performance of molecular polarization methods
DESCRIPTION
Performance of Molecular Polarization Methods. Marco Masia. Overview. Nonpolarizable Models Algorithms Incorporating Polarizability Fluctuacting Charges (FQ) Point Dipoles (PD) Shell Models (SH) Comparison Among Methods: Case of a Positive Point Charge Case of Cations Damping Methods - PowerPoint PPT PresentationTRANSCRIPT
Performance of Molecular Polarization Methods
Marco Masia
Performance of Molecular Polarization Methods - BCN: april 2005
Overview
Nonpolarizable ModelsAlgorithms Incorporating Polarizability
Fluctuacting Charges (FQ) Point Dipoles (PD) Shell Models (SH)
Comparison Among Methods: Case of a Positive Point Charge Case of Cations Damping Methods
Conclusions
Performance of Molecular Polarization Methods - BCN: april 2005
A: repulsive short range term
B: attractive term depending on the (dipole-dipole) London dispersion
Nonpolarizable Models
ij
jiqq
LJ
qqLJ
rqq
rU
rB
BArr
rU
UUU
)(
4)(
6
2
612
qO
qH
qH
Performance of Molecular Polarization Methods - BCN: april 2005
Nonpolarizable Models
Drawback: no dynamical response to the fluctuations of the electric fields is considered!We need to implement polarizability in an explicit way!
O
H
H
E
Performance of Molecular Polarization Methods - BCN: april 2005
Algorithms Incorporating Polarizability
Several methods have been developed for the last 30 years.
0
),...,,(0
2100
i
n
xU
EUU
xxxUU
Minimization of the energy respect to some parameter
Performance of Molecular Polarization Methods - BCN: april 2005
Fluctuacting Charges (FQ)
Charges are allowed to fluctuate according to the electronic properties of the molecule as atomic electronegativity and atomic hardness.
jj
i
qqU
0
0
E=0 E=E(r)
q1
q2
q3
q1+dq1
q2+dq2
q3 +dq3
dq1 + dq2 + dq3 = 0
Performance of Molecular Polarization Methods - BCN: april 2005
Point Dipoles (PD)
E=0 E=E(r)
q1
q2
q3
q1
q2
q3
Atomic polarizabilities i are assigned to some molecular site
The electric field induces the formation of a point dipole i
Performance of Molecular Polarization Methods - BCN: april 2005
Point Dipoles (PD)
iii
ijij
ijijijij
ij
ijij
jiijjijji
E
rrrr
TT
rr
T
TTqE
35
3
3 The calculation is repeated iteratively till convergence.
Charge and
Dipole Field Tensors
Performance of Molecular Polarization Methods - BCN: april 2005
Molecular Polarizability
3336
33323332
3)(
)(sin16)(sin82)(sin32)(sin32)(sin16)2(
),,,,,,(
000000
2
dddd
ZYXzyxf
HOH
HOHOHOHHO
OHzz
iiiati
Tr
zz
yy
xx
mol
mol
Dependence of the molecular polarizability tensor from the atomic polarizabilities
Performance of Molecular Polarization Methods - BCN: april 2005
Shell Model (SH)
The point dipole is mapped to a system of two point charges linked by a spring.
i
Sii
iSii
qk
rq
2,
,
Performance of Molecular Polarization Methods - BCN: april 2005
Comparison Among Methods
Water:• Low polarizability (1.47 Å3)• Anisotropic
Carbon Tetrachloride:• High polarizability (10.5 Å3)• Isotropic
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Charge Close to Water
Five configurations were considered:
1 2 3 4
-400
-200
0
200
400
C2v-face
trans
top
cis
po
tent
ial e
nerg
y (k
J mol
-1)
distance (+)-O (Å)
C2v-back
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Point Charge Close to Water
2 3 4 52
3
4
5 G03 PDM-H2O PD2-H2O SH-H2O
distance (+)-O (Å)
dipo
le m
omen
t (D
ebye
)
Similar results were obtained for all the other configurations considered
O
HH M
dOH
dOM
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Point Charge Close to Water
What about the performance with double point charges?
