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Stanley Meyer breaks the Covalent Bonds of the Water Molecule H2O Dipole using a 600 Cycle Per Second Square Wave Gated Pulsating 42.8Khz Square Wave High Voltage Direct Currentless Method [* the Patent is Expired* ~:-)>

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A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms, or between atoms and other covalent bonds. In short, attraction-to-repulsion stability that forms between atoms when they share electrons is known as covalent bonding. [1]

Covalent bonding includes many kinds of interaction, including σ-bonding, π-bonding, metal to non-metal bonding, agostic interactions, and three-center two-electron bonds.[2][3] The term covalent bond dates from 1939.[4] The prefix co- means jointly, associated in action, partnered to a lesser degree, etc.; thus a "co-valent bond", essentially, means that the atoms share "valence", such as is discussed in valence bond theory. In the molecule H2, the hydrogen atoms share the two electrons via covalent bonding. Covalency is greatest between atoms of similar electronegativities. Thus, covalent bonding does not necessarily require the two atoms be of the same elements, only that they be of comparable electronegativity. Although covalent bonding entails sharing of electrons, it is not necessarily delocalized. Furthermore, in contrast to electrostatic interactions ("ionic bonds") the strength of covalent bond depends on the angular relation between atoms in polyatomic molecules.

Contents

[edit] History

The term "covalence" in regard to bonding was first used in 1919 by Irving Langmuir in a Journal of American Chemical Society article entitled The Arrangement of Electrons in Atoms and Molecules:[5]

(p.926)… we shall denote by the term covalence the number of pairs of electrons which a given atom shares with its neighbors.

The idea of covalent bonding can be traced several years prior to 1919 to Gilbert N. Lewis, who in 1916 described the sharing of electron pairs between atoms. He introduced the so called Lewis notation or electron dot notation or The Lewis Dot Structure in which valence electrons (those in the outer shell) are represented as dots around the atomic symbols. Pairs of electrons located between atoms represent covalent bonds. Multiple pairs represent multiple bonds, such as double and triple bonds. Some examples of Electron Dot Notation are shown in the following figure. An alternative form of representation, not shown here, has bond-forming electron pairs represented as solid lines.

Early concepts in covalent bonding arose from this kind of image of the molecule of methane. Covalent bonding is implied in the Lewis structure that indicates sharing of electrons between atoms.

While the idea of shared electron pairs provides an effective qualitative picture of covalent bonding, quantum mechanics is needed to understand the nature of these bonds and predict the structures and properties of simple molecules. Walter Heitler and Fritz London are credited with the first successful quantum mechanical explanation of a chemical bond, specifically that of molecular hydrogen, in 1927.[6] Their work was based on the valence bond model, which assumes that a chemical bond is formed when there is good overlap between the atomic orbitals of participating atoms. These atomic orbitals are known to have specific angular relationships between each other, and thus the valence bond model can successfully predict the bond angles observed in simple molecules.

[edit] Bond order

Bond order is a number that indicates the number of pairs of electrons shared between atoms forming a covalent bond. The term is only applicable to diatomic molecules, but is used to describe bonds within polyatomic compounds as well.

  1. The most common type of covalent bond is the single bond, the sharing of only one pair of electrons between two atoms. It usually consists of one sigma bond. All bonds with more than one shared pair are called multiple bonds.
  2. Sharing two pairs is called a double bond. An example is in ethylene (between the carbon atoms). It usually consists of one sigma bond and one pi bond.
  3. Sharing three pairs is called a triple bond. An example is in hydrogen cyanide (between C and N). It usually consists of one sigma bond and two pi-bonds.
  4. Quadruple bonds are found in the transition metals. Molybdenum and rhenium are the elements most commonly observed with this bonding configuration. An example of a quadruple bond is also found in Di-tungsten tetra(hpp).
  5. Quintuple bonds have been found to exist in certain dichromium compounds.
  6. Sextuple bonds are found in diatomic molybdenum and tungsten.

Most bonding of course, is not localized, so the above classification, while powerful and pervasive, is of limited validity. Three-center bonds do not conform readily to the above conventions.

