Accurate energy eigenvalues and eigenfunctions for the two‐dimensional confined hydrogen atom

A study of the two‐dimensional hydrogen atom confined within a circle of impenetrable walls is presented. The potential inside the box is Coulomb type, whereas outside it is infinite. The energy eigenvalues and some radial wave function properties are computed with high accuracy for different box sizes. We derive the polarizability in the Kirkwood approximation, calculate the Fermi contact term as a function of the confinement radius, and investigate the filling order of the one‐electron states. When the electronic configuration of many electrons is constructed by means of the Aufbau principle, the model predicts the inversion 2s–3d levels in the N atom. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Static field ionization of the spherically confined hydrogen atom

The ionization of the hydrogen atom confined in a spherical potential well and subjected to a static electric field is studied, using the diffusion Monte Carlo (DMC) method. Atomic ionization within a potential well is found to be a stationary, gradual, and reversible process. The value of the electric field at the onset of ionization is of the order of 0.1 atomic units, and depends on the symmetry of the atomic wave function and on the confinement dimension. By decreasing the confinement sphere, the difference between the bound and ionized states disappears, showing that strict confinement leads to pressure ionization of the atom. The off-center case is studied characterizing the potential energy surface (PES), and the transition between field-induced and pressure-induced ionization is confirmed. Except for very weak fields, the minimum of the PES is reached when the proton is in contact with the boundary of the well.     

Information‐entropic measures in free and confined hydrogen atom

Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T), Fisher information (I), and Onicescu energy (E) have been explored extensively in both free H atom (FHA) and confined H atom (CHA). For a given quantum state, accurate results are presented by employing respective exact analytical wave functions in r space. The p‐space wave functions are generated from respective Fourier transforms—for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. Exact mathematical expressions of , are derived for circular states of a FHA. Pilot calculations are done taking order of entropic moments (α, β) as in r and p spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices n, l, and with confinement radius (r_c) for the latter. In a CHA, at small r_c, kinetic energy increases, whereas decrease with growth of n, signifying greater localization in high‐lying states. At moderate r_c, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.     

Variational approach to the confined hydrogen atom with a moving nucleus

We calculate the ground‐state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and show that the total, kinetic, and potential energies for the moving nucleus model are greater than those for the case in which the nucleus is clamped at the box center. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Revisiting the generalized pseudospectral method: Radial expectation values,fine structure,and hyperfine splitting of confined atom

This paper revisits the generalized pseudospectral (GPS) method on the calculation of various radial expectation values of atomic systems, especially on the spatially confined hydrogen atom and harmonic oscillator. As one of the collocation methods based on global functions, the powerfulness and robustness of the GPS method has been well established in solving the radial Schrödinger equation with high accuracy. However, in our recent work, it was found that the previous calculations based on the GPS method for the radial expectation values of confined systems show significant discrepancies with other theoretical methods. In this work we have tackled such a problem by tracing its source to the GPS method and found that the method itself may not be able to obtain the system wave function at the origin. Combined with an extrapolation method developed here, the GPS method can fully reproduce the radial quantities obtained by other theoretical methods, but with more flexibility, efficiency, and accuracy. We apply the GPS-extrapolation method to investigate the relatievistic fine structure and hyperfine splitting of confined hydrogen atom in s-wave states where the zero-point wave function dominates. Good agreement with previous predictions is obtained for confined hydrogen in low-lying states, and benchmark results are obtained for high-lying excited states. The perturbation treatment of the fine and hyperfine interactions is validated in the confining environment.     

Integral evaluation in the case of a helium atom positioned off‐center in a spherical box

A variational approach to the problem of multielectron atoms placed off‐center in a spherical box leads to the difficult evaluation of electron repulsion integrals in an environment where spherical symmetry is no longer present. A technique for the evaluation of the electron repulsion integrals generated by this situation is developed and tested for the case of a helium atom placed off‐center in a spherical box. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 459–467, 1999     

A two‐state reactivity rationale for the reaction of ta atom with acetonitrile in the gas phase

The spin‐forbidden reaction mechanism of Ta (⁴F, 5d³6s²) with CH₃CN, on two different potential surfaces (PESs) has been investigated at the B3LYP, MP2, and CCSD level of theory. Crossing points between the PESs are located using different methods, and possible spin inversion processes are discussed by means of spin‐orbit coupling calculations. As a result, the reaction system will change its spin multiplicities near this crossing seam, leading to a significant decrease in the barrier of ^2‐4TS3 from 24.17 to 5.36 kcal/mol, which makes the reaction access to a lower energy pathway and accelerate the reaction rate. © 2012 Wiley Periodicals, Inc.     

