Determining the appropriate exchange-correlation functional for time-dependent density functional theory studies of charge-transfer excitations in organic dyes

A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes

In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)  ⋆ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.

Toward Consistent Predictions of Core/Valence Ionization Potentials and Valence Excitation Energies by MRSF-TDDFT

Optimizing exchange-correlation functionals for both core/valence ionization potentials (cIPs/vIPs) and valence excitation energies (VEEs) at the same time in the framework of MRSF-TDDFT is self-contradictory. To overcome the challenge, within the previous "adaptive exact exchange" or double-tuning strategy on Coulomb-attenuating XC functionals (CAM), a new XC functional specifically for cIPs and vIPs was first developed by enhancing exact exchange to both short- and long-range regions. The resulting DTCAM-XI functional achieved remarkably high accuracy in its predictions with errors of less than half eV. An additional concept of "valence attenuation", where the amount of exact exchange for the frontier orbital regions is selectively suppressed, was introduced to consistently predict both VEEs and IPs at the same time. The second functional, DTCAM-XIV, exhibits consistent overall prediction accuracy at ∼0.64 eV. By preferentially optimizing VEEs within the same "valence attenuation" concept, a third functional, DTCAM-VAEE, was obtained, which exhibits improved performance as compared to that of the previous DTCAM-VEE and DTCAM-AEE in the prediction of VEEs, making it an attractive alternative to BH&HLYP. As the combination of "adaptive exchange" and "valence attenuation" is operative, it would be exciting to explore its potential with a more tunable framework in the future.

Optimal Transport Distances to Characterize Electronic Excitations

Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very useful in a plethora of classification problems and, therefore, seem a natural tool to try to tackle this challenge. We propose and investigate a new diagnostic Θ based on the Sinkhorn divergence from optimal transport. We evaluate a k-NN classification algorithm on Θ, the popular Λ diagnostic, and their combination, and assess their performance in labeling excitations, finding that (i) the combination only slightly improves the classification, (ii) Rydberg excitations are not separated well in any setting, and (iii) Θ breaks down for charge transfer in small molecules. We then define a length-scale-normalized version of Θ and show that the result correlates closely with Λ for results obtained with Gaussian basis functions. Finally, we discuss the orbital dependence of our approach and explore an orbital-independent version. Using an optimized combination of the optimal transport and overlap diagnostics together with a different metric is in our opinion the most promising for future classification studies.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory

The density functional theory (DFT) and linear response (LR) time-dependent (TD)-DFT are of the utmost importance for routine computations. However, the single reference formulation of DFT suffers in the description of open-shell singlet systems such as diradicals and bond-breaking. LR-TDDFT, on the other hand, finds difficulties in the modeling of conical intersections, doubly excited states, and core-level excitations. In this Perspective, we demonstrate that many of these limitations can be overcome by recently developed mixed-reference (MR) spin-flip (SF)-TDDFT, providing an alternative yet accurate route for such challenging situations. Empowered by the practicality of the LR formalism, it is anticipated that MRSF-TDDFT can become one of the major workhorses for general routine tasks.

High-performance strategies for the recent MRSF-TDDFT in GAMESS

Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. This paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios.

Performance of Common Density Functionals for Excited States of Tetraphenyldibenzoperiflanthene

Time-dependent density functional theory is the method of choice to efficiently calculate excitation spectra with the functional and basis set choice allowing one to compromise between accuracy and computational cost. In this work, the performance of different functionals as well as the second-order approximate coupled cluster singles and doubles model CC2 is evaluated by comparing the results to experimental results of the example molecule tetraphenyldibenzoperiflanthene (DBP). The choice of the functional has a significant impact on the calculated spectrum of DBP. The performance of a number of different functionals was evaluated, quantified, and, where possible, discussed. The best functional, tuned-CAM-B3LYP, is used to investigate DBP on a surface of hexagonal boron nitride (h-BN). The resulting spectrum shows excellent agreement with experimental results for a monolayer of DBP on h-BN.

