Coupled cluster theory with the polarizable continuum model of solvation

The environment may significantly affect molecular properties. Thus, it is desirable to account explicitly for these effects on the wave function and its derivatives, especially when the latter are evaluated with accurate methods, such as those belonging to coupled cluster (CC) theory. In this tutorial review, we discuss how to combine CC methods with the polarizable continuum model of solvation (PCM). We describe useful approximations that include the solvent response to the correlation and excited state equations while maintaining the computational cost comparable to in vacuo calculations. Although applied to PCM, the theoretical framework presented in this review is general and can be used with any polarizable embedding model. Representative applications of the CC-PCM method to ground and excited state properties of solvated molecules are presented, and comparisons with experiment, and between the full and approximate schemes are discussed.     

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution.     

Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model

In this paper, we present the theory and implementation of a nonequilibrium solvation model for the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method in the polarizable continuum model. For nonequilibrium solvation, we adopted the Pekar partition scheme in which solvent charges are divided into dynamical and inertial components. With this nonequilibrium solvation scheme, a vertical transition from an initial state to a final state may be described as follows: the initial state is described by equilibrium solvation, while in the final state, the inertial component remains in the solvation for the initial state; the dynamical component will be calculated self-consistently for the final state. The present method was applied to the vertical photoemission and absorption of s-trans acrolein and methylenecyclopropene. The effect of nonequilibrium solvation was significant for a polar solvent.     

Influence of electron correlation effects on the solvation of Cu2+

Hybrid QM/MM MD simulations including electron correlation effects at MP2 level were performed to obtain an accurate picture of the solvation structure and the Jahn-Teller effect of the Cu2+ ion.     

Solvation effects on reaction profiles by the polarizable continuum model coupled with the Gaussian density functional method

An efficient version of the polarizable continuum model for solvation has been implemented in the Gaussian density-functional-based code called deMon. Solvation free energies of representative compounds have been calculated as a preliminary test. The hydration effects on the reaction profile of the Cl⁻+CH₃Cl→ClCH₃+Cl⁻ reaction and the thermodynamics of the Menschutkin reaction have also been investigated. Finally, the conformational behavior of the 1,2-diazene cis–trans isomerization process in water was examined. Comparisons between the results obtained and the available experimental data and previous theoretical computations have been made. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 290–299, 1998     

On the calculations of interaction energies and induced electric properties within the polarizable continuum model

In this work we investigate the influence of a polarizable environment on the interaction energies and the interaction-induced (excess) static electric dipole properties for the selected model hydrogen-bonded complexes. The excess properties were estimated for water and hydrogen fluoride dimers using the supermolecular approach and assuming the polarizable continuum model (PCM) as a representation of the polarizable environment. We analyze in this context the performance of the counterpoise correction and the consequences of various possible monomer cavity choices. The polarizable environment reduces the absolute magnitudes of interaction energies and interaction-induced dipole moments, whereas an increase is observed for the absolute magnitudes of induced polarizabilities and first hyperpolarizabilities. Our results indicate that the use of either monomeric (MC) or dimeric (DC) cavities in calculations of monomer properties does not change qualitatively the resultant excess properties. We conclude that the DC scheme is more consistent with the definition of the interaction energy and consequently also the interaction-induced property, whereas the MC scheme corresponds to the definition of stabilization energy. Our results indicate also a good performance of the counterpoise correction scheme for the self-consistent methods in the case of all studied properties.     

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.     

Towards an accurate description of anharmonic infrared spectra in solution within the polarizable continuum model: reaction field, cavity field and nonequilibrium effects

We present a newly developed and implemented methodology to perturbatively evaluate anharmonic vibrational frequencies and infrared (IR) intensities of solvated systems described by means of the polarizable continuum model (PCM). The essential aspects of the theoretical model and of the implementation are described and some numerical tests are shown, with special emphasis towards the evaluation of IR intensities, for which the quality of the present method is compared to other methodologies widely used in the literature. Proper account of an incomplete solvation regime in the treatment of the molecular vibration is also considered, as well as inclusion of the coupling between the solvent and the probing field (cavity field effects). In order to assess the quality of our approach, comparison with experimental findings is reported for selected cases.     

Solvent effect on the stability and properties of platinum-substituted borirene and boryl isomers: The polarizable continuum model

The structure and properties of platinum borirene complex trans-[Cl(PMe₃)₂Pt{μ-BN(SiMe₃)₂C=C}Ph] and its isomer the platinum boryl complex trans–[Cl(PMe₃)₂PtBN(SiMe₃)₂C≡CPh] were investigated theoretically. The solvent effect on the stability, structural parameters, frontier orbital energies, HOMO–LUMO gaps, and hardness of isomers was investigated using the polarizable continuum model (PCM). It was found that borirene isomer is the most stable isomer in the gas phase and solvent. The calculated results show that the presence of solvent reduces the frontier orbital energy of the studied molecules. Geometries obtained from calculations were used to perform NBO analysis.     

