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In this work, the theory of the modified unit sphere representation (mUSR) has been proposed as a computational tool suitable for the three-dimensional representation of the pure electric-dipole [ ß λ µ ν ( - 2 ω ; ω , ω ) $$ {\beta}_{\lambda \mu \nu}\left(-2\omega; \omega, \omega \right) $$ ] as well as of the mixed electric-dipole/magnetic-dipole [ α J λ µ ν ( - 2 ω ; ω , ω ) $$ {}^{\alpha }{J}_{\lambda \mu \nu}\left(-2\omega; \omega, \omega \right) $$ and ß J λ µ ν ( - 2 ω ; ω , ω ) $$ {}^{\beta }{J}_{\lambda \mu \nu}\left(-2\omega; \omega, \omega \right) $$ ] or electric-dipole/electric-quadrupole [ α K λ µ ν o ( - 2 ω ; ω , ω ) $$ {}^{\alpha }{K}_{\lambda \mu \nu o}\left(-2\omega; \omega, \omega \right) $$ and ß K λ µ ν o ( - 2 ω ; ω , ω ) $$ {}^{\beta }{K}_{\lambda \mu \nu o}\left(-2\omega; \omega, \omega \right) $$ ] first hyperpolarizabilities. These five quantities are Cartesian tensors and they are responsible for the chiral signal in the chiroptical version of the hyper-Rayleigh scattering (HRS) spectroscopy, namely the HRS optical activity (HRS-OA) spectroscopy. For the first time, for each hyperpolarizability, alongside with the three-dimensional representation of the whole (i.e., reducible) Cartesian tensors, the mUSRs are developed for each of the irreducible Cartesian tensors (ICTs) that constitute them. This scheme has been applied to a series of three (chiral) hexahelicene molecules containing different degrees of electron-withdrawing (quinone) groups and characterized by the same (positive) handedness. For these molecules, the mUSR shows that, upon substitution, the most remarkable qualitative and semi-quantitative (enhancement of the molecular responses) effects are obtained for the pure electric-dipole and for the mixed electric-dipole/magnetic-dipole hyperpolarizabilities.
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A multistep computational approach has been employed to study a multimillion all-atom dyed plasma membrane, with no less than 42 different lipid species spanning the major head groups and a variety of fatty acids, as well as cholesterol, with the objective of investigating its structure and dynamics, as well as its impact on the embedded di-8-ANEPPS dyes. The latter are commonly used as bioimaging probes and serve as local microscopes. So, they provide information on membrane morphology via their second harmonic nonlinear optical (NLO) responses, which have the advantage of being specific to interface regions and sensitive to the chromophore environment. In previous studies, this chromophore has only been studied in simpler membrane models, far from the complexity of real lipid bilayers, while, owing to the ever-increasing computational resources, multimillion lipid bilayers have been studied, giving access to the effects of its heterogeneity. First, using molecular dynamics (MD) simulations, it is found that the combination of lipids produces a more ordered and denser membrane compared to its homogeneous model counterparts, while the local environment of the embedded dyes becomes enriched in phosphatidylcholine. Subsequently, the second harmonic first hyperpolarizability of the probes was calculated at the TDDFT level on selected frames of MD, highlighting the influence of the lipid environment. Due to the complexity of the system, machine learning (ML) tools have been employed to establish relationships between the membrane structural parameters, the orientation of the probes, and their NLO responses. These ML approaches have revealed influential features, including the presence of diacylglycerol lipids close to the dye. On the whole, this work provides a first step toward understanding the cooperation, synergy, and interactions that occur in such complex guest-host environments, which have emerged as new targets for drug design and membrane lipid therapy.
