Density coupling constants

A = cross peak intensity B = magnetic flux density / = coupling constant = population of rotamer i R y= relaxation rate between spins i and / r = internuclear distance 0 = probability of double- and zero-quantum transitions, respectively, in the rotating frame W2, Wq = transition probability for double- and zero-quantum transitions, respectively y = gyromagnetic ratio, o = cross-relaxation rate r, t2 = correlation times = correlation time tjjj = mixing time (j) ip a) = peptide backbone angles X = bond angles of peptide side-chains (Oq = Larmor frequency. 

Hence, a measurement of hyperfme coupling constants provides infonnation on spin densities at certain positions in the molecule and thus renders a map of tlie electronic wavefiinction. 

The CIDNP spectrum is shown in figure B 1.16.1 from the introduction, top trace, while a dark spectrum is shown for comparison in figure B 1.16.1 bottom trace. Because the sign and magnitude of the hyperfine coupling constant can be a measure of the spin density on a carbon, Roth et aJ [10] were able to use the... 

A simple, non-selective pulse starts the experiment. This rotates the equilibrium z magnetization onto the v axis. Note that neither the equilibrium state nor the effect of the pulse depend on the dynamics or the details of the spin Hamiltonian (chemical shifts and coupling constants). The equilibrium density matrix is proportional to F. After the pulse the density matrix is therefore given by and it will evolve as in equation (B2.4.27). If (B2.4.28) is substituted into (B2.4.30), the NMR signal as a fimction of time t, is given by (B2.4.32). In this equation there is a distinction between the sum of the operators weighted by the equilibrium populations, F, from the unweighted sum, 7. The detector sees each spin (but not each coherence ) equally well. 

Experimental confirmation of the metal-nitrogen coordination of thiazole complexes was recently given by Pannell et al. (472), who studied the Cr(0), Mo(0), and W(0) pentacarbonyl complexes of thiazole (Th)M(CO)5. The infrared spectra are quite similar to those of the pyridine analogs the H-NMR resonance associated with 2- and 4-protons are sharper and possess fine structure, in contrast to the broad, featureless resonances of free thiazole ligands. This is expected since removal of electron density from nitrogen upon coordination reduces the N quad-rupole coupling constant that is responsible for the line broadening of the a protons. 

Spin densities help to predict the observed coupling constants in electron spin resonance (ESR) spectroscopy. From spin density plots you can predict a direct relationship between the spin density on a carbon atom and the coupling constant associated with an adjacent hydrogen. 

Calculated rr-bond orders are summarized in Table 1. These calculations are supported by chemical evidence that the S—N bond is the one most easily cleaved. Attempts have been made to relate bond orders and electron densities to NMR coupling constants (74CJC833, 77aC6i9> and CNMR (75CJC596, 75CJC1677> and NNMR (78JOC4693> chemical shifts, with limited success. 

Assignment of the signals is completed in Table 30.2. The criteria for assignment are the shift values (resonance effects on the electron density on C and N), multiplicities and coupling constants. Because the difference between them is so small, the assignment of N-8 and N-9 is interchangeable. 

The EPR spectrum of the ethyl radical presented in Fig. 12.2b is readily interpreted, and the results are relevant to the distribution of unpaired electron density in the molecule. The 12-line spectrum is a triplet of quartets resulting from unequal coupling of the electron spin to the a and P protons. The two coupling constants are = 22.38 G and Op — 26.87 G and imply extensive delocalization of spin density through the a bonds Note that EPR spectra, unlike NMR and IR spectra, are displayed as the derivative of absorption rather than as absorption. 

Compute the isotropic hyperfine coupling constant for each of the atoms in HNCN with the HF, MP2, MP4(SDQ) and QCISD methods, using the D95(d,p) basis set Make sure that the population analysis for each job uses the proper electron density by including the Density=Current keyword in the route section. Also, include the 5D keyword in each job s route sectionfas was done in the original study). 

The electron densities for a spin electrons and for spin electrons are always equal in a singlet spin state, but in non-singlet spin states the densities may be different, giving a resultant spin density. If we evaluate the spin density function at the position of certain nuclei, it gives a value proportional to the isotropic hyperfine coupling constant that can be measured from electron spin resonance experiments. 

Barone also introduces two new basis sets, EPR-Il and EPR-llI. These are optimized for the calculation of hyperfine coupling constants by density functional methods. EPR-Il is a double zeta basis set with a single set of polarization functions and an enhanced s part. EPR-III is a triple zeta set including diffuse functions, double d polarization functions and a single set off functions. 

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

Tile ESR spectra of the radical anions, generated by one-electron reduction of the a-oxothioketone 173 and the dithiete 172, were determined, and spin densities were calculated from the coupling constants and, especially, from the anisotropic values (87CB575). 

In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

Table 2 shows the hyperfine coupling constants obtained at the B3-LYP/6-311+G(2df,p)//B3-LYP/6-31G(d) level. The calculations reiterate the results cf reference [9], that the largest spin density is on H], which is consistent with the... 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

Isotropic Hyperfine coupling constants an are related to the spin densities p(rN) at the corresponding nuclei by... 

Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized.

A great deal of information on the electronic structure and geometry of radicals in solution can be extracted from their ESR spectra, as it is well established that the values of hyperfine coupling constants (hfcc), arising from the spin density of the s-orbitals, markedly increase with increasing of the SOMO s-character. The pyramidalization of the radicals is manifested in higher values of their hfccs (o-radicals), whereas smaller values of the hfccs are indicative of the more planar radicals (tt-radicals). 

The anionic Si atom is nearly tetrahedral, being bonded to the two Si atoms of substituents and two Li atoms. The resonance of this Si anionic center in the Si NMR spectrum of 55 Li2 was observed at a very high field (-292.0ppm) as a quintet due to coupling with the 2 equivalent Li atoms (/ = 1) with a coupling constant of 15.0Hz. This chemical shift is largely shifted upheld compared with that of (MesSOsSiLi (-189.4ppm), ° because of the sharply increased electron density... 

---