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.

Application to nonlinear optical properties of the RSX-QIDH double-hybrid range-separated functional

The effective calculation of static nonlinear optical properties requires a considerably high accuracy at a reasonable computational cost, to tackle challenging organic and inorganic systems acting as precursors and/or active layers of materials in (nano-)devices. That trade-off implies to obtain very accurate electronic energies in the presence of externally applied electric fields to consequently obtain static polarizabilities (α i j ) and hyper-polarizabilities (β i j k andγ i j k l ). Density functional theory is known to provide an excellent compromise between accuracy and computational cost, which is however largely impeded for these properties without introducing range-separation techniques. We thus explore here the ability of a modern (double-hybrid and range-separated) Range-Separated eXchange Quadratic Integrand Double-Hybrid exchange-correlation functional to compete in accuracy with more costly and/or tuned methods, thanks to its robust and parameter-free nature.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

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.

High-throughput virtual screening of organic second-order nonlinear optical chromophores within the donor-π-bridge-acceptor framework

In view of the theoretical importance and huge application potential of second-order nonlinear optical (NLO) materials, it is of great significance to conduct high-throughput virtual screening (HTVS) on a compound library to find candidate NLO chromophores. Under the donor-π-bridge-acceptor structural framework, a virtual compound library (size = 27 090) was constructed by enumeration of structural fragments. The kernel property adopted for optimization is the static first hyperpolarizability (β0). By combining machine learning and quantum chemical calculations, we have performed an HTVS procedure to sieve NLO chromophores out, and the response mechanism of the selected optimal NLO chromophores was examined. We have found: (a) The multi-layer perceptron/extended connectivity fingerprint combination with 20% selection ratio gives the highest prediction accuracy for the studied systems. (b) The two optimal donors are bis(4-diphenylaminophenyl)aminyl and bis(4-tert-butylphenyl)aminyl; the optimal π-bridges are composed of two thiophenyl, selenophenyl or furanyl units; and the two optimal acceptors are tri-s-triazinyl and 2,3-dicyanopyrazinyl. (c) The no. 1 candidate molecule can exhibit a calculated β0 equal to 8.55 × 104 a.u. (d) The difference in NLO responses of the optimal 16 molecules comes from the synergistic interaction of ES1, Δμ and f, by employing the two-level model. In addition, the sizable Δμ and f allow the studied optimal molecules to obtain a large NLO response in the meantime keeping a not-too-low excitation energy (retaining good optical transparency in the restricted range of the visible spectrum region). (e) With further modification on the acceptor, the designed DPA-π-TRZ-A' (A' = CN or NO2, π = oligo-thiophenyl or selenophenyl) systems can exhibit a rather large NLO response (maximum β0 = 3.17 × 105 a.u.), hence should have considerable potential as second-order NLO chromophores. With the above observations, we expect to provide some insight for the research community into the HTVS of organic second-order NLO chromophores.

Fabrication of Two-Dimensional Homo-Bimetallic Porphyrin Framework Thin Films for Optimizing Nonlinear Optical Limiting

Developing efficient metal-organic framework (MOF) optical devices with tunable third-order nonlinear optical (NLO) properties is an important challenge for scientific research and practical application. Herein, 2D monometallic and hetero/homo-bimetallic porphyrin MOF thin films (ZnTCPP(M) M = H2, Fe, Zn) were fabricated using the liquid-phase epitaxial (LPE) layer-by-layer (LBL) method to investigate the metal substitution dependent third-order NLO behavior. The prepared homo-bimetallic ZnTCPP(Zn) thin film exhibited enhanced third-order NLO performance with a higher third-order nonlinear susceptibility of ∼4.21 × 10-7 esu compared to monometallic and hetero-bimetallic counterparts. Additionally, theoretical calculations were performed to complement the experimental findings and revealed that the enhanced NLO effect of the ZnTCPP(Zn) thin film is mainly attributed to the enhanced local excitation. These findings not only provide a comprehensive understanding of the relationship between metal types and the NLO behavior of porphyrin MOF thin films but also offer valuable insights into the design and optimization of NLO devices.

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.

