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

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.

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

The ability of trimethylamine N-oxide to resist pressure induced perturbations to water structure

Trimethylamine N-oxide (TMAO) protects organisms from the damaging effects of high pressure. At the molecular level both TMAO and pressure perturb water structure but it is not understood how they act in combination. Here, we use neutron scattering coupled with computational modelling to provide atomistic insight into the structure of water under pressure at 4 kbar in the presence and absence of TMAO. The data reveal that TMAO resists pressure-induced perturbation to water structure, particularly in retaining a clear second solvation shell, enhanced hydrogen bonding between water molecules and strong TMAO - water hydrogen bonds. We calculate an 'osmolyte protection' ratio at which pressure and TMAO-induced energy changes effectively cancel out. Remarkably this ratio translates across scales to the organism level, matching the observed concentration dependence of TMAO in the muscle tissue of organisms as a function of depth. Osmolyte protection may therefore offer a molecular mechanism for the macroscale survival of life in extreme environments.

Studying and exploring potential energy surfaces of compressed molecules: a fresh theory from the eXtreme Pressure Polarizable Continuum Model

We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the XP-PCM framework. The effective potential energy surface is defined by the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform, in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining of the optimized geometry of compressed methane and the transition state of electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.

Implementation and Optimization of the Embedded Cluster Reference Interaction Site Model with Atomic Charges

In this work, we implemented the embedded cluster reference interaction site model (EC-RISM) originally developed by Kloss, Heil, and Kast (J. Phys. Chem. B2008, 112, 4337–4343). This method combines quantum mechanical calculations with the 3D reference interaction site model (3D-RISM). Numerous options, such as buffer, grid space, basis set, charge model, water model, closure relation, and so forth, were investigated to find the best settings. Additionally, the small point charges, which are derived from the solvent distribution from the 3D-RISM solution to represent the solvent in the QM calculation, were neglected to reduce the overhead without the loss of accuracy. On the MNSOL[a], MNSOL, and FreeSolv databases, our implemented and optimized method provides solvation free energies in water with 5.70, 6.32, and 6.44 kJ/mol root-mean-square deviations, respectively, but with different settings, 5.22, 6.08, and 6.63 kJ/mol can also be achieved. Only solvent models containing fitting parameters, like COSMO-RS and EC-RISM with universal correction and directly used electrostatic potential, perform better than our EC-RISM implementation with atomic charges.

The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium

The theoretical description of water properties continues to be a challenge. Using quantum cluster equilibrium (QCE) theory, we combine state-of-the-art quantum chemistry and statistical thermodynamic methods with the almost historical Clausius-Clapeyron relation to study water self-dissociation and the thermodynamics of vaporization. We pay particular attention to the treatment of internal rotations and their impact on the investigated properties by employing the modified rigid-rotor-harmonic-oscillator (mRRHO) approach. We also study a novel QCE parameter-optimization procedure. Both the ionic product and the vaporization enthalpy yield an astonishing agreement with experimental reference data. A significant influence of the mRRHO approach is observed for cluster populations and, consequently, for the ionic product. Thermodynamic properties are less affected by the treatment of these low-frequency modes.

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.

Evaluation of an Efficient 3D-RISM-SCF Implementation as a Tool for Computational Spectroscopy in Solution

The 3D-RISM-SCF solvent-model implementation of Gusarov et al. [ J. Phys. Chem. A 2006, 110, 6083-6090] in the Amsterdam density functional program has been improved and extended. In particular, an accurate yet efficient representation of the solute electrostatic potential is provided. The Coulomb-potential fitting of many DFT codes can be used advantageously in this context. The extra effort compared to a point-charge representation is small for a given SCF cycle and compensated by faster SCF convergence. This allows applications to large solutes, as demonstrated by evaluation of the solvatochromism of Reichardt's dye. In general, TDDFT applications to excitation energies in solution stand out and are highlighted. Applications to the ¹⁷O NMR chemical shifts of N-methylformamide in different solvents also demonstrate the distinct advantages of 3D-RISM over continuum solvents. Limitations are observed in this case for water solvent, where the solvent shielding is overestimated. This shortcoming applies also to the ¹⁷O gas-to-liquid shift of water, where we used localized molecular orbital analyses for a deeper understanding. For such cases of extremely strong solute-solvent interactions, couplings between solute and solvent orbitals induced by the magnetic perturbation are relevant. These clearly require a quantum-mechanical treatment of the most closely bound solvent molecules. Except for such extreme cases, 3D-RISM-SCF is very well suited to treat solvent effects on NMR parameters. More serious limitations pertain to the treatment of vibrational spectra, where the absence of the coupling between solute and solvent vibrational modes limits the accuracy of applications of 3D-RISM-SCF. The reported extended, efficient, and numerically accurate 3D-RISM-SCF implementation should provide a useful tool to study chemical and spectroscopic properties of molecules of appreciable size in a realistic solvent environment.

