Dissertations / Theses on the topic 'Quantum States - Diatomic Molecules'

Through continual advancement in laser pulse technology. experimentalists now have al their disposal higher intensities (> 1015 W cm!) and shon.er pulse durations « 10 fs) than ever before. Using sllch technology it is possible to probe and manipulate the electronic and nuclear Illotions in even the smallest fastest-moving diatomic molecules. The first pan. of this thesis presents a simplified theoretical model that allows one to adequately treat the nuclear vibrational and photodissociation dynamics of the O2 ' molecular ion, when subjected to typical infrared wavelengths. Direct comparison between the predictions of this theoretical model and recent experimental observations is provided. The same model is then used as a basis for the proposal of a number of novel techniques that utilize ultrashort laser pulses to l;:ontrol both the dissociation pathway and the population ofthe bound vibrational levels. One of the main areas of theoretical and experimental advancement in recent decades has been the area of cold atom trapping and manipulation. The second part of this thesis considers the theoretical treatment of two interacting particles, confined in various one-dimensioDal potentials. These systems represent a fundamental building block that has been made accessible through recent developments in the field of ultracold atomic physics: The numerical scheme for the treatment of the two-particle system is described and results are presented for two-paJ1icles in a harmonic trap, a o-split harmonic trap. and a double-well potential. Propel1ies of the two-particle ground state and low-energy excited states are examined including the energy spectra, eigenfunctions, reduced single-particle density matrices, momentum distributions and entanglement. ]n particular, focussing upon how these quantities depend upon the two parameters, particle-particle interaction strength and barrier height. In this way, the present work relates to the scope of quantum state control, in such systems, through variation of 'experimentally accessible' control parameters.

The work carried out during this thesis focuses on the quantum dynamics of the diffusion of hydrogen atoms on a surface of palladium (111). The study of the 3D system allowed us to detail the infrared spectrum of H/Pd (111), showing the existence of different adsorption sites on which localized states exist that are strongly coupled (Fermi resonance). This phenomenon governs the diffusion of hydrogen atoms in an ultra-fast time scale (fs).The study of the (6D) H2/Pd(111) system has shown that the transitions observed are in fact transition bands between several quasi-degenerate adsorption states. The agreement between the calculated and measured values is significantly less good than that between the data calculated for the 3D system and the measured data. Does adsorbed hydrogen on palladium exist in the form of a weakly bound H2 molecule? This thesis has provided some answers to this question, which remains open, hovewer, to some extent.

The main theme covered in this thesis is experimentalstudies of quantum dynamics and coherent control in homonuclearalkali diatomic molecules by ultrafast laser spectroscopy iththe implementation of pump-probe techniques.

A series of experiments have been performed on the Rb2molecules in a molecular beam as well as in a thermal oven. Thereal-time molecular quantum dynamics of the predissociatingelectronically excited D(3)¹Πu state of Rb₂, which couples to/intersects several otherneighbouring states, is investigated using wavepackets. Thepredissociation of the D state, explored by this wavepacketmethod, arises from two independent states, the (4)³Σ_u⁺and (1)³∆_u, for which the second corresponds to a much fasterdecay channel above a sharp energy threshold around 430 nm. Thelifetime of the D state above the energy threshold is obtained,τ ≈ 5 ps, by measuring the decay time of thewavepacket in a thermal oven. Further experimentalinvestigation performed in a molecular beam together withquantum calculations of wavepacket dynamics on the D state haveexplored new probe channels of wavepacket evolution: theD′(3)1Σu+ channel, which exhibits vibrational motionin a shelf state and the (4)³Σu+ channel, where direct build-up of thewavefunction is observed due to its spin-orbit oupling to the Dstate.

The real-time quantum dynamics of wavepackets confined totwo bound states, A¹Σ_u⁺(0_u⁺) and b³Π_u(0_u⁺), have been studied by experiment andcalculations. It is shown that these two states are fullycoupled by spin-orbit interaction, characterised by itsintermediate strength. The intermediate character of thedynamics is established by complicated wavepacket oscillationatterns and a value of 75 cm^-1is estimated for the coupling strength at thestate crossing.

