The complexification and degree of a semi-algebraic set

The complexification of a semi-algebraic set is the smallest complex algebraic set containing S. Let S be defined by s polynomials of degrees less than d. We prove that the geometric degree of the complexification is less than . Received: 9 January 1997; in final form: 11 August 2000 / Published online: 17 May 2001     

Group additive values for the gas phase standard enthalpy of formation of hydrocarbons and hydrocarbon radicals

A complete and consistent set of 95 Benson group additive values (GAV) for the standard enthalpy of formation of hydrocarbons and hydrocarbon radicals at 298 K and 1 bar is derived from an extensive and accurate database of 233 ab initio standard enthalpies of formation, calculated at the CBS-QB3 level of theory. The accuracy of the database was further improved by adding newly determined bond additive corrections (BAC) to the CBS-QB3 enthalpies. The mean absolute deviation (MAD) for a training set of 51 hydrocarbons is better than 2 kJ mol(-1). GAVs for 16 hydrocarbon groups, i.e., C(C(d))(3)(C), C-(C(d))(4), C-(C(t))(C(d))(C)(2), C-(C(t))(C(d))(2)(C), C-(C(t))(C(d))(3), C-(C(t))(2)(C)(2), C-(C(t))(2)(C(d))(C), C-(C(t))(2)(C(d))(2), C-(C(t))(3)(C), C-(C(t))(3)(C(d)), C-(C(t))(4), C-(C(b))(C(d))(C)(H), C-(C(b))(C(t))(H)(2), C-(C(b))(C(t))(C)(H), C-(C(b))(C(t))(C)(2), C(d)-(C(b))(C(t)), for 25 hydrocarbon radical groups, and several ring strain corrections (RSC) are determined for the first time. The new parameters significantly extend the applicability of Benson's group additivity method. The extensive database allowed an evaluation of previously proposed methods to account for non-next-nearest neighbor interactions (NNI). Here, a novel consistent scheme is proposed to account for NNIs in radicals. In addition, hydrogen bond increments (HBI) are determined for the calculation of radical standard enthalpies of formation. In particular for resonance stabilized radicals, the HBI method provides an improvement over Benson's group additivity method.     

Detailed experimental and kinetic modeling study of 3-carene pyrolysis

3-Carene is an important potential biofuel with properties similar to the jet-propellant JP-10. Its thermal decomposition and combustion behavior is to date unknown, which is essential to assess its quality as a fuel. A combined experimental and kinetic modeling study has been conducted to understand the initial decomposition of 3-carene. The pyrolysis of 3-carene was investigated in a jet-stirred quartz reactor at atmospheric pressure, at temperatures varying from 650 to 1050 K, covering the complete conversion range. The decomposition of 3-carene was observed to start around 800 K, and it is almost complete at 970 K. Online gas chromatography shows that primarily aromatics are generated which suggests that 3-carene is not a good fuel candidate. The potential energy surface for the initial decomposition pathways determined by KinBot shows that a hydrogen elimination reaction dominates, giving primarily cara-2,4-diene. Next to this molecular pathway, radical pathways lead to aromatics via ring opening. The kinetic model was automatically generated with Genesys and consists of 2565 species and 9331 reactions. New quantum chemical calculations at the CBS-QB3 level of theory were needed to calculate rate coefficients and thermodynamic properties relevant for the primary decomposition of 3-carene. Both the conversion of 3-carene and the yields of the primary products (ie, benzene and hydrogen gas) are well predicted with this kinetic model. Rate of production analyses shows that the dominant pathways to convert 3-carene are hydrogen elimination reaction and radical chemistry.     

QUANTIS: Data quality assessment tool by clustering analysis

Automatically generated kinetic networks are ideally validated against a large set of accurate, reproducible, and easy-to-model experimental data. However, although this might seem simple, it proves to be quite challenging. QUANTIS, a publicly available Python package, is specifically developed to evaluate both the precision and accuracy of experimental data and to ensure a uniform, quick processing, and storage strategy that enables automated comparison of developed kinetic models. The precision is investigated with two clustering techniques, PCA and t-SNE, whereas the accuracy is probed with checks for the conservation laws. First, the developed tool processes, evaluates, and stores experimental yield data automatically. All data belonging to a given experiment, both unprocessed and processed, are stored in the form of an HDF5 container. The demonstration of QUANTIS on three different pyrolysis cases showed that it can help in identifying and overcoming instabilities in experimental datasets, reduce mass and molar balance closure discrepancies, and, by evaluating the visualized correlation matrices, increase understanding in the underlying reaction pathways. Inclusion of all experimental data in the HDF5 file makes it possible to automate simulating the experiment with CHEMKIN. Because of the employed InChI string identifiers for molecules, it is possible to automate the comparison experiment/simulation. QUANTIS and the concepts demonstrated therein is a potentially useful tool for data quality assessment, kinetic model validation, and refinement.     

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.