Pemodelan molekul: komputasi kimia
Contoh: molekul air dengan 3 titik muatan
1. Koordinat internal molekul air:
H3
H
O1
O
H
H2
O1
H2 O1 R1
H3 O1 R2
R1=1.
R2=1.
A1=105.
H2 A1
2. Koordinat internal terdiri atas 3 ordinat yaitu jarak
antara titik muatan (atom), R, sudut antara 3 titik
muatan (atom, A, dan sutut (torsi, dihedral) antara 4
titik muatan (atom), D.
3. Harga R1, R2, A1, dan D1 (bila molekul lebih besar
dari 3 atom) dapat dipilih sembarang tetapi tidak
terlalu jauh dari harga eksperimen.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 1
Pemodelan molekul: komputasi kimia
4. Perhitungan mekanika kuantum ab initio:
Input file: misalnya air_opt.g03
#T RHF/6-31G(D,P) opt
air opt
0 1
o1
h2 o1 1.
h3 o1 1. h2 105.
Perintah perhitungan (harus)
Tidak harus ditulis
Muatan dan multiplisitas (harus)
Koordinat internal (harus)
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 2
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Output file: misalnya air_opt.out
Bagian awal output:
#T RHF/6-31G(D,P) opt
air opt
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
o1
h2 o1
1.
h3 o1
1. h2 105.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 3
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Output file: misalnya air_opt.out
Bagian output (lanjut):
Perhitungan awal: koordinat internal diubah menjadi
koordinat kartesian pertama.
awal:
Standard orientation:
------------------------------------------------------Center
Atomic
Atomic
Coordinates (Angstroms)
Number
Number
Type
X
Y
Z
------------------------------------------------------1
8
0
0.000000
0.000000
0.121752
2
1
0
0.000000
0.793353 -0.487009
3
1
0
0.000000 -0.793353 -0.487009
------------------------------------------------------Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 4
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
perhitungan awal: konstanta rotasi hingga momen
dipol.
Rotational constants (GHZ): 761.8214656 398.3536020 261.5763201
SCF Done: E(RHF)=-76.0172883749 A.U. after 10 cycles
Convg= 0.4337D-08 -V/T = 2.0048 S**2 = 0.0000
Mulliken atomic charges:
1
O -0.687056
2
H
0.343528
3
H
0.343528
Dipole moment (field-independent basis, Debye):
X= 0.0000 Y= 0.0000 Z= -2.2089 Tot= 2.2089
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 5
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 1: konvergensi.
Step number 1 out of a maximum of 20
Variable
Old X
-DE/DX
Delta X
Delta X
(Linear)
(Quad)
R1
1.88973 -0.05532 0.00000 -0.11303
R2
1.88973 -0.05532 0.00000 -0.11303
A1
1.83260 -0.00316 0.00000 -0.01833
Item
Value
Threshold
Maximum Force
0.055321
0.000450
RMS
Force
0.045207
0.000300
Maximum Displacement
0.090403
0.001800
RMS
Displacement
0.085525
0.001200
Delta X
(Total)
-0.11303
-0.11303
-0.01833
Converged?
NO
NO
NO
NO
New X
1.77670
1.77670
1.81426
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 6
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 1: koordinat kartesian baru (kedua).
Standard orientation:
-----------------------------------------------------Center
Atomic
Atomic
Coordinates (Angstroms)
Number
Number
Type
X
Y
Z
------------------------------------------------------1
8
0
0.000000
0.000000
0.115833
2
1
0
0.000000
0.740624 -0.463330
3
1
0
0.000000 -0.740624 -0.463330
------------------------------------------------------Rotational constants (GHZ): 841.6775412
457.0952421
296.2233305
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 7
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 1: Energi.
SCF Done: E(RHF) =-76.0234723584 A.U. after 10 cycles
Convg=0.3593D-08 -V/T = 2.0019
S**2 = 0.0000
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 8
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 2: konvergensi.
Step number 2 out of a maximum of 20
Variable
Old X
-DE/DX
