Polarizabilities of π-Conjugated Chains Revisited: Improved Results from Broken-Symmetry Range-Separated DFT and New CCSD(T) Benchmarks

A Strategy for Modeling Nonstatistical Reactivity Effects: Combining Chemical Activation Estimates with a Vibrational Relaxation Model

The kinetics of many chemical reactions can be readily explained with a statistical approach, for example, using a form of transition state theory and comparing calculated Gibbs energies along the reaction coordinate(s). However, there are cases where this approach fails, notably when the vibrational relaxation of the molecule to its statistical equilibrium occurs on the same time scale as the reaction dynamics, whether it is caused by slow relaxation, a fast reaction, or both. These nonstatistical phenomena are then often explored computationally using (quasi)classical ab initio molecular dynamics by calculating a large number of trajectories while being prone to issues such as zero-point energy leakage. On the other side of the field, we see resource-intensive quantum dynamics simulations, which significantly limit the size of explorable systems. We find that using a Fermi's golden rule type of model for vibrational relaxation, based on anharmonic coupling constants, we can extract the same qualitative information while giving insights into how to enhance (or destroy) the bottlenecks causing the phenomena. We present this model as a middle ground for exploring complex nonstatistical behavior, capable of treating medium-sized organic molecules or biologically relevant fragments. We also cover the challenges involved, in particular quantifying the excess energy in terms of vibrational modes. Relying on readily available electronic structure methods and providing results in a simple master equation form, this model shows promise as a screening tool for opportunities in mode-selective chemistry without external control.

Why Does the Optimal Tuning Method of the Range Separation Parameter of a Long-Range Corrected Density Functional Fail in Intramolecular Charge Transfer Excitation Calculations?

We performed intra- and intermolecular charge transfer (CT) excitation energy calculations of (a) conjugated carbon chain [H2N-(CH=CH)n-X] and (b) its equidistant H2NH∙∙∙HX (n = 2~8) with various electron acceptors (X = NH2, OH, Cl, CHO, CN, and NO2) using EOM-CCSD, time-dependent (TD) Hartree-Fock (HF) and various density functional theory (DFT) functionals, such as BLYP, B3LYP, long-range corrected (LC) DFT, and LC-DFT with an optimally tuned (OT) range separation parameter (µ) using Koopman's theorem to investigate the effect of the electron-withdrawing (or -donating) strength of end-capped functional group (X) and CT distance (R) on intra- and intermolecular CT excitation energies. As the electron-withdrawing strength of X increases, both intra- and intermolecular CT excitation energies tend to decrease, since energy gaps between orbitals corresponding to CT excitations (e.g., HOMO and LUMO) decrease. However, the effect of the electron-withdrawing group on intramolecular CT excitation energy is negligible (at most 0.5 eV). OT-LC-DFT shows accurate intermolecular CT excitation energy, but worse results in intramolecular CT excitation energy than LC-DFT with the default µ value (0.47). Therefore, we conclude that the optimal tuning method is not effective in predicting intramolecular CT excitation energy. While intermolecular CT excitation energy has excitonic binding energy with asymptotic behavior to CT distance that is not affected by the choice of range separation parameter, intramolecular CT excitation energy is affected by orbital relaxation energy, which strongly depends on the choice of range separation parameter, which makes the OT method of range separation parameter ineffective in predicting intramolecular CT excitation energy as well as local excitation with high accuracy.

Molecular Insights into the Quenching Mechanism of the Triplet Excited State of Rose Bengal through Oxidative and Reductive Organic Compounds

In oxygenated aquatic environments, the predominant scavenging of the triplet excited state of chromophoric dissolved organic matter (3CDOM*) involves dissolved ground-state oxygen, diverting attention away from the scavenging mechanisms of 3CDOM* mediated through specific organic compounds. Previous studies demonstrated that model 3CDOM* exhibited quantum yields (i.e., 1-56%) in the formation of radical ions, resulting from the competition between physical and chemical quenching through a common exciplex intermediate. Physical quenching was rationalized through the reverse intersystem crossing of the exciplex, followed by back electron transfer, yielding ground-state reactants. Despite this, direct experimental evidence for exciplex involvement has been elusive, owing to detection challenges. Herein, employing density functional theory (DFT) and time-dependent DFT specifically for excited state surrogate CDOM and organic scavengers, we unveil, for the first time, the underlying mechanisms responsible for the quenching of Rose Bengal through oxidative and reductive scavengers. Our computational findings provide evidence for the involvement of exciplexes during the quenching process of the excited triplet state of Rose Bengal, highlighting the impact of electronic coupling between Rose Bengal and quenchers on the quantum yield for radical ion formation.

