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In chemistry, molecular orbital theory (MO theory) is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.[1] In this theory, each molecule has a set of molecular orbitals, in which it is assumed that the molecular orbital wave function ψf may be written as a simple weighted sum of the n constituent atomic orbitals χi, according to the following equation:[2] For other uses, see Chemistry (disambiguation). ...
For other uses, see Electron (disambiguation). ...
A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ...
Properties For other meanings of Atom, see Atom (disambiguation). ...
In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ...
A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ...
 The cij coefficients may be determined numerically by substitution of this equation into the Schrödinger equation and application of the variational principle. This method is called the linear combination of atomic orbitals approximation and is used in computational chemistry. An additional unitary transformation can be applied on the system to accelerate the convergence in some computational schemes. Molecular orbital theory was seen as a competitor to valence bond theory in the 1930s, before it was realized that the two methods are closely related and that when extended they become equivalent. For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ...
A variational principle is a principle in physics which is expressed in terms of the calculus of variations. ...
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. ...
Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to complement the information obtained by actual chemical experiments, predict hitherto unobserved chemical phenomena, and solve related problems. ...
In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. ...
History
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Molecular orbital theory was developed, in the years after valence bond theory (1927) had been established, primarily through the efforts of Friedrich Hund, Robert Mulliken, John C. Slater, and John Lennard-Jones.[3] MO theory was originally called the Hund-Mulliken theory.[4] The word orbital was introduced by Mulliken in 1932.[4] By 1933, the molecular orbital theory had become accepted as a valid and useful theory.[5] According to German physicist and physical chemist Erich Hückel, the first quantitative use of molecular orbital theory was the 1929 paper of Lennard-Jones.[6] The first accurate calculation of a molecular orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen molecule.[7] By 1950, molecular orbitals were completely defined as eigenfunctions (wave functions) of the self-consistent field Hamiltonian and it was at this point that molecular orbital theory became fully rigorous and consistent.[8] This rigorous approach is known as the Hartree-Fock method for molecules although it had its origins in calculations on atoms. In calculations on molecules, the molecular orbitals are expanded in terms of an atomic orbital basis set, leading to the Roothaan equations.[9] This led to the development of many ab initio quantum chemistry methods. Parallel to this rigorous development, molecular orbital theory was applied in an approximate manner using some empirically derived parameters in methods now known as semi-empirical quantum chemistry methods.[10] Niels Bohr’s 1913 quantum model of the atom, which incorporated an explanation of Johannes Rydbergs 1888 formula, Max Planck’s 1900 quantum hypothesis, i. ...
Carl von Weizacker & Friedrich Hund, Goettingen DPI Friedrich Hund (February 4, 1896 - March 31, 1997) : German physicist known for his work on atoms and molecules. ...
Robert Sanderson Mulliken (June 7, 1896-October 31, 1986) was an American physicist and chemist, primarily responsible for the elaboration of the molecular orbital method of computing the structure of molecules. ...
John Clark Slater (1900-1976) was a major physicist and theoretical chemist. ...
John Edward Lennard-Jones (October 27, 1894 - November 1, 1954) was a mathematician who held a chair of theoretical physics at Bristol University, and then a chair of theoretical science at Cambridge University. ...
Erich Armand Arthur Joseph Hückel (August 9, 1896 - February 16, 1980) was a German physicist and physical chemist. ...
Charles Alfred Coulson (1910-1974) was a prominent researcher in the field of theoretical chemistry. ...
In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ...
In mathematics, an eigenfunction f of a linear operator A on a function space is an eigenvector of the linear operator; it satisfies for some scalar λ, the corresponding eigenvalue. ...
In physics, Hamiltonian has distinct but closely related meanings. ...
In computational physics, the Hartree-Fock calculation scheme is a self-consistent iterative procedure to calculate the so-called best possible single determinant solution to the time-independent Schrödinger equation of a many-electron system in a Coulombic potential of fixed nuclei. ...
In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ...
