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	Molecular orbital - Wikipedia, the free encyclopedia
		For hand-waving (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 (using eventually the concept of hybridized orbitals).
		The linear combination of atomic orbitals approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones.
		The equation for the coefficients of these linear combinations is a generalized eigenvalue equation known as the Roothaan equations which are in fact a particular representation of the Hartree-Fock equation.
	en.wikipedia.org /wiki/Molecular_orbital (796 words)

	The Linear Combination of Atomic Orbitals (Site not responding. Last check: 2007-10-12)
		The atomic orbitals can be the original atomic orbitals of the atoms, but often the geometry of these orbitals is such that effective overlap cannot occur in the known geometry of the molecule.
		This method of linearly combining atomic orbitals is particularly useful when the bonding in a molecule is essentially determined by one of the atoms in it, unlike the case of molecular oxygen where both of the atoms are significantly involved and no atom is located at the center of symmetry of the molecule.
		The hybridized atomic orbitals on one atom overlap with either normal or hybridized orbitals on another atom, or with both, depending on the molecular geometry.
	www.3rd1000.com /chem301/chem301i.htm (1233 words)

	Molecular Orbital Theory (Site not responding. Last check: 2007-10-12)
		The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.
		Where the atomic orbitals overlap, the in-phase interaction leads to an increase in the intensity of the negative charge in the region where they overlap.
		Because electrons in the molecular orbital are lower potential energy than in separate atomic orbitals, energy would be required to shift the electrons back into the 1s orbitals of separate atoms.
	www.mpcfaculty.net /mark_bishop/molecular_orbital_theory.htm (1632 words)

	Linear combination of atomic orbitals molecular orbital method - Wikipedia, the free encyclopedia
		The linear combination of atomic orbitals molecular orbital method (usually called the LCAO MO method) is a technique for calculating molecular orbitals in quantum chemistry.
		The orbitals are expressed as linear combinations of basis functions, and the basis functions are one-electron functions centered on nuclei of the component atoms of the molecule.
		By minimizing the energy, an appropriate set of coefficients of the linear combinations is determined.
	www.netipedia.com /index.php/LCAO_MO_Method (160 words)

	[No title]
		atomic orbitals H is the Hamiltonian operator; a differential operator which describes both the kinetic energy and potential energy of the nuclei and electrons that make up the atom.
		Eatom is the energy of system and fatom is a wavefunction or atomic orbital which determines the positions and momenta of all the particles in the atom.
		The square of the atomic orbitals fatom2 is a mathematical functions describing the position of the electron as a function of its distance from the nucleus of the atom.
	community.middlebury.edu /~chem/chemistry/software/ftp/docs/handouts_wt97/d-Quantum_Mechanics.doc (2343 words)

	Molecular Orbitals in MOE (Site not responding. Last check: 2007-10-12)
		Hence the total density of the orbital at a point in space is the sum of those of the constituent atomic orbitals at that point, multiplied by the weighting coefficient taken from the eigenvector matrix.
		The Cartesian variables (x, y, z) are the displacements from the center of the atomic orbital (the center being the position of the atom) and r is the magnitude of distance from the center.
		These orbitals have two node-planes, which is a qualitative rationalization for their higher energy relative to the lower orbital of p-type symmetry.
	www.chemcomp.com /Journal_of_CCG/Articles/molorbs.htm (2672 words)

	Atomic orbital
		In the quantum-chemical treatment of molecules, it is usually necessary to express the solutions as linear combinations of one-electron functions which are centered on the nuclei of the constituent atoms of the molecule.
		This method is referred to as the linear combination of atomic orbitals molecular orbital method (LCAO MO method).
		The orbitals used in the LCAO method are usually either exponentially decreasing from the atomic center (radial component of the form r=e
	www.sciencedaily.com /encyclopedia/atomic_orbital (244 words)

	Molecular Mechanics
		is a wavefunction or atomic orbital which determines the positions and momenta of all the particles in the atom.
		Molecular orbitals are represented as a linear combination of atomic orbitals (LCAO).
		For example, hybrid orbitals are linear combinations of atomic orbitals on a single atom.
	community.middlebury.edu /~chem/chemistry/class/winterm/handouts_wt97/d-Quantum_Mechanics.html (2206 words)

