A one-dimensional model for hydrogen bonding is proposed based on the potential function V = D[1—exp(—nΔr2/2r)]. The energy associated with both the weak and strong bonds of the configuration RO – H – – – OR2 is obtained through application of this function. A repulsive Van der Waals potential and an attractive electrostatic potential are also assumed to exist between the two electronegative atoms of the hydrogen bond. Through application of the conditions describing a stable equilibrium, relations are obtained which permit a calculation of OH frequency shifts, OH bonded distances, hydrogen bond energies and ko — — — o force constants, all as a function of the O – – – O distance R. The calculated quantities agree well with those obtained from neutron diffraction, infrared, and other experimental studies. Because of the assumptions involved, this model is best used to describe the properties of hydrogen bonds in crystals. The model is also capable of extention to describe the properties of other types of hydrogen bonds such as HFH, NHN, NHO, OHN, etc.
The infrared sp ectra of coesite, low-temperature tridymite, low-temperature cristobalitelow-~emperature quartz, vitreous silica, hexagonal Oe02, tetragonal Ge02, and vitreous germallla are reported from ~,OO O to 300 C~-l. Wherever possible an assignment of frequencies has been made on t he basls of the selectlOn rules for the crystal symmetry. Three characteris.tic gro up frequencies. near 1,lOq, 800, and 480 cm-1 are common to all the polymorphs of Sl02. Thes.e frequ~nCle.s respectlvely correspond to a str~tching mode i nvolving displacements assoclated prnnanly wlth the oxygen atoms, a stretclung mode involving displacements associated primarily . wi~h the. sil~co~ atoms, and a Si-O bending mode. The presence of these gro up frequencles III coeslte mdlcates that t he coordination of silicon in coesite is tetrahedral and that its high density is associated with the packinrr of tetrahedral units at an angle approximatiI?g 120 degrees.. The tetragonal and hexagon~l GC02 polymorphs show a marked dlfference III spectra due III part to the change from sixfold to fourfold coordination. The assignment of obscrved frequencies in hexagonal Ge02 is consistent with that made for low-temperature quartz if allowance is made for the heavier mass of t he Ge atom.
Infrared absorption spectra have been obtained on the alk ali nitrates, the divalent m etal carbonates, a nd t he rare eart h borates which assume t he aragoni te, calcitc, or vaterite cr ystal struct ures. It was observed t hat simi lar str uct ures gi ve rise to analogo us spectra except for t he carbonate and borates having the vaterite str uct ure. The marked differences o~scr~e d in t hese latter spectra. a re disc ussed. Frequency s hifts produ ced by cation s ubs t ltutlOn are ascnbed to repulslOn between closed electro n shells of oxyge n atoms . It is concluded t h at t his repulsive force determines the s tru cture type in the rare earth b~rates .
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