based on TDDFT

To enhance the understanding of photochemical reactivity and its mechanisms, it is essential to analyze bonding interactions in excited-state reactions. Such insights can aid in optimizing these reactions. This paper presents an energy decomposition analysis method for excited states (exc-EDA), integrating the ground state EDA approach by Morokuma, Ziegler and Rauk with time-dependent density functional theory (TDDFT). The methodology focuses on calculating excitation energies, particularly for the intermediate states of the EDA. We introduce two variants: the first uses non-relaxed excitation coefficients (exc-u-EDA), where the excitation coefficients of the excited fragment are used directly; the second optimizes these coefficients for the intermediate states (exc-r-EDA). Exc-EDA can be applied with various density functionals, but the accuracy depends on the functional's ability to describe the excited state properly. Smaller basis sets result in lower energy values due to fewer virtual orbitals, while larger basis sets produce consistent relative results but may involve different excited states in intermediate steps leading to artificial increase of energy terms in the EDA. The method's convergence behavior resembles that of TDDFT, with a computational cost approximately three times that of the underlying TDDFT calculation. At the current stage, the method requires that the excitation is localized on one of the fragments, but it also enables an analysis of the subsequent charge-transfer effects. Application of exc-EDA to singlet fission in pentacene clusters demonstrates its practical value, offering quantitative insights into excited-state bonding and revealing clear, intuitive trends.

Ensemble Density Functional Theory of Ground and Excited Energy Levels

A Kohn-Sham (KS) density-functional energy expression is derived for any (ground or excited) state within a given many-electron ensemble along with the stationarity condition it fulfills with respect to the ensemble density, thus giving access to both physical energy levels and individual-state densities, in principle exactly. We also provide working equations for the evaluation of the latter from the true static ensemble density-density linear response function. Unlike in Gould's recent ensemble potential functional approach to excited states [arXiv:2404.12593], we use the ensemble density as sole basic variable. While a state-specific KS potential naturally emerges from the present formalism, at the exact ensemble Hartree-exchange-only (Hx) level of approximation, the standard implementation of orbital-optimized density functional theory for excited states is recovered when recycling the regular ground-state Hx-correlation functional in this context.

Capturing the Elusive Curve-Crossing in Low-Lying States of Butadiene with Dressed TDDFT

A striking example of the need to accurately capture states of double-excitation character in molecules is seen in predicting photoinduced dynamics in small polyenes. Due to the coupling of electronic and nuclear motions, the dark 21Ag state, known to have double-excitation character, can be reached after an initial photoexcitation to the bright 11Bu state via crossings of their potential energy surfaces. However, the shapes of the surfaces are so poorly captured by most electronic structure methods, that the crossing is missed or substantially mis-located. We demonstrate that the frequency-dependent kernel of dressed TDDFT beyond Tamm-Dancoff successfully captures the curve-crossing, providing an energy surface close to the highly accurate but more expensive δ-CR-EOMCC(2,3) benchmark reference. This, along with its accurate prediction of the excitation character of the state makes dressed TDDFT a practical and accurate route to electronic structure quantities needed in modeling ultrafast dynamics in molecules.

A Cost-Effective Computational Strategy for the Electronic Layout Characterization of a Second Generation Light-Driven Molecular Rotary Motor in Solution