The experiments on the Li₂molecule are performed by coherent control ofrovibrational molecular wavepackets. First, the Deutsch-Jozsaalgorithm is experimentally demonstrated for three-qubitfunctions using a pure coherent superposition of Li₂rovibrational eigenstates. The function’scharacter, either constant or balanced, is evaluated by firstimprinting the function, using a phase-tailored femtosecond(fs) pulse, on a coherent superposition of the molecularstates, and then projecting the superposition onto an ionicfinal state using a second fs pulse at a specific delay time.Furthermore, an amplitude-tailored fs pulse is used to exciteselected rovibrational eigenstates and collision induceddephasing of the wavepacket signal, due to Li₂-Ar collisions, is studied experimentally. Theintensities of quantum beats decaying with the delay time aremeasured under various pressures and the collisional crosssections are calculated for each well-defined rovibrationalquantum beat, which set the upper limitsfor ure dephasingcross sections.

Keywords:Ultrafast laser spectroscopy, pump-probetechnique, predissociation, wavepacket, pin-orbit interaction,coherent control, (pure) dephasing

In this work an attempt has been made to develop a computer program package that can be used to simulate/model spectra and other properties of the majority of diatomic molecules. Specifically, the program package aims at: (i) providing a general tool for the interpretation of experimental spectra and for pointing out any perturbation that may exist in them; and (ii) to help researchers in setting up their experiment and know in advance optimum conditions to perform it. The program package under development at present includes the following features: 1. Generation of molecular potentials; 2. Calculation of Frank-Condon factors and transition probabilities; 3. Simulation of spectra in adsorption, emission, laser-induced fluorescence and resonance ionisation; 4. The inclusion of thermal and non-thermal level population distribution; 5. In case of perturbations, the ability to read the energies of the levels as input parameters, rather than calculating them for inadequate formulas based on standard spectroscopic constants. The program package was tested for a few diatomic molecules, selected specifically to be representative for typical cases in laser absorption and emission spectroscopy.

Cette thèse s'articule autour de développements méthodologiques sur l'évaluation théorique des énergies quantiques et relativistes d'état électroniquement excité d'atome ou de molécule. La méthode basée sur la fonction d'onde "Coupled Cluster" (CC) est à l'heure actuelle, une des méthodes les plus précise pour calculer ces états pour les systèmes à N-corps. L'implémentation présentée est basée sur un Hamiltonien relativiste à N-corps: Dirac-Coulomb à 4 composantes et une fonction d'onde "Coupled Cluster" au rang d'excitation arbitraire. Les états excités sont évalués via la théorie de la réponse linéaire, en diagonalisant la matrice Jacobienne Coupled Cluster. L'accent des travaux se porte sur l'évaluation de ses éléments en seconde quantification via un nouvel algorithme basé sur les commutateurs, et sur son adaptation au formalisme relativiste de Dirac à 4 composantes. Enfin, des applications du code à des molécules diatomiques non triviales seront présentées
This thesis focuses on methodological developments of the theoretical evaluation of the quantum and relativistic energy of electronically excited states of an atom or a molecule. The wave-function method Coupled Cluster (CC) is currently one of the most accurate methods to calculate these states for many-body systems. The implementation presented is based on the many-body relativistic 4-component Dirac-Coulomb Hamiltonian and a Coupled Cluster wave function at arbitrary excitation rank. The excited states are evaluated using linear response theory by diagonalizing the Coupled Cluster Jacobian matrix. The work focuses on the evaluation of these second-quantized elements using a new commutator-based algorithm, and on its adaptation to a Dirac 4-component relativistic formalism. Finally, I present some applications of the code to challenging diatomic molecules

