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

Photocaging of N-pyridinyl amide scaffold-based PIM inhibitors for spatiotemporal controlled anticancer bioactivity

Photocaging is an ideal way to enable spatiotemporal control over the release of bioactive compounds for cancer treatments. In this work, a series of photocaged N-pyridinyl amide scaffold-based PIM inhibitors were developed by rendering the amino group unable to bind to the Asp128/Glu171 sites of PIM kinase with a photoremovable protecting group (PPG). Upon light irradiation, our studies revealed the structure-dependent photouncaging efficiency and screened out the photocaged PIM inhibitor FD1024-PPG. Its spatiotemporally controlled bioactivity was confirmed by cell-based in-vitro assays and revealed that it exerts the antiproliferation and induction of cell apoptosis through inhibition of PIM kinase upon light irradiation. Furthermore, the spatiotemporal control over the in-vivo anticancer activity was demonstrated using zebrafish xenograft model.

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.

Excited-State Absorption: Reference Oscillator Strengths, Wave Function, and TDDFT Benchmarks

Excited-state absorption (ESA) corresponds to the transition between two electronic excited states and is a fundamental process for probing and understanding light-matter interactions. Accurate modeling of ESA is indeed often required to interpret time-resolved experiments. In this contribution, we present a dataset of 53 ESA oscillator strengths in three different gauges and the associated vertical transition energies between 71 excited states of 21 small- and medium-sized molecules from the QUEST database. In a few cases, we additionally investigated the effect of geometry relaxation on excited-state geometries. The reference values were obtained within the quadratic response (QR) CC3 formalism using eight different Dunning basis sets. We found that the d-aug-cc-pVTZ basis set is always adequate while its more compact double-ζ counterpart, d-aug-cc-pVDZ, performs well in most cases. These QR-CC3 data allow us to assess the performance of QR-TDDFT, with and without applying the Tamm-Dancoff approximation, using a panel of global and range-separated hybrids (B3LYP, BH&HLYP, CAM-B3LYP, LC-BLYP33, and LC-BLYP47), as well as several lower-order wave function methods, i.e., QR-CCSD, QR-CC2, EOM-CCSD, ISR-ADC(2), and ISR-ADC(3). We show that QR-TDDFT delivers acceptable errors for ESA oscillator strengths with CAM-B3LYP showing particular promise, especially for the largest molecules of our set, and in the Franck-Condon (FC) region. We also find that ISR-ADC(3) exhibits excellent performance in this region. When using excited-state optimal geometries, the relative performance of wave function-based approaches remains consistent with trends observed in the Franck-Condon region. However, for TD(A)-DFT, the accuracy varies more significantly, as the performance of different exchange-correlation functionals significantly depends on the chosen geometry.

Optimal-Reference Excited State Methods: Static Correlation at Polynomial Cost with Single-Reference Coupled-Cluster Approaches

Accurate yet efficient modeling of chemical systems with pronounced static correlation in their excited states remains a significant challenge in quantum chemistry, as most electronic structure methods that can adequately capture static correlation scale factorially with system size. Researchers are often left with no option but to use more affordable methods that may lack the accuracy required to model critical processes in photochemistry such as photolysis, photocatalysis, and nonadiabatic relaxation. A great deal of work has been dedicated to refining single-reference descriptions of static correlation in the ground state via "addition-by-subtraction" coupled cluster methods such as pair coupled cluster with double substitutions (pCCD), singlet-paired CCD (CCD0), triplet-paired CCD (CCD1), and CCD with frozen singlet- or triplet-paired amplitudes (CCDf0/CCDf1). By combining wave functions derived from these methods with the intermediate state representation (ISR), we gain insights into the extensibility of single-reference coupled cluster theory's coverage of static correlation to the excited state problem. Our CCDf1-ISR(2) approach is robust in the face of static correlation and provides enough dynamical correlation to accurately predict excitation energies to within about 0.2 eV in small organic molecules. We also highlight distinct advantages of the Hermitian ISR construction, such as the avoidance of pathological failures of equation-of-motion methods for excited state potential energy surface topology. Our results prompt us to continue exploring optimal single-reference theories (excited state approaches that leverage dependence on the initial reference wave function) as a potentially economical approach to the excited state static correlation problem.

Heterometallic CuCd and Cu2Zn complexes with o-vanillin and its Schiff-base derivative: slow magnetic relaxation and catalytic activity associated with Cu(II) centres