Light-driven molecular rotary motors are nanometric machines able to convert light into unidirectional motions. Several types of molecular motors have been developed to better respond to light stimuli, opening new avenues for developing smart materials ranging from nanomedicine to robotics. They have great importance in the scientific research across various disciplines, but a detailed comprehension of the underlying ultrafast photophysics immediately after photo-excitation, that is, Franck-Condon region characterization, is not fully achieved yet. For this aim, it is first required to rely on an accurate description at ab initio level of the system in this potential energy region before performing any further step, that is, dynamics. Thus, we present an extensive investigation aimed at accurately describing the electronic structure of low-lying electronic states (electronic layout) of a molecular rotor in the Franck-Condon region, belonging to the class of overcrowded alkenes: 9-(2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-ylidene)-9H-fluorene. This system was chosen since its photophysics is very interesting for a more general understanding of similar compounds used as molecular rotors, where low-lying electronic states can be found (whose energetic interplay is crucial in the dynamics) and where the presence of different substituents can tune the HOMO-LUMO gap. For this scope, we employed different theory levels within the time-dependent density functional theory framework, presenting also a careful comparison adopting very accurate post Hartree-Fock methods and characterizing also the different conformations involved in the photocycle. Effects on the electronic layout of different functionals, basis sets, environment descriptions, and the role of the dispersion correction were all analyzed in detail. In particular, a careful treatment of the solvent effects was here considered in depth, showing how the implicit solvent description can be accurate for excited states in the Franck-Condon region by testing both linear-response and state-specific formalisms. As main results, we chose two cost-effective (accurate but relatively cheap) theory levels for the ground and excited state descriptions, and we also verified how choosing these different levels of theory can influence the curvature of the potential via a frequency analysis of the normal modes of vibrations active in the Raman spectrum. This theoretical survey is a crucial step towards a feasible characterization of the early stage of excited states in solution during photoisomerization processes wherein multiple electronic states might be populated upon the light radiation, leading to a future molecular-level interpretation of time-resolved spectroscopies.

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. II. Density-based methods

In this paper, we demonstrate the performance of several density-based methods in predicting the inversion of S1 and T1 states of a few N-heterocyclic triangulene based fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cost-effective preliminary screening method. Both conventional linear-response time-dependent density functional theory (LR-TDDFT) and ΔSCF methods (namely maximum overlap method, square-gradient minimization method, and restricted open-shell Kohn-Sham) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against fully internally contracted multireference configuration interaction singles and doubles and/or equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the most important feature being the capture of spin-polarization in the presence of correlation. A set of functionals with the least mean absolute error is proposed for both the approaches, LR-TDDFT and ΔSCF, which can be more cost-effective alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the domain-based local pair natural orbital-similarity transformed EOM-CCSD (STEOM-CCSD), which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination, and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models, which identify the minimal physics governing the interactions in these molecules.

Electric Fields in Polymeric Systems

Polymer-based electronic devices are limited by slow transport and recombination of newly separated charges. Built-in electric fields, which arise from compositional gradients, are known to improve charge separation, directional charge transport, and to reduce recombination. Yet, the optimization of these fields through the rational design of polymeric materials is not prevalent. Indeed, polymers are disordered and generate nonuniform electric fields that are hard to measure, and therefore, hard to optimize. Here, we review work focusing on the intentional optimization of electric fields in polymeric systems with applications to catalysis, energy conversion, and storage. This includes chemical tuning of constituent monomers, linkers, morphology, etc. that result in stronger molecular dipoles, polarizability or crystallinity. We also review techniques to characterize electric fields in polymers and emerging processing strategies based on electric fields. These studies demonstrate the benefits of optimizing electric fields in polymers. However, rational design is often restricted to the molecular scale, deriving new pendants on, or linkers between, monomers. This does not always translate in strong electric fields at the polymer level, because they strongly depend on the monomer orientation. A better control of the morphology and monomer-to-polymer scaling relationship is therefore crucial to enhance electric fields in polymeric materials.

Highly Accurate and Robust Constraint-Based Orbital-Optimized Core Excitations

We adapt our recently developed constraint-based orbital-optimized excited-state method (COOX) for the computation of core excitations. COOX is a constrained density functional theory (cDFT) approach based on excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT), and has been shown to provide accurate excitation energies and excited-state properties for valence excitations within a spin-restricted formalism. To extend COOX to core-excited states, we introduce a spin-unrestricted variant which allows us to obtain orbital-optimized core excitations with a single constraint. Using a triplet purification scheme in combination with the constrained unrestricted Hartree-Fock formalism, scalar-relativistic zero-order regular approximation corrections, and a semiempirical treatment of spin-orbit coupling, COOX is shown to produce highly accurate results for K- and L-edge excitations of second- and third-period atoms with subelectronvolt errors despite being based on LR-TDDFT, for which core excitations pose a well-known challenge. L- and M-edge excitations of heavier atoms up to uranium are also computationally feasible and numerically stable, but may require more advanced treatment of relativistic effects. Furthermore, COOX is shown to perform on par with or better than the popular ΔSCF approach while exhibiting more robust convergence, highlighting it as a promising tool for inexpensive and accurate simulations of X-ray absorption spectra.

