Spin-orbit ionization

LICS control over branching reactions was also demonstrated in the two spin-orbit ionization continua of Xe [88]. The photo-ionization of Xe atom to yield the two spin-orbit Xe+ -I- continua can be varied by electromagnetically embedding into the continua an atomic bound state. The dressed Pi/2 continuum, when probed by a three-photon absorption from the ground state, exhibits a pronounced induced structure, whereas the Pz/2 continuum possesses no such structure, as demonstrated... 

The analytical continuation in the complex plane of the radial coordinate r corresponding to the complex scaling transformation preserves that the spin densities r ain real quantities for the real values of r [61]. That is why all the contributions to the right-hand side of Equation 3.18 are real, except the eigenvalues e. Thus, the total ionization rate can be expressed as a sum of spin-orbital ionization rates [61] ... 

So, within the limitations of the single-detenninant, frozen-orbital model, the ionization potentials (IPs) and electron affinities (EAs) are given as the negative of the occupied and virtual spin-orbital energies, respectively. This statement is referred to as Koopmans theorem [47] it is used extensively in quantum chemical calculations as a means for estimating IPs and EAs and often yields results drat are qualitatively correct (i.e., 0.5 eV). 

When the states P1 and P2 are described as linear combinations of CSFs as introduced earlier ( Fi = Zk CiKK), these matrix elements can be expressed in terms of CSF-based matrix elements < K I eri IOl >. The fact that the electric dipole operator is a one-electron operator, in combination with the SC rules, guarantees that only states for which the dominant determinants differ by at most a single spin-orbital (i.e., those which are "singly excited") can be connected via electric dipole transitions through first order (i.e., in a one-photon transition to which the < Fi Ii eri F2 > matrix elements pertain). It is for this reason that light with energy adequate to ionize or excite deep core electrons in atoms or molecules usually causes such ionization or excitation rather than double ionization or excitation of valence-level electrons the latter are two-electron events. 

The He I ultraviolet photoelectron spectra of Kr and Xe appear similar to that of Ar but the ionization energy decreases and the spin-orbit coupling increases with increasing atomic number, as illustrated by the data in Table 8.1. 

The Brueckner-reference method discussed in Section 5.2 and the cc-pvqz basis set without g functions were applied to the vertical ionization energies of ozone [27]. Errors in the results of Table IV lie between 0.07 and 0.17 eV pole strengths (P) displayed beside the ionization energies are approximately equal to 0.9. Examination of cluster amplitudes amd elements of U vectors for each ionization energy reveals the reasons for the success of the present calculations. The cluster operator amplitude for the double excitation to 2bj from la is approximately 0.19. For each final state, the most important operator pertains to an occupied spin-orbital in the reference determinant, but there are significant coefficients for 2h-p operators. For the A2 case, a balanced description of ground state correlation requires inclusion of a 2p-h operator as well. The 2bi orbital s creation or annihilation operator is present in each of the 2h-p and 2p-h operators listed in Table IV. Pole strengths are approximately equal to the square of the principal h operator coefiScient and contributions by other h operators are relatively small. 

Element E Ionization energy E2 bond dissociation energy Spin-orbit 3P2 3Po... 

Koopmann s theorem establishes a connection between the molecular orbitals of the 2jV-electron system, just discussed, and the corresponding (2N- 1 Electron system obtained by ionization. The theorem states If one expands the (2N - 1) molecular spin-orbitals of the ground state of the ionized system in terms of the 2N molecular spin-orbitals of the ground state of the neutral system, then one finds that the orbital space of the ionized system is spanned by the (2N - 1) canonical orbitals with the lowest orbital energies ek i.e. to this approximation the canonical self-consistent-field orbital with highest orbital energy is vacated upon ionization. This theorem holds only for the canonical SCF orbitals. 13>... 

For systems in degenerate states, first-order corrections may need to be computed. In our work [26] we found that this significantly reduced the mean absolute error for the G2-1 and G2-2 test sets for ionization potentials and electron affinities, in no small part due to the preponderance of atoms and linear molecules in these sets. We found that CISD/MTsmall generally yields quite satisfactory spin-orbit correc-... 

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].

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