Long-range Corrected Density Functional Theory Research Articles

Unveiling the Nature of Chemical Bonds in Real Space.

Recent advent of diverse chemical entities necessitates a re-evaluation of chemical bond concepts, underscoring the importance of experimental evidence. Our prior study introduced a general methodology, termed Core Differential Fourier Synthesis (CDFS), for mapping the distribution of valence electron density (VED) in crystalline substances within real space. In this study, we directly compare the VED distributions obtained through CDFS with those derived from high-accuracy theoretical calculation using long-range corrected density functional theory, which quantitatively reproduces accurate orbital energies. This comparison serves to demonstrate the precision of the CDFS in replicating complex details. The VED patterns observed experimentally exhibited detailed structures and phases of wave functions indicative of sp3 hybrid orbitals, closely aligning with theoretical predictions. This alignment underscores the utility of our approach in gathering quantum chemical data experimentally, a crucial step for discussing the chemical properties, such as reaction mechanisms.

Impact of the alkyl side-chain length on solubility, interchain packing, and charge-transport properties of amorphous π-conjugated polymers

Increasing the length of alkyl side chains is a typical way to improve the solubility of π-conjugated polymers designed for use in solution-processed devices. However, these modifications have also been reported to alter the film morphology. Given that the mechanism leading to improved solubility is not well documented yet and the nanoscale (local) morphologies of amorphous π-conjugated polymer films are difficult to characterize experimentally, here, we combine molecular dynamics simulations and long-range corrected density functional theory calculations to examine at the molecular scale the impact that the alkyl side-chain length has on polymer solubility and film morphologies. As a representative example, we consider poly(thieno[3,4-c]pyrrole-4,6-dione-alt-3,4-difluorothiophene) (PTPD[2F]T) with two different lengths of the alkyl side chains on the thieno[3,4-c]pyrrole-4,6-dione (TPD) moieties, i.e., 2-hexyldecyl (2HD) and 2-decyltetradecyl (2DT). A detailed analysis of polymer–solvent and polymer–polymer interactions provides a picture that describes the underlying mechanism for improved solubility in going from 2HD to 2DT. We then underline an intrinsic characteristic that decreasing the side-chain length brings a greater extent of backbone planarity and lesser side chain-TPD interactions, which leads to higher interchain π-π packing density and order, while the interchain π-π packing patterns remain similar in the two films. These morphologies are discussed in terms of the charge-transport properties between neighboring PTPD[2F]T chains, which point to a higher electron mobility in the PTPD[2F]T films with shorter alkyl side chains. Overall, our findings offer guidance in the field of solution-processed electronic devices by pointing out that the polymer alkyl side-chain length could be minimized to improve carrier mobility while ensuring polymer solubility.

Long-range Corrected Density Functional Theory Including a Two-Gaussian Hartree-Fock Operator for High Accuracy Core-excitation Energy Calculations of Both the Second- and Third-Row Atoms (LC2gau-core-BOP).

In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree-Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.

Singlet Fission as the Gateway to Triplet Generation in Heavy Atom-Free Organic Molecules.

Triplet generations in heavy atom-free organic molecules are primarily revealed to proceed through singlet fissions (SFs) by investigating the contributions of SFs and intersystem crossings to the generation rates. The spin-flip long-range corrected time-dependent density functional theory calculations on 11 organic molecules known for triplet generation under photoirradiation are performed. The correlation between the descriptors for SF and the experimental singlet-to-triplet conversion rates strongly supports the predominance of SF progressions in all these molecules, corroborated by experimental observations of their triplet-triplet annihilations. Based on these findings, we propose updated conditions for SF progression: There is a high-absorption singlet state just above the triplet-triplet excitation of the chromophore dimer, or the singlet (triplet-triplet) excitation itself is responsible for photoabsorption. To the best of our knowledge, all organic molecules known for rapid triplet state generation fulfill these conditions.

Singlet fission initiating organic photosensitizations

The feasibility of singlet fission (SF) in organic photosensitizers is investigated through spin-flip long-range corrected time-dependent density functional theory. This study focuses on four major organic photosensitizer molecules: benzophenone, boron-dipyrromethene, methylene blue, and rose bengal. Calculations demonstrate that all these molecules possess moderate pi-stacking energies and closely-lying singlet (S) and quintet (triplet–triplet, TT) excitations, satisfying the essential conditions for SF: (1) Near-degenerate low-lying S and (TT) excitations with a significant S–T energy gap, and (2) Moderate pi-stacking energy of chromophores, slightly higher than solvation energy, enabling dissociation for triplet-state chromophore generation. Moreover, based on the El-Sayed rule, intersystem crossing is found to simultaneously proceed at very slow rates in all these photosensitizers. This is attributed to the fact that the lowest singlet excitation of the monomers partly involves npi ^* transitions alongside the main pi pi ^* transitions. The proposed mechanisms are strongly substantiated by comparisons with experimental studies.