Building on the strengths of a double-hybrid density functional for excitation energies and inverted singlet-triplet energy gaps

It is demonstrated that a double hybrid density functional approximation, ωB88PTPSS, that incorporates equipartition of density functional theory and the non-local correlation, however with a meta-generalized gradient approximation correlation functional, as well as with the range-separated exchange of ωB2PLYP, provides accurate excitation energies for conventional systems, as well as correct prescription of negative singlet-triplet gaps for non-conventional systems with inverted gaps, without any necessity for parametric scaling of the same-spin and opposite-spin non-local correlation energies. Examined over "safe" excitations of the QUESTDB set, ωB88PTPSS performs quite well for open-shell systems, correctly and fairly accurately [relative to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) reference] predicts negative gaps for 50 systems with inverted singlet-triplet gaps, and is one of the leading performers for intramolecular charge-transfer excitations and achieves near-second-order approximate coupled cluster (CC2) and second-order algebraic diagrammatic construction quality for the Q1 and Q2 subsets. Subsequently, we tested ωB88PTPSS on two sets of real-life examples from recent computational chemistry literature-the low energy bands of chlorophyll a (Chl a) and a set of thermally activated delayed fluorescence (TADF) systems. For Chl a, ωB88PTPSS qualitatively and quantitatively achieves DLPNO-STEOM-CCSD-level performance and provides excellent agreement with experiment. For TADF systems, ωB88PTPSS agrees quite well with spin-component-scaled CC2 (SCS-CC2) excitation energies, as well as experimental values, for the gaps between the S₁ and T₁ excited states.

Computational investigations on acceptor substituent influence of metal-free efficient chromophores for optoelectronic properties

In this study, the computational studies of the PO₃H₂, CONHOH, and SO₂H (A1-A3) molecules were investigated for optoelectronic applications on the basis of tetrahydroquinoline (C1-1) dye. Besides, a detailed calculation of the molecular structures, energy levels, driving force of injection, regeneration, non-linear optical (NLO) property, chemical hardness, excitation binding energy, light-harvesting efficiency (LHE), absorption spectra, and photovoltaic (PV) parameters were all discussed in details using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods. The optoelectronic properties of C1-1-based A1-A3 molecules are originated to be tuned by changing the position of the acceptor. To get a maximum absorption spectrum of C1-1, Becke's three-parameter and Lee-Yang-Parr (B3LYP), Coulomb-attenuating method-B3LYP (CAM-B3LYP), and Head-Gordon model (ωB97XD) were used for the TD-DFT method. Results reveal that the TD-ɷB97XD and 6-31G(d) combined functionals were provided reliable effects to the C1-1. Therefore, absorption spectra of the A1-A3 dyes were followed by the TD-ɷB97XD/6-31G(d) techniques. The designed A1 (PO₃H₂) dye displayed a smaller energy gap and red-shifted broadened spectra than the other dyes and C1-1 can be utilized to get a better PV properties. In addition, NLO properties of the A1-A3 chromophores were calculated by the polarizability and first-order hyperpolarizability. Consequently, A1 dye has a superior value of the NLO activity. This study will deliver a valuable reference to the upcoming molecular proposal of tetrahydroquinoline dyes for optoelectronic applications.

Design of new hole transport materials based on triphenylamine derivatives using different π-linkers for the application in perovskite solar cells. A theoretical study

New organic molecules containing five different compounds, commonly called p-linkers, located between the triphenylamine units, were theoretically designed and analyzed in order to be proposed as new hole transport materials (HTMs) in perovskite solar cells, in total ten new molecules were analyzed. The electronic, optical and hole transport properties were determined, similarly, the relationship of these properties with their molecular structure was also investigated by Density Functional Theory (DFT) and Density Functional Tight Binding (DFTB) calculations. Eight of the ten analyzed compounds exhibited the main absorption band out of the visible region; therefore these compounds did not present an overlap with the absorption spectra of the typical methylammonium lead iodide (MAPI) hybrid-perovskite. The results showed that the Highest occupied molecular orbital (HOMO) levels of the compounds are higher than the perovskite HOMO level, and in some cases these are even higher than the Spiro-OMeTAD HOMO. The calculated electronic couplings and the reorganization energy values provided useful information in order to determine if the systems were hole or electron transport materials.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange–correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Application of TD-DFT Theory to Studying Porphyrinoid-Based Photosensitizers for Photodynamic Therapy: A Review

