Reference Energies for Intramolecular Charge-Transfer Excitations

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.

Electronic excitation behavior and anharmonic IR spectrum characteristics of RDX

CONTEXT

RDX, a typical nitro-based energetic material, has a wide range of applications. In recent years, the frequent occurrence of production accidents has created an urgent need for effective early detection technologies, which rely heavily on its spectral characteristics. This research systematically discusses the ultraviolet spectrum and electronic excitation behavior of RDX using charge transfer spectrum, hole-electron analysis, and NBO analysis methods. It also conducts anharmonic calculations to systematically explore various vibrational forms related to the -NO2 characteristic bands in the infrared spectrum of RDX. Additionally, considering the requirements of actual production scenarios, the impact of solvents on spectral changes is examined. The findings can provide a theoretical basis for the safe production detection methods of energetic materials.

METHOD

All calculations on the structures and NBO analysis were conducted using Gaussian 16 software. Additionally, further calculations on electronic excitations were performed using Multiwfn, while VMD was employed for visualization.

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.

Performance of the Bethe-Salpeter Equation for Electronic Excitations in First-Row Transition Metal Complexes

The performance of the Green's function-Bethe-Salpeter Equation (BSE@GW) approach has been systematically tested on a series of first-row transition metal complexes. Special attention was paid to the interplay between metal-centered (MC) and charge transfer (CT) transitions and their ordering in the excited singlet and triplet state manifolds. Here, the commonly used time-dependent density functional theory (DFT) reaches its limits and in particular shows a strong dependence on the exchange-correlation functional. In contrast, the present BSE@GW ultraviolet-visible (UV-vis) spectra show a good agreement with experimental results as far as the absorption spectra and their assignment are concerned. This is achieved independently of the exchange-correlation functional underlying the initial guess of the GW iteration. These conclusions are drawn on the basis of an investigation of a test set including nearly pure MC transitions in triazacyclononane with different metal centers and mixed MC-CT transitions in Fe(II) complexes with different numbers of N-heterocyclic carbene ligands. Furthermore, important aspects of the calculations such as the dependence on the ground state equilibrium geometry or the influence of the Tamm-Dancoff approximation are highlighted.

The Amsterdam Modeling Suite

In this paper, we present the Amsterdam Modeling Suite (AMS), a comprehensive software platform designed to support advanced molecular and materials simulations across a wide range of chemical and physical systems. AMS integrates cutting-edge quantum chemical methods, including Density Functional Theory (DFT) and time-dependent DFT, with molecular mechanics, fluid thermodynamics, machine learning techniques, and more, to enable multi-scale modeling of complex chemical systems. Its design philosophy allows for seamless coupling between components, facilitating simulations that range from small molecules to complex biomolecular and solid-state systems, making it a versatile tool for tackling interdisciplinary challenges, both in industry and in academia. The suite also emphasizes user accessibility, with an intuitive graphical interface, extensive scripting capabilities, and compatibility with high-performance computing environments.

Rational design of a near-infrared fluorescent probe for rapid monitoring of carboxylesterase in live cells and drug-induced liver injury mice

BACKGROUND

Carboxylesterase (CE) is an important enzyme that mainly exists in liver cells and can catalyze the hydrolysis of esters in a variety of pharmaceuticals and xenobiotics. Real-time and non-invasive imaging of CE is of great significance for the study of CE-related metabolic diseases. Although fluorescence sensing technology is considered a promising candidate, the slow response rate (> 60 min), low sensitivity, and short emission wavelength (<650 nm) of most CE probes limit their practical application. Therefore, it is significant and urgent to develop novel fluorescent probes for the rapid diagnosis of CE-related diseases.

RESULTS

Herein, a near-infrared fluorescent probe, CF3-BDP-CE, has been developed by introducing acetyl as the CE recognition unit into the fluorophore meso-trifluoromethyl-BODIP for the detection of CE. CF3-BDP-CE exhibited a remarkable fluorescence enhancement at 690 nm for CE with a limit of detection of 7.9 × 10-4 U/mL. Importantly, the fast response kinetics (within 3 min) make CF3-BDP-CE superior to most reported probes. The emission turn-on mechanism was confirmed by theoretical calculation, revealing that after the hydrolysis of CF3-BDP-CE, the intramolecular charge transfer process leads to strong fluorescence. Furthermore, CF3-BDP-CE has been successfully applied to real-time imaging of endogenous CE changes in living cells and to imaging CE activity differences between tumor and normal cells. In addition, CF3-BDP-CE has been successfully used to track CE abnormalities in acetaminophen-induced liver injury model mice.

