Calculation of Linear and Non-linear Electric Response Properties of Systems in Aqueous Solution: A Polarizable Quantum/Classical Approach with Quantum Repulsion Effects

Elucidating the Photophysics and Nonlinear Optical Properties of a Novel Azo Prototype for Possible Photonic Applications: A Quantum Chemical Analysis

The photophysics and nonlinear optical responses of a novel nitrothiazol-methoxyphenol molecule were investigated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methods with the polarizable continuum model to take the solvent effect into account. Special attention is paid to the description of the lowest absorption band, characterized as a strong π → π* state in the visible region of the spectrum. The TD-DFT emission spectrum analysis reveals a significant Stokes shift of more than 120 nm for the π → π* state in gas phase condition. The results show a great influence of the solvent polarity on the nonlinear optical (NLO) response of the molecule. Specifically, the second harmonic generation hyperpolarizability β(-2ω; ω, ω) shows a large variation from gas to aqueous solvent (82 × 10-30 to 162 × 10-30 esu), exhibiting notably higher values than those reported for standard compounds such as urea (0.34 × 10-30 esu) and p-nitroaniline (6.42 × 10-30 esu). Furthermore, a two-photon absorption analysis indicates a large cross-section (δ2PA = 77 GM) with superior performance compared to several dyes. These results make the molecule quite interesting for nonlinear optics.

Close-Up Look at Electronic Spectroscopic Signatures of Common Pharmaceuticals in Solution

Simulating electronic properties and spectral signals requires robust computational approaches that need tuning with the system's peculiarities. In this paper, we test implicit and fully atomistic solvation models for the calculation of UV-vis and electronic circular dichroism (ECD) spectra of two pharmaceutically relevant molecules, namely, (2S)-captopril and (S)-naproxen, dissolved in aqueous solution. Room temperature molecular dynamics simulations reveal that these two drugs establish strong contacts with the surrounding solvent molecules via hydrogen bonds. Such specific interactions, which play a major role in the spectral response and are neglected in implicit approaches, are further characterized and quantified with natural bond orbital methods. Our calculations show that simulated spectra, and especially ECD, are in good agreement with experiments solely when conformational and configurational dynamics, mutual polarization, and solute-solvent repulsion effects are considered.

Assessment of an Electrostatic Energy-Based Charge Model for Modeling the Electrostatic Interactions in Water Solvent

The protein force field based on the restrained electrostatic potential (RESP) charges has limitations in accurately describing hydrogen bonding interactions in proteins. To address this issue, we propose an alternative approach called the electrostatic energy-based charges (EEC) model, which shows improved performance in describing electrostatic interactions (EIs) of hydrogen bonds in proteins. In this study, we further investigate the performance of the EEC model in modeling EIs in water solvent. Our findings demonstrate that the fixed EEC model can effectively reproduce the quantum mechanics/molecular mechanics (QM/MM)-calculated EIs between a water molecule and various water solvent environments. However, to achieve the same level of computational accuracy, the electrostatic potential (ESP) charge model needs to fluctuate according to the electrostatic environment. Our analysis indicates that the requirement for charge adjustments depends on the specific mathematical and physical representation of EIs as a function of the environment for deriving charges. By comparing with widely used empirical water models calibrated to reproduce experimental properties, we confirm that the performance of the EEC model in reproducing QM/MM EIs is similar to that of general purpose TIP4P-like water models such as TIP4P-Ew and TIP4P/2005. When comparing the computed 10,000 distinct EI values within the range of -40 to 0 kcal/mol with the QM/MM results calculated at the MP2/aug-cc-pVQZ/TIP3P level, we noticed that the mean unsigned error (MUE) for the EEC model is merely 0.487 kcal/mol, which is remarkably similar to the MUE values of the TIP4P-Ew (0.63 kcal/mol) and TIP4P/2005 (0.579 kcal/mol) models. However, both the RESP method and the TIP3P model exhibit a tendency to overestimate the EIs, as evidenced by their higher MUE values of 1.761 and 1.293 kcal/mol, respectively. EEC-based molecular dynamics simulations have demonstrated that, when combined with appropriate van der Waals parameters, the EEC model can closely reproduce oxygen-oxygen radial distribution function and density of water, showing a remarkable similarity to the well-established TIP4P-like empirical water models. Our results demonstrate that the EEC model has the potential to build force fields with comparable accuracy to more sophisticated empirical TIP4P-like water models.

Solvation Effects on Polarizability of Aromatic Fluids

Elucidating solvation effects on polarizability in condensed phases is important for the description of the optical and dielectric behavior of high-refractive-index molecular materials. We study these effects via the polarizability model combining electronic, solvation, and vibrational contributions. The method is applied to well-characterized highly polarizable liquid precursors: benzene, naphthalene, and phenanthrene. We find that the solvation and vibrational terms are of opposite signs and cancel almost exactly for benzene, but for naphthalene and phenanthrene, a 2.5 and 5.0% decrease relative to the equilibrium electronic polarizability of the respective monomer, α₁^e, is predicted, respectively. The increase in electronic polarizability affects interaction polarizability of all contacts, which is the main reason for the increasing importance of solvation contribution. The calculated refractive indices agree very well with experiment for all three systems.

Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems

We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.

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.

