Accelerated approach to self-consistency in molecular-orbital methods

Interpolation between two successive approximations for the bond-order matrix is used in a method of deducing corrections to the matrix; a matrix equation for the corrections is derived and solved. It is shown by reference to pyridine that the correction greatly accelerates the approach to self-consistency.Read at the Symposium on Quantum Chemistry, Palanga, June 1965.     

Simple implementation of complex functionals: scaled self-consistency

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of self-consistent implementation of simpler functionals: (i) post-local-density approximation (LDA) evaluation of complex functionals at the LDA densities (or those of other simple functionals) (ii) application of a global scaling factor to the potential of the simple functional, and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in density-functional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez [Phys. Rev. A 71, 042505 (2005)]. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of density-functional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully self-consistent implementations for Hartree, local-density, generalized-gradient, self-interaction corrected, and meta-generalized-gradient approximations, for atoms, ions, quantum wells, and model Hamiltonians. Scaled approaches turn out to be, on average, better than post approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled self-consistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.     

Approaching the self-consistency challenge of electrocatalysis with theory and computation

This opinion piece centers around challenges involved in developing first-principles electrochemical methods. In recent years, theory and computation have become indispensable tools to navigate the parameter space that controls the activity and stability of electrocatalytic materials and electrochemical devices. Viable methods process as input details on materials structure, composition and reaction conditions. Their output includes metrics for stability and activity, phase diagrams, as well as mechanistic insights on reaction mechanisms and pathways. The core challenge, connecting input to output, is a self-consistency problem that couples the electrode potential to variables for the electronic structure of the solid electrode, solvent properties and ion distributions in the electrolyte as well as specific properties of a boundary region in-between. We will discuss a theoretical framework and computational approaches that strive to accomplish this feat.     

Acid base contributions to interfacial free energy: self-consistency considerations

The evaluation of interfacial free energies is a subject of much discussion. Of recent times, the role of acid/base interactions has been much debated and a mathematical model devised by van Oss et al. is now commonly used. In this work, we study several polymers using recognised probe liquids and, exploiting an extended matrix analysis, obtain values of solid surface characteristics in agreement with literature values. However, by ‘inverting’ the method, and using accepted solid surface characteristics to ‘rederive’ surface free energy parameters for probe liquids, inconsistencies become apparent. Despite the conceptual interest of acid/base interactions, clearly the mathematical formulation of van Oss et al. is incomplete and further development is required.     

On the accuracy of the many-points local procedures

As until now proposed in the literature, in the local energy calculations we can distinguish “few-points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many-points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many-points” calculation M points/N functions (M > N) can be connected in a simple way with the errors of the (^M_N) partial calculations N points/N functions. This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.     

On optimization procedures based upon the atomic thomas-fermi energy

For the total atomic Thomas-Fermi (TF) energy many expressions in terms of the kinetic and potential energy contributions can be given. Thirty of these expressions exhibit either a maximum or a minimum if some variational approximation to the TF function is used. Three of these expressions, to note E, G, and J (see text) have been used in an optimization procedure, in which four two-parameter and two three-parameter approximate TF functions have been considered. One-parameter functions cannot be optimized, as the one parameter must be fixed to ensure proper normalization. It is found that optimization of E and G give reasonable and similar results, whereas the results of optimization of J are generally not very impressive. Where possible, expectation values of the type 〈rⁿ〉 (with n = ?1, 1, 2, and 3) have been calculated from ten approximate TF functions. A new estimate of the exact atomic TF energy, as well as of the derivative of the TF function at the origin, has been obtained.     

Redox cycling in nanogap electrochemical cells

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The problem of critical damping in nanofriction

The progress that has been made in describing atomic friction in terms of mechanical instabilities of the stick-slip type masks the role of damping and makes researchers ignore the true mechanisms of dissipation. This study shows that there is a necessary condition for the realization of regular stick-slips occurring with atomic periodicity, which are observed in friction force microscopy (a variant of atomic force microscopy) experiments. This condition lies in the existence of a direct relation between the rate of dissipation and the characteristic frequency of a measuring system, i.e., its stiffness and mass (??critical damping??). The conclusion seems to be paradoxical; it indicates a nontrivial dissipation mechanism, which, according to the proposed explanation, essentially depends on memory effects.     

Optical damping constants in narrow gap semiconductors

Optical damping constants due to free carriers of HgSe, Zn _x Hg_1–x and Cd _x Hg_1–x Se were estimated from far infrared reflection spectra at 5 and 10 K. The damping mechanism was explained by the Drude type scattering below plasma frequency and by doubly ionized impurity scattering in the higher frequency range.     

用诱导自洽方法计算振动力常数的研究

本文提出一种迭代方法计算振动力常数,可以比较清楚地显示基频与振动力常数之间的关系,从而能方便地选择合适的力常数限制条件,得到合理的结果.用本方法对一系列不同分子作了计算,结果比较满意,对计算中一些具体问题作了讨论.     

On the accuracy of micro Winkler titration procedures: a case study

Accuracy data (expressed as precision and trueness) presented by the authors of three different micro modifications of the Winkler titration procedure for dissolved oxygen concentration determination are critically evaluated. Tentative uncertainty estimates are extracted from the data based on the single-laboratory validation approach (originally published in the Nordtest Technical Report 537) and they lead to expanded uncertainty (k = 2) estimates in the range from 0.13 to 0.27 mg l⁻¹ for the three procedures. It is demonstrated that, in all cases, the authors have presented the accuracy and/or precision estimates of the procedures in a way that can lead to too optimistic conclusions about the uncertainty of their procedures. This case study demonstrates the usefulness and flexibility of the single-laboratory validation approach to uncertainty estimation, even in the case of insufficient data, and can be of interest to laboratory workers dealing with measurement procedures from the literature. It is also expected to be of interest to university instructors of analytical chemistry and metrology in chemistry as a real-life example of the critical evaluation of the literature data. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control

Numerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a by-product we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.     

On the nonlinear isoconversional procedures to evaluate the activation energy of nonisothermal reactions in solids

A general procedure for deriving the equations that underlie various isoconversional nonlinear methods for evaluating the activation energy is presented. A new integral isoconversional nonlinear method with integration over a given range of conversion is suggested. This method was applied to simulated nonisothermal data as well as to data for the nonisothermal decomposition of ammonium perchlorate. The obtained dependencies of the activation energy on the degree of conversion were compared with those resulting from other nonlinear and linear methods of analysis. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 87–93 2004     

Numerical procedures in electrochemical simulation

The use of both the Laplace transformation technique and the finite element method has been analyzed in an electrochemical system. The diffusion-controlled adsorption process of a species onto an electrode surface is studied in detail. © 1994 John Wiley & Sons, Inc.     

Scaling procedures in colloidal electro-optics

In a series of recent papers, we demonstrate the possibility to use the complete electro-optic saturation curves (or arbitrary part of them) to analyse the polarization mechanisms of charged colloidal particles. Scaling of the electro-optic saturation curves by field intensity permits to find the frequency range in which the functional dependence of the effects, hence the orientation mechanism remains unchanged. Similar procedure can be applied to verify the changes of this dependence with variation of particle electric parameters. When different polarization mechanisms are involved the new scale helps their analysis.

The aim of the present paper is to summarize the basic applications and advantages of the scaling method in the electro-optic investigation of charged colloids.