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The descriptive and utility power of linear combinations of special construction of connectivity indices (LCXCI) derived by a trial-and-error procedure from a medium-sized set of eight connectivity indices or from a subset of it has been tested on several properties of different classes of bioorganic and inorganic compounds. Two techniques have been tested to choose the appropriate combination of indices:  the forward selection and the complete combinatorial technique. While the latter searches the entire combinatorial space and the first searches only a subspace of it, this last, nevertheless, has many advantages among which to be a good tool for an elementary and direct test for newly defined indices. The modeling of the side-chain volume V of 18 amino acids (AA) is perfectly achieved by a composite index together with a connectivity index, and, while the modeling of pI of 21 amino acids is satisfactorily accomplished by special 0χv-fractional indices that are also rather good descriptors of the melting T m points of 20 amino acids, the solubility S of 16 and 20 amino acids is nicely described by reciprocal and suprareciprocal connectivity indices, respectively, a description that seems to have nothing in common with the modeling of the same property for 23 purines and pyrimidines (PP) achieved by squared supraconnectivity indices. Nevertheless, the modeling of the solubility of the entire heterogeneous class of n = 43 amino acids, purines, and pyrimidines could be satisfactorily achieved with a set of supracomposite indices based on the χt v index mainly. The modeling of the motor octane MON number of 30 alkanes and of the melting points of 17 and 14 alkanes shows how far a minimum set of four connectivity indices can positively replace a larger set of 17 indices, while the modeling of the lattice ΔH L φ enthalpies of 20 metal halides by a mixed set of normal and composite indices introduces and stimulates the problem of the definition of a connectivity model for inorganic compounds. The utility of the given LCXCI is generally rather high as many properties can be satisfactorily modeled by one or just two indices (V, pI, S(AA), S(PP), and ΔH L φ) and it can be enhanced, especially when the modeling requires more than three or four indices, with the introduction of the corresponding orthogonal indices.

The barometric formula, relating the pressure p(z) of an isothermal, ideal gas of molecular mass m at some height z to its pressure p͑0͒ at height zϭ0, is discussed. After a brief historical review, several derivations are given. Generalizations of the barometric formula for a nonuniform gravitational field and for a vertical temperature gradient are also presented. © 1997 American Association of Physics Teachers.

The modeling power of the method of linear combinations of connectivity indexes (LCCI), based on a minimal and on an expanded set of connectivity indexes, has been tested on several properties of different classes of organic compounds: the melting points and motor octane numbers of alkanes, the melting points and solubilities of caffein homologues, and four different physicochemical properties of organophosphorus compounds. The modeling of the first property, a classical shape-dependent property and up to date a challenging problem of molecular modeling, was resolved by partitioning the entire set of alkanes into congruent subsets. A minimal set of normal and valence connectivity indexes was able to model the melting points of caffein homologues that have quite similar molecular shapes and sizes, while the modeling of the solubilities of these homologues was unravelled by taking into consideration their association in solution and by employing linear combinations of squared connectivity indexes. The very effective modeling of the two different types (shape-and sizedependent) of properties of the organophosphorus compounds, with a minimal set of connectivity indexes, delineates also a test for the proposed valence 6" value of phosphorus in organophosphorus derivatives. Linear LCOCI combinations of orthogonal connectivity indexes were also tested to improve, if possible, the modeling of the properties of the given classes of compounds. Modeled properties show that the connectivity indexes can be highly dependent on the detailed knowledge of the physicochemical state of the investigated system and that, usually, LCCIs with a minimal basis set yield quite adequate modeling.

A molecular connectivity model of the crystal densities and specific rotations of some natural amino acids and of the longitudinal relaxation rates of some natural amino acids and cyclic dipeptides is presented. While crystal densities and relaxation rates are better described by a set of three valence molecular connectivity indices {D (v),(0) X (v),(1) X (v)}, specific rotations are better described by a set of two simple molecular connectivity indices {(1) X,(0) X}. Relaxation rates are, also, well described by the simple molecular connectivity {D,(1) X} index set. Use of orthogonal indices, derived from the corresponding ordinary indices shows, in the case of specific rotations, the possibility to condense the information by the aid of a single high quality descriptor underlining, thus, the versatility of these indices and also their dependence on the orthogonalisation process.

A b initio CI calculations have been carried out in a double-zeta AO basis for the simultaneous torsion and pyramidalization energy and dipole moment surfaces of the two lowest (V and Z) singlet excited states of ethylene. In nonpyramidalized geometries these two electronic states are found to undergo a potential crossing for a twisting angle of ϑ=82 °, with the Z(1A1) species being the more stable for the perpendicular D2d conformation. The dipole moments of these states are found to increase quite rapidly with pyramidalization for the entire range of twisting angle from ϑ=75 ° to ϑ=90 °, but this effect is found to reach a definite maximum in the neighborhood of the 82 ° crossing region for the unpyramidalized species and it is argued that these two phenomena are in fact closely related to one another. The CI results are found to be strongly dependent on the choice of one-electron basis in the significant portion of key structural regions and it is concluded that the use of natural orbitals optimized for one of the two nearly degenerate singlet states leads to excessively ionic charge distributions. Finally, the minimum-to-minimum energy difference (Te) between the ground and lowest singlet excited state is calculated to be 5.83 eV, suggesting a corresponding T0 value for this transition of 5.6–5.7 eV which is in very good agreement with McDiarmid’s recent experimental determination of this quantity.

The molecular connectivity index combinations used to describe the physicochemical properties of the a-amino acids were specifically analyzed in terms of their statistical meaning and, especially, of their Q (quality) value. Combinations of ordinary connectivity indexes provide a good description of nearly every physicochemical property examined but especially of the isoelectric point, side-chain volume, and crystal density of the a-amino acids. Some features of these combinations of connectivity indices are as follows: (i) the combination with the maximum number of molecular connectivity indexes does not always show the best quality, (ii) successive inclusion of the next good index to the best combination of indexes does not always produce the next best combination of indexes, and (iii) even highly intercorrelated indexes can contribute to the best combination of indexes. It was also detected that valence molecular connectivity indexes by themselves provide a rather good description of nearly every property with the exception of specific rotation of amino acids, which is better described by a set of two simple connectivity indexes. Orthogonal indexes, obtained from the ordinary molecular connectivity indexes, show in some cases the best single-index regressions and the best multi-index description of the molecular weights and relaxation rates. The best description of the specific rotation and solubility of the a-amino acids is, instead, achieved by the aid of the nonconnectivity Kidera, Konishi, Oka, Ooi, and Scheraga indexes.