Intermolecular Charge-transfer Excitations Research Articles

Why Does the Optimal Tuning Method of the Range Separation Parameter of a Long-Range Corrected Density Functional Fail in Intramolecular Charge Transfer Excitation Calculations?

We performed intra- and intermolecular charge transfer (CT) excitation energy calculations of (a) conjugated carbon chain [H2N-(CH=CH)n-X] and (b) its equidistant H2NH∙∙∙HX (n = 2~8) with various electron acceptors (X = NH2, OH, Cl, CHO, CN, and NO2) using EOM-CCSD, time-dependent (TD) Hartree-Fock (HF) and various density functional theory (DFT) functionals, such as BLYP, B3LYP, long-range corrected (LC) DFT, and LC-DFT with an optimally tuned (OT) range separation parameter (µ) using Koopman's theorem to investigate the effect of the electron-withdrawing (or -donating) strength of end-capped functional group (X) and CT distance (R) on intra- and intermolecular CT excitation energies. As the electron-withdrawing strength of X increases, both intra- and intermolecular CT excitation energies tend to decrease, since energy gaps between orbitals corresponding to CT excitations (e.g., HOMO and LUMO) decrease. However, the effect of the electron-withdrawing group on intramolecular CT excitation energy is negligible (at most 0.5 eV). OT-LC-DFT shows accurate intermolecular CT excitation energy, but worse results in intramolecular CT excitation energy than LC-DFT with the default µ value (0.47). Therefore, we conclude that the optimal tuning method is not effective in predicting intramolecular CT excitation energy. While intermolecular CT excitation energy has excitonic binding energy with asymptotic behavior to CT distance that is not affected by the choice of range separation parameter, intramolecular CT excitation energy is affected by orbital relaxation energy, which strongly depends on the choice of range separation parameter, which makes the OT method of range separation parameter ineffective in predicting intramolecular CT excitation energy as well as local excitation with high accuracy.

Assessing intra- and inter-molecular charge transfer excitations in non-fullerene acceptors using electroabsorption spectroscopy

Organic photovoltaic cells using Y6 non-fullerene acceptors have recently achieved high efficiency, and it was suggested to be attributed to the charge-transfer (CT) nature of the excitations in Y6 aggregates. Here, by combining electroabsorption spectroscopy measurements and electronic-structure calculations, we find that the charge-transfer character already exists in isolated Y6 molecules but is strongly increased when there is molecular aggregation. Surprisingly, it is found that the large enhanced charge transfer in clustered Y6 molecules is not due to an increase in excited-state dipole moment, Δμ, as observed in other organic systems, but due to a reduced polarizability change, Δp. It is proposed that such a strong charge-transfer character is promoted by the stabilization of the charge-transfer energy upon aggregation, as deduced from density functional theory and four-state model calculations. This work provides insight into the correlation between molecular electronic properties and charge-transfer characteristics in organic electronic materials.

Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations.

Intermolecular charge-transfer is a highly important process in biology and energy-conversion applications where generated charges need to be transported over several moieties. However, its theoretical description is challenging since the high accuracy required to describe these excited states must be accessible for calculations on large molecular systems. In this benchmark study, we identify reliable low-scaling computational methods for this task. Our reference results were obtained from highly accurate wavefunction calculations that restrict the size of the benchmark systems. However, the density-functional theory based methods that we identify as accurate can be applied to much larger systems. Since targeting charge-transfer states requires the unambiguous classification of an excited state, we first analyze several charge-transfer descriptors for their reliability concerning intermolecular charge-transfer and single out the charge-transfer distance calculated based on the variation of electron density upon excitation (DCT) as an optimal choice for our purposes. In general, best results are obtained for orbital-optimized methods and among those, the maximum overlap method proved to be the most numerically stable variant when using the initial MOs as reference orbitals. Favorable error cancellation with optimally-tuned range-separated hybrid functionals and a rather small basis set can provide an economical yet reasonable wavefunction when using time-dependent density functional theory, which provides relevant information about the excited-state character to be used in the orbital-optimized methods. The qualitative agreement makes these fast calculations attractive for high-throughput screening applications.

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States.

