Describing long-range charge-separation processes with subsystem density-functional theory

Electronic Transport Properties of Molecular Clusters Sb4O6, P4Se3, and P4O6

Inorganic molecular crystal (IMC) is a trending class of materials in which structural units comprise molecular cages or clusters bonded via van der Waal forces. The structure-property relationship in IMCs is less known due to the unusual assembly of molecular clusters in these materials. In this paper, the density functional theory-calculated electronic transport properties of the molecular clusters of antimony oxide (Sb4O6), phosphorus triselenide (P4Se3), and phosphorus trioxide (P4O6) are described in detail. The calculated values of highest occupied molecular orbital-lowest unoccupied molecular orbital gaps appeared as 5.487, 2.296, and 4.425 eV for Sb4O6, P4Se3, and P4O6, respectively. The work was carried out to explore the charge transport mechanism in IMCs in order to disclose their potential in practical applications. The calculations involved charge-transfer integral based on Marcus theory to compute the electronic coupling (V), reorganization energies (λ), and hopping rate (k) in the structures. The hopping rate for Sb4O6, P4Se3, and P4O6 is found as 8.49 × 10-12, 1.28 × 10-14, and 2.51 × 10-20 s-1, respectively. The transport properties of Sb4O6 are found better, which predicts the application of the relevant IMC for device grade applications. The findings of this study are important for future application of the IMCs in electronic and optoelectronic applications.

Evolution of the ionisation energy with the stepwise growth of chiral clusters of [4]helicene

Polycyclic aromatic hydrocarbons (PAHs) are widely established as ubiquitous in the interstellar medium (ISM), but considering their prevalence in harsh vacuum environments, the role of ionisation in the formation of PAH clusters is poorly understood, particularly if a chirality-dependent aggregation route is considered. Here we report on photoelectron spectroscopy experiments on [4]helicene clusters performed with a vacuum ultraviolet synchrotron beamline. Aggregates (up to the heptamer) of [4]helicene, the smallest PAH with helical chirality, were produced and investigated with a combined experimental and theoretical approach using several state-of-the-art quantum-chemical methodologies. The ionisation onsets are extracted for each cluster size from the mass-selected photoelectron spectra and compared with calculations of vertical ionisation energies. We explore the complex aggregation topologies emerging from the multitude of isomers formed through clustering of P and M, the two enantiomers of [4]helicene. The very satisfactory benchmarking between experimental ionisation onsets vs. predicted ionisation energies allows the identification of theoretically predicted potential aggregation motifs and corresponding energetic ordering of chiral clusters. Our structural models suggest that a homochiral aggregation route is energetically favoured over heterochiral arrangements with increasing cluster size, hinting at potential symmetry breaking in PAH cluster formation at the scale of small grains.

High Electronic Coupling between Cu Complexes and Oxidized Dyes Confirmed by Measurements of Driving Force Dependent Regeneration Kinetics in Minimal Electrolyte System

We confirm fast regeneration kinetics between copper complexes and oxidized organic dyes and the major contribution of electronic coupling (HDA). The highest efficiency of dye-sensitized TiO2 solar cells has been shown by employing Cu complex redox couples. Various groups have reported a fast regeneration rate of oxidized dyes by Cu complexes giving a low driving force attributed to low reorganization energy (λ), but the effect of HDA has not been evaluated. The values of HDA and λ can be derived from driving force dependent transient absorption (TA) measurements. However, analyzing TA decay using Cu complexes is not trivial because accelerated recombination by the presence of Cu2+ complexes and biphasic TA decay often complicates the analysis. Here we employ 16 Cu1+ and Co2+ complexes and two dyes. To simplify the system, i.e., making a minimal electrolyte system, Cu2+ and Co3+ complexes and a common additive of 4-tert-butylpyridine are not used. From the driving force dependent TA decays of oxidized dyes by both Cu1+ and Co2+ complexes, λ for the combination of the Cu complexes and dyes is found to be about 0.15 eV lower than that of Co complexes. Approximately 3 to 5 times higher HDA values of Cu complexes than those of Co complexes are obtained, which is the dominant factor for faster rates. The values vary with the structure of the molecules, showing the possibility of increasing the HDA values further. The higher HDA values of a Cu complex than that of a Co complex are also reproduced by quantum chemical calculations.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Static embedding with pair coupled cluster doubles based methods

Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.

