By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each zone of the self-discipline.
themes integrated during this quantity comprise fresh advancements in classical density useful concept, nonadiabatic chemical dynamics in intermediate and excessive laser fields, and bilayers and their simulation.Content:
Chapter 1 fresh advancements in Classical Density practical thought (pages 1–92): James F. Lutsko
Chapter 2 Nonadiabatic Chemical Dynamics in Intermediate and extreme Laser Fields (pages 93–156): Kazuo Takatsuka and Takehiro Yonehara
Chapter three Liquid Bilayer and its Simulation (pages 157–219): J. Stecki
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Extra resources for Advances in Chemical Physics, Volume 144
DbFex ½n rðmÞgðr1 ; r2 ; mÞ ¼ exp bmÀbvðr1 ; r2 ÞÀ ð52Þ dnðr2 Þ nðrÞ¼rðr;m;½f0r Þ 1 These relations are often used in practical calculations to get the PDF from a DFT calculation. Furthermore, since the same DFT allows one to calculate both the PDF and the DCF and since they are related via the Ornstein–Zernike relation, this gives a method to check the self-consistency of model calculations analogous to the comparison of the virial and compressibility routes to the equation of state in liquid-state theory.
The excess free energy per unit area, the surface free energy g which is often assumed to be the same as the surface tension, can then be calculated from ! Z 1 1 drðzÞ 2 g¼ f ðrðzÞÞ þ g À mrðzÞ À vð rv ; mÞ dz ð70Þ 2 dz À1 If the profile is monotonic, one can solve Eq. (69) for dr=dz and write this as pﬃﬃﬃﬃﬃ Z rl pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ g ¼ 2g f ðrÞÀmrÀvð rv ; mÞ dn ð71Þ rv so that the surface free energy can be determined by a simple integration without even solving for the profile.
F. Exact General Expression for the Excess Part of the Free Energy Functional Recall the relation À drðr1 ; ½fÞ ¼ rðr1 Þdðr1 À r2 Þ þ rðr1 Þrðr2 Þhðr1 ; r2 Þ dbfðr2 Þ ð38Þ derived above (see Eq. 8). Let us write the inverse relation as dbfðr2 ; ½rÞ 1 ¼À dðr1 À r2 Þ þ Gðr1 ; r2 ; ½rÞ drðr1 Þ rðr1 Þ ð39Þ JAMES F. LUTSKO 12 where we must clarify the nature of Gðr1 ; r2 Þ. Substituting these into the functional chain rule, Z drðr1 ; ½fÞ dbfðr2 ; ½rÞ dðr1 Àr3 Þ ¼ dr2 dbfðr2 Þ drðr3 Þ gives the relation Z hðr1 ; r3 Þ ¼ Gðr1 ; r3 ; ½rÞ þ hðr1 ; r2 Þrðr2 ÞGðr2 ; r3 ; ½rÞdr2 ð40Þ This is recognized as the Ornstein–Zernike equation for an inhomogeneous system  so that we can identify the unknown function G as the (two-body) direct correlation function (DCF), Gðr2 ; r3 Þ ¼ c2 ðr2 ; r3 ; ½rÞ.