In this work, two novel heterometallic mixed-ligand mixed-anion complexes [CuIICdIIClL(o-Van)(OAc)]·3H2O (1) and [CuII2ZnIICl2L2(o-Van)(OAc)] (2) were prepared by reacting fine copper powder and Cd(II) or Zn(II) acetate with an ethanol solution of the Schiff-base ligand HL formed in situ in the condensation reaction of 2-hydroxy-3-methoxy-benzaldehyde (o-VanH) and CH3NH2·HCl. The compounds were thoroughly characterized by elemental analysis, FT-IR, UV/Vis and EPR spectroscopy, cyclic voltammetry, and single-crystal X-ray diffraction, revealing the neutral molecular nature of both the compounds. Catalytic properties of 1 and 2 were studied in the oxidation of hydrocarbons with H2O2 under mild conditions, showing the maximum reaction rate of 4 × 10-5 M s-1 and TOF up to 640 h-1. Both compounds undergo complex transformations in solution as evidenced by kinetic analysis and time-dependent UV/Vis spectroscopy, indicating that the reduced Cu(I) form of 1 is unexpectedly unfavorable. Complex 1 demonstrates slow magnetic relaxation dominated by the direct relaxation process between T = 1.8 and 7 K under an external DC field of 0.2 and 0.4 T, a very rarely observable effect in the coordination compounds of Cu(II). Complex 2 possesses weak ferromagnetism (J = 4.50 cm-1, zJ' = -0.201 cm-1 for H = -JS1S2 formalism) occurring through the Cu-O-Cu pathways. Theoretical CASSCF, DFT and TDDFT calculations were applied to investigate the electronic structures of 1 and 2 and rationalize their behavior in solution.

Application of the noncollinear Scalmani-Frisch formalism to current density functional theory

We generalize the noncollinear formalism proposed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)] to include the particle and spin current densities for meta-generalized gradient approximations and local hybrid functionals. This allows us to fully include the impact of spin-orbit coupling in relativistic calculations and for applications to finite magnetic fields. For the latter, we use London atomic orbitals to ensure gauge origin invariance. It is shown that this formalism is superior to the more common canonical noncollinear approach in relativistic calculations, as it naturally includes all three spin current densities in the closed-shell limit and avoids the projection onto the spin magnetization vector. This is important to easily restore rotational invariance in this limit. In addition, the Scalmani-Frisch approach can be made numerically stable and may lead to a nonvanishing local magnetic torque. However, both formalisms are rotationally invariant for open-shell systems and in finite magnetic fields.

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

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

Molecular engineering on tyrian puprle natural dye as TiO2 based fined tuned photovoltaic dye material: DFT molecular analysis

In this research, molecular modification is employed to see the enhancement in the efficiency of Tyrian Purple (TP), a natural dye, for organic photovoltaic materials. By using Density Functional Theory (DFT) based molecular modeling, seven new structures are designed with pi spacer to extend electron donor moieties. Teheir Frontier Molecular Orbital (FMO) analysis demonstartes their charges with a similar pattern of distributions over their Highest Occupied and Lowed Unocuupied Molecular Orbitals (HOMO/lUMO). This analysls also show their energy gaps (Egaps) to range around 2.97-3.02 eV. Their maximum absorption wavelength (λmax) demosntartes 486-490 nm range to indicate their tendency of absorbing light efficiently. Their Transition Density Matrix (TDM) analysis also reveals their facile electronic transitions without a significant charges over spacers. From calculating their photovoltaic paramters, their Light Harvesting Efficiency (LHE) reaches to 72.4-95.5 %. Also their Open Circuit Voltage (Voc) varies across 1.16-1.34 V. It is found that dyes actively adsorb onto TiO2 clusters to demonstrate their promise for tuning their Conduction Band (CB). This research is an effort for to evaluate the structural correlations to the develop photovoltaic materials through molecular-level design and optimization.

Calibration of several first excited state properties for organic molecules through systematic comparison of TDDFT with experimental spectra

Time-dependent density functional theory (TDDFT) is a powerful computational tool for investigating excitation properties in organic electronics, and it holds significant potential for high-throughput virtual screening (HTVS) in this field. While most benchmarks focus on excitation energies, less attention has been paid to evaluating the accuracy of computed oscillator strengths and exciton reorganization energies against experimental data. In this work, we provide a systematic approach to evaluate in parallel the accuracy of these three quantities on the basis of a suitable fitting of the experimental absorption spectra of 71 molecules in solution. After considering 18 computational methodologies, the results from the M06-2X/def2-TZVP/PCM method demonstrate the strongest correlation with experimental data across the desired properties. For HTVS, the M06-2X/6-31G(d)/PCM method appears to be a particularly convenient choice among all methodologies due to its balance of computational efficiency and accuracy. Our results provide an additional benchmark needed before employing TDDFT methods for the discovery and design of organic electronic molecules.

Efficient Ground-State Recovery of UV-Photoexcited p-Nitrophenol in Aqueous Solution by Direct and Multistep Pathways

