We report a systematic computational investigation of the (chiro)ptical properties of a series of intrinsically chiral organic ketones, considering the prediction of one-photon absorption, electronic circular dichroism, fluorescence, and circularly polarized luminescence spectra, together with the absorption and luminescence dissymmetry factors, gabs and glum, typically used to quantify chiral responses. A set of TD-DFT functionals, namely B3LYP, MN15, M06-2X, CAM-B3LYP, and ωB97X-D, is first assessed within the vertical approximation. Such an approach qualitatively reproduces the main trends in dipole and rotatory strengths, but provides rather unreliable gabs and glum factors. For the same set of functionals, vibrationally resolved spectra were then simulated using a panel of vibronic models. For absorption and electronic circular dichroism spectra, vertical hessian and vertical gradient vibronic models reproduce the experimental vibronic structure more accurately than the adiabatic hessian model, which often yields overly broad and blueshifted bands. The inclusion of Herzberg-Teller effects significantly improves the prediction of gabs, mainly by increasing the computed absorption dipole strength associated with the weak n → π* transition, with the range separated functionals, ωB97X-D and CAM-B3LYP, providing the best overall results. In contrast, the fluorescence and circularly polarized luminescence spectra are less sensitive to the vibronic model, as they are dominated by a single broad emission band. Nevertheless, Herzberg-Teller effects allow improving glum values for all the tested functionals. Overall, this work shows that reliable predictions of dissymmetry factors in chiral ketones require a balanced treatment of electronic-structure and vibronic effects. While non-Condon contributions are essential for accurately describing gabs, the calculation of glum is comparatively more dependent on the electronic-structure method for the investigated set of compounds.

We present a comprehensive benchmark of excited-state polarizabilities for a representative set of more than 40 singlet states from 27 small organic molecules. Reference data were obtained using the high-level coupled-cluster CC3 model in combination with the aug-cc-pVTZ atomic basis set, providing the first systematic data set of excited-state polarizabilities at this level of theory. The studied set includes both valence and Rydberg states, the latter exhibiting significantly larger polarizabilities, reflecting their diffuse character and enhanced sensitivity to external electric fields. The benchmark analysis includes lower-level wave function-based methods, namely, CCSD and CC2, as well as Time-Dependent Density Functional Theory (TD-DFT) with several common density functional approximations (B3LYP, MN15, M06-2X, CAM-B3LYP, and LC-BLYP). The statistical analysis enables the evaluation of the impact of orbital relaxation and highlights method-dependent differences across the different kinds of excited states. The results indicate that CCSD, in both its relaxed and unrelaxed forms, provides the most accurate description of excited-state polarizabilities, closely followed by CC2, which can therefore be generally employed as a computationally efficient yet reliable alternative. Among the TD-DFT functionals, range-separated hybrids─particularly LC-BLYP─perform best, while larger errors are observed for the three evaluated global hybrids.

A series of twenty-two acceptor-donor-acceptor chromophores, comprising both dicationic and neutral dyes, were synthesized and characterized. These compounds were designed with a wide range of electron-withdrawing end groups to explore the balance between acceptor-donor-acceptor aromatic structures and hypothetical nonaromatic coupled polymethine electronic structures within the central six-membered ring. Structural, electrochemical, photophysical, and computational investigations were conducted to gain insights into the structure-property relationships of these systems. The experimental data revealed that the redox and optical properties were most consistent with acceptor-donor-acceptor aromatic structures, significantly impacted by the nature of the end groups. Solvatochromic studies further indicated that the dyes were unlikely to lose their aromatic character in favor of a coupled polymethine structure. Theoretical calculations suggested that a few dicationic derivatives exhibited a slightly reduced aromatic character, hinting at minor coupled polymethine contributions. However, the majority of the chromophores retained a predominantly aromatic central ring.

The conformational behavior and nonlinear optical properties of a donor–acceptor Stenhouse adduct (DASA) derivative in chloroform solution is investigated by combining molecular dynamics (MD) simulations with quantum chemistry calculations. MD simulations are carried out at three different temperatures in order to assess the thermal effects on the structural fluctuations of the solute and the shape of the solvation shell. Next, time-dependent DFT calculations combined either with implicit or explicit solvation models are performed on statistical samples of geometries extracted from the MD runs to assess the impact of temperature on the second harmonic response of the DASA molecule. We show that geometrical distortions, which push the molecule out of its cyanine-like equilibrium geometry, largely enhance the second harmonic intensity of the DASA, and that these effects become more important with increasing temperature.

