Dependence of Spurious Charge-Transfer Excited States on Orbital Exchange in TDDFT: Large Molecules and Clusters

Unveiling the potential of TPA-based molecules to tune the optoelectronic properties and enhance the efficiency of dye-sensitized solar cells

CONTEXT

The world's energy and environmental requirements are changing due to rapid population growth and industrial growth, and solar cells can be used to meet these demands. Dye-sensitized solar cells (DSSCs) are solar cells in which energy conversion occurs via a process similar to photosynthesis in plants. DSSC development is still in its infancy. DSSCs can operate under cloudy conditions and indirect sunlight and have attracted considerable attention due to their low cost and high efficiency. We designed two metal-free TPA-based dyes (Dye2 and Dye3) based on the reference dye Mg207 (Dye1) by increasing the donor strength of the molecule, as such dyes have shown enhanced efficiency in DSSCs. Moreover, the triphenylamine (TPA) moiety has been demonstrated to be a good donor that prevents charge recombination. Intramolecular charge transfer (ICT) from the donor to acceptor moiety was found in the sensitizers, and electrons were promoted to the conduction band (CB) of the TiO2 semiconductor. The negative binding energy of the dye@TiO2 clusters indicated that dye adsorption on the semiconductor surface was stable. The double donor increased the electron injection and electronic coupling constants in Dye2 and Dye3, indicating that these newly designed dyes have superior charge injection capacity. Accordingly, the efficiencies of DSSCs with Dye2 and Dye3 were 9.77% and 9.62%, respectively, and substitution with the TPA unit at the -R1 and -R2 positions in Dye1 resulted in better power conversion compared to the parent compound (9.09%). Increased donor strength improved photovoltaic performance by increasing current density and light-harvesting efficiency. This is a good molecular design approach for preparing targeted donor- π -acceptor (D- π -A) organic dyes with high DSSC efficiency.

METHODS

To predict the charge transport and optoelectronic characteristics of the TPA dyes, quantum chemical calculations were carried out using Gaussian16. The ground-state (S0) optimized geometries of the sensitizers were computed by utilizing DFT at the B3LYP/6-31G** level. The absorption spectra ( λ max) were computed by employing TD-DFT with various functionals (B3LYP, PBE1PBE, CAM-B3LYP, and BHandHLYP) in the gas and solvent (DCM) phases. Among the studied functionals, BHandHLYP was found to be best at successfully reproducing the experimental data. Thus, the absorption spectra of the newly designed dyes and dye@TiO2 were calculated at the BHandHLYP/6-31G** level. The dye@TiO2 cluster optimizations were carried out at the B3LYP/6-31G**(LANL2DZ) level.

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

Evidence of Excited-State Vibrational Mode Governing the Photorelaxation of a Charge-Transfer Complex

Modern, nonlinear, time-resolved spectroscopic techniques have opened new doors for investigating the intriguing but complex world of photoinduced ultrafast out-of-equilibrium phenomena and charge dynamics. The interaction between light and matter introduces an additional dimension, where the complex interplay between electronic and vibrational dynamics needs the most advanced theoretical-computational protocols to be fully understood on the molecular scale. In this study, we showcase the capabilities of ab initio molecular dynamics simulation integrated with a multiresolution wavelet protocol to carefully investigate the excited-state relaxation dynamics in a noncovalent complex involving tetramethylbenzene (TMB) and tetracyanoquinodimethane (TCNQ) undergoing charge transfer (CT) upon photoexcitation. Our protocol provides an accurate description that facilitates a direct comparison between transient vibrational analysis and time-resolved spectroscopic signals. This molecular level perspective enhances our understanding of photorelaxation processes confined in the adiabatic regime and offers an improved interpretation of vibrational spectra. Furthermore, it enables the quantification of anharmonic vibrational couplings between high- and low-frequency modes, specifically the TCNQ "rocking" and "bending" modes. Additionally, it identifies the primary vibrational mode that governs the adiabaticity between the ground state and the CT state. This comprehensive understanding of photorelaxation processes holds significant importance in the rational design and precise control of more efficient photovoltaic and sensor devices.

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.