Nitroaromatic compounds are found in brown carbon aerosols emitted to the Earth's atmosphere by biomass burning, and are important organic chromophores for the absorption of solar radiation. Here, transient absorption spectroscopy spanning 100 fs-8 μs is used to explore the pH-dependent photochemical pathways for aqueous solutions of p-nitrophenol, chosen as a representative nitroaromatic compound. Broadband ultrafast UV-visible and infrared probes are used to characterize the excited states and intermediate species involved in the multistep photochemistry, and to determine their lifetimes under different pH conditions. The assignment of absorption bands, and the dynamical interpretation of our experimental measurements are supported by computational calculations. After 320 nm photoexcitation to the first bright state, which has 1ππ* character in the Franck-Condon region, and ultrafast (∼200 fs) structural relaxation in the adiabatic S1 state to a region with 1nπ* electronic character, the S1 p-nitrophenol population decays on a time scale of ∼12 ps. This decay involves competition between direct internal conversion to the S0 state (∼40%) and rapid intersystem crossing to the triplet manifold (∼60%). Population in the T1-state decays by excited-state proton transfer (ESPT) to the surrounding water and relaxation of the resulting triplet-state p-nitrophenolate anion to its S0 electronic ground state in ∼5 ns. Reprotonation of the S0-state p-nitrophenolate anion recovers p-nitrophenol in its electronic ground state. Overall recovery of the S0 state of aqueous p-nitrophenol via these competing pathways is close to 100% efficient. The experimental observations help to explain why nitroaromatic compounds such as p-nitrophenol resist photo-oxidative degradation in the environment.

Electronic Spectroscopy of Ovalene: Reassignment of the S2(B3u)- S0(Ag) Transition

As part of our experiments to characterize solid para-hydrogen (para-H2) as a matrix host for electronic spectroscopy with potential applications in the ongoing quest for the carriers of the diffuse interstellar bands (DIB), we studied dispersed fluorescence and fluorescence excitation spectra of ovalene (C32H14), a planar polycyclic aromatic hydrocarbon (PAH) of D2h symmetry. Although generally in good agreement with previously reported data for jet-cooled C32H14, our results, in conjunction with quantum-chemical calculations, indicate that the observed spectral progressions are associated with the S2(B3u)-S0(Ag) electronic transition instead of the originally assigned S1-S0 transition for C32H14 in a supersonic jet, and that the previously reported origin band was misassigned and should be located at ∼21050 cm-1. The reassignment is further supported by the comparably long fluorescence lifetime of ∼1.7 μs. From an analysis of spectral features located >1600 cm-1 in the fluorescence excitation spectrum, we estimate an S2(B3u)-S3(B1g) energy gap of ∼350 cm-1.

Stable Meisenheimer Complexes as Powerful Photoreductants Readily Obtained from Aza-Hetero Aromatic Compounds

Excited states of radical anions derived from the photoreduction of stable organic molecules are suggested to serve as potent reductants. However, excited states of these species are too short-lived to allow bimolecular quenching processes. Recently, the singlet excited state of Meisenheimer complexes, which possess a long-lived excited state, was identified as the competent species for the reduction of challenging organic substrates (-2.63 V vs. SCE, saturated calomel electrode). To produce reasonably stable and simply accessible different Meisenheimer complexes, the addition of nBuLi to readily available aromatic heterocycles was investigated, and the photoreactivity of the generated species was studied. In this paper, we present the straightforward preparation of a family of powerful photoreductants (*Eox<-3 V vs. SCE in their excited states, determined by DFT and time-dependent TD-DFT calculations; DFT, density functional theory) that can induce dehalogenation of electron-rich aryl chlorides and to form C-C bond through radical cyclization. Photophysical analyses and computational studies in combination with experimental mechanistic investigations demonstrate the ability of the adduct to act as a strong electron donor under visible light irradiation.

A Constraint-Based Orbital-Optimized Excited State Method (COOX)

In this work, we present a novel method to directly calculate targeted electronic excited states within a self-consistent field calculation based on constrained density functional theory (cDFT). The constraint is constructed from the static occupied-occupied and virtual-virtual parts of the excited state difference density from (simplified) linear-response time-dependent density functional theory calculations (LR-TDDFT). Our new method shows a stable convergence behavior, provides an accurate excited state density adhering to the Aufbau principle, and can be solved within a restricted SCF for singlet excitations to avoid spin contamination. This also allows the straightforward application of post-SCF electron-correlation methods like MP2 or direct RPA methods. We present the details of our constraint-based orbital-optimized excited state method (COOX) and compare it to similar schemes. The accuracy of excitation energies will be analyzed for a benchmark of systems, while the quality of the resulting excited state densities is investigated by evaluating excited state nuclear forces and excited state structure optimizations. We also investigate the performance of the proposed COOX method for long-range charge transfer excitations and conical intersections with the ground-state.

Effect of Leaving Centrosymmetric Character on Spectral Properties in Mono-, Bi-, and Triphotonic Absorption Spectroscopies

Numerical simulations of the absorption bands of photoswitch E-o-tetrafluoroazobenzene in DMSO solution under one-, two-, and three-photon absorption conditions combined with the analysis of the behavior of transition probability under distortion of planarity reveal many similarities between the mono- and triphoton spectroscopic behaviors with a two-photon spectrum being set apart. The position of the absorption peak for the studied nπ* and ππ* transitions appears shifted to lower energies (longer wavelengths) than the conventional estimate based on vertical excitation from the ground-state potential energy minimum.

