Timothy J. Giese

Many-body force field models based solely on pairwise Coulomb screening do not simultaneously reproduce correct gas-phase and condensed-phase polarizability limits

It is demonstrated that many-body force field models based solely on pairwise Coulomb screening cannot simultaneously reproduce both gas-phase and condensed-phase polarizability limits. Several many-body force field model forms are tested and compared with basis set-corrected ab initio results for a series of bifurcated water chains. Models are parameterized to reproduce the ab initio polarizability of an isolated water molecule, and pairwise damping functions are set to reproduce the polarizability of a water dimer as a function of dimer separation. When these models are applied to extended water chains, the polarization is over-predicted, and this over-polarization increased as a function of the overlap of molecular orbitals as the chains are compressed. This suggests that polarizable models based solely on pairwise Coulomb screening have some limitations, and that coupling with non-classical many-body effects, in particular exchange terms, may be important.

Improvement of semiempirical response properties with charge-dependent response density

The present work outlines a new method for treatment of charge-dependent polarizability in semiempirical quantum models for use in combined quantum-mechanical/molecular mechanical simulations of biological reactions. The method addresses a major shortcoming in the performance of conventional semiempirical models for these simulations that is tied to the use of a localized minimal atomic-orbital basis set. The present approach has the advantages that it uses a density basis that retains a set of linear-response equations, does not increase the atomic-orbital basis, and avoids the problem of artificial charge transfer and scaling of the polarizability seen in related models that allow atomic charges to fluctuate. The model introduces four new atom-based parameters and has been tested with the modified neglect of differential overlap d-orbital Hamiltonian against 1132 molecules and ions and shown to decrease the dipole moment and polarizability errors by factors of 2 and 10, respectively, with respect to density-functional results. The method performs impressively for a variety of charge states (from 2+ to 2-), and offers a potentially powerful extension in the design of next generation semiempirical quantum models for accurate simulations of highly charged biological reactions.

Extended Polarization in Third-Order SCC-DFTB from Chemical-Potential Equalization

In this work, we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical-potential equalization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for the NDDO type of methods by Giese and York, has been shown to significantly emend minimal basis methods with respect to the response properties and has been applied to SCC-DFTB recently. CPE allows this inherent limitation of minimal basis methods to be overcome by supplying an additional response density. The systematic underestimation is thereby corrected quantitatively without the need to extend the atomic orbital basis (i.e., without increasing the overall computational cost significantly). The dependency of polarizability as a function of the molecular charge state, especially, was significantly improved from the CPE extension of DFTB3. The empirical parameters introduced by the CPE approach were optimized for 172 organic molecules in order to match the results from density functional theory methods using large basis sets. However, the first-order derivatives of molecular polarizabilities (e.g., required to compute Raman activities) are not improved by the current CPE implementation (i.e., Raman spectra are not improved).

A Semiempirical Quantum Model for Hydrogen-Bonded Nucleic Acid Base Pairs.

An exploratory semiempirical Hamiltonian (PM3BP) is developed to model hydrogen bonding in nucleic acid base pairs. The PM3BP Hamiltonian is a novel reparametrization of the PM3 Hamiltonian designed to reproduce experimental base pair dimer enthalpies and high-level density-functional results. The parametrization utilized a suite of integrated nonlinear optimization algorithms interfaced with a d-orbital semiempirical program. Results are compared with experimental values and with benchmark density-functional (mPWPW91/MIDI!) calculations for hydrogen-bonded nucleic acid dimers and trimers. The PM3BP Hamiltonian is demonstrated to outperform the AM1, PM3, MNDO, and MNDO/H Hamiltonians for dimer and trimer structures and interaction enthalpies and is shown to reproduce experimental dimer interaction enthalpies that rival density-functional results for an over 3 orders of magnitude reduction in computational cost. The tradeoff between a high accuracy gain for hydrogen bonding at the expense of sacrificing some generality is discussed. These results provide insight into the limits of conventional semiempirical forms for accurate modeling of biological interactions.

