Excited-state Calculations Research Articles

Structural, electronic, and magnetic properties of bulk and epitaxial LaCoO3 through diffusion Monte Carlo

Magnetism in lanthanum cobaltite (LCO, LaCoO$_3$) appears to be strongly dependent on strain, defects, and nanostructuring. LCO on strontium titanate (STO, SrTiO$_3$) is a ferromagnet with an interesting strain relaxation mechanism that yields a lattice modulation. However, the driving force of the ferromagnetism is still controversial. Experiments debate between a vacancy-driven or strain-driven mechanism for the ferromagnetism of epitaxial LCO. We found that a weak lateral modulation of the superstructure is sufficient to promote ferromagnetism. We find that ferromagnetism appears under uniaxial compression and expansion. Although earlier experiments suggest that bulk LCO is nonmagnetic, we find an antiferromagnetic ground state for bulk LCO. We discuss the recent experiments which indicate a more complicated picture for bulk magnetism and a closer agreement with our calculations. Role of defects are also discussed through excited state calculations.

Absolutely Localized Projection-Based Embedding for Excited States.

We present a quantum embedding method that allows for calculation of local excited states embedded in a Kohn-Sham density functional theory (DFT) environment. Projection-based quantum embedding methodologies provide a rigorous framework for performing DFT-in-DFT and wave function in DFT (WF-in-DFT) calculations. The use of absolute localization, where the density of each subsystem is expanded in only the basis functions associated with the atoms of that subsystem, provide improved computationally efficiency for WF-in-DFT calculations by reducing the number of orbitals in the WF calculation. In this work, we extend absolutely localized projection-based quantum embedding to study localized excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding results are highly accurate compared to the corresponding canonical EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently more accurate than canonical TDDFT. The absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge-transfer states and prevent overdelocalization of excited states. Additionally, we attempt to recover the environment response caused by the electronic excitations in the high-level subsystem using different schemes and compare their accuracy. Finally, we apply this method to the calculation of the excited-state energy of green fluorescent protein and show that we systematically converge to the full system results. Here we demonstrate how this method can be useful in understanding excited states, specifically which chemical moieties polarize to the excitation. This work shows absolutely localized projection-based quantum embedding can treat local electronic excitations accurately and make computationally expensive WF methods applicable to systems beyond current computational limits.

Density function theory (DFT) calculated infrared absorption spectra for nitrosamines.

Absorption spectra within the infrared (IR) range of frequencies for nitrosamines in water are calculated using density function theory (DFT). Calculated in this study, are the IR spectra of C2H6N2O, C4H10N2O, C6H14N2O, C4H8N2O, C3H8N2O, and C8H18N2O. DFT calculated absorption spectra corresponding to vibration excited states of these molecules in continuous water background can be correlated with additional information obtained from laboratory measurements. The DFT software Gaussian was used for the calculations of excited states presented here. This case study provides proof of concept, viz., that such DFT calculated spectra can be used for their practical detection in environmental samples. Thus, DFT calculated spectra may be used to construct templates, for spectral-feature comparison, and thus detection of spectral-signature features associated with target materials.

Theoretical design of new triphenylamine based dyes for the fabrication of DSSCs: A DFT/TD-DFT study

A series of rigid triphenylamine (TPA) dyes have been designed with the donor(D)-π-acceptor(A) architecture. The rigid TPA unit is designed by locking the two phenyl rings with alkyl and ethylene chain to attain better planarity and to minimize its rotation. Four different acceptor units viz. BTz, BBTz, PzT and PyT are used to design four parent dye systems. The study reveals that all four dyes show low ΔH−L values whereas only BTz, PyT and PzT dyes show small dihedral angles. Moreover, excited state calculation of these three dyes show excellent electronic transition properties with a sharp absorption (λmax) in the range of 507–540 nm at the UV–vis spectra. The λmax values of BTz, PyT and PzT dyes show a red shift to that of the reference dye which signifies better electronic transition from HOMO to LUMO orbitals. It is further supported by the MO diagrams of the dyes where the MOs of BBTz dye shows less overlap between the occupied and unoccupied orbitals. It is also evident from the low EA and IP values that the three dye systems (excluding BBTz) should show excellent transfer of injected electron to the semiconducting surface. Low λ+ and high kCT+ values imply the hole transporting nature of the designed dyes. Hence, these dyes will act as potential candidates for fabrication of dye-sensitized solar cells (DSSCs).