Application of Inverse Design Approaches to the Discovery of Nonlinear Optical Switches

Molecular switches, in which a stimulus induces a large and reversible change in molecular properties, are of significant interest in the domain of photonics. Due to their commutable redox states with distinct nonlinear optical (NLO) properties, hexaphyrins have emerged as a novel platform for multistate switches in nanoelectronics. In this study, we employ an inverse design algorithm to find functionalized 26R→28R redox switches with maximal βHRS contrast. We focus on the role of core modifications, since a synergistic effect with meso-substitutions was recently found for the 30R-based switch. In contrast to these findings, the inverse design optima and subsequent database analysis of 26R-based switches confirm that core modifications are generally not favored when high NLO contrasts are targeted. Moreover, while push-pull combinations enhance the NLO contrast for both redox switches, they prefer a different arrangement in terms of electron-donating and electron-withdrawing functional groups. Finally, we aim at designing a three-state 26R→28R→ 30R switch with a similar NLO response for both ON states. Even though our best-performing three-state switch follows the design rules of the 30R-based component, our chemical compound space plots show that well-performing three-state switches can be found in regions shared by high-responsive 26R and 30R structures.

Efficient calculation of electronic coupling integrals with the dimer projection method via a density matrix tight-binding potential

Designing organic semiconductors for practical applications in organic solar cells, organic field-effect transistors, and organic light-emitting diodes requires understanding charge transfer mechanisms across different length and time scales. The underlying electron transfer mechanisms can be efficiently explored using semiempirical quantum mechanical (SQM) methods. The dimer projection (DIPRO) method combined with the recently introduced non-self-consistent density matrix tight-binding potential (PTB) [Grimme et al., J. Chem. Phys. 158, 124111 (2023)] is used in this study to evaluate charge transfer integrals important for understanding charge transport mechanisms. PTB, parameterized for the entire Periodic Table up to Z = 86, incorporates approximate non-local exchange, allowing for efficient and accurate calculations for large hetero-organic compounds. Benchmarking against established databases, such as Blumberger's HAB sets, or our newly introduced JAB69 set and comparing with high-level reference data from ωB97X-D4 calculations confirm that DIPRO@PTB consistently performs well among the tested SQM approaches for calculating coupling integrals. DIPRO@PTB yields reasonably accurate results at low computational cost, making it suitable for screening purposes and applications to large systems, such as metal-organic frameworks and cyanine-based molecular aggregates further discussed in this work.

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.

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.

Designing hexaphyrins for high-potential NLO switches: the synergy of core-modifications and meso-substitutions

Due to the enormous size of the chemical compound space, usually only small regions are traversed with traditional direct molecular design approaches making the discovery for novel functionalized molecules for nonlinear optical applications challenging. By applying inverse molecular design algorithms, we aim to efficiently explore larger regions of the compound space in search of promising hexaphyrin-based molecular switches as measured by their first-hyperpolarizability (β_HRS) contrast. We focus on the 28R → 30R switch with a functionalization pattern allowing for centrosymmetric OFF states yielding zero β_HRS response. This switch is particularly challenging as full meso-substitution with a single type of functional group or core-modifications result in almost no contrast enhancement. We carried out four inverse design procedures during which two sets of core-modifications and three sets of meso-substitutions sites were systematically optimized. All 4 optimal switches are characterized by a mix of meso-substitutions and core-modifications, of which the best performing switch yields a 10-fold improvement over the parent macrocycle. Throughout the inverse design procedures, we collected and analyzed a database biased towards high NLO contrasts that contains 277 different patterns for hexaphyrin-based switches. We derived three design rules to obtain highly functional 28R → 30R NLO switches: (I) a combination of 2 strong EWG and 1 EDG group is the ideal recipe for increasing the NLO contrast, though their position also plays an important role. (II) The type of core-modification is less important when only the diagonal positions are core-modified. Switches with 4 core-modifications show a clear preference for oxygen. (III) Keeping centrosymmetry in the OFF state remains highly beneficial given the investigated functionalization pattern. Finally, we have demonstrated that combining meso-substitutions with core-modifications can synergistically improve the NLO contrast.