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

Is charge-transfer excitation through a polyalkane single-bond chain an intramolecular charge-transfer?: EOM-CCSD and LC-BOP study

We performed intra- and intermolecular charge-transfer (CT) excitation calculations of (a) H2N–(CH2–CH2)n–NO2 and (b) its equidistant H2N-H……H-NO2 using EOM-CCSD (n = 1 ∼ 5) and time-dependent long-range corrected density functional theory (n = 1 ∼ 10). The calculation results show that polyalkane [polyethylene oligomer] chain has almost no effect on CT excitation energy between donor and acceptor. That is, CT excitation energy through the polyalkane chain behaves closely to intermolecular CT excitation. Decomposition of the optical excitation energies of (a) and (b) into HOMO-LUMO gap and excitonic binding energy revealed that alkane chain does not affect HOMO-LUMO gaps, while conjugated polyene [polyethylene oligomer] chain medium reduces HOMO-LUMO gaps by delocalization.

Assessing challenging intra- and inter-molecular charge-transfer excitations energies with double-hybrid density functionals.

We investigate the performance of a set of recently introduced range-separated double-hybrid functionals, namely ωB2-PLYP, ωB2GP-PLYP, RSX-0DH, and RSX-QIDH models for hard-to-calculate excitation energies. We compare with the parent (B2-PLYP, B2GP-PLYP, PBE0-DH, and PBE-QIDH) and other (DSD-PBEP86) double-hybrid models as well as with some of the most widely employed hybrid functionals (B3LYP, PBE0, M06-2X, and ωB97X). For this purpose, we select a number of medium-sized intra- and inter-molecular charge-transfer excitations, which are known to be challenging to calculate using time-dependent density-functional theory (TD-DFT) and for which accurate reference values are available. We assess whether the high accuracy shown by the newest double-hybrid models is also confirmed for those cases too. We find that asymptotically corrected double-hybrid models yield a superior performance, especially for the inter-molecular charge-transfer excitation energies, as compared to standard double-hybrid models. Overall, the PBE-QIDH and its corresponding range-separated RSX-QIDH functional are recommended for general-purpose TD-DFT applications, depending on whether long-range effects are expected to play a significant role.

Global double hybrids do not work for charge transfer: A comment on “Double hybrids and time‐dependent density functional theory: An implementation and benchmark on charge transfer excited states”

We comment on the results published by Ottochian et al. in J. Comput Chem. 2020, 41, 1242. Therein, the authors claim that the second-order, perturbative correlation correction applied to the time-dependent version of the PBE-QIDH global double-hybrid functional approximation (DHDFA) enables the description of charge-transfer (CT) excitations. Herein, we point out some inadvertent oversights related to what had already been previously known and achieved in the field of time-dependent DHDFAs. Exemplified for the same four systems that Ottochian et al. have used to analyze intermolecular CT excitations, we show how a systematic and unacceptably large redshift in global DHDFAs is rectified when using the latest long-range corrected DHDFAs published earlier in J. Chem. Theory Comput. 2019, 15, 4735.

Aggregation-induced emission spectra of triphenylamine salicylaldehyde derivatives via excited-state intramolecular proton transfer revealed by molecular spectral and dynamics simulations.

Aggregation-induced emission (AIE) spectra accompanied by excited state intramolecular proton transfer (ESIPT) for two triphenylamine salicylaldehyde derivatives (namely, TS and TS-OMe) are investigated by performing molecular spectral and dynamics simulations associated with the hybrid quantum mechanics/molecular mechanics (QM/MM) at the quantum level of the time-dependent density functional theory. The simulated emission spectral peaks and Stokes' shifts are in good agreement with the experimental results for both TS and TS-OMe. Furthermore, the AIE spectral mechanisms are well explained to be associated with the ESIPT processes for both TS and TS-OMe monomers in the aggregated crystal state, while the AIE spectra mechanism for the TS-OMe (TS) dimer is accompanied by intermolecular charge-transfer excitation process. Besides, the TS dimers also contributed to the AIE mechanisms in the crystal with the intermolecular charge-transfer from one monomer to another. In addition, the TS dimers are contributed to the AIE mechanisms in the crystal with the intermolecular charge-transfer from one monomer to another. On the other hand, simulated emission spectra for both the TS and TS-OMe monomers in acetonitrile solution are involved in mixed emission with and without the ESIPT process, as interpreted by nonadiabatic molecular dynamics simulation. It is also briefly addressed that the emission spectra in the solution are weak and enhanced in the crystal. The present study provides a great physical insight into the design of highly efficient AIE compounds.

