The accuracy limit of chemical shift predictions for species in aqueous solution.

Interpreting NMR experiments benefits from first-principles predictions of chemical shifts. Reaching the accuracy limit of theory is relevant for unambiguous structural analysis and dissecting theoretical approximations. Since accurate chemical shift measurements are based on using internal reference compounds such as trimethylsilylpropanesulfonate (DSS), a detailed comparison of experimental with theoretical data requires simultaneous consideration of both target and reference species ensembles in the same solvent environment. Here we show that ab initio molecular dynamics simulations to generate liquid-state ensembles of target and reference compounds, including explicitly their short-range solvation environments and combined with quantum-mechanical solvation models, allows for predicting highly accurate 1H (∼0.1-0.5 ppm) and aliphatic 13C (∼1.5 ppm) chemical shifts for aqueous solutions of the model compounds trimethylamine N-oxide (TMAO) and N-methylacetamide (NMA), referenced to DSS without any system-specific adjustments. This encompasses the two peptide bond conformations of NMA identified by NMR. The results are used to derive a general-purpose guideline set for predictive NMR chemical shift calculations of NMA in the liquid state and to identify artifacts of force field models. Accurate predictions are only obtained if a sufficient number of explicit water molecules is included in the quantum-mechanical calculations, disproving a purely electrostatic model of the solvent effect on chemical shifts.

Solvent-Controlled Separation of Integratively Self-Sorted Pd2LA2LB2 Coordination Cages.

The integrative implementation of multiple different components into metallosupramolecular self-assemblies requires sophisticated strategies to avoid the formation of statistical mixtures. Previously, the key focus was set on thermodynamically driven reactions of simple homoleptic into complex heteroleptic structures. Using Pd2LA2LB2-type coordination cages, we herein show that integrative self-sorting can be reversed by a change of solvent (from DMSO to MeCN) to favor narcissistic re-segregation into coexisting homoleptic species Pd2LA4 and Pd3LB6. Full separation ("unsorting") back to a mixture of the homoleptic precursors was finally achieved by selective precipitation of Pd3LB6with anionic guest G1 from MeCN, keeping pure Pd2LA4 in solution. When a mixture of homoleptic Pd3LB6 and heteroleptic Pd2LA2LB2 is exposed to a combination of two different di-anions (G1 and G2) in DMSO, selective guest uptake gives rise to two defined coexisting host-guest complexes. A joint experimental and deep theoretical investigation via liquid-state integral equation theory of the reaction thermodynamics on a molecular level accompanied by solvent distribution analysis hints at solvent expulsion from Pd2LA4 to favor the formation of Pd2LA2LB2 in DMSO as the key entropic factor for determining the solvent-specific modulation of the cage conversion equilibrium.

Dissecting the Molecular Origin of g-Tensor Heterogeneity and Strain in Nitroxide Radicals in Water: Electron Paramagnetic Resonance Experiment versus Theory.

Nitroxides are common EPR sensors of microenvironmental properties such as polarity, numbers of H-bonds, pH, and so forth. Their solvation in an aqueous environment is facilitated by their high propensity to form H-bonds with the surrounding water molecules. Their g- and A-tensor elements are key parameters to extracting the properties of their microenvironment. In particular, the gxx value of nitroxides is rich in information. It is known to be characterized by discrete values representing nitroxide populations previously assigned to have different H-bonds with the surrounding waters. Additionally, there is a large g-strain, that is, a broadening of g-values associated with it, which is generally correlated with environmental and structural micro-heterogeneities. The g-strain is responsible for the frequency dependence of the apparent line width of the EPR spectra, which becomes evident at high field/frequency. Here, we address the molecular origin of the gxx heterogeneity and of the g-strain of a nitroxide moiety (HMI: 2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water. To treat the solvation effect on the g-strain, we combined a multi-frequency experimental approach with ab initio molecular dynamics simulations for structural sampling and quantum chemical EPR property calculations at the highest realistically affordable level, including an explicitly micro-solvated HMI ensemble and the embedded cluster reference interaction site model. We could clearly identify the distinct populations of the H-bonded nitroxides responsible for the gxx heterogeneity experimentally observed, and we dissected the role of the solvation shell, H-bond formation, and structural deformation of the nitroxide in the creation of the g-strain associated with each nitroxide subensemble. Two contributions to the g-strain were identified in this study. The first contribution depends on the number of hydrogen bonds formed between the nitroxide and the solvent because this has a large and well-understood effect on the gxx-shift. This contribution can only be resolved at high resonance frequencies, where it leads to distinct peaks in the gxx region. The second contribution arises from configurational fluctuations of the nitroxide that necessarily lead to g-shift heterogeneity. These contributions cannot be resolved experimentally as distinct resonances but add to the line broadening. They can be quantitatively analyzed by studying the apparent line width as a function of microwave frequency. Interestingly, both theory and experiment confirm that this contribution is independent of the number of H-bonds. Perhaps even more surprisingly, the theoretical analysis suggests that the configurational fluctuation broadening is not induced by the solvent but is inherently present even in the gas phase. Moreover, the calculations predict that this broadening decreases upon solvation of the nitroxide.

