Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

Role of free valences and spin densities on the migrating atom in location of saddle points in radical-exchange reactions

The principle of the conservation of bond orders during radical-exchange reactions is examined using Mayer's definition of bond orders. This simple intuitive approximation is not valid in a quantitative sense. Ab initio results reveal that free valences (or spin densities) develop on the migrating atom during reactions. For several examples of hydrogen-transfer reactions, the sum of the reaction coordinate bond orders in the transition state was found to be 0.92 +/- 0.04 instead of the theoretical 1.00 because free valences (or spin densities) develop on the migrating atom during reactions. It is shown that free valence is almost equal to the square of the spin density on the migrating hydrogen atom and the maxima in the free valence (or spin density) profiles coincide (or nearly coincide) with the saddle points in the corresponding energy profiles.

Halogen Bonds in Crystal Engineering: Like Hydrogen Bonds yet Different

CONSPECTUS: The halogen bond is an attractive interaction in which an electrophilic halogen atom approaches a negatively polarized species. Short halogen atom contacts in crystals have been known for around 50 years. Such contacts are found in two varieties: type I, which is symmetrical, and type II, which is bent. Both are influenced by geometric and chemical considerations. Our research group has been using halogen atom interactions as design elements in crystal engineering, for nearly 30 years. These interactions include halogen center dot center dot center dot halogen interactions (X center dot center dot center dot X) and halogen center dot center dot center dot heteroatom interactions (X center dot center dot center dot B). Many X center dot center dot center dot X and almost all X center dot center dot center dot B contacts can be classified as halogen bonds. In this Account, we illustrate examples of crystal engineering where one can build up from previous knowledge with a focus that is provided by the modern definition of the halogen bond. We also comment on the similarities and differences between halogen bonds and hydrogen bonds. These interactions are similar because the protagonist atoms halogen and hydrogen are both electrophilic in nature. The interactions are distinctive because the size of a halogen atom is of consequence when compared with the atomic sizes of, for example, C, N, and O, unlike that of a hydrogen atom. Conclusions may be drawn pertaining to the nature of X center dot center dot center dot X interactions from the Cambridge Structural Database (CSD). There is a clear geometric and chemical distinction between type I and type II, with only type II being halogen bonds. Cl/Br isostructurality is explained based on a geometric model. In parallel, experimental studies on 3,4-dichlorophenol and its congeners shed light on the nature of halogen center dot center dot center dot halogen interactions and reveal the chemical difference between Cl and Br. Variable temperature studies also show differences between type I and type II contacts. In terms of crystal design, halogen bonds offer a unique opportunity in the strength, atom size and interaction gradation; this may be used in the design of ternary cocrystals. Structural modularity in which an entire crystal structure is defined as a combination of modules is rationalized on the basis of the intermediate strength of a halogen bond. The specific directionality of the halogen bond makes it a good tool to achieve orthogonality in molecular crystals. Mechanical properties can be tuned systematically by varying these orthogonally oriented halogen center dot center dot center dot halogen interactions. In a further development, halogen bonds are shown to play a systematic role in organization of LSAMs (long range synthon aufbau module), which are bigger structural units containing multiple synthons. With a formal definition in place, this may be the right time to look at differences between halogen bonds and hydrogen bonds and exploit them in more subtle ways in crystal engineering.

Hydrogen behavior in GaN epilayers grown by NH3-MBE

Hydrogen behavior in unintentionally doped GaN epilayers on sapphire substrates grown by NH3-MBE is investigated. Firstly, we find by using nuclear reaction analysis (NRA) that with increasing hydrogen concentration the background electron concentration increases, which suggests that there exists a hydrogen-related donor in undoped GaN, Secondly, Fourier transform infrared (FTIR) absorption and X-ray photoelectron spectroscopy (XPS) reveal Further that hydrogen atom is bound to nitrogen atom in GaN with a local vibrational mode at about 3211 cm(-1) Hence, it is presumed that the hydrogen-related complex Ga. . .H-N is a hydrogen-related donor candidate partly responsible for high n-type background commonly observed in GaN films. Finally, Raman spectroscopy results of the epilayers show that ill addition to the expected compressive biaxial strain, in some cases GaN films suffer from serious tensile biaxial strain. This anomalous behavior has been well interpreted in terms of interstitial hydrogen lattice dilation. (C) 2001 Elsevier Science B.V. All rights reserved.

