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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]

The integral equation formulation of the polarizable continuum model is extended to the calculation of solvent effects on vibrational Raman optical activity (ROA) spectra. Results indicate that solvent effects on the ROA differential scattering intensities are substantial, and vary in sign and magnitude for different vibrational modes.

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]

The theory and implementation of the solvent contribution to the cubic response function of a molecular solute for the polarizable continuum model in its integral equation formulation which could be used to compute the solvent effect for the degenerate four-wave mixing process for different classes of heteroaromatic chromophores are described.

A new quantum mechanical model is described to introduce Pauli repulsion interaction between a molecular solute and the surrounding solvent in the framework of the Polarizable Continuum Model. The new model is derived to allow naturally for a position-dependent solvent density, which makes it possible to employ the derived expression for the calculation of molecular properties at the interface between two different dielectrics.

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]

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 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. [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]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present a parallel and linear scaling implementation of the calculation of the electrostatic potential arising from an arbitrary charge distribution. Our approach is making use of the multi-resolution basis of multiwavelets. The potential is obtained as the direct solution of the Poisson equation in its Green's function integral form. In the multiwavelet basis, the formally non local integral operator decays rapidly to negligible values away from the main diagonal, yielding an effectively banded structure where the bandwidth is only dictated by the requested accuracy. This sparse operator structure has been exploited to achieve linear scaling and parallel algorithms. Parallelization has been achieved both through the shared memory (OpenMP) and the message passing interface (MPI) paradigm. Our implementation has been tested by computing the electrostatic potential of the electronic density of long-chain alkanes and diamond fragments showing (sub)linear scaling with the system size and efficent parallelization. [ABSTRACT FROM AUTHOR]

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 for a number of UNIX 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 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]

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]