SAMPL7 physical property prediction from EC-RISM theory.

Inspired by the successful application of the embedded cluster reference interaction site model (EC-RISM), a combination of quantum-mechanical calculations with three-dimensional RISM theory to predict Gibbs energies of species in solution within the SAMPL6.1 (acidity constants, pKa) and SAMPL6.2 (octanol-water partition coefficients, log P) the methodology was applied to the recent SAMPL7 physical property challenge on aqueous pKa and octanol-water log P values. Not part of the challenge but provided by the organizers, we also computed distribution coefficients log D7.4 from predicted pKa and log P data. While macroscopic pKa predictions compared very favorably with experimental data (root mean square error, RMSE 0.72 pK units), the performance of the log P model (RMSE 1.84) fell behind expectations from the SAMPL6.2 challenge, leading to reasonable log D7.4 predictions (RMSE 1.69) from combining the independent calculations. In the post-submission phase, conformations generated by different methodology yielded results that did not significantly improve the original predictions. While overall satisfactory compared to previous log D challenges, the predicted data suggest that further effort is needed for optimizing the robustness of the partition coefficient model within EC-RISM calculations and for shaping the agreement between experimental conditions and the corresponding model description.

Quantum-mechanical property prediction of solvated drug molecules: what have we learned from a decade of SAMPL blind prediction challenges?

Joint academic-industrial projects supporting drug discovery are frequently pursued to deploy and benchmark cutting-edge methodical developments from academia in a real-world industrial environment at different scales. The dimensionality of tasks ranges from small molecule physicochemical property assessment over protein-ligand interaction up to statistical analyses of biological data. This way, method development and usability both benefit from insights gained at both ends, when predictiveness and readiness of novel approaches are confirmed, but the pharmaceutical drug makers get early access to novel tools for the quality of drug products and benefit of patients. Quantum-mechanical and simulation methods particularly fall into this group of methods, as they require skills and expense in their development but also significant resources in their application, thus are comparatively slowly dripping into the realm of industrial use. Nevertheless, these physics-based methods are becoming more and more useful. Starting with a general overview of these and in particular quantum-mechanical methods for drug discovery we review a decade-long and ongoing collaboration between Sanofi and the Kast group focused on the application of the embedded cluster reference interaction site model (EC-RISM), a solvation model for quantum chemistry, to study small molecule chemistry in the context of joint participation in several SAMPL (Statistical Assessment of Modeling of Proteins and Ligands) blind prediction challenges. Starting with early application to tautomer equilibria in water (SAMPL2) the methodology was further developed to allow for challenge contributions related to predictions of distribution coefficients (SAMPL5) and acidity constants (SAMPL6) over the years. Particular emphasis is put on a frequently overlooked aspect of measuring the quality of models, namely the retrospective analysis of earlier datasets and predictions in light of more recent and advanced developments. We therefore demonstrate the performance of the current methodical state of the art as developed and optimized for the SAMPL6 pKa and octanol-water log P challenges when re-applied to the earlier SAMPL5 cyclohexane-water log D and SAMPL2 tautomer equilibria datasets. Systematic improvement is not consistently found throughout despite the similarity of the problem class, i.e. protonation reactions and phase distribution. Hence, it is possible to learn about hidden bias in model assessment, as results derived from more elaborate methods do not necessarily improve quantitative agreement. This indicates the role of chance or coincidence for model development on the one hand which allows for the identification of systematic error and opportunities toward improvement and reveals possible sources of experimental uncertainty on the other. These insights are particularly useful for further academia-industry collaborations, as both partners are then enabled to optimize both the computational and experimental settings for data generation.

