Combinaison linéaire d'orbitales atomiques

Résumé

En chimie quantique, une combinaison linéaire d'orbitales atomiques (CLOA) représente la superposition d'orbitales atomiques et permet de calculer les orbitales moléculaires. En effet, dans une molécule le nuage d'électrons est modifié et dépend des atomes participant aux liaisons chimiques : la CLOA permet d'approximer cette nouvelle fonction d'onde en se basant sur celles de chaque élément pris individuellement. Cette méthode a été introduite en 1929 par John Lennard-Jones pour décrire les liaisons des molécules diatomiques de la première ligne du tableau périodique des éléments, mais elle a été utilisée auparavant par Linus Pauling pour H2+. Elle est aussi utilisée en physique du solide pour établir la structure de bande d'un matériau. Formulation mathématique Les fonctions de base combinent les fonctions d'onde pour représenter une orbitale moléculaire. Considérons un système composé de plusieurs éléments de base i (par exemple des atomes) centrés en

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, ,

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

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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

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, , ,

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

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