Tuning Optoelectronic Properties of Dithienopyrrole Donor Molecules for Organic Solar Cells

Theoretical analysis of physical properties of organic solar cells (OSCs) are important in order to reveal the correlation between power conversion efficiencies (PCE), structure and properties. Five new A‒D‒A type small molecules M1, M2, M3, M4, and M5 were designed by using dithienopyrrole (DTP) as electron rich donor unit with different types of π-spacers and end capped acceptor units. Functional MPW1PW91/6-31G(d,p) level of theory was used to optimize the geometry of all molecules. For excited state calculation TD-MPW1PW91/6-31G(d,p) level of theory was used. The geometries, electronic structures, dipole moment, open circuit voltage, reorganization energies and charge transport properties of designed molecules (M1 $$ - $$ M5) have been scrutinized comparing with the reported compound R. The results revealed that the HOMO energy levels of molecules M1, M2, M3, and M5 were lower while M4 was of high energy level thus facilitate the donation of electron as compared to references molecule R. While LUMO energy level of all the molecules were slightly high energy due electron withdrawing effects of spacer and acceptor moiety. Highest energy gap of HOMO–LUMO was observed in M1 which was 2.48 eV and M3 showed low energy gap (2.11 eV) as compared to other designed molecules. All molecules showed low values for λe, so they have high rate of electron transfer as compared to R. All designed molecules exhibited higher value of dipole moment as compared to reference molecule R except M1. Higher value of dipole moment of donor molecules contrary to reference means good solubility towards organic solvents which is beneficial for further solar cell device fabrication. All designed molecules show higher Voc values except M4 which has comparable Voc with respect to reference molecule R. In short, choice of appropriate electron withdrawing and donating groups is very important for improving power conversion efficiencies of OSCs.

Reduced-Scaling Correlation Methods for the Excited States of Large Molecules: Implementation and Benchmarks for the Second-Order Algebraic-Diagrammatic Construction Approach.

A framework for reduced-scaling implementation of excited-state correlation methods is presented. An algorithm is introduced to construct excitation-specific local domains, which include all important molecular orbitals for the excitation as well as for electron correlation. The orbital space dimensions of the resulting compact domains are further decreased utilizing our reduced-cost techniques developed previously [J. Chem. Phys. 148, 094111 (2018)] based on the natural auxiliary function and local natural orbital approaches. Additional methodological improvements for the evaluation of density matrices are also discussed. Benchmark calculations are presented at the second-order algebraic-diagrammatic construction level. Compared to our reduced-cost algorithm significant, up to 3-9-fold speedups are achieved even for systems of smaller than 100 atoms. At the same time, additional errors introduced by domain approximations are highly acceptable, being about 2-4 meV on the average. The presented reduced-scaling algorithm allows us to carry out correlated excited-state calculations using triple-ζ basis sets with diffuse functions for systems of up to 400 atoms or 13 000 atomic orbitals in a matter of days using an 8-core processor.

Calculation of Free-Energy Barriers with TD-DFT: A Case Study on Excited-State Proton Transfer in Indigo

The performance of time-dependent density functional theory (TD-DFT) for the calculation of excited states of molecular systems has been the subject of many benchmark studies. Often, these studies focus on excitation energies or, more recently, excited-state equilibrium geometries. In this work, we take a different angle by instead exploring how well TD-DFT reproduces experimental free-energy barriers of a well-known photochemical reaction: the excited-state proton transfer (ESPT) in indigo. Specifically, by exploiting the possibility of using TD-DFT to locate and compute free energies of first-order saddle points in excited states, we test the performance of several popular density functionals in reproducing recently determined experimental free-energy barriers for ESPT in indigo and in an N-hexyl substituted derivative thereof. Through the calculations, it is found that all of the tested functionals perform quite well, uniformly overestimating the experimental values by 1.4-3.5 (mean error) and 2.5-5.5 kcal mol-1 (maximum error) only. Given that these errors are not larger than those typically observed when barriers for ground-state proton transfer reactions are calculated in ground-state DFT, the results highlight the potential of TD-DFT to enable accurate modeling of ESPT reactions based on free energies and explicit localization of transition states.