Combining Local Range Separation and Local Hybrids: A Step in the Quest for Obtaining Good Energies and Eigenvalues from One Functional

Some of the most successful exchange-correlation approximations in density functional theory are "hybrids", i.e., they rely on combining semilocal density functionals with exact nonlocal Fock exchange. In recent years, two classes of hybrid functionals have emerged as particularly promising: range-separated hybrids on the one hand, and local hybrids on the other hand. These functionals offer the hope to overcome a long-standing "observable dilemma", i.e., the fact that density functionals typically yield either a good description of binding energies, as obtained, e.g., in global and local hybrids, or physically interpretable eigenvalues, as obtained, e.g., in optimally tuned range-separated hybrids. Obtaining both of these characteristics from one and the same functional with the same set of parameters has been a long-standing challenge. We here discuss combining the concepts of local range separation and local hybrids as part of a constraint-guided quest for functionals that overcome the observable dilemma.

Theoretical design of alkaline earthides M+(36 adz) Be- (M+ = V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) with excellent nonlinear optical response and ultraviolet transparency

A novel series of alkaline earthides containing eight complexes based upon 36adz complexant are designed by placing carefully transition metals (V-Zn) on inner side and alkaline earth metal outer side of the complexant i.e., M+(36adz) Be- (M+ = V, Cr, Mn, Fe, Co, Ni, Cu and Zn). All the designed compounds are electronically and thermodynamically stable as evaluated by their interaction energy and vertical ionization potential respectively. Moreover, the true nature of alkaline earthides is verified through NBOs and FMO study, showing negative charge and excess electrons on alkaline earth metal respectively. Furthermore, true alkaline earthides characteristics are evaluated graphically by spectra of partial density state (PDOS). The energy gap (HOMO -LUMO gap) is very small (ranging 2.95 eV-1.89 eV), when it is compared with pure cage 36adz HOMO-LUMO gap i.e., 8.50 eV. All the complexes show a very small value of transition energy ranging from 1.68eV to 0.89eV. Also, these possess higher hyper polarizability values up to 2.8 x 105au (for Co+(36adz) Be-). Furthermore, an increase in hyper polarizability was observed by applying external electric field on complexes. The remarkable increase of 100fold in hyper polarizability of Zn+(36adz) Be- complex is determined after application of external electric field i.e., from 1.7 x 104 au to 1.7 x 106 au when complex is subjected to external electric field of 0.001 au strength. So, when external electric field is applied on complexes it enhances the charge transfer, polarizability and hyper polarizability of complexes and proves to be effective for designing of true alkaline earthides with remarkable NLO response.

Polaronic state of conducting oligomer as a new approach to design non-lieaner optical materials: A case study of oligofurans

The geometric, electronic and nonlinear optical properties of neutral and polaron based oligofurans are studied comparatively. We have reported the role of polaron to trigger the nonlinear optical response of oligofurans (nFu). The polaron based oligomers show excellent opto-electronic properties. The effect of polaron on nFu* chains is measured by electronic properties i.e (ionization energy, electron affinity, band gap) and global reactivity descriptors like softness, hardness and chemical potential than their neutral counterpart. An interesting trends of reactivity descriptors have been observed. Lower band gaps (EH-L = 4.66 and 4.41 eV) are observed for polaronic systems as compared to their neutral counterpart. On the other hand, the TD-DFT study further demonstrated that, as the size of chain increases, the absorption maxima (λmax) also increases with significant reduction in excitation energies (ΔE). Furthermore, the nonlinear optical response is confirmed through the linear polarizability (αo), static first order hyperpolarizability (βo) and dynamic (frequency denepndent) hyperpolarizability. Electric filed induced second harmonic generation (EFISHG) and electro-optic pockle effect (EOPE) at 532 nm and 1064 nm, commonly used lasers frequencies have also been employed. Our results showed that the maximum hyperpolarizabilities are observed for polaron based 7Fu* and 9Fu* i.e 1.3 × 104, and 3.1 × 104 au. This study concluded that these polaron based organic polymers (nFu*) are useful as an efficient NLO material with vast applications in different fields.

Frequency-dependent nonlinear optical response and refractive index investigation of lactone-derived thermochromic compounds

Nonlinear optical (NLO) switchable materials play a crucial role in the fields of electronics and optoelectronics. The selection of an appropriate switching approach is vital in designing such materials to enhance their NLO response. Among various approaches, thermos-switching materials have shown a 4-fold increase in NLO response compared to other photo-switching materials. In this study, we computationally investigated the geometric, electronic, and nonlinear optical properties of reversible lactone-based thermochromic compounds using the ωB97XD/6-311+G (d,p) level of theory. Molecular orbital studies are employed to analyze the electronic properties of the close and open isomers of these compounds, while time-dependent density functional theory (TD-DFT) analysis is utilized to evaluate their molecular absorption. Our findings reveal that the π-electronic conjugation-induced delocalization significantly influences the ON-OFF switchable nonlinear optical response of the lactone-based thermochromic compounds. Notably, among all compounds, the open isomer of lactone 2 exhibits the highest hyperpolarizability value (6596.69 au). Furthermore, we extended our analysis to investigate the frequency-dependent second and third-order hyperpolarizabilities. The most pronounced frequency-dependent NLO response is observed at 532 nm. Additionally, we calculated the refractive index of these thermochromic compounds to further assess their nonlinear optical response. The open isomer of lactone 1 demonstrates the highest refractive index value (3.99 × 10-14 cm2/W). Overall, our study highlights the excellent potential of reversible thermochromic compounds as NLO molecular thermos-switches for future applications.