Nonlinear Optical Responses of Photoswitchable Donor-Acceptor Stenhouse Adducts

This work combines hyper-Rayleigh scattering (HRS) experiments performed in the NIR range (1.30 and 1.60 μm) and quantum chemical calculations to provide a comprehensive description of the second harmonic generation (SHG) responses of donor-acceptor Stenhouse adducts (DASAs). Representative derivatives of the three generations of DASAs, which differ by the nature of their electron-donating and withdrawing moieties and also include clickable species, have been synthesized and their photoswitching behavior fully characterized. The HRS measurements allow us to establish relationships between the magnitude of the SHG response of open forms and the nature of the donor and acceptor groups. The largest SHG responses are obtained for derivatives incorporating either a barbituric acid or an indanedione acceptor unit, while N-methylaniline appears as the most efficient donor group. The calculations support well the experimental data and show that high hyperpolarizabilities are associated to low excitation energies and large extent of the photoinduced intramolecular charge transfer, which enhances the dipole moment variation between the ground and first dipole-allowed electronic excited state. In addition, a complete investigation of the photoswitching kinetics of DASAs in chloroform solution shows important differences, highlighting in particular the role of the donor group on the photoswitching efficiency.

Coordination-Induced Symmetry Breaking on Metal-Porphyrinic Framework Thin Films for Enhanced Nonlinear Optical Limiting

Structural asymmetry affecting the nonlinear optics (NLO) of metal-organic frameworks (MOFs) is very important in fundamentals and applications but is still a challenge. Herein we develop a series of indium-porphyrinic framework (InTCPP) thin films and provide the first study on the coordination-induced symmetry breaking on their third-order NLO. The continuous and oriented InTCPP(H₂) thin films were grown on quartz substrates and then postcoordinated with different cations (Fe²⁺ or Fe³⁺Cl^-) in InTCPP(H₂) (named InTCPP(Fe²⁺) and InTCPP(Fe³⁺Cl^-)). The third-order NLO results reveal the Fe²⁺ and Fe³⁺Cl^- coordinated InTCPP thin films have substantially enhanced NLO performance. Moreover, InTCPP(Fe³⁺Cl^-) thin films cause symmetry breaking of microstructures, resulting in a 3-fold increase in the nonlinear absorption coefficient (up to 6.35 × 10^-6 m/W) compared to InTCPP(Fe²⁺). This work not only develops a series of nonlinear optical MOF thin films but also provides new insight into symmetry breaking on MOFs for nonlinear optoelectronic applications.

Effects of external field wavelength and solvation on the photophysical property and optical nonlinearity of 1,3-thiazolium-5-thiolates mesoionic compound

The photophysical property and optical nonlinearity of an electronic push-pull mesoionic compound, 2-(4-trifluoromethophenyl)-3-methyl-4-(4-methoxyphenyl)-1,3-thiazole-5-thiolate, were theoretically investigated with a reliable computing strategy. The essence of the optical properties were then explored through a variety of wavefunction analysis methods, including the natural transition orbital analysis, hole-electron analysis, (hyper)polarizability density analysis, decomposition of the (hyper)polarizability contribution, and (hyper)polarizability tensor analysis, at the level of electronic structure. The influences of the electric field and solvation on the absorption spectrum and (hyper)polarizability of the molecule are highlighted and clarified. The results are expected to provide guidance for people to understand the effects of external field wavelength and solvation on the optical properties of mesoscopic molecules.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

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.

The Importance of the Density Functional Theory Exchange-Correlation Hartree-Fock Term in Magnetic Resonance: Application to an Aqueous Environment

Within the framework of Density Functional Theory (DFT), the relevance of the term Hartree-Fock exchange (HFE) for a variety of molecular properties is a critical point. For this reason, we spend efforts to understand these relationships in nuclear magnetic resonance (NMR) parameters in a water solvent. This work takes advantage of the appropriate aug-cc-pVTZ-J basis set and the Minnesota family of DFT methods, which consider different portions of HFE contributions. With regard to solvent participation, the results are based on a sequential Monte Carlo/Quantum Mechanics procedure, which builds the structures of the liquid under realistic thermodynamic conditions. Compared to the accurate results of second-order polarization propagator approximation (SOPPA) and experimental data, all NMR parameters show a huge dependence on the size of the HFE contribution. For instance, the inclusion of this term in ¹J_OH and ²J_HH indirect spin-spin couplings does vary with 49.661 and 25.459 Hz, respectively. The M06-HF method accounts for 100% of HFE and better matches the σ_O and σ_H shielding constants. On the other hand, ¹J_OH and ²J_HH demand a medium contribution (54% of HFE), the best description being associated with the M06-2X method. Thus, the dependence varies regarding the phenomenology of the property in focus and the order for independent treatments. For elements that participate in hydrogen bonds simultaneously as donor and acceptor actors, the results indicate that explicit solvent molecules must be considered in the quantum mechanical calculations for better modeling of paramagnetic shielding constants.