SIGNIFICANCE

A NIR fluorescent probe CF3-BDP-CE was developed to effectively track the dynamic change of CE fluctuation in living cells and mice, with potential applications in the diagnosis of CE-related diseases.

Triplet states nurture the long-lived emission at room temperature of a chlorine-containing tetraphenylimidazole derivative when aggregation occurs in water/acetonitrile mixtures

In recent years, there have been numerous reports on the synthesis and applications of 1,2,4,5-tetraphenylimidazole (TEPI) derivatives, particularly due to the photophysical properties of such systems. However, the long-lived emission behavior of TEPIs has not been studied, with research largely limited to attempts at 77 K. In this study, the compound 1-(4-chlorophenyl)-2,4,5-triphenyl-1H-imidazole (TEPI-Cl) was prepared and characterized using experimental techniques (i.e., absorption spectra, steady-state, and long-lived emission), as well as computationally, using a combination of Extended Tight Binding (xTB), Density Functional Theory (DFT), and Time-Dependent (TD-DFT) methods. TEPI-Cl exhibited a low solvatochromic effect, both in absorption and steady-state emission in organic solvents, which is typical of a locally excited transition; this was confirmed by the performed calculations. However, in its aggregated state (observed in water/acetonitrile mixtures with >80% of water, in volume), the compound displayed the emergence of a new band in the absorption spectrum, as well as aggregate-induced enhanced emission in the steady-state emission analysis. The long-lived emission spectrum of TEPI-Cl recorded at room temperature shows two signals (at 380 and 540 nm) and the presence of benzil enables the generation of triplet excited states of the latter, likely through an energy transfer process. The sensitivity of these signals to the presence of oxygen suggested that the related excited states are of a triplet nature; moreover, the calculated electronic transitions for the optimized structures of the T1 and T2 states are comparable to the experimentally observed long-lived emission wavelengths. This newly observed behavior of TEPI-Cl comes as a novel photophysical property added to this class of molecules, demonstrating its significant potential for further applications in complex matrices.

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.

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.

Beyond Quasi-Particle Self-Consistent GW for Molecules with Vertex Corrections

We introduce the ΣBSE@LBSE self-energy in the quasi-particle self-consistent GW (qsGW) framework (qsΣBSE@LBSE). Here, L is the two-particle response function, which we calculate by solving the Bethe-Salpeter equation with the static, first-order GW kernel. The same kernel is added to Σ directly. For a set of medium organic molecules, we show that including the vertex both in L and Σ is crucial. This approach retains the good performance of qsGW for predicting first ionization potentials and fundamental gaps, while it greatly improves the description of electron affinities. Its good performance places qsΣBSE@LBSE among the best-performing electron propagator methods for charged excitations. Adding the vertex in L only, as commonly done in the solid-state community, leads to devastating results for electron affinities and fundamental gaps. We also test the performance of BSE@qsGW and qsΣBSE@LBSE for neutral charge-transfer excitation and find both methods to perform similar. We conclude that ΣBSE@LBSE is a promising approximation to the electronic self-energy beyond GW. We hope that future research on dynamical vertex effects, second-order vertex corrections, and full self-consistency will improve the accuracy of this method, both for charged and neutral excitation energies.

Using an aromatic linker to optimize charge-resonance states, photodimerization and reversibility in covalent anthracene dimers

