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The theory and an implementation of the solvent contribution to the cubic response function for the polarizable continuum model for multiconfigurational self-consistent field wave functions is presented. The excited-state polarizability of benzene, para-nitroaniline, and nitrobenzene has been obtained from the double residue of the cubic response function calculated in the presence of an acetonitrile and dioxane solvent. The calculated excited-state polarizabilities are compared to results obtained from the linear response function of the explicitly optimized excited states. [ABSTRACT FROM AUTHOR]

The two-photon absorption of a class of [2.2]paracyclophane derivatives has been studied using quadratic response and density functional theories. For the molecules investigated, several effects influencing the two-photon absorption spectra have been investigated, such as side-chain elongation, hydrogen bonding, the use of ionic species, and solvent effects, the latter described by the polarizable continuum model. The calculations have been carried out using a recent parallel implementation of the polarizable continuum model in the DALTON code. Special attention is given to those aspects that could explain the large solvent effect on the two-photon absorption cross sections observed experimentally for this class of compounds. [ABSTRACT FROM AUTHOR]

Using a recently developed quadratic response methodology for the calculation of frequency-dependent third-order properties of molecules in solution, we investigate the Buckingham birefringence of furan, thiophene, and selenophene in cyclohexane solution. These systems are chosen since accurate experimental data are available, allowing for a direct comparison of experimental observations with our theoretical estimates. Our model for describing the solvent effects is based on a dielectric continuum approach for the solvent, and uses a molecule-shaped cavity. Our results show qualitatively different Buckingham constants and effective quadrupole centers calculated with and without the solvent, and only when the solvent is included are the qualitative trends observed experimentally reproduced. It is demonstrated that a significant part of this effect arises from the geometry relaxation of the molecules in the solvent. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present the first implementation of the quadratic response function for multiconfigurational self-consistent-field wave functions of solvated molecules described by a polarizable continuum model employing a molecule-shaped cavity. We apply the methodology to the first hyperpolarizability β and, in particular, the second-harmonic generation process for a series of conjugated push-pull oligomers, as well as for para-nitroaniline. The effect of solvation on the dispersion of the hyperpolarizability and the change in the hyperpolarizability for increasing chain length of the oligomers in vacuum and in solution is considered. The effect of a correlated description is analyzed by comparing the Hartree-Fock hyperpolarizabilities to the multiconfigurational self-consistent-field hyperpolarizabilities. The effect of geometry relaxation in the solvent on the properties of the solvated molecules are also investigated. [ABSTRACT FROM AUTHOR]

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 π 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 π, D-π-D, A-π-D, and A-π-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. [ABSTRACT FROM AUTHOR]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper presents the linear response (LR) function for a multiconfigurational self-consistent field (MCSCF) molecular wave function for the integral equation formalism version of the polarizable continuum model (PCM). Both equilibrium and nonequilibrium PCM solvation schemes are described: The nonequilibrium scheme is applied to the calculation of excited state wave functions (Franck–Condon states) and/or of dynamic response properties. An important characteristic of the LR-PCM-MCSCF theory is the explicit inclusion of the effects of solvent dynamics, and this allows us to treat a large variety of time-dependent phenomena. Here, in particular, the theory is applied to the study of the solvent effect on transition energies and on static and dynamic polarizabilities of para-nitroaniline (pNA). The study of the polarizability dispersion of pNA is performed for the ground state and for low-lying electronic excited states including the charge transfer state. We compare our results with available experimental and theoretical data. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present a new implementation of the polarizable continuum model (PCM) at the multiconfigurational self-consistent field (MCSCF) level. This new MCSCF-PCM implementation is based on a second-order algorithm for the optimization of the wave function of the solvated molecule. The robust convergence properties of this approach allows for fast convergence of the PCM-MCSCF wave function for large MCSCF expansions as well as for excited states of solvated molecules. Our implementation also enables us to treat nonequilibrium solvation—that is, to treat excited molecular states generated in a fast excitation process such that not all degrees of freedom of the solvent have relaxed. To demonstrate the applicability of the approach we present calculations of solvation effects on 1,3-dipolar systems and on the ground and excited states of methylenecyclopropene. [ABSTRACT FROM AUTHOR]

Wavelets and multiwavelets have lately been adopted in quantum chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few), they provide a framework that narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for multiwavelet calculations (algebra and integral and differential operator application) and exposes the required functionality to write a simple Python code to solve, among others, the Hartree–Fock equations, the generalized Poisson equation, the Dirac equation, and the time-dependent Schrödinger equation up to any predefined precision. In this study, we will outline the main features of multiresolution analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms. [ABSTRACT FROM AUTHOR]

