Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

Localized Orbital Scaling Correction to Linear-Response Time-Dependent Density Functional Approximations

The localized orbital scaling correction (LOSC) method, which was developed for eliminating the delocalization error in density functional approximations (DFAs), is extended to the linear-response regime for calculating excitation energies with time-dependent density functional theory (TDDFT). Corrections to the exchange-correlation kernel are derived within the frozen-orbitalet approximation. Extensive numerical tests on various data sets show that LOSC-DFAs are able to maintain the good performance of parent DFAs for valence excitations while systematically improving the excitation energies for Rydberg and charge-transfer excitations by reducing the delocalization error. For charge-transfer excitations, LOSC can produce correct asymptotic behaviors with the donor-acceptor separation R as well as the excitation energy at the infinite separation limit. Moreover, through the example of trans-polyacetylene oligomers, we demonstrate that the performance of LOSC does not deteriorate with increasing system size, holding promise for application in bulk systems.

Hybrid Functional DFTB Parametrizations for Modeling Organic Photovoltaic Systems

Density functional tight binding (DFTB) is a quantum chemical simulation method based on an approximate density functional theory (DFT), known for its low computational cost and comparable accuracy to DFT. For several years, the application of DFTB in organic photovoltaics (OPV) has been limited by the absence of an appropriate set of parameters that adequately account for the relevant elements and necessary corrections. Here we have developed new parametrizations using hybrid functionals, including B3LYP and CAM-B3LYP, for OPV applications within the DFTB method in order to overcome the self-interaction error present in DFT functionals lacking long-range correction. These parametrizations encompass electronic and repulsive parameters for the elements H, C, N, O, F, S, and Cl. A Bayesian optimization approach was employed to optimize the free atom eigenenergies of unoccupied shells. The effectiveness of these new parametrizations was evaluated by a data set of 12 OPV donor and acceptor molecules, showing consistent performance when compared with their corresponding DFT references. Frontier molecular orbitals and optimized geometries were examined to evaluate the performance of the new parametrizations in predicting ground-state properties. Furthermore, the excited-state properties of monomers and dimers were investigated by means of real-time time-dependent DFTB (real-time TD-DFTB). The appearance of charge-transfer (CT) excitations in the dimers was observed, and the influence of alkyl side-chains on the photoinduced CT process was explored. This work paves the way for studying ground- and excited-state properties, including band alignments and CT mechanisms at donor-acceptor interfaces, in realistic OPV systems.

Signature of electronically excited states in Raman spectra of azobenzene derivatives. Computational and experimental approaches

Raman spectroscopy can provide highly sensitive and detailed information about the structural fingerprint of molecules, enabling their identification. In this study, our aim is to understand the enhanced intensity observed in experimental Raman measurements. Five azobenzene derivatives were selected, each substituted with different functional groups, for both experimental and theoretical investigations. To reproduce the experimental trend, we employed various levels of theory using the QM-DFT approach. Theoretical results were compared to experimental data through both qualitative and quantitative analyses. A good correlation between theoretical and experimental results was achieved when considering electronic transitions to predict the theoretical Raman spectra and interpret the experimental data. Our theoretical results indicate that even dark (nπ*) transitions, which are forbidden and have an oscillator strength close to zero, can have a signature in the Raman spectra due to the resonance effect with incident energy. Additionally, the vibrational modes stimulated by the presence of ππ* bright states, being at the pre-resonance with the incident energy, was clearly separated from the vibrational frequencies of the dark states, which was evinced in the Raman fingerprint. Theoretical Raman spectra of azobenzene derivatives, substituted with push-pull moieties, revealed contributions from the charge transfer transitions (nπ*CT, ππ*CT) as well as back-donation of electron density, observed for the first time in an azobenzene derivative. Our protocol, proposing a quantitative and qualitative overlap between theoretical and experimental data, confirms the presence of combination modes between vibrational levels and electronically excited states.

Simplified Tuning of Long-Range Corrected Time-Dependent Density Functional Theory

Range-separated hybrid functionals have dramatically improved the description of charge-transfer excitations in time-dependent density functional theory (TD-DFT), especially when the range-separation parameter is adjusted in order to satisfy the ionization energy (IE) criterion, εHOMO = -IE. However, this "optimal tuning" procedure is molecule-specific, inconvenient, expensive for large systems, and problematic in extended or periodic systems. Here, we consider an alternative procedure known as global density-dependent (GDD) tuning, which sets the range-separation parameter in an automated way based on properties of the exchange hole. In small molecules, we find that long-range corrected functionals with either IE or GDD tuning afford remarkably similar TD-DFT excitation energies, for both valence and charge-transfer excitations. However, GDD tuning is more efficient and is well-behaved even for large systems. It provides a black-box solution to the optimal-tuning problem that can replace IE tuning for many applications of TD-DFT.

Assessment of Charge Transfer Energies of Noncovalently Bounded Ar-TCNE Complexes Using Range-Separated Density Functionals and Double-hybrid Density Functionals

Charge Transfer (CT) molecular complexes have recently received much attention in a broad variety of fields. The time-dependent density functional theory (TDDFT), which is essential for studying CT complexes, is a well-established tool to study the excited states of relatively large molecular systems. However, when dealing with donor-acceptor molecules with CT characteristics, TDDFT calculations based on standard functionals can severely underestimate the excitation energies. The TDDFT methodology, combined with range-separated DFT and range-separated double-hybrid DFT functionals, had previously been used by different research groups to reliably predict the excitation energies of different charge transfer molecular complexes. We follow the same path to calculate the excited state charge transfer energy of some selected molecular complexes, such as, Ar-TCNE (TCNE=tetracyanoethylene; Ar= benzene, naphthalene, anthracene, etc.). The interactions between the donor-acceptor moieties of these molecular complexes are also studied and the relationship between the interaction and the charge transfer energies are shown here.