The intramolecular [4+4] photodimerization of anthracene chromophores in covalent assemblies can be harnessed to create negative photochromic systems. This paper reports the characterization of the photophysical and photochemical properties of a new class of asymmetric phenyl-linked bis(anthracene) photochromes and compares their behavior with that of a previously studied symmetric ethylene-linked analog. Steady-state and femtosecond time-resolved spectroscopic experiments show that both types of bis(anthracenes) support a neutral bright state along with a lower-energy charge resonance state. After photoexcitation, both states relax on sub-10 ps timescales, but with significantly different photodimerization quantum yields: 0.83 using 532 nm excitation of the charge-resonance state versus 0.46 for 400 nm excitation of the neutral bright state. The phenyl-linked bis(anthracene) derivatives exhibit superior thermal stability and reversibility due to a lower activation energy for dimer dissociation (94 kJ mol-1versus 110 kJ mol-1). Quantum chemical calculations reveal the structure of the neutral and charge-resonance excited states and can rationalize the higher photodimerization quantum yield of the latter. The phenyl linker enforces close alignment of the anthracene moieties, shifting the charge resonance state to lower energy and extending the wavelength range of the photochrome while also raising the energy of the photodimer ground state to enhance the backward reaction rate. The phenyl-linked bis(anthracenes) provide a promising system to harness the [4+4] photodimerization reaction with high quantum yield, room temperature reversibility, and cyclability.

QUEST#4X: An Extension of QUEST#4 for Benchmarking Multireference Wave Function Methods

Given a number of data sets for evaluating the performance of single reference methods for the low-lying excited states of closed-shell molecules, a comprehensive data set for assessing the performance of multireference methods for the low-lying excited states of open-shell systems is still lacking. For this reason, we propose an extension (QUEST#4X) of the radical subset of QUEST#4 (J. Chem. Theory Comput. 2020, 16, 3720) to cover 110 doublet and 39 quartet excited states. Near-exact results obtained by iterative configuration interaction with selection and second-order perturbation correction (iCIPT2) are taken as benchmark to calibrate static-dynamic-static configuration interaction (SDSCI) and static-dynamic-static second-order perturbation theory (SDSPT2), which are minimal MRCI and CI-like perturbation theory, respectively. It is found that SDSCI is very close in accuracy to internally contracted multireference configuration interaction with singles and doubles (ic-MRCISD), although its computational cost is just that of one iteration of the latter. Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and performs similarly to multistate n-electron valence second-order perturbation theory (MS-NEVPT2). These findings put SDSCI and SDSPT2 on a firm basis.

A study on indolo[3,2,1-jk]carbazole donor-based dye-sensitized solar cells and effects from addition of auxiliary donors

Density functional theory has been employed to study indolo[3,2,1-jk]carbazole donor-based dyes, incorporating one and two units of 2,4-dimethoxybenzene auxiliary donors. Electrostatic potential analysis highlights the dye with one auxiliary donor (D2) as having the highest charge-donating capability. Structural analysis shows that auxiliary donors enhance planarity, reduce steric hindrance, and improve π-conjugation. Highest occupied molecular orbital (-6.025 to -5.660 eV) and lowest unoccupied molecular orbital (-2.927 to -2.844 eV) of all dyes support efficient electron injection into the semiconductor and dye regeneration process. Auxiliary donors enhance chemical reactivity parameters, improving the suitability of these dyes for dye-sensitized solar cells (DSSCs). Inclusion of extra donors reduces the excitonic binding energy, minimizing recombination losses, and increases polarization, enhancing the charge injection efficiency. Additional analyses explored properties such as charge separation, charge transfer length, transition density matrix and non-covalent interactions. All dyes exhibit strong absorption (410-440 nm) in the visible region, confirming their applicability to DSSCs, while emission spectra provide insights into their fluorescence lifetimes. D2 demonstrates improved performance in specific properties. However, D3, with two auxiliary donors, achieves the best overall balance across other computed parameters. Indeed, the inclusion of auxiliary donors induces significant changes and may be considered as a valuable strategy for designing efficient DSSCs.

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/GW, and Wave Function Methods

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O ( N 5 ) and O ( N 6 ) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

Accurate computation of quantum excited states with neural networks

We present an algorithm to estimate the excited states of a quantum system by variational Monte Carlo, which has no free parameters and requires no orthogonalization of the states, instead transforming the problem into that of finding the ground state of an expanded system. Arbitrary observables can be calculated, including off-diagonal expectations, such as the transition dipole moment. The method works particularly well with neural network ansätze, and by combining this method with the FermiNet and Psiformer ansätze, we can accurately recover excitation energies and oscillator strengths on a range of molecules. We achieve accurate vertical excitation energies on benzene-scale molecules, including challenging double excitations. Beyond the examples presented in this work, we expect that this technique will be of interest for atomic, nuclear, and condensed matter physics.

A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes

In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)  ⋆ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.

