Excited terms

For separable initial states the single excitation terms can be set to zero at all times at this level of approximation. Eqs. (32),(33),(34) together with the CSP equations and with the ansatz (31) for the total wavefunction are the working equations for the approach. This form, without further extension, is valid only for short time-domains (typically, a few picoseconds at most). For large times, higher correlations, i.e. interactions between different singly and doubly excited states must be included. 

For /2(Ar)i7, an extensive CI-CSP simulation was carried out, and the results were compared with those of the simple CSP approximation. Both calculations are for the ultrafast dynamics following excitation of the I2 into the B state. We found that the CI-CSP calculation, including doubly excited configurations , is close to converged for times up to t 500 fs, when 1500 configurations are included. Fig. 2 shows co(t)p, the coefficient of the CSP term and the doubly excited terms in the full CI-CSP wavefunction,... 

For excited terms splif by spin-orbif interaction fhere are no general rules regarding normal or inverted mulfiplefs. For example, in Fie, excited sfafes form mosfly inverted mulfiplefs whereas in fhe alkaline earth mefals. Be, Mg, Ca,..., fhey are mosfly normal. 

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

The presence of the h(z, P) factor makes Eq. (7.44) different from a Laplace transform of C(z). If the z dependence of h(z, P) is ignored,(34 36) then calculated concentrations of fluorophore near an interface derived from collected fluorescence are approximations. Also, the P dependence in the tf1,11 causes the integral in Eq. (7.44) to differ from the form of a Laplace transform even after the excitation term is factored out. 

A AZPE = AZPEii — AZPEd AZPEt) corresponds to the terms for the reactions of monodeuteriated aldehydes. Terms defined by IE = MMl x EXC x EXP (IE is the Isotopic exchange equilibrium, MMl is the mass moment of inertia term representing the rotational and translational partition function ratios, EXC is the vibrational excitation term and EXP is the exponential zero point energy). 

The ground term of a molecule is prefixed by the letter X. Excited terms that have the same multiplicity as the ground term are usually prefixed by A, B, C,. The letters a,b,c,. .. usually denote excited terms of different multiplicity than the ground term. 

Excited terms with the some spin Configuration Ground term" multiplicity os the ground term"... 

Calculation of excited term spin—orbit coupling splittings are available for the configurations d d%), (d6) and d5, with d3(dT) and dl(d9) being trivial cases.67 71-82... 

Consider the spin-allowed transitions possible from the 3Tig(F) ground term of an octahedral d2 complex, ignoring the g -g selection rule and vibrational complications. The candidates are the 3TXg(P), 3T2g(F) and 3A2g(F) excited terms. We note that r transforms as Tiu in Oh. In the Group O... 

Figure 20 Potential wells and vibrational levels for the ground and an excited term of a complex...

In principle, it is possible to relate the excited term splittings Ae, the ground term splitting Ag, and to express the ZFS value of D in terms of A and Ae. For example, for tetragonal symmetry one can deduce Ae = 3Ag/4 and D = 412(AX 1 - A 1), where Ax = A + /2Ag - /3Ae and Ap = A + VjAg + 2/3Ae. However, in practice, as is known from spectral studies, these relationships do not hold well, particularly for the calculation of D, to which many excited terms including those of different multiplicity contribute. To evaluate D with any accuracy from the ligand field parameters it appears to be necessary to use the entire relevant dh manifold.89,90... 

Fig. 21.18 Effect of overlap interference in the Mg 3pnd 7 = 3 spectrum (a) synthesized spectrum including interference, (b) same as (a) but using only direct-excitation terms, (c) measured spectrum, and (d) corresponding overlap integral squared (from ref. 12).

CCSD coupled-cluster theory with single and double excitation terms... 

CCSD(T) same as CCSD plus a perturbative estimate of triple excitation terms... 

With a weaker axial CF the ground CFT is 3 g and cannot be treated correctly within the SH formalism. The first excited term is 3A2g separated by I Aaxl /he = 425 cm x Aax < 0. The situation is somehow analogous to the case of a compressed d1 system. 

The perturbation theory brings the SH formalism the excited terms bearing the angular momentum fill the components of the A-tensor and con-... 

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