Ghosh, Pradip N

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Jndimi J. Phys. 51B, 279-282 (1977)Potential function of (X-H..X) hydrogen bondsP r a d ip  N . G h o s hDeparVment o f  Physics, University CoUene o f  Science. 92, Acharya Prafulla du m du i Road, ( alcutla-lQQ 0()9T h e one dimensional potemial model for hydrogen bonding has been used to calculate the dilferent crystal structure and spec- troscc^iO parameters associated with X -H  . . X  type H-Bonds in crystalline hydrogen halides and ice. It is found that the model potential cannot predict the intermolccular force and the hydrogen bond energy accurately. We suggest that the X - X  electrostatic part o f this potential should be modified to take account o f the different hieher (nder terms.I. I n iro im k tio nThe presently held view of the nature of hydrogen bonding is that it consists of four interactions. T hese are :( 1 ) eledtrostatic interactions, ( 2 ) nembemded interactions including the attrac­tive dispersion forces, f3 )  the shor* range repulsive forces and (4 )  thecovalent charge transfer contributions. But there .seems to be no unanimity in literature regarding the nature o f hydrogen bonding. A faithful model potential function for hydrogen bonding X - - H  . . Y  should reproducethe observed quantities like the X -H  frequency shift, the intermolccular force for X — . . Y — ^stretching, the hyd re^ n  bond energy etc.A  model potential function given by l.ippincotl and Schroedcr (195/5) (hereafter refered to L S )  for O — H —O  bonding and later extended to N— H  . . O , O — H . . N, N —H  . . Cl, N— H . . N bonds is found to describe these observed features quite accurately (Schroedcr and Lippincott 1957). Thispotential function has been very widely used for a number of hydrogenbonds (R eid  1959, K ing and Nixon 1968). M ost of these calculations api^y to organic systems, and very little attention has been paid to the intermole- cular hydrogen bonding in hydrogen halide crystals. T h e Ram an and infratied spectroscopy. X -ray  and neutron diffraction experiment, dielectric constant measurements etc. provide enormous data for check of the applicability of a  model potential to these X — H  . . X  (X -h a lo g e n )  hydrogen bonds. In addition, it is to  be noted that these small molecules H X  possess large values o f dipole and quadrupole moments, plarizaWlities etc. In the present note.280 P ra d ip  N . G h o shwe use the one dimensional model potential to see if it can satisfacjtorily reproduce the observed properties of X — H . . X  bonds. In Section 2 we introduce the LS potential function, define the paramaters and calculate the different quanititics characterising the H bonds. In section 3 we discuss the failure of LS potential to reproduce all tl-.e features simultaneously and suggest some modifications which can improve the model potential for these strongly polar molecules.2. T h F L ll 'P IN fO 'n -S (  IlKOlDf R PoltlNTIAt.The one dimensional potential dehned by Lippincott and Schroeder for X — H . . X  hydrogen bonds isV (r ,R ) =r V ,(r )  H V ,(R ,r )  -f V ,(R )  -I V ,(R )f n(r -- r,,)- 1 — exp  —2rV ,.(R ,r) n„* exp- n * ( R - r - r „ ) -  |2 ( R - r )  ’V : , ( R )  -  A c and V , ( R )  B/R}]( 1)r and R  codrespond to the distances X —H and X  .. X  respectively, n =: Kpr<yDo where Ko, fo and Do arc respectively the force constant, intcmuclear disitance and dissociation energy of the unperturbed X — bond, Do* iss the dissociation energy' of the unperturbed H bond, for which the force constant and inlemuclear distance arc assumed to remain the same as in unperturbed X — bond, hence nD “  n*Do*. Thus the first term represents a slightly stretched typiad covalent bond X —H and the second term corresponds to the highly stretched tx>nd H— The third term represents the Van der Waals repulskm be t^ween the halogen altoms and the last tenn is the elec­trostatic potential between the two halogen altoms.We use the potential function defined by cq. (1) for the calculation of X -H  distance, X — H frequency, X — H , . X  stretching fottte constant and hydrogen bond energy for the intermolecular hydrogen in H F polymer, crys­talline HF, HCl HBr and ice. TTie parameters Ko, ro and Do are obtained from standard works (Table— 1), tniese paramdters define the amstant n. The constant n* is chosen to give the best value of the X — frequency shift, this constant in turn determines D o *; the constant A has been evaluated from the equilibrium condition (dV/dR) =  0. For the constant b  we use the value 4.8 as suggested by LS. Thus the potential is ccMnpletely defined. TTie calculated parameters are given in Table 2.Potential function of {X‘H.  , X)  hydrogen bonds 2 8 1T ab le  1. Assumed parameters o f L S  potenitialF-H—F Cl-H---- Cl Br-H— Br O-H—-OKo (mdyn/A) r« (A )Do (eV )n* (A -n  (d) b (A-M (cm-*)9.66(»)0.917(b)6.40(b)14.3i54.8(041 40 (04.81(b)1.275(b)4.43(b)12.874.8(02889(b)3.84(b)l.413<b)3.7S<b)13 914 « ( 07.76(0 0 97(0 5A2ic)13.324 .8 ( 03700(c)(a) Coulson 1953.(b) Herzberg 1935.(c) Lippincott and wSchroedcr (1955)(d) Adjusted values.3. D i s c  u s s i o n  a n d  I ^ o p o s e o  M o d i f k  a t i o n  o f  LS P o t f m i a lThe good agreenieat with the observed values for both X — frequency and X — H distance shows that the properties of internal X — H bond are described wdl by the L S  function. But in case of miermolecular X  . . X  bonds the agreement is good only for the X  . . X  stretching forde constant Kx. A lth ou ^  the experimental values of hydrogen bond energies are not available for all the cases considered, yet it is found that in the two cases of H F polymer and ice, for which these values are available, the agreement is not at all good. A leadjuslment of the value (^ f the constant b can be done to improve the agreement of hydrogen bond energy, but this will be associated with a decrease in the agreement of the force constant Kx-This failure of the L S  function to reproduce both me energy and the force ocHisitant of the hydrogen bond may be inherent in the choice of X  electrostatic term in the L S  function. The choice of type term isexplained by L S as arising due to fractional charges on the two X  atoms. This may be true, but, as has been aigued by Reid (1959), R “® type dispersion term should also be importanit.2 8 20>e2Soi ’gT3 ^o ^1 1 ':§ 100 § 5p g X 83SI•52 ^XXSil iretf o<o8COUP r a d ip  N ;. G h o s h5-r-VOrir^ t 3; ©©Tf *r>31 TT s© or-rf'.©v> sO © ©'a*i O© © ©+1 +1 +13 s:©»/*<ri*o'VTis;©r~ OOr^ l «oSvn *—00Ow-iOOoo'o+1^ I Irvl M£r<C'l©Olxe« €>% -o*o»3 ' -S1 1 1 C/5S §haOQ»Potential junction o f  (X-H ■ ■ X)  hydrogen bonds 283We feel that since the X-H donor group in a hydrogen bond X-H . .  X  is very strongly polar (i.e. have permanent nwlecular moments), tlicir moments will interact with the charge of the acceptor atom X. This would mean that one shctild consider the higher order terms in an expansion of the Coulombic interartion. Thus the electrostatic part of the potential, Vi, shpuld be modified to incorporate the terms depending on h i^ c  inverse powers of R. This may be taken asV, (R )[I- 1  m = lWhere p is the maximum value of m i.c. the maximum number of terms one can retain in the series. Calculations with this and other modified forms of LS function arc being done by us and will be reported elsewhere.The author thanks the Computer Centre, Calcutta bniversJty for providing computation facilities. The author thanks Professor P. C. Bhattadiarya for his encouragement and Professor D. L. Bhattacherya for helpful comments.RF.FKRtNCFSCoulam C. A. 1952, Valemr, (Oxford)Grahn R 19.59 Arkiv Fysik 15, 257.Herzberg G, 1935 Spectra of diaiomic molecules (D Van Noslrond). Suzuki M. & Yokojama T. 1%9. J, Chem. Phys. 50, 2949.Jolinson M. W., Sandor E  and Arzi E  1975 Acta Crysl B31, 199S.King C. M. and Nixon E. R. 19&8, Chcin. Phy’i 48, 168S.Kittelberger J. S. and Homig D. F. 1967, J. Chem. rhys. 47, 3099. Lippincott E. R. and Schroeder R. 1955, J. Chem. Phys. 23, 1099, Pauling L. 1960, The nature of the chemical bond, [Cornell Univ.). Reid C. 1959, J. Can. Phys. 30, 182.Sandor E  and Farrow R. F. C. 1967, Nature 213, 171.Sandor E  and Johnson M. W., 1968, Nature, 217, 541.Savoie R. and Anderson A. 1966, /. Chem. Phys. 44, 548.

Potential Function of (X-H..X) Hydrogen Bonds

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Potential Function of (X-H..X) Hydrogen Bonds

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