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.

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.

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's functionG W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, theG W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

A DFT/MRCI Hamiltonian parameterized using only ab initio data: I. valence excited states

A new combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian parameterized solely using the benchmark ab initio vertical excitation energies obtained from the QUEST databases is presented. This new formulation differs from all previous versions of the method in that the choice of the underlying exchange-correlation (XC) functional employed to construct the one-particle (orbital) basis is considered, and a new XC functional, QTP17, is chosen for its ability to generate a balanced description of core and valence vertical excitation energies. The ability of the new DFT/MRCI Hamiltonian, termed QE8, to furnish accurate excitation energies is confirmed using benchmark quantum chemistry computations, and a mean absolute error of 0.16 eV is determined for the wide range of electronic excitations included in the validation dataset. In particular, the QE8 Hamiltonian dramatically improves the performance of DFT/MRCI for doubly excited states. The performance of fast approximate DFT/MRCI methods, p-DFT/MRCI and DFT/MRCI(2), is also evaluated using the QE8 Hamiltonian, and they are found to yield excitation energies in quantitative agreement with the parent DFT/MRCI method, with the two methods exhibiting a mean difference of 0.01 eV with respect to DFT/MRCI over the entire benchmark set.

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

The eXact integral simplified time-dependent density functional theory (XsTD-DFT)

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14 eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.

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.

Intramolecular Charge Transfer and Stimuli-Responsive Emission in Cholesterol-Appended Phenothiazine-Cyanostyryl-Based Donor-Acceptor Systems

Organic fluorescent molecules have received considerable attention owing to their various optoelectronic applications. Herein, we report the design and synthesis of two cholesterol-functionalized cyanostyrene-phenothiazine-based D-π-A systems that are emissive in both the solution and solid states. The newly synthesized cholesterol-appended phenothiazine-cyanostyrene diads PTCS-1 and PTCS-2 vary in the N-alkylation of phenothiazine, respectively, with─octyl and─hexyl chains. Both molecules are highly fluorescent and show reasonably good quantum yields in nonpolar solvents because of twisted intramolecular charge transfer (TICT). The molecules exhibit aggregation-induced emission in the solid state. Due to the presence of flexible alkyl chains in the phenothiazine and cholesterol moieties, PTCS-1 and PTCS-2 show mechanochromic luminescence switching in response to external shear stress and emission recovery under methanol vapor. Powder X-ray diffraction studies prove that the emission switching on the applied stimuli in both PTCS-1 and PTCS-2 is attributed to the reversible transformation between the crystalline and amorphous states. Time-dependent density functional theory (TD-DFT) studies are carried out to gain insight into the ICT interactions. TD-DFT analysis at the TD-M06-2X/def2-TZVP level further revealed that in both molecules, the lowest unoccupied molecular orbital (LUMO) + 2, LUMO, highest occupied molecular orbital (HOMO), and HOMO - 1 orbitals are responsible for the charge transfer interactions. These ICT interactions are identified as π-π* type interactions.

Beyond Explored Functionals: A Computational Journey of Two-Photon Absorption

We present a thorough investigation into the efficacy of 19 density functional theory (DFT) functionals, relative to RI-CC2 results, for computing two-photon absorption (2PA) cross sections (σ2PA) and key dipole moments (|μ00|, |μ11|, |Δμ|, |μ01|) for a series of coumarin dyes in the gas-phase. The functionals include different categories, including local density approximation (LDA), generalized gradient approximation (GGA), hybrid-GGA (H-GGA), range-separated hybrid-GGA (RSH-GGA), meta-GGA (M-GGA), and hybrid M-GGA (HM-GGA), with 14 of them being subjected to analysis for the first time with respect to predicting σ2PA values. Analysis reveals that functionals integrating both short-range (SR) and long-range (LR) corrections, particularly those within the RSH-GGA and HM-GGA classes, outperform the others. Furthermore, the range-separation approach was found more impactful compared to the varying percentages of Hartree-Fock exchange (HF Ex) within different functionals. The functionals traditionally recommended for 2PA do not appear among the top 9 in our study, which is particularly interesting, as these top-performing functionals have not been previously investigated in this context. This list is dominated by M11, QTP variants, ωB97X, ωB97X-V, and M06-2X, surpassing the performance of other functionals, including the commonly used CAM-B3LYP.

