Performance of DFT functionals for calculating the second-order nonlinear optical properties of dipolar merocyanines

Evolution of the static HRS hyperpolarizability of a tricyanopropylidene-based merocyanine dye with the length of the polyenic bridge, as calculated using various ab initio and DFT approximations.

Finding the optimal exchange–correlation functional to describe the excited state properties of push–pull organic dyes designed for thermally activated delayed fluorescence

In view of designing organic dyes for TADF, TD-DFT calculations are performed on 10 prototypical donor-acceptor compounds and are benchmarked against riCC2 calculations, demonstrating that modified range-separated hybrids perform best.

Periodic DFT Study of the Effects of Co-Crystallization on a N-Salicylideneaniline Molecular Switch

This work aims at better understanding the complex effects of co-crystallization on a single salicylideneaniline molecular switch, (E)-2-methoxy-6-(pyridine-3-yliminomethyl)phenol (PYV3), which can tautomerize between an enol and a keto form. A combination of periodic boundary conditions DFT and molecular wavefunction calculations has been adopted for examining a selection of PYV3 co-crystals, presenting hydrogen bonds (H-bonds) or halogen bonds (X-bonds), for which X-ray diffraction data are available. Three aspects are targeted: i) the energy (H-bond strength, enol to keto relative energy, and geometry relaxation energies), ii) the geometrical structure (PYV3 to co-crystal and enol to keto geometrical variations), and iii) the electron distribution (PYV3 to co-crystal and enol to keto Mulliken charge variations). These allow i) explaining the preference for forming H-bonds with the nitrogen of the pyridine of PYV3 with respect to the oxygens and the importance of the crystal field, ii) distinguishing the peculiar behavior of the SulfonylDiPhenol (SDP) coformer, which stabilizes the keto form of PYV3, iii) describing the relative stabilization of the enol form upon co-crystallization (with the exception of SDP) and therefore iv) substantiating the co-crystallization-induced reduction of thermochromism observed for several PYV3 co-crystals.

Theoretical Assessment of the Second-Order Nonlinear Optical Responses of Lindqvist-Type Organoimido Polyoxometalates

The second-order nonlinear optical properties of Lindqvist-type organoimido polyoxometalates bearing donor and acceptor substituents are evaluated by employing density functional theory and time-dependent density functional theory using the ωB97X-D range-separated hybrid exchange-correlation functional to describe accurately the field-induced effects. The hyper-Rayleigh scattering responses, β_HRS (-2ω; ω, ω), and the depolarization ratio are the targeted quantities. They are analyzed by resorting to the two-state model, which reduces the full summation-over-state expression to a single diagonal term and relates the response to a few spectroscopic quantities. The validity of this model is demonstrated by its ability to reproduce the β_HRS variations as a function of the nature of the ligand, owing to the dominant 1D character of these organic-inorganic hybrids. The calculated values are in good agreement with the recent experimental work of Al-Yasari et al. (Inorg. Chem. 2017, 56, 10181-10194), which demonstrates that the hexamolybdate moiety plays the role of an electron acceptor group. On the contrary, they contradict previous studies, which attributed an electron donor character to the polyoxometalate moiety. Calculations highlight that (i) combining the hexamolybdate unit with an organic ligand bearing a strong donor substituent leads to an enhanced first hyperpolarizability, associated with a dominant low-energy excited state, characterized by a large excitation-induced electron transfer from the donating ligand to the hexamolybdate, therefore coupling the polyoxometalate (POM) and its substituted ligand; (ii) in the case of weaker donor substituents, the hexamolybdate still behaves as an electron acceptor, but the first hyperpolarizability is smaller and the coupling has a reduced spatial extension; and, on the contrary, (iii) in the presence of an acceptor substituent, there is a competition between the hexamolybdate and this group so that the first hyperpolarizability becomes very small. The whole set of results demonstrates that polyoxometalate moieties are good candidates to achieve large second-order nonlinear optical (NLO) responses while keeping a rather large transparency window and also that there remains space to improve their integration into NLO efficient organic-inorganic hybrids.

