20 ' LINUS PAULING [1 



(A^-acetylglycine,2^ A'^jA'^'-diglycyl-L-cysteine dihydrate,^^ glycyl-L-tryptophan 

 hydrate^^), and even some in which the N — H--0 hydrogen bond involving 

 the NH and O of the peptide groups is not formed, as for one of the peptide 

 oxygens in glycyl-L-asparagine.^* It should not be surprising that the mole- 

 cules of a simple substance, in seeking the way of arranging themselves in 

 a crystal that minimizes the free energy of the crystal, should occasionally 

 have to sacrifice the most favorable circumstances for hydrogen-bond forma- 

 tion in order to satisfy some other structural features leading to stabiUty. 



In many of these substances the N — H---0 hydrogen bonds that are 

 formed by oxygen atoms other than those in peptide groups involve angles 

 of about 120°, with the atoms adjacent to the oxygen atom coplanar. Further 

 examples of this sort are the carboxyl oxygens in the amino acids glycine,^^ 

 alanine,^^ Lg-threonine,^' and DL-serine.^^ 



A simple theoretical consideration can be made that supports the pro- 

 posed principle that under ordinary circumstances an oxygen atom attached 

 to a carbon atom by a double bond tends to form hydrogen bonds that lie 

 in the plane formed by the carbonyl group and adjacent atoms, with the 

 angle at the oxygen atom equal approximately to 120°, whereas in hydrogen 

 bonds formed by a peptide group the angle tends to be a straight angle. Let 

 us consider the electrons of the oxygen atom in a carbonyl group. There 

 are two electrons involved in the double bond (shared with two electrons 

 of the carbon atom), and two electron pairs occupy the remaining two 

 Orbitals of the neon shell of the oxygen atom. We may discuss the deviation 

 of the electronic structure from spherical symmetry by considering only the 

 distribution of one electron in each of the two orbitals for unshared pairs 

 inasmuch as there is, as a first approximation, spherical symmetry when 

 one electron is placed in each of the four orbitals of the neon shell. Also, 

 as a first approximation, we may treat the orbitals as tetrahedral sp^ or- 

 bitals. The treatment of the double bond as involving two bent tetrahedral 

 bonds is mathematically equivalent to its treatment as a sigma bond and 

 a pi bond. 



When the orbitals for the shared pairs are taken as ^s-\ — j^Pz+^Px and 



2 V2 ^ 



~s — 7=Pz-^^Px (the bond direction being the x axis), it is found that the 



2 V2 2 



electron distribution for one electron in each of these orbitals, with arbitrary 

 normalization, is given by the expression 



p(,rz) = l + 6 sin2 Öcos2 <^+3 cos^ ö+2\/3 cos 6 (1) 



When this is differentiated with respect to the angle 6 and the angle (f>, it 

 is found that there are two maxima in the density, both lying in the plane 

 determined by the atoms around the carbon atom and at the angle 125° 16' 

 with the C — O axis. 

 In discussing the distribution of the electrons around the oxygen atom 