We report the synthesis of a new family of chromophores based on benzothiazole, indandione, and tricyanofuran moieties, forming aromatic neutral precursors or negatively charged quinoidal counterparts. Upon deprotonation, these dyes undergo marked bathochromic shifts, leading to highly delocalized coupled polymethine structures, particularly in their moderatly antiaromatic dianionic forms. The evolution of optical properties was systematically studied through pH-dependent absorption measurements and supported by TD-DFT and CC2 calculations. Distinct behaviors were identified across the series: ESIPT in benzothiazole dyes, photoacidity in indandione derivatives, and spirocyclization in tricyanofuran-containing dyes. These findings provide insights into structure-property relationships in anionic polymethine systems.

Computer simulations play a pivotal role in interpreting experimental two-photon absorption (2PA) spectra. One of the key aspects of the simulation of these spectra is to take into account the vibrational fine structure of the bands in electronic spectra. This is typically done by employing Franck-Condon (FC) term and low-order terms in the Herzberg-Teller (HT) expansion. In this work, we present a systematic study of first-order HT effects on the vibronic structure of π → π* electronic bands in 2PA spectra of 13 common fluorophores. We begin by evaluating the performance of several density functional approximations (DFAs) against the second-order coupled cluster singles and doubles model (CC2) for reproducing two-photon transition moments and their first- and second-order derivatives with respect to normal modes of vibration on a set of six donor-acceptor molecules. Our findings reveal that most DFAs produce inaccurate values for these derivatives, with the exception of the LC-BLYP functionals with range-separation parameters of 0.33 and 0.47. Although these functionals underestimate the HT contribution to the 2PA total intensities of the π → π* electronic bands, they offer a reasonable qualitative reproduction of the HT vibrational fine structure of the reference spectra. We further explore HT effects on fluorescent chromophores, finding that HT contributions are secondary to FC effects, leading to small shifts of the wavelengths peaks, and minimal changes in the intensities. Additionally, the adiabatic Hessian, vertical Hessian, and vertical gradient vibronic models are assessed. The general agreement among these models confirms that the harmonic approximation is suitable for studying the selected fluorophores.

Just four steps are required to transform 2-nitrobenzaldehyde into centrosymmetric, quadrupolar N,B-doped nanographenes possessing two nitrogen-boron dative bonds. A convergent fragment coupling strategy allowed rapid access to key intermediates bearing the 1,4-dihydropyrrolo[3,2-b]pyrrole core. 2,6-Di-tert-butylpyridine turned out to be the best base for the formation of B←N bonds. This synthetic strategy can be extended to encompass double helicenes possessing two [7]helicene units bearing four five-membered rings. The size of the peripheral arm influences the reaction output: in the case of replacing benzene with dibenzothiophene, the yield decreases from 75% to 16%. Interestingly only two enantiomers and not meso form are formed in the latter case. The obtained double helicene containing 14 fused rings, exhibits green emission characterized by reasonable fluorescence quantum yield reaching 0.38. This dye has average circularly polarized luminescence brightness (B CPL) of about 15 M-1 cm-1. The analysis of the electronic structure of the dyes with quantum chemical methods reveals highly-delocalized excited states with the core of the dye acting as a electron-donating moiety.

Owing to their unique combination of magnetic and optical properties, luminescent polychlorinated radicals are promising candidates for advanced applications in both optoelectronics and quantum technologies. In this study, we employ the lineshape formalism within a computational protocol based on time-dependent density functional theory (TD-DFT) to investigate the excited-state properties of six representative members of this family presenting different sizes and excited-state characters. We explore a wide range of density functionals, applying or not the Tamm-Dancoff approximation (TDA), combined with different vibronic models, namely, the vertical gradient (VG), vertical Hessian (VH), and adiabatic Hessian (AH), as well as dipole moment expansions using the Franck-Condon (FC) and Herzberg-Teller (HT) approximations. This systematic approach allows us to assess how these methodological choices influence the spectral shapes, excited-state energies, radiative and non-radiative decay rates, and emission yields. Our results show that although TDA effectively reduces spin contamination, it generally leads to poorer predictions of emission energies, radiative rates, and internal conversion rates. The VH model within the FC approximation emerged as the most balanced approach for reproducing both spectral profiles and radiative rates; the inclusion of HT contributions had a minor effect only. Internal conversion rates were found to be highly sensitive to the choice of the vibronic model and spectral broadening, which in turn strongly impacted the predicted fluorescence quantum yields, suggesting that incorporating higher-order expansions and anharmonic corrections could be crucial for more reliable estimates. Among the functionals tested, LC-ωHPBE emerged as the most suited for consistently reproducing all key features, including emission shapes, energies, and decay trends. In short, this study demonstrates that despite the challenges posed by spin contamination and the open-shell character of these systems, TD-DFT remains a powerful and versatile framework for qualitatively capturing the emission properties of radical emitters even when the harmonic approximation is challenged.

