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{{essay |date=October 2010}}
{{primary sources |date=July 2011}}
'''Periodic systems of molecules''' are charts of molecules similar to the [[periodic table]] of the elements. Construction of such charts was initiated in the early 20th century and is still ongoing.

It is commonly believed that the [[periodic law]], represented by the periodic chart, is echoed in the behavior of [[molecule]]s, at least [[small molecule]]s. For instance, if one replaces any one of the atoms in a [[triatomic molecule]] with a [[rare gas]] 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 just a few atoms, for use as a [[teaching aid]] 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 [[Elementary particle|fundamental particles]].<ref>{{cite arxiv |author=Chung, D.-Y. |year= 2000 |title= The Periodic Table of Elementary Particles |eprint=0003023}}</ref>

==Physical periodic systems of molecules==
Periodic systems (or charts or tables) of molecules are the subjects of two reviews.<ref name=r2>Hefferlin, R. and Burdick, G.W. 1994. Fizicheskie i khimicheskie periodicheskie sistemy Molekul, Zhurnal Obshchei Xhimii, vol. 64, pp. 1870–1885. English translation: {{cite journal |title=Periodic Systems of Molecules: Physical and Chemical |journal= Russ. J. Gen. Chem. |volume=64 |pages=1659–1674}}</ref><ref name=r3>Hefferlin, R. 2006. The Periodic Systems of Molecules [http://books.google.com/books?id=gDSg9VQNIPcC&pg=PA221 pp. 221 ff], in Baird, D., Scerri, E., and McIntyre, L. (Eds.) “The Philosophy of Chemistry, Synthesis of a New Discipline,” Springer, Dordrecht ISBN 1-4020-3256-0.</ref> The systems of [[diatomic molecule]]s include those of (1) H. D. W. Clark,<ref>{{cite journal |author=Clark, C. H. D. |year= 1935 |title= The periodic Groups of Non-Hydride Di-Atoms |journal= Trans. Faraday Soc |volume=31 |pages=1017–1036 |doi=10.1039/tf9353101017}}</ref><ref>{{cite journal |author=Clark, C. H. D |year= 1940 |title= Systematics of Band-Spectral Constants. Part V. Interrelations of Dissociation Energy and Equilibrium Internuclear Distance of Di-Atoms in Ground States |journal= Trans. Faraday Soc. |volume=36 |pages= 370–376}}</ref> and (2) F.-A. Kong,<ref>{{cite journal |author=Kong, F |year= 1982 |title= The Periodicity of Diatomic Molecules |journal= J. Mol. Struct |volume=90 |pages=17–28 |doi=10.1016/0022-2860(82)90199-5|bibcode = 1982JMoSt..90...17K }}</ref><ref name=r7>Kong, F. and Wu, W. 2010. Periodicity of Diatomic and Triatomic Molecules, Conference Proceedings of the 2010 Workshop on Mathematical Chemistry of the Americas.</ref> which somewhat resemble the atomic chart. The system of R. Hefferlin ''et al.''<ref>{{cite journal |author=Hefferlin, R., Campbell, D. Gimbel, H. Kuhlman, and T. Cayton |year=1979 |doi=10.1016/0022-4073(79)90063-3 |journal= Quant. Spectrosc. Radiat. Transfer |volume=21 |pages=315–336 |title=The periodic table of diatomic molecules—I an algorithm for retrieval and prediction of spectrophysical properties |issue=4|bibcode = 1979JQSRT..21..315H }}</ref><ref name=r9>{{cite journal |author=Hefferlin, R |year= 2008 |title= Kronecker-Product Periodic Systems of Small Gas-Phase Molecules and the Search for Order in Atomic Ensembles of Any Phase |journal= Comb. Chem. High Through. Screen |volume=11 |pages=690–706}}</ref> was developed from (3) a three-dimensional to (4) a four-dimensional system [[Kronecker product]] of the element chart with itself.

{| align=right style="margin-left:1em"
|<math>
\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}
</math>
|-
| width=60em style="font-size:90%" |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 atoms.<ref>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, ISBN 978-1-61209-712-1</ref>
|}

A totally different kind of periodic system is (5) that of G. V. Zhuvikin,<ref>{{cite journal |author=Zhuvikin, G.V. and R. Hefferlin |year= 1983 |title= Periodicheskaya Sistema Dvukhatomnykh Molekul: Teoretiko-gruppovoi Podkhod, Vestnik Leningradskovo Universiteta |issue =16 |pages=10–16}}</ref><ref name=r11>{{cite journal |author=Carlson, C.M., Cavanaugh, R.J, Hefferlin, R.A, and of Zhuvikin, G.V. |year=1996 |title= Periodic Systems of Molecular States from the Boson Group Dynamics of SO(3)xSU(2)s |journal= Chem. Inf. Comp. Sci |volume=36 |pages=396–398}}</ref> which is based on [[group dynamics]]. 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<ref name=r7/> and Hefferlin <ref>{{cite journal |author=Hefferlin, R. ''et al.'' |year=1984 |title=Periodic Systems of N-atom Molecules |journal= J. Quant. Spectrosc. Radiat. Transfer |volume= 32 |pages=257–268 |doi=10.1016/0022-4073(84)90098-0 |issue=4|bibcode = 1984JQSRT..32..257H }}</ref> to include ionized species, and expanded by Kong,<ref name=r7/> Hefferlin,<ref name=r9/> and Zhuvikin and Hefferlin<ref name=r11/> to the space of triatomic molecules. These architectures are mathematically related to the chart of the elements. They were first called “physical” periodic systems.<ref name=r2/>