Examination of the correlation energy and second virial coefficients from accurate ab initio calculations of rare-gas dimers

Calculations of rare-gas dimers (He–He, Ne–Ne, Ar–Ar, He–Ne, He–Ar, and Ne–Ar) at the coupled-cluster single double (triple) level of theory with large basis sets including bond functions and counterpoise corrections are reported over a wide range of 100 internuclear separations. These results are compared to experimental curves obtained from fitting to rovibrational spectra, and to second virial coefficients and Boyle temperatures. Accurate analytic potentials are developed for the total interaction energy, Hartree–Fock (exchange) energy, and correlation (dispersion) energy; the transferability of the latter is demonstrated to very high accuracy even in the region of considerable wave function overlap. These calculations represent an important set of benchmarks that can be used to develop improved empirical molecular mechanical force fields and new quantum models.

Parametrization of an Orbital-Based Linear-Scaling Quantum Force Field for Noncovalent Interactions.

We parametrize a linear-scaling quantum mechanical force field called mDC for the accurate reproduction of nonbonded interactions. We provide a new benchmark database of accurate ab initio interactions between sulfur-containing molecules. A variety of nonbond databases are used to compare the new mDC method with other semiempirical, molecular mechanical, ab initio, and combined semiempirical quantum mechanical/molecular mechanical methods. It is shown that the molecular mechanical force field significantly and consistently reproduces the benchmark results with greater accuracy than the semiempirical models and our mDC model produces errors twice as small as the molecular mechanical force field. The comparisons between the methods are extended to the docking of drug candidates to the Cyclin-Dependent Kinase 2 protein receptor. We correlate the protein–ligand binding energies to their experimental inhibition constants and find that the mDC produces the best correlation. Condensed phase simulation of mDC water is performed and shown to produce O–O radial distribution functions similar to TIP4P-EW.

Density-functional expansion methods: grand challenges

We discuss the source of errors in semiempirical density-functional expansion (VE) methods. In particular, we show that VE methods are capable of well reproducing their standard Kohn-Sham density-functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

Multipolar Ewald Methods, 1: Theory, Accuracy, and Performance

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Evidence for the role of active site residues in the hairpin ribozyme from molecular simulations along the reaction path.

The hairpin ribozyme accelerates a phosphoryl transfer reaction without catalytic participation of divalent metal ions. Residues A38 and G8 have been implicated as playing roles in general acid and base catalysis, respectively. Here we explore the structure and dynamics of key active site residues using more than 1 μs of molecular dynamics simulations of the hairpin ribozyme at different stages along the catalytic pathway. Analysis of results indicates hydrogen bond interactions between the nucleophile and proR nonbridging oxygen are correlated with active inline attack conformations. Further, the simulation results suggest a possible alternative role for G8 to promote inline fitness and facilitate activation of the nucleophile by hydrogen bonding, although this does not necessarily exclude an additional role as a general base. Finally, we suggest that substitution of G8 with N7- or N3-deazaguanosine which have elevated pKa values, both with and without thio modifications at the 5′ leaving group position, would provide valuable insight into the specific role of G8 in catalysis.

Complete basis set extrapolated potential energy, dipole, and polarizability surfaces of alkali halide ion-neutral weakly avoided crossings with and without applied electric fields.

Complete basis set extrapolations of alkali halide (LiF, LiCl, NaF, NaCl) energy, dipole, and polarizability surfaces are performed with and without applied fields along the internuclear axis using state-averaged multireference configuration interaction. Comparison between properties (equilibrium separation, dissociation energy, crossing distance, diabatic coupling constant, dipole, and polarizability) derived from the extrapolated potential energy (or dipole) surfaces are made with those obtained from direct extrapolation from the basis set trends. The two extrapolation procedures are generally found to agree well for these systems. Crossing distances from this work are compared to those of previous work and values obtained from the Rittner potential. Complete basis set extrapolated crossing distances agree well with those derived from the Rittner potential for LiF, but were significantly larger for LiCl, NaF, and NaCl. The results presented here serve as an important set of benchmark data for the development of new-generation many-body force fields that are able to model charge transfer.