Quantum chemical benchmark databases of gold-standard dimer interaction energies.

Advances in computational chemistry create an ongoing need for larger and higher-quality datasets that characterize noncovalent molecular interactions. We present three benchmark collections of quantum mechanical data, covering approximately 3,700 distinct types of interacting molecule pairs. The first collection, which we refer to as DES370K, contains interaction energies for more than 370,000 dimer geometries. These were computed using the coupled-cluster method with single, double, and perturbative triple excitations [CCSD(T)], which is widely regarded as the gold-standard method in electronic structure theory. Our second benchmark collection, a core representative subset of DES370K called DES15K, is intended for more computationally demanding applications of the data. Finally, DES5M, our third collection, comprises interaction energies for nearly 5,000,000 dimer geometries; these were calculated using SNS-MP2, a machine learning approach that provides results with accuracy comparable to that of our coupled-cluster training data. These datasets may prove useful in the development of density functionals, empirically corrected wavefunction-based approaches, semi-empirical methods, force fields, and models trained using machine learning methods.

Mechanism of Na+/H+ antiporting.

Na+/H+ antiporters are central to cellular salt and pH homeostasis. The structure of Escherichia coli NhaA was recently determined, but its mechanisms of transport and pH regulation remain elusive. We performed molecular dynamics simulations of NhaA that, with existing experimental data, enabled us to propose an atomically detailed model of antiporter function. Three conserved aspartates are key to our proposed mechanism: Asp164 (D164) is the Na+-binding site, D163 controls the alternating accessibility of this binding site to the cytoplasm or periplasm, and D133 is crucial for pH regulation. Consistent with experimental stoichiometry, two protons are required to transport a single Na+ ion: D163 protonates to reveal the Na+-binding site to the periplasm, and subsequent protonation of D164 releases Na+. Additional mutagenesis experiments further validated the model.

Transesterification thio effects of phosphate diesters: free energy barriers and kinetic and equilibrium isotope effects from density-functional theory.

Primary and secondary kinetic and equilibrium isotope effects are calculated with density-functional methods for the in-line dianionic methanolysis of the native (unsubstituted) and thio-substituted cyclic phosphates. These reactions represent reverse reaction models for RNA transesterification under alkaline conditions. The effect of solvent is treated with explicit (single and double) water molecules and self-consistently with an implicit (continuum) solvation model. Singly substituted reactions at the nonbridging O(P1) position and bridging O(2)('), O(3)('), and O(5)(') positions and a doubly substituted reaction at the O(P1) and O(P2) positions were considered. Aqueous free energy barriers are calculated, and the structures and bond orders of the rate-controlling transition states are characterized. The results are consistent with available experimental data and provide useful information for the interpretation of measured isotope and thio effects used to probe mechanism in phosphoryl transfer reactions catalyzed by enzymes and ribozymes.

QCRNA 1.0: a database of quantum calculations for RNA catalysis.

This work outlines a new on-line database of quantum calculations for RNA catalysis (QCRNA) available via the worldwide web at http://theory.chem.umn.edu/QCRNA. The database contains high-level density functional calculations for a large range of molecules, complexes and chemical mechanisms important to phosphoryl transfer reactions and RNA catalysis. Calculations are performed using a strict, consistent protocol such that a wealth of cross-comparisons can be made to elucidate meaningful trends in biological phosphate reactivity. Currently, around 2000 molecules have been collected in varying charge states in the gas phase and in solution. Solvation was treated with both the PCM and COSMO continuum solvation models. The data can be used to study important trends in reactivity of biological phosphates, or used as benchmark data for the design of new semiempirical quantum models for hybrid quantum mechanical/molecular mechanical simulations.

A charge-scaling implementation of the variational electrostatic projection method.

