Performance of correlation functionals in ab initio chemisorption cluster-model calculations: Alkali metals on Si(111)

The performance of different correlation functionals has been tested for alkali metals, Li to Cs, interacting with cluster models simulating different active sites of the Si(111) surface. In all cases, the ab initio Hartree-Fock density has been obtained and used as a starting point. The electronic correlation energy is then introduced as an a posteriori correction to the Hartree-Fock energy using different correlation functionals. By making use of the ionic nature of the interaction and of different dissociation limits we have been able to prove that all functionals tested introduce the right correlation energy, although to a different extent. Hence, correlation functionals appear as an effective and easy way to introduce electronic correlation in the ab initio Hartree-Fock description of the chemisorption bond in complex systems where conventional configuration interaction techniques cannot be used. However, the calculated energies may differ by some tens of eV. Therefore, these methods can be employed to get a qualitative idea of how important correlation effects are, but they have some limitations if accurate binding energies are to be obtained.

Polarization and correlation phenomena in the radiative electron capture by bare highly-charged ions

In dieser Arbeit wird die Wechselwirkung zwischen einem Photon und einem Elektron im starken Coulombfeld eines Atomkerns am Beispiel des radiativen Elektroneneinfangs beim Stoß hochgeladener Teilchen untersucht. In den letzten Jahren wurde dieser Ladungsaustauschprozess insbesondere für relativistische Ion–Atom–Stöße sowohl experimentell als auch theoretisch ausführlich erforscht. In Zentrum standen dabei haupsächlich die totalen und differentiellen Wirkungsquerschnitte. In neuerer Zeit werden vermehrt Spin– und Polarisationseffekte sowie Korrelationseffekte bei diesen Stoßprozessen diskutiert. Man erwartet, dass diese sehr empfindlich auf relativistische Effekte im Stoß reagieren und man deshalb eine hervorragende Methode zu deren Bestimmung erhält. Darüber hinaus könnten diese Messungen auch indirekt dazu führen, dass man die Polarisation des Ionenstrahls bestimmen kann. Damit würden sich neue experimentelle Möglichkeiten sowohl in der Atom– als auch der Kernphysik ergeben. In dieser Dissertation werden zunächst diese ersten Untersuchungen zu den Spin–, Polarisations– und Korrelationseffekten systematisch zusammengefasst. Die Dichtematrixtheorie liefert hierzu die geeignete Methode. Mit dieser Methode werden dann die allgemeinen Gleichungen für die Zweistufen–Rekombination hergeleitet. In diesem Prozess wird ein Elektron zunächst radiativ in einen angeregten Zustand eingefangen, der dann im zweiten Schritt unter Emission des zweiten (charakteristischen) Photons in den Grundzustand übergeht. Diese Gleichungen können natürlich auf beliebige Mehrstufen– sowie Einstufen–Prozesse erweitert werden. Im direkten Elektroneneinfang in den Grundzustand wurde die ”lineare” Polarisation der Rekombinationsphotonen untersucht. Es wurde gezeigt, dass man damit eine Möglichkeit zur Bestimmung der Polarisation der Teilchen im Eingangskanal des Schwerionenstoßes hat. Rechnungen zur Rekombination bei nackten U92+ Projektilen zeigen z. B., dass die Spinpolarisation der einfallenden Elektronen zu einer Drehung der linearen Polarisation der emittierten Photonen aus der Streuebene heraus führt. Diese Polarisationdrehung kann mit neu entwickelten orts– und polarisationsempfindlichen Festkörperdetektoren gemessen werden. Damit erhält man eine Methode zur Messung der Polarisation der einfallenden Elektronen und des Ionenstrahls. Die K–Schalen–Rekombination ist ein einfaches Beispiel eines Ein–Stufen–Prozesses. Das am besten bekannte Beispiel der Zwei–Stufen–Rekombination ist der Elektroneneinfang in den 2p3/2–Zustand des nackten Ions und anschließendem Lyman–1–Zerfall (2p3/2 ! 1s1/2). Im Rahmen der Dichte–Matrix–Theorie wurden sowohl die Winkelverteilung als auch die lineare Polarisation der charakteristischen Photonen untersucht. Beide (messbaren) Größen werden beträchtlich durch die Interferenz des E1–Kanals (elektrischer Dipol) mit dem viel schwächeren M2–Kanal (magnetischer Quadrupol) beeinflusst. Für die Winkelverteilung des Lyman–1 Zerfalls im Wasserstoff–ähnlichen Uran führt diese E1–M2–Mischung zu einem 30%–Effekt. Die Berücksichtigung dieser Interferenz behebt die bisher vorhandene Diskrepanz von Theorie und Experiment beim Alignment des 2p3/2–Zustands. Neben diesen Ein–Teichen–Querschnitten (Messung des Einfangphotons oder des charakteristischen Photons) wurde auch die Korrelation zwischen den beiden berechnet. Diese Korrelationen sollten in X–X–Koinzidenz–Messungen beobbachtbar sein. Der Schwerpunkt dieser Untersuchungen lag bei der Photon–Photon–Winkelkorrelation, die experimentell am einfachsten zu messen ist. In dieser Arbeit wurden ausführliche Berechnungen der koinzidenten X–X–Winkelverteilungen beim Elektroneneinfang in den 2p3/2–Zustand des nackten Uranions und beim anschließenden Lyman–1–Übergang durchgeführt. Wie bereits erwähnt, hängt die Winkelverteilung des charakteristischen Photons nicht nur vom Winkel des Rekombinationsphotons, sondern auch stark von der Spin–Polarisation der einfallenden Teilchen ab. Damit eröffnet sich eine zweite Möglichkeit zur Messung der Polaristion des einfallenden Ionenstrahls bzw. der einfallenden Elektronen.