An important focus for innovation in photodynamic therapy (PDT) is theoretical investigations. They employ mostly methods based on Time-Dependent Density Functional Theory (TD-DFT) to study the photochemical properties of photosensitizers. In the current article we review the existing state-of-the-art TD-DFT methods (and beyond) which are employed to study the properties of porphyrinoid-based systems. The review is organized in such a way that each paragraph is devoted to a separate aspect of the PDT mechanism, e.g., correct prediction of the absorption spectra, determination of the singlet-triplet intersystem crossing, and interaction with molecular oxygen. Aspects of the calculation schemes are discussed, such as the choice of the most suitable functional and inclusion of a solvent. Finally, quantitative structure-activity relationship (QSAR) methods used to explore the photochemistry of porphyrinoid-based systems are discussed.

Are all charge-transfer parameters created equally? A study of functional dependence and excited-state charge-transfer quantification across two dye families

Small molecule organic dyes have many potential uses in medicine, textiles, forensics, and light-harvesting technology. Being able to computationally predict the spectroscopic properties of these dyes could greatly expedite screening efforts, saving time and materials. Time-dependent density functional theory (TD-DFT) has been shown to be a good tool for this in many instances, but characterizing electronic excitations with charge-transfer (CT) character has historically been challenging and can be highly sensitive to the chosen exchange-correlation functional. Here we present a combined experimental and computational study of the excited-state electronic structure of twenty organic dyes obtained from the Max Weaver Dye Library at NCSU. Results of UV-vis spectra calculations on these dyes with six different exchange-correlation functionals, BP86, B3LYP, PBE0, M06, BH and HLYP, and CAM-B3LYP, were compared against their measured UV-vis spectra. It was found that hybrid functionals with modest amounts (20-30%) of included Hartree-Fock exchange are the most effective at matching the experimentally determined λ_max. The interplay between the observed error, the functional chosen, and the degree of CT was analyzed by quantifying the CT character of λ_max using four orbital and density-based metrics, Λ, Δr, S_C and D_CT, as well as the change in the dipole moment, Δμ. The results showed that the relationship between CT character and the functional dependence of error is not straightforward, with the observed behavior being dependent both on how CT was quantified and the functional groups present in the molecules themselves. It is concluded that this may be a result of the examined excitations having intermediate CT character. Ultimately it was found that the nature of the molecular "family" influenced how a given functional behaved as a function of CT character, with only two of the examined CT quantification methods, Δr and D_CT, showing consistent behavior between the different molecular families. This suggests that further work needs to be done to ensure that currently used CT quantification methods show the same general trends across large sets of multiple dye families.

Exploring organic semiconductors in solution: the effects of solvation, alkylization, and doping

The first-principles simulation of the electronic structure of organic semiconductors in solution poses a number of challenges that are not trivial to address simultaneously. In this work, we investigate the effects and the mutual interplay of solvation, alkylization, and doping on the structural, electronic, and optical properties of sexithiophene, a representative organic semiconductor molecule. To this end, we employ (time-dependent) density functional theory in conjunction with the polarizable-continuum model. We find that the torsion between adjacent monomer units plays a key role, as it strongly influences the electronic structure of the molecule, including energy gap, ionization potential, and band widths. Alkylization promotes delocalization of the molecular orbitals up to the first methyl unit, regardless of the chain length, leading to an overall shift of the energy levels. The alterations in the electronic structure are reflected in the optical absorption, which is additionally affected by dynamical solute-solvent interactions. Taking all these effects into account, solvents decrease the optical gap by an amount that depends on its polarity, and concomitantly increase the oscillator strength of the first excitation. The interaction with a dopant molecule promotes planarization. In such scenario, solvation and alkylization enhance charge transfer both in the ground state and in the excited state.

