A variation principle for energy differences between states of two different Hamiltonians

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ??] = 〈X₀| ??_x – W_x|X₁〉 – 〈Y₀|??_y – W_y|y₁〉 + 〈X₀| Δ ??|Y₀〉 · 〈X₀| Y₀〉^?1. Δ ?? = ??_y – ??_x, |X₀〉 and |Y₀〉 are the wave functions for the X and Y states and |X₁〉 and |Y₁〉 are functions defined in the text. The principle is applied to a few simple examples.     

Molybdenum triamidoamine complexes that contain hexa-tert-butylterphenyl, hexamethylterphenyl, or p-bromohexaisopropylterphenyl substituents. An examination of some catalyst variations for the catalytic reduction of dinitrogen

Three new tetramines, (ArNHCH(2)CH(2))(3)N, have been synthesized in which Ar = 3,5-(2,4,6-t-Bu(3)C(6)H(2))(2)C(6)H(3) (H(3)[HTBTN(3)N]), 3,5-(2,4,6-Me(3)C(6)H(2))(2)C(6)H(3) (H(3)[HMTN(3)N]), or 4-Br-3,5-(2,4,6-i-Pr(3)C(6)H(2))(2)C(6)H(2) (H(3)[pBrHIPTN(3)N]). The diarylated tetramine, [3,5-(2,4,6-t-Bu(3)C(6)H(2))(2)C(6)H(3)NHCH(2)CH(2)](2)NCH(2)CH(2)NH(2), has also been isolated, and the "hybrid" tetramine [3,5-(2,4,6-t-Bu(3)C(6)H(2))(2)C(6)H(3)NHCH(2)CH(2)](2)NCH(2)CH(2)NH(4-t-BuC(6)H(4)) has been prepared from it. Monochloride complexes, [(TerNCH(2)CH(2))(3)N]MoCl, have been prepared, as well as a selection of intermediates that would be expected in a catalytic dinitrogen reduction such as [(TerNCH(2)CH(2))(3)N]Mo[triple bond]N and [[(TerNCH(2)CH(2))(3)N]Mo(NH(3))][BAr'(4)] (Ter = HTBT, HMT, or pBrHIPT and Ar' = 3,5-(CF(3))(2)C(6)H(3))). Intermediates that contain the new terphenyl-substituted ligands are then evaluated for their efficiency for the catalytic reduction of dinitrogen under conditions where analogous [HIPTN(3)N]Mo species give four turnovers to ammonia under "standard" conditions with an efficiency of approximately 65%. Only [pBrHIPTN(3)N]Mo compounds are efficient catalysts for dinitrogen reduction. The reasons are explored and discussed.     

Variational bounds on the radius of convergence of the born series

The radius of convergence of the Born series for potential scattering problems is discussed in terms of the eigen-values of the scattering integral equation. Variational procedures yielding upper and lower bounds for these eigen-values are introduced. These bounds axe calculated using various trial functions and compared to the exact values for the square well, exponential repulsive, and Yukawa potentials.     

The role of the putative catalytic base in the phosphoryl transfer reaction in a protein kinase: first-principles calculations

