Orbit Coupling Constant Research Articles

Theoretical Study on Anisotropic Magnetoresistance Effects ofI// [100],I// [110], andI// [001] for Ferromagnets with a Crystal Field of Tetragonal Symmetry

Using the electron scattering theory, we obtain analytic expressions for anisotropic magnetoresistance (AMR) ratios for ferromagnets with a crystal field of tetragonal symmetry. Here, a tetragonal distortion exists in the [001] direction, the magnetization ${\mbox{\boldmath $M$}}$ lies in the (001) plane, and the current ${\mbox{\boldmath $I$}}$ flows in the [100], [010], or [001] direction. When the ${\mbox{\boldmath $I$}}$ direction is denoted by $i$, we obtain the AMR ratio as ${\rm AMR}^i (\phi_i)= C_0^i + C_2^i \cos 2\phi_i + C_4^i \cos 4 \phi_i \ldots = \sum_{j=0,2,4,\ldots} C_j^i \cos j\phi_i$, with $i=[100]$, $[110]$, and $[001]$, $\phi_{[100]} = \phi_{[001]}=\phi$, and $\phi_{[110]}=\phi'$. The quantity $\phi$ ($\phi'$) is the relative angle between ${\mbox{\boldmath $M$}}$ and the $[100]$ ($[110]$) direction, and $C_j^i$ is a coefficient composed of a spin--orbit coupling constant, an exchange field, the crystal field, and resistivities. We elucidate the origin of $C_j^i \cos j\phi_i$ and the features of $C_j^i$. In addition, we obtain the relation $C_4^{[100]} = -C_4^{[110]}$, which was experimentally observed for Ni, under a certain condition. We also qualitatively explain the experimental results of $C_2^{[100]}$, $C_4^{[100]}$, $C_2^{[110]}$, and $C_4^{[110]}$ at 293 K for Ni.

Moment Analysis Method As Applied to the 2S → 2P Transition in Cryogenic Alkali Metal/Rare Gas Matrices

The moment analysis method (MA) has been tested for the case of 2S --> 2P ([core]ns1 --> [core]np1) transitions of alkali metal atoms (M) doped into cryogenic rare gas (Rg) matrices using theoretically validated simulations. Theoretical/computational M/Rg system models are constructed with precisely defined parameters that closely mimic known M/Rg systems. Monte Carlo (MC) techniques are then employed to generate simulated absorption and magnetic circular dichroism (MCD) spectra of the 2S --> 2P M/Rg transition to which the MA method can be applied with the goal of seeing how effective the MA method is in re-extracting the M/Rg system parameters from these known simulated systems. The MA method is summarized in general, and an assessment is made of the use of the MA method in the rigid shift approximation typically used to evaluate M/Rg systems. The MC-MCD simulation technique is summarized, and validating evidence is presented. The simulation results and the assumptions used in applying MA to M/Rg systems are evaluated. The simulation results on Na/Ar demonstrate that the MA method does successfully re-extract the 2P spin-orbit coupling constant and Landé g-factor values initially used to build the simulations. However, assigning physical significance to the cubic and noncubic Jahn-Teller (JT) vibrational mode parameters in cryogenic M/Rg systems is not supported.

Assignment of the Electronic Spectra of [Mo(CN)8]4‐ and [W(CN)8]4‐ by ab initio Calculations.

CASPT2 calculations are performed on the dodecahedral and square antiprismatic isomers of the [Mo(CN)8]4- and [W(CN)8]4- complexes. The high-energy experimental bands above 40000 cm-1 are assigned to MLCT transitions. The experimental observed trend of the extinction coefficients for the molybdenum and tungsten complex is reproduced by our CASSCF oscillator strengths. All bands below 40000 cm-1 can be ascribed to ligand-field transitions, although small contributions from forbidden MLCT transitions cannot be excluded. In order to account for all experimental bands in the electronic spectrum of these octacyanocomplexes, a dynamic equilibrium in solution between the two isomeric forms must be hypothesized. Spin−orbit coupling effects are found to be more important for the square antiprismatic isomers; in particular, large singlet−triplet mixings are calculated for this isomer of [W(CN)8]4-. Ligand-field and Racah parameters as well as spin−orbit coupling constants are determined on the basis of the calculat...

