Molecular nuclei

The random diffusion of molecules in a magnetic field gradient causes an irreversible loss of phase coherence in the transverse magnetization of the molecular nuclei—i.e., it causes a decrease in a measurable signal h according to the relation 12) ... 

The last point regarding basis sets that will be important for the discussion here is the inclusion of diffuse functions. As the name implies, diffuse functions are used to describe electron density far from a nucleus. The role of electrons far from molecular nuclei is especially important in two cases. Anionic models require diffuse... 

Both newly generated HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) levels of fluorinated compounds are lower than those of a hydrogen compound. These lower orbital energy levels of the fluorinated compound indicate a high reactivity toward the reductant (electron donor to the LUMO) and a low reactivity toward the oxidant (electron acceptor from the HOMO). Moreover, a lower HOMO suggests strongly that the valence electrons captured by the molecular nuclei in the fluorinated... 

If the quantity (3.171) weakly depends on R, which is the case for sufficiently intense dipole transitions, it can be considered as a constant taken at a certain value R = Rq, Ro being the molecular nuclei configuration at the ground state, and removed from integration in (3.170). Thus we obtain... 

Not taking into account the electron charge, eEMP acts as a positive definite (PD) distribution, with maxima located at molecular nuclei. Thus, the... 

It can be concluded that KE can be considered related to the norm of the QO wavefunctions gradient. As a consequence it could be interesting, to obtain KE DF, K, maps or images in the same way as they are customarily obtained for the eDF, p 9. A complementary information to eDF will surely be obtained from these representations. Similar shapes of both functions at large distances from the molecular nuclei shall be expected, but having very different behaviour near the nuclei. 

FuUy reversible melting, as just shown for LLDPE and many other polymers. This reversible melting is either caused by short, decoupled segments of the molecules (see Figs. 3.75 and 3.91) or indicates remaining molecular nuclei. 

It was implicitly assumed in the discussion so far that the motion of the molecular nuclei is determined by a single Born-Oppenheimer potential energy surface. However, in vibronic coupling systems, there are several coupled electronic states of importance. The MCTDH algorithm hence has to be extended to deal with more than one electronic state. 

The feature of the all considered experimental methods is that they allow us to define the values of the molecular polarizabilify only at the equilibrium position of molecular nuclei. To obtain the dependencies of molecular polarizabilities on the mutual location of nuclei in a molecule, the Raman effect can be used The line intensities of Raman spectra depend on the values of polarizability derivatives with respect to the nuclei displacements. The first works to define the polarizability derivatives of molecules have appeared immediately after the creation of the theory of Raman light scattering (Placzek theory of polarizability) [17]. However, the experimental technique of pre-laser period could not obtain the high-quality results. Some experimental results of this period are summarized in [18]. Currently, these data have only a historical interest. Now, laser technologies allow to increase the measurement accuracy and, as a result, significantly improve and revise the pre-laser data. Nevertheless, up to day the experimental data on flie polarizability derivatives of molecules are fragmentary and do not give the impression of systematic studies of the polarizability of molecules as a function of the nuclei coordinates, even for diatomic molecules [19-39]. 

The molecular nuclei, 3-cephem (8) and penam (21) are considered first. As is well known (Sweet, 1973), the p-lactam amide portion of these nuclei is essentially planar, although one carbon of the p-lactam ring, C5(6) of penicillins (cephalosporins), can be displaced up to 0.4 A toward the p face of the molecule (i.e., toward sulfur). The ring has little conformational flexibility. Likewise, the dihydrothiazine ring of 3-ce-phems is rather rigid and exists in only one conformation. The sulfur lies above the plane formed roughly by the other five atoms of the ring. 

It may be concluded that any correlation between p-lactam carbonyl stretching frequency with some other property, such as antibacterial activity or basic hydrolysis rates (Indelicate et al., 1974), will emerge more distinctly if different molecular nuclei are embraced in the comparison (D. B. Boyd, unpublished data, 1980). 

D. Excited Electronic States of the 3-Cephem and Penam Molecular Nuclei... 

Now, all molecules exhibit this electronic polarisabiUty, the effect being greatest when there are most electrons least strongly bound to the molecular nuclei. For polymer units this means that ... 

In NMR, the pulse of frequencies generates a new magnetic field when it interacts with the molecular nuclei which then gradually decays. The receiver detects this and records the free induction decay (FID) pattern as a function of time. 

Gavezzotti and his co-workers have pioneered the concept of the molecular nuclei. Given a molecular stmcture, clusters of molecules (nuclei) are built using various symmetry operators, including glide, inversion, and screw elements. These symmetry operations accompanied by translations account for around 80% of the space groups and, more importantly, all the important space groups for molecular materials (see Section 5.2). The relative stability of each of these clusters is appraised... 

The concept of charge flux arises in empirical molecular force fields in connection with the calculation of electrostatic forces on the molecular nuclei. 

This clearly was, at least, a very uncomfortable situation and Sidgwick attempted to avoid the difficulty by shifting the argument away from atomic structure as such, to the idea of molecular structure in which pairs of electrons had common orbits of the Bohr-Sommerfeld type involving the molecular nuclei. He... 

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