Hydrogen related defects in InP

Local vibrational modes(LVMs) in tenths of InP samples reveal clearly existence of complexes related to hydrogen. Complexes of vacancy at indium site with one to four hydrogen atom(s) and isolated hydrogen or hydrogen dimers and complexes of hydrogen with various impurities and intrinsic defects are investigated by FTIR. Especially hydrogen related complexes between various transition metals and hydrogen or hydrogen related complexes between hydrogen with point defects. New LVMs related to hydrogen will be reported in this paper. Dynamical formation mechanism of defects in the annealed nominally undoped semiinsulating InP obtained by high pressure, high temperature annealing of ultra purity materials is proposed. Hydrogen can acts as actuator for antistructure defects production. Structural, electronic and vibrational properties of LVMs related to hydrogen as well as their temperature effects are discussed.

Hydrogen behavior in GaN epilayers grown by NH3-MBE

Hydrogen behavior in unintentionally doped GaN epilayers on sapphire substrates grown by NH3-MBE is investigated. Firstly, we find by using nuclear reaction analysis (NRA) that with increasing hydrogen concentration the background electron concentration increases, which suggests that there exists a hydrogen-related donor in undoped GaN, Secondly, Fourier transform infrared (FTIR) absorption and X-ray photoelectron spectroscopy (XPS) reveal Further that hydrogen atom is bound to nitrogen atom in GaN with a local vibrational mode at about 3211 cm(-1) Hence, it is presumed that the hydrogen-related complex Ga. . .H-N is a hydrogen-related donor candidate partly responsible for high n-type background commonly observed in GaN films. Finally, Raman spectroscopy results of the epilayers show that ill addition to the expected compressive biaxial strain, in some cases GaN films suffer from serious tensile biaxial strain. This anomalous behavior has been well interpreted in terms of interstitial hydrogen lattice dilation. (C) 2001 Elsevier Science B.V. All rights reserved.

Enabling science through emerging HPC technologies: accelerating numerical quadrature using a GPU

The R-matrix method when applied to the study of intermediate energy electron scattering by the hydrogen atom gives rise to a large number of two electron integrals between numerical basis functions. Each integral is evaluated independently of the others, thereby rendering this a prime candidate for a parallel implementation. In this paper, we present a parallel implementation of this routine which uses a Graphical Processing Unit as a co-processor, giving a speedup of approximately 20 times when compared with a sequential version. We briefly consider properties of this calculation which make a GPU implementation appropriate with a view to identifying other calculations which might similarly benet.

Production of ultracold hydrogen and deuterium via Doppler-cooled Feshbach molecules

A counterintuitive scheme to produce ultracold hydrogen via fragmentation of laser cooled diatomic hydrides is presented where the final atomic H temperature is inversely proportional to the mass of the molecular parent. In addition, the critical density for formation of a Bose-Einstein condensate (BEC) at a fixed temperature is reduced by a factor (mH/mMH)3/2 over directly cooled hydrogen atoms. The narrow Feshbach resonances between a S01 atom and hydrogen are well suited to a tiny center of mass energy release necessary during fragmentation. With the support of ab initio quantum chemistry, it is demonstrated that BaH is an ideal diatomic precursor that can be laser cooled to a Doppler temperature of ∼26μK with just two rovibronic transitions, the simplest molecular cooling scheme identified to date. Preparation of a hydrogen atom gas below the critical BEC temperature Tc is feasible with present cooling technology, with optical pulse control of the condensation process.

