Charge Transfer Excitation Research Articles

How the Interplay among Conformational Disorder, Solvation, Local, and Charge-Transfer Excitations Affects the Absorption Spectrum and Photoinduced Dynamics of Perylene Diimide Dimers: A Molecular Dynamics/Quantum Vibronic Approach.

In this contribution we present a mixed quantum-classical dynamical approach for the computation of vibronic absorption spectra of molecular aggregates and their nonadiabatic dynamics, taking into account the coupling between local excitations (LE) and charge-transfer (CT) states. The approach is based on an adiabatic (Ad) separation between the soft degrees of freedom (DoFs) of the system and the stiff vibrations, which are described by the quantum dynamics (QD) of wave packets (WPs) moving on the coupled potential energy surfaces (PESs) of the LE and CT states. These PESs are described with a linear vibronic coupling (LVC) Hamiltonian, parameterized by an overlap-based diabatization on the grounds of time-dependent density functional theory computations. The WPs time evolution is computed with the multiconfiguration time-dependent Hartree method, using effective modes defined through a hierarchical representation of the LVC Hamiltonian. The soft DoFs are sampled with classical molecular dynamics (MD), and the coupling between the slow and fast DoFs is included by recomputing the key parameters of the LVC Hamiltonians, specifically for each MD configuration. This method, named Ad-MD|gLVC, is applied to a perylene diimide (PDI) dimer in acetonitrile and water solutions, and it is shown to accurately reproduce the change in the vibronic features of the absorption spectrum upon aggregation. Moreover, the microscopic insight offered by the MD trajectories allows for a detailed understanding of the role played by the fluctuation of the aggregate structure on the shape of the vibronic spectrum and on the population of LE and CT states. The nonadiabatic QD predicts an extremely fast (∼50 fs) energy transfer between the two LEs. CT states have only a moderate effect on the absorption spectrum, despite the fact that after photoexcitation they are shown to acquire a fast and non-negligible population, highlighting their relevance in dictating the charge separation and transport in PDI-based optical devices.

Solvent Effects on the Photophysical Properties of a Donor-acceptor Based Schiff Base.

In this work, a donor-acceptor substituted aromatic system ((E)-N-((E)-3-(4 (dimethylamino)phenyl) allylidene)-4-(trifluoromethyl) benzenamine (DPATB) has been synthesized and its detailed photophysics of intramolecular charge transfer process have been explored on the basis of steady state absorption, fluorescence and time resolved spectroscopy in combination with density functional theory calculations. Large solvent dependency fluorescence spectral shift and the calculated large excited state dipole moment clearly indicate an efficient charge transfer occurring from the donor group to the acceptor moiety in the excited state. Effect on addition of acid and pH on steady state spectral properties further reveals excited state charge transfer character. Quantum chemical calculations were performed in order to study the conformation and polarity of DPATB at their ground as well as excited electronic states. The HOMO and LUMO molecular orbital pictures are obtained at DFT level using B3LYP functional and 6-311 + g(d,p) basis set which clearly support excited state intramolecular charge transfer process. The molecular electrostatic potential maps for the optimized ground state, donor twisted and acceptor twisted geometry shed insight on the electrostatic potential and charge distribution in a system which gives information about the reacting site of the probe and nature of the reaction. In this work, detailed photophysics of excited state intramolecular charge transfer process in donor-acceptor system (DPATB) was evaluated using steady state and time-resolved fluorescence spectroscopy in combination with density functional theory calculations. Large solvent dependency fluorescence spectral shift and the calculated large excited state dipole moment clearly indicate an efficient charge transfer occurring in DPATB. Molecular orbital pictures as obtained from DFT based computational analysis reveals a significant change in the distribution of electron density upon transition from HOMO to LUMO which confirms an ICT process occurring from the donor group to the acceptor moiety in the excited state.

