An attempt on the calculation of relativistic potential energy curves: noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr - F and Xe - F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF_2 may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF_2 and XeF_2 to within 2 eV.

Relativistic effects in physics and chemistry of element 105. [Part] I.

A detailed study of the electronic structure and bonding of the pentahalides of group 5 elements V, Nb, Ta, and element 105, hahnium (and Pa) has been carried out using relativistic molecular cluster Dirac-Slater discrete-variational method. A number of calculations have been performed for different geometries and molecular bond distances. The character of the bonding has been analyzed using the Mulliken population analysis of the molecular orbitals. It is shown that hahnium is a typical group 5 element. In a great number of properties it continues trends in the group. Some peculiarities in the electronic structure of HaCl_5 result from relativistic effects.

Relativistic effects in physics and chemistry of element 105. [Part] II.

Relativistic self-consistent charge Dirac-Slater discrete variational method calculations have been done for the series of molecules MBr_5, where M = Nb, Ta, Pa, and element 105, Ha. The electronic structure data show that the trends within the group 5 pentabromides resemble those for the corresponding pentaclorides with the latter being more ionic. Estimation of the volatility of group 5 bromides has been done on the basis of the molecular orbital calculations. According to the results of the theoretical interpretation HaBr_5 seems to be more volatile than NbBr_5 and TaBr_5.

Relativistic effects in physics and chemistry of element 105. [Part] III.

Electronic structures of MOCl_3 and MOBr_3 molecules, where M = V, Nb, Ta, Pa, and element 105, hahnium, have been calculated using the relativistic Dirac-Slater discrete variational method. The character of bonding has been analyzed using the Mulliken population analysis of the molecular orbitals. It was shown that hahnium oxytrihalides have similar properties to oxytrihalides of Nb and Ta and that hahnium has the highest tendency to form double bond with oxygen. Some peculiarities in the electronic structure of HaOCl_3 and HaOBr_3 result from relativistic effects. Volatilities of the oxytrihalides in comparison with the corresponding pentahalides were considered using results of the present calculations. Higher ionic character and lower covalency as well as the presence of dipole moments in MOX_3 (X = Cl, Br) molecules compared to analogous MX_5 ones are the factors contributing to their lower volatilities.

Electronic structure and properties of the group 4, 5 and 6 highest chlorides including elements 104, 105, and 106

Results of the Dirac-Slater discrete variational calculations for the group 4, 5, and 6 highest chlorides including elements 104, 105, and 106 have shown that the groups are not identical with respect to trends in the electronic structure and bonding. The charge density distribution data show that notwithstanding the basic increase in covalency within the groups this increase diminishes in going from group 4 to group 6. As a result, E106Cl_6 will be less stable toward thermal decomposition than WCl_6, which is confirmed by an estimated low E106-Cl bond energy. \delta H_form equal to -90.3 ± 6 kcal/rnol is obtained for E106Cl_6 in the gas phase, which is indicative of a very low stability of this compound. The stability of the maximum oxidation state is shown to decrease in the direction E104(+4) > E105(+5) > E106(+6).

Non-relativistic and relativistic molecular calculations for the chalcogen hexafluorides: SF_6, SeF_6, TeF_6, PoF_6

Non-relativistic Hartree-Fock-Slater and relativistic Dirac-Slater self-consistent orbital models are applied for the analysis of the electronic structure of the chalcogen hexafluorides: SF_6, SeF_6, TeF_6 and PoF_6. The molecular eigenfunctions and eigenvalues are generated using the discrete variational method (DVM) with numerical basis functions. The results obtained for SF_6 are compared with other ab initio calculations. Information about relativistic level shifts and spin-orbit splitting has been obtained by comparison between the non-relativistic and relativistic results.

