Charge-transfer Excitation Energies Research Articles

Introducing constricted variational density functional theory in its relaxed self-consistent formulation (RSCF-CV-DFT) as an alternative to adiabatic time dependent density functional theory for studies of charge transfer transitions.

We have applied the relaxed and self-consistent extension of constricted variational density functional theory (RSCF-CV-DFT) for the calculation of the lowest charge transfer transitions in the molecular complex X-TCNE between X = benzene and TCNE = tetracyanoethylene. Use was made of functionals with a fixed fraction (α) of Hartree-Fock exchange ranging from α = 0 to α = 0.5 as well as functionals with a long range correction (LC) that introduces Hartree-Fock exchange for longer inter-electronic distances. A detailed comparison and analysis is given for each functional between the performance of RSCF-CV-DFT and adiabatic time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation. It is shown that in this particular case, all functionals afford the same reasonable agreement with experiment for RSCF-CV-DFT whereas only the LC-functionals afford a fair agreement with experiment using TDDFT. We have in addition calculated the CT transition energy for X-TCNE with X = toluene, o-xylene, and naphthalene employing the same functionals as for X = benzene. It is shown that the calculated charge transfer excitation energies are in as good agreement with experiment as those obtained from highly optimized LC-functionals using adiabatic TDDFT. We finally discuss the relation between the optimization of length separation parameters and orbital relaxation in the RSCF-CV-DFT scheme.

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.

Influence of the Delocalization Error and Applicability of Optimal Functional Tuning in Density Functional Calculations of Nonlinear Optical Properties of Organic Donor–Acceptor Chromophores

Nonempirically tuned hybrid density functionals with range-separated exchange are applied to calculations of the first hyperpolarizability (β//) and charge-transfer (CT) excitations of linear "push-pull" donor-acceptor-substituted organic molecules with extended π-conjugated bridges. An unphysical delocalization with increasing chain length in density functional calculations can be reduced significantly by enforcing an asymptotically correct exchange-correlation potential adjusted to give frontier orbital energies representing ionization potentials. The delocalization error for a number of donor-acceptor systems is quantified by calculations with fractional electron numbers and from orbital localizations. Optimally tuned hybrid variants of the PBE functional incorporating range-separated exchange can produce similar magnitudes for β// as Møller-Plesset second-order perturbation (MP2) correlated calculations. Improvements are also found for CT excitation energies, with results similar to an approximate coupled-cluster model (CC2).

Electronic excitations from a linear-response range-separated hybrid scheme

We study linear-response time-dependent density-functional theory (DFT) based on the single-determinant range-separated hybrid (RSH) scheme, i.e. combining a long-range Hartree–Fock exchange kernel with a short-range DFT exchange-correlation kernel, for calculating electronic excitation energies of molecular systems. It is an alternative to the more common long-range correction (LC) scheme which combines a long-range Hartree–Fock exchange kernel with a short-range DFT exchange kernel and a standard full-range DFT correlation kernel. We discuss the local-density approximation (LDA) to the short-range exchange and correlation kernels, and assess the performance of the linear-response RSH scheme for singlet → singlet and singlet → triplet valence and Rydberg excitations in the N2, CO, H2CO, C2H4 and C6H6 molecules, and for the first charge-transfer excitation in the C2H4–C2F4 dimer. For these systems, the presence of long-range LDA correlation in the ground-state calculation and in the linear-response kernel has only a small impact on the excitation energies and oscillator strengths, so that the RSH method gives results very similar to the ones given by the LC scheme. Like in the LC scheme, the introduction of long-range HF exchange in the present method corrects the underestimation of charge-transfer and high-lying Rydberg excitation energies obtained with standard (semi)local density-functional approximations, but also leads to underestimated excitation energies to low-lying spin-triplet valence states. This latter problem is largely cured by the Tamm–Dancoff approximation which leads to a relatively uniform accuracy for all excitation energies. This work thus suggests that the present linear-response RSH scheme is a reasonable starting approximation for describing electronic excitation energies, even before adding an explicit treatment of long-range correlation.