[edit] Resonance

Many bonding situations can be described with more than one valid Lewis Dot Structure (for example, ozone, O3). In an LDS diagram of O3, the center atom will have a single bond with one atom and a double bond with the other. The LDS diagram cannot tell us which atom has the double bond; the first and second adjoining atoms have equal chances of having the double bond. These two possible structures are called resonance structures. In reality, the structure of ozone is a resonance hybrid between its two possible resonance structures. Instead of having one double bond and one single bond, there are actually two 1.5 bonds with approximately three electrons in each at all times.

A special resonance case is exhibited in aromatic rings of atoms (for example, benzene). Aromatic rings are composed of atoms arranged in a circle (held together by covalent bonds) that may alternate between single and double bonds according to their LDS. In actuality, the electrons tend to be disambiguously and evenly spaced within the ring. Electron sharing in aromatic structures is often represented with a ring inside the circle of atoms.

Lewis Dot Structures for molecules with resonance are shown by creating the dot structure for every possible form, placing brackets around each structure,and connecting the boxes with double-headed arrows.

[edit] Current theory

Today the valence bond model has been supplanted by the molecular orbital model. In this model, as atoms are brought together, the atomic orbitals interact to form molecular orbitals, which are linear sums and differences of the atomic orbitals. These molecular orbitals are a cross between the original atomic orbitals and generally extend between the two bonding atoms.

Using quantum mechanics it is possible to calculate the electronic structure, energy levels, bond angles, bond distances, dipole moments, and electromagnetic spectra of simple molecules with a high degree of accuracy. Bond distances and angles can be calculated as accurately as they can be measured (distances to a few pm and bond angles to a few degrees). For small molecules, calculations are sufficiently accurate to be useful for determining thermodynamic heats of formation and kinetic activation energy barriers.

[edit] See also

[edit] Notes

  1. ^ Campbell, Neil A.; Brad Williamson; Robin J. Heyden (2006). Biology: Exploring Life. Boston, Massachusetts: Pearson Prentice Hall. ISBN 0-13-250882-6. http://www.phschool.com/el_marketing.html. 
  2. ^ March, J. “Advanced Organic Chemistry” 4th Ed. J. Wiley and Sons, 1991: New York. ISBN 0-471-60180-2.
  3. ^ G. L. Miessler and D. A. Tarr “Inorganic Chemistry” 3rd Ed, Pearson/Prentice Hall publisher, ISBN 0-13-035471-6.
  4. ^ Merriam-Webster - Collegiate Dictionary (2000).
  5. ^ Langmuir, I. (1919). J. Am. Chem. Soc.; 1919; 41; 868-934.
  6. ^ W. Heitler and F. London, Zeitschrift für Physik, vol. 44, p. 455 (1927). English translation in H. Hettema, Quantum Chemistry, Classic Scientific Papers, World Scientific, Singapore (2000).

[edit] References

[edit] External links

[edit] Overview

A molecular orbital (MO) can be used to specify the spatial distribution and energy of one (or one pair of) electron(s). Most commonly an MO is represented as a linear combination of atomic orbitals (the LCAO-MO method), especially in qualitative or very approximate usage. They are invaluable in providing a simple model of bonding in molecules.

Most methods in computational chemistry today start 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. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals (see configuration interaction).

[edit] Qualitative discussion

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. In this approach, 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.[1][2] The linear combination of atomic orbitals approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones.[3]. 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.

Some properties:

  • The number of molecular orbitals is equal to the number the atomic orbitals included in the linear expansion,
  • If the molecule has some symmetry, the degenerate atomic orbitals (with the same atomic energy) are grouped in linear combinations (called symmetry adapted atomic orbitals (SO)) which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations (SALC).
  • The number of molecular orbitals belonging to one group representation is equal to the number of symmetry adapted atomic orbitals belonging to this representation,
  • Within a particular representation, the symmetry adapted atomic orbitals mix more if their atomic energy level are closer.

[edit] Examples

[edit] H2

H2 1sσ* antibonding molecular orbital

As a simple example consider the hydrogen molecule, H2 (see molecular orbital diagram), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:

1s' - 1s" Antisymmetric combination: negated by reflection, unchanged by other operations
1s' + 1s" Symmetric combination: unchanged by all symmetry operations

The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. Because the H2 molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (and hence more stable) than two free hydrogen atoms. This is called a covalent bond. The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms.

