How does theory compare to experiment for oscillator strengths in electronic spectra? Proposing range-separated hybrids with reliable accountability

As an important quantity in atomic and molecular spectroscopy, oscillator strength should be mentioned. Oscillator strength is linked to the transition dipole moment and consequently to the transition probability between two states, where its magnitude is directly connected to the intensity of the peaks in ultraviolet-visible spectra. However, accurately accounting for oscillator strengths still remains one of the greatest challenges in theory and experiment. Given previous efforts in the context of investigations into oscillator strengths, the related theoretical treatments are relatively limited and have proven to be challenging. In this work, the oscillator strengths in the electronic spectra of organic compounds have thoroughly been investigated with the help of optimally tuned range-separated hybrids (OT-RSHs). In particular, variants of the OT-RSHs combined with the polarizable continuum model (PCM), OT-RSHs-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the dielectric constant, OT-SRSHs-PCM, are proposed for reliable prediction of the oscillator strengths. The role of the involved ingredients in the proposed methods, namely the underlying density functional approximations, short-range and long-range Hartree-Fock (HF) exchange, as well as the range-separation parameter, has been examined in detail. It is shown that any combination of the parameters in the proposed approximations does not render the reliable oscillator strengths, but a particular compromise among them is needed to describe the experimental data well. Perusing all the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM, coupled with the linear response theory in the non-equilibrium solvation regime, with the correct asymptotic behavior and incorporating no (low) HF exchange contributions in the short-range part. The best proposed approximations also reveal superior performances not only with respect to their standard counterparts with the default parameters but also as compared to earlier range-separated functionals. Finally, the applicability of the best approximation is also put into broader perspective, where it is used for predicting the oscillator strengths in other sets of compounds not included in the process of developing the approximations. Hopefully, our proposed method can function as an affordable alternative to the expensive wave function-based methods for both theoretical modeling and confirming the experimental observations in the field of electronic spectroscopy.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Spin state and magnetic coupling in polynuclear Ni(II) complexes from density functional theory: is there an optimal amount of Fock exchange?

Reliable prediction of the ground-state spin and magnetic coupling constants in transition-metal complexes is a well-known challenge for density functional theory (DFT). One popular strategy for addressing this long-standing issue involves the modification of the fraction of Fock exchange in a hybrid functional. Here we explore the viability of this approach using three polynuclear metal-organic complexes based on a Ni4O4 cubane motif, having different ground state spin values (S = 0, 2, 4) owing to the use of different ligands. We systematically search for an optimum fraction of Fock exchange, across various global, range-separated, and double hybrid functionals. We find that for all functionals tested, at best there only exists a very narrow range of Fock exchange fractions which results in a correct prediction of the ground-state spin for all three complexes. The useful range is functional dependent, but general trends can be identified. Typically, at least two similar systems must be used in order to determine both an upper and lower limit of the optimal range. This is likely owing to conflicting demands of minimizing delocalization errors, which typically requires a higher percentage of Fock exchange, and addressing static correlation, which typically requires a lower one. Furthermore, we find that within the optimal range of Fock exchange, the sign and relative magnitude of Ni-Ni magnetic coupling constants are reasonably well reproduced, but there is still room for quantitative improvement in the prediction. Thus, the prediction of spin state and magnetic coupling in polynuclear complexes remains an ongoing challenge for DFT.

Spin-Crossover and Fragmentation of Fe(neoim)2 on Silver and Gold

The neutral spin crossover complex Fe(neoim)2, neoim being the deprotonated form of the ionogenic ligand 2-(1H-imidazol-2-yl)-9-methyl-1,10-phenanthroline (neoimH), is investigated on the (111) surfaces of Au and Ag using scanning tunneling microscopy and density functional theory calculations. The complex sublimates and adsorbs intact on Ag(111), where it exhibits an electron-induced spin crossover. However, it fragments on Au. According to density functional theory calculations, the adsorbed complex is drastically distorted by the interactions with the substrates, in particular by van der Waals forces. Dispersion interaction is also decisive for the relative stabilities of the low- and high-spin states of the adsorbed complex. The unexpected instability of the complex on the gold substrate is attributed to enhanced covalent bonding of the fragments to the substrate.

