Theoretical investigation of excited states of molecules. An application on the nitrogen molecule

Diverse existing lines for the calculation of excited states are exposed, with an emphasis on those methods that consider both types of correlation energy: the dynamic and the non-dynamic one. We analyze the possibility of to calculate the dynamic correlation energy using a correlation energy density functional applied to a multi-determinantal wavefunction, which would include the non-dynamic correlation energy, versus the use of mono-determinantal wavefunctions, which are not able to include the long-range correlation energy, and versus the use of variational or perturbative calculations from multi-determinantal wavefunctions, with their excessive computational cost. The results obtained with several methods are compared. Contribution to the Serafin Fraga Memorial Issue.     

Distributed Gaussian discrete variable representation

A discrete variable representation (DVR) made from distributed Gaussians g_n(x) = e, (n = ?∞, …, ∞) and its infinite grid limit is described. The infinite grid limit of the distributed Gaussian DVR (DGDVR) reduces to the sinc function DVR of Colbert and Miller in the limit c → 0. The numerical performance of both finite and infinite grid DGDVRs and the sinc function DVR is compared. If a small number of quadrature points are taken, the finite grid DGDVR performs much better than both infinite grid DGDVR and sinc function DVR. The infinite grid DVRs lose accuracy due to the truncation error. In contrast, the sinc function DVR is found to be superior to both finite and infinite grid DGDVRs if enough grid points are taken to eliminate the truncation error. In particular, the accuracy of DGDVRs does not get better than some limit when the distance between Gaussians d goes to zero with fixed c, whereas the accuracy of the sinc function DVR improves very quickly as d becomes smaller, and the results are exact in the limit d → 0. An analysis of the performance of distributed basis functions to represent a given function is presented in a recent publication. With this analysis, we explain why the sinc function DVR performs better than the infinite grid DGDVR. The analysis also traces the inability of Gaussians to yield exact results in the limit d → 0 to the incompleteness of this basis in this limit. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Energy Recovery from Municipal Solid Waste in Small Communities

The heating values of municipal solid waste generated in three towns with a population of less than 50 000, situated in Galicia (Spain), were measured with a static bomb calorimeter. Samples of raw refuse were burnt either as received or after sorting of the different combustible components. A study was made of samples from controlled and uncontrolled landfills. The calorific values were compared with those corresponding to a commercial residual derived fuel in order to study the possibility of using municipal solid waste as a source of recovered energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermodynamics of molecular interactions in ethyl iodide+toluene mixtures

The excess Gibb's free energy of mixing, G^E, for ethyl iodide+toluene at 25°C have been obtained from the measured vapor pressuure data. The H^E and G^E values for ethyl iodide+toluene are positive throughout the ethyl iodide concentration range and G^E>H^E. The results have been analyzed in terms of Flory and ideal associated model theory of nonelectrolyte solutions. It has been observed that the ideal associated model approach which assumes the presence of AN and A₂B molecular species describes well (within±10 J-mol^–1 in the worst case) the general dependence of H^E on X_A (mole fraction of ethyl iodide) over the whole composition range for ethyl iodide+toluene mixtures. The equilibrium constants for A+A AB and 2A+BA₂B reactions along with the enthalpies of formation of AB and A₂B molecular species have been calculated.     

Image analysis in the electron microscopy of cellulose protofibrils II. Digital correlation methods

Electron micrographs of parallel arrays of negatively stained ramie cellulose protofibrils were analyzed using the two-dimensional digital autocorrelation function (ACF). The method is based upon the statistical analysis of images in real space. The ACF shows strong parallel streaks of high correlation, and the lateral distance between adjacent streaks allows the mean interfibrillar distance to be estimated as 3.7 nm. The intensity profile along the streaks shows a weak modulation with peaks occurring at integral multiples of 3 or 6 nm. These results provide direct evidence that there is a regular axial texture in the protofibrils, and corroborate the conclusions previously drawn from optical diffraction analysis. Using the difference vectors found in the ACF it has been possible to reduce the picture noise level by linear integration, thereby obtaining an enhanced image. A preliminary result obtained in this way suggests that the projected protofibril morphology associated with the observed axial periodicity is a ribbon-like zigzag structure. Possible applications of the method for future work are discussed.     