The Excited State and Charge Transfer of Two Nonfullerene Acceptors from First-Principles Many-Body Green’s Function Theory

Nonfullerene acceptors (NFAs) have shown an outstanding performance upon producing highly efficient and sustainable organic solar cells (OSC). Recently, a growing group of researchers denoted to modify the structures of acceptor−donor−acceptor-type NFAs to raise the power conversion efficiencies (PCEs) when they are blended with a variety of polymer donors in OSC. In 2020, the ketone on the ending groups of BTP-IC were substituted for sulfonyl; the new NFA named BTP-IS was synthetized. The PCE of BTP-IS based OSC is 5.25% higher than that of the BTP-IC device. Based on this, the many-body Green’s function theory, combined with other quantum chemical methods, is conducted to study their ground electronic structures, excited states, and absorption spectra. The ground-state geometries, ionization energies, and the excited state energies are deeply sensitive to exchange-correlation functionals used in calculations. The lowest excited state energies calculated by full-BSE method using DFT-PBE as the starting point is 0.07~0.14 eV smaller than that by TDDFT-PBE method, which is more consistent with experimental data. This provided a methodology for future research on similar NFA systems. The first charge-transfer states and transfer mechanism of two molecules are proposed in this paper. Furthermore, we found that the reason for more efficient charge transport in BTP-IS-based OSC is the larger ionization energies and much weaker electron-hole interaction in BTP-IS. This finding is conducive to the better application of BTP-IS in OSC field.

Near‐IR Intramolecular Charge Transfer in Strongly Interacting Diphenothiazene‐TCBD and Diphenothiazene‐DCNQ Push‐Pull Triads

AbstractThree types of phenothiazines dimers (PTZ‐PTZ, 1–3), covalently linked with one or two acetylene linkers, were synthesized by copper‐mediated Eglinton and Pd‐catalyzed Sonogashira coupling reactions in excellent yields. The dimers 1–3 were further engaged in [2+2] cycloaddition‐retroelectrocyclization reactions with strong electron acceptors, tetracyanoethylene (TCNE) and 7,7,8,8‐tetracyanoquinodimethane (TCNQ) to yield tetracyanobutadiene (TCBD, 1 a–3 a), and dicyanoquinodimethane (DCNQ, 1 b–3 b) functionalized donor‐acceptor (D‐A) conjugates, respectively. The conjugates were examined by a series of spectral, computational, and electrochemical studies. Strong ground state polarization leading to new optical transitions was witnessed in both series of D‐A conjugates. In the case of DCNQ derived D‐A system 1 b, the optical coverage extended until 1200 nm in benzonitrile, making this a rare class of D‐A ICT system. Multiple redox processes were witnessed in these D‐A systems, and the frontier orbitals generated on DFT optimized structures further supported the ICT phenomenon. Photochemical studies performed using femtosecond pump‐probe studies confirmed solvent polarity dependent excited state charge transfer and separation in these novel multi‐modular D‐A conjugates. The charge‐separated states lasted up to 70 ps in benzonitrile while in toluene slightly prolonged lifetime of up to 100 ps was witnessed. The significance of phenothiazine dimer in wide‐band optical capture all the way into the near‐IR region and promoting ultrafast photoinduced charge transfer in the D‐A‐D configured multi‐modular systems, and the effect of donor‐acceptor distance and the solvent polarity was the direct outcome of the present study.

Microscopic Study of Molecular Double Doping

Double doping, in which a single dopant molecule induces two charge carriers in an organic semiconductor (OSC), was recently experimentally observed and promises to enhance the efficiency of molecular doping. Here we present a theoretical investigation of p-type molecular double doping in a CN6-CP:bithiophene-thienothiophene OSC system. Our analysis is based on density functional theory (DFT) calculations for the electronic ground state. In a molecular complex with two OSC oligomers and one CN6-CP dopant molecule, we explicitly demonstrate double integer charge transfer and find the formation of two individual polarons on the OSC molecules and a dianion dopant molecule. We show that the vibrational modes and related infrared absorption spectrum of this complex can be traced back to those of the charged dopant and OSC molecules in their isolated forms. The near-infrared optical absorption spectrum calculated by time-dependent DFT shows features of both typical intramolecular polaron excitations and weak intermolecular charge transfer excitations associated with the doping-induced polaron states.

