A-doublets

The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

This establishes our assertion that the former roots are overwhelmingly more numerous than those of the latter kind. Before embarking on a formal proof, let us illustrate the theorem with respect to a representative, though specific example. We consider the time development of a doublet subject to a Schrodinger equation whose Hamiltonian in a doublet representation is [13,29]... 

Thus, we can use the approximate quantum number m to label such levels. Moreover, it may be shown [11] that (1) 3/m is one-half of an integer for the case with consideration of the GP effect, while it is an integer or zero for the case without consideration of the GP effect (2) the lowest level must have m = 0 and be a singlet with Ai symmetry in 53 when the GP effect is not taken into consideration, while the first excited level has m = 1 and corresponds to a doublet E conversely, with consideration of the GP effect, the lowest level must have m = j and be a doublet with E symmetry in S, while the first excited level corresponds to m = and is a singlet Ai. Note that such a reversal in the ordering of the levels was discovered previously by Hancock et al. [59]. Note further thatj = 3/m has a meaning similar to thej quantum numbers described after Eq. (59). The full set of quantum numbers would then be... 

WFth all semi-empirical methods, IlyperChem can also perform psendo-RIfF calculations for open -shell systems. For a doublet stale, all electrons except one are paired. The electron is formally divided into isvo "half electron s" with paired spins. Each halfelec-... 

Closed-sh ell inolceiiles h avc a multiplicity of on c (a sin glet), A radical, with on e un paii ed deetroii, h as a m ultiplieity of two (a doublet),. A iTiolceiilar system with two unpaired eleelrons (usually a triplet) has a m u Itip licity o f ihrec. In some cases, however, such as a biradieal, two unpaired electrons may also be a singlet. 

To define the state yon want to calculate, you must specify the m u Itiplicity. A system with an even ii n m ber of electron s n sn ally has a closed-shell ground state with a multiplicity of I (a singlet). Asystem with an odd niim her of electrons (free radical) nsnally has a multiplicity of 2 (a doublet). The first excited state of a system with an even ii nm ber of electron s usually has a m n Itiplicity of 3 (a triplet). The states of a given m iiltiplicity have a spectrum of states —the lowest state of the given multiplicity, the next lowest state of the given multiplicity, and so on. 

The keyword is in the route section, line 1 of the input file. Lines 2, 3, and 4 are blank, comment, blank, respectively. Line 5 designates a charge of 1 and a spin multiplicity of 2 (a doublet). Line 6 specifies one atom as hydrogen, and line 7 specifies the second atom as hydrogen, attached to atom 1 at a distance of 1.32 A(2.49 bohr). Among several G2 energies printed out in about the last 25 lines of output are... 

Band 5, 6-25y. (1601 cm. i). Aromatic (phenyl) ring absorption. The weak shoulder at 6-33p. (1580 cm. i) may be noted. When the aromatic ring is conjugated, as in the present example, the aromatic (phenyl) band is often split into a doublet and is usually more pronounced (Table III). 

MHz H NMR spectrum of 1 1 dichloroethane (CI2CHCH3) showing the me thine proton as a quartet and the methyl protons as a doublet The peak multiplici ties are seen more clearly in the scale expanded insets... 

The NMR spectrum of isopropyl chloride (Figure 13 17) illustrates the appearance of an isopropyl group The signal for the six equivalent methyl protons at 8 1 5 is split into a doublet by the proton of the H—C—Cl unit In turn the H—C—Cl proton signal at 8 4 2 IS split into a septet by the six methyl protons A doublet-septet pattern is char acteristic of an isopropyl group... 

Section 13 9 The methyl protons of an isopropyl group appear as a doublet and the methine proton as a septet in compounds of the type (CH3)2CHX... 

Section 13 10 A doublet of doublets characterizes the signals for the protons of the type shown (where W X Y and Z are not H or atoms that split H themselves)... 

IS the only phosphorus isotope present at natural abundance and has a nuclear spin of The H NMR spectrum of tnmethyl phosphite (CH30)3P exhibits a doublet for the methyl protons with a splitting of 12 Hz... 

Closed-shell molecules have a multiplicity of one (a singlet). Arad-ical, with one unpaired electron, has a spin multiplicity of two (a doublet). Amolecular system with two unpaired electrons (usually... 

If you add a single electron to the LUMO orbital above to create an anion, you obtain total spin S=l/2 (a doublet). 

---