We have developed and implemented a general formalism for fast numerical solution of time-independent linear partial differential equations as well as integral equations through the application of numerically separable integral operators ind≥ 1 dimensions using the non-standard (NS) form. The proposed formalism is universal, compact and oriented towards the practical implementation into a working code using multiwavelets. The formalism is applied to the case of Poisson and bound-state Helmholtz operators ind= 3. Our algorithms are fully adaptive in the sense that the grid supporting each function is obtained on the fly while the function is being computed. In particular, when the functiong=O fis obtained by applying an integral operatorO, the corresponding grid is not obtained by transferring the grid from the input functionf. This aspect has significant implications that will be discussed in the numerical section. The operator kernels are represented in a separated form with finite but arbitrary precision using Gaussian functions. Such a representation combined with the NS form allows us to build a sparse, banded representation of Green’s operator kernel. We have implemented a code for the application of such operators in a separated NS form to a multivariate function in a finite but, in principle, arbitrary number of dimensions. The error of the method is controlled, while the low complexity of the numerical algorithm is kept. The implemented code explicitly computes all the 22dcomponents of thed-dimensional operator. Our algorithms are described in detail in the paper through pseudo-code examples. The final goal of our work is to be able to apply this method to build a fast and accurate Kohn–Sham solver for density functional theory. [ABSTRACT FROM AUTHOR]

We present the first theoretical investigation of solvent effects on the Faraday $${\mathcal{B}}$$ term of magnetic circular dichroism (MCD) at the density–functional level of theory. In our model, the solvent is described by the polarizable continuum model in its integral-equation formulation. We present the extensions required for including electron correlation effects using density–functional theory (DFT) as well as the necessary extensions for including the effects of a dielectric continuum. The new code is applied to the study of the Faraday $${\mathcal{B}}$$ term of MCD in a series of benzoquinones. It is demonstrated that electron correlation effects, as described by DFT, are essential in order to recover the experimentally observed signs of the $${\mathcal{B}}$$ term. Dielectric continuum effects increase, in general, the magnitude of the $${\mathcal{B}}$$ term, leading to an overestimation of the experimental observations in most cases. [ABSTRACT FROM AUTHOR]

Abstract: Density-functional theory and the polarizable continuum model have been used to calculate the electric-field-induced second harmonic generation of a series of push–pull phenylpolyenes in chloroform solution. The calculations have been performed using both the Becke 3-parameter Lee–Yang–Parr functional and the recently developed Coulomb-attenuated method functional. Solvation has been investigated by examining the effects of the reaction field, non-equilibrium solvation, geometry relaxation, and cavity field. The inclusion of solvent effects leads to significantly better agreement with experimental observations. [Copyright &y& Elsevier]

We present an extension of the Polarizable Continuum Model to compute nonlinear optical (NLO) macroscopic susceptibilities of pure liquids. The procedure is based on the interpretation of the molar property (i.e. the macroscopic susceptibilities) in terms of effective molecular dipoles and (hyper)polarizabilities for a system immersed in the surrounding medium, represented by a continuum dielectric. The effective quantities are obtained through an ab initio description of the molecule under scrutiny interacting with the macroscopic field at the fundamental frequency and with the nonlinear macroscopic polarization at the output frequency. [Copyright &y& Elsevier]

Solvent effects on the two-photon absorption of a symmetrical diamino substituted distyrylbenzene chromophore have been studied using the density functional response theory in combination with the polarizable continuum model. It is shown that the dielectric medium has a rather small effect both on the bond length alternation and on the one-photon absorption spectrum, but it affects significantly the two-photon absorption cross section. It is found that both one- and two-photon absorptions are extremely sensitive to the planarity of the molecule, and the absorption intensity can be dramatically reduced by the conformation distortion. It has led to the conclusion that the experimentally observed anomalous solvent effect on the two-photon absorption of dialkylamino substituted distyrylbenzene chromophores cannot be attributed to the intrinsic properties of a single molecule and its interaction with solvents. [ABSTRACT FROM AUTHOR]

The magnetic-field-induced axial birefringence (magnetochirality) of five closed-shell chiral molecules (three substituted oxiranes, carvone, and limonene) is studied at the density functional theory level using Becke’s 3-parameter Lee-Yang-Parr functional and frequency-dependent quadratic response theory. The influence of the environment and the conformational distribution on the property is also studied. The environment effects are described by the polarizable continuum model in its integral-equation formulation. The effect of the conformational distribution is investigated by performing calculations on several conformers—for carvone and limonene—followed by Boltzmann averaging. The calculated values for the magnetochiral birefringence are compared to previous ab initio results and experimental data where available. The refined model presented here brings the ab initio values closer to experiment. Still, disagreements remain in some cases and it appears difficult to resolve these discrepancies. [ABSTRACT FROM AUTHOR]

