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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Electrochemical solvent reorganization energies in the framework of the polarizable continuum model

Electron transfer reactions at electrochemical interfaces play a critical role in a wide range of catalytic processes. A key parameter in the rate constant expressions for such processes is the reorganization energy, which reflects the energetic cost of the solute and solvent rearrangements upon electron transfer. In this paper, we present dielectric continuum methods for calculating the solvent reorganization energy for electrochemical processes. We extend the simple approach in which the solute is represented as a point charge located a specified distance from the electrode surface to the representation of the solute as a collection of point charges corresponding to the partial atomic charges of the molecule. We also develop a method for calculating the electrochemical solvent reorganization energies with molecular-shaped cavities within the framework of the polarizable continuum model (PCM). The electronic and inertial responses of the solvent are separated according to their respective time scales, and two limiting cases of the relation between the solute and solvent electrons are examined. The effects of the electrode are included with the integral equations formalism PCM (IEF-PCM), in which the molecule-solvent boundary is treated explicitly, but the effects of the electrode-solvent boundary are included through an external Green’s function. This approach accounts for the effects of detailed molecular charge redistribution in a molecular-shaped cavity, as well as the electronic and inertial solvent responses and the effects of the electrode. The calculated total reorganization energies are in reasonable agreement with experimental measurements for a series of electrochemical systems. Inclusion of the effects of the electrode is found to be essential for obtaining even qualitatively accurate solvent reorganization energies. These approaches are applicable to a wide range of systems and can be extended to include other types of boundaries, such as a self-assembled monolayer or double layer separating the electrode and the molecule. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.

Ghosh, Soumya↗
DOE OSTI2018

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

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

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Challenges in Modeling Electrochemical Reaction Energetics with Polarizable Continuum Models

A major challenge in the modeling of electrochemical phenomena is the accurate description of the interface between an electrolyte and a charged conductor. Polarizable continuum models (PCM) have been gaining popularity because they offer a computationally inexpensive method of modeling the electrolyte. In this Perspective, we discuss challenges from using one such model which treats the ions using a linearized Poisson–Boltzmann (LPB) distribution. From a physical perspective, this model places charge unphysically close to the surface and adsorbates, and it includes excessively steep ramping of the dielectric constant from the surface to the bulk solvent. Both of these issues can be somewhat mitigated by adjusting parameters built into the model, but in doing so, the resultant capacitance deviates from experimental values. Likewise, hybrid explicit-implicit approaches to the solvent may offer a more realistic description of hydrogen bonding and solvation to reaction intermediates, but the corresponding capacitances also deviate from experimental values. These deviations highlight the need for a careful adjustment of parameters in order to reproduce not only solvation energies but also other physical properties of solid–liquid interfaces. Continuum approaches alone also necessarily do not capture local variations in the electric field from cations at the interface, which can affect the energetics of intermediates with substantial dipoles or polarizability. Finally, since the double-layer charge can be varied continuously, LPB/PCM models provide a way to determine electrochemical barriers at constant potential. However, double-layer charging and the atomic motion associated with reaction events occur on significantly different timescales. As a result, we suggest that more detailed approaches, such as the modified Poisson–Boltzmann model and/or the addition of a Stern layer, may be able to mitigate some but not all of the challenges discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Perspective: Polarizable continuum models for quantum-mechanical descriptions

Polarizable continuum solvation models are nowadays the most popular approach to describe solvent effects in the context of quantum mechanical calculations. Unexpectedly, despite their widespread use in all branches of quantum chemistry and beyond, important aspects of both their theoretical formulation and numerical implementation are still not completely understood. In particular, in this perspective we focus on the numerical issues of their implementation when applied to large systems and on the theoretical framework needed to treat time dependent problems and excited states or to deal with electronic correlation. Possible extensions beyond a purely electrostatic model and generalizations to environments beyond common solvents are also critically presented and discussed. Finally, some possible new theoretical approaches and numerical strategies are suggested to overcome the obstacles which still prevent a full exploitation of these models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Electronic excitation spectra of molecules in solution calculated using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model with perturbative approach

