Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

Tuning ultrafast time-evolution of photo-induced charge-transfer states: A real-time electronic dynamics study in substituted indenotetracene derivatives

Photo-induced charge transfer (CT) states are pivotal in many technological and biological processes. A deeper knowledge of such states is mandatory for modeling the charge migration dynamics. Real-time time-dependent density functional theory (RT-TD-DFT) electronic dynamics simulations are employed to explicitly observe the electronic density time-evolution upon photo-excitation. Asymmetrically substituted indenotetracene molecules, given their potential application as n-type semiconductors in organic photovoltaic materials, are here investigated. Effects of substituents with different electron-donating characters are analyzed in terms of the overall electronic energy spacing and resulting ultrafast CT dynamics through linear response (LR-)TD-DFT and RT-TD-DFT based approaches. The combination of the computational techniques here employed provided direct access to the electronic density reorganization in time and to its spatial and rational representation in terms of molecular orbital occupation time evolution. Such results can be exploited to design peculiar directional charge dynamics, crucial when photoactive materials are used for light-harvesting applications.

Watching the Interplay between Photoinduced Ultrafast Charge Dynamics and Nuclear Vibrations

Here is presented the ultrafast hole-electron dynamics of photoinduced metal to ligand charge-transfer (MLCT) states in a Ru(II) complex, [Ru(dcbpy)2(NCS)2]4- (dcbpy = 4,4'-dicarboxy-2,2'-bipyridine), a photoactive molecule employed in dye sensitized solar cells. Via cutting-edge computational techniques, a tailored computational protocol is here presented and developed to provide a detailed analysis of the electronic manifold coupled with nuclear vibrations to better understand the nonradiative pathways and the resulting overall dye performances in light-harvesting processes (electron injection). Thus, the effects of different vibrational modes were investigated on both the electronic levels and charge transfer dynamics through a theoretical-computational approach. First, the linear response time-dependent density functional (LR-TDDFT) formalism was employed to characterize excitation energies and spacing among electronic levels (the electronic layouts). Then, to understand the ultrafast (femtosecond) charge dynamics on the molecular scale, we relied on the nonperturbative mean-field quantum electronic dynamics via real-time (RT-) TDDFT. Three vibrational modes were selected, representative for collective nuclear movements that can have a significant influence on the electronic structure: two involving NCS- ligands and one involving dcbpy ligands. As main results, we observed that such MLCT states, under vibrational distortions, are strongly affected and a faster interligand electron transfer mechanism is observed along with an increasing MLCT character of the adiabatic electronic states approaching closer in energy due to the vibrations. Such findings can help both in providing a molecular picture of multidimensional vibro-electronic spectroscopic techniques, used to characterize ultrafast coherent and noncoherent dynamics of complex systems, and to improve dye performances with particular attention to the study of energy or charge transport processes and vibronic couplings.

The low-lying electronic states and ultrafast relaxation dynamics of the monomers and J-aggregates of meso-tetrakis (4-sulfonatophenyl)-porphyrins

The electronic and vibrational spectra of the meso-tetrakis(4-sulfonatophenyl)-porphyrins (TSPP) have been studied computationally using the PFD-3B functional with time-dependent density functional theory for the excited states. The calculated UV-vis absorption and emission spectra in aqueous solution are in excellent agreement with the experimental measurements of both H2TSPP-4 (monomer) at high pH and H4TSPP-2 (forming J-aggregate) at low pH. Moreover, our calculations reveal an infrared absorption at 1900 cm-1 in the singlet and triplet excited states that is absent in the ground state, which is chosen as a probe for transient IR absorption spectroscopy to investigate the vibrational dynamics of the excited state. Specifically, the S2 to S1 excited state internal conversion process time, the S1 state vibrational relaxation time, and the lifetime of the S1 excited electronic state are all quantitatively deduced.

Effects of aggregation on the structures and excited-state absorption for zinc phthalocyanine

In the present paper, the aggregated structures of zinc phthalocyanine (ZnPc) have been investigated by considering its dimers and trimers. Based on the density functional theory calculations, two stable conformations are obtained for the ZnPc dimer and trimer, respectively. The IGMH (independent gradient model based on the Hirshfeld partition of molecular density) analysis reveals that the π-π interaction between the ZnPc molecules causes the aggregation. Normally, stacked structures with a slight displacement are favorable for aggregation. In addition, the planar structure of the ZnPc monomer is largely maintained in the aggregated conformations. For the presently obtained structures, the first singlet excited state absorption (ESA) spectra of these aggregated conformations of ZnPc were calculated based on the linear-response time-dependent density functional theory (LR-TDDFT), which has been well applied by our group. The results of the excited state absorption spectra reveal that the aggregation causes the ESA band to blue shift compared to the ZnPc monomer. By using the conventional description of the interaction between monomer transition dipoles, this blue shift is elucidated by the side-by-side transition dipole moments in the constituted monomers. The present results for the ESA combined with the previously reported results for ground state absorption (GSA) will provide guidelines to tune the window of the optical-limiting effect for the ZnPc based materials.

