Understanding the Uniqueness of 2p Elements in Periodic Tables

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)approximate to r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n >= 3 exhibit r(ns) MUCH LESS-THAN r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) >> r(2p) by +20 to +30 %, whereas r(3s)greater than or similar to r(3p)greater than or similar to r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.Peer reviewe

Molecular electronic structures : an introduction

The present book is an introduction to molecular electronic structural theory. It is aimed at students who have reasonable familiarity with differential and integral calculus and are beginning a study of the physical description of chemical systems. We have decided to concentrate on the description of ground state electronic structures, or, in other words, the principles of chemical bonding in molecules. In this important respect the present volume differs from our earlier book "Molecular Orbital Theory" (Benjamin, 1964), which included a strong emphasis on the description of electronic excited states. In our treatment of molecular wave functions we make use of "symmetry operators", the latter being operators that leave the Hamiltonian unchanged. By using such symmetry operators, it is possible to characterize the electronic structures of molecules. In our opinion, this approach provides good preparation for later studies that may be undertaken in which formal group theory is employed. The heart of the book is Chapter 4, where we discuss in some detail the bonding in several selected molecules. Examples from both organic and inorganic chemistry are included in an attempt to make the coverage as general as possible. Our objective here is to provide an introduction to molecular bonding that will serve as a foundation for more advanced study of electronic structures. Suggested reading and problems are included in each chapter. Some of the problems are challenging, but working them will give the student a much better feeling for the principles involved. The suggested reading is of two types, books (and reviews) and original papers. And we urge students to examine at least some of the older papers in the field, as muck can be learned from them

Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory

The package fhi98PP allows one to generate norm-conserving pseudopotentials adapted to density-functional theory total-energy calculations for a multitude of elements throughout the periodic table, including first-row and transition metal elements. The package also facilitates a first assessment of the pseudopotentials' transferability, either in semilocal or fully separable form, by means of simple tests carried out for the free atom. Various parameterizations of the local-density approximation and the generalized gradient approximation for exchange and correlation are implemented.Comment: 44 pages, 5 Postscript figures, epsfig, elsart, psfrag, submitted to Comput. Phys. Commun. Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Expanding the scope of density derived electrostatic and chemical charge partitioning to thousands of atoms

The density derived electrostatic and chemical (DDEC/c3) method is implemented into the onetep program to compute net atomic charges (NACs), as well as higher-order atomic multipole moments, of molecules, dense solids, nanoclusters, liquids, and biomolecules using linear-scaling density functional theory (DFT) in a distributed memory parallel computing environment. For a >1000 atom model of the oxygenated myoglobin protein, the DDEC/c3 net charge of the adsorbed oxygen molecule is approximately -1e (in agreement with the Weiss model) using a dynamical mean field theory treatment of the iron atom, but much smaller in magnitude when using the generalized gradient approximation. For GaAs semiconducting nanorods, the system dipole moment using the DDEC/c3 NACs is about 5% higher in magnitude than the dipole computed directly from the quantum mechanical electron density distribution, and the DDEC/c3 NACs reproduce the electrostatic potential to within approximately 0.1 V on the nanorod’s solvent-accessible surface. As examples of conducting materials, we study (i) a 55-atom Pt cluster with an adsorbed CO molecule and (ii) the dense solids Mo2C and Pd3V. Our results for solid Mo2C and Pd3V confirm the necessity of a constraint enforcing exponentially decaying electron density in the tails of buried atoms

Quantum Chemical Investigation of Electronic and Structural Properties of Crystalline Bismuth and Lanthanide Triborates

The origins of the optical effects and the chemical stability of BiB3O6 are studied by gradient-corrected hybrid B3PW density functional theory within the Gaussian-orbital-based CO-LCAO scheme. Including spin-orbit coupling, B3PW yields an estimate of the indirect band gap of 4.29~4.99 eV which is closer to the experimental value of 4.3 eV than the HF, LDA or GGA results. The crystal orbital overlap population is carried out to give a detailed first-principles analysis of chemical bonding. It is found that the Bi 6s couples with the O 2p in the primary interaction, which eventually forms both bonding and antibonding orbitals below the Fermi level. The Bi 6p is further involved in the secondary interaction with the filled Bi 6s-O 2p antibonding orbitals. The stereochemical activity of the Bi lone-pairs mainly originates from the primary interaction for the occupied Bi 6s-O 2p antibonding orbitals. It is found that the Bi 6p orbitals are not critically responsible for the non-spherical shape of the Bi lone-pairs. The densities of optical absorptions for the total BiB3O6 crystal, [BiO4]5- and [BO3]3- and [BO4]5- subunits are individually calculated by convoluting the total occupied density of states and the virtual densities of states of the corresponding unit. It is found that the [BiO4]5- units are mainly responsible for the optics of BiB3O6 in the long wavelength region. The reason is that the Bi-O covalent bonds lead to large spatial orbital overlappings and thus favor the electronic transfer from the occupied O 2p to the empty Bi 6p orbitals. The relativistic and correlation effects lead to fundamental differences of the band structure, chemical bonds and optical effects for BiB3O6 compared with non-relativistic and uncorrelated calculations. The harmonic frequencies of BiB3O6 are calculated by applying the numerical-difference technique. The complete 13 A and 14 B vibrational modes are assigned, graphically visualized and classified according to the Bi-O and B-O motions. Comparisons with previous experimental reports are discussed in detail. Crystal orbital adapted Gaussian (4s4p3d), (5s5p4d) and (6s6p5d) valence primitive basis sets are derived, in line with relativistic energy-consistent 4f-in-core lanthanide pseudopotentials of the Stuttgart-Köln variety, for calculating periodic bulk materials containing trivalent lanthanide ions, particularly in this thesis for the investigation of the relative stability of C2 and I2 phases of LnB3O6. Different segmented contraction schemes are calibrated on A-type Pm2O3 studying the basis set size effects. Further applications to the geometry optimization of other A-type Ln2O3 (Ln=La-Nd) show a satisfactory agreement with experimental data using the lanthanide valence basis sets (6s6p5d)/[4s4p4d]. The cohesive energies of A-Ln2O3 within both conventional Kohn-Sham DFT and the a posteriori-HF correlation DFT schemes are evaluated by using the corresponding augmented sets (8s7p6d)/[6s5p5d] with additional diffuse functions for the atomic energies of free lanthanide atoms. The I2 phases of LaB3O6 and GdB3O6 crystals are more stable than C2 phases according to both of the calculated energetic data and first-principles bond analysis. This is in agreement with the experimental results. A new method is developed to calculate the optical properties for large systems based on available wavefunction correlation approaches in the framework of the incremental scheme. The convergence behaviors of first- and second-order polarizabilities with respect to the domain distances and incremental expansion orders are examined and discussed for the model system Ga4As4H18

