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Topic: Linear combination of atomic orbitals molecular orbital method

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	Molecular orbital - Wikipedia, the free encyclopedia
		The linear combination of atomic orbitals approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones.
		The most common method to obtain such functions is the Hartree-Fock method which expresses the molecular orbitals as eigenfunctions of the Fock operator.
		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 (848 words)

	Linear combination of atomic orbitals molecular orbital method - Wikipedia, the free encyclopedia
		The LCAO molecular orbital method or LCAO MO 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.
		In this case, the shape of the molecular orbitals and their respective energies are deduced approximately from comparing the energies of the atomic orbitals of the individual atoms (or molecular fragments) and applying some recipes known as level repulsion and the like.
	en.wikipedia.org /wiki/LCAO_MO_Method (460 words)

	Atomic orbital (Site not responding. Last check: 2007-10-23)
		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.1-free-software.com /en/wikipedia/a/at/atomic_orbital.html (183 words)

	Molecular orbital Information Center - nitrogen trifluoride molecular orbital diagram
		The linear combination of atomic orbitals approximation for molecular orbitals was bh3 molecular orbital diagram introduced in 1929 by Sir John Lennard-Jones.
		When the energy difference between the atomic molecular orbital nitric oxide orbitals of two atoms is quite large, one atom's orbitals contribute almost entirely to the bonding orbitals, and the other's c3v molecular molecular orbital diagram helium orbital diagram almost entirely to the antibonding orbitals.
		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 molecular orbital theory and carbon representation nf3 molecular orbital diagram of the Hartree-Fock ethylene molecular orbital equation.
	www.scipeeps.com /Sci-Chemistry_Topics_Mi_-_O/Molecular_orbital.html (896 words)

	Atomic orbital Information Center - number of electrons in atomic orbital
		The atomic orbital concept is therefore a key concept for visualizing the excitation process associated to a given transition.
		In this case the atomic orbitals are the eigenstates of the hydrogen Hamiltonian.
		An atomic orbital is uniquely identified by the values of the three quantum numbers, and each set of the three quantum numbers corresponds to exactly one orbital, but the quantum numbers only occur in certain combinations of values.
	www.scipeeps.com /Sci-Biochemistry_Topics_A/Atomic_orbital.html (1692 words)

	Orbital hybridisation Did You Mean orbital_hybridisation (Site not responding. Last check: 2007-10-23)
		In chemistry, hybridisation is the mixing of atomic orbitals belonging to a same electron shell to form new orbitals suitable for the qualitative description of atomic bonding properties.
		Hybridized orbitals are very useful for rationalizing in hand waving discussions the shape of molecular orbitals for molecules made of atoms of the groups 2,3,4 of the periodic families of elements.
		Hydrogen orbitals are used as a basis for simple schemes of hybridisation because it is one of the few examples of orbitals for which an exact analytic solution to its Schrödinger equation is known.
	www.did-you-mean.com /Orbital_hybridisation.html (947 words)

	Business Ebook More Info - Atomic orbital - Free For You. (Site not responding. Last check: 2007-10-23)
		orbitals Atomic orbitals are the quantum state s of the individual electrons in the electron cloud around a single atom.
		The simplest atomic orbitals are those that occur in an atom with a single electron, such as the hydrogen atom.
		The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics.
	atomic.orbital.en.lmoney.org (1838 words)

	Orbit Room
		In molecular physics, 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 terms ''sub-orbital'' and ''orbital spaceflights'' refer to the latter: an orbital spaceflight is one which completes an orbit fully around the central body.
		An orbital spaceflight is achieved when the spacecraft travels around the Earth in space at sufficient lateral velocity (or equivalently, enough angular velocity) for the centrifugal force to cancel out the pull of Earth's gravity.
	www.artistbooking.com /trips/150/orbit-room.html (1418 words)

	Molecular Orbital Theory
		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.
		Molecular orbitals are formed from the overlap of atomic orbitals.
		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)

	Molecular Orbitals in MOE (Site not responding. Last check: 2007-10-23)
		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.
		From a molecular orbital point of view, either of these two reaction orientations is favorable: the shape and symmetry of the diene HOMO and the dienophile LUMO are ideally matched for maximum in-phase overlap.
	www.chemcomp.com /Journal_of_CCG/Articles/molorbs.htm (2672 words)

	Intute sciences - Chemical Sciences: Hybridization of Atomic Orbitals
		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.intute.ac.uk /sciences/reference/plambeck/chem1/p02201.htm (1256 words)

	Atomic orbital Information Center - number of electrons in atomic orbital
		These states are labelled by a set of quantum numbers summarized in the model atomic de orbital tippo d term symbol and usually associated to particular electron configurations, i.e.
		However, in general, an electron's behavior is not fully described by a number of electrons in atomic orbital single orbital.
		Generally atomic orbital speaking, the number n determines the size and energy of the orbital: as n increases, the size of the orbital increases.
	www.scipeeps.com /Sci-Chemistry_Topics_Ap_-_B/Atomic_orbital.html (1758 words)