Two new charge-scaling methods for efficient modeling of the solvated macromolecular environment in hybrid QM/MM calculations of biological reactions are presented. The methods are extensions of the variational electrostatic projection (VEP) method, and allows a subset of atomic charges in the external environment to be adjusted to mimic, in the active dynamical region, the electrostatic potential and field due to the large surrounding macromolecule and solvent. The method has the advantages that it offers improved accuracy, does not require the use of a three-dimensional grid or auxiliary set of fitting points, and requires only minor molecular simulation code modifications. The VEP-cs and VEP-RVM+cs methods are able to attain very high accuracy (relative force errors of 10(-7) or better with appropriate choice of control parameters), and take advantage of a recently introduced set of high-order discretization schemes and Gaussian exponents for boundary element solvation and VEP methods. The methods developed here serve as potentially powerful tools in the arsenal of computational techniques used in multiscale computational modeling problems.

High-order discretization schemes for biochemical applications of boundary element solvation and variational electrostatic projection methods.

A series of high-order surface element discretization schemes for variational boundary element methods are introduced. The surface elements are chosen in accord with angular quadrature rules for integration of spherical harmonics. Surface element interactions are modeled by Coulomb integrals between spherical Gaussian functions with exponents chosen to reproduce the exact variational energy and Gauss's law for a point charge in a spherical cavity. The present work allows high-order surface element expansions to be made for variational methods such as the conductorlike screening model for solvation and the variational electrostatic projection method for generalized solvent boundary potentials in molecular simulations.

Density functional study of the in-line mechanism of methanolysis of cyclic phosphate and thiophosphate esters in solution: insight into thio effects in RNA transesterification.

Density functional calculations of thio effects on the in-line mechanism of methanolysis of ethylene phosphate (a reverse reaction model for RNA phosphate transesterification) are presented. A total of 12 reaction mechanisms are examined using the B3LYP functional with large basis sets, and the effects of solvation were treated using the PCM, CPCM, and SM5 solvation models. Single thio substitutions at all of the distinct phosphoryl oxygen positions (2', 3', 5', pro-R) and a double thio substitution at the nonbridging (pro-R/pro-S) positions were considered. Profiles for each reaction were calculated in the dianionic and monoanionic/monoprotic states, corresponding to reaction models under alkaline and nonalkaline conditions, respectively. These models provide insight into the mechanisms of RNA transesterification thio effects and serve as a set of high-level quantum data that can be used in the design of new semiempirical quantum models for hybrid quantum mechanical/molecular mechanical simulations and linear-scaling electronic structure calculations.

Variational electrostatic projection (VEP) methods for efficient modeling of the macromolecular electrostatic and solvation environment in activated dynamics simulations.

New methods for the calculation of electrostatic interactions between the active dynamical region and surrounding external solvated macromolecular environment in hybrid quantum mechanical/molecular mechanical (QM/MM) simulations are presented. The variational electrostatic projection (VEP) method, and related variational reverse-mapping procedure (VEP-RVM) utilize an expansion in Gaussian surface elements for representation of electrostatic interactions. The use of a discretized surface that surrounds the active dynamical region greatly reduces the number of interactions with the particles of the external environment. The methods are tested on two catalytic RNA systems: the hammerhead and the hairpin ribozymes. It is shown that with surface elements numbering from 302 to 1202 points the direct VEP and VEP-RVM methods are able to obtain relative force errors in the range of 0.5-0.05% and 0.09-0.0001%, respectively, using a 4.0 A projection buffer. These results are encouraging and provide an essential step in the development of new variational macromolecular solvent-boundary methods for QM/MM calculations of enzyme reactions.

Smooth solvation method for d-orbital semiempirical calculations of biological reactions. 1. Implementation.

The present paper describes the extension of a recently developed smooth conductor-like screening model for solvation to a d-orbital semiempirical framework (MNDO/d-SCOSMO) with analytic gradients that can be used for geometry optimizations, transition state searches, and molecular dynamics simulations. The methodology is tested on the potential energy surfaces for separating ions and the dissociative phosphoryl transfer mechanism of methyl phosphate. The convergence behavior of the smooth COSMO method with respect to discretization level is examined and the numerical stability of the energy and gradient are compared to that from conventional COSMO calculations. The present method is further tested in applications to energy minimum and transition state geometry optimizations of neutral and charged metaphosphates, phosphates, and phosphoranes that are models for stationary points in transphosphorylation reaction pathways of enzymes and ribozymes. The results indicate that the smooth COSMO method greatly enhances the stability of quantum mechanical geometry optimization and transition state search calculations that would routinely fail with conventional solvation methods. The present MNDO/d-SCOSMO method has considerable computational advantages over hybrid quantum mechanical/molecular mechanical methods with explicit solvation, and represents a potentially useful tool in the arsenal of multi-scale quantum models used to study biochemical reactions.

