Energy isosbestic points in third-row transition metal alloys.

A method is presented for solution of the spatially inhomogeneous Boltzmann equation in the two-term approximation for low-pressure inductively coupled plasmas (ICP). The total electron energy \ensuremath{\varepsilon}=w-e\ensuremath{\varphi} (the sum of kinetic energy w and potential energy e\ensuremath{\varphi} in an electrostatic field) is used as an independent variable in the kinetic equation. Two energy ranges are distinguished. In the elastic energy range w${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{*}}$, where ${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{*}}$ is the first excitation energy, the problem is effectively reduced to one variable (total electron energy) by performing an appropriate spatial average. The electron distribution function (EDF) in this energy range is a function solely of \ensuremath{\varepsilon} and does not depend explicitly on the coordinates. In the inelastic energy range, the kinetic equation in the variables (r,z,\ensuremath{\varepsilon}) (two spatial coordinates and the total energy) is solved for trapped and free electrons in a cylindrically symmetric ICP with a given spatial distribution of electric fields. The EDF and the spatial distributions of the electron current density and the ionization rate are calculated as functions of pressure, plasma density, and the profile of the electrostatic field. Explanations of some available experimental observations are given.

SKF makes group changes

New insight into the structure, internal rotation barrier and vibrational analysis of 2-fluorostyrene

On the quantum-mechanical virial theorem for molecular bending motions

Phase stability of the intermetallic compound Al3Nb is investigated as a function of nickel additions by band structure calculations based on an extended Hueckel tight-binding method. With this method, the electronic structure and total energies of the Al6-n -Ni n Nb2 compounds (where n is an integer from 0 to 6) are calculated for both D022 and L12 structures under the assumption that nickel substitutes for aluminium. The electronic total energies obtained from integration of the energy states of all electrons considered have shown that the D022 structure is stable in the binary Al3Nb compound as compared with the L12 structure; conversely, the L12 structure is stable for compounds with n values greater than 1. These calculations are in good agreement with X-ray diffraction results reported by Schubert and co-workers. Differences in the electronic total energy per atom between D022 and L12 are - 0·79 eV and 0·56 eV for n equal to 0 and 2, respectively.

New estimation of non-thermal electron energetics in the giant solar flare on 28 October 2003 based on Mars Odyssey observations

The Robinson–Schaad approximate formula relating the total electronic energy and the sum of orbital energies of a scaled system is rederived and generalized using a Radau-type quadrature.

In this study, it has been demonstrated that there are additive rules corresponding to ab initio derived total electronic energies between members of triple sets of some extended sulfur diimides and their mono- and bi-derivatives. It has been shown that the additive rules are insensitive to the combination of methods and basis sets used to derive the total electronic energies. This insensitivity to the level of calculation is demonstrated to be the case for some linear alkanes also. It has been found that the total electronic energies of certain members of extended sulfur diimide sets ((ZZ)k and (EE)k conformers) follow a linear relation although chemical accuracy may be achieved only by excluding the smallest members of these sets. The details of this deviation have been employed to quantify the “Z-effect” proposed previously by the same authors.

Total electronic energy by tight binding approximation and experimental toughness of three different hybrid polymers

Local geometry and orientation of intercalated molecules of formamide (FA) and N-methylformamide (NMFA) in the clay mineral dickite (D) was studied by means of Density Functional Theory (DFT) calculations. Ten configurations with different orientation of the intercalated molecule were investigated for both D_FA and D_NMFA intercalates. Four groups of relaxed structures sorted by the calculated total electronic energy were found in both cases. The experimental geometry of the D_FA intercalate was denoted as the most stable structure from the investigated models. The differences in the total electronic energy of all D_FA configurations are within the interval of ∼92 kJ/mol. On one hand FA forms intercalates specifically and a close relation between the orientation of the FA molecules in the interlayer space and the stability of a particular configuration has been observed. On the other hand, N-methylformamide forms intercalated structures non-specifically. Small differences in the total energy, not larger than 18 kJ/mol, are observed for different orientations of the NMFA molecules The reorientation of the intercalated molecules has only a small effect on the stabilization of the D_NMFA intercalate what is in contrast with the D_FA intercalate. It was also observed that the experimental D_NMFA configuration is not the most stable. A small variation of the total electronic energy of different configurations correlates with small changes of the orientation of the dipole moment of the intercalated NMFA molecule.