Building cavities in a fluid of spherical or rod-like particles: a contribution to the solvation free energy in isotropic and anisotropic polarizable continuum model

A general formalism for the calculation of cavitation energies in the framework of the scaled particle theory has been implemented in the Polarizable Continuum Model (PCM), contributing to the nonelectrostatic part of the molecular free energy in solution. The solute cavity and the solvent molecules are described as hard spherocylinders, whose radius and length are related to the actual molecular shape, while the solvent density is estimated from experimental data, or from the solvent molecular volume, suitably scaled. The present model can describe isotropic solutions of spherical and rod-like molecules in spherical or rod-like solvents, and also anisotropic solutions in which the solvent molecules are oriented in space: in this case, the cavitation energy also depends on the relative orientation of solute and solvent molecules. Test calculations have been performed on simple systems to evaluate the accuracy of the present approach, in comparison with other methods and with the available experimental estimates of the cavitation energy, giving encouraging results.     

Evaluation of the dispersion contribution to the solvation energy. A simple computational model in the continuum approximation

We present a simple computational method for the evaluation of solute-solvent dispersion energy contributions in dilute isotropic solutions, supplementing the method with an analysis of its sensitivity with respect to several parameters (or features of the solvation model) which are left free in the general formulation. The method is a natural complement of the electrostatic solvation procedure described in preceding articles.     

Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

A coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Two-photon absorption in solution by means of time-dependent density-functional theory and the polarizable continuum model

We present the first study of two-photon absorption (TPA) of solvated molecules based on direct evaluation of TPA cross sections from the quadratic response of time-dependent perturbations. A set of prototypical two-photon (TP) chromophores has been selected and analyzed: a pure pi system (t-stilbene) and its substituted homologs obtained employing a donor (D) and an acceptor (A) group to probe the solvent effects along the series pi, D-pi-D, A-pi-D, and A-pi-A. For the selected systems we have calculated the TPA cross sections in different environments by means of the polarizable continuum model. The data have been analyzed to evaluate how the structural and environmental parameters contribute to the final two-photon absorption cross section. These include molecular structure, geometry relaxation in solution, polarity, and refractive index of the solvent. The performances of the three common functionals SVWN, BLYP, and B3LYP have been compared. The results show a significant solvent dependence of the TPA cross section and an unusual trend when passing from cyclohexane to water. The data have also been rationalized in terms of the main orbital excitations leading to the transitions. Finally, trends along the series have been described and comparison with experiments and previous calculations has been drawn.     

Steric effects in RNA interference: probing the influence of nucleobase size and shape

Nonpolar nucleosides with varying size and shape have been used to study the hydrogen-bonding stabilization and steric effects on RNA interference. The uracil and adenine residues of siRNA guide strands have been replaced by nonpolar isosteres of uracil and adenine and by steric variants. RNAi experiments targeting Renilla luciferase mRNA have shown close correlation between siRNA thermal stability and gene suppression. Interestingly, siRNA modified at position 7 on the guide strand does not follow this correlation, having substantial RNAi activity despite low thermal stability. Sequence-selectivity studies were carried out at this position with mutated target mRNAs and nucleobase analogues with varied size (2,4-difluoro- and 2,4-dichlorobenzene) and different shape (2,3-dichlorobenzene, 4-methylbenzimidazole). The results point out the importance of nucleobase shape and steric effects in RNA interference.     

Continuous medium theory for nonequilibrium solvation: IV. Solvent reorganization energy of electron transfer based on conductor-like screening model

In this work the authors present some evidences of defects in the popular continuous medium theories for nonequilibrium solvation. Particular attention has been paid to the incorrect reversible work approach. After convincing reasoning, the nonequilibrium free energy has been formulated to an expression different from the traditional ones. In a series of recent works by the authors, new formulations and some analytical application models for ultrafast processes were developed. Here, the authors extend the new theory to the cases of discrete bound charge distributions and present the correct form of the nonequilibrium solvation energy in such cases. A numerical solution method is applied to the evaluation of solvent reorganization energy of electron transfer. The test calculation for biphenyl-cyclohexane-naphthalene anion system achieves excellent agreement with the experimental fitting. The central importance presented in this work is the very simple and a consistent form of nonequilibrium free energy for both continuous and discrete charge distributions, based on which the new models can be established.     

Effective modeling of intrinsic and environmental effects on the structure and electron plaramagnetic resonance parameters of nitroxides by an integrated quantum mechanical/molecular mechanics/polarizable continuum model approach

 Experimental and density functional theory geometries have been used to extend the AMBER force field to nitroxides. An optimum set of transferable atomic charges for the calculation of electrostatic interactions both in vacuo and in aqueous solution has been obtained by averaging the charges obtained by a restrained electrostatic potential fitting of representative compounds. Besides reliable structural data, our implementation allows the computation of accurate spectromagnetic properties by single-point B3LYP computations on geometries optimized at the AMBER level. Solvent shifts in aqueous solution can be reproduced quantitatively by a mixed model in which specific solvent effects are described by two water molecules strongly coordinated to the nitroxide oxygen, while bulk effects are described by the polarizable continuum model. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 29 June 2000     

Solvent effects in electronically excited states using the continuum solvation model COSMO in combination with multireference configuration interaction with singles and doubles (MR-CISD)

An implementation of the COSMO continuum solvation model into the MCSCF and MR-CISD programs of the COLUMBUS program system is reported. Equilibrium solvation and non-equilibrium solvation models for the treatment of electronic excitations have been used. Solvatochromic effects have been computed for a representative set of n-* and -* states of formaldehyde, acrolein and pyrazine using several solvents ranging from some with apolar character to water. Agreement with experimental shifts is good within the limits of a continuum model.Contribution to the Jacopo Tomasi Honorary Issue