Contrasting the excited state properties of different conformers of trans- and cis-2,2'-bipyridine oligomers in the gas phase

In this article, we present conformation-dependent photophysical and excited state properties of trans- and cis- BPY oligomers. Oligomers up to tetramers for three conformers, namely, o-, m-, and p-, are constructed and optimized at the B3LYP-D3/def2-SVPD level. The photophysical and excited state properties are interpreted in terms of UV and CD spectra at the RI-ADC(2)/def2-TZVPD level. The UV spectra of oligomers of the m-conformer show high-intensity and red-shifted UV bands compared to o- and p-oligomers. The CD spectra of p-oligomers show intense CD bands compared to o- and p-oligomers in the case of trans-structures. In contrast, oligomers of each conformer of cis-structures show high-intensity CD bands. The excited states of (BPY)2 and (BPY)4 are also characterized by analysis of one-electron transition density matrix considering three descriptors: ωCT, dexc, and PRNTO. The ωCT values of dimers are in the range of 0.06-0.32, which indicates the excited states are mainly LE states, whereas, for (BPY)4, the ωCT values range from 0.17 to 0.53, indicating the possibility of partial CT in the excited states. These observations are also explained using the NTOs and e-h correlation plots.

Comparative assessment of structure-property relationships of new Cu(II) complex in selected density functionals

In order to evaluate the structure-property relationships of Cu(II) complex by using DFT methods, the structure of the newly synthesized Cu(II) complex, [Cu(6-Brpic)2(bpy)], was investigated by XRD, FTIR, UV-Vis, and fluorescence spectroscopic methods. In addition, Hirshfeld surface and NBO analyses were fulfilled to identify possible interactions in the intermolecular and coordination environment. The five different DFT methods (HCTH, M06L, TPSSTPSS, B3LYP, and CAM-B3LYP levels), having four different functionalities (the GGA, meta-GGA, hybrid-GGA, and range-separated hybrid), were carried out so as to investigate the structure-property relationship, considering the geometric parameters (bond lengths and angles), vibrational frequencies, electronic absorption wavelengths, electronic transitions, and linear and nonlinear optical parameters. The R2 for structural and vibrational parameters, as well as MPD%, MAD, an optimal scaling factor (λ) and overall root mean square (RMS) deviation, were considered only at vibration frequencies. While it was determined that M06-L and TPSSTPSS levels gave the best results for the bond lengths and angles of the Cu(II) complex, the best results for vibrational frequencies were obtained in the HCTH method along with these methods. In NLO parameters, the static and dynamic first-order hyperpolarizability (<β(0;0,0)> and β(-ω;ω,0)/<β(-2ω;ω,ω)>) values, the largest values were obtained in the HCTH method (38.817 × 10-30 and 437.86 × 10-30/201.55 × 10-30 esu), whereas the smallest values were found to be in the CAM-B3LYP/TPSSTPSS levels (6.118 × 10-30 esu, 8.270 × 10-30/11.730 × 10-30 esu). By regarding the static γ (<γ(0;0,0,0)>) and dynamic (<γ(-ω;ω,0,0)> parameters, the largest values were calculated in the M06L (232.101 × 10-36) and HCTH (1711.52 × 10-36) methods and the smallest values were obtained in the CAM-B3LYP (43.281 × 10-36 and 60.844 × 10-36) method. In fact, it is obviously seen that the β and γ values obtained by the aforementioned DFT levels are many times higher than that of the standard molecule of urea. These results indicate that the Cu(II) complex may be used as a potential NLO material to evolve optoelectronic devices.

Conformational Effect on the Excitonic States of 2-Phenylpyridine Oligomers: Ab Initio Studies and Analysis

In this work, we report the effect of different conformations of 2-phenylpyridine oligomers ((PhPy)n=1-5) on the excited state properties from the results obtained at the RI-ADC(2)/def2-TZVP level. Three different conformers, namely, A, B, and C, are considered for each oligomer. All the oligomers of conformer A have linear-type structures, whereas conformers B and C form helical structures at n = 5 and n = 3, respectively. The differences in the geometries of the three conformers are reflected in the UV and CD spectra. The UV spectra of conformer A show high-intensity peaks compared to the conformers B and C, for each oligomer. While the helical oligomers of conformers B and C show high-intensity CD bands, the intensities of CD bands for all of the oligomers of conformer A are weaker. Analysis of the properties of the first five excited states in (PhPy)5 is carried out using three descriptors, and the results reveal that these are partially charge transfer states.

