Gupta, N P

Sinha, Aruna Kumari

IACS Institutional Repository

Indian J. Phys. 73A (2). 249-252 (1999) LU P  Aan internatJODal jounialLattice energy of some organic m olecular crystalsN P Gupta and Aruna Kumari SinhaDepartment of Physics, Ranchi University, Ranchi-834 008*Bihar, IncbaReceived 12 December 1997, accepted 26 June 1998Abstract ; Latuce energies of the crystals of biphenyl and pyracene have been calculated using MKB and William sets of 6-exponential non-bonded pioteniial parameters. The comparison oi the calculated values of lattice energy with tlie corresponding values of heat of sublimation shows Uiat MKB set is more suitable than the William set of parameters. The proposed potential parameters tiir urea take care of hydrogen bond energy in the form of van der Waals interaction energy and give accurate values of lattice energy, lattice parameter and conformation energy.Keywords ; Non-bonded interatonuc potential, latuce energy, organic molecular crystalsPACSNos. ; 63.lO.+a, 34.20.CfThe structure and properties o f Organic M olecular Crystals can be calculated using •suiuiblc non-bonded interaction potential parameters. The interaction potential between two non-bonded atoms separated by distance r is given by the equation0  = -A r* ' + Be~^,where A, B and a  are potential parameters. The lattice energy is the sum of the interaction potential energies o f all atoms o f the reference molecule with ail atoms o f the surrounding molecules. The space group symmetry operation is perform ed on the reference molecule to generate the surrounding m olecules. The sum m ation is continued till the lattice energy attains a  constant value. The straight forward method o f selecting suitable parameters is to calculate lattice energy and com pare it with the experim ental value of heat of sublimation. M irskaya, K ozlova and B ereznitskaya [1] abbrev iated  as MKB obtained potential param eters for C  • • C, C  • ■ • H and H • -H interactions using the structure and heat o f  sublim ation data and latest elasticity data o f  the crystals o f benzene, naphthalene and anthracene all extrapolated to ab.solute zero where the effects o f m olecular and lattice® 1999 lACS250 N P Gupta and Aruna Kumari Sinhavibrations are minimised and the crystal properties are mainly determined by the interaction potential energy. M irasky f2] used these parameters to calculate lattice parameter, lattice energy o f the crystals o f m ethane, 2,2-paracyclophane and 3,3-paracyclophane. The calculated values agreed satisfactorily with the experim ental values. He also studied successfully the solid phase transition peculiarity o f adam antane crystals. W illiam  (3] obtained these parameters using the structure data of 18 hydrtKarbon crystals half o f them arom atic and half saturated hydrocarbons and the heat o f sublim ation of benzene and naphthalene reduced to absolute zero. The steepness o f the corresponding curves is the stune but the coordinates of minima differ slightly. Trotter [4] reported that the crystals of biphenyl are monoclinic of space group P2|/a. There are two m olecules per unit cell o f dimension a = 8.12 A, b = 5.64 A, c = 9.47 A and p  = 95.4®. Simmons and Lingafelter [5] show ed that pyracene crystals are m onoclinic of space group P2j//i containing two molecules per unit cell of dimensions a = 12.56 k ,b  = 5.64 A, c = 7.32 A and j3= 95°14 '. Nauilie el al [6] found that urea crystals arc tetragonal o f space group P 4 2 1 , m. There are two molecules in the unit cell o f dimensions a = 5.662 A and c = 4.71 A. The molecules are planar and linked to each other through N —  H O bonds in the crystal structure. The calculation of lattice energy o f urea is interesting because the crystal is of chem ical importance and lattice energy consists of van der W aals interaction energy and hydrogen bond energy. In urea, there are N N, O O, O N. C' O, C N, O H, N H in terac tions in addition  to C ■ C, C H a n d H  H in terac tions. Theparam eters o f  Dashevsky [7] for N N and O O interactions were com bined with MKB set o f  parameters for C C and H H interactions to deduce parameters for the above interactions according to the formulaA\2 —(A i i <422) B\2 — ^ 2 2 ) ^' ttnd cx\2 = l/2{oc\ \ + (2^ 2 2 )W hen tliese param eters were used to calculate the lattice eneigy ol urea, low value was obtained because