Spin-crossover complexes: Self-interaction correction vs density correction

Complexes containing a transition metal atom with a 3d⁴-3d⁷ electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-Löwdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Toward a Reliable Theory Benchmark

A new composite method for the calculation of spin-crossover energies in 3d transition-metal complexes based on multireference methods is presented. The method reduces to MRCISD+Q at the complete-basis-set (CBS) level for atomic ions, for which it gives excitation energies with a mean absolute error of only ca. 0.01 eV. For molecular complexes, the CASPT2+δMRCI composite approach corresponds to a CASPT2/CBS calculation augmented by a high-level MRCISD+Q-CASPT2 correction with a smaller ligand basis set. For a set of [Fe(He)6]n+ test complexes, the approach reproduces full MRCISD+Q/CBS results to within better than 0.04 eV, without depending on any arbitrary IPEA shifts. The high-quality CASPT2+δMRCI method has then been applied to a series of 3d transition-metal hexaqua complexes in aqueous solution, augmented by an elaborate 3D-RISM-SCF solvent treatment of the underlying structures. It provides unprecedented agreement with experiment for the lowest-lying vertical spin-flip excitation energies, except for the Fe³⁺ system. Closer examination of the latter case provides strong evidence that the observed lowest-energy excitation at 1.56 eV, which has been used frequently for evaluating quantum-chemical methods, does not arise from the iron(III) hexaqua complex in solution, but from its singly deprotonated counterpart, [Fe(H2O)5OH]2+.

Mean Value Ensemble Hubbard-U Correction for Spin-Crossover Molecules

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the U_eff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of U_eff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble U_eff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional U_eff values. Based on the observation that the U_eff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged U_eff values for high-throughput calculations.

Electronic Coupling and Electrocatalysis in Redox Active Fused Iron Corroles

Conjugated arrays composed of corrole macrocycles are increasingly more common, but their chemistry still lags behind that of their porphyrin counterparts. Here, we report on the insertion of iron(III) into a β,β-fused corrole dimer and on the electronic effects that this redox active metal center has on the already rich coordination chemistry of [H3tpfc] COT, where COT = cyclo-octatetraene and tpfc = tris(pentafluorophenyl)corrole. Synthetic manipulations were performed for the isolation and full characterization of both the 5-coordinate [FeIIItpfc(py)]2COT and 6-coordinate [FeIIItpfc(py)2]2COT, with one and two axial pyridine ligands per metal, respectively. X-Ray crystallography reveals a dome-shaped structure for [FeIIItpfc(py)]2COT and a perfectly planar geometry which (surprisingly at first) is also characterized by shorter Fe-N (corrole) and Fe-N (pyridine) distances. Computational investigations clarify that the structural phenomena are due to a change in the iron(III) spin state from intermediate (S = 3/2) to low (S = 1/2), and that both the 5- and 6-coordinated complexes are enthalpically favored. Yet, in contrast to iron(III) porphyrins, the formation enthalpy for the coordination of the first pyridine to Fe(III) corrole is more negative than that of the second pyridine coordination. Possible interactions between the two corrole subunits and the chelated iron ions were examined by UV-Vis spectroscopy, electrochemical techniques, and density functional theory (DFT). The large differences in the electronic spectra of the dimer relative to the monomer are concluded to be due to a reduced electronic gap, owing to the extensive electron delocalization through the fusing bridge. A cathodic sweep for the dimer discloses two redox processes, separated by 230 mV. The DFT self-consistent charge density for the neutral and cationic states (1- and 2-electron oxidized) reveals that the holes are localized on the macrocycle. A different picture emerges from the reduction process, where both the electrochemistry and the calculated charge density point toward two consecutive electron transfers with similar energetics, indicative of very weak electron communication between the two redox active iron(III) sites. The binuclear complex was determined to be a much better catalyst for the electrochemical hydrogen evolution reaction (HER) than the analogous mononuclear corrole.