Automatic Active Space Selection for Calculating Electronic Excitation Energies Based on High-Spin Unrestricted Hartree–Fock Orbitals

Multireference perturbation theory (MR-PT2, e.g., MS-CASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) use a multiconfigurational wave function as the reference wave function, and this can be generated, for example, by the complete active space self-consistent field (CASSCF) method or restricted active space self-consistent field (RASSCF) method. The MR-PT2 and MC-PDFT methods have proved successful in many previous studies, but their performance depends on the quality of the reference wave function, and the quality of a CASSCF or RASSCF wave function depends on the active space. Even for a given number of active electrons and active orbitals, the orbitals obtained at the end of the self-consistent field iterations of the CASSCF calculation may be different for different sets of initial guess orbitals. Consequently, it is a worthwhile goal to automate active space selection, including the choice of orbitals to start the iterations, and here we examine the question of whether we can devise a broadly applicable automatic scheme for producing guess orbitals that lead to an active space that gives accurate excitation energies. Such a scheme depends on the target number of excitation energies that one is trying to calculate, and here our target is the first two spin-conserving excited electronic states of a closed-shell molecule or a doublet radical. For this target, we propose a scheme called ABC2 to automatically select an active space for MC-PDFT calculations and MS-CASPT2 calculations; the scheme uses high-spin-state unrestricted Hartree-Fock (UHF) natural orbitals as guess orbitals. A novel feature of the ABC2 scheme is that it contains a reliability test that should be passed for the results to be considered reliable. This test requires that the MC-PDFT or CASPT2 excitation energy be within 1.1 eV of the CASSCF excitation energy for the result to be considered reliable. We evaluated the performance of ABC2 for the two lowest excitation energies (or only the lowest when an accurate value of the second lowest state is not available) of 16 singlet systems and 10 doublet systems. We compared the performance of ABC2 to that of our previous ABC scheme, which finds active orbitals through a more expensive (multiconfigurational) excited-state calculation, to the use of ground-state UHF natural orbitals, and to the default scheme in OpenMolcas. We found that the new scheme is more robust than previous methods for a variety of systems.

Experimental and theoretical studies on the absorption spectra of n-dodecane in the IR and VUV regions

We report here a comprehensive spectroscopic study of the absorption spectrum of the n-dodecane molecule using synchrotron radiation based photoabsorption and FTIR spectroscopy. Quantum chemical calculations using the DFT and TDDFT methodologies are used to predict relevant ground and excited state properties and correlate them with the experimental results. In the IR spectrum, assignment of the prominent CH stretching bands in the 2800–3000 cm−1 region are consolidated while a few new vibrational assignments are made in the 700–1500 cm−1 region. The electronic absorption spectrum of n-dodecane lies entirely in the vacuum ultraviolet (VUV) region and consists of a broad continuous absorption band starting from ∼7.5 eV, with no discernible structure. TDDFT calculations of vertical excited states predict that most of the excited states are Rydberg in nature. Potential energy curves of the first few excited states with respect to various bond lengths and bond angles are studied in order to gain additional insights into the nature of the excited states. The broad nature of the absorption is attributed partly to the effect of several conformers as well as hot bands from low frequency modes in the ground state and partly due to overlap of several Rydberg series converging to the first few ionization potentials (IPs). Energy separation between the first and second IP is theoretically predicted to be ∼0.65 eV, while successive separation between the second, third, fourth and fifth IPs is ∼0.03 eV. To the best of our knowledge this is the first report of the VUV absorption spectrum of n-dodecane in the region from 6 to 10 eV, as also the first report of theoretical calculations of its electronically excited states.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions.

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

Far Red Fluorescent Proteins: Where Is the Limit of the Acylimine Chromophore?

