Stereo-electronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: a feasible anharmonic protocol

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.

Analytical second derivatives of the free energy in solution by the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution

The application of analytical derivative methods to solution systems is important because several chemical reactions occur in solution. The reference interaction site model (RISM) is one of the solvation theories used to study solution systems and has shown good performance, especially in the polar solvent systems. Although the analytical first derivative based on the RISM coupled with quantum methods (RISM-SCF) has already been derived, the analytical second derivative has not been proposed yet. Therefore, in this study, the analytical second derivative was derived using RISM-SCF explicitly including constrained spatial electron density distribution (RISM-SCF-cSED). The performance of this method was validated with the Hessian calculations of formaldehyde and para-nitroaniline in solution, and the results demonstrated that the method accurately calculated frequency values at a small computational cost.

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

We present a computational study of polarizabilities and hyperpolarizabilities of organic molecules in aqueous solutions, focusing on solute-water interactions and the way they affect a molecule's linear and non-linear electric response properties. We employ a polarizable quantum mechanics/molecular mechanics (QM/MM) computational model that treats the solute at the QM level while the solvent is treated classically using a force field that includes polarizable charges and dipoles, which dynamically respond to the solute's quantum-mechanical electron density. Quantum confinement effects are also treated by means of a recently implemented method that endows solvent molecules with a parametric electron density, which exerts Pauli repulsion forces upon the solute. By applying the method to a set of aromatic molecules in solution we show that, for both polarizabilities and first hyperpolarizabilities, observed solution values are the result of a delicate balance between electrostatics, hydrogen-bonding, and non-electrostatic solute solvent interactions.

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions

In this work, we investigate how geometric changes influence the static dipole polarizability (α) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C ₆ dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H₂O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic (α _iso) and nearly 50% to the anisotropic (α _aniso) polarizability values. In doing so, we find that α _iso = 9.8307 bohr³, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr³ provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

A 4,4'-bis(2-benzoxazolyl)stilbene luminescent probe: assessment of aggregate formation through photophysics experiments and quantum-chemical calculations

A combination of experimental and quantum mechanical investigations is applied to the study of the optical features of 4,4'-bis(2-benzoxazolyl)stilbene (BBS) dissolved in solution or in a poly(l-lactic acid) (PLA) thermoplastic matrix at different concentrations. The experimental analyses allow the characterization of BBS solutions and dispersions in terms of absorption and emission features, along with the collection of some key parameters such as fluorescence quantum yield, anisotropy and lifetime, while the computational approach gives a detailed description of the photophysical behavior of BBS in the different environments. For the 10^-5 M BBS solution, the fluorescence spectra show the expected peaks at 425 and 455 nm of the non-interacting BBS molecules with a single fluorescence lifetime of 0.85 ns without revealing any aggregation phenomena, prevented by the short lifetime and fast diffusion rate of the monomer. Moreover, the calculated spectra are in excellent agreement with the experiments, thus showing the reliability of the computational approach. In time-resolved emission experiments (TRES) on more concentrated solutions (10^-4 M) and on BBS crystals, the presence of an excimer is revealed by the appearance of a broad peak around 540 nm, followed by the disappearance of the two main peaks at 460 nm on a time scale of about 10 ns. The computational analysis attributes this behavior to the formation of aggregates of different geometries. The BBS dispersions in PLA reveal the presence of different BBS architectures depending on the fluorophore content. Even at low concentrations, BBS is mainly dispersed as a monomer in the matrix, spheroid aggregates of about 800-900 nm in diameter are also present and the relevant fluorescence spectra arise from the combination of monomer and aggregate contributions. At higher concentrations, BBS starts forming crystals of a peculiar helicoidal shape, with a diameter of about 2 μm, variable length up to several hundreds of μm and emission spectra similar to those of isolated BBS crystals.