Roles of Singlet Fission in the Photosensitization of Silicon Phthalocyanine.

The roles of singlet fission in the triplet generation of silicon phthalocyanine (SiPc), a compound analogous to the IRDye700DX photosensitizer used in near-infrared photoimmunotherapy, are investigated by considering the energetical relation between the excitations of this compound. These excitations are obtained through spin-flip long-range corrected time-dependent density functional theory calculations. To initiate singlet fission, chromophores must meet two conditions: (1) near-degenerate low-lying singlet and quintet (triplet-triplet) excitations with a considerable energy gap of the lowest singlet and triplet excited states and (2) moderate π-stacking energy of chromophores, which is higher than but not far from the solvation energy, to facilitate the dissociation and generation of triplet-state chromophores. The present calculations demonstrate that SiPc satisfies both of these conditions after the formation of π-stacking irrespective of the presence of an axial ligand(s), suggesting that singlet fission plays a crucial role in the triplet generation process, although intersystem crossing occurs simultaneously at a very slow rate.

Computational design of efficient corannulene-based Non-Fullerene acceptors for organic solar cells applications

In our study, we aimed to enhance the optoelectronic properties of corannulene through functionalization for use as a non-fullerene acceptor (NFA) in organic solar cells. To achieve this, we designed new corannulene derivatives by introducing various electron-donating and electron-withdrawing groups onto the corannulene core. Geometric, electronic, optical, and charge transport properties of newly designed molecules are analyzed using long-range corrected density functional theory methods. The potential NFA is identified by conducting extensive analysis, such as light absorption properties, ground-state dipole moments, and the energy difference between LUMO and LUMO+1 orbitals. Also, a model donor–acceptor interface is constructed by considering PTQ10 oligomer as the donor and corannulene derivatives as acceptors. Charge-transfer states and exciton dissociation processes are analyzed at the polymer chain and NFA interface. Overall, the results obtained from this study can provide useful guidance in designing high-performing NFAs.

Singlet fission initiating triplet generations of BODIPY derivatives through pi -stacking: a theoretical study

The role of singlet fission (SF) in the triplet-state generation mechanism of 1,3,5,7-tetramethyl-boron-dipyrromethene derivatives is revealed by exploring the cause for the solvent dependence of the generation rate. Comparing the adsorption energy calculations of solvent molecules, i.e., cyclohexane, chloroform and acetonitrile molecules, to the derivatives with the pi -stacking energies of these derivatives surprisingly show that the hierarchy of the solvation energies and pi -stacking energies strongly correlates with the experimentally-suggested solvent dependence of the triplet-state generation of these derivatives for five and more adsorbing solvent molecules. Following this finding, the excitation spectra of these derivatives in acetonitrile solvent are explored using the proprietary spin-flip long-range corrected time-dependent density functional theory. It is, consequently, confirmed that the pi -stacking activates the second lowest singlet excitation to trigger the spin-allowed transition to the singlet doubly-excited tetraradical (TT)_1 state, which generates the long-lived quintet (TT)_1 state causing the SF. However, it is also found that the pi -stacking also get a slow intersystem crossing active around the intersections of the lowest singlet excitations with the lowest triplet T_1 excitations in parallel with the SF due to the charge transfer characters of the lowest singlet excitations. These results suggest that SF initiates the triplet-state generations through near-degenerate low-lying singlet and (TT) excitations with a considerable singlet-triplet energy gap after the pi -stacking of chromophores stronger than but not far from the solvation. Since these derivatives are organic photosensitizers, this study proposes that SF should be taken into consideration in developing novel heavy atom-free organic photosensitizers, which will contribute to a variety of research fields such as medical care, photobiology, energy science, and synthetic chemistry.