Functional Assessment for Predicting Charge-Transfer Excitations of Dyes in Complexed State: A Study of Triphenylamine–Donor Dyes on Titania for Dye-Sensitized Solar Cells

Time-dependent density functional theory (TD-DFT) was employed to calculate the UV/vis spectra for three of the triphenylamine (TPA)-donor dyes, TC1, L1, and LJ1, in isolation as well as when complexed with a titania nanoparticle. TPA-donor dyes are a class of promising organic dyes for use in dye-sensitized solar cells (DSSCs). The three dyes studied here are among the smallest of these molecules and provide important insight into the entire series of TPA dyes that are being explored as possible sensitizers in titania-based DSSCs. An attempt to calculate the optical spectra for these dyes within the B3LYP approximation to the exchange correlation functional produces erroneous results. However, Coulomb attenuated approximation (CAM-B3LYP) captures the correct photophysics of the dyes and produces more accurate charge-transfer excitation energies of their complexes with titania. This work shows that the extent to which a given approximation fails or succeeds to correctly predict the charge-transfer excitation energies in the isolated dyes is propagated in that it fails (or succeeds) to correctly predict the values of the excitation energies for the complexes. It is, therefore, important to determine the most appropriate functional for a dye before considering it in more complicated structures such as dye-titania complexes.

Effect of geometrical orientation on the charge-transfer energetics of supramolecular (tetraphenyl)-porphyrin/C60 dyads

The charge transfer (CT) excited state energies of donor-acceptor (D∕A) pairs determine the achievable open-circuit voltage of D∕A-based organic solar cell devices. Changes in the relative orientation of donor-acceptor pairs at the interface influence the frontier orbital energy levels, which impacts the dissociation of bound excitons at the D∕A-interface. We examine the effect of relative orientation on CT excited state energies of porphyrin-fullerene dyads. The donors studied are base- and Zn-tetraphenyl porphyrin coupled to C60 as the acceptor molecule in an end-on configuration. We compare the energetics of a few low-lying CT states for the end-on geometry to our previously calculated CT energetics of a co-facial orientation. The calculated CT excitation energies are larger for the end-on orientation in comparison to the co-facial structure by about 0.7 eV, which primarily occurs due to a decrease in exciton binding energy in going from the co-facial to the end-on orientation. Furthermore, changes in relative donor-acceptor orientation have a larger impact on the CT energies than changes in donor-acceptor distance.

An accurate and linear-scaling method for calculating charge-transfer excitation energies and diabatic couplings

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Ångstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.

Many-body Green's function study of coumarins for dye-sensitized solar cells

We study within the many-body Green's function $GW$ and Bethe-Salpeter formalisms the excitation energies of several coumarin dyes proposed as an efficient alternative to ruthenium complexes for dye-sensitized solar cells. Due to their internal donor-acceptor structure, these chromophores present low-lying excitations showing a strong intramolecular charge-transfer character. We show that combining $GW$ and Bethe-Salpeter calculations leads to charge-transfer excitation energies and oscillator strengths in excellent agreement with reference range-separated functional studies or coupled-cluster calculations. The present results confirm the ability of this family of approaches to describe accurately Frenkel and charge-transfer photo-excitations in both extended and finite size systems without any system-dependent adjustable parameter, paving the way to the study of dye-sensitized semiconducting surfaces.

Reliable Quantum Chemical Prediction of the Localized/Delocalized Character of Organic Mixed-Valence Radical Anions. From Continuum Solvent Models to Direct-COSMO-RS.

A recently proposed quantum-chemical protocol for the description of the character of organic mixed-valence (MV) compounds, close from both sides to the localized/delocalized borderline, is evaluated and extended for a series of dinitroaryl radical anions 1-6. A combination of global hybrid functionals with exact-exchange admixtures of 35% (BLYP35) or 42% (BMK) with appropriate solvent modeling allows an essentially quantitative treatment of, for example, structural symmetry-breaking in Robin/Day class II systems, thermal electron transfer (ET) barriers, and intervalence charge-transfer (IV-CT) excitation energies, while covering also the delocalized class III cases. Global hybrid functionals with lower exact-exchange admixtures (e.g., B3LYP, M05, or M06) provide a too delocalized description, while functionals with higher exact-exchange admixtures (M05-2X, M06-2X) provide a too localized one. The B2PLYP double hybrid gives reasonable structures but far too small barriers in class II cases. The CAM-B3LYP range hybrid gives somewhat too high ET barriers and IV-CT energies, while the range hybrids ωB97X and LC-BLYP clearly exhibit too much exact exchange. Continuum solvent models describe the situation well in most aprotic solvents studied. The transition of 1,4-dinitrobenzene anion 1 from a class III behavior in aprotic solvents to a class II behavior in alcohols is not recovered by continuum solvent models. In contrast, it is treated faithfully by the novel direct conductor-like screening model for real solvents (D-COSMO-RS). The D-COSMO-RS approach, the TURBOMOLE implementation of which is reported, also describes accurately the increased ET barriers of class II systems 2 and 3 in alcohols as compared to aprotic solvents and can distinguish at least qualitatively between different aprotic solvents with identical or similar dielectric constants. The dominant role of the solvent environment for the ET character of these MV radical anions is emphasized, as in contrast to some previous computational suggestions essentially all of the present systems have delocalized class III character in the gas phase. The present approach allows accurate estimates from the gas phase to aprotic and protic solvent environments, without the need for explicit ab initio molecular dynamics simulations, and without artificial constraints.