Single- and co-sensitization of triphenylamine-based and asymmetrical squaraine dyes on the anatase (001) surface for DSSC applications: Periodic DFT calculations

Dye aggregation causes poor performance of dye-sensitized solar cell (DSSC) applications through faster charge recombination of the photosensitizer with electrolyte. Triphenylamine (TBA)-based dyes feature a higher molar absorption coefficient and broadened wavelength but cannot absorb sunlight in the near-infrared (NIR) region. In contrast, the squaraine (SQ) photosensitizer, which is also called an NIR photosensitizer, has a maximum wavelength in the NIR region with high intensity. However, SQ dye suffers from dye aggregation due to its planar structure. The use of a co-sensitizer is one well-tested way to increase the power conversion efficiency (η) of solar cells by reducing dye aggregation and charge recombination. Using density functional theory (DFT) and time-dependent DFT (TDDFT), this work explains from a theoretical perspective the higher η values of the TZC1 and TZC2 dyes compared to that of asymmetric the SQ sensitizer (YR6) as free dyes. The electronic properties, reorganization energies, absorption and emission spectra, ICT parameters, and photovoltage parameters of the TZC1, TZC2, and YR6 dyes were computed using the M06/6-31G(d,p) level of theory in the gas phase and CH₂Cl₂ solvent (CPCM method). Additionally, the mono- and co-adsorption processes of TZC-based sensitizers with YR6 on the anatase (001) surface were investigated using periodic DFT calculations with the PBE + U/PAW method and the dispersion correction of the Grimme method D3. The results reveal that the use of the co-sensitized led to significant stabilization of the formed complexes by at least 1.21 eV, the panchromatic effect on the absorption spectra, and an increase in the light-harvesting ability in the NIR region, which improves the performance of DSSCs.

Designing and understanding light-harvesting devices with machine learning

Understanding the fundamental processes of light-harvesting is crucial to the development of clean energy materials and devices. Biological organisms have evolved complex metabolic mechanisms to efficiently convert sunlight into chemical energy. Unraveling the secrets of this conversion has inspired the design of clean energy technologies, including solar cells and photocatalytic water splitting. Describing the emergence of macroscopic properties from microscopic processes poses the challenge to bridge length and time scales of several orders of magnitude. Machine learning experiences increased popularity as a tool to bridge the gap between multi-level theoretical models and Edisonian trial-and-error approaches. Machine learning offers opportunities to gain detailed scientific insights into the underlying principles governing light-harvesting phenomena and can accelerate the fabrication of light-harvesting devices.

Solvent effect on excited state potential energy surfaces of Thioflavin T. Qualitatively different results by TDDFT and SA-2-CASSCF methods

Thioflavin T (ThT) is a viscosity-sensitive fluorescent dye and its emission intensity undergoes a significant enhancement upon binding to DNA or amyloid fibrils. This fluorescence light-up feature has been attributed earlier to restriction of structural rearrangements in the excited state that are coupled to an intramolecular charge transfer (ICT) reaction. In this work TDDFT (using B3LYP and CAM-B3LYP functionals) and SA-2-CASSCF calculations were carried out to obtain relaxed excited-state potential energy surfaces (PES) along twisting φ and wagging δ angles that describe mutual orientation of benzothiazole (BTZ) and dimethylaniline (DMA) fragments in ThT. For isolated ThT molecule both methods predict that during structural rearrangements of the initially excited Franck-Condon state, besides twisting along CC bond which connects BTZ and DMA fragments, a considerable wagging motion is expected to occur. Account for solvent effect using polarized continuum model showed qualitative differences in the excited state PES features calculated by SA-2-CASSCF and TDDFT methods. Single-reference TDDFT calculations failed to describe solvation of TICT state and predicted increase of its energy in more polar media.

Aromaticity-Photovoltaic Property Relationship of Triphenylamine-Based D-π-A Dyes: Leads from DFT Calculations

