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.

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.

A Joint Venture of Ab Initio Molecular Dynamics, Coupled Cluster Electronic Structure Methods, and Liquid-State Theory to Compute Accurate Isotropic Hyperfine Constants of Nitroxide Probes in Water.

The isotropic hyperfine coupling constant (HFCC, Aiso) of a pH-sensitive spin probe in a solution, HMI (2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water, is computed using an ensemble of state-of-the-art computational techniques and is gauged against X-band continuous wave electron paramagnetic resonance (EPR) measurement spectra at room temperature. Fundamentally, the investigation aims to delineate the cutting edge of current first-principles-based calculations of EPR parameters in aqueous solutions based on using rigorous statistical mechanics combined with correlated electronic structure techniques. In particular, the impact of solvation is described by exploiting fully atomistic, RISM integral equation, and implicit solvation approaches as offered by ab initio molecular dynamics (AIMD) of the periodic bulk solution (using the spin-polarized revPBE0-D3 hybrid functional), embedded cluster reference interaction site model integral equation theory (EC-RISM), and polarizable continuum embedding (using CPCM) of microsolvated complexes, respectively. HFCCs are obtained from efficient coupled cluster calculations (using open-shell DLPNO-CCSD theory) as well as from hybrid density functional theory (using revPBE0-D3). Re-solvation of "vertically desolvated" spin probe configuration snapshots by EC-RISM embedding is shown to provide significantly improved results compared to CPCM since only the former captures the inherent structural heterogeneity of the solvent close to the spin probe. The average values of the Aiso parameter obtained based on configurational statistics using explicit water within AIMD and from EC-RISM solvation are found to be satisfactorily close. Using either such explicit or RISM solvation in conjunction with DLPNO-CCSD calculations of the HFCCs provides an average Aiso parameter for HMI in aqueous solution at 300 K and 1 bar that is in good agreement with the experimentally determined one. The developed computational strategy is general in the sense that it can be readily applied to other spin probes of similar molecular complexity, to aqueous solutions beyond ambient conditions, as well as to other solvents in the longer run.

Pressure-dependent electronic structure calculations using integral equation-based solvation models.

Recent methodological progress in quantum-chemical calculations using the "embedded cluster reference interaction site model" (EC-RISM) integral equation theory is reviewed in the context of applying it as a solvation model for calculating pressure-dependent thermodynamic and spectroscopic properties of molecules immersed in water. The methodology is based on self-consistent calculations of electronic and solvation structure around dissolved molecules where pressure enters the equations via an appropriately chosen solvent response function and the pure solvent density. Besides specification of a dispersion-repulsion force field for solute-solvent interactions, the EC-RISM approach derives the electrostatic interaction contributions directly from the wave function. We further develop and apply the method to a variety of benchmark cases for which computational or experimental reference data are either available in the literature or are generated specifically for this purpose in this work. Starting with an enhancement to predict hydration free energies at non-ambient pressures, which is the basis for pressure-dependent molecular population estimation, we demonstrate the performance on the calculation of the autoionization constant of water. Spectroscopic problems are addressed by studying the biologically relevant small osmolyte TMAO (trimethylamine N-oxide). Pressure-dependent NMR shifts are predicted and compared to experiments taking into account proper computational referencing methods that extend earlier work. The experimentally observed IR blue-shifts of certain vibrational bands of TMAO as well as of the cyanide anion are reproduced by novel methodology that allows for weighing equilibrium and non-equilibrium solvent relaxation effects. Taken together, the model systems investigated allow for an assessment of the reliability of the EC-RISM approach for studying pressure-dependent biophysical processes.

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.