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.

Reply to the 'Comment on "Designing potentially singlet fission materials with an anti-Kasha behaviour"' by K. Jindal, A. Majumdar and R. Ramakrishnan, Phys. Chem. Chem. Phys., 2025, , DOI: 10.1039/D4CP02863E

In this reply to the preceding paper by K. Jindal, A. Majumdar, and R. Ramakrishnan, we argue that the results obtained in our original manuscript with the time-dependent density functional theory (TD-DFT) are reasonable and that they are not only in agreement with experimental results but also with reliable ab initio calculations.

Review on the DFT computation of bulk heterojunction and dye-sensitized organic solar cell properties

CONTEXT

Organic solar cells (OSCs) represent a promising renewable energy technology due to their flexibility, low production cost, and environmental sustainability. To advance OSC efficiency and stability, density functional theory (DFT) has emerged as a powerful computational tool, enabling the prediction and optimization of critical properties at the molecular and device levels. This review highlights the key properties of bulk heterojunction solar (BHJ) solar cells and dye-sensitized solar cells (DSSCs) that can be accurately computed using DFT, including electronic structure properties (HOMO-LUMO energy levels, bandgap energies, and exciton binding energies, which influence charge separation and transport); optical properties (absorption spectra and light-harvesting efficiency, essential for maximizing photon capture); charge transport properties (reorganization energies, electron, and hole mobilities, and charge transfer rates that govern carrier dynamics within devices); interfacial properties (energy alignment at donor-acceptor interfaces, contributing to efficient charge separation and minimizing recombination); and chemical reactivity descriptors (ionization potential, electron affinity, chemical hardness, and electrophilicity, which facilitate material screening for OSC applications). We also show how to compute OSCs' power conversion efficiency (PCE) from DFT.

METHODS

The review also discusses the importance of selecting appropriate exchange-correlation functionals and basis sets to ensure the accuracy of DFT predictions. By providing reliable computational insights, DFT accelerates the rational design of OSC materials, guides experimental efforts, and reduces resource demands. This work underscores DFT's pivotal role in optimizing OSC performance and fostering the development of next-generation photovoltaic technologies.

Insight into the Excited States in Monomers and π-Stacked Dimers of Azulene-Fused Acenes: ADC(2) and TD-DFT Studies

Charge transfer (CT) states in polycyclic aromatic hydrocarbons play crucial roles in determining their electronic properties and their potential applications in organic electronics. In this work, we investigate the nature of the excited states in monomers and π-stacked dimers of azulene-fused naphthalene and anthracene systems, focusing on the interplay between structure and excited-state properties. Four different isomers for azulene-fused naphthalene (NapAz-A, NapAz-B, NapAz-C, and NapAz-D) and anthracene (AntAz-A, AntAz-B, AntAz-C, and AntAz-D) are considered. The excited-state studies are performed at the SCS-ADC(2) level and at the TD-DFT level using CAM-B3LYP, SCS-ωB2GP-PLYP, and SCS-RSX-QIDH functionals. For the monomers, the SCS-ADC(2) results reveal that states with CT characters are different in naphthalene- and anthracene-based systems. In π-stacked dimers, a few of the excited states are of the charge resonance (CR) type in NapAz-A, NapAz-B, and NapAz-C and the intermolecular CT type in NapAz-D. Similarly, AntAz-A, AntAz-B, and AntAz-D have some CR type excited states, whereas the AntAz-C isomer has intramolecular CT type excited states. Overall, among the three DFT functionals considered, CAM-B3LYP has been found to reproduce well the SCS-ADC(2) excited results in both monomers and π-stacked dimers.

Probing the Design Rules for Optimizing Electron Spin Relaxation in Densely Packed Triplet Media for Quantum Applications

Quantum technologies using electron spins have the advantage of employing chemical qubit media with tunable properties. The principal objective of material engineers is to enhance photoexcited spin yields and quantum spin relaxation. In this study, we demonstrate a facile synthetic approach to control spin properties in charge-transfer cocrystals consisting of 1,2,4,5-tetracyanobenzene (TCNB) and acetylated anthracene. We find that the extent and position of acetylation control the degree of charge-transfer and the optical band gap by modifying crystal packing and electronic structure. We further reveal that while the spin polarization of the triplet state is slightly reduced compared to prototypical Anthracene:TCNB, the phase memory (T m) and, for 9-acetylanthracene:TCNB spin-lattice relaxation (T 1) time, could be enhanced up to 2.4 times. Our findings are discussed in the context of quantum microwave amplifiers, known as masers, and show that acetylation could be a powerful tool for improving organic materials for quantum sensing applications.