Precise calculations of atomic electron binding energies in fermium

The comparison between the experimental binding energies for the K, L, and M electrons for fermium and the results of our Dirac-Fock calculation, taking into account all tractable corrections, leads to agreement within about 20 eV. This shows that the present method of calculation is an adequate description of this problem and that nonlinear electrodynamical effects will not be present in nature or will be smaller than 1% compared to the values recently proposed. It is found that the energies of electronic transitions can now be used to estimate the nuclear radius.

Realistic many electron coupled channel calculations in heavy ion scattering

The time dependent Dirac equation which describes a heavy ion-atom collision system is solved via a set of coupled channel equations with energy eigenvalues and matrix elements which are given by a selfconsistent field many electron calculation. After a brief discussion of the theoretical approximations and the connection of the many particle with the one particle interpretation we discuss first results for the systems F{^8+} - Ne and F{^6+} - Ne. The resulting P(b) curves for the creation of a Ne K-hole are in good agreement with the experimental results.

Many electron coupled channel calculations for the system F{^8+} - Ne

To describe the time dependence of an atomic collision system the Dirac equation usually is rewritten in a coupled channel equation. We first discuss part of the approximation used in this approach and the connection of the many particle with the one particle interpretation. The coupled channel equations are solved for the system F{^8+} - Ne using static selfconsistent many electron Dirac-Fock-Slater wavefunctions as basis. The resulting P(b) curves for the creation of a Ne K-hole are in reasonable agreement with the experimental results.

The molecular structure of hexamethyldigermane determined by gas-phase electron diffraction with theoretical calculations for (CH3)3M-M(CH3)3 Where M = C, Si, and Ge

Gas-phase electron diffraction (GED) data together with results from ab initio molecular orbital calculations (HF and MP2/6-311+G(d,p)) have been used to determine the structure of hexamethyldigermane ((CH3)3Ge-Ge(CH3)3). The equilibrium symmetry is D3d, but the molecule has a very low-frequency, largeamplitude, torsional mode (φCGeGeC) that lowers the thermal average symmetry. The effect of this largeamplitude mode on the interatomic distances was described by a dynamic model which consisted of a set of pseudoconformers spaced at even intervals. The amount of each pseudoconformer was obtained from the ab initio calculations (HF/6-311+G(d,p)). The results for the principal distances (ra) and angles (∠h1) obtained from the combined GED/ab initio (with estimated 1σ uncertainties) are r(Ge-Ge) ) 2.417(2) Å, r(Ge-C) ) 1.956(1) Å, r(C-H) ) 1.097(5) Å, ∠GeGeC ) 110.5(2)°, and ∠GeCH ) 108.8(6)°. Theoretical calculations were performed for the related molecules ((CH3)3Si-Si(CH3)3 and (CH3)3C-C(CH3)3).