Alkali metals doped cycloparaphenylene nanohoops: Promising nonlinear optical materials with enhanced performance

In the ongoing pursuit of novel and efficient NLO materials, the potential of alkali metal-doped {6}cycloparaphenylene ({6}CPP) and methylene bridged {6} cycloparaphenylene (MB{6}CPP) nanohoops as excellent NLO candidates has been explored. The geometric, electronic, linear, and nonlinear optical properties of designed systems have been investigated theoretically. All the nanohoops demonstrated thermodynamic stability, with remarkable interaction energies reaching up to -1.39 eV (-0.0511 au). Notably, the introduction of alkali metals led to a significant reduction in the HOMO-LUMO energy gaps, with values as low as 2.92 eV, compared to 6.80 eV and 6.06 eV for undoped {6}CPP and MB{6}CPP, respectively. Moreover, the alkali metal-doped nanohoops exhibited exceptional NLO response, with the K@r6-{6}CPP complex achieving the highest first hyperpolarizability of 56,221.7 × 10-30 esu. Additionally, the frequency-dependent first hyperpolarizability values are also computed at two commonly used wavelengths of 1550 nm and 1907 nm, respectively. These findings highlight the potential of designed nanohoops as promising candidates for advanced NLO materials with high-tech applications.

Effects of Au6 and Au20 Adsorption Sites of Cyromazine-Au Complexes by Raman Spectroscopy and Density Functional Theory

Cyromazine, when used as an insect growth regulator and low-toxicity insecticide, may degrade into melamine and pose a potential threat to the environment and soil health, which has thus attracted extensive research on eliminating such a harmful effect. In this paper, density functional theory (DFT)/LC-BLYP/6-311G(d,p) is used to optimize the geometric structure and analyze the vibration of cyromazine. The DFT/LC-BLYP/def2-SVP is used for the cyromazine-Au complex optimization and vibration analysis. The molecular electrostatic potential (MEP), frontier molecular orbitals (FMOs), vibration frequency, electrophilicity-based charge transfer (ECT) descriptor, binding energy (BE), polarizability, normal Raman spectroscopy (NRS), and surface-enhanced Raman spectroscopy (SERS) of cyromazine adsorbing on Au6 and Au20 are calculated. The study of the chemical enhancement mechanism of SERS of cyromazine at different adsorption sites of Au6 or Au20 confirms the existence of a charge transfer between cyclopromazine and Au6 and Au20, which can adsorb and form stable cyromazine-Au complexes. The results show that N2, H13, and N4 are the adsorption sites of Au6 and Au20. The Raman spectra of the cyromazine-Au complex can be selectively enhanced with a factor up to 9.07. Compared with those of cyromazine-Au6, the Raman spectra of cyromazine-Au20 are enhanced more significantly.

A quantum chemical investigation of the second hyperpolarizability of p-nitroaniline

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure-property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange-correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree-Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange-correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, β, and vice versa. In fact, the β of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange-correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

A three orders of magnitude increase in nonlinear optical response by external electric field on Cryptand[2.2.2] (C222) based alkaline earthides

A new series of alkaline earthides based on Cryptand [2.2.2] (C222) containing nine complexes is designed by carefully placing alkali metals and alkaline earth metals inside and outside the C222 complexant, respectively i.e., M1(C222)M2 (M1 = Li, Na, K; M2 = Be, Mg, Ca). The designed complexes are reasonably stable both electronically and thermodynamically, as revealed through their vertical ionization potentials (VIPs) and interaction energies, respectively. Moreover, the true alkaline earthide nature of the complexes is confirmed through NBO and FMO analyses showing the negative charges and HOMOs over the alkaline earth metals, respectively. The further validity of true earthide characteristic is represented graphically by the spectra of partial density of states (PDOS). HOMO-LUMO gaps of the compounds are also very small (from 2.23 to 2.83 eV) when compared with pure cage's (C222) H-L gap i.e., 5.63 eV. All these features award these complexes with very small values of transition energies (ΔE) ranging from 0.68 to 2.06 eV ultimately resulting in remarkably high hyperpolarizability values up to 2.7 × 10⁵ au (for Na⁺(C222)Mg^-). Furthermore, applying external electric field (EEF) on the complexes enhances hyperpolarizability further. A remarkable increase of 1000 folds has been seen when hyperpolarizability of K⁺(C222)Ca^- is calculated after EEF application i.e., from 8.79 × 10⁴ au to 2.48 × 10⁷ au; when subjected to 0.001 au external electric field.

