Contact Distances

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Covalent bond distances and angles tell us how the atomic nuclei are arranged in space but they do not tell us anything about the outside surfaces of molecules. The distance from the center of an atom to the point at which it contacts an adjacent atom in a packed structure such as a crystal is known as the vander Waals radius. The ways in which biological molecules fit together are determined largely by the van der Waals contact radii. In every case they are approximately equal to the covalent radius plus 0.08 nm. Van der Waals radii are not as constant as covalent radii because atoms can be“squeezed” a little, but only enough to decrease
the contact radii by 0.005–0.01 nm. The radii of spacefilling molecular models are usually made a little smaller than the actual scaled van der Waals radii to permit easier assembly.

Packing of molecules of suberic acid HOOC–(CH2) 6 –COOH in a crystal lattice as determined by neutron diffraction. 2 Notice the pairs of hydrogen bonds that join the carboxyl groups at the ends of the molecules and also the close contact of hydrogen atoms between the chains. Only the positions of the hydrogen nuclei were determined; the van der Waals radii have been drawn around them. However, the radii were originally determined from X-ray and neutron diffraction data obtained from many different crystalline compounds.

Bond Lengths

Chemists describe bond lengths as the distances between the nuclei of bonded atoms. The C–C single bond has a length of 0.154 nm (1.54 Å). The C–O bond is ∼0.01 nm shorter (0.143 nm), and the typical C–H bond has a length of ∼0.109 nm. The C–N bond distance is halfway between that for C–C and C–O (0.149 nm). Other lengths, such as that of O–H, can be stimated from the covalent radii given.
The length of a double bond between any two atoms (e.g., C=C) is almost exactly 0.020 nm less than that for a single bond between the same atoms. If there is resonance, hence only partial double bond character, the shortening is less. For example, the length of the C–C bond in benzene is 0.140 nm; the C–O distances in the carboxylate anion are 0.126 nm.
Using simple geometry, it is easy to calculate overall lengths of molecules; here are two distances worth remembering:
In the preceding simplified structural formula for benzene the six hydrogen atoms have been omitted. Resonance between the two possible arrangements of the three double bonds1 is indicated by the circle. Chemical shorthand of the following type is used throughout the book. Carbon atoms may be represented by an angle or the end of a line, but other atoms will always be shown.

Bond Angles

Because of the tetrahedral arrangement of the four bonds around single-bonded carbon atoms and most phosphorus atoms, all six of the bond angles about the central atom have nearly the same tetrahedral angle of 109.5°.


Bond angles within chains of carbon atoms in organic compounds vary only slightly from this, and even atoms that are attached to fewer than four groups usually have similar angles; for example, the H–O–H angle in a water molecule is 105°, and the H–N–H angles of ammonia are 107°. In ethers the C–O–C angle is 111°. However, bond angles of only 101° are present in H2O2 and of 92° in H2S and PH3.
The presence of double bonds leads to planarity and to compounds with bond angles of 120°, the internal angle in a hexagon. The planar geometry imposed upon an atom by a double bond is often transmitted to an adjacent nitrogen or oxygen atom as a result of
resonance. For example, the amide groups that form the peptide linkage in proteins are nearly planar and the angles all fall within four degrees of 120°.

Structural Principles for Small Molecules

Stable organic molecules are held together by covalent bonds which are usually very strong. The standard Gibbs energies of formation (∆Gf °) † of many covalent single bonds are of the order of –400 kJ/mol (96 kcal/mol). The bonds have definite directions, which are measured by bond angles and definite bond lengths.

Amino Acids, Peptides, and Proteins.

Thousands of different proteins make up a very large fraction of the “machinery” of a cell. Protein molecules catalyze chemical reactions, carry smaller molecules through membranes, sense the presence of hormones, and cause muscle fibers to move. Proteins serve as structural materials within cells and between cells. Proteins of blood transport oxygen to the tissues, carry hormones between cells, attack invading bacteria, and serve in many other ways. No matter what biological process we consider, we find that a group of
special proteins is required. The amino acid units that make up a protein molecule are joined together in a precise sequence when the protein is made on a ribosome. The chain is then folded, often into a very compact form. Sometimes the chain is then cut in specific places. Pieces may be discarded and parts may be added. A metal ion, a coenzyme derived from a vitamin, or even a single methyl group may be attached to form the biologically active protein. The final product is a complex and sophisticated machine, often with moving parts, that is exquisitely designed for its particular role.
The biological functioning of a protein is determined both by the properties of the chemical groups in the amino acids that are joined to form the protein chain and by the way the chain is folded. The ways in which the different parts of the protein interact with each other
and with other molecules are equally important. These interactions play a major role in determining the folding pattern and also provide much of the basis for the biological functioning of proteins. Similar considerations apply also to carbohydrates, nucleic acids, and other biopolymers. For these reasons it is appropriate to review some fundamentals of molecular structure and geometry.