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

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

Exploring non-covalent interactions in excited states: beyond aromatic excimer models

Time-dependent density functional theory (TD-DFT) offers a relatively accurate and inexpensive approach for excited state calculations. However, conventional TD-DFT may suffer from the same poor description of non-covalent interactions (NCIs) which is known from ground-state DFT. In this work we present a comprehensive benchmark study of TD-DFT for excited-state NCIs. This is achieved by calculating dissociation curves for excited complexes ('exciplexes'), whose binding strength depends on excited-state NCIs including electrostatics, Pauli repulsion, charge-transfer, and London dispersion. Reference dissociation curves are calculated with the reasonably accurate wave function method SCS-CC2/CBS(3,4) which is used to benchmark a range of TD-DFT methods. Additionally, we test the effect of ground-state dispersion corrections, DFT-D3(BJ) and VV10, for exciplex binding. Overall, we find that TD-DFT methods generally under-bind exciplexes which can be explained by the missing dispersion forces. Underbinding errors reduce going up the rungs of Jacob's ladder. Further, the D3(BJ) dispersion correction is essential for good accuracy in most cases. Likewise, the VV10-type non-local kernel yields relatively low errors and has comparable performance in either its fully self-consistent implementation or as a post-SCF additive correction, but its impact is solely on ground-state energies and not on excitation energies. From our analysis, the most robust TD-DFT methods for exciplexes with localised excitations in their equilibrium and non-equilibrium geometries are the double hybrids B2GP-PLYP-D3(BJ) and B2PLYP-D3(BJ). Their range-separated versions ωB2(GP-)PLYP-D3(BJ) or the spin-opposite scaled, range-separated double hybrid SOS-ωB88PP86 can be recommended when charge transfer plays a role in the excitations. We also identify the need for a state-specific dispersion correction as the next step for improved TD-DFT performance.

Non-Degenerate Two-Photon Absorption of Fluorescent Protein Chromophores

Two-photon absorption (2PA), where a pair of photons are absorbed simultaneously, is recognized as a potent bioimaging technique, which depends on the quantified 2PA probability, defined as cross-section (σ2PA). The absorbed photons either have equivalent (ω1 = ω2) or different frequencies (ω1 ≠ ω2), where the former is degenerate 2PA (D-2PA) and the latter is nondegenerate 2PA (ND-2PA). ND-2PA is of particular interest since it is a promising imaging technology with flexibility of photon frequencies and enhanced cross sections, however, it remains a relatively unexplored area compared to D-2PA. This work utilizes time-dependent density functional theory (TD-DFT) and second-order approximate coupled-cluster with the resolution-of-identity approximation (RI-CC2), for the excitation from S0 to S1, to investigate σD-2PA and σND-2PA of FP chromophore models. Interestingly, comparing CAM-B3LYP with the RI-CC2 computations shows qualitative and, in fact, near quantitative agreement in the computed improvements of σND-2PA for comparable (relative) frequency detunings, despite the known underestimations of 2PA cross sections, for TD-DFT results relative to RI-CC2 values. As expected from the 2-state model, the computed values of σND-2PA are quantitatively larger than σD-2PA, where chromophores with the largest values of σD-2PA show greater potential for σND-2PA improvement. Anionic chromophores demonstrated improvements up to 14%, while substantial enhancements were observed in neutral chromophores with some achieving a 30% increase. This work investigates the ND-2PA photophysical characteristics of FP chromophores and identifies qualitative patterns in the computed properties of ND-2PA relative to D-2PA.

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.

An Improved Penalty-Based Excited-State Variational Monte Carlo Approach with Deep-Learning Ansatzes

We introduce several improvements to the penalty-based variational quantum Monte Carlo (VMC) algorithm for computing electronic excited states of Entwistle et al. [Nat. Commun. 14, 274 (2023)] and demonstrate that the accuracy of the updated method is competitive with other available excited-state VMC approaches. A theoretical comparison of the computational aspects of these algorithms is presented, where several benefits of the penalty-based method are identified. Our main contributions include an automatic mechanism for tuning the scale of the penalty terms, an updated form of the overlap penalty with proven convergence properties, and a new term that penalizes the spin of the wave function, enabling the selective computation of states with a given spin. With these improvements, along with the use of the latest self-attention-based ansatz, the penalty-based method achieves a mean absolute error below 1 kcal/mol for the vertical excitation energies of a set of 26 atoms and molecules, without relying on variance matching schemes. Considering excited states along the dissociation of the carbon dimer, the accuracy of the penalty-based method is on par with that of natural-excited-state (NES) VMC, while also providing results for additional sections of the potential energy surface, which were inaccessible with the NES method. Additionally, the accuracy of the penalty-based method is improved for a conical intersection of ethylene, with the predicted angle of the intersection agreeing well with both NES-VMC and multireference configuration interaction.

GPU-accelerated on-the-fly nonadiabatic semiclassical dynamics

GPU-accelerated on-the-fly nonadiabatic dynamics is enabled by interfacing the linearized semiclassical dynamics approach with the TeraChem electronic structure program. We describe the computational workflow of the "PySCES" code interface, a Python code for semiclassical dynamics with on-the-fly electronic structure, including parallelization over multiple GPU nodes. We showcase the abilities of this code and present timings for two benchmark systems: fulvene solvated in acetonitrile and a charge transfer system in which a photoexcited zinc-phthalocyanine donor transfers charge to a fullerene acceptor through multiple electronic states on an ultrafast timescale. Our implementation paves the way for an efficient semiclassical approach to model the nonadiabatic excited state dynamics of complex molecules, materials, and condensed phase systems.