Toward highly efficient hyperfluorescence-based emitters through excited-states alignment using novel optimally tuned range-separated models

Hyperfluorescence has recently been introduced as a promising strategy to achieve organic light-emitting diodes (OLEDs) with high color purity and enhanced stability. In this approach, fluorescent emitters (FEs) with strong and narrow band fluorescence are integrated in thin films containing sensitizers exhibiting thermally activated delayed fluorescence (TADF). Toward highly efficient hyperfluorescence-based emitters, the excited-states ordering of the FEs should be well-aligned. Given some recent endeavors in this context, the related theoretical explorations are relatively limited and have proven to be challenging. In this work, alignments of the corresponding excited-states, crucial for both the fast Förster resonance energy transfer and suppression of the Dexter energy transfer from TADF sensitizers to FEs, have theoretically been investigated using optimally tuned range-separated hybrid functionals (OT-RSHs). We have proposed and validated several variants of the models including OT-RSHs, their coupled versions with the polarizable continuum model, OT-RSHs-PCM, as well as the screened versions accounting for the screening effects by the electron correlation through the scalar dielectric constant, OT-SRSHs, for a reliable description of the excited-states ordering in the FEs of the hyperfluorescence-based materials. Particular attention is paid to the influence of the underlying density functional approximations as well as the short- and long-range Hartree-Fock (HF) exchange contributions and the range-separation parameter. Considering a series of experimentally known hyperfluorescence-based emitters as working models, it is unveiled that any combination of the ingredients in the proposed models does not render the correct order of the excited-states of the FEs, but a particular compromise among the involved parameters is needed to more accurately account for the relevant excited-states alignment. Perusing the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM with the correct asymptotic behavior and incorporating no (low) HF exchange contribution at the short-range regime. The proposed models show superior performances not only with respect to their standard counterparts with the default parameters but also as compared to other range-separated approximations. Accountability of the best-proposed model is also put into broader perspective, where it has been employed for the computational design of several molecules as promising FE candidates prone to be utilized in hyperfluorescence-based materials. Summing up, the proposed models in this study can be recommended for both the theoretical modeling and confirming the experimental observations in the field of hyperfluorescence-based OLEDs.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T₁) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.

Excited-state properties of organic semiconductor dyes as electrically pumped lasing candidates from new optimally tuned range-separated models

Even though many efforts have been devoted to optical lasing in recent years, the realization of lasing by direct electrical excitation of organic semiconductors is hampered mainly due to optical losses from electrical contacts and electrical losses induced by triplets and polarons at high current densities. Hereby, accurately accounting for the electrically pumped organic semiconductor laser diodes (OSLDs) still remains one of the greatest challenges in optoelectronics. In this work, the excited-state characteristics of the organic semiconductor dyes used in the electrically pumped OSLDs have thoroughly been investigated using optimally tuned range-separated hybrids (OT-RSHs). Considering several experimentally known compounds of the electrically pumped OSLDs as working models, several variants of OT-RSHs, their combination forms with the polarizable continuum model (PCM), OT-RSH-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the scalar dielectric constant, OT-SRSHs, have been proposed for reliable prediction of their emission energies and oscillator strengths in both the gas and solvent phases. The role of involved ingredients in the models, namely, the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, has been examined in detail. It is shown that the newly designed OT-RSHs with the correct behavior of asymptotic exchange-correlation potential outperform the standard RSHs and other density functionals with both fixed and interelectronic distance-dependent exact-like exchange for describing the excite-state properties of compounds of the electrically pumped OSLDs. Concerning the computational cost of the models, it is unveiled that performing both the optimal tuning procedure and subsequent excited-state computations using OT-RSHs in the gas phase can be considered as a more reliable and affordable framework. Finally, the applicability of the proposed models is also put into a broader perspective for the computational design of several compounds as promising candidates to be used in the OSLD materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the related theoretical modeling and confirming the experimental observations in the field of electrically pumped OSLDs.