Interplay between Intra- and Intermolecular Charge Transfer in the Optical Excitations of J-Aggregates.

In a first-principles study based on density functional theory and many-body perturbation theory, we address the interplay between intra- and intermolecular interactions in a J-aggregate formed by push–pull organic dyes by investigating its electronic and optical properties. We find that the most intense excitation dominating the spectral onset of the aggregate, i.e., the J-band, exhibits a combination of intramolecular charge transfer, coming from the push–pull character of the constituting dyes, and intermolecular charge transfer, due to the dense molecular packing. We also show the presence of a pure intermolecular charge-transfer excitation within the J-band, which is expected to play a relevant role in the emission properties of the J-aggregate. Our results shed light on the microscopic character of optical excitations of J-aggregates and offer new perspectives to further understand the nature of collective excitations in organic semiconductors.

The effect of electronic excitation on London dispersion

Atomic and molecular dispersion coefficients can now be calculated routinely using density-functional theory. In this work, we present the first determination of how electronic excitation affects molecular C6 London dispersion coefficients from the exchange-hole dipole moment (XDM) dispersion model. Excited states are typically found to have larger dispersion coefficients than the corresponding ground states, due to their more diffuse electron densities. A particular focus is both intramolecular and intermolecular charge-transfer excitations, which have high absorbance intensities and are important in organic dyes, light-emitting diodes, and photovoltaics. In these classes of molecules, the increase in C6 for the electron-accepting moiety is largely offset by a decrease in C6 for the electron-donating moiety. As a result, the change in dispersion energy for a chromophore interacting with neighbouring molecules in the condensed phase is minimal.

Validation of local hybrid functionals for TDDFT calculations of electronic excitation energies.

The first systematic evaluation of local hybrid functionals for the calculation of electronic excitation energies within linear-response time-dependent density functional theory (TDDFT) is reported. Using our recent efficient semi-numerical TDDFT implementation [T. M. Maier et al., J. Chem. Theory Comput. 11, 4226 (2015)], four simple, thermochemically optimized one-parameter local hybrid functionals based on local spin-density exchange are evaluated against a database of singlet and triplet valence excitations of organic molecules, and against a mixed database including also Rydberg, intramolecular charge-transfer (CT) and core excitations. The four local hybrids exhibit comparable performance to standard global or range-separated hybrid functionals for common singlet valence excitations, but several local hybrids outperform all other functionals tested for the triplet excitations of the first test set, as well as for relative energies of excited states. Evaluation for the combined second test set shows that local hybrids can also provide excellent Rydberg and core excitations, in the latter case rivaling specialized functionals optimized specifically for such excitations. This good performance of local hybrids for different excitation types could be traced to relatively large exact-exchange (EXX) admixtures in a spatial region intermediate between valence and asymptotics, as well as close to the nucleus, and lower EXX admixtures in the valence region. In contrast, the tested local hybrids cannot compete with the best range-separated hybrids for intra- and intermolecular CT excitation energies. Possible directions for improvement in the latter category are discussed. As the used efficient TDDFT implementation requires essentially the same computational effort for global and local hybrids, applications of local hybrid functionals to excited-state problems appear promising in a wide range of fields. Influences of current-density dependence of local kinetic-energy dependent local hybrids, differences between spin-resolved and "common" local mixing functions in local hybrids, and the effects of the Tamm-Dancoff approximation on the excitation energies are also discussed.

Resonance Raman spectra of organic molecules absorbed on inorganic semiconducting surfaces: Contribution from both localized intramolecular excitation and intermolecular charge transfer excitation.

The time-dependent correlation function approach for the calculations of absorption and resonance Raman spectra (RRS) of organic molecules absorbed on semiconductor surfaces [Y. Zhao and W. Z. Liang, J. Chem. Phys. 135, 044108 (2011)] is extended to include the contribution of the intermolecular charge transfer (CT) excitation from the absorbers to the semiconducting nanoparticles. The results demonstrate that the bidirectionally interfacial CT significantly modifies the spectral line shapes. Although the intermolecular CT excitation makes the absorption spectra red shift slightly, it essentially changes the relative intensities of mode-specific RRS and causes the oscillation behavior of surface enhanced Raman spectra with respect to interfacial electronic couplings. Furthermore, the constructive and destructive interferences of RRS from the localized molecular excitation and CT excitation are observed with respect to the electronic coupling and the bottom position of conductor band. The interferences are determined by both excitation pathways and bidirectionally interfacial CT.

Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme.

Photoinduced charge-transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for an accurate and computationally inexpensive treatment of charge-transfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys. 138, 124107 (2013)] to allow for the description of intermolecular charge-transfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the Hartree-Fock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest charge-transfer excitation energies for a set of tetracyanoethylene-hydrocarbon complexes that have been used earlier as a test set for such kind of excitations.

What makes differences between intra- and inter-molecular charge transfer excitations in conjugated long-chained polyene? EOM-CCSD and LC-BOP study

We performed intra- and inter-molecular charge transfer (CT) excitation calculations of H2N–(CH=CH) n –NO2 (a) and its equidistant H2N–H···H–NO2 (b) using EOM-CCSD (n = 1–9), time-dependent (TD) long-range corrected (LC) density functional theory (DFT) (n = 1–10). It was shown that LC-BOP and LCgau-BOP outperform all the tested DFT functionals on inter- and intra-CT excitation energy and oscillator strength, regardless of CT interaction distance (R). Decomposition of TD-DFT optical excitation energies of (a) and (b) into HOMO–LUMO gap and excitonic binding energy disclosed that HOMO–LUMO gap reduction resulting from delocalization of HOMO and LUMO through bridged polyene conjugation is mainly responsible for the decreasing of intra-molecular CT excitation energy with chain number, while inter-molecular CT increases linearly with −1/R, which is wholly due to the decrease in excitonic energy between HOMO and LUMO. We found that success of exchange correlation functional on long-distanced intra-molecular CT calculations depends on correct descriptions of (1) Koopmans’ energy of donor and acceptor and (2) excitonic energy between donor and acceptor, and (3) correct far-nucleus asymptotic behavior, −1/R. We found that LC scheme can satisfy (3), but needs an appropriate choice of long-range parameter able to satisfy (1) and (2). On the other hand, the pure, conventional hybrid, and screened hybrid functionals show near-zero intra- and inter-molecular excitonic energy regardless of R, which means optical band gap coincide with HOMO–LUMO gap. Therefore, we conclude that 100 % long-range Hartree–Fock exchange inclusion is indispensable for correct descriptions of intra-molecular CT excitations as well as inter-molecular CT.

Frenkel and Charge-Transfer Excitations in Donor-acceptor Complexes from Many-Body Green's Functions Theory.

Excited states of donor-acceptor dimers are studied using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. For a series of prototypical small-molecule based pairs, this method predicts energies of local Frenkel and intermolecular charge-transfer excitations with the accuracy of tens of meV. Application to larger systems is possible and allowed us to analyze energy levels and binding energies of excitons in representative dimers of dicyanovinyl-substituted quarterthiophene and fullerene, a donor-acceptor pair used in state of the art organic solar cells. In these dimers, the transition from Frenkel to charge transfer excitons is endothermic and the binding energy of charge transfer excitons is still of the order of 1.5-2 eV. Hence, even such an accurate dimer-based description does not yield internal energetics favorable for the generation of free charges either by thermal energy or an external electric field. These results confirm that, for qualitative predictions of solar cell functionality, accounting for the explicit molecular environment is as important as the accurate knowledge of internal dimer energies.

Vibronic Spectra of Perylene Bisimide Oligomers: Effects of Intermolecular Charge-Transfer Excitation and Conformational Flexibility