Evaluation of log P, pKa, and log D predictions from the SAMPL7 blind challenge.

The Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges focuses the computational modeling community on areas in need of improvement for rational drug design. The SAMPL7 physical property challenge dealt with prediction of octanol-water partition coefficients and pKa for 22 compounds. The dataset was composed of a series of N-acylsulfonamides and related bioisosteres. 17 research groups participated in the log P challenge, submitting 33 blind submissions total. For the pKa challenge, 7 different groups participated, submitting 9 blind submissions in total. Overall, the accuracy of octanol-water log P predictions in the SAMPL7 challenge was lower than octanol-water log P predictions in SAMPL6, likely due to a more diverse dataset. Compared to the SAMPL6 pKa challenge, accuracy remains unchanged in SAMPL7. Interestingly, here, though macroscopic pKa values were often predicted with reasonable accuracy, there was dramatically more disagreement among participants as to which microscopic transitions produced these values (with methods often disagreeing even as to the sign of the free energy change associated with certain transitions), indicating far more work needs to be done on pKa prediction methods.

Chemically Stabilized DNA Barcodes for DNA-Encoded Chemistry.

DNA-encoded compound libraries are a widely used small molecule screening technology. One important aim in library design is the coverage of chemical space through structurally diverse molecules. Yet, the chemical reactivity of native DNA barcodes limits the toolbox of reactions for library design. Substituting the chemically vulnerable purines by 7-deazaadenine, which exhibits tautomerization stability similar to natural adenine with respect to the formation of stable Watson-Crick pairs, yielded ligation-competent, amplifiable, and readable DNA barcodes for encoded chemistry with enhanced stability against protic acid- and metal ion-promoted depurination. The barcode stability allowed for straightforward translation of 16 exemplary reactions that included isocyanide multicomponent reactions, acid-promoted Pictet-Spengler and Biginelli reactions, and metal-promoted pyrazole syntheses on controlled pore glass-coupled barcodes for diverse DEL design. The Boc protective group of reaction products offered a convenient handle for encoded compound purification.

The SAMPL6 challenge on predicting octanol-water partition coefficients from EC-RISM theory.

Results are reported for octanol-water partition coefficients (log P) of the neutral states of drug-like molecules provided during the SAMPL6 (Statistical Assessment of Modeling of Proteins and Ligands) blind prediction challenge from applying the "embedded cluster reference interaction site model" (EC-RISM) as a solvation model for quantum-chemical calculations. Following the strategy outlined during earlier SAMPL challenges we first train 1- and 2-parameter water-free ("dry") and water-saturated ("wet") models for n-octanol solvation Gibbs energies with respect to experimental values from the "Minnesota Solvation Database" (MNSOL), yielding a root mean square error (RMSE) of 1.5 kcal mol-1 for the best-performing 2-parameter wet model, while the optimal water model developed for the pKa part of the SAMPL6 challenge is kept unchanged (RMSE 1.6 kcal mol-1 for neutral compounds from a model trained on both neutral and ionic species). Applying these models to the blind prediction set yields a log P RMSE of less than 0.5 for our best model (2-parameters, wet). Further analysis of our results reveals that a single compound is responsible for most of the error, SM15, without which the RMSE drops to 0.2. Since this is the only compound in the challenge dataset with a hydroxyl group we investigate other alcohols for which Gibbs energy of solvation data for both water and n-octanol are available in the MNSOL database to demonstrate a systematic cause of error and to discuss strategies for improvement.

Structure of a Therapeutic Full-Length Anti-NPRA IgG4 Antibody: Dissecting Conformational Diversity.