Magnetically-induced current density investigation in carbohelicenes and azahelicenes

A computational study of the magnetically-induced current (MIC) density has been carried out for a variety of ortho fused polycyclic aromatic molecules at the density functional theory level with the gauge including magnetically induced current (GIMIC) method. With this method, the aromatic character of each ring in a homologous series of carbohelicenes with an increasing number of fused benzene rings is assessed and compared with other aromaticity criteria such as the Nucleus Independent Chemical Shift [NICS(0), NICSzz(0)] and Bond Length Alternation (BLA) parameters. All criteria indicate that the two outer rings are the most aromatic ones [i.e. higher induced current, more negative NICS(0) and NICSzz(0) values, and smaller BLA values]. For the large helicenes (n > 10), the current drops along the following four rings and then rises again. Additionally, we have proven that this behavior is not due to a difference of the local magnetic field coming from a difference of orientation of the ring with respect to the external magnetic field (oriented along the helical axis). Upon fusing additional benzene rings to form hexa-peri-hexabenzo[7]helicene, some rings (B, D, and F) are a lot less aromatic (even non-aromatic) than the others. The NICS(0) and NICSzz(0) values exaggerate this behavior because they are all positive values, which is a signature of antiaromaticity. Then, when substituting one, three, or four benzene rings with pyrrole ones to form mono-aza-[7]-helicene, tri-aza-[7]-helicene, and tetra-aza-[7]-helicene, remarkable changes in the electronic structures of the helicenes are observed. Indeed, the induced currents are always smaller in the pyrrole rings than in the benzene ones. This has been further investigated using the streamline and the color map representations, which indicate that the diatropic current density passing through the plane cutting the C-N bonds in the pyrrole rings is stronger but is more localized than the current density passing through the plane cutting the C-C bonds in the benzene rings. This gives a positive but smaller total induced current for the pyrrole rings than for the benzene ones. For these systems, the NICS(0) and even more the NICSzz(0) values are not fully reliable to probe the local aromaticity, contrary to the induced current. Indeed, the NICSzz(0) values for the tri-aza-[7]-helicene molecule range from -14.23 to 1.14 ppm, which cannot lead to the same conclusion as the induced current values (10.03 to 12.87 nA T-1).

Second-order nonlinear optical properties of Stenhouse photoswitches: insights from density functional theory

We report the first investigation of the second-order nonlinear optical (NLO) properties of donor-acceptor Stenhouse adducts (DASAs), an emerging class of colored photochromes that undergo photoswitching with visible light to a colorless form. By using time-dependent density functional theory, we provide insights into the relationships linking the nature of the chemical substituents to the amplitude and contrasts of the NLO response. Solvent and frequency dispersion effects are also analyzed. The calculations predict that DASAs behave as high contrast NLO switches, a finding that extends their potential applications to photo-responsive NLO materials and devices.

Aromaticity as a Guiding Concept for Spectroscopic Features and Nonlinear Optical Properties of Porphyrinoids