Transition metal-catalyzed reactions invariably include steps where ligands associate or dissociate. In order to obtain reliable energies for such reactions, sufficiently large basis sets need to be employed. In this paper, we have used high-precision multiwavelet calculations to compute the metal–ligand association energies for 27 transition metal complexes with common ligands, such as H2, CO, olefins, and solvent molecules. By comparing our multiwavelet results to a variety of frequently used Gaussian-type basis sets, we show that counterpoise corrections, which are widely employed to correct for basis set superposition errors, often lead to underbinding. Additionally, counterpoise corrections are difficult to employ when the association step also involves a chemical transformation. Multiwavelets, which can be conveniently applied to all types of reactions, provide a promising alternative for computing electronic interaction energies free from any basis set errors. [ABSTRACT FROM AUTHOR]

We present the explicit derivation of an approach to the multiscale description of molecules in complex environments that combines frozen-density embedding (FDE) with continuum solvation models, in particular the conductor-like screening model (COSMO). FDE provides an explicit atomistic description of molecule-environment interactions at reduced computational cost, while the outer continuum layer accounts for the effect of long-range isotropic electrostatic interactions. Our treatment is based on a variational Lagrangian framework, enabling rigorous derivations of ground- and excited-state response properties. As an example of the flexibility of the theoretical framework, we derive and discuss FDE + COSMO analytical molecular gradients for excited states within the Tamm-Dancoff approximation (TDA) and for ground states within second-order Møller-Plesset perturbation theory (MP2) and a second-order approximate coupled cluster with singles and doubles (CC2). It is shown how this method can be used to describe vertical electronic excitation (VEE) energies and Stokes shifts for uracil in water and carbostyril in dimethyl sulfoxide (DMSO), respectively. In addition, VEEs for some simplified protein models are computed, illustrating the performance of this method when applied to larger systems. The interaction terms between the FDE subsystem densities and the continuum can influence excitation energies up to 0.3 eV and, thus, cannot be neglected for general applications. We find that the net influence of the continuum in presence of the first FDE shell on the excitation energy amounts to about 0.05 eV for the cases investigated. The present work is an important step toward rigorously derived ab initio multilayer and multiscale modeling approaches. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We have implemented a self-consistent field solver for Hartree–Fock calculations, by making use of Multiwavelets and Multiresolution Analysis. We show how such a solver is inherently a preconditioned steepest descent method and therefore a good starting point for rapid convergence. A distinctive feature of our implementation is the absence of any reference to the kinetic energy operator. This is desirable when Multiwavelets are employed, because differential operators such as the Laplacian in the kinetic energy are challenging to represent correctly. The theoretical framework is described in detail and the implemented algorithm is both presented in the paper and made available as a Python notebook. Two simple examples are presented, highlighting the main features of our implementation: arbitrary predefined precision, rapid and robust convergence, absence of the kinetic energy operator. [ABSTRACT FROM AUTHOR]

Wepresent a formulation of four-component relativistic self-consistentfield (SCF) theory for a molecular solute described within the frameworkof the polarizable continuum model (PCM) for solvation. The linearresponse function for a four-component PCM-SCF state is also derived,as well as the explicit form of the additional contributions to thefirst-order response equations. The implementation of such a four-componentPCM-SCF model, as carried out in a development version of the DIRACprogram package, is documented. In particular, we present the newlydeveloped application programming interface PCMSolver used in theactual implementation with DIRAC. To demonstrate the applicabilityof the approach, we present and analyze calculations of solvationeffects on the geometries, electric dipole moments, and static electricdipole polarizabilities for the group 16 dihydrides H2X(X = O, S, Se, Te, Po). [ABSTRACT FROM AUTHOR]

We present a parallel implementation of the Polarizable Embedding (PE) method, an advanced quantum mechanics/molecular mechanics (QM/MM) approach, for Hartree–Fock (PE-HF) and density functional theory (PE-DFT). The parallelization includes calculations of energies and linear, quadratic, and cubic response functions. The couplings to the QM system due to the polarizable embedding potential have been implemented using a master/slave approach. The implementation shows good scaling behaviour, demonstrated through calculations on a small (a water molecule in a bulk of water molecules) and a larger system (Green Fluorescent Protein (GFP)). [ABSTRACT FROM AUTHOR]

