Generation of Molecular Fields, Quantum Similarity Measures and Related Questions

A straightforward discussion on how to generate molecular fields is developed within the postulates of quantum mechanics. The theoretical formalism points towards the generalization and extension of the well-known molecular field forms, associated to density function and electrostatic molecular potential (EMP), including another category of fields associated to quantum molecular similarity measures. The results show that the new formalism can be easily applied to obtain an unlimited number of new information about molecular behavior.     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

Completely soft molecular electrostatic potentials (CoSMEP) and total density functions

Soft molecular electrostatic potentials (SMEP or SEMP) have been recently defined substituting the point-like proton by a Gaussian positive charge distribution. In the present paper an additional step is taken forward, transforming SMEP into a completely soft MEP (CoSMEP). Such transformation is carried out using a charge distributed proton as in SMEP and also a Gaussian positive nuclear charge distribution, instead of the classical point-like nuclear charges. The general form of MEP is roughly preserved, but new features can be noticed. Such new point of view is also associated to the possibility to redefine the molecular charge density. Definition of CoSMEP is thus connected to the definition of total molecular density functions (DF), where to the negative electronic DF is summed up the soft nuclear DF, made of linear combinations of Gaussian distributions of nuclear charges.     

On the nature of atomic shell approximation (ASA) electrostatic molecular potentials (EMP)

General properties of the electrostatic molecular potential (EMP) when obtained by means of the atomic shell approximation (ASA) density function (DF) are discussed. In the present study it is proved that in general and without exceptions promolecular ASA DF provide EMP which are everywhere repulsive. The polarized ASA DF version, providing an alternative enhanced kind of EMP, behaves in such a way that in the neighborhood of negative charged atoms, attractive regions appear resembling the ab initio results.     

A naive look on the Hohenberg–Kohn theorem

A generalised Hohenberg–Kohn theorem is described in terms of the sign of the secondorder energy variation. Independently, it is also corroborated within the perturbation theoretical framework. An alternative formulation of the Hohenberg–Kohn theorem, based on the relationships involving the matrix representations of density functions and the Hamiltonian operator variations, is shown to extend the validity of the theorem to the excited states of the Hamiltonian operators possessing nondegenerate spectra. Finally, a connection with Brillouin's theorem when energy variation becomes stationary is also outlined.     

Odour-causing organic compounds in wastewater treatment plants: evaluation of headspace solid-phase microextraction as a concentration technique

Odorous emissions from wastewater collection systems and treatment facilities affecting quality of life have given local populations reasons to complain for decades. In order to characterise the composition of such malodorous emissions, a method based on headspace solid-phase microextraction (HS-SPME) and gas chromatography coupled to mass spectrometry (GC-MS) has been developed to determine a list of compounds belonging to different chemical families, which have been previously described as potentially responsible for odour complaints, in wastewater matrices. Some parameters affecting the chromatographic behaviour of the target compounds were studied (e.g. splitless time). Experimental conditions affecting the extraction process (temperature, time and salt content) were evaluated by applying a factorial design at two levels. Using a DVB/CAR/PDMS fibre and the optimised HS-SPME conditions, calibration curves were constructed with detection limits in the range of 0.003-0.6 μg L(-1). Recovery values higher than 70% and relative standard deviation values between 5 and 16% (n=5) were obtained for all compounds and found to be satisfactory. In wastewater samples, a decrease in the concentration of the analysed compounds through the different treatments was observed. Most of the target analytes were found in influent samples while only octanal and carvone were detected in samples from the plant effluent.     

Calculation of clustered eigenvalues of large matrices using variance minimization method

The autoadjusting perturbation theory method is presented and developed to calculate eigenpairs of a square matrix. The procedures to simultaneously compute a cluster of eigenpairs by variance minimization are also given. Finally, numerical examples are reported. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1777–1785, 1998     

Nested summation symbols and perturbation theory

A new mathematical concept, the nested summation symbol (NSS) has been developed. This concept is attached to a mathematical linear operator directly related to the summation symbols. After a discussion on its properties, we investigate the potential usefulness of this symbol in the developing of sequential and parallel computational algorithms, constituting a powerful link between mathematical formalism and high level languages programming. A NSS is well suited in order to express some kind of mathematical formulae and to implement them in any computational environment. In this sense, NSSs are directly related toartificial intelligence techniques. Nested sums are connected withgeneralized nested do loop (GNDL) structures, a programming concept developed in our laboratory. This paper shows an application of the NSS. The NSS concept has been used to obtain in a compact form the expressions of the general energy and wavefunction corrections associated to the perturbation theory under the Brillouin-Wigner or the Rayleigh-Schrödinger formalisms.     

Extending molecular similarity to energy surfaces: Boltzmann similarity measures and indices

Maxwell-Boltzmann statistics provides the adequate mathematical background allowing to define similarity measures involving molecular energy surfaces and electrostatic potential maps. Boltzmann similarity measures are described and various illustrative examples are used to show the practical viability of the theory. A new molecular similarity index is also presented. Finally, hybrid measures involving Boltzmann and density distributions are defined.