We report the x-ray crystal structure of intact, full-length human immunoglobulin (IgG4) at 1.8 Å resolution. The data for IgG4 (S228P), an antibody targeting the natriuretic peptide receptor A, show a previously unrecognized type of Fab-Fc orientation with a distorted λ-shape in which one Fab-arm is oriented toward the Fc portion. Detailed structural analysis by x-ray crystallography and molecular simulations suggest that this is one of several conformations coexisting in a dynamic equilibrium state. These results were confirmed by small angle x-ray scattering in solution. Furthermore, electron microscopy supported these findings by preserving molecule classes of different conformations. This study fosters our understanding of IgG4 in particular and our appreciation of antibody flexibility in general. Moreover, we give insights into potential biological implications, specifically for the interaction of human anti-natriuretic peptide receptor A IgG4 with the neonatal Fc receptor, Fcγ receptors, and complement-activating C1q by considering conformational flexibility.

The SAMPL6 challenge on predicting aqueous pKa values from EC-RISM theory.

The "embedded cluster reference interaction site model" (EC-RISM) integral equation theory is applied to the problem of predicting aqueous pKa values for drug-like molecules based on an ensemble of tautomers. EC-RISM is based on self-consistent calculations of a solute's electronic structure and the distribution function of surrounding water. Following-up on the workflow developed after the SAMPL5 challenge on cyclohexane-water distribution coefficients we extended and improved the methodology by taking into account exact electrostatic solute-solvent interactions taken from the wave function in solution. As before, the model is calibrated against Gibbs energies of hydration from the "Minnesota Solvation Database" and a public dataset of acidity constants of organic acids and bases by adjusting in total 4 parameters, among which only 3 are relevant for predicting pKa values. While the best-performing training model yields a root-mean-square error (RMSE) of 1 pK unit, the corresponding test set prediction on the full SAMPL6 dataset of macroscopic pKa values using the same level of theory exhibits slightly larger error (1.7 pK units) than the best test set model submitted (1.7 pK units for corresponding training set vs. test set performance of 1.6). Post-submission analysis revealed a number of physical optimization options regarding the numerical treatment of electrostatic interactions and conformational sampling. While the experimental test set data revealed after submission was not used for reparametrizing the methodology, the best physically optimized models consequentially result in RMSEs of 1.5 if only improved electrostatic interactions are considered and of 1.1 if, in addition, conformational sampling accounts for quantum-chemically derived rankings. We conclude that these numbers are probably near the ultimate accuracy achievable with the simple 3-parameter model using a single or the two best-ranking conformations per tautomer or microstate. Finally, relations of the present macrostate approach to microstate pKa results are discussed and some illustrative results for microstate populations are presented.

Identification of Intrahelical Bifurcated H-Bonds as a New Type of Gate in K+ Channels.

Gating of ion channels is based on structural transitions between open and closed states. To uncover the chemical basis of individual gates, we performed a comparative experimental and computational analysis between two K+ channels, KcvS and KcvNTS. These small viral encoded K+ channel proteins, with a monomer size of only 82 amino acids, resemble the pore module of all complex K+ channels in terms of structure and function. Even though both proteins share about 90% amino acid sequence identity, they exhibit different open probabilities with ca. 90% in KcvNTS and 40% in KcvS. Single channel analysis, mutational studies and molecular dynamics simulations show that the difference in open probability is caused by one long closed state in KcvS. This state is structurally created in the tetrameric channel by a transient, Ser mediated, intrahelical hydrogen bond. The resulting kink in the inner transmembrane domain swings the aromatic rings from downstream Phes in the cavity of the channel, which blocks ion flux. The frequent occurrence of Ser or Thr based helical kinks in membrane proteins suggests that a similar mechanism could also occur in the gating of other ion channels.

Thermodynamic Characterization of Hydration Sites from Integral Equation-Derived Free Energy Densities: Application to Protein Binding Sites and Ligand Series.

