Total spin density

Total spin density reflects the excess probability of finding a versus (3 electrons in an open-shell system. For a system in which the a electron density is equal to the (3 electron density (for example, a closed-shell system), the spin density is zero. 

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You can also plot ihe electrostatic polenlial. the total charge density. or the total spin density determined during a semi-enipincal or ah initio calculation. This information is useful in determining reactivity and correlating calculalional results with experimental data. Th ese examples illustrate uses of lb ese plots ... 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

Figure 3. Two-dimensional contours of total spin density of Ag°(C2Fl4) and Ag°(C2Fl4)2 complexes as the result of DFT calculations (B3LYP/A1CF//R-level)...

The most convincing evidence for the BC model of Mu in III-V materials comes from the nuclear hyperfine structure in GaAs. The hyperfine parameters for the nearest-neighbor Ga and As on the Mu symmetry axis and the corresponding s and p densities are given in Table I. One finds a total spin density on the As(Ga) of 0.45 (0.38) with the ratio of p to 5 density of 23 (4) respectively. The fact that 83% of the spin density is on the two nearest-neighbor nuclei on the Mu symmetry axis agrees with the expectations of the BC model. From the ratios of p to s one can estimate that the As and Ga are displaced 0.65 (17) A and 0.14(6) A, respectively, away from the bond center. The uncertainties of these estimates were calculated from spin polarization effects, which are not known accurately, and they do not reflect any systematic uncertainties in the approximation. These displacements imply an increase in the Ga—As bond of about 32 (7)%, which is similar to calculated lattice distortions for Mu in diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987) and Si (Estreicher, 1987). 

The tin hyperfine coupling constants for the hexaphenylditin radical anion enable values for the occupancy of the unpaired electron in the tin 5s and 5p orbitals of 0.10 and 0.34, respectively, to be calculated. This would imply that the electron occupies a tin sp3 hybrid orbital. Since the radical contains two tin atoms, the total spin density residing with the tin centres is ca 0.9. There is very little spin density residing with the ligands, and the... 

Comparing electrochemical behavior and biological transformations of purine bases, Japanese chemists (Yao and Musha 1974, Ohya-Nishiguchi et al. 1980) have considered the anion-radicals of purine, its 8-deutero and 6,8-dideutero derivatives. As it turned out, up to 40% of the total spin density is localized in position 6 of the purine anion-radical (see Scheme 3.7). Ohya-Nishiguchi et al. (1980) noted that such a large localized spin density is very rare in a n electron system of the purine s size and should have important application in relation to its chemical reactivity. Protonation should... 

Atom % K-electron density % total spin density ... 

Selected 17 O Hyperfine Constants and Total Spin Densities for Diatomic Oxygen Species with Equivalent Oxygen Nuclei... 

When adding the spin density matrices P and P3 to yield the total density matrix P, P = P + P3 and the total spin density matrix Ps being the difference of P and P 3, Ps = P - P3, we... 

The distribution of the total spin density in radicals was calculated using the UB3LYP16-31g method. In systems 1, 3, 4, and 8-11, the spin density is localized on the -S-N-S- fragment with minor spin distribution onto the Jt-framework, presumably through a spin polarization mechanism. For instance, in 1,3,2-dithiazolyl 1, virtually all positive spin density is localized on the -S-N-S- array due to the two polar resonance structures shown in Equation (2). A very similar spin distribution is observed in ring-fused derivatives 3, 4 and 9-11 <2001PCA7615>. 

In addition, we will present the mechanistic aspects concerning the electron-entry on four-coordinated phosphorus compounds. There are indications promoting the concept that a TBP is involved with the odd electron in an equatorial position. This presumption is based on the temperature-dependent ESR spectra of the radicals derived from 5. X-irradiation of a single crystal of 5 at liquid nitrogen temperature (77 K) yields the spectrum of radical 13 exclusively with ap//= 1120 G, api = 930 G, while,splitting is not resolved. From these values one calculates apls° = 993 G, indicating the phosphorus 3s spin density is 0.27, while the anisotropic contribution places 0.61 of the spin density in its 3p orbital, giving a total spin density of 0.88 on phosphorus. 

For a more detailed analysis, it is helpful to distinguish between direct and indirect contributions. In treatments which employ a one particle basis to describe the electronic structure, two different contributions to the spin density at a given center can be distinguished. The first part is proportional to the spin density of the singly occupied orbital (SOMO) at the center under consideration. In the following, this will be called the direct contribution . The difference between the direct contribution and the total spin density at the given center is summarized as indirect contributions , and arise from spin polarization and correlation effects (cf. section 2). 

The spin density (pi) at the unsubstituted end of the radical can be calculated directly from the proton hyperfine coupling constants, using the relationship, A = 2i-lp (McConnell and Chesnut, 1958 Fessenden and Schuler, 1963). The spin density (ps) at the substituted end of the radicals can be calculated if it is assumed that the total spin density in the conjugated 77-electron system of the radical is unaffected by substitution. Then ... 

For some other molecular properties the wave function must be accurate in the proximity of nuclei. Such a property is for example the hyperfine splitting caused by Fermi contact term which is proportional to the total spin density at the nucleus. Among the one-electron pro-... 

Here denotes the density matrbc of the spin surroundings, while / , B, and C, are the constants that denote the state of ith subensemble after the preparation. This decomposition of the total spin density matrbc into a sum... 

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