P-terms

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

Nowadays there is a tendency to use the word term to describe that which arises from an approximate treatment of an electron configuration, whereas the word state is used to describe something that is observable experimentally. For example, we can say that the s 2s 2p 3d configuration of C gives rise to a term which, when spin-orbit coupling is taken into account, splits into Pi, 2 Pj, states. Since spin-orbit coupling can be excluded only in theory but never in practice there can be no experimental observation associated with the P term. ... 

In an ociiihcOraJ field (he free-ion ground F lerm of a d ion is split into an A and two T terms which, along with the excited T(P) term (Fig. A), give rise to the possibility of three spin-allowed d-d transitions of which (he one of lowest eneigy is a direct measure of the ciystal field splitting, A or 10 Dq ... 

The parameter ais the ionization energy of an electron from the p,th atomic orbital located on the Ath atom and ft is the so-called resonance integral (represented here by a simple exponential). The QB and P terms of represent corrections to the effective ionization potential due to the residual charges on the different atoms. The charges are determined by... 

The three p orbitals are directed along the three cartesian axes and so, in an octahedral crystal field, suffer equal repulsion from point charges sited on those axes. The energies of the three p orbitals, therefore, remain degenerate. Similarly, a free-ion P term remains unsplit in octahedral or tetrahedral crystal fields and is labelled Tig or Ti respectively. 

Figure 3-22. Orgel diagram for energies of octahedral or tetrahedral terms arising from free-ion F or P terms.

Strictly, L is defined only as a quantum number for a spherical environment - the free ion. The use of L ff = 0 for A terms or Leff = 1 for L terms on the grounds that (2Leff + 1) equals the degeneracy of these terms is, however, legitimate as used here. There is a close parallel between the quantum mechanics of T terms in octahedral or tetrahedral symmetry on the one hand, and of P terms in spherical symmetry on the other. 

From the condition Eq. (5) it is readily seen that for linearly polarized light the P term vanishes from Eq. (4) and the more familiar form of Eq. (2) is recovered for linear polarization. Evidently, for linear polarization is just equivalent to the... 

Davies and Rideal proposed the p term to consist of three components ... 

The negative Clog P term shows that the highly hydrophihc molecules for this data set would present better inhibitory activities against topo II. 

In words, the integral of equation (7-33) for the exchange-correlation potential is approximated by a sum of P terms. Each of these is computed as the product of the numerical values of the basis functions and rp, with the exchange-correlation potential Vxc at each point rp on the grid. Each product is further weighted by the factor Wp, whose value depends on the actual numerical technique used. 

The product P, termed the (real or thermodynamic) solubility product, is a constant dependent only on the temperature. The analogous (apparent)... 

Calculated from the weighted average of the p- terms of the atom and of the p1 terms of the ion data from Reference 49. 

The E, N, and P terms are then obtained from the density matrix P of the aqueous-phase SCF calculation as... 

For models containing a P term, the sum of squares due to the factors has p - I degrees of freedom associated with it, where p is the number of parameters in the model. For models that do not contain a Pq term, SSf has p degrees of freedom. 

Figure 9.2 summarizes the additivity of sums of squares and degrees of freedom for models containing a Pq term. For models that do not include a P term, the partitioning is shown in Figure 9.3. 

ANOVA table for linear models lacking a P, term. 

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