Long-range electrostaticinteraction
0-0.2-0.4-0.6-0.8-1

105-100-5
0-55• First we learn what means “long range”? It is10-10very important concept for simulation. !!

Consider 1D ionic crystal-+R+-+-+

2N ions
N cations: q+ = e
N anions: q- = -e
We can cal. the coulomb interaction U0 which involve the ↑ anion(2 means int. to left and right is the same)

4π"0 U0e2!

"!
"
11112
1 1 1
= 2 − +−+− ... = −1 − + − + ...
R 2R 3R 4R
R2 3 4223
4= − ln 2xxx
Rln(1 + x) ! x −+−+ ...
234

The interaction is the same for all 2N ions, then
1
1 ! qi qj
e2 2 ln 2= 2N U0 = −N
U=2 i,j 4π"0 rij
24π"0 R

Madelung constantq0 qiIf we plot 2
e r0i

very long-range !!
remember R (2- 3 Å) is ion-ion distance! q0 qi

If we plot total energyie2 r0islow convergence!!
remember R is ion-ion distance− ln 2− ln 2 = −0.693147− ln 2

• So if we simply use the cut-off (I. Benjamin use 3 nmcutoff) we may get not-accurate (sometimes wrong)answer!!

• Some special care should be taken to handle the longrange interaction!!

Ewald method
I want to skip the formulation.
If you like, please refer pp.35-42 of
http://www.users.kudpc.kyoto-u.ac.jp/~d54649/web_material/MDselfstudy.pdf(Prof. Kano told me that one of the B4 students in his lab always say that she is happy when she handles equations!)

But One very important thing:short range part ☞direct Coulomb sum (R space)long range part ☞ k-space sum (reciprocal space)(long range r

short range k)

In the Ewald method the electrostatic potential becomes
VI−I=
 1 4π %()2 )2 ( NN%
1 − |G|22  %e24κZi sin(G · ri ) e
Zi cos(G · ri ) +24π"0 2 Ωcell|G|i=1i=1G"=0


,-.
/

+1 %%
2ij

Zi Zj 000erfc(κx)00x%! 12κπ− √ δij − 2κ ΩcellπR12|S(G)|2x=|R+rj −ri |The practical points: we should give1) cutoff of G sum2) cutoff R sum3) κ value
Don’t worry! In DL-POLY these parameters are optimized
inside the program, so just set,
ewald precision 1d-6
(If you don’t like it, you can set “ewald sum κ k1 k2 k3”)

MD Simulations ofHigh Temperature Molten Salts
cf. S. Okazaki, Y. Miyamoto, and I. Okada, PRB, 45, 1992, 2055-2062
LiCl and LiCl-CsCl

Potential : Coulomb + Born-Huggins-Meyer(Tosi-Fumi potential)
zi zj e2φij (r) =+ Aij b exp
r $! "#!
Coulomb%

σi0 + σj0 − r
ρ"#BHM&cijdij− 6 − 8rr$Tosi-Fumi potential parameters for alkali-halides

岡田勲

溶融塩の分子動力学シミュレーション

計算物理学と計算化学

８章

134-157 KAIBUNDO

LiCl molten salts: physical properties
ρ / 103 kg m-3
LiCl 1.884 - 4.328x10-4 T (910-1050 K)
金属データブック1.463 g cm-3 at 973 K
fcc cubic lattice 5.774 Åsolid->
fcc cubic lattice 5.14 Å

融解塩イオンD0/10-7 m2 s-1

Q / kJ mol-1

温度 T / K

LiCl

Li+1.2318.00

883〜1033

Cl-0.7118.43

883〜1033

Li+ 1.3D-8 m2s-1 at 973K
Cl- 0.7D-8 m2s-1 at 973K

LiCl potential parameters
LiAij : Pauling parameterzjzi++ 1)(?? =ninj

Li+ Li+Li+ ClCl- Cl-2
1.25
4/3 1
2/3 0.75

zLi+ = 1, zCl− = −1
nLi+ = 2, nCl− = 6
nLi+ = 8??, nCl− = 8??

b = 0.338 × 10−19 J = 20.35 kJ mol−100σLi+ = 0.816 Å, σCl− = 1.585 Å, ρLiCl = 0.342 Å