Towards the description of charge transfer states in solubilised LHCII using subsystem DFT

Light harvesting complex II (LHCII) in plants and green algae have been shown to adapt their absorption properties, depending on the concentration of sunlight, switching between a light harvesting and a non-harvesting or quenched state. In a recent work, combining classical molecular dynamics (MD) simulations with quantum chemical calculations (Liguori et al. in Sci Rep 5:15661, 2015) on LHCII, it was shown that the Chl611-Chl612 cluster of the terminal emitter domain can play an important role in modifying the spectral properties of the complex. In that work the importance of charge transfer (CT) effects was highlighted, in re-shaping the absorption intensity of the chlorophyll dimer. Here in this work, we investigate the combined effect of the local excited (LE) and CT states in shaping the energy landscape of the chlorophyll dimer. Using subsystem Density Functional Theory over the classical [Formula: see text]s MD trajectory we look explicitly into the excitation energies of the LE and the CT states of the dimer and their corresponding couplings. Upon doing so, we observe a drop in the excitation energies of the CT states, accompanied by an increase in the couplings between the LE/LE and the LE/CT states facilitated by a shorter interchromophoric distance upon equilibration. Both these changes in conjunction, effectively produces a red-shift of the low-lying mixed exciton/CT states of the supramolecular chromophore pair.

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

State-specific solvation for restricted active space spin-flip (RAS-SF) wave functions based on the polarizable continuum formalism

The restricted active space spin-flip (RAS-SF) formalism is a particular form of single-reference configuration interaction that can describe some forms of strong correlation at a relatively low cost and which has recently been formulated for the description of charge-transfer excited states. Here, we introduce both equilibrium and nonequilibrium versions of a state-specific solvation correction for vertical transition energies computed using RAS-SF wave functions, based on the framework of a polarizable continuum model (PCM). Ground-state polarization is described using the solvent's static dielectric constant and in the nonequilibrium solvation approach that polarization is modified upon vertical excitation using the solvent's optical dielectric constant. Benchmark calculations are reported for well-studied models of photo-induced charge transfer, including naphthalene dimer, C₂H₄⋯C₂F₄, pentacene dimer, and perylene diimide (PDI) dimer, several of which are important in organic photovoltaic applications. For the PDI dimer, we demonstrate that the charge-transfer character of the excited states is enhanced in the presence of a low-dielectric medium (static dielectric constant ɛ₀ = 3) as compared to a gas-phase calculation (ɛ₀ = 1). This stabilizes mechanistic traps for singlet fission and helps to explain experimental singlet fission rates. We also examine the effects of nonequilibrium solvation on charge-separated states in an intramolecular singlet fission chromophore, where we demonstrate that the energetic ordering of the states changes as a function of solvent polarity. The RAS-SF + PCM methodology that is reported here provides a framework to study charge-separated states in solution and in photovoltaic materials.

Quantum dynamics of the photoinduced charge separation in a symmetric donor–acceptor–donor triad: The role of vibronic couplings, symmetry and temperature

The photoinduced charge separation in a symmetric donor–acceptor–donor (D–A–D) triad is studied quantum mechanically using a realistic diabatic vibronic coupling model. The model includes a locally excited DA*D state and two charge-transfer states D+A−D and DA−D+ and is constructed according to a procedure generally applicable to semirigid D–A–D structures and based on energies, forces, and force constants obtained by quantum chemical calculations. In this case, the electronic structure is described by time-dependent density functional theory, and the corrected linear response is used in conjunction with the polarizable continuum model to account for state-specific solvent effects. The multimode dynamics following the photoexcitation to the locally excited state are simulated by the hybrid Gaussian-multiconfigurational time-dependent Hartree method, and temperature effects are included using thermo field theory. The dynamics are connected to the transient absorption spectrum obtained in recent experiments, which is simulated and fully assigned from first principles. It is found that the charge separation is mediated by symmetry-breaking vibrations of relatively low frequency, which implies that temperature should be accounted for to obtain reliable estimates of the charge transfer rate.

Multi-state formulation of the frozen-density embedding quasi-diabatization approach

We present a multi-state implementation of the recently developed frozen-density embedding diabatization (FDE-diab) methodology [D. G. Artiukhin and J. Neugebauer, J. Chem. Phys. 148, 214104 (2018)] in the Serenity program. The new framework extends the original approach such that any number of charge-localized quasi-diabatic states can be coupled, giving an access to calculations of ground and excited state spin-density distributions as well as to excitation energies. We show that it is possible to obtain results similar to those from correlated wave function approaches such as the complete active space self-consistent field method at much lower computational effort. Additionally, we present a series of approximate computational schemes, which further decrease the overall computational cost and systematically converge to the full FDE-diab solution. The proposed methodology enables computational studies on spin-density distributions and related properties for large molecular systems of biochemical interest.

