A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules

Adiabatic-Molecular Dynamics Generalized Vertical Hessian Approach: A Mixed Quantum Classical Method To Compute Electronic Spectra of Flexible Molecules in the Condensed Phase

We present a general mixed quantum classical method that couples classical molecular dynamics (MD) and vibronic models to compute the shape of electronic spectra of flexible molecules in the condensed phase without, in principle, any phenomenological broadening. It is based on a partition of the nuclear motions of the solute + solvent system in "soft" and "stiff" vibrational modes and an adiabatic hypothesis that assumes that stiff modes are much faster than soft ones. In this framework, the spectrum is rigorously expressed as a conformational integral of quantum vibronic spectra along the stiff coordinates only. Soft modes enter at the classical level through the conformational distribution that is sampled with classical MD runs. In each configuration, reduced-dimensionality quadratic Hamiltonians are built in the space of the stiff coordinates only, thanks to a generalization of the Vertical Hessian harmonic model and an iterative application of projectors in internal coordinates to remove soft modes. Quantum vibronic spectra, specific for each sampled configuration of the soft coordinates, are then computed at the desired temperature with efficient time-dependent techniques, and the global spectrum simply arises from their average. For consistency of the whole procedure, classical MD runs are performed with quantum-mechanically derived force fields, parameterized at the same level of theory selected for generating the quadratic Hamiltonians along the stiff coordinates. Application to N-methyl-6-oxyquinolinium betaine in water, dithiophene in ethanol, and cyanidine in water is presented to show the performance of the method.

Quantum algorithm for simulating molecular vibrational excitations

We introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. The algorithm is used to simulate vibrational excitations of pyrrole and butane during photochemical and mechanochemical excitations.

Boosting the hole transport of conductive polymers by regulating the ion ratio in ionic liquid additives

Poly(3,4-ethylenedioxythiophene) (PEDOT) has aroused great interest in organic electrics because of its high electrical conductivity and mechanical flexibility.

Role of specific solute–solvent interactions on the photophysical properties of distyryl substituted BODIPY derivatives

The role played by specific solute–solvent interactions on the spectroscopic properties of experimentally available BODIPY derivatives has been investigated.

Strong optical response and light emission from a monolayer molecular crystal

Excitons in two-dimensional (2D) materials are tightly bound and exhibit rich physics. So far, the optical excitations in 2D semiconductors are dominated by Wannier-Mott excitons, but molecular systems can host Frenkel excitons (FE) with unique properties. Here, we report a strong optical response in a class of monolayer molecular J-aggregates. The exciton exhibits giant oscillator strength and absorption (over 30% for monolayer) at resonance, as well as photoluminescence quantum yield in the range of 60–100%. We observe evidence of superradiance (including increased oscillator strength, bathochromic shift, reduced linewidth and lifetime) at room-temperature and more progressively towards low temperature. These unique properties only exist in monolayer owing to the large unscreened dipole interactions and suppression of charge-transfer processes. Finally, we demonstrate light-emitting devices with the monolayer J-aggregate. The intrinsic device speed could be beyond 30 GHz, which is promising for next-generation ultrafast on-chip optical communications.

The optical response of inorganic two-dimensional semiconductors is dominated by Wannier-Mott excitons, but molecular systems can host localised Frenkel excitons. Here, the authors report strong optical response in a class of monolayer molecular J-aggregates due to the coherent Coulomb interaction between localised Frenkel excitons.

Theoretical study and experimental validation on the optical emission processes in "free" and "locked" pyrazine derivatives

The excited-state properties of the "free" and "locked" pyrazine derivatives are investigated in solution. DCFP with "free" phenyls is theoretically calculated to be non-emissive due to the non-radiative energy dissipation through strong Duschinsky rotation effect, in agreement with the available experimental result. Surprisingly, DCBP with "bi-locked" phenyls is also calculated to be nonluminous. The emission of DCAP with "conjoined" architecture is predicted to be weaker than DCPP with "single-locked" phenyls, quite contrary to our intuition but further validated by the experimental measurement. The construction of four-, five- and six-membered ring respectively in DCBP, DCAP and DCPP is found to be the major structural origin for the descending relaxation energy in these "locked" systems, thus giving rise to the ascending luminescence order. Our work not only provides strategy for the molecular design of efficient organic light-emitting materials, but also offers valuable insight into the aggregation-induced emission phenomena.