Notre travail de recherche concerne l’étude théorique de la structure électronique des molécules diatomiques telles que les mono-halogénures d’Aluminium AlX(X=Br,I) et les mono-halogénures de Lutécium LuX(X=F,Cl). Les méthodes ab-initio sont utilisées pour réaliser notre étude. Il s’agit des méthodes Hartree-Fock SCF, CASSCF (Complete Active-Space Self-Consistent Field) et les méthodes d’interaction de configuration multi-référence MRCI avec et sans la correction de Davidson. Ces calculs sont effectués à l’aide du progiciel en chimie quantique MOLPRO, en bénéficiant de l’usage de l’interface graphique GABEDIT. Nos résultats ont regroupé les courbes d’énergie potentielle CEPs, les constantes spectroscopiques, y compris la fréquence harmonique ωe (cm-1), la distance internucléaire à l’équilibre Re (Å) et la valeur énergétique Te(cm-1) pour un ensemble des états électroniques singulets et triplets de représentation 2s+1Λ(+/-) (L’effet de spin-orbite est négligeable) pour ces quatre molécules. Par comparaison entre nos résultats obtenus et ceux apportés de la littérature, on a trouvé un bon accord avec un faible pourcentage d’erreur ne dépassent pas le 3% par rapport à la valeur expérimentale considérée comme valeur exacte
Our research concerns the theoretical study of the electronic structure of diatomic molecules such as Aluminum mono-halides AlX (X = Br,I) and Lutetium mono-halides LuX (X = F, Cl). The ab-initio methods are used for our study. These methods SCF, CASSCF (Complete Active-Space Self-Consistent Field) and interaction of configuration multi-reference MRCI with and without Davidson correction. These calculations are performed using the quantum chemistry software package MOLPRO, benefiting from the use of graphic interface GABEDIT. Our findings have consolidated the potential energy curves PECs, spectroscopic constants, including harmonic frequency ωe(cm-1), the internuclear distance at equilibrium Re(Å) and energy Te(cm-1) for a set of singlet and triplet electronic states in the representation 2s +1 Λ (+/-) (neglecting spin-orbit effects) for these four molecules. By comparison between our results and those contributed to the literature, we found a good agreement with a low percentage of error does not exceed 3% from the experimental value was considered as exact

Nesta tese de doutorado apresentamos os resultados de quatro tópicos referentes a estudos de propriedades elétricas que são interpretados com o auxílio da Teoria Quântica de Átomos em Moléculas (QTAIM). No primeiro deles, foram calculados momentos de dipolo e suas derivadas através de um novo formalismo de divisão de átomos em moléculas, baseado em campos de forças de Ehrenfest (CFE), sendo que estes dados são comparados com aqueles advindos da QTAIM. Desta forma, um modelo alternativo de partição em carga - fluxo de carga - fluxo de dipolo (CFCFD) é discutido para derivadas do momento dipolar. Os resultados gerais obtidos pelo formalismo CFE foram satisfatórios em termos quantitativos, embora QTAIM ainda fornece uma descrição mais apropriada destes fenômenos das polarizações atômicas e de suas variações durante vibrações. Na sequência, investigamos os Atratores Não Nucleares (NNAs), que são identificados através de uma análise QTAIM da densidade eletrônica. O nosso intuito foi descobrir novas moléculas que apresentam essa peculiaridade, bem como encontrar padrões entre os casos encontrados que permitam contribuir para o entendimento dos fatores que levam ao seu aparecimento. Para isso trabalhamos com moléculas diatômicas homonucleares de elementos representativos com números atômicos que variavam de Z=1 até Z=38 e moléculas heteronucleares formadas pela combinação dos mesmos. Os nossos dados mostram que NNAs podem ser encontrados em alguns pontos dentro da faixa de distâncias internucleares investigada para quase todos os sistemas diatômicos homonucleares, exceto para as moléculas de Hidrogênio, Hélio e Estrôncio. Por sua vez, encontramos trinta casos de NNAs em sistemas heteronucleares, muitos dos quais ainda inéditos na literatura. Descobrimos também que a polarizabilidade atômica aparentemente tem um papel importante na explicação dos casos encontrados. Tratamos também de moléculas contendo interações fracas como as de Van der Waals (moléculas tri-atômicas contendo um gás nobre ligado a um composto diatômico iônico) de modo a investigar os valores de dipolos atômicos QTAIM de uma maneira mais direta, ou seja, via comparação com um modelo simples para estes compostos. Por fim, estudamos moléculas em estados excitados, sendo que nossa análise focou em dois casos peculiares (CO e de CF2N2) que apresentam momento de dipolo nulo no estado fundamental, enquanto valores significativos desta propriedade são observados em seus primeiros estados excitados. Desta forma, QTAIM foi fundamental para compreender como o processo de excitação pode levar à mudanças tão significativas em tais propriedades elétricas.
In this PhD thesis we present the results of four different topics that refer to a study of electric properties interpreted with The Quantum Theory of Atoms and Molecules (QTAIM). First, dipole moments and their derivatives were calculated from a new formalism based on Ehrenfest Force Fields (EFF) and a comparison with data from QTAIM is carried out. Therefore, the Charge-Charge Flux-Dipole Flux (CCFDF) model was discussed for the dipole moment derivatives. The results from EFF were satisfactory in quantitative terms although QTAIM still seems to be better for the description of atomic polarization and its variations during vibrations. In the sequence, we investigated the Non-Nuclear Attractors (NNAs) that could be identified with the QTAIM formalism. Our intention was to discover new molecules that present this peculiarity, as well as to find trends among these cases that allow contributing for the understanding of the factors that lead to their appearance. For this purpose, we selected homonuclear diatomic molecules of elements presenting atomic numbers ranging from Z=1 to Z=38 and heteronuclear diatomic molecules containing these same elements. Our data shows that NNAs could be found in almost every homonuclear molecule expect by the systems formed by Hydrogen, Helium, and Strontium. On other hand, we have found 30 cases of NNAs in heteronuclear molecules, many of them seen for the first time. We also have noticed that the atomic polarizabilities play a main role in the understanding of these cases. We also treated molecules containing weak Van der Waals interactions (triatomic complexes presenting a noble gas bonded to a diatomic ionic molecule) in order to investigate the atomic dipole values obtained with QTAIM in a direct way, that is, by means of a comparison using a simple model for this kind of bonding. Finally, we studied molecules in excited states. Our focus was in two peculiar cases (CO and CF2N2), which present null dipole moments in their ground states but exhibit significant dipole moment values in their first excited states. Therefore, QTAIM was fundamental to understand how the excitation process can lead to important changes in electric properties.