Exploration of the effect of multiple acceptor and π-spacer moieties coupled to indolonaphthyridine core for promising organic photovoltaic properties: a first principles framework

Herein, the indolonaphthyridine-based molecules (INDTD1-INDTD8) with A1-π-A2-π-A1 configuration were designed by the end-capped modification of INDTR reference with various acceptors. The density functional theory (DFT) and time-dependent DFT (TD-DFT) analyses at M06/6-31G(d,p) level were reported in this research to explore their optoelectronic and photovoltaic features. Their geometrical structures were initially optimized at the afore-said level and followed by various calculations such as the frontier molecular orbitals (FMOs), UV-Visible, density of states (DOS), transition density matrix (TDM), binding energy (Eb), open circuit voltage (Voc) and fill factor (FF). Moreover, their global reactivity parameters (GRPs) were depicted by using the HOMO-LUMO band gaps obtained from the FMOs study. The tailored molecules demonstrated lower band gaps (2.183-2.269 eV) than INDTR (2.288 eV). They also showed bathochromic shifts in the visible region in chloroform (735.937-762.318 nm) and gas phase (710.384-729.571 nm) as compared to INDTR (724.710 and 698.498 nm, respectively). Further, intramolecular charge transfer (ICT) was demonstrated via the DOS and TDM graphical maps. Among all the entitled chromophores, INDTD7 showed significantly reduced band gap (2.183 eV), red-shifted absorption value (760.914 nm) in chloroform solvent and minimal Eb value (0.554 eV). The presence of -SO3H groups on the terminal acceptors of INDTD7  may enhance the mobility of charges. The results suggested that the newly designed chromophores can be effective candidates for the future organic solar cell applications. Moreover, this study may encourage the experimentalists to develop photovoltaic materials.

Femtosecond Core-Level Spectroscopy Reveals Involvement of Triplet States in the Gas-Phase Photodissociation of Fe(CO)5

Excitation of iron pentacarbonyl [Fe(CO)5], a prototypical photocatalyst, at 266 nm causes the sequential loss of two CO ligands in the gas phase, creating catalytically active, unsaturated iron carbonyls. Despite numerous studies, major aspects of its ultrafast photochemistry remain unresolved because the early excited-state dynamics have so far eluded spectroscopic observation. This has led to the long-held assumption that ultrafast dissociation of gas-phase Fe(CO)5 proceeds exclusively on the singlet manifold. Herein, we present a combined experimental-theoretical study employing ultrafast extreme ultraviolet transient absorption spectroscopy near the Fe M2,3-edge, which features spectral evolution on 100 fs and 3 ps time scales, alongside high-level electronic structure theory, which enables characterization of the molecular geometries and electronic states involved in the ultrafast photodissociation of Fe(CO)5. We assign the 100 fs evolution to spectroscopic signatures associated with intertwined structural and electronic dynamics on the singlet metal-centered states during the first CO loss and the 3 ps evolution to the competing dissociation of Fe(CO)4 along the lowest singlet and triplet surfaces to form Fe(CO)3. Calculations of transient spectra in both singlet and triplet states as well as spin-orbit coupling constants along key structural pathways provide evidence for intersystem crossing to the triplet ground state of Fe(CO)4. Thus, our work presents the first spectroscopic detection of transient excited states during ultrafast photodissociation of gas-phase Fe(CO)5 and challenges the long-standing assumption that triplet states do not play a role in the ultrafast dynamics.

A new parameterization of the DFT/CIS method with applications to core-level spectroscopy

Time-dependent density functional theory (TD-DFT) within a restricted excitation space is an efficient means to compute core-level excitation energies using only a small subset of the occupied orbitals. However, core-to-valence excitation energies are significantly underestimated when standard exchange-correlation functionals are used, which is partly traceable to systemic issues with TD-DFT's description of Rydberg and charge-transfer excited states. To mitigate this, we have implemented an empirically modified combination of configuration interaction with single substitutions (CIS) based on Kohn-Sham orbitals, which is known as "DFT/CIS." This semi-empirical approach is well-suited for simulating x-ray near-edge spectra, as it contains sufficient exact exchange to model charge-transfer excitations yet retains DFT's low-cost description of dynamical electron correlation. Empirical corrections to the matrix elements enable semi-quantitative simulation of near-edge x-ray spectra without the need for significant a posteriori shifts; this should be useful in complex molecules and materials with multiple overlapping x-ray edges. Parameter optimization for use with a specific range-separated hybrid functional makes this a black-box method intended for both core and valence spectroscopy. Results herein demonstrate that realistic K-edge absorption and emission spectra can be obtained for second- and third-row elements and 3d transition metals, with promising results for L-edge spectra as well. DFT/CIS calculations require absolute shifts that are considerably smaller than what is typical in TD-DFT.