Strategy for tuning the up-conversion intersystem crossing rates in a series of organic light-emitting diodes emitters relevant for thermally activated delayed fluorescence

Accurate prediction on the up-conversion intersystem crossing rate (k_UISC) is a critical issue for the molecular design of an efficient thermally activated delayed fluorescence (TADF) emitter, and the k_UISC rate is considered to be mainly determined by the spin-orbit coupling matrix element (SOCME) and the singlet-triplet energy difference (∆E_ST). In the present contribution, we strategically designed a series of organic molecules, bearing an isoindole-dione core as the electron acceptor (A) unit and dinitrocarbazolyl, carbazolyl, diphenylcarbazolyl, dicarbazolyl and tercarbazolyl groups as the electron donor (D) units, respectively. Their SOCME and ∆E_ST values between the S₁ and T₁ states were calculated by the DFT and TD-DFT methodes, and the k_UISC rates were estimated by using the semiclassical Marcus theory. The present studies indicate that as the π-conjugation in the D unit enhances, the ∆E_ST value gradually decreases, and the k_UISC rate gradually increases. The molecule using tercarbazolyl as the D moiety is found to exhibit the largest k_UISC in the present computations, as high as 1.22 × 10⁶ s^-1, which is of the same order of magnitude as an experimentally observed highly-efficient TADF emitter using a 4-benzoylpyridine as the A unit and the same tercarbazolyl group as the D moiety. The present results sufficiently prove the necessity of introducing strong electron-rich substituent groups when designing highly efficient TADF emitters.

p-Doped Conducting Polyelectrolyte as an Anode Interlayer Enables High Efficiency for 1 cm2 Printed Organic Solar Cells

Manufacturing large-area devices through a low-cost and large batch printing technique is the key to the commercialization of organic solar cells (OSCs). However, the lack of printable anode interlayer (AIL) materials severely impedes the development of high-efficiency printed OSCs. Herein, we synthesize three p-type self-doped conjugated polyelectrolytes (CPEs), namely, PCP-B, PCP-2B, and PCP-3B, as printable AIL materials for fabricating high-performance and large-area OSCs. By increasing the number of benzene units in the polymer backbone, the work function of the CPEs was enhanced from 4.57 to 5.01 eV, and the optical transparency was also improved because of the enlarged polymer band gap. The improved photoelectronic properties as well as a good film-forming capacity make the PCP-3B an ideal AIL material to be processed by the printing technique. By using PCP-3B, a 1 cm² printed device was fabricated in which all the functional layers, including the AIL, active layer, and cathode interlayer were processed by blade-coating, achieving a power conversion efficiency (PCE) of 9.67%. The PCE belongs to the highest efficiency at present for printable large-area OSCs, showing a promising prospect for the OSC mass production.

Molecular Dynamics of Excited State Intramolecular Charge Transfer in Solution by Coherent Nuclear Wave Packets

Revealing a proper reaction coordinate in a chemical reaction is the key step towards elucidation of the molecular reaction dynamics. In this report, we investigated the dynamics of intramolecular charge transfer (ICT) of 8-aminopyrene-1,3,6-trisulfonic acid (APTS) occurring in the excited state by time-resolved fluorescence (TF) and TF spectra. Accurate reaction rates and rate-dependent nuclear wave packets in the product state allow detailed investigation of the molecular reaction dynamics. The ICT rate is solvent dependent: (34 fs)^-1 , (87 fs)^-1 , and (∞)^-1 in water, formamide, and dimethylformamide, respectively. By recording spectra of the nuclear wave packets for different reaction rates, chemical species responsible for the emission spectra can be positively identified. The origin of the wave packets can be deduced from the amplitude change of the wave packets at different reaction rates, and the vibrational modes that are associated with the reaction coordinate could be identified. Theoretical calculations of the vibrational reorganization energies reproduce the experimental spectrum of the nuclear wave packets and corroborate the conclusions.