Does the Traditional Band Picture Correctly Describe the Electronic Structure of n-Doped Conjugated Polymers? A TD-DFT and Natural Transition Orbital Study

Doped conjugated polymers have a variety of potential applications in thermoelectric and other electronic devices, but the nature of their electronic structure is still not well understood. In this work, we use time-dependent density functional theory (TD-DFT) calculations along with natural transition orbital (NTO) analysis to understand electronic structures of both p-type (e.g., poly(3-hexylthiophene-2,5-diyl), P3HT) and n-type (e.g., poly{[N,N'-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,5'-(2,2'-bithiophene)}, N2200) conjugated polymers that are both p-doped and n-doped. Of course, the electronic transitions of doped conjugated polymers are multiconfigurational in nature, but it is still useful to have a one-electron energy level diagram with which to interpret their spectroscopy and other electronic behaviors. Based on the NTOs associated with the TD-DFT transitions, we find that the "best" one-electron orbital-based energy level diagram for doped conjugated polymers such as P3HT is the so-called traditional band picture. We also find that the situation is more complicated for donor-acceptor-type polymers like N2200, where the use of different exchange-correlation functionals leads to different predicted optical transitions that have significantly less one-electron character. For some functionals, we still find that the "best" one-electron energy level diagram agrees with the traditional picture, but for others, there is no obvious route to reducing the multiconfigurational transitions to a one-electron energy level diagram. We also see that the presence of both electron-rich and electron-poor subunits on N2200 breaks the symmetry between n- and p-doping, because different types of polarons reside on different subunits leading to different degrees of charge delocalization. This effect is exaggerated by the presence of dopant counterions, which interact differently with n- and p-polarons. Despite these complications, we argue that the traditional band picture suffices if one wishes to employ a simple one-electron picture to explain the spectroscopy of n- and p-doped conjugated polymers.

Importance of Orbital Invariance in Quantifying Electron-Hole Separation and Exciton Size

A fundamental tenet of quantum mechanics is that properties should be independent of representation. In self-consistent field methods such as density functional theory, this manifests as a requirement that properties be invariant with respect to unitary transformations of the occupied molecular orbitals and (separately) the unoccupied molecular orbitals. Various ad hoc measures of excited-state charge separation that are commonly used to analyze time-dependent density-functional calculations violate this requirement, as they are based on incoherent averages of excitation amplitudes rather than expectation values involving coherent superpositions. As a result, these metrics afford markedly different values in various common representations, including canonical molecular orbitals, Boys-localized orbitals, and natural orbitals. Numerical values can be unstable with respect to basis-set expansion and may afford nonsensical results in the presence of extremely diffuse basis functions. In contrast, metrics based on well-defined expectation values are stable, representation-invariant, and physically interpretable. Use of natural transition orbitals improves the stability of the incoherent averages, but numerical values can only be interpreted as expectation value in the absence of superposition. To satisfy this condition, the particle and hole density matrices must each be dominated by a single eigenvector so that the transition density is well described by a single pair of natural transition orbitals. Counterexamples are readily found where this is not the case. Our results suggest that ad hoc charge-transfer diagnostics should be replaced by rigorous expectation values, which are no more expensive to compute.

A Critical Evaluation of the Hybrid KS DFT Functionals Based on the KS Exchange-Correlation Potentials

We have developed a critical methodology for the evaluation of the quality of hybrid exchange-correlation (XC) density functional approximations (DFAs) based on very fundamental quantities, i.e., Kohn-Sham (KS) XC potentials, self-consistent electron densities, first ionization potentials (IPs), and total energies. Since the XC potentials, the primary objects in the current study, are not directly accessible for the hybrids, we calculate them by inverting the KS electron densities. Utilizing this methodology, we tested 155 hybrid DFAs available in the LIBXC library using FCI and CCSD(T) methods as a reference. We have found that a group of functionals produces very decent XC potentials, mainly those with a large mixture of Hartree-Fock exchange. Moreover, the value of IP strongly depends on the XC potential quality. On the other hand, we show that the XC energy is dominated by functional-driven error, which in some cases leads to substantial errors in electronic densities. The study shows new directions for constructing more accurate XC functionals within the KS-DFT framework.

Unveiling the impact of enhanced hydrophobicity of ZIF-71 on butanol purification: insights from experimental and molecular simulations

Biofuels offer significant potential for reducing carbon emissions and enhancing energy sustainability, but their efficient purification remains a significant challenge. In this study, the performance of a hydrophobic zeolitic imidazolate framework, ZIF-71(ClBr)-SE, in the adsorptive separation of butanol from single- and ternary-component systems (acetone, butanol, and ethanol) was investigated and compared with ZIF-8 and ZIF-71. Physicochemical characterization techniques, including XRD, SEM, BET, TGA, and DVS, confirmed that the modified ZIF-71 is hydrophobic, isostructural with ZIF-71, and has a higher surface area. Adsorption tests in aqueous solutions revealed that ZIF-71(ClBr)-SE unexpectedly showed a higher affinity for acetone over butanol. DFT molecular simulations provided insights into solute-ZIF interactions, highlighting preferential sites for ZIF interaction.

