A new all-round density functional based on spin states and SN2 barriers

We report here a new empirical density functional that is constructed based on the performance of OPBE and PBE for spin states and SN 2 reaction barriers and how these are affected by different regions of the reduced gradient expansion. In a previous study [Swart, Sol̀, and Bickelhaupt, J. Comput. Methods Sci. Eng. 9, 69 (2009)] we already reported how, by switching between OPBE and PBE, one could obtain both the good performance of OPBE for spin states and reaction barriers and that of PBE for weak interactions within one and the same (SSB-sw) functional. Here we fine tuned this functional and include a portion of the KT functional and Grimme's dispersion correction to account for π- π stacking. Our new SSB-D functional is found to be a clear improvement and functions very well for biological applications (hydrogen bonding, π -π stacking, spin-state splittings, accuracy of geometries, reaction barriers)

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+ 1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Relations among several nuclear and electronic density functional reactivity indexes

A set of connections among several nuclear and electronic indexes of reactivity in the framework of the conceptual Density Functional Theory by using an expansion ofthe energy functional in terms of the total number of electrons and the normal coordinates within a canonical ensemble was derived. The relations obtained provided explicit links between important quantities related to the chemical reactivity of a system. This paper particularly demonstrates that the derivative of the electronic energy with respect to the external potential of a system in its equilibrium geometry was equal to the negative of the nuclear repulsion derivative with respect to the external potential

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

One- and two-center physical space partitioning of the energy in the density functional theory

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (Hartree-Fock) exchange for the same Kohn-Sham orbitals

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor–acceptorsubstituted azobenzene. It is observed that both electronic and vibrational contributions to the electricdipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected densityfunctional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange correlation potentials amend the drawbacks of their conventional counterparts

Do orthopaedic shoes improve local dynamic stability of gait? An observational study in patients with chronic foot and ankle injuries.

BACKGROUND: Complex foot and ankle fractures, such as calcaneum fractures or Lisfranc dislocations, are often associated with a poor outcome, especially in terms of gait capacity. Indeed, degenerative changes often lead to chronic pain and chronic functional limitations. Prescription footwear represents an important therapeutic tool during the rehabilitation process. Local Dynamic Stability (LDS) is the ability of locomotor system to maintain continuous walking by accommodating small perturbations that occur naturally during walking. Because it reflects the degree of control over the gait, LDS has been advocated as a relevant indicator for evaluating different conditions and pathologies. The aim of this study was to analyze changes in LDS induced by orthopaedic shoes in patients with persistent foot and ankle injuries. We hypothesised that footwear adaptation might help patients to improve gait control, which could lead to higher LDS: METHODS: Twenty-five middle-aged inpatients (5 females, 20 males) participated in the study. They were treated for chronic post-traumatic disabilities following ankle and/or foot fractures in a Swiss rehabilitation clinic. During their stay, included inpatients received orthopaedic shoes with custom-made orthoses (insoles). They performed two 30s walking trials with standard shoes and two 30s trials with orthopaedic shoes. A triaxial motion sensor recorded 3D accelerations at the lower back level. LDS was assessed by computing divergence exponents in the acceleration signals (maximal Lyapunov exponents). Pain was evaluated with Visual Analogue Scale (VAS). LDS and pain differences between the trials with standard shoes and the trials with orthopaedic shoes were assessed. RESULTS: Orthopaedic shoes significantly improved LDS in the three axes (medio-lateral: 10% relative change, paired t-test p < 0.001; vertical: 9%, p = 0.03; antero-posterior: 7%, p = 0.04). A significant decrease in pain level (VAS score -29%) was observed. CONCLUSIONS: Footwear adaptation led to pain relief and to improved foot & ankle proprioception. It is likely that that enhancement allows patients to better control foot placement. As a result, higher dynamic stability has been observed. LDS seems therefore a valuable index that could be used in early evaluation of footwear outcome in clinical settings.

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

Thermal nucleation and cavitation in 3He and 4He

Density functionals that reproduce the helium liquid-gas interface as a function of temperature have been used, within an improved homogeneous nucleation approach, to investigate thermal nucleation and cavitation in both helium isotopes. The results are compared with available experimental data on cavitation in 3He and 4He. Predictions are made for cavitation in 3He at negative pressures and for nucleation in both isotopes.

Quantized vortices in mixed 3He-4He drops

Using density functional theory, we investigate the structure of mixed 3HeN3-4HeN4 droplets with an embedded impurity (Xe atom or HCN molecule) which pins a quantized vortex line. We find that the dopant+vortex+4HeN4 complex, which in a previous work [F. Dalfovo et al., Phys. Rev. Lett. 85, 1028 (2000)] was found to be energetically stable below a critical size Ncr, is robust against the addition of 3He. While 3He atoms are distributed along the vortex line and on the surface of the 4He drop, the impurity is mostly coated by 4He atoms. Results for N4 = 500 and a number of 3He atoms ranging from 0 to 100 are presented, and the binding energy of the dopant to the vortex line is determined.

Probing vortices in 4He nanodroplets

We present static and dynamical properties of linear vortices in 4He droplets obtained from density functional calculations. By comparing the adsorption properties of different atomic impurities embedded in pure droplets and in droplets where a quantized vortex has been created, we suggest that Ca atoms should be the dopant of choice to detect vortices by means of spectroscopic experiments.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Local size segregation in polydisperse hard sphere fluids

The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of density fields. The case of continuous polydispersity thereby becomes tractable. We predict, generically, an oscillatory size segregation close to the wall, and connect this, by a perturbation theory for narrow distributions, with the reversible work for changing the size of one particle in a monodisperse reference fluid.

Manifolds on the verge of a hyperbolicity breakdown

We study numerically the disappearance of normally hyperbolic invariant tori in quasiperiodic systems and identify a scenario for their breakdown. In this scenario, the breakdown happens because two invariant directions of the transversal dynamics come close to each other, losing their regularity. On the other hand, the Lyapunov multipliers associated with the invariant directions remain more or less constant. We identify notable quantitative regularities in this scenario, namely that the minimum angle between the two invariant directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws seem to be universal.