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Corantes , Bicamadas Lipídicas , Bicamadas Lipídicas/química , Membrana Celular , Compostos de Piridínio , Simulação de Dinâmica MolecularRESUMO
Liquid-air interfaces have extensive implications in different areas of interest because the dynamical processes at the interface can be different from those in bulk. Thus, its characterization, understanding, and control may be pivotal in advancing discoveries. However, characterizing the interface requires special and selective tools to avoid signals from the bulk region. This surface specificity and versatility is achieved by using the second harmonic generation (SHG) responses. This study adopts multiscale simulation methods to evaluate the surface SHG responses of methanol-air interfaces with submonolayer resolution tackled by sequentially using classical molecular dynamics simulations under different temperatures and then employing quantum chemistry methods to compute the molecular first hyperpolarizabilities (ß). This approach ensures the configurational diversity required to evaluate the average ß values. The main achievements are (i) a quasi-absence of surface sensitivity of the mean polarizability ãαã with values about 2% larger than those obtained in bulk, (ii) conversely, smooth variations on the polarizability anisotropy Δα are observed up to the fourth molecular layer at around 20 Å from the interface, and (iii) narrow interfacial effects on the SHG responses, ß(-2ω;ω,ω), which are limited to the first molecular layer (â¼3.0 Å) and characterized by a high contrast in the ßZZZ(-2ω;ω,ω) tensor component between the first and the subsequent layers. Similar trends are obtained at different temperatures or when increasing the number of methanol molecules treated at the quantum chemistry level, indicating the robustness of the approach for describing the dipolar molecular responses of air-liquid interfaces.
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The second hyperpolarizabilities (γ) of the stilbene molecular switch in its trans and cis forms have been calculated using quantum chemistry methods to address their third-order nonlinear optical contrasts, to assess the reliability of lower-cost DFT methods, and to make comparisons with experiments. First, the reference CCSD(T) method shows that trans-stilbene presents a γâ value twice larger than its cis isomer (its γTHS value is 2.7 times larger). Among more cost-effective methods, reliable results are obtained at MP2 as well as with DFT, provided the CAM-B3LYP or ωB97X-D XCFs are employed. Supplementary DFT calculations have investigated the relationships between the accuracy of the exchange-correlation functionals, the fulfillment of Koopmans' theorem, and the delocalization error, and they demonstrated that satisfying Koopmans' theorem is not the condition for the best accuracy but that functionals with small delocalization errors are generally efficient. Using the selected CAM-B3LYP, large γ enhancements by about 70% (trans-stilbene) and 50% (cis-stilbene) have been evidenced when accounting for solvent effects using an implicit solvation model (IEFPCM), even for apolar solvents. Then, the frequency dispersion of the γ responses has been described using Bishop polynomial expansions, allowing comparisons with a broad set of experimental data. To a certain extent, no systematic agreement between the calculations and the measured values was found. On the one hand, the agreement is satisfactory for the γ(-ω;ω,-ω,ω) quantities, provided that the dominant vibrational contribution is taken into account. On the other hand, the agreement is poor for the γ(-2ω;ω,ω,0) and γ(-3ω;ω,ω,ω) quantities, while some inconsistencies between experimental values are also highlighted.
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This work reports an investigation of the second-order NLO properties of two isomer series of X-shaped pyrazine derivatives, by means of HRS measurements and DFT calculations. The systems differ in the relative position of the donor and acceptor substituents with respect to the axis formed by the nitrogen atoms of the central pyrazine ring. Although the magnitude of the second harmonic signal is similar, HRS measurements revealed that the anisotropy of the NLO response strongly differs in the two chromophore series, the one of the 2,3-isomers being strikingly dipolar, while the one of the 2,6-isomers is mostly octupolar. The experimental observations are well supported by DFT calculations. In particular, the sum-over-states approach allows us to rationalize the different NLO anisotropies observed in the two isomer series through a detailed analysis of the symmetry of the low-lying excited states.
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In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H2O, SO2, ClO2, HS2, and ZnOH. The method solves the classically hard problem of estimating the Franck-Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.
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Sterically hindered pyridines embedded in a three-dimensional triptycene framework have been synthesized, and their resolution by chiral HPLC enabled access to unprecedented enantiopure pyridines exceeding the known steric limits. The design principles for new axially chiral pyridine derivatives are then described. To rationalize their associations with Lewis acids and transition metals, a comprehensive determination of the steric and electronic parameters for this new class of pyridines was performed. This led to the general parameterization of the steric parameters (percent buried volume %VBur, Tolman cone angle θ, and He8_steric descriptor) for a large set of two- and three-dimensional pyridine derivatives. These parameters are shown to describe quantitatively their interactions with carbon- and boron-centered Lewis acids and were used to predict the ΔG° of association with the prototypical B(C6F5)3 Lewis acid widely used in frustrated Lewis pair catalysis. This first parameterization of pyridine sterics is a fundamental basis for the future development of predictive reactivity models and for guiding new applications of bulky and chiral pyridines in organocatalysis, frustrated Lewis pairs, and transition-metal catalysis.
