Ionization potentials, spin-orbit coupling

Figure 4. Schematic of the potential energy curves of the relevant electronic states The pump pulse prepares a coherent superposition of vibrational states in the electronic A 1 EJ state at the inner turning point. Around v = 13 this state is spin-orbit coupled with the dark b 3n state, causing perturbations. A two-photon probe process transfers the wavepacket motion into the ionization continuum via the (2) llg state [7].

Another important effect due to the spin-orbit coupling comes into play whether the upper ionic core is specifically involved or not. This is because the excitation dynamics is very sensitive not only to the ionization potential or binding energy of the active electron but also to m, the projection of the orbital angular momentum along the polarization axis. Since spin-orbit terms are not... 

There are several theoretical studies on LaO and related lanthanide oxides. We have already mentioned the ligand-field theory model calculations of Field (1982) as well as Carette and Hocquet (1988). More recently, Kotzian et al. (1991a,b) have applied the INDO technique (Pople et al. (1967) extended to include spin-orbit coupling [see also Kotzian et al. (1989a, b)] to lanthanide oxides (LaO, CeO, GdO and LuO). The authors call it INDO/S-CI method. The INDO parameters were derived from atomic spectra, model Dirac Fock calculations on lanthanide atoms and ions to derive ionization potentials, Slater-Condon factors and basis sets. The spin-orbit parameter is derived from atomic spectra in this method. 

The third critical point is the choice of the appropriate electronic structure method to treat the species in gas phase. The change of electronic configuration from the oxidized to the reduced species implies that electronic correlation effects are different and that spin-orbit coupling is likely to contribute differently for the two species. Most studies rely on DFT using either the PBE functional, a hybrid functional, or more recently a meta-functional of the Minnesota M06 family. Changing the functional can yield changes of the gas-phase ionization potential up to an eV. Unfortunately, we cannot compare these DFT values to the most reliable... 

Figure 16.3 Fourth ionization potentials IP4 of Ce and Th (eV) as well as corresponding relativistic and electron correlation contributions (eV) from basis set extrapolated all-electron HF and CCSD(T) calculations without and with the DKH2 Hamiltonian [24], Arrows from left to right denote relativistic, those from top to bottom correlation contributions. Spin-orbit coupling contributions (as shown in Figure 16.4) were not considered...

Atomic spectra, which historically contributed extensively to the development of the theory of the structure of the atom and led 10 the discovery of the electron and nuclear spin, provide a method of measuring ionization potentials, a method for rapid and sensitive qualitative and quantitative analysis, and data for the determination of the dissociation energy of a diatomic molecule. Information about the type of coupling of electron spin and orbital momenta in the atom can be obtained with an applied magnetic field. Atomic spectra may be used to obtain information about certain regions of interstellar space from the microwave frequency emission by hydrogen and to examine discharges in thermonuclear reactions. 

One of the great strengths of MO theory is the guidance it provides for the assignment of photoelectron spectra by means of Koopmans theorem. Using physical assumptions which closely parallel those of Koopmans theorem, we have used the spin-coupled orbitals to examine simple valence bond estimates of the ionization potentials. We find that the results for the lowest ionization potentials are at least as good as those derived from Koopmans theorem, while the higher potentials appear to be considerably more reliable. 

This procedure provides a model of the xenon atom which accounts only for the manifold of singly excited states based on the lowest ionic core, P3/2- For all rare gases, a second manifold of states converges to the next spin-orbit component of the ion, the Pi/2 state. For example, these two ionization limits in xenon are separated by 1.3 eV corresponding to different total angular momenta, J, of the 5p configuration. The lower ionization potential is 12.15 eV. We assume that multiphoton excitations into these two manifolds are very weakly coupled so they can be treated separately. This assumption is reasonable because once one of the electrons is excited outside a particular core configuration, transitions... 

Equations for the Fock space coupled cluster method, including all single, double, and triple excitations (FSCCSDT) for ionization potentials [(0,1) sector], are presented in both operator and spin orbital form. Two approximations to the full FSCCSDT equations are described, one being the simplest perturbative inclusion of triple excitation effects, FSCCSD+T(3), and a second that indirectly incorporates certain higher-order effects, FSCCSD+T (3). 

The ionization potentials and electron affinities of the atoms H, C, N, O and F have been computed by means of coupled-cluster methods using doubly augmented correlation-consistent one-electron basis sets in conjunction with explicitly correlated Slater-type geminals. Excitations up to the level of connected quintuples have been accounted for, and all orbitals in the core and valence shells have been correlated. Relativistic effects (spin-orbit as well as scalar) and diagonal Born-Oppenheimer corrections have been included. 

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