Calcul des courbes de potentiel adiabatiques pour les géométries colinéaires et perpendiculaires, à l'aide d'un pseudopotentiel dépendant du moment orbital électronique et d'une approche à deux centres; bon accord avec les calculs ab initio existants. Examen des différentes symétries de ces systèmes dans le formalisme de la théorie des groupes, afin d'étudier les valeurs propres et facteurs propres de l'hamiltonien électronique. Calcul quantique des sections efficaces relatives des transitions de structure fine de Rb induites par collision avec H(2) ou D(2). En tenant compte des niveaux rotationnels moléculaires, obtention d'un très bon accord avec les résultats expérimentaux et interprétation de l'effet isotopique

碩士
國立交通大學
電子物理系
89
This thesis studies basically the behaviors of the rotational states of an adsorbed diatomic molecule on the surface of a solid under the acting of the external electric field. The content of this thesis is main by divided into three points. In the first points we calculate the rotational energy of a rotator that is hindered inside a finite conical well and finite quadrilateral conical well. In the next point we calculate the behaviors of the rotational energy levels of the hindered rotor generated by the external electric fields. In the final point, we calculate the distribution of the rotational spectra of the rotor caused by the electric field. By comparing the calculating result of finite conical well and that of finite quadrilateral conical well, we can find out the effect caused by the symmetry change of the solid surface. Our results can be also proved by drawing the 3-D distribution of the wave function. The calculated rotational states and spectra under the electric field manifest that they depend quite sensitively on the electric fields. We explain this phenomenon by using the distribution of the wave function and breakdown of symmetry of the system. The calculating results of this thesis can provide very useful data for future studies of experimenters .

碩士
國立交通大學
電子物理系
88
This thesis is devoted to the studies on the rotational states of adsorbed diatomic molecules under the external electric fields. By using the matrix method, the rotational state energies of the hindered rotor were obtained. Our results show that the rotational states of adsorbed diatomic molecules have large energy shifts as well as the free dipole molecules in the very large external electric field. When the field strength is smaller compared with the hindering potential, the Stark effect is suppressed by the conical well and is not prominent. We have also found that the energy levels possess abrupt turning points. The pit and concave places between adjacent levels are very close but do not cross to each other. We convert the hindering potential into the one-dimensional periodic potential and successfully explain the circumstances that the energy levels vary with the electric strengths. For the energy turning points, a simple model is employed to each other to explain this phenomenon. The angular distributions of the wave functions also manifest that adjacent levels are so close at the turning places. Besides, from the Hellmann-Feynman theorem, it is clearly able to point out how many turning places are there for the same level. A complete description about the rotational states of adsorbed diatomic molecules under the external electric fields is presented in the thesis.