Theoretical study of cis-trans isomer of 2-hydroxy-5-methyl-2'-nitroazobenzene: DFT insight

CONTEXT

The synthesis of azobenzene materials is an important aspect of the research in the field of photo-switch materials. It is currently thought that azobenzene molecules exist in the cis and trans form of molecular structure configuration. However, the reaction process allowing for reversible energy switches from trans to cis form is still challenging. Therefore, it is crucial to understand the molecular properties of the azobenzene compounds in order to provide reference for future synthesis and application. Affirmation supporting this perspective has been substantially derived from theoretical results in the isomerization process and whether these molecular structures may affect the electronic properties entirely needs to be confirmed. In this study, I give my effort to understand the molecular structure properties of the cis and trans form of azobenzene molecule from 2-hydroxy-5-methyl-2'-nitroazobenzene (HMNA). Their chemistry phenomena are investigated using the density functional theory (DFT) method. This study shows that the trans-HMNA has a molecular size of 9.0 Å and the cis-HMNA has a molecular size of 6.6 Å. The trans-HMNA exhibits an electronic transition of π → π* type driven by an azo bond, whereas the cis-HMNA exhibits an electronic transition of n → π* type with respect to the non-bonding electrons of oxygen and nitrogen atoms. Therefore, the HMNA mechanism pathway from trans to cis form is feasible to undergo at the inversion pathway in the ground state.

METHODS

All DFT calculations were performed using the Gaussian Software Packages (Gaussian 09 Revision-A.02 and GaussView 5.0.8). Gaussum 3.0 software was selected to visualize the molecular orbital levels in the density of states diagram. The optimized molecular geometrical parameter was calculated using B3LYP/cc-pVTZ level in the gas phase. TD-DFT with M06-2X/cc-pVTZ level was used as a method for the precise interpretation of excited states in molecular systems.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

The analytic energy gradient of energy with respect to nuclear coordinates is derived for the fragment molecular orbital (FMO) method combined with time-dependent density functional theory (TDDFT). The response terms arising from the use of a polarizable embedding are derived. The obtained analytic FMO-TDDFT gradient is shown to be accurate in comparison to both numerical FMO-TDDFT and unfragmented TDDFT gradients, at the level of two- and three-body expansions. The gradients are used for geometry optimizations, molecular dynamics, vibrational calculations, and simulations of IR and Raman spectra of excited states. The developed method is used to optimize the geometry of the ground and excited electronic states of the photoactive yellow protein (PDB: 2PHY).

Charge-Transfer Luminescence in a Molecular Donor-Acceptor Complex: Computational Insights

Donor-acceptor molecular complexes are a popular class of materials utilizing charge-transfer states for practical applications. A recent class of donor-acceptor dyads based on the fluorescent BODIPY functionalized with triphenylamine (TPA) shows the peculiar property of dual fluorescence. It is hypothesized that instead of the sensitized charge-transfer state being optically dark, it provides an additional bright radiative pathway. Here we use time-dependent density functional theory to characterize the energetic alignment of excitonic and charge-transfer states in a BODIPY-TPA molecular complex. We observe that using a long-range exchange corrected functional in combination with state-specific solvation scheme gives a qualitatively correct alignment of the exciton and charge-transfer states and an enhancement in oscillator strength for the equilibrium solvated charge-transfer state, in agreement with experiment. This work provides rationalization of charge-transfer state emission and provides a foundation to explore charge-transfer using ab initio excited-state nonadiabatic dynamics.

