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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., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.

New techniques in core-electron spectroscopy are necessary to resolve the structures of oxides of f -elements and other strongly correlated materials that are present only as powders and not as single crystals. Thus, accurate quantum chemical methods must be developed to calculate core spectroscopic properties in such materials. In this contribution, we present an important development in this direction, extending our fully adaptive real-space multiwavelet basis framework to tackle the four-component Dirac-Coulomb-Breit Hamiltonian. We show that multiwavelets can reproduce one-dimensional grid-based approaches. They are however a fully three-dimensional approach which can later be extended to molecules and materials. Our multiwavelet implementation attained precise results irrespective of the chosen nuclear model, provided that the error threshold is tight enough and that the chosen polynomial basis is sufficiently large. Furthermore, our results confirmed that in two-electron species, the magnetic and Gauge contributions from s -orbitals are identical in magnitude and can account for the experimental evidence from K and L edges.

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree-Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

We present a multiwavelet-based implementation of a quantum/classical polarizable continuum model. The solvent model uses a diffuse solute-solvent boundary and a position-dependent permittivity, lifting the sharp-boundary assumption underlying many existing continuum solvation models. We are able to include both surface and volume polarization effects in the quantum/classical coupling, with guaranteed precision, due to the adaptive refinement strategies of our multiwavelet implementation. The model can account for complex solvent environments and does not need a posteriori corrections for volume polarization effects. We validate our results against a sharp-boundary continuum model and find a very good correlation of the polarization energies computed for the Minnesota solvation database.

MRChem is a code for molecular electronic structure calculations, based on a multiwavelet adaptive basis representation. We provide a description of our implementation strategy and several benchmark calculations. Systems comprising more than a thousand orbitals are investigated at the Hartree-Fock level of theory, with an emphasis on scaling properties. With our design, terms that formally scale quadratically with the system size in effect have a better scaling because of the implicit screening introduced by the inherent adaptivity of the method: all operations are performed to the requested precision, which serves the dual purpose of minimizing the computational cost and controlling the final error precisely. Comparisons with traditional Gaussian-type orbitals-based software show that MRChem can be competitive with respect to performance.

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 H 2 , 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.

Benchmarking molecular properties with Gaussian-type orbital (GTO) basis sets can be challenging, because one has to assume that the computed property is at the complete basis set (CBS) limit, without a robust measure of the error. Multiwavelet (MW) bases can be systematically improved with a controllable error, which eliminates the need for such assumptions. In this work, we have used MWs within Kohn-Sham density functional theory to compute static polarizabilities for a set of 92 closed-shell and 32 open-shell species. The results are compared to recent benchmark calculations employing the GTO-type aug-pc4 basis set. We observe discrepancies between GTO and MW results for several species, with open-shell systems showing the largest deviations. Based on linear response calculations, we show that these discrepancies originate from artifacts caused by the field strength and that several polarizabilies from a previous study were contaminated by higher order responses (hyperpolarizabilities). Based on our MW benchmark results, we can affirm that aug-pc4 is able to provide results close to the CBS limit, as long as finite difference effects can be controlled. However, we suggest that a better approach is to use MWs, which are able to yield precise finite difference polarizabilities even with small field strengths.

We present the extension of the quantum/classical polarizable fluctuating charge model to the calculation of single residues of quadratic response functions, as required for the computational modeling of two-photon absorption cross sections. By virtue of a variational formulation of the quantum/classical polarizable coupling, we are able to exploit an atomic orbital-based quasienergy formalism to derive the additional coupling terms in the response equations. Our formalism can be extended to the calculation of arbitrary order response functions and their residues. The approach has been applied to the challenging problem of one- and two-photon spectra of rhodamine 6G (R6G) in aqueous solution. Solvent effects on one- and two-photon spectra of R6G in aqueous solution have been analyzed by considering three different approaches, from a continuum (QM/PCM) to two QM/MM models (nonpolarizable QM/TIP3P and polarizable QM/FQ). Both QM/TIP3P and QM/FQ simulated OPA and TPA spectra show that the inclusion of discrete water solvent molecules is essential to increase the agreement between theory and experiment. QM/FQ has been shown to give the best agreement with experiments.

Mixed multiscale quantum/molecular mechanics (QM/MM) models are widely used to explore the structure, reactivity, and electronic properties of complex chemical systems. Whereas such models typically include electrostatics and potentially polarization in so-called electrostatic and polarizable embedding approaches, respectively, nonelectrostatic dispersion and repulsion interactions are instead commonly described through classical potentials despite their quantum mechanical origin. Here we present an extension of the Tkatchenko-Scheffler semiempirical van der Waals (vdW TS ) scheme aimed at describing dispersion and repulsion interactions between quantum and classical regions within a QM/MM polarizable embedding framework. Starting from the vdW TS expression, we define a dispersion and a repulsion term, both of them density-dependent and consistently based on a Lennard-Jones-like potential. We explore transferable atom type-based parametrization strategies for the MM parameters, based on either vdW TS calculations performed on isolated fragments or on a direct estimation of the parameters from atomic polarizabilities taken from a polarizable force field. We investigate the performance of the implementation by computing self-consistent interaction energies for the S22 benchmark set, designed to represent typical noncovalent interactions in biological systems, in both equilibrium and out-of-equilibrium geometries. Overall, our results suggest that the present implementation is a promising strategy to include dispersion and repulsion in multiscale QM/MM models incorporating their explicit dependence on the electronic density.