Li+ Li+Li+ ClCl- Cl-c / 10-79 J m60.073
2.0111.0d 10-99 J m80.03
2.4
223.066

1.0 × 10−79 J m6 = 1.0 × 10−19 J Å = 60.221 kJ mol−1 Å
88
1.0 × 10−99 J m8 = 1.0 × 10−19 J Å = 60.221 kJ mol−1 Å

ClDL-POLY parameters (Please check the values!)ABσC

DkJ mol-1

Å-1

ÅkJ mol-1 Å6kJ mol-1 Å8

Li+ - Li+25.44

2.924

1.632

4.40

1.81

Li+ - Cl-20.352.924

2.401

120.44144.53Cl- - Cl-

15.26

2.924

3.170

6684.57

13429.36

start configuration
NaCl structure:
Li fcc + 1-basis Li-Cl

256 Li cation+256 Cl anion

CONFIG
LiCl Tosi-Fumi coulomb 973 K
2
1
23.0949137651.0000000000.0000000000.0000000000
23.0949137651.0000000000.0000000000.0000000000
23.0949137651
Li 1-11.5474568825-11.5474568825-11.5474568825-10.6165397575-9.2381425951
2.3127320988.0000000000.0000000000.0000000000
Cl 2-8.6605926619-11.5474568825-11.5474568825-3.8343057133
3.3861251245-.2857354079.0000000000.0000000000.0000000000
Li 3-8.6605926619-8.6605926619-11.5474568825-2.4627326782-10.9204233616-10.5006199708.0000000000.0000000000.0000000000
Cl 4-11.5474568825-8.6605926619-11.5474568825.3993300091
8.0160734289-5.3483995294.0000000000.0000000000.0000000000...
Li 5115.7737284413
8.6605926619
8.6605926619
10.1377456936-13.03660257479.8671728482.0000000000.0000000000.0000000000
Cl 5128.6605926619
8.6605926619
8.6605926619.7285484771
1.4579165760.5758900933.0000000000.0000000000.0000000000

FIELD
LiCl Tosi-Fumi+Ewald
units kJ
molecules 1
LiClnummols 256
atoms 2
Li 6.941
1.00
Cl 35.453 -1.00
finishvdW 3
LiLi bhm
25.44 2.924 1.632 4.40 1.81
LiCl bhm
20.35 2.924 2.401 120.44 144.53
ClCl bhm
15.26 2.924 3.170 6684.57 13429.36
close

CONTROL
LiCl Tosi-Fumi+Ewaldunits kJ
molecules 1
LiClnummols 256
atoms 2
Li 6.941
1.00
Cl 35.453 -1.00
finishvdW 3
LiLi bhm
25.44 2.924 1.632 4.40 1.81
LiCl bhm
20.35 2.924 2.401 120.44 144.53
ClCl bhm
15.26 2.924 3.170 6684.57 13429.36
close

You can download the three input files and the
CONFIG generation program DLPOLY_LiClinput.f
from/home/d/d54649/DL_POLY/data_LiCl_TosiFumiEwald
Please sftp d54649@sakura.kudpc.kyoto-u.ac.jp

results

4

Cl - ClRDF

3210246810distance / Angstrom
4

Li - ClRDF

3210246810

distance / Angstrom
4

Li - LiRDF

3210246
distance / Angstrom

810

Approximate 3D Diffusion coefficients ( m^2 / s)ion
Li+Cl-D
9.0 x10^-97.5 x10^-9exp
Li+ 1.3D-8 m2s-1 at 973K
Cl- 0.7D-8 m2s-1 at 973K

So what’s ? ===>It seems very easy to run the simulation!! ===>
The analysis of the calculation results are very important. ===>
Thermal average, space-time correlation and so on.

mixing system
M.Y. did not cal. this system.
Please do it
by yourself if you have an interest.

• LiCl-KCl case？
• Li-K？
LiClKρ / 103 kg m-3
LiCl 1.884 - 4.328x10-4 T (910-1050 K)
KCl 2.136 - 5.832x10-4 T (910-1050 K)
LiCl(58.8)-KCl(41.2) 2.0286-5.2676x10-4 T (680-860 K)
金属データブック

融解塩イオン

D0/10-7 m2
s-1

Q/kJ mol-1

温度 T/ K

KCl

K+

1.80

28.79

1070〜1260

Cl-1.8029.83

1065〜1260

Li+

1.23

18.00

883〜1033

Cl-0.7118.43

883〜1033

LiClFor the mixing rule, please refer toB. Larson et al.
Mol. Phys. 1973, 26, 1521-1532