Following the density evolution using real time density functional theory and density based indexes: Application to model push-pull molecules

Considering as test case a family of organic rod like push-pull molecules, we derived and applied density based index enabling the description and diagnostic of the electronic density evolution in real time-time dependent density functional theory (RT-TDDFT) simulations. In particular, both the charge transfer (CT) distance and a diagnostic index, the D_CT and M_AC ^RT respectively, were computed on the fly from the density distribution obtained at a given time and the reference ground state density and their mean values were compared with what obtained at Linear Response-TDDFT level. Besides giving a way of analyzing the density redistribution occurring in time, these tools allowed to show how RT-TDDFT, which is definitely a powerful method to model the evolution of the density in CT or charge separation processes, can be affected by the same artifacts known for LR-TDDFT approaches and, particularly, to those related to the use of approximate exchange correlation functionals. The analysis here performed allowed to identify and discard on fly the electronic configurations corresponding to spurious situations.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Effects of Heterocyclic Ring Fusion and Chain Elongation on Chiroptical Properties of Polyaza[9]helicene: A Computational Study

In the present work, the effect of lateral and helical extensions on the physical and chiroptical properties of azahelicenes is reported. Starting with the experimentally reported polyaza[9]helicene (9Ha), three derivatives, two with laterally fused electron-withdrawing rings and the third with larger helical length, are designed. For the excited-state properties such as UV-vis and CD spectra, performances of different DFT functionals are evaluated by comparing the energies and characters of the excited states against the ADC(2) results. CPL properties are calculated at DFT level. Among the three designed systems, pyrazine-based 9HaP shows an improved g_CPL value compared to that for parent 9Ha. However, quinoxaline-based 9HaQ is found to be the worst CPL emitter with the lowest dissymmetry factor. The helically extended derivative, 11Ha, shows good CPL results, but g_CPL remains smaller than that for the parent system. The CPL results are analyzed in terms of electric dipole transition moment (EDTM) and magnetic dipole transition moment (MDTM) vectors, and angles between these two vectors.

Theoretical Study on the Structure and Spectral Properties of Several Classical and Non-Classical C76 Isomers and Their Newly Synthesized Derivatives

X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectra, as well as the ground-state electronic/geometrical structures of the newly discovered two non-classical isomers C₂-C₇₆(NC2) and C₁-C₇₆(NC3) with their derivatives C₂-C₇₆(NC2)(CF₃)₁₄ and C₁-C₇₆(NC3)Cl₂₄, as well as the non-IPR(isolated pentagon rule) isomer C₁-^#17418C₇₆ with its embedded metal fullerene U@C₁-^#17418C₇₆ have been calculated at the density functional theory (DFT) level. The electronic structure after chlorination is significantly different in the simulated X-ray spectrum. Both XPS and NEXAFS spectra reflect obvious isomer dependence, indicating that the "fingerprint" in X-ray spectroscopy can provide an effective means for the identification of the above-mentioned fullerene isomers. Time-dependent DFT was used to simulate the ultraviolet-visible absorption spectrum of U@C₁-^#17418C₇₆. The calculated results are in good agreement with the experimental consequence. This work reveals that theoretically simulated X-ray and UV-vis spectroscopy techniques can provide valuable information to help researchers explore the electronic structure of fullerenes and the identification of isomers in future experimental and theoretical fields.

On the inclusion of one double within CIS and TDDFT

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

Structural and Spectral Properties of a Nonclassical C66 Isomer with Its Hydrogenated Derivative C66H4 in Theory

X-ray photoelectron and near-edge X-ray absorption fine structure (NEXAFS) spectra, as well as the ground-state electronic/geometrical structures of a newly discovered nonclassical isomer C 2v -C66(NC), and two classical fullerene isomers C 2-#4466C66 and C s -#4169C66 with their hydrogenated derivatives [C 2v -C66H4(NC), C 2-#4466C66H4, and C s -#4169C66H4] have been calculated at the density functional theory (DFT) level. Significant differences were observed in the electronic structures and simulated X-ray spectra after hydrogenation. Simultaneously, both X-ray photoelectron and NEXAFS spectra reflected conspicuous isomer dependence, indicating that the "fingerprints" in the X-ray spectra can offer an effective method for identifying the above-mentioned fullerene isomers. The simulated ultraviolet-visible (UV-vis) absorption spectroscopy of C 2v -C66H4(NC) has also been generated by means of the time-dependent DFT method, and the calculations are well consistent with the experimental results. Consequently, this work reveals that X-ray and UV-vis spectroscopy techniques can provide valuable information to help researchers explore the fullerene electronic structure and isomer identification on the future experimental and theoretical fullerene domains.

