Isoelectronic and isolobal relationship questions

Isolobal principle - Wikipedia

The isolobal definition may be extended to isoelectronic fragments having the A potential application of this relationship is to seek phosphorous- containing. The relation between formal oxidation state and d electron configuration. , ∏ Bonding in Isoelectronic and isolobal analogies. 3, read sections below. Isolobal compounds are analogues to isoelectronic compounds that share the same . Figure 7: Isolobal relationship between octahedral and square planar complexes. .. and examined problems in organo-metallic and solid-state chemistry.

Isolobal principle

This concept has one of the most powerful tools of theoretical physics. See Noethers theorem, and also, Wigners classification, which says that the symmetries of the laws of physics determine the properties of the found in nature. Important symmetries in physics include continuous symmetries and discrete symmetries of spacetime, internal symmetries of particles, in biology, the notion of symmetry is mostly used explicitly to describe body shapes. Bilateral animals, including humans, are more or less symmetric with respect to the plane which divides the body into left 2.

Quantum mechanical properties of the include a intrinsic angular momentum of a half-integer value, expressed in units of the reduced Planck constant. As it is a fermion, no two electrons can occupy the same state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of particles and waves, they can collide with other particles and can be diffracted like light.

Since an electron has charge, it has an electric field. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law, electrons radiate or absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields, special telescopes can detect electron plasma in outer space.

Electrons are involved in applications such as electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, gaseous ionization detectors.

Interactions involving electrons with other particles are of interest in fields such as chemistry.

Isolobal principle - Wikiwand

The Coulomb force interaction between the positive protons within atomic nuclei and the negative electrons without, allows the composition of the two known as atoms, ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system.

The exchange or sharing of the electrons between two or more atoms is the cause of chemical bonding. InBritish natural philosopher Richard Laming first hypothesized the concept of a quantity of electric charge to explain the chemical properties of atoms.

Irish physicist George Johnstone Stoney named this charge electron inelectrons can also participate in nuclear reactions, such as nucleosynthesis in stars, where they are known as beta particles.

Electrons can be created through beta decay of isotopes and in high-energy collisions. The antiparticle of the electron is called the positron, it is identical to the electron except that it carries electrical, when an electron collides with a positron, both particles can be totally annihilated, producing gamma ray photons. The ancient Greeks noticed that amber attracted small objects when rubbed with fur, along with lightning, this phenomenon is one of humanitys earliest recorded experiences with electricity.

Nobel Prize — The Nobel Prize is a set of annual international awards bestowed in a number of categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances. The will of the Swedish inventor Alfred Nobel established the prizes inthe prizes in Chemistry, Literature, Peace, Physics, and Physiology or Medicine were first awarded in Medals made before were struck in 23 carat gold, between andthe Nobel Prizes and the Prize in Economic Sciences were awarded times to people and organisations.

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With some receiving the Nobel Prize more than once, this makes a total of 23 organisations, the prize ceremonies take place annually in Stockholm, Sweden. Each recipient, or laureate, receives a medal, a diploma. The Nobel Prize is widely regarded as the most prestigious award available in the fields of literature, medicine, physics, chemistry, peace, and economics. The prize is not awarded posthumously, however, if a person is awarded a prize and dies before receiving it, though the average number of laureates per prize increased substantially during the 20th century, a prize may not be shared among more than three people.

Alfred Nobel was born on 21 October in Stockholm, Sweden and he was a chemist, engineer, and inventor. InNobel purchased the Bofors iron and steel mill and this invention was a precursor to many smokeless military explosives, especially the British smokeless powder cordite.

As a consequence of his patent claims, Nobel was eventually involved in a patent infringement lawsuit over cordite, Nobel amassed a fortune during his lifetime, with most of his wealth from his inventions, of which dynamite is the most famous. InNobel was astonished to read his own obituary, titled The merchant of death is dead, as it was Alfreds brother Ludvig who had died, the obituary was eight years premature.