With their versatile molecular topology and aromaticity, porphyrinoid systems combine remarkable chemistry with interesting photophysical properties and nonlinear optical properties. Hence, the field of application of porphyrinoids is very broad ranging from near-infrared dyes to opto-electronic materials. From previous experimental studies, aromaticity emerges as an important concept in determining the photophysical properties and two-photon absorption cross sections of porphyrinoids. Despite a considerable number of studies on porphyrinoids, few investigate the relationship between aromaticity, UV/vis absorption spectra and nonlinear properties. To assess such structure-property relationships, we performed a computational study focusing on a series of Hückel porphyrinoids to: (i) assess their (anti)aromatic character; (ii) determine the fingerprints of aromaticity on the UV/vis spectra; (iii) evaluate the role of aromaticity on the NLO properties. Using an extensive set of aromaticity descriptors based on energetic, magnetic, structural, reactivity and electronic criteria, the aromaticity of [4n+2] π-electron porphyrinoids was evidenced as was the antiaromaticity for [4n] π-electron systems. In agreement with previous studies, the absorption spectra of aromatic systems display more intense B and Q bands in comparison to their antiaromatic homologues. The nature of these absorption bands was analyzed in detail in terms of polarization, intensity, splitting and composition. Finally, quantities such as the average polarizability and its anisotropy were found to be larger in aromatic systems, whereas first and second hyperpolarizability are influenced by the interplay between aromaticity, planarity and molecular symmetry. To conclude, aromaticity dictates the photophysical properties in porphyrinoids, whereas it is not the only factor determining the magnitude of NLO properties.

The Impact of Acceptor-Acceptor Homocoupling on the Optoelectronic Properties and Photovoltaic Performance of PDTSQxff Low Bandgap Polymers

Push-pull-type conjugated polymers applied in organic electronics do not always contain a perfect alternation of donor and acceptor building blocks. Misscouplings can occur, which have a noticeable effect on the device performance. In this work, the influence of homocoupling on the optoelectronic properties and photovoltaic performance of PDTSQx_ff polymers is investigated, with a specific focus on the quinoxaline acceptor moieties. A homocoupled biquinoxaline segment is intentionally inserted in specific ratios during the polymerization. These homocoupled units cause a gradually blue-shifted absorption, while the highest occupied molecular orbital energy levels decrease only significantly upon the presence of 75-100% of homocouplings. Density functional theory calculations show that the homocoupled acceptor unit generates a twist in the polymer backbone, which leads to a decreased conjugation length and a reduced aggregation tendency. The virtually defect-free PDTSQx_ff affords a solar cell efficiency of 5.4%, which only decreases substantially upon incorporating a homocoupling degree over 50%.

DFT Investigation of the Diastereoselectivity of the MX2 and MX3 Lewis-Acid-Catalyzed Mukaiyama Aldol Reaction between C,O,O-Tris(trimethylsilyl)ketene Acetal and Aldehydes

The kinetics and diastereoselectivity of the Mukaiyama aldol reaction between C,O,O-tris(trimethylsilyl)ketene acetal and aldehydes bearing alkyl, vinyl, and aromatic substituents is influenced by the nature of Lewis acid catalysts. A density functional theory investigation using the M06-2X exchange-correlation functional and the PCM scheme to account for solvent effects has been carried out to characterize the structure and energetics of the transition state when the Lewis acid is ZnBr₂ (MX₂) or GaCl₃ (MX₃) in comparison to the uncatalyzed reaction. The main observations are that (i) the pro-syn transition states are always more stable than the pro-anti ones; (ii) for MX₂, the transition state presents a cyclic structure, whereas it is open for MX₃, owing to steric interactions; (iii) the difference of activation free enthalpy between the pro-anti and pro-syn transition states decreases when the reaction is catalyzed, by either MX₂ or MX₃, demonstrating a reduction of the diastereoselectivity with respect to the uncatalyzed reaction; (iv) this decrease of diastereoselectivity is larger for MX₃- than for MX₂-catalyzed reactions; and (v) the MX₃-catalyzed reactions are kinetically favored by 1-2 kcal mol^-1 with respect to the MX₂ ones.

Nonlinear optical responses of self-assembled monolayers functionalized with indolino–oxazolidine photoswitches

The second harmonic generation responses of photoresponsive self-assembled monolayers based on indolino–oxazolidine derivatives are computed using a sequential MD/DFT approach.

Acidochromic spiropyran–merocyanine stabilisation in the solid state

Stabilizing the open-ring merocyanine form of a spiropyran compound based on co-crystallisation with inorganic acids.

