Earth Mover's Charge Transfer Distance: A General and Robust Approach for Describing Excited State Locality

A novel approach for assessing the extent of electron displacement in optical transitions is proposed by implementing the Earth Mover's Distance (EMD) method, which quantifies the spatial dissimilarity between ground and excited state electron density distributions. In contrast to previous descriptors, this index provides a representative and intuitively understandable distance under a robust and computationally efficient scheme for all possible forms of locality, even in the most difficult to dissect topological cases. The theoretical differences among the existing indices and our method are first illustrated with the help of a simplified model system, followed by a benchmarking of several partial atomic charge models using experimentally relevant push-pull compounds with diverse symmetries. These same molecules are finally employed to further demonstrate the principal advantages of the EMD index and its capabilities in rationalizing charge transfer phenomena.

Disentangling the molecular polarizability and first hyperpolarizability of methanol-air interfaces

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 (β). This approach ensures the configurational diversity required to evaluate the average β values. The main achievements are (i) a quasi-absence of surface sensitivity of the mean polarizability 〈α〉 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, β(-2ω;ω,ω), which are limited to the first molecular layer (∼3.0 Å) and characterized by a high contrast in the βZZZ(-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.

Bridge improvement work: maximising non-linear optical performance in polyoxometalate derivatives

New phenyl and stilbene-bridged polyoxometalate (POM) charge-transfer chromophores with diphenylamino donor groups produce, respectively, the highest intrinsic and absolute quadratic hyperpolarisabilities measured for such species. The β0,zzz obtained for the phenyl bridge - at 180 × 10-30 esu - is remarkable for a short conjugated system while changing to the stilbene (260 × 10-30 esu) produces a substantial increase in non-linearity for a minimal red-shift in the absorption profile. Together with TD-DFT calculations, the results show that maximising conjugation in the π-bridge is vital to high performance in such "POMophores".

Multimillion Atom Simulations of Di-8-ANEPPS Chromophores Embedded in a Model Plasma Membrane: Toward the Investigation of Realistic Dyed Cell Membranes

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.

Second-order nonlinear optical properties of X-shaped pyrazine derivatives

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.

Three-Dimensional Rotational Averaging Using Irreducible Sets of Linearly Independent Fundamental Isotropic Cartesian Tensors: A Computational Approach

The theoretical formulation of linear and nonlinear molecular spectroscopies applied to isotropic samples (e.g., liquid or gas solutions) goes through a fundamental step known as the rotational averaging of Cartesian tensors. Rotational averaging of Cartesian tensors is a mathematical procedure from which the expressions for the rotationally invariant observables (e.g., rates or intensities), associated with a given spectroscopic process, can be found. In this work, the mathematical/computational procedure for finding the rotational averages of Cartesian tensors of any rank n, which is based on the use of the fundamental isotropic Cartesian tensors (FICTs), is discussed. Moreover, for the first time, a heuristic computational method for finding a set of linearly independent FICTs is proposed. The procedure has been tested for 2 ≤ n ≤ 12, where most of the linear and nonlinear molecular spectroscopies apply (e.g., one-photon and multiphoton absorption, emission, electronic circular dichroism, Raman optical activity, coherent and incoherent mth-harmonic generation, etc.). Finally, it is shown how this computational procedure can be extended for n > 12.

Intramolecular locking and coumarin insertion: a stepwise approach for TADF design

Three novel TADF (thermally activated delayed fluorescence) emitters based on the well-studied Qx-Ph-DMAC fluorophore are designed and synthesized. The photophysical properties of these materials are studied from a theoretical and experimental point of view, demonstrating the cumulative effects of multiple small modifications that combine to afford significantly improved TADF performance. First, an extra phenyl ring is added to the acceptor part of Qx-Ph-DMAC to increase the conjugation length, resulting in BQx-Ph-DMAC, which acts as an intermediate molecular structure. Next, an electron-deficient coumarin unit is incorporated to fortify the electron accepting ability, affording ChromPy-Ph-DMAC with red-shifted emission. Finally, the conjugated system is further enlarged by 'locking' the molecular structure, generating DBChromQx-DMAC with further red-shifted emission. The addition of the coumarin unit significantly impacts the charge-transfer excited state energy levels with little effect on the locally excited states, resulting in a decrease of the singlet-triplet energy gap. As a result, the two coumarin-based emitters show considerably improved TADF performance in 1 w/w% zeonex films when compared to the initial Qx-Ph-DMAC structure. 'Locking' the molecular structure further lowers the singlet-triplet energy gap, resulting in more efficient reverse intersystem crossing and increasing the contribution of TADF to the total emission.