Density Functional Calculations Based on the Exponential Ansatz

This work explores the application of the singles-based exponential ansatz to density functional calculations. In contrast to the standard approach where Kohn-Sham (KS) orbitals are determined prior to computing molecular quantities of interest, we consider the single-reference Hartree-Fock wave function as a starting point. Applying the exponential ansatz to this single reference gives an auxiliary wave function that is employed to calculate the electronic properties of the system. This wave function is determined self-consistently through the standard KS Hamiltonian but evaluated over the Hartree-Fock molecular orbital basis. By using spin-symmetry breaking, we recover size-consistent results free of unphysical fractional charges in the dissociation limit. Our method shows consistency with standard KS density functional calculations when the system geometry is similar to the equilibrium one or in repulsive configurations. For moderately long distances between atoms, not at dissociation, because of self-interaction the exponential ansatz may give instabilities in the form of large cluster amplitudes. To avoid these, this work introduces a relatively simple regularization method that preserves size-consistency and penalizes high amplitudes of the cluster operator, whereas the results remain physically meaningful. We also present the time-dependent extension of our theory and show that it can feature quantum states where multiple electrons are excited.

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.

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory

Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system. Thus, within TD-DFT, no definite separation of the subsystems (the single MNP or the emitter) and their couplings is directly available. This important feature is obtained here using the subsystem formulation of TD-DFT, which has been originally developed in the context of weakly interacting organic molecules. In subsystem TD-DFT, interacting MNPs are treated independently, thus allowing us to compute the plasmon couplings directly from the subsystem TD-DFT transition densities. We show that subsystem TD-DFT, as well as a simplified version of it in which kinetic contributions are neglected, can reproduce the reference TD-DFT calculations for gap distances greater than about 6 Å or even smaller in the case of hybrid plasmonic systems (i.e., molecules interacting with MNPs). We also show that the subsystem TD-DFT can be also used as a tool to analyze the impact of charge-transfer effects.

Hidden Hemibonding in the Aqueous Hydroxyl Radical

The existence of a two-center, three-electron hemibond in the first solvation shell of ^•OH(aq) has long been a matter of debate. The hemibond manifests in ab initio molecular dynamics simulations as a small-r feature in the oxygen radial distribution function (RDF) for H₂O···^•OH, but that feature disappears when semilocal density functionals are replaced with hybrids, suggesting a self-interaction artifact. Using periodic simulations at the PBE0+D3 level, we demonstrate that the hemibond is actually still present (as evidenced by delocalization of the spin density) but is obscured by the hydrogen-bonded feature in the RDF due to a slight elongation of the hemibond. Computed electronic spectra for ^•OH(aq) are in excellent agreement with experiment and confirm that hemibond-like configurations play an outsized role in the spectroscopy due to an intense charge-transfer transition that is strongly attenuated in hydrogen-bonded configurations. Apparently, 25% exact exchange (as in PBE0) is insufficient to eliminate delocalization of unpaired spins.

Electronic relaxation of aqueous aminoazobenzenes studied by time-resolved photoelectron spectroscopy and surface hopping TDDFT dynamics calculations

Studies of ultrafast relaxation of molecular chromophores are complicated by the fact that most chromophores of biological and technological importance are rather large molecules and are strongly affected by their environment, either solvent or a protein cage. Here we present an approach which allows us to follow transient electronic structure of complex photoexcited molecules. We use the method of time-resolved photoelectron spectroscopy in solution to follow relaxation of two prototypical aqueous chromophores, Methyl Orange and Metanil Yellow, both of which are aminoazobenzene derivatives. Using excitation by 400 nm laser pulses and ionization by wavelength-selected 46.7 nm XUV pulses from high-order harmonic generation we follow relaxation of both molecules via the dark S1 state. The photoelectron spectra yield binding energies of both ground and excited states. We combine the experimental results with surface hopping time-dependent density functional theory (TDDFT) calculations employing B3LYP+D3 and ωB97X-D functionals. The results demonstrate that the method is generally suitable for description of ultrafast dynamics in these molecules and can recover absolute binding energies observed in the experiment. The B3LYP+D3 functional appears to be better suited for these systems, especially in the case of Metanil Yellow, where it indicates the importance of an intramolecular charge transfer state. Our results pave the way towards quantitative understanding of evolving electronic structure in photo-induced relaxation processes.