A perturbative approximation of the state specific polarizable continuum model (PCM) symmetry-adapted cluster-configuration interaction (SAC-CI) method is proposed for efficient calculations of the electronic excitations and absorption spectra of molecules in solutions. This first-order PCM SAC-CI method considers the solvent effects on the energies of excited states up to the first-order with using the zeroth-order wavefunctions. This method can avoid the costly iterative procedure of the self-consistent reaction field calculations. The first-order PCM SAC-CI calculations well reproduce the results obtained by the iterative method for various types of excitations of molecules in polar and nonpolar solvents. The first-order contribution is significant for the excitation energies. The results obtained by the zeroth-order PCM SAC-CI, which considers the fixed ground-state reaction field for the excited-state calculations, are deviated from the results by the iterative method about 0.1 eV, and the zeroth-order PCM SAC-CI cannot predict even the direction of solvent shifts in n-hexane for many cases. The first-order PCM SAC-CI is applied to studying the solvatochromisms of (2,2{sup ′}-bipyridine)tetracarbonyltungsten [W(CO){sub 4}(bpy), bpy = 2,2{sup ′}-bipyridine] and bis(pentacarbonyltungsten)pyrazine [(OC){sub 5}W(pyz)W(CO){sub 5}, pyz = pyrazine]. The SAC-CI calculations reveal the detailed character of the excited states and the mechanisms of solvent shifts. The energies of metal to ligand charge transfer states are significantly sensitive to solvents. The first-order PCM SAC-CI well reproduces the observed absorption spectra of the tungsten carbonyl complexes in several solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Combining the GW formalism with the polarizable continuum model: A state-specific non-equilibrium approach

We have implemented the polarizable continuum model within the framework of the many-body Green’s function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupled-cluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The virial theorem for the polarizable continuum model

The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Polarization consistent dielectric screening in polarizable continuum model calculations of solvation energies

A polarization consistent framework, where dielectric screening is affected consistently in polarizable continuum model (PCM) calculations, is employed for the study of solvation energies. The computational framework combines a screened range-separated-hybrid functional (SRSH) with PCM calculations, SRSH-PCM, where dielectric screening is imposed in both PCM self-consistent reaction field (SCRF) iterations and the electronic structure Hamiltonian. We begin by demonstrating the impact of modifying the Hamiltonian to include such dielectric screening in SCRF iterations by considering the solutions of electrostatically embedded Hartree–Fock (HF) exact exchange equations. Long-range screened HF-PCM calculations are shown to capture properly the linear dependence of gap energy of frontier orbitals on the inverse of the dielectric constant, whereas unscreened HF-PCM orbital energies are fallaciously semi-constant with respect to the dielectric constant and, therefore, inconsistent with the ionization energy gaps. Similar trends affect density functional theory (DFT) calculations that aim to achieve predictive quality. Importantly, the dielectric screened calculations are shown to significantly affect DFT- and HF PCM-based solvation energies, where screened solvation energies are smaller compared to the unscreened values. Importantly, SRSH-PCM, therefore, appears to reduce the tendency of DFT-PCM to overestimate solvation energies, where we find the effect to increase with the dielectric constant and the polarity of the molecular solute, trends that enhance the quality of DFT-PCM calculations of solvation energy. Understanding the relationship of dielectric screening in the Hamiltonian and DFT-PCM calculations can ultimately benefit on-going efforts for the design of predictive and parameter free descriptions of solvation energies.