An electronic structure investigation of the BNO-BON-NBO system

The potential energy hypersurface of the ground triplet states of the BNO-BON-NBO system has been investigated using traditional ab initio electronic structure theory. The molecules studied have the molecular formula BON and include three linear and three angular species, and two transition states for the isomerization of an angular N-B-O to an angular B-O-N and a linear B-NO, respectively. All stationary points on the BNO-BON-NBO isomerization potential energy surface have been characterized employing UMP2, UMP4, and Gaussian-2 (G2) theory with the 6-311G(d), 6-311G(2d), and TZ2P basis sets. The isomerization for an angular N-BO to the linear B-NO has a lower energy barrier than that of the former to an angular B-ON. Energetics are presented with G2 energies. Two sets of resonance structures for both bent B-NO (boron nitrosyl) and B-ON (boron isonitrosyl) were proposed and the bonding in the two species was analyzed. For the purpose of comparison, the density functional theory based hybrid methods B3LYP/6-311G(d) and B3LYP/TZ2P have also been applied to both geometry optimization and single-point calculations. It is found that the B3LYP prediction of the nature of the linear B-O is contradictory to that made by all MPn(n = 2 and 4) calculations. The cause for this contradiction is discussed.     

Vibrational partition functions for H2O derived from perturbation-theory energy levels

Purely vibrational energy levels and partition functions are calculated using three different potential energy surfaces for the H₂O molecule. Results obtained with perturbation-theory, independent-normal-mode (INM), and harmonic approximations are compared with accurate values. For the cases considered here, the expected improvement that perturbation theory provides over the corresponding harmonic treatment is found to be substantial, while the INM approximation leads to results which are worse than the corresponding harmonic ones. In fact, we show that reliable partition functions for these potential surfaces can be obtained when resonance contributions are removed from the perturbation-theory treatment, and we propose a theoretical criterion for deciding when a particular interaction should be treated as resonant.     

Electron kinetics of collision dominated r.f. bulk plasma in CO: The role of second-kind collisions

Electron energy distribution functions (EEDF) and related properties in the bulk region of the rf CO plasma at the reduced rf field frequency /p₀=×10⁷ sec^–1 torr^–1 have been calculated by solving the time-dependent spatially homogeneous Boltzmann equation in the presence of second-kind collisions and have been interpreted on a microphysical basis. The results show that second-kind collisions (vibrational and electronic) strongly affect the temporal evolution of EEDF, of the mean energy, and of the mean collision frequencies for vibrational and electronic excitation processes, as well as for ionization. In particular, second-kind collisions in the CO rf bulk plasma strongly decrease the modulation of the mean ionization frequency during its periodical alteration in the rf field. Furthermore, the effect of second-kind collisions on an approximate determination of the time-averaged EEDF in the rf bulk plasma using the so-called effective-field appriximation has been estimated.     

Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides

Summary The effective core potential and model potential methods were used in post-SCF calculations on HC1, HBr, Cl₂, and Br₂ in order to gain insight into the effect of insufficient representation of inner nodes in the valence orbitals of the approximate methods. The results show that while the correlation energy may be slightly overestimated (by 1–7%), both the electric moment functions and the quantities depending on energy differences are consistently similar for the methods studied and close to the results from all-electron calculations.Dedicated to Prof. Klaus Ruedenberg     

About compensation effect by thermal decomposition of some catalyst precursors

Summary In order to obtain catalysts, the thermal decomposition of the precursors is a compulsory step. However, kinetic analysis of the decomposition data obtained under non-isothermal conditions lead very seldom to the intimate reaction mechanism. There is also a lack of information because in non-isothermal kinetics, the compensation effect, is rather a rule and unfortunately a source of debate. In order to discriminate between these processes, and the influence of conversion, respectively temperature on the reaction rate, the NPK (non-parametric kinetic - Sempere and Nomen) method was used. This method is based on the singular value decomposition algorithm (SVD) applied on the matrix of reaction rate at corresponding conversion and temperature. This method allows a less speculative determination of the conversion functions and of the kinetic parameters.