Optimal-tuning of range-separated density functionals to describe the optical and photophysical properties of rhodamine B dimers

Setting up computational approaches enabling the correct prediction of the photophysical properties of rhodamine B (RB) derivatives and their aggregates (referred to as dimers here) is of fundamental importance to rationally drive the design of novel systems of applicative relevance, such as artificial light-harvesting nanosystems. Currently, approaches rooted in time-dependent density functional theory (TD-DFT), which are appealing for their relatively low computational cost, nonetheless have limitations in terms of accuracy, especially while considering RB dimeric species. In this work, we investigated the performances of optimally tuned range-separated hybrid functionals for describing the excited states of RB and its H dimer, focusing on dimeric charge-transfer (CT) states. We compared different optimal-tuning (OT) procedures including or not solvent screening. The results show that the properties of CT states, such as their CT extent, brightness and relative energy ordering, are crucially affected by the Hartree-Fock exchange amount dictated by OT, which is in turn driven by the chosen asymptotic behavior. Finally, to understand the dissimilar pictures provided for the CT states by different tuning approaches, we performed an extensive analysis aimed at elucidating how CT states are affected by range-separation parameters. As a result, a simple procedure is finally provided for easily achieving a unique functional to be applied on both monomer and dimers, its current limitations are highlighted and possible perspectives for future development are envisaged.

Structural Fine-Tuning to Achieve Highly Fluorescent Organic and Water-Soluble Thiazolo[5,4-d]thiazole Chromophores

Fluorescent molecular systems are important for various applications such as sensing of analytes, probes for biologically relevant processes and as optoelectronic materials. Achieving high fluorescence quantum yield across the spectrum of solvent polarity and in solid-state is challenging in molecular materials. Herein, we present a strategy to achieve strongly fluorescent molecular materials based on weak intramolecular charge-transfer (ICT) in a family of unsymmetrical donor-thiazolo[5,4-d]thiazole-acceptor systems (both neutral and cationic). Detailed photophysical studies reveal that the delicate balance between the donor and acceptor result in high solution-state fluorescence quantum yield (>80 %) in both polar protic and apolar solvents. Quantum chemical computations uncover a hitherto unappreciated insight that the extent of ICT is aptly represented by the change in Mulliken charges between the ground and excited state for different fragments rather than the classical approach of monitoring the change in dipole moment for the entire molecule. This insight rationalizes the observed photophysical properties and can have implications in the design of tuneable donor-π-acceptor systems.

Influence of Substituents on the Vectorial Difference Static Dipole Upon Excitation in Synthetic Bacteriochlorins

Organic dye aggregates have been shown to exhibit exciton delocalization in natural and synthetic systems. Such dye aggregates show promise in the emerging area of quantum information science (QIS). We believe that the difference in static dipole (Δd) is an essential dye parameter in the development of molecular QIS systems. However, a foundational understanding of the structural factors influencing Δd remains elusive. Bacteriochlorins play a vital role in photosynthesis due to their exceptional photophysical properties. Therefore, bacteriochlorins are particularly suitable dyes for the construction of aggregate systems for QIS. Synthetic bacteriochlorins further offer stability and tunability via chemical modifications. Here, the influence of substituents on the Δd of monomeric (nonaggregated) dyes was investigated via density functional theory (DFT) and time-dependent (TD)DFT in a set of 5-methoxybacteriochlorins progressively substituted with ethynyl, phenyl, and phenylethynyl substituents at the 3,13 and 3,13,15 positions of the macrocycle. Symmetrically substituted 5-methoxybacteriochlorins were shown to have the largest Δd. The increase in Δd in the series of dyes was largely due to changes in the orientation of the static dipole upon excitation rather than large changes in magnitude. In addition, the transition dipole (μ) and the angle between Δd and μ (ζ) were calculated. Three 5-methoxybacteriochlorins with large predicted Δd and μ values were synthesized and characterized spectroscopically. The trend in Δd values empirically determined using the solvatochromic Stokes shift method was comparable to the DFT calculations.

Molecular interactions of photosystem I and ZIF-8 in bio-nanohybrid materials

Bio-nanohybrid devices featuring natural photocatalysts bound to a nanostructure hold great promise in the search for sustainable energy conversion. One of the major challenges of integrating biological systems is protecting them against harsh environmental conditions while retaining, or ideally enhancing their photophysical properties. In this mainly computational work we investigate an assembly of cyanobacterial photosystem I (PS I) embedded in a metal-organic framework (MOF), namely the zeolitic imidazolate framework ZIF-8. This complex has been reported experimentally [Bennett et al., Nanoscale Adv., 2019, 1, 94] but so far the molecular interactions between PS I and the MOF remained elusive. We show via absorption spectroscopy that PS I remains intact throughout the encapsulation-release cycle. Molecular dynamics (MD) simulations further confirm that the encapsulation has no noticeable structural impact on the photosystem. However, the MOF building blocks frequently coordinate to the Mg2+ ions of chlorophylls in the periphery of the antenna complex. High-level quantum mechanical calculations reveal charge-transfer interactions, which affect the excitonic network and thereby may reversibly change the fluorescence properties of PS I. Nevertheless, our results highlight the stability of PS I in the MOF, as the reaction center remains unimpeded by the heterogeneous environment, paving the way for applications in the foreseeable future.

Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations

Intermolecular charge-transfer is a highly important process in biology and energy-conversion applications where generated charges need to be transported over several moieties. However, its theoretical description is challenging since the high accuracy required to describe these excited states must be accessible for calculations on large molecular systems. In this benchmark study, we identify reliable low-scaling computational methods for this task. Our reference results were obtained from highly accurate wavefunction calculations that restrict the size of the benchmark systems. However, the density-functional theory based methods that we identify as accurate can be applied to much larger systems. Since targeting charge-transfer states requires the unambiguous classification of an excited state, we first analyze several charge-transfer descriptors for their reliability concerning intermolecular charge-transfer and single out the charge-transfer distance calculated based on the variation of electron density upon excitation (DCT) as an optimal choice for our purposes. In general, best results are obtained for orbital-optimized methods and among those, the maximum overlap method proved to be the most numerically stable variant when using the initial MOs as reference orbitals. Favorable error cancellation with optimally-tuned range-separated hybrid functionals and a rather small basis set can provide an economical yet reasonable wavefunction when using time-dependent density functional theory, which provides relevant information about the excited-state character to be used in the orbital-optimized methods. The qualitative agreement makes these fast calculations attractive for high-throughput screening applications.

Fluorescence quenching of deprotonated phenylurea through twisting motion induced by an electron-donating substituent group

The excited-state proton transfer (ESPT) reaction between anthracen-2-yl-3-phenylurea (PUA) derivatives and tetrabutylammonium acetate (TBAAc) in dimethyl sulfoxide (DMSO) solvent was theoretically investigated using time-dependent density functional theory. The electron-donating methoxy group (OMe) and electron-withdrawing trifluoromethyl group (CF3) were bonded to 2PUA to form OMe-2PUA and CF3-2PUA, respectively. Two hydrogen bonds formed in the 1 : 1 hydrogen-bonded complexes between the 2PUA derivative and acetate ion (AcO-), namely N1-H1⋯O1 and N2-H2⋯O2. Strong charge transfer (CT) due to the electron-donating OMe group led to H1 transfer in the S1 state for the OMe-2PUA:AcO- hydrogen-bonded complex. On the contrary, weak CT due to the electron-withdrawing CF3 group led to H2 transfer in the S1 state for CF3-2PUA. After the ESPT reaction, the binding energies of the hydrogen-bonded complexes strongly decreased in both cases, and this promoted the separation of contact-ion pairs (CIPs*) and formed different types of anionic species. CF3-2PUA- could keep its nearly planar structure in the S1 state and emit "abnormal" fluorescence. On the other hand, the anionic OMe-2PUA- underwent a twisting motion to form a twisted structure in the S1 state with very low energy, and this led to a rapid internal conversion (IC) to quench long-wave fluorescence in the emission spectra.

Benchmarking Charge-Transfer Excited States in TADF Emitters: ΔDFT Outperforms TD-DFT for Emission Energies

Charge-transfer (CT) excited states are crucial to organic light-emitting diodes (OLEDs), particularly to those based on thermally activated delayed fluorescence (TADF). However, accurately modeling CT states remains challenging, even with modern implementations of (time-dependent) density functional theory [(TD-)DFT], especially in a dielectric environment. To identify shortcomings and improve the methodology, we previously established the STGABS27 benchmark set with highly accurate experimental references for the adiabatic energy gap between the lowest singlet and triplet excited states (ΔEST). Here, we diversify this set to the STGABS27-EMS benchmark by including experimental emission energies (Eem) and use this new set to (re)-evaluate various DFT-based approaches. Surprisingly, these tests demonstrate that a state-specific (un)restricted open-shell Kohn-Sham (U/ROKS) DFT coupled with a polarizable continuum model for perturbative state-specific nonequilibrium solvation (ptSS-PCM) provides exceptional accuracy for predicting Eem over a wide range of density functionals. In contrast, the main workhorse of the field, Tamm-Dancoff-approximated TD-DFT (TDA-DFT) paired with the same ptSS-PCM, is distinctly less accurate and strongly functional-dependent. More importantly, while TDA-DFT requires the choice of two very different density functionals for good performance on either ΔEST or Eem, the time-independent U/ROKS/PCM approaches deliver excellent accuracy for both quantities with a wide variety of functionals.

Exploiting Mixed Valence Charge Transfer for Electrochromic and Electrofluorochromic Use

An asymmetric mixed valence fluorophore with two different electron rich termini was investigated as a dual-role active material for electrochromism and electrofluorochromism. The fluorescence quantum yield (Φfl) and emission wavelength of the fluorophore were dependent on solvent polarity. The quantum yield of the material in an electrolyte gel, on a glass substrate and in a device was 40 %, 20 % and 13 % respectively. The fluorophore further underwent two near-simultaneous electrochemical oxidations. The first oxidation resulted in a 1000 nm red shift in the absorption to broadly absorb in the NIR, corresponding to the intervalence charge transfer (IVCT). Whereas the second oxidation led to a perceived green color at 715 nm with the extinction of the NIR absorbing IVCT. Owing to the dissymmetry of the fluorophore along with its two unique oxidation sites, the IVCT gives rise to a mixed valence transfer charge (MVCT). The coloration efficiency of the fluorophore in both solution and a device was 1433 and 200 cm2 C-1, respectively. The fluorescence intensity could be reversibly modulated electrochemically. The photoemission intensity of the fluorophore was modulated with applied potential in an operating electrochromic/electrofluorochromic device. Both the dual electrochromic and the electrofluorochromic behavior of the fluorophore were demonstrated.