碩士
國立臺灣大學
物理研究所
97
We present an ab initio study of the time-dependent density-functional theory (TDDFT) with proper asymptotic long-range potential for nonperturbative treatment of multi-photon processes of diatomic molecules in strong laser field. For accurate and efficient treatment of the TDDFT equations, the generalized pseudospectral method (GPS) is extended to two-center molecules system. The procedure allows nonuniform and optimal spatial grid discretization of the Hamiltonian in prolate spheroidal coordinates and the time propagation using the split-operator technique in the energy representation. The multiphoton ionization and high-order harmonic generation (HHG) of diatomic molecules N2, CO, and O2 in intense short laser pulse fields are calculated in detail. We observe both the electronic binding energy and the orientation of the orbitals affect the ionization rate. In the analysis of HHG, the highest occupied molecular orbital (HOMO) has dominant contribution, but accurate results have to be obtained with all-electron study. The CO molecule has a small permanent dipole moment cause the different nonlinear optical response to homonuclear molecules such as generating both even and odd harmonics. We also practice the optimal control theory using time-dependent targets on the two-level system with use of the conjugate gradient algorithm, therefore greatly reducing the number of iterations to reach convergence.

Ultrazimne molekuły, tj. molekuły schłodzone do temperatur ponizej 1 mK, stanowiazupełnie nowe pole badawcze na granicy chemii i fizyki. Wiele fascynujacychzastosowan ultrazimnych molekuł zostało opublikowane w literaturze w kontekscie dokładnejspektroskopii, poszukiwan efektów fizycznych poza Modelem Standardowym,kontroli reakcji chemicznych i wielu innych. Wiekszosc eksperymentów przeprowadzanychz uzyciem zimnych molekuł wymaga pewnej formy wsparcia teoretycznego. Tareguła stosuje sie zarówno na etapie projektowania nowych eksperymentów, jak i interpretacjijuz istniejacych. Metody teoretyczne uzywane w tym celu musza spełniacszereg waznych wymagan m.in. musza byc stosowalne do lekkich i ciezkich atomów,a takze musza byc dokładne i dawac wiarygodne wyniki.Głównym celem niniejszej pracy jest zastosowanie orbitali Slatera do obliczenab initio układów dwuatomowych, które sa bardzo czesto badane w rezimie ultrazimnym.Orbitale Slatera stanowia naturalna baze dla rozwiniecia funkcji falowejwieloelektronowych atomów i molekuł. Orbitale the wywodza sie z dokładnego analitycznegorozwiazania równania Schr¨odingera dla atomu wodoru i posiadaja szeregoptymalnych własnosci analitycznych np. ostrze w połozeniu jadra i prawidłowy zanikdalekozasiegowy.Wzwiazku z tym mozna oczekiwac istotnych korzysci w dokładnoscii wydajnosci obliczen jesli orbitale Slatera zastosuje sie jako baze do rozwiniecia orbitalimolekularnych. Własciwie jedynym powodem dla którego orbitale Slatera nie sastosowane rutynowo w obliczeniach kwantowo-chemicznych sa trudnosci w obliczaniuwielocentrowych elementów macierzowych powstajacych jako skutek oddziaływaniakulombowskiego miedzy elektronami.Stworzenie nowych, ogólnych technik wydajnego obliczania tych elementów macierzowychdla układów dwuatomowych jest pierwszym wyzwaniem niniejszej pracy.Zaproponowano szereg nowych metod rozwiazania tego problemu, które zostałyzaprogramowane z uzyciem nowoczesnych technik programistycznych (paralelizacjaetc.) i przetestowane