The sound velocities in dense fluids from distribution functions

The sound velocities and adiabatic compressibilities in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs). Using such approach not only tests the power of distribution functions theory in predicting the sound velocities and adiabatic compressibilities, but also specifies better expressions in determining these properties. To calculate these quantities, the variation of RDF with density and temperature is required. Therefore, we should have analytical expressions which explicitly present RDF as a function of temperature, density and interparticle distance. It is shown that if an expression is used which properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate sound velocities and adiabatic compressibilities from distribution function theory.     

Impulse/response functions of individual components of flow-injection manifolds

The dispersion behaviour of the various individual parts making up a flow-injection manifold is often difficult to establish because it is virtually impossible to obtainthe required very small injection and detection volumes. It is shown that it is possible, under suitable experimental conditions, to find the impulse/response functionof each component by means of a deconvolution process of the response functions have been established, the response function of any arrangement can be predicted by convoluting the impulse/response functions of all the individuaol parts involved. Convolution and deconvolution were done in the Fourier domain, by using a fast FT algorithm.     

Mathematical functions for the analysis of luminescence decays with underlying distributions: 2. Becquerel (compressed hyperbola) and related decay functions

The Becquerel (compressed hyperbola) decay law is analyzed in detail and shown to be an interesting approach for the analysis of complex luminescence decays. A decay function unifying the modified Kohlrausch and Becquerel decay laws is also introduced. It is proposed that the analysis of luminescence decays with a sum of Becquerel functions is a powerful alternative to the usual sum of exponentials. It is also shown that some complex decay laws can be written as a sum of an infinite number of exponentials and have for this reason an infinite but discrete spectrum of rate constants.     

Theory of the wavelet analysis for electrochemical noise by use of the Laguerre functions

It is shown that the wavelet transform that uses the Laguerre function as a basis function is a useful tool to analyse the stationary electrochemical noise. Knowledge of the variance of the Laguerre wavelet of noise allows the Laplace transform of the correlation function to be found. The Laplace transform of the correlation function may be referred to the spectral density in the Laplace domain as well as to the operational spectral density of noise. It is shown that the operational spectral density of noise can be found not only by averaging over the ensemble of realizations of the noise process but also by averaging over the ensemble of Laguerre wavelets. The results obtained can be useful not only for analysis of electrochemical noise but also for analysis of any stationary random process, in particular for the time series analysis in econometric research.     

The use of site symmetry in constructing symmetry adapted functions

It is shown that the application of a projection operator from a given group to a function is equivalent to the successive application of projection operators from factor groups of the starting group to that function. When used with the factor groups representing the site symmetry of a position and the simplest group of interchanges of positions, this concept provides a very simple method for obtaining symmetry adapted linear combinations of basis functions.     

Ring functions,as polarization functions,forab initio calculations on small rings: Dioxirane

The exponents and relative positions have been optimized for bond functions to be used as polarization functions in the theoretical treatment of small cycles. The transferability of the conventional bond functions to this type of “compact” systems is analyzed for the particular case of dioxirane and it is shown that they can be replaced by a single function located inside the ring (ring function) which describes equally well the polarization effects on the equilibrium geometry, charge distribution and dipole moment. These conclusions are corroborated by the characteristics exhibited by the corresponding localized molecular orbitals.     

Blip function calculation of the radial distribution functions for a binary liquid mixture

It is shown that the use of the high temperature approximation to blip function theory together with a two-component hard sphere reference fluid leads to reasonably accurate predictions for the radial distribution functions in a moderate temperature, moderate density, binary Lennard-Jones mixture.     

Decomposition of DSC curves of dairy products with Gaussian functions

Summary DSC measurements have wide application in the field of biochemical/biophysical research to look into the melting behaviour of muscle proteins in different intermediate states of ATP hydrolysis cycle as well as in the field to develop dairy products. It was a demand to develop a deconvolution program to evaluate and interpret the background of DSC scans such a way that the decomposition into a proper function has to be simple and quick. There should be possible to choose the proper parameters as well as to calculate the data of decomposing curves with the simultaneous graphic representation of them including the resultant DSC scan as the sum of decomposing functions. In most cases Gaussian function is used for this purpose. Our main field of interest is the food physics where e.g. the proliferation of different probiotic bacteria follows a lognormal distribution, its first derivative is a Gaussian one, for this reason we have chosen it. The main parts of this PC program are: -the process of fitting and calculation of Gaussian functions, a multiple step correction of these function (optimal fitting), graphic representation of all functions. An example is shown for its application how to analyse the melting of butter fat.     

On the use ofT H[1s] and 1s functions as expansion functions

It is shown by a numerical calculation that although aT _H [1s] function (0s orbital) is a much better approximation to the exact Hartree-Fock 1s orbital than a usual 1s function, the set ofT _H [1s] functions does not have markable advantage over the set of 1s functions as expansion functions.NRCC No. 12092.NRCC Postdoctoral Fellow, 1969–71.     

Anomalous coherence functions in collective resonance fluorescence

The anomalous coherence functions (ACF) of collective resonance fluorescence are calculated analytically forN two-level atoms, coherently driven by a strong laser field and distributed in a region much smaller than the resonant wavelength. It is shown that the anomalous coherence functions are nonzero for transient as well as steady-state resonance fluorescence. The values of ACF are dependent on the number of atoms and the initial atomic populations. For one-atom resonance fluorescence, the one-time ACF vanishes whereas the two-time ACF differ from zero irrespective of the number of atoms. Moreover, it is found that information about the higher-order resonance at 2Θ, where Θ is the Rabi frequency, is conveyed by the ACF's only in the transient régime of resonance fluorescence. For steady-state resonance fluorescence, the ACF's carry information similar to that carried by the correlation function that yields the fluorescent spectrum. We also discuss the possibility of measuring the ACF's using photon-counting techniques.     

