Self-consistent effective local potentials

An effective local potential (ELP) is a multiplicative operator whose deviation from a given nonlocal potential has the smallest variance evaluated with a prescribed single-determinant wave function. ELPs are useful in density functional theory as alternatives to optimized effective potentials (OEPs) because they do not require special treatment in finite basis set calculations as OEPs do. We generalize the idea of variance-minimizing potentials by introducing the concept of a self-consistent ELP (SCELP), a local potential whose deviation from its nonlocal counterpart has the smallest variance in terms of its own Kohn-Sham orbitals. A semi-analytical method for computing SCELPs is presented. The OEP, ELP, and SCELP techniques are applied to the exact-exchange-only Kohn-Sham problem and are found to produce similar results for many-electron atoms.     

The effective local potential method: implementation for molecules and relation to approximate optimized effective potential techniques

We have recently formulated a new approach, named the effective local potential (ELP) method, for calculating local exchange-correlation potentials for orbital-dependent functionals based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart [V. N. Staroverov et al., J. Chem. Phys. 125, 081104 (2006)]. Here we show that under a mildly simplifying assumption of frozen molecular orbitals, the equation defining the ELP has a unique analytic solution which is identical with the expression arising in the localized Hartree-Fock (LHF) and common energy denominator approximations (CEDA) to the optimized effective potential. The ELP procedure differs from the CEDA and LHF in that it yields the target potential as an expansion in auxiliary basis functions. We report extensive calculations of atomic and molecular properties using the frozen-orbital ELP method and its iterative generalization to prove that ELP results agree with the corresponding LHF and CEDA values, as they should. Finally, we make the case for extending the iterative frozen-orbital ELP method to full orbital relaxation.     

Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations

Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size is the highest, whereas an increase of the pore size and the density of hydrogen volumetric energy causes the polymer swelling up to a value slightly below the one computed from the bulk phase. Quantum confinement-inducing polymer shrinking is of great importance for realizing the potential of quantum molecular sieves.     

On calculating a polymer's enthalpy of formation with quantum chemical methods

Calculating the enthalpy of formation of a polymer with ab initio methods requires two choices. The first decision is whether to use oligomeric extrapolation or periodic boundary conditions to model the extended system, and the second choice is between formation reactions to be modeled, for example, formation from atoms, formation from standard states, or formation from some set of molecular systems. Utilizing trans-polyacetylene and polyethylene as examples, the oligomeric and periodic techniques are contrasted, leading to a discussion of the larger than minimal unit cell required when frequency calculations only include in-phase vibrations, that is, only the k = 0 frequencies, in an enthalpy of formation calculation. The accuracy of calculating the enthalpy of formation, in light of density functional theory's increased error with larger systems and with respect to various reference states, is also discussed. The calculation of the enthalpy of formation for a polymer is most accurate when the reference states are chosen carefully and most efficient when using periodic boundary conditions.     

Structure sensitivity of alkynol hydrogenation on shape- and size-controlled palladium nanocrystals: which sites are most active and selective?

The activity and selectivity of structure-sensitive reactions are strongly correlated with the shape and size of the nanocrystals present in a catalyst. This correlation can be exploited for rational catalyst design, especially if each type of surface atom displays a different behavior, to attain the highest activity and selectivity. In this work, uniform Pd nanocrystals with cubic (in two different sizes), octahedral, and cuboctahedral shapes were synthesized through a solution-phase method with poly(vinyl pyrrolidone) (PVP) serving as a stabilizer and then tested in the hydrogenation of 2-methyl-3-butyn-2-ol (MBY). The observed activity and selectivity suggested that two types of active sites were involved in the catalysis--those on the planes and at edges--which differ in their coordination numbers. Specifically, semihydrogenation of MBY to 2-methyl-3-buten-2-ol (MBE) occurred preferentially at the plane sites regardless of their crystallographic orientation, Pd(111) and/or Pd(100), whereas overhydrogenation occurred mainly at the edge sites. The experimental data can be fit with a kinetic modeling based on a two-site Langmuir-Hinshelwood mechanism. By considering surface statistics for nanocrystals with different shapes and sizes, the optimal catalyst in terms of productivity of the target product MBE was predicted to be cubes of roughly 3-5 nm in edge length. This study is an attempt to close the material and pressure gaps between model single-crystal surfaces tested under ultra-high-vacuum conditions and real catalytic systems, providing a powerful tool for rational catalyst design.     

