*1Che mist ry Dep artm ent of Fud an Univ ersit yPhysical ChemistryChapter VI Interaction between Molecules*2Che mist ry Dep artm ent of Fud an Univ ersit y61 Intermolecular interaction 1873-van der Waals1910 Noble Prize in PhysicsWeak interactions between molecules (18371923) (P+a/V2)(V-b)=RT *3Chemistry Department of Fudan University(1) Electrostatic interactionElectrostatic interactionKeesom 1912Dipole-dipole interactions between two polar molecules(1876-1956),*4Chemistry Department of Fudan UniversityDebye 1920-1921A molecule with permanent dipole can induce a dipole of a neighboring polarizability molecule (polarizability ). The interaction of the induced dipole with the permanent dipole can be written as:(2) (2) Dipole-Induced-dipole Dipole-Induced-dipole interactioninteraction1884-19661936 Noble Prize in Chemistry*5Che mist ry Dep artm ent of Fud an Univ ersit yFor similar molecules, if 1=2=, 1=2=, then*6Chemistry Department of Fudan University(3) Dispersion interactionTransient dipole interactions1930-London1900-1954*7Che mist ry Dep artm ent of Fud an Univ ersit y(4) Total Energy of intermolecular interactions*8Che mist ry Dep artm ent of Fud an Univ ersit yPartition of van der Waals interactionDipole momentPolarizabilitymolecule*9Che mist ry Dep artm ent of Fud an Univ ersit yThe interaction energy of AB can be obtained using Variational Principle (Quantum mechanics)*10Chemistry Department of Fudan University(5) Intermolecular potential energy(n=8-16)*11Che mist ry Dep artm ent of Fud an Univ ersit yn=6, m=12Lennard-Jones potential energyJohn Edward Lennard-Jones1894-1954 *12Che mist ry Dep artm ent of Fud an Univ ersit yLennard-Jones potential energy curve*13Che mist ry Dep artm ent of Fud an Univ ersit yConversion between SLM and GMC5vOhFinal Pathway 1 -173.252378 -170.522309 -172.877736Final Pathway 2 -172.877736 -170.049554 -170.217678Final Pathway 3 -170.217678 -169.576060 -170.361742Final Pathway 4 -170.361742 -170.197572 -170.262953Final Pathway 5 -170.262953 -170.172264 -170.215483Final Pathway 6 -170.215482 -170.006935 -170.327349Final Pathway 7 -170.327349 -169.655903 -173.928427In total 55000 pathwaysIdentify 30 pathways with the lowest barrier3.67 e from C5v 4.35 e from Oh-169.576060 -173.252378 -173.928427It can be done !But, huge computer resources icosahedronTruncated octahedronLJ38 cluster*16Che mist ry Dep artm ent of Fud an Univ ersit yVan der Waals radiusPrimary alkane*17Che mist ry Dep artm ent of Fud an Univ ersit y62 Intermolecular interactions of gasFor ideal gas :*18Chemistry Department of Fudan University(1) Real gas and van der Waals equationFor ideal gas, Z=1*19Che mist ry Dep artm ent of Fud an Univ ersit yIdeal gas*20Chemistry Department of Fudan UniversityVirial equation of stateB, C, D: the second, third and fourth Virial coefficient*21Che mist ry Dep artm ent of Fud an Univ ersit y100K273K373K600KHe11.412.011.310.4Ne-6.010.412.313.8Ar187.021.74.211.9Kr-62.9-28.71.7Xe-153.7-81.7-19.6H2-2.013.715.6N2-160.0-10.56.221.7O2-197.5-22.0-3.712.9CO2-142-72.2-12.4CH4-53.6-21.28.1Air-167.3-13.53.419.0the second virial coefficient*22Che mist ry Dep artm ent of Fud an Univ ersit yVm= V / nVan der Waals equation:*23Che mist ry Dep artm ent of Fud an Univ ersit yHe0.034572.370H2O5.5363.049Ne0.21351.709H2S4.4904.287Ar1.3633.219CO23.6404.267Kr2.3493.978SO26.8035.636Xe4.2505.105NH34.2253.707H20.24762.661CH42.2834.278N21.4083.913C2H44.5305.714O21.3783.183C2H65.5626.380Cl26.5795.622C6H618.2411.54CO1.5053.985Van der Waals constants:*24Che mist ry Dep artm ent of Fud an Univ ersit y(2) Critical and supercriticalCritical pointCritical pressureCritical volume*25Che mist ry Dep artm ent of Fud an Univ ersit y(3) Corresponding state lawReduced variables:*26Che mist ry Dep artm ent of Fud an Univ ersit ymethan enitroge npropan eethylen e*27Chemistry Department of Fudan UniversityAt the critical point, pr, Tr and Vr all equal to 1*28Chemistry Department of Fudan University*29Che mist ry Dep artm ent of Fud an Univ ersit y63 Intermolecular interactions in liquid1. The structure of liquid and radial distribution function J(R)Long range- disorderedShort range- ordered but components vary all the timeThe structure of liquid is the spatial distribution and arrangement of liquid molecules*30Che mist ry Dep artm ent of Fud an Univ ersit yThe structure of liquid can usually be described by the radial distribution function, J(R) or the pair-correlation function g(R)：-average particle density of liquid J(R)dR is the probability of finding another particle within a spherical shell with radius R and thickness dR defined by the center particle. *31Che mist ry Dep artm ent of Fud an Univ ersit yTypical radia