Water molecules play an essential role for mediating interactions between ligands and protein binding sites. Displacement of specific water molecules can favorably modulate the free energy of binding of protein-ligand complexes. Here, the nature of water interactions in protein binding sites is investigated by 3D RISM (three-dimensional reference interaction site model) integral equation theory to understand and exploit local thermodynamic features of water molecules by ranking their possible displacement in structure-based design. Unlike molecular dynamics-based approaches, 3D RISM theory allows for fast and noise-free calculations using the same detailed level of solute-solvent interaction description. Here we correlate molecular water entities instead of mere site density maxima with local contributions to the solvation free energy using novel algorithms. Distinct water molecules and hydration sites are investigated in multiple protein-ligand X-ray structures, namely streptavidin, factor Xa, and factor VIIa, based on 3D RISM-derived free energy density fields. Our approach allows the semiquantitative assessment of whether a given structural water molecule can potentially be targeted for replacement in structure-based design. Finally, PLS-based regression models from free energy density fields used within a 3D-QSAR approach (CARMa - comparative analysis of 3D RISM Maps) are shown to be able to extract relevant information for the interpretation of structure-activity relationship (SAR) trends, as demonstrated for a series of serine protease inhibitors.

The hpCADD NDDO Hamiltonian: Parametrization.

A neglect of diatomic differential overlap (NDDO) Hamiltonian has been parametrized as an electronic component of a polarizable force field. Coulomb and exchange potentials derived directly from the NDDO Hamiltonian in principle can be used with classical potentials, thus forming the basis for a new generation of efficiently applicable multipolar polarizable force fields. The new hpCADD Hamiltonian uses force-field-like atom types and reproduces the electrostatic properties (dipole moment, molecular electrostatic potential) and Koopmans' theorem ionization potentials closely, as demonstrated for a large training set and an independent test set of small molecules. The Hamiltonian is not intended to reproduce geometries or total energies well, as these will be controlled by the classical force-field potentials. In order to establish the hpCADD Hamiltonian as an electronic component in force-field-based calculations, we tested its performance in combination with the 3D reference interaction site model (3D RISM) for aqueous solutions. Comparison of the resulting solvation free energies for the training and test sets to atomic charges derived from standard procedures, exact solute-solvent electrostatics based on high-level quantum-chemical reference data, and established semiempirical Hamiltonians demonstrates the advantages of the hpCADD parametrization.

The SAMPL5 challenge for embedded-cluster integral equation theory: solvation free energies, aqueous pK a, and cyclohexane-water log D.

We predict cyclohexane-water distribution coefficients (log D 7.4) for drug-like molecules taken from the SAMPL5 blind prediction challenge by the "embedded cluster reference interaction site model" (EC-RISM) integral equation theory. This task involves the coupled problem of predicting both partition coefficients (log P) of neutral species between the solvents and aqueous acidity constants (pK a) in order to account for a change of protonation states. The first issue is addressed by calibrating an EC-RISM-based model for solvation free energies derived from the "Minnesota Solvation Database" (MNSOL) for both water and cyclohexane utilizing a correction based on the partial molar volume, yielding a root mean square error (RMSE) of 2.4 kcal mol-1 for water and 0.8-0.9 kcal mol-1 for cyclohexane depending on the parametrization. The second one is treated by employing on one hand an empirical pK a model (MoKa) and, on the other hand, an EC-RISM-derived regression of published acidity constants (RMSE of 1.5 for a single model covering acids and bases). In total, at most 8 adjustable parameters are necessary (2-3 for each solvent and two for the pK a) for training solvation and acidity models. Applying the final models to the log D 7.4 dataset corresponds to evaluating an independent test set comprising other, composite observables, yielding, for different cyclohexane parametrizations, 2.0-2.1 for the RMSE with the first and 2.2-2.8 with the combined first and second SAMPL5 data set batches. Notably, a pure log P model (assuming neutral species only) performs statistically similarly for these particular compounds. The nature of the approximations and possible perspectives for future developments are discussed.

Design principles for high-pressure force fields: Aqueous TMAO solutions from ambient to kilobar pressures.

Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures--while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields.

Toward Extreme Biophysics: Deciphering the Infrared Response of Biomolecular Solutions at High Pressures.

Biophysics under extreme conditions is the fundamental platform for scrutinizing life in unusual habitats, such as those in the deep sea or continental subsurfaces, but also for putative extraterrestrial organisms. Therefore, an important thermodynamic variable to explore is pressure. It is shown that the combination of infrared spectroscopy with simulation is an exquisite approach for unraveling the intricate pressure response of the solvation pattern of TMAO in water, which is expected to be transferable to biomolecules in their native solvent. Pressure-enhanced hydrogen bonding was found for TMAO in water. TMAO is a molecule known to stabilize proteins against pressure-induced denaturation in deep-sea organisms.