Sensitive and selective fluorescence detection of guanosine nucleotides by nanoparticles conjugated with a naphthyridine receptor

Novel fluorescent nanosensors, based on a naphthyridine receptor, have been developed for the detection of guanosine nucleotides, and both their sensitivity and selectivity to various nucleotides were evaluated. The nanosensors were constructed from polystyrene nanoparticles functionalized by (N-(7-((3-aminophenyl)ethynyl)-1,8-naphthyridin-2-yl)acetamide) via carbodiimide ester activation. We show that this naphthyridine nanosensor binds guanosine nucleotides preferentially over adenine, cytosine, and thymidine nucleotides. Upon interaction with nucleotides, the fluorescence of the nanosensor is gradually quenched yielding Stern–Volmer constants in the range of 2.1 to 35.9 mM⁻¹. For all the studied quenchers, limits of detection (LOD) and tolerance levels for the nanosensors were also determined. The lowest (3σ) LOD was found for guanosine 3’,5’-cyclic monophosphate (cGMP) and it was as low as 150 ng/ml. In addition, we demonstrated that the spatial arrangement of bound analytes on the nanosensors’ surfaces is what is responsible for their selectivity to different guanosine nucleotides. We found a correlation between the changes of the fluorescence signal and the number of phosphate groups of a nucleotide. Results of molecular modeling and ζ-potential measurements confirm that the arrangement of analytes on the surface provides for the selectivity of the nanosensors. These fluorescent nanosensors have the potential to be applied in multi-analyte, array-based detection platforms, as well as in multiplexed microfluidic systems.     

On algebrability of nonabsolutely convergent series

We prove that the set of all complex series which are nonabsolutely convergent is c-algebrable. We establish a similar result for the set of all divergent complex series with bounded partial sums.     

The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes

We prove exponential contraction of renormalization along hybrid classes of infinitely renormalizable unimodal maps (with arbitrary combinatorics), in any even degree d. We then conclude that orbits of renormalization are asymptotic to the full renormalization horseshoe, which we construct. Our argument for exponential contraction is based on a precompactness property of the renormalization operator (“beau bounds”), which is leveraged in the abstract analysis of holomorphic iteration. Besides greater generality, it yields a unified approach to all combinatorics and degrees: there is no need to account for the varied geometric details of the dynamics, which were the typical source of contraction in previous restricted proofs.     

How reliable are GIAO calculations of 1H and 13C NMR chemical shifts? A statistical analysis and empirical corrections at DFT (PBE/3z) level

Reliability of calculated (1)H and (13)C NMR chemical shifts for various classes of organic compounds obtained with gauge-invariant atomic orbital (GIAO) approach has been studied at the PBE/3ζ level (as implemented in PRIRODA code) using linear regression analysis with experimental data. Empirical corrections for the calculated chemical shifts δ(H,calc) = δ(PBE/3ζ) - 0.08 ppm (RMS 0.18 ppm, MAD 0.66 ppm) and δ(C,calc) = δ(PBE/) (3) (ζ) - 6.35 ppm (RMS 3.09 ppm, MAD 9.42 ppm) have been developed using the sets of 263 and 308 experimental values for (1)H and (13)C chemical shifts, respectively. The confidence intervals of NMR chemical shifts at 95% confidence probability are δ(H,calc) ± 0.35 ppm for (1)H and δC,calc) ± 6.05 ppm for (13)C.