952 resultados para idrogeno ionizzato lcao orbitali legame antilegame born oppenheimer rayleigh ritz


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The Born-Oppenheimer approximation is the keystone for molecular dynamics simulations of radiation damage processes; however, actual materials response involves nonadiabatic energy exchange between nuclei and electrons. In this work, time dependent density functional theory is used to calculate the electronic excitations produced by energetic protons in Al. We study the influence of these electronic excitations on the interatomic forces and find that they differ substantially from the adiabatic case, revealing a nontrivial connection between electronic and nuclear stopping that is absent in the adiabatic case. These results unveil new effects in the early stages of radiation damage cascades.

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Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a combined quantum electron-nuclear dynamics is still missing. In this work, we aim to elucidate the theoretical basis for the widely used hopping rules. Naturally, we concentrate thereby on the formal aspects of the TSH. Using a Gaussian wave packet limit, we derive the transition rates governing the hopping process at a simple avoided level crossing. In this derivation, which gives insight into the physics underlying the hopping process, some essential features of the standard TSH algorithm are retrieved, namely (i) non-zero electronic transition rate ("hopping probability") at avoided crossings; (ii) rescaling of the nuclear velocities to conserve total energy; (iii) electronic transition rates linear in the nonadiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770280]

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Cette thèse présente une série d'études qui visent la compréhension de la structure électronique de complexes de métaux de transition en employant diverses méthodes de spectroscopie. L'information sur la structure électronique aide à comprendre et développer des nouveaux matériaux, des nouvelles voies de synthèses, ainsi que des nouveaux modèles théoriques. Habituellement, afin d'explorer la structure électronique d'un système qui comporte en son centre un métal de transition, l'information fournie par les spectres d'un seul composé n'est pas suffisante. On étudie une série de composés similaires, qui ont le même métal de transition à un degré d'oxydation donné, ainsi que des ligands qui forment des liaisons de différentes forces et caractéristiques avec le métal. Cependant, ces changements, bien qu'on les désire de faible impact, créent une grande perturbation de la structure électronique visée par les études. Afin d'étudier en profondeur une seule structure électronique, nous employons une stratégie d'analyse moins perturbante. Nous appliquons une pression hydrostatique sur les complexes de métaux de transition. Cette pression perturbe le système suffisamment pour nous livrer davantage d'informations sur la structure électronique, sans la « dénaturer ». Afin d'étudier précisément ces systèmes perturbés, la technique d'application de pression est conjuguée, dans la littérature, aux diverses techniques de spectroscopie d'absorption UV-visible, de luminescence, ainsi que de diffusion Raman. Pour extraire un maximum d'informations de ces expériences, on emploie des techniques de calculs de structure électronique ainsi que de dynamique des noyaux. Dans cette thèse, on tente de mettre en lumière la structure électronique de composés de molybdène(IV), de platine(II) et palladium(II) à l'aide de la technique de pression couplée aux spectroscopies de luminescence et de diffusion Raman. Dans le chapitre 3, on observe un déplacement de la bande de luminescence de +12 cm-1/kbar entre la pression ambiante et 25 kbar pour le complexe trans-[MoOCl(CN-t-Bu)4]BPh4, dont le centre métallique molybdène(IV)est de configuration électronique 4d2. Il s'agit de la première variation positive observée pour un complexe de type métal-oxo. À des pressions plus élevées, la tendance s'inverse. Le maximum d'énergie de la bande de luminescence se déplace de -8 cm-1/kbar. Ce changement de variation présage d'une compétition interne entre les ligands situés sur les différents axes de l'octaèdre. À l'aide de calculs basés sur la théorie de la fonctionnelle de la densité, on propose un mécanisme pour expliquer ce phénomène. Au cours du chapitre 4, on étudie des complexes de palladium(II) et de platine(II) qui ont les mêmes ligands. Un de ces ligands est le 1,4,7-trithiacyclononane (ttcn). On constate qu'à basse pression le ligand est bidentate. Par contre, lorsque la pression augmente, on constate, par exemple à l'aide du complexe [Pt(ttcn)Cl2], qu'une interaction anti-liante supplémentaire se produit entre le ligand ttcn et le métal, ce qui change la nature de l'orbitale HOMO. On observe un déplacement de la bande de luminescence de -19 cm-1/kbar. Tel que pour le complexe de molybdène(IV), le déplacement de la bande de luminescence dépend de la compétition entre les ligands situés sur les différents axes de l'octaèdre. L'interaction liante entre l'ion platine(II) et l'atome de soufre axial est l'effet le plus plausible qui peut induire un déplacement de la bande de luminescence vers les basses énergies. Ceci nous indique que cette interaction domine. Par contre, pour ce qui est du complexe palladium(II), la compétition est remportée par d'autres effets, car le déplacement de la bande de luminescence est de +6 cm-1/kbar. Encore une fois, des calculs, basés sur la théorie de la fonctionnelle de la densité, aident à explorer les causes de ces observations en suggérant des explications corroborées simultanément par les diverses expériences de spectroscopie. Lors du chapitre 5, une étude plus exacte de la structure électronique ainsi que de la dynamique des noyaux de complexes de métaux de transition est présentée. En effet, les complexes de palladium(II) et de platine(II), de type [M(X)4]2-, ont une structure simple, très symétrique. Le premier état excité de ces molécules subit la distorsion Jahn-Teller. On veut établir un protocole de travail pour les expérimentateurs afin d'analyser des spectres de molécules pour lesquelles l'approximation de Born-Oppenheimer n'est pas valide. On utilise la théorie de la fonctionnelle de la densité dépendante du temps ainsi que le modèle de Heidelberg afin de décrire des effets non adiabatique. On tente d'établir l'influence des effets non adiabatiques sur les spectres de ce type de complexe.