The Simulation of Solvent Polarizabilities and Dipolarities with Polarizable Continuum Model

The ability of polarizable continuum models (PCM) to simulate nonspecific solvent effects (dipolarity and polarizability) was evaluated by calculating the transition energies of 1,1,10,10-tetrabutyldecanonaene (ttbp9) and 2-N,N-dimethylamino-7-nitrofluorene (DMANF), basis of Catalán's polarizability (SP) and dipolarity (SdP) solvent scales, respectively. Time-dependent density-functional theory (TD-DFT) calculations were performed at different levels of theory, employing four basis sets in 10 different solvents, covering the full range of the normalized SP and SdP scales. Transition energies were calculated using linear response (LR) and corrected linear response (cLR2) schemes. Although these methods yielded variable mean absolute errors, the LR-PCM calculations reproduced medium polarizability and dipolarity trends. While calculated ttbp9 transition energies correlated with SP and Laurence's dispersion-induced (DI) scales, the DMANF transition energies correlated poorly with SdP or Laurence's ES dipolarity scales. This result agrees with the fact that DMANF solvatochromism is "contaminated" by solvent polarizability and HB acidity. The incorporation of SP or DI contributions led to much better (r2 > 0.95) correlations with the DMANF-calculated transitions. The results offer a clearer picture of the limitations of continuum models in simulating the behavior of solvatochromic dyes in solution by pointing out their poor performance when specific solvent effects, such as hydrogen-bond interactions, play a significant role in their solvatochromism.

Screened optimally tuned range separated hybrid functional for solvated low bandgap molecular systems

The description of electronic properties of low bandgap molecular system is often performed by using density functional theory (DFT) and time dependent (TD) DFT calculations with the optimally tuned range-separated hybrid (OT-RSH) functional, as it contains the necessary ingredients to reliably predict charge transfer excitations. However, the range separating parameter (ω) is system-dependent and its optimization, including the chemical environment, is intricate. Refaely-Abramson et al. demonstrated that the gap renormalization in molecular crystals, a ground state property, can be represented by an OT-RSH functional screened by ɛstatic [Phys. Rev. B 88, 081204(R) (2013)], the zero frequency scalar dielectric constant. In this study, we propose the use of an OT-RSH functional screened by the scalar dielectric constant in the high frequency limit (OT-sRSH), ɛ∞, an appropriate constraint for vertical ionization energies or excitations in a dielectric environment. We have performed calculations for S,N-heteroacene derivatives in tetrahydrofuran and dichloromethane. The "unscreened" OT-RSH functional tends to underestimate experimental ionization potentials (IPs) and optical gaps (Egs) by up to 1.5 and 0.5 eV, respectively. In contrast, OT-sRSH functional calculations underestimate IPs and Egs by only 0.4 and 0.2 eV. We also compared the OT-sRSH results to explicitly solvated OT-RSH functional calculations for oligothiophenes in dioxane, benzene in ammonia, and methylene blue in water. We observe that both the approaches perform similarly for weakly interacting intermolecular systems and deviate for solvent-solute interacting systems, as expected. In conclusion, the OT-sRSH functional can describe molecular systems with environmental polarization effects accurately, a step toward describing realistic molecular systems.

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.

Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

Comment on: "Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation"

A recent benchmark study of two-photon absorption (2PA) strengths using meta-generalized gradient approximation (MGGA) exchange-correlation functionals by Ahmadzadeh, Li, Rinkevicius, Norman, and Zaleśny (ALRNZ24) [ J. Phys. Chem. Lett. 2024, 15, 969] misrepresents the state of the field in this area. Not only was an assessment of 2PA strengths for the exact same benchmark published previously; ALRNZ24 also uses a gauge-variant form of MGGA response theory which produces erratic behavior for certain benchmark systems. Applications of MGGAs to optical and magnetic response properties should use a gauge-invariant extension of MGGA functionals such as paramagnetic current-dependent MGGAs.

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

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

COMPAS-3: a dataset of peri-condensed polybenzenoid hydrocarbons

We introduce the third installment of the COMPAS Project - a COMputational database of Polycyclic Aromatic Systems, focused on peri-condensed polybenzenoid hydrocarbons. In this installment, we develop two datasets containing the optimized ground-state structures and a selection of molecular properties of ∼39k and ∼9k peri-condensed polybenzenoid hydrocarbons (at the GFN2-xTB and CAM-B3LYP-D3BJ/cc-pvdz//CAM-B3LYP-D3BJ/def2-SVP levels, respectively). The manuscript details the enumeration and data generation processes and describes the information available within the datasets. An in-depth comparison between the two types of computation is performed, and it is found that the geometrical disagreement is maximal for slightly-distorted molecules. In addition, a data-driven analysis of the structure-property trends of peri-condensed PBHs is performed, highlighting the effect of the size of peri-condensed islands and linearly annulated rings on the HOMO-LUMO gap. The insights described herein are important for rational design of novel functional aromatic molecules for use in, e.g., organic electronics. The generated datasets provide a basis for additional data-driven machine- and deep-learning studies in chemistry.