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.

Molecular Electrides: An In Silico Perspective

Electrides are defined as the ionic compounds where the electron(s) serves as an anion. These electron(s) is (are) not bound to any atoms, bonds, or molecules rather than they are localized into the space, crystal voids, or interlayer between two molecular slabs. There are three major categories of electrides, known as organic electriades, inorganic electrides, and molecular electrides. The computational techniques have proven as a great tool to provide emphasis on the electride materials. In this review, we have focused on the computational methodologies and criteria that help to characterize molecular electrides. A detailed account of the computational methods and basis sets applicable for molecular electrides have been discussed along with their limitation(s) in this field. The main criterion for the identification of the electrides has also been discussed thoroughly with proper examples. The molecular electrides presented here have been justified with all the required criteria that support and proved their electride characteristics. We have also presented a few systems which have similar properties but are not considered as molecular electrides. Moreover, the applicability of the electrides in catalytic processes has also been presented.

Silver-Templated γ-Keggin Alkyltin-Oxo Cluster: Electronic Structure and Optical Limiting Effect

As one of the most representative polyoxometalate (POM) structures, Keggin clusters have attracted considerable attention. Nevertheless, the noble-metal-templated Keggin structure has not been reported to date. In this work, for the first time, a Ag atom was successfully incorporated to template the formation of a γ-Keggin alkytin-oxo cluster. Moreover, the central Ag atom has brought a significant heavy atom effect, showing the important influence on the electronic structure and optical properties. Theoretical calculations demonstrate that the Ag atom affects the frontier molecular orbitals and excited states of the AgSn₁₂ cluster, and also the process of electron transfer. The solid structure of the AgSn₁₂ cluster exhibits a significant third-order nonlinear optical (NLO) response, and an excellent optical limiting effect has been experimentally verified. The success of this work opens the way for the construction and optical properties modulation of noble metal templated Keggin structures.

How Reliable Are Modern Density Functional Approximations to Simulate Vibrational Spectroscopies?

We show that properties of molecules with low-frequency modes calculated with density functional approximations (DFAs) suffer from spurious oscillations along the nuclear displacement coordinate due to numerical integration errors. Occasionally, the problem can be alleviated using extensive integration grids that compromise the favorable cost-accuracy ratio of DFAs. Since spurious oscillations are difficult to predict or identify, DFAs are exposed to severe performance errors in IR and Raman intensities and frequencies or vibrational contributions to any molecular property. Using Fourier spectral analysis and digital signal processing techniques, we identify and quantify the error due to these oscillations for 45 widely used DFAs. LC-BLYP and BH&H are revealed as the only functionals showing robustness against the spurious oscillations of various energy, dipole moment, and polarizability derivatives with respect to a nuclear displacement coordinate. Given the ubiquitous nature of molecules with low-frequency modes, we warrant caution in using modern DFAs to simulate vibrational spectroscopies.

A DFT analysis of electronic, reactivity, and NLO responses of a reactive orange dye: the role of Hartree-Fock exchange corrections

An experimental and theoretical study based on DFT/TD-DFT approximations is presented to understand the nature of electronic excitations, reactivity, and nonlinear optical (NLO) properties of reactive orange 16 dye (RO16), an azo chromophore widely used in textile and pharmacological industries. The results show that the solvent has a considerable influence on the electronic properties of the material. According to experimental results, the absorption spectrum is formed by four intense transitions, which have been identified as [Formula: see text] states using TD-DFT calculations. However, the TD-DFT results reveal a weak [Formula: see text] in the low-lying spectral region. Continuum models of solvation indicate that these states suffer from bathochromic (ca. 15 nm) and hypsochromic shifts (ca. 4 nm), respectively. However, the expected blue shift for the absorption [Formula: see text] is only described using long-range or dispersion-corrected DFT methods. RO16 is classified as a strong electrophilic system, with electrophilicity ω > 1.5 eV. Concerning the nucleophilicity parameter (N), from vacuum to solvent, the environment is active and changes the nucleophilic status from strong to moderate nucleophile (2.0 ≤ N ≤ 3.0 eV). The results also suggest that all electrical constants are strongly dependent on long-range and Hartree-Fock exchange contributions, and the absence of these interactions gives results far from reality. In particular, the results for the NLO response show that the chromophore presents a potential application in this field with a low refractive index and first hyperpolarizability ca. 214 times bigger than the value usually reported for urea (β = 0.34 × 10^- 30 esu), which is a standard NLO material. Concerning the solvent effects, the results indicate that the polarizability increases [Formula: see text] esu from gas to solvent while the first hyperpolarizability is calculated as [Formula: see text] esu, ca. 180%, regarding the vacuum. The results suggest RO16 is a potential compound in NLO applications. Graphical Abstract The frontier molecular orbitals, and the inverse relation between the energy-gap (E_gap) and the first hyperpolarizability (β).