BSE@GW Prediction of Charge Transfer Exciton in Molecular Complexes: Assessment of Self-Energy and Exchange-Correlation Dependence

The Bethe-Salpeter equation using the GW approximation to the self-energy (BSE@GW) is a computationally attractive method for studying electronic excitation from first principles within the many-body Green's function theory framework. We examine its dependence on the underlying exchange-correlation (XC) approximation as well as on the GW approximation for predicting the charge transfer exciton formation at representative type-II interfaces between molecular systems of tetrachloro-1,2-benzoquinone (TCBQ) and acene derivatives. For the XC approximation, we consider several widely used generalized gradient approximation (GGA) and hybrid GGA functionals. For the GW self-energy approximation, we examine the recently proposed renormalized singles approach by Yang and coauthors [J. Phys. Chem. Lett. 2019, 10 (3), 447-452; J. Chem. Theory Comput. 2022, 18, 7570-7585] in addition to other commonly employed approximated GW schemes. We demonstrate a reliable prediction of the charge transfer exciton within the BSE@GW level of theory.

How do spin-scaled double hybrids designed for excitation energies perform for noncovalent excited-state interactions? An investigation on aromatic excimer models

Time-dependent double hybrids with spin-component or spin-opposite scaling to their second-order perturbative correlation correction have demonstrated competitive robustness in the computation of electronic excitation energies. Some of the most robust are those recently published by our group (M. Casanova-Páez, L. Goerigk, J. Chem. Theory Comput. 2021, 20, 5165). So far, the implementation of these functionals has not allowed correctly calculating their ground-state total energies. Herein, we define their correct spin-scaled ground-state energy expressions which enables us to test our methods on the noncovalent excited-state interaction energies of four aromatic excimers. A range of 22 double hybrids with and without spin scaling are compared to the reasonably accurate wavefunction reference from our previous work (A. C. Hancock, L. Goerigk, RSC Adv. 2023, 13, 35964). The impact of spin scaling is highly dependent on the underlying functional expression, however, the smallest overall errors belong to spin-scaled functionals with range separation: SCS- and SOS- ω PBEPP86, and SCS-RSX-QIDH. We additionally determine parameters for DFT-D3(BJ)/D4 ground-state dispersion corrections of these functionals, which reduce errors in most cases. We highlight the necessity of dispersion corrections for even the most robust TD-DFT methods but also point out that ground-state based corrections are insufficient to completely capture dispersion effects for excited-state interaction energies.

Cobalt-Mediated Photochemical C-H Arylation of Pyrroles

Precious metal complexes remain ubiquitous in photoredox catalysis (PRC) despite concerted efforts to find more earth-abundant catalysts and replacements based on 3d metals in particular. Most otherwise plausible 3d metal complexes are assumed to be unsuitable due to short-lived excited states, which has led researchers to prioritize the pursuit of longer excited-state lifetimes through careful molecular design. However, we report herein that the C-H arylation of pyrroles and related substrates (which are benchmark reactions for assessing the efficacy of photoredox catalysts) can be achieved using a simple and readily accessible octahedral bis(diiminopyridine) cobalt complex, [1-Co](PF6)2. Notably, [1-Co]2+ efficiently functionalizes both chloro- and bromoarene substrates despite the short excited-state lifetime of the key photoexcited intermediate *[1-Co]2+ (8 ps). We present herein the scope of this C-H arylation protocol and provide mechanistic insights derived from detailed spectroscopic and computational studies. These indicate that, despite its transient existence, reduction of *[1-Co]2+ is facilitated via pre-assembly with the NEt3 reductant, highlighting an alternative strategy for the future development of 3d metal-catalyzed PRC.

Ab initio investigation of excited state charge transfer pathways in differently capped bithiophene cages

The electronic excitations of conformationally constrained bithiophene cage systems as previously investigated by Lewis et al. (J. Am. Chem. Soc. 143, 18548 (2021)) are revisited, employing the correlated ab initio Scaled Opposite-Spin Algebraic Diagrammatic Construction Second Order electronic structure method. Quantitative descriptors are determined to assess the extent of charge transfer between the bithiophene moieties and the capping domains, represented by either phenyl or triazine groups. The investigation substantiates intrinsic differences in the photophysical behavior of these two structural variants and reveals the presence of lower-energy excited states characterized by noteworthy charge transfer contributions in the triazine cage system. The manifestation of this charge transfer character is discernible even at the Franck-Condon geometry, persisting throughout the relaxation of the excited state. By examining isolated monomer building blocks, we confirm the existence of analogous charge transfer contributions in their excitations. Employing this methodological approach facilitates the prospective identification of potential wall/cap chromophore pairs, wherein charge transfer pathways can be accessed within the energetically favorable regime.

Theoretical insights into dopamine photochemistry adsorbed on graphene-type nanostructures

The equilibrium geometry structures and light absorption properties of the dopamine (DA) and dopamine-o-quinone (DAQ) adsorbed on the graphene surface have been investigated using the ground state and linear-response time-dependent density functional theories. Two types of graphene systems were considered, a rectangular form of hexagonal lattice with optimized C-C bond length as the model system for graphene nanoparticles (GrNP) and a similar system but with fixed C-C bond length (1.42 Å) as the model system for graphene 2D sheet (GrS). The analysis of the vertical excitations showed that three types of electronic transitions are possible, namely, localized on graphene, localized on the DA or DAQ, and charge transfer (CT). In the case of the graphene-DA complex, the charge transfer excitations were characterized by the molecule-to-surface (MSCT) character, whereas the graphene-DAQ was characterized by the reverse, i.e. surface-to-molecule (SMCT). The difference between the two cases is given by the presence of an energetically low-lying unoccupied orbital (LUMO+1) that allows charge transfer from the surface to the molecule in the case of DAQ. However, it was also shown that the fingerprints of excited electronic states associated with the adsorbed molecules cannot be seen in the spectrum, as they are mostly suppressed by the characteristic spectral shape of graphene.

