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md2011-05-note_Part_7

# md2011-05-note_Part_7 - Then absolute internal energy A can...

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I Then, absolute internal energy A can be calculated for any λ with A ( λ ) - A ( λ 0 ) = Z λ λ 0 U ∂λ d λ . (40) I The real potential function, for which we want to calculate A is U 0 . I So, constructed U interpolates between U 0 and a harmonic lattice U ( r , λ ) = U 0 ( r ) + λ i ( r i - r 0 ) 2 A ( λ = 0 ) = A ( λ ) - R λ 0 U ∂λ d λ 0 . (41) I Because at large λ we now have harmonic lattice, for which we know the solution, we can integrate the real solution A ( λ = 0 ) from h U /∂λ i . Notes

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R F I Response functions describe how the system reacts to a change in some thermodynamic variables. I Some of the most important response functions are: Constant volume heat capacity: C V = ( E T ) V Constant pressure heat capacity: C P = ( H T ) P Thermal expansion coefficient: α P = V - 1 ( V T ) P Isothermal compressivity: β T = - V - 1 ( V P ) T Bulk modulus: B = 1 T Thermal pressure coefficient: γ V = ( P T ) V I Many of them can be directly calculated with an MD simulation.
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