Error bounds for the overlap of approximate wave functions

Variational upper and lower bounds for the overlap between an approximate and the true wave function are proposed, and it is shown that the error bounds introduced recently by Gordon are special cases of the variational formulas.     

Considerations on Gaussian expanded generator coordinate wave functions

The recently developed integral discretization technique for the generator coordinate method is applied to discuss some features of Gaussian expanded wave functions. Using the hydrogen atom ground state, it is shown that the nuclear cusp problem has an interesting relation with the generator coordinator weight function, which allows the production of accurate wave functions by an integration criterion.     

Time-dependence of wave functions and the calculation of transition intensities

The standard formalism of the perturbation theory for time-dependent perturbations follows from the assumption that the exact solution of the unperturbed time-independent problem is known. The consequences of this assumption are analyzed. Particular attention is given to the methods used for the evaluation of transition intensities. It is shown that the traditional intensity formula in most cases violates the assumptions underlying its derivation. It is shown that for the given ansatz concerning the form of the approximate wave function, the transition intensities should be determined from the variation treatment of the corresponding time-dependent problem. The wave functions of both states involved in the transition should be given the same amount of variation flexibility. This condition is satisfied if the transition intensity expression follows from the complete timedependent perturbation treatment of the perturbed system.     

An effect of symmetry on the time dependence of correlation functions

In this work it is shown that because of the different symmetry of the variables the time dependence of the auto-correlation function of the time derivative of the anisotropic polarizability density can be different from that of the molecular angular momentum density auto-correlation function. Thus the information on this angular momentum correlation function that can be deduced from that of the time derivative of the anisotropic polarizability density can be limited.     

Quadratic response functions in the relativistic four-component Kohn-Sham approximation

A formulation and implementation of the quadratic response function in the adiabatic four-component Kohn-Sham approximation is presented. The noninteracting reference state is time-reversal symmetric and formed from Kramers pair spinors, and the energy density is gradient corrected. Example calculations are presented for the optical properties of disubstituted halobenzenes in their meta and ortho conformations. It is demonstrated that correlation and relativistic effects are not additive, and it is shown that relativity alone reduces the mubeta-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. Of the employed functionals, CAM-B3LYP shows the best performance and gives hyperpolarizabilities beta distinctly different from B3LYP.     

Calculation of thermodynamic solution functions in gas-liquid chromatography

The solubility of m- and p-isomers of xylene and fluorotoluene in aromatic stationary phases is investigated. It is shown that orientation interaction can be calculated from a lattice model, with the results compared with experiment. By calculating the orientation and dispersion forces it is possible to construct an enthalpy diagram for molecular rotation, on the basis of which the differences in heats of solution and rotational entropies of the isomers can be determined. An example is cited in which hydrogen bonding was found in systems containing fluorotoluenes. From increments in the heats of solution and rotational entropies of the homologous n-paraffins it is possible to determine the structural characteristics of the solvent, and the accuracy of the proposed structure can be evaluated by calculating the individual heats of solution. The presence of aromatic nuclei and aliphatic radicals in the molecule of the stationary phase can be determined from characteristic variations in the heat-of-solution increments. The size of the natural cavity in the solvent structure can be determined from the rotational entropy increment. It is shown that the selectivity of the stationary phase with respect to the n-paraffin homologs does not remain constant. Aromatic solvents give the highest selectivity.     

Energy transfer between polyatomic molecules. 3. Energy transfer quantities and probability density functions in self-collisions of benzene, toluene, p-xylene and azulene

This paper is the third and last in a series of papers that deal with collisional energy transfer, CET, between aromatic polyatomic molecules. Paper 1 of this series (J. Phys. Chem. B 2005, 109, 8310) reports on the mechanism and quantities of CET between an excited benzene and cold benzene and Ar bath. Paper 2 in the series (J. Phys. Chem., in press) discusses CET between excited toluene, p-xylene and azulene with cold benzene and Ar and CET between excited benzene colliding with cold toluene, p-xylene and azulene. The present work reports on CET in self-collisions of benzene, toluene, p-xylene and azulene. Two modes of excitation are considered, identical excitation energies and identical vibrational temperatures for all four molecules. It compares the present results with those of papers 1 and 2 and reports new findings on average vibrational, rotational, and translational energy, , transferred in a single collision. CET takes place mainly via vibration to vibration energy transfer. The effect of internal rotors on CET is discussed and CET quantities are reported as a function of temperature and excitation energy. It is found that the temperature dependence of CET quantities is unexpected, resembling a parabolic function. The density of vibrational states is reported and its effect on CET is discussed. Energy transfer probability density functions, P(E,E'), for various collision pairs are reported and it is shown that the shape of the curves is convex at low temperatures and can be concave at high temperatures. There is a large supercollision tail at the down wing of P(E,E'). The mechanisms of CET are short, impulsive collisions and long-lived chattering collisions where energy is transferred in a sequence of short internal encounters during the lifetime of the collision complex. The collision complex lifetimes as a function of temperature are reported. It is shown that dynamical effects control CET. A comparison is made with experimental results and it is shown that good agreement is obtained.     

Quadratic response functions in the time-dependent four-component Hartree-Fock approximation

The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process beta(-2omega;omega,omega). It is shown that relativistic corrections to property values are substantial in these cases--the orientationally averaged hyperpolarizabilities in the static limit beta(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown.