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

Excited-State Forces with the Gaussian and Augmented Plane Wave Method for the Tamm-Dancoff Approximation of Time-Dependent Density Functional Theory

Augmented plane wave methods enable an efficient description of atom-centered or localized features of the electronic density, circumventing high energy cutoffs and thus prohibitive computational costs of pure plane wave formulations. To complement existing implementations for ground-state properties and excitation energies, we present the extension of the Gaussian and augmented plane wave method to excited-state nuclear gradients within the Tamm-Dancoff approximation of time-dependent density functional theory and its implementation in the CP2K program package. Benchmarks for a test set of 35 small molecules demonstrate that maximum errors in the nuclear forces for excited states of singlet and triplet spin multiplicity are smaller than 0.1 eV/Å. The method is furthermore applied to the calculation of the zero-phonon line of defective hexagonal boron nitride. This spectral feature is reproduced with an error of 0.6 eV in comparison to GW-Bethe-Salpeter reference computations and 0.4 eV in comparison to experimental measurements. Accuracy assessments and applications thus demonstrate the potential use of the outlined developments for large-scale applications on excited-state properties of extended systems.

Thiocarbonyl-Bridged N-Heterotriangulenes for Energy Efficient Triplet Photosensitization: A Theoretical Perspective

Structurally-rigid metal-free organic molecules are of high demand for various triplet harvesting applications. However, inefficient intersystem crossing (ISC) due to large singlet-triplet gap (Δ E S - T ${\Delta {E}_{S-T}}$ ) and small spin-orbit coupling (SOC) between lowest excited singlet and triplet often limits their efficiency. Excited electronic states, fluorescence and ISC rates in several thiocarbonyl-bridged N-heterotriangulene ( m ${m}$ S-HTG) with systematically increased thione content (m = ${m=}$ 0-3) are investigated implementing polarization consistent time-dependent optimally-tuned range-separated hybrid. All m ${m}$ S-HTGs are dynamically stable and also thermodynamically feasible to synthesize. Relative energies of several low-lying singlets (S n ${{S}_{n}}$ ) and triplets (T n ${{T}_{n}}$ ), and their excitation nature (i. e.,n π * ${n{\pi }^{^{\ast}}}$ orπ π * ${\pi {\pi }^{^{\ast}}}$ ) and SOC are determined for these m ${m}$ S-HTGs in dichloromethane. Low-energy optical peak displays gradual red-shift with increasing thione content due to relatively smaller electronic gap resulted from greater degree of orbital delocalization. Significantly large SOC due to different orbital-symmetry and heavy-atom effect produces remarkably high ISC rates (k I S C ${{k}_{ISC}}$ ~1012 s-1) for enthalpically favouredS 1 n π * → T 2 ${{S}_{1}\left(n{\pi }^{^{\ast}}\right)\to {T}_{2}}$ (π π * ${\pi {\pi }^{^{\ast}}}$ ) channel in these m ${m}$ S-HTGs, which outcompete radiative fluorescence rates (~108 s-1) even directly from higher lying optically brightπ π * ${\pi {\pi }^{^{\ast}}}$ singlets. Importantly, high energy triplet excitons of ~1.7 eV resulting from such significantly large ISC rates from non-fluorescentS 1 n π * ${{S}_{1}\left(n{\pi }^{^{\ast}}\right)}$ make these thiocarbonylated HTGs ideal candidates for energy efficient triplet harvest including triplet-photosensitization.

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

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

Nature and energetics of low-lying excited singlets/triplets and intersystem crossing rates in selone analogs of perylenediimide: A theoretical perspective

