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.     

On the accuracy of correlation energy calculated by the correlation factor method: first- and second-row atoms

Summary The correlation energy of two- and four-isoelectronic series, a representative example for which the existing spin-density functionals fails, is calculated using the Colle and Salvetti method, considering mono- and multideterminantal wave functions. The results are in agreement with experimental data, and show the potentiality of this method when it is applied to wave functions including the most relevant configurational features. Also, results for the ionization energies and electron affinities of first- and second-row atoms are reported.     

Performance of hollow-fiber flow field-flow fractionation in protein separation

Since hollow-fiber flow field-flow fractionation (HF FIFFF) utilizes a cylindrical channel made of a hollow-fiber membrane, which is inexpensive and simple in channel assembly and thus disposable, interests are increasing as a potential separation device in cells, proteins, and macromolecules. In this study, performance of HF FIFFF of proteins is described by examining the influence of flow rate conditions and length of fiber (polyacrylonitrile or PAN in this work) on sample recovery as well as experimental plate heights. The interfiber reproducibility in terms of separation time and recovery was also studied. Experiments showed that sample recovery was consistent regardless of the length of fiber when the effective field strength (equivalent to the mean flow velocity at the fiber wall) and the channel void time were adjusted to be equivalent for channels of various fiber lengths. This supported that the majority of sample loss in HF FIFFF separation of apoferritin and their aggregates may occur before the migration process. It is finally demonstrated that HF FIFFF can be applied for characterizing the reduction in Stokes' size of low density lipoproteins from blood plasma samples obtained from patients having coronary artery disease and from healthy donors.     

乙烯-α-烯烃共聚物的结晶性能及其临界序列结晶长度的研究

本文用DSC、WAXD及偏光显微镜(PLM)方法,研究了化学反应法催化剂合成的乙烯-α-烯烃共聚物的结晶性能及其临界序列结晶长度。结果表明,随共聚物中α-烯烃含量增大,共聚物的微晶尺寸、结晶度及熔点均逐渐减小,而晶胞参数增大。变化的辐度戊烯>辛烯。共聚物的临界结晶序列长度(n)和k值均戊烯<辛烯。上述结果表明影响支链进入晶格的主要因素是α-烯烃支链长度和结构。     

Determination of trace elements in the Lavender inflorescence (Lavandula angustifolia Mill.) — Lavender oil system

Bulgaria is a famous world producer of essential oils. Quality control of the lavender oils produced is an important analytical task in view of their wide use in perfumery and cosmetics, the food industry and aromatherapy. The present paper studies the relationship between the trace elements content in lavender inflorescence (Lavandula angustifolia Mill.) and in lavender oil derived from this inflorescence. Three model regions were investigated: two of them are situated far from industrial areas — the village of Zelenikovo and the town of Pavel Banya, and one region is located near the Plovdiv Non-Ferrous Metallurgical Plant. The content of the elements Cd, Cr, Cu, Fe, Mn and Pb in plants was determined after acid digestion by flame and electrothermal atomic absorption spectrometry (ETAAS). Lavender oils were analyzed directly by ETAAS. The results undoubtedly show that there is no strong correlation between the trace elements content in inflorescence and in essential oils. It might be assumed that the trace elements present and accumulated in the inflorescence do not pass in lavender oil during the production by steam distillation.     

Fluorinated nitroxides as ESR probes of solvation

Some newly synthesized fluorinated nitroxides, such as t-butyl perfluoroalkyl nitroxides Bu^tN(O) R_f (R_f=CF₃, 5; C₂F₅, 6; n-C₃F₇, 7) and s-butyl perfluoroacyl nitroxides Bu^sN(O) COR_f (R_f=CF₃, 9; n-C₃F₇, 10) have been employed as ESR probes of solvation in different common organic solvents. In aprotic solvents, the measured a_N values for each of the nitroxyl probes show a linear correlation with the cybotactic polar solvent parameters E_T (Dimroth) and Z (Kosowar), i.e. a_N=bE_T+c, and a_N=b′Z+c′. The physical significance for the slope (b or b′), the slope×E_T or slope×Z, the extrapolated intercept on a_N axis, c or c′, are linked, respectively, to the sensitivity of a specific nitroxide toward solvation, the magnitude of the overall solvation effect on the a_N value, and the intrinsic a_N value of each nitroxide in the ideal gaseous state. The intercept on the a_N axis may also serve as a new measure of electronegativity for perfluoroalkyl groups, CF₃, C₂F₅, n-C₃F₇, and perfluoroacyl groups, CF₃CO, n-C₃F₇CO. In protic solvents, i.e. alcohols and carboxylic acids, however, a_N values of all the probes, kept almost no change with the increase in E_T and Z. Furthermore, the plots of a_N versus non-cybotactic solvent constants, such as dipolar moment (μ) and dielectric constant (ε), all show random variations.     

Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

The covariance matrix of the Potts model: A random cluster analysis

We consider the covariance matrix,G ^mm =q ²<(_x,m);(_y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point _o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at _o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure.     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.