Nature of the Ultrafast Interligands Electron Transfers in Dye-Sensitized Solar Cells

Charge-transfer dynamics and interligand electron transfer (ILET) phenomena play a pivotal role in dye-sensitizers, mostly represented by the Ru-based polypyridyl complexes, for TiO₂ and ZnO-based solar cells. Starting from metal-to-ligand charge-transfer (MLCT) excited states, charge dynamics and ILET can influence the overall device efficiency. In this letter, we focus on N3^4- dye ( [Ru(dcbpy)₂(NCS)₂]^4-, dcbpy = 4,4'-dicarboxy-2,2'-bipyridine) to provide a first direct observation with high time resolution (<20 fs) of the ultrafast electron exchange between bpy-like ligands. ILET is observed in water solution after photoexcitation in the ∼400 nm MLCT band, and assessment of its ultrafast time-scale is here given through a real-time electronic dynamics simulation on the basis of state-of-the-art electronic structure methods. Indirect effects of water at finite temperature are also disentangled by investigating the system in a symmetric gas-phase structure. As main result, remarkably, the ILET mechanism appears to be based upon a purely electronic evolution among the dense, experimentally accessible, MLCT excited states manifold at ∼400 nm, which rules out nuclear-electronic couplings and proves further the importance of the dense electronic manifold in improving the efficiency of dye sensitizers in solar cell devices.

Understanding Charge Dynamics in Dense Electronic Manifolds in Complex Environments

Photoinduced charge transfer (CT) excited states and their relaxation mechanisms can be highly interdependent on the environment effects and the consequent changes in the electronic density. Providing a molecular interpretation of the ultrafast (subpicosecond) interplay between initial photoexcited states in such dense electronic manifolds in condensed phase is crucial for improving and understanding such phenomena. Real-time time-dependent density functional theory is here the method of choice to observe the charge density, explicitly propagated in an ultrafast time domain, along with all time-dependent properties that can be easily extracted from it. A designed protocol of analysis for real-time electronic dynamics to be applied to time evolving electronic density related properties to characterize both in time and in space CT dynamics in complex systems is here introduced and validated, proposing easy to be read cross-correlation maps. As case studies to test such tools, we present the photoinduced charge-transfer electronic dynamics of 5-benzyluracil, a mimic of nucleic acid/protein interactions, and the metal-to-ligand charge-transfer electronic dynamics in water solution of [Ru(dcbpy)2(NCS)2]4-, dcbpy = (4,4'-dicarboxy-2,2'-bipyridine), or "N34-", a dye sensitizer for solar cells. Electrostatic and explicit ab initio treatment of solvent molecules have been compared in the latter case, revealing the importance of the accurate modeling of mutual solute-solvent polarization on CT kinetics. We observed that explicit quantum mechanical treatment of solvent slowed down the charge carriers mobilities with respect to the gas-phase. When all water molecules were modeled instead as simpler embedded point charges, the electronic dynamics appeared enhanced, with a reduced hole-electron distance and higher mean velocities due to the close fixed charges and an artificially increased polarization effect. Such analysis tools and the presented case studies can help to unveil the influence of the electronic manifold, as well as of the finite temperature-induced structural distortions and the environment on the ultrafast charge motions.

A computational investigation about the effect of metal substitutions on the electronic spectra of porphyrin donors in the visible and near infrared regions

Porphyrin compounds have unique advantages because of their wide absorption range (about 300-1000 nm) and good planarity. At present, the effects of metal substitutions of porphyrin compounds on their photovoltaic properties are still not clear. In this paper, we have systematically modelled a series of porphyrin donors MP-TBO (M = 2H, Mg, Cu, Fe, Co, Zn and Ni), in which ZnP-TBO has been experimentally synthesized and the power conversation efficiency of organic solar cell based on it is up to 12.08 %. The photovoltaic properties of these MP-TBO molecules have been investigated via density functional theory (DFT) and time-dependent DFT. We find that CoP-TBO and NiP-TBO both have worse planarity and smaller dipole moments than other compounds. The electronic absorption spectra of these porphyrin donors all show three main absorption peaks. However, metal substitutions blue-shift the wavelength of absorption peaks and lower total absorption strength in the visible and near-infrared regions. Finally, we find that MgP-TBO and H₂P-TBO seem to be potential donors because both have more red-shifted wavelength of absorption peaks and higher absorption strength than other metal substitutions.