Theoretical Study of Oxygen Isotope Exchange and Quenching in the O(1D) + CO2 Reaction

Ab initio multireference configuration interaction calculations have been carried out for the CO3 system in singlet and triplet electronic states to investigate the mechanism of the O(1D) + CO2 reaction. The reaction has been shown to occur through the formation of an O−CO2 complex s0, which then isomerizes to a cyclic O(CO2) structure s1 over a barrier at s-TS0 located ∼0.3 kcal/mol below the reactants. The cyclic isomer s1, 48.8 kcal/mol lower in energy than O(1D) + CO2, can in turn rearrange to a D3h structure s2, only slightly higher in energy. The isomers s1 and s2 formed in the reaction possess high internal energy and can decompose into the initial reactants or undergo singlet−triplet intersystem crossing to form the triplet isomer t1, which can dissociate to O(3P) + CO2. If the attacking oxygen atom is isotope-labeled, isotope exchange can occur due to symmetry properties of s1 and s2. The ab initio energies, molecular parameters, and spin−orbit coupling constants were employed in statistical calculations of various isomerization and dissociation reaction rates. For intersystem crossing rates, we used the theory of radiationless transitions, in which the rates are determined as a product of the overlap of electronic wave functions (spin−orbit coupling) and the overlap of vibrational wave functions (Franck−Condon factor). The calculated rate constants were then used to compute the product branching ratios both for the case of the 16O(1D) + 44CO2 reaction and for the isotope-labeled 18O(1D) + 44CO2 reaction. For the latter, the calculated relative branching ratios of the 16O(1D) + 46CO2 and 16O(3P) + 46CO2 products at collision energies of 4.2 and 7.7 kcal/mol, 17/83 and 42/58, agree reasonably well with the experimental values of 16/84 and 33/67 (ref 4), respectively, and reproduce the qualitative trend with Ecol. The overall relative yields computed for 44CO2 and 46CO2 show that the attacking O(1D) atom can be incorporated into the product CO2 molecule with a near-statistical probability of 2/3.

Theoretical Studies of Regioselectivity in the Photochemical Cycloaddition of Allene to Cyclopentenone

In the photocycloaddition of allene to cyclopentenone, four different triplet 1,4-biradicals can form, two of which contain an allylic moiety from addition to the central carbon of allene, while two others result from addition to a terminal carbon of the allene. The two biradicals containing the allyl fragment are predicted to be approximately 20 kcal/mol lower in energy than the other two. Using a model for the reaction mechanism in which the relaxed triplet excited state of allene reacts with ground state cyclopentenone, the reaction barriers to forming these allylic substituted systems are lower by ca. 8−10 kcal/mol in comparison to the other two. The conformation of the biradicals upon spin inversion is in all probability one important factor in determining whether the biradicals close to products or revert to starting materials. The sp3 hybridization at the bond-forming carbon in the vinyl (nonallylic) systems leads to nearly free rotation about that bond, and three shallow minima and the corresponding transition states for internal rotation were located. One minimum has the two carbon centers which carry the excess spin density about 3.8 Å, apart while in the other two minima the distances are ∼3.1 Å. Taking these distances into account, it is estimated that very few of the intermediates formed from the addition α to the carbonyl close to products. In contrast, a high percentage of the systems formed from attack β to the carbonyl are predicted to yield products. In the allylic substituted systems, carbon centers with some radical character are always relatively close to the site of radical character in the cyclopentenone ring. The relative ratio of cycloadducts can be estimated from the distribution of the biradicals. Important factors considered in this study include energetics, conformations, spin−orbit coupling constants, and the singlet−triplet energy splittings of the intermediate biradicals.