Is charge-transfer excitation through a polyalkane single-bond chain an intramolecular charge-transfer?: EOM-CCSD and LC-BOP study

We performed intra- and intermolecular charge-transfer (CT) excitation calculations of (a) H2N–(CH2–CH2)n–NO2 and (b) its equidistant H2N-H……H-NO2 using EOM-CCSD (n = 1 ∼ 5) and time-dependent long-range corrected density functional theory (n = 1 ∼ 10). The calculation results show that polyalkane [polyethylene oligomer] chain has almost no effect on CT excitation energy between donor and acceptor. That is, CT excitation energy through the polyalkane chain behaves closely to intermolecular CT excitation. Decomposition of the optical excitation energies of (a) and (b) into HOMO-LUMO gap and excitonic binding energy revealed that alkane chain does not affect HOMO-LUMO gaps, while conjugated polyene [polyethylene oligomer] chain medium reduces HOMO-LUMO gaps by delocalization.

Higher-order transition state approximation.

We generalize Slater's transition state concept by deriving systematic higher-order transition state approximations. Numerical validation is performed by the calculation of transition energies for various excitations, including core, valence, and charge-transfer excitations, at Hartree-Fock and Kohn-Sham density functional theory levels. All higher-order transition state approximations introduced in this study accurately reproduce the results from delta self-consistent-field calculations. In particular, we demonstrate that the third-order generalized transition state (GTS3) approximation is a promising alternative to the original, owing to a good balance between the accuracy and computational cost. We also demonstrate that accurate and reliable results can be obtained with a low computational cost by combining the GTS3 approximation with the transition potential scheme.

Super-Exchange Charge Transfer in One-Photon and Two-Photon Absorption of Multibranched Compounds

In this work, density functional theory is used to study organic molecules in a donor–acceptor (D–A) system centered on phenothiazine with strip and trigonal structures. The transition modes of the one-photon absorption (OPA) and two-photon absorption (TPA) processes of the two molecules are studied. The calculations show that the molar absorption coefficient of OPA for trigonal molecule TPPO and the cross section of TPA are both larger than those for strip molecule M1 due to the increase in the number of branches of the system. A special local excitation-enhanced charge-transfer excitation appears in strip-type molecule M1. In the charge-transfer process of trigonal D–A structure molecule TPPO, there are not only local excitation-enhanced charge-transfer excitation but also super-exchange charge transfer between the three branches that occurs due to the increase in the planarity of the system.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems.

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

A spectroscopic study of benzonitrile

A spectroscopic study on benzonitrile has been carried out by recording photoabsorption spectra in the 36,000–90,000 cm−1 (4.5–11 eV) region using the synchrotron light source Indus 1 and infrared spectra in the 500–4000 cm−1 region using a Fourier transform infrared spectrometer. The observed electronic spectrum encompasses rich vibrational spectra corresponding to the π→π* valence transition in the 36,000–62,000 cm−1 region. Further, the 62000–90000 cm−1 region predominantly comprises of weak Rydberg transitions of the ns and np type riding on a broad continuum. Vertical excited states calculated using the TDDFT methodology give new insights into the interpretation of the valence and Rydberg transitions by corelating them with the observed spectral peaks and shifted benzene transitions. Excited electronic states of benzonitrile are classified as local excitations and /or charge transfer excitations from the percentage contributions predicted with the aid of quantum chemical calculations. A reinvestigation of the titled compound with quantum chemical calculations using DFT methodology predict the equilibrium geometry and ground state vibrational modes, while normal coordinate analysis establishes a good agreement with the observed molecular vibrations. Theoretically generated potential energy curves of low lying excited states provide additional insights into UV spectral features, photodissociation dynamics for formation of C5H5• and CN• radicals and could establish the identity of the hidden (dark) state postulated in an earlier work. For the first time, a comprehensive study of benzonitrile in the IR and UV-VUV regions is summarized in this paper.