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods

The emergence of state-of-the-art X-ray light sources has paved the way for novel spectroscopies that take advantage of their atomic specificity to shed light on fundamental physical, chemical, and biological processes both in the static and time domains. The success of these experiments hinges on the ability to interpret and predict core-level spectra, which has opened avenues for theory to play a key role. Over the last two decades, linear-response time-dependent density functional theory (LR-TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this context, we focus our discussion on LR-TDDFT approaches for the computation of X-ray Near-Edge Structure (XANES), Valence-to-Core X-ray Emission (VtC-XES), and Resonant Inelastic X-ray Scattering (RIXS) spectroscopies in molecular systems with an emphasis on Gaussian basis set implementations. We illustrate these approaches with applications and provide a brief outlook of possible new directions.

Excited state absorption of DNA bases in the gas phase and in chloroform solution: a comparative quantum mechanical study

We study the excited state absorption (ESA) properties of the four DNA bases (thymine, cytosine, adenine, and guanine) by different single reference quantum mechanical methods, namely, equation of motion coupled cluster singles and doubles (EOM-CCSD), singles, doubles and perturbative triples (EOM-CC3), and time-dependent density functional theory (TD-DFT), with the long-range corrected CAM-B3LYP functional. Preliminary results at the Tamm-Dancoff (TDA) CAM-B3LYP level using the maximum overlap method (MOM) are reported for thymine. In the gas phase, the three methods predict similar One Photon Absorption (OPA) spectra, which are consistent with the experimental results and with the most accurate computational studies available in the literature. The ESA spectra are then computed for the ππ* states (one for pyrimidine, two for purines) associated with the lowest-energy absorption band, and for the close-lying nπ* state. The EOM-CC3, EOM-CCSD and CAM-B3LYP methods provide similar ESA spectral patterns, which are also in qualitative agreement with literature RASPT2 results. Once validated in the gas phase, TD-CAM-B3LYP has been used to compute the ESA in chloroform, including solvent effects by the polarizable continuum model (PCM). The predicted OPA and ESA spectra in chloroform are very similar to those in the gas phase, most of the bands shifting by less than 0.1 eV, with a small increase of the intensities and a moderate destabilization of the nπ* state. Finally, ESA spectra have been computed from the minima of the lowest energy ππ* state, and found in line with the available experimental transient absorption spectra of the nucleosides in solution, providing further validation of our computational approach.

Three-Photon-Induced Singlet Excited-State Absorption for the Tunable Ultrafast Optical-Limiting in Distyrylbenzene: A First-Principles Study

The ground and first singlet excited state absorption in distyrylbenzene(DSB) are simulated based on the linear-response time dependent density functional theory(LR-TDDFT). It is found that distyrylbenzene shows strong reverse saturable...

In Silico Ultrafast Nonlinear Spectroscopy Meets Experiments: The Case of Perylene Bisimide Dye

Spectroscopy simulations are of paramount importance for the interpretation of experimental electronic spectra, the disentangling of overlapping spectral features, and the tracing of the microscopic origin of the observed signals. Linear and nonlinear simulations are based on the results drawn from electronic structure calculations that provide the necessary parameterization of the molecular systems probed by light. Here, we investigate the applicability of excited-state properties obtained from linear-response time-dependent density functional theory (TDDFT) in the description of nonlinear spectra by employing the pseudowavefunction approach and compare them with benchmarks from highly accurate RASSCF/RASPT2 calculations and with high temporal resolution experimental results. As a test case, we consider the prediction of femtosecond transient absorption and two-dimensional electronic spectroscopy of a perylene bisimide dye in solution. We find that experimental signals are well reproduced by both theoretical approaches, showing that the computationally cheaper TDDFT can be a suitable option for the simulation of nonlinear spectroscopy of molecular systems that are too large to be treated with higher-level RASSCF/RASPT2 methods.