The Roothaan equations are a representation of the Hartree-Fock equation in a non orthonormalized basis set which can be of Gaussian type. ...
Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. ...
Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. ...
Overview Molecular orbital (MO) theory uses a linear combination of atomic orbitals to form molecular orbitals which cover the whole molecule. These are often divided into bonding orbitals, anti-bonding orbitals, and non-bonding orbitals. A molecular orbital is merely a Schrödinger orbital which includes several, but often only two nuclei. If this orbital is of type in which the electron(s) in the orbital have a higher probability of being between nuclei than elsewhere, the orbital will be a bonding orbital, and will tend to hold the nuclei together. If the electrons tend to be present in a molecular orbital in which they spend more time elsewhere than between the nuclei, the orbital will function as an anti-bonding orbital and will actually weaken the bond. Electrons in non-bonding orbitals tend to be in deep orbitals (nearly atomic orbitals) associated almost entirely with one nucleus or the other, and thus they spend equal time between nuclei or not. These electrons neither contribute nor detract from bond strength. In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ...
In chemistry, an atomic orbital is the region in which an electron may be found around a single atom. ...
Antibonding (or anti-bonding) is a type of chemical bonding. ...
In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ...
Antibonding (or anti-bonding) is a type of chemical bonding. ...
An atomic orbital is the description of the behavior of an electron in an atom according to quantum mechanics. ...
Molecular orbitals are further divided according the types of atomic orbitals combining to form a bond. These orbitals are results of electron-nucleus interactions that are caused by the fundamental force of electromagnetism. Chemical substances will form a bond if their orbitals become lower in energy when they interact with each other. Different chemical bonds are distinguished that differ by electron cloud shape and by energy levels. The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ...
A fundamental interaction or fundamental force is a mechanism by which particles interact with each other, and which cannot be explained in terms of another interaction. ...
Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ...
Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure (, a crystal). ...
A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ...
MO theory provides a global, delocalized perspective on chemical bonding. For example, in the MO theory for hypervalent molecules, it is no longer necessary to invoke a major role for d-orbitals. In MO theory, any electron in a molecule may be found anywhere in the molecule, since quantum conditions allow electrons to travel under the influence of an arbitrarily large number of nuclei, so long as permitted by certain quantum rules. Although in MO theory some molecular orbitals may hold electrons which are more localized between specific pairs of molecular atoms, other orbitals may hold electrons which are spread more uniformly over the molecule. Thus, overall, bonding (and electrons) are far more delocalized (spread out) in MO theory, than is implied in VB theory. This makes MO theory more useful for the description of extended systems. A hypervalent molecule is a molecule that contains one or more typical elements (group 1, 2, 13-18) formally bearing more than eight electrons in their valence shells. ...
An example is that in the MO picture of benzene, composed of a hexagonal ring of 6 carbon atoms. In this molecule, 24 of the 30 total valence bonding electrons are located in 12 σ (sigma) bonding orbitals which are mostly located between pairs of atoms (C-C or C-H), similar to the valence bond picture. However, in benzene the remaining 6 bonding electrons are located in 3 π (pi) molecular bonding orbitals that are delocalized around the ring. Two are in a MO which has equal contributions from all 6 atoms. The other two have a vertical nodes at right angles to each other. As in the VB theory, all of these 6 delocalized pi electrons reside in a larger space which exists above and below the ring plane. All carbon-carbon bonds in benzene are chemically equivalent. In MO theory this is a direct consequence of the fact that the 3 molecular pi orbitals form a combination which evenly spreads the extra 6 electrons over 6 carbon atoms.[11] For benzine, see petroleum ether. ...