First hyperpolarizability of the di-8-ANEPPS and DR1 nonlinear optical chromophores in solution. An experimental and multi-scale theoretical chemistry study

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 (βHRS). 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 βHRS 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 βHRS 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.

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.

Third-harmonic scattering optical activity: QED theory, symmetry considerations, and quantum chemistry applications in the framework of response theory

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.

Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications

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.

Electric-field induced second harmonic generation responses of push-pull polyenic dyes: experimental and theoretical characterizations

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.

Balanced Energy Gaps as a Key Design Rule for Solution-Phase Organic Room Temperature Phosphorescence

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.

Second Harmonic Generation Signatures of Supramolecular Assemblies Based on Amide Moieties

Targeting the use of the second harmonic generation (SHG) as a bioimaging technique to unravel the formation of aggregates, the SHG first hyperpolarizabilities (β) of assemblies of benzene-1,3,5-tricarboxamide derivatives have been evaluated at the density functional theory level. Calculations have revealed that i) 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 βHRS of B4 when going from the monomer to the pentamer, that ii) the intrinsic SHG responses described by the hyper-Rayleigh Scattering  are enhanced in presence of iodine atoms on the phenyl core, that iii) 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) the radial component to β 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.

First-principles evaluation of the second harmonic generation response of reference organic and inorganic crystals

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 χ_ZXX ⁽²⁾ of LiNbO₃. The agreement is more questionable for χ_ZZZ ⁽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.

Investigating the Mechanism of the Catalytic Intramolecular Aza-Wittig Reaction Involved in the Synthesis of 2-Methylbenzothiazole from the Perspective of Bonding Evolution Theory

The Bonding Evolution Theory has been used at the Density Functional Theory level [ωB97X-D exchange-correlation functional, 6-311G(d,p) basis set, and solvent (toluene) effects with polarizable continuum model] to unravel the reaction mechanism of the intramolecular aza-Wittig reaction of 2-(acetylthio)phenyl isocyanate (1) catalyzed by 3-methyl-1-phenyl-2-phospholene 1-oxide (2) to form 2-methylbenzothiazole (3). The reaction involves four steps (transition states) corresponding to i) the formation of a cycloadduct (O-C then P-N bonds), ii) then a decarboxylation leading to the formation of an iminophosphorane, and iii) an intramolecular [2+2] cycloaddition (N-C then P-O bonds) followed by iv) a retro [2+2] cycloaddition (cleavage of the P-N then O-C bonds) to get the product and regenerate the catalyst. Step 1 is the rate determining step with an activation Gibbs free enthalpy of 21 kcal mol-1 and it is favored with respect to a competitive pathway leading to the formation of another cycloadduct (P-C then O-N bonds). The whole reaction is exergonic with a Gibbs free energy decrease of 31 kcal mol-1, associated with the liberation of a CO2 molecule and the formation of the aromatic benzothiazole. Following the scale of Domingo, the successive steps of the reaction have a polar nature.

Electrochemically-Switched 2nd Order Non-Linear Optical Response in an Arylimido-Polyoxometalate with High Contrast and Cyclability

Electrochemically switched 2^nd 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.

Influence of the Nature of the Lipid Building Blocks on the Second-Order Nonlinear Optical Responses of an Embedded Di-8-ANEPPS Probe