Determining Excited-State Absorption Properties of a Quinoid Flavin by Polarization-Resolved Transient Spectroscopy

As important naturally occurring chromophores, photophysical/chemical properties of quinoid flavins have been extensively studied both experimentally and theoretically. However, little is known about the transition dipole moment (TDM) orientation of excited-state absorption transitions of these important compounds. This aspect is of high interest in the fields of photocatalysis and quantum control studies. In this work, we employ polarization-associated spectra (PAS) to study the excited-state absorption transitions and the underlying TDM directions of a standard quinoid flavin compound. As compared to transient absorption anisotropy (TAA), an analysis based on PAS not only avoids diverging signals but also retrieves the relative angle for ESA transitions with respect to known TDM directions. Quantum chemical calculations of excited-state properties lead to good agreement with TA signals measured in magic angle configuration. Only when comparing experiment and theory for TAA spectra and PAS, do we find deviations when and only when the S0 → S1 of flavin is used as a reference. We attribute this to the vibronic coupling of this transition to a dark state. This effect is only observed in the employed polarization-controlled spectroscopy and would have gone unnoticed in conventional TA.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

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.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

A step toward density benchmarking-The energy-relevant "mean field error"

Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that are precise enough to be predictive in many instances, as validated by large- and small-scale benchmarking efforts. However, assessing the quality of densities has been the subject of far less attention, in part because reliable error measures are difficult to define. To this end, this work introduces the mean-field error, which directly assesses the quality of densities from approximations. The mean-field error is contextualized within existing frameworks of density functional error analysis and understanding and shown to be part of the density-driven error. It is demonstrated in several illustrative examples. Its potential use in future benchmarking protocols is discussed, and some conclusions are drawn.

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.

Earth Mover's Distance as a Metric to Evaluate the Extent of Charge Transfer in Excitations Using Discretized Real-Space Densities

This paper presents a novel theoretical measure, μEMD, based on the earth mover's distance (EMD), for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized ground- and excited-state electron densities in real space, rendering it compatible with almost all electronic structure methods used to calculate excited states. The EMD metric is compared against other popular theoretical metrics for describing the extent of electron-hole separation in a wide range of excited states (valence, Rydberg, charge transfer, etc.). The results showcase the EMD metric's effectiveness across all excitation types and suggest that it is useful as an additional tool to characterize electronic excitations. The study also reveals that μEMD can function as a promising diagnostic tool for predicting the failure of pure exchange-correlation functionals. Specifically, we show statistical relationships among the functional-driven errors, the exact exchange content within the functional, and the magnitude of μEMD values.

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.

Recent Advances in Real-Time Time-Dependent Density Functional Theory Simulations of Plasmonic Nanostructures and Plasmonic Photocatalysis

Plasmonic catalysis provides a possible means for driving chemical reactions under relatively mild conditions. Rational design of these systems is impeded by the difficulty in understanding the electron dynamics and their interplay with reactions. Real-time, time-dependent density functional theory (RT-TDDFT) can provide dynamic information on excited states in plasmonic systems, including those relevant to plasmonic catalysis, at time scales and length scales that are otherwise out of reach of many experimental techniques. Here, we discuss previous RT-TDDFT studies of plasmonic systems, focusing on recent work that gains insight into plasmonic catalysis. These studies provide insight into plasmon dynamics, including size effects and the role of specific electronic states. Further, these studies provide significant insight into mechanisms underlying plasmonic catalysis, showing the importance of charge transfer between metal and adsorbate states, as well as local field enhancement, in different systems.

Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i) A linearized scheme of the quadratic equation used to determine the cluster amplitudes. ii) The effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods.

Excitation energies of polycylic aromatic hydrocarbons by double-hybrid functionals: Assessing the PBE0-DH and PBE-QIDH models and their range-separated versions

A family of non-empirical double-hybrid (DH) density functionals, such as Perdew-Burke-Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet ¹L_a and ¹L_b states of linear oligoacenes as well as the triplet ³L_a and ³L_b states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S₀-T₁ singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive results.

Building on the strengths of a double-hybrid density functional for excitation energies and inverted singlet-triplet energy gaps

It is demonstrated that a double hybrid density functional approximation, ωB88PTPSS, that incorporates equipartition of density functional theory and the non-local correlation, however with a meta-generalized gradient approximation correlation functional, as well as with the range-separated exchange of ωB2PLYP, provides accurate excitation energies for conventional systems, as well as correct prescription of negative singlet-triplet gaps for non-conventional systems with inverted gaps, without any necessity for parametric scaling of the same-spin and opposite-spin non-local correlation energies. Examined over "safe" excitations of the QUESTDB set, ωB88PTPSS performs quite well for open-shell systems, correctly and fairly accurately [relative to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) reference] predicts negative gaps for 50 systems with inverted singlet-triplet gaps, and is one of the leading performers for intramolecular charge-transfer excitations and achieves near-second-order approximate coupled cluster (CC2) and second-order algebraic diagrammatic construction quality for the Q1 and Q2 subsets. Subsequently, we tested ωB88PTPSS on two sets of real-life examples from recent computational chemistry literature-the low energy bands of chlorophyll a (Chl a) and a set of thermally activated delayed fluorescence (TADF) systems. For Chl a, ωB88PTPSS qualitatively and quantitatively achieves DLPNO-STEOM-CCSD-level performance and provides excellent agreement with experiment. For TADF systems, ωB88PTPSS agrees quite well with spin-component-scaled CC2 (SCS-CC2) excitation energies, as well as experimental values, for the gaps between the S₁ and T₁ excited states.

