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  2. Isovalent hybridization - Wikipedia

    en.wikipedia.org/wiki/Isovalent_hybridization

    For example, the C−H bond length is 110.2 pm in ethane, 108.5 pm in ethylene and 106.1 pm in acetylene, with carbon hybridizations sp 3 (25% s), sp 2 (33% s) and sp (50% s) respectively. To determine the degree of hybridization of each bond one can utilize a hybridization parameter (λ).

  3. Molecular orbital diagram - Wikipedia

    en.wikipedia.org/wiki/Molecular_orbital_diagram

    Two atomic orbitals in phase create a larger electron density, which leads to the σ orbital. If the two 1s orbitals are not in phase, a node between them causes a jump in energy, the σ* orbital. From the diagram you can deduce the bond order, how many bonds are formed between the two atoms. For this molecule it is equal to one.

  4. Orbital hybridisation - Wikipedia

    en.wikipedia.org/wiki/Orbital_hybridisation

    Chemist Linus Pauling first developed the hybridisation theory in 1931 to explain the structure of simple molecules such as methane (CH 4) using atomic orbitals. [2] Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and a fourth weaker bond ...

  5. Ball-and-stick model - Wikipedia

    en.wikipedia.org/wiki/Ball-and-stick_model

    Double and triple bonds are usually represented by two or three curved rods, respectively, or alternately by correctly positioned sticks for the sigma and pi bonds. In a good model, the angles between the rods should be the same as the angles between the bonds , and the distances between the centers of the spheres should be proportional to the ...

  6. Bonding molecular orbital - Wikipedia

    en.wikipedia.org/wiki/Bonding_molecular_orbital

    The MO diagram for dihydrogen. In the classic example of the H 2 MO, the two separate H atoms have identical atomic orbitals. When creating the molecule dihydrogen, the individual valence orbitals, 1s, either: merge in phase to get bonding orbitals, where the electron density is in between the nuclei of the atoms; or, merge out of phase to get antibonding orbitals, where the electron density ...

  7. Square planar molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Square_planar_molecular...

    Representative d-orbital splitting diagrams for square planar complexes featuring σ-donor (left) and σ+π-donor (right) ligands. A general d-orbital splitting diagram for square planar (D 4h) transition metal complexes can be derived from the general octahedral (O h) splitting diagram, in which the d z 2 and the d x 2 −y 2 orbitals are degenerate and higher in energy than the degenerate ...

  8. Metal–ligand multiple bond - Wikipedia

    en.wikipedia.org/wiki/Metal–ligand_multiple_bond

    Increasing the bond order to two by involving another lone pair changes the hybridization at the oxygen to an sp 2 center with an expected expansion in the M-O-R bond angle and contraction in the M-O bond length. If all three lone pairs are included for a bond order of three than the M-O bond distance contracts further and since the oxygen is a ...

  9. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...