Shannon-information entropy sum in the confined hydrogenic atom

The appearance of critical points in the Shannon entropy sum as a function of confinement radius, in ground and excited state confined hydrogenic systems, is discussed. We illustrate that the Coulomb potential in tandem with the hard sphere confinement are responsible for these points. The positions of these points are observed to vary with the intensity of the potential. The effects of the Coulomb potential on the system are further probed, by examining the differences between the densities of the confined atom and those of the particle confined in a spherical box, for the same confinement radius. These differences are quantified by using Kullback-Leibler and cumulative residual Kullback-Leibler distance measures from information theory. These measures detect that the effects of the Coulomb potential are squeezed out of the system as the confinement radius decreases. That is, the confined atom densities resemble the particle in a box ones, for smaller confinement radii. Furthermore, the critical points in the entropy sum lie in the same regions where there are changes in the distance measures, as the atom behaves more particle in a spherical box-like. The analysis is further complemented by examination of the derivative of the entropy sum with respect to confinement radius. This study illustrates the inhomogeneity in the magnitudes of the derivatives of the entropy sum components and their dependence on the Coulomb potential. A link between the derivative and the entropic force is also illustrated and discussed. Similar behaviors are observed when the virial ratio is compared to the entropic power one, as a function of confinement radius.     

Study of a confined hydrogen‐like atom by the asymptotic iteration method

The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen‐like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no longer bound, are also calculated. The results are compared with those in the literature. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Dynamic changing features of the molecular face for interaction of a rare gas atom with a hydrogen molecule

We perform a systematical investigation on the dynamic changing feature of the molecular shape and size and electron density distribution in the process of a rare‐gas atom (He, Ne, Ar, and Kr) approaching a hydrogen molecule by an ab initio method. In terms of the molecular face (MF) theory, the polarization effect in the above processes is vividly demonstrated. There is a good linear correlation between our average variation rate (S_aver) of molecular intrinsic characteristic radius at the contacting point and the experimental polarizability of the rare‐gas atoms. This indicates that the MF theory can well represent the intermolecular polarization effect. Interestingly, the pictures of shape changing, charge‐flow, and exchange repulsion processes especially on the reacting active areas have been clearly observed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field

A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 183–192, 1998     

Noninnocence of the ligand atoms in iron‐porphine: Chemical consequences of the delocalized electron spin

It is well recognized that the electronic spin density in transition metal complexes in high‐spin states, tends to delocalize from the metal ion itself to the donor atoms of the ligand. In square planar iron‐porphine [PFe]⁺ the delocalization occurs even further and spin corresponding to roughly one electron is delocalized over a large part of the ligand. In this article, density functional theory is applied to explore the chemical consequences of the delocalized spin in four‐coordinate iron‐porphine. It is shown that the porphine ligand has a moderate affinity for radicals, and that covalent bonds can form through spin‐pairing of the unpaired delocalized electron on the porphine ligand and the unpaired electron of another radical species. The hydrogen atom is used as a probe to evaluate the radical affinity of the different nitrogen and carbon atoms that constitute the porphine ligand. It is computationally predicted that the porphine ligand of four‐coordinate iron‐porphine is kinetically capable of activating weak C? H bonds of, for example, unsaturated organic compounds. Hydrogen atom transfer becomes spontaneous via subsequent homo‐coupling of the organic radical created. Whether or not the radical affinity of the porphine ligand has any mechanistic implications for heme‐containing enzymes is left as an open question.     

The effect of confinement on the electronic energy and polarizability of a hydrogen molecular ion

The electronic energy and the polarizability of a confined hydrogen molecular ion in the ground state and the first excited state, for cavities of different volumes, are calculated using the variational method. In the treatment adopted an alternative molecular wave function is introduced with only one variational parameter and based on wave functions used for confined atoms. © 2016 Wiley Periodicals, Inc.     

A DFT and AIM analysis of the spin–spin couplings across the hydrogen bond in the 2‐fluorobenzamide and related compounds

In 1975 a large number of coupling constants were measured in 2‐fluorobenzamide labeled with ¹⁵N. Some of them were assigned to couplings through intramolecular N? H···F hydrogen bonds (HBs). These couplings change dramatically when CDCl₃ is replaced by DMSO‐d₆. In this theoretical paper we provide density functional theory (DFT) calculations that justify the existence of a weak HB in the absence of solvent, while solvents that act as HB acceptors break down the intramolecular hydrogen bond (IMHB) of 2‐fluorobenzamide. Atoms in molecules (AIM) analyses and Steiner‐Limbach plots were used to analyze the structure of the compounds. Copyright © 2009 John Wiley & Sons, Ltd.