dla szerokiego zakresu wystepujacych parametrów. Pozwoliło towykonywac rutynowe obliczenia dla molekuł dwuatomowych w bazach orbitali Slaterazawierajacych wysokie momenty pedu (l ¬ 6). Nastepnie przedstawione zostałyogólne zasady konstrukcji i optymalizacji baz Slatera przeznaczonych do obliczen abinitio o wysokiej dokładnosci. Liczne obliczenia testowe i porównania z danymi referencyjnymidowodza poprawnosci zaproponowanego schematu. Rozwazone zostałyrówniez sposoby ekstrapolacji wyników do granicy bazy zupełnej.Kolejnym waznym celem niniejszej pracy było połaczenie bazy orbitali Slatera zteoria efektywnych potencjałów rdzenia. Potencjały efektywne sa szeroko stosowane wobliczeniach kwantowo-chemicznych, szczególnie dla ciezkich atomów, w celu usunieciaczesci elektronów rdzeniowych i wprowadzenia efektów relatywistycznych do opisuteoretycznego. Pokazano, ze elementy macierzowe potencjałów efektywnych w bazieorbitali Slatera moga byc obliczane z uzyciem metody przesuniec Barnetta-Coulsona.Co istotne, w koncowych wyrazeniach nie pojawiaja sie nieskonczone sumowania. Topodejscie zostało zastosowane równiez do obliczen z wykorzystaniem tzw. potencjałówpolaryzacji rdzenia i efektywnych operatorów spin-orbita.W celu ilustracji przydatnosci metod opracowanych w niniejszej pracy wykonanospektroskopowo dokładne obliczenia kompletnych krzywych energii oddziaływaniadla dwóch układów molekularnych (dimer litu w stanie a3+u i dimer berylu w staniepodstawowym) z wykorzystaniem baz orbitali Slatera. W przypadku czasteczkiLi2 wyznaczone teoretycznie parametry spektroskopowe (energia wiazania, geometriarównowagowa, energie poziomów wibracyjnych, etc.) róznia sie od najdokładniejszychwyników doswiadczalnych o mniej niz jedna czesc na tysiac. Czasteczka Be2 stanowitroche bardziej skomplikowany układ jednak uzyskana dokładnosc pozwoliła potwierdzicistnienie słabo zwiazanego dwunastego poziomu wibracyjnego. W opisie obuukładów uwzgledniono subtelne efekty relatywistyczne i elektrodynamiki kwantowej.Rozprawa napisana jest w jezyku angielskim. Piec oryginalnych artykułów badawczychopublikowanych w czasopismach naukowych o zasiegu miedzynarodowym(Phys. Rev. A, Phys. Rev. E, J. Math. Chem.) i dwa (jeszcze nieopublikowane) przeddrukistanowia rdzen niniejszej pracy i zawieraja dokładny opis uzyskanych wyników.Pozostałe nieopublikowane wyniki sa opisane w osobnej sekcji pracy i zostana opublikowanew bliskiej przyszłosci.
Ultrazimne molekuły, tj. molekuły schłodzone do temperatur ponizej 1 mK, stanowiazupełnie nowe pole badawcze na granicy chemii i fizyki. Wiele fascynujacychzastosowan ultrazimnych molekuł zostało opublikowane w literaturze w kontekscie dokładnejspektroskopii, poszukiwan efektów fizycznych poza Modelem Standardowym,kontroli reakcji chemicznych i wielu innych. Wiekszosc eksperymentów przeprowadzanychz uzyciem zimnych molekuł wymaga pewnej formy wsparcia teoretycznego. Tareguła stosuje sie zarówno na etapie projektowania nowych eksperymentów, jak i interpretacjijuz istniejacych. Metody teoretyczne uzywane w tym celu musza spełniacszereg waznych wymagan m.in. musza byc stosowalne do lekkich i ciezkich atomów,a takze musza byc dokładne i dawac wiarygodne wyniki.Głównym celem niniejszej pracy jest zastosowanie orbitali Slatera do obliczenab initio układów dwuatomowych, które sa bardzo czesto badane w rezimie ultrazimnym.Orbitale Slatera stanowia naturalna baze dla rozwiniecia funkcji