Theoretical Investigations into the Electron and Ambipolar Transport Properties of Anthracene-Based Derivatives

To obtain anthracene-based derivatives with electron transport behavior, two series of anthracene-based derivatives modified by trifluoromethyl groups (-CF₃) and cyano groups (-CN) at the 9,10-positions of the anthracene core were studied. Their electronic structures and crystal packings were also analyzed and compared. The charge-carrier mobilities were evaluated by quantum nuclear tunneling theory based on the incoherent charge-hopping model. Our results suggest that introducing -CN groups at 9,10-positions of the anthracene core is more favorable than introducing -CF₃ to maintain great planar rigidity of the anthracene skeleton, decreasing more lowest unoccupied molecular orbital energy levels (0.45-0.55 eV), reducing reorganization energies, and especially forming a tight packing motif. Eventually, the excellent electron transport materials could be obtained. The molecule 1-B in Series 1 containing -CF₃ groups is an ambipolar organic semiconductor (OSC) material with a 2D transport network, and its value of μ_h-max/μ_e-max is 1.75/0.47 cm² V^-1 s^-1 along different directions; 2-A and 2-C in Series 2 with -CN groups are excellent n-type OSC candidates with the maximum intrinsic mobilities of 3.74 and 2.69 cm² V^-1 s^-1 along the π-π stacking direction, respectively. Besides, the Hirshfeld surface and quantum theory of atoms in molecules analyses were applied to reveal the relationship between noncovalent interactions and crystal stacking.

Regulating vibrational modes to improve quantum efficiency: insights from theoretical calculations on iridium(iii) complexes bearing tridentate NCN and NNC chelates

We reported a theoretical study on [(NCN)Ir(iii)(NNC)]+ tridentate Ir(iii) complexes for organic light-emitting diode (OLED) applications. With appropriate chemical modifications onto the NCN ligand of [(NCN)Ir(iii)(NNC)]+, several rotational and stretching vibration modes were weakened or even eliminated, resulting in a weaker vibrational coupling between the emissive state and the ground state, therefore slowing down the non-radiative decay process, ultimately improving the quantum efficiency. We hope that these theoretical studies and the semi-quantitative prediction on phosphorescence efficiency could provide inspiration for the design of highly efficient phosphorescent materials.

Singlet/triplet exciton dissociation and charge recombination in donor-acceptor ThQs-C60 /PDIxCN2 complexes

The donor-acceptor interface plays a critically important role in determining the power conversion efficiency of organic solar cells via controlling charge separation (CS) and recombination (CR) processes. Here, we combine the electronic structure calculations with electron transfer rate theory to clarify the CS and CR processes in ThQs-C₆₀ /PDIxCN₂ donor-acceptor complexes. The results reveal that in ThQs-PDIxCN₂ the CS comes from both the dissociations of photo-induced singlet exciton and singlet fission-induced triplet exciton with a high efficiency, whereas in ThQs-C₆₀ only the singlet exciton dissociation can take place because the triplet exciton lies below the charge-transfer exciton. However, very high CR rates in ThQs-PDIxCN₂ obliterate the benefit of fast CS, inversely leading to the ThQ-C₆₀ complex with a better cell efficiency. The present results are consistent with experimental observation and may furnish a possible patten to improve the overall conversion efficiency. © 2018 Wiley Periodicals, Inc.

Excited State Frequencies of Chlorophyll f and Chlorophyll a and Evaluation of Displacement through Franck-Condon Progression Calculations

We present ground and excited state frequency calculations of the recently discovered extremely red-shifted chlorophyll f. We discuss the experimentally available vibrational mode assignments of chlorophyll f and chlorophyll a which are characterised by particularly large downshifts of 13¹-keto mode in the excited state. The accuracy of excited state frequencies and their displacements are evaluated by the construction of Franck–Condon (FC) and Herzberg–Teller (HT) progressions at the CAM-B3LYP/6-31G(d) level. Results show that while CAM-B3LYP results are improved relative to B3LYP calculations, the displacements and downshifts of high-frequency modes are underestimated still, and that the progressions calculated for low temperature are dominated by low-frequency modes rather than fingerprint modes that are Resonant Raman active.

