Modeling solvent effects on chiroptical properties.

In this article, the most advanced extensions of solvation models to chiroptical properties of solvated systems will be reviewed. The main aspects determining the complex phenomenon of solvation will be first discussed in terms of the physical interactions beyond them and successively translated in a computational language introducing the specific models. A particular attention will be devoted to the family of solvation models which couple a quantum-mechanical description of the molecular solute and a continuum description of the solvent. The theoretical analysis will be supported with examples of applications showing the potentialities of the models and their accuracy in capturing the essence of solvent effects on optically active molecules.

Structure versus solvent effects on nonlinear optical properties of push-pull systems: a quantum-mechanical study based on a polarizable continuum model.

A quantum mechanical investigation on the effects of the solvent and the structure on nonlinear optical activity of a class of merocyanine compounds has been conducted. The interplay of the two effects on the first hyperpolarizability, computed at density functional theory and second-order Møller-Plesset level, has been analyzed in combination with ground state properties and geometries and excited state energies and dipoles. A critical analysis of the simplified two-level model has also been presented.

On the performance of continuum solvation methods. A comment on "Universal approaches to solvation modeling".

In a recent Account, Cramer and Truhlar presented a comparison between the SM8 method and standard versions of other continuum solvation models implemented in widely available quantum mechanical programs. In that Account, the SM8 model was found to lead to "considerably smaller errors for aqueous and nonaqueous free energies of solvation for neutrals, cations, and anions, with particularly good performance for nonaqueous data". Here, we demonstrate that competing solvation methods are indeed as accurate as the SM8 method, if they are applied with the same rigor.

Structures and properties of electronically excited chromophores in solution from the polarizable continuum model coupled to the time-dependent density functional theory.

This paper provides an overview of recent research activities concerning the quantum-mechanical description of structures and properties of electronically excited chromophores in solution. The focus of the paper is on a specific approach to include solvent effects, namely the polarizable continuum model (PCM). Such a method represents an efficient strategy if coupled to proper quantum-mechanical descriptions such as the time-dependent density functional theory (TDDFT). As a result, the description of molecules in the condensed phase can be extended to excited states still maintaining the computational efficiency and the physical reliability of the ground-state calculations. The most important theoretical and computational aspects of the coupling between PCM and TDDFT are presented and discussed together with an example of application to the study of the low-lying electronic excited states of push-pull chromophores in different solvents.

Response of Scalar Fields and Hydrogen Bonding to Excited-State Molecular Solvation of Carbonyl Compounds.

An attempt has been made to understand the mechanism of excited-state molecular solvation and its effect on hydrogen bonding in carbonyl compounds in aqueous solution. The correlation between solvation and electronic transitions has been investigated by comparing results obtained either with a supermolecular description in terms of hydrogen-bonded clusters or with a combined method embedding such clusters with a polarizable continuum dielectric mimicking the bulk water. Popular scalar fields such as molecular electrostatic potential and molecular electron density have been used as useful tools to probe the changes in the hydrogen bonding passing from ground to excited states in the gas as well as solvent phase.

How the environment controls absorption and fluorescence spectra of PRODAN: a quantum-mechanical study in homogeneous and heterogeneous media.

The spectroscopic behavior of 6-propionyl-2-(N,N-dimethyl)aminonaphthalene (PRODAN) is investigated in different environments, ranging from homogeneous solutions of different polarities to diffuse interfaces mimicking membranes. The variety of experimental data as well as computational results present in the literature still do not clarify the nature of the emission process; in particular, it is not well-established whether fluorescence in such a molecule occurs from a planar or from a twisted intramolecular charge transfer state. The first part of the work is thus devoted to better understand how the electronic transition processes occur in homogeneous solvents. The effect of the medium polarity as well as the hydrogen bond formation are studied. In the second part of the paper, a first attempt to interpret the experimental results of PRODAN in unilamellar vesicles is carried out. The complexity of the still-open questions about the photophysics of PRODAN has prompted us to base the study on quantum-mechanical calculations performed at various levels of theory, namely, DFT, TDDFT, CIS, and SAC-CI, and to include the effects of the environment in a self-consistent way. This is achieved by using the integral equation formalism version of the polarizable continuum model (IEFPCM). IEFPCM is a quite versatile approach, being able to treat equilibrium and nonequilibrium solvation in both homogeneous and heterogeneous media.

How solvent controls electronic energy transfer and light harvesting.

