Spatial electron

Stem, P. S., M. Chorev, M. Goodman, and A. T. Hagler. 1983. Computer Simulation of the Conformational Properties of Retro-Inverso Peptides. II Ab Initio Study, Spatial Electron Distribution, and Population Analysis of N-Formylglycine Methylamide, N-Formyl N -Acetyldiaminomethane, and N-Methylmalonamide. Biopolymers 22, 1901-1917. 

A. T. Hagler, A. Lapicirella, Spatial Electron Distribution and Population Analysis of Amides, Carboxylic Acid, and Peptides, and Their Relation to Empirical Potential Functions , Biopolymers 1976, 1167-1200 A. T. Hagler, L. Leiserowitz, M. Tuval, Experimental and Theoretical Studies of the Barrier to Rotation about the N-C° and Ca-C Bonds ([Pg.369]

For a given total electron spin quantum number (S), the multiplicity is the number of possible orientations of the spin angular momentum for the same spatial electronic wavefunction. Thus, the multiphcity equals 25 -F 1. For... 

The key descriptors used to predict the likelihood of a CYP inhibition are incredibly vast. Descriptors can, for example, be defined as spatial, electronic or conformational. Some of the key structural properties include lipophilicity, pKa and PSA and are relatively easy to interpret, while others are more complex. For further information on descriptors used in DDI modeling, please refer to De Groot et al. [6]. 

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

The valence MO energies and Mulliken populations for H3PCH2 at various theory levels are shown in Table 6. The low HOMO energy is consistent with the first ionization potentials determined for substituted ylides which are in the range 6-7 eV (Section II.B.l.f). The Mulliken populations show that there is a build-up of electron density on carbon, also reflected in the integrated spatial electron population (ISEP) value of 9.2 at the 3-21G level 65, with a corresponding decrease in electron density of phosphorus. The semiquantitative approach of Jardine et a/.190 gives a similar result. 

The zero-order, spin-free Hamiltonian HSF commutes with the symmetric group SnF of permutations on the N different spatial electronic indices,... 

The use of the conventional spin formulation in conjunction with a spin-free Hamiltonian HSF merely assures symmetry adaptation to a given spin-free permutational symmetry [Asp] without recourse to group theory. In fact, one may symmetry adapt to a given spin-free permutational symmetry without recourse to spin. This is the motivation behind the Spin-Free Quantum Chemistry series.107-116 In this spin-free formulation one uses a spatial electronic ket which is symmetry adapted to a given spin-free permutational symmetry by the application of an appropriate projector. The Pauli-allowed partitions are given by eq. (2-12) and the correspondence with spin by eqs. (2-14) and (2-15). Finally, since in this formulation [Asp] is the only type of permutational symmetry involved, we suppress the superscript SF on [Asp],... 

Recalling that the elements of S F act only on the spatial electron coordinates, it follows that for the permutation (12) e SiF... 

J. B. Collins and A. Streitwieser Jr., J. Comput. Chem., 1, 81 (1980). Integrated Spatial Electron Populations in Molecules Applications to Simple Molecules. 

Microseconds to nanoseconds As previously mentioned, gated intensified vidicons can provide temporal resolutions as low as 40 nsec. New intensifiers, e.g., microchannel plates, may extend this range to 1-5 nsec or less. However, by far, the most useful tool for ns to ps spectroscopy is the streak camera, i.e., an ultra-rapid temporal-to-spatial electronic image sweeper (16). Streak cameras convert an optical signal, e.g., a spectrum, into... 

Angular or spatial electron shift induced by excitation results, in general, in weakening of some bonds within the molecule. The probability of the effective photochemical... 

Multiplicity Spin Multiplicity) The number of possible orientations, calculated as 2S -L 1, of the spin angular momentum corresponding to a given total spin quantum number (S), for the same spatial electronic wavefunction. A state of singlet multiplicity has S = 0 and 2S -i- 1 = 1. A doublet state has S = 1/2, 2S -i- 1 = 2, etc. Note that when S > L (the total orbital angular momentum quantum number) there are only 21 -t 1 orientations of total angular momentum possible. 

For a characterization of the electronic structure, the spatial electron density distributions, the bond order between atoms and ionicities of each atom in the cluster are estimated according to the Mulliken population analysis [35]. The overlap population, (2 ., of electrons between two atoms v and v is defined as,... 

Spatial electron density distributions in pure Mg Ni hydride The contour map of the electron densities on the (110) atomic plane is shown in Fig.7 for pure Mg Ni hydride. As shown in this figure, it is evident that relatively high electron-density regions extend from the H atom site towards the Ni atom site, but do not towards the Mg atom site. Also, the electron density distributions around the Mg atom site seem to show an extension towards the Ni atom site but does not towards the H atom site, although the Mg-H distance is shorter than the Mg-Ni distance. These results clearly indicate that hydrogen atoms exhibit a larger affinity with Ni atoms rather than Mg atoms in this system. 

When transformed to complex-valued spatial electronic basis functions... 

The study of the spatial electron relaxation in uniform fields has demonstrated its complexity and its sensitive dependence on the field strength. In these relaxation studies, a local disturbance at z = 0 has been initiated by the choice of the boundary value/j(L/) for the anisotropic distribution according to Eq. (59), and the succeeding spatial relaxation in a uniform electric field has been analyzed. 

On the basis of the space-dependent two-term approximation, including elastic and conservative inelastic electron collision processes, substantial aspects of the inhomogeneous electron kinetics, such as the spatial relaxation behavior in uniform electric fields and the response of the electron component to spatially limited pulselike field disturbances, have been demonstrated and the complex mechanism of spatial electron relaxation has been briefly explained. In these cases, starting from a specific choice of the boundary condition for the velocity distribution, the succeeding spatial evolution of the electrons in the field acceleration direction up to their establishment of a steady state has been studied. 

The spin-paired closed-shell case for which the spatial electron density is... 

For completeness we must take spin into account by multiplying each spatial electronic wave function by a or (3, depending on whether the component of electron spin along the internuclear axis is + 0T (in atomic units). Inclusion of spin doubles the degeneracy of all levels. 

The participation of the outer electrons in the chemical bonds, accompanied by a change in the spatial electron density distribution, has an effect on the position of the K level. As Karal nik [6] showed, the level displacement caused by a change in the screening of the nucleus by the valence electrons is as high as 1 eV. Our investigation of the position of the K line of silicon in the chromium silicides showed that, within the limits of experimental error, it coincides with its position in the pure element. 

The chemical composition of the IF phase deviates only very slightly, if at all, from the composition of the bulk layered compound. Deviations from stoichiometry can only occur in the cap of the nanotube. In fact, even the most modern analytical techniques such as scanning probe techniques and high-resolution (spatial) electron energy loss spectroscopy are unable to resolve such tiny deviations from the stoichiometry, like the excess or absence of a single Mo (W) or S (Se) atom in the nano tube cap. 

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