Computational Predictions of the Stability of Fluorinated Calcium Aluminate and Borate Salts

Energy storage concepts based on multivalent ions, such as calcium, have great potential to become next-generation batteries due to their low cost and comparable cell voltage and energy density to Li-ion batteries. However, the development of Ca batteries is still hindered by the lack of suitable materials that grant a long cycle life. Specific to electrolyte materials, developing a calcium salt that is chemically stable under ambient conditions and enables reversible electrodeposition of Ca is critical. In this work, we use first-principles calculations to study the intrinsic and reductive stability of twelve Ca salts with fluorinated aluminate and borate anions and analyze the decomposition products formed on the metal anode surface that are critical to early-stage solid electrolyte interphase formation. We found anions with significant steric hindrance and a high degree of fluorination are intrinsically less stable and deemed unviable designs for Ca salt. Aluminate salts are generally less reactive with the Ca anode than their borate counterparts, and a high degree of fluorination leads to weaker reductive stability. Calcium fluoride is the most prominent decomposition product on the anode surface, and carbide-like motifs were also found from the decomposition of the designed salts.

Transition metalides based on facially polarized all-cis-1,2,3,4,5,6-hexafluorocyclohexane - a new class of high performance second order nonlinear optical materials

Continuous attempts are being made to discover new approaches to design materials with extraordinary nonlinear optical responses. Herein, for the first time, we report the geometric, electronic, and nonlinear optical properties of novel Janus transition metalides AM-J-TM (where AM = Li, Na and K, and TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) containing alkali metals as a source of excess electrons for transition metals to generate metalides. The Janus organic complexant used for the study is all cis 1,2,3,4,5,6-hexafluorocyclohexane F₆C₆H₆ (J). These complexes contain the unique involvement of alkali metals (AM = Li, Na and K) as a source of excess electrons, which significantly affects the hyperpolarizability values of the resulting transition metalides. The NBO analysis reveals the charge transfer from alkali metals to the transition metals, thereby confirming the metalide behavior of the complexes. Moreover, the metalide nature of these complexes is validated through frontier molecular orbital (FMO) analysis. The values of interaction energies, vertical ionization potential (VIP) and vertical electron affinity (VEA) illustrate the stability of the metalide complexes. Ultimately, the hyperpolarizability values confirm the excellent nonlinear optical response of the designed transition metalides. The remarkable static first hyperpolarizability (β₀) response up to 4 × 10⁸ a.u. is observed for complexes of vanadium. Similarly, the complexes of AM-J-Mn and Li/Na-J-Sc show significantly high NLO response. These compounds besides providing a new entry into excess electron compounds will also pave the way for the design and synthesis of further novel NLO materials.

Toward highly efficient hyperfluorescence-based emitters through excited-states alignment using novel optimally tuned range-separated models

Hyperfluorescence has recently been introduced as a promising strategy to achieve organic light-emitting diodes (OLEDs) with high color purity and enhanced stability. In this approach, fluorescent emitters (FEs) with strong and narrow band fluorescence are integrated in thin films containing sensitizers exhibiting thermally activated delayed fluorescence (TADF). Toward highly efficient hyperfluorescence-based emitters, the excited-states ordering of the FEs should be well-aligned. Given some recent endeavors in this context, the related theoretical explorations are relatively limited and have proven to be challenging. In this work, alignments of the corresponding excited-states, crucial for both the fast Förster resonance energy transfer and suppression of the Dexter energy transfer from TADF sensitizers to FEs, have theoretically been investigated using optimally tuned range-separated hybrid functionals (OT-RSHs). We have proposed and validated several variants of the models including OT-RSHs, their coupled versions with the polarizable continuum model, OT-RSHs-PCM, as well as the screened versions accounting for the screening effects by the electron correlation through the scalar dielectric constant, OT-SRSHs, for a reliable description of the excited-states ordering in the FEs of the hyperfluorescence-based materials. Particular attention is paid to the influence of the underlying density functional approximations as well as the short- and long-range Hartree-Fock (HF) exchange contributions and the range-separation parameter. Considering a series of experimentally known hyperfluorescence-based emitters as working models, it is unveiled that any combination of the ingredients in the proposed models does not render the correct order of the excited-states of the FEs, but a particular compromise among the involved parameters is needed to more accurately account for the relevant excited-states alignment. Perusing the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM with the correct asymptotic behavior and incorporating no (low) HF exchange contribution at the short-range regime. The proposed models show superior performances not only with respect to their standard counterparts with the default parameters but also as compared to other range-separated approximations. Accountability of the best-proposed model is also put into broader perspective, where it has been employed for the computational design of several molecules as promising FE candidates prone to be utilized in hyperfluorescence-based materials. Summing up, the proposed models in this study can be recommended for both the theoretical modeling and confirming the experimental observations in the field of hyperfluorescence-based OLEDs.