Dynamical Model for the Counteracting Effects of Trimethylamine N-Oxide on Urea in Aqueous Solutions under Pressure

Of cosolutes found in living cells, urea denatures and trimethylamine N-oxide (TMAO) stabilizes proteins; furthermore, these effects cancel at a 2:1 ratio of urea to TMAO. Interestingly, cartilaginous fish use urea and TMAO as osmolytes at similar ratios at the ocean surface but with increasing fractions of TMAO at increasing depths. Here, molecular dynamics simulations of aqueous solutions with different urea:TMAO ratios show that the diffusion coefficients of water in the solutions vary with pressure if the urea:TMAO ratio is constant, but strikingly, they are almost pressure independent at the ratio found in these fish as a function of depth. This suggests that this ratio may be maintaining a homeostasis of water dynamics. In addition, diffusion is determined by hydrogen-bond lifetimes of the different species in the solution. Based on these observations, a dynamical model in terms of hydrogen-bond lifetimes is developed for the hydrogen bonding propensities of cosolutes and water in an aqueous solution to proteins. This model provides an explanation for both the counteracting effects of TMAO on urea denaturation and the depth-dependent urea:TMAO ratio found in cartilaginous fish.

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 pK_a 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 and thermodynamics of aqueous urea solutions from ambient to kilobar pressures: From thermodynamic modeling, experiments, and first principles simulations to an accurate force field description

Molecular simulations based on classical force fields are a powerful method for shedding light on the complex behavior of biomolecules in solution. When cosolutes are present in addition to water and biomolecules, subtle balances of weak intermolecular forces have to be accounted for. This imposes high demands on the quality of the underlying force fields, and therefore force field development for small cosolutes is still an active field. Here, we present the development of a new urea force field from studies of urea solutions at ambient and elevated hydrostatic pressures based on a combination of experimental and theoretical approaches. Experimental densities and solvation shell properties from ab initio molecular dynamics simulations at ambient conditions served as the target properties for the force field optimization. Since urea is present in many marine life forms, elevated hydrostatic pressure was rigorously addressed: densities at high pressure were measured by vibrating tube densitometry up to 500 bar and by X-ray absorption up to 5 kbar. Densities were determined by the perturbed-chain statistical associating fluid theory equation of state. Solvation properties were determined by embedded cluster integral equation theory and ab initio molecular dynamics. Our new force field is able to capture the properties of urea solutions at high pressures without further high-pressure adaption, unlike trimethylamine-N-oxide, for which a high-pressure adaption is necessary.

High pressure response of 1H NMR chemical shifts of purine nucleotides

The study of the pressure response by NMR spectroscopy provides information on the thermodynamics of conformational equilibria in proteins and nucleic acids. For obtaining a database for expected pressure effects on free nucleotides and nucleotides bound in macromolecular complexes, the pressure response of ¹H chemical shifts and J-coupling constants of the purine 5'-ribonucleotides AMP, ADP, ATP, GMP, GDP, and GTP were studied in the absence and presence of Mg²⁺-ions. Experiments are supported by quantum-chemical calculations of populations and chemical shift differences in order to corroborate structural interpretations and to estimate missing data for AMP. The preference of the ribose S puckering obtained from the analysis of the experimental J-couplings is also confirmed by the calculations. In addition, the pressure response of the non-hydrolysable GTP analogues GppNHp, GppCH₂p, and GTPγS was examined within a pressure range up to 200 MPa. As observed earlier for ³¹P NMR chemical shifts of these nucleotides the pressure dependence of chemical shifts is clearly non-linear in most cases. In di- and tri-phospho nucleosides, the resonances of the two protons bound to the ribose 5' carbon are non-equivalent and can be observed separately. The gg-rotamer at C4'- C5' bond is strongly preferred and the downfield shifted resonance can be assigned to the H5″ proton in the nucleotides. In contrast, in adenosine itself the frequencies of the two resonances are interchanged.