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The last 30 years have witnessed an ever-growing application of computational chemistry for rationalizing the nonlinear optical (NLO) responses of organic chromophores. More specifically, quantum chemical calculations proved highly helpful in gaining fundamental insights into the factors governing the magnitude and character of molecular first hyperpolarizabilities (ß), be they either intrinsic to the chromophore molecular structure and arising from symmetry, chemical substitution, or π-electron delocalization, or induced by external contributions such as the laser probe or solvation and polarization effects. Most theoretical reports assumed a rigid picture of the investigated systems, the NLO responses being computed solely at the most stable geometry of the chromophores. Yet, recent developments combining classical molecular dynamics (MD) simulations and DFT calculations have evidenced the significant role of structural fluctuations, which may induce broad distributions of NLO responses, and even generate them in some instances.This Account presents recent case studies in which theoretical simulations have highlighted these effects. The discussion specifically focuses on the simulation of the second-order NLO properties that can be measured experimentally either from Hyper-Rayleigh Scattering (HRS) or Electric-Field Induced Second Harmonic Generation (EFISHG). More general but technical topics concerning several aspects of the calculations of hyperpolarizabilities are instead discussed in the Supporting Information.Selected examples include organic chromophores, photochromic systems, and ionic complexes in the liquid phase, for which the effects of explicit solvation, concentration, and chromophore aggregation are emphasized, as well as large flexible systems such as peptide chains and pyrimidine-based helical polymers, in which the relative variations of the responses were shown to be several times larger than their average values. The impact of geometrical fluctuations is also illustrated for supramolecular architectures with the examples of nanoparticles formed by organic dipolar dyes in water solution, whose soft nature allows for large shape variations translating into huge fluctuations in time of their NLO response, and of self-assembled monolayers (SAMs) based on indolino-oxazolidine or azobenzene switches, in which the geometrical distortions of the photochromic molecules, as well as their orientational and positional disorder within the SAMs, highly impact their NLO response and contrast upon switching. Finally, the effects of the rigidity and fluidity of the surrounding are evidenced for NLO dyes inserted in phospholipid bilayers.
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Corantes , Simulação de Dinâmica Molecular , Estrutura MolecularRESUMO
Metal-free organic emitters that display solution-phase room temperature phosphorescence (sRTP) remain exceedingly rare. Here, we investigate the structural and photophysical properties that support sRTP by comparing a recently reported sRTP compound (BTaz-Th-PXZ) to two novel analogous materials, replacing the donor group by either acridine or phenothiazine. The emissive triplet excited state remains fixed in all three cases, while the emissive charge-transfer singlet states (and the calculated paired charge-transfer T2 state) vary with the donor unit. While all three materials show dominant RTP in film, in solution different singlet-triplet and triplet-triplet energy gaps give rise to triplet-triplet annihilation followed by weak sRTP for the new compounds, compared to dominant sRTP throughout for the original PXZ material. Engineering both the sRTP state and higher charge-transfer states therefore emerges as a crucial element in designing emitters capable of sRTP.
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Targeting the use of the second harmonic generation (SHG) as a bioimaging technique to unravel the formation of aggregates, the SHG first hyperpolarizabilities ( ß ${\beta }$ ) of assemblies of benzene-1,3,5-tricarboxamide derivatives have been evaluated at the density functional theory level. Calculations have revealed that i)â the assemblies exhibit SHG responses and the total first hyperpolarizability responses of the aggregates are evolving with their size. The largest aggregation effect is a 18-times increase for ß H R S ${{\beta }_{HRS}}$ of B4 when going from the monomer to the pentamer, that ii)â the intrinsic SHG responses described by the hyper-Rayleigh Scattering ß ${\beta }$ are enhanced in presence of iodine atoms on the phenyl core, that iii)â the side chains affect the relative orientation of the dipole moment and first hyperpolarizability vectors, which impacts more the EFISHG quantities than their moduli, and that iv)â the radial component to ß ${\beta }$ is dominant for the compounds having the largest responses. These results have been obtained using the sequential molecular dynamics then quantum mechanics approach to account for dynamic structural effects on the SHG responses.