Evaluating fast methods for static polarizabilities on extended conjugated oligomers

Given the importance of accurate polarizability calculations to many chemical applications, coupled with the need for efficiency when calculating the properties of sets of molecules or large oligomers, we present a benchmark study examining possible calculation methods for polarizable materials. We first investigate the accuracy of the additive model used in GFN2, a highly-efficient semi-empirical tight-binding method, and the D4 dispersion model, comparing its predicted additive polarizabilities to ωB97XD results for a subset of PubChemQC and a compiled benchmark set of molecules spanning polarizabilities from approximately 3 ų to 600 ų, with some compounds in the range of approximately 1200-1400 ų. Although we find additive GFN2 polarizabilities, and thus D4, to have large errors with polarizability calculations on large conjugated oligomers, it would appear an empirical quadratic correction can largely remedy this. We also compare the accuracy of DFT polarizability calculations run using basis sets of varying size and level of augmentation, determining that a non-augmented basis set may be used for large, highly polarizable species in conjunction with a linear correction factor to achieve accuracy extremely close to that of aug-cc-pVTZ.

Zinc oxide nanoclusters and their potential application as CH4 and CO2 gas sensors: Insight from DFT and TD-DFT

We have investigated the adsorption of CH₄ and CO₂ gases on zinc oxide nanoclusters (ZnO NCs) using density functional theory (DFT). It was found that the CH₄ tends to be physically adsorbed on the surface of all the ZnO NCs with adsorption energy in the range -11 to -14 kcal/mol. Even though, the CO₂ is favorably chemisorbed on the Zn₁₂ O₁₂ and Zn₁₅ O₁₅ NCs, with adsorption energy about -38 kcal/mol at B3LYP/6-311G(d,p) level of theory. When the CH₄ and CO₂ gases are adsorbed on the ZnO NCs, their electrical conductivities are decreased, and thus the studied ZnO NCs do not generate an electrical signal in the presence of CH₄ and CO₂ gases. Interestingly, both pure and gas adsorbed Zn₂₂ O₂₂ NC exhibited more favorable electronic and reactive properties than other NCs. Comparison of the structural, electronic, and optical data predicted by DFT/B3LYP and TD-DFT/CAM-B3LYP calculations with those experimentally obtained show good agreement.

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

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

Excited-state properties of organic semiconductor dyes as electrically pumped lasing candidates from new optimally tuned range-separated models

Even though many efforts have been devoted to optical lasing in recent years, the realization of lasing by direct electrical excitation of organic semiconductors is hampered mainly due to optical losses from electrical contacts and electrical losses induced by triplets and polarons at high current densities. Hereby, accurately accounting for the electrically pumped organic semiconductor laser diodes (OSLDs) still remains one of the greatest challenges in optoelectronics. In this work, the excited-state characteristics of the organic semiconductor dyes used in the electrically pumped OSLDs have thoroughly been investigated using optimally tuned range-separated hybrids (OT-RSHs). Considering several experimentally known compounds of the electrically pumped OSLDs as working models, several variants of OT-RSHs, their combination forms with the polarizable continuum model (PCM), OT-RSH-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the scalar dielectric constant, OT-SRSHs, have been proposed for reliable prediction of their emission energies and oscillator strengths in both the gas and solvent phases. The role of involved ingredients in the models, namely, the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, has been examined in detail. It is shown that the newly designed OT-RSHs with the correct behavior of asymptotic exchange-correlation potential outperform the standard RSHs and other density functionals with both fixed and interelectronic distance-dependent exact-like exchange for describing the excite-state properties of compounds of the electrically pumped OSLDs. Concerning the computational cost of the models, it is unveiled that performing both the optimal tuning procedure and subsequent excited-state computations using OT-RSHs in the gas phase can be considered as a more reliable and affordable framework. Finally, the applicability of the proposed models is also put into a broader perspective for the computational design of several compounds as promising candidates to be used in the OSLD materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the related theoretical modeling and confirming the experimental observations in the field of electrically pumped OSLDs.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor–acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure–property studies across large series of dipolar compounds.

Germanium-based superatom clusters as excess electron compounds with significant static and dynamic NLO response; a DFT study

Herein, the geometric, electronic, and nonlinear optical properties of excess electron zintl clusters Ge₅AM₃, Ge₉AM₅, and Ge₁₀AM₃ (AM = Li, Na, and K) are investigated. The clusters under consideration demonstrate considerable electronic stability as well as superalkali characteristics. The NBO charge is transferred from the alkali metal to the Ge-atoms. The FMO analysis shows fabulous conductive properties with a significant reduction in SOMO-LUMO gaps (0.79-4.04 eV) as compared with undoped systems. The designed clusters are completely transparent in the deep UV-region and show absorption in the visible and near-IR region. Being excess electron compounds these clusters exhibit remarkable hyperpolarizability response up to 8.99 × 10^-26 esu, where a static second hyperpolarizability (γ _o) value of up to 2.15 × 10^-30 esu was recorded for Ge₉Na₅ superatom clusters. The excitation energy is the main controlling factor for hyperpolarizability as revealed from the two-level model study. The electro-optical Pockel's effect and the second harmonic generation phenomenon (SHG) are used to investigate dynamic nonlinear optical features. At a lower applied frequency (=532 nm), the dynamic hyperpolarizability and second hyperpolarizability values are significantly higher for the studied clusters. Furthermore, for the Ge₉K₅ cluster, the hyper Rayleigh scattering (HRS) increases to 5.03 × 10^-26 esu.