OpenQP: A Quantum Chemical Platform Featuring MRSF-TDDFT with an Emphasis on Open-Source Ecosystem

The OpenQP (Open Quantum Platform) is a new open-source quantum chemistry library developed to tackle sustainability and interoperability challenges in the field of computational chemistry. OpenQP provides various popular quantum chemical theories as autonomous modules such as energy and gradient calculations of HF, DFT, TDDFT, SF-TDDFT, and MRSF-TDDFT, thereby allowing easy interconnection with third-party software. A scientifically notable feature is the innovative mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) and its customized exchange-correlation functionals such as the DTCAM series of VAEE, XI, XIV, AEE, and VEE, which significantly expand the applicability scope of DFT and TDDFT. OpenQP also supports parallel execution and is optimized with BLAS and LAPACK for high performance. Future enhancements such as extended Koopman's theorem (EKT)-MRSF-TDDFT and spin-orbit coupling (SOC)-MRSF-TDDFT will further expand OpenQP's capabilities. Additionally, a Python wrapper PyOQP is provided that performs tasks such as geometry optimization, conical intersection searches, and nonadiabatic coupling calculations, among others, by prototyping the modules of the OpenQP library in combination with third-party libraries. Overall, OpenQP aligns with modern trends in high-performance scientific software development by offering flexible prototyping and operation while retaining the performance benefits of compiled languages like Fortran and C. They enhance the sustainability and interoperability of quantum chemical software, making OpenQP a crucial platform for accelerating the development of advanced quantum theories like MRSF-TDDFT.

Classification and quantitative characterisation of the excited states of π-conjugated diradicals

Diradicals are of high current interest as emerging materials for next generation optoelectronic applications. To tune their excited-state properties it would be greatly beneficial to have a detailed understanding of the wave functions of the different states involved but this endeavour is hampered by formal and practical barriers. To tackle these challenges, we present a formal analysis as well as concrete results on diradical excited states. We start with a detailed investigation of the available states of a two-orbital two-electron model viewed from both the valence-bond and molecular orbital perspectives. We highlight the presence of diradical and zwitterionic states and illustrate their connections to the states found in closed-shell molecules. Subsequently, we introduce practical protocols for analysing states from realistic multireference computations applying these to the para-quinodimethane (pQDM) molecule. The analysis reveals four different categories of states - diradical, zwitterionic, HOMO-SOMO as well as biexciton - while also providing insight into their energetics and optical properties. Twisting the CH2 groups allows us to interconvert between the closed- and open-shell forms of pQDM illustrating the connection between the states in both forms. More generally, we hope that this work will lay the foundations for a more powerful rational design approach to diradicals for photophysical applications.

UMRSF-TDDFT: Unrestricted Mixed-Reference Spin-Flip-TDDFT

An unrestricted version of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (UMRSF-TDDFT) was developed based on unrestricted Kohn-Sham orbitals (UKS) with a new molecular orbital (MO) reordering scheme. Additionally, a simple yet accurate method for estimating ⟨S2⟩ expectation values was devised. UMRSF-TDDFT was benchmarked against cases where DFT, TDDFT, and SF-TDDFT traditionally fail to provide accurate descriptions. In an application to the ground and excited states of a Be atom, UMRSF-TDDFT successfully recovers the degenerate states, with its energies slightly reduced compared to its RO counterpart, due to the additional variational flexibility of UKS. A clear difference between UMRSF and U-SF-TDDFT is evident in the bond breaking of the hydrogen fluoride system, as the latter misses an important configuration. In the case of the Jahn-Teller distortion of trimethylenemethane (TMM), the relative singlet energy compared to the triplet is lower by 0.1 and 0.2 eV for UMRSF and U-SF-TDDFT, respectively, than that of MRSF-TDDFT. The reduction in UMRSF energy is attributed to spatial orbital relaxations, whereas the reduction in U-SF-TDDFT energy results from spin contamination. Overall, the additional orbital relaxations afforded by unrestricted Kohn-Sham (UKS) orbitals in UMRSF-TDDFT lead to lower total system energies compared to their restricted open-shell counterparts. This enhancement adds a practical and accurate quantum chemical theory to the existing RO variant for addressing challenging systems where traditional quantum theories suffer.

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.

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.

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).

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.

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.

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.