Hyperpolarizabilities of Push-Pull Chromophores in Solution: Interplay between Electronic and Vibrational Contributions

Contemporary design of new organic non-linear optical (NLO) materials relies to a large extent on the understanding of molecular and electronic structure-property relationships revealed during the years by available computational approaches. The progress in theory-hand-in-hand with experiment-has enabled us to identify and analyze various physical aspects affecting the NLO responses, such as the environmental effects, molecular vibrations, frequency dispersion, and system dynamics. Although it is nowadays possible to reliably address these effects separately, the studies analyzing their mutual interplay are still very limited. Here, we employ density functional theory (DFT) methods in combination with an implicit solvent model to examine the solvent effects on the electronic and harmonic as well as anharmonic vibrational contributions to the static first hyperpolarizability of a series of push-pull α,ω-diphenylpolyene oligomers, which were experimentally shown to exhibit notable second-order NLO responses. We demonstrate that the magnitudes of both vibrational and electronic contributions being comparable in the gas phase significantly increase in solvents, and the enhancement can be, in some cases, as large as three- or even four-fold. The electrical and mechanical anharmonic contributions are not negligible but cancel each other out to a large extent. The computed dynamic solute NLO properties of the studied systems are shown to be in a fair agreement with those derived from experimentally measured electric-field-induced second-harmonic generation (EFISHG) signals. Our results substantiate the necessity to consider concomitantly both solvation and vibrational effects in modeling static NLO properties of solvated systems.

Assessing the quality of QM/MM approaches to describe vacuo-to-water solvatochromic shifts

The performance of different quantum mechanics/molecular mechanics embedding models to compute vacuo-to-water solvatochromic shifts is investigated. In particular, both nonpolarizable and polarizable approaches are analyzed and computed results are compared to reference experimental data. We show that none of the approaches outperform the others and that errors strongly depend on the nature of the molecular transition to be described. Thus, we prove that the best choice of embedding model highly depends on the molecular system and that the use of a specific approach as a black box can lead to significant errors and, sometimes, totally wrong predictions.

Multiple Facets of Modeling Electronic Absorption Spectra of Systems in Solution

In this Perspective, we outline the essential physicochemical aspects that need to be considered when building a reliable approach to describe absorption properties of solvated systems. In particular, we focus on how to properly model the complexity of the solvation phenomenon, arising from dynamical aspects and specific, strong solute-solvent interactions. To this end, conformational and configurational sampling techniques, such as Molecular Dynamics, have to be coupled to accurate fully atomistic Quantum Mechanical/Molecular Mechanics (QM/MM) methodologies. By exploiting different illustrative applications, we show that an effective reproduction of experimental spectral signals can be achieved by delicately balancing exhaustive sampling, hydrogen bonding, mutual polarization, and nonelectrostatic effects.

The negative solvatochromism of Reichardt`s dye B30 - a complementary study

The UV/Vis spectra of a hypothetical negative solvatochromic dye in a solvent are theoretically calculated assuming the classical damped harmonic oscillator model and the Lorentz‐Lorenz relation. For the simulations, the oscillator strength of the solvent was varied, while for the solute all oscillator parameters were kept constant. As a result, a simple change of the oscillator strength of the solute can explain the redshift and intensity increase of the UV/Vis band of the solute. Simulated results are compared with measured UV/Vis spectroscopic data of 2,6‐diphenyl‐4‐(2,4,6‐triphenylpyridinium‐1‐yl) phenolate B30 (Reichardt‘s dye) Significant correlations of the absorption energy (1/λ_max) with the molar absorption coefficient ϵ as function of solvent polarity are demonstrated for several derivatives of B30. The approach presented is only applicable to negative solvatochromism. Therefore, while the approach is vital to fully understand solvatochromism, it needs to be complemented by other approaches, e. g., to describe the changes of the chemical interactions based on the nature of the solvent, to explain all its various aspects.

All-Atom Quantum Mechanical Calculation of the Second-Harmonic Generation of Fluorescent Proteins

Fluorescent proteins (FPs) are biotags of choice for second-harmonic imaging microscopy (SHIM). Because of their large size, computing their second-harmonic generation (SHG) response represents a great challenge for quantum chemistry. In this contribution, we propose a new all-atom quantum mechanics methodology to compute SHG of large systems. This is now possible because of two recent implementations: the tight-binding GFN2-xTB method to optimize geometries and a related version of the simplified time-dependent density functional theory (sTD-DFT-xTB) to evaluate quadratic response functions. In addition, a new dual-threshold configuration selection scheme is introduced to reduce the computational costs while retaining overall similar accuracy. This methodology was tested to evaluate the SHG of the proteins iLOV and bacteriorhodopsin (bR). In the case of bR, quantitative agreement with respect to experiment was reached for the out-of-resonance low-energy part of the β_HRS frequency dispersion. This work paves the way toward an accurate prediction of the SHG of large structures-a requirement for the design of new and improved SHIM biotags.

A polarizable three-layer frozen density embedding/molecular mechanics approach

We present a novel multilayer polarizable embedding approach in which the system is divided into three portions, two of which are treated using density functional theory and their interaction is based on frozen density embedding (FDE) theory, and both also mutually interact with a polarizable classical layer described using an atomistic model based on fluctuating charges (FQ). The efficacy of the model is demonstrated by extending the formalism to linear response properties and applying it to the simulation of the excitation energies of organic molecules in aqueous solution, where the solute and the first solvation shell are treated using FDE, while the rest of the solvent is modeled using FQ charges.