Level schemes

Figure Al.6.20. (Left) Level scheme and nomenclature used in (a) single time-delay CARS, (b) Two-time delay CARS ((TD) CARS). The wavepacket is excited by cOp, then transferred back to the ground state by with Raman shift oij. Its evolution is then monitored by tOp (after [44])- (Right) Relevant potential energy surfaces for the iodine molecule. The creation of the wavepacket in the excited state is done by oip. The transfer to the final state is shown by the dashed arrows according to the state one wants to populate (after [44]).

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

Figure B2.5.12. Hyperfine structure energy level scheme and spectrum for the...

Before we look at the various methods of pumping we shall consider the types of energy level scheme encountered in lasing materials. 

Laser action fakes place befween excifed levels of fhe neon atoms, in a four-level scheme, fhe helium atoms serving only fo mop up energy from fhe pump source and fransfer if fo neon atoms on collision. The energy level scheme is shown in Figure 9.12. 

The spectroscopy of ion lasers is generally less well understood than that of neutral atom lasers because of the lack of detailed knowledge of ion energy-level schemes. Indeed, ion lasers were first produced accidentally and attempts to assign the transitions came later. 

Figure 9.1 8 Energy level scheme for a dye molecule showing nine processes important in laser action...

Figure 9.30 Vibrational energy level scheme for multiphoton dissociation...

Fig. 2.35. Typical EEL spectrum and corresponding energy-level scheme.

Tietze et al. investigated the Diels-Alder reaction between 44 and 2-methylbut-2-ene at the B3-LYP/6-31G level (Scheme 30) [98EJ02733]. 

The vibrational spectra of 1,2-dithiole-3-thione 46 and 1,2-dithiol-3-one 47 were computed at the DFT and MP2 levels (Scheme 31) [98VS77]. Most remarkably, the uniformly scaled MP2 fundamentals are in better agreement with experimental data than the corresponding DFT frequencies. 

The reactions of the diazine radicals with O2 were studied at the B3-LYP/6-311-1- G level (Scheme 59) [00JPC(A)6088]. Formation of dioxiranyl radical intermediates was found to be the most important pathway from the peroxy precursor. DFT-derived geometric parameters of pyrimidiniumolate are in good agreement with experimental data obtained for 1,2,3,5-tetraphenylpyrimidiniumolate [97MI1]. 

Figure 12-8. Encigy level scheme of a iriluyer LF.D consistin of polylliiciiylvinylcnc (PTV). 1.4-/M.v(4 -dipliL-nylaiiiiiioslyiyl)-2.5-dinieilioxy-ben/cne (DASMI5) and 2-(4-hipheiiyl)-5-(4-lcit-hutylphcnyl)- 1,3.4-oxadiazolc (PliD) (Ref. 127p.

Recent observations of fluorescence in NpF6 and PuF6 (46) are consistent with the energy-level scheme proposed. However, comparison of the calculated level structure with high-resolution spectra of PuFg (44) confirms that much of the observed structure is vibronic in character, built on electronic transitions that are forbidden by the inversion symmetry at the Pu site. 

Fig. 15 Energy level scheme of the isotopic line splitting of V9 in terms of the free molecules ( Sg and 81 87 as the main contributions) and of the orthorhombic crystal with natural abundance of isotopomers, after [109], Numerical values are observed wavenumbers (in cm ), values in brackets came from MD simulations on free rings [131] and in the case of au from LD calculations [116, 117]...

Scheme 3). The qualitative energy levels (Scheme 4) show the number of valence electrons necessary to obtain closed-shell electronic structures. Each orbital in the. y-orbital set is assumed to be occupied by a pair of electrons since the 5-orbital energies are low and separate from those of the p-orbital ones, especially for heavy atoms. The total number of valence electrons for the closed-shell structures... 

The i-orbital array of three and four-membered rings is of the Hiickel conjugation. (Scheme 2). The splitting patterns of the orbital energy levels (Scheme 3) show that the total number of valence electrons for the closed-shell structures is 4Af + 2 for the three- N= 0) and four-membered rings (N= 0, 1). 

All molecules of a particular type have orbital energy level schemes that are qualitatively similar but differ in the number of valence electrons for example, BH2 and NHj belong to the same diagram. 

Figure 10. Electron excitations in radicals (a) Collective representation of one-electron transitions of the A, B, and C types if denotes MO (b) LCI energy-level scheme (Jablonski diagram) for doublet and quartet states indicating why with radicals fluorescence (- - -) but not phosphorescence is observed. Spin-forbidden transitions are represented by dashed lines.

Figure 13. Orbital energy-level scheme for the biphenyl anion radical (A) and biphenyl cation radical (C) based on the SCF calculations (59) by the Pople and Longuet-Higgins method. Pairing of MO s is indicated. Thick lines with arrows represent the five lowest transition energies. All entries are given in eV.

The colors of fireworks displays are produced by emission from atomic ions as described in Chapter 7. The explosions of fireworks promote electrons to excited states. The energy level scheme of every element is different, so fireworks manufacturers can change colors by incorporating different elements. Sodium ions emit... 

Finally, the rotational partition function of a diatomic molecule follows from the quantum mechanical energy level scheme ... 

Figure 3.5. Energy level scheme of two hypothetical molecules...

FIGURE 8.2 (a) Simplified energy-level scheme of a carotenoid molecule. The solid arrow represents the... 

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