In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region; the term orbital was introduced by Robert S. Mulliken in 1932 as an abbreviation for one-electron orbital wave function. At an elementary level, it is used to describe the region of space in which the function has a significant amplitude. Molecular orbitals are constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms, they can be quantitatively calculated using the Hartree -- self-consistent field methods. A molecular orbital can be used to represent the regions in a molecule where an electron occupying that orbital is to be found. Molecular orbitals are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom.

A molecular orbital can specify the electron configuration of a molecule: the spatial distribution and energy of one electron. Most a MO is represented as a linear combination of atomic orbitals in qualitative or approximate usage, they are invaluable in providing a simple model of bonding in molecules, understood through molecular orbital theory. Most present-day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. In the case of two electrons occupying the same orbital, the Pauli principle demands that they have opposite spin; this is an approximation, accurate descriptions of the molecular electronic wave function do not have orbitals. Molecular orbitals are, in general, delocalized throughout the entire molecule. Moreover, if the molecule has symmetry elements, its nondegenerate molecular orbitals are either symmetric or antisymmetric with respect to any of these symmetries.

In other words, application of a symmetry operation S to molecular orbital ψ results in the molecular orbital being unchanged or reversing its mathematical sign: Sψ = ±ψ. In planar molecules, for example, molecular orbitals are either symmetric or antisymmetric with respect to reflection in the molecular plane. If molecules with degenerate orbital energies are considered, a more general statement that molecular orbitals form bases for the irreducible representations of the molecule's symmetry group holds; the symmetry properties of molecular orbitals means that delocalization is an inherent feature of molecular orbital theory and makes it fundamentally different from valence bond theory, in which bonds are viewed as localized electron pairs, with allowance for resonance to account for delocalization. In contrast to these symmetry-adapted canonical molecular orbitals, localized molecular orbitals can be formed by applying certain mathematical transformations to the canonical orbitals; the advantage of this approach is that the orbitals will correspond more to the "bonds" of a molecule as depicted by a Lewis structure.

As a disadvantage, the energy levels of these localized orbitals no longer have physical meaning. Molecular orbitals arise from allowed interactions between atomic orbitals, which are allowed if the symmetries of the atomic orbitals are compatible with each other. Efficiency of atomic orbital interactions is determined from the overlap between two atomic orbitals, significant if the atomic orbitals are close in energy; the number of molecular orbitals formed must be equal to the number of atomic orbitals in the atoms being combined to form the molecule. For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the "Linear combination of atomic orbitals molecular orbital method" ansatz. Here, the molecular orbitals are expressed as linear combinations of atomic orbitals. Molecular orbitals were first introduced by Friedrich Hund and Robert S. Mulliken in 1927 and 1928; the linear combination of atomic orbitals or "LCAO" approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones.

His ground-breaking paper showed how to derive the electronic structure of the fluorine and oxygen molecules from quantum principles. This qualitative approach to molecular orbital theory is part of the start of modern quantum chemistry. Linear combinations of atomic orbitals can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation. For simple diatomic molecules, the wavefunctions obtained are represented mathematically by the equations Ψ = c a ψ a + c b ψ b {\displaystyle \Psi

Grand Ayatollah Mohammad Ebrahim Jannaati is an Iranian Twelver Shia Marja. He has studied in seminaries of Qom and Najaf under Grand Ayatollahs Khomeini, he is known for his progressive fatwas on women and youth issues, such as: Allowing women to be an Islamic judge, Marja Allowing youth to get married without parental permission Unlike conservative Shias, he declares all humans, including kafirs clean Allowing betting on horse racing and archery competition. Allows Muslim men to marry non-Muslim yet religious women. Allows Muslims to consume non-halal meats provided by non-Muslims yet religious groups such as Christians and Jews. Allows Muslim men to shake hands with non-Muslim women if avoiding shaking hands is a bad habit in that culture or makes Islam to be viewed badly. Allowing woman to hold a judicial position provided she bears all necessary conditions. Women dancing for Women and men for men in Wedding ceremonies and Happiness is no problem. In Qom, In Fiqh courseSeyyed Hossein Borujerdi And soul out Ruhollah Khomeini Used.

