Sakir Erkoc

STRUCTURAL STABILITY AND ENERGETICS OF SULPHUR MICROCLUSTERS : AN MNDO CALCULATION

Abstract The structural stability and energetics of sulphur microclusters of 2–13 atoms were studied. The semiempirical MNDO method was used to calculate the lowest lying triplet state of S 2 and the singlet states of S 3 -S 13 . The binding energy and ionization potentials of these clusters were calculated. The results agree qualitatively with the available data.

Structural and electronic properties of borazine cyclacenes

Abstract The structural and electronic properties of borazine cyclacenes (BNn) have been investigated by performing semiempirical molecular orbital self-consistent field calculations at the level of AM1 method within the RHF formulation. It has been found that as the number of borazine rings increases in the arenoid belt the structures become more exothermic.

Fundamentals of quantum mechanics

HISTORICAL EXPERIMENTS AND THEORIES Dates of Important Discoveries and Events Blackbody Radiation Photoelectrice Effect Quantum Theory of Spectra TheComptone Effect Matterwaves, the de Broglie Hypothesis The Davisson -Germer Experiment Heisenbergs Uncertainity Principle Difference Between Particles and Waves Interpretation of the Wavefunction AXIOMATIC STRUCTURE OF QUANTUM MECHANICS The Necessity of Quantum Theory Function Spaces Postulates of Quantum Mechanics The Kronecker Delta and the Dirac Delta Function Dirac Notation OBSERVABLES AND SUPERPOSITION Free Particle Particle In A Box Ensemble Average Hilbert -Space Interpretation The Initial Square Wave Particle Beam Superposition and Uncertainty Degeneracy of States Commutators and Uncertainty TIME DEVELOPMENT AND CONSERVATION THEOREMS Time Development of State Functions, The Discrete Case The Continuous Case, Wave Packets Particle Beam Gaussian Wave Packet Free Particle Propagator The Limiting Cases of the Gaussian Wave Packets Time Development of Expectation Values Conservation of Energy and Momentum Conservation of Parity BOUND AND UNBOUND STATES IN ONE-DIMENSION One-Dimensional Schrodinger Equation The Simple Harmonic Oscillator Unbound States One-Dimensional Barrier Problems The Finite Potential Well N-PARTICLE SYSTEMS The Schrodinger Equation for N-Particle Systems Identical Particles The Pauli Principle Fermions and Bosons THE SCHRODINGER EQUATION IN THREE-DIMENSIONS The Two-Body Systems Separation of Variables in the Two-Body Systems Rotational Invariance The Schrodinger Equation for Non-Central Potentials ANGULAR MOMENTUM Commutation Relations Raising and Lowering Operators Eigen Solutions of Angular Momentum Operators Kinetic Energy and Angular Momentum THE RADIAL EQUATION FOR FREE AND BOUND PARTICLES The Radial Schrodinger Equation The Free Particle Three-Dimensional Square Well Potential The Hydrogenatom The Spectra of Hydrogenic Atoms The Virial Theorem INTERACTION OF ELECTRONS WITH ELECTROMAGNETIC FIELD Maxwell s Equations and Gauge Transformations Motion of a Free Electron in a Uniform Magnetic Field Motion of a Bound Electron in a Uniform Magnetic Field The Principal of Gauge Invariance and Flux Quantization MATRIX REPRESENTATIONS Matrix Representations of Wave Functions and Operators Matrix Algebra Types of Matrix Representations Harmonic Oscillator in Matrix Representations Matrix Representations of Angular Momentum Operators SPIN AND THE ADDITION OF ANGULAR MOMENTA Systems with Spin One-Half The Addition of Angular Momenta TIME-INDEPENDENT PERTURBATION THEORY Nondegenerate Perturbation Theory Degenerate Perturbation Theory THE VARIATIONAL METHOD The Variational Principle Linear Variation Functions THE WKB APPROXIMATION Turning Points The Connection Formulas The WKB Approximation to a Potential Well The WKB Approximation to a Potential Barrier TIME-DEPENDENT PERTURBATION THEORY Time -Dependent Schrodinger Equation Time -Dependent Perturbation Approximations Sinusoidal Perturbations Emission and Absorption of Radiation Incoherent Perturbations Selection Rules THE ADIABATIC APPROXIMATION The Adiabatic Processes The Adiabatic Theorem Nonholonomic Processes Experimental Evidences of Nonholonomic Processes PATH-INTEGRATION METHOD An Approximation to Time -Evolution for a Free Particle Path Integral Evaluation of the Free Particle Propagator Equivalence to the Schrodinger Equation SCATTERING THEORY Classical Scattering Theory Center-of-Mass and Laboratory Frames Quantum Scattering Theory The Method of Partial waves (Low -Energy Case) Expansion of a Plane Wave into Spherical Waves Expansion of the Scattering Amplitude Scattering from a Delta Potential Scattering from a Square -Well Potential Scattering from a Hardsphere Scattering of Identical Particles Energy Dependence and Resonance Scattering The Lippman-Schwinger Equation (High-Energy Case) The Greens Function for the Scattering Problem Born Approximation INELASTIC SCATTERING Bibliography and References 409 Appendix 413 Index 417