Accurate Modeling of the Polarizability of Dyes for Electromagnetic Calculations

The wavelength-dependent complex linear polarizability of a dye is a crucial input for the modeling of the optical properties of dye-containing systems. We here propose and discuss methods to obtain an accurate polarizability model by combining absorption spectrum measurements, Kramers-Kronig (KK) tranformations, and density functional theory (DFT) calculations. We focus, in particular, on the real part of the polarizability and its link with static polarizability. In addition, we introduce simple KK-consistent analytic functions based on the theory of critical points as a much more accurate approach to model dye polarizabilities compared with existing models based on Lorentz oscillators. Accurate polarizability models based on critical points and DFT calculations of the static polarizability are derived for five commonly used dyes: Rhodamine 6G, Rhodamine 700, Crystal Violet, Nile Blue A, and Methylene Blue. Finally, we demonstrate explicitly, using examples of Mie Theory calculations of nanoparticle-dye interactions, how an inaccurate polarizability model can result in fundamentally different predictions, further emphasizing the importance of accurate models, such as the one proposed here.

Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route

We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.

Understanding the interplay between the solvent and nuclear rearrangements in the negative solvatochromism of a push–pull flexible quinolinium cation

The main effects (solvation, vibronic progression) affecting the band position and shape of a push–pull flexible quinolinium cation OPA are highlighted.

Effective Fully Polarizable QM/MM Approach To Model Vibrational Circular Dichroism Spectra of Systems in Aqueous Solution

We propose a methodology, based on the combination of classical Molecular Dynamics (MD) simulations with a fully polarizable Quantum Mechanical (QM)/Molecular Mechanics (MM)/Polarizable Continuum Model (PCM) Hamiltonian, to calculate Vibrational Circular Dichroism (VCD) spectra of chiral systems in aqueous solution. Polarization effects are included in the MM force field by exploiting an approach based on Fluctuating Charges (FQ). By performing the MD, the description of the solvating environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions. On the other hand, the QM/FQ/PCM calculation of the VCD spectrum ensures an accurate description of the electronic density of the solute and a proper account for the specific interactions in solution. The application of our approach to (R)-methyloxirane and (l)-alanine in aqueous solution gives calculated spectra in remarkable agreement with their experimental counterparts and a substantial improvement with respect to the same spectra calculated with the PCM.

Comparison of Property-Oriented Basis Sets for the Computation of Electronic and Nuclear Relaxation Hyperpolarizabilities

In the present work, we perform an assessment of several property-oriented atomic basis sets in computing (hyper)polarizabilities with a focus on the vibrational contributions. Our analysis encompasses the Pol and LPol-ds basis sets of Sadlej and co-workers, the def2-SVPD and def2-TZVPD basis sets of Rappoport and Furche, and the ORP basis set of Baranowska-Łączkowska and Łączkowski. Additionally, we use the d-aug-cc-pVQZ and aug-cc-pVTZ basis sets of Dunning and co-workers to determine the reference estimates of the investigated electric properties for small- and medium-sized molecules, respectively. We combine these basis sets with ab initio post-Hartree-Fock quantum-chemistry approaches (including the coupled cluster method) to calculate electronic and nuclear relaxation (hyper)polarizabilities of carbon dioxide, formaldehyde, cis-diazene, and a medium-sized Schiff base. The primary finding of our study is that, among all studied property-oriented basis sets, only the def2-TZVPD and ORP basis sets yield nuclear relaxation (hyper)polarizabilities of small molecules with average absolute errors less than 5.5%. A similar accuracy for the nuclear relaxation (hyper)polarizabilites of the studied systems can also be reached using the aug-cc-pVDZ basis set (5.3%), although for more accurate calculations of vibrational contributions, i.e., average absolute errors less than 1%, the aug-cc-pVTZ basis set is recommended. It was also demonstrated that anharmonic contributions to first and second hyperpolarizabilities of a medium-sized Schiff base are particularly difficult to accurately predict at the correlated level using property-oriented basis sets. For instance, the value of the nuclear relaxation first hyperpolarizability computed at the MP2/def2-TZVPD level of theory is roughly 3 times larger than that determined using the aug-cc-pVTZ basis set. We link the failure of the def2-TZVPD basis set with the difficulties in predicting the first-order field-induced coordinates. On the other hand, the aug-cc-pVDZ and ORP basis sets overestimate the property in question only by roughly 30%. In this study, we also propose a low-cost composite treatment of anharmonicity that relies on the combination of two basis sets, i.e., a large-sized basis set is employed to determine lowest-order derivatives with respect to the field-induced coordinates, and a medium-sized basis set is used to compute the higher-order derivatives. The results of calculations performed at the MP2 level of theory demonstrate that this approximate scheme is very successful at predicting nuclear relaxation hyperpolarizabilities.