Gauge-origin-independent magnetizabilities of solvated molecules using the polarizable continuum model

We present an implementation of the polarizable continuum model in its integral equation formulation for the calculation of the magnetizabilities of solvated molecules. The gauge-origin independence of the calculated magnetizabilities and the fast basis set convergence are ensured through the use of London atomic orbitals. Our implementation can use Hartree-Fock and multiconfigurational self-consistent-field (MCSCF) wave functions as well as density-functional theory including hybrid functionals such as B3LYP. We present the results of dielectric continuum effects on water and pyridine using MCSCF wave functions, as well as dielectric medium effects on the magnetizability of the aromatic amino acids as a model for how a surrounding protein environment affects the magnetizability of these molecules. It is demonstrated that the dielectric medium effects on the magnetizability anisotropies of the aromatic amino acids may be substantial, being as large as 25% in the case of tyrosine.     

Electronic g-tensors of solvated molecules using the polarizable continuum model

We present the implementation of density functional response theory combined with the polarizable continuum model (PCM), enabling first principles calculations of molecular g-tensors of solvated molecules. The calculated g-tensor shifts are compared with experimental g-tensor shifts obtained from electron paramagnetic resonance spectra for a few solvated species. The results indicate qualitative agreement between the calculations and the experimental data for aprotic solvents, whereas PCM fails to reproduce the electronic g-tensor behavior for protic solvents. This failure of PCM for protic solvents can be resolved by including into the model those solvent molecules which are involved in hydrogen bonding with the solute. The results for the protic solvents show that the explicit inclusion of the solvent molecules of the first solvation sphere is not sufficient in order to reproduce the behavior of the electronic g-tensor in protic solvents, and that better agreement with experimental data can be obtained by including the long-range electrostatic effects accounted for by the PCM approach on top of the explicit hydrogen-bonded complexes.     

Modeling ultrafast solvated electronic dynamics using time-dependent density functional theory and polarizable continuum model

A first-principles solvated electronic dynamics method is introduced. Solvent electronic degrees of freedom are coupled to the time-dependent electronic density of a solute molecule by means of the implicit reaction field method, and the entire electronic system is propagated in time. This real-time time-dependent approach, incorporating the polarizable continuum solvation model, is shown to be very effective in describing the dynamical solvation effect in the charge transfer process and yields a consistent absorption spectrum in comparison to the conventional linear response results in solution.     

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     

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.     

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.     

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.     

Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models

The conductor-like polarizable continuum model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C-PCM solvation for Hartree-Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU-based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM-related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C-PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time-dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)-based implementation. In addition, our C-PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed-ups of up to 130× for restricted ESP-based atomic charge evaluations, when compared to CPU-based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.     

Wavelet formulation of the polarizable continuum model

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF‐PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N^1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effective generation of molecular cavities in polarizable continuum model by DefPol procedure

A new computational strategy for the building of molecular cavities (named DefPol) has been linked to the most recent implementation of the polarizable continuum model (PCM) for the representation of solvent effects on physicochemical properties of large molecules. Free energies, analytical gradients, and Hessians can be computed in this framework in the rigid cavity approximation. Coupling DefPol cavities with a number of other recent improvements of the standard algorithm (e.g., effective use of symmetry, iterative procedures with linear scaling) significantly enlarges the dimensions of systems amenable to refined computations and strongly reduces the gap between computations for isolated molecules and in solution. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1693–1701, 1999     

Improving performance of polarizable continuum model for study of large molecules in solution

We present a new implementation of the polarizable continuum model (PCM) that significantly improves its performance, especially for large solutes. This approach avoids the separation between electronic and nuclear sources in the calculation of the solvation charges, allowing the extension of iterative procedures to all the PCM versions [dielectric (D), conductor (C), and integral equation formalism (IEF)], so that the best method and/or algorithm can be selected, depending on the system at hand. In particular, the new balanced two-term iterative procedure with total charges avoids any nonlinear computational step and memory occupation. Furthermore, it also shows a good convergence for the C-PCM and IEF-PCM versions, which were quite problematic for the conventional separate charges approach. Also, first and second analytical derivatives are available in this context for Hartree–Fock and Kohn–Sham models. A number of examples are analyzed; they show that the new algorithms couple fully satisfactory numerical accuracy with remarkable computational efficiency. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1186–1198, 1999     

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.     

A study of amino-protecting groups using the polarizable continuum model (PCM)

In order to better understand the performance of 1,2-dimethyl-5-acetyl barbituric acid (DMB) as an amino protecting group relative to 5,5-dimethylcyclohexane-1,3-dione (DMD), ab initio calculations were performed. pK_a calculations using the PCM model indicated that both molecules are more acidic in the enol form. Therefore, the protecting reaction of these molecules should involve the anions formed from the loss of a proton from the enol compounds. Contrary to what would be expected, the larger efficiency exhibited by the DMB molecule cannot be attributed to an extension of the electronic conjugation effect. In the absence of any other noticeable effect that could be responsible for the greater efficiency of the DMB molecule, we are inclined to believe that the difference could be accounted for by the presence of two independent centers of conjugation.This paper is dedicated to Jacopo Tomasi in recognition of his outstanding contribution to the field of computational chemistry in solution. The authors are honored to contribute to this volume; especially so for two of them (COS and MACN) who have the privilege of his friendship.Acknowledgements The authors would like to thank the Brazilian research agencies CNPq, CAPES and FAPERJ for the financial support. C. O. da Silva thanks the Dipartimento di Chimica e Chimica Industriale, University of Pisa, where the MCSCF calculations were performed.     