Chemistry↗
DOE OSTI2014

Development of multicomponent hybrid density functional theory with polarizable continuum model for the analysis of nuclear quantum effect and solvent effect on NMR chemical shift

We have developed the multicomponent hybrid density functional theory [MC-(HF+DFT)] method with polarizable continuum model (PCM) for the analysis of molecular properties including both nuclear quantum effect and solvent effect. The chemical shifts and H/D isotope shifts of the picolinic acid N-oxide (PANO) molecule in chloroform and acetonitrile solvents are applied by B3LYP electron exchange-correlation functional for our MC-(HF+DFT) method with PCM (MC-B3LYP/PCM). Our MC-B3LYP/PCM results for PANO are in reasonable agreement with the corresponding experimental chemical shifts and isotope shifts. We further investigated the applicability of our method for acetylacetone in several solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Electronic excitation of molecules in solution calculated using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

The effects from solvent environment are specific to the electronic states; therefore, a computational scheme for solvent effects consistent with the electronic states is necessary to discuss electronic excitation of molecules in solution. The PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (configuration interaction) methods are developed for such purposes. The PCM SAC-CI adopts the state-specific (SS) solvation scheme where solvent effects are self-consistently considered for every ground and excited states. For efficient computations of many excited states, we develop a perturbative approximation for the PCM SAC-CI method, which is called corrected linear response (cLR) scheme. Our test calculations show that the cLR PCM SAC-CI is a very good approximation of the SS PCM SAC-CI method for polar and nonpolar solvents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The cavity electromagnetic field within the polarizable continuum model of solvation

Cavity field effects can be defined as the consequences of the solvent polarization induced by the probing electromagnetic field upon spectroscopies of molecules in solution, and enter in the definitions of solute response properties. The polarizable continuum model of solvation (PCM) has been extended in the past years to address the cavity-field issue through the definition of an effective dipole moment that couples to the external electromagnetic field. We present here a rigorous derivation of such cavity-field treatment within the PCM starting from the general radiation-matter Hamiltonian within inhomogeneous dielectrics and recasting the interaction term to a dipolar form within the long wavelength approximation. To this aim we generalize the Göppert-Mayer and Power-Zienau-Woolley gauge transformations, usually applied in vacuo, to the case of a cavity vector potential. Our derivation also allows extending the cavity-field correction in the long-wavelength limit to the velocity gauge through the definition of an effective linear momentum operator. Furthermore, this work sets the basis for the general PCM treatment of the electromagnetic cavity field, capable to describe the radiation-matter interaction in dielectric media beyond the long-wavelength limit, providing also a tool to investigate spectroscopic properties of more complex systems such as molecules close to large nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Applications of Polarizable Continuum Models To Determine Accurate Solution-Phase Thermochemical Values Across a Broad Range of Cation Charge – The Case of U(III–VI)

Contributing factors to the solution-phase correction to the free energy of the molecular clusters U(H 2 O) n 3+/4+ and UO 2 (H 2 O) m 1+/2+ ( n = 8, 9, 30, 41, 77; m = 4, 5, 30, 41, 77) have been examined as a function of cavity type in the integrated-equation-formalism-protocol (IEF) and SMD polarizable continuum models (PCMs). It is observed that the free energy correction, G corr , does not smoothly converge to zero as the number of explicitly solvating water molecules approaches the bulk limit, and the convergence behavior varies significantly with cavity and model. The rates of convergence of the gas-phase hydration energy, Δ G hyd , wherein the bare metal ion is inserted into a molecular water cluster and Δ G corr for the reaction exhibit wide variations as a function of ion charge, cavity, and model. This is the likely source of previously reported discrepancies in predicted free energies of solvation for metal ions when using different PCM cavities and/or models. The cancellation of errors in Δ G hyd and Δ G corr is optimal for clusters consisting of only a second solvation shell of explicit water molecules ( n = m = 30). Finally, the UFF cavity within IEF, in particular, exhibits the most consistent cancellation of errors when using a molecular cluster consisting of a second shell of solvating water for all oxidation states of uranium, leading to accurate free energies of solvation Δ G solv for these species.

chemistry↗
DOE OSTI2020

Screened Range-Separated Hybrid Functional with Polarizable Continuum Model Overcomes Challenges in Describing Triplet Excitations in the Condensed Phase Using TDDFT

