Calculation of two-photon absorption spectra of donor-π-acceptor compounds in solution using quadratic response time-dependent density functional theory

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/GW, and Wave Function Methods

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O ( N 5 ) and O ( N 6 ) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

Hyperpolarizabilities of Push-Pull Chromophores in Solution: Interplay between Electronic and Vibrational Contributions

Contemporary design of new organic non-linear optical (NLO) materials relies to a large extent on the understanding of molecular and electronic structure-property relationships revealed during the years by available computational approaches. The progress in theory-hand-in-hand with experiment-has enabled us to identify and analyze various physical aspects affecting the NLO responses, such as the environmental effects, molecular vibrations, frequency dispersion, and system dynamics. Although it is nowadays possible to reliably address these effects separately, the studies analyzing their mutual interplay are still very limited. Here, we employ density functional theory (DFT) methods in combination with an implicit solvent model to examine the solvent effects on the electronic and harmonic as well as anharmonic vibrational contributions to the static first hyperpolarizability of a series of push-pull α,ω-diphenylpolyene oligomers, which were experimentally shown to exhibit notable second-order NLO responses. We demonstrate that the magnitudes of both vibrational and electronic contributions being comparable in the gas phase significantly increase in solvents, and the enhancement can be, in some cases, as large as three- or even four-fold. The electrical and mechanical anharmonic contributions are not negligible but cancel each other out to a large extent. The computed dynamic solute NLO properties of the studied systems are shown to be in a fair agreement with those derived from experimentally measured electric-field-induced second-harmonic generation (EFISHG) signals. Our results substantiate the necessity to consider concomitantly both solvation and vibrational effects in modeling static NLO properties of solvated systems.

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.

Calculated linear and nonlinear optical absorption spectra of phosphine-ligated gold clusters

Although prediction of optical excitations of ligated gold clusters by time-dependent density functional theory (TDDFT) is relatively well-established, limitations still exist, for example in the choice of the exchange-correlation functional....

Exciton coupling effects on the two-photon absorption of squaraine homodimers with varying bridge units

Excitonically coupled squaraine dimers show high two-photon absorption cross sections.

Tuning of hyperpolarizability, and one- and two-photon absorption of donor-acceptor and donor-acceptor-acceptor-type intramolecular charge transfer-based sensors

The present work aims to study the effect of solvent as well as arrangement of donor-acceptor groups on linear and non-linear optical (NLO) response properties of two experimentally studied intramolecular charge-transfer (ICT)-based fluorescent sensors. One of them (molecule 1) is a donor-acceptor (D-A) system with hemicyanine and dimethylanilino as electron withdrawing and donating groups, respectively, while the other one (molecule 3) is molecule 1 fused with a boron-dipyrromethene (BODIPY) moiety. BODIPY acts as the electron acceptor group of molecule 2 that as well consists of dimethylanilino as the electron donor. Density functional theory (DFT) as well as time-dependent DFT has been employed to optimize the geometry of the molecules, followed by computation of dipole moment (μ), static first hyperpolarizability (β_total), and one- and two-photon absorption (TPA) strengths. The results reveal that dipole moment as well as total static first hyperpolarizability (β_total) of the studied molecules is dominated by the respective components in the direction of charge transfer. The ratio of vector component of first hyperpolarizability (β_vec) to β_total also supports the unidirectional charge transfer in the studied systems. In molecule 3, which is a donor-acceptor-acceptor (D-A-A)-type system, the BODIPY moiety is found to play a major role in controlling the NLO response over the other acceptor group. Solvents are also found to play an important role in controlling the linear as well as NLO response of the studied systems. A significant increase in the first hyperpolarizability as well as TPA cross-section of the studied molecules is predicted due to an increase in the dielectric constant of the medium. The results presented are expected to provide a clue in tuning the NLO response of many ICT-based chromophores, especially those with D-A-A arrangements.

Interplay of twist angle and solvents with two-photon optical channel interference in aryl-substituted BODIPY dyes

Channel interference plays a crucial role in understanding the physics behind multiphoton absorption processes. In this work, we study the role of channel interference and solvent effects on the two-photon absorption in aryl-substituted boron dipyrromethene (BODIPY) dyes, a class of intramolecular charge-transfer (ICT) molecules. For this purpose, we consider fourteen dyes of this class with various donor/acceptor substitutions at the para position of the phenyl ring and with or without methyl (-CH₃) substitution on the BODIPY moiety. The presence of a methyl group on the BODIPY moiety affects the dihedral angle significantly, which in turn affects the one- (OPA) and two-photon absorption (TPA) properties of the molecules. Among the molecules studied, the one having the strong electron-donating dimethylamino group and no methyl substitution at the BODIPY moiety is found to have the highest TPA cross section. Our few-state model analysis shows that the large TPA activity of this molecule is due to the all positive contributions from different channel interference terms. Change in dielectric constant of the medium is found to have a profound impact on both the magnitude and sign of the channel interference terms. The magnitude of destructive channel interference gradually decreases with decreasing solvent polarity and becomes constructive in a low-polarity solvent. We also study the effect of rotating the phenyl ring with respect to the BODIPY moiety on the TPA activity. In the gas phase and in different solvents, we found that channel interference is changed from destructive to constructive on twisting the molecule. These results are explained by considering different dipole-, energy- and angle-terms appearing in the expression of a two-state model.

