Chapter 2 wave function the mathematical description of an orbital the square of the wave function is proportional to the electron density the plus sign and the minus sign of these wave functions are not charges they are the instantaneous phase of the constantly changing wave function if you picture the wave function as a string the two halves are out of phase Picture it as the p orbital the two lobes are out of phase with each other when one has a plus sign the other has a minus sign node non bonding plane bond length is the internuclear distance where attraction and repulsion are balanced which also gives the minimum energy the strongest bond keep in mind that there is always an optimum distance between 2 nuclei this must be true because if they re too far their attraction for the bonding electrons is diminished but if they re too close their electrostatic repulsion pushes them apart bonding molecular orbital bonding MO places a large amount of electron density in the bonding region between the nuclei the energy of an electron in a bonding MO is lower than it is in an atomic orbital sigma bond ALSO known as cylindrically symmetrical bond most common bonds in organic compounds all single bonds in organic compounds are sigma bonds every double or triple bond contains at least one sigma bond antibonding molecular orbital places most of the electron density outside the bonding region the energy of an electron in an antibonding MO is higher than it is in an atomic orbital the presence of a node separating the two nuclei usually indicates that the orbital is antibonding both bonding and antibonding orbitals exist in all molecules but antibonding orbitals are usually vacant in stable molecules antibonding orbitals often participate in reactions pi bond results from overlap between two p orbitals oriented perpendicular to the line connecting the nuclei double bonds requires the presence of 4 electrons obviously in the bonding region between the nuclei of the two atoms that are going to have the double bond the first pair of electrons goes into sigma bonding MO forming a strong sigma bond the second pair of electrons cannot go into the same orbital or the same space so it goes into a pi bonding MO with its electron density centered above and below the sigma bond VSEPR theory bonds and lone pairs around a central atom tend to be separated by the largest possible angles about 180 deg for 2 120 deg for 3 and 109 5 deg for 4 sp hybrid orbitals are associated with 180 deg bond angle which means a linear bonding arrangement sp2 hybrid orbitals are composed of 1 s and 2 p orbitals they re associated with a 120 deg bond angle and have trigonal geometry sp3 hybrid orbitals are associatd with 109 5 deg bond angles and tetrahedral geometry general rules for determining the hybridization of orbitals and the bond angles of atoms in organic molecules 1 Both sigma bonding electrons and lone pairs can occupy hybrid orbitals The number of hybrid orbitals on an atom is computed by adding the sigma bonds and the lone pairs of electrons on that atom 2 Use the hybridization and geometry that give the widest possible separation of the calculated number of bonds and lone pairs so basically atoms want to be as far away from each other as possible 3 In double and triple bonds the first bond is always a sigma bond formed by a hybrid orbital The second bond is a pi bond consisting of two lobes above and below the sigma bond formed by two unhybridized p orbitals The third bond of a triple bond is another pi bond perpendicular to the first pi bond conformations are different structures of the same molecule that only differ in how one group is twisted in relation to the other like ethane for example note rotation about single bonds is allowed but double bonds are rigid and cannot be twisted in double bonds we can separate and isolate compound that differ only in how their substituents are arranged on a double bond cis trans C C bond cis is when they re on the same side trans is when they re across from each other constitutional isomers aka structural isomers differ in their bonding sequence such as n butane and isobutane stereoisomers differ only in how their atoms are oriented in space so cis and trans the study of this is called stereochemistry another term for cis trans isomers is geometric isomers because they differ in the geometry of the groups on a double bond bond dipole moment a measure of the polarity of an individual bond in a molecule defined by the following equation in debyes 4 8 x electron charge x d in angstroms they re measured experimentally and are used to calculate other info like bond lengths and charge separations molecular dipole moment the dipole moment of the molecule taken as a whole good indicator of the molecule s overall polarity another definition claims that it s the vector sum of the individual bond dipole moments three major kinds of attractive forces cause molecules to associate into solids and liquids 1 dipole dipole forces of polar molecules 2 London dispersion forces that affect all molecules 3 hydrogen bonds that link molecules having OH or NH groups dipole dipole forces are generally attractive intermolecular forces resulting from the attraction of the positive and negative ends of the dipole moments of polar molecules London dispersion forces intermolecular forces resulting from the attraction of correlated temporary dipole moments induced in adjacent molecules hydrogen bonds the only ones that really mean anything are H O H N and H F alcohols with OH bonds form stronger hydrogen bonds than amines with NH bonds probably because oxygen is more EN than nitrogen polar solute in a polar solvent dissolves because like dissolves like which means that polar solute in a nonpolar solvent doesn t dissolve and so on hydrocarbons are compounds composed entire of carbon and hydrogen alkanes only have single bonds cycloalkanes form a ring still only single bonds alkanes usually undergo few reactions because they lack a functional group which is the part where reactions usually occur alkyl group alkane portion of a molecule with one hydrogen atom removed to allow bonding to the rest of the molecule alkenes hydrocarbons with C C double bonds the double bond is considered the functional group of the alkene unless rings are very large cycloalkenes are always the cis isomers but since they re so common the cis is omitted from the name in the case that it s a large ring a trans double bond may