The search for new near-infrared probes for fluorescence imaging applications is a rapidly growing field of research. Monomeric fluorescent proteins that autocatalyze their chromophore are the most versatile markers for in vivo applications, but the development of bright far-red fluorescent proteins (RFPs) has proven difficult. In this contribution, we search for the theoretical limit of the red shift and how it can be reached without sacrificing the fluorescence quantum yield. Through extensive excited-state pathway calculations, molecular dynamics sampling, and statistical modeling using QM/MM schemes, we provide a new understanding of the chromophore's photophysics including the role of its acylimine extension, which is the main difference from other families of fluorescent proteins. The excited-state dynamics of the mPlum RFP and its mutants provide an ideal basis due to mPlum's flexible binding pocket and extended dynamic Stokes shift. We found a large number of structural species with red-shifted emission that differ in rotamer states and H-bonds between key amino acid residues in the binding pocket. By analyzing their spectral and structural features, we derive guidelines for future rational genetic design strategies.

QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra.

Cyanobacteriochromes are compact and spectrally diverse photoreceptor proteins that are promising candidates for biotechnological applications. Computational studies can contribute to an understanding at a molecular level of their wide spectral tuning and diversity. In this contribution, we benchmark methods to model a 110 nm shift in the UV/Vis absorption spectrum from a red- to a green-absorbing form of the cyanobacteriochrome Slr1393g3. Based on an assessment of semiempirical methods to describe the chromophore geometries of both forms in vacuo, we find that DFTB2+D leads to structures that are the closest to the reference method. The benchmark of the excited state calculations is based on snapshots from quantum mechanics/molecular mechanics molecular dynamics simulations. In our case, the methods RI-ADC(2) and sTD-DFT based on CAM-B3LYP ground state calculations perform the best, whereas no functional can be recommended to simulate the absorption spectra of both forms with time-dependent density functional theory. Furthermore, the difference in absorption for the lowest energy absorption maxima of both forms can already be modelled with optimized structures, but sampling is required to improve the shape of the absorption bands of both forms, in particular for the second band. This benchmark study can guide further computational studies, as it assesses essential components of a protocol to model the spectral tuning of both cyanobacteriochromes and the related phytochromes.

Multicomponent equation-of-motion coupled cluster singles and doubles: Theory and calculation of excitation energies for positronium hydride.

The calculation of excited states in multicomponent systems, in which more than one type of particle is described quantum mechanically, is important for a wide range of applications in chemistry and physics. The nuclear-electronic orbital (NEO) approach has been used to treat all electrons and key protons, or the positron for positronic systems, quantum mechanically on the same level with density functional theory or wavefunction-based methods. The NEO coupled cluster singles and doubles (NEO-CCSD) method has been shown to provide accurate densities, energies, and optimized geometries for multicomponent systems. Herein, the multicomponent equation-of-motion CCSD (NEO-EOM-CCSD) method is developed for the calculation of excitation energies in multicomponent systems. The working equations are derived and implemented, and the programmable equations are provided to enable others to implement this method. This approach is validated by the comparison of the ground state and first three excited state energies of positronium hydride computed with the NEO-EOM-CCSD method to the values calculated with the NEO full configuration interaction and full coupled cluster methods. The development of the NEO-EOM-CCSD method paves the way for a wide range of applications in excited state multicomponent quantum chemistry.

Photosynthetic Pigments with Potential for a Photosynthetic Antenna: A DFT Analysis