Charge transfer excited state energies by perturbative delta self consistent field method

We use our recently outlined perturbative approach to compute the lowest charge transfer excitation energies for a set of tetracynoehylene (TCNE)-hydrocarbon complexes, C(2)H(4)-C(2)F(4), NH(3)-F(2), pentacene-C(60), and tetraphenyl porphyrin-C(60) complexes. Results show that the method can provide a reliable description of charge transfer excitation energies, which are comparable to that obtained by time-dependent density functional theory using specially optimized range-corrected functionals. As the calculation cost of excited state is comparable to the ground state and the calculation of each excited state is independent of others, the method can be easily used to describe the charge transfer excited states of large donor-acceptor complexes containing 200 or more atoms.

Charge transfer excitations in cofacial fullerene-porphyrin complexes

Porphyrin and fullerene donor-acceptor complexes have been extensively studied for their photo-induced charge transfer characteristics. We present the electronic structure of ground states and a few charge transfer excited states of four cofacial porphyrin-fullerene molecular constructs studied using density functional theory at the all-electron level using large polarized basis sets. The donors are base and Zn-tetraphenyl porphyrins and the acceptor molecules are C(60) and C(70). The complexes reported here are non-bonded with a face-to-face distance between the porphyrin and the fullerene of 2.7 to 3.0 Å. The energies of the low lying excited states including charge transfer states calculated using our recent excited state method are in good agreement with available experimental values. We find that replacing C(60) by C(70) in a given dyad may increase the lowest charge transfer excitation energy by about 0.27 eV. Variation of donor in these complexes has marginal effect on the lowest charge transfer excitation energy. The interfacial dipole moments and lowest charge transfer states are studied as a function of face-to-face distance.

Charge-Transfer Excitations in Uranyl Tetrachloride ([UO2Cl4]2–): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory?

Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange-correlation functional for the [UO(2)Cl(4)](2-) system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approximate exchange-correlation functionals: BLYP, B3LYP, and CAM-B3LYP.

A non-self-consistent range-separated time-dependent density functional approach for large-scale simulations

We propose an efficient method for carrying out time-dependent density functional theory (TDDFT) calculations using range-separated hybrid exchange–correlation functionals. Based on a non-self-consistent range-separated Hamiltonian, the method affords large-scale simulations at a fraction of the computational time of conventional hybrid TDDFT approaches. For typical benchmark molecules including N2, CO, C6H6, H2CO and the C2H4–C2F4 dimer, the method possesses the same level of accuracy as the conventional approaches for the valence, Rydberg, and charge-transfer excitation energies when compared to the experimental results. The method is used to determine π → π* excitations in both disordered and crystalline poly(3-hexylthiophene) (P3HT) conjugated polymers with more than six hundred atoms and it yields excitation energies and charge densities that are in excellent agreement with experiments. The simulation of the crystalline P3HT reveals that the phase of the wavefunctions could have an important effect on the excitation energy; a hypothesis based on π–π stacking is proposed to explain this novel effect in conjugated polymers.

A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97)

We applied an improved long-range correction scheme including a short-range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau-B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long-range portion of Hartree-Fock (HF) exchange to excitation energies of large molecules (Chai and Head-Gordon, J Chem Phys 2008, 128, 084106) and additional short-range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short-range to mid-range (0.5-3 Å) to ground state properties achieved high performances of LCgau-B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x-family. We also found that while a small μ value (∼0.2) in LC-DFT is appropriate to the local excitation and intramolecular charge-transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation-energy calculations.

Nonempirically Tuned Long-Range Corrected Density Functional Theory Study on Local and Charge-Transfer Excitation Energies in a Pentacene/C60 Model Complex

The local and charge-transfer excitation energies in a pentacene/C60 complex, which is prototypical of the minimal structural unit of the donor–acceptor heterojunction in pentacene/C60 organic cells, are evaluated using the time-dependent long-range corrected density functional theory (TD-LC-BLYP) method in comparison with those estimated from the experimental data for pentacene and C60. In the framework of the tuned range-separated hybrid (Livshits et al. J. Phys. Chem. A2008, 112, 12789), we tune the range separating parameter (μ) of the LC-BLYP functional by imposing the many-electron self-interaction-free (ME-SIF) condition on the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of pentacene and C60. The TD-LC-BLYP method with μ = 0.20 is found to succeed in the semiquantitative description of both the local and charge-transfer excitation energies in the pentacene/C60 complex.