We present the theory and an implementation of the combined quantum mechanics/molecular mechanics/polarizable dielectric continuum (QM/MM/PCM) method. This is a fully polarizable layered model designed for effective inclusion of a medium in a quantum-mechanical calculation. The short-range part of the solvent electrostatic potential is described by an atomistic model while the long-range part of this potential is described by a dielectric continuum. The QM/MM/PCM method has been implemented in combination with QM linear response techniques allowing for the assessment of, e.g., vertical electronic excitation energies and linear dipole−dipole polarizabilities, in all cases using a nonequilibrium formulation of the environmental response. The model is general, but is here implemented for the case of density functional theory. Numerical examples are given for solvatochromic shifts relating to a set of organic molecules in aqueous solution. We find in general the QM/MM/PCM interface to exhibit a faster convergence with respect to the system size as compared to the use of QM/MM only. [ABSTRACT FROM AUTHOR]

We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Green's function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Green's function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Many treatment options for stress urinary incontinence are difficult to apply to neurological patients. Urolastic is a new agent that is primarily indicated for women with mild stress urinary incontinence or men after prostate surgery. In this report, we present a series of 5 cases describing the first use of Urolastic to treat neurological patients. All patients were evaluated with a voiding diary and the use of auxiliary devices as the main indicators of continence. The median operative time was 30.8 minutes, and no complications were observed. Of the 5 patients, 4 reported improved incontinence: 2 switched from diapers to small pads, while the other 2 patients were able to discontinue urinary condom use. The only instance of treatment failure occurred in a patient with a low-compliance bladder. The advantages of this procedure appear to include a soft-cuff effect, reversibility, and minimal invasiveness. However, a future randomized study would be necessary to validate this treatment option. [ABSTRACT FROM AUTHOR]

The description of chemical phenomena in solution is as challenging as it is important for the accurate calculation of molecular properties. Here, we present the implementation of the polarisable continuum model (PCM) in the four-component Dirac–Kohn–Sham density functional theory framework, offering a cost-effective way to concurrently model solvent and relativistic effects. The implementation is based on the matrix representation of the Dirac–Coulomb Hamiltonian in the basis of restricted kinetically balanced Gaussian-type functions, exploiting a non-collinear Kramer's unrestricted formalism implemented in the program ReSpect, and the integral equation formalism of the PCM available through the stand-alone library PCMSolver. Calculations of electron paramagnetic resonance parameters (g-tensors and hyperfine couplingA-tensors), as well as of the temperature-dependent contribution to paramagnetic nuclear magnetic resonance (pNMR) shifts, are presented to validate the model and to demonstrate the importance of taking both relativistic and solvent effects into account for magnetic properties. As shown for selected Ru and Os complexes, the solvent shifts may amount to as much as 25% of the gas-phase values forg-tensor components and even more for pNMR shifts in some extreme cases. [ABSTRACT FROM AUTHOR]

We have developed a new strategy to reduce the storage requirements of a multivariate function in a multiwavelet framework. We propose that alongside the commonly used adaptivity in the grid refinement one can also vary the order of the representation k as a function of the scale n . In particular the order is decreased with increasing refinement scale. The consequences of this choice, in particular with respect to the nesting of scaling spaces, are discussed and the error of the approximation introduced is analyzed. The application of this method to some examples of mono- and multivariate functions shows that our algorithm is able to yield a storage reduction up to almost 60%. In general, values between 30 and 40% can be expected for multivariate functions. Monovariate functions are less affected but are also much less critical in view of the so called “curse of dimensionality”. [ABSTRACT FROM AUTHOR]

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 N1.5 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 [ABSTRACT FROM AUTHOR]

An analytical theory for the energy second derivatives at second-order Mø øller–Plesset level for solvated molecules described within the polarizable continuum model is presented. The method, which is based on the differentiation of relaxed density equations for the first derivatives, is firstly presented in its formal aspects and is then applied to the study of the rate-determining step of the electrophilic bromination of ethylene in aqueous solution. [ABSTRACT FROM AUTHOR]

PCMSolver is an open‐source library for continuum electrostatic solvation. It can be combined with any quantum chemistry code and requires a minimal interface with the host program, greatly reducing programming effort. As input, PCMSolver needs only the molecular geometry to generate the cavity and the expectation value of the molecular electrostatic potential on the cavity surface. It then returns the solvent polarization back to the host program. The design is powerful and versatile: minimal loss of performance is expected, and a standard single point self‐consistent field implementation requires no more than 2 days of work. We provide a brief theoretical overview, followed by two tutorials: one aimed at quantum chemistry program developers wanting to interface their code with PCMSolver, the other aimed at contributors to the library. We finally illustrate past and ongoing work, showing the library's features, combined with several quantum chemistry programs. PCMSOLVER is an open‐source library for continuum electrostatic solvation. It can be combined with any quantum chemistry code and requires a minimal interface with the host program, greatly reducing programming effort. Communication and data movement between the two is limited to the molecular electrostatic potential and apparent surface charge. This affords a significantly streamlined interface, with minimal loss of performance. A standard single point self‐consistent field implementation requires no more than 2 days of work. [ABSTRACT FROM AUTHOR]