The extensive collection of lipids found in cell membranes is justified by the fact that each lipid contributes to their overall structure, dynamics, and properties and so to the biological processes taking place within them. It also showcases that, in order to deepen our understanding of membranes, we need to have a tool to differentiate lipid bilayers of varying composition. In this work, we investigate a suite of single-component saturated glycerophospholipids varying only in their headgroup structure by analyzing the second harmonic generation (SHG) nonlinear optical (NLO) response of a probe, di-8-ANEPPS, embedded into the membranes. The seven hydrophilic heads chosen (phosphatidylcholine (PC), phosphatidylethanolamine (PE), diaglycerol (GL), phosphatidylserine (PS), phosphatidylglycerol (PG), phosphatidylinositol (PI), and phosphatidyc acid (PA)) represent all the major headgroups that are part of mammalian plasma membranes and provide an assortment of neutral, zwiterrionic, and charged species. First, molecular dynamics simulations revealed that the lipidic arrangement is strongly sensitive to the nature of the hydrophilic head and less to the variety in the hydrophobic region. Membranes exhibiting drastically opposite structural properties can be pointed out: 1,2-dihexadecanoyl-rac-glycerol (DPGL) is the thickest and most ordered and aligned system, whereas 1,2-diacyl-sn-glycero-3-phospho-(1'-sn-glycerol) (DPPG) is thinnest and least ordered and aligned system. The structural analyses are then confronted with the molecular NLO responses, β, computed at the time-dependent density functional theory (TDDFT) level. As the orientation of the chromophore is impacted by the various degrees of order within the lipid bilayers, the diagonal component of the β tensor parallel to the bilayer normal, β_ZZZ, is as well. In the end, this computational approach provides insights into the link between lipid building blocks and the NLO responses of the embedded dye.

Investigation of the Second Harmonic Generation at the Water-Vacuum Interface by Using Multi-Scale Modeling Methods

Invited for this month's cover picture are Dr. Tárcius N. Ramos and Prof. Benoît Champagne at the University of Namur (Belgium). The cover picture shows the interfacial selectivity of second harmonic generation at the water-vacuum interface, which is targeted in this work. In more details, the molecular first hyperpolarizability responses have been calculated by combining classical molecular dynamics and quantum chemistry simulations, and our model was able to distinguish between the bulk and the interfacial contributions. Read the full text of their Research Article at 10.1002/open.202200045.

Predicting the Second-Order Nonlinear Optical Responses of Organic Materials: The Role of Dynamics

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 (β), 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.

Investigation of the Second Harmonic Generation at the Water-Vacuum Interface by Using Multi-Scale Modeling Methods

The Sequential Quantum Mechanics/Molecular Mechanics scheme has been enacted to perform a systematic investigation of the polarizability (α) and first hyperpolarizability (β) responses at the water-vacuum interface. After performing classical molecular dynamics simulations to provide snapshots of the structures, quantum chemistry calculations of the linear and nonlinear optical responses have been performed for clusters of five water molecules at the time-dependent DFT level in combination with different embedding schemes, ranging from point charges to polarizable point charges, with and without local field effects. When going from the bulk to the interface, the main observations of these calculations encompass i) a modest increase of the average polarizability but an increase by about a factor of two of its anisotropy, ii) an increase by about 20 % of the β_HRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the β tensor normal to the interface (β_zzz ) as well as of β_// . Globally, the interfacial effects on β are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.

9-Phosphatriptycene Derivatives: From Their Weak Basicity to Their Application in Frustrated Lewis Pair Chemistry

The accurate prediction of the basicity of tertiary phosphines in acetonitrile and water is reported by the linear correlation between computed ΔpK_a's obtained by density functional theory (DFT) and experimental values extracted from the literature. This method is applied to the prediction of pK_a 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.

TDDFT Investigation of the Raman and Resonant Raman Spectra of Fluorescent Protein Chromophore Models

The off-resonance and resonant Raman spectra have been simulated for models of fluorescent protein chromophores, those of the green fluorescent protein (GFP, called FP1) and of DsRed (called FP2), which presents a longer π-conjugated path, with the aim of providing a systematic investigation of structural but also computational aspects. These were performed at the (time-dependent) density functional theory [(TD)DFT] level. The off-resonance intensities have been calculated from the derivatives of the frequency-dependent polarizability with respect to the normal coordinates while the resonant ones have been evaluated using Huang-Rhys factors determined from the gradients of the excitation energies with respect to the normal coordinates. When applied with the M05 meta-GGA exchange-correlation functional, this simple computational scheme can reproduce most of the experimental Raman signatures of FP1 in its protonated and deprotonated forms, the differences of vibrational signatures of the cis (Z) and trans (E) isomers, as well as their changes as a function of the excitation wavelength. On the other hand, testing the predictions made for FP2 would require new experimental work. It was also observed that simulations with methods that inadequately predict the resonant Raman spectra could nevertheless produce a UV-vis absorption spectrum that is quite similar to the one obtained with better methods, once realistic peak broadening has been applied.

