Electronic stress tensor of the hydrogen molecular ion: Comparison between the exact wave function and approximate wave functions using Gaussian basis sets

We investigate the electronic stress tensor of the hydrogen molecular ion for the ground state using the exact wave function and wave functions approximated by gaussian function basis set expansion. The spatial distribution of the largest eigenvalue, corresponding eigenvectors, tension and kinetic energy density are compared. We find that the cc-pV6Z basis set gives the spindle structure very close to the one calculated from the exact wave function. Similarly, energy density at the Lagrange point is very well approximated by the cc-pV5Z or cc-pV6Z basis sets.Comment: 22 pages, 8 figure

Taft, Frankfurter, and the First Presidential For-Cause Removal

In the fall of 1912—while one of the most consequential presidential campaigns in United States history raged around them— William Howard Taft, Felix Frankfurter, and a handful of officials within the federal government initiated a process to remove two members of the Board of General Appraisers (“Board”) for inefficiency, neglect of duty, and malfeasance in office. The process culminated in President Taft’s for-cause dismissal of the two members, Thaddeus Sharretts and Roy Chamberlain, on the very last day that he served as President, after he received a report recommending their firing from a “committee of inquiry” that included Frankfurter

The Attorney General and Early Appointments Clause Practice

This Article proceeds as follows. In Part I, I provide an overview of the Appointments Clause and the officer-employee line as it currently stands in caselaw and in executive branch practice. I also summarize the Appointments Clause practices of the First Congress. In Part II, I address the opinions of the Attorneys General, and their attempt to rationalize and to explain the statutes enacted by the First Congress and the appointments practices of the nation. In Part III, I derive some implications and conclusions, generally for the Appointments Clause and specifically for the Administrative Law Judge controversy that is currently the subject of a Supreme Court case in Lucia

Electronic stress tensor analysis of molecules in gas phase of CVD process for GeSbTe alloy

We analyze the electronic structure of molecules which may exist in gas phase of chemical vapor deposition process for GeSbTe alloy using the electronic stress tensor, with special focus on the chemical bonds between Ge, Sb and Te atoms. We find that, from the viewpoint of the electronic stress tensor, they have intermediate properties between alkali metals and hydrocarbon molecules. We also study the correlation between the bond order which is defined based on the electronic stress tensor, and energy-related quantities. We find that the correlation with the bond dissociation energy is not so strong while one with the force constant is very strong. We interpret these results in terms of the energy density on the "Lagrange surface", which is considered to define the boundary surface of atoms in a molecule in the framework of the electronic stress tensor analysis.Comment: 32 pages, 9 figure

On the Original Proof by Reductio ad Absurdum of the Hohenberg-Kohn Theorem for Many-Electron Coulomb Systems

It is shown that, for isolated many-electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg-Kohn theorem is unsatisfactory since the to-be-refuted assumption made about the one-electron densities and the assumption about the external potentials are not compatible with the Kato cusp condition. The theorem is, however, provable by more sophisticated means and it is shown here that the Kato cusp condition actually leads to a satisfactory proof.Comment: 14 pages. Int. J. Quantum Chem. to appea

Debs and the Federal Equity Jurisdiction

The United States can sue for equitable relief without statutory authorization. The leading case on this question is In re Debs, and how to understand that case is of both historical and contemporary importance. Debs was a monumental opinion that prompted responses in the political platforms of major parties, presidential addresses, and enormous academic commentary. In the early twentieth century, Congress enacted several pieces of labor legislation that reduced Debs’s importance in the specific context of strikes. But in other contexts, the question whether the United States can bring suit in equity remains disputed to this day. The United States has expressly invoked, or implicitly relied on, Debs in some of the most high-profile cases in recent years, including United States v. Texas. This Article explains the equitable principles at work in Debs and shows how these principles still have a normative basis today. Collecting materials from traditional equity practice and historic treatments of Debs that have escaped the attention of the recent academic literature, this Article especially considers the connection that the Debs Court draws between equitable relief and a proprietary interest. It shows how the equity-property connection works as an empowering and limiting principle for the ability of the United States to bring a suit in equity. And it offers guidance to the federal courts by explaining and defending the traditional contours of their equity jurisdiction

Effects of certain growth substances and boric acid on germination, tube growth and storage of grape pollen (Vitis ssp.)

Investigations on the ,effects of growth substances (GA, IAA and IBA) and boric acid on grape pollen have shown that maximum germination and tube growth was obtained rwith boric acid at lower concentrations (5, 10 and 20 ppm) as compared to GA, IAA, IBA and control. Although GA showed lesser pollen germination, pollen tube growth was enhanced at 5, 10 and 20 ppm in the grape cultivars under study. Pollen grains of Pusa Seedless were stored for 12 months and Pearl of Csaba for four months at different combinations of temperature and ihumidity. The pollen viability was highest when sfored at -12° to -10° C with 25 per cent R.H. which was followed by 4° to 8° C ,and 25 per cent R.H. The pollen germination increased throughout the storage period by boric acid at 5, 10 and 20 ppm