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The second-order nonlinear optical properties of four series of amphiphilic cationic chromophores involving different push-pull extremities and increasingly large polyenic bridges have been investigated both experimentally, by means of electric field induced second harmonic (EFISH) generation, and theoretically, using a computational approach combining classical molecular dynamics (MD) and quantum chemical (QM) calculations. This theoretical methodology allows to describe the effects of structural fluctuations on the EFISH properties of the complexes formed by the dye and its iodine counterion, and provides a rationale to EFISH measurements. The good agreement between experimental and theoretical results proves that this MD + QM scheme constitutes a useful tool for a rational, computer-aided, design of SHG dyes.
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In this work, expressions for the third-harmonic scattering optical activity (THS-OA) spectroscopic responses are derived by combining molecular quantum electrodynamics (QED) and response theory, allowing their computational implementation. The QED theory of THS-OA presented here is meant to be an extension of a previous study by Andrews [Symmetry 12, 1466 (2020)]. In particular, the THS-OA phenomena are described within the Power-Zienau-Woolley multipolar Hamiltonian by including the electric-dipole, magnetic-dipole, and electric-quadrupole interactions for the absorption as well as the emission processes between the dynamic electromagnetic field (the photons) and matter. Moreover, we derive the expressions for the differential scattering ratios as a function of the scattering angle defined by the wavevectors of the incident and scattered photons. We show how the pure and mixed second hyperpolarizabilities can be obtained in the framework of response theory as specific cases of a generic cubic response function, thus enabling the computational implementation of THS-OA spectroscopy. We prove the origin-independence of the theory for exact wavefunctions. Preliminary computations on a prototype chiral molecule (methyloxirane) are considered together with an analysis of the basis set convergence and of the origin-dependence.
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Using the CRYSTAL17 package at the coupled-perturbed Kohn-Sham (CPKS) level, periodic boundary conditions first-principles calculations are enacted to predict the second harmonic generation second-order nonlinear optical (NLO) susceptibility, χ(2), values of six historical NLO crystals. This selection allowed the comparison between state-of-the-art calculations and experiment. Several computational aspects are tackled to define conditions where the results are converged with respect to the range of lattice summations, to the number of k-points in the first Brillouin zone, to the order of the multipole expansions for evaluating the long-range part of the electrostatic interactions, as well as to the atomic basis set size. A valence triple zeta basis set supplemented with polarization functions has been selected. Then, χ(2) calculations have been performed using a range of exchange-correlation functionals (XCFs). Results show the large impact of the amount of Hartree-Fock (HF) exchange on the amplitude but also on the sign on the χ(2) tensor components. To a given extent, these amplitude effects are consistent with results on molecules, but the sign reversal effects and the non-monotonic behavior of the χ(2) tensor components as a function of the amount of HF exchange are scarcely found for molecules. Then, using the recommended range-separated hybrid XCFs, the CPKS scheme leads to good agreement with experimental data for potassium dihydrogenophosphate, urea, and χZXX (2) of LiNbO3. The agreement is more questionable for χZZZ (2) of LiNbO3 whereas it remains poor for ammonium dihydrogenophosphate and 2-methyl-4-nitroaniline, with large underestimations by about a factor of 3, opening a path to further fine-tuning of the ranges of inclusion of HF exchange.
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This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.
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The solvent effects on the linear and second-order nonlinear optical properties of an aminonaphtylethenylpyridinium (ANEP) dye are investigated by combining experimental and theoretical chemistry methods. On the one hand, deep near infrared (NIR) hyper-Rayleigh scattering (HRS) measurements (1840-1950 nm) are performed on solutions of di-8-ANEPPS in deuterated chloroform, dimethylformamide, and dimethylsulfoxide to determine their first hyperpolarizablity (ßHRS). For the first time, these HRS experiments are carried out in the picosecond regime in the deep NIR with very moderate (≤3 mW) average input power, providing a good signal-to-noise ratio and avoiding solvent thermal effects. Moreover, the frequency dispersion of ßHRS is investigated for Disperse Red 1 (DR1), a dye commonly used as HRS external reference. On the other hand, these are compared with computational chemistry results obtained by using a sequential molecular dynamics (MD) then quantum mechanics (QM) approach. The MD method allows accounting for the dynamical nature of the molecular structures. Then, the QM part is based on TDDFT/M06-2X/6-311+G* calculations using solvation models ranging from continuum to discrete ones. Measurements report a decrease of the ßHRS of di-8-ANEPPS in more polar solvents and these effects are reproduced by the different solvation models. For di-8-ANEPPS and DR1, comparisons show that the use of a hybrid solvation model, combining the description of the solvent molecules around the probe by point charges with a continuum model, already achieves quasi quantitative agreement with experiment. These results are further improved by using a polarizable embedding that includes the atomic polarizabilities in the solvent description.