they were not taking care of hydrogen bond energy As tlie depth of the interaction potential is responsible for the lattice energy, it becam e essential to increase the A values o f all interactions. A ccording to Pauling and W ilson [8], the van der W aals interaction energy between two atoms 1 and 2 separated by distance r is given by the equationW =  - 6 ( r t | / i 2 Z f  + / 2 ) .Therefore A = (en , rij Z f  Z ^ e * ) / ( / ,  + 12 ),where /i] and h2 are effective number o f electrons, /] and I2 are the first ionisation energies. e the charge o f an electron, , Z |  are the average o f the square of the coordinates o f the electrmis in the field direction relative to the nuclues. Thus, A is prqKwtional to the product o f the effective numba* of electrons. In H ■ • H interaction, this product is unity. Therefore, A for H ' -H interaction becomes constant o f proportionality. In MKB set, it is 29 whereas it is 40.2 in W illiam set. The average of these two is 35 which has been taken as A value for H ■ - H . As the effective num ber o f electrons in carbon, nitrogen and oxygen atoms are 4, 5Lattice energy of some organic molecular crystals 251and 6, the A  values for C • • -C, N  • • • N  and O  • • 0  interactions become 560, 875 and 1260 respectively. The D ashevsky’s values o f B and a  for N  • • • N  —  O • -O interactions were so adjusted that the interaction energy attains minimum value at observed crystallographic distances. The potential param eters obtained according to ^ o v e  com bination rules are given in Table 1.Table 1. Potential parameters.Atom pair A (K cal A^/mole) B (K cal/mole) a(A"')c c 560 7.16x10^ 3 68c- •H 140 1.86x10'* 3.94H- H 35 0.49 X 10^ 4.29N-- .-If 875 7.62 X 10** 4.060 - •() 1260 9.69 X 10^ 4.090 - ••N 1050 8.59 X 10* 4.09c- O 840 8.33 X 10* 3.69c ■•N 700 7.39 X 10* 3.87o H 210 2.18x10* 4.34H 175 1.93 X 10* 4.18The calculated values o f lattice energy, the heat o f sublim tion and the chem ical fonnula o f the crystals are given in Table 2.Table 2. Chemical formula and lattice parameters.Name of crystalQiemicalformulaU (K cal/mole) Hq (K cal/mole)Biphenyl C i2Hio 19.6 19.5Pyracene C14H12 20.7 20,7Urea CON2H4 20.92 21As the charge d istribu tion  o f the overlapping e lectfon  cloud o f tw o atom s responsible for the repulsive force is represented by the exponential density function, the 6-exponential potential is m ore accurate than the 6 -1 2  potential. The lattice energy is m inim um  at 4.68 A which is close to c = 4.71 A. The non-bonded part o f the conformation energy on the basis o f the proposed parameters is -1 .9  K cal/mole.The lattice energies o f  biphenyl and pyracene obtained on the basis o f W illiam set o f param eters are 16.8 and 17.34 K cal/mole. This shows that the MKB set is more suitable than the W illiam  set o f  parameters.Recently, W endy et al [9] proposed force field for the simulation o f proteins, nuclic acids and organic m olecules. O n the basis o f that force field, the C  ■ C, N  • • N and O — O  contributions to lattice energy o f urea are -0 .283 , -0 .228  and -1 .9 3 4  K cal/m ole252 N P Gupta and Aruna Kuman Sinhawhich are greater than the corresponding values -0.338, -0.797 and -3.281 K cal/mole obtained on the basis of the proposed parameters.AcknowledgmentWc thank Dr. C Prasad and Dr. A A Khan for extending library facility and making fruitfulsuggestions from time to time.References(11 K V Miiskaya, I E Kozlova and V P Berezniiskaya P hys Slot. Sol. (b ) 62 291 (1974)(2) K Mirasky A cta C n s t , A32 199 (1976)[^ 1 1) E Wjlham A cta C m t  A30 71 (1974)14] J Trotter Affa Cryst. 14 1135 (1961)|5| G L Simmons and E C Lingafclier Acfa C n s t  14 872 (1961)|6] Natalie Sklar, Michael E Senko and Ben Post A cta  Cryst. 14 716 (1961)[7] V G Dashevsky and A 1 Kitaigorodsky Theor Exp C h m i 3 43 (1967)|8) I Pauling and E B Wilson Introduction to Q u a n tu m M n h a m e s (New York McGraw Hill) p 388 (1935)[9] D (Virnell Wendy and Poiir Cleplak Ginstopher, 1 Bayly, Ian R Couuld Kenneth, M Merz (Jr) M David Perguson, David C Spdlmeyer lliomas Fox, Jame^ j WCaldwell and Peter Kollman J  Am, Chem. Soc. 117 5179(1995)

Lattice Energy of Some Organic Molecular Crystals

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Lattice Energy of Some Organic Molecular Crystals

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