Cyclo[18]carbon‐A new class of electron acceptor for organic solar cells applications

The all-carboatomic ring, cyclo[18]carbon (C18), has the potential to act as an electron acceptor due to promising electronic and optical properties. In this study, we first illustrated the geometrical, electronic, and excited-state properties of C18 using various hybrid and long-range corrected density functional theory (DFT) methods. Further, we studied the nature of intermolecular interactions between dimers of C18 to gain insights into packing configurations of cyclo[18] in dimer and trimer configurations. Also, using the state-of-the-art DFT methods, we have reported the thorough characterization of the lowest excited-state (i.e. charge-transfer state) in various donor-acceptor model complexes based on pentacene and C18. We established an interplay between the molecular packing of C18 and pentacene molecules on the energy of charge transfer state. All these results could help in the designing of more efficient organic solar cells.

Theoretical Protocol Based on Long-Range Corrected Density Functional Theory and Tuning of Range-Split Parameter for Two-Electron Two-Proton Reduction of Phenylazocarboxylates.

A theoretical protocol based on long-range corrected density functional theory is suggested for a highly accurate estimation of the two-electron two-proton (2e2p) reduction potential of ethyl 2-phenylazocarboxylate derivatives. Geometry optimization and single-point energy refinement with ωB97X-D are recommended. The impact of polarization and diffusion functions in the basis sets on the 2e2p reduction potential is discussed. Further improvements can be achieved by tuning the range-split parameter based on the linear relationship between the Hammett constant of phenyl substituents and the optimal ω value that most accurately reproduces the experiments. The suggested protocol can accurately predict the 2e2p reduction potential of five ethyl 2-phenylazocarboxylate derivatives. Based on these findings, 22 additional candidates are suggested to enlarge the electrochemical window and to increase the selectivity of 2e2p reactions. This study contributes to the development of a theoretical approach to accurately estimate the 2e2p reduction potential of azo groups.

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.

ANTIOXIDANT POTENTIAL OF EIGHT PHENOLIC ACIDS USING HIGH-PERFORMANCE DENSITY FUNCTIONAL THEORY

Phenolic acids are one of the major fractions identified in the extract of several vegetable seed oils which present interesting antioxidant properties. A density functional theory (DFT) study on the antioxidant potential of eight phenolic acids including gallic, vanillic, isovanillic, ferulic, caffeic, b-coumaric, cinnamic, and chlorogenic acids, is presented in this paper. The bond dissociation enthalpies (BDEs) of C–H and O–H bonds, the proton affinities (PA) and the ionization energies (IEs) were calculated in detail by using the LC-wPBE functional coupled with the 6-311++G(d,p) basis set. The standard Gibbs free energies (DrG0) for the scavenging reactions towards HOO· radical were calculated. In addition, the kinetics of H-atom transfer reaction was evaluated. As a result, the chosen long-range corrected DFT LC-wPBE functional is shown as the highly reliable computational approaches in calculating geometrical properties as well as the thermochemical parameters by comparison with CCSD(T)/aug-cc-pVDZ results. The differences of bond length are about 0.1 Angstroms, while the ones of BDE are only from 0.1 to 0.6 kcal/mol. Furthermore, gallic, caffeic, ferulic and chlorogenic acids represent as the most reactive antioxidants in the reaction with HOO· radical in water occurring via H transfer process with the negative DrG0 ranging from -3.3 kcal/mol for caffeic to -5.9 kcal/mol for ferulic compounds. Kinetic calculations in the gas phase based on transition state theory (TST) for the studied compound confirm that chlorogenic acid is shown as the most reactive antioxidant via HAT process with the lowest activation free energy (i.e. 17.9 kcal/mol) and the highest reaction rate (i.e. 4.20 × 10-19 cm3/molecule/s).

Pseudospectral implementations of long-range corrected density functional theory.

We have implemented pseudospectral density-functional theory (DFT) with long-range corrected DFT functionals (PS-LRC) in quantum mechanics package Jaguar, and applied it in the calculations of geometry optimizations, dimmer interaction energies, polarizabilities and first-order hyperpolarizabilities, harmonic vibrational frequencies, S1 and T1 excitation energies, singlet-triplet gaps, charge transfer numbers, oscillator strengths, reaction barrier heights, electron-transfer couplings, and charge-transfer excitation energies. From our accuracy benchmark analysis, PS grids, PS dealiasing functions, PS atomic corrections, PS multigrid strategy, PS length scales, and PS cutoff scheme perform well in PS DFT with LRC density functionals with very small and ignorable deviations when compared to the conventional spectral (CS) method. The timing benchmark study of S1 excitation energy calculations of fullerenes (Cn , n up to 540) demonstrates that PS-LRC achieves 1.4-8.4-fold speedups in SCF, 22-32-fold speedups in Tamm-Dancoff approximation, and 6-15-fold speedups in total wall clock time with an average error 0.004 eV of excitation energies compared to the CS method.

