Linear combination of atomic orbitals

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions. In a mathematical sense, these wave functions are the basis set of functions, the basis functions, which describe the electrons of a given atom. In chemical reactions, orbital wavefunctions are modified, i.e. the electron cloud shape is changed, according to the type of atoms participating in the chemical bond. It was introduced in 1929 by Sir John Lennard-Jones with the description of bonding in the diatomic molecules of the first main row of the periodic table, but had been used earlier by Linus Pauling for H2+. Mathematical description An initial assumption is that the number of molecular orbitals is equal to the number of atomic orbitals included in the linear expansion. In a sense, n atomic orbitals combine to form n

Design of a Flexure Based Low Frequency Foucault Pendulum

Patrick Robert Flückiger, Simon Nessim Henein, Ilan Vardi

The Foucault pendulum is a well-known mechanism used to demonstrate the rotation of the Earth. It consists in a pendulum launched on linear orbits and, following Mach’s Principle, this line of oscillation will remain fixed with respect to absolute space but appear to slowly precess for a terrestrial observer due to the turning of the Earth. The theoretical proof of this phenomenon uses the fact that, to first approximation, the Foucault pendulum is a harmonic isotropic two degree of freedom (2-DOF) oscillator. Our interest in this mechanism follows from our research on flexure-based implementations of 2-DOF oscillators for their application as time bases for mechanical timekeeping. The concept of the Foucault pendulum therefore applies directly to 2-DOF flexure based harmonic oscillators. In the Foucault pendulum experiment, the rotation of the Earth is not the only source of precession. The unavoidable defects in the isotropy of the pendulum along with its well-known intrinsic isochronism defect induce additional precession which can easily mask the precession due to Earth rotation. These effects become more prominent as the frequency increases, that is, when the length of the pendulum decreases. For this reason, short Foucault pendulums are difficult to implement, museum Foucault pendulum are typically at least 7 meters long. These effects are also present in our flexure based oscillators and reducing these parasitic effects, requires decreasing their frequency. This paper discusses the design and dimensioning of a new flexure based 2-DOF oscillator which can reach low frequencies of the order of 0.1[Hz]. The motion of this oscillator is approximatelyplanar, like the classical Foucault pendulum, and will have the same Foucault precession rate. The construction of a low frequency demonstrator is underway and will be followed by quantitative measurements which will examine both the Foucault effect as well as parasitic precession.

2020

Using X-ray absorption spectra to monitor specific radiation damage to anomalously scattering atoms in macromolecular crystallography

Marc Fleurant, Philip Pattison

Radiation damage in macromolecular crystals is not suppressed even at 90 K. This is particularly true for covalent bonds involving an anomalous scatterer (such as bromine) at the

peak wavelength'. It is shown that a series of absorption spectra recorded on a brominated RNA faithfully monitor the extent of cleavage. The continuous spectral changes during irradiation preserve an

isosbestic point', each spectrum being a linear combination of zero' and infinite' dose spectra. This easily yields a good estimate of the partial occupancy of bromine at any intermediate dose. The considerable effect on the near-edge features in the spectra of the crystal orientation versus the beam polarization has also been examined and found to be in good agreement with a previous study. Any significant influence of the (C-Br bond/beam polarization) angle on the cleavage kinetics of bromine was also searched for, but was not detected. These results will be useful for standard SAD/MAD experiments and for the emerging radiation-damage-induced phasing' method exploiting both the anomalous signal of an anomalous scatterer and the isomorphous' signal resulting from its cleavage.

2007

Valence and conduction band tuning in halide perovskites for solar cell applications

Negar Ashari Astani, Simone Meloni, Giulia Palermo, Ursula Röthlisberger

We performed density functional calculations aimed at identifying the atomistic and electronic structure origin of the valence and conduction band, and band gap tunability of halide perovskites ABX(3) upon variations of the monovalent and bivalent cations A and B and the halide anion X. We found that the two key ingredients are the overlap between atomic orbitals of the bivalent cation and the halide anion, and the electronic charge on the metal center. In particular, lower gaps are associated with higher negative antibonding overlap of the states at the valence band maximum (VBM), and higher charge on the bivalent cation in the states at the conduction band minimum (CBM). Both VBM orbital overlap and CBM charge on the metal ion can be tuned over a wide range by changes in the chemical nature of A, B and X, as well as by variations of the crystal structure. On the basis of our results, we provide some practical rules to tune the valence band maximum, respectively the conduction band minimum, and thus the band gap in this class of materials.

2016

Design of a Flexure Based Low Frequency Foucault Pendulum

Patrick Robert Flückiger, Simon Nessim Henein, Ilan Vardi

2020