Geometrical and electronic properties of the main photosynthetic pigments in higher plants such as chlorophylls and xanthophylls were studied to find potential candidates that were able to participate in an eventual zeolite-dye artificial antenna. CRDFT (chemical reactivity density functional theory) and TD-DFT (time-dependent DFT) methods were employed in ground-state and excited-state calculations, respectively. The evaluated electronic properties at the gas phase included (a) energies such as HOMO-LUMO band gap (H-L, ranging from 2.168 to 2.504 eV), adiabatic ionization potential (I, ranging from 5.964 to 7.207 eV), and adiabatic electronic affinity (A, ranging from 2.176 to 2.741 eV); (b) global chemical reactivity indexes such as electronegativity (χ, ranging from 4.121 to 4.974 eV), hardness (η, ranging from 1.812 to 2.233 eV), electrophilicity index (ω, ranging from 4.365 to 5.541 eV), and electroaccepting-electrodonating powers (ω+, ranging from 1.671 to 2.115 eV, and ω−, ranging from 4.375 to 5.273 eV); (c) electron-hole reorganization energies (λ, ranging from 0.225 to 0.519 eV and ranging from 0.168 to 0.425 eV, respectively) and electron-hole extraction potentials (EEP, ranging from 2.570 to 2.966 eV, and HEP, ranging from 5.538 to 7.012 eV, respectively); and (d) local chemical reactivity indexes like condensed Fukui functions (fk), condensed dual descriptor (f2r), and condensed local softness (sk). These electronic properties allowed the association between molecules and reactivity-selectivity criteria, under the context of charge transfer and electronic transitions. Also, the aforementioned electronic properties were determined for combinations made with the selected molecules (β-cryptoxanthin and zeaxanthin) and 5 solvents (n-hexane, diethyl ether, acetone, ethanol, and methanol) with upward dielectric constants (ε). From frequency calculations, IR spectra were obtained for combinations. Finally, excited-state computations were carried out to acquire UV-Vis spectra of the combinations. We conclude that the selection of dyes is controlled mainly by geometrical constraints rather than by electronic properties.

Excitation Energies from the Single-Particle Green’s Function with the GW Approximation

Quasi-particle energies are important in predicting molecular ionization energies and bulk band structures. The state-of-the-art method for quasi-particle energy calculations, particularly for bulk systems, is the GW approximation. For excited state calculations, one needs to go beyond the GW approximation. The Bethe-Salpeter equation (BSE) is the commonly used approach for bulk-system excited state calculations beyond the GW approximation, which is accurate but computationally cumbersome. In this Article, we develop a new method to extract excitation energies directly from the quasi-particle energies based on the GW approximation. Starting from the ( N - 1)-electron system, we are able to calculate molecular excitation energies with orbital energies at the GW level for HOMO excitations. Our calculations demonstrate that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. Our method is shown to outperform the time-dependent density functional theory (TDDFT) and are comparable with higher level excited state calculations, including the equation-of-motion couple cluster (EOM-CC) theory and the BSE, but with less computational effort. This new approach provides an efficient alternative to the BSE method for accurate excited state calculations.

Bridge‐ and Double‐Bonded O and NH on Fully OH‐ and NH2‐Terminated Silicon Nanocrystals: Ground and Excited State Properties

The authors model fully hydroxyl‐ (OH‐) and amino‐ (NH2‐) terminated silicon nanocrystals (Si‐NCs) by time‐dependent density functional theory (TD‐DFT), and replace OH or NH2 groups by respective double‐ (=) or bridge‐bonded (>) groups  >/ = O or >/ = NH. Investigating ground state (GS) gaps and interface charge transfers (ICTs) from Si‐NCs to anion groups, the authors show the impact of >/ = O and >/ = NH. Excited state (ES) calculations yielded transition energies Etrans, oscillator strengths fosc and transition rates . The exciton binding energy R* increases with ICT modulation in particular for >/ = O. Increase of is high for =O and comparatively low for >O which correlates with increased (decreased) ionisation of =O (>O), as compared to nominal OH termination. Findings are also met by >/=NH on Si‐NCs, though the authors find the results there to be less apparent which is arguably originating from the specific anionic nature of N. As a result, Si‐NCs with >O and in particular =O bonds show significantly increased optical activity, but also higher R* values. The latter hampers exciton dissociation, hence carrier transport, and results in an increased redshift in photoluminescence (PL). These statements apply also to Si3N4‐embedded Si‐NCs, though the differences there are less articulate.

