Periodic systems of molecules are charts of molecules similar to the

periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...

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 Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element. They were discovered by the Russian chemist Dmitri Mendeleev in the year 1863. Major periodic trends include atom ...

, represented by the periodic chart, is echoed in the behavior of

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

s, at least small molecules. For instance, if one replaces any one of the atoms in a

triatomic molecule Triatomic molecules are molecules composed of three atoms, of either the same or different chemical elements. Examples include H2O, CO2 (pictured), HCN and O3 (ozone) Molecular vibrations The vibrational modes of a triatomic molecule can be d ...

with a

rare gas The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical elements with similar properties; under standard conditions, they are all odorless, colorless, monatomic gases with very low chemi ...

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 A teacher, also called a schoolteacher or formally an educator, is a person who helps students to acquire knowledge, competence, or virtue, via the practice of teaching. ''Informally'' the role of teacher may be taken on by anyone (e.g. wh ...

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

fundamental particles In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, a ...

Physical periodic systems of molecules

Periodic systems (or charts or tables) of molecules are the subjects of two reviews.Hefferlin, R. and Burdick, G.W. 1994. Fizicheskie i khimicheskie periodicheskie sistemy Molekul, Zhurnal Obshchei Xhimii, vol. 64, pp. 1870–1885. English translation: Hefferlin, R. 2006. The Periodic Systems of Molecule
pp. 221 ff
in Baird, D., Scerri, E., and McIntyre, L. (Eds.) “The Philosophy of Chemistry, Synthesis of a New Discipline,” Springer, Dordrecht . The systems of

diatomic molecule Diatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear. Ot ...

s include those of (1) H. D. W. Clark, and (2) F.-A. Kong,Kong, F. and Wu, W. 2010. Periodicity of Diatomic and Triatomic Molecules, Conference Proceedings of the 2010 Workshop on Mathematical Chemistry of the Americas. which somewhat resemble the atomic chart. The system of R. Hefferlin ''et al.'' was developed from (3) a three-dimensional to (4) a four-dimensional system

Kronecker product In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a generalization of the outer product (which is denoted by the same symbol) from vectors to ...

of the element chart with itself. A totally different kind of periodic system is (5) that of G. V. Zhuvikin, which is based on

group dynamics Group dynamics is a system of behaviors and psychological processes occurring within a social group (''intra''group dynamics), or between social groups ( ''inter''group dynamics). The study of group dynamics can be useful in understanding decision- ...

. 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.

Chemical periodic systems of molecules

Other investigators have focused on building structures that address specific kinds of molecules such as

alkane In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which ...

s (Morozov);

benzenoid In organic chemistry, benzenoids are a class of organic compounds with at least one benzene ring. These compounds have increased stability due resonance in the benzene rings. Most aromatic hydrocarbons are benzenoid. Notable counterexamples are cyc ...

s (Dias);

functional group In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest ...

s containing

fluorine Fluorine is a chemical element with the symbol F and atomic number 9. It is the lightest halogen and exists at standard conditions as a highly toxic, pale yellow diatomic gas. As the most electronegative reactive element, it is extremely reacti ...

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...

nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...

and

sulfur Sulfur (or sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula ...

(Haas); or a combination of

core charge Core charge is the effective nuclear charge experienced by an outer shell electron. In other words, core charge is an expression of the attractive force experienced by the valence electrons to the core of an atom which takes into account the shiel ...

, number of shells,

redox Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate (chemistry), substrate change. Oxidation is the loss of Electron, electrons or an increase in the oxidation state, while reduction ...

potentials, and acid-base tendencies (Gorski). These structures are not restricted to molecules with a given number of

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

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 In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwee ...

s (Dias),

Grimm's hydride displacement law Grimm's Hydride Displacement Law is an early hypothesis, formulated in 1925, to describe bioisosterism, the ability of certain chemical groups to function as or mimic other chemical groups. :“Atoms anywhere up to four places in the periodic syste ...

(Haas),

reduced potential curve Reduction, reduced, or reduce may refer to: Science and technology Chemistry * Reduction (chemistry), part of a reduction-oxidation (redox) reaction in which atoms have their oxidation state changed. ** Organic redox reaction, a redox reacti ...

s (Jenz), a set of

molecular descriptor Molecular descriptors play a fundamental role in chemistry, pharmaceutical sciences, environmental protection policy, and health researches, as well as in quality control, being the way molecules, thought of as real bodies, are transformed into num ...

s (Gorski), and similar strategies.

Hyperperiodicity

E. V. Babaev 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 Bohr–

Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...

“

solar system The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...

”

atomic model Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter an ...

(with

electron spin In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin (physics), spin and electric charge. The value of the ...

and the 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 The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...

, 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–Sommerfeld model The Bohr–Sommerfeld model (also known as the Sommerfeld model or Bohr–Sommerfeld theory) was an extension of the Bohr model to allow elliptical orbits of electrons around an atomic nucleus. Bohr–Sommerfeld theory is named after Danish ph ...

should not be ignored: it gave explanations for the wealth of spectroscopic data that were already in existence before the advent of

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...

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 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, and Hefferlin

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 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 atomic group numbers (the sum of the column numbers 1 to 8 in the

p-block A block of the periodic table is a set of elements unified by the atomic orbitals their valence electrons or vacancies lie in. The term appears to have been first used by Charles Janet. Each block is named after its characteristic orbital: s-blo ...

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 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).

References