Accurate calculation of spin-state energy gaps in Fe(III) spin-crossover systems using density functional methods

Fe(III) complexes are receiving ever-increasing attention as spin crossover (SCO) systems because they are usually air stable, as opposed to Fe(II) complexes, which are prone to oxidation. Here, we present the first systematic study exclusively devoted to assess the accuracy of several exchange-correlation functionals when it comes to predicting the energy gap between the high-spin (S = 5/2) and the low-spin (S = 1/2) states of Fe(III) complexes. Using a dataset of 24 different Fe(III) hexacoordinated complexes, it is demonstrated that the B3LYP* functional is an excellent choice not only for predicting spin-state energy gaps for Fe(III) complexes undergoing spin-transitions but also for discriminating Fe(III) complexes that are either low- or high-spin in the whole range of temperatures. Our benchmark study has led to the identification of a very versatile Fe(III) compound whose SCO properties can be engineered upon changing a single axial ligand. Overall, this work demonstrates that B3LYP* is a reliable functional for screening new spin-crossover systems with tailored properties.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density

We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.

Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.

Accurate Molecular Geometries in Complex Excited-State Potential Energy Surfaces from Time-Dependent Density Functional Theory

The interplay of electronic excitations and structural changes in molecules impacts nonradiative decay and charge transfer in the excited state, thus influencing excited-state lifetimes and photocatalytic reaction rates in optoelectronic and energy devices. To capture such effects requires computational methods providing an accurate description of excited-state potential energy surfaces and geometries. We suggest time-dependent density functional theory using optimally tuned range-separated hybrid (OT-RSH) functionals as an accurate approach to obtain excited-state molecular geometries. We show that OT-RSH provides accurate molecular geometries in excited-state potential energy surfaces that are complex and involve an interplay of local and charge-transfer excitations, for which conventional semilocal and hybrid functionals fail. At the same time, the nonempirical OT-RSH approach maintains the high accuracy of parametrized functionals (e.g., B3LYP) for predicting excited-state geometries of small organic molecules showing valence excited states.

Singlet fission relevant energetics from optimally tuned range-separated hybrids

As a promising idea to design high-efficiency organic photovoltaics, singlet fission (SF) mechanism, i.e., generating two triplet excitons out of a single photon absorption, has recently come into the spotlight. Even though much effort has been devoted to this arena, accurately accounting for the SF process from the theoretical perspective has proven to be challenging. Herein, the SF energetics have thoroughly been investigated with the help of optimally tuned range-separated hybrid functionals (OT-RSHs) in both gas and solvent phases. Taking a series of experimentally known SF chromophores as working models, we have proposed and validated several variants of OT-RSH approximations for the reliable prediction of the energy levels which match the crucial criteria for the SF process, namely, the negative singlet-triplet and triplet-triplet energy gaps. We scrutinize the role of the OT-RSH ingredients, i.e., the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, for our purpose. The newly designed OT-RSHs outperform the standard RSHs and other related schemes such as screened-exchange approximations as well as other density functionals from different rungs for describing the SF energetics. More importantly, it is unveiled that although the OT-RSH coupled with the polarizable continuum model, OT-RSH-PCM, as well as the screened versions, OT-SRSHs, which account for the screening effect by the electron correlation through the scalar dielectric constant have some advantages over gas-phase computations using OT-RSHs, the energetics criteria of the SF process may not necessarily be satisfied. This in turn corroborates the idea of performing both the optimal tuning procedure and subsequent computations of the SF relevant energetics using OT-RSHs as a more reliable and affordable framework, at least for the present purpose. The applicability of the proposed models is also put into broader perspective, where they are used for the computational design of several chromophores as promising candidates prone to utilization in the SF-based materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the theoretical modeling of SF chromophores and confirming the experimental observations in the field.

Unveiling the role of short-range exact-like exchange in the optimally tuned range-separated hybrids for fluorescence lifetime modeling