BODIPY-Based Polymers of Intrinsic Microporosity for the Photocatalytic Detoxification of a Chemical Threat.

Effective heterogeneous photocatalysts capable of detoxifying chemical threats in practical settings must exhibit outstanding device integrity. We report a copolymerization that yields robust, porous, processible, chromophoric BODIPY (BDP; boron-dipyrromethene)-containing polymers of intrinsic microporosity (BDP-PIMs). Installation of a pentafluorophenyl at the meso position of a BDP produced reactive monomer that when combined with 5,5,6,6-tetrahydroxy-3,3,3,3-tetramethyl-1,1-spirobisindane (TTSBI) and tetrafluoroterephthalonitrile (TFTPN) yields PIM-1. Postsynthetic modification of these polymers yields Br-BDP-PIM-1a and -1b─polymers containing bromine at the 2,6-positions. Remarkably, the brominated polymers display porosity and processability features similar to those of H-BDP-PIMs. Gas adsorption reveals molecular-scale porosity and Brunette-Emmet-Teller surface areas as high as 680 m2 g-1. Electronic absorption spectra reveal charge-transfer (CT) bands centered at 660 nm, while bands arising from local excitations, LE, of BDP and TFTPN units are at 530 and 430 nm, respectively. Fluorescence spectra of the polymers reveal a Förster resonance energy-transfer (FRET) pathway to BDP units when TFTPN units are excited at 430 nm; weak phosphorescence at room temperature indicates a singlet-to-triplet intersystem crossing. The low-lying triplet state is well positioned energetically to sensitize the conversion of ground-state (triplet) molecular oxygen to electronically excited singlet oxygen. Photosensitization capabilities of these polymers toward singlet-oxygen-driven detoxification of a sulfur-mustard simulant 2-chloroethyl ethyl sulfide (CEES) have been examined. While excitation of CT and LEBDP bands yields weak catalytic activity (t1/2 > 15 min), excitation to higher energy states of TFTPN induces significant increases in photoactivity (t1/2 ≅ 5 min). The increase is attributable to (i) enhanced light collection, (ii) FRET between TFTPN and BDP, (iii) the presence of heavy atoms (bromine) having large spin-orbit coupling energies that can facilitate intersystem crossing from donor-acceptor CT-, FRET-, or LE-generated BDP singlet states to BDP-related triplet states, and (iv) polymer triplet excited-state sensitization of the formation of CEES-reactive, singlet oxygen.

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.

Charge Transfer-Mediated Dramatic Enhancement of Raman Scattering upon Molecular Point Contact Formation.

Charge-transfer enhancement of Raman scattering plays a crucial role in current-carrying molecular junctions. However, the microscopic mechanism of light scattering in such nonequilibrium systems is still imperfectly understood. Here, using low-temperature tip-enhanced Raman spectroscopy (TERS), we investigate how Raman scattering evolves as a function of the gap distance in the single C60-molecule junction consisting of an Ag tip and various metal surfaces. Precise gap-distance control allows the examination of two distinct transport regimes, namely tunneling regime and molecular point contact (MPC). Simultaneous measurement of TERS and the electric current in scanning tunneling microscopy shows that the MPC formation results in dramatic Raman enhancement that enables one to observe the vibrations undetectable in the tunneling regime. This enhancement is found to commonly occur not only for coinage but also transition metal substrates. We suggest that the characteristic enhancement upon the MPC formation is rationalized by charge-transfer excitation.

