Using a set of oscillator strengths and excited-state dipole moments of near full configuration interaction (FCI) quality determined for small compounds, we benchmark the performances of several single-reference wave function methods (CC2, CCSD, CC3, CCSDT, ADC(2), and ADC(3/2)) and time-dependent density-functional theory (TD-DFT) with various functionals (B3LYP, PBE0, M06-2X, CAM-B3LYP, and $ω$B97X-D). We consider the impact of various gauges (length, velocity, and mixed) and formalisms: equation of motion (EOM) \emph{vs} linear response (LR), relaxed \emph{vs} unrelaxed orbitals, etc. Beyond the expected accuracy improvements and a neat decrease of formalism sensitivy when using higher-order wave function methods, the present contribution shows that, for both ADC(2) and CC2, the choice of gauge impacts more significantly the magnitude of the oscillator strengths than the choice of formalism, and that CCSD yields a notable improvement on this transition property as compared to CC2. For the excited-state dipole moments, switching on orbital relaxation appreciably improves the accuracy of both ADC(2) and CC2, but has a rather small effect at the CCSD level. Going from ground to excited states, the typical errors on dipole moments for a given method tend to roughly triple. Interestingly, the ADC(3/2) oscillator strengths and dipoles are significantly more accurate than their ADC(2) counterparts, whereas the two models do deliver rather similar absolute errors for transition energies. Concerning TD-DFT, one finds: i) a rather negligible impact of the gauge on oscillator strengths for all tested functionals (except for M06-2X); ii) deviations of ca.~0.10 D on ground-state dipoles for all functionals; iii) the better overall performance of CAM-B3LYP for the two considered excited-state properties.
In this work we propose a chemically-informed data-driven approach to benchmark the approximate density-functional tight-binding (DFTB) excited state (ES) methods that are currently available within the DFTB+ suite. By taking advantage of the large volume of low-detail ES-data in the machine learning (ML) dataset, QM8, we were able to extract valuable insights regarding the limitations of the benchmarked methods in terms of the approximations made to the parent formalism, density-functional theory (DFT), while providing recommendations on how to overcome them. For this benchmark, we compared t…
Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is however not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motiv…
Optical spectra (UV-vis and fluorescence) are sensitive to the chemical environment and conformation of fluorophores and therefore, are ideal probes for their conformation and solvent responses. Tyrosine kinase inhibitors (TKI) such as AG-1478 of epidermal growth factor receptor (EGFR) when containing a quinazolinamine scaffold are fluorophores. Conformers of AG-1478 have been confirmed by both experiment and theory. It is, however, very important to benchmark computational methods such as DFT functionals against optical spectral measurements, when time-dependent density functional theory (TD-…
A derivation of non-adiabatic coupling vectors for the density functional based tight binding method (DFTB) between ground and excited states is presented. The analytical result is valid both for semi-local and long-range corrected DFTB and includes all required Pulay terms. Electron-translation factors lead to a conceptual simplification of the Slater-Koster scheme for precomputed integrals. Compared to scalar couplings obtained from numerical derivatives, the present approach is computationally more efficient and can be applied to systems with hundreds of atoms. The accuracy of DFTB derivati…
Excited state electron and hole transfer underpin fundamental steps in processes such as exciton dissociation at photovoltaic heterojunctions, photoinduced charge transfer at electrodes, and electron transfer in photosynthetic reaction centers. Diabatic states corresponding to charge or excitation localized species, such as locally excited and charge transfer states, provide a physically intuitive framework to simulate and understand these processes. However, obtaining accurate diabatic states and their couplings from adiabatic electronic states generally leads to inaccurate results when combi…
Benchmarking and contrasting exchange-correlation functional differences in response to static correlation in unrestricted Kohn-Sham and a hybrid 1-electron reduced density matrix functional theory
The increasing need to simulate the dynamics of photoexcited molecular and nanosystems in the sub-picosecond regime demands new efficient tools able to describe the quantum nature of matter at a low computational cost. By combining the power of the approximate DFTB method with the semiclassical Ehrenfest method for nuclear-electron dynamics we have achieved a real-time time-dependent DFTB (TD-DFTB) implementation that fits such requirements. In addition to enabling the study of nuclear motion effects in photoinduced charge transfer processes, our code adds novel features to the realm of static…