Calculation of One-Photon and Two-Photon Absorption Spectra of Porphyrins Using Time-Dependent Density Functional Theory

Time-dependent density functional theory has been used to calculate the one-photon and two-photon absorption spectra of free-base porphyrin, a substituted zinc porphyrin, and a zinc porphyrin dimer, in order to assess the validity of the method to reproduce the large increase in the two-photon absorption (TPA) cross-section for the dimer. Three hybrid functionals with varying amounts of exact exchange were tested, and the calculated one-photon absorption spectra for each of the molecular systems were shown to be in qualitative agreement with the measured spectra. All three functionals predict a large enhancement in the TPA cross-section for the dimer relative to the monomer, in agreement with experimental results. However, because of the sensitivity of the resonance enhancement factor to small differences in the relevant state energies, quantitative prediction of the TPA cross-section by this method is still a challenge.

Photoinduced Charge Transport in a BHJ Solar Cell Controlled by an External Electric Field

This study investigated theoretical photoinduced charge transport in a bulk heterojunction (BHJ) solar cell controlled by an external electric field. Our method for visualizing charge difference density identified the excited state properties of photoinduced charge transfer, and the charge transfer excited states were distinguished from local excited states during electronic transitions. Furthermore, the calculated rates for the charge transfer revealed that the charge transfer was strongly influenced by the external electric field. The external electric field accelerated the rate of charge transfer by up to one order when charge recombination was significantly restrained. Our research demonstrated that photoinduced charge transport controlled by an external electric field in a BHJ solar cell is efficient, and the exciton dissociation is not the limiting factor in organic solar cells.Our research should aid in the rational design of a novel conjugated system of organic solar cells.

New trans-stilbene derivatives with large two-photon absorption cross-section and non-linear optical susceptibility values – a theoretical investigation

In the present study, newly designed TSB derivatives decorated with suitable donor–acceptor groups have large TPA cross-sections and can be used as potential two-photon active materials.

Triply twisted Möbius annulene: a new class of two-photon active material – a computational study

The present study clearly reveals that the triply twisted Möbius annulene molecules decorated with suitable donor–acceptor groups can be used as a potential two-photon active material.

Chemical control of channel interference in two-photon absorption processes

The two-photon absorption (TPA) process is the simplest and hence the most studied nonlinear optical phenomenon, and various aspects of this process have been explored in the past few decades, experimentally as well as theoretically. Previous investigations have shown that the two-photon (TP) activity of a molecular system can be tuned, and at present, performance-tailored TP active materials are easy to develop by monitoring factors such as length of conjugation, dimensionality of charge-transfer network, strength of donor-acceptor groups, polarity of solvents, self-aggregation, H-bonding, and micellar encapsulation to mention but a few. One of the most intriguing phenomena affecting the TP activity of a molecule is channel interference. The phrase "channel interference" implies that if the TP transition from one electronic state to another involves more than one optical pathway or channel, characterized by the corresponding transition dipole moment (TDM) vectors, the channels may interfere with each other depending upon the angles between the TDM vectors and hence can either increase (constructive interference) or decrease (destructive interference) the overall TP activity of a system to a significant extent. This phenomenon was first pointed out by Cronstrand, Luo, and Ågren [Chem. Phys. Lett. 2002, 352, 262-269] in two-dimensional systems (i.e., only involving two components of the transition moment vectors). For three-dimensional molecules, an extended version of this idea was required. In order to fill this gap, we developed a generalized model for describing and exploring channel interference, valid for systems of any dimensionality. We have in particular applied it to through-bond (TB) and through-space (TS) charge-transfer systems both in gas phase and in solvents with different polarities. In this Account, we will, in addition to briefly describing the concept of channel interference, discuss two key findings of our recent work: (1) how to control the channel interference by chemical means, and (2) the role of channel interference in the anomalous solvent dependence of certain TP chromophores. For example, we will show that simple structurally induced changes in certain dihedral angles of the well-known betaine dye (TB type) will help fine-tune the constructive channel interference and hence increase the overall TP activity of molecules with this general TP channel structure. Another intriguing result we will discuss is observed for a tweezer-trinitrofluorinone complex (TS type) where, on moving from polar to essentially nonpolar solvents, the nature of the channel interference switches from destructive to constructive, leading to a net abnormal solvent dependence of the TP activity of the system. The present Account highlights the usefulness of the channel interference effect and establishes it as a new and unique way of controlling the TP transition probability in different types of three-dimensional molecules.

