Tuned range separated hybrid functionals for solvated low bandgap oligomers

Screened optimally tuned range separated hybrid functional for solvated low bandgap molecular systems

The description of electronic properties of low bandgap molecular system is often performed by using density functional theory (DFT) and time dependent (TD) DFT calculations with the optimally tuned range-separated hybrid (OT-RSH) functional, as it contains the necessary ingredients to reliably predict charge transfer excitations. However, the range separating parameter (ω) is system-dependent and its optimization, including the chemical environment, is intricate. Refaely-Abramson et al. demonstrated that the gap renormalization in molecular crystals, a ground state property, can be represented by an OT-RSH functional screened by ɛstatic [Phys. Rev. B 88, 081204(R) (2013)], the zero frequency scalar dielectric constant. In this study, we propose the use of an OT-RSH functional screened by the scalar dielectric constant in the high frequency limit (OT-sRSH), ɛ∞, an appropriate constraint for vertical ionization energies or excitations in a dielectric environment. We have performed calculations for S,N-heteroacene derivatives in tetrahydrofuran and dichloromethane. The "unscreened" OT-RSH functional tends to underestimate experimental ionization potentials (IPs) and optical gaps (Egs) by up to 1.5 and 0.5 eV, respectively. In contrast, OT-sRSH functional calculations underestimate IPs and Egs by only 0.4 and 0.2 eV. We also compared the OT-sRSH results to explicitly solvated OT-RSH functional calculations for oligothiophenes in dioxane, benzene in ammonia, and methylene blue in water. We observe that both the approaches perform similarly for weakly interacting intermolecular systems and deviate for solvent-solute interacting systems, as expected. In conclusion, the OT-sRSH functional can describe molecular systems with environmental polarization effects accurately, a step toward describing realistic molecular systems.

Thiocarbonyl-Bridged N-Heterotriangulenes for Energy Efficient Triplet Photosensitization: A Theoretical Perspective

Structurally-rigid metal-free organic molecules are of high demand for various triplet harvesting applications. However, inefficient intersystem crossing (ISC) due to large singlet-triplet gap (Δ E S - T ${\Delta {E}_{S-T}}$ ) and small spin-orbit coupling (SOC) between lowest excited singlet and triplet often limits their efficiency. Excited electronic states, fluorescence and ISC rates in several thiocarbonyl-bridged N-heterotriangulene ( m ${m}$ S-HTG) with systematically increased thione content (m = ${m=}$ 0-3) are investigated implementing polarization consistent time-dependent optimally-tuned range-separated hybrid. All m ${m}$ S-HTGs are dynamically stable and also thermodynamically feasible to synthesize. Relative energies of several low-lying singlets (S n ${{S}_{n}}$ ) and triplets (T n ${{T}_{n}}$ ), and their excitation nature (i. e.,n π * ${n{\pi }^{^{\ast}}}$ orπ π * ${\pi {\pi }^{^{\ast}}}$ ) and SOC are determined for these m ${m}$ S-HTGs in dichloromethane. Low-energy optical peak displays gradual red-shift with increasing thione content due to relatively smaller electronic gap resulted from greater degree of orbital delocalization. Significantly large SOC due to different orbital-symmetry and heavy-atom effect produces remarkably high ISC rates (k I S C ${{k}_{ISC}}$ ~1012 s-1) for enthalpically favouredS 1 n π * → T 2 ${{S}_{1}\left(n{\pi }^{^{\ast}}\right)\to {T}_{2}}$ (π π * ${\pi {\pi }^{^{\ast}}}$ ) channel in these m ${m}$ S-HTGs, which outcompete radiative fluorescence rates (~108 s-1) even directly from higher lying optically brightπ π * ${\pi {\pi }^{^{\ast}}}$ singlets. Importantly, high energy triplet excitons of ~1.7 eV resulting from such significantly large ISC rates from non-fluorescentS 1 n π * ${{S}_{1}\left(n{\pi }^{^{\ast}}\right)}$ make these thiocarbonylated HTGs ideal candidates for energy efficient triplet harvest including triplet-photosensitization.