Polycyclic Aromatic Hydrocarbons (PAHs) in Interstellar Ices: A Computational Study into How the Ice Matrix Influences the Ionic State of PAH Photoproducts.

It has been experimentally observed that water–ice-embedded polycyclic aromatic hydrocarbons (PAHs) form radical cations when exposed to vacuum UV irradiation, whereas ammonia-embedded PAHs lead to the formation of radical anions. In this study, we explain this phenomenon by investigating the fundamental electronic differences between water and ammonia, the implications of these differences on the PAH–water and PAH–ammonia interaction, and the possible ionization pathways in these complexes using density functional theory (DFT) computations. In the framework of the Kohn–Sham molecular orbital (MO) theory, we show that the ionic state of the PAH photoproducts results from the degree of occupied–occupied MO mixing between the PAHs and the matrix molecules. When interacting with the PAH, the lone pair-type highest occupied molecular orbital (HOMO) of water has poor orbital overlap and is too low in energy to mix with the filled π-orbitals of the PAH. As the lone-pair HOMO of ammonia is significantly higher in energy and has better overlap with filled π-orbitals of the PAH, the subsequent Pauli repulsion leads to mixed MOs with both PAH and ammonia character. By time-dependent DFT calculations, we demonstrate that the formation of mixed PAH–ammonia MOs opens alternative charge-transfer excitation pathways as now electronic density from ammonia can be transferred to unoccupied PAH levels, yielding anionic PAHs. As this pathway is much less available for water-embedded PAHs, charge transfer mainly occurs from localized PAH MOs to mixed PAH–water virtual levels, leading to cationic PAHs.

Charge-Transfer Excitation within a Hybrid-(G)KS Framework through Cartesian Grid DFT.

Organic molecules that exhibit charge-transfer (CT) excited states are known to play an important role in processes linked to electron transfer properties and molecular conductance. In this article, we present a simple technique based on "Becke's excitation theorem" that offers an accurate picture of these electronic states. It expresses the correlated energy splitting between triplet and its corresponding singlet states by a two-electron integral, which is numerically evaluated by our recently developed strategy on Cartesian grid. We first examine the consistency of our adopted numerical strategy to evaluate the integral with the original prescribed technique. Then we assess the method on weakly bound CT complexes with three different functionals (BLYP, B3LYP, and LC-BLYP). The accuracy on asymptotic limit of CT excitation is also explored. Finally in order to illustrate the strength and feasibility, it is further extended to a few "challenging" molecules. The method, when employed with hybrid B3LYP functional, turns out to be quite accurate to describe CT excitation energy.

Role of the Backbone when Optimizing Functional Groups─A Theoretical Study Based on an Improved Inverse-Design Approach.

We present an improved inverse-design approach for automatically identifying molecular (or other) systems with optimal values for prechosen properties. The new approach uses SMILES (simplified molecular input line entry system) to describe molecular structures efficiently, a genetic algorithm to optimize the molecules automatically, and the DFTB+ (self-consistent charge density functional tight-binding) method to calculate electronic properties. Thereby, almost every class of materials─even macromolecules or monomers─can be studied easily. Without crossover operators but with only mutation operators, the genetic algorithm is more adaptive to SMILES while keeping its efficiency. DFTB+ is more accurate than the DFTB method used in our previous inverse-design approach for the study of excited states and charge transfer processes. The improved approach is applied to optimize benzene, pyridine, pyridazine, pyrimidine, and pyrazine derivatives for seven electronic properties, which all are highly relevant and important for the performance of molecules in solar cells. We found that for some electronic properties, the precise composition and structure of the backbone have remarkable impacts on the value of the electronic properties and/or on the set of functional groups that leads to the best performance. On the contrary, for other properties, these effects are less pronounced. The reasonable optimal functional groups and/or substitution patterns are reported.