Delta X
(Linear)
R1
1.77670 0.00455 0.00791
R2
1.77670 0.00455 0.00791
A1
1.81426 0.00674 0.00128
Item
Value
Maximum Force
0.006742
RMS
Force
0.005383
Maximum Displacement
0.024153
RMS
Displacement
0.022831
Delta X Delta X
(Quad)
(Total)
-0.00302 0.00489
-0.00302 0.00489
0.03657 0.03785
Threshold
Converged?
0.000450
NO
0.000300
NO
0.001800
NO
0.001200
NO
New X
1.78159
1.78159
1.85212
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 9
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 2: koordinat kartesian baru (ketiga).
Standard orientation:
-------------------------------------------------------Center
Atomic
Atomic
Coordinates (Angstroms)
Number
Number
Type
X
Y
Z
-------------------------------------------------------1
8
0
0.000000
0.000000
0.113319
2
1
0
0.000000
0.753520 -0.453278
3
1
0
0.000000 -0.753520 -0.453278
-------------------------------------------------------Rotational constants (GHZ): 879.4252319
441.5831829
293.9719298
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 10
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 2: Energi.
SCF Done: E(RHF) =-76.0236143166 A.U. after 8 cycles
Convg=0.6467D-08 -V/T = 2.0021
S**2 = 0.0000
Bandingkan dengan perhitungan awal dan step 1:
SCF Done: E(RHF)=-76.0172883749 A.U. after 10 cycles
Convg= 0.4337D-08 -V/T = 2.0048 S**2 = 0.0000
SCF Done: E(RHF) =-76.0234723584 A.U. after 10 cycles
Convg=0.3593D-08 -V/T = 2.0019
S**2 = 0.0000
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 11
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 3: konvergensi.
Step number 3 out of a maximum of 20
Variable
Old X
-DE/DX
Delta X Delta X Delta X
(Linear)
(Quad) (Total)
R1
1.78159 0.00026 -0.00022 0.00091 0.00069
R2
1.78159 0.00026 -0.00022 0.00091 0.00069
A1
1.85212 -0.00043 -0.00171 -0.00109 -0.00280
Item
Value
Threshold
Converged?
Maximum Force
0.000434
0.000450
YES
RMS
Force
0.000326
0.000300
NO
Maximum Displacement
0.001271
0.001800
YES
RMS
Displacement
0.001373
0.001200
NO
New X
1.78227
1.78227
1.84932
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 12
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 3: koordinat kartesian baru (ketiga).
Standard orientation:
-------------------------------------------------------Center
Atomic
Atomic
Coordinates (Angstroms)
Number
Number
Type
X
Y
Z
-------------------------------------------------------1
8
0
0.000000
0.000000 0.113574
2
1
0
0.000000
0.753017 -0.454295
3
1
0
0.000000 -0.753017 -0.454295
-------------------------------------------------------Rotational constants (GHZ): 875.4913660 442.1729232
293.7915065
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 13
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 3: Energi.
SCF Done: E(RHF) =-76.0236150032
A.U. after
Convg =0.5596D-08
-V/T = 2.0021
S**2
7 cycles
= 0.0000
Bandingkan dengan perhitungan awal, step 1, dan step 2:
SCF Done: E(RHF)=-76.0172883749 A.U. after 10 cycles
Convg= 0.4337D-08 -V/T = 2.0048 S**2 = 0.0000
SCF Done: E(RHF) =-76.0234723584 A.U. after 10 cycles
Convg=0.3593D-08 -V/T = 2.0019
S**2 = 0.0000
SCF Done: E(RHF) =-76.0236143166 A.U. after 8 cycles
Convg=0.6467D-08 -V/T = 2.0021
S**2 = 0.0000
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 14
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 4: konvergensi.
Step number 4 out of a maximum of 20
Variable
Old X
-DE/DX
Delta X Delta X Delta X
(Linear)
(Quad) (Total)
R1
1.78227 -0.00009 -0.00007 -0.00008 -0.00016
R2
1.78227 -0.00009 -0.00007 -0.00008 -0.00016
A1
1.84932 0.00002
0.00030 -0.00013 0.00018
Item
Value
Threshold Converged?
Maximum Force
0.000092
0.000450
YES
RMS
Force
0.000076
0.000300
YES
Maximum Displacement
0.000117
0.001800
YES
RMS
Displacement
0.000107
0.001200
YES
Optimization completed.
New X
1.78212
1.78212
1.84950
