Orbital parameters

Thiel W and A A Voityuk 1994. Extension of MNDO to d Orbitals Parameters and Results for Silicon. 

It is difficult to treat the effect of a heteroatom on the localization energies of aromatic systems, but Brown has derived molecular orbital parameters from which he has shown that the rates of attack of the phenyl radical at the three positions of pyridine relatively to benzene agree within 10% with the experimental results. He and his co-workers have shown that the formation of 1-bromoisoquinoline on free-radical bromination of isoquinoline is in agreement with predictions from localization energies for physically reasonable values of the Coulomb parameters, but the observed orientation of the phcnylation of quinoline cannot be correlated with localization ener-... 

In the realistic case where the potential is spin-dependent, the spin-orbit method is in trouble (should the spin-orbit parameter be calculated with the up or the down spin potential ). The present formalism allows for the use of spin-dependent potential and wavefunctions. 

There is an interesting similarity in the character of the solution absorption spectra of the isoelectronic ions Np3+ and Pu1 even though the absorption bands in Pu1 + are all shifted toward higher energies due to increases in both the electrostatic (Fk) and spin-orbit ( ) parameters, Table VI. We have also examined the spectra of complex alkali-metal Pu(IV)... 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

Reminder The one-electron spin-orbit coupling coefficient, is intrinsically positive. The many-electron spin-orbit parameter X is defined by... 

The binary pulsar PSR1913+16. In 1974 Russell Hulse and Joseph Taylor discovered a very special pulsar PSR1916+13. A striking feature that was revealed just after its discovery was a large shift of the pulses rate with a period of a few hours. This was explained by Doppler shift, so PSR1916-H13 is in fact a binary system in which a pulsar orbits about the center of mass of the system. Thanks to the presence of this very stable local clock, Hulse and Taylor were able to obtain all the orbital parameters of this system. By studying the variations of those parameters over nearly twenty years, they... 

Fig. 18-2 Orbital parameters that control the seasonal and annual receipt of radiation at the Earth s surface. The Earth s rotational axis tilts and wobbles as shown. The eccentricity of the orbit is dp — d )/ (dp + da) which is zero for a circle but for the Earth s orbit is sometimes as large as 0.06. (After Hartmann (1994, p. 303) and Turekian (1996, p. 80).)...

A sample of 823 stars with abundances of several elements (Fe,0,Mg,Ti,Si, Na,Ni,Al) was compiled from several papers (Ref 1 to 10) after checking the lack significant differences between their results. The velocities (U,V,W) and orbital parameters were computed for 640 Hipparcos stars having <0.25, to make a large database combining kinematics and detailed abundances. Ages of 442 stars were retrieved from Nordstrom et al(2004). 

These applications show how easy it is to modify a program, once it has been developed, to explore such questions. Another application, not undertaken here, would be to explore Milankovitch perturbations in the Earth s orbital parameters, eccentricity, obliquity, and date of perihelion. These parameters are specified as constants at the beginning of the program, and it would be simple to change their values as predicted by astronomical calculations, in order to see how the seasonal variation of temperature is affected at various latitudes. 

Recently, molecular orbital calculations on some iron complexes have been made by Gray and his co-workers (2, 30). These values for ferrous complexes are plotted in Figure 2 as the dashed line [3d 4s (MO)]. Hence, Mossbauer spectroscopy provides estimates for the 4s electron contribution for molecular orbital calculations. This correlation does not hold for high spin complexes such as FeCb" and FeFe ". Bersuker (3, 4) has attempted to relate both S and AEq directly to molecular orbital parameters. Using the equations developed from this approach, Bersuker, Gordanskii, and Makarov (5) have concluded that in tin tetrahalides the role of dx-Px bonding is significant. 

In these first studies, resort was done to the OLPA scheme to estimate 4 for tho CAB contributions to the molecular mean ionization energy. By combining equations (8), (11), and (13) 4 was obtained using the scaling parameter 1 yielding the following simple expression in terms of the orbital parameters [42] ... 

We have applied the above procedure to a selected number of free atoms with Z< 36 not reported in Ref. [52]. Table 1 displays the optimized orbital parameters and total ground state energies as compared to corresponding Hartree-Fock estimates [61]. Note that for most of the systems, the TFD(1/8)W energies are systematically below the HF values by about 0.1% difference indicating a possible best value for the 2 parameter close to 2 = 1/8. 

Using the obtained values of the orbital parameters contained in Table 1 and those reported in Ref. [52] for all atoms with 2corresponding orbital and total mean excitation energies using equations (5), (9), (28), and (29). Table 2 shows the results calculated here (TFDW) as compared to those by Oddershede and Sabin (OS) and Meltzer, Sabin, and Trickey (MST). In general, the Is, 2s, 3s, and 3p orbital mean excitation energies obtained through the TFDW method are closer to the OS values as compared to the MST estimates. Major differences are observed for the 2p, 3d, 4s, and 4p orbitals, with the MST values closer to those by OS except for the 4s orbital for atoms from Zn to Kr. 

Table 1. Best orbital parameters and total energies tfd(i/s)w for the ground state of selected free atoms obtained through the TFD(1/8)W energy density functional... 

Local-Scaling Transformation Version of Density Functional Theory Talbe 3. Orbital parameters for function... 

The intra-orbit optimization process is carried out by varying the density parameters uj, 6,-, cj while keeping the wavefunction (or orbital) parameters fixed. Alternatively, inter-orbit optimization is accomplished by optimizing the wavefunction parameters for the energy functional... 

A variety of different approaches to the prediction of toxicity have been developed under the sponsorship of the Predictive Toxicology Evalnation project of the National Institnte of Environmental Health Sciences. The widespread application of compnta-tional techniqnes to stndies in biology, chemistry, and environmental sciences has led to a qnest for important, characteristic molecnlar parameters that may be directly derived from these compntational methods. Theoretical linear solvation energy relationships combine compntational molecular orbital parameters with the linear solvation energy relationship of Kamlet and Taft to characterize, nnderstand, and predict biological, chemical, and physical properties of chemical componnds (Eamini and Wilson, 1997). 

In an attempt to answer this question, we have calculated the probability for a nova outburst not to occur (in 50 years) in 86 DN systems (for which at least some of the orbital parameters are known). 

The metal ions which form Square planar complexes with simple ligands have a -electronic configuration. The five degenerate d-orbitals of the uncomplexed metal ion split into four different levels in a square planar complex. Thus three orbital parameters are needed. to describe the ligand field d-sputtings. 

Here the sum is over all Z values for which there is a known R(Z) value. As expected, the values of the parameter q, obtained in this way, as a rule are very close to the corresponding quantities, following from the hydrogenic approximation q = 1 for the integrals of the electrostatic interaction, 2 for average energies, 4 for spin-orbit parameter and q = —k for mean values of rk. 

Table 7.1 Atomic orbital parameters used in extended Huckel calculations. Single zeta STO functions are used for B and C and double zeta STO functions are used for the transition metals...

The curves in Fig. 4 demonstrate the dependence of the normalized critical current / Jc° s (0) on the spin-orbit parameter Aa for asymmetric (a)... 

Fig.4. Potential hypersurfaces of T, (3P0) and r4 (3P,) levels in the e (Q2, Q3) subspace calculated from the Fukuda coupling matrix with the vibronic coupling parameter Are t = 4x 10 9 J/m from Eq. (5) (denoted by b in [84]), the electron (exchange) repulsion parameter G and spin-orbit parameter are both set equal to 0.3 eV...

---