Orbitali molecolari di legame e antilegame per lo ione molecolare idrogeno H2+: risoluzione esatta e approssimazione LCAO

In questo lavoro di tesi si intende fornire un'analisi in chiave quantomeccanica di una serie di caratteristiche della molecola di idrogeno ionizzata. Il fatto che l'equazione di Schrödinger per l'elettrone sia nel caso di H2+ risolvibile in maniera esatta rende questo sistema fisico un prezioso banco di prova per qualsiasi metodo di approssimazione. Il lavoro svolto in questa trattazione consisterà proprio nella risoluzione dell'equazione d'onda per l'elettrone nel suo stato fondamentale, dapprima in maniera esatta poi mediante LCAO, e successivamente nell'analisi dei risultati ottenuti, che verranno dapprima discussi e interpretati in chiave fisica, e infine messi a confronto per la verifica della bontà dell'approssimazione. Il metodo approssimato fornirà approssimazioni relative anche al primo stato elettronico eccitato; anche questo verrà ampiamente discusso, e ci si soffermerà in particolare sulla caratterizzazione di orbitali di "legame" e di "antilegame", e sul loro rapporto con la stabilità dello ione molecolare.

Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: Influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a global analysis (that is to say that all non-negligible interactions are explicitely included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are rCC 120.2958(7) pm and rCH 106.164(1) pm. © 2011 American Institute of Physics.

Non-Born-Oppenheimer Dynamics of Hydrogen Molecules in Strong Laser-Fields

Die Arbeit behandelt die numerische Untersuchung von Wasserstoff-Moleküldynamik in starken Laserfeldern. Im Speziellen wird die Struktur von Ionisationsspektren bei Einfach-Photoionisation betrachtet. Korrelationen zwischen Elektron- und Kernbewegung werden identifiziert und mit Effekten in den Energiespektren in Verbindung gebracht. Dabei wird stets auf die Integration der zeitabhängigen Schrödingergleichung zurückgegriffen.

Born-Oppenheimer failure in the separation of low frequency vibrations

Changes in the effective potential function of a low-frequency large-amplitude molecular vibration, resulting from excitation of a high-frequency vibration, are discussed. It is shown that in some situations a significant contribution to such changes may arise from failure of the Born-Oppenheimer separation of the low-frequency mode. In the particular example of the HF dimer, recent evidence that the tunneling barrier increases on exciting either of the H-stretching vibrations is probably due to this effect.

Electronic properties of liquid hydrogen fluoride: A sequential quantum mechanical/Born-Oppenheimer molecular dynamics approach

The electronic properties of liquid hydrogen fluoride (HF) were investigated by carrying out sequential quantum mechanics/Born-Oppenheimer molecular dynamics. The structure of the liquid is in good agreement with recent experimental information. Emphasis was placed on the analysis of polarisation effects, dynamic polarisability and electronic excitations in liquid HF. Our results indicate an increase in liquid phase of the dipole moment (similar to 0.5 D) and isotropic polarisability (5%) relative to their gas-phase values. Our best estimate for the first vertical excitation energy in liquid HF indicates a blue-shift of 0.4 +/- 0.2 eV relative to that of the gas-phase monomer (10.4 eV). (C) 2010 Elsevier B.V. All rights reserved.

Numerical test of Born-Oppenheimer approximation in chaotic systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators. we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space. (C) 2009 Elsevier B.V. All rights reserved.

Portrait of four generations of women: Henny Molling nee Meyerhof, Elizabeth Gottschalk, Julie Meyerhof nee Oppenheimer and Therese Gottschalk nee Molling Portraits; Family

From left to right: Henny Molling, born Meyerhof, Elizabeth Gottschalk, Julie Meyerhof born Oppenheimer, and Therese Gottschalk, born Molling.

Portrait of four generations of women: Henny Molling nee Meyerhof, Elizabeth Gottschalk, Julie Meyerhof nee Oppenheimer and Therese Gottschalk nee Molling Portraits; Family

From left to right: Henny Molling, born Meyerhof, Elizabeth Gottschalk, Julie Meyerhof born Oppenheimer, and Therese Gottschalk, born Molling.

On the models for deuterium long-range isotope effects in13C NMR spectroscopy

The long-range deuterium isotope effects on13C nuclear shielding are physically not yet completely understood. Two existing models for explaining these effects, vibrational and substituent, are compared here. The vibrational model is based on the Born-Oppenheimer approximation, but it can explain only one-bond deuterium effects. To the contrary, the substituent model may explain many long-range isotope effects, but it is controversial due to the assumption of some distinct electronic properties of isotopes. We explain how long-range deuterium isotope effects may be rationalized by the subtle electronic changes induced by isotope substitution, which does not violate the Born-Oppenheimer approximation.