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A. David Andrews is an Irish astronomer, he studied at Oriel College University of Dublin. He spent the early 1960s in Denmark working with the astrophysicist M. Rudkjobing at the Aarhus Observatory, he moved on in 1963 to Armagh Observatory in Northern Ireland. Dr Andrews discovered the minor planet 1727 Mette whilst at the Boyden Observatory located in Bloemfontein, South Africa, where he was Acting Director, it was while at Boyden Observatory. He was the first to make full use of computers, at Armagh Observatory. Andrews was Editor of the Irish Astronomical Journal following Ernst Öpik, in 1967 became a founder member of Commission 27 Working Group on Flare Stars of the International Astronomical Union; the Boyden Station was created by Harvard University in 1889 in Arequipa, using Uriah A. Boyden's bequest to Harvard. In 1927 the renamed Boyden Observatory moved across continents to its present location in South Africa; this became the site of the Armagh-Dunsink-Harvard 36-inch Baker-Schmidt telescope utilized by Dr.

E. M. Lindsay and other Irish and international astronomers. In 1976 the Observatory was handed over to the University of the Orange Free State and the famous ADH telescope was dismantled; some of its optical parts, including a 32-inch prism, were transferred to Dunsink Observatory, Dublin. Andrews turned his attention to the new international astronomical facilities in Chile, to available satellite technologies. Whilst 1727 Mette is by no means unique, it has been found that it belongs to the Hungaria family of asteroids which cross the orbit of Mars, that it has a small companion orbiting it once every 21 days; this update comes from the Palmer Divide Observatory in Colorado Springs U. S. A. Asteroid 1727 Mette is 10 kilometers in diameter and rotates on its axis with a period of 2.98 hours. Its companion is about 2 kilometers in diameter, it has been suggested that 1727 Mette could make a close encounter with Mars in 2023 even a collision. This impact scenario sounds much like that on Earth 65 million years ago when our dinosaurs were destroyed.

In the Irish Astronomical Journal Andrews reported a suspected outburst of a B7 spectral type star in Auriga, BD +31 1048. This enigmatic object was referred to by Prof. G. Haro as "Andrews' Star"; this was a discovery made in his earliest work on flare stars and solar-related phenomena which he pioneered at Armagh Observatory. Andrews collaborated with several groups in U. K. U. S. A. with Dr. D. J. Mullan, S. America, Armenia and Greece, he cooperated with Prof. G. Haro, director at the Tonantzintla Observatory in Mexico on stellar flares in young stellar clusters. Collaboration with Dr. W. E. Kunkel and Sir Bernard Lovell at the Jodrell Bank radio telescope led to one of the earliest detections of large radio flares in UV Ceti-type stars, in the dMe star YZ CMi. What Andrews had fortuitously observed at Armagh in 1968 turns out to have been what is now termed a stellar megaflare. In 1981 Andrews published from the Armagh Observatory his multi-colour measurements of over 16000 stars in a region rich in flare stars on Schmidt photographic plates, "A Photometric Atlas of the Orion Nebula".

He used material from the SRC/UK Schmidt in Australia and the European Southern Observatory and the Las Campanas Observatory in Chile. In the Irish Astronomical Journal he published a "Cyclopaedia of Telescope Makers" in seven parts in the 1990s. From 1984 he was engaged in the search for quasi-periodic ultraviolet and infrared variations in flare stars indicative of active regions and stellar rotation, he collaborated with the Armagh astronomers, Drs. C. J. Butler, P. B. Byrne, J. G. Doyle and P. Panagi, Japanese, Italian, U. K. and U. S. astronomers Prof. J. Linsky, in observations of the chromospheric rotation of RS CVn and BY Dra stars with the International Ultraviolet Explorer satellite. Andrews, now retired, his asteroidal wife, live in Dore, a village on the outskirts of the beautiful S. Yorkshire and Derbyshire border, near Sheffield U. K. where he enjoys a life of painting, music and his family. A. D. Andrews own account on Boyden Observatory Former Armagh Observatory Staff