Theoretical Insights into the Structural and Optical Properties of D-π-A-based Cyanostilbene Systems of α and β Variants

The π-conjugated organic molecules containing cyanostilbene motifs have been extensively investigated due to their great potential applications in several optoelectronic and biological fields. Developing efficient molecules in this respect requires strategic structural engineering and a deep understanding of the structure-property relationship at the molecular level. In this context, understanding the impact of positional isomerism in cyanostilbene systems is a fundamental aspect of designing desired materials with improved photophysical properties. Herein, we designed ten donor-π-acceptor (D-π-A) type cyanostilbene derivatives (P1 - P10) with different π linkers and compared their structural and optoelectronic properties arising from the positional variations of the -CN group (α and β- variations) through the utilization of density functional theory (DFT) and time-dependent DFT (TDDFT) methods. The topological analyses of the electron density are used to explain the relatively high stability of α isomer compared to that of β. Frontier molecular orbital analysis reveals that 17 molecules tend to show a reduced highest occupied molecular orbital-lowest unoccupied molecular orbital gap, and most of them showed a greater nonlinear optical (NLO) character compared to the parent molecule. TDDFT calculations indicate that β isomers show higher absorption maxima compared to their α counterparts. Among all the scrutinized molecules, the absorption maximum extended up to 602 nm for P9 and it possesses the highest first-order hyperpolarizability. This study sheds light on positional isomers and their reactivity, absorption spectra, and NLO properties of D-π-A type architecture that can be suitably tuned by appropriating the π-bridge for practical applications.

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.

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.

Search for Chirality in Hydrogenated Magnesium Nanosilicates: A DFT and TD-DFT Investigation

The formation of silicate grains in the interstellar medium (ISM), especially those containing chiral surfaces such as clinopyroxenes, is poorly understood. Moreover, silicate interactions with various forms of hydrogen-proton (H+), neutral H (HI), and molecular hydrogen (H2) are of high importance as hydrogen comprises >90% of the ISM gas budget, and these species play important roles in the formation of new molecules in space. Furthermore, silicate surfaces catalyze the formation of H2 in the interstellar medium formed on dust grain surfaces by H-H association. The technical difficulty of in situ laboratory investigations of nanosilicate nucleation using astrophysically relevant environmental conditions makes computational chemistry a useful tool for studying potential nanosilicate structures. Furthermore, chiral surfaces interacting with chiral organic molecules could serve as templates that lead to the enantiomeric excess of l-amino acids and d-polyols detected in carbonaceous meteorites. However, in order for this effect to take place, an excess of one chiral form of a mineral is required to break the symmetry. This symmetry-breaking event could have been due to the asymmetric absorption of circularly polarized light by the nanosilicate as it traverses star-forming regions. We investigate this possibility using a metastable chiral form of an enstatite dimer as an input for density functional theory (DFT) and time-dependent (TD)-DFT calculations to obtain various properties and circular dichroism spectra. All in all, twenty-six magnesium nanosilicate structures were studied using varying degrees of hydrogenation: none, with HI, with H+, and with H2. The HSE06/aug-cc-pVQZ level of theory was used for the DFT calculations. TD-DFT calculations utilized the CAM-B3LYP/cc-pVQZ and ωB97X-D3/cc-pVQZ functional and basic set pairings. Results show that (1) all twenty-six structures have absorption bands that fall within the 0.6-28.3 μm range available with the newly launched James Webb Space Telescope and (2) there is a small enantioselective effect by UV-CPL on the eight chiral enstatite dimers (predicted g-values of up to 0.007). While the observed effect is small, it opens up the possibility that it is the inorganic material that becomes enantiomerically biased by UV-CPL, driving chiral enhancements in meteoric organic molecules.

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.

Activating the Fluorescence of a Ni(II) Complex by Energy Transfer

Luminescence of open-shell 3d metal complexes is often quenched due to ultrafast intersystem crossing (ISC) and cooling into a dark metal-centered excited state. We demonstrate successful activation of fluorescence from individual nickel phthalocyanine (NiPc) molecules in the junction of a scanning tunneling microscope (STM) by resonant energy transfer from other metal phthalocyanines at low temperature. By combining STM, scanning tunneling spectroscopy, STM-induced luminescence, and photoluminescence experiments as well as time-dependent density functional theory, we provide evidence that there is an activation barrier for the ISC, which, in most experimental conditions, is overcome. We show that this is also the case in an electroluminescent tunnel junction where individual NiPc molecules adsorbed on an ultrathin NaCl decoupling film on a Ag(111) substrate are probed. However, when an MPc (M = Zn, Pd, Pt) molecule is placed close to NiPc by means of STM atomic manipulation, resonant energy transfer can excite NiPc without overcoming the ISC activation barrier, leading to Q-band fluorescence. This work demonstrates that the thermally activated population of dark metal-centered states can be avoided by a designed local environment at low temperatures paired with directed molecular excitation into vibrationally cold electronic states. Thus, we can envisage the use of luminophores based on more abundant transition metal complexes that do not rely on Pt or Ir by restricting vibration-induced ISC.