Smooth solvation method for d-orbital semiempirical calculations of biological reactions. 2. Application to transphosphorylation thio effects in solution.

Density-functional and semiempirical quantum methods and continuum dielectric and explicit solvation models are applied to study the role of solvation on the stabilization of native and thio-substituted transphosphorylation reactions. Extensive comparison is made between results obtained from the different methods. For the semiempirical methods, explicit solvation was treated using a hybrid quantum mechanical/molecular mechanical (QM/MM) approach and the implicit solvation was treated using a recently developed smooth solvation model implemented into a d-orbital semiempirical framework (MNDO/d-SCOSMO) within CHARMM. The different quantum and solvation methods were applied to the transesterification of a 3'-ribose,5'-methyl phosphodiester that serves as a nonenzymatic model for the self-cleavage reaction catalyzed by the hammerhead and hairpin ribozymes. Thio effects were studied for a double sulfur substitution at the nonbridging phosphoryl oxygen positions. The reaction profiles of both the native and double sulfur-substituted reactions from the MNDO/d-SCOSMO calculations were similar to the QM/MM results and consistent with the experimentally observed trends. These results underscore the need for a d-orbital semiempirical representation for phosphorus and sulfur for the study of experimentally observed thio effects in enzymatic and nonenzymatic phosphoryl transfer reactions. One of the major advantages of the present approach is that it can be applied to model chemical reactions at a significantly lower computational cost than either the density-functional calculations with implicit solvation or the semiempirical QM/MM simulations with explicit solvent.

Hybrid QM/MM study of thio effects in transphosphorylation reactions: the role of solvation.

Transphosphorylation thio effects in solution are studied using hybrid QM/MM calculations with a d-orbital semiempirical Hamiltonian. Activated dynamics simulations were performed for a 3' ribose-phosphate model in an explicit 20 A sphere of TIP3P water surrounded by a solvent boundary potential, and free energy analysis was performed using the weighted histogram analysis method. Single thio-substitutions at all of the phosphoryl oxygen positions and a double thio-substitution at the nonbridging positions were considered. The reaction free energy profiles are compared with available experimental data, and the role of solvation on the barrier heights and reaction coordinate is discussed. These results provide an important step in the characterization of thio effects in reactions of biological phosphates that may aid in the interpretation of kinetic data and ultimately help to unravel the catalytic mechanisms of ribozymes.

Hybrid QM/MM study of thio effects in transphosphorylation reactions.

Results of a series of hybrid quantum mechanical/molecular mechanical (QM/MM) activated dynamics simulations of thio effects in the transphosphorylation (methanolysis) of a 2'-ribose, 5'-methyl phosphate-diester under basic conditions are presented. Single and double substitutions in the nonbridging oxygen positions exhibit thio effects in accord with experimental data and show the existence of a stable intermediate. Thio substitution at the 2' and 5' positions resulted in reactions having a single transition state with increased and decreased free energy barriers, respectively, relative to the unsubstituted reaction. In all of the reactions except for the 5' substitution, the rate-limiting step corresponds to exocyclic cleavage. In the 5' substitution reaction, the rate-limiting step corresponds to endocyclic cleavage and shows a considerable reverse thio effect, in accord with experimental observations of phosphates with enhanced leaving groups. Thio substitution at the 3' position results in a mild reverse thio effect that arises from electronic stabilization of the dianionic transition state. The results presented here provide an important step toward the development and application of new hybrid QM/MM methods that, combined with experiment, may provide a detailed picture of the molecular mechanisms of RNA catalysis.