The article disconcerted Nobel and made him apprehensive about how he would be remembered and this inspired him to change his will. Because of skepticism surrounding the will, it was not until 26 April that it was approved by the Storting in Norway. The executors of Nobels will, Ragnar Sohlman and Rudolf Lilljequist, formed the Nobel Foundation to take care of Nobels fortune, Nobels instructions named a Norwegian Nobel Committee to award the Peace Prize, the members of whom were appointed shortly after the will was approved in April Soon thereafter, the other prize-awarding organisations were designated or established and these were Karolinska Institutet on 7 June, the Swedish Academy on 9 June, and the Royal Swedish Academy of Sciences on 11 June.

The Nobel Foundation reached an agreement on guidelines for how the prizes should be awarded, and, ininthe personal union between Sweden and Norway was dissolved 4. He has also published plays and poetry and he is the Frank H. After Germany invaded Poland and occupied the town, his family was placed in a camp where his father. His father remained at the camp, but was able to occasionally visit.

While in hiding his mother kept Hoffmann entertained by teaching him to read and having him memorize geography from textbooks stored in the attic and he referred to the experience as having been enveloped in a cocoon of love. Most of the rest of the family perished in the Holocaust, though one grandmother and they migrated to the United States on the troop carrier Ernie Pyle in Ina monument to Holocaust victims was built in Zolochiv on Hoffmanns initiative, Hoffmann graduated in from New York Citys Stuyvesant High School, where he won a Westinghouse science scholarship.

He received his bachelor of degree at Columbia University in This method was extended by Hoffmann. He went to Cornell in and has remained there, becoming professor emeritus, Hoffmanns research and interests have been in the electronic structure of stable and unstable molecules, and in the study of transition states in reactions.

He has investigated the structure and reactivity of organic and inorganic molecules, and examined problems in organo-metallic and solid-state chemistry. They realized that chemical transformations could be predicted from subtle symmetries and asymmetries in the electron orbitals of complex molecules.

Their rules predict differing outcomes, such as the types of products that will be formed when two compounds are activated by heat compared with those produced under activation by light.

For this work Hoffmann received the Nobel Prize in chemistry, sharing it with Japanese chemist Kenichi Fukui, in his Nobel Lecture, Hoffmann introduced the isolobal analogy for predicting the bonding properties of organometallic compounds 5. Molecular geometry — Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule.

It determines several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism and biological activity. The angles between bonds that an atom forms depend only weakly on the rest of molecule, i. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques.

X-ray crystallography, neutron diffraction and electron diffraction can give molecular structure for crystalline solids based on the distance between nuclei and concentration of electron density, gas electron diffraction can be used for small molecules in the gas phase. NMR and FRET methods can be used to determine complementary information including relative distances, dihedral angles, angles, molecular geometries are best determined at low temperature because at higher temperatures the molecular structure is averaged over more accessible geometries.

Larger molecules often exist in multiple stable geometries that are close in energy on the energy surface. Geometries can also be computed by ab initio quantum chemistry methods to high accuracy, the molecular geometry can be different as a solid, in solution, and as a gas. The position of each atom is determined by the nature of the bonds by which it is connected to its neighboring atoms. Since the motions of the atoms in a molecule are determined by quantum mechanics, the overall quantum mechanical motions translation and rotation hardly change the geometry of the molecule.

In addition to translation and rotation, a type of motion is molecular vibration. The molecular vibrations are harmonic, and the atoms oscillate about their equilibrium positions, at higher temperatures the vibrational modes may be thermally excited, but they oscillate still around the recognizable geometry of the molecule.

To put this in perspective, the lowest excitation vibrational energy in water is the bending mode, thus, at room temperature less than 0. As stated above, rotation hardly influences the molecular geometry, but, as a quantum mechanical motion, it is thermally excited at relatively low temperatures.

From a classical point of view it can be stated that at temperatures more molecules will rotate faster. Octahedron — In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices. A regular octahedron is a Platonic solid composed of eight equilateral triangles, a regular octahedron is the dual polyhedron of a cube.

