Direct-excitation configuration

In Fig. 11.19a, the most simple of ED-XRF instrumental configurations is shown. A low power X-ray tube (e. g., 50 W) and a Si(Li) detector are both placed at an angle of 45° with respect to the sample. Collimators are used to confine the excited and detected beam to a sample area between 0.5 and 2 cm. In such a direct-excitation configuration, the distance between the components can be fairly small (typically a few cm) and since both the tube anode lines and the bremsstrah-... 

The direct product of Bx and Ax for 62o is Bx. Including spin, we see that the first excited configuration of water gives rise to BX and XBX electronic terms. 

Starting with the method described above, extensive tables of the numerical values of mean energies, integrals of electrostatic and constant of spin-orbit interactions are presented in [137] for the ground and a large number of excited configurations, for atoms of boron up to nobelium and their positive ions. They are obtained by approximation of the corresponding Hartree-Fock values by polynomials (21.20) and (21.22). Such data can be directly utilized for the calculation of spectral characteristics of the above-mentioned elements or they can serve as the initial parameters for semi-empirical calculations [138]. 

Once the proper spin-coupled excited reference state has been obtained, the type of optimization procedure described in the previous Section may be used to generate virtual orbitals, and thus to introduce dynamical correlation directly into the excited states of interest. It should be noted that such optimization has to be modified slightly to avoid the collapse of the doubly-excited configuration towards the ground state. The modifications consist simply in a set of additional orthogonality constraints, analogous to the previous ones, to be imposed during the virtual orbital optimization procedure. 

Fig. 4 Process of dye sensitization of AgX. A Light absorbed by dye and subsequent charge injection into AgX levels from dye levels B final state has the same result configuration as if AgX was directly excited by light...

The comparison of the Mfiu values with those of Mabs allows one to obtain information about the changes in the electronic structure and molecular conformation between the Franck-Condon excited state initially reached upon excitation and the solvent-equilibrated fluorescent state [14]. Electronic transition dipole moments are mainly determined by the direct interactions between the lowest CT state and the ground state (So), and by the contributions from the locally excited configurations [14, 54, 56, 57]. For example, for the fluorescent CT state one can obtain... 

In HF theory, one has the Brillouin theorem (BT) stating that singly excited configurations do not interact with the ground state determinant [130], The proof commonly proceeds by utilizing the properties of the HF wave function. An alternative route was followed by Mayer [131, 132, 133] who derived the BT directly from the variational principle, permitting one to obtain the HF... 

Zeros in the first column of H are a consequence of the fact that the cluster operator T satisfies the XCC system of equations, Eq. (78). Their presence allows us to solve the EOMXCC eigenvalue problem in the space spanned by excited configurations only and obtain energy differences ujk directly. 

As explained in Section 4 (cf., also, Section 5), the three- and four-body components of the operator Hp entering the EOMXCCSD equations (recall that P is a projector on the subspace spanned by singly and doubly excited configurations) are computed directly by forming the quantities 3Aj, 3A 6,... 

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