[edit] He2

On the other hand, consider the hypothetical molecule of He2 (see molecular orbital diagram) with the atoms labelled He' and He". Again, the lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule, while the following symmetry adapted atomic orbitals do:

1s' - 1s" Antisymmetric combination: negated by reflection, unchanged by other operations
1s' + 1s" Symmetric combination: unchanged by all symmetry operations

Similar to the molecule H2, the symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. However, in its neutral ground state, each Helium atom contains two electrons in its 1s orbital, combining for a total of four electrons. Two electrons fill the lower energy bonding orbital, while the remaining two fill the higher energy antibonding orbital. Thus, the resulting electron density around the molecule does not support the formation of a bond between the two atoms (called a sigma bond), and the molecule does therefore not exist. Another way of looking at it is that there are two bonding electrons and two antibonding electrons; therefore, the bond order is 0 and no bond exists.

[edit] Noble gases

Considering a hypothetical molecule of He2, since the basis set of atomic orbitals is the same as in the case of H2, we find that both the bonding and antibonding orbitals are filled, so there is no energy advantage to the pair. HeH would have a slight energy advantage, but not as much as H2 + 2 He, so the molecule exists only a short while. In general, we find that atoms such as He that have completely full energy shells rarely bond with other atoms. Except for short-lived Van der Waals complexes, there are very few noble gas compounds known.

[edit] Ionic bonds

Main article: Ionic bond

When the energy difference between the atomic orbitals of two atoms is quite large, one atom's orbitals contribute almost entirely to the bonding orbitals, and the other's almost entirely to the antibonding orbitals. Thus, the situation is effectively that some electrons have been transferred from one atom to the other. This is called a (mostly) ionic bond.

[edit] MO diagrams

For more complicated molecules, the wave mechanics approach loses utility in a qualitative understanding of bonding (although is still necessary for a quantitative approach). The qualitative approach of MO uses a molecular orbital diagram. In this type of diagram, the molecular orbitals are represented by horizontal lines; the higher a line, the higher the energy of the orbital, and degenerate orbitals are placed on the same level with a space between them. Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity (only 2 electrons, having opposite spins, per orbital; have as many unpaired electrons on one energy level as possible before starting to pair them).

[edit] More quantitative approach

To obtain quantitative values for the molecular energy levels, one needs to have molecular orbitals which are such that the configuration interaction (CI) expansion converges fast towards the full CI limit. The most common method to obtain such functions is the Hartree-Fock method which expresses the molecular orbitals as eigenfunctions of the Fock operator. One usually solves this problem by expanding the molecular orbitals as linear combinations of gaussian functions centered on the atomic nuclei (see linear combination of atomic orbitals and basis set (chemistry)). 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.

Simple accounts often suggest that experimental molecular orbital energies can be obtained by the methods of ultra-violet photoelectron spectroscopy for valence orbitals and X-ray photoelectron spectroscopy for core orbitals. This however is incorrect as these experiments measure the ionization energy, the difference in energy between the molecule and one of the ions resulting from the removal of one electron. Ionization energies are linked approximately to orbital energies by Koopmans' theorem. While the agreement between these two values can be close for some molecules, it can be very poor in other cases.

[edit] See also

[edit] References

  1. ^ Friedrich Hund and Chemistry, Werner Kutzelnigg, on the occasion of Hund's 100th birthday, Angewandte Chemie, 35, 573 - 586, (1996)
  2. ^ Robert S. Mulliken's Nobel Lecture, Science, 157, no. 3785, 13 - 24, (1967)
  3. ^ J. E. Lennard-Jones, Transactions of the Faraday Society, 25, 668, (1929)

[edit] External links

Stanley Allen Meyer Water Fuel Cell

Molecular orbital

From Wikipedia, the free encyclopedia

Jump to: navigation, search

In chemistry, a molecular orbital (or MO) is a mathematical function that describes 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 use of the term "orbital" was first used in english by Robert S. Mulliken in 1925 as the English translation of Schrödinger's use of the german word, 'Eigenfunktion'. It has since been equated with the "region" generated with the function. Molecular orbitals are usually 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-Fock or Self-Consistent Field method.

H2 1sσ bonding molecular orbital
Complete acetylene (H–C≡C–H) molecular orbital set

Contents

[edit] Overview

A molecular orbital (MO) can be used to specify the spatial distribution and energy of one (or one pair of) electron(s). Most commonly an MO is represented as a linear combination of atomic orbitals (the LCAO-MO method), especially in qualitative or very approximate usage. They are invaluable in providing a simple model of bonding in molecules.