falowejwieloelektronowych atomów i molekuł. Orbitale the wywodza sie z dokładnego analitycznegorozwiazania równania Schr¨odingera dla atomu wodoru i posiadaja szeregoptymalnych własnosci analitycznych np. ostrze w połozeniu jadra i prawidłowy zanikdalekozasiegowy.Wzwiazku z tym mozna oczekiwac istotnych korzysci w dokładnoscii wydajnosci obliczen jesli orbitale Slatera zastosuje sie jako baze do rozwiniecia orbitalimolekularnych. Własciwie jedynym powodem dla którego orbitale Slatera nie sastosowane rutynowo w obliczeniach kwantowo-chemicznych sa trudnosci w obliczaniuwielocentrowych elementów macierzowych powstajacych jako skutek oddziaływaniakulombowskiego miedzy elektronami.Stworzenie nowych, ogólnych technik wydajnego obliczania tych elementów macierzowychdla układów dwuatomowych jest pierwszym wyzwaniem niniejszej pracy.Zaproponowano szereg nowych metod rozwiazania tego problemu, które zostałyzaprogramowane z uzyciem nowoczesnych technik programistycznych (paralelizacjaetc.) i przetestowane dla szerokiego zakresu wystepujacych parametrów. Pozwoliło towykonywac rutynowe obliczenia dla molekuł dwuatomowych w bazach orbitali Slaterazawierajacych wysokie momenty pedu (l ¬ 6). Nastepnie przedstawione zostałyogólne zasady konstrukcji i optymalizacji baz Slatera przeznaczonych do obliczen abinitio o wysokiej dokładnosci. Liczne obliczenia testowe i porównania z danymi referencyjnymidowodza poprawnosci zaproponowanego schematu. Rozwazone zostałyrówniez sposoby ekstrapolacji wyników do granicy bazy zupełnej.Kolejnym waznym celem niniejszej pracy było połaczenie bazy orbitali Slatera zteoria efektywnych potencjałów rdzenia. Potencjały efektywne sa szeroko stosowane wobliczeniach kwantowo-chemicznych, szczególnie dla ciezkich atomów, w celu usunieciaczesci elektronów rdzeniowych i wprowadzenia efektów relatywistycznych do opisuteoretycznego. Pokazano, ze elementy macierzowe potencjałów efektywnych w bazieorbitali Slatera moga byc obliczane z uzyciem metody przesuniec Barnetta-Coulsona.Co istotne, w koncowych wyrazeniach nie pojawiaja sie nieskonczone sumowania. Topodejscie zostało zastosowane równiez do obliczen z wykorzystaniem tzw. potencjałówpolaryzacji rdzenia i efektywnych operatorów spin-orbita.W celu ilustracji przydatnosci metod opracowanych w niniejszej pracy wykonanospektroskopowo dokładne obliczenia kompletnych krzywych energii oddziaływaniadla dwóch układów molekularnych (dimer litu w stanie a3+u i dimer berylu w staniepodstawowym) z wykorzystaniem baz orbitali Slatera. W przypadku czasteczkiLi2 wyznaczone teoretycznie parametry spektroskopowe (energia wiazania, geometriarównowagowa, energie poziomów wibracyjnych, etc.) róznia sie od najdokładniejszychwyników doswiadczalnych o mniej niz jedna czesc na tysiac. Czasteczka Be2 stanowitroche bardziej skomplikowany układ jednak uzyskana dokładnosc pozwoliła potwierdzicistnienie słabo zwiazanego dwunastego poziomu wibracyjnego. W opisie obuukładów uwzgledniono subtelne efekty relatywistyczne i elektrodynamiki kwantowej.Rozprawa napisana jest w jezyku angielskim. Piec oryginalnych artykułów badawczychopublikowanych w czasopismach naukowych o zasiegu miedzynarodowym(Phys. Rev. A, Phys. Rev. E, J. Math. Chem.) i dwa (jeszcze nieopublikowane) przeddrukistanowia rdzen niniejszej pracy i zawieraja dokładny opis uzyskanych wyników.Pozostałe nieopublikowane wyniki sa opisane w osobnej sekcji pracy i zostana opublikowanew bliskiej przyszłosci.

