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703:{\displaystyle {\begin{pmatrix}{\rm {Li}}&{\rm {Be}}\\{\rm {Na}}&{\rm {Mg}}\end{pmatrix}}\otimes {\begin{pmatrix}{\rm {Li}}&{\rm {Be}}\\{\rm {Na}}&{\rm {Mg}}\end{pmatrix}}={\begin{pmatrix}{\rm {Li_{2}}}&{\rm {LiBe}}&{\rm {BeLi}}&{\rm {Be_{2}}}\\{\rm {LiNa}}&{\rm {LiMg}}&{\rm {BeNa}}&{\rm {BeMg}}\\{\rm {NaLi}}&{\rm {NaBe}}&{\rm {MgLi}}&{\rm {MgBe}}\\{\rm {Na_{2}}}&{\rm {NaMg}}&{\rm {MgNa}}&{\rm {Mg_{2}}}\\\end{pmatrix}}}
883:, R1 and R2; for triatomic molecules, the monotonicity is close with respect to R1R2+R2R3 (which reduces to R1R2 for diatomic molecules). Therefore, the coordinates x, y, and z of the collapsed-coordinate system are C1+C2+C3, C2, and R1R2+R2R3. Multiple-regression predictions of four property values for molecules with tabulated data agree very well with the tabulated data (the error measures of the predictions include the tabulated data in all but a few cases).
725:. In all but the first of these cases, other researchers provided invaluable contributions and some of them are co-authors. The architectures of these systems have been adjusted by Kong and Hefferlin to include ionized species, and expanded by Kong, Hefferlin, and Zhuvikin and Hefferlin to the space of triatomic molecules. These architectures are mathematically related to the chart of the elements. They were first called “physical” periodic systems.
91:
33:
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molecular-orbital, and other fundamental theories, and (c) summing of atomic period and group numbers (Kong), the
Kronecker product and exploitation of higher dimensions (Hefferlin), formula enumerations (Dias), the hydrogen-displacement principle (Haas), reduced potential curves (Jenz), and similar strategies.
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systems of molecules include some predictions of molecular properties, but starting at the turn of the
Century there have been serious attempts to use periodic systems for the prediction of progressively more precise data for various numbers of molecules. Among these attempts are those of Kong, and Hefferlin
213:
atom, there will be a drastic change in the molecule’s properties. Several goals could be accomplished by constructing an explicit representation of this periodic law as manifested in molecules: (1) a classification scheme for the vast number of molecules that exist, starting with small ones having
865:
has three independent variables instead of the six demanded by the
Kronecker-product system. The reduction of independent variables makes use of three properties of gas-phase, ground-state, triatomic molecules. (1) In general, whatever the total number of constituent atomic valence electrons, data
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The
Kronecker product of a hypothetical four-element periodic chart. The sixteen molecules, some of which are redundant, suggest a hypercube, which in turn suggests that the molecules exist in a four-dimensional space; the coordinates are the period numbers and group numbers of the two constituent
878:
of the periodic chart of the elements, C1+C2+C3). (2) Linear/bent triatomic molecules appear to be slightly more stable, other parameters being equal, if carbon is the central atom. (3) Most physical properties of diatomic molecules (especially spectroscopic constants) are closely monotonic with
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A chronological list of the contributions to this field contains almost thirty entries dated 1862, 1907, 1929, 1935, and 1936; then, after a pause, a higher level of activity beginning with the 100th anniversary of
Mendeleev’s publication of his element chart, 1969. Many publications on periodic
848:
Each of the molecular systems listed above, and those not cited, is also supported by three legs: (a) physical and chemical data arranged in graphical or tabular patterns (which, for physical periodic systems at least, echo the appearance of the element chart), (b) group dynamic, valence-bond,
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Gary W. Burdick and Ray
Hefferlin, "Chapter 7. Data Location in a Four-Dimensional Periodic System of Diatomic Molecules", in Mihai V Putz, Ed., Chemical Information and Computational Challenges in the 21st Century, NOVA, 2011,
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Babaev, E.V. and R. Hefferlin 1996. The
Concepts of Periodicity and Hyper- periodicity: from Atoms to Molecules, in Rouvray, D.H. and Kirby, E.C., “Concepts in Chemistry,” Research Studies Press Limited, Taunton, Somerset,
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Carlson, C., Gilkeson, J., Linderman, K., LeBlanc, S. Hefferlin, R., and Davis, B (1997). "Estimation of
Properties of Triatomic Molecules from Tabulated Data Using Least-Squares Fitting".
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Hefferlin, R., Campbell, D. Gimbel, H. Kuhlman, and T. Cayton (1979). "The periodic table of diatomic molecules—I an algorithm for retrieval and prediction of spectrophysical properties".
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and tool for archiving data, (2) forecasting data for molecular properties based on the classification scheme, and (3) a sort of unity with the periodic chart and the periodic system of
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and they bear little resemblance to the element chart; they are called “chemical” systems. Chemical systems do not start with the element chart, but instead start with, for example,
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Clark, C. H. D (1940). "Systematics of Band-Spectral
Constants. Part V. Interrelations of Dissociation Energy and Equilibrium Internuclear Distance of Di-Atoms in Ground States".
