Electrophilic additions to a 2-methylenebicyclo[2.1.1]hexane system: probing pi-face selectivity for electrostatic and orbital effects

[reaction: see text] 5-exo-Bicyclo[2.1.1]hexane derivatives with remote electron-withdrawing substituents exhibit very modest face selectivity during electrophilic additions due to interplay of several electronic factors. These experimental results have been probed through ab initio MESP maps, bond density calculations, and energetics involved in pre-reaction complexation.     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

Molecular tailoring approach for geometry optimization of large molecules: energy evaluation and parallelization strategies

A linear-scaling scheme for estimating the electronic energy, gradients, and Hessian of a large molecule at ab initio level of theory based on fragment set cardinality is presented. With this proposition, a general, cardinality-guided molecular tailoring approach (CG-MTA) for ab initio geometry optimization of large molecules is implemented. The method employs energy gradients extracted from fragment wave functions, enabling computations otherwise impractical on PC hardware. Further, the method is readily amenable to large scale coarse-grain parallelization with minimal communication among nodes, resulting in a near-linear speedup. CG-MTA is applied for density-functional-theory-based geometry optimization of a variety of molecules including alpha-tocopherol, taxol, gamma-cyclodextrin, and two conformations of polyglycine. In the tests performed, energy and gradient estimates obtained from CG-MTA during optimization runs show an excellent agreement with those obtained from actual computation. Accuracy of the Hessian obtained employing CG-MTA provides good hope for the application of Hessian-based geometry optimization to large molecules.     

Atop-the-barrier localization in periodically driven double wells: A minimization of information entropic sums in conjugate spaces

The spatio-temporal localization of a system in the presence of an oscillating electric field for a symmetric double-well potential is examined via numerical simulations of the time-dependent Schrödinger equation. For an initial state with equal probability densities in both the wells, stabilized localization atop the barrier can be achieved on a periodic high-frequency driving. The barrier localization is characterized using Shannon information entropies in position and momentum spaces, defined as S_ρ = − ∫ |ψ|² ln |ψ|² dx and S_γ = − ∫ |ϕ|² ln |ϕ|² dp , where ψ and ϕ refer to position and momentum space wave functions, respectively. The information entropy sum, S_ρ + S_γ, goes through a minimum indicating the formation of the barrier-localized state, when the peak intensity of the oscillating field is reached. The generalized uncertainty via the Białynicki-Birula-Mycielski inequality ( S_ρ + S_γ ≥ 1 + lnπ ) is saturated upon this minimization. This serves as a signature of the formation of the barrier-atop localized state, in terms of Shannon entropies of measurable densities.     

Why are carborane acids so acidic? An electrostatic interpretation of Brønsted acid strengths

Acidity of Br?nsted acids is explained in terms of the electrostatic potentials of the corresponding conjugate bases. The electrostatic potential distribution on the zero-flux surface of the strongest isolable carborane anions is seen to provide a good measure of their acidities. Increasing value of the lowest minimum in the electrostatic potential is observed to be a signature of increasing acidity.     

Can ring strain be realized in momentum space?

An increased electron momentum density (EMD) at low momentum is proposed to be an indicator of ring strain, with the nature of the function tending toward a maximum. A p-space Hirshfeld atomic partitioning scheme is applied for analyzing the effect of strain on molecular EMDs. The Hirshfeld momentum densities for a strained system show an increase in the population for the carbons with the hydrogens becoming more positive in comparison with an unstrained reference molecule. The manifestation of strain in cage-like hydrocarbons such as tetrahedrane, cubane, prismane, etc. as well as their nitrogen-substituted analogues is clearly seen in terms of EMDs.     

Topography of molecular scalar fields. II. An appraisal of the hierarchy principle for electron momentum densities

The previously observed hierarchy principle for nondegenerate critical points (CPs) of the electron momentum density (EMD) of molecules [Kulkarni, Gadre, and Pathak, Phys. Rev. A. 45, 4399 (1992)] is verified at a reliable level of theory. Application of Morse inequalities and the Poincare-Hopf relation to EMD leads to some rigorous results viz (i) for total number of CPs, NCP=3,7,11,15, ...there must be either a (3,+3) or a (3,-1) CP at the center of symmetry, (ii) for N(CP)=1,5,9,13, ...there must be either a (3,-3) or a (3,+1) CP at the center of symmetry. A single directional maximum on every ray, starting from p=0 has been observed for all the test molecules and is suggested as a working topographical principle in p space. This working principle is shown to satisfy the sufficiency condition for the hierarchy principle.     

Electrostatic potential topography for exploring electronic reorganizations in 1,3 dipolar cycloadditions

Topographical analysis of the molecular electrostatic potential (MESP) along a reaction path is employed for bringing out sequential electronic reorganizations for 1,3-dipolar cycloadditions of ethyne to fulminic acid as well as diazomethane. A simple and consistent set of rules for portraying electronic mechanisms of chemical reactions using the MESP topography is applied for this purpose. The MESP topography at each point on the concerted reaction path is associated with a classical electronic structure yielding a clear picture of the electronic reorganization along the reaction path.