Simulation and Analysis of the Transient Absorption Spectrum of 4-(N,N-Dimethylamino)benzonitrile (DMABN) in Acetonitrile

4-(N,N-Dimethylamino)benzonitrile (DMABN) is a well-known model compound for dual fluorescence-in sufficiently polar solvents, it exhibits two distinct fluorescence emission bands. The interpretation of its transient absorption (TA) spectrum in the visible range is the subject of a long-standing controversy. In the present study, we resolve this issue by calculating the TA spectrum on the basis of nonadiabatic molecular dynamics simulations. An unambiguous assignment of spectral signals to specific excited-state structures is achieved by breaking down the calculated spectrum into contributions from twisted and nontwisted molecular geometries. In particular, the much-discussed excited-state absorption band near 1.7 eV (ca. 700 nm) is attributed to the near-planar locally excited (LE) minimum on the S1 state. On the technical side, our study demonstrates that the second-order approximate coupled cluster singles and doubles (CC2) method can be used successfully to calculate the TA spectra of moderately large organic molecules, provided that the system in question does not approach a crossing between the lowest excited state and the singlet ground state within the time frame of the simulation.

Minimizing the Time-Dependent Density Functional Error in Ehrenfest Dynamics

Simulating electron-ion dynamics using time-dependent density functional theory within an Ehrenfest dynamics scheme can be done in two ways that are in principle exact and identical: propagating time-dependent electronic Kohn-Sham equations or propagating electronic coefficients on surfaces obtained from linear-response. We show here that using an approximate functional leads to qualitatively different dynamics in the two approaches. We argue that the latter is more accurate because the functionals are evaluated on domains close to the ground state where currently used approximations perform better. We demonstrate this on an exactly solvable model of charge transfer and discuss implications for time-resolved spectroscopy.

Molecular light-upconversion: we have had a problem! When excited state absorption (ESA) overcomes energy transfer upconversion (ETU) in Cr(III)/Er(III) complexes

Nine-coordinate [ErN₉] or [ErN₃O₆] chromophores found in triple helical [Er(L)₃]³⁺ complexes (L corresponds to 2,2′,6′,2′′-terpyridine (tpy), 2,6-(bisbenzimidazol-2-yl)pyridine (bzimpy), 2,6-diethylcarboxypyridine (dpa-ester) or 2,6-diethylcarboxamidopyridine (dpa-diamide) derivatives), [Er(dpa)₃]³⁻ (dpa is the 2,6-dipicolinate dianion) and [GaErGa(bpb-bzimpy)₃]⁹⁺ (bpb-bzimpy is 2,6-bis((pyridin-2-benzimidazol-5-yl)methyl-(benzimidazol-2-yl))pyridine) exhibit NIR (excitation at 801 nm) into visible (emission at 542 nm) linear light upconversion processes in acetonitrile at room temperature. The associated quantum yields 5.5(6) × 10⁻¹¹ ≤ ϕ^up_tot(ESA) ≤ 1.7(2) × 10⁻⁹ appear to be 1–3 orders of magnitude larger than those predicted by the accepted single-center excited-state absorption mechanism (ESA). Switching to the alternative energy transfer upconversion mechanism (ETU), which operates in multi-centers [CrErCr(bpb-bzimpy)₃]⁹⁺, leads to an improved quantum yield of ϕ^up_tot(ETU) = 5.8(6) × 10⁻⁸, but also to an even larger discrepancy by 4–6 orders of magnitude when compared with theoretical models. All photophysical studies point to Er(⁴I_13/2) as being the only available ‘long-lived’ (1.8 ≤ τ ≤ 6.3 μs) and emissive excited state, which works as an intermediate relay for absorbing the second photon, but with an unexpected large cross-section for an intrashell 4f → 4f electronic transition. With this in mind, the ETU mechanism, thought to optimize upconversion via intermetallic Cr → Er communication in [CrErCr(bpb-bzimpy)₃]⁹⁺, is indeed not crucial and the boosted associated upconversion quantum yield is indebted to the dominant contribution of the single-center erbium ESA process. This curious phenomenon is responsible for the successful implementation of light upconversion in molecular coordination complexes under reasonable light power intensities, which paves the way for applications in medicine and biology. Its origin could be linked with the presence of metal–ligand bonding.

Near-infrared to visible molecular upconversion exhibits quantum yields which are 2–6 orders of magnitude larger than those modeled with the accepted linear excited state absorption (ESA) or energy transfer (ETU) mechanisms: we have had a problem!

