Development of new cross intermolecular pair potential ab initio and prediction of cross second virial coefficients for dimer h2o-Ch4

Journal of Chemistry, Vol. 47 (6), P. 786 - 790, 2009 DEVELOPMENT OF NEW CROSS INTERMOLECULAR PAIR POTENTIAL AB INITIO AND PREDICTION OF CROSS SECOND VIRIAL COEFFICIENTS FOR DIMER H2O-CH4 Received 2 May 2008 PHAM VAN TAT Department of Chemistry, University of Dalat Abstract The site-site intermolecular pair potential of dimer H2O-CH4 was constructed from the ab initio calculations at high level of theory CCSD(T) with basis set cc-pVTZ. The cross second virial coefficients of this system were calculated accurately using this ab initio pair potential. These results were compared with experimental data and those from literatures. The discrepancies between them are insignificant. Keywords: cross intermolecular pair potential, cross second virial, ab initio potential. I - INTRODUCTION The thermodynamic data needed for designing processes of gaseous fuels in several industrial applications. The methods for predicting the physical properties of the natural gas mixtures are need that can be used with the great significance for a wide range of temperatures, pressures and compositions. The empirical methods are also useful for correlation of quantities of data on specific components. But these were not generated the properties of new components accurately. In recent years computer simulations have become indispensable tools for studying fluids and fluid mixtures. One of the first attempts Nasrabad and Deiters predicted phase high-pressure vapor- liquid phase equilibria of noble-gas mixtures [1,2] from the global Monte Carlo simulations using the intermolecular potential ab initio. These simulations are to predict the thermodynamic properties of microscopic systems using the intermolecular potentials, and we can be understood macroscopic behaviours [3]. The reliability of these depends only on the accuracy of intermolecular potentials. In this work we report the development of an accurate cross potential ab initio between molecules water and methane using the high level of theory CCSD(T) with the Dunning’s contracted basis set cc-pVTZ. The cross second virial coefficients of dimer H2O-CH4 are predicted using this cross intermolecular potential. The cross second virial results are compared with the experimental data and those from literatures. II - COMPUTATIONAL DETAILS 1. Potential energy surface Six orientations for dimer H2O-CH4 were chosen with the fixed molecule methane at the origin. One atom H of methane is on the X axis and another H is in the plane XY. The intermolecular pair potential is a function of distance r (between the center of gravity of two molecules) and the angular coordinates α, β and φ, as are explained in Fig. 1. Intermolecular 786 energies were calculated for all values of r from 6 to 15 Å with increment 0.5 Å; the angles α and β for molecular plane H2O was varied from 0 to 180o with increment 30o along Y and Z axis. Figure 1: Dimer orientation for ab initio calculation 2. Ab initio calculations The CCSD(T) method appears to account for the most significant electron correlation effects. The Dunning’s contracted correlation-consistent basis set cc-pVTZ (for hydrogen: 5s,2p,1d/3s,2p,1d; for oxygen: 10s,5p,2d,1f/4s,3p,2d,1f; carbon: 10s,5p,2d,1f/4s,3p,2d,1f) were used in this work [4, 5]. The ab initio energies were corrected for BSSE with the counterpoise correction method proposed by Boys and Bernardi [6]: C O α β φ ΔEint = EAB - (EAb + EaB) (1) where EAB denotes the total electronic energy of a dimer AB, EAb the energy of a dimer consisting of an A atom and a B ghost atom (an atom without nucleus and electrons, but having its orbitals), and EaB vice versa. Ab initio calculations were carried out with the Gaussian03 program package [7]. The potential energy surfaces for six orientations resulting from ab initio interaction energies are depicted in Fig. 2. 6 9 12 15 -600 0 600 1200 E H / μ H r/Å B C D E F G C O O C C CC O C O O O A B CD E F Figure 2: Potential energy surface of six special orientations for ab initio calculations The geometry parameters of monomers methane and water obtained by quantum calculations ab initio at the level of theory CCSD(T)/ cc-pVTZ, as given in table 1. Table 1: Optimization geometry of monomers methane and water methane water No parameter ab initio Exp.[15] parameter ab initio Exp.[15] 1 angle H-C-H 109.49 109.5 angle H-O-H 104.62 104.0 2 bond length H-C 1.091 Ǻ 1.10 Ǻ bond length H-O 0.946 Ǻ 0.95 Ǻ 3 charge on C -0.144 charge on O -0.292 4 charge on H 0.036 charge on H 0.146 787 3. Potential function The new cross intermolecular potential function for dimer H2O-CH4 was developed in this work by incorporating the interaction contribution from the terms of the site-site potentials in publications [3, 8], as shown in Eq. 2. The adjustable parameters of this potential function can be estimated by nonlinear least-square fitting to the 800 ab initio interaction energy values. 