Periodic Systems of Small Molecules
Encyclopedia
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. What could be accomplished by constructing an explicit representation of this periodic law as manifested in molecules? Several goals could be accomplished: (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 fundamental particles
.
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
. 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.
s (Morozov); benzenoids (Dias); functional group
s containing fluorine
, oxygen
, nitrogen
and sulfur
(Haas); or a combination of core charge
, number of shells, redox
potentials, and acid-base tendencies (Gorski). 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 enumerations (Dias), the hydrogen-displacement principle (Haas), reduced potential curves (Jenz), a set of molecular descriptor
s (Gorski), and similar strategies.
” atomic model
(with electron spin 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 Schroedinger 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-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 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
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 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).
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
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
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s, at least small molecule
Small molecule
In the fields of pharmacology and biochemistry, a small molecule is a low molecular weight organic compound which is by definition not a polymer...
s. For instance, if one replaces any one of the atoms in a triatomic molecule
Triatomic molecule
Triatomic molecules are formed by three atoms. Examples include H2O, CO2, HCN etc.-Molecular vibrations:The vibrational modes of a triatomic molecule can be determined in specific cases.- Symmetric linear molecules :...
with a rare gas atom, there will be a drastic change in the molecule’s properties. What could be accomplished by constructing an explicit representation of this periodic law as manifested in molecules? Several goals could be accomplished: (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 fundamental particles
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
.
Physical periodic systems of molecules
Periodic systems (or charts or tables) of molecules are the subjects of two reviews. The systems of diatomic molecules include those of (1) H. D. W. Clark, and (2) F.-A. Kong, 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 productKronecker product
In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It gives the matrix of the tensor product with respect to a standard choice of basis. The Kronecker product should not be confused with the usual matrix...
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
Group dynamics refers to a system of behaviors and psychological processes that occur within a social group , or between social groups...
. 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 alkaneAlkane
Alkanes are chemical compounds that consist only of hydrogen and carbon atoms and are bonded exclusively by single bonds without any cycles...
s (Morozov); benzenoids (Dias); functional group
Functional group
In organic chemistry, functional groups are specific groups of atoms within molecules that are responsible for the characteristic chemical reactions of those molecules. The same functional group will undergo the same or similar chemical reaction regardless of the size of the molecule it is a part of...
s containing fluorine
Fluorine
Fluorine is the chemical element with atomic number 9, represented by the symbol F. It is the lightest element of the halogen column of the periodic table and has a single stable isotope, fluorine-19. At standard pressure and temperature, fluorine is a pale yellow gas composed of diatomic...
, oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
, nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
and sulfur
Sulfur
Sulfur or sulphur is the chemical element with atomic number 16. In the periodic table it is represented by the symbol S. It is an abundant, multivalent non-metal. Under normal conditions, sulfur atoms form cyclic octatomic molecules with chemical formula S8. Elemental sulfur is a bright yellow...
(Haas); or a combination of core charge
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 shielding effect of core electrons...
, number of shells, redox
Redox
Redox reactions describe all chemical reactions in which atoms have their oxidation state changed....
potentials, and acid-base tendencies (Gorski). These structures are not restricted to molecules with a given number of atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
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 enumerations (Dias), the hydrogen-displacement principle (Haas), reduced potential curves (Jenz), a set of molecular descriptor
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 numbers, allowing some mathematical treatment of the...
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 “solar systemSolar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
” atomic model
Atomic model
In model theory, an atomic model is a model such that the complete type of every tuple is axiomatized by a single formula. Such types are called principal types, and the formulas that axiomatize them are called complete formulas.-Definitions:...
(with electron spin 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 Schroedinger 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-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 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 moleculesIsoelectronicity
Two or more molecular entities are described as being isoelectronic with each other if they have the same number of electrons or a similar electron configuration and the same structure , regardless of the nature of the elements involved.The term valence isoelectronic is used when these molecular...
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
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
(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 atomic period (or row) numbers
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
, 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).