Nature and energetics of low-lying excited singlets/triplets and intersystem crossing rates in selone analogs of perylenediimide: A theoretical perspective

The structural rigidity and chemical diversity of the highly fluorescent perylenediimide (PDI) provide wide opportunities for developing triplet photosensitizers with sufficiently increased energy efficiency. Remarkably high intersystem crossing (ISC) rates with a complete fluorescence turn-off reported recently for several thione analogs of PDI due to substantially large spin-orbit coupling garners huge attention to develop other potential analogs. Here, several selone analogs of PDI, denoted as mSe-PDIs (m = 1-4) with varied Se content and positions, are investigated to provide a comprehensive and comparative picture down the group-16 using density functional theory (DFT) and time-dependent DFT implementing optimally tuned range-separated hybrid in toluene dielectric. All mSe-PDIs are confirmed to be dynamically stable and also thermodynamically feasible to synthesize from their oxygen and thione congeners. The first excited-state singlet (S1) of mSe-PDI with relatively low Se-content (m = 1, 2) is of nπ* character with an expected fluorescence turn-off. Whereas, the ππ* nature of the S1 for 3Se-PDI and 4Se-PDI suggests a possible fluorescence turn-on in the absence of any other active nonradiative deactivation pathways. However, ∼4-6 orders greater ISC rates (∼1012-1014 s-1) than the fluorescence ones (∼108 s-1) for all mSe-PDIs signify highly efficient triplet harvest. Importantly, significantly higher ISC rates for these mSe-PDIs than their thione congeners render them efficient triplet photosensitizers.

Does the Intersystem Crossing Rate of β-Iodinated Phosphorus Corrole Depend on Iodine Numbers and/or Positions?

The heavy-atom effect is known to enhance the intersystem crossing (ISC) in organic molecular systems. Effects of iodine numbers and positions on the ISC rate of a few meso-difluorophenyl substituted β-iodinated phosphorus corroles (PCs) with axially ligated fluorine atoms (mI-FPC; m = 1-4) are studied using a time-dependent optimally tuned range-separated hybrid. Solvent effects are accounted for through a polarizable continuum model with a toluene dielectric. Calculations suggest similar thermodynamic stability for all mI-FPCs and also reproduce the experimentally measured 0-0 energies for some of the freebase phosphorus corrole (FPC) systems studied here. Importantly, our results reveal that all mI-FPCs display 10 times larger ISC rate (∼109 s-1) than the fluorescence rate (∼108 s-1), and the higher ISC rate stems from the improved spin-orbit coupling (SOC) introduced by lighter heteroatoms like central P and biaxial F rather than the I heavy-atom effect. However, an enhanced SOC is found with increasing I content for El-Sayed forbidden ISC channels. Research findings reported in this study unveil the impact of light heteroatoms and heavy atoms in promoting ISC in several iodinated PCs, which help in designing visible-light-driven efficient triplet photosensitizers.

Understanding Primary Charge Separation in the Heliobacterial Reaction Center

The homodimeric reaction center of heliobacteria retains features of the ancestral reaction center and can thus provide insights into the evolution of photosynthesis. Primary charge separation is expected to proceed in a two-step mechanism along either of the two reaction center branches. We reveal the first charge-separation step from first-principles calculations based on time-dependent density functional theory with an optimally tuned range-separated hybrid and ab initio Born-Oppenheimer molecular dynamics: the electron is most likely localized on the electron transfer cofactor 3 (EC3, OH-chlorophyll a), and the hole on the adjacent EC2. Including substantial parts of the surrounding protein environment into the calculations shows that a distinct structural mechanism is decisive for the relative energetic positioning of the electronic excitations: specific charged amino acids in the vicinity of EC3 lower the energy of charge-transfer excitations and thus facilitate efficient charge separation. These results are discussed considering recent experimental insights.

Screening the Band Shape of Molecules by Optimal Tuning of Range-Separated Hybrid Functional with TD-DFT: A Molecular Designing Approach

In the present article we have demonstrated the effectiveness of optimally tuned range-separated hybrid (RSH) functional to determine the electronic transitions from two fluorophore moieties (blue and yellow/orange) within a single white light emitter (WLE). First, the optimally tuned range separation parameter (ω) is calculated for two white emitting fluorophores (W1 and W2) already reported in the literature. The success of the optimally tuned RSH functional ω*B97XD, used in the TDDFT study, encouraged the authors to design eight new single organic white light emitters with frustrated energy transfer between the two individual fluorophore moieties (blue and yellow/orange). The simulated spectra (the band shapes, to be more specific) generated by TDDFT study and outcomes through natural transition orbital (NTO) and natural bond orbital (NBO) studies clearly demonstrate that all the designed eight organic molecules are potential white light emitters and can be synthesized in future.