==Chemical periodic systems of molecules==
Other investigators have focused on building structures that address specific kinds of molecules such as [[alkane]]s (Morozov);<ref>Morozov, N. 1907. Stroeniya Veshchestva, I. D. Sytina Publication, Moscow.</ref> [[benzenoid]]s (Dias);<ref>{{cite journal |author=Dias, J.R. |year=1982 |title= A periodic Table of Polycyclic Aromatic Hydrocarbons. Isomer Enumeration of Fused Polycyclic Aromatic Hydrocarbons |journal= Chem. Inf. Comput. Sci. |volume=22 |pages=15–22}}</ref><ref>{{cite journal |author=Dias, J. R. |year=1994 |title= Benzenoids to Fullerines and the Circumscribing and Leapfrog Algorithms |journal= New J. Chem. |volume=18 |pages=667–673}}</ref> [[functional group]]s containing [[fluorine]], [[oxygen]], [[nitrogen]] and [[sulfur]] (Haas);<ref>{{cite journal |author=Haas, A. |year= 1982 |title= A new classification principle: the periodic system of functional groups |journal= Chemicker-Zeitung |volume=106 |pages=239–248}}</ref><ref>{{cite journal |author=Haas, A. |year=1988 |title= Das Elementverscheibungsprinzip und siene Bedeutung fur die Chemie der p-Block Elemente |journal= Kontakte (Darmstadt) |volume=3 |pages=3–11}}</ref> or a combination of [[core charge]], number of shells, [[redox]] potentials, and acid-base tendencies (Gorski).<ref>{{cite journal |author=Gorski, A |year=1971 |title= Morphological Classification of Simple Species. Part I. Fundamental Components of Chemical Structure |volume=45 |pages=1981–1989 |journal= Roczniki Chemii}}</ref><ref>{{cite journal |author=Gorski, A |year= 1973 |title= Morphological Classification of Simple Species. Part V. Evaluation of Structural Parameters of Species |journal= Roczniki Chemii |volume=47 |pages=211–216}}</ref> These structures are not restricted to molecules with a given number of [[atom]]s 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, [[formula enumeration]]s (Dias), the [[hydrogen-displacement principle]] (Haas), [[reduced potential curve]]s (Jenz),<ref>{{cite journal |author=Jenz, F |year= 1996 |title= The Reduced Potential Curve (RPC) Method and its Applications |journal= Int. Rev. Phys. Chem. |volume=15 |pages=467–523 |doi=10.1080/01442359609353191 |issue=2|bibcode = 1996IRPC...15..467J }}</ref> a set of [[molecular descriptor]]s (Gorski), and similar strategies.

==Hyperperiodicity==
E. V. Babaev<ref>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, England.</ref> has erected a [[hyperperiodic system]] which in principle includes all of the systems described above except those of Dias, Gorski, and Jenz.

==Bases of the element chart and periodic systems of molecules==
The periodic chart of the elements, like a small stool, is supported by three legs: (a) the [[Niels Bohr|Bohr]]–[[Arnold Sommerfeld|Sommerfeld]] “[[solar system]]” [[atomic model]] (with [[electron spin]] and the [[Aufbau principle|Madelung principle]]), 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 [[Schrödinger equation]], which provide the same information, and (c) data provided by experiment, by the solar system model, and by solutions to the Schroedinger equation. The [[Bohr model#Refinements|Bohr–Sommerfeld model]] should not be ignored: it gave explanations for the wealth of spectroscopic data that were already in existence before the advent of [[wave function|wave]] mechanics.

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, 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.

A chronological list of the contributions to this field<ref name=r3/> 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 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,<ref name=r7/> and Hefferlin<ref>{{cite journal |author=Hefferlin, R. |year=2010 |title= Vibration Frequencies using Least squares and Neural Networks for 50 new s and p Electron Diatomics |journal= Quant. Spectr. Radiat. Transf. |volume=111 |pages=71–77 |doi=10.1016/j.jqsrt.2009.08.004|bibcode = 2010JQSRT.111...71H }}</ref><ref>{{cite journal |author=Hefferlin, R. |year=2010 |title=Internuclear Separations using Least squares and Neural Networks for 46 new s and p Electron Diatomics}}</ref>

==A collapsed-coordinate system for triatomic molecules==
The [[collapsed-coordinate system]] 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 for [[Isoelectronicity|isoelectronic molecules]] 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 [[Periodic table|atomic group numbers]] (the sum of the column numbers 1 to 8 in the [[p-block]] 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 respect to the product of the two [[Periodic table|atomic period (or row) numbers]], 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).<ref>{{cite journal |author=Carlson, C., Gilkeson, J., Linderman, K., LeBlanc, S. Hefferlin, R., and Davis, B |year= 1997 |title= Estimation of Properties of Triatomic Molecules from Tabulated Data Using Least-Squares Fitting |journal= Croatica Chemica Acta |volume=70 |pages=479–508}}</ref>

==References==

{{Reflist|35em}}

{{DEFAULTSORT:Periodic Systems Of Small Molecules}}
[[Category:Chemical compounds]]

Prime integer topology - Revision history

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