2 3 4 5 6 72
4
6
8
PDM-H2O SH-H2O G03
distance (++)-O (Å)
dipo
le m
omen
t (D
ebye
)
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Point ChargeClose to Carbon Tetrachloride
2 3 4 5 6 7
-300
-200
-100
0
100
face
edge
corner
po
tent
ial e
nerg
y (k
J mol
-1)
distance (+)-C (Å)
Three configurations were considered:
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Point ChargeClose to Carbon Tetrachloride
3 4 5 6 7
2
4
6
8 G03 FQ PD PD-C PD opt SH opt
distance (+)-C (Å)
dipo
le m
omen
t (D
ebye
)
C
Cl
Cl Cl
Cl
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Point ChargeClose to Carbon Tetrachloride
2 3 4 5 6 70
4
8
12
16
20 PD opt SH opt G03
distance (++)-C (Å)
dipo
le m
omen
t (D
ebye
)
Performance of Molecular Polarization Methods - BCN: april 2005
Case of a Positive Point Charge
PD and SH models can be reparametrized to reproduce the polarizability tensor of the molecule & the dipole moment induced by a point charge;
Also at short distances there is no need to use damping functions;
High electric fields cause the linear models to fail due to hyperpolarizability effects;
Performance of Molecular Polarization Methods - BCN: april 2005
Case of Cations
2 3 4 5-200
-150
-100
-50
0
distance ion-O (Å)
Pote
ntia
l Ene
rgy
(kJ
mol
-1)
3 4 5-200
-150
-100
-50
0
(+); Li+; Na+; K+
distance ion-C (Å)
Potential energy: importance of electron repulsion
Performance of Molecular Polarization Methods - BCN: april 2005
Case of Cations
2 3 4 52.0
2.5
3.0
3.5
4.0
4.5 (+) Li+
Na+
K+
distance ion-O (Å)
dipo
le m
omen
t (D
ebye
)
2 3 4 52
3
4
5
2 3 4 52
3
4
5
6
7
8 PDM-H2O; PD2-H2O; SH-H2O; G03
dip
ole
mom
ent (
Deb
ye)
distance ion-O (Å)
Li+ Ca2+
distance ion-O (Å)
Performance of Molecular Polarization Methods - BCN: april 2005
Case of Cations
3 4 5
2
3
4
5
6
3 4 5
4
6
8
10
12
PD opt; SH opt; PD; G03
Li+
distance ion-C (Å)
dip
ole
mom
ent (
Deb
ye)
Mg2+
distance ion-C (Å)
Performance of Molecular Polarization Methods - BCN: april 2005
Damping Functions
Thole (1981): for intramolecular interactions the molecular polarizability diverges at short distances
r
=(r,)
Many functional forms for the charge density have been proposed.
The most used are the exponential and the linear forms.
Performance of Molecular Polarization Methods - BCN: april 2005
Damping Functions
35
3
3
ijij
ijijijij
ij
ijij
jiijjijji
rrrr
TT
rr
T
TTqE
Performance of Molecular Polarization Methods - BCN: april 2005
Damping Functions
),,,(
)(3
)(
;)(
3553
31
wrf
rf
rrr
fTT
rr
fT
jiij
ij
ij
ij
ijijijijij
ij
ijijij
Performance of Molecular Polarization Methods - BCN: april 2005
Damping Functions
2 3 4 52.0
2.5
3.0
3.5
4.0
4.5
2 3 4 52
3
4
5
6
7
PDM; PDM-exp; PDM-lin; G03
distance ion-O (Å)
Na+
dipo
le m
omen
t (D
ebye
)
Ca2+
distance ion-O (Å)
Performance of Molecular Polarization Methods - BCN: april 2005
Conclusions and Future Work
Dimers with cations show a different behaviour from the case of positive point charges;
In the case of cations the use of damping functions for the electrostatic interactions is needed;
The Thole linear and exponential models have been applied to intermolecular interactions and reparametrized for the interactions cation-water and cation-CCl4.
Study the performance of the same methods with
anions (high polarizabilities!)
Performance of Molecular Polarization Methods - BCN: april 2005
Bibliography
Review Rev. in Comput. Chem. 18, 89 (2002).
Methods FQ: J. Chem. Phys. 101, 6141 (1994) PD: J. Am. Chem. Soc. 94, 2952 (1972) SH: The Theory of Optics (Longmans, N. Y., 1902) Damping: Chem. Phys. 59, 341 (1981)
Results J. Chem. Phys. 121, 7362 (2004) Comp. Phys. Commun. In press Manuscript in preparation
Performance of Molecular Polarization Methods - BCN: april 2005
Aknowledgements
Rossend ReyMichael Probst
EUMinisterio EspañolRegione Sardegna
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