On the Low-Lying Electronically Excited States of Azobenzene Dimers: Transition Density Matrix Analysis

Azobenzene-containing molecules may associate with each other in systems such as self-assembled monolayers or micelles. The interaction between azobenzene units leads to a formation of exciton states in these molecular assemblies. Apart from local excitations of monomers, the electronic transitions to the exciton states may involve charge transfer excitations. Here, we perform quantum chemical calculations and apply transition density matrix analysis to quantify local and charge transfer contributions to the lowest electronic transitions in azobenzene dimers of various arrangements. We find that the transitions to the lowest exciton states of the considered dimers are dominated by local excitations, but charge transfer contributions become sizable for some of the lowest ππ* electronic transitions in stacked and slip-stacked dimers at short intermolecular distances. In addition, we assess different ways to partition the transition density matrix between fragments. In particular, we find that the inclusion of the atomic orbital overlap has a pronounced effect on quantifying charge transfer contributions if a large basis set is used.

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.

Exploring the Franck-Condon region of a photoexcited charge transfer complex in solution to interpret femtosecond stimulated Raman spectroscopy: excited state electronic structure methods to unveil non-radiative pathways

We present electronic structure methods to unveil the non-radiative pathways of photoinduced charge transfer (CT) reactions that play a main role in photophysics and light harvesting technologies. A prototypical π-stacked molecular complex consisting of an electron donor (1-chloronaphthalene, 1ClN) and an electron acceptor (tetracyanoethylene, TCNE) was investigated in dichloromethane solution for this purpose. The characterization of TCNE:π:1ClN in both its equilibrium ground and photoinduced low-lying CT electronic states was performed by using a reliable and accurate theoretical-computational methodology exploiting ab initio molecular dynamics simulations. The structural and vibrational time evolution of key vibrational modes is found to be in excellent agreement with femtosecond stimulated Raman spectroscopy experiments [R. A. Mathies et al., J. Phys. Chem. A, 2018, 122, 14, 3594], unveiling a correlation between vibrational fingerprints and electronic properties. The evaluation of nonadiabatic coupling matrix elements along generalized normal modes has made possible the interpretation on the molecular scale of the activation of nonradiative relaxation pathways towards the ground electronic state. In particular, two low frequency vibrational modes such as the out of plane bending and dimer breathing and the TCNE central C[double bond, length as m-dash]C stretching play a prominent role in relaxation phenomena from the electronic CT state to the ground state one.

Assessing the Performance of DFT Functionals for Excited-State Properties of Pyridine-Thiophene Oligomers

In this article, we have examined the accuracy of various density functional theory (DFT) functionals to reproduce the absorption and CD spectra of pyridine-thiophene oligomers. The performance of different levels of approximations in DFT functionals is discussed with reference to the ADC(2) results. Starting from a linear system, like monomer, calculations are carried out at ADC(2) and DFT levels till a helical system, like pentamer, is formed. For vertical excitation energies, results obtained with functionals, like CAM-B3LYP, ωB97XD, and M06-2X, are closer to the ADC(2) results. However, analysis of excited-state properties shows that the state ordering patterns or results regarding natural transition orbitals from these DFT functionals sometimes differ from the ADC(2) results. Global hybrid functionals like B3LYP and PBE0 produce excitation energies which are far away from the ADC(2) benchmark results. Similarly, pure functionals and their long-range corrected versions produce either redshifted or blueshifted energies. For the CD spectra, the above three mentioned functionals, CAM-B3LYP, ωB97XD, and M06-2X, again produce spectra closer to the benchmark spectra.