The time-dependent density functional theory (TDDFT) has been broadly used to investigate the excited-state properties of various molecular systems. However, the current TDDFT heavily relies on outcomes from the corresponding ground-state density functional theory (DFT) calculations which may be prone to errors due to the lack of proper treatment in the non-dynamical correlation effects. Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, \textit{J. Chem. Phys.} \textbf{136}, 154104 (2012)], a DFT with fractional orbital occupations, was proposed, explicitl…
The study of the Aromatic Infrared Bands (AIBs) in astronomical environments has opened interesting spectroscopic questions on the effect of anharmonicity on the infrared (IR) spectrum of hot polycyclic aromatic hydrocarbons (PAHs) and related species in isolated conditions. The forthcoming James Webb Space Telescope will unveil unprecedented spatial and spectral details in the AIB spectrum; significant advancement is thus necessary now to model the infrared emission of PAHs, their presumed carriers, with enough detail to exploit the information content of the AIBs. This requires including anh…
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the a…
Excited-state potential-energy surfaces of metal-adsorbed organic molecules from Linear Expansion Δ-Self-Consistent Field Density-Functional Theory (ΔSCF-DFT)
准确、高效地模拟金属表面的激发态性质是研究金属表面吸附动力学的重要基础。为此，Gavnholt等人最近提出的线性展开Δ自洽场（leΔSCF）方法[Phys. Rev. B 78，075441（2008）]为耗时的准粒子计算提供了一种有效的替代方案。在该方法中，密度泛函理论的标准Kohn-Sham方程在类似于吸附质的气相轨道的Hilbert空间区域中的非平衡占据的约束下求解。在这项工作中，我们讨论了这种方法的适用性金属表面安装的有机吸附物的激发态动力学，特别是在分子开关的背景下。我们提出了必要的进步，以允许激发态势能面（PES）的质量一致的描述，并说明了与应用程序的概念，偶氮苯吸附在Ag（111）和Au（111）表面。我们发现，明确列入基板电子状态修改的拓扑结构的分子内激发态PES的分子，由于图像电荷和杂化效应。虽然气相中的分子显示出诱导异构化和逆反应的共振的清晰的能量分离，但表面吸附的分子没有。伴随的可能同时诱导两个过程将导致这种机制的转换效率显著降低。
Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density-functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficienc…
We present an investigation of the performance of the relativistic multi-reference Fock-space coupled cluster (FSCC) method for predicting molecular hyperfine structure (HFS) constants, including a thorough computational study to estimate the associated uncertainties. In particular, we considered the $^{19}$F HFS constant in the ground and excited states of BaF. Due to a larger basis set dependence, the uncertainties on the excited state results (16-85%) were found to be significantly larger than those on the ground state constants ($\sim$2%). The ab initio values were compared to the recent e…
Electronically Excited States of Vitamin B12: Benchmark Calculations Including Time-Dependent Density Functional Theory and Correlated Ab Initio Methods
We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the $N$-electron system as the sum of the ($N-2$)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition …
The computational investigation of photochemical processes often entails the calculation of excited state geometries, energies, and energy gradients. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons, thereby including the associated nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations. The multicomponent density functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) methods allow efficient calculations of ground and excited states, respectively. Here…
Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way for testing electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relations were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen to the purpose, adopting a large basis set to ensure high quality results. A general agreement with previous benchm…
Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
Gross-Oliveira-Kohn密度泛函理论（GOK-DFT）是DFT到激发态的扩展，其中基本变量是系综密度，即基态和激发态密度的加权和。系综能量（即基态和激发态能量的加权和）可以作为系综密度的函数而变分获得。与DFT类似，GOK-DFT中建模的关键成分是交换相关泛函。发展密度泛函近似（DFA）的合奏是一项复杂的任务，密度和重量的依赖关系，原则上应该重现。在最近的一篇论文[Phys. Rev. B 95，035120（2017）]中，作者将精确的GOK-DFT应用于简单但非平凡的Hubbard二聚体，以研究（数值）重量依赖性在计算激发能中的重要性。在这项工作中，我们推导出各种密度和相关制度的分析DFA的Legendre-Fenchel变换形式主义。功能和密度驱动的错误进行评估，为每个DFA。有趣的是，当使用系综精确交换功能时，这些误差可能很大，特别是如果二聚体是对称的，但它们相互抵消，使得通过线性插值获得的激发能总是准确的，即使在强相关的制度。
Excited state orbital optimization via minimizing the square of the gradient: General approach and application to singly and doubly excited states via density functional theory
Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
Laboratoire de Chimie Quantique, Institut de Chimie, CNRS / Université de Strasbourg（斯特拉斯堡大学化学研究所量子化学实验室）；University of Strasbourg Institute for Advanced Study（斯特拉斯堡大学高等研究院）；Université de Lorraine, CNRS, LPCT（洛林大学CNRS LPCT）
The choice of Gaussian basis functions for computing the ground-state properties of molecules, and clusters, employing wave-function-based electron-correlated approaches, is a well-studied subject. However, the same cannot be said when it comes to the excited-state properties of such systems, in general, and optical properties, in particular. The aim of the present study is to understand how the choice of basis functions affects the calculations of linear optical absorption in clusters, qualitatively, and quantitatively. For this purpose, we have calculated linear optical absorption spectra of…