1 2 0 ( ) ( ) ( ) 4 ij ij A r i jn ij ij ij ijn ij ijij ij q qCu r D e f r f r B r r α α α πε −= + +∑ ∑ ∑ (2) With and . 2( 2) 15 1( ) (1 )ij ij r ijf r e δ− − −= + ijijrij erf β−−= 1)(2 The fit has to be carried out by means of the Genetic algorithm (GA) and the Levenberg- Marquardt algorithm [9]. The values of root mean-square deviations (rms) of 0.1325 and multiple correlation (R2) of 0.9987 are appeared here to be important for assessing the fitting quality. This fit turns out to be very satisfactory. 4. Cross second virial coefficients The fitted cross potential Eq. 2 was used to calculate the cross second virial coefficients B2(T) for dimer H2O-CH4. These virial coefficients B2(T) were also corrected quantum effects using the formula proposed by Pack [10] and Wang [11] for this cross potential: 2 0 1 2 12 1 2 1( ) 1 exp( ( ) / ) 1 ( ) 12( )2 ( ) A B B N 2B T u r k T H u rk Tu r d d ⎧ ⎫⎡ ⎤⎪ ⎪= − − +⎨ ⎬⎢ ⎥Ω Ω ⎪ ⎪⎣ ⎦⎩ ⎭∫ ∫ ∫ ∫∫∫ dr dr d dΩ Ω (3) Here NA is Avogradro’s constant, kB Boltzmann’s constant, T the temperature, and u(r, α, β, φ) the pair potential; H B 0 is the translation-rotation Hamiltonian for a pair of molecules. This expression can be broken down into a classical term and first-order quantum corrections (radial part, angular part proportional to I (moment of inertia), angular part proportional to μ (reduced mass)): -1 -1 0 1 1 1 2 cl a a( ) ( ) ( ) ( ) ( )r IB T B T B T B T B Tm= + + + (4) Where 0cl ( )B T the classical second virial coefficient is given by 2 0 2 cl 0 0 0 0 ( ) d sin d sin d exp 1 d 4 A B N uB T r k T π π π φ β β α α ∞ ⎛ ⎞⎛ ⎞= − − −⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠∫ ∫ ∫ ∫ r⎟⎟ (5) All these integrals were estimated numerically with a Gaussian quadrature method [12] over the molecular orientation vectors r, α, β and φ. The cross second virial coefficients, BB2(T) including quantum corrections are given in table 2. The cross 2nd virial coefficients B2(T) including quantum corrections at the level of theory CCSD(T) with basis set cc-pVTZ are illustrated in Fig. 3. 788 Table 2: Cross second virial coefficient, B2(T) (cm 3/mol); Beck: calculated by Beck potential [13]; exp.: experimental data [14]; D1-EOS: Deiters equation of state [16] T(K) Eq.2 (this work) Beck [13] D1-EOS[16] Exp.[14] 200.0 -115.292 -116.07 -122.154 240.0 -84.152 -84.232 -81.925 298.2 -56.086 -55.594 -47.757 -63 323.2 -47.378 -46.939 -38.709 -46 348.2 -39.979 -39.708 -31.896 -37 373.2 -33.625 -33.579 -26.771 -30 423.2 -23.373 -23.777 -20.027 498.2 -12.443 -13.168 -14.987 598.2 -3.332 -3.584 -12.465 100 200 300 400 500 600 700 -350 -280 -210 -140 -70 0 B 2(T )/ cm 3 .m ol -1 T (K) Figure 3: Cross second virial coefficients B2(T) of dimer H2O-CH4; : potential Eq. 2 at CCSD(T)/cc-pVTZ (this work); ●: experimental data [14]; ○: ab initio potential proposed by Beck [13]; ∗: D1-EOS Deiters equation of state [16] III - CONCLUSION The cross second virial coefficients of dimer H2O-CH4 obtained from the cross pair potential Eq.2 are very close to experimental data, as described in Fig 3. The discrepancies between them are insignificant. The results are generated almost within the uncertainties of the experimental measurements. The quantum corrections contributed significantly to the virial coefficients at temperatures. The new ab initio cross pair potential of the dimer H2O-CH4 is reliable for predicting the thermodynamic properties. References 1. E. Nasrabad and U. K. Deiters. J. Chem. Phys., 119, 947 - 952 (2003). 2. E. Nasrabad, R. Laghaei, and U. K. Deiters. J. Chem. Phys., 121, 6423 - 6434 (2004). 3. K. Leonhard and U. K. Deiters, Mol. Phys., 100, 2571 - 2585 (2002). 4. D. E. Woon and T. H. Dunning Jr. J. Chem. Phys. 98, 1358 (1993). 5. T.H. Dunning, Jr. J. Chem. Phys. 90, 1007 (1989). 6. S. F. Boys and F. Bernardi. Mol. Phys., 19, 553 - 566 (1970). 7. Gaussian03, Revision B.02. Gaussian Inc., Wallingford, CT, USA (2003). 8. K. T. Tang and J. P. Toennies. J. Chem. Phys., 80, 3726 - 3741 (1984). 9. D. M. Bates and D. G. Watts. Nonlinear Regression and Its Applications. New York: Wiley (1988). 10. R. T. Pack. J. Chem. Phys., 78, 7217 - 7222 (1983). 11. W. F. Wang. J. Quant. Spectrosc. Radiat. Transfer, 76, 23 - 30 (2003). 12. W. Squire. Integration for Engineers and Scientists. Elsevier, New York (1970). 13. D. R. Beck. Development of ab initio molecular potentials for certain alkanes (1992). 789 14. J. H. Dymond and E. B. Smith. Virial Coefficients of Pure Gases and Mixtures. Clarendon Press, Oxford (1980). 15. L. E. Sutton, Table of Interatomic Distances and Configurations in Molecules and Ions. Chemical Society, London, 18 (1965). 16. U. K. Deiters, ThermoC project homepage: 790