	Intute sciences - Chemical Sciences: Introduction to Molecular Orbitals
		The molecular orbital approach, at the qualitative and descriptive level at which we shall introduce it, is useful primarily as a method of determining energy levels in molecules and the distribution of electrons among these energy levels.
		The principle of the molecular orbital theory is that the electronic structures of molecules are determined primarily by the nuclei of the atoms which constitute them and the arrangement of those nuclei in space.
		As a consequence the electrons in the molecule will prefer to occupy the bonding molecular orbital and the difference in energy between the bonding molecular orbital and the two original atomic orbitals is the bond enthalpy of the hydrogen molecule.
	www.psigate.ac.uk /newsite/reference/plambeck/chem1/p02211.htm (1024 words)

	Intute sciences - Chemical Sciences: Geometry of Hybridized Orbitals
		In the formation of covalent bonds, the electrons in the atomic orbitals on one atom interact with the electrons in the atomic orbitals on another atom to accomplish the sharing of electrons between the atoms.
		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 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.
	www.psigate.ac.uk /newsite/reference/plambeck/chem1/p02202.htm (837 words)

	M
		Molecular entity is used in this glossary as a general term for singular entities, irrespective of their nature, while chemical species stands for sets or ensembles of molecular entities.
		The method is based on the assumption of "natural" bond lengths and angles, deviation from which leads to strain, and the existence of torsional interactions and attractive and/or repulsive van der Waals and dipolar forces between non-bonded atoms.
		Molecular orbitals can also be described, in terms of the number of nuclei (or "centres") encompassed, as two-centre, multi-centre, etc. molecular orbitals, and are often expressed as a linear combination of atomic orbitals.
	www.chem.qmul.ac.uk /iupac/gtpoc/M.html (2808 words)

	Molecular Orbitals for Heteronuclear Molecules
		The molecular orbital is said to be approximated mathematically by a linear combination of atomic orbitals and the technique is known as the LCAO-MO method.
		Density diagrams of the molecular orbitals for the LiH, CH, and HF molecules are illustrated in Fig.
		The molecular orbitals which involve ps orbitals are characteristically strongly polarized in a direction away from the bond in the region of the nucleus on which the p orbital is centred.
	www.cartage.org.lb /en/themes/Sciences/Physics/MolecularPhysics/MolecularSpectra/Orbitals/Heteronuclear/Heteronuclear.htm (1628 words)

	Atomic orbital - More Info (Site not responding. Last check: 2007-10-23)
		Orbitals with the same value of n and also the same value of l are even more closely related; and are said to comρrise a " electron subshell ".
		Any discussion of the shaρes of electron orbitals is necessarily imρrecise; because a given electron; regardless of which orbital it occuρies; can at any moment be found at any distance from the nucleus and in any direction due to the Uncertainty Princiρle.
		The shaρes of atomic orbitals in one-electron atom are related to 3-dimensional sρherical harmonics.
	bg_688.bg.host-news.info (1892 words)

	Hartree-Fock Theory (Site not responding. Last check: 2007-10-23)
		The mathematics behind it is that each MO is made of a linear combination of atom-centered basis functions.
		Unfortunately, you are probably under the illusion that molecular orbitals are somehow ``real'' or ``true.'' Except for the special case of the hydrogen atom, this is completely false.
		Molecular orbitals are the product of Hartree-Fock theory, and Hartree-Fock is not an exact theory: it is an approximation to the electronic Schrödinger equation.
	vergil.chemistry.gatech.edu /courses/chem4681/background/node6.html (335 words)

	SparkNotes: Molecular Orbitals: Molecular Orbital Theory
		Molecular orbital theory posits the notion that electrons in molecules likewise exist in different orbitals that give the probability of finding the electron at particular points around the molecule.
		Notice that the orbitals of the separated atoms are written on either side of the diagram as horizontal lines at heights denoting their relative energies.
		From the orbital correlation diagram above you should notice that the amount of stabilization due to bonding is equal to the amount of destabilization due to antibonding, because there are two electrons in the bonding orbital and two electrons in the antibonding orbital.
	www.sparknotes.com /chemistry/bonding/molecularorbital/section1.html (1814 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)

	Computation Synopsis
		The atomic wavefunctions are combined proportionately using the Linear Combination of Atomic Orbitals (LCAO) approximation to generate a set of molecular wavefunctions (one for each atomic orbital).
		The extent to which the orbitals of each atom contribute to a given molecular orbital (expressed as a set of molecular orbital coefficients) is estimated using the method of "linear variation".
		The effects of electron-electron repulsion tend to be underestimated by SCF methods, limiting the accuracy of the calculated wavefunctions and energies.
	cmm.info.nih.gov /modeling/guide_documents/tocs/computation_synopsis.html (578 words)

	Molecular orbital Did You Mean molecular_orbital (Site not responding. Last check: 2007-10-23)
		In quantum chemistry, the molecular electronic states, i.e.
		The spatial components of these one-electron functions are called molecular orbitals.
		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).
	www.did-you-mean.com /Molecular_orbital.html (770 words)

	[No title]
		Molecular and solid-state quantum computations can be simplified considerably if the symmetry of the systems with respect to the rotation and inversion of the coordinates is taken into account.
		These so-called symmetry orbitals are invariant with respect to the symmetry operations of the group and are different for the point and double groups, i.e.
		Projection operator techniques are applied to generate the symmetry-adapted orbital functions as a linear combination of atomic orbitals.
	www.cpc.cs.qub.ac.uk /summaries/ADUH_v2_0.html (534 words)

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