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Interaction element

The only nonvanishing matrix elements HKL associated with the SCF determinant will thus be the diagonal element, which is identical with the Hartree-Fock energy, and the interaction elements with the doubly excited determinants... [Pg.284]

Datta-Mannan A, Stone MJ. Chemokine-binding specificity of soluble chemokine-receptor analogues identification of interacting elements by chimera complementation. Biochemistry 2004 43 14602-11. [Pg.28]

The link between the ecological/ecotoxicological risk assessment and the risk management frameworks is demonstrated. The ecological risk assessment consists of seven interactive elements (Fig. 17). The quantitative and descriptive science used to conduct ERA (Table 5) does not answer, in a direct way, the question of what should be done to manage the risk. Science determines adversity, but the public determines acceptability (Fig. 18). But acceptable risk is a highly subjective and relative term. It is time and space-specific and depends upon definitions of quality of life and robustness of the environment. [Pg.409]

A valuable feature of the overlapping PNHO hybrids hA and hB is that they allow the (hA A hB) NHO interaction elements to be estimated in terms of the corresponding PNHO overlap integral hA hB) by a Mulliken-type approximation49 of the form... [Pg.31]

Figure 3.2 An energy-level-splitting diagram (cf. Fig. 1.3) for interaction of orbitals A F Figure 3.2 An energy-level-splitting diagram (cf. Fig. 1.3) for interaction of orbitals <Pa and with degenerate energy e and interaction element Fab = (<f>A F <h).
We can also verify that the usual ECAO-MO description (3.2) and (3.4) leads to predicted hybridizations that are generally consistent with the donor-acceptor estimates (3.8). Suppose that each H atom is associated with a valence spin-orbital of hybridized form (3.6). According to Eq. (3.2), the optimal electronic energy of bond formation is obtained by choosing the hybridization parameter k to maximize the magnitude of the interaction element... [Pg.95]

How can (CMO) E L) despite the fact that energies of occupied CMO and NBO differ significantly The answer is suggested in Fig. 3.13, which depicts the interaction between filled NBOs and L2b with interaction element... [Pg.117]

Figure 3.13 The energy-level-splitting diagram (cf. Figs. 1.3 and 3.2) for interaction of filled NBOs l a and l b (with energies ea(L) = < b(L) and interaction element F ab = (f2a F f2b>) to form MO levels e , Eq. (3.48). Figure 3.13 The energy-level-splitting diagram (cf. Figs. 1.3 and 3.2) for interaction of filled NBOs l a and l b (with energies ea(L) = < b(L) and interaction element F ab = (f2a F f2b>) to form MO levels e , Eq. (3.48).
Using, e.g., the NAO Fock-matrix elements for Li2+ quoted in note 11 (together with the corresponding value for /ss/ = (lsA F lsB) = —0.0668), we obtain the estimate Fab — —0.0910. This somewhat underestimates the magnitude of the actual interaction element (—0.1191), but shows the general direction and strength of the hybridization effect. [Pg.354]

Ed71- is obtained by a DEL keylist (a standard option of the NBO program) that deletes the possible 7t—7t interaction elements from the density matrix and recalculates the SCF energy in the absence of such interactions. For all model DEL calculations described in this section we employed the simpler RHF/6-31 + G level of theory. [Pg.356]

Figure 4.96 Contour plots (left) and radial-profile plots (right) of overlapping hM and hH NHOs of ctMh bonds for group 10 dihydrides (NiH2, PdH2, and PtH2). Numerical (hM F, hH> Fock-matrix interaction elements are shown for each case. Figure 4.96 Contour plots (left) and radial-profile plots (right) of overlapping hM and hH NHOs of ctMh bonds for group 10 dihydrides (NiH2, PdH2, and PtH2). Numerical (hM F, hH> Fock-matrix interaction elements are shown for each case.
Neural networks are systems built of basic, mutually interacting elements, called neurons. The two key features of a neural network model that are of interest to us here are the properties of each neuron and the connectivity between neurons. In this section the construction of biochemical networks... [Pg.78]

The characters x r f°rm a reducible representation of the molecular orbitals of this molecule that is, the orbitals still have finite interaction elements between them, and the secular determinant must be reduced further to diagonal form. The number of times af that a reducible representation occurs in an irreducible representation is given by (140)... [Pg.38]

The idea of treating complex systems of interacting elements in Boolean (= logical) terms is far from new see, for instance, in the particular case of biological systems Refs. 17-19 and especially Refs. 15, 20, and 21. [Pg.252]

Knowing the quasi-spin properties of F we can now turn our attention to the associated selection rules. According to the Wigner-Eckart theorem acting in quasi-spin space the selection of an interaction element of an operator K0 ... [Pg.38]

Interaction elements between half-filled shell states with different quasispin character will be zero for time-odd one-electron operators. [Pg.39]

Diagonal interaction elements will be zero for time-even one-electron operators that are non-totally symmetric scalars in spin and orbit space. [Pg.39]

Off-diagonal interaction elements between half-filled shell states of identical (C/) parity will be zero if //,)f is symmetric under time reversal. [Pg.39]

The diagonal matrix elements between half-filled shell states are now considered. If it is assumed that the interaction operator is symmetric under time reversal (also as in case 2), then thm = +1. The diagonal interaction elements are just the expectation value of in the closed shell, which is zero if is not totally symmetric under spatial operations (Another way of saying this is that (H%) vanishes if Mr K X K KMKr ), but obviously has time reversal parity +1. It now follows that if the above criteria are met then the diagonal matrix elements must vanish. [Pg.40]


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See also in sourсe #XX -- [ Pg.204 ]




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