In molecules such as methane, the 8 valence electrons are in 4 MOs that are spread out over all 5 atoms. However, it is possible to transform this picture, without altering the total wavefunction and energy, to one with 8 electrons in 4 localized orbitals that are similar to the normal bonding picture of four two-electron covalent bonds. This is what has been done above for the σ (sigma) bonds of benzene, but it is not possible for the π (pi) orbitals. The delocalised picture is more appropriate for ionisation and spectroscopic properties. Upon ionization, a single electron is taken from the whole molecule. The resulting ion does not have one bond different from the other three Similarly for electronic excitations, the electron that is excited is found over the whole molecule and not in one bond. Methane is a chemical compound with the molecular formula CH4. ...
As in benzene, in substances such as beta carotene, chlorophyll or heme, some electrons the π (pi) orbitals are spread out in molecular orbitals over long distances in a molecule, giving rise to light absorption in lower energies (visible colors), a fact which is observed. This and other spectroscopic data for molecules are better explained in MO theory, with an emphasis on electronic states associated with multicenter orbitals, including mixing of orbitals premised on principles of orbital symmetry matching. The same MO principles also more naturally explain some electrical phenomena, such as high electrical conductivity in the planar direction of the hexagonal atomic sheets that exist in graphite. In MO theory, "resonance" (a mixing and blending of VB bond states) is a natural consequence of symmetry. For example, in graphite, as in benzene, it is not necessary to invoke the sp2 hybridization and resonance of VB theory, in order to explain electrical conduction. Instead, MO theory simply recognizes that some electrons in the graphite atomic sheets are completely delocalized over arbitrary distances, and reside in very large molecular orbitals that cover an entire graphite sheet, and some electrons are thus as free to move and conduct electricity in the sheet plane, as if they resided in a metal. Beta-carotene is a form of carotene with β-rings at both ends. ...
Chlorophyll gives leaves their green color Space-filling model of the chlorophyll molecule Chlorophyll is a green pigment found in most plants, algae, and cyanobacteria. ...
Structure of Heme b A heme or haem is a prosthetic group that consists of an iron atom contained in the center of a large heterocyclic organic ring called a porphyrin. ...
Electrical conductivity or specific conductivity is a measure of a materials ability to conduct an electric current. ...
For other uses, see Graphite (disambiguation). ...
In chemistry, delocalized electrons are electrons in a molecule that do not belong to a single atom or a covalent bond. ...
This article is about metallic materials. ...
See also Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. ...
In chemistry, an atomic orbital is the region in which an electron may be found around a single atom. ...
Configuration interaction (CI) is a post Hartree-Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a quantum chemical multi-electron system. ...
This article needs to be cleaned up to conform to a higher standard of quality. ...
In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...
In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ...
A molecular orbital diagram or MO diagram for short is a simple qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the Linear combination of atomic orbitals molecular orbital method (LCAO method) in particular [1] [2] [3]. This tool is very well...
Møller-Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree-Fock ab initio quantum chemistry methods in the field of computational chemistry. ...
Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. ...
References - ^ Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. ISBN 0-19-860918-3.
- ^ Licker, Mark, J. (2004). McGraw-Hill Concise Encyclopedia of Chemistry. New York: McGraw-Hill. ISBN 0-07-143953-6.
- ^ Coulson, Charles, A. (1952). Valence. Oxford at the Clarendon Press.
- ^ a b Spectroscopy, Molecular Orbitals, and Chemical Bonding - Robert Mulliken's 1966 Nobel Lecture
- ^ Lennard-Jones Paper of 1929 - Foundations of Molecular Orbital Theory.
- ^ Hückel, E. (1934). Trans. Faraday Soc. 30, 59.
- ^ Coulson, C.A. (1938). Proc. Camb. Phil. Soc. 34, 204.
- ^ Hall, G.G. Lennard-Jones, Sir John. (1950). Proc. Roy. Soc. A202, 155.
- ^ Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 65 - 69, ISBN 0 471 98055
- ^ Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 81 - 92, ISBN 0 471 98055
- ^ Introduction to Molecular Orbital Theory - Imperial College London
Robert Sanderson Mulliken (June 7, 1896-October 31, 1986) was an American physicist and chemist, primarily responsible for the elaboration of the molecular orbital method of computing the structure of molecules. ...
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