Performance of Density Functionals for Excited-State Properties of Isolated Chromophores and Exciplexes: Emission Spectra, Solvatochromic Shifts, and Charge-Transfer Character

This study assesses the performance of various meta-generalized gradient approximation (meta-GGA), global hybrid, and range-separated hybrid (RSH) density functionals in capturing the excited-state properties of organic chromophores and their excited-state complexes (exciplexes). Motivated by their uses in solar energy harvesting and photoredox CO2 reduction, we use oligo-(p-phenylenes) and their excited-state complexes with triethylamine as model systems. We focus on the fluorescence properties of these systems, specifically emission energies. We also consider solvatochromic shifts and wave function characteristics. The latter is described by using reduced quantities such as natural transition orbitals (NTOs) and exciton descriptors. The functionals are benchmarked against the experimental fluorescence spectra and the equation-of-motion coupled-cluster method with single and double excitations. Both in isolated chromophores and in exciplexes, meta-GGA functionals drastically underestimate the emission energies and exhibit significant exciton delocalization and anticorrelation between electron and hole motion. The performance of global hybrid functionals is strongly dependent on the percentage of exact exchange. Our study identifies RSH GGAs as the best-performing functionals, with ωPBE demonstrating the best agreement with experimental results. RSH meta-GGAs often overestimate emission energies in exciplexes and yield larger hole NTOs. Their performance can be improved by optimally tuning the range-separation parameter.

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

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

Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning

Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification of molecules in gas, solution, and solid-state phases. However, accurate prediction of chemical shifts using the gold-standard coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] method with a complete basis set (CBS) can be prohibitively expensive. By contrast, machine learning (ML) methods offer inexpensive alternatives for chemical shift predictions but are hampered by generalization to molecules outside the original training set. Here, we propose several new ideas in ML of the chemical shift prediction for H, C, N, and O that first introduce a novel feature representation, based on the atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics (QM) method, and train it to predict NMR chemical shieldings of a high-level composite theory that approaches the accuracy of CCSD(T)/CBS. In addition, we train the ML model through a new progressive active learning workflow that reduces the total number of expensive high-level composite calculations required while allowing the model to continuously improve on unseen data. Furthermore, the algorithm provides an error estimation, signaling potential unreliability in predictions if the error is large. Finally, we introduce a novel approach to keep the rotational invariance of the features using tensor environment vectors (TEVs) that yields a ML model with the highest accuracy compared to a similar model using data augmentation. We illustrate the predictive capacity of the resulting inexpensive shift machine learning (iShiftML) models across several benchmarks, including unseen molecules in the NS372 data set, gas-phase experimental chemical shifts for small organic molecules, and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.

Density functional theory for doped TiO2: current research strategies and advancements

Since the inception of the density functional theory (DFT) by Hohenberg and Kohn in 1964, it rapidly became an indispensable theoretical tool across various disciplines, such as chemistry, biology, and materials science, among others. This theory has ushered in a new era of computational research, paving the way for substantial advancements in fundamental understanding. Today, DFT is routinely employed for a diverse range of applications, such as probing new material properties and providing a profound understanding of the mechanisms underlying physical, chemical, and biological processes. Even after decades of active utilization, the improvement of DFT principles has never been slowed down, meaning that more accurate theoretical results are continuously generated with time. This work highlights the latest achievements acquired by DFT in the specific research field, namely the theoretical investigations of doped TiO2systems, which have not been comprehensively reviewed and summarized yet. Successful progress in this niche is currently hard to imagine without the support by DFT. It can accurately reveal new TiO2properties after introducing the desired dopant and help to find the optimal system design for a specific application prior to proceeding to more time-consuming and expensive experimental research. Hence, by evaluating a selection of the most recent research studies, we aim to highlight the pertinent aspects of DFT as they relate to the study of doped TiO2systems. We also aim to shed light on the strengths and weaknesses of DFT and present the primary strategies employed thus far to predict the properties of various doped TiO2systems reliably.

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.

Data-Driven Discovery of Organic Electronic Materials Enabled by Hybrid Top-Down/Bottom-Up Design

The high-throughput exploration and screening of molecules for organic electronics involves either a 'top-down' curation and mining of existing repositories, or a 'bottom-up' assembly of user-defined fragments based on known synthetic templates. Both are time-consuming approaches requiring significant resources to compute electronic properties accurately. Here, 'top-down' is combined with 'bottom-up' through automatic assembly and statistical models, thus providing a platform for the fragment-based discovery of organic electronic materials. This study generates a top-down set of 117K synthesized molecules containing structures, electronic and topological properties and chemical composition, and uses them as building blocks for bottom-up design. A tool is developed to automate the coupling of these building blocks at their C(sp2/sp)-H bonds, providing a fundamental link between the two dataset construction philosophies. Statistical models are trained on this dataset and a subset of resulting top-down/bottom-up compounds, enabling on-the-fly prediction of ground and excited state properties with high accuracy across organic compound space. With access to ab initio-quality optical properties, this bottom-up pipeline may be applied to any materials design campaign using existing compounds as building blocks. To illustrate this, over a million molecules are screened for singlet fission. tThe leading candidates provide insight into the features promoting this multiexciton-generating process.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory

Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [Maitra et al., J. Chem. Phys. 120, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra, and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here, we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations.

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.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.