Structural and Electronic Origin of Bis-Lactam-Based High-Performance Organic Thin-Film Transistors

We describe herein the comprehensive theoretical and experimental studies on the transistor mobility of organic semiconductors by correlating a two-dimensional (2D) intermolecular interaction with thin-film morphology and the electronic coupling structure. We developed a novel bis-lactam-based small molecule, 1,5-dioctyl-3,7-di(thiophen-2-yl)-1,5-naphthyridine-2,6-dione (C8-NTDT), with a 2D-type C-H···O═C intermolecular interaction along the in-plane directions of the crystal packing structure, which is characteristically different from the one-dimensional-type intermolecular interaction shown in the typical bis-lactam molecule of 2,5-dioctyl-3,6-di(thiophen-2-yl)pyrrolo[3,4- c]pyrrole-1,4-dione (C8-DPPT). Experimentally and theoretically, C8-NTDT exhibited more favorable thin-film morphology and an electronic coupling structure for charge transport because of its unique 2D intermolecular interactions compared with C8-DPPT. In fact, C8-NTDT exhibited a hole mobility of up to 1.29 cm² V^-1 s^-1 and an on/off ratio of 10⁷ in a vacuum-processed device. Moreover, the high solubility with the 2D electronic coupling structure of C8-NTDT enables versatile solution processing for device fabrication without performance degradation compared to the vacuum-processed device. As an example, we could demonstrate a hole mobility of up to 1.10 cm² V^-1 s^-1 for the spin-coated devices, which is one of the best performances among the solution-processed organic field-effect transistors based on bis-lactam-containing small molecules.

Revealing the mechanism of contrasting charge transport properties for phenyl and thienyl substituent organic semiconductors

The aromatic substituents such as phenyl and thienyl have a direct impact on the structure-property relationship of conjugated semiconducting molecules and thus play a significant role in determining the performance of organic thin film transistors (OTFTs). To design a molecule with good charge transport properties, it is essential to understand the charge transfer process. Herein, through the study of two groups of classical OTFT materials with different substituents, we demonstrate the fundamental reasons for the contrasting carrier mobilities between the materials in each group by means of DFT calculations. The results from our theoretical analysis on the two groups of molecules provide very good estimates of their charge transfer properties and the numerical trend from our calculation is consistent with that from the corresponding experimental results. We reveal in detail the impacts of the subtle geometric differences caused by different substituents from two aspects including (i) the significant influence of steric hindrance on reorganization energy and (ii) the overlap of the adjacent molecular orbitals (MOs) on electron coupling. Overall, our systematic investigation into the charge transfer mechanism and geometry effects allows us to employ a reliable theoretical methodology for the prediction of the material performance, which is crucial for the design of high performance OTFT materials.

Effect of intermolecular interaction on excited-state properties of thermally activated delayed fluorescence molecules in solid phase: A QM/MM study

Recently, thermally activated delayed fluorescence (TADF) molecules have attracted great attention since nearly 100% exciton usage efficiency was obtained in TADF molecules. Most TADF molecules used in organic light-emitting diodes are in aggregation state, so it is necessary to make out the intermolecular interaction on their photophysical properties. In this work, the excited-state properties of the molecule AI-Cz in solid phase are theoretically studied by the combined quantum mechanics and molecular mechanics (QM/MM) method. Our results show that geometry changes between the ground state (S₀) and the first singlet excited state (S₁) are limited due to the intermolecular π-π and CH-π interactions. The energy gap between S₁ and the first triplet excited state is broadened and the transition properties of excited states are changed. Moreover, the Huang-Rhys factors and the reorganization energy between S₀ and S₁ are decreased in solid phase, because the vibration modes and rotations are hindered by intermolecular interaction. The non-radiative rate has a large decrease in solid phase which improves the light-emitting performance of the molecule. Our calculation provides a reasonable explanation for experimental measurements and highlights the effect of intermolecular interaction on excited-states properties of TADF molecules.

Cd(II) enhanced fluorescence and Zn(II) quenched fluorescence with phenylenevinylene terpyridine: A theoretical investigation

Phenylenevinylene terpyridine (mepvpt) shows chelation enhanced fluorescence (CHEF) with Cd(II) and chelation quenched fluorescence (CHQF) with Zn(II), respectively. To understand the behaviors, we studied their intrinsic optical properties using DFT/TDDFT methods. The results show that fluorescence quantum yields (FQY) of mepvpt, mepvpt-Cd and mepvpt-Zn are low due to high ISC rates from higher excited states rather than the S₁ excited state. When mepvpt chelates Cd(II), the molecular structure becomes more planar and S_3,4 → S₀ radiation rates become higher than that of mepvpt, which results in CHEF. When mepvpt chelates Zn(II), a new S₄ → S₀ emission with low oscillator strength occurs and high S₄ → T_n ISC rates appear, which leads to CHQF. This proposed mechanism of metal fluorescence enhancing/quenching suggests a design strategy for single-molecular multi-analyte sensors.