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 15
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 4: parameter optimasi.
-- Stationary point found.
---------------------------! Optimized Parameters !
! (Angstroms and Degrees) !
----------------------------------! Name Definition
Value
Derivative Info.
! ------------------------------------------------------! R1
R(1,2)
0.9431
-DE/DX = -0.0001
!
! R2
R(1,3)
0.9431
-DE/DX = -0.0001
!
! A1
A(2,1,3)
105.9583
-DE/DX = 0.0
!
-------------------------------------------------------Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 16
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 4: koordinat kartesian baru
(keempat).
1
2
3
O
H
H
Distance matrix (angstroms):
1
2
3
0.000000
0.943138 0.000000
0.943138 1.506035
0.000000
Framework group C2V[C2(O),SGV(H2)]
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 17
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 4: koordinat kartesian baru (keempat).
Standard orientation:
-------------------------------------------------------Center
Atomic
Atomic
Coordinates (Angstroms)
Number Number Type
X
Y
Z
-------------------------------------------------------1
8
0
0.000000
0.000000
0.113574
2
1
0
0.000000
0.753017 -0.454295
3
1
0
0.000000 -0.753017 -0.454295
-------------------------------------------------------Rotational constants (GHZ):
875.4913660
442.1729232
293.7915065
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 18
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 4: analisis populasi.
****************************************************************
Population analysis using the SCF density.
****************************************************************
Orbital symmetries:
Occupied (A1) (A1) (B2) (A1) (B1)
Virtual
(A1) (B2) (B2) (A1) (A1) (B1) (B2) (A1) (A2) (A1)
(B1) (B2) (A1) (B2) (B1) (A2) (A1) (A1) (B2) (A1)
The electronic state is 1-A1.
Alpha occ. eigenvalues -- -20.55729 -1.34643 -0.71383 -0.56829 -0.49760
Alpha virt. eigenvalues -0.21531 0.30842 1.01682 1.09298 1.13457
Alpha virt. eigenvalues -1.16898 1.29552 1.41170 1.80255 1.82943
Alpha virt. eigenvalues -1.93143 2.58264 2.58874 2.84147 2.99751
Alpha virt. eigenvalues -3.00620 3.40640 3.74549 3.94511 4.12833
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 19
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Bagian output (lanjut):
Step perhitungan 4: muatan atom Mullikan dan momen
dipol.
****************************************************************
Population analysis using the SCF density.
****************************************************************
Mulliken atomic charges: (step awal)
1 O -0.670704
2 H
0.335352
3 H
0.335352
Mulliken atomic charges: (step 4)
1
O -0.687056
2
H
0.343528
3
H
0.343528
Dipole moment (field-independent basis, Debye):
X= 0.0000
Y= 0.0000
Z= -2.1478 Tot= 2.1478
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 20
Pemodelan molekul: komputasi kimia
5. Perhitungan mekanika kuantum ab initio:
Output file: misalnya air_opt.out
AND HERE I AM, FOR ALL MY LORE, THE WRETCHED FOOL I
WAS BEFORE. CALLED MASTER OF ARTS, AND DOCTOR TO
BOOT, FOR TEN YEARS ALMOST I CONFUTE AND UP AND
DOWN, WHEREVER IT GOES I DRAG MY STUDENTS BY THE
NOSE -- AND SEE THAT FOR ALL OUR SCIENCE AND ART WE
CAN KNOW NOTHING. IT BURNS MY HEART.
-- FAUST
Job cpu time: 0 days 0 hours 0 minutes 4.2 seconds.
File lengths (MBytes): RWF= 11 Int= 0 D2E= 0 Chk= 4 Scr= 1
Normal termination of Gaussian 03 at Wed Apr 8 11:35:24 2009.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 21
Polarisasi
The polarization, P (Cm/m3) of a sample is the electric
dipole moment density, the mean electric dipole
moment of molecules,<μ>, multiplied by the number
density, N (m-3):
P  N
Persamaan 6
Pada temperatur T:
z 