The way that solvent (or host medium) modifies the rate of electronic energy transfer (EET) has eluded researchers for decades. By applying quantum chemical methods that account for the way solvent (in general any host medium including liquid, solid, or protein, etc.) responds to the interaction between transition densities, we quantify the solvent screening. We find that it attains a striking exponential attenuation at separations less than about 20 A, thus interpolating between the limits of no apparent screening and a significant attenuation of the EET rate. That observation reveals a previously unidentified contribution to the distance dependence of the EET rate.

Dispersion and repulsion contributions to the solvation free energy: comparison of quantum mechanical and classical approaches in the polarizable continuum model.

We report a systematic comparison of the dispersion and repulsion contributions to the free energy of solvation determined using quantum mechanical self-consistent reaction field (QM-SCRF) and classical methods. In particular, QM-SCRF computations have been performed using the dispersion and repulsion expressions developed in the framework of the integral equation formalism of the polarizable continuum model, whereas classical methods involve both empirical pairwise potential and surface-dependent approaches. Calculations have been performed for a series of aliphatic and aromatic compounds containing prototypical functional groups in four solvents: water, octanol, chloroform, and carbon tetrachloride. The analysis is focused on the dependence of the dispersion and repulsion components on the level of theory used in QM-SCRF computations, the contribution of those terms in different solvents, and the magnitude of the coupling between electrostatic and dispersion-repulsion components. Finally, comparison is made between the dispersion-repulsion contributions obtained from QM-SCRF calculations and the results determined from classical approaches.

Formation and relaxation of excited states in solution: a new time dependent polarizable continuum model based on time dependent density functional theory.

In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, epsilonomega. The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations (and emissions), as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.

Geometries and properties of excited states in the gas phase and in solution: theory and application of a time-dependent density functional theory polarizable continuum model.

In this paper we present the theory and implementation of analytic derivatives of time-dependent density functional theory (TDDFT) excited states energies, both in vacuo and including solvent effects by means of the polarizable continuum model. The method is applied to two case studies: p-nitroaniline and 4-(dimethyl)aminobenzonitrile. For both molecules PCM-TDDFT is shown to be successful in supporting the analysis of experimental data with useful insights for a better understanding of photophysical and photochemical pathways in solution.

A time-dependent polarizable continuum model: theory and application.

This work presents an extention of the polarizable continuum model to explicitly describe the time-dependent response of the solvent to a change in the solute charge distribution. Starting from an initial situation in which solute and solvent are in equilibrium, we are interested in modeling the time-dependent evolution of the solvent response, and consequently of the solute-solvent interaction, after a perturbation in this equilibrium situation has been switched on. The model introduces an explicit time-dependent treatment of the polarization by means of the linear-response theory. Two strategies are tested to account for this time dependence: the first one employs the Debye model for the dielectric relaxation, which assumes an exponential decay of the solvent polarization; the second one is based on a fitting of the experimental data of the solvent complex dielectric permittivity. The first approach is simpler and possibly less accurate but allows one to write an analytic expression of the equations. By contrast, the second approach is closer to the experimental evidence but it is limited to the availability of experimental data. The model is applied to the ionization process of N,N-dimethyl-aniline in both acetonitrile and water. The nonequilibrium free-energy profile is studied both as a function of the solvent relaxation coordinate and as a function of time. The solvent reorganization energy is evaluated as well.

Solvation dynamics in acetonitrile: a study incorporating solute electronic response and nuclear relaxation.

The solvent reorganization process after electronic excitation of a polar solute in a polar solvent such as acetonitrile is related mainly to the time evolution of the solute-solvent electrostatic interaction. Modern laser-based techniques have sufficient time resolution to follow this decay in real time, providing information to be confirmed and interpreted by theories and models. We present here a study aimed at the investigation of the different steps involved in the process taking place after a vertical S(0) --> S(1) excitation of a large size chromophore, coumarin 153 (C153), in acetonitrile, from both the solute and the solvent points of view. To do this, we use accurate quantum mechanical calculations for the solute properties within the polarizable continuum model (PCM) and classical molecular dynamics (MD) simulations, both equilibrium and nonequilibrium, for C153 in the presence of the solvent. The geometry of the solute is allowed to change in order to study the role of internal motions in the time-dependent solvation process. The solvent response function has been obtained from the simulation data and compared to experiment, while the comparison between equilibrium and nonequilibrium MD results for the solvation response confirms the validity of the linear response approximation in the C153-acetonitrile system. The MD trajectories have also been used to monitor the structure of the solvation shell and to determine its change in response to the change in the solute partial charges.