The electronic structure of anionic halide complexes of element 105 in aqueous solutions and their extraction by aliphatic amines

To study the complex formation of group 5 elements (Nb, Ta, Ha, and pseudoanalog Pa) in aqueous HCI solutions of medium and high concentrations the electronic structures of anionic complexes of these elements [MCl_6]^-, [MOCl_4]^-, [M(OH)-2 Cl_4]^-, and [MOCl_5]^2- have been calculated using the relativistic Dirac-Slater Discrete-Variational Method. The charge density distribution analysis has shown that tantalum occupies a specific position in the group and has the highest tendency to form the pure halide complex, [TaCl_6-. This fact along with a high covalency of this complex explains its good extractability into aliphatic amines. Niobium has equal trends to form pure halide [NbCl_6]^- and oxyhalide [NbOCl_5]^2- species at medium and high acid concentrations. Protactinium has a slight preference for the [PaOCl_5]^2- form or for the pure halide complexes with coordination number higher than 6 under these conditions. Element 105 at high HCl concentrations will have a preference to form oxyhalide anionic complex [HaOCl_5]^2- rather than [HaCl_6]^-. For the same sort of anionic oxychloride complexes an estimate has been done of their partition between the organic and aqueous phases in the extraction by aliphatic amines, which shows the following succession of the partition coefficients: P_Nb < P_Ha < P_Pa.

The electronic structure of the group 6 oxyanions [MO_4]^2-, where M = Cr, Mo, W, and element 106

The electronic structure of the group 6 oxyanions [MO_4]^2-, where M = Cr, Mo, W, and element 106 have been calculated using the Dirac-Slater Discrete Variational method. Results of the calculations show a relative decrease in the metal-oxygen bond strengths for the [E106O_4]^2- ion in the solid state compared to that for the [WO_4]^2- anion. Calculated energies of the electronic charge-transfer transitions are indicative of a strong possible luminescence of [El06O_4]^2- in the blue-violet area. In solutions [El06O_4]^2- will be the most stable ion out of the entire series. Estimated reduction potential E^0 (El06O^2-_4/E106O^3-_4) equal to -1.60V shows only a slightly increased stability of the +6 oxidation state for element 106 in comparison with W.

Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen

Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von großer Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen präsentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer Lösungen von q-holonomen Rekursionen beschrieben. Das fünfte Kapitel beschäftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung für die Koeffizienten ermittelt. Ferner können wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung für die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der nützlich ist, um q-holonome Rekursionen für bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schließlich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden können. ________________________________________________________________________________________________________________

Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

Electron-Nuclear Correlation in Laser-Driven Diatomic Molecules

The interaction of short intense laser pulses with atoms/molecules produces a multitude of highly nonlinear processes requiring a non-perturbative treatment. Detailed study of these highly nonlinear processes by numerically solving the time-dependent Schrodinger equation becomes a daunting task when the number of degrees of freedom is large. Also the coupling between the electronic and nuclear degrees of freedom further aggravates the computational problems. In the present work we show that the time-dependent Hartree (TDH) approximation, which neglects the correlation effects, gives unreliable description of the system dynamics both in the absence and presence of an external field. A theoretical framework is required that treats the electrons and nuclei on equal footing and fully quantum mechanically. To address this issue we discuss two approaches, namely the multicomponent density functional theory (MCDFT) and the multiconfiguration time-dependent Hartree (MCTDH) method, that go beyond the TDH approximation and describe the correlated electron-nuclear dynamics accurately. In the MCDFT framework, where the time-dependent electronic and nuclear densities are the basic variables, we discuss an algorithm to calculate the exact Kohn-Sham (KS) potentials for small model systems. By simulating the photodissociation process in a model hydrogen molecular ion, we show that the exact KS potentials contain all the many-body effects and give an insight into the system dynamics. In the MCTDH approach, the wave function is expanded as a sum of products of single-particle functions (SPFs). The MCTDH method is able to describe the electron-nuclear correlation effects as the SPFs and the expansion coefficients evolve in time and give an accurate description of the system dynamics. We show that the MCTDH method is suitable to study a variety of processes such as the fragmentation of molecules, high-order harmonic generation, the two-center interference effect, and the lochfrass effect. We discuss these phenomena in a model hydrogen molecular ion and a model hydrogen molecule. Inclusion of absorbing boundaries in the mean-field approximation and its consequences are discussed using the model hydrogen molecular ion. To this end, two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full many-particle Hamiltonian and (ii) an approach in the spirit of time-dependent density functional theory (TDDFT), including complex absorbing potentials in the single-particle equations. It is elucidated that for small grids the TDDFT approach is superior to the variational approach.