Protein kinases are important enzymes controlling the majority of cellular signaling events via a transfer of the gamma-phosphate of ATP to a target protein. Even after many years of study, the mechanism of this reaction is still poorly understood. Among many factors that may be responsible for the 1011-fold rate enhancement due to this enzyme, the role of the conserved aspartate (Asp166) has been given special consideration. While the essential presence of Asp166 has been established by mutational studies, its function is still debated. The general base catalyst role assigned to Asp166 on the basis of its position in the active site has been brought into question by the pH dependence of the reaction rate, isotope measurements, and pre-steady-state kinetics. Recent semiempirical calculations have added to the controversy surrounding the role of Asp166 in the catalytic mechanism. No major role for Asp166 has been found in these calculations, which have predicted the reaction process consisting of an early transfer of a substrate proton onto the phosphate group. These conclusions were inconsistent with experimental observations. To address these differences between experimental results and theory with a more reliable computational approach and to provide a theoretical platform for understanding catalysis in this important enzyme family, we have carried out first-principles structural and dynamical calculations of the reaction process in cAPK kinase. To preserve the essential features of the reaction, representations of all of the key conserved residues (82 atoms) were included in the calculation. The structural calculations were performed using the local basis density functional (DFT) approach with both hybrid B3LYP and PBE96 generalized gradient approximations. This kind of calculation has been shown to yield highly accurate structural information for a large number of systems. The optimized reactant state structure is in good agreement with X-ray data. In contrast to semiempirical methods, the lowest energy product state places the substrate proton on Asp166. First-principles molecular dynamics simulations provide additional support for the stability of this product state. The latter also demonstrate that the proton transfer to Asp166 occurs at a point in the reaction where bond cleavage at the PO bridging position is already advanced. This mechanism is further supported by the calculated structure of the transition state in which the substrate hydroxyl group is largely intact. A metaphoshate-like structure is present in the transition state, which is consistent with the X-ray structures of transition state mimics. On the basis of the calculated structure of the transition state, it is estimated to be 85% dissociative. Our analysis also indicates an increase in the hydrogen bond strength between Asp166 and substrate hydroxyl and a small decrease in the bond strength of the latter in the transition state. In summary, our calculations demonstrate the importance of Asp166 in the enzymatic mechanism as a proton acceptor. However, the proton abstraction from the substrate occurs late in the reaction process. Thus, in the catalytic mechanism of cAPK protein kinase, Asp166 plays a role of a "proton trap" that locks the transferred phosphoryl group to the substrate. These results resolve prior inconsistencies between theory and experiment and bring new understanding of the role of Asp166 in the protein kinase catalytic mechanism.     

The Aqueous Ca2+ System,in Comparison with Zn2+, Fe3 +, and Al3 +: An Ab Initio Molecular Dynamics Study

Herein, we report on the structure and dynamics of the aqueous Ca²⁺ system studied by using ab initio molecular dynamics (AIMD) simulations. Our detailed study revealed the formation of well‐formed hydration shells with characteristics that were significantly different to those of bulk water. To facilitate a robust comparison with state‐of‐the‐art X‐ray absorption fine structure (XAFS) data, we employ a 1st principles MD‐XAFS procedure and directly compare simulated and experimental XAFS spectra. A comparison of the data for the aqueous Ca²⁺ system with those of the recently reported Zn²⁺, Fe³⁺, and Al³⁺ species showed that many of their structural characteristics correlated well with charge density on the cation. Some very important exceptions were found, which indicated a strong sensitivity of the solvent structure towards the cation′s valence electronic structure. Average dipole moments for the 2nd shell of all cations were suppressed relative to bulk water.     

Parallel implementation of γ‐point pseudopotential plane‐wave DFT with exact exchange

Semi‐local functionals commonly used in density functional theory (DFT) studies of solids usually fail to reproduce localized states such as trapped holes, polarons, excitons, and solitons. This failure is ascribed to self‐interaction which creates a Coulomb barrier to localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid‐DFT, e.g., B3LYP and PBE0) have shown to promise in rectifying this type of failure, as well as producing more accurate band gaps and reaction barriers. The evaluation of exact exchange is challenging for large, solid state systems with periodic boundary conditions, especially when plane‐wave basis sets are used. We have developed parallel algorithms for implementing exact exchange into pseudopotential plane‐wave DFT program and we have implemented them in the NWChem program package. The technique developed can readily be employed in Γ‐point plane‐wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car‐Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Computational investigation of rules governing selective adsorption intensities

Rules previously derived by Wolfe and Weare governing selective adsorption scattering intensities are investigated computationally via the attractive corrugated wall (ACW) model of Harvie and Weare. These rules, which correlate features of the scattering intensity with the form of the atom surface potential, correctly predict intensity features seen in the ACW calculation.