D-π-A-based dyes find a wide range of applications in molecular electronics and photovoltaics in general and dye-sensitized solar cells (DSSC) in particular. We speculated whether there exists a relationship between the degree of aromaticity of the π-spacers used in the D-π-A type dyes and their structural, electronic, energetic, photophysical, and intramolecular charge transfer properties. Triphenylamine (TPA) and cyanoacrylic acid (CAA) have been chosen as the donor and acceptor, respectively. In order to carry out the investigation systematically the π-spacers have been logically chosen based on their experimental resonance energies, which follows the order, furan < pyrrole < thiophene < pyridine < benzene. All the properties have been discussed based on the degree of aromaticity of the π-spacers. Geometric properties such as dihedral angles and bond lengths have been discussed extensively. Energy levels of the frontier molecular orbitals, electrochemical properties, namely, ground and excited state oxidation potentials (GSOP/ESOP), and change in Gibbs free energy for electron injection and regeneration (ΔG_inj/ΔG_reg) have also been evaluated. Photophysical properties like wavelength of maximum absorption (λ_max), oscillator strength (f), light harvesting efficiency (LHE), and intramolecular charge transfer properties, viz., charge transfer distance (D_CT), fraction of charge transferred (q_CT), and change in dipole moment (μ_CT) have been assessed. The adsorption characteristics of dye with (TiO₂)₉ nanocluster have been studied along with their optical properties. Results reveal that the nature of the relationship between the aforementioned properties and the extent of aromaticity of the π-spacers is inherently multifaceted. It thus turns out that it is highly difficult to quantify the relationship. These properties of D-π₁-π₂-A molecules can be regarded to be arising from two groups, namely, π-spacers with lower and higher resonance energies. This results in a natural trade-off in selection of competing properties. The qualitative aromaticity photovoltaic property relationship thus obtained may serve as a guide to tailor-design various properties of D-π-A type dyes for application in the intramolecular charge transfer devices.

Distortion-Controlled Redshift of Organic Dye Molecules

It is shown, quantum chemically, how structural distortion of an aromatic dye molecule can be leveraged to rationally tune its optoelectronic properties. By using a quantitative Kohn-Sham molecular orbital (KS-MO) approach, in combination with time-dependent DFT (TD-DFT), the influence of various structural and electronic tuning parameters on the HOMO-LUMO gap of a benzenoid model dye have been investigated. These parameters include 1) out-of-plane bending of the aromatic core, 2) bending of the bridge with respect to the core, 3) the nature of the bridge itself, and 4) π-π stacking. The study reveals the coupling of multiple structural distortions as a function of bridge length and number of bridges in benzene to be chiefly responsible for a decreased HOMO-LUMO gap, and consequently, red-shifting of the absorption wavelength associated with the lowest singlet excitation (λ≈560 nm) in the model cyclophane systems. These physical insights together with a rational approach for tuning the oscillator strength were leveraged for the proof-of-concept design of an intense near-infrared (NIR) absorbing cyclophane dye at λ=785 nm. This design may contribute to a new class of distortion-controlled NIR absorbing organic dye molecules.

Benchmarking the Performance of Time-Dependent Density Functional Theory Methods on Biochromophores

Quantum chemical calculations are important for elucidating light-capturing mechanisms in photobiological systems. The time-dependent density functional theory (TDDFT) has become a popular methodology because of its balance between accuracy and computational scaling, despite its problems in describing, for example, charge transfer states. As a step toward systematically understanding the performance of TDDFT calculations on biomolecular systems, we study here 17 commonly used density functionals, including seven long-range separated functionals, and compare the obtained results with excitation energies calculated at the approximate second order coupled-cluster theory level (CC2). The benchmarking set includes the first five singlet excited states of 11 chemical analogues of biochromophores from the green fluorescent protein, rhodopsin/bacteriorhodopsin (Rh/bR), and the photoactive yellow protein. We find that commonly used pure density functionals such as BP86, PBE, M11-L, and hybrid functionals with 20-25% of Hartree-Fock (HF) exchange (B3LYP, PBE0) have a tendency to consistently underestimate vertical excitation energies (VEEs) relative to the CC2 values, whereas hybrid density functionals with around 50% HF exchange such as BHLYP, PBE50, and M06-2X and long-range corrected functionals such as CAM-B3LYP, ωPBE, ωPBEh, ωB97X, ωB97XD, BNL, and M11 overestimate the VEEs. We observe that calculations using the CAM-B3LYP and ωPBEh functionals with 65% and 100% long-range HF exchange, respectively, lead to an overestimation of the VEEs by 0.2-0.3 eV for the benchmarking set. To reduce the systematic error, we introduce here two new empirical functionals, CAMh-B3LYP and ωhPBE0, for which we adjusted the long-range HF exchange to 50%. The introduced parameterization reduces the mean signed average (MSA) deviation to 0.07 eV and the root mean square (rms) deviation to 0.17 eV as compared to the CC2 values. In the present study, TDDFT calculations using the aug-def2-TZVP basis sets, the best performing functionals relative to CC2 are ωhPBE0 (rms = 0.17, MSA = 0.06 eV); CAMh-B3LYP (rms = 0.16, MSA = 0.07 eV); and PBE0 (rms = 0.23, MSA = -0.14 eV). For the popular range-separated CAM-B3LYP functional, we obtain an rms value of 0.31 eV and an MSA value of 0.25 eV, which can be compared with the rms and MSA values of 0.37 and -0.31 eV, respectively, as obtained at the B3LYP level.