The Chemical Shift Baseline for High-Pressure NMR Spectra of Proteins.

High-pressure (HP) NMR spectroscopy is an important method for detecting rare functional states of proteins by analyzing the pressure response of chemical shifts. However, for the analysis of the shifts it is mandatory to understand the origin of the observed pressure dependence. Here we present experimental HP NMR data on the (15) N-enriched peptide bond model, N-methylacetamide (NMA), in water, combined with quantum-chemical computations of the magnetic parameters using a pressure-sensitive solvation model. Theoretical analysis of NMA and the experimentally used internal reference standard 4,4-dimethyl-4-silapentane-1-sulfonic (DSS) reveal that a substantial part of observed shifts can be attributed to purely solvent-induced electronic polarization of the backbone. DSS is only marginally responsive to pressure changes and is therefore a reliable sensor for variations in the local magnetic field caused by pressure-induced changes of the magnetic susceptibility of the solvent.

Viral potassium channels as a robust model system for studies of membrane-protein interaction.

The viral channel KcvNTS belongs to the smallest K(+) channels known so far. A monomer of a functional homotetramer contains only 82 amino acids. As a consequence of the small size the protein is almost fully submerged into the membrane. This suggests that the channel is presumably sensitive to its lipid environment. Here we perform a comparative analysis for the function of the channel protein embedded in three different membrane environments. 1. Single-channel currents of KcvNTS were recorded with the patch clamp method on the plasma membrane of HEK293 cells. 2. They were also measured after reconstitution of recombinant channel protein into classical planar lipid bilayers and 3. into horizontal bilayers derived from giant unilamellar vesicles (GUVs). The recombinant channel protein was either expressed and purified from Pichia pastoris or from a cell-free expression system; for the latter a new approach with nanolipoprotein particles was used. The data show that single-channel activity can be recorded under all experimental conditions. The main functional features of the channel like a large single-channel conductance (80pS), high open-probability (>50%) and the approximate duration of open and closed dwell times are maintained in all experimental systems. An apparent difference between the approaches was only observed with respect to the unitary conductance, which was ca. 35% lower in HEK293 cells than in the other systems. The reason for this might be explained by the fact that the channel is tagged by GFP when expressed in HEK293 cells. Collectively the data demonstrate that the small viral channel exhibits a robust function in different experimental systems. This justifies an extrapolation of functional data from these systems to the potential performance of the channel in the virus/host interaction. This article is part of a Special Issue entitled: Viral Membrane Proteins-Channels for Cellular Networking.

3D RISM theory with fast reciprocal-space electrostatics.

The calculation of electrostatic solute-solvent interactions in 3D RISM ("three-dimensional reference interaction site model") integral equation theory is recast in a form that allows for a computational treatment analogous to the "particle-mesh Ewald" formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.

Solvation effects on chemical shifts by embedded cluster integral equation theory.

The accurate computational prediction of nuclear magnetic resonance (NMR) parameters like chemical shifts represents a challenge if the species studied is immersed in strongly polarizing environments such as water. Common approaches to treating a solvent in the form of, e.g., the polarizable continuum model (PCM) ignore strong directional interactions such as H-bonds to the solvent which can have substantial impact on magnetic shieldings. We here present a computational methodology that accounts for atomic-level solvent effects on NMR parameters by extending the embedded cluster reference interaction site model (EC-RISM) integral equation theory to the prediction of chemical shifts of N-methylacetamide (NMA) in aqueous solution. We examine the influence of various so-called closure approximations of the underlying three-dimensional RISM theory as well as the impact of basis set size and different treatment of electrostatic solute-solvent interactions. We find considerable and systematic improvement over reference PCM and gas phase calculations. A smaller basis set in combination with a simple point charge model already yields good performance which can be further improved by employing exact electrostatic quantum-mechanical solute-solvent interaction energies. A larger basis set benefits more significantly from exact over point charge electrostatics, which can be related to differences of the solvent's charge distribution.