Most methods in computational chemistry today start 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. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals (see configuration interaction).

[edit] Qualitative discussion

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. In this approach, 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.[1][2] The linear combination of atomic orbitals approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones.[3]. 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.

Some properties:

  • The number of molecular orbitals is equal to the number the atomic orbitals included in the linear expansion,
  • If the molecule has some symmetry, the degenerate atomic orbitals (with the same atomic energy) are grouped in linear combinations (called symmetry adapted atomic orbitals (SO)) which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations (SALC).
  • The number of molecular orbitals belonging to one group representation is equal to the number of symmetry adapted atomic orbitals belonging to this representation,
  • Within a particular representation, the symmetry adapted atomic orbitals mix more if their atomic energy level are closer.

[edit] Examples

[edit] H2

H2 1sσ* antibonding molecular orbital

As a simple example consider the hydrogen molecule, H2 (see molecular orbital diagram), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:

1s' - 1s" Antisymmetric combination: negated by reflection, unchanged by other operations
1s' + 1s" Symmetric combination: unchanged by all symmetry operations

The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. Because the H2 molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (and hence more stable) than two free hydrogen atoms. This is called a covalent bond. The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms.

[edit] He2

On the other hand, consider the hypothetical molecule of He2 (see molecular orbital diagram) with the atoms labelled He' and He". Again, the lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule, while the following symmetry adapted atomic orbitals do:

1s' - 1s" Antisymmetric combination: negated by reflection, unchanged by other operations
1s' + 1s" Symmetric combination: unchanged by all symmetry operations

Similar to the molecule H2, the symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. However, in its neutral ground state, each Helium atom contains two electrons in its 1s orbital, combining for a total of four electrons. Two electrons fill the lower energy bonding orbital, while the remaining two fill the higher energy antibonding orbital. Thus, the resulting electron density around the molecule does not support the formation of a bond between the two atoms (called a sigma bond), and the molecule does therefore not exist. Another way of looking at it is that there are two bonding electrons and two antibonding electrons; therefore, the bond order is 0 and no bond exists.

[edit] Noble gases

Considering a hypothetical molecule of He2, since the basis set of atomic orbitals is the same as in the case of H2, we find that both the bonding and antibonding orbitals are filled, so there is no energy advantage to the pair. HeH would have a slight energy advantage, but not as much as H2 + 2 He, so the molecule exists only a short while. In general, we find that atoms such as He that have completely full energy shells rarely bond with other atoms. Except for short-lived Van der Waals complexes, there are very few noble gas compounds known.

[edit] Ionic bonds

Main article: Ionic bond

When the energy difference between the atomic orbitals of two atoms is quite large, one atom's orbitals contribute almost entirely to the bonding orbitals, and the other's almost entirely to the antibonding orbitals. Thus, the situation is effectively that some electrons have been transferred from one atom to the other. This is called a (mostly) ionic bond.

[edit] MO diagrams

For more complicated molecules, the wave mechanics approach loses utility in a qualitative understanding of bonding (although is still necessary for a quantitative approach). The qualitative approach of MO uses a molecular orbital diagram. In this type of diagram, the molecular orbitals are represented by horizontal lines; the higher a line, the higher the energy of the orbital, and degenerate orbitals are placed on the same level with a space between them. Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity (only 2 electrons, having opposite spins, per orbital; have as many unpaired electrons on one energy level as possible before starting to pair them).

[edit] More quantitative approach

To obtain quantitative values for the molecular energy levels, one needs to have molecular orbitals which are such that the configuration interaction (CI) expansion converges fast towards the full CI limit. The most common method to obtain such functions is the Hartree-Fock method which expresses the molecular orbitals as eigenfunctions of the Fock operator. One usually solves this problem by expanding the molecular orbitals as linear combinations of gaussian functions centered on the atomic nuclei (see linear combination of atomic orbitals and basis set (chemistry)). 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.

Simple accounts often suggest that experimental molecular orbital energies can be obtained by the methods of ultra-violet photoelectron spectroscopy for valence orbitals and X-ray photoelectron spectroscopy for core orbitals. This however is incorrect as these experiments measure the ionization energy, the difference in energy between the molecule and one of the ions resulting from the removal of one electron. Ionization energies are linked approximately to orbital energies by Koopmans' theorem. While the agreement between these two values can be close for some molecules, it can be very poor in other cases.