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.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels

We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.

A novel isophorone-based fluorescent probe for recognizing Al3+ and its bioimaging in plants

Aluminium ions (Al3+) are widely present in industries and daily life and are closely related to human health and environmental protection. Therefore, it is crucial to detect their concentration. In this paper, a convenient and reliable small molecule fluorescent probe based on a dicyanoisophorone Schiff base and 2-pyridinecarbohydrazide has been developed. The probe is capable of selectively detecting Al3+ with the advantages of near-infrared emission (maximum emission wavelength of 625 nm), good selectivity, high sensitivity (detection limit of 2.18 × 10-7 M) and fast response time (15 s). It has good potential for rapid detection and visual tracking of Al3+ in aqueous solutions and plant bodies.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

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.

Reference Vertical Excitation Energies for Transition Metal Compounds

To enrich and enhance the diversity of the quest database of highly accurate excitation energies [Véril, M.; et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with a singlet or doublet ground state containing a fourth-row transition metal (CuCl, CuF, CuH, ScF, ScH, ScO, ScS, TiN, ZnH, ZnO, and ZnS) are considered, and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely, CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In many cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of the CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported.

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.

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

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

A Hammett's analysis of the substituent effect in functionalized diketopyrrolopyrrole (DPP) systems: Optoelectronic properties and intramolecular charge transfer effects

Diketopyrrolopyrrole (DPP) systems have promising applications in different organic electronic devices. In this work, we investigated the effect of 20 different substituent groups on the optoelectronic properties of DPP-based derivatives as the donor ( D )-material in an organic photovoltaic (OPV) device. For this purpose, we employed Hammett's theory (HT), which quantifies the electron-donating or -withdrawing properties of a given substituent group. Machine learning (ML)-basedσ m ,σ p ,σ m 0 ,σ p 0 ,σ p + ,σ p - ,σ I , andσ R Hammett's constants previously determined were used. Mono- (DPP-X1 ) and di-functionalized (DPP-X2 ) DPPs, where X is a substituent group, were investigated using density functional theory (DFT), time-dependent DFT (TDDFT), and ab initio methods. Several properties were computed using CAM-B3LYP and the second-order algebraic diagrammatic construction, ADC(2), an ab initio wave function method, including the adiabatic ionization potential ( I P A ), the electron affinity ( E A A ), the HOMO-LUMO gaps (E g ), and the maximum absorption wavelengths (λ max ), the first excited state transition 1 S0 → 1 S1 energies ( ∆ E ) (the optical gap), and exciton binding energies. From the optoelectronic properties and employing typical acceptor systems, the power conversion efficiency ( PCE ), open-circuit voltage (V OC ), and fill factor ( FF ) were predicted for a DPP-based OPV device. These photovoltaic properties were also correlated with the machine learning (ML)-based Hammett's constants. Overall, good correlations between all properties and the different types of σ constants were obtained, except for theσ I constants, which are related to inductive effects. This scenario suggests that resonance is the main factor controlling electron donation and withdrawal effects. We found that substituent groups with large σ values can produce higher photovoltaic efficiencies. It was also found that electron-withdrawing groups (EWGs) reducedE g and ∆ E considerably compared to the unsubstituted DPP-H. Moreover, for every decrease (increase) in the values of a given optoelectronic property of DPP-X1 systems, a more significant decrease (increase) in the same values was observed for the DPP-X2 , thus showing that the addition of the second substituent results in a more extensive influence on all electronic properties. For the exciton binding energies, an unsupervised machine learning algorithm identified groups of substituents characterized by average values (centroids) of Hammett's constants that can drive the search for new DDP-derived materials. Our work presents a promising approach by applying HT on molecular engineering DPP-based molecules and other conjugated molecules for applications on organic optoelectronic devices.

Full theoretical protocol for the design of metal-free organic electron donor-spacer-acceptor systems

A user-friendly (time-dependent) density functional theory based algorithm is proposed to design new donor-spacer-acceptor systems for electron transfer reactions. This algorithm is focused on metal-free organic compounds, most of which contain aromatic or alkene moieties. The oxidation and reduction potentials are calculated, together with the excited-state energy difference including the zero-point energy and the structural properties required to calculate an electron transfer Gibbs free energy change. The proposed algorithm has been tested on well-known systems, while two new compounds are suggested for photoinduced intramolecular electron transfer reactions using this scheme. The methodology here presented is intended to be a tool for synthetic physical-chemists, allowing them to evaluate the properties of hypothetical systems before the synthesis, enabling the study of limitless combinations of donor-spacer-acceptor arrangements.