Organic Photovoltaics: Understanding the Preaggregation of Polymer Donors in Solution and Its Morphological Impact.

In bulk-heterojunction organic solar cells, it is well established that the active-layer morphology significantly impacts device performance. However, morphology control remains very challenging. An interesting step in that direction was recently provided by the development of polymer donors that display a temperature-dependent aggregation behavior in solution; the aggregation characteristics were found indeed to play a determining role in the eventual active-layer morphology. Here, a combination of thermodynamic analyses, molecular dynamics simulations, and long-range corrected density functional theory calculations enables us (i) to establish the Flory-Huggins interaction parameter, χ, as a useful figure of merit that allows us to integrate the contributions from all inter-related molecular interactions and to describe the extent of polymer preaggregation in solution at room temperature; (ii) to correlate the χ values for various polymer solutions to the extent of polymer aggregation and the morphological characteristics of the active layers; and (iii) to assess how polymer-polymer and polymer-solvent intermolecular interactions contribute to the variations in χ values among different polymer solutions. We have chosen to examine four representative polymer donors (PBT4T-2OD, PBTff4T-2OD, PffBT4T-2OD, and PffBTff4T-2DT) in solution in chlorobenzene or dichlorobenzene. With χ as a robust bridge, our results provide an unprecedented, detailed description of the relationships among intermolecular interactions, extent of polymer solution aggregation, and morphological features of the active layers.

Assessment of long-range corrected density functional theory on the absorption and vibrationally resolved fluorescence spectrum of carbon nanobelts.

Time-dependent (TD) density functional theory (DFT) and Franck-Condon Hertzberg-Teller (FCHT) calculations of various DFT functionals [B3LYP, CAM-B3LYP, ωB97XD, and optimally tuned (OT) long-range corrected (LC)-BLYP] were performed to examine how well DFT functionals can predict the experimental absorption and fluorescence spectra of a 12-carbon nanobelt (CNB). OT-LC-BLYP reproduced the experimental absorption spectrum well in terms of the peak position and intensity in the case of using a basis set with a diffuse function, such as 6-31+G(d,p) and 6-311+G(d,p), whereas B3LYP showed a red-shift in the peak positions and CAM-B3LYP and ωB97XD, which have a long-range HF exchange, showed blue shifts. Regarding the fluorescence spectrum calculations with FCHT using 6-311+G(d,p), the OT-LC-BLYP reproduced both the peak intensities and positions closest to the experimental spectrum. B3LYP, however, showed red-shifted peaks, and ωB97XD showed blue-shifted peaks. CAM-B3LYP provided less blue-shifted peaks, but the relative peak intensities mismatched the experimental ones. Furthermore, calculations of the absorption and vibrationally resolved fluorescence spectra of 16-CNB and 24-CNB using OT-LC-BLYP/6-311+G(d,p) showed absorption and fluorescence spectra close to the experimental spectra with high accuracy. Moreover, the application of a polarizable continuum model (dichloromethane) produced a red shift in the peak positions of the absorption spectrum with increasing intensity but an increase in the peak intensities of the fluorescence calculations without shifting the peak position.

Impact of secondary donor units on the excited-state properties and thermally activated delayed fluorescence (TADF) efficiency of pentacarbazole-benzonitrile emitters.

The performance of organic light-emitting diodes based on thermally activated delayed fluorescence emitters depends on the efficiency of reverse intersystem crossing (RISC) processes, which are promoted by a small energy gap between the lowest singlet (S1) and triplet (T1) excited states and large spin-orbit couplings. Recently, it was proposed that the introduction of secondary donor units into 2,3,4,5,6-penta(9H-carbazol-9-yl)benzonitrile (5CzBN) can significantly increase the mixing between triplet states with charge-transfer (CT) and local-excitation characteristics and consequently increase the spin-orbit couplings. Here, the results of long-range corrected density functional theory calculations show that the main impact on the RISC rates of substituting 5CzBN with secondary donors is due to a decrease in adiabatic singlet-triplet energy gaps and intramolecular reorganization energies rather than to a change in spin-orbit couplings. Our calculations underline that at least two singlet and three triplet excited states contribute to the ISC/RISC processes in 5CzBN and its derivatives. In addition, we find that in all emitters, the lowest singlet excited-state potential energy surface has a double-minimum shape.