Two compact far-red cationic benzoquinone diimine dyes were synthesized, having molecular weights lower than 400 or 300 Da and featuring light absorption properties centered around 700 nm. Their redox and optical properties were investigated experimentally, alongside theoretical studies of their structural and excited-state characteristics.

The second-order nonlinear optical (NLO) responses of a donor-acceptor stenhouse adduct (DASA) are investigated by using a computational approach combining molecular dynamics simulations and density functional theory (DFT) calculations. Specific force fields for the open and closed photoswitching forms are first parameterized and validated according to the Joyce protocol, in order to finely reproduce the geometrical features and potential energy surfaces of both isomers in chloroform solution. Then, DFT calculations are performed on structural snapshots extracted at regular time steps of the MD trajectories to address the influence of the thermalized conformational dynamics on the NLO responses related to hyper-Rayleigh scattering (HRS) experiments. We show that accounting for the structural dynamics largely enhances the HRS hyperpolarizability (beta HRS) compared to DFT calculations considering solely equilibrium geometries, and greatly improves the agreement with experimental measurements. Furthermore, we show that the NLO responses of the NLO-active open form are correlated with the bond order alternation along the triene bridge connecting the donor and acceptor moieties, which is rationalized using simple essential state models. The second-order nonlinear optical (NLO) responses of a donor-acceptor stenhouse adduct (DASA) are investigated by using a computational approach combining molecular dynamics simulations and density functional theory (DFT) calculations.

We present a large dataset of highly accurate two-photon transition strengths (δTPA) determined for standard small molecules. Our reference values have been calculated using the quadratic response implementation of the third-order coupled cluster method including iterative triples (Q-CC3). The aug-cc-pVTZ atomic basis set is used for molecules with up to five non-hydrogen atoms, while larger molecules are assessed with aug-cc-pVDZ; the differences due to the basis sets are discussed. This dataset, encompassing 82 singlet transitions of various characters (Rydberg, valence, and double excitations), enables a comprehensive benchmark of smaller basis sets and alternative wavefunction methods when Q-CC3 calculations become beyond reach as well as time-dependent density functional theory (TD-DFT) approaches. The evaluated wavefunction methods include quadratic response and equation-of-motion CCSD approximations, Q-CC2, and second-order algebraic diagrammatic construction in its intermediate state representation (I-ADC2). In the TD-DFT framework, a set of five commonly used exchange-correlation functionals are evaluted. This extensive analysis provides a quantitative assessment of these methods, revealing how different system sizes, response intensities, and types of transitions affect their performances.

We present the largest dataset of highly-accurate vertical and degenerate two-photon transition strengths ($\delta^{\mbox{\tiny TPA}}$) for standard small- and medium-sized organic molecules, calculated using the quadratic response implementation of the third-order coupled cluster method that includes iterative triples (Q-CC3). The aug-cc-pVTZ basis set was used for all small molecules, while medium-sized molecules were assessed with aug-cc-pVDZ and the differences due to the basis sets are discussed. This dataset, encompassing 82 singlet transitions of various characters (Rydberg, valence, and double excitations), enables a comprehensive benchmark of both small basis sets and, alternative wavefunction methods when Q-CC3 calculations become beyond reach. These methods include quadratic (Q) response and equation of motion CCSD approximations, Q-CC2, second-order algebraic diagrammatic construction in its intermediate state representation (I-ADC2), as well as time-dependent density functional theory (TD-DFT) with a set of 5 commonly used exchange-correlation functionals. This extensive analysis provides a quantitative assessment of these methods, revealing how different system sizes, response intensities, and types of transitions affect their performances.

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.

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.

In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.

The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in meta-position with functional groups of different bulkiness are investigated using various abinitio and DFT levels of approximation. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that Londondispersion interactions existing between bulky meta-substituents stabilize the Z con-former. The !B97-X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of themolecules. We show that density functional approximations should include no less than50% 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-substituentscan enhance it.