Unraveling the Symmetry Effects on the Second-Order Nonlinear Optical Responses of Molecular Switches: The Case of Ruthenium Complexes

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 (β_HRS), 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 Ru^II/III redox-triggered switching effects. The one-dimensional and Λ-shaped NLOphores present β_HRS values ∼3 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 β_HRS 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 β 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 Ru^II/III oxidations lead to a strong decrease in the β_HRS 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 β responses of the oxidized species, as revealed by the DR values, further evidences a clear evolution from dipolar to octupolar NLOphores.

Unveiling the relationship between structural and polarization effects on the first hyperpolarizability of a merocyanine dye

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.

Unveiling the [3+2] cycloaddition between difluoromethyl diazomethane and 3-ylideneoxindole from the perspective of molecular electron density theory

Evolution of some key ELF basins along the IRC of the most favorable ortho/endo reaction path.

Simulation of absorption and scattering spectra of crystalline organic nanoparticles with the discrete dipole approximation: Effects of crystal shape, crystal size, and refractive index of the medium

The effect of the shape (habit) of crystalline organic nanoparticles on their absorption spectra is studied by simulations using the discrete dipole approximation, focusing, in particular, on the vibronic structure of the absorption bands in the spectra. Simulations predict a significant effect that, for sufficiently small particles, can be simply rationalized by the depolarization factor. The crystal size and the refractive index of the medium in which the nanoparticles are embedded are also found to have an effect on the absorption spectra. All factors mentioned are found to influence also the spectra of scattered light. These effects, already broadly documented for metallic nanoparticles, are here demonstrated theoretically for the first time for crystalline organic nanoparticles, providing novel insight into the optical response of such particles. The effects are expected to be displayed by all organic nanoparticles, as long as they have a well-defined crystal structure and are large enough for the optical properties to be understandable using a macroscopic dielectric tensor. The effects demonstrated here should be taken into account when rationalizing differences in absorption spectra of a substance in solution and in nanoparticle form, e.g., in deducing the type of intermolecular packing. The effects are much less pronounced for optically isotropic nanoparticles.

Self-assembling, structure and nonlinear optical properties of fluorescent organic nanoparticles in water

Owing to their intense emission, low toxicity and solubility in aqueous medium, fluorescent organic nanoparticles (FONs) have emerged as promising alternatives to inorganic ones for the realization of exogenous probes for bioimaging applications. However, the intimate structure of FONs in solution, as well as the role played by intermolecular interactions on their optical properties, remains challenging to study. Following a recent Second-Harmonic Scattering (SHS) investigation led by two of us [Daniel et al., ACS Photonics, 2015, 2, 1209], we report herein a computational study of the structural organization and second-order nonlinear optical (NLO) properties of FONs based on dipolar chromophores incorporating a hydrophobic triphenylamine electron-donating unit and a slightly hydrophilic aldehyde electron-withdrawing unit at their extremities. Molecular dynamics simulations of the FON formation in water are associated with quantum chemical calculations, to provide insight into the molecular aggregation process, the molecular orientation of the dipolar dyes within the nanoparticles, and the dynamical behavior of their NLO properties. Moreover, the impact of intermolecular interactions on the NLO responses of the FONs is investigated by employing the tight-binding version of the recently developed simplified time-dependent density functional theory (sTD-DFT) approach, allowing the all-atom quantum mechanics treatment of nanoparticles.

All-Atom Quantum Mechanical Calculation of the Second-Harmonic Generation of Fluorescent Proteins

Fluorescent proteins (FPs) are biotags of choice for second-harmonic imaging microscopy (SHIM). Because of their large size, computing their second-harmonic generation (SHG) response represents a great challenge for quantum chemistry. In this contribution, we propose a new all-atom quantum mechanics methodology to compute SHG of large systems. This is now possible because of two recent implementations: the tight-binding GFN2-xTB method to optimize geometries and a related version of the simplified time-dependent density functional theory (sTD-DFT-xTB) to evaluate quadratic response functions. In addition, a new dual-threshold configuration selection scheme is introduced to reduce the computational costs while retaining overall similar accuracy. This methodology was tested to evaluate the SHG of the proteins iLOV and bacteriorhodopsin (bR). In the case of bR, quantitative agreement with respect to experiment was reached for the out-of-resonance low-energy part of the β_HRS frequency dispersion. This work paves the way toward an accurate prediction of the SHG of large structures-a requirement for the design of new and improved SHIM biotags.

