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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]

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 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]

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]

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]

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 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]

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]

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.