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.
.Infrar ed abso rp t ion spectra of a n h ydr ou s, crystalline, ino rgani c borates were obtained lLl ~h e .2000 cm-I to 300 cm-I ra n ge. Compounds wit h B'O a nd B " isoto pes we re prepa red to ass Ist lI1 terpr etatlOn . Spectra l bands for all or t hobo rates and py roborates a nd som e meLaborates could be assign ed sat isfacto rily . Borates wit h complex rin g-ty p e an ion s gener a lly e~'(hlbl te d spectra of su ch co mplex ity t hat on ly s u perfi cial in terp retatio n WItS attempLed. }< rom correlatlOlI s between s pectra a nd stru cture It a ppears t hat boro n in 3-fold or in 4-fold coordin at ion can be iden t ifi ed wi t h r easo nable ass uran ce on t he bas is of t he infrared s pectrum alon e. Absorp t ion bands ar c ta,bulated for about 80 bo rates a lld typ ical sp ectra a rc s hown .
Potential Function Model of Hydrogen Bonds 921 pear as if two endothermic peaks are occurring.This explanation is consistent with the observation that the small peak occurred in the pattern of CuS04-5H20 in Fig. 1 only when the doublet appeared, that is, only when liquid formed in the sample and only at high rates of temperature rise.18 Since the sample wells in this work are very small, thermal gradients are reduced to a minimum. In order to establish an appreciable gradient high heat-(13) Taylor and Klug* observed several small peaks prior to dehydration which they attributed to second-order transitions in CuSOrSHjO. These were observed at sensitivities much higher than those used in the present work and are apparently not the same as the anomalous peak described above.ing rates are necessary.The results of this investigation emphasize precautions which are necessary in the interpretations of some differential thermal analysis measurements.
Infra red absorpt ion spectra of in orga ni c ni trates an d carbon ates have bee n obtained on s in~le cr ystals at. room te r,nperaL ure, under liquid n! troge n refri ge ratio n a nd unde r liquid heltum ref rIgeratIOn. DIffuse a bsorptIOn observed 111 t he room te mperature spectra between a bout 1400 cm-[ a nd 700 cm-[ is resolved under liquid helium refrigeration into a large number of ba nds not att ribu table to fundamentals or co mbinat ions of fundamental frequenci es of t he a nions. Almost all of t hese bands arc read ily in terpreted as summation bands of fundamental freque nci es wi t h successive levels of a libmLing oscillato r. The li b ration is cons ide red to represe nt a pla na r torsio nal oscill aL ion of Lhe anion abo u L the Lr igo na l axis. The libraLional freq ue ncy depends in pa rt on Lhe crystal structur(' a nd on the ions. In a give n maLe ri a l t he lib mtional frequency as dete rm ined fro m successive bands is reaso mlbl y co nsLa nL. In t he substances studied the libraL iona l frequency va ri ed from ~"\bout 15 em-[ to 30 cm-[. Band limi Ls observ('d ill t he specLra are i nterpreted as rep" es(' nting rotaL ional e nergy ba rri ers. These bar rier heig hts a re approx imate ly 200 cm-J w iLh so me depe ndence on the crysta l st ru ctu1"C an d t lte ions in volved. Barri('" heighLs calcu laLed from a cosin e potential funct ion agree reasonably well with the obse rve d ba rri e rs for the cubic and caleiLe st ru cL ures. Similar calculaLio ns have not been made for other st ructures stu d ied beca use of doubtful assign me nLs or unk no wn structural details. In parLicular, spectra of the aragon iLe stru ctu res a re re ma rk a ble in d etail a nd complexity, and have not bee n analyzed. H owever, the details of t hese and a ll ot her spectra studied appear to involve simila r phenomena.
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