Cubical atom
Encyclopedia
The cubical atom was an early atom
ic model in which electron
s were positioned at the eight corners of a cube in a non-polar atom or molecule. This theory was developed in 1902 by Gilbert N. Lewis
and published in 1916 in the famous article "The Atom and the Molecule" and used to account for the phenomenon of valency.
Lewis's theory was based on Abegg's rule
. It was further developed in 1919 by Irving Langmuir
as the cubical octet atom. The figure below shows structural representations for elements of the second row of the periodic table
.
Although the cubical model of the atom was soon abandoned in favor of the quantum mechanical model based on the Schrödinger equation
, and is therefore now principally of historical interest, it represented an important step towards the understanding of the chemical bond. The 1916 article by Lewis also introduced the concept of the electron pair in the covalent bond
, the octet rule
, and the now-called Lewis structure
.
Double bonds are formed by sharing a face between two cubic atoms. This results in sharing four electrons:
Triple bonds could not be accounted for by the cubical atom model, because there is no way of having two cubes share three parallel edges. Lewis suggested that the electron pairs in atomic bonds have a special attraction, which result in a tetrahedral structure, as in the figure below (the new location of the electrons is represented by the dotted circles in the middle of the thick edges). This allows the formation of a single bond by sharing a corner, a double bond by sharing an edge, and a triple bond by sharing a face. It also accounts for the free rotation around single bonds and for the tetrahedral geometry of methane. Remarkably, it could be said that there was a grain of truth in this idea, because it was later shown that the Pauli exclusion principle
results in a "Fermi hole
" of decreased repulsion between a pair of electrons with opposite spins in the same orbital.
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...
ic model in which electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s were positioned at the eight corners of a cube in a non-polar atom or molecule. This theory was developed in 1902 by Gilbert N. Lewis
Gilbert N. Lewis
Gilbert Newton Lewis was an American physical chemist known for the discovery of the covalent bond , his purification of heavy water, his reformulation of chemical thermodynamics in a mathematically rigorous manner accessible to ordinary chemists, his theory of Lewis acids and...
and published in 1916 in the famous article "The Atom and the Molecule" and used to account for the phenomenon of valency.
Lewis's theory was based on Abegg's rule
Abegg's rule
In chemistry, Abegg’s rule states that the difference between the maximum positive and negative valence of an element is frequently eight. The rule used a historic meaning of valence which resembles the modern concept of oxidation state in which an atom is an electron donor or receiver...
. It was further developed in 1919 by Irving Langmuir
Irving Langmuir
Irving Langmuir was an American chemist and physicist. His most noted publication was the famous 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on Gilbert N. Lewis's cubical atom theory and Walther Kossel's chemical bonding theory, he outlined his...
as the cubical octet atom. The figure below shows structural representations for elements of the second row of the periodic table
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...
.
Although the cubical model of the atom was soon abandoned in favor of the quantum mechanical model based on the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
, and is therefore now principally of historical interest, it represented an important step towards the understanding of the chemical bond. The 1916 article by Lewis also introduced the concept of the electron pair in the covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
, the octet rule
Octet rule
The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low (The octet rule is a chemical rule of thumb that states that atoms of low (...
, and the now-called Lewis structure
Lewis structure
Lewis structures are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds...
.
Bonding in the cubical atom model
Single covalent bonds are formed when two atoms share an edge, as in structure C below. This results in the sharing of two electrons. Ionic bonds are formed by the transfer of an electron from one cube to another, without sharing an edge (A). An intermediate state B where only one corner is shared was also postulated by Lewis.Double bonds are formed by sharing a face between two cubic atoms. This results in sharing four electrons:
Triple bonds could not be accounted for by the cubical atom model, because there is no way of having two cubes share three parallel edges. Lewis suggested that the electron pairs in atomic bonds have a special attraction, which result in a tetrahedral structure, as in the figure below (the new location of the electrons is represented by the dotted circles in the middle of the thick edges). This allows the formation of a single bond by sharing a corner, a double bond by sharing an edge, and a triple bond by sharing a face. It also accounts for the free rotation around single bonds and for the tetrahedral geometry of methane. Remarkably, it could be said that there was a grain of truth in this idea, because it was later shown that the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
results in a "Fermi hole
Fermi hole
The idea of a Fermi hole requires some background in the idea of anti-symmetrized wavefunctions. The Pauli exclusion principle is the "rule" that no more than two electrons can be in the same orbital. The "rule" traces to a deep algebraic property of nature that has nothing whatsoever to do with...
" of decreased repulsion between a pair of electrons with opposite spins in the same orbital.