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

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

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.

Fine-Tuning of Nonlinear Optical Contrasts of Hexaphyrin-Based Molecular Switches Using Inverse Design

In the search for new nonlinear optical (NLO) switching devices, expanded porphyrins have emerged as ideal candidates thanks to their tunable chemical and photophysical properties. Introducing meso-substituents to these macrocycles is a successful strategy to enhance the NLO contrasts. Despite its potential, the influence of meso-substitution on their structural and geometrical properties has been scarcely investigated. In this work, we pursue to grasp the underlying pivotal concepts for the fine-tuning of the NLO contrasts of hexaphyrin-based molecular switches, with a particular focus on the first hyperpolarizability related to the hyper-Rayleigh scattering (β_HRS). Building further on these concepts, we also aim to develop a rational design protocol. Starting from the (un)substituted hexaphyrins with various π-conjugation topologies and redox states, structure-property relationships are established linking aromaticity, photophysical properties and β_HRS responses. Ultimately, inverse molecular design using the best-first search algorithm is applied on the most favorable switches with the aim to further explore the combinatorial chemical compound space of meso-substituted hexaphyrins in search of high-contrast NLO switches. Two definitions of the figure-of-merit of the switch performance were used as target objectives in the optimization problem. Several meso-substitution patterns and their underlying characteristics are identified, uncovering molecular symmetry and the electronic nature of the substituents as the key players for fine-tuning the β_HRS values and NLO contrasts of hexaphyrin-based switches.

Oriented Assembly of 2D Metal-Pyridylporphyrinic Framework Films for Giant Nonlinear Optical Limiting

The development of metal-organic frameworks (MOFs) with nonlinear optical (NLO) properties is of pronounced significance for optical devices. Herein, a series of 2D MOFs ZnTPyP(M) (TPyP = 5,10,15,20-tetrakis(4-pyridyl)porphyrin, M = Cu, Ni, Mn, H₂) films with [010]-orientation growth composed of ultrathin nanosheets from a pyridylporphyrinic ligand are first obtained by using a liquid-phase epitaxial (LPE) layer-by-layer (lbl) growth approach. ZnTPyP(M) films show a giant nonlinear optical limiting (OL) response and can be modulated by tuning the type of metalloporphyrinic ligands. As a result, ZnTPyP(Cu) film exhibits the highest nonlinear absorption coefficient of 5.7 × 10^-6 m/W compared to other reported NLO materials. Density functional theory calculations were consistent with the experimental results, revealing that the tunable π-π* local excitation and the increased delocalization of the metalloporphyrinic group regulate the NLO performance of ZnTPyP(M) films. These findings provide new insight into the effect of 2D porphyrinic MOFs toward the NLO response and offer new film candidates for nonlinear OL application.

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.

Interpenetrated Metal-Porphyrinic Framework for Enhanced Nonlinear Optical Limiting

