Phosphorus predictive modeling

Bjorsvik, H.R., Hansen, U.M. and Carlson, R. (1997). Principal Properties of Monodentate Phosphorus Ligands. Predictive Model for the Carbonyl Absorption Frequencies in Ni(Co)(3)l Complexes. Acta Chem.Scand.,51,733-741. 

Table 9.6. Selected regressions illustrating the key role of lake total phosphorus in predictive models. Many biological variables that would normally require determinations from extensive and expensive field and laboratory work may be estimated/predicted from one key, abiotic state variable, total-P. Some variables may be predicted with great precision, others with low. (Peters 1986 H kanson and Peters 1995)...

So far, we have not considered whether terminal atoms, such as the Cl atoms in PC15, are hybridized. Because they are bonded to only one other atom, we cannot use bond angles to predict a hybridization scheme. However, spectroscopic data and calculation suggest that both s- and p-orbitals of terminal atoms take part in bond formation, and so it is reasonable to suppose that their orbitals are hybridized. The simplest model is to suppose that the three lone pairs and the bonding pair are arranged tetrahedrally and therefore that the chlorine atoms bond to the phosphorus atom by using sp hybrid orbitals. 

Figure 14 The predicted uptake of phosphorus by maize over a 22 day period. The Barber-Cushman model (F, ), u.ses an average root radius calculated at the end of the simulation period, while the F, model uses a population of roots of different radius. Identical parameter values were used by both simulation models with the exception of root radius.

P. C. R. Fontes, S. A. Barber, and G. E. Wilcox, Prediction of phosphorus uptake by two tomato cultivars growing under sufficient and insufficient phosphorus soil conditions using a mechanistic mathematical model. Plant Soil. 94 81 (1986). 

The stable configuration for the H—P pair is predicted by all of the quantum-mechanical calculations to have a hydrogen located at the silicon antibonding site (Si—AB). A model is shown in Fig. 7b, where a phosphorus lone pair lies along the (111) axis and is energetically in the valence band. Here, the theoretical predictions of the H vibrational frequency have been mixed, with the H—Si interaction and frequency overestimated by Hartree-Fock and Hartree-Fock-like methods and lower by local-density calculations. 

Carbodiphosphoranes (R3P = C = PR3) are known,79 but ylides with a P-H bond are rare.80 Therefore, the spectroscopic characterization of 77 was unexpected. Even more surprising was the characterization of the carbodiphosphorane 79 featuring two P-H bonds.31 This compound, prepared by treatment of 2d with tert-butyllithium, rearranged in solution at room temperature over a period of 16 h to afford the phosphorus ylide 80 with one remaining P-H bond. This compound was also unstable and transformed completely into the diphosphinomethane 81 overnight. Note that calculations for the model compounds where R = NH2 predicted 79 to be 28 kcal/mol less stable than 80, which is also 34 kcal/mol above 81.16 The surprising stability of 79 and 80 is probably due to the presence of bulky substituents, since tetracoordinate phosphorus atoms can more readily accommodate the increased steric constraints than can their tricoordinate counterparts. 

The reason for this behavior in the case of the double-bonded structures ( A -type phosphorus) is the easy dimerization of the P=C bond. Tricoordinate planar (or nearly planar) phosphorus ( B - and C -type bonding) can be stabilized by repyramidalization when the cyclic electron delocalization is disturbed or lost (e.g., in a chemical reaction). The fine balance between these energetic effects cannot easily be predicted by using analogies or other simple models. Such predictions, however, can be made by using the sophisticated methods of computational chemistry, leaving the field of the chemistry of the aromatic phosphorus compounds an interesting research area with unexpected results in the future. 

The objective of this work Is to establish a reaction mechanism between sodium perborate and several organophosphorus esters. By analogy we can then describe Its probable effects upon other phosphorus-based Insecticides. We conclude that the reactivity of sodium perborate toward five model compounds Is attributable to the nucleophilic reactions of hydroperoxyl anion, HO2 , produced by perborate dissociation In water. On this basis we predict that sodium perborate solutions will be effective chemical detoxicants for phosphorus ester Insecticides. 

TABLE 9.2 Summary of Mathematical Models for Predicting Phosphorus Reactions in Soils... 

Mansell, R. S., and Selim, H. M. (1981). Mathematical models for predicting reactions and transport of phosphorus applied to soils. "In Modeling Wastewater Renovation (I. K. Iskander, ed.), pp. 600-640. Wiley, New York. 

Enfield, C. G. (1978). Evaluation of phosphorus models for prediction of percolate water quality in land treatment. In State of the Knowledge in Land Treatment of Wastewater (H. L. McKim, ed.), Vol. 1, pp. 153-162. U.S. Army Cold Reg. Res. Eng. Lab.) Hanover, New Hampshire. 

Fig. 4. The phosphazene ring (a) island delocalization model predicting nodes in TT-density at the phosphorus atoms (b) dynamic deformation density (at 0.1 eA 3) in the plane of the ring (c) theoretical deformation density (at 0.05 eA-3) of cyclic phosphazene was used as a model (reproduced with permission from Cameron et al. [43]).

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