Resonant Inelastic X-ray Scattering Calculations of Transition Metal Complexes Within a Simplified Time-Dependent Density Functional Theory Framework

We present a time-dependent density functional theory (TDDFT) approach to compute the light-matter couplings between two different manifolds of excited states relative to a common ground state in the context of 4d transition metal systems. These quantities are the necessary ingredients to solve the Kramers-Heisenberg (KH) equation for resonant inelastic X-ray scattering (RIXS) and several other types of two-photon spectroscopies. The procedure is based on the pseudo-wavefunction approach, where the solutions of a TDDFT calculation can be used to construct excited-state wavefunctions, and on the restricted energy window approach, where a manifold of excited states can be rigorously defined based on the energies of the occupied molecular orbitals involved in the excitation process. Thus, the present approach bypasses the need to solve the costly TDDFT quadratic-response equations. We illustrate the applicability of the method to 4d transition metal molecular complexes by calculating the 2p4d RIXS maps of three representative ruthenium complexes and comparing them to experimental results. The method can capture all the experimental features in all three complexes to allow the assignment of the experimental peaks, with relative energies correct to within ∼0.6 eV at the cost of two independent TDDFT calculations.

Nonlinear light absorption in many-electron systems excited by an instantaneous electric field: a non-perturbative approach

Applications of low-cost non-perturbative approaches in real time, such as time-dependent density functional theory, for the study of nonlinear optical properties of large and complex systems are gaining increasing popularity. However, their assessment still requires the analysis and understanding of elementary dynamical processes in simple model systems. Motivated by the aim of simulating optical nonlinearities in molecules, here exemplified by the case of the quaterthiophene oligomer, we investigate light absorption in many-electron interacting systems beyond the linear regime by using a single broadband impulse of an electric field; i.e. an electrical impulse in the instantaneous limit. We determine non-pertubatively the absorption cross section from the Fourier transform of the time-dependent induced dipole moment, which can be obtained from the time evolution of the wavefunction. We discuss the dependence of the resulting cross section on the magnitude of the impulse and we highlight the advantages of this method in comparison with perturbation theory by working on a one-dimensional model system for which numerically exact solutions are accessible. Thus, we demonstrate that the considered non-pertubative approach provides us with an effective tool for investigating fluence-dependent nonlinear optical excitations.

Excited-State Absorption of Uracil in the Gas Phase: Mapping the Main Decay Paths by Different Electronic Structure Methods

We present a computational study of the one-photon and excited-state absorption (ESA) from the two lowest energy excited states of uracil in the gas phase: an nπ* dark state (1n) and the lowest energy bright ππ* state (1π). The predictions of six different linear response electronic structure methods, namely, TD-CAM-B3LYP, EOM-CCSD, EOM-CC3, ADC(2), ADC(2)-x, and ADC(3) are critically compared. In general, the spectral shapes predicted by TD-CAM-B3LYP, EOM-CCSD, EOM-CC3, and ADC(3) are fairly similar, though the quality of TD-CAM-B3LYP slightly deteriorates in the high-energy region. By computing the spectra at some key structures on different potential energy surfaces (PES), that is, the Franck-Condon point, the 1n minimum, and structures representative of different regions of the 1π PES, we obtain important insights into the shift of the ESA spectra, following the motion of the wavepacket on the excited-state PES. Though 1π has larger ESA than 1n, some spectral regions are dominated by these latter signals. Aside from its methodological interest, we thus obtain interesting indications to interpret transient absorption spectra to disentangle the photoactivated dynamics of nucleobases.

NWChem: Past, present, and future

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

Excited-state absorption for zinc phthalocyanine from linear-response time-dependent density functional theory

The mechanism for zinc phthalocyanine (ZnPc) showing optical-limiting character is related to the first singlet excited-state absorption (ESA). Two distinct band peaks in this ESA spectrum (1.97 eV and 2.56 eV) were observed in experiments. However, the origin of the absorption is not well understood. In the present work, we perform accurate quantum mechanical calculations and analysis of the absorption of ZnPc in the first singlet excited state. It is found that the transitions of S₁ → S₃ and S₁ → S₂₄ are the origin of the first and second band peaks, respectively. Charge transfer character is observed between the edges and central parts of ZnPc for those two transitions, but occurs in opposite directions. It is gratifying to note that the absorption can be modified smoothly through the substitution of nitrogen atoms in ZnPc with methyne or benzene rings. The aggregation phenomenon is also investigated with ZnPc dimers. The present calculations show that the absorptions of two ZnPc molecules with cofacially stacked and slightly shifted cofacially stacked configurations both result in an obvious blueshift compared with the zinc phthalocyanine monomer. The present observations may be utilized in tuning the optical-limiting character of ZnPc.

We perform accurate quantum mechanical calculations and analysis for the absorption of ZnPc in the first singlet excited state.

Identifying Electronic Modes by Fourier Transform from δ-Kick Time-Evolution TDDFT Calculations

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.