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Zhuvikin, G.V. & R. Hefferlin (1983). "Periodicheskaya
Sistema Dvukhatomnykh Molekul: Teoretiko-gruppovoi Podkhod, Vestnik Leningradskovo Universiteta" (16): 10–16.
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Hefferlin, R. and Burdick, G.W. 1994. Fizicheskie i khimicheskie periodicheskie sistemy Molekul, Zhurnal Obshchei Xhimii, vol. 64, pp. 1870–1885. English translation:
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Carlson, C.M., Cavanaugh, R.J, Hefferlin, R.A, and of Zhuvikin, G.V. (1996). "Periodic Systems of Molecular States from the Boson Group Dynamics of SO(3)xSU(2)s".
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Kong, F. and Wu, W. 2010. Periodicity of Diatomic and Triatomic Molecules, Conference Proceedings of the 2010 Workshop on Mathematical Chemistry of the Americas.
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tend to be more similar than for adjacent molecules that have more or fewer valence electrons; for triatomic molecules, the electron count is the sum of the
837:, which provide the same information, and (c) data provided by experiment, by the solar system model, and by solutions to the Schroedinger equation. The
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Hefferlin, R (2008). "Kronecker-Product Periodic Systems of Small Gas-Phase Molecules and the Search for Order in Atomic Ensembles of Any Phase".
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833:), which provides the magic-number elements that end each row of the table and gives the number of elements in each row, (b) solutions to the
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Dias, J.R. (1982). "A periodic Table of Polycyclic Aromatic Hydrocarbons. Isomer Enumeration of Fused Polycyclic Aromatic Hydrocarbons".
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should not be ignored: it gave explanations for the wealth of spectroscopic data that were already in existence before the advent of
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Hefferlin, R. (2010). "Internuclear Separations using Least squares and Neural Networks for 46 new s and p Electron Diatomics".
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include those of (1) H. D. W. Clark, and (2) F.-A. Kong, which somewhat resemble the atomic chart. The system of R. Hefferlin
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Hefferlin, R. (2010). "Vibration Frequencies using Least squares and Neural Networks for 50 new s and p Electron Diatomics".
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Gorski, A (1973). "Morphological Classification of Simple Species. Part V. Evaluation of Structural Parameters of Species".
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Gorski, A (1971). "Morphological Classification of Simple Species. Part I. Fundamental Components of Chemical Structure".
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potentials, and acid-base tendencies (Gorski). These structures are not restricted to molecules with a given number of
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Haas, A. (1988). "Das Elementverscheibungsprinzip und siene Bedeutung fur die Chemie der p-Block Elemente".
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of the elements. Construction of such charts was initiated in the early 20th century and is still ongoing.
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Other investigators have focused on building structures that address specific kinds of molecules such as
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that states a Knowledge (XXG) editor's personal feelings or presents an original argument about a topic.
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which in principle includes all of the systems described above except those of Dias, Gorski, and Jenz.
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Periodic systems (or charts or tables) of molecules are the subjects of two reviews. The systems of
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Dias, J. R. (1994). "Benzenoids to Fullerines and the Circumscribing and Leapfrog Algorithms".
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Haas, A. (1982). "A new classification principle: the periodic system of functional groups".
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A totally different kind of periodic system is (5) that of G. V. Zhuvikin, which is based on
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The periodic chart of the elements, like a small stool, is supported by three legs: (a) the
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Jenz, F (1996). "The Reduced Potential Curve (RPC) Method and its Applications".
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was developed from (3) a three-dimensional to (4) a four-dimensional system
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Hefferlin, R.; et al. (1984). "Periodic Systems of N-atom Molecules".
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Morozov, N. 1907. Stroeniya Veshchestva, I. D. Sytina Publication, Moscow.
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Clark, C. H. D. (1935). "The periodic Groups of Non-Hydride Di-Atoms".
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Chung, D.-Y. (2000). "The Periodic Table of Elementary Particles".
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Bases of the element chart and periodic systems of molecules
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personal reflection, personal essay, or argumentative essay
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Kong, F (1982). "The Periodicity of Diatomic Molecules".
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Hefferlin, R. 2006. The Periodic Systems of Molecules
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A collapsed-coordinate system for triatomic molecules
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1019:: 370–376.
845:mechanics.
763:core charge
745:containing
737:(Morozov);
1555:: 479–508.
1424:: 211–216.
1367:: 239–248.
1348:: 667–673.
964:pp. 221 ff
904:References
815:Sommerfeld
739:benzenoids
135:newspapers
102:references
1321:: 15–22.
1046:: 17–28.
319:⊗
203:molecules
165:July 2011
1580:Category
1470:England.
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887:See also
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747:fluorine
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211:rare gas
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767:redox
156:JSTOR
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1567:link
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1256:link
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