Application of the Computationally Efficient Self-Consistent-Charge Density-Functional Tight-Binding Method to Magnesium-Containing Molecules

Mechanisms of ATP to cAMP Conversion Catalyzed by the Mammalian Adenylyl Cyclase: A Role of Magnesium Coordination Shells and Proton Wires

We report a mechanism of adenosine triphosphate (ATP) to cyclic adenosine monophosphate (cAMP) conversion by the mammalian type V adenylyl cyclase revealed in molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) simulations. We characterize a set of computationally derived enzyme-substrate (ES) structures showing an important role of coordination shells of magnesium ions in the solvent accessible active site. In the lowest energy ES conformation, the coordination shell of Mg_A²⁺ does not include the O_δ1 atom of the conserved Asp440 residue. Starting from this conformation, a one-step reaction mechanism is characterized that includes proton transfer from the ribose O^3'H^3' group in ATP to Asp440 via a shuttling water molecule concerted with P^A-O^3A bond cleavage and O^3'-P^A bond formation. The energy profile of this route is consistent with the observed reaction kinetics. The computed energy profiles initiated from higher energy ES complexes are characterized by larger energy expenses to complete the reaction. Consistent with experimental data, we show that the Asp440Ala mutant of the enzyme should exhibit a reduced but retained activity. All considered reaction pathways include proton wires from the O^3'H^3' group via shuttling water molecules.

Quantum mechanical force fields for condensed phase molecular simulations

Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.

Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications

Semiempirical (SE) methods can be derived from either Hartree-Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

Parametrization of DFTB3/3OB for magnesium and zinc for chemical and biological applications

We report the parametrization of the approximate density functional theory, DFTB3, for magnesium and zinc for chemical and biological applications. The parametrization strategy follows that established in previous work that parametrized several key main group elements (O, N, C, H, P, and S). This 3OB set of parameters can thus be used to study many chemical and biochemical systems. The parameters are benchmarked using both gas-phase and condensed-phase systems. The gas-phase results are compared to DFT (mostly B3LYP), ab initio (MP2 and G3B3), and PM6, as well as to a previous DFTB parametrization (MIO). The results indicate that DFTB3/3OB is particularly successful at predicting structures, including rather complex dinuclear metalloenzyme active sites, while being semiquantitative (with a typical mean absolute deviation (MAD) of ∼3–5 kcal/mol) for energetics. Single-point calculations with high-level quantum mechanics (QM) methods generally lead to very satisfying (a typical MAD of ∼1 kcal/mol) energetic properties. DFTB3/MM simulations for solution and two enzyme systems also lead to encouraging structural and energetic properties in comparison to available experimental data. The remaining limitations of DFTB3, such as the treatment of interaction between metal ions and highly charged/polarizable ligands, are also discussed.

Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications

We report the parametrization of the approximate density functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of organic and biologically relevant molecules. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of molecules of biological relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these molecules; vibrational frequencies are also examined, although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, especially for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant reduction of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calculations, DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination number of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary solution; this suggests that the current DFTB3 methodology has limited transferability for complex phosphorus chemistry at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodology are needed for a reliable method that describes phosphorus chemistry without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calculations for studying phosphorus/sulfur chemistry in condensed phase systems, especially as a low-level method that drives the sampling in a dual-level QM/MM framework.

A modified QM/MM Hamiltonian with the Self-Consistent-Charge Density-Functional-Tight-Binding Theory for highly charged QM regions

To improve the description of electrostatic interaction between QM and MM atoms when the QM is SCC-DFTB, we adopt a Klopman-Ohno (KO) functional form which considers the finite size of the QM and MM charge distributions. Compared to the original implementation that used a simple Coulombic interaction between QM Mulliken and MM point charges, the KO based QM/MM scheme takes charge penetration effect into consideration and therefore significantly improves the description of QM/MM interaction at short range, especially when the QM region is highly charged. To be consistent with the third-order formulation of SCC-DFTB, the Hubbard parameter in the KO functional is dependent on the QM charge. As a result, the effective size of the QM charge distribution naturally adjusts as the QM region undergoes chemical transformations, making the KO based QM/MM scheme particularly attractive for describing chemical reactions in the condensed phase. Together with the van der Waals parameters for the QM atom, the KO based QM/MM model introduces four parameters for each element type. They are fitted here based on microsolvation models of small solutes, focusing on negatively charged molecular ions, for elements O, C, H and P with a specific version of SCC-DFTB (SCC-DFTBPR). Test calculations confirm that the KO based QM/MM scheme significantly improves the interactions between QM and MM atoms over the original point charge based model and it is transferable due to the small number of parameters. The new form of QM/MM Hamiltonian will greatly improve the applicability of SCC-DFTB based QM/MM methods to problems that involve highly charged QM regions, such as enzyme catalyzed phosphoryl transfers.

Density-functional expansion methods: generalization of the auxiliary basis

The formulation of density-functional expansion methods is extended to treat the second and higher-order terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the self-consistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

An implicit solvent model for SCC-DFTB with Charge-Dependent Radii

Motivated by the need of rapidly exploring the potential energy surface of chemical reactions that involve highly charged species, we have developed an implicit solvent model for the approximate density functional theory, SCC-DFTB. The solvation free energy is calculated using the popular model that employs Poisson-Boltzmann for electrostatics and a surface-area term for non-polar contributions. To balance the treatment of species with different charge distributions, we make the atomic radii that define the dielectric boundary and solute cavity depend on the solute charge distribution. Specifically, the atomic radii are assumed to be linearly dependent on the Mulliken charges and solved self-consistently together with the solute electronic structure. Benchmark calculations indicate that the model leads to solvation free energies of comparable accuracy to the SM6 model (especially for ions), which requires much more expensive DFT calculations. With analytical first derivatives and favorable computational speed, the SCC-DFTB based solvation model can be effectively used, in conjunction with high-level QM calculations, to explore the mechanism of solution reactions. This is illustrated with a brief analysis of the hydrolysis of mono-methyl mono-phosphate ester (MMP) and tri-methyl mono-phosphate ester (TMP). Possible future improvements are also briefly discussed.