Ultrafast Spectroscopies of Nitrophenols and Nitrophenolates in Solution: From Electronic Dynamics and Vibrational Structures to Photochemical and Environmental Implications

Nitrophenols are a group of small organic molecules with significant environmental implications from the atmosphere to waterways. In this work, we investigate a series of nitrophenols and nitrophenolates, with the contrasting ortho-, meta-, and para-substituted nitro group to the phenolic hydroxy or phenolate oxygen site (2/3/4NP or NP-), implementing a suite of steady-state and time-resolved spectroscopic techniques that include UV/Visible spectroscopy, femtosecond transient absorption (fs-TA) spectroscopy with probe-dependent and global analysis, and femtosecond stimulated Raman spectroscopy (FSRS), aided by quantum calculations. The excitation-dependent (400 and 267 nm) electronic dynamics in water and methanol, for six protonated or deprotonated nitrophenol molecules (three regioisomers in each set), enable a systematic investigation of the excited-state dynamics of these functional "nanomachines" that can undergo nitro-group twisting (as a rotor), excited-state intramolecular or intermolecular proton transfer (donor-acceptor, ESIPT, or ESPT), solvation, and cooling (chromophore) events on molecular timescales. In particular, the meta-substituted compound 3NP or 3NP- exhibits the strongest charge-transfer character with FSRS signatures (e.g., C-N peak frequency), and thus, does not favor nitroaromatic twist in the excited state, while the ortho-substituted compound 2NP can undergo ESIPT in water and likely generate nitrous acid (HONO) after 267 nm excitation. The delineated mechanistic insights into the nitro-substituent-location-, protonation-, solvent-, and excitation-wavelength-dependent effects on nitrophenols, in conjunction with the ultraviolet-light-induced degradation of 2NP in water, substantiates an appealing discovery loop to characterize and engineer functional molecules for environmental applications.

Theoretical Study of the Structural, Optoelectronic, and Reactivity Properties of N-[5′-Methyl-3′-Isoxasolyl]-N-[(E)-1-(-2-)]Methylidene] Amine and Some of Its Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ Complexes for OLED and OFET Applications

Herein, we report the structural, electronic, and charge transfer properties of N-[5′-methyl-3′-isoxasolyl]-N-[(E)-1-(-2-thiophene)] methylidene] amine (L) and its Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ complexes (dubbed A, B, C, D, and E, respectively) using the density functional theory (DFT). All molecules investigated were optimized at the BP86/def2-TZVP/RI level of theory. Single point energy calculations were carried out at the M06-D3ZERO/def2-TZVP/RIJCOSX level of theory. Reorganization energies of the hole and electron (λh and λe) and the charge transfer mobilities of the electron and hole (μe and μh) have been computed and reported. The λe and λh values vary in the order D > E > A > B > C > L and E > A > D > L > C > B, respectively, while μe and μh vary in the order B > C > L > A > E > D and C > B > A > L > E > D, respectively. μh of B (39.5401 cm2·V−1S−1) and C (366.4740 cm2·V−1s−1) is remarkably large, suggesting their application in organic light-emitting diode (OLED) and organic field-effect transistor (OFET) technologies. Electron excitation analysis based on time-dependent (TD)-DFT calculations revealed that charge transfer excitations may significantly affect charge transfer mobilities. Based on charge transfer mobility results, B and C are outstanding and are promising molecules for the manufacture of electron and hole-transport precursor materials for the construction of OLED and OFET devices as compared to L. The results also show that L and all its complexes interestingly have higher third-order NLO activity than those of para-nitroaniline, a prototypical NLO molecule.

Exchange Spin Coupling in Optically Excited States

In optically excited states in molecules and materials, coupling between local electron spins plays an important role for their photoemission properties and is interesting for potential applications in quantum information processing. Recently, it was experimentally demonstrated that the photogenerated local spins in donor-acceptor metal complexes can interact with the spin of an attached radical, resulting in a spin-coupling-dependent mixing of excited doublet states, which controls the local spin density distributions on donor, acceptor, and radical subunits in optically excited states. In this work, we propose an energy-difference scheme to evaluate spin coupling in optically excited states, using unrestricted and spin-flip simplified time-dependent density functional theory. We apply it to three platinum complexes which have been studied experimentally to validate our methodology. We find that all computed coupling constants are in excellent agreement with the experimental data. In addition, we show that the spin coupling between donor and acceptor in the optically excited state can be fine-tuned by replacing platinum with palladium and zinc in the structure. Besides the two previously discussed excited doublet states (one bright and one dark), our calculations reveal a third, bright excited doublet state which was not considered previously. This third state possesses the inverse spin polarization on donor and acceptor with respect to the previously studied bright doublet state and is by an order of magnitude brighter, which might be interesting for optically controlling local spin polarizations with potential applications in spin-only information transfer and manipulation of connected qubits.

Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent density functional theory excitation energies, though hybrid meta generalized-gradient approximations (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.