Computational prediction of the supramolecular self-assembling properties of organic molecules: the role of conformational flexibility of amide moieties

Two families of organic molecules with different backbones have been considered. The first family is based on a macrolactam-like unit that is constrained in a particular conformation. The second family is composed by a substituted central phenyl that allows a larger mobility for its substituents. They have however a common feature, three amide moieties (within the cycle for the macrolactam-like molecule and as substituents for the phenyl) that permit hydrogen bonding when molecules are stacked. In this study we propose a computational protocol to unravel the ability of the different families to self-assemble into organic nanotubes. Starting from the monomer and going towards larger assemblies like dimers, trimers, and pentamers we applied the different protocols to rationalize the behavior of the different assemblies. Both structures and thermodynamics were investigated to give a complete picture of the process. Thanks to the combination of a quantum mechanics approach and molecular dynamics simulations along with the use of tailored tools (non covalent interaction visualization) and techniques (umbrella sampling), we have been able to differentiate the two families and highlight the best candidate for self-assembling purposes.

Unravelling the Effects of Cholesterol on the Second-Order Nonlinear Optical Responses of Di-8-ANEPPS Dye Embedded in Phosphatidylcholine Lipid Bilayers

Cholesterol is known for its role in maintaining the correct fluidity and rigidity of the animals cell membranes and thus their functions. Assessing the content and the role of cholesterol in lipid bilayers is therefore of crucial importance for a deeper understanding and control of membrane functioning. In this computational work, we investigate bilayers built from three types of glycerophospholipid phosphatidylcholine (PC) lipids, namely dipalmitoylphosphatidylcholine (DPPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), and dioleoylphosphatidylcholine (DOPC), and containing different amounts of cholesterol by analyzing the second-harmonic generation (SHG) nonlinear optical (NLO) response of a probe molecule, di-8-ANEPPS, inserted into the membranes. This molecular property presents the advantage to be specific to interfacial regions such as lipid bilayers. To unravel these effects, Molecular Dynamics (MD) simulations have been performed on both DPPC and DOPC lipids by varying the cholesterol mole fraction (from 0 to 0.66), while POPC was only considered as a pure bilayer. In the case of the structural properties of the bilayers, all the analyses converge toward the same conclusion: as the mole fraction of cholesterol increases, the systems become more rigid, confirming the condensing effect of cholesterol. In addition, the chromophore is progressively more aligned with respect to the normal to the bilayer. On the contrary, addition of unsaturation disorders the lipid bilayers, with barely no impact on the alignment of the chromophore. Then, using the frames obtained from the MD simulations, the first hyperpolarizability β of the dye in its environment has been computed at the TDDFT level. On the one hand, the addition of cholesterol induces a progressive increase of the diagonal component the β tensor parallel to the bilayer normal. On the other hand, larger β values have been calculated for the unsaturated than for the saturated lipid systems. In summary, this study illustrates the relationship between the composition and structure of the bilayers and the NLO responses of the embedded dye.

Polar and Helical Isomorphous Crystals of Proline Derivatives: Influence of a Fluorine Atom on the Electric Susceptibility

Two novel nonlinear optical isomorphous crystals of proline derivatives with alkyne functionality have been obtained (Boc-L-ProNH(CH2)2CCH and Boc-cis-4-fluoro-L-ProNH(CH2)2CCH). Both derivatives, which differ only by the substitution of a H atom to a F atom, adopt the same polar and columnar right-handed helix arrangement in the crystalline state. In addition, adjacent polar helical columns all point in the same direction, thus generating a macrodipole and a crystalline system conducive for second harmonic generation (SHG) properties. This isomorphous crystal system constitutes an interesting tool to study the effect of the fluorine atom on the dipole moment and on the first hyperpolarizability. Starting from the PBC optimized geometries of the crystals, the macroscopic second-order nonlinearity, χ(2), of the newly synthesized crystals has been estimated by quantum chemical calculations. These χ(2) responses are of the same order of magnitude as those of inorganic proline derivatives while smaller than those observed in crystals of push–pull π-conjugated molecules.

