Density-Dependent Onset of the Long-Range Exchange: A Key to Donor–Acceptor Properties

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.

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.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

Reverse Designing the Wavelength-Specific Thermally Activation Delayed Fluorescent Molecules Using a Genetic Algorithm Coupled with Cheap QM Methods

Genetic algorithm (GA) optimization coupled with the semiempirical intermediate neglect of differential overlap (INDO)/CIS method is presented to inversely design the red thermally activation delayed fluorescent (TADF) molecules. According to the predefined donor-acceptor (DA) library to build an AD_n-type TADF candidate, we utilized the chemical notation language SMILES code to generate a TADF molecule and apply the RDKit program to produce the initial 3D molecular structure. A combined fitness function is proposed to evaluate the performance of the functional-lead TADF molecule. The fitness function includes three key parameters, i.e., the emission wavelength, the energy gap (ΔE_ST) between the lowest singlet (S₁)- and triplet (T₁)-excited states, and the oscillator strengths for electron transition from S₀ and S₁. A cheap QM method, i.e., INDO/CIS, on the basis of an xTB-optimized molecular geometry is applied to quickly calculate the fitness function. Finally, the GA approach is utilized to globally search for the wavelength-specific TADF molecules under our predefined DA library, and the optimum 630 nm red and 660 nm deep red TADF molecules are inversely designed according to the evolution of molecular fitness functions.

Birth of the Hydrated Electron via Charge-Transfer-to-Solvent Excitation of Aqueous Iodide

A primary means to generate hydrated electrons in laboratory experiments is excitation to the charge-transfer-to-solvent (CTTS) state of a solute such as I^-(aq), but this initial step in the genesis of e^-(aq) has never been simulated directly using ab initio molecular dynamics. We report the first such simulations, combining ground- and excited-state simulations of I^-(aq) with a detailed analysis of fluctuations in the Coulomb potential experienced by the nascent solvated electron. What emerges is a two-step picture of the evolution of e^-(aq) starting from the CTTS state: I^-(aq) + hν → I^-*(aq) → I^•(aq) + e^-(aq). Notably, the equilibrated ground state of e^-(aq) evolves from I^-*(aq) without any nonadiabatic transitions, simply as a result of solvent reorganization. The methodology used here should be applicable to other photochemical electron transfer processes in solution, an important class of problems directly relevant to photocatalysis and energy transfer.

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

Hybrid or "extended" symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT's treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that "compromise" basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. The "δ(Hartree-Fock)" correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Simplified tuning of long-range corrected density functionals for use in symmetry-adapted perturbation theory

Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn-Sham orbitals, or SAPT0(KS), can be resurrected for semiquantitative purposes using long-range corrected density functionals whose asymptotic behavior is adjusted separately for each monomer. As in other contexts, correct asymptotic behavior can be enforced via "optimal tuning" based on the ionization energy theorem of density functional theory, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using a fast, convenient, and automated tuning procedure based on the size of the exchange hole. In conjunction with "extended" (X)SAPT methods that improve the description of dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.

Natural Charge-Transfer Analysis: Eliminating Spurious Charge-Transfer States in Time-Dependent Density Functional Theory via Diabatization, with Application to Projection-Based Embedding

For many types of vertical excitation energies, linear-response time-dependent density functional theory (LR-TDDFT) offers a useful degree of accuracy combined with unrivaled computational efficiency, although charge-transfer excitation energies are often systematically and dramatically underestimated, especially for large systems and those that contain explicit solvent. As a result, low-energy electronic spectra of solution-phase chromophores often contain tens to hundreds of spurious charge-transfer states, making LR-TDDFT needlessly expensive in bulk solution. Intensity borrowing by these spurious states can affect intensities of the valence excitations, altering electronic bandshapes. At higher excitation energies, it is difficult to distinguish spurious charge-transfer states from genuine charge-transfer-to-solvent (CTTS) excitations. In this work, we introduce an automated diabatization that enables fast and effective screening of the CTTS acceptor space in bulk solution. Our procedure introduces "natural charge-transfer orbitals" that provide a means to isolate orbitals that are most likely to participate in a CTTS excitation. Projection of these orbitals onto solvent-centered virtual orbitals provides a criterion for defining the most important solvent molecules in a given excitation and be used as an automated subspace selection algorithm for projection-based embedding of a high-level description of the CTTS state in a lower-level description of its environment. We apply this method to an ab initio molecular dynamics trajectory of I^-(aq) and report the lowest-energy CTTS band in the absorption spectrum. Our results are in excellent agreement with the experiment, and only one-third of the water molecules in the I^-(H₂O)₉₆ simulation cell need to be described with LR-TDDFT to obtain excitation energies that are converged to <0.1 eV. The tools introduced herein will improve the accuracy, efficiency, and usability of LR-TDDFT in solution-phase environments.

