Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator.

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.

On the third-order nonlinear optical responses of cis and trans stilbenes - a quantum chemistry investigation.

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 γ‖ 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.

Reactivity and Steric Parameters from 2D to 3D Bulky Pyridines : Increasing Steric Demand at Nitrogen with Chiral Azatriptycenes.

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.

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 (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 〈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, ß(-2ω;ω,ω), which are limited to the first molecular layer (∼3.0 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.

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.

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 ß0,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.

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 (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.

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.

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, 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.

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.

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.

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.

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 ( 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) 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) 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) 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 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.

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 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.

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, ß, 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 ß tensor parallel to the bilayer normal, ßZZZ, 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.

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 (ß) 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 ßHRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the ß tensor normal to the interface (ßzzz ) as well as of ß// . Globally, the interfacial effects on ß are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.