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Wir entwickeln die Starkfeldnäherung für die Erzeugung hoher Harmonischer in Wasserstoffmolekülen, wobei die Vibrationsbewegung berücksichtigt wird, sowie die laserinduzierte Kopplung zwischen den beiden untersten Born-Oppenheimer-Zuständen im Molekülion, das durch die anfängliche Ionisation des Moleküls erzeugt wird. Wir zeigen, dass die Kopplung bei längeren Laserwellenlängen (≈ 2 μm) wichtig wird und zu einer Reduzierung der Erzeugung von Harmonischen führt, sowie zu einer Änderung des Verhältnisses von Harmonischen in verschiedenen Isotopen. ----------------------------------------------------------------------- We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths (≈ 2 μm), leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.

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We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

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The triatomic spin-rovibronic variational code RVIB3 has been extended to include the effect of two uncoupled electrons, for both (3)Sigma(-) and (3)Pi (Renner-Teller) electronic states. The spin-orbital-rotational kinetic energy is included in the usual way, via terms (J+L+S). The phenomenological terms AL.S and lambda 2/3(3S(z)(2)) are introduced to reproduce the 3 spin-orbit and spin-spin splittings, respectively. Calculations are performed to evaluate the spin-rovibronic energy levels of CCO (X) over tilde (3) Sigma(-) and CCO (A) over tilde (3) Pi for which the Born-Oppenheimer potentials are derived from high-accuracy ab initio calculations.

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We study the elastic scattering of positronium atoms by hydrogen atoms at medium energies using partial-wave Born-Oppenheimer (BO) exchange amplitudes and report accurate BO cross sections in the energy range 0 to 60 eV. The present BO results agree with a 22-state R-matrix and a five-state coupled-channel model potential calculation, but disagree strongly with a conventional close-coupling calculation as well as its input BO amplitudes at medium energies.

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In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Using the hyperspherical adiabatic approach in a coupled-channel calculation, we present precise binding energies of excitons trapped by impurity donors in semiconductors within the effective-mass approximation. Energies for such three-body systems are presented as a function of the relative electron-hole mass sigma in the range 1 less than or equal to1/sigma less than or equal to6, where the Born-Oppenheimer approach is not efficiently applicable. The hyperspherical approach leads to precise energies using the intuitive picture of potential curves and nonadiabatic couplings in an ab initio procedure. We also present an estimation for a critical value of sigma (sigma (crit)) for which no bound state can be found. Comparisons are given with results of prior work by other authors.

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We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schrödinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The BO expression is derived using separable potentials and yields a concise adiabatic potential between the two heavy particles. The BO potential is Coulomb-like and exponentially decreasing at small and large distances, respectively. While we find similar qualitative features to previous studies, we find important quantitative differences. Our results demonstrate that mass-imbalanced systems that are accessible in the field of ultracold atomic gases can have a rich three-body bound state spectrum in two-dimensional geometries. Small light-heavy mass ratios increase the number of bound states. For 87Rb-87Rb-6Li and 133Cs- 133Cs-6Li we find respectively three and four bound states. © 2013 IOP Publishing Ltd.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Si considera nell'approssimazione di Born-Oppenheimer una molecola pluriatomica, di cui due livelli elettronici presentano la configurazione di una buca stabile sovrapposta a una instabile. Si dimostra che, con un errore inversamente proporzionale alla massa dei nuclei, le risonanze coincidono con autovalori di due specifici operatori scalari autoaggiunti.

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Lo spazio fra le stelle nelle galassie non è vuoto, ma è composto da gas rarefatto, particelle di polvere, un campo magnetico, elettroni, protoni e altri nuclei atomici relativistici; spesso questi elementi possono essere considerati come un’unica entità di- namica: il mezzo interstellare o più semplicemente ISM. Nel primo capitolo vedremo come il mezzo si distribuisce generalmente all’interno delle galassie a spirale, in fasce di temperatura sempre minore man mano che ci si allontana dal centro (HIM, WIM, WNM, CNM). La conoscenza della distribuzione del mezzo è utile per poter comprendere maggiormente i processi di emissione e le varie zone in cui questi avvengono in una tipica galassia a spirale, che è lo scopo di questa tesi. L’ISM infatti entra in gioco in quasi tutti i processi emissivi, in tutte le bande di emis- sione dello spettro elettromagnetico che andremo ad analizzare. Il nostro modo di vedere le galassie dell’universo è molto cambiato infatti nel corso dell’ultimo secolo: l’utilizzo di nuovi telescopi ci ha permesso di andare ad osservare le galassie anche in bande dello spettro diverse da quella visibile, in modo da raccogliere informazioni impossibili da ottenere con la sola banda ottica. Nel secondo capitolo andremo ad analizzare cinque bande di emissione (banda X, ot- tica, radio, gamma e infrarossa) e vedremo come appaiono tipicamente le galassie a spirale a lunghezze d’onda differenti, quali sono i processi in gioco e come il mezzo interstellare sia fondamentale in quasi ogni tipo di processo. A temperature elevate, esso è responsabile dell’emissione X della galassia, mentre re- gioni più fredde, formate da idrogeno ionizzato, sono responsabili delle righe di emis- sione presenti nello spettro ottico. Il campo magnetico, tramite le sue interazioni con elettroni relativistici è la principale fonte dell’emissione radio nel continuo di una galas- sia a spirale, mentre quella in riga è dovuta a idrogeno atomico o a gas freddo. Vedremo infine come raggi cosmici e polvere, che fanno sempre parte del mezzo inter- stellare, siano rispettivamente la causa principale dell’emissione gamma e infrarossa.