Poisoning density functional theory with benchmark sets of difficult systems

Large benchmark sets like GMTKN55 [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] let us analyse the performance of density functional theory over a diverse range of systems and bonding types. However, assessing over a large and diverse set can miss cases where approaches fail badly, and can give a misleading sense of security. To this end we introduce a series of 'poison' benchmark sets, P30-5, P30-10 and P30-20, comprising systems with up to 5, 10 and 20 atoms, respectively. These sets represent the most difficult-to-model systems in GMTKN55. We expect them to be useful in developing new approximations, identifying weak points in existing ones, and to aid in selecting appropriate DFAs for computational studies involving difficult physics, e.g. catalysis.

Hybrid functionals with local range separation: Accurate atomization energies and reaction barrier heights

Range-separated hybrid approximations to the exchange-correlation density functional mix exact and semi-local exchange in a position-dependent manner. In their conventional form, the range separation is controlled by a constant parameter. Turning this constant into a density functional leads to a locally space-dependent range-separation function and thus a more powerful and flexible range-separation approach. In this work, we explore the self-consistent implementation of a local range-separated hybrid, taking into account a one-electron self-interaction correction and the behavior under uniform density scaling. We discuss different forms of the local range-separation function that depend on the electron density, its gradient, and the kinetic energy density. For test sets of atomization energies, reaction barrier heights, and total energies of atoms, we demonstrate that our best model is a clear improvement over common global range-separated hybrid functionals and can compete with density functionals that contain multiple empirical parameters. Promising results for equilibrium bond lengths, harmonic vibrational frequencies, and vertical ionization potentials further underline the potential and flexibility of our approach.

Linear fractional charge behavior in density functional theory through dielectric tuning of conductor-like polarizable continuum model

A property of exact density functional theory is linear fractional charge behavior as electrons are added or removed from a molecule. Typical density functional approximations (DFAs) exhibit delocalization error, which overstabilizes this fractional charge. Conversely, solvent corrections have been shown to erroneously destabilize this fractional charge. This work will show that an implicit solvent correction with a tuned dielectric can be used as an ad hoc correction to offset the delocalizing character of DFAs and achieve linear fractional charge behavior. While desirable, in principle, we find that this linear charge behavior degrades the vertical ionization energies reported by DFAs. Our results reveal that the localizing character of the solvent correction and the Hartree-Fock (HF) exchange offset each other. This helps explain the decreased ratios of HF exchange to DFA exchange in long-range hybrid tuning studies that use a solvent correction.

First principles theoretical spectroscopy of methylene blue: Between limitations of time-dependent density functional theory approximations and its realistic description in the solvent

Methylene blue [3,7-Bis(di-methylamino) phenothiazin-5-ium chloride] is a phenothiazine dye with applications as a sensitizer for photodynamic therapy, photoantimicrobials, and dye-sensitized solar cells. Time-dependent density functional theory (TDDFT), based on (semi)local and global hybrid exchange-correlation functionals, fails to correctly describe its spectral features due to known limitations for describing optical excitations of π-conjugated systems. Here, we use TDDFT with a non-empirical optimally tuned range-separated hybrid functional to explore the optical excitations of gas phase and solvated methylene blue. We compute solvated configurations using molecular dynamics and an iterative procedure to account for explicit solute polarization. We rationalize and validate that by extrapolating the optimized range separation parameter to an infinite amount of solvating molecules, the optical gap of methylene blue is well described. Moreover, this method allows us to resolve contributions from solvent-solute intermolecular interactions and dielectric screening. We validate our results by comparing them to first-principles calculations based on the GW+Bethe-Salpeter equation approach and experiment. Vibronic calculations using TDDFT and the generating function method account for the spectra's subbands and bring the computed transition energies to within 0.15 eV of the experimental data. This methodology is expected to perform equivalently well for describing solvated spectra of π-conjugated systems.

Beyond Koopmans' theorem: electron binding energies in disordered materials

The topical review focuses on calculating ionization energies (IE), or electronic polarons in quasi-particle terminology, in large disordered systems, e.g. for a solute dissolved in a molecular solvent. The simplest estimate of the ionization energy is provided by one-electron energies in the Hartree-Fock theory, but the calculated quantities are not accurate. Density functional theory as many-body theory provides a principal opportunity for calculating one-electron energies including correlation and relaxation effects, i.e. the true energies of electronic polarons. We argue that such a principal possibility materializes within the concept of optimally tuned range-separated hybrid functionals (OT-RSH). We describe various schemes for optimal tuning. Importantly, the OT-RSH scheme is investigated for systems capped with dielectric continuum, providing a consistent picture on the QM/dielectric boundary. Finally, some limitations and open issues of the OT-RSH approach are addressed.