Emergence of Nonlinear Optical Activity by Incorporation of a Linker Carrying the p-Nitroaniline Motif in MIL-53 Frameworks

p-Nitroaniline presents the typical motif of a second-order nonlinear optically (NLO) active molecule. However, because of its crystallization in an antiparallel and hence centrosymmetric structure, the NLO activity is lost. In this contribution, the p-nitroaniline motif was built successfully into the MIL-53 metal-organic framework. More precisely, MIL-53 was synthesized with 2-amino-5-nitroterephthalate as organic linker, with Al³⁺, Ga³⁺, or In³⁺ as inorganic cation. The Al and Ga structures are polar, as confirmed by second-harmonic generation microscopy, yielding stable NLO materials. Indeed, they contain a 22-36% surplus of the dipolar 2-amino-5-nitro-terephthalate oriented in a parallel fashion. The indium compound was shown to be less crystalline and centrosymmetric. Ab initio modeling of the second-order NLO response shows that the Al and Ga materials show a response comparable to typical inorganic commercial NLO materials such as KDP. As a hybrid material, capable of low-temperature synthesis and processing and the ultrafast NLO responses associated with organic materials, this material can potentially provide an interesting venue for applications with respect to traditional inorganic NLO materials.

Coupled-cluster sum-frequency generation nonlinear susceptibilities of methyl (CH3) and methylene (CH2) groups

The first vibrational sum frequency generation (SFG) spectra based on molecular properties calculated at the coupled cluster singles and doubles (CCSD) level of approximation have been simulated for interfacial model alkyl chains, providing benchmark data for comparisons with approximate methods, including density functional theory (DFT). The approach proceeds in three steps. In the first two steps, the molecular spectral properties are determined: the vibrational normal modes and frequencies and then the derivatives of the dipole moment and of the polarizability with respect to the normal coordinates. These derivatives are evaluated with a numerical differentiation approach, of which the accuracy was monitored using Romberg's procedure. Then, in the last step, a three-layer model is employed to evaluate the macroscopic second-order nonlinear optical responses and thereby the simulated SFG spectra of the alkyl interface. Results emphasize the following facts: (i) the dipole and polarizability derivatives calculated at the DFT level with the B3LYP exchange-correlation functional can differ, with respect to CCSD, by as much as ±10 to 20% and ±20 to 50% for the CH₃ and CH₂ vibrations, respectively; (ii) these differences are enhanced when considering the SFG intensities as well as their variations as a function of the experimental configuration (ppp versus ssp) and as a function of the tilt and rotation angles, defining the orientation of the alkyl chain at the interface; (iii) these differences originate from both the vibrational normal coordinates and the Cartesian derivatives of the dipole moment and polarizability; (iv) freezing the successive fragments of the alkyl chain strongly modifies the SFG spectrum and enables highlighting the delocalization effects between the terminal CH₃ group and its neighboring CH₂ units; and finally (v) going from the free chain to the free methyl model, and further to C_3v constraints on leads to large variations of two ratios that are frequently used to probe the molecular orientation at the interface, the (r + r)/r⁺ ratio for both antisymmetric and symmetric CH₃ vibrations and the I_ppp/I_ssp ratio.

A theoretical study on quasi-one-dimensional open-shell singlet ladder oligomers: multi-radical nature, aromaticity and second hyperpolarizability

Quasi-one-dimensional open-shell singlet ladder oligomers composed of indenofluorene-like units show strong correlation between multiradical nature, aromaticity and second hyperpolarizability.

Origin of the Enhancement of the Second Hyperpolarizabilities of Metal-Carbon Bonds

The spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (γ) in model systems involving metal-carbon bonds with various bond lengths as a function of their diradical character (y) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to γ, (ii) the π electrons contribution to γ is negative, (iii) when the bond length increases, γ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum γ amplitude per σ bond is about 7 times larger than that per π bond. These features are significantly different from those observed in pure organic systems.