Structural interpenetration in metal-organic frameworks (MOFs) significantly impacts on their properties and functionalities. However, understanding the interpenetration on third-order nonlinear optics (NLO) of MOFs have not been reported to date. Herein, we report two 3D porphyrinic MOFs, a 2-fold interpenetrated [Zn₂(TPyP)(AC)₂] (ZnTPyP-1) and a noninterpenetrated [Zn₃(TPyP)(H₂O)₂(C₂O₄)₂] (ZnTPyP-2), constructed from 5,10,15,20-tetra(4-pyridyl)porphyrin (TPyP(H₂)) and Zn(NO₃)₂ (AC = acetate, C₂O₄ = oxalate). ZnTPyP-1 achieves excellent optical limiting (OL) performance with a giant nonlinear absorption coefficient (3.61 × 10⁶ cm/GW) and large third-order susceptibility (7.73 × 10^-7 esu), which is much better than ZnTPyP-2 and other reported OL materials. The corresponding MOFs nanosheets are dispersed into a polydimethylsiloxane (PDMS) matrix to form highly transparent and flexible MOFs/PDMS glasses for practical OL application. In addition, the OL response optimized by adjusting the MOFs concentration in the PDMS matrix and the type of metalloporphyrin are discussed in the ZnTPyP-1 system. The theoretical calculation confirmed that the abundant π-π interaction from porphyrinic groups in the interpenetrated framework increased the electron delocalization/transfer and boosted the OL performance. This study opens a new avenue to enhance OL performance by the construction of interpenetrated structures and provides a new approach for the preparation of transparent and flexible MOF composites in nonlinear optical applications.

Impact of van der Waals interactions on the structural and nonlinear optical properties of azobenzene switches

The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in the meta-position with functional groups of different bulkiness are investigated using various ab initio and density functional approximations. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that London dispersion interactions existing between bulky meta-substituents stabilize the Z conformer. The ωB97X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of the molecules. We show that density functional approximations should include no less than 50% of Hartree-Fock exchange to provide accurate hyperpolarizabilities. A property-structure analysis of the azobenzene derivatives reveals that the main contribution to the first hyperpolarizability comes from the azo bond, but phenyl meso-substituents can enhance it.

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.

Density Functional Theory Study of Substitution Effects on the Second-Order Nonlinear Optical Properties of Lindquist-Type Organo-Imido Polyoxometalates

Density functional theory and time-dependent density functional theory have been enacted to investigate the effects of donor and acceptor on the first hyperpolarizability of Lindquist-type organo-imido polyoxometalates (POMs). These calculations employ a range-separated hybrid exchange-correlation functional (ωB97X-D), account for solvent effects using the implicit polarizable continuum model, and analyze the first hyperpolarizabilities by using the two-state approximation. They highlight the beneficial role of strong donors as well as of π-conjugated spacers (CH=CH rather than C≡C) on the first hyperpolarizabilities. Analysis based on the unit sphere representation confirms the one-dimensional push-pull π-conjugated character of the POMs substituted by donor groups and the corresponding value of the depolarization ratios close to 5. Furthermore, the use of the two-state approximation is demonstrated to be suitable for explaining the origin of the variations of the first hyperpolarizabilities as a function of the characteristics of a unique low-energy charge-transfer excited state and to attribute most of the first hyperpolarizability changes to the difference of dipole moment between the ground and that charge-transfer excited state.

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.

Applicability of DFT functionals for evaluating the first hyperpolarizability of phenol blue in solution

The first electronic hyperpolarizability (β) of phenol blue (PB) in several solvents in a wide range of dielectric constants is investigated using the density functional theory (DFT). The reliability of various exchange-correlation functionals is assessed by a comparison to reference Møller-Plesset second-order perturbation theory (MP2) calculations. The equilibrium geometry of PB in each solvent is obtained by using the average solvent electrostatic configuration/free energy gradient method, which performs optimizations on the free energy hyper-surface by employing iteratively the sequential quantum mechanics/molecular mechanics methodology. The dependence of β on the bond length alternation (BLA) coordinate is rationalized by means of the two-level model. Within the employed exchange-correlation functionals, the LC-BLYP functional shows the best performance for describing the static and dynamic MP2 results of β, which increases as the BLA diminishes, reaching a maximum in an intermediate value of BLA. The results also illustrate the role played by the difference between the ground- and excited-state dipole moments (Δμ) in determining the hyperpolarizability behavior in solution. Particularly, in the aqueous solution case, Δμ goes to around zero when BLA is near zero, leading to an abrupt decline in the β value. The DFT results of this study, therefore, indicate a clear relationship between the first hyperpolarizability and the BLA coordinate for the PB in solution, in agreement with experiment.

Functional ligand directed assembly and electronic structure of Sn18-oxo wheel nanoclusters

The bilayer hexagonal Sn₁₈-oxo cluster, as the largest tin-oxo wheel, was constructed by a ligand templating method. Moreover, the ligands also show important effects on electronic structure and third-order nonlinear optical property of the wheel.