We have recently presented a theoretical study on the temperature-dependent absorption and photoluminescence spectroscopy of rubrene multichromophores by combining the time-dependent long-range-corrected density functional theory with the Frenkel exciton model (Gao; et al. J. Phys. Chem. A2009, 113, 12847). The spectra of rubrene multichromophores up to heptamers have been calculated and the effects of exciton-phonon coupling and temperature on the photophysical properties of both H- and J-aggregated oligomers were addressed. However, in that work the contribution of intermolecular charge-transfer excitons (CTEs) to vibronic spectra was not addressed. Here we take into account the effect of CTEs for the absorption and emission spectra of the aggregated perylene bisimide (PBI) oligomers in order to have a quantitative explanation to the experimental absorption and emission spectra of the PBI dyes. The role of intermolecular CTEs is discussed for different intermolecular orientations and distances. The simulations demonstrate that the contribution of CTEs becomes significant when the intermolecular distance is less than 4.5 Å for the π-π stacked PBI aggregates, and the mixed exciton model is prerequisite to explain the experimentally observed red-shift of the absorption spectra in this case. The large Stokes shift of the emission spectra can be reproduced by our model, and it is induced by the asymmetric nature of the lowest excitonic state of the H-aggregated oligomers. The experimentally observed broad emission bands come from two species with different conformations. As for J-aggregated PBI oligomers, the interactions of FEs induce the red-shift and the increase of the relative intensity of 0-0 peak of the absorption spectra with more aggregated units.

Correlated-electron description of the photophysics of thin films ofπ-conjugated polymers

We extend the Mulliken theory of ground-state charge transfer in a donor-acceptor complex to excited-state charge transfer between pairs of identical $\ensuremath{\pi}$-conjugated oligomers, one of which is in the optically excited state and the other is in the ground state, leading to the formation of a charge-transfer exciton. Within our theory, optical absorptions from the charge-transfer exciton should include a low-energy intermolecular charge-transfer excitation, as well as distinct intramolecular excitations from both the neutral delocalized exciton component and the Coulombically bound polaron-pair component of the charge-transfer exciton. We report high-order configuration-interaction calculations for pairs of oligomers of polyparaphenylenevinylene (PPV) that go beyond our previous single configuration-interaction calculation and find all five excited-state absorptions predicted using heuristic arguments based on the Mulliken concept. Our calculated excited-state absorption spectrum exhibits strong qualitative agreement with the complete wavelength-dependent ultrafast photoinduced absorption in films of PPV derivatives, suggesting that a significant fraction of the photoinduced absorption here is from the charge-transfer exciton. We make detailed comparisons to experiments and a testable experimental prediction.

A well-tempered density functional theory of electrons in molecules

This Invited Article reports extensions of a recently developed approach to density functional theory with correct long-range behavior (R. Baer and D. Neuhauser, Phys. Rev. Lett., 2005, 94, 043002). The central quantities are a splitting functional gamma[n] and a complementary exchange-correlation functional E[n]. We give a practical method for determining the value of gamma in molecules, assuming an approximation for E is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond lengths of the molecules in the G2(1) database. The optimized values are gamma = 0.5 a and w = 0.1. We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations.

Nonlinear Infrared and Optical Responses of a Holstein−Peirls−Hubbard Dimer

A simple model based on the Holstein-Peierls-Hubbard Hamiltonian has been used to calculate the nonlinear responses at infrared and optical frequencies. The model is applied to a molecular ion radical dimer in order to account for the contribution to the nonlinear responses arising from the intermolecular charge transfer excitations and from their coupling to both intramolecular and intermolecular phonons. A similar calculation has been performed on a model quadrupolar conjugated molecule characterized by intramolecular charge transfer excitations. The calculations are performed according to a collective electronic oscillator scheme by solving the Liouville equation for the bielectronic density matrix. Such a choice allows us to retain the ability, inherent in the Hubbard type models, to fully account for the on-site electron correlation effects. Calculated spectra are reported for one-photon and two-photon absorption (the latter in the form of the imaginary part of the Kerr susceptibility) and for third harmonic generation. Narrow resonances are observed in the infrared, related mostly to the coupling with intramolecular modes. The off-resonant contribution to the nonlinear susceptibility arising from the electron-phonon interactions appears to be marginal (in the order of 1%) in all cases.

Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory

Charge-transfer (CT) electronic excitation energies are known to be very poorly predicted by time-dependent density functional theory (TDDFT) using local exchange-correlation functionals. Insight into this observation is provided by a simple analysis of intermolecular CT excitations at infinite separation. It is argued that the first TDDFT CT excitation energy approximately underestimates the experimental excitation by the average of the integer discontinuities of the donor and acceptor molecules; errors are of the order of several electron volts.