Vacuum values

Fig. 5. The /rSR spectra from fused quartz at room temperature and silicon at 77 K, each in a magnetic field of 10 mT. For quartz, the two high-frequency lines result from muonium with a hyperfine parameter close to that in vacuum. The two high-frequency lines in Si result from Mu, and their larger splitting arises because the hyperfine parameter is less than the vacuum value (0.45 Afree). The lowest line in each sample comes from muons in diamagnetic environments. The lines from 40 to 50 MHz in Si arise from Mu. From Brewer et al. (1973).

In diamond, Sahoo et al. (1983) investigated the hyperfine interaction using an unrestricted Hartree-Fock cluster method. The spin density of the muon was calculated as a function of its position in a potential well around the T site. Their value was within 10% of the experimental number. However, the energy profiles and spin densities calculated in this study were later shown to be cluster-size dependent (Estreicher et al., 1985). Estreicher et al., in their Hartree-Fock approach to the study of normal muonium in diamond (1986) and in Si (1987), found an enhancement of the spin density at the impurity over its vacuum value, in contradiction with experiment this overestimation was attributed to the neglect of correlation in the HF method. 

The magnitude of the injection barrier is open to conjecture. Meanwhile there is consensus that energy barriers can deviate significantly from the values estimated from vacuum values of the work-function of the electrode and from the center of the hole and electron transporting states, respectively. The reason is related to the possible formation of interfacial dipole layers that are specific for the kind of material. Photoelectron spectroscopy indicates that injection barriers can differ by more than 1 eV from values that assume vacuum level alignment [176, 177]. Photoemission studies can also delineate band bending close to the interface [178]. 

The transfer of the energy associated with this true vacuum charge current density to a matter current is achieved by adjusting the value of the coupling constant g such that the vacuum value g = f/,4i0 becomes e/h in matter. The resulting equation is... 

Let us compare first the calculated VCoul in water solvent versus vacuum for a model 7r-electron system, the ethane dimer. It is apparent that the medium strongly modifies the molecular transition densities in this example, actually increasing the electronic coupling VCoul relative to the vacuum value. However, the precise effect of solvent on VCoul has been found to depend on the chromophore and it is difficult to formulate predictive rules. 

Here, rDA is the donor-acceptor distance, H% 0) is the interaction at constant distance r0, and [1 is the so-called attenuation factor. In vacuum, values of [1 are relatively large in the range of 2-5 A-1 [21]. Consequently, at donor-acceptor distances commonly found in molecular dyads, the through space couplings will be negligible. 

In several examples for gases and dilute suspensions, we expand the dielectric response e around its vacuum value of 1 or around its pure-solvent value em, respectively, for the suspending medium. In those cases, the dimensionless x for the gas or for the suspension as a whole will be proportional to the number density of particles (units 1/length3), and the contribution to the polarizability from individual particles will have volume units (length3). 

Figure 3-15. Fluctuations in effective linear polarizability (a), first (b) and second (c) hyperpolarizability as function of simulation time from 50 ps MD runs. Vacuum values (

In the table, the laser wavelengths are air values and the wavenumbers for the I2 transitions are vacuum values from Ref. 11. The assignments are based on a calculation of the transition wavenumbers using the molecular parameters in Ref. 12. 

The first and fourth terms in the dispersion equations represent the difference between the square of the wavevectors Kq and Kg inside the crystal and the square K, which is the vacuum value k corrected for the mean inner potential. If there is no difference, there is no unique solution. Thus, the refractive index for Kq and Kg waves must be different from the average refractive index. This is the crux of the dynamical theory. 

For R > 8 nm the lifetime approached its. .vacuum" value (140 ns), however, with R increase certain changes of the spectrum still occurred. Ortho-positronium locates not only in the pores but also in small voids in the amorphous structure of the bulk medium. The lifetime of o-Ps in these voids (1.3 ns in Vycor. up to 2.5 ns in polymers) is by two orders of the magnitude shorter than in the pores. These small free volumes always appear at a high concentration and effectively trap the positronium only those of Ps atoms which were formed close to the surface, or on it. had the chance to outdiffuse there. One can expect that the fraction of Ps annihilating in pores will rise with the specific surface. A series of Vycor glasses with specific surfaces from 17 to 190 m"/g was studied. It was found that the intensity ratio of the 140 ns component to the sum of intensities 1.3 and 140 ns k = 1, / (F + 1 ,) increased systematically from 9% at the smallest surface to 90% at the largest one. I he dependence of k on specific pore surface area observed in our experiments seems to follow well the equation given by Brandt and Paulin [13] and modified by Venkateswaran [14]. 

Note that is the donor ionization potential in the polar solvent that may be different from the vacuum value. 

Except for narrow regions of the length A+ (np) 1 /l k y/2(np) ]e rn nearby the peaks the dynamical energy density is less than its initial vacuum value, in agreement with other results [112,164,165,168] obtained in the framework of different approaches. The minimum values of Wo far off peak are given by [taking into account the contributions of both the functions Fq(u) and Fq(u)]... 

This synopsis summarises three applications of the hybrid method, two of which actually involve chemical reactions. The combination of a semiempirical kernel and a force-field environment has been very successful in these application and has yielded information that could - at present - be obtained by other means (experimental or computational) only with considerable difficulty or not at all. One has to realise, though, that in practice there is a window of usefulness of the method If the energy differences are large enough the energetics will be mainly determined by vacuum values, i.e. environment effects will be negligible. If, on the other hand, the energy differences are small compared to the intrinsic inaccuracies of semiempirical method and force field the results cannot be trusted. 

---