Demonstrating the Potential of Alkali Metal-Doped Cyclic C6O6Li6 Organometallics as Electrides and High-Performance NLO Materials

In this report, the geometric and electronic properties and static and dynamic hyperpolarizabilities of alkali metal-doped C6O6Li6 organometallics are analyzed via density functional theory methods. The thermal stability of the considered complexes is examined through interaction energy (E int) calculations. Doping of alkali metal derives diffuse excess electrons, which generate the electride characteristics in the respective systems (electrons@complexant, e-@M@C6O6Li6, M = Li, Na, and K). The electronic density shifting is also supported by natural bond orbital charge analysis. These electrides are further investigated for their nonlinear optical (NLO) responses through static and dynamic hyperpolarizability analyses. The potassium-doped C6O6Li6 (K@C6O6Li6) complex has high values of second- (βtot = 2.9 × 105 au) and third-order NLO responses (γtot = 1.6 × 108 au) along with a high refractive index at 1064 nm, indicating that the NLO response of the corresponding complex increases at a higher wavelength. UV-vis absorption analysis is used to confirm the electronic excitations, which occur from the metal toward C6O6Li6. We assume that these newly designed organometallic electrides can be used in optical and optoelectronic fields for achieving better second-harmonic-generation-based NLO materials.

Inorganic electrides of alkali metal doped Zn12O12 nanocage with excellent nonlinear optical response

Finding new materials with exceptionally large nonlinear optical response is an interesting and challenging avenue for scientific research. Here, we report the alkali metal doped Zn₁₂O₁₂ nanocages as inorganic electrides with excellent nonlinear optical response. Density functional theory calculations have been performed for geometric, electronic and nonlinear optical response of exo- and endohedrally alkali metal doped Zn₁₂O₁₂ nanoclusters. For exohedral doping, all different possible doping sites are considered for decoration of alkali metal on the nanocage. The electride nature of the complexes is highly dependent on the position of alkali metal doping. All exohedral complexes except for alkali metal doping on six membered ring (r₆) are electride in nature, as revealed from frontier molecular orbital analysis. Interaction energies reveal that all doped nanoclusters except endo-K@Zn₁₂O₁₂ are thermodynamically stable. The exothermic encapsulation of alkali metals in Zn₁₂O₁₂ nanocages is in marked contradiction with other inorganic fullerenes where encapsulation is an endothermic process. The barriers for boundary crossing are also evaluated in order study the interconversion of exo- and endohedral complexes. Doping of alkali metal significantly influences the properties of nanocages. HOMO-LUMO (H-L) gap is reduced significantly whereas hyperpolarizability is increased several orders of magnitude. The NLO response of exohedrally doped complexes is higher than the corresponding endohedral complexes, which is in mark contradiction with the behavior of phosphide or nitride nanocages. The highest first hyperpolarizability of 1.0 × 10⁵ au is calculated for K@r₆-Zn₁₂O₁₂ complex. Third order NLO response of these complexes is calculated and compared with the best systems reported in the literature at the same level of theory.

Dissociation of dinitrogen on iron clusters: a detailed study of the Fe16 + N2 case

The coalescence of two Fe8N as well as the structure of the Fe16N2 cluster were studied using density functional theory with the generalized gradient approximation and a basis set of triple-zeta quality. It was found that the coalescence may proceed without an energy barrier and that the geometrical structures of the resulting clusters depend strongly on the mutual orientations of the initial moieties. The dissociation of N2 is energetically favorable on Fe16, and the nitrogen atoms share the same Fe atom in the lowest energy state of the Fe16N2 species. The attachment of two nitrogen atoms leads to a decrease in the total spin magnetic moment of the ground-state Fe16 host by 6 μB due to the peculiarities of chemical bonding in the magnetic clusters. In order to gain insight into the dependence of properties on charge and to estimate the bonding energies of both N atoms, we performed optimizations of Fe16N and the singly charged ions of both Fe16N2 and Fe16N. It was found that the electronic properties of the Fe16N2 cluster, such as electron affinity and ionization energy, do not appreciably depend on the attachment of nitrogen atoms but that the average binding energy per atom changes significantly. The lowering in total energy due to the attachment of two N atoms was found to be nearly independent of charge. The IR and Raman spectra were simulated for Fe16N2 and its ions, and it was found that the positions of the most intense peaks in the IR spectra strongly depend on charge and therefore present fingerprints of the charged states. The chemical bonding in the ground-state Fe16N20,±1 species was described in terms of the localized molecular orbitals.