Borazine embedded cyclacenes-MINDO3 treatment

Abstract The Huckel type cyclacenes having embedded borazine moiety are considered for the semiempirical molecular orbital treatment at the level of MINDO3 type calculations. The structures considered possess three to 10 arenoid rings. It has been found that they should be thermally stable but the endogenicity increases as the size increases. No cryptoannulenic effect is exhibited by these structures on the energies considered, however, on the dipole moments the effect is influential.

Resveratrol and its analogues resveratrol-dihydroxyl isomers: semi-empirical SCF-MO calculations

The structural and electronic properties of resveratrol and its three analogues resveratrol-dihydroxyl isomers have been investigated theoretically by performing semi-empirical self-consistent field molecular orbital theory calculations. The geometry of the systems have been optimized and the electronic properties have been calculated at the level of AM1 method.

Study of the Influence of Transition Metal Atoms on Electronic and Magnetic Properties of Graphyne Nanotubes Using Density Functional Theory

Density functional theory calculations were used to study the adsorption of three transition metal atoms (Fe, Co, and Ni) on the external surface of two zigzag and two armchair graphyne nanotubes. The most stable position for the adsorption of all three metal atoms on all nanotubes is on the acetylenic ring. The metal atom remains in the plane of the acetylenic ring and makes six bonds with neighboring carbon atoms. Fe and Co complexes are magnetic and show different properties such as metal, semimetal, half-semimetal, and half-semiconductor. Ni complexes are nonmagnetic and semiconductive, with a narrower bandgap in comparison to bare tubes. The results of these calculations are relevant for spintronics and the design of future electronic devices.

Quantum mechanical calculations of vibrational transition probabilities in collinear atom-polyatom collisions

Abstract Quantum vibrational transition probabilities for collinear He + C 2 H 2 collisions are reported. The transition (001 → 100) has a relatively large probability, while the probabilities for the transitions (000 → 001) and (000 → 100) are relatively small.

S Autoionizing States of H

1,3S autoionizing states of H- above the n = 1, 2, and 3 ionization threholds are calculated using the time stability theory of autoionization.

Cluster, Surface and Bulk Properties of ZnCd Binary Alloys: Molecular-Dynamics Simulations

The structural and electronic properties of isolated neutral ZnmCdn clusters for m+n £ 3 have been investigated by performing density functional theory calculations at B3LYP level. The optimum geometries, vibrational frequencies, electronic structures, and the possible dissosiation channels of the clusters considered have been obtained. An empirical many-body potential energy function (PEF), which comprices two- and three-body atomic interactions, has been developed to investigate the structural features and energetics of ZnmCdn (m+n=3,4) microclusters. The most stable structures were found to be triangular for the three-atom clusters and tetrahedral for the four-atom clusters. On the other hand, the structural features and energetics of Znn-mCdm (n=7,8) microclusters, and Zn50, Cd50, Zn25Cd25, Zn12Cd38, and Zn38Cd12 nanoparticles have been investigated by performing molecular-dynamics computer simulations using the developed PEF. The most stable structures were found to be compact and three-dimensional for all elemental and mixed clusters. An interesting structural feature of the mixed clusters is that Zn and Cd atoms do not mix in mixed clusters, they come together almost without mixing. Surface and bulk properties of Zn, Cd, and ZnCd systems have been investigated too by performing molecular-dynamics simulations using the developed PEF. Surface reconstruction and multilayer relaxation on clean surfaces, adatom on surface, substitutional atom on surface and bulk materials, and vacancy on surface and bulk materials have been studied extensively.

Structural and electronic properties of perchlorocoronene

Abstract The structural and electronic properties of perchlorocoronene (C24Cl12) have been investigated theoretically by using semiempirical molecular orbital theory at the level of AM1 calculations. The optimized structure and the electronic structure of the molecule are obtained.