Valence Virtual Orbitals: An unambiguous ab initio quantification of the LUMO concept

Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two “frontier orbitals”, which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today’s quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set’s polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. The utility of VVOs is demonstrated for construction of qualitative MO diagrams, for prediction of valence excited states, and as starting orbitals for more sophisticated calculations. This suggests that VVOs are a suitable realization of the LUMO, LUMO + 1, ... concept. VVO generation requires no expert knowledge, as the number of VVOs sought is found by counting s-block atoms as having only a valence s orbital, transition metals as having valence s and d, and main group atoms as being valence s and p elements. Closed shell, open shell, or multireference wave functions and elements up to xenon may be used in the present program

Unconventional and Exotic Magnetism in Carbon-Based Structures and Related Materials

The detailed analysis of the problem of possible magnetic behavior of the carbon-based structures was fulfilled to elucidate and resolve (at least partially) some unclear issues. It was the purpose of the present paper to look somewhat more critically into some conjectures which have been made and to the peculiar and contradictory experimental results in this rather indistinct and disputable field. Firstly the basic physics of magnetism was briefly addressed. Then a few basic questions were thoroughly analyzed and critically reconsidered to elucidate the possible relevant mechanism (if any) which may be responsible for observed peculiarities of the "magnetic" behavior in these systems. The arguments supporting the existence of the intrinsic magnetism in carbon-based materials, including pure graphene were analyzed critically. It was concluded that recently published works have shown clearly that the results of the previous studies, where the "ferromagnetism" was detected in pure graphene, were incorrect. Rather, graphene is strongly diamagnetic, similar to graphite. Thus the possible traces of a quasi-magnetic behavior which some authors observed in their samples may be attributed rather to induced magnetism due to the impurities, defects, etc. On the basis of the present analysis the conclusion was made that the thorough and detailed experimental studies of these problems only may shed light on the very complicated problem of the magnetism of carbon-based materials. Lastly the peculiarities of the magnetic behavior of some related materials and the trends for future developments were mentioned.Comment: 40 pages, 5 tables, 221 Reference

Atomic and electronic structure studies of nano-structured systems : Carbon and related materials

Modeling in the framework of density functional theory has been conducted on carbon nanotubes and graphene nano-structures. The results have been extended to non-carbon systems such as boron nanostructures. Computational studies are complemented by experimental methods to refine the structural models and obtain a better understanding of the electronic structure. It is observed that the zigzag edged bilayered graphene nanoribbons are highly unstable as compared to their armchair counterparts. A novel approach has been proposed for the patterning of chirality/diameter controlled single walled carbon nanotubes. Nanotube formation is found to be assisted by edge ripples along with the intrinsic edge reactivity of different types of bilayered GNRs. The effect of bundling on the electronic structure of single walled carbon nanotubes in zigzag single walled carbon nanotubes has been studied. Hydrostatic pressure effects were examined on bundled single walled carbon nanotubes. Nanotubes with chiral indices (3n + 3, 3n + 3) acquire hexagonal cross-sections on application of hydrostatic pressures. The formation of a novel quasi two-dimensional phase of carbon during hydrostatic compression of small and large nanotubes under extreme conditions of pressure is modeled and is understood to be dictated by breaking of symmetry during compression. Nanoscale materials with anisotropic compressibility do not exhibit symmetric compression as in bulk materials. Structural stability of boron nanoribbons derived from \u27α-sheet\u27 and reconstructed {1221} sheets was studied. Antiaromatic instabilities were found to destabilize nanoribbons constructed from reconstructed {1221} sheets when compared to those obtained from the \u27α-sheet\u27. The stability of the nanoribbons was found to increase with increasing width and increase in the hole density (η) of the boron nanoribbons. The study of electronic structure reveals the presence of semiconducting nanostructures. The presence of nanoscale crystalline domains due to random functionalization has made it difficult to resolve the chemical structure of graphene oxide and it remains a much debated topic to date. A combination of analytical, spectroscopic and density functional techniques have been used to determine the structure and properties of such nano materials. Graphene oxide has unusual exotic properties and belongs to this class of materials. Investigations reveal that the chemical structure of graphene oxide can be visualized as puckered graphene sheets linked by oxygen atoms. Density functional theory has been used to calculate the site projected partial density of states for carbon and oxygen atoms involved in different types of bonding. A comparison of these simulations with carbon and oxygen K-edge absorption spectra has led to an understanding of the basic electronic structure of this material