The novel polarizable FQFμ force field is proposed and coupled to a quantum mechanical (QM) SCF Hamiltonian. The peculiarity of the resulting QM/FQFμ approach stands in the fact the polarization effects are modeled in terms of both fluctuating charges and dipoles, which vary as a response to the external electric field/potential. Remarkably, QM/FQFμ is defined in terms of three parameters: electronegativity and chemical hardness, which are well-defined in density functional theory, and polarizability, which is physically observable. Such parameters are numerically adjusted to reproduce full QM reference electrostatic energy values. The model is challenged against test molecular systems in aqueous solution, showing remarkable accuracy and thus highlighting its potentialities for future extensive applications.

Fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles, named QM/FQFµ (J. Chem. Theory Comput. 2019, 15 2233-2245), 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 1 arXiv:1906.03852v1 [physics.chem-ph] 10 Jun 2019 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. IntroductionExcited-state phenomena play a crucial role in many application fields, as for instance photocatalysis, optical information storage and solar cells. In the past decades, theoretical modeling of excited-state properties of molecules in the gas-phase has become a widespread strategy of investigation, 1 giving precious information on, for instance, the nature of the electronic excitation, 2-4 nuclei-electron coupling effects 5-7 and excited state electron dynamics. [8][9][10] However, for electronic phenomena taking place in the condensed phase, 11-19 the interplay between the molecule and its environment can substantially alter the electronic response to external electromagnetic fields. Therefore, any accurate modeling of excited states of solvated systems asks for reliable theoretical approaches to include the effects of the environment at all levels of the excitation phenomenon.Most of the currently available approaches to describe the effects of the external environment on molecular properties belong to the class of the so-called focused models; 20-25 the attention is focused on the molecule and the environment is treated a lower level of sophistication as it modifies, but not determines, the molecular response to the external radiation. In order to keep the atomistic description of the environment, thus substantially overcoming well-known and amply used continuum solvent descriptions, 23,25-29 multiscale QM/Molecular Mechanics (MM) approaches have been developed. 30,31 In such models, the molecule (solute) is treated at the QM level, whereas the environment (solvent) is modelled by means of classical MM force fields (FF). The interaction between the QM and MM portions is usually described in terms of electrostatic forces, although approaches to include non-electrostatic QM/MM interactions have been proposed recently. [32][33][34] In order to fully capure the physics of solute-

We demonstrate the pivotal role of QM density confinement effects on solvatochromic shifts. In particular, by resorting to a QM/MM approach capable of accounting for confinement effects we successfully reproduce vacuo-to-water solvatochromic shifts for dark n → π * and bright π → π * transitions of acrolein and dark n → π * transitions of pyridine and pyrimidine without the need of including explicit water molecules in the QM portion. Remarkably, our approach is also able to dissect the effects of the single forces acting on the solute-solvent couple, and allows for a rationalization of the experimental findings in terms of physico-chemical quantities.

We present a computational study on the spectroscopic properties of UV-Vis absorbing dyes in water solution. We model the solvation environment by using both continuum and discrete models, with and without polarization, to establish how the physical and chemical properties of the solute-solvent interaction may affect the spectroscopic response of aqueous systems. Seven different compounds were chosen, representing different classes of organic molecules. The classical atomistic description of the solvent molecules was enriched with polarization effects treated by means of the fluctuating charges (FQ) model, propagated to the first-order response function of the quantum-mechanical (QM) solute to include its effects withing the modeling of the electronic excitations of the systems. Results obtained with the QM/FQ model were compared with those from continuum solvation models as well as nonpolarizable atomistic models, and then confronted with the experimental values to determine the accuracy that can be expected with each level of theory. Moreover, a thorough structural analysis using molecular dynamics simulations is provided for each system. K E Y W O R D S excitation energies, QM/FQ, QM/MM, QM/PCM, solvent effects, TD-DFT 1 | I N TR O DU C TI O N One-photon absorption spectroscopy within the UV-Visible range is often the most direct and inexpensive analytical tool that can be used to study the electronic properties of a system. Most commonly, such measurements are carried out on solvated samples, with water being a ubiquitous choice.With the gradual increase in the complexity of the systems under investigation, the correct interpretation of experimental data is increasingly reliant on their calculated ab initio counterparts. Many theoretical models based on quantum mechanics (QM), accompanied by their computational implementations, have been presented over the years offering different levels of compromise between the computational cost and the accuracy of the results. [1][2][3] At present, methods based on density functional theory (DFT) and its time-dependent counterpart (TD-DFT) have become the most popular choice for the simulation of absorption spectra of medium-large organic molecular systems thanks to their versatility stemming from the freedom of choice of density functional and basis set, as well as the favorable scaling with system size which allows their application to increasingly large systems. [1,[4][5][6] Many benchmarks studies have been presented elaborating on the merits and limitations of TD-DFT for the simulation of UV-Vis spectroscopy, as well as on the most appropriate choice of functional and basis set combination for different types of system. [6][7][8][9][10][11][12][13][14][15][16] And though many computational studies are carried out on isolated systems, solvent effects should not be neglected for the presence of the solvation environment can significantly alter the electronic absorption properties of a system, both qualitatively and quantitatively. [17][18][19][20][21][22][23][24][25][2...

Despite the potentialities of the quantum mechanics (QM)/fluctuating charge (FQ) approach to model the spectral properties of solvated systems, its extensive use has been hampered by the lack of reliable parametrizations of solvents other than water. In this paper, we substantially extend the applicability of QM/FQ to solvating environments of different polarities and hydrogen-bonding capabilities. The reliability and robustness of the approach are demonstrated by challenging the model to simulate solvatochromic shifts of four organic chromophores, which display large shifts when dissolved in apolar, aprotic or polar, protic solvents.

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The fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles, named QM/FQFµ (J. Chem. Theory Comput. 2019, 15, 2233-2245, is extended to the evaluation of nuclear gradients and the calculation of IR spectra of molecular systems in condensed phase. To this end, analytical equations defining first and second energy derivatives with respect to nuclear coordinates are derived and discussed. The potentialities of the approach are shown by applying the model to the calculation of IR spectra of Methlyoxirane, Glycidol and Gallic Acid in aqueous solution. The results are compared with the continuum QM/PCM and the polarizable QM/FQ, which is based on Fluctuating Charges only.

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