Remarkable static and dynamic NLO response of alkali and superalkali doped macrocyclic [hexa-]thiophene complexes; a DFT approach

In this study, the nonlinear optical (NLO) response of alkali metal atom (Li, Na and K) and their corresponding superalkali (Li₃O, Na₃O and K₃O) doped six membered cyclic thiophene (6CT) has been explored. The optimized geometries of complexes; Li@6CT, Na@6CT, K@6CT, Li₃O@6CT, Na₃O@6CT and K₃O@6CT depict that the superalkalis and alkali metals interact through the active cavity of 6CT. Interaction energies reveal that superalkalis have higher interaction with 6CT than alkali metals. The nonlinear optical (NLO) response of the reported complexes is estimated via both static and dynamic hyperpolarizabilities which are further rationalized by the HOMO–LUMO gap, natural bond orbital (NBO) charge transfer, dipole moment, polarizabilities and β_vec. A remarkably high NLO response is computed for Na₃O@6CT among all of the complexes. The static hyperpolarizability of the Na₃O@6CT complex is 5 × 10⁴ au along with the highest β_vec value (2.5 × 10⁴ au). High charge transfer (1.53e⁻) and small E_H–L gap (2.96 eV) is responsible for such a large NLO response. For dynamic NLO responses, electro-optic Pockel's effect (EOPE) and second-harmonic generation (SHG) are explored. A very large quadratic nonlinear optical response (3.8 × 10⁻¹² au) is observed for the Na₃O@6CT complex. Moreover, the absorption spectrum of the Na₃O@6CT complex shows ultra-high transparency in the ultraviolet and visible regions unlike any other of its counterparts.

In this study, the nonlinear optical (NLO) response of alkali metal atom (Li, Na and K) and their corresponding superalkali (Li₃O, Na₃O and K₃O) doped six membered cyclic thiophene (6CT) has been explored.

Endohedral metallofullerene electrides of Ca12O12 with remarkable nonlinear optical response

Herein, the structural, electronic, thermodynamic, linear and nonlinear optical properties of inorganic electrides, generated by alkali metal doping in group II–VI Ca₁₂O₁₂ fullerene, are studied. Endohedral doping of alkali metal leads to the formation of electrides whereas no such phenomenon is seen for exohedral doping. The electride nature of the endohedral fullerenes is confirmed through the analysis of frontier molecular orbitals. The results show that doping of alkali metal atoms leads to a reduction of the HOMO–LUMO gap and increase of the dipole moment, polarizability and hyperpolarizability of nanocages. Doping causes shifting of electrons from alkali metal atoms towards the Ca₁₂O₁₂ nanocage, which serve as excess electrons. Furthermore, the participation of excess electrons for enhancing the NLO response of these nanocages has been confirmed through the calculation of hyperpolarizability (β_o). For exploring the controlling factors of hyperpolarizability, a two level model has been employed and the direct relation of hyperpolarizability with Δμ & f_o, while an inverse relation of hyperpolarizability with ΔE has been studied. The electrides possess remarkable nonlinear response where the highest hyperpolarizability can reach up to 1.0 × 10⁶ a.u. for endo-K@Ca₁₂O₁₂. This electride has the lowest ΔE of 0.63 eV among all compounds studied here. These intriguing results will be expedient for promoting the potential applications of the Ca₁₂O₁₂-based nano systems in high-performance nonlinear optical (NLO) materials.

Electride formation by alkali metal doping with a drastic increase in hyperpolarizability

Surface functionalization of twisted graphene C32H15 and C104H52 derivatives with alkalis and superalkalis for NLO response; a DFT study

Herein, we present the detailed comparative study on geometric, electronic, optical and non-linear optical response of alkalis and superalkalis doped twisted graphene. The results illustrate that alkali metals and superalkalis interact with the central ring of the twisted graphene through non-covalent interactions which demonstrate the stability of the resultant complexes. NBO charges indicate the transfer of electrons from dopant (alkali metal atoms and superalkalis) towards twisted graphene sheet. Superalkalis doped twisted graphene complexes exhibit higher first hyperpolarizability values compared to alkali metals analogues. Among superalkalis doped complexes, K₃O@C₁₀₄H₅₂ shows the highest β_o value of 1.68 × 10⁵ au. In frequency dependent first hyperpolarizability analysis, strong second harmonic generation (SHG) response of K₃O@C₃₂H₁₅ complex is observed at both selected resonance frequency values (532 nm and1064 nm) whereas EOPE value of K₃O@C₃₂H₁₅ complex shows higher induced response at 1064 nm wavelength. The static hyperpolarizability (β_o) further increases under the influence of applied electric field. Among all complexes, Li₃O@C₃₂H₁₅ graphene complex has the highest β_o value (1.40 × 10⁵ au) under applied electric field along x axis when sheet is in y-z plane. This analysis will be an important guideline for future studies on twisted graphene based NLO materials.