Radiative and nonradiative decay rates of a molecule close to a metal particle of complex shape.

We present a model to evaluate the radiative and nonradiative lifetimes of electronic excited states of a molecule close to a metal particle of complex shape and, possibly, in the presence of a solvent. The molecule is treated quantum mechanically at Hartree-Fock (HF) or density-functional theory (DFT) level. The metal/solvent is considered as a continuous body, characterized by its frequency dependent local dielectric constant. For simple metal shapes (planar infinite surface and spherical particle) a version of the polarizable continuum model based on the integral equation formalism has been used, while an alternative methodology has been implemented to treat metal particles of arbitrary shape. In both cases, equations have been numerically solved using a boundary element method. Excitation energies and nonradiative decay rates due to the energy transfer from the molecule to the metal are evaluated exploiting the linear response theory (TDHF or TDDFT where TD--time dependent). The radiative decay rate of the whole system (molecule + metal/solvent) is calculated, still using a continuum model, in terms of the response of the surrounding to the molecular transition. The model presented has been applied to the study of the radiative and nonradiative lifetimes of a lissamine molecule in solution (water) and close to gold spherical nanoparticles of different radius. In addition, the influence of the metal shape has been analyzed by performing calculations on a system composed by a coumarin-type molecule close to silver aggregates of complex shape.

Excitation energy transfer (EET) between molecules in condensed matter: a novel application of the polarizable continuum model (PCM).

We present a quantum-mechanical theory to study excitation energy transfers between molecular systems in solution. The model is developed within the time-dependent (TD) density-functional theory and the solvent effects are introduced in terms of the polarizable continuum model (PCM). Unique characteristic of this model is that both "reaction field" and screening effects are included in a coherent and self-consistent way. This is obtained by introducing proper solvent-specific operators in the Kohn-Sham equations and in the corresponding TD scheme. The solvation model exploits the integral equation formalism (IEF) version of PCM and it defines the solvent operators on a molecular cavity modeled on the real three-dimensional (3D) structure of the solute systems. Applications to EET in dimers of ethylene and naphtalene are presented and discussed.

A polarizable continuum model for molecules at diffuse interfaces.

In this work we illustrate an extension of the polarizable continuum model to describe solvation effects on molecules at the interface between two fluid phases (liquid/liquid, liquid/vapor). This extension goes beyond the naive picture of the interface as a plane dividing two distinct dielectrics, commonly employed in continuum models. The main feature of the model is the use of a diffuse interface with an electric permittivity depending on the position. This characteristic clearly allows the study of simple interfaces as well as more complex membrane or multilayer structures. Moreover the smooth variation of the permittivity in the diffuse interface, in contrast to the sharp boundary between two regions, overcomes the numerical divergences due to charges placed at the boundary. The implementation of the model relies on the integral equation formalism, which allows one to calculate the reaction field acting on a molecule immersed in a dielectric environment once the proper Green's function is known. In the present case, such a Green's function is obtained numerically, allowing a large flexibility in the choice of the dielectric permittivity profile. The applications have been selected with the aim of illustrating the capabilities of the model; its present limitations are also discussed.

New developments in the symmetry-adapted algorithm of the Polarizable Continuum Model.

We present recent developments in the symmetry implementation of the Polarizable Continuum Model (PCM). The structure of the matrix, which defines the PCM solvent response, is examined, and we demonstrate how this matrix can be transformed to a block diagonal form where each block belongs to different irreducible representations of the molecular point group. This development is especially important at the Multi-configurational Self-Consistent Field (MCSCF) level where symmetry is needed to avoid problems with symmetry breaking in the wave function and facilitate the optimization of electronic excited states. Moreover, although only the totally symmetric part of the solvent interaction is needed for energy calculations, in response or perturbation theory calculations of molecular properties, other irreps play an important role and the classification of solvent interaction terms by irrep is, therefore, desirable. In addition, the use of symmetry reduces the computational cost. The implementation presented here is illustrated with a series of calculations of absorption and emission processes in solution on the diazines pyrazine, pyrimidine, and pyridazine. These calculations allow us to illustrate both formal aspects of the implementation such as the choice of active spaces based on orbital symmetry as well as practical aspects such as the speed-up of the calculation.