1

機能性溶液化学

Al3+

TCNQ

TCNQ-

Fe(CN)64-

Fe(CN)63-

N

O-

3 x-

2

gas

liquid

solid

Static :radial distribution functionDynamic: Self-diffusion constant

Phase diagram

3

相律F = C - P + 2

4

VdW Equation of State

5

Thermodynamics

Statistical mechanics

Mechanics, Quantum MechanicsExample:■VdW Equation of State■Statistical Mechanical Perturbation Theory■Hard Sphere Model + Pair Potential

6

Liquid Theory

Integral Equation Theorymany-body interaction

1---2 1 23

J.P. Hansen and I. R. MacdonaldTheory of Simple Liquids 1986 Academic

Molecular SimulationMolecular DynamicsMonte Carlo１）M. P. Allen and D. J. Tildesley

Computer Simulation of Liquids 1987, Oxford２）岡崎進 コンピュータシミュレーションの基礎 2000化学同人

7

OH H

OH H

OH H

OH H

OH H

OH H

OH H

OH

H

OH

H

OH

H

OH

H

OH

H

δ+δ+

δ+δ+

δ+

δ+

δ+

δ+

δ-

δ-

δ-

δ-

8

H2O dimerAb-initio calculation

674 cm-1 liberational motionHydrogen bond

9

SPC model(simple point charge/flexible) water model

[J. Lobaugh and G. A. Voth,

J. Chem. Phys. 106 (1997) 2400]

10

11

12

13

Xe固体 Xe液体

14Molecular Dynamics Simulation, J. M. Haile John&Wiley 1992

+ +

gasliquid

solid

Lennard-Jones Reduced Unit System

15

16

17

18

solid

liquid

19

solid

liquid

20

LJ-Liquid movie

21

LJ-Solid Snapshot

12

i

j

{ri} :position{vi}:velocity{Fi}:Force

Molecular Dynamics

Monte Carlo(Energy only)

Φij (ri,rj) = Φij (| ri-rj |)

k

position

velocity

Force

23

24

Periodic Boundary Condition

25

Minimum image convention

Cutoff rcutoff < L / 2

L:PBC box length

26

27

28

Nature 414, 73 - 77 (2001); Energetics of ion conduction through the K+ channel

Simulations and parameters All simulations were carried out using the program CHARMM23. The total number of atoms in the simulation system is slightly above 40,000 (KcsA, 112 dipalmitoylphosphatidylcholine (DPPC), 6,532 water molecules, 3 K+ in the pore, and 12 K+ and 23 Cl- in the bulk solution).