Unraveling the Concerted Reaction Mechanism of the Noncatalyzed Mukaiyama Reaction between C,O,O-Tris(trimethylsilyl)ketene Acetal and Aldehydes Using Density Functional Theory

The uncatalyzed Mukaiyama aldol reaction between C,O,O-tris(trimethylsilyl)ketene acetal and aldehydes bearing alkyl, vinyl, and aromatic substituents has been studied theoretically using density functional theory with the M06-2X exchange-correlation functional. These DFT calculations mostly demonstrate that (i) the syn product is both kinetically and thermodynamically favored, (ii) the diastereoselectivity of the uncatalyzed reaction is larger than observed for the reaction catalyzed by HgI2 and it is inverted with respect to the latter, (iii) solvents with larger dielectric constants increase the activation barrier but reduce the diastereoselectivity, (iv) the concerted reaction is preferred over the stepwise reaction, and (v) the OSiMe3 group in geminal lowers the activation barrier and increases the energy of reaction. Analyzing the concerted mechanism unravels four types of cyclic transition states, two pro-anti and two pro-syn. Then, the relative energy of the most stable transition state of each type as well as of the corresponding anti and syn products shows that the syn reaction path is located at lower Gibbs enthalpy than the anti reaction path for all substituents.

Challenging compounds for calculating molecular second hyperpolarizabilities: the triplet state of the trimethylenemethane diradical and two derivatives

The second hyperpolarizability γ of trimethylenemethane (TMM) and two 1,3-dipole derivatives (NXA and OXA) in their triplet ground state has been evaluated at the UCCSD(T) level with the d-aug-cc-pVDZ extended basis set, highlighting that γ decreases from TMM to NXA and OXA, following the opposite order of their permanent dipole moments. These results are then used to benchmark a broad range of levels of approximation. So, the UMP2, UMP4, and UCCSD methods can be used to characterize γ of TMM and NXA but not of OXA. In that case, the large field-induced charge transfer contribution is difficult to handle using the MPn methods and only the UCCSD method provides values close to the UCCSD(T) reference. Turning to the performance of DFT with typical exchange-correlation functionals, the UM06-2X functional, which contains 54% of HF exchange, performs very well with a maximum of 4.5% of difference with respect to the reference values. On the other hand, employing less HF exchange leads to an overestimation of the responses whereas range-separated hybrids generally underestimate the second hyperpolarizabilities. Finally, the use of spin-projected methods for these 1,3-dipole triplet molecules has a little impact since the spin contamination is almost negligible.

Nonlinear optical properties in open-shell molecular systems

For more than 30 years, nonlinear optical (NLO) properties of molecular systems have been actively studied both theoretically and experimentally due to their potential applications in photonics and optoelectronics. Most of the NLO molecular systems are closed-shell species, while recently open-shell molecular species have been theoretically proposed as a new class of NLO systems, which exhibit larger NLO properties than the traditional closed-shell NLO systems. In particular, the third-order NLO property, the second hyperpolarizability γ, was found to be strongly correlated to the diradical character y, which is a quantum-chemically defined index of effective bond weakness or of electron correlation: the γ values are enhanced in the intermediate y region as compared to the closed-shell (y = 0) and pure open-shell (y = 1) domains. This principle has been exemplified by accurate quantum-chemical calculations for polycyclic hydrocarbons including graphene nanoflakes, multinuclear transition-metal complexes, main group compounds, and so on. Subsequently, some of these predictions have been substantiated by experiments, including two-photon absorption. The fundamental mechanism of the y-γ correlation has been explained by using a simple two-site model and the valence configuration interaction method. On the basis of this y-γ principle, several molecular design guidelines for controlling γ have been proposed. They consist in tuning the diradical characters through chemical modifications of realistic open-shell singlet molecules. These results open a new path toward understanding the structure-NLO property relationships and toward realizing a new class of highly efficient NLO materials. WIREs Comput Mol Sci 2016, 6:198-210. doi: 10.1002/wcms.1242.