Performance of TDDFT Vertical Excitation Energies of Core-Substituted Naphthalene Diimides

We have evaluated the performance of various density functionals, covering generalized gradient approximation (GGA), global hybrid (GH) and range‐separated hybrid (RSH), using time dependent density functional theory (TDDFT) for computing vertical excitation energies against experimental absorption maximum (λ_max) for a set of 10 different core‐substituted naphthalene diimides (cNDI) recorded in dichloromethane. The computed excitation in case of GH PBE0 is most accurate while the trend is most systematic with RSH LCY‐BLYP compared to λ_max. We highlight the importance of including solvent effects for optimal agreement with the λ_max. Increasing the basis set size from TZ2P to QZ4P has a negligible influence on the computed excitation energies. Notably, RSH CAMY‐B3LYP gave the least error for charge‐transfer excitation. The poorest agreement with λ_max is obtained with semi‐local GGA functionals. Use of the optimally‐tuned RSH LCY‐BLYP* is not recommended because of the high computational cost and marginal improvement in results.

Theoretical study on novel superalkali doped graphdiyne complexes: Unique approach for the enhancement of electronic and nonlinear optical response

Based on DFT calculations, we have explored the changes in geometric, electronic and nonlinear optical (NLO) properties of M₃O and M₃S (M = Li, Na and K) doped graphdiyne. The doping of superalkalis not only changes the electronic properties of GDY but also remarkably alters the NLO properties. Stabilities of doped GDY are evaluated through interaction energies. HOMO-LUMO gap, NBO, polarizability and first hyperpolarizability (β_o) calculations at hybrid (B3LYP) and long-range corrected methods (CAM-B3LYP, LC-BLYP and ωB97XD) are performed for studying the NLO properties of doped GDY complexes. Significantly high values of β_o are observed for all doped structures, especially for Na₃S@GDY (1.36×10⁵ au). Reduction in HOMO-LUMO gap concomitant with increase of β_o value is attributed to the strong interaction of Na₃S with GDY. The partial density of states (PDOS) spectra strongly support the existence of excess electrons. To rationalize the trends in first hyperpolarizability of doped GDY, two level model calculations are also performed. This study of super alkalis doped GDY will be advantageous for promoting the potential applications of the nanostructures in designing new types of electronic nanodevices and production of high performance nonlinear optical materials.

Superhalogen doping: a new and effective approach to design materials with excellent static and dynamic NLO responses

The first-ever example where superhalogen doping alone is introduced as a new and effective approach to impart large NLO responses.

A new tuned range-separated density functional for the accurate calculation of second hyperpolarizabilities

Among the nine functionals benchmarked, the most accurate γ are obtained by Tα-LC-BLYP, reducing about half the errors of LC-BLYP.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

Theoretical study on a boron phosphide nanocage doped with superalkalis: novel electrides having significant nonlinear optical response

Three series of compounds Li₂F@B₁₂P₁₂, Li₃O@B₁₂P₁₂ and Li₄N@B₁₂P₁₂ are theoretically designed and investigated for their nonlinear optical response using density functional theory (DFT).

A theoretical study on the formation and oxidation mechanism of hydroxyalkylsulfonate in the atmospheric aqueous phase

Hydroxymethanesulfonate (HMS) is an important organosulfur compound in the atmosphere. In this work, we studied the formation mechanism of HMS via the reaction of formaldehyde with dissolved SO₂ using the quantum chemistry calculations. The results show that the barrier (9.7 kcal mol⁻¹) of the HCHO + HSO₃⁻ reaction is higher than that (1.6 kcal mol⁻¹) of the HCHO + SO₃²⁻ reaction, indicating that the HCHO + SO₃²⁻ reaction is easier to occur. For comparison, the reaction of acetaldehyde with dissolved SO₂ also was discussed. The barriers for the CH₃CHO + HSO₃⁻ reaction and CH₃CHO + SO₃²⁻ reaction are 16.6 kcal mol⁻¹, 2.5 kcal mol⁻¹, respectively. This result suggests that the reactivity of HCHO with dissolved SO₂ is higher than that of CH₃CHO. The further oxidation of CH₂(OH)SO₃⁻ and CH₃CH(OH)SO₃⁻ by an OH radical and O₂ shows that the SO₅˙⁻ radical can be produced.

We report the formation of an important organosulfur compound HMS and its oxidation using theoretical calculation.

Partition of optical properties into orbital contributions

A new tool to analyze the response property through the partition of nonlinear optical properties in terms of orbital contributions (PNOC), valuable in the assessment of the electronic structure methods in the NLOPs computations, is presented.