Studies on Non-Resonant Multiphoton Processes in Atomic Hydrogen

In the present thesis we have formulated the Dalgarno-Lewis procedure for two-and three-photon processes and an elegant alternate expressions are derived. Starting from a brief review on various multiphoton processes we have discussed the difficulties coming in the perturbative treatment of multiphoton processes. A small discussion on various available methods for studying multiphoton processes are presented in chapter 2. These theoretical treatments mainly concentrate on the evaluation of the higher order matrix elements coming in the perturbation theory. In chapter 3 we have described the use of Dalgarno-Lewis procedure and its implimentation on second order matrix elements. The analytical expressions for twophoton transition amplitude, two-photon ionization cross section, dipole dynamic polarizability and Kramers-Heiseberg are obtained in a unified manner. Fourth chapter is an extension of the implicit summation technique presented in chapter 3. We have clearly mentioned the advantage of our method, especially the analytical continuation of the relevant expressions suited for various values of radiation frequency which is also used for efficient numerical analysis. A possible extension of the work is to study various multiphoton processcs from the stark shifted first excited states of hydrogen atom. We can also extend this procedure for studying multiphoton processes in alkali atoms as well as Rydberg atoms. Also, instead of going for analytical expressions, one can try a complete numerical evaluation of the higher order matrix elements using this procedure.

Interatomic potential structures in highly ionized scattering systems

The interatomic potential of the ion-atom scattering system I^N+-I at small intermediate internuclear distances is calculated for different charge states N from atomic Dirac-Focker-Slater (DFS) electron densities within a statistical model. The behaviour of the potential structures, due to ionized electronic shells, is studied by calculations of classical elastic differential scattering cross-sections.

Metal cluster expansion by addition of low-valent group 4B reagents: crystal and molecular structure of [Os3SnH2(CO)10{CH(SiMe3)2}2]; a compound with hydrogen bridging osmium and tin

Cluster expansion of [Os3H2(CO)10] with [SnR2][R = CH(SiMe3)2] take place in high yield to give [Os3SnH2(CO)10R2], the first closed triosmium–main-group metal cluster to be structurally characterized; a novel feature is the presence of a hydrogen atom bridging the tin atom and one of the osmium atoms.

High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Role of Mie scattering in the seeding of matter-wave superradiance

Matter-wave superradiance is based on the interplay between ultracold atoms coherently organized in momentum space and a backscattered wave. Here, we show that this mechanism may be triggered by Mie scattering from the atomic cloud. We show how the laser light populates the modes of the cloud and thus imprints a phase gradient on the excited atomic dipoles. The interference with the atoms in the ground state results in a grating that in turn generates coherent emission, contributing to the backward light wave onset. The atomic recoil "halos" created by the Mie-scattered light exhibit a strong anisotropy, in contrast to single-atom scattering.

Guessing Solutions to the H-atom Schrodinger Equation

In teaching elementary quantum chemistry, the concept of eigenfunctionality is explored using the H-atom's Hamiltonian and various guessed functions. This is done in Cartesian coordinates, in Spherical Polar coordinates, and in Confocal Elliptical coordinates.

On the electronic nature of low-barrier hydrogen bonds in enzymatic reactions

The electronic nature of low-barrier hydrogen bonds (LBHBs) in enzymatic reactions is discussed based on combined low temperature neutron and x-ray diffraction experiments and on high level ab initio calculations by using the model substrate benzoylacetone. This molecule has a LBHB, as the intramolecular hydrogen bond is described by a double-well potential with a small barrier for hydrogen transfer. From an “atoms in molecules” analysis of the electron density, it is found that the hydrogen atom is stabilized by covalent bonds to both oxygens. Large atomic partial charges on the hydrogen-bonded atoms are found experimentally and theoretically. Therefore, the hydrogen bond gains stabilization from both covalency and from the normal electrostatic interactions found for long, weak hydrogen bonds. Based on comparisons with other systems having short-strong hydrogen bonds or LBHBs, it is proposed that all short-strong and LBHB systems possess similar electronic features of the hydrogen-bonded region, namely polar covalent bonds between the hydrogen atom and both heteroatoms in question.