• Bulletin of the Korean Chemical Society
• /
• v.30 no.4
• /
• pp.891-896
• /
• 2009

Giusti-Suzor and Fano introduced translations of the scales of Lu-Fano plots by phase renormalization in order to decouple the intra- and inter-channel couplings in multichannel quantum defect theory (MQDT). Their theory was further developed by others to deal with systems involving a larger number of channels. In different directions, MQDT was reformulated into forms with a one-to-one correspondence to those in Fano's configuration mixing theory of resonance for photofragmentation processes involving one closed and many open channels. In this study, the theory was further developed to fully reveal the coupling nature, decoupling of the background and resonance scattering in physical scattering matrices as well as to further extract the dynamic parameters undiscovered by Fano and his colleagues. This theory was applied to the photoabsorption spectrum of $H_2$ observed by Herzberg's group.

• Bulletin of the Korean Chemical Society
• /
• v.23 no.7
• /
• pp.971-984
• /
• 2002

The multichannel quantum defect theory (MQDT) is reformulated into the form of the configuration mixing (CM) method using the geometrical construction of the S matrix developed for the system involving two open and one closed channels. The reformulation is done by the phase renormalization method of Giusti-Suzor and Fano. The rather unconventional short-range reactance matrix K whose diagonal elements are not zero is obtained though the Lu-Fano plot becomes symmetrical. The reformulation of MQDT yields the partial cross section formulas analogous to Fano's resonance formula, which has not easily been available in other's work.

• Bulletin of the Korean Chemical Society
• /
• v.30 no.8
• /
• pp.1783-1792
• /
• 2009

Although overlapping resonances have been studied extensively in conventional resonance theories, there have not been many studies on them in multichannel quantum defect theories (MQDT). In MQDT, overlapping resonances occur between the channels instead of states, which pose far greater difficulty. Their systematic treatment was obtained for cases involving degenerate closed channels by applying our previous theory, which decouples background scattering from the resonance scattering in the MQDT formulation. The use of mathematical theory on con-diagonalization and con-similarity was essential for handling the non-Hermitian symmetric complex matrix. Overlapping resonances in rare gas spectra of Ar, Kr and Xe were analyzed using this theory and the results were compared with the ones of the previous alternative parameterizations of MQDT which make the open-open part $K^{oo}$ and closed-closed part $K^{cc}$ of reactance submatrices zero. The comparison revealed that separation of background and resonance scatterings achieved in our formulation in a systematic way was not achieved in the representation of $K^{oo}\;=\;0\;and\;K^{cc}$ = 0 when overlapping resonances are present.

• Bulletin of the Korean Chemical Society
• /
• v.35 no.5
• /
• pp.1422-1432
• /
• 2014

Convergent all-electron multi-reference configuration-interaction (MRCI) calculations are performed for a lithium dimer with Kaufmann's Rydberg basis functions. A comparison of the results of these calculations with those of the effective core potential/core polarization potential (ECP/CPP) method and experimental data reveals the deficiency of the all-electron ab initio method. The deficiency is related to the mere 51.9% attainment of electron correlation for the ground state. The percent attainment of electron correlation for the first excited state is slightly better than that for the ground state, preventing us from obtaining better agreements with experimental data by means of increasing the size of basis sets. The Kaufmann basis functions are then used with the ECP/CPP method to obtain the accurate convergent potential energy curves for the $^1\prod_u$ states correlated to Li(2p) + Li(2p) and Li(2s) + Li(n = 2, 3, 4). Quantum defect curves (QDCs) calculated for both the $X^2\sum_g$ and 1 $^2\prod_u$ states of the $Li{_2}^+$ ion and the Lu-Fano plot reveal a strong series-series interaction between the two $2snp{\pi}$ and $2pnp{\pi}$ Rydberg series. The QDCs are then used to resolve assignment problems in the literature. The reassignments, performed by Jedrzejewski-Szemek et al., of the dissociation product of the D $^1\prod$ state from (2s+3d) to (2s+3p) and that of the 6 $^1\prod_u$ from (2s+4d) to (2s+4p) are found to be incorrect. It may be more natural to assign their $2snp{\pi}$ Rydberg series as a $2snd{\pi}$ series. The state, assigned as 5p $^1\prod_u$ by Ross et al. and 4d $^1\prod$ by Jedrzejewski-Szemek et al., is assigned as the 7 $^1\prod_u$ state, correlated to the Li(2s) + Li(4f) limit.