Theoretical Assessment of Hinge-Type Models for Electron Donors in Reaction Centers of Photosystems I and II as well as of Purple Bacteria

Hinge-type molecular models for electron donors in reaction centers of Photosystems I and II and purple bacteria were investigated using a two-state computational approach based on frozen-density embedding (FDE). This methodology, dubbed FDE-diab, is known to avoid consequences of the self-interaction error as far as intermolecular phenomena are concerned, which allows a prediction of qualitatively correct spin densities for large biomolecular systems. The calculated spin density distributions are in a good agreement with available experimental results and demonstrated a very high sensitivity to changes in the relative orientation of cofactors and amino acid protonation states. This allows a validation of the previously proposed hinge-type models providing hints on possible protonation states of axial histidine molecules.

Quantifying Uncertainties in Solvation Procedures for Modeling Aqueous Phase Reaction Mechanisms

Computational quantum chemistry provides fundamental chemical and physical insights into solvated reaction mechanisms across many areas of chemistry, especially in homogeneous and heterogeneous renewable energy catalysis. Such reactions may depend on explicit interactions with ions and solvent molecules that are nontrivial to characterize. Rigorously modeling explicit solvent effects with molecular dynamics usually brings steep computational costs while the performance of continuum solvent models such as polarizable continuum model (PCM), charge-asymmetric nonlocally determined local-electric (CANDLE), conductor-like screening model for real solvents (COSMO-RS), and effective screening medium method with the reference interaction site model (ESM-RISM) are less well understood for reaction mechanisms. Here, we revisit a fundamental aqueous hydride transfer reaction-carbon dioxide (CO₂) reduction by sodium borohydride (NaBH₄)-as a test case to evaluate how different solvent models perform in aqueous phase charge migrations that would be relevant to renewable energy catalysis mechanisms. For this system, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations almost exactly reproduced energy profiles from QM simulations, and the Na⁺ counterion in the QM/MM simulations plays an insignificant role over ensemble averaged trajectories that describe the reaction pathway. However, solvent models used on static calculations gave much more variability in data depending on whether the system was modeled using explicit solvent shells and/or the counterion. We pinpoint this variability due to unphysical descriptions of charge-separated states in the gas phase (i.e., self-interaction errors), and we show that using more accurate hybrid functionals and/or explicit solvent shells lessens these errors. This work closes with recommended procedures for treating solvation in future computational efforts in studying renewable energy catalysis mechanisms.

Electronic couplings for photo-induced processes from subsystem time-dependent density-functional theory: The role of the diabatization

Subsystem time-dependent density-functional theory (sTDDFT) making use of approximate non-additive kinetic energy (NAKE) functionals is known to be capable of describing excitation energy transfer processes in a variety of applications. Here, we show that sTDDFT, especially when combined with projection-based embedding (PbE), can be employed for the entire range of photo-induced electronic couplings essential for modeling photophysical properties of complex chemical and biological systems and therefore represents a complete toolbox for this class of problems. This means that it is capable of capturing the interaction/coupling associated with local- and charge-transfer (CT) excitons. However, this requires the choice of a reasonable diabatic basis. We therefore propose different diabatization strategies of the virtual orbital space in PbE-sTDDFT and show how CT excitations can be included in sTDDFT using NAKE functionals via a phenomenological approach. Finally, these electronic couplings are compared to couplings from a multistate fragment excitation difference (FED)-fragment charge difference (FCD) diabatization procedure. We show that both procedures, multistate FED-FCD and sTDDFT (with the right diabatization procedure chosen), lead to an overall good agreement for the electronic couplings, despite differences in their general diabatization strategy. We conclude that the entire range of photo-induced electronic couplings can be obtained using sTDDFT (with the right diabatization procedure chosen) in a black-box manner.

Nonlocal Subsystem Density Functional Theory

By invoking a divide-and-conquer strategy, subsystem DFT dramatically reduces the computational cost of large-scale, ab initio electronic structure simulations of molecules and materials. The central ingredient setting subsystem DFT apart from Kohn-Sham DFT is the nonadditive kinetic energy functional (NAKE). Currently employed NAKEs are at most semilocal (i.e., they only depend on the electron density and its gradient), and as a result of this approximation, so far large-scale simulations only included systems composed of weakly interacting subsystems. In this work, we advance the state-of-the-art by introducing fully nonlocal NAKEs in subsystem DFT simulations for the first time. A benchmark analysis based on the S22-5 test set shows that nonlocal NAKEs considerably improve the computed interaction energies and electron densities compared to commonly employed GGA NAKEs, especially when increasing intersubsystem electron density overlap is considered. Most importantly, we resolve the long-standing problem of too attractive interaction energy curves typically resulting from the use of GGA NAKEs.

