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              Organic Chemical Systems, Theory                                                            437

              TABLE I Typical Bond Energies in Organic Molecules a  The sum total of formal charges on atoms in a molecule
                                                                is equal to its net charge, and this is always indicated.
               X    X H    X C    X N    X O    X C    X C
                                                                Negativelychargedmoleculesarecalledanions,positively
               C     100     81    69      84    148    194     charged ones cations. The electrostatic force of attrac-
               N      93     69    38      43    148    213     tion between two oppositely charged ions is sometimes
               O     110     84    43      33    172            referred to as an ionic bond.
               F     135    105    65      50                     Typical bonding situations in which atoms of elements
               Si     72     69           103                   that are most commonly found in organic molecules find
               P      77     63                                 themselves in molecular structures are listed in Table II.
               S      83     65                  128            Analogous bonding situations are found throughout each
               Cl    103     79    48      50                   column of the periodic table, except that atoms of second-
               Br     88     67            53                   row elements resist hypervalency.
               I      71     57            57                     The hydrogen atom does not suffer from steric con-
              N N     38    N N    100    N N    226            straints in its ordinary univalent state, in which it makes
              O O     33    N O    145                          only one bond. It can enter into a special kind of weak hy-
              S S     54    O O     96                          pervalent interaction known as the hydrogen bond, which
                                                                attaches it to a lone-pair-carrying second atom. The hy-
                a
                 In kilocalories per mole; 1 kcal = 4.184 kJ.
                                                                drogen bond is indicated by a dotted line. As usual for
                                                                hypervalent interactions, hydrogen bonding is particularly
                                                                important if the neighbors of the hydrogen atom are highly
              atom in 4; the electronegativity of an element increases as
                                                                electronegative.
              one moves up and to the right in the periodic table).
                Those molecules that contain an odd number of elec-
              trons cannot satisfy the rules for all of their atoms and are  B. Molecular Geometries
              known as free radicals (e.g., 2).
                                                                Classical structural formulas imply molecular geometries.
                In addition to atomic symbols and symbols for bonds,
                                                                These are determined by bond lengths, valence angles, and
              lone pairs, and unpaired electrons, the classical struc-
                                                                dihedral angles and describe the average nuclear positions
              tural formulas of organic chemistry also indicate atomic
                                                                when the molecule is at equilibrium.
              charges (e.g., 3–5):
                                                                  In real molecules, at least some vibrational and inter-
                                 CH 3          H  H             nal rotational motion is always present. In many organic
                      CH 3  H 3 C                       O
              CH 3  C            Sn    CH 3  H  N     C  C      molecules, this can be neglected in the first approxima-
                            H 3 C                               tion, and the molecules can be considered rigid. Some,
                      CH 3                     H  H      O
                                 CH 3                           particularly those lacking rings and multiple bonds, are
                    3            4              5               definitely floppy at room temperature due to nearly free
                                                                rotation around single bonds but can be viewed as rigid at
              The way to determine the charge on an atom is to count  sufficiently low temperatures.
              the valence-electron ownership of an atom in the molecule
              and compare it with the number of valence electrons on a  1. Bond Lengths
              neutral isolated atom of the same element. If the two agree,
              the formal charge is zero. If there is one more electron on  Bond lengths are generally determined by the nature of
              the atom in the molecule than on an isolated atom, the  the two atoms bonded, with minor variations depending
              formal charge is minus one and so on.             on the environment. Each kind of atom can be associated
                In order to determine the valence-electron ownership of  with the value of its “covalent radius.” A bond length is
              an atom in a molecular structure, one counts all electrons  approximately equal to the sum of the covalent radii of the
              indicated as lone pairs as well as unpaired electrons on the  participating atoms. Typical lengths of the most common
              atom, plus one for each bond in which the atom partici-  bonds in organic molecules are listed in Table III.
              pates. Thus, one assumes that the two electrons of a bond
              are shared equally between the two atoms that it joins. To
                                                                  2. Valence Angles
              indicate that this is unrealistic when the two atoms differ
              in their electronegativity, the charges are referred to as for-  Valence angles are the angles between two bonds on the
              mal. For molecules containing transition metal elements,  same atom, generally dictated by the coordination number
              the individual formal charges are frequently not indicated  of the atom. However, if lone pairs are present on an atom,
              at all.                                           each of these counts for yet another neighbor. On the other
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