Arylamine-coumarin based donor-acceptor dyads: Unveiling the relationship between two-photon absorption cross-section and lifetime of singlet excited state intramolecular charge separation

Two-photon absorption (2 PA) with three-dimensional (3D) resolution and deep penetration of light into absorbing materials hold great promise for many applications such as 3D microscopy, 3D microfabrication, polymerization and optical data storage. We herein designed and synthesized two novel series of arylamine-coumarin based donor-acceptor dyads that showed good two-photon absorption activities. Tested by an open/close aperture Z-scan technique, the largest 2 PA cross-section value is 103.6 GM and the largest two-photon absorption coefficient (β) is 7.84 × 10−12 cm W−1. Fluorometric and electrochemical studies further reveal the formation of intramolecular charge transfer (ICT) among two dyads. Photoinduced singlet excited state intramolecular charge separation states were confirmed by ultrafast laser flash photolysis analyses coupled with TD-DFT excited state calculations. Surprisingly, the experimental measured lifetime of singlet excited state intramolecular charge separation state may be a diagnostic criterion for 2 PA cross-section of donor-acceptor systems. This work provides a new strategy for designing high-efficiency 2 PA materials.

Exact two-component equation-of-motion coupled-cluster singles and doubles method using atomic mean-field spin-orbit integrals.

A new semi-atomic-orbital- based algorithm for a two-component spin-orbit (SO) equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method using mean-field SO integrals is reported. The new algorithm removes the major computational bottlenecks of a SO-EOM-CCSD calculation associated with the evaluation, storage, and processing of the H¯ab,cd elements in the similarity-transformed Hamiltonian involving four virtual orbital labels. The partial recovery of spin symmetry in the present algorithm reduces the storage requirement by an order of magnitude and the floating point operation count for the evaluation of the ladder-like term by a factor of three to four. EOM-CCSD calculations of excited states in the triiodide ion (I3 -) using the exact two-component Hamiltonian in combination with atomic mean-field SO integrals (X2CAMF) are reported as a validation of the implementation and also as a demonstration of the capability of the new algorithm to correlate extended virtual spaces. X2CAMF-EOM-CCSD calculations of the ground and excited states in As2, Sb2, and Bi2 are also presented and compared with the available experimental studies. An analysis based on the computed spectroscopic constants as well as the compositions of the excited-state wavefunctions strongly supports a new assignment for the lowest 2u and 0u - levels in the photoelectron spectrum of Bi2.

Inelastic excitation and charge transfer processes for oxygen in collision with H atoms.

Potential energy functions of the OH molecule are investigated from small to large inter-atomic distances R. The electronic problem is treated using an efficient Full Configuration Interaction (Full CI) approach that avoids orbital jumps found usually in multi-configuration self-consistent-field followed by multi-reference configuration interaction calculations of excited states. The calculations are performed for all the doublet, quartet, and sextet OH molecular states, up to the O(2p34s 3S) + H(1s 2S) asymptote, and for the lowest O- + H+ and O+ + H- ionic states. Inter-atomic distances, ranging from 0.5 Å to 20 Å, are spanned with a very small step in order to describe accurately the avoided crossings between the adiabatic potential energy functions. The accuracy of the potentials at small and large R values is analyzed. These Full CI calculations provide for the first time a global description of the 40 lowest molecular states of OH, well suited for dynamical calculations. The resulting potentials are used to obtain first estimates of cross sections and rate coefficients for different inelastic processes through the multichannel approach. This method, based on a Landau-Zener formalism taking into account the ionic-covalent avoided crossings at large distances, gives reliable results for the most intense transitions. It is shown that the largest rate coefficients correspond to mutual neutralization and ion-pair production processes.

Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory Calculations Using Hybrid Functionals.

An approximation is presented which can efficiently decrease the computational expenses of configuration interaction singles (CIS) and time-dependent density functional theory (TDDFT) methods employing hybrid functionals. The approach is the adaptation of the local density fitting scheme developed for Hartree-Fock (HF) calculations for excited states and reduces the quartic scaling of the methods to cubic. It can also be applied to related methods, such as the time-dependent HF and Tamm-Dancoff approximation TDDFT approaches. Our benchmark calculations show that, for molecules of 50-100 atoms, average speedups of 2-4 can be achieved for CIS and TDDFT calculations at the expense of negligible errors in the calculated excitation energies and oscillator strengths, but for bigger systems or molecules of localized electronic structure significantly larger speedups can be gained. We also demonstrate that the approximation enables excited-state calculations on a single processor even for molecules of 1000 atoms using basis sets augmented with diffuse functions including more than 17 000 atomic orbitals.