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CHEM6670Notes8 - Fundamentals of statistical mechanics...

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Fundamentals of statistical mechanics 1 CHEM 6670 Computational Chemistry & Biophysics Fundamentals of Statistical Mechanics Feb 12, 2008 Course instructor: Dr. Jana Khandogin [email protected] Course web site: http://ccb.ou.edu/teaching.aspx Experiment, theory and simulation Make models Real liquids Model liquids Wet lab experiments Computer simulations Approximate theories Experimental results Exact results for models Theoretical predictions 2 compare compare Test of models Test of theories Allen & Tildesley What is statistical mechanics Relationship between microscopic dynamics of individual particles and observed macroscopic properties Mechanical properties: Internal energy; conformation Heat capacity; pressure etc (depends on coordinates only) Statistical mechanics 6N variables! A handful of variables! 3 Thermal properties: Free energy; Chemical potential, etc (depends on volume and evokes temperature) Known: Laws (Schrödinger or Newton’s equation) describing particles and particle particle interactions Phase space A classical system of N particles can be defined by 6 N variables (3N position and 3N momenta). Each combination of 3N positions and3N momenta can be considered as a point ( microscopic state Γ ) in the phase space. The hamiltonian contains the momenta dependent kinetic energy and the coordinate dependent potential energy ) ,... , ; ,... , ( ) , ( 2 1 2 1 N N N N p p p r r r p r r r r r r r r r = energy and the coordinate dependent potential energy. 4 = + = N i i i N N N N N m p p K r V p K r p H 2 / ) ( ) ( ) ( ) , ( 2 r r r r r
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