Recent Advances in Fluorescent Probes for Zinc Ions Based on Various Response Mechanisms

Zinc is a vital metal element with extensive applications in various fields such as industry, metallurgy, agriculture, food, and healthcare. For living organisms, zinc ions are indispensable, and their deficiency can lead to physiological and metabolic abnormalities that cause multiple diseases. Hence, there is a significant need for selective recognition and effective detection of free zinc ions. As a probe method with high sensitivity, high selectivity, real-time monitoring, safety, harmlessness and ease of operation, fluorescent probes have been widely used in metal ion identification studies, and many convenient, low-cost and easy-to-operate fluorescent probes for Zn2+ detection have been developed. This article reviews the latest research advances in fluorescent chemosensors for Zn2+ detection from 2019 to 2023. In particular, sensors working through photo-induced electron transfer (PET), excited state intramolecular proton transfer (ESIPT), intramolecular charge transfer (ICT), fluorescence resonance energy transfer (FRET), chelation-enhanced fluorescence (CHEF), and aggregation-induced emission (AIE) mechanisms are described. We discuss the use of various recognition mechanisms in detecting zinc ions through specific cases, some of which have been validated through theoretical calculations.

A Similarity Renormalization Group Approach to Green's Function Methods

The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.

Synthesis and Characterization of Novel Thienothiadiazole-Based D-π-A-π-D Fluorophores as Potential NIR Imaging Agents

As fluorescence bioimaging has increased in popularity, there have been numerous reports on designing organic fluorophores with desirable properties amenable to perform this task, specifically fluorophores with emission in the near-infrared II (NIR-II) region. One such strategy is to utilize the donor-π-acceptor-π-donor approach (D-π-A-π-D), as this allows for control of the photophysical properties of the resulting fluorophores through modulation of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels. Herein, we illustrate the properties of thienothiadiazole (TTD) as an effective acceptor moiety in the design of NIR emissive fluorophores. TTD is a well-known electron-deficient species, but its use as an acceptor in D-π-A-π-D systems has not been extensively studied. We employed TTD as an acceptor unit in a series of two fluorophores and characterized the photophysical properties through experimental and computational studies. Both fluorophores exhibited emission maxima in the NIR-I that extends into the NIR-II. We also utilized electron paramagnetic resonance (EPR) spectroscopy to rationalize differences in the measured quantum yield values and demonstrated, to our knowledge, the first experimental evidence of radical species on a TTD-based small-molecule fluorophore. Encapsulation of the fluorophores using a surfactant formed polymeric nanoparticles, which were studied by photophysical and morphological techniques. The results of this work illustrate the potential of TTD as an acceptor in the design of NIR-II emissive fluorophores for fluorescence bioimaging applications.

Automated Active Space Selection with Dipole Moments

Multireference calculations can provide accurate information of systems with strong correlation, which have increasing importance in the development of new molecules and materials. However, selecting a suitable active space for multireference calculations is nontrivial, and the selection of an unsuitable active space can sometimes lead to results that are not physically meaningful. Active space selection often requires significant human input, and the selection that leads to reasonable results often goes beyond chemical intuition. In this work, we have developed and evaluated two protocols for automated selection of the active space for multireference calculations based on a simple physical observable, the dipole moment, for molecules with nonzero ground-state dipole moments. One protocol is based on the ground-state dipole moment, and the other is based on the excited-state dipole moments. To evaluate the protocols, we constructed a dataset of 1275 active spaces from 25 molecules, each with 51 active space sizes considered, and have mapped out the relationship between the active space, dipole moments, and vertical excitation energies. We have demonstrated that, within this dataset, our protocols allow one to choose among a number of accessible active spaces one that is likely to give reasonable vertical excitation energies, especially for the first three excitations, with no parameters manually decided by the user. We show that, with large active spaces removed from consideration, the accuracy is similar and the time-to-solution can be reduced by more than 10 fold. We also show that the protocols can be applied to potential energy surface scans and determining the spin states of transition metal oxides.