Eliminating nonradiative decay in Cu(I) emitters: >99% quantum efficiency and microsecond lifetime

Luminescent complexes of heavy metals such as iridium, platinum, and ruthenium play an important role in photocatalysis and energy conversion applications as well as organic light-emitting diodes (OLEDs). Achieving comparable performance from more-earth-abundant copper requires overcoming the weak spin-orbit coupling of the light metal as well as limiting the high reorganization energies typical in copper(I) [Cu(I)] complexes. Here we report that two-coordinate Cu(I) complexes with redox active ligands in coplanar conformation manifest suppressed nonradiative decay, reduced structural reorganization, and sufficient orbital overlap for efficient charge transfer. We achieve photoluminescence efficiencies >99% and microsecond lifetimes, which lead to an efficient blue-emitting OLED. Photophysical analysis and simulations reveal a temperature-dependent interplay between emissive singlet and triplet charge-transfer states and amide-localized triplet states.

Range-Separated Double-Hybrid Functional from Nonempirical Constraints

On the basis of our previous developments in the field of nonempirical double hybrids, we present here a new exchange-correlation functional based on a range-separated model for the exchange part and integrating a nonlocal perturbative correction to the electron correlation contribution. Named RSX-QIDH, the functional is free from any kind of empirical parametrization. Its range-separation parameter is set to recover the total energy of the hydrogen atom, thus eliminating the self-interaction error for this one-electron system. Subsequent tests on some relevant benchmark data sets confirm that the self-interaction error is particularly low for RSX-QIDH. This new functional provides also correct dissociation profiles for charged rare-gas dimers and very accurate ionization potentials directly from Kohn-Sham orbital energies. Above all, these good results are not obtained at the expense of other properties. Indeed, further tests on standard benchmarks show that RSX-QIDH is competitive with the more empirical ωB97X-2 double hybrid and outperforms the parent LC-PBE long-range corrected hybrid, thus underlining the important role of the nonlocal perturbative correlation.

The nature of three-body interactions in DFT: Exchange and polarization effects

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar₂-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Energy Decomposition Analysis with a Stable Charge-Transfer Term for Interpreting Intermolecular Interactions

Many schemes for decomposing quantum-chemical calculations of intermolecular interaction energies into physically meaningful components can be found in the literature, but the definition of the charge-transfer (CT) contribution has proven particularly vexing to define in a satisfactory way and typically depends strongly on the choice of basis set. This is problematic, especially in cases of dative bonding and for open-shell complexes involving cation radicals, for which one might expect significant CT. Here, we analyze CT interactions predicted by several popular energy decomposition analyses and ultimately recommend the definition afforded by constrained density functional theory (cDFT), as it is scarcely dependent on basis set and provides results that are in accord with chemical intuition in simple cases, and in quantitative agreement with experimental estimates of the CT energy, where available. For open-shell complexes, the cDFT approach affords CT energies that are in line with trends expected based on ionization potentials and electron affinities whereas some other definitions afford unreasonably large CT energies in large-gap systems, which are sometimes artificially offset by underestimation of van der Waals interactions by density functional theory. Our recommended energy decomposition analysis is a composite approach, in which cDFT is used to define the CT component of the interaction energy and symmetry-adapted perturbation theory (SAPT) defines the electrostatic, polarization, Pauli repulsion, and van der Waals contributions. SAPT/cDFT provides a stable and physically motivated energy decomposition that, when combined with a new implementation of open-shell SAPT, can be applied to supramolecular complexes involving molecules, ions, and/or radicals.

Range-Separated meta-GGA Functional Designed for Noncovalent Interactions

The accuracy of applying density functional theory to noncovalent interactions is hindered by errors arising from low-density regions of interaction-induced change in the density gradient, error compensation between correlation and exchange functionals, and dispersion double counting. A new exchange-correlation functional designed for noncovalent interactions is proposed to address these problems. The functional consists of the range-separated PBEsol exchange considered in two variants, pure and hybrid, and the semilocal correlation functional of Modrzejewski et al. (J. Chem. Phys. 2012, 137, 204121) designed with the constraint satisfaction technique to smoothly connect with a dispersion term. Two variants of dispersion correction are appended to the correlation functional: the atom-atom pairwise additive DFT-D3 model and the density-dependent many-body dispersion with self-consistent screening (MBD-rsSCS). From these building blocks, a set of four functionals is created to systematically examine the role of pure versus hybrid exchange and the underlying models for dispersion. The new functional is extensively tested on benchmark sets with diverse nature and size. Truly outstanding performance is demonstrated for water clusters of varying size, ionic hydrogen bonds, and thermochemistry of isodesmic n-alkane fragmentation reactions. The merits of each component of the new functional are discussed.

Charge-transfer excited states in phosphorescent organo-transition metal compounds: a difficult case for time dependent density functional theory?

A series of 17 platinum(ii) and iridium(iii) complexes have been investigated theoretically and experimentally to elucidate the charge-transfer character in emission from the lowest triplet state. TDDFT is found to be surprisingly accurate.