Rational design of near-infrared absorbing organic dyes: Controlling the HOMO-LUMO gap using quantitative molecular orbital theory

Principles are presented for the design of functional near-infrared (NIR) organic dye molecules composed of simple donor (D), spacer (π), and acceptor (A) building blocks in a D-π-A fashion. Quantitative Kohn-Sham molecular orbital analysis enables accurate fine-tuning of the electronic properties of the π-conjugated aromatic cores by effecting their size, including silaaromatics, adding donor and acceptor substituents, and manipulating the D-π-A torsional angle. The trends in HOMO-LUMO gaps of the model dyes correlate with the excitation energies computed with time-dependent density functional theory at CAMY-B3LYP. Design principles could be developed from these analyses, which led to a proof-of-concept linear D-π-A with a strong excited-state intramolecular charge transfer and a NIR absorption at 879 nm. © 2018 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Human Aquaporin 4 Gating Dynamics under Perpendicularly-Oriented Electric-Field Impulses: A Molecular Dynamics Study

Human aquaporin 4 has been studied using molecular dynamics (MD) simulations in the absence and presence of pulses of external static electric fields. The pulses were 10 ns in duration and 0.012-0.065 V/Å in intensity acting along both directions perpendicular to the pores. Water permeability and the dipolar response of all residues of interest (including the selectivity filter) within the pores have been studied. Results showed decreased levels of water osmotic permeability within aquaporin channels during orthogonally-oriented field impulses, although care must be taken with regard to statistical certainty. This can be explained observing enhanced "dipolar flipping" of certain key residues, especially serine 211, histidine 201, arginine 216, histidine 95 and cysteine 178. These residues are placed at the extracellular end of the pore (serine 211, histidine 201, and arginine 216) and at the cytoplasm end (histidine 95 and cysteine 178), with the key role in gating mechanism, hence influencing water permeability.

Multi-state extrapolation of UV/Vis absorption spectra with QM/QM hybrid methods

In this work, we present a simple approach to simulate absorption spectra from hybrid QM/QM calculations. The goal is to obtain reliable spectra for compounds that are too large to be treated efficiently at a high level of theory. The present approach is based on the extrapolation of the entire absorption spectrum obtained by individual subcalculations. Our program locates the main spectral features in each subcalculation, e.g., band peaks and shoulders, and fits them to Gaussian functions. Each Gaussian is then extrapolated with a formula similar to that of ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics). However, information about individual excitations is not necessary so that difficult state-matching across subcalculations is avoided. This multi-state extrapolation thus requires relatively low implementation effort while affording maximum flexibility in the choice of methods to be combined in the hybrid approach. The test calculations show the efficacy and robustness of this methodology in reproducing the spectrum computed for the entire molecule at a high level of theory.

A structure-property study toward π-extended phosphole chromophores with ambipolar redox properties

We report the synthesis of a series of π-extended dithienophospholes with phenyl or biphenyl terminal groups via Suzuki Miyaura cross-coupling procedures. The incorporation of the dithienophosphole core into the scaffold on oligophenylenes was found to lead to pronounced luminescence properties in solution and the solid state, the latter of which also responded to different solid-state morphologies, i.e., powder versus crystal. More importantly, the investigated molecular architectures also allowed — for the first time — the observation of ambipolar redox behavior of such species, with the biphenyl-extended species in particular showing quasi-reversible reduction and oxidation processes; the observed experimental features were correlated with computational density functional theory studies.

Novel styrylbenzothiazolium dye-based sensor for mercury, cyanide and hydroxide ions

We report the design and synthesis of a novel styrylbenzothiazolium (3) derivative developed as a fluorescent and colorimetric chemodosimeter with high selectivity toward Hg(2+), CN(-) and OH(-) ions. An obvious loss of pink color in the presence of Hg(2+) and CN(-) ions could make it a suitable "naked eye" indicator. We propose a sensing mechanism whereby the benzenoid form is changed to a quinoid form upon Hg(2+) binding in a 1:1 stoichiometric ratio. More significantly, the styrylbenzothiazolium-Hg(2+) and styrylbenzothiazolium-CN(-) complexes exhibited a dual-channel chromo-fluorogenic response. The sensors exhibit remarkable Hg(2+)-, CN(-)-, and OH(-)-selective red fluorescence but remain dark-green in the presence of a wide range of tested metal ions and anions.