3kT
Persamaan 7
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 22
Polarisabilitas
An applied electric field can distort a molecule as well
as align its permanent electric dipole moment. The
induced dipole moment, μ* (Cm), is generally
proportional to the field strength, E, and we write:
  

Persamaan 8
The constant of proportionality is the polarizability of
the molecule. The greater the polarizability, the
larger is the induced dipole moment for a given
applied field.
In a formal treatment, we should use vector quantities
and allow for the possibility that the induced dipole
moment might not lie parallel to the applied field,
but for simplicity we discuss polarizabilities in
terms of (scalar) magnitudes.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 23
Polarisabilitas Volume
Polarizability has the units (coulomb metre)2 per joule
(C2m2J-1).
That collection of units is awkward, so α is often
expressed as a polarizability volume, α’, by using
the relation:

 
4 o
'
Persamaan 9
where εo is the vacuum permittivity. Because the units of
are coulomb-squared per joule per metre (C2J-1m-1), it
follows that α has the dimensions of volume (hence its
name). Polarizability volumes are similar in magnitude
to actual molecular volumes (of the order of 10-30 m3,
10-3 nm3, 1 Ao3.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 24
Momen Dipol Listrik
Tabel 3: Polarizability volumes (α’)
Molecules
CCl4
H2
H2O
HCl
HI
(1,2)
α’/(10-30 m3)
10.5
0.819
1.48
2.63
5.45
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 25
Polarisabilitas Volume
Polarizability volumes correlate with the HOMO-LUMO
separations in atoms and molecules.
The electron distribution can be distorted readily if
the LUMO lies close to the HOMO in energy, so
the polarizability is then large.
If the LUMO lies high above the HOMO, an applied
field cannot perturb the electron distribution
significantly, and the polarizability is low.
Molecules with small HOMO-LUMO gaps are typically
large, with numerous electrons.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 26
Polarisabilitas dan Struktur Molekul
The contribution to the Hamiltonian when a dipole
moment is exposed to an electric field in the zdirection is
(1)
Persamaan 11
H   
z
By
a series of the mathematical operation, the
polarizability of the molecule in the z-direction is
  2
n
 z ,0 n
(0)
n
E
2
E
(0)
0
Persamaan 12
where μz,0n is the transition electric dipole moment in
the z-direction.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 27
Polarisabilitas dan Struktur Molekul
The content of eqn previous can be appreciated by
approximating the exitation energies by a mean
value ΔE (an indication of the HOMO-LUMO
separation), and supposing that the most important
transition dipole moment is approximately equal to
the charge of an electron multiplied by the radius,
R, of the molecule. Then is
2e2 R 2

E
Persamaan 13
This expression shows that α increases with size of the
molecule and with the ease with which it can be
excited (the smaller the value of ΔE).
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 28
Polarisabilitas dan Struktur Molekul
If the excitation energy is approximated by the energy
needed to remove an electron to invinity from a
distance R from a single positive charge, we can
write:
2
Persamaan 14
o
E  e 4 R
When this expression is substituted into the equation
previous, and 9, and the factor 2 ignored in this
approximation, we obtain,
 R
'
3
Persamaan 15
which is of the same order of magnitude as the
molecular volume).
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 29
Polarisabilitas dan Struktur Molekul
For most molecules, the polarizability is anisotropic, by
which is meant that its value depends on the
orientation of the molecule relative to the field.
The polarizability volume of benzene when the field is
applied perpendicular to the ring is 0.0067 nm3 and
it is 0.0123 nm3 when the field is applied in the
plane of the ring.
The anisotropy of the polarizability determines whether
a molecule is rotationally Raman active.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 30
Permitivitas Relatif
Potential energy of interaction of two charges q1 and
q2 which are separated by a distance r
in a
vacuum is
q1q2
V
4 o r
Persamaan 16
where εo is the vacuum permittivity.
In a medium such as air or a liquid:
q1q2
V
4 r
Persamaan 17
where ε is the permittivity of the medium.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 31
Permitivitas Relatif
Permitivitas dapat dinyatakan dalam permitivitas relatif
(tak berdimensi), εr, (tetapan dielektrik) medium:

r 
o
Persamaan 18
The relative permittivity can have a very significant
effect on the strength of the interactions between
ions in solutions.
For instance, water has a relative permittivity of 78
at 25 oC, so the interionic Coulombic interaction
energy is reduced by nearly two orders (102) of
magnitude from its vacuum value.
Some of the consequences of this reduction for
electrolyte solutions were explored in chapter of
simple mixtures.
.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 32
Permitivitas Relatif
The relative permittivity of a substance is large if its
molecules are polar or highly polarizable.
The quantitative relation between the relative
permittivity and the electric properties of the
molecules
is
obtained
by
considering
the
polarization of a medium, and is expressed by the
Debye equation:
 r  1  Pm

r  2 M
Persamaan 19
where ρ is the mass density of the sample, M is the molar mass
of the molecules, and Pm is the molar polarization.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 33
Permitivitas Relatif
Pm is the molar polarization, which defined as:
2