Long range-corrected (LRC) or range-separated hybrid (RSH) functionals where the long-range (LR) limit of electronic interactions is set to the exact exchange have been shown to correct the tendency of traditional density functional theory (DFT) to underestimate the frontier orbital gap. Consequently, the use of such functionals in calculating electronic excited states using linear response based time-dependent DFT (TDDFT) has been successful in correcting the tendency for underestimating the energies of charge transfer states by DFT-based calculations. More recently formulations of functionals that attenuate the LR limit to address condensed-phase effects to polarize the electronic density have been reported. In particular screened RSH (SRSH) combined with polarizable continuum model (PCM) was benchmarked successfully in reproducing the fundamental gap and charge transfer state energies of molecular systems in the condensed phase. Here we use SRSH-PCM to address triplet excited states, and show its success in obtaining correspondence of the low-lying triplet states to the singlet–triplet gap in a similar way that the fundamental orbital gap corresponds to electron removal and addition energies. Importantly, the accuracy of the SRSH-PCM in calculating triplet excitations stands on the polarization consistent framework in addressing the scalar dielectric constant and without affecting the optimal tuning by triplet energies. Finally, the prospect of even further improving the SRSH-PCM accuracy in calculating triplet states can be achieved by optimal tuning on the basis of the spin multiplicity gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

How Aqueous Solvation Impacts the Frequencies and Intensities of Infrared Absorption Bands in Flavin: The Quest for a Suitable Solvent Model

FTIR spectroscopy accompanied by quantum chemical simulations can reveal important information about molecular structure and intermolecular interactions in the condensed phase. Simulations typically account for the solvent either through cluster quantum mechanical (QM) models, polarizable continuum models (PCM), or hybrid quantum mechanical/molecular mechanical (QM/MM) models. Recently, we studied the effect of aqueous solvent interactions on the vibrational frequencies of lumiflavin, a minimal flavin model, using cluster QM and PCM models. Those models successfully reproduced the relative frequencies of four prominent stretching modes of flavin’s isoalloxazine ring in the diagnostic 1450–1750 cm−1 range but poorly reproduced the relative band intensities. Here, we extend our studies on this system and account for solvation through a series of increasingly sophisticated models. Only by combining elements of QM clusters, QM/MM, and PCM approaches do we obtain an improved agreement with the experiment. The study sheds light more generally on factors that can impact the computed frequencies and intensities of IR bands in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Comparison of the Marcus and Pekar partitions in the context of non-equilibrium, polarizable-continuum solvation models

The Marcus and Pekar partitions are common, alternative models to describe the non-equilibrium dielectric polarization response that accompanies instantaneous perturbation of a solute embedded in a dielectric continuum. Examples of such a perturbation include vertical electronic excitation and vertical ionization of a solution-phase molecule. Here, we provide a general derivation of the accompanying polarization response, for a quantum-mechanical solute described within the framework of a polarizable continuum model (PCM) of electrostatic solvation. Although the non-equilibrium free energy is formally equivalent within the two partitions, albeit partitioned differently into “fast” versus “slow” polarization contributions, discretization of the PCM integral equations fails to preserve certain symmetries contained in these equations (except in the case of the conductor-like models or when the solute cavity is spherical), leading to alternative, non-equivalent matrix equations. Unlike the total equilibrium solvation energy, however, which can differ dramatically between different formulations, we demonstrate that the equivalence of the Marcus and Pekar partitions for the non-equilibrium solvation correction is preserved to high accuracy. Differences in vertical excitation and ionization energies are <0.2 eV (and often <0.01 eV), even for systems specifically selected to afford a large polarization response. Numerical results therefore support the interchangeability of the Marcus and Pekar partitions, but also caution against relying too much on the fast PCM charges for interpretive value, as these charges differ greatly between the two partitions, especially in polar solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