Parallelization of the integral equation formulation of the polarizable continuum model for higher-order response functions

We present a parallel implementation of the integral equation formalism of the polarizable continuum model for Hartree-Fock and density functional theory calculations of energies and linear, quadratic, and cubic response functions. The contributions to the free energy of the solute due to the polarizable continuum have been implemented using a master-slave approach with load balancing to ensure good scalability also on parallel machines with a slow interconnect. We demonstrate the good scaling behavior of the code through calculations of Hartree-Fock energies and linear, quadratic, and cubic response function for a modest-sized sample molecule. We also explore the behavior of the parallelization of the integral equation formulation of the polarizable continuum model code when used in conjunction with a recent scheme for the storage of two-electron integrals in the memory of the different slaves in order to achieve superlinear scaling in the parallel calculations.     

Solvent effects on Raman optical activity spectra calculated using the polarizable continuum model

The integral equation formulation of the polarizable continuum model (IEFPCM) has been extended to the calculation of solvent effects on vibrational Raman optical activity spectra. Gauge-origin independence of the differential scattering intensities of right and left circularly polarized light is ensured through the use of London atomic orbitals. Density functional theory (DFT) calculations have been carried out for bromochlorofluoromethane, methyloxirane, and epichlorhydrin. The results indicate that solvent effects on the ROA differential scattering intensities can be substantial, and vary in sign and magnitude for different vibrational modes. It is demonstrated that both direct and indirect effects are important in determining the total solvent effects on the ROA differential scattering intensities. Local field effects are shown to be in general small, whereas electronic nonequilibrium solvation has a profound effect on the calculated solvent effects compared to an equilibrium solvation model. For molecules with several conformations, the changes in the relative stability of the different conformers also lead to noticeable changes in the ROA spectra.     

On the performance of time-dependent density functional theory and polarizable continuum model in the study of aqueous formaldehyde

In this paper Time-Dependent Density Functional Theory (TD-DFT) with Becke's three-parameter hybrid method using the Lee–Yang–Parr correlation functional (B3LYP) in conjunction with different basis sets is applied to calculate the solvatochromic shift on the lowest singlet transition of formaldehyde in vacuum and in solution. Our results, in excellent agreement with solvent excitation energy shift of acetone in water at 298–300 K (no experimental data on formaldehyde in water are available so far) and with previous high level quantum chemical calculations, help in appreciating the potentialities of the combined DFT/PCM approach on aquo-complexes for the study of structural and spectroscopic properties of molecule in solution.     

Conformational simulations of aqueous solvated alpha-conotoxin GI and its single disulfide analogues using a polarizable force field model

The solution conformation of alpha-conotoxin GI and its two single disulfide analogues are simulated using a polarizable force field in combination with the molecular fragmentation quantum chemical calculation. The polarizability is explicitly described by allowing the partial charges and fragment dipole moments to be variables, with values coming from the linear-scaling energy-based molecular fragmentation calculations at the B3LYP/6-31G(d) level. In comparison with the full quantum chemical calculations, the fragmentation approaches can yield precise ground-state energies, dipole moments, and static polarizabilities for peptides. The B3LYP/6-31G(d) charges and fragment-centered dipole moments are introduced in calculations of electrostatic terms in both AmberFF03 and OPLS force fields. Our test calculations on the gas-phase glucagon (PDB code: 1gcn) and solvated alpha-conotoxin GI (PDB code: 1not) demonstrate that the present polarization model is capable of describing the structural properties (such as the relative conformational energies, intramolecular hydrogen bonds, and disulfide bonds) with accuracy comparable to some other polarizable force fields (ABEEM/MM and OPLS-PFF) and the quantum mechanics/molecular mechanics (QM/MM) hybrid model. The employment of fragment-centered dipole moments in calculations of dipole-dipole interactions can save computational time in comparison with those polarization models using atom-centered dipole moments without much loss of accuracy. The molecular dynamics simulations using the polarizable force field demonstrate that two single disulfide GI analogues are more flexible and less structured than the native alpha-conotoxin GI, in agreement with NMR experiments. The polarization effect is important in simulations of the folding/unfolding process of solvated proteins.     

Achieving linear-scaling computational cost for the polarizable continuum model of solvation

This work describes a new and low-scaling implementation of the polarizable continuum model (PCM) for computing the self-consistent solvent reaction field. The PCM approach is both general and accurate. It is applicable in the framework of both quantum and classical calculations, and also to hybrid quantum/classical methods. In order to further extend the range of applicability of PCM we addressed the problem of its computational cost. The generation of the finite-elements molecular cavity has been reviewed and reimplemented, achieving linear scaling for systems containing up to 500 atoms. Linear scaling behavior has been achieved also for the iterative solution of the PCM equations, by exploiting the fast multipole method (FMM) for computing electrostatic interactions. Numerical results for large (both linear and globular) chemical systems are discussed.