Excited states using the simplified Tamm-Dancoff-Approach for range-separated hybrid density functionals: development and application

The recently introduced sTDA methodology [S. Grimme, J. Chem. Phys., 2013, 138, 244104] to compute excitation spectra of huge molecular systems is extended to range-separated hybrid (RSH) density functionals. The three empirical parameters of the method which describe a screened two-electron interaction are obtained for some common RSH functionals (ωB97 family, CAM-B3LYP, LC-BLYP) from a fit to theoretical SCS-CC2 reference vertical excitation energies for a set of small to medium-sized chromophores. The method is cross-validated on a set of inter- and intramolecular charge transfer states and a set composed of typical valence transitions. Overall small deviations from reference data of only about 0.2-0.4 eV are found with best performance for CAM-B3LYP and ωB97X-D3. To demonstrate versatility and robustness of the new methodology, applications (the UV/Vis spectrum of the pyridine polymer and the ECD spectrum of (P)-[11]helicene) and frequently used charge transfer examples are discussed. In one case, 11 000+ excited electronic states of a system containing 330 atoms were calculated. We show that the asymptotically correct sTDA-RSH combination yields results often superior to those based on global hybrids and that it opens up new possibilities for the computation of excited states in materials science and bio-molecular systems.

Dye chemistry with time-dependent density functional theory

In this perspective, we present an overview of the determination of excited-state properties of "real-life" dyes, and notably of their optical absorption and emission spectra, performed during the last decade with time-dependent density functional theory (TD-DFT). We discuss the results obtained with both vertical and adiabatic (vibronic) approximations, choosing relevant examples for several series of dyes. These examples include reproducing absorption wavelengths of numerous families of coloured molecules, understanding the specific band shape of amino-anthraquinones, optimising the properties of dyes used in solar cells, mimicking the fluorescence wavelengths of fluorescent brighteners and BODIPY dyes, studying optically active biomolecules and photo-induced proton transfer, as well as improving the properties of photochromes.

Theoretical design of triphenylamine-based derivatives with asymmetric D-D-π-A configuration for dye-sensitized solar cells

The use of theoretical techniques in the structural development of dye-sensitized solar cells helps in the efficient screening of the dyes. To properly rationalize the dye's design process, benchmark calculations were conducted using long-range corrected exchange-correlation (xc) functionals with varying separation parameters to be able to predict the excited-state energies of triphenylamine-based dyes, namely: PPS, PSP, and PSS, wherein they differ at the π-conjugated bridge using thiophene and/or phenyl moieties. The results show that LC-ωPBE xc functional with an optimized parameter provided better correlation with the experimental results compared to the other functionals. The relative shifts of the absorption spectra, light harvesting efficiency, normal dipole moments, as well as the ionization potentials and electron affinities of the dyes were well-correlated with the experimental data. A new set of dyes was designed in an effort to increase its solar cell efficiency that was patterned after PSS with an additional donor moiety such as fluorene, cyclopentaindole, and pyrene attached asymmetrically at the triphenylamine ring. Among the newly designed dyes, analogs that contain 4-phenyl-1,2,3,4-tetrahydrocyclopenta[b]indole (I) and pyrido[2,3,4-5-imn]phenanthridine-5,10(4H,9H)-dione (P2) as the additional donor moiety produced the best photophysical properties and charge-transfer characteristics for a promising dye for solar cell applications.

Study of chemical reactivity in relation to experimental parameters of efficiency in coumarin derivatives for dye sensitized solar cells using DFT

A group of dyes derived from coumarin was studied, which consisted of nine molecules using a very similar manufacturing process of dye sensitized solar cells (DSSCs).

Structure–property relationship of donor–acceptor acridones – an optical, electrochemical and computational study

The effect of changing acceptor strength on intramolecular charge transfer absorption and its implication towards organic materials are investigated.