Electronically Excited States of Vitamin B12: Benchmark Calculations Including Time-Dependent Density Functional Theory and Correlated ab Initio Methods

Time-dependent density functional theory (TD-DFT) and correlated ab initio methods have been applied to explore the electronically excited states of vitamin B(12) (cyanocobalamin or CNCbl). Different experimental techniques have been used to probe the excited states of CNCbl, revealing many issues that remain poorly understood from an electronic structure point of view. Due to its efficient scaling with size, TD-DFT emerges as one of the most practical tools that can be used to study the electronic properties of these fairly complex molecules. However, the description of excited states is strongly dependent on the type of functional used in the calculations. In the present contribution, the choice of a proper functional for vitamin B(12) was evaluated in terms of its agreement with both experimental results and correlated ab initio calculations. Three different functionals, i.e., B3LYP, BP86, and LC-BLYP, were tested. In addition, the effect of the relative contributions of DFT and HF to the exchange-correlation functional was investigated as a function of the range-separation parameter, μ. The issues related to the underestimation of charge-transfer excitation energies by TD-DFT were validated by the Λ diagnostic, which measures the spatial overlap between occupied and virtual orbitals involved in the particular excitation. The nature of the low-lying excited states was also analyzed based on a comparison of TD-DFT and ab initio results. Based on an extensive comparison with experimental results and ab initio benchmark calculations, the BP86 functional was found to be the most appropriate in describing the electronic properties of CNCbl. Finally, an analysis of electronic transitions and reassignment of some excitations were discussed.

Charge-transfer separability and size-extensivity in the equation-of-motion coupled cluster method: EOM-CCx

We study the charge-transfer separability (CTS) property of the Fock space (FS) and equation-of-motion (EOM) coupled cluster (CC) methods by analysing the charge-transfer (CT) excitation energy versus the donor-acceptor (D-A) distance. All FS-CC approaches fulfill the CT separability condition which is not the case for the standard EOM-CC approaches. This defect of the EOM-CC scheme can be fixed by slight modification of the H matrix's diagrammatic structure, namely by adding some "dressing" composed of disconnected terms. The latter guarantee CTS of the respective EOM-CC scheme and marginally improve local excitations. The newly proposed variant of the EOM-CCSD approach is termed EOM-CCSDx (size-extensive EOM-CCSD).

Computational and spectroscopic studies of organic mixed-valence compounds: where is the charge?

This article discusses recent progress by a combination of spectroscopy and quantum-chemical calculations in classifying and characterizing organic mixed-valence systems in terms of their localized vs. delocalized character. A recently developed quantum-chemical protocol based on non-standard hybrid functionals and continuum solvent models is evaluated for an extended set of mixed-valence bis-triarylamine radical cations, augmented by unsymmetrical neutral triarylamine-perchlorotriphenylmethyl radicals. It turns out that the protocol is able to provide a successful assignment to class II or class III Robin-Day behavior and gives quite accurate ground- and excited-state properties for the radical cations. The limits of the protocol are probed by the anthracene-bridged system 8, where it is suspected that specific solute-solvent interactions are important and not covered by the continuum solvent model. Intervalence charge-transfer excitation energies for the neutral unsymmetrical radicals are systematically overestimated, but dipole moments and a number of other properties are obtained accurately by the protocol.

ChemInform Abstract: Aromatic Nitration with Electrophilic N-Nitropyridinium Cations. Transitory Charge-Transfer Complexes as Key Intermediates.

Electrophilic aromatic nitration of various arenes (ArH) is shown to be critically dependent on labile charge-transfer complexes derived from N-nitropyridinium cations. The electrophiles XPyNO 2 + ,with X=CN, CO 2 CH 3 , Cl, H, CH 3 , and OCH 3 , form a highly graded series of electron acceptors that produce divers [ArH,XPyNO 2 + ] complexes, with charge-transfer excitation energies (h CT ) spanning a range of almost 50 kcal mol -1

DFT calculations of molecular excited states using an orbital-dependent nonadiabatic exchange kernel

A density functional method for computing molecular excitation spectra is presented that uses a frequency-dependent kernel and takes into account the nonlocality of exchange interaction. Owing to its high numerical stability and the use of a nonadiabatic (frequency-dependent) exchange kernel, the proposed approach provides a qualitatively correct description of the asymptotic behavior of charge-transfer excitation energies.