	No Title
		Linear Combination of Atomic Orbitals - Molecular Orbitals.
		Early, the Slater Type Orbitals (STO's) were used as basis functions due to their similarity to atomic orbitals of the hydrogen atom.
		The term contraction means "a linear combination of gaussian primitives to be used as basis function." Such a basis function will have its coefficients and exponents fixed.
	www.chem.arizona.edu /~lichtend/c518.dir/s2001.dir/basissets.dir/basisb.html (5439 words)

	Covalent Bonding (Site not responding. Last check: 2007-10-12)
		Atomic orbitals must overlap and they must have the same sign in order to form a bonding molecular orbital.
		Sigma or single bonds are formed by overlap of atomic orbitals between the nuclei (x axis).
		Pi bonds or multiple bonds are formed by the overlap of atomic orbitals perpendicular to the bond axis.
	www.humboldt.edu /~dp6/chem110/covalent/covalent.html (243 words)

	SparkNotes: Organic Molecular Orbitals: Molecular Orbital Theory
		Molecular orbital theory holds, as its name suggests, that electrons reside in molecular orbitals that are distributed over the entire molecule.
		The bonding molecular orbital is "bonding" in the sense that it is lower in energy than its component atomic orbitals.
		The total number of orbitals is conserved; the number of molecular orbitals equals the number of original atomic orbitals.
	www.sparknotes.com /chemistry/organic1/orbitals/section2.rhtml (891 words)

	No Title
		Basis functions are not usually atomic orbitals, and in many cases, they do not even resemble orbitals of isolated atoms.
		DZ sets have two basis functions per orbital, etc. Since valence orbitals of atoms are more affected by forming a bond than the inner (core) orbitals, more basis functions are assigned frequently to describe valence orbitals.
		Frequently, the core orbitals are long contractions consisting of many primitive Gaussians to represent well the "cusp" of s type function at the position of the nucleus.
	www.chem.arizona.edu /~dll518/BasisSets/basisDLL.html (5334 words)

	Organic Chemistry at Penn State: Quantum Primer III (Site not responding. Last check: 2007-10-12)
		All atoms in the molecule provide their atomic orbitals for construction of MO, but not all atomic orbitals must participate in all MO. The number of MO is equal to the number of atomic orbitals used to generate them.
		We have to use each atomic orbital completely, we have to generate normalized molecular orbitals (MOs), and the number of MOs must be equal to the number of atomic orbitals that we have started with.
		The usual energy order of MO is as follows: σ-type orbitals (the lowest energy), π-type orbitals, n-type orbitals (nonbonding, such as lone pairs), π-type orbitals* and σ-type orbitals* (the highest in energy).
	courses.chem.psu.edu /chem38/quantum/quantum3.html (1337 words)

	SparkNotes: Organic Molecular Orbitals: Terms
		This is in contrast to molecular orbitals, which are spread across a collection of atoms.
		In terms of Molecular Orbital theory, it is the number of bonding electron pairs minus the number of antibonding electron pairs.
		Molecular orbital - Orbitals that, in contrast to atomic orbitals, are distributed over an entire molecule instead of being localized to specific atoms.
	www.sparknotes.com /chemistry/organic1/orbitals/terms.html (412 words)

	Molecular orbitals of diatomic molecules.
		The formation of bonds from the linear combination of atomic orbitals is the same as that of the valence bond theory.
		In the discusion of electronic configurations of many-electron atoms, the variation of energy levels of the atomic orbitals was given.
		The combination of the 2s orbitals from the two atoms form a sigma bonding and sigma antibonding orbitals in a way very similar to the case of the hydrogen molecules, because the 2p orbitals have little to do with the 2s orbitals.
	www.science.uwaterloo.ca /~cchieh/cact/c120/molitof.html (746 words)

	[No title]
		A linear approximation of the functions is then feasible and the ensuing integrals are evaluated analytically.
		This is the approach of the commonly employed 'linear tetrahedron method' [Lehman and Andersen 1972], which is by far inferior in performance to the quadratic one [Wiesenekker et al.
		Nvertk is the number of points associated with each simplex; this depends on the type of approximation and on the dimensionality; in two dimensions for instance nvertk is 3 for the linear approximation (vertices only) and 6 for the quadratic approximation (with the midpoints).
	www.scm.com /Doc/BAND_thesis/BAND_Thesis.doc (3942 words)

	Linear Combinations of Atomic Orbitals (Site not responding. Last check: 2007-10-12)
		This one assumes the electron orbitals for a given molecule are linear combinations of the atomic orbitals surrounding each of the nuclei of the molecule.
		The fluorine 2px and 2s orbitals have the correct symmetry to overlap with the hydrogen 1s orbital.
		The 3px, 3py, and 3s orbitals on each of the chlorine atoms overlap to produce sp2 hybridized orbitals.
	user.mc.net /~buckeroo/LCAO.html (440 words)

	Seventh quiz CHEM3504 Oct
		In the LCAO method, linear combinations of atomic orbitals, or more often atomic-like orbitals, are used to approximate the (unknown) molecular orbitals.
		For full accuracy, one should in principle use an infinite number of atomic orbitals, but in practice three different radial functions for each occupied atomic function suffice, plus a few polarization functions which are not occupied in the atom but are needed in the molecule, like d functions for carbon etc.
		molecule, the occupied molecular orbital is the normalized sum of two hydrogen 1s atomic orbitals, centered at the positions of the protons (the LCAO coefficients must be equal because of symmetry).
	www.uark.edu /campus-resources/pulay/PChem03/quiz7k.htm (491 words)

	Chemical Sciences: Geometry of Hybridized Orbitals (Site not responding. Last check: 2007-10-12)
		One approach which does this is called the "hybridization" of atomic orbitals, which was introduced in a previous section and whose discussion is continued here.
		This sp type of hybridization is the reason for the existence of the basic linear shape found for two electron pairs in the valence shell using the valence shell electron pair repulsion approach.
		The trigonal bipyramid is the basic shape assumed by five bonding pairs of electrons in the outer (valence) shell of an atom in the valence shell electron pair repulsion approach.
	www.ualberta.ca /~jplambec/che/p102/p02202.htm (834 words)

	Chem 241 - EXPERIMENT D4 (Site not responding. Last check: 2007-10-12)
		Use the applet to display the molecular orbitals derived from the 2s atomic orbitals on two atoms.
		There is also a little contribution from the 2s orbitals to the most antibonding molecular orbital (at the top of the diagram), and a little contribution by the 2p orbitals to the most bonding molecular orbital (at the bottom).
		Feel free to play with the applet to examine some of the other combinations of atomic orbitals that are possible.
	artsandscience.concordia.ca /facstaff/a-c/bird/c241/D4.html (1616 words)

	Valence bond theory-Molecular orbital theory-Theories Of Chemical Bonding-Sigma bond-Pi bond-Formation of sigma ...
		A covalent bond is formed by the overlapping of atomic orbitals which form molecular orbital.
		Sigma bond is formed by the linear or head to head or end on overlapping of orbitals.
		The relative strength of a sigma bond is related to the extent of overlap of the atomic orbitals.
	www.citycollegiate.com /bond_theoryXIa.htm (492 words)

	G.G. Hall about Lennard-Jones, Sir John Edward - concerning : Early Ideas in the History of Quantum Chemistry.
		Thus his first approximation to the molecular orbital is a linear combination of H-like atomic orbitals suitably normalized using the overlap integral.
		In effect, this Lennard-Jones approach implied that the inner electrons in these molecules remained in atomic orbitals and only the valence electrons needed to be in MO involving both nuclei.
		As a final contribution, the paper also argued that the notation for the MO should begin with the principal quantum nurnber of the atomic orbital of the separated atom instead of using that of the united atom, as was the custom at that time.
	quantum-chemistry-history.com /LeJo_Dat/LJ-Hall1.htm (1553 words)

	Glossary - L (Site not responding. Last check: 2007-10-12)
		Ligand Field Theory: The description of the effect on the metal ion energy levels when in a complex, based on the molecular orbital description of covalent bond formation between the ligands and the metal ion center.
		Linear Combination of Atomic Orbitals (LCAO): An approximate procedure for forming molecular orbitals, by writing them as linear combinations of atomic orbital wavefunctions.
		Linear Combination: A linear combination of two quantities means simply their sum or their difference.
	www.everyscience.com /Chemistry/Glossary/L.php (447 words)

	Chemical Sciences: Geometry of Hybridized Orbitals
		This method of combining atomic orbitals is particularly useful when the bonding in all or part of a molecule is essentially determined by one of the atoms in it, located at the center.
		The square plane was not a basic shape in the valence shell electron pair approach, which explained square planar molecules as distortions of the octahedral geometry arising when six electron pairs are in the valence shell of the atom.
		2, the s, and all three of the p orbitals; one of the p orbitals is perpendicular to the xy plane.
	www.psigate.ac.uk /newsite/reference/plambeck/chem1/p02203.htm (823 words)

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