The three lowest-lying electronic states of the aluminum dihydride anion (AlH2-) were systematically investigated using ab initio electronic structure theory. Self-consistent-field (SCF), two-configuration self-consistent-field (TCSCF), complete active space self-consistent-field (CASSCF), configuration interaction including single and double excitations (CISD), and CASSCF-based second-order configuration interaction (SOCI) levels of theory were employed with five basis sets of triple-ζ quality. All three electronic states were predicted to possess bent equilibrium geometries. Total electronic energies as well as physical properties including dipole moments, harmonic vibrational frequencies, and associated infrared (IR) intensities were determined for each state. At the CISD level with the largest basis set employed, triple-ζ plus triple polarization augmented with two sets of higher angular momentum functions and two sets of diffuse functions [TZ3P(2f,2d)+2diff)], the equilibrium geometries of the three states were predicted to be re = 1.681 Å and θe = 95.6° (X̃ 1A1), re = 1.617 Å and θe = 117.8° (ã 3B1), and re = 1.594 Å and θe = 118.7° (Ã 1B1). At the same level of theory, the dipole moments with respect to the center of mass were predicted to be 0.64 (X̃ 1A1), 0.03 (ã 3B1), and 0.24 D (Ã 1B1). The energy separations (T0) between the ground (X̃ 1A1) and first two excited states predicted at the CASSCF-SOCI level with the TZ3P(2f,2d)+2diff basis set were 14.1 (ã 3B1 ← X̃ 1A1) and 29.0 kcal mol-1 (Ã 1B1 ← X̃ 1A1).

Article On the Constancy of the Second Differences in Total Electronic Energies within Atomic Isoelectronic Series was published on January 1, 1984 in the journal Zeitschrift für Physikalische Chemie (volume 265O, issue 1).

DFT/B3LYP study of O–H bond dissociation enthalpies of para and meta substituted phenols: Correlation with the phenolic C–O bond length

In this work, we have explored the validity of the hypotheses on which rest the Hammett's approach to quantify the substituent effect on a reaction center, by applying two DFT energy decomposition schemes. This is performed by studying the change in the total electronic energy, ΔΔE, associated with a proton transfer isodesmic equilibrium. For this reaction, two sets of substituted benzoic acids and their corresponding benzoate anions have been considered. One of these sets contains para- and meta-substitutions, whereas the other one includes ortho-substituted benzoic acids. For each case, the gas phase change in the total electronic energy has been calculated, and two DFT energy decomposition schemes have been applied. The experimental σ(X) was found to be nearly proportional to the computed ΔΔE. The results for the para- and meta-substituted benzoic acids lead to the conclusion that it is possible to treat separately and, in an additive manner, the electrostatic and steric contributions; and also that the Hammett constant depends mainly on the electronic contributions to the free energy, while the steric contribution is negligible. However, the results for the ortho-substituted cases lead to the conclusion, as was assumed by Hammett, that there are significant qualitative differences between the effects on a reaction site of substituents in the meta- and para-positions and those in the ortho-position.

The density functional theory B3LYP/6-311++G(3df,3pd) has been used to optimize the geometry of homologues of a series of sulfoxylic acid ester radicals and to obtain the electron density distributions of the first nine compounds. The hydrogen bond presented in the initial molecules of the unbranched esters of sulfoxylic acid between the hydrogen of the second carbon atom of the alkyl chain (from the ester bond) and the oxygen of the hydroxyl group of the sulfur-containing fragment (-C(Н)H-CH2-O-S-ОН) and the corresponding cycle are not observed in the radicals. The fragmentation of the structures into topological groups of CH3, CH2, and (-O-S-O)● has been proposed and their electron integral characteristics are presented including charges, unpaired electron density, energy, and volume. The steric effect of the fragment (-O-S-O)● has been established and its inductive effect has been considered based on the groups charge parameters changes triggered by an increase in the hydrocarbon chain. The scale of group electronegativities of the studied homologues has been constructed by comparing the charges of topological groups. The fact that the radical center corresponds to the fragment (-O-S-O)● has been demonstrated by the spin density delocalization results (having the largest fraction on the sulfur atom (0.57), slightly less fraction on the oxygen atom with a free valence (0.32) and an insignificant fraction on oxygen atom using the ether bond (0.10)). The increment value of the total energy contributed by the CH2 group of each subsequent homologue of the series under the study has been estimated. It is 103260 kJ/mol. The evaluation of the “standard” value of the groups’ total electron energy and the use of their relative energy (ΔE(R)) for comparing with ΔE(R) of molecules and radicals of other homologous series have been described. A decrease in the volumes of the two closest to the sulfur-containing fragment CH2 groups caused by an outflow of electron density from them toward the fragment (-O-S-O)● has been noted.