Graphic Abstract

Rational Development of a Metal-Free Bifunctional System for the C-H Activation of Methane: A Density Functional Theory Investigation

The activation or heterolytic splitting of methane, a challenging substrate usually restricted to transition metals, has so far proven elusive in experimental frustrated Lewis pair (FLP) chemistry. In this article, we demonstrate, using density functional theory (DFT), that 1-aza-9-boratriptycene is a conceptually simple intramolecular FLP for the activation of methane. Systematic comparison with other FLP systems allows to gain insight into their reactivity with methane. The thermodynamics and kinetics of methane activation are interpreted by referring to the analysis of the natural charges and by employing the distortion-interaction/activation strain (DIAS) model. These showed that the nature of the Lewis base influences the selectivity over the reaction pathway, with N Lewis bases favoring the deprotonation mechanism and P bases the hydride abstraction one. The lower barrier of activation for 1-aza-9-boratriptycene and the higher products stability are due to a better interaction energy than its counterparts, itself due to electrostatic interactions with the methane moiety, favorable orbital overlaps allowed by the side-attack, and space proximity between the B and N atoms.

Heavy-Atom-Free Bay-Substituted Perylene Diimide Donor-Acceptor Photosensitizers

Perylene diimide (PDI) dyes are extensively investigated because of their favorable photophysical characteristics for a wide range of organic material applications. Fine-tuning of the optoelectronic properties is readily achieved by functionalization of the electron-deficient PDI scaffold. Here, we present four new donor-acceptor type dyads, wherein the electron donor units - benzo[1,2-b : 4,5-b']dithiophene, 9,9-dimethyl-9,10-dihydroacridine, dithieno[3,2-b : 2',3'-d]pyrrole, and triphenylamine-are attached to the bay-positions of the PDI acceptor. Intersystem crossing occurs for these systems upon photoexcitation, without the aid of heavy atoms, resulting in singlet oxygen quantum yields up to 80 % in toluene solution. Furthermore, this feature is retained when the system is directly irradiated with energy corresponding to the intramolecular charge-transfer absorption band (at 639 nm). Geometrical optimization and (time-dependent) density functional theory calculations afford more insights into the requirements for intersystem crossing such as spin-orbit coupling, dihedral angles, the involvement of charge-transfer states, and energy level alignment.

Combining Benzazolo-Oxazolidine Twins toward Multi-state Nonlinear Optical Switches

Molecular switches are chemical compounds exhibiting the possibility of reversible transformations between their different forms accompanied by a modification in their properties. Among these, switching of multi-addressable Benzazolo-OXazolidines (BOXs) from a closed form to an open form results in drastic modifications in their linear and nonlinear optical properties. Here, we target molecules containing two identical BOX units (DiBOX) connected by different π-conjugated linkers, and we combine synthesis, UV/visible absorption, and hyper-Rayleigh scattering (HRS) measurements, together with density functional theory (DFT) calculations. Three derivatives have been considered, which differ by the linker: (i) a bithiophene moiety (Bt), (ii) two 3,4-ethylenedioxythiopene (EDOT) units, and (iii) a triad composed of an EDOT-thiophene-EDOT sequence (TtO). As a matter of fact, these systems can adopt three states (CF-CF, POF-POF, and CF-POF) depending on the closed form (CF) or the protonated open form (POF) of each BOX unit. Despite chemical equivalence, stepwise switching of such systems under the addition of a chemical acid or an oxidant has been experimentally evidenced for two of them (DiBOX-Bt and DiBOX-TtO). Then, DFT calculations show that the first BOX opening leads to the formation of a push-pull π-conjugated segment, exhibiting a huge increase in the first hyperpolarizability (β) and a bathochromic shift with respect to the fully closed form. On the contrary, the second BOX opening induces not only a slight bathochromic shift but also a reduction in their β values conferring the great and uncommon abilities to modulate their linear and nonlinear properties over three discrete levels. Among these results, those on DiBOX-Bt agree with the experimental data obtained by HRS measurements and further shed light on their structure-property relationship.

