Second order interaction coefficients

In the same way it was found through analysis incorporating second-order interaction coefficients that the aldehyde AfT is not conditioned by the CHO effect on the close hydrocarbon groups as was the case with ketonic carbonyl, but by the effect of close groups on aldehydic C-H. 

Tg = 125-140°C, and was stable in a N2 atmosphere to 220°C. The 13C NMR spectrum revealed the presence of 7t-interaction between those chromophoric groups that are in isotactic relationship to each other ( 30-35% of total). The orientation of the chromophores in a PPNA sample (Tg = 125°C) was achieved in a thin film by the corona poling technique at temperatures above Tg. The subsequent freezing process resulted in a polymeric film that exhibited an initial high second-order nonlinear coefficient, d33=31 pm/V, as measured by Maker-fringe technique with 1.06 im fundamental. 

In the second-order interaction model cross-product terms have also been included. A significant estimated cross-product coefficient, bVj, shows that the influence of variable X is dependent on the settings of variable xp i.e. there is an interaction effect between these variables. Geometrically this corresponds to a twist of the response surface over the xi x3 plane. 

If also interaction effects are to be evaluated, second-order interaction models can be determined from a limited number of runs four variables in (3/4 x24) twelve runs (constant term, four linear coefficients, and six cross-product coefficients) five variables in sixteen runs (constant term, five linear coefficients, and ten cross-product coefficients). 

Knowing the molecular permanent multipole moments and transition moments (or closure moments derived from sum rules, such as (36)), the computation of the fust and second order interaction energies in the multipole expansion becomes very easy. One just substitutes all these multipole properties into the expressions (16), (20), (21) and (22), together with the algebraic coefficients (24) (tabulated up to terms inclusive in ref. in a somewhat different form ), and one calculates the angular functions (lb) for given orientations of the molecules. 

Since the ground state second order Zeeman coefficient is proportional to — 1/A, this vibronic interaction has a profound influence on the magnetic properties of the [Ti(OH2)6] + cation [50, 54, 55], With just the ground state populated, the susceptibility and effective magnetic moment have the form ... 

When linear and second order interaction models are determined from a two-level design, the estimate of the constant term will be an alias in which the "true" intercept fig is confounded with all square coefficients. 

A least squares fit of a second order interaction model (without the constant term, as the data had been centred prior to computing the PC model) to the score values afforded the estimated coefficients shown in Table 17.4. 

In principle if all the second order virial coefficients of the pure components and the interaction coefficients of all the pairs of the molecules are known, the second order virial coefficient can be calculated. For the third order virial coefficient, 112 and 122 interactions... 

The coefficient Po is the constant term. The coefficient Pj is called the main effect of the variable (or the factor) X. The coefficient P,2 is a 2-factor interaction or a first-order interaction effect The coefficient P,23 is called a 3-factor interaction or a second-order interaction effect The coefficient P12.2 is called the general interaction effect. Thus P123 is the general interaction effect for a 3 factor model and P1234 is the general interaction effect for a 4 factor model. 

---