The electron acceptor effect of end group on charge transfer excitation energy calculations using long-range corrected density functional theory

The electron acceptor effect of end group on charge transfer excitation energy calculations using long-range corrected density functional theory

Copper(II) and Nickel(II) Complexes of Tridentate Hydrazide and Schiff Base Ligands Containing Phenyl and Naphthalyl Groups: Synthesis, Structural, Molecular Docking and Density Functional Study

In the present study, we report the synthesis, characterization, molecular docking and theoretical studies of two new copper(II) [Cu2(L1)2(py)2]·H2O (1) and nickel(II) [Ni(L2)2] (2) coordination complexes, which are made through the coordination of (E)-N′-(5-bromo-2-hydroxybenzylidene) benzohydrazide (H2L1) and 1-((E)-(2-methoxyphenylimino) methyl) naphthalene-2-ol (HL2), respectively. The H2L1 and HL2 acts as deprotonated tridentate hydrazide and Schiff base ligands containing phenyl and naphthalyl groups, respectively. The molecular structure of (1) and (2) have been confirmed by single crystal X-ray diffraction studies and belongs to the monoclinic and triclinic system of the space group C2/c and P-1, respectively. The X-ray structural determination showed that the structure around Cu(II) was phenoxo-bridged distorted square pyramidal geometry for (1), while complex (2) display octahedral geometry around Ni(II). Binding affinity of (1) and (2) with the DNA generated from molecular docking was − 8.2 and − 9.2 kcal/mol, respectively, while H-pylori urease with binding affinity of − 9.3 and − 12.8 kcal/mol, respectively as predicted with Auto Dock Vina using DFT. The absorption and vibrational analysis of (1) and (2) have been carried out by the long-range corrected density functional theory (LC-DFT). The natural bonding orbital (NBO) analysis has been used to get insight into non-covalent interactions. From LC-DFT calculations, various parameters such as natural population analysis, atomic charges, and HOMO–LUMO energies have been obtained.

Nonlinear optical activity of imino-dyes with furan, thiophene or thiazole moieties as π-conjugated bridge: a computational investigation

ABSTRACT The electronic, linear and nonlinear optical properties of some heterocycle-containing imino-dyes, namely, the synthesised dyes 1–3 and the designed dye 4, were evaluated using suitable long-range corrected DFT functionals. HOMO–LUMO gaps, dipole moments, polarisabilities, and first hyperpolarisabilities were calculated using CAM-B3LYP, ωB97XD and LC-ωPBE methods combined with the 6-311++G(d,p) basis set using CAM-B3LYP/6-31G(d,p) optimised geometries. The calculated molecular hyperpolarisabilities, µβ, increase in the order 1 < 2 < 3 as expected experimentally. The enhancement of µβ when passing from dye 1 to dye 2 is due to the replacement of furan by thiophene and the increase of µβ when passing from dye 2 to dye 3 is due to the change of the thiophene position from the acceptor side to the donor side. Interestingly, the replacement of thiophene (dye 2) by thiazole (dye 4) leads to a notable increase of the NLO response. The electronic transitions data of dyes 1–4 were calculated at the CIS/6-31G(d,p) level of theory and the predicted order 1 < 2<3 < 4 of µβ values is conveniently explained using the two-level model based on the calculation of the dipole moment absolute change, |ΔµEG |, from the ground to the excited state. Consequently, dye 4 could be a promising candidate for organic NLO devices.

Application of accelerated long-range corrected exchange functional [LC-DFT(2Gau)] to periodic boundary condition systems: CO adsorption on Cu(111) surface.

Several different types of density functional theory (DFT) exchange correlation functionals were applied to a periodic boundary condition (PBC) system [carbon monoxide (CO) adsorbed on Cu(111): CO/Cu(111)] and the differences in the results calculated using these functionals were compared. The exchange correlation functionals compared were those of Perdew-Burke-Ernzerhof (PBE) and those of long-range corrected density functional theory (LC-DFT), such as LC-ωPBE(2Gau) and LC-BLYP(2Gau). Solid state properties such as the partial density of states were calculated in order to elucidate the detailed adsorption mechanisms and back-bonding peculiar to the CO/Cu(111) system. In addition, our benchmark analysis of the correlations among the orbitals of CO and Cu metal using LC-DFT reasonably was in line with the experimentally observed adsorption site. The computation time was reasonable, and other numerical results were found to agree well with the experimental results and also with the theoretical results of other researchers. This suggests that the long-range Hartree-Fock exchange integral should be included to correctly predict the electronic nature of PBC systems.