Complexes of divalent europium with dotp and dotpph

Structures, electron spectroscopy and theoretical (DFT and TD DFT) analyses of two complexes of Eu(ii) with phosphonate and phosphinate ligands based on cyclen ring are presented.

Experimental and theoretical study of energy transfer in a chromophore triad: What makes modeling dynamics successful?

Simulation of electronic dynamics in realistically large molecular systems is a demanding task that has not yet achieved the same level of quantitative prediction already realized for its static counterpart. This is particularly true for processes occurring beyond the Born-Oppenheimer regime. Non-adiabatic molecular dynamics (NAMD) simulations suffer from two convoluted sources of error: numerical algorithms for dynamics and electronic structure calculations. While the former has gained increasing attention, particularly addressing the validity of ad hoc methodologies, the effect of the latter remains relatively unexplored. Indeed, the required accuracy for electronic structure calculations to reach quantitative agreement with experiment in dynamics may be even more strict than that required for static simulations. Here, we address this issue by modeling the electronic energy transfer in a donor-acceptor-donor (D-A-D) molecular light harvesting system using fewest switches surface hopping NAMD simulations. In the studied system, time-resolved experimental measurements deliver complete information on spectra and energy transfer rates. Subsequent modeling shows that the calculated electronic transition energies are "sufficiently good" to reproduce experimental spectra but produce over an order of magnitude error in simulated dynamical rates. We further perform simulations using artificially shifted energy gaps to investigate the complex relationship between transition energies and modeled dynamics to understand factors affecting non-radiative relaxation and energy transfer rates.

Asymmetry in the Q y Fluorescence and Absorption Spectra of Chlorophyll a Pertaining to Exciton Dynamics

Significant asymmetry found between the high-resolution Q_y emission and absorption spectra of chlorophyll-a is herein explained, providing basic information needed to understand photosynthetic exciton transport and photochemical reactions. The Q_y spectral asymmetry in chlorophyll has previously been masked by interference in absorption from the nearby Q_x transition, but this effect has recently been removed using extensive quantum spectral simulations or else by analytical inversion of absorption and magnetic circular dichroism data, allowing high-resolution absorption information to be accurately determined from fluorescence-excitation spectra. To compliment this, here, we measure and thoroughly analyze the high-resolution differential fluorescence line narrowing spectra of chlorophyll-a in trimethylamine and in 1-propanol. The results show that vibrational frequencies often change little between absorption and emission, yet large changes in line intensities are found, this effect also being strongly solvent dependent. Among other effects, the analysis in terms of four basic patterns of Duschinsky-rotation matrix elements, obtained using CAM-B3LYP calculations, predicts that a chlorophyll-a molecule excited into a specific vibrational level, may, without phase loss or energy relaxation, reemit the light over a spectral bandwidth exceeding 1,000 cm⁻¹ (0.13 eV) to influence exciton-transport dynamics.

DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum-classical description. To this end, Born-Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna-Matthews-Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

Theoretical investigation using DFT of quinoxaline derivatives for electronic and photovoltaic effects

Photovoltaic properties of solar cells based on fifteen organic dyes have been studied in this work. B3LYP/6-311G (d,p) methods are realized to obtain geometries and optimize the electronic properties, optical and photovoltaic parameters for some quinoxaline derivatives. The results showed that time dependent DFT investigations using the CAM-B3LYP method with the polarized split-valence 6-311G (d,p) basis sets and the polarizable continuum model PCM model were sensibly able to predict the excitation energies, the spectroscopy of the compounds. HOMO and LUMO energy levels of these molecules can make a positive impact on the process of electron injection and dye regeneration. Gaps energy ΔE_g, short-circuit current density J_sc, light-harvesting efficiency LHE, injection driving force ΔG^inject, total reorganization energy λ_total and open-circuit photovoltage V_oc enable qualitative predictions about the reactivity of these dyes.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Quantitative Design of Bright Fluorophores and AIEgens by the Accurate Prediction of Twisted Intramolecular Charge Transfer (TICT)

Inhibition of TICT can significantly increase the brightness of fluorescent materials. Accurate prediction of TICT is thus critical for the quantitative design of high-performance fluorophores and AIEgens. TICT of 14 types of popular organic fluorophores were modeled with time-dependent density functional theory (TD-DFT). A reliable and generalizable computational approach for modeling TICT formations was established. To demonstrate the prediction power of our approach, we quantitatively designed a boron dipyrromethene (BODIPY)-based AIEgen which exhibits (almost) barrierless TICT rotations in monomers. Subsequent experiments validated our molecular design and showed that the aggregation of this compound turns on bright emissions with ca. 27-fold fluorescence enhancement, as TICT formation is inhibited in molecular aggregates.