Towards an exact factorization of the molecular wave function

An exact single-product factorisation of the molecular wave function for the timedependent Schrodinger equation is investigated by using an ansatz involving a phasefactor. By using the Frenkel variational method, we obtain the Schrodinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.

The theory of long distance electron transfer reactions

The rate of electron transport between distant sites was studied. The rate depends crucially on the chemical details of the donor, acceptor, and surrounding medium. These reactions involve electron tunneling through the intervening medium and are, therefore, profoundly influenced by the geometry and energetics of the intervening molecules. The dependence of rate on distance was considered for several rigid donor-acceptor "linkers" of experimental importance. Interpretation of existing experiments and predictions for new experiments were made.

The electronic and nuclear motion in molecules is correlated. A Born-Oppenheimer separation is usually employed in quantum chemistry to separate this motion. Long distance electron transfer rate calculations require the total donor wave function when the electron is very far from its binding nuclei. The Born-Oppenheimer wave functions at large electronic distance are shown to be qualitatively wrong. A model which correctly treats the coupling was proposed. The distance and energy dependence of the electron transfer rate was determined for such a model.

Spectroscopic investigations of inter- and intramolecular processes in crystalline benzene

I. Introductory Remarks

A brief discussion of the overall organization of the thesis is presented along with a discussion of the relationship between this thesis and previous work on the spectroscopic properties of benzene.

II. Radiationless Transitions and Line broadening

Radiationless rates have been calculated for the ³B_1u→¹A_1g transitions of benzene and perdeuterobenzene as well as for the ¹B_2u→¹A_1g transition of benzene. The rates were calculated using a model that considers the radiationless transition as a tunneling process between two multi-demensional potential surfaces and assuming both harmonic and anharmonic vibrational potentials. Whenever possible experimental parameters were used in the calculation. To this end we have obtained experimental values for the anharmonicities of the carbon-carbon and carbon-hydrogen vibrations and the size of the lowest triplet state of benzene. The use of the breakdown of the Born-Oppenheimer approximation in describing radiationless transitions is critically examined and it is concluded that Herzberg-Teller vibronic coupling is 100 times more efficient at inducing radiationless transitions.

The results of the radiationless transition rate calculation are used to calculate line broadening in several of the excited electronic states of benzene. The calculated line broadening in all cases is in qualitative agreement with experimental line widths.

III. ³B_1u←¹A_1g Absorption Spectra

The ³B_1u←¹A_1g absorption spectra of C₆H₆ and C₆D₆ at 4.2˚K have been obtained at high resolution using the phosphorescence photoexcitation method. The spectrum exhibits very clear evidence of a pseudo-Jahn-Teller distortion of the normally hexagonal benzene molecule upon excitation to the triplet state. Factor group splitting of the 0 – 0 and 0 – 0 + v exciton bands have also been observed. The position of the mean of the 0 – 0 exciton band of C₆H₆ when compared to the phosphorescence origin of a C₆H₆ guest in a C₆D₆ host crystal indicates that the “static” intermolecular interactions between guest and hose are different for C₆H₆ and C₆D₆. Further investigation of this difference using the currently accepted theory of isotopic mixed crystals indicates that there is a 2cm^-1 shift of the ideal mixed crystal level per hot deuterium atom. This shift is observed for both the singlet and triplet states of benzene.

IV. ³E_1u←¹A_1g, Absorption Spectra

The ³E_1u←¹A_1g absorption spectra of C₆H₆ and C₆D₆ at 4.2˚K have been obtained using the phosphorescence photoexcitation technique. In both cases the spectrum is broad and structureless as would be expected from the line broadening calculations.

Spectroscopic analysis of atoms and molecules

151 p.

Quantum revivals in ultrashort intense field dissociation of molecular ions

Ultrashort (<15 fs) high intensity (1014-1016 W cm-2) laser pulses have provided novel methods for investigation of the dynamics of simple molecular ions such as H2+ and D2+. In this paper we report on simulations carried out for the D2+ molecular ion, within the Born- Oppenheimer and two-state approximations. These simulations allow one to investigate the dissociation dynamics of the D2+ molecular ion when subjected to such ultrashort, intense laser pulses. In particular, these simulations are compared to the results from recent pump-probe experiments, in which, the nuclear vibrational motion of D2+ has been imaged. Simulations suggest that the nature of the dissociation process, be it 1- or 2-photon, may be influenced by the tuning of the pump-probe delay time.