Ω r ωr functional minimization thermodynamic

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 Ω r , 0 Ω r , 0 Functional minimization: Thermodynamic equilibrium D. Mermin Thermal properties of the inhomogeneous electron gas », Phys. Rev., 137 (1965)) Intrinsic to a given solvent
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In analogy to electronic DFT, how to use classical DFT as a « theoretical chemist » tool to compute the solvation properties of molecules, in particular their solvation free-energy ? 0 Ω r , 0 F energy free Solvation min F 0 , c ) , ( , Ω r ext c V But what is the functional ??
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The exact functional ext exc id F F F F x 0 1 0 1 1 1 ln x x x x d T k F B id 1 1 1 x x x ext ext V d F , , 1 2 1 1 2 1 x x x x x x  C d d T k F B exc 0 x x ; , 1 , 2 1 ) 2 ( 1 0 2 1 x x x x c d C x x 0 ) , ( Ω r x ) , ( Ω r
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The homogeneous reference fluid approximation Neglect the dependence of c (2) ( x 1 , x 2 ,[ ]) on the parameter , i.e use direct correlation function of the homogeneous system 2 1 0 2 1 ) 2 ( 2 1 ) 2 ( , ; , ; , x x x x x x c c c c ( x 1 , x 2 ) connected to the pair correlation function h ( x 1 , x 2 ) through the Ornstein-Zernike relation 2 3 3 1 3 0 2 1 2 1 , , , , x x x x x x x x x h c d c h 1 , , 2 1 2 1 x x x x g h g(r) h(r)
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The homogeneous reference fluid approximation Neglect the dependence of c (2) ( x 1 , x 2 ,[ ]) on the parameter , i.e use direct correlation function of the homogeneous system 2 1 0 2 1 ) 2 ( 2 1 ) 2 ( , ; , ; , x x x x x x c c c c ( x 1 , x 2 ) connected to the pair correlation function h ( x 1 , x 2 ) through the Ornstein-Zernike relation 2 3 32 3 1 13 3 3 0 2 1 12 2 1 12 , , ) , , ( , , , , Ω Ω r Ω Ω r Ω r Ω Ω r Ω Ω r h c d d c h 1 , , 2 1 2 1 x x x x g h g(r) h(r)
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) , , ( h 2 1 12 Ω Ω r ) , , ( c 2 1 12 Ω Ω r The picture Functional minimization
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Rotational invariants expansion ) , , ˆ ( ) , , ( 2 1 12 12 2 1 12 Ω Ω r Ω Ω r lmn lmn r h h   ) , , ˆ ( ) , , ( 2 1 12 12 2 1 12 Ω Ω r Ω Ω r lmn lmn r c c   1 Ω 2 Ω 12 r
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2 1 12 1 12 1 112 2 1 110 000 ) )( ( 3 , , 1 Ω Ω r Ω r Ω Ω Ω The case of dipolar solvents The Stockmayer solvent 1 Ω 2 Ω 12 r 112 12 112 110 12 110 000 12 000 2 1 12 ) ( ) ( ) ( ) , , ( r c r c r c c Ω Ω r
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Particle density Polarization density Ω r Ω r , d n Ω r Ω Ω r P , 0 d Ω r , F r P r , n F density solvent n orientatio position/ , Ω r R. Ramirez et al, Phys. Rev E,
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  • Fall '19
  • Computational chemistry, Molecular dynamics, Implicit solvation, Biomolecule solvation

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