PISA model

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

Solvent effects were evaluated by different self consistent reaction field (SCRF) procedures i) the parametrisation AM1-SM4 for cyclohexane and AM1-SM2.1 for water, implemented on the AMSOL-V suite of programs,ii) the ab initio Pisa model (interlocking spheres) implemented in the Gamess (Rev,97) package and, with different options, in the Gaussian 94 package. 

We acknowledge financial support by the MIUR SPARX and MIUR-FSRIS project Impianti Innovativi multiscopo per la produzione di radiazione X and by the INFN project PLASMON-X. Access to the IOQ installation was supported by LASERLAB. We thank F. Cornolti from the Physics Department of the University of Pisa for fruitful discussion and suggestions on the preliminary modeling of the data. 

Backx, T. O. Bosgra and W. Marguardt. Integration of Model Predictive Control and Optimization of Processes. ADCHEM Proceedings, pp. 249-259, Pisa, Italy (2000). Baker, T. E. An Integrated Approach to Planning and Scheduling. In Foundations of Computer Aided Process Operations (FOCAPO), D. W. T. Rippin J. C. Hale and J. F. Davis, eds. CACHE Corporation, Austin, TX (1993), pp. 237-252. 

In the standard continuum solvation model, exemplified by the Polarizable Continuum Model (PCM) we developed in Pisa [9], the solute-solvent interaction energies are described by four Qx operators, each having a clearly defined physical nature. Each term gives a contribution to the solvation energy which has the nature of a free energy. The free energy of M in solution is thus defined as the sum of these four terms, supplemented by a fifth describing contributions due to thermal motions of the molecular framework ... 

Apart from the ASC-PCM method developed by the Pisa group, there are several other methods based on the polarizable continuum model the MPE (multipole expansion method) by the Nancy group [19,20] and by Mikkelsen and co-workers [21,22], the GBA (generalized Bom approximation) by the Minneapolis group - Cramer and Truhlar [23-26] and others. 

We end our contribution to this editorial initiative of the European Academy of Science by recalling the leading role played by the European quantum chemistry community in the development of quantum mechanical (QM) solvation models. We cite, as an example, the first quantum chemistry continuum solvation code developed by Rivail s group in Nancy in 1973 [43], However, this initiative to address the solvation problem from a QM point of view was not entirely out-of-the-blue. It was, on the contrary, a response to the challenges stimulated by a limited number of scientists working in France and in Italy (Paris, Nancy, Pisa), with strong contact, in competition and also in collaboration to each others [44], More than 30 years later, the European quantum chemistry community is still at the forefront in the development of QM continuum solvation models, and we hope that the present contribution can be considered as a testimony of this activity. 

Lucia Band and Peter Comba, Molecular Modeling and Dynamics of Bioinorganic Systems. Proceedings of the NATO Advanced Research Workshop, held 15-21 March 1997, in San Miniato (Pisa), Italy, in NATO ASI Series, Ser. 3, Vol. 41, Kluwer, Dordrecht, 1997. 

For this purpose, the PISA continuum model developed by Tomasi and coworkers [72] can be utilized as was shown by Cremer and co-workers. [34,38,41-47]... 

Kuznetsov, V.V., Shamirzaev, A.S., (1999), Two-phase flow pattern and boiling heat transfer in noncircular channel with a small gap, Proc. of Two-Phase Flow Modeling and Experimentation, Pisa, V.l, pp. 249-253. 

There are several versions of EH-CSD models. To make the exposition less cumbersome, in the next pages we shall only summarize one version, that was elaborated in Pisa and known with the acronym PCM (Polarizable Continuum Model) (Miertus et al., 1981 Miertus and Tomasi, 1982). We shall consider other versions later, and the differences with respect to PCM will be highlighted. Other approaches, based on effective Hamiltonians expressed in terms of discrete solvent distributions, EH-DSD, or not relying on effective Hamiltonians, will also be considered. 

Tomiyama, a. 2004 Drag, lift and virtual mass forces acting on a single bubble, in 3rd International Symposium on Two-Phase Flow Modeling and Experiments, Pisa. 

An alternative to the use of finite differences or finite elements to discretize the differential operator is to use boundary element methods (BEM). " One of the most popular of these is the polarizable continuum model (PCM) developed originally by the Pisa group of Tomasi and co-workers. The main aspect of PCM is to reduce the electrostatic Poisson equation (1) into a boundary element problem with apparent charges (ASCs) on the solute cavity surface. 

Gallego, E., Garcia, J., Migoya, E., Crespo, A., Kotchourko, A., Yanez, J., Beccantini, A. (2005), An inter-comparison exercise on the capabilities of CFD models to predict deflagration of a large-scale H2-Air mixture in open atmosphere . First International Conference on Hydrogen Safety, 8-10 set, Pisa, Italy. 

R.C. Corcoran, D.D. Jones, I. Vatter, S.R. Ortner and P. Nenonen, Technique comparison of Auger and FEGSTEM measurement of grain boundary composition in pressure vessel steels and model alloys , EURATOM Fifth Framework Report On Project PISA (Phosphorous Influence on Steel Ageing), PISA/R(12)/WP7/D8, March, 2005. 

Furthermore, Areepattamannil, Freeman, and Klinger (2011) used hierarchical linear modeling to analyze the Canadian PISA data. They compared the effects of different student-level variables on science achievement, including enjoyment of science, general interest in science, instrumental motivation to learn science, future-oriented motivation to learn science, self-efficacy in science, and self-concept in science. They reported that science self-efficacy had the largest predictive effect on science achievement. Pajares (1996) also pointed out that... 

Sur Texistence et unicite de solutions d un modele agproxime des equations d e volution tridimensionelles d un cristal liquide nematique, Ann. S.N.S. Pisa, 5.1 (1978), 1-13. 

Repke, J.-U., Wozny, G., 2000, A Nonequilibrium Model for Three-Phase Distillation in a Packed Column. ADCHEM 2000, Pisa, Italy, 14.-16.06.2000, pp. 1031 -1036. 

D. Tyner, M. Soroush, M. C. Grady, J. R. Richards, J. P. Congalidis, Mathematical modeling and optimization of a semi-batch polymerization reactor . Proceedings lEAC Symposium on Advanced Control of Chemical Processes, Pisa. Italy, 2001, 3, 983. 

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