The structural rigidity and chemical diversity of the highly fluorescent perylenediimide (PDI) provide wide opportunities for developing triplet photosensitizers with sufficiently increased energy efficiency. Remarkably high intersystem crossing (ISC) rates with a complete fluorescence turn-off reported recently for several thione analogs of PDI due to substantially large spin-orbit coupling garners huge attention to develop other potential analogs. Here, several selone analogs of PDI, denoted as mSe-PDIs (m = 1-4) with varied Se content and positions, are investigated to provide a comprehensive and comparative picture down the group-16 using density functional theory (DFT) and time-dependent DFT implementing optimally tuned range-separated hybrid in toluene dielectric. All mSe-PDIs are confirmed to be dynamically stable and also thermodynamically feasible to synthesize from their oxygen and thione congeners. The first excited-state singlet (S1) of mSe-PDI with relatively low Se-content (m = 1, 2) is of nπ* character with an expected fluorescence turn-off. Whereas, the ππ* nature of the S1 for 3Se-PDI and 4Se-PDI suggests a possible fluorescence turn-on in the absence of any other active nonradiative deactivation pathways. However, ∼4-6 orders greater ISC rates (∼1012-1014 s-1) than the fluorescence ones (∼108 s-1) for all mSe-PDIs signify highly efficient triplet harvest. Importantly, significantly higher ISC rates for these mSe-PDIs than their thione congeners render them efficient triplet photosensitizers.

Accurate Non-Adiabatic Couplings from Optimally-Tuned Range-Separated Hybrid Functionals

Precise theoretical calculations of non-adiabatic couplings, which describe the interaction between two Born-Oppenheimer surfaces, are important for the modeling of radiationless decay mechanisms in photochemical processes. Here, we demonstrate that accurate non-adiabatic couplings can be calculated in the framework of linear-response time-dependent density functional theory by using non-empirical, optimally-tuned range-separated hybrid (OT-RSH) functionals. We focus on molecular radicals, in which ultrafast non-radiative decay plays a crucial role, to find that the OT-RSH functional compares well to wave-function based reference data and competes with the accuracy of semi-empirical CAM-B3LYP calculations. Our findings show that the OT-RSH approach provides very accurate non-adiabatic couplings and, therefore, provides a computationally efficient alternative to wave-function based techniques.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

Reliability of computed molecular structures

When the structures of 1342 molecules are optimized by 30 methods and 7 basis sets, there appear 289 (21.54%) problematic molecules and 112 (8.35%) failed ones. When 278 problematic molecules are compared, the best methods are BHandH and LC-wPBE, while B97D, BP86, HFS, VSXC, and HCTH are very unreliable. When 179 problematic molecules are computed with larger basis sets, the smallest mean absolute deviation (MAD) of bond angle (2.3°) is shown by QCISD(T)/cc-pVTZ, while the smallest MAD of bond length (0.021 Å), the best SUM1 (4.9 unit), and the best SUM2 (2.4 unit) are shown by DSDPBEP86(Full), DSDPBEP86, PBE1PBE-D3, MP2, and MP2(Full) in combination with aug-cc-pVQZ, cc-pVQZ, Def2QZVP, Def2TZVPP, and/or 6-311++G(3df,3pd). Very large basis sets, for example, larger than cc-pVTZ usually have to be used to obtain very good structures and the performances of many density-functional theory methods are encouraging. The best results may be the limit of modern computational chemistry.

Micro-Solvated DMABN: Excited State Quantum Dynamics and Dual Fluorescence Spectra

In this work, we report a complete analysis by theoretical and spectroscopic methods of the short-time behaviour of 4-(dimethylamino)benzonitrile (DMABN) in the gas phase as well as in cyclohexane, tetrahydrofuran, acetonitrile, and water solution, after excitation to the La state. The spectroscopic properties of DMABN were investigated experimentally using UV absorption and fluorescence emission spectroscopy. The computational study was developed at different electronic structure levels and using the Polarisable Continuum Model (PCM) and explicit solvent molecules to reproduce the solvent environment. Additionally, excited state quantum dynamics simulations in the diabatic picture using the direct dynamics variational multiconfigurational Gaussian (DD-vMCG) method were performed, the largest quantum dynamics "on-the-fly" simulations performed with this method until now. The comparison with fully converged multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) dynamics on parametrised linear vibronic coupling (LVC) potentials show very similar population decays and evolution of the nuclear wavepacket. The ring C=C stretching and three methyl tilting modes are identified as the responsible motions for the internal conversion from the La to the Lb states. No major differences are observed in the ultrafast initial decay in different solvents, but we show that this effect depends strongly on the level of electronic structure used.