Low excited state

Table J Transition energy (in au) between the ground states and some low-excited states of He. Reprinted with permission from [189], Copyright 2006John Wiley Sons, Inc.

A rather characteristic feature of nuclei off the line of stability is that many of them have relatively long-lived low-excited states, and others have prominent isomeric states. For example, even-even nuclei in the vicinity of shells belonging to group (a) above have 4 f states with T l-4 nsec and... 

The problems for quantum chemists in the mid-forties were how to improve the methods of describing the electronic structure of molecules, valence theory, properties of the low excited states of small molecules, particularly aromatic hydrocarbons, and the theory of reactions. It seemed that the physics needed was by then all to hand. Quantum mechanics had been applied by Heitler, London, Slater and Pauling, and by Hund, Mulliken and Hiickei and others to the electronic structure of molecules, and there was a good basis in statistical mechanics. Although quantum electrodynamics had not yet been developed in a form convenient for treating the interaction of radiation with slow moving electrons in molecules, there were semi-classical methods that were adequate in many cases. 

For this molecule, few theoretical studies [87,89] have been applied to the relatively low excited states. Fig. 39.11 shows a comparison of the theoretical results for the excitation spectrum of Cr02Cl2 with the experimental spectrum. Among the theoretical spectra, the SAC-CI result agrees well with the experimental spectrum and the quantitative assignments are possible in the whole energy region. 

Non-polar solvents, such as hexane and benzene, produce high yields of excited states via ion recombination, and relatively low yields of radical ions. In contrast, polar solvents like methanol, acetonitrile and water support high yields of radical ions with low excited state yields, due to solvation and stabilisation of the initial ions, particularly the electrons, leading to a slow rate of ion recombination. In intermediate polarity solvents, such as acetone, approximately equal amounts of radicals and excited states are generated. Hence, generally it is better to study solute excited states with pulse radiolysis in non-polar solvents and solute radicals or radical ions in polar solvents. This is often not possible due to insolubility in the preferred solvent, but if the transients are being monitored via transient absorption spectroscopy and they have high molar absorption coefiicients then low yields need not be problematic. 

The formation of rare earth metal sulfide ions, particularly poly sulfides, in reactions of the singly charged metal cations with Sg was studied by Dance, Fisher, and Willett using FTICR-MS. The authors examined Sc (Dance et al., 1995, 1996), Y " (Dance et ah, 1996), La" " (Dance et al., 1996 Fisher et al., 1998), and the lanthanide ions Ln" " (Fisher et al., 1998). A series of [RSJ product ions were formed, with n starting at 2-A and increasing up to 21 for longer reaction times, as observed for the cases of La and Pr the reaction rates correlated approximately with the occurrence of a ground or low excited state with two unpaired non-f electrons, as observed with other substrates. 

The direction of the transition dipole with respect to the molecular axis is determined by the symmetry of the lower and upper electronic states. is the projection of the angular momentum of the electrons on the intemuclear axis. A parallel transition excites from = 0 of the groimd state to an upper state with 2 = 0. A perpendicular transition will lead to a state with = 1. Figures 7.5 and 7.8 show the ground and low excited states of ICl. From the symmetry of the states, transitions in the longer visible wavelengths (say about 560 nm) are... 

The modified WKB method can also be applied to low excited states. This is discussed for the case of a multidimensional problem in Chapter 6. 

The symmetry-correct anion orbitals can also be utilized in calculations of states of the N03 cation. The primary purpose of this work is to examine the NO3 ionization spectrum and the ground and low excited states of the N03 cation system by the DIP-STEOM-CCSD method (40) (double ionization potential similarity transformed equation-of-motion coupled-cluster singles and doubles). The DIP-STEOM-CCSD method is built upon the IP-EOM-CCSD method (32) (ionization potential equation-of-motion coupled-cluster singles and doubles), which in turn, has been shown to be equivalent (41,42) to singly ionized FSMRCC, such as the example of Kaldor above. The DIP-STEOM-CCSD method generates ground and excited states of the cation by deletion of... 

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