博士
國立交通大學
電子物理系所
94
In this dissertation, we study the rotational states of adsorbed diatomic molecules and some physical properties of quantum dots. In part I, an adsorbed dipole molecule confined by a conical well is subject to strong laser fields. The crossover from field-free to hindered rotation motion is observed by varying the hindering angle. Moreover, the rotational states of coupled free and adsorbed molecules with dipolar interaction are further studied. It is shown that the orientation is significantly different from that of an isolated one due to the dipole-dipole interaction. In addition, the von Neumann entropy is calculated to characterize the degree of entanglement. It is also found that the entanglement can be influenced by the inter-molecule distance, the strength and number of laser pulses, and the confinement effect. In part II, we investigate the spin relaxation and electron transport in quantum dot systems. When a quantum dot is embedded in a semiconductor slab, the spin relaxation rate shows peculiar behaviors due to the confined phonons. Second, to observe the phonon effect on the transport, we have also considered a double-dot device embedded in a single phonon environment. It is shown that the transport behavior is deeply influenced by the Coulomb or phonon field. Finally, the transport of a double-dot device irradiated by an external field is considered. The enhanced or suppressed current is found due to the interplay between the energy states and external field.

博士
雲林科技大學
工程科技研究所博士班
97
PART I Based on the current spin density functional theory with non-parabolic effective mass approximation, Ben Daniel-Duke boundary conditions, and finite hard-wall confinement potential, a three-dimensional model is presented to study the multi-electron system in two different types of InAs/GaAs quantum dots (QDs). For the first type, we study electronic configurations in a vertically stacked quantum triple-dot molecule (QDM) holding six electrons. We demonstrate theoretically a possibility to drive dynamically coupled electronic states, i.e., to relocate electrons from one dot to another with adjustable energy levels by means of both external magnetic and electric fields. The second type is a charge-tunable QD for which the electron spectra have been obtained from the capacitance-voltage (CV) measurements by Miller et al. [Phys. Rev. B 56 (1997) 6764]. Our model is an extension of the single-electron model proposed by Filikhin et al. [Solid State Comm. 140 (2006) 483]. Our results can quantitatively well interpret the experimental CV data. It is shown that the energy differences between the parabolic and nonparabolic approximations are comparable with the exchange-correlation energies. Moreover, the nonparabolic effect is shown to be increasingly more significant than that of parabolic case in higher magnetic fields. It is also more pronounced for larger number of electrons. PART II Reaction injection molding involves the injection of two or more kinds of liquid polymers into a mold at relative high speed. Such high inertia effect may result in air pocket inside the mold or non-uniform velocity distribution. How to design the mold entry geometry to provide uniform velocity distribution becomes one of the major topics in reaction injection molding process. Thus a new and simple method was developed in this work to optimize the reaction mold entry design. Several regulation islands were located in a fish tail entrance to help distribute the flow more even. Dimensions and locations of the islands will affect the flow uniformity and become the factors to be optimized. Taguchi’s design of experiments coupled with computer flow simulation was used to achieve die geometry optimization. Effects of different dimensions of the islands on the flow uniformity can also be evaluated through statistical analyses in the flow simulation. Flow visualization technique was done by capturing flow images with high speed CCD. The experimental results showed very good agreements with the Fluent simulation results. The design methodology proposed here can help the molders in designing different reaction injection mold entries for better uniformity and performance.

Quantum chromodynamics (QCD), the theory of quarks and gluons, is known to be

the correct description of strong nuclear interactions. At high energy and momenta,

one can use QCD directly to compute quantities of physical interest related to the

strong force. At low energies and momenta, one should use a different description in

terms of the degrees of freedom relevant at that scale. Two approaches to achieve

this end are effective field theories and gauge/gravity dualities. The former involves

a field theory more or less like QCD itself, but with states which are composites

of quarks and gluons. Then a perturbative expansion is made not in terms of the

gauge coupling but instead in terms of the momentum of the fields. This approach

dates back to the 1970s and is on firm theoretical footing. Gauge/gravity dualities

are a newer and less understood technique, which relates the physics of the strong

interactions to a different but likely equivalent theory in a higher dimensional space-

time, where the quantity of interest can be computed more readily. We employ

both effective field theories and gauge/gravity dualities to study the physics of ex-

otic quarkonium states, that is bound states containing a heavy quark-antiquark pair

which nevertheless cannot be be understood working only with the standard quark

model of hadrons. Candidates for such states, long speculated to exist, have recently

been observed at particle colliders, so that the theory of exotic quarkonium is now

of great experimental importance.

Dissertation