Solvatochromic Shifts in UV–Vis Absorption Spectra: The Challenging Case of 4-Nitropyridine N-Oxide

A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes

In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)  ⋆ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Predicting Solvatochromism of Chromophores in Proteins through QM/MM and Machine Learning

Solvatochromism occurs in both homogeneous solvents and more complex biological environments, such as proteins. While in both cases the solvatochromic effects report on the surroundings of the chromophore, their interpretation in proteins becomes more complicated not only because of structural effects induced by the protein pocket but also because the protein environment is highly anisotropic. This is particularly evident for highly conjugated and flexible molecules such as carotenoids, whose excitation energy is strongly dependent on both the geometry and the electrostatics of the environment. Here, we introduce a machine learning (ML) strategy trained on quantum mechanics/molecular mechanics calculations of geometrical and electrochromic contributions to carotenoids' excitation energies. We employ this strategy to compare solvatochromism in protein and solvent environments. Despite the important specifities of the protein, ML models trained on solvents can faithfully predict excitation energies in the protein environment, demonstrating the robustness of the chosen descriptors.

Biosynthesis Optimization of Antibacterial-Magnetic Iron Oxide Nanoparticles from Bacillus megaterium

The occurrence of antibiotic resistance on common bacterial agents and the need to use new generations of antibiotics have led to the use of various strategies for production. Taking inspiration from nature, using bio-imitation patterns, in addition to the low cost of production, is advantageous and highly accurate. In this research, we were able to control the temperature, shake, and synthesis time of the synthesis conditions of Bacillus megaterium bacteria as a model for the synthesis of magnetic iron nanoparticles and optimize the ratio of reducing salt to bacterial regenerating agents as well as the concentration of salt to create iron oxide nanoparticles with more favorable properties and produced with more antibacterial properties. Bacterial growth was investigated by changing the incubation times of pre-culture and overnight culture in the range of the logarithmic phase. The synthesis time, salt ratio, and concentration were optimized to achieve the size, charge, colloidal stability, and magnetic and antibacterial properties of nanoparticles. The amount of the effective substance produced by the bacteria was selected by measuring the amount of the active substance synthesized using the free radical reduction (DPPH) method. With the help of DPPH, the duration of the synthesis was determined to be one week. Characterizations such as UV-vis spectroscopy, FTIR, FESEM, X-ray, and scattering optical dynamics were performed and showed that the nanoparticles synthesized with a salt concentration of 80 mM and a bacterial suspension to salt ratio of 2:1 are smaller in size and have a light scattering index, a PDI index close to 0.1, and a greater amount of reducing salt used in the reaction during one week compared to other samples. Moreover, they had more antibacterial properties than the concentration of 100 mM. As a result, better characteristics and more antibacterial properties than common antibiotics were created on E. coli and Bacillus cereus.

Simple Protocol for Capturing Both Linear-Response and State-Specific Effects in Excited-State Calculations with Continuum Solvation Models

We present an effective computational protocol (cLR²) to describe both solvatochromism and fluorosolvatochromism. This protocol, which couples the polarizable continuum model to time-dependent density functional theory, simultaneously accounts for both linear-response and state-specific solvation effects. A series of test cases, including solvatochromic and fluorosolvatochromic compounds and excited-state intramolecular proton transfers, are used to highlight that cLR² is especially beneficial for modeling bright excitations possessing a significant charge-transfer character, as well as cases in which an accurate balance between states of various polarities should be restored.

Ab initio effective one-electron potential operators: Applications for charge-transfer energy in effective fragment potentials

The concept of effective one-electron potentials (EOPs) has proven to be extremely useful in efficient description of electronic structure of chemical systems, especially extended molecular aggregates such as interacting molecules in condensed phases. Here, a general method for EOP-based elimination of electron repulsion integrals is presented, that is tuned toward the fragment-based calculation methodologies such as the second generation of the effective fragment potentials (EFP2) method. Two general types of the EOP operator matrix elements are distinguished and treated either via the distributed multipole expansion or the extended density fitting (DF) schemes developed in this work. The EOP technique is then applied to reduce the high computational costs of the effective fragment charge-transfer (CT) terms being the bottleneck of EFP2 potentials. The alternative EOP-based CT energy model is proposed, derived within the framework of intermolecular perturbation theory with Hartree-Fock noninteracting reference wavefunctions, compatible with the original EFP2 formulation. It is found that the computational cost of the EFP2 total interaction energy calculation can be reduced by up to 38 times when using the EOP-based formulation of CT energy, as compared to the original EFP2 scheme, without compromising the accuracy for a wide range of weakly interacting neutral and ionic molecular fragments. The proposed model can thus be used routinely within the EFP2 framework.

Optical Absorption of Atomically-Precise Sn14 Nanoclusters: The Antagonistic Interplay of Ligand Stabilization, Molecular Symmetry, and Solvatochromism

The synthesis of atomically precise clusters is nowadays well established. The study of isolated clusters in the gas phase has also become an approved field of research. Although both approaches examine the same research objects, namely nanoclusters, little is known about to what extent results from gas phase studies can be transferred to colloidal systems and vice versa. In particular, it is not yet sufficiently understood how ligands influence the geometric and electronic structure of clusters from an experimental point of view. By comparing a ligand-stabilized tin nanocluster in solution with an isolated species in the gas phase and considering different geometric arrangements with the same number of tin atoms, the impacts of ligand stabilization, molecular symmetry, and solvatochromism on the optical behavior are thoroughly worked out for the first time.