Fast-Response, Highly Air-Stable, and Water-Resistant Organic Photodetectors Based on a Single-Crystal Pt Complex

Organic semiconductors demonstrate several advantages over conventional inorganic materials for novel electronic and optoelectronic applications, including molecularly tunable properties, flexibility, low-cost, and facile device integration. However, before organic semiconductors can be used for the next-generation devices, such as ultrafast photodetectors (PDs), it is necessary to develop new materials that feature both high mobility and ambient stability. Toward this goal, a highly stable PD based on the organic single crystal [PtBr₂ (5,5'-bis(CF₃ CH₂ OCH₂ )-2,2'-bpy)] (or "Pt complex (1o)") is demonstrated as the active semiconductor channel-a material that features a lamellar molecular structure and high-quality, intraligand charge transfer. Benefitting from its unique crystal structure, the Pt-complex (1o) device exhibits a field-effect mobility of ≈0.45 cm² V^-1 s^-1 without loss of significant performance under ambient conditions even after 40 days without encapsulation, as well as immersion in distilled water for a period of 24 h. Furthermore, the device features a maximum photoresponsivity of 1 × 10³ A W^-1 , a detectivity of 1.1 × 10¹² cm Hz^1/2 W^-1 , and a record fast response/recovery time of 80/90 µs, which has never been previously achieved in other organic PDs. These findings strongly support and promote the use of the single-crystal Pt complex (1o) in next-generation organic optoelectronic devices.

Description of intermolecular charge transfer with subsystem density-functional theory

Efficient quantum-chemical methods that are able to describe intermolecular charge transfer are crucial for modeling organic semiconductors. However, the correct description of intermolecular charge transfer with density-functional theory (DFT) is hampered by the fractional charge error of approximate exchange-correlation (xc) functionals. Here, we investigate the charge transfer induced by an external electric field in a tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) complex as a test case. For this seemingly simple model system, a supermolecular DFT treatment fails with most conventional xc functionals. Here, we present an extension of subsystem DFT to subsystems with a fractional number of electrons. We show that within such a framework, it becomes possible to overcome the fractional charge error by enforcing the correct dependence of each subsystem's total energy on the subsystem's fractional charge. Such a subsystem DFT approach allows for a correct description of the intermolecular charge transfer in the TTF-TCNQ model complex. The approach presented here can be generalized to larger molecular aggregates and will thus allow for modeling organic semiconductor materials accurately and efficiently.

Charge transfer dynamics at the boron subphthalocyanine chloride/C60 interface: non-adiabatic dynamics study with Libra-X

The Libra-X software for non-adiabatic molecular dynamics is reported. It is used to comprehensively study the charge transfer dynamics at the boron subphtalocyanine chloride (SubPc)/fullerene (C₆₀) interface.

Charge transfer in time-dependent density functional theory

Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Constricted variational density functional theory for spatially clearly separated charge-transfer excitations

Constricted Variational Density Functional Theory (CV-DFT) is known to be one of the successful methods in predicting charge-transfer excitation energies. In this paper, we apply the CV-DFT method to the well-known model systems ethylene-tetrafluoroethylene (C₂H₄ × C₂F₄) and the zincbacteriochlorin-bacteriochlorin complex (ZnBC-BC). The analysis of the CV-DFT energies enables us to understand the -1/R charge-transfer behaviour in CV-DFT for large separation distances R. With this we discuss the importance of orbital relaxations using the relaxed version of CV(∞)-DFT, the R-CV(∞)-DFT method. Possible effects of the optimization of the transition matrix for the relaxed self-consistent field version of CV(∞)-DFT, RSCF-CV(∞)-DFT in the case of large fragment separations are shown and we introduce two possible gradient restrictions to avoid the unwanted admixing of other transitions.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Constrained subsystem density functional theory

Constrained Subsystem Density Fucntional Theory (CSDFT) allows to compute diabatic states for charge transfer reactions using the machinery of the constrained DFT method, and at the same time is able to embed such diabatic states in a molecular environment via a subsystem DFT scheme.