A novel structure of grid spirofluorene: a new organic semiconductor with low reorganization energy

The lower charge mobility of organic semiconductors relative to that of inorganic semiconductors is a thorny problem that still has not been resolved.

Theoretical study on the light-emitting mechanism of circularly polarized luminescence molecules with both thermally activated delayed fluorescence and aggregation-induced emission

The light-emitting mechanism of circularly polarized luminescence molecules with both TADF and AIE.

Theoretical study of synergetic effect between halogenation and pyrazine substitutions on transport properties of silylethynylated pentacene

Combining quantum-tunneling-effect-enabled hopping theory with kinetic Monte Carlo simulation and dynamic disorder effects, the charge transport properties of a series of N-hetero 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-PEN) derivatives with halogen substitutions were studied.

Unraveling the marked differences of the phosphorescence efficiencies of blue-emitting iridium complexes with isomerized phenyltriazole ligands

Quantum chemical insights into the marked quantum efficiencies of blue-emitting iridium complexes with isomerized ptz ligands.

Theoretical investigations of the substituent effect on the electronic and charge transport properties of butterfly molecules

Introducing different substituents into the pyrene core leads to different crystal packing motifs, and the charge carrier mobility can be effectively modulated by the introduction of electron-donating and electron-withdrawing groups.

The influence of external electric fields on charge reorganization energy in organic semiconductors

Charge reorganization energies (λ) of inter-ring carbon–carbon (IRCC) bond connected conjugated polycyclics are shown to exhibit an electric-field-driven anisotropic character.

Time-Dependent Formulation of Resonance Raman Optical Activity Spectroscopy

In this work, we extend the theoretical framework recently developed for the simulation of resonance Raman (RR) spectra of medium-to-large sized systems to its chiral counterpart, namely, resonance Raman optical activity (RROA). The theory is based on a time-dependent (TD) formulation, with the transition tensors obtained as half-Fourier transforms of the appropriate cross-correlation functions. The implementation has been kept as general as possible, supporting adiabatic and vertical models for the PES representation, both in Cartesian and internal coordinates, with the possible inclusion of Herzberg-Teller (HT) effects. Thanks to the integration of this TD-RROA procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects can be included in an effective way. The implementation is validated on one of the smallest chiral molecule (methyloxirane). Practical applications are illustrated with three medium-size organic molecules (naproxen-OCD₃, quinidine and 2-Br-hexahelicene), whose simulated spectra are compared to the corresponding experimental data.

A computational study of the vibrationally-resolved electronic circular dichroism spectra of single-chain transoid and cisoid oligothiophenes in chiral conformations

We simulate the vibronic profile of the electronic circular dichroism (ECD) spectra of oligothiophenes in cisoid and transoid chiral arrangements. We consider oligomers of different lengths, from two to fifteen units, and investigate extensively how the ECD spectral shapes depend on the inter-ring torsions. In general, the molecular structures we consider are not stationary points of the ground state potential energy surface. Therefore, in order to perform vibronic calculations, we present a new computational protocol able to define reduced-dimensionality models where the effect of the off-equilibrium modes is removed. This is done adopting a description of the vibrational motions in curvilinear internal coordinates, and vertical harmonic models coupled with an iterative application of projectors to define energy Hessians, and therefore effective normal modes, in the space complementary to the one of the off-equilibrium coordinates. Although we consider both Franck-Condon and Herzberg-Teller contributions, the results show that transoid twisted ribbons always give rise to monosignated ECD spectra, while bi-signated and multi-signated spectra are expected for cisoid helices. These findings are explained on the basis of the different transition strengths of the lowest electronic states imparted by the different spatial arrangement, that is almost linear for transoid structures and more globular for cisoid ones. We predicted the chiroptical response of a large number of possible molecular arrangements. These data are employed to critically discuss the experimental ECD of polythiophenes in different experimental conditions, forming either aggregates or host-guest complexes. The method here proposed to perform vibronic calculations in reduced-dimensionality models is of general applicability and its potential interest goes beyond the practical application presented here.