Excited state potential energy surfaces of N-phenylpyrrole upon twisting: reference values and comparison between BSE/GW and TD-DFT

The puzzling case of the mixing between the charge transfer (CT) and local excited (LE) characters upon twisting of the geometry of N-phenylpyrrole (N-PP) is investigated considering the six low-lying singlet excited states (ES). The theoretical calculations of the potential energy surfaces (PES) have been performed for these states using a Coupled Cluster method accounting for the impact of the contributions from the triples, many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, as well as Time-Dependent Density Functional Theory (TD-DFT) using various exchange-correlation functionals. Our findings confirm that the BSE formalism is more reliable than TD-DFT for close-lying ES with mixed CT/LE nature. More specifically, BSE/GW yields a more accurate evolution of the excited state PES than TD-DFT when compared to the reference coupled cluster values. BSE/GW PES curves also show negligible exchange-correlation functional starting point dependency in sharp contrast with their TD-DFT counterparts.

Ultrafast Photoelimination of Nitrogen from Upper Excited States of Diazoalkanes and the Fate of Carbenes Formed in the Reaction

The photochemical reactivity of diphenyldiazomethane 1 and phenyl 1- and 2-adamantyl diazomethanes 2 and 3, respectively, was investigated by transient absorption spectroscopy (TA). Photoelimination of N₂ upon UV excitation takes place in the anti-Kasha ultrafast photochemical reaction from the upper excited singlet states to deliver singlet carbenes, which were, in the case of 1 and 2, detected by fs-TA. The reactivity of the carbenes differs with respect to the substituent at the carbene center. The singlet car-1 in a nonpolar solvent delivers the triplet carbene by intersystem crossing (ISC). Singlet car-2 does not undergo ISC but reacts in the intermolecular insertion reactions into C-H bonds. Car-3 has an α-C-H bond next to the carbene center and reacts rapidly in the intramolecular C-H insertion reaction to deliver alkene, precluding its detection by fs-TA. However, the isolation of ketone photoproducts from 3 is highly indicative of triplet car-3's intermediate formation. The TA spectra from the S₁-S₃ states of 1-3 were computed using time-dependent density functional theory, while the multiconfigurational perturbation theory to the second order was used for the absorption spectra of the corresponding singlet and triplet carbenes. The modeled and measured spectra are in good agreement, and the computations corroborate the assignments of the key short-lived intermediates.

Optimization Stability in Excited-State-Specific Variational Monte Carlo

We investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

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.

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

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

TDDFT versus GW/BSE Methods for Prediction of Light Absorption and Emission in a TADF Emitter

Design concepts for organic light emitting diode (OLED) emitters, which exhibit thermally activated delayed fluorescence (TADF) and thereby achieve quantum yields exceeding 25%, depend on singlet-triplet splitting energies of order kT to allow reverse intersystem crossing at ambient temperatures. Simulation methods for these systems must be able to treat relatively large organic molecules, as well as predict their excited state energies, transition energies, singlet-triplet splittings, and absorption and emission cross sections with reasonable accuracy, in order to prove useful in the design process. Here we compare predictions of TDDFT with M06-2X and ωB97X-D exchange-correlation functionals and a G_oW_o@HF/BSE method for these quantities in the well-studied DPTZ-DBTO2 TADF emitter molecule. Geometry optimization is performed for ground state (GS) and lowest donor-acceptor charge transfer (CT) state for each functional. Optical absorption and emission cross sections and energies are calculated at these geometries. Relaxation energies are on the order of 0.5 eV, and the importance of obtaining excited state equilibrium geometries in predicting delayed fluorescence is demonstrated. There are clear trends in predictions of G_oW_o@HF/BSE, and TDDFT/ωB97X-D and M06-2X methods in which the former method favors local exciton (LE) states while the latter favors DA CT states and ωB97X-D makes intermediate predictions. G_oW_o@HF/BSE suffers from triplet instability for LE states but not CT states relevant for TADF. Shifts in HOMO and LUMO levels on adding a conductor-like polarizable continuum model dielectric background are used to estimate changes in excitation energies on going from the gas phase to a solvated molecule.

Connections between many-body perturbation and coupled-cluster theories

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.