Do water's electrons care about electrolytes?

Ions have a profound effect on the geometrical structure of liquid water and an aqueous environment is known to change the electronic structure of ions. Here we combine photoelectron spectroscopy measurements from liquid microjets with molecular dynamical and quantum chemical calculations to address the reverse question, to what extent do ions affect the electronic structure of liquid water? We study aqueous solutions of sodium iodide (NaI) over a wide concentration range, from nearly pure water to 8 M solutions, recording spectra in the 5 to 60 eV binding energy range to include all water valence and the solute Na+ 2p, I- 4d, and I- 5p orbital ionization peaks. We observe that the electron binding energies of the solute ions change only slightly as a function of electrolyte concentration, less than 150 ± 60 meV over an ∼8 M range. Furthermore, the photoelectron spectrum of liquid water is surprisingly mildly affected as we transform the sample from a dilute aqueous salt solution to a viscous, crystalline-like phase. The most noticeable spectral changes are a negative binding energy shift of the water 1b2 ionizing transition (up to -370 ± 60 meV) and a narrowing of the flat-top shape water 3a1 ionization feature (up to 450 ± 90 meV). A novel computationally efficient technique is introduced to calculate liquid-state photoemission spectra using small clusters from molecular dynamics (MD) simulations embedded in dielectric continuum. This theoretical treatment captured the characteristic positions and structures of the aqueous photoemission peaks, reproducing the experimentally observed narrowing of the water 3a1 feature and weak sensitivity of the water binding energies to electrolyte concentration. The calculations allowed us to attribute the small binding energy shifts to ion-induced disruptions of intermolecular electronic interactions. Furthermore, they demonstrate the importance of considering concentration-dependent screening lengths for a correct description of the electronic structure of solvated systems. Accounting for electronic screening, the calculations highlight the minimal effect of electrolyte concentration on the 1b1 binding energy reference, in accord with the experiments. This leads us to a key finding that the isolated, lowest-binding-energy, 1b1, photoemission feature of liquid water is a robust energetic reference for aqueous liquid microjet photoemission studies.

Dielectric Screening Meets Optimally Tuned Density Functionals

A short overview of recent attempts at merging two independently developed methods is presented. These are the optimal tuning of a range-separated hybrid (OT-RSH) functional, developed to provide an accurate first-principles description of the electronic structure and optical properties of gas-phase molecules, and the polarizable continuum model (PCM), developed to provide an approximate but computationally tractable description of a solvent in terms of an effective dielectric medium. After a brief overview of the OT-RSH approach, its combination with the PCM as a potentially accurate yet low-cost approach to the study of molecular assemblies and solids, particularly in the context of photocatalysis and photovoltaics, is discussed. First, solvated molecules are considered, with an emphasis on the challenge of balancing eigenvalue and total energy trends. Then, it is shown that the same merging of methods can also be used to study the electronic and optical properties of molecular solids, with a similar discussion of the pros and cons. Tuning of the effective scalar dielectric constant as one recent approach that mitigates some of the difficulties in merging the two approaches is considered.

Direct observation of backbone planarization via side-chain alignment in single bulky-substituted polythiophenes

The backbone conformation of conjugated polymers affects, to a large extent, their optical and electronic properties. The usually flexible substituents provide solubility and influence the packing behavior of conjugated polymers in films or in bad solvents. However, the role of the side chains in determining and potentially controlling the backbone conformation, and thus the optical and electronic properties on the single polymer level, is currently under debate. Here, we investigate directly the impact of the side chains by studying the bulky-substituted poly(3-(2,5-dioctylphenyl)thiophene) (PDOPT) and the common poly(3-hexylthiophene) (P3HT), both with a defined molecular weight and high regioregularity, using low-temperature single-chain photoluminescence (PL) spectroscopy and quantum-classical simulations. Surprisingly, the optical transition energy of PDOPT is significantly (∼2,000 cm-1 or 0.25 eV) red-shifted relative to P3HT despite a higher static and dynamic disorder in the former. We ascribe this red shift to a side-chain induced backbone planarization in PDOPT, supported by temperature-dependent ensemble PL spectroscopy. Our atomistic simulations reveal that the bulkier 2,5-dioctylphenyl side chains of PDOPT adopt a clear secondary helical structural motif and thus protect conjugation, i.e., enforce backbone planarity, whereas, for P3HT, this is not the case. These different degrees of planarity in both thiophenes do not result in different conjugation lengths, which we found to be similar. It is rather the stronger electronic coupling between the repeating units in the more planar PDOPT which gives rise to the observed spectral red shift as well as to a reduced calculated electron-hole polarization.