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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, ß, and vice versa. In fact, the ß 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.
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Electrochemically switched 2nd order non-linear optical responses have been demonstrated for the first time in polyoxometalates (POMs), with an arylimido-derivative showing a leading combination of high on/off contrast (94 %), high visible transparency, and cyclability. Spectro-electrochemical and TD-DFT studies indicate that the switch-off results from weakened charge transfer (CT) character of the electronic transitions in the reduced state. This represents the first study of an imido-POM reduced state, and demonstrates the potential of POM hybrids as electrochemically activated molecular switches.
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Owing to their odd order, second-order nonlinear optical (NLO) responses are very sensitive to symmetry. Therefore, within hyper-Rayleigh scattering (HRS) technique, the symmetry impacts the amplitude of the molecular responses, the HRS first hyperpolarizability (ßHRS), and the depolarization ratio (DR). Starting from a challenging octupolar structure bearing six ruthenium(II) ammine centers π-conjugated via quaterpyridyl moieties to a tris-chelated zinc(II) core, together with its Λ shape and one-dimensional analogues built by replacing one or two Ru-quaterpyridyl moieties with bipyridine moieties, (time-dependent) density functional theory calculations have been enacted to unravel the symmetry-NLO response relationships as well as their RuII/III redox-triggered switching effects. The one-dimensional and Λ-shaped NLOphores present ßHRS values â¼3 times larger than those of the octupolar system, for both Ru oxidation states. However, using the few-state valence bond-charge transfer models demonstrates that the ßHRS response of the octupolar complex cation can become larger than those of its one-dimensional and Λ-shaped analogues provided stronger donor-acceptor groups are employed. In parallel, the DRs decrease from a strong dipolar character (DR ≈ 6) for the one-dimensional chromophore to a weaker dipolar character (DR ≈ 5) for the Λ-shaped one and to a clear octupolar character (DR ≈ 1.7) for the last one. In all cases, the ß responses originate mostly from metal-to-ligand charge transfer excited states, as revealed using a new scheme for analyzing the variations in electron density upon excitation. The RuII/III oxidations lead to a strong decrease in the ßHRS responses, which is attributed to the loss of the donor character of the Ru centers and therefore to the reduction of the push-pull π-conjugation. These results demonstrate that the NLO contrast and the NLO switching behavior of these Ru cations are maintained for the different molecular symmetries. Finally, the character of the ß responses of the oxidized species, as revealed by the DR values, further evidences a clear evolution from dipolar to octupolar NLOphores.
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The accurate prediction of the basicity of tertiary phosphines in acetonitrile and water is reported by the linear correlation between computed ΔpKa's obtained by density functional theory (DFT) and experimental values extracted from the literature. This method is applied to the prediction of pKa values of 9-phosphatriptycene derivatives and showed that they are weaker Brønsted bases than their triphenylphosphine analogues. This lower reactivity is attributed to their high pyramidalization that increases their lone pair 3s character, stabilizing its energy level. Their potential application in frustrated Lewis pair chemistry is then considered by investigating the hydrogenation of 1,1-diphenylethylene by the tris(pentafluorophenyl)borane/1-chloro-9-phosphatriptycene frustrated Lewis pair.
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The nonlinear optical response, more specifically the Hyper-Rayleigh Scattering (HRS) response of the Brooker's merocyanine, has been calculated at the time-dependent density functional theory level and rationalized in terms of the structural changes and polarization effects induced by applied external electric fields. The structural change leads to large changes in the HRS response, while only slight variations were observed due to the polarization effects on the fixed quinoid form. Considering both structural and polarization contributions concurrently, the HRS response is dominated by cooperative behavior of those effects for weak and intermediate electric field strengths. At the same time, the competition between both effects was a crucial factor in the region of strong electric fields. The obtained results can lead to an easier understanding for upcoming studies considering more realistic models of solvents where it is not simple to disentangle these contributions.