One- and two-photon absorption of fluorescein dianion in water: a study using S-QM/MM methodology and ZINDO method

One- and two-photon absorption (1PA and 2PA) of fluorescein dianion (FSD) in water were studied using a combined and sequential Quantum Mechanics/Molecular Dynamics methodology. Different sets of 250 statistically relevant (uncorrelated) configurations composed by the solute and several solvent molecules were sampled from the classical simulation. On these configurations, the electronic properties were calculated a posteriori using the Zerner's intermediate neglect of differential overlap (ZINDO) method. The linear and nonlinear absorption of FSD in water were calculated using discrete and explicit solvent models. In the largest case, the relevant configurations are composed by FSD and 47 explicit water molecules embedded in the electrostatic field of all remaining water molecules. Both INDO/CIS and INDO/CISD calculations were performed to study the absorption processes of FSD and the Sum-Over-States (SOS) model was used to describe the 2PA process. A semi-classical method for spectrum simulations was employed to simulate the 1PA and 2PA cross-section spectra of FSD in water. For comparison purposes, in the case of the 2PA process two approaches, the "full expression" and "resonant expression" methods, were employed to simulate the nonlinear spectrum. The last method assumes resonant conditions and on the computation point of view it represents an interesting option to study the 2PA process. The INDO/CI calculations give a satisfactory description of the 1PA spectrum of FSD and properly describe the unusual blue-shift of its first π→π(*) transition in water. In the case of 2PA, the introduction of doubly excited configuration interactions (INDO/CISD) has proven to be essential for an appropriate description of the process at the higher energy spectral region. It was observed that the solvent effects do not drastically change the cross-sections of both processes. The simulated 2PA cross-section spectrum provided by the "full expression" method presents a better definition of the bands which appear along the experimental spectrum than the one provided by the "resonant expression" method. However, both approaches provide similar description for the effect of the solvent environment on the 2PA process of FSD in water.

On the origin of large two-photon activity of DANS molecule

In this work, using the quadratic response theory and two-state model approach, we have explained the origin of high two-photon activity and the corresponding solvent dependence of 4,4'-dimethyl-amino-nitro-stilbene (DANS) molecule. For this purpose, we have made two structural modifications in the DANS molecule (1) at the donor-acceptor part and (2) at the unsaturated bridge between the two rings and calculated the one- and two-photon (OP and TP) absorption parameters of all the systems in gas phase and in three different solvents, viz., MeCN, THF, and toluene. We found that the removal of donor-acceptor groups from the original DANS molecule vanishes the transition moment between the ground and excited states and also the corresponding dipole moment difference, and the saturation of the π-conjugation bridge between the two rings keeping the donor-acceptor groups intact causes a large decrease in the ground to excited state transition moment. These changes, in turn, decrease the overall TP activity of the molecules as compared to DANS. On the basis of our analysis, we have concluded that neither the donor-acceptor pair nor the π-conjugation bridge between the two, rather their cooperative involvement leads to a large overlap between the ground and virtual and also the virtual and charge-transfer states, which are eventually responsible for the very large TP activity of DANS.

The role of molecular conformation and polarizable embedding for one- and two-photon absorption of disperse orange 3 in solution

Solvent effects on the one- and two-photon absorption (1PA and 2PA) of disperse orange 3 (DO3) in dimethyl sulfoxide (DMSO) are studied using a discrete polarizable embedding (PE) response theory. The scheme comprises a quantum region containing the chromophore and an atomically granulated classical region for the solvent accounting for full interactions within and between the two regions. Either classical molecular dynamics (MD) or hybrid Car-Parrinello (CP) quantum/classical (QM/MM) molecular dynamics simulations are employed to describe the solvation of DO3 in DMSO, allowing for an analysis of the effect of the intermolecular short-range repulsion, long-range attraction, and electrostatic interactions on the conformational changes of the chromophore and also the effect of the solute-solvent polarization. PE linear response calculations are performed to verify the character, solvatochromic shift, and overlap of the two lowest energy transitions responsible for the linear absorption spectrum of DO3 in DMSO in the visible spectral region. Results of the PE linear and quadratic response calculations, performed using uncorrelated solute-solvent configurations sampled from either the classical or hybrid CP QM/MM MD simulations, are used to estimate the width of the line shape function of the two electronic lowest energy excited states, which allow a prediction of the 2PA cross-sections without the use of empirical parameters. Appropriate exchange-correlation functionals have been employed in order to describe the charge-transfer process following the electronic transitions of the chromophore in solution.