Hot and Cold Charge-Transfer Mechanisms in Organic Photovoltaics: Insights into the Excited States of Donor/Acceptor Interfaces

The evolution of the excited-state manifold in organic D/A aggregates (e.g., the prototypical P3HT/PCBM) is investigated through a bottom-up approach via first-principles calculations. We show how the excited-state energies, the charge transfer (CT) states, and the electron-hole density distributions are strongly influenced by the size, the orientation, and the position (i.e., on-top versus on-edge phases) of P3HT/PCBM domains. We discuss how the structural order influences the excited-state electronic structure, providing an atomistic interpretation of the photophysics of organic blends. We show how the simultaneous presence of on-top and on-edge phases does not alter the optical absorption spectrum of the blend but does affect the photophysics. Photovoltaic processes such as (i) the simultaneous charge generation obtained from hot and cold excitations, (ii) the instantaneous and delayed charge separation, and (iii) the pump-push-probe charge generation can be interpreted based on our study.

Effect of Solid-State Polarization on Charge-Transfer Excitations and Transport Levels at Organic Interfaces from a Screened Range-Separated Hybrid Functional

We develop a robust approach for the description of the energetics of charge-transfer (CT) excitations and transport levels at organic interfaces based on a screened range-separated hybrid (SRSH) functional. We find that SRSH functionals correctly capture the effect of solid-state electronic polarization on transport gap renormalization and on screening of the electrostatic electron-hole interaction. With respect to calculations based on nonscreened optimally tuned RSH (long-range corrected) functionals, the SRSH-based calculations can be performed for both isolated molecular complexes and systems embedded in a dielectric medium with the same range-separation parameter, which allows a clear physical interpretation of the results in terms of solid-state polarization without any perturbation of the molecular electronic structure. By considering weakly interacting donor/acceptor complexes of pentacene with C₆₀ and poly-3-hexylthiophene (P3HT) with PCBM, we show that this new approach provides CT-state energies that compare very well with experimental data.

Description of the Charge Transfer States at the Pentacene/C60 Interface: Combining Range-Separated Hybrid Functionals with the Polarizable Continuum Model

Density functional theory (DFT) approaches based on range-separated hybrid functionals are currently methods of choice for the description of the charge-transfer (CT) states in organic donor/acceptor solar cells. However, these calculations are usually performed on small-size donor/acceptor complexes and as result do not account for electronic polarization effects. Here, using a pentacene/C60 complex as a model system, we discuss the ability of long-range corrected (LCR) hybrid functionals in combination with the polarizable continuum model (PCM) to determine the impact of the solid-state environment on the CT states. The CT energies are found to be insensitive to the interactions with the dielectric medium when a conventional time-dependent DFT/PCM (TDDFT/PCM) approach is used. However, a decrease in the energy of the CT state in the framework of LRC functionals can be obtained by using a smaller range-separated parameter when going from an isolated donor/acceptor complex to the solid-state case.

Excited-State Properties of Molecular Solids from First Principles

Molecular solids have attracted attention recently in the context of organic (opto)electronics. These materials exhibit unique charge carrier generation and transport phenomena that are distinct from those of conventional semiconductors. Understanding these phenomena is fundamental to optoelectronics and requires a detailed description of the excited-state properties of molecular solids. Recent advances in many-body perturbation theory (MBPT) and density functional theory (DFT) have made such description possible and have revealed many surprising electronic and optical properties of molecular crystals. Here, we review this progress. We summarize the salient aspects of MBPT and DFT as well as various properties that can be described by these methods. These properties include the fundamental gap and its renormalization, hybridization and band dispersion, singlet and triplet excitations, optical spectra, and excitonic properties. For each, we present concrete examples, a comparison to experiments, and a critical discussion.

Theoretical investigations of the small molecular acceptor materials based on oligothiophene – naphthalene diimide in organic solar cells

The electronic transmission paths of NDI-T3DCRD with the centroid distance from core molecule to ambient molecules marked.

Rational computing of energy levels for organic electronics: the case of 2-benzylidene-1,3-indandiones

To compute ionization potential and electron affinity (HOMO & LUMO levels by tradition), diffuse functions are redundant, while range-separated hybrid DFT is not always better than B3LYP. Solvent modelling is essential and can be cheap with CPCM.