We propose and validate several variants of the optimally tuned range-separated hybrid functionals (OT-RSHs) including different density functional approximations for predicting the fluorescence lifetimes of different categories of fluorophores within the time-dependent density functional theory (TD-DFT) framework using both the polarizable continuum and state-specific solvation models. Our main idea originates from performing the optimal tuning in the presence of a contribution of the exact-like exchange at the short-range part, which, in turn, leads to the small values of the range-separation parameter, and computing the fluorescence lifetimes using the models including no or small portions of the short-range exact-like exchange. Particular attention is also paid to the influence of the geometries of emitters on fluorescence lifetime computations. It is shown that our developed OT-RSHs along with the polarizable continuum model can be considered as the promising candidates within the TD-DFT framework for the prediction of fluorescence lifetimes for various fluorophores. We find that the proposed models not only outperform their standard counterparts but also provide reliable data better than or comparable to the conventional hybrid functionals with both the fixed and interelectronic distance-dependent exact-like exchanges. Furthermore, it is also revealed that when the excited state geometries come into play, more accurate descriptions of the fluorescence lifetimes can be achieved. Hopefully, our findings can give impetus for future developments of OT-RSHs for computational modeling of other characteristics in fluorescence spectroscopy as well as for verification of the related experimental observations.

The effect of N-heterocyclic carbene units on the absorption spectra of Fe(ii) complexes: a challenge for theory

The absorption spectra of five Fe(ii) homoleptic and heteroleptic complexes containing strong sigma-donating N-heterocyclic carbene (NHC) and polypyridyl ligands have been theoretically characterized using a tuned range-separation functional.

Appraising spin-state energetics in transition metal complexes using double-hybrid models: accountability of SOS0-PBESCAN0-2(a) as a promising paradigm

Through a comprehensive survey, reliable double-hybrid models have been validated and proposed for spin-state energetics in transition metal complexes.

Toward photophysical characteristics of triplet-triplet annihilation photon upconversion: a promising protocol from the perspective of optimally tuned range-separated hybrids

The photon upconversion (UC) process assisted by the triplet-triplet annihilation (TTA) mechanism has recently come into the spotlight. Given the rich collection of efforts in this area, theoretical explorations regarding TTA-UC are relatively limited and have proven to be challenging for its control in devices. In this contribution, the photophysical properties crucial for TTA-UC, such as triplet excited state energies and triplet-triplet energy transfer gaps of the essential ingredients involved in the process, namely sensitizers, annihilators and their pairs, have theoretically been investigated using optimally tuned range-separated hybrid functionals (OT-RSHs) and their screened exchange counterparts, OT-SRSHs. Taking a series of experimentally proven-to-work sensitizer/annihilator pairs as working models, we have constructed and validated several variants of OT-RSHs using both full time-dependent and Tamm-Dancoff formalisms for a reliable description of the TTA-UC photophysics. Given the bimolecular biphotonic nature of the TTA-UC process under study, particular attention is paid to the influence of the factors like the underlying density functional approximations and the tunable parameters such as short- and long-range exact-like exchanges as well as the range-separation parameter for both the sensitizers and annihilators separately. Dissecting all the aspects and relying on the appropriate choices from the tested models, we propose an OT-RSH with the correct asymptotic behavior as a cost-effective yet useful tool for this purpose. Not only against the standard RSHs but also in comparison to the conventional hybrids, the newly developed OT-RSH yields a more reliable description for the TTA-UC energetics in the gas phase and dielectric medium. Accountability of the proposed model has further been confirmed for several theoretically designed sensitizer/annihilator pairs prone to be used in the TTA-UC process. Summing up, in light of this study additional pieces of convincing evidence on the quality of OT-(S)RSHs for computational modeling and experimental verifications of the photophysics of the photon UC based on TTA and other possible technologies are showcased.

Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT

Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.

Photoelectron spectra of copper oxide cluster anions from first principles methods

We present results and analyses for the photoelectron spectra of small copper oxide cluster anions (CuO^-, Cu O2- , Cu O3- , and Cu₂O^-). The spectra are computed using various techniques, including density functional theory (DFT) with semi-local, global hybrid, and optimally tuned range-separated hybrid functionals, as well as many-body perturbation theory within the GW approximation based on various DFT starting points. The results are compared with each other and with the available experimental data. We conclude that as in many metal-organic systems, self-interaction errors are a major issue that is mitigated by hybrid functionals. However, these need to be balanced against a strong role of non-dynamical correlation-especially in smaller, more symmetric systems-where errors are alleviated by semi-local functionals. The relative importance of the two phenomena, including practical ways of balancing the two constraints, is discussed in detail.