Solvent Effect on the Excited Charge Transfer State of Naphthylamine Sulfonate Derivatives: Steady State and Time resolved studies

Solvent Effect on the Excited Charge Transfer State of Naphthylamine Sulfonate Derivatives: Steady State and Time resolved studies

Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation

The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the exciton states of molecular aggregates, and it has been shown to provide reliable results when coupled with the appropriate choice of the functional. Here we apply a general procedure to analyze the aggregates’ exciton states derived from TDDFT calculations in terms of diabatic states chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space. We apply the approach to study energy profiles, interstate couplings, and the charge-transfer character of singlet and triplet exciton states of perylene di-imide aggregates (PDI). We focus on the intermolecular displacement along the longitudinal translation coordinate, which mimics different amounts of slip-stacking observed in PDI crystals. The analysis, in terms of symmetry-adapted Frenkel excitations (FE) and charge-resonance (CR) states and their interactions, discloses how the interchange of the H/J character for small longitudinal shifts, previously reported for singlet exciton states, also occurs for triplet excitons.

LibSC: Library for Scaling Correction Methods in Density Functional Theory.

In recent years, a series of scaling correction (SC) methods have been developed in the Yang laboratory to reduce and eliminate the delocalization error, which is an intrinsic and systematic error existing in conventional density functional approximations (DFAs) within density functional theory (DFT). On the basis of extensive numerical results, the SC methods have been demonstrated to be capable of reducing the delocalization error effectively and producing accurate descriptions for many critical and challenging problems, including the fundamental gap, photoemission spectroscopy, charge transfer excitations, and polarizability. In the development of SC methods, the SC methods were mainly implemented in the QM4D package that was developed in the Yang laboratory for research development. The heavy dependency on the QM4D package hinders the SC methods from access by researchers for broad applications. In this work, we developed a reliable and efficient implementation, LibSC, for the global scaling correction (GSC) method and the localized orbital scaling correction (LOSC) method. LibSC will serve as a lightweight and open-source library that can be easily accessed by the quantum chemistry community. The implementation of LibSC is carefully modularized to provide the essential functionalities for conducting calculations of the SC methods. In addition, LibSC provides simple and consistent interfaces to support multiple popular programing languages, including C, C++, and Python. In addition to the development of the library, we also integrated LibSC with two popular and open-source quantum chemistry packages, the Psi4 package and the PySCF package, which provides immediate access for general users to perform calculations with SC methods.

Tunable Conductance of MoS2 and WS2 Quantum Dots by Electron Transfer with Redox-Active Quinone.

Due to their uniqueness in tunable photophysics, transition metal dichalcogenide (TMD) based quantum dots (QDs) have emerged as the next-generation quantum materials for technology-based semiconductor applications. This demands frontline research on the rational synthesis of the TMD QDs with controlled shape, size, nature of charge migration at the interface, and their easy integration in optoelectronic devices. In this article, with a controlled solution-processed synthesis of MoS2 and WS2 QDs, we demonstrate the disparity in their structural, optical, and electrical characteristics in bulk and confinement. With a series of steady-state and time-resolved spectroscopic measurements in different media, we explore the uncommon photophysics of MoS2 and WS2 QDs such as excitation-dependent photoluminescence and assess their excited state charge transfer kinetics with a redox-active biomolecule, menadione (MQ). In comparison to the homogeneous aqueous medium, photoinduced charge transfer between the QDs and MQ becomes more plausible in encapsulated cetyltrimethylammonium bromide (CTAB) micelles. Current sensing atomic force microscopy (CS-AFM) measurements at a single molecular level reveal that the facilitated charge transfer of QDs with MQ strongly correlates with an enhancement in their charge transport behavior. An increase in charge transport further depends on the density of states of the QDs directing a change in Schottky emission to Fowler-Nordheim (FN) type of tunneling across the metal-QD-metal junction. The selective response of the TMD QDs while in proximity to external molecules can be used to design advanced optoelectronic devices and applications involving rectifiers and tunnel diodes for future quantum technology.