Benzothiazoles with tunable electron-withdrawing strength and reverse polarity: a route to triphenylamine-based chromophores with enhanced two-photon absorption

A series of dipolar and octupolar triphenylamine-derived dyes containing a benzothiazole positioned in the matched or mismatched fashion have been designed and synthesized via palladium-catalyzed Sonogashira cross-coupling reactions. Linear and nonlinear optical properties of the designed molecules were tuned by an additional electron-withdrawing group (EWG) and by changing the relative positions of the donor and acceptor substituents on the heterocyclic ring. This allowed us to examine the effect of positional isomerism and extend the structure-property relationships useful in the engineering of novel heteroaromatic-based systems with enhanced two-photon absorption (TPA). The TPA cross-sections (δ(TPA)) in the target compounds dramatically increased with the branching of the triphenylamine core and with the strength of the auxiliary acceptor. In addition, a change from the commonly used polarity in push-pull benzothiazoles to a reverse one has been revealed as a particularly useful strategy (regioisomeric control) for enhancing TPA cross-sections and shifting the absorption and emission maxima to longer wavelengths. The maximum TPA cross-sections of the star-shaped three-branched triphenylamines are ∼500-2300 GM in the near-infrared region (740-810 nm); thereby the molecular weight normalized δ(TPA)/MW values of the best performing dyes within the series (2.0-2.4 GM·g(-1)·mol) are comparable to those of the most efficient TPA chromophores reported to date. The large TPA cross-sections combined with high emission quantum yields and large Stokes shifts make these compounds excellent candidates for various TPA applications, including two-photon fluorescence microscopy.

A critical theoretical study on the two-photon absorption properties of some selective triaryl borane-1-naphthylphenyl amine based charge transfer molecules

In the present work, we have studied the two-photon absorption (TPA) properties of some selective molecules containing triarylborane and 1-naphthylphenylamine as the acceptor and donor moiety, respectively. The calculations are performed by using the state-of-the-art linear and quadratic response theory in the framework of the time dependent density functional theoretical method. The TPA parameters are calculated with CAMB3LYP functional and the cc-pVDZ basis set. The one-photon results indicate that both the electronic transitions (S(0)-S(1) and S(0)-S(2)) are associated with the charge transfer interaction between the donor and acceptor moieties along with the reorganization of the π-electron density. All these chromophores are found to have very strong two-photon active modes. In order to find out the origin of large TP transition probability of these molecules, we have performed two-state model (TSM) and sum-over-states (SOS) calculations. We have found that the TSM failed to reproduce the correct trend of the TP transition probability of the molecules obtained from the response theory, while SOS is quite successful in doing so. The whole study indicates that the transition moments between the excited states play a pivotal role in controlling the TP transition probabilities of these molecules. The role of solvent in the TP transition probability of these molecules has meticulously been scrutinized within the polarized continuum model (PCM). Further more, we have benchmarked our theoretical findings by calculating the TPA cross-section of a boron and nitrogen containing a charge transfer molecule for which the experimental result is available and we found that our theoretical result is in good agreement with the experimental one which definitely demonstrates the potential of all these light-emitting diode molecules as TP active materials too.

DFT study of linear and nonlinear optical properties of donor-acceptor substituted stilbenes, azobenzenes and benzilideneanilines

A theoretical analysis of the linear and nonlinear optical properties of six push-pull pi-conjugated molecules with stilbene, azobenzene and benzilideneaniline as a backbone is presented. The photophysical properties of the investigated systems were determined by using response functions combined with density functional theory (DFT). Several different exchange-correlation potentials were applied in order to determine parameters describing the one- and two-photon spectra of the studied molecules. In particular, the recently proposed Coulomb-attenuated model (CAM-B3LYP) was used to describe charge-transfer (CT) excited states. In order to compare theoretical predictions with available experimental data, calculations with inclusion of solvent effects were performed. The BLYP and the CAM-B3LYP functionals were found to yield values of two-photon absorption (TPA) probabilities closer to experimental values than the B3LYP functional or the HF wavefunction. Moreover, molecular static hyperpolarisabilities were determined using both DFT and second-order Møller-Plesset perturbation (MP2) theory. Likewise, the CAM-B3LYP functional was found to outperform other applied exchange-correlation potentials in determining first hyperpolarisability (beta). Moreover, it was confirmed on a purely theoretical basis that the presence of a -C=C- bridge between the phenyl rings leads to a much larger nonlinear optical response in comparison with a -N=N- bridge.