Determination of excited state dipole moments in solution via thermochromic methods

The method basically combines the existing ideas of excited state dipole moment determination via thermochromic fluorescence spectroscopy with the determination of the solvent cavity volume via concentration dependent density measurements of the solution densities at different weight fractions. Additionally, the determination of the cavity volume in dependence of the solvent temperature is included here, which provides a better accuracy of the excited state dipole moment determination. With this step two major sources of errors are eliminated: the use of the very imprecise Onsager radius and the assumption, that the cavity size is temperature independent.•

Thermochromic absorption and fluorescence spectroscopy.

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Cavity volume determination by density measurements.

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Temperature dependent cavity volume determination.

The Bethe-Salpeter formalism with polarisable continuum embedding: reconciling linear-response and state-specific features

The Bethe-Salpeter equation (BSE) formalism has been recently shown to be a valuable alternative to time-dependent density functional theory (TD-DFT) with the same computing time scaling with system size. In particular, problematic transitions for TD-DFT such as charge-transfer, Rydberg and cyanine-like excitations were shown to be accurately described with BSE. We demonstrate here that combining the BSE formalism with the polarisable continuum model (PCM) allows us to include simultaneously linear-response and state-specific contributions to solvatochromism. This is confirmed by exploring transitions of various natures (local, charge-transfer, etc.) in a series of solvated molecules (acrolein, indigo, p-nitro-aniline, donor-acceptor complexes, etc.) for which we compare BSE solvatochromic shifts to those obtained by linear-response and state-specific TD-DFT implementations. Such a remarkable and unique feature is particularly valuable for the study of solvent effects on excitations presenting a hybrid localised/charge-transfer character.

Development of a Novel Index for Analysis of Electronically Excited States

Concerning the major factors in the context of excited states analyses, namely charge centroids of the orbitals involved in the excitations, the distance between orbital centroids, and overlap integrals, a new metric-the Ω index-is proposed to assign the character and optical properties of electronically excited states. Using several molecules from different classes and also a well-studied standard database for time-dependent density functional theory (TD-DFT) studies as benchmark criteria, accountability of the developed index is numerically assessed for local, charge transfer, and Rydberg excitations. It is shown that the nature of excited states can be discriminated using the Ω index, where its superior performance for those situations in which the previous descriptors were not helpful is also unveiled. Relationships are also examined between the Ω index and optical properties of some molecules under study in the framework of the sum-over-state approach. It is observed that there are correlations between the proposed index and computed hyperpolarizabilities based on the sum-over-state scheme. These findings offer the possibility of estimating excited-state properties of large systems from simple descriptors without explicitly performing calculations of high-order response functions.

Molecular and thin film properties of cobalt half-sandwich compounds for optoelectronic application

The structure and electronic properties of a novel cobalt half sandwich complex of cyclopentadiene (Cp) and diaminonaphthalene (DAnap) [CpCo(DAnap)] are described and compared to the previously reported diaminobenzene derivative [CpCo(DAbnz)] in view of their potential for (opto)electronic device application. Both complexes show stable redox processes, tunable through the diaminoacene ligand, and show strong absorption in the visible region, with additional transitions stretching into the near infrared (NIR). CpCo(DAnap) crystallises with a particularly large unit cell (9301 ų), comprising 32 molecules, with a gradual rotation over 8 molecules along the long c-axis. In the solid state the balance of the optical transitions in both complexes is reversed, with a suppression of the visible band and an enhancement of the NIR band, attributed to extensive intermolecular electronic interaction. In the case of CpCo(DAnap), highly crystalline thin films could be formed under physical vapor deposition, which show a photocurrent response stretching into the NIR, and p-type semiconductor behavior in field effect transistors with mobility values of the order 1 × 10^-4 cm² V^-1 s^-1. The device performance is understood through investigation of the morphology of the grown films.

Bethe-Salpeter study of cationic dyes: Comparisons with ADC(2) and TD-DFT

We present a theoretical investigation of the excited-state properties of a large series of structurally diverse arylcarbonium derivatives that are known to be challenging for theoretical models. More specifically, we compare the pros and cons of TD-DFT (TD-M06-2X), ADC(2), and BSE/GW approaches for a large panel of compounds, using two different solvent models. Both 0-0 and vertical transition energies are considered and compared to the experimental values. All approaches reasonably reproduce the auxochromic and acidochromic shifts, although in most cases both TD-DFT and BSE/GW return larger correlation with experimental values than ADC(2) for these shifts. In contrast, the absolute transition energies obtained with ADC(2) tend to be closer to the measurements, TD-DFT using the M06-2X functional largely overestimating the experimental references (by ca. 0.5 eV), and BSE/GW providing intermediate values. In addition, we show that the selected solvent model has a significant impact on the results, the corrected linear-response approach providing larger transition energies than its linear-response counterpart.