It is a square bipyramid in any of three orthogonal orientations and it is also a triangular antiprism in any of four orientations. An octahedron is the case of the more general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan metric, the second and third correspond to the B2 and A2 Coxeter planes. The octahedron can also be represented as a tiling. This projection is conformal, preserving angles but not areas or lengths, straight lines on the sphere are projected as circular arcs on the plane.

Correspondingly, an octahedron is the result of cutting off from a regular tetrahedron. One can also divide the edges of an octahedron in the ratio of the mean to define the vertices of an icosahedron. There are five octahedra that define any given icosahedron in this fashion, octahedra and tetrahedra can be alternated to form a vertex, edge, and face-uniform tessellation of space, called the octet truss by Buckminster Fuller.

This is the only such tiling save the regular tessellation of cubes, another is a tessellation of octahedra and cuboctahedra. The octahedron is unique among the Platonic solids in having a number of faces meeting at each vertex.

Consequently, it is the member of that group to possess mirror planes that do not pass through any of the faces. Using the standard nomenclature for Johnson solids, an octahedron would be called a square bipyramid, truncation of two opposite vertices results in a square bifrustum.

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The octahedron is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices and it is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size 7. Coordination complex — Many metal-containing compounds, especially those of transition metals, are coordination complexes. A coordination complex whose centre is an atom is called a metal complex. Coordination complexes are so pervasive that their structures and reactions are described in many ways, the atom within a ligand that is bonded to the central metal atom or ion is called the donor atom.

In a typical complex, an ion is bonded to several donor atoms. A polydentate ligand is a molecule or ion that bonds to the atom through several of the ligands atoms. These complexes are called chelate complexes, the formation of complexes is called chelation, complexation.

The central atom or ion, together with all ligands comprise the coordination sphere, the central atoms or ion and the donor atoms comprise the first coordination sphere. Coordination refers to the covalent bonds between the ligands and the central atom. Originally, a complex implied a reversible association of molecules, atoms, as applied to coordination chemistry, this meaning has evolved. Some metal complexes are formed virtually irreversibly and many are bound together by bonds that are quite strong, the number of donor atoms attached to the central atom or ion is called the coordination number.

The oxidation state and the number reflect the number of bonds formed between the metal ion and the ligands in the complex ion. Coordination complexes have been known since the beginning of modern chemistry, early well-known coordination complexes include dyes such as Prussian blue.

The removal of a hydrogen atom from methane generates a methyl radical. The molecule retains its molecular geometry as the frontier orbital points in the direction of the missing hydrogen atom. Further removal of hydrogen results in the formation of a second frontier orbital. This process can be repeated until only one bond remains to the molecule's central atom. Figure 2 demonstrates this example of step-by-step generation of isolobal fragments.

Construction of frontier orbitals from methane. The isolobal fragments of octahedral complexes, such as ML6, can be created in a similar fashion. Transition metal complexes should initially satisfy the eighteen electron rulehave no net charge, and their ligands should be two electron donors Lewis bases.

Consequently, the metal center for the ML6 starting point must be d6. Removal of a ligand is analogous to the removal of hydrogen of methane in the previous example resulting in a frontier orbital, which points toward the removed ligand.

In order to satisfy the zero-charge criteria the metal center must be changed. For example, a MoL6 complex is d6 and neutral. To remedy this, Mo can be exchanged for Mn, which would form a neutral d7 complex in this case, as shown in Figure 3. This trend can continue until only one ligand is left coordinated to the metal center. Production of a frontier orbital in an octahedral complex. Since the process is not charge producing, the metal center must change from d6 Mo to d7 Mn to retain the neutral charge.

Relationship between tetrahedral and octahedral fragments[ edit ] Figure 4: Isolobal fragments of tetrahedral and octahedral geometries. Isolobal fragments of tetrahedral and octahedral molecules can be related. Structures with the same number of frontier orbitals are isolobal to one another.