Role of hemibonding in the structure and ultraviolet spectroscopy of the aqueous hydroxyl radical

The presence of a two-center, three-electron hemibond in the solvation structure of the aqueous hydroxl radical has long been debated, as its appearance can be sensitive to self-interaction error in density functional theory.

Theoretical study on functionalized acrylonitrile compounds with a large second-order nonlinear optical response

The nonlinear optical properties of the studied compounds were studied with the help of DFT calculations.

Understanding plasmon coupling in nanoparticle dimers using molecular orbitals and configuration interaction

We perform a theoretical investigation of the electronic structure and optical properties of atomic nanowire and nanorod dimers using DFT and TDDFT. In both systems at separation distances larger than 0.75 nm, optical spectra show a single feature that resembles the bonding dipole plasmon (BDP) mode. A configuration interaction (CI) analysis shows that the BDP mode arises from constructive coupling of transitions, whereas the destructive coupling does not produce significant oscillator strength for such separation distances. At shorter separation distances, both constructive and destructive coupling produce oscillator strength due to wave-function overlap, which results in multiple features in the calculated spectra. Our analysis shows that a charge-transfer plasmon (CTP) mode arises from destructive coupling of transitions, whereas the BDP results from constructive coupling of the same transitions at shorter separation distances. Furthermore, the coupling elements between these transitions are shown to depend heavily on the amount of exact Hartree-Fock exchange (HFX) in the functional, which affects the splitting of CTP and BDP modes. With 50% HFX or more, the CTP and BDP modes mainly merge into a single feature in the spectra. These findings suggest that the effects of exact exchange must be assessed during the prediction of CTP modes in plasmonic systems.

Étude structurale des systèmes dissymétriques de structure D-π-A à base de thiénopyrazine destinés aux cellules solaires organiques de type « bulk heterojunction » (BHJ)

Onze nouvelles molécules organiques de structure donneurs-espaceur-accepteurs (D-π-A) utilisées pour les cellules solaires organiques (OSC) basées sur la thiénopyrazine et le thiophène ont été étudiées par la théorie de la densité fonctionnelle (DFT) et la théorie de la densité fonctionnelle dépendante de temps DFT (TD-DFT), pour expliquer comment l’ordre de conjugaison influe sur les performances des cellules solaires. Le groupe accepteur d’électrons (ancrage) était composé de 2-cyanoacrylique pour tous les composés, tandis que l’unité donneuse d’électrons était variée et que son influence fut étudiée. Les résultats théoriques ont montré que les calculs TD-DFT, avec une fonction hybride d’échange – corrélation utilisant la méthode d’atténuation de Coulomb (CAM-B3LYP) en conjonction avec un modèle de solvatation à cycle continu polarisable (modèle de continuum polarisable, PCM) combinée avec la base 6-31G(d,p), était raisonnablement capable de prédire les énergies d’excitation, les spectres d’absorption et d’émission des molécules étudiées. Les niveaux d’énergie des orbitales moléculaires frontières (orbitale moléculaire occupée de plus haute énergie (HOMO) et orbitale moléculaire inoccupée de plus basse énergie (LUMO) de ces composés peuvent avoir un effet positif sur le processus d’injection et de régénération d’électrons. La tendance des lacunes calculées HOMO-LUMO se compare bien avec les données spectrales. En outre, les valeurs estimées de photovoltage en circuit ouvert (Voc) pour ces composés ont été présentées. L’étude des propriétés structurelles, électroniques et optiques de ces composés pourrait aider à concevoir des matériaux organiques photovoltaïques fonctionnels plus efficaces.