Molecular structure of 2,5-dihydropyrrole (C4NH7), obtained by gas-phase electron diffraction and theoretical calculations

The structure of 2,5-dihydropyrrole (C4NH7) has been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing third-order Moller-Plesset (MP3) level of theory and the 6-311+G(d,p) basis set. Several theoretical calculations were performed. From theoretical calculations using MP3/6-311+G(d,p) evidence was obtained for the presence of an axial (63%) (N-H bond axial to the CNC plane) and an equatorial conformer (37%) (N-H bond equatorial to the CNC plane). The five-membered ring was found to be puckered with the CNC plane inclined at 21.8 (38)° to the plane of the four carbon atoms.

Molecular structures of benzoic acid and 2-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of benzoic acid (C6H5COOH) and 2-hydroxybenzoic acid (C6H4OHCOOH) have been determined in the gas phase by electron diffraction using results from quantum chemical calculations to inform restraints used on the structural parameters. Theoretical methods (HF and MP2/6-311+G(d, p)) predict two conformers for benzoic acid, one which is 25.0 kJ mol(-1) (MP2) lower in energy than the other. In the low-energy form, the carboxyl group is coplanar with the phenyl ring and the O-H group eclipses the C=O bond. Theoretical calculations (HF and MP2/6-311+ G(d, p)) carried out for 2-hydroxybenzoic acid gave evidence for seven stable conformers but one low-energy form (11.7 kJ mol-1 lower in energy (MP2)) which again has the carboxyl group coplanar with the phenyl ring, the O-H of the carboxyl group eclipsing the C=O bond and the C=O of the carboxyl group oriented toward the O-H group of the phenyl ring. The effects of internal hydrogen bonding in 2-hydroxybenzoic acid can be clearly observed by comparison of pertinent structural parameters between the two compounds. These differences for 2-hydroxybenzoic acid include a shorter exocyclic C-C bond, a lengthening of the ring C-C bond between the substituents, and a shortening of the carboxylic single C-O bond.

Molecular structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid have been determined by gas-phase electron diffraction using results from quantum chemical calculations to inform the choice of restraints applied to some of the structural parameters. The results from the study presented here demonstrate that resonance hybrids are not as helpful in rationalizing the structures of 2-, 3-, and 4-hydroxybenzoic acids as are models based upon electrostatic effects.

The molecular structure of propylene sulphide (methylthiirane) by gas-phase electron diffraction and theoretical calculations: a molecule used in MOCVD

Gas-phase electron-diffraction (GED) data together with results from ab initio molecular orbital calculations have been used to determine the structure of propylene sulphide. Values found for the main structural parameters for the molecule are consistent with those obtained from microwave studies and are compared here with those found for similar sulphur containing rings of general formula S(CH2)n (n = 2–5). A high ring strain enthalpy was calculated for propylene sulphide which is consistent with the small C–S–C angle (48.2(6)degrees) and the relatively long C–S bond lengths (ra = 1.831(2) Å). This is thought to account for the ease of ring opening in propylene sulphide observed in MOCVD reactions and the ready polymerisation of the molecule.

Hydrogen bonding in the gas-phase: the molecular structures of 2‑hydroxybenzamide (C7H7NO2) and 2‑methoxybenzamide (C8H9NO2), obtained by gas-phase electron diffraction and theoretical calculations

The structures of 2-hydroxybenzamide(C7H7NO2) and 2-methoxybenzamide (C8H9NO2) have been determined in the gas-phase by electron diffraction using results from quantum chemical calculations to inform restraints used on the structural parameters. Theoretical methods (HF and MP2/6-311+G(d,p)) predict four stable conformers for both 2-hydroxybenzamide and 2-methoxybenzamide. For both compounds, evidence for intramolecular hydrogen bonding is presented. In 2-hydroxybenzamide, the observed hydrogen bonded fragment is between the hydroxyl and carbonyl groups, while in 2-methoxybenzamide, the hydrogen bonded fragment is between one of the hydrogen atoms of the amide group and the methoxy oxygen atom.