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., (© 2017 Wiley Periodicals, Inc.)

Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.

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.

The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

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.

The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the integral equation formulation (IEF) of the polarizable continuum model (PCM), generally lead to working equations which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the IEFPCM with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module PCMSolver and interfaced with LSDalton, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any QC software with minimal effort.

We present a formulation of four-component relativistic self-consistent field (SCF) theory for a molecular solute described within the framework of the polarizable continuum model (PCM) for solvation. The linear response function for a four-component PCM-SCF state is also derived, as well as the explicit form of the additional contributions to the first-order response equations. The implementation of such a four-component PCM-SCF model, as carried out in a development version of the DIRAC program package, is documented. In particular, we present the newly developed application programming interface PCMSolver used in the actual implementation with DIRAC. To demonstrate the applicability of the approach, we present and analyze calculations of solvation effects on the geometries, electric dipole moments, and static electric dipole polarizabilities for the group 16 dihydrides H2X (X = O, S, Se, Te, Po).

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

A theoretical study of the one-photon absorption of five fluorescent proteins (FPs) is presented. The absorption properties are calculated using a polarizable embedding approach combined with density functional theory (PE-DFT) on the wild-type green fluorescent protein (wtGFP) and several of its mutants (BFP, eGFP, YFP and eCFP). The observed trends in excitation energies among the FPs are reproduced by our approach when performing calculations directly on the crystal structures or when using structures extracted from molecular dynamics simulations. However, in the former case, QM/MM geometry optimization of the chromophores within a frozen protein environment is needed in order to reproduce the experimental trends. An explicit account of polarization in the force field is not needed to yield the correct trend between the different FPs, but it is necessary for reproducing the experimentally observed red shift from vacuum to protein. This is the first computational study of a range of fluorescent proteins using a polarizable embedding potential.

We present for the first time a QM/MM study of the one- and two-photon absorption spectra of the GFP chromophore embedded in the full protein environment described by an advanced quantum mechanically derived polarizable force field. The calculations are performed on a crystal structure of the green fluorescent protein (GFP) using the polarizable embedding density functional theory (PE-DFT) scheme. The importance of treating the protein environment explicitly with a polarizable force field and higher-order multipoles is demonstrated, as well as the importance of including water molecules close to the chromophore in the protein barrel. For the most advanced description we achieve good agreement with experimental findings, with a peak at 405 nm for the neutral and a peak at 475 nm for the anionic form of the GFP chromophore. The presence of a dark OPA state, as suggested by other studies to explain the discrepancies between OPA and TPA spectra, is not supported by our calculations., (This journal is © the Owner Societies 2012)

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.

We revised the quantum model of Amovilli and Mennucci (J. Phys. Chem. B 1997, 101, 1051) to include the dispersion contribution to the solvation free energy within the framework of continuum models. Our revised formulation makes use of a single adjustable solvent-dependent parameter, and it can be readily generalized to different quantum mechanical descriptions. In particular, we made use of DFT and applied the model to investigate dispersion effects on vertical excitation energies within a time-dependent DFT framework. Our findings show that dispersion effects constitute a significant component of the absolute solvent effect but when relative solvent-solvent shifts are considered a cancellation effect is observed.

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., (Copyright 2009 Wiley Periodicals, Inc.)

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.

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.

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.

We have derived and implemented the solvent contribution to the cubic response function for the polarizable continuum model in its integral equation formulation. The present formulation is valid both at the Hartree-Fock and at the Kohn-Sham density functional levels of theory, because both bear the same formal description of the solvent contribution through an additional additive term in the Hamiltonian operator. This new implementation is used to compute the solvent effect for the degenerate four-wave mixing process on three different classes of heteroaromatic chromophores: (I) triazine, benzoxazole, benzimidazole, and benzothiazole; (II) three benzothiazole derivatives; and (III) three tri-s-triazine derivatives. The results are first discussed in terms of the solvent effects on the calculated property and then compared to experimental data for the substrates of class (I) and (II).

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.

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.

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.

We present a new quantum mechanical model to introduce Pauli repulsion interaction between a molecular solute and the surrounding solvent in the framework of the Polarizable Continuum Model. The new expression is derived in a way to allow naturally for a position-dependent solvent density. This development makes it possible to employ the derived expression for the calculation of molecular properties at the interface between two different dielectrics. The new formulation has been tested on the azide anion (N3-) for which we have calculated the solvation energy, the dipole moment, and the static polarizability at the interface as a function of the ion position. The calculations have been carried out for different ion-surface orientations, and the results have also been compared with the parallel electrostatic-only solvation 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.

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.

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 beta 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.

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.

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., ((c) 2004 American Institute of Physics.)

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., (Copyright 2003 Wiley Periodicals, Inc.)