Second Harmonic Generation Responses of Ion Pairs Forming Dimeric Aggregates

A sequential approach combining molecular dynamics and density functional theory calculations has been worked out to unravel the second harmonic generation responses of anion-cation (AC) pairs when they form dimeric aggregates, where the cation is a stilbazolium derivative and the anions range from small inorganic iodide to medium-size organic p-toluenesulfonate. These complexes showed a strong self-aggregation behavior in molecular dynamics simulations within high-concentration conditions and formed stable dimeric aggregates, (AC)₂, which can adopt different structural shapes from stacked, Λ, to head-to-head configurations. These various structures are associated with different symmetries, which are shown to modulate the second- and third-order nonlinear optical (NLO) responses. By consolidating the NLO results of this work with those previously obtained for single AC pairs [ J. Chem. Inf. Model. 2020, 60, 4817-4826], we have been able to explain the experimentally observed variations of the electrical-field-induced second harmonic generation (EFISHG) responses of these complexes as a function of concentration [ ChemPhysChem 2010, 11, 495-507]. Moreover, results have highlighted that (i) the second-order contribution, μβ_//, dominates the global EFISHG response; (ii) the μβ_// responses of dimers are about half of those computed for the parent AC pairs, while the third-order contributions, γ_//, are reduced by only 10%; (iii) these distinct trends are ascribed to the formation of dimers adopting mainly Λ and head-to-head shapes, increasing the centrosymmetric character, in comparison to the monomers, a situation in which the second-order response cancels out as well as influences the dipole moment on μβ_//; (iv) the presence of a strong amino donor group in the cation enhances the μβ_// response by 1 order of magnitude and γ_// by about a factor of 2; and finally, (v) dimeric aggregation has similar effects on the hyper-Rayleigh scattering response, β_HRS, as on μβ_//, while it reduces the one-dimensional character of β_HRS. This work constitutes a step forward for the modeling of the NLO responses of AC aggregates in solution.

Methylene Bridging Effect on the Structures, Lewis Acidities and Optical Properties of Semi-planar Triarylboranes

Three synthetic methods towards semi-planar triarylboranes with two aryl rings connected by a methylene bridge have been developed. The fine-tuning of their stereoelectronic properties and Lewis acidities was achieved by introducing fluorine, methyl, methoxy, n-butyl and phenyl groups either at their exocyclic or bridged aryl rings. X-ray diffraction analysis and quantum-chemical calculations provided quantitative information on the structural distortion experienced by the near planar hydro-boraanthracene skeleton during the association with Lewis bases such as NH₃ and F^- . Though the methylene bridge between the ortho-positions of two aryl rings of triarylboranes decreased the Gibbs free energies of complexation with small Lewis bases by less than 5 kJ mol^-1 relative to the classical Lewis acid BAr₃ , the steric shielding of the CH₂ bridge is sufficient to avoid the formation of Lewis adducts with larger Lewis bases such as triarylphosphines. A newly synthesized spirocyclic amino-borane with a long intramolecular B-N bond that could be dissociated under thermal process, UV-irradiation, or acidic conditions might be a potential candidate in Lewis pairs catalysis.

Topological investigation of the reaction mechanism of glycerol carbonate decomposition by bond evolution theory

The reaction mechanisms of the decomposition of glycerol carbonate have been investigated at the density functional theory level within the bond evolution theory. The four reaction pathways yield to 3-hydroxypropanal (TS1), glycidol (TS2a and TS2b), and 4-methylene-1,3-dioxolan-2-one (TS3). The study reveals non-concerted processes with the same number (four) of structural stability domains for each reaction pathway. For the two decarboxylation mechanisms, the two first steps are similar. They correspond to the cleavage of two single CO bonds to the detriment of the increased population of the lone pairs of two O atoms. These are followed, along TS1, by the transformation of a CO single bond into a double bond together with a proton transfer to create a CH bond. For TS2a and TS2b, the last step is a cyclization by CO bond formation. For the TS3 pathway, the first stage consists in the cleavage of a CH bond and the transfer of its electron population to both a proton and a C atom, the second step corresponds to the formation of an OH bond, and the last one describes the formation of a CC double bond. Moreover, the analysis of the energies, enthalpies, and free enthalpies of reaction and of activation leads to the conclusion that 3-hydroxypropanal is both the thermodynamic and kinetic product, independent of the method of calculation.

ELFs of glycerol carbonate and of its kinetic and thermodynamic decomposition product, 3-hydroxypropanal (+CO₂).