Intramolecular Vibrations Complement the Robustness of Primary Charge Separation in a Dimer Model of the Photosystem II Reaction Center

The energy conversion of oxygenic photosynthesis is triggered by primary charge separation in proteins at the photosystem II reaction center. Here, we investigate the impacts of the protein environment and intramolecular vibrations on primary charge separation at the photosystem II reaction center. This is accomplished by combining the quantum dynamic theories of condensed phase electron transfer with quantum chemical calculations to evaluate the vibrational Huang-Rhys factors of chlorophyll and pheophytin molecules. We report that individual vibrational modes play a minor role in promoting charge separation, contrary to the discussion in recent publications. Nevertheless, these small contributions accumulate to considerably influence the charge separation rate, resulting in subpicosecond charge separation almost independent of the driving force and temperature. We suggest that the intramolecular vibrations complement the robustness of the charge separation in the photosystem II reaction center against the inherently large static disorder of the involved electronic energies.

Excited-state vibrational dynamics toward the polaron in methylammonium lead iodide perovskite

Hybrid organic–inorganic perovskites have attractive optoelectronic properties including exceptional solar cell performance. The improved properties of perovskites have been attributed to polaronic effects involving stabilization of localized charge character by structural deformations and polarizations. Here we examine the Pb–I structural dynamics leading to polaron formation in methylammonium lead iodide perovskite by transient absorption, time-domain Raman spectroscopy, and density functional theory. Methylammonium lead iodide perovskite exhibits excited-state coherent nuclear wave packets oscillating at ~20, ~43, and ~75 cm⁻¹ which involve skeletal bending, in-plane bending, and c-axis stretching of the I–Pb–I bonds, respectively. The amplitudes of these wave packet motions report on the magnitude of the excited-state structural changes, in particular, the formation of a bent and elongated octahedral PbI₆⁴⁻ geometry. We have predicted the excited-state geometry and structural changes between the neutral and polaron states using a normal-mode projection method, which supports and rationalizes the experimental results. This study reveals the polaron formation via nuclear dynamics that may be important for efficient charge separation.

Elucidating electron-phonon coupling in hybrid organic-inorganic perovskites may help us to understand the high photovoltaic efficiency. Here, the authors observe low-frequency Raman modes and related nuclear displacements of the Pb–I framework, indicating how these vibrational motions lead to polaron formation in perovskites.

Molecular quantum cellular automata cell design trade-offs: latching vs. power dissipation

The use of molecules to enact quantum cellular automata (QCA) cells has been proposed as a new way for performing electronic logic operations at sub-nm dimensions. A key question that arises concerns whether chemical or physical processes are to be exploited. The use of chemical reactions allows the state of a switch element to be latched in molecular form, making the output of a cell independent of its inputs, but costs energy to do the reaction. Alternatively, if purely electronic polarization is manipulated then no internal latching occurs, but no power is dissipated provided the fields from the inputs change slowly compared to the molecular response times. How these scenarios pan out is discussed by considering calculated properties of the 1,4-diallylbutane cation, a species often used as a paradigm for molecular electronic switching. Utilized are results from different calculation approaches that depict the ion either as a charge-localized mixed-valence compound functioning as a bistable switch, or else as an extremely polarizable molecule with a delocalized electronic structure. Practical schemes for using molecular cells in QCA and other devices emerge.

On the theoretical prediction of fluorescence rates from first principles using the path integral approach

In this work, we present and implement the theory for calculating fluorescence rates and absorption and emission spectra from first principles, using the path integral approach. We discuss some approximations and modifications to the full set of equations that improve speed and numerical stability for the case when a large number of modes are considered. New methods to approximate the excited state potential energy surface are also discussed and it is shown that for most purposes, these can be used instead of a full geometry optimization to obtain the rates mentioned above. A few examples are presented and the overall performance of the method is discussed. It is shown that the rates and spectra computed in this way are well within the acceptable range of errors and can be used in future predictions, particularly for screening purposes, with the only limitation on size being that of the electronic structure calculation itself.