NA
 
Pm 
 

3 o 
3kT 
Persamaan 20
The term  2 3kT stems from the termal averaging of the electric
dipole moment in the presence of the applied field (eqn 7).
The corresponding expression without the contribution from the
permanent dipole moment is called the Clausius-Mossotti equation:
 r  1  N A

 r  2 3M  o
Persamaan 21
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 34
Permitivitas Relatif
The Clausius-Mossotti equation is used when there is no
contribution from permanent electric dipole moment to the
polarization, either because the molecules are non-polar or
because the frequency of the applied field is so high that the
molecule can not orientate quickly enough to follow the change in
direction of the field.
Contoh:
Permitivitas relatif suatu zat diukur dengan membandingkan
kapasitansi kapasitor dengan dan tanpa adanya sampel masingmasing C dan Co menggunakan hubungan:
 r  C Co
Permitivitas relatif kamper diukur pada berbagai temperatur,
tabel 4. Tentukan momen dipol dan polarisabilitas volume molekul.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 35
Contoh:
T/oC
ρ/(gcm-3)
0
20
40
60
80
100
120
140
160
200
0.99
0.99
0.99
0.99
0.99
0.99
0.97
0.96
0.95
0.91
εr=C/Co
12.50
11.40
10.80
10.00
9.50
8.90
8.10
7.60
7.11
6.21
Equation 19 implies that the
polarizability
and
permanent
electric dipole moment of the
molecules in a sample can be
determined by measuring  r at a
series of temperatures, calculating Pm, and plotting it against
1/T. The slope of the graph is
N A  2 9 o k
and its intercept at 1/T=0 is
N A 3 o
We need to calculate  r  1  r  2 at each temperature, and then
multiply by M/ρ to form Pm.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 36
Jawab:
T/oC
0
20
40
60
80
100
120
140
160
200
(103 K)/T
3.66
3.41
3.19
3.00
2.83
2.68
2.54
2.42
2.31
2.11
εr
(εr -1)/(εr +2)
12.50
0.793
11.40
0.776
10.80
0.766
10.00
0.750
9.50
0.739
8.90
0.725
8.10
0.703
7.60
0.688
7.11
0.670
6.21
0.634
Pm/(cm3 mol-1)
122
119
118
115
114
111
110
109
107
106
Hasilnya adalah:
1. momen dipol μ= 4,46.10
-30
2. Polarizabilitas, α’ = 3,3.10
Cm = 1,34 D.
-23
3
cm .
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 37
Tugas 1
1. Gunakan software kimia untuk menentukan kepolaran
molekul:
•
ClF3, O3, H2O2.
•
SO3, XeF4, SF4.
•
Metil benzena (toluena), dimetil benzena.
2. Polarisasi molar (persamaan 20) uap fluorobenzena
berubah secara linier terhadap T-1, yaitu 70,62
cm3/mol
pada
351,0K
dan 62,47 cm3/mol pada
423,2K. Hitung polarisabilitas dan momen dipol molekul.
3. Pada 0oC, polarisasi molar trifluoroklorida cair adalah
27,18 cm3/mol dan kerapatannya 1,89 g/cm3. Hitung
permitivitas relatif cairan.
4. Polarisabilitas volume H2O adalah 1,48.10-24 cm3.
Hitung momen dipol molekul (tambahan pada momen
dipol permanen) yang diinduksi oleh medan listrik
dengan kekuatan 1,0 kV/cm.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 38
Tugas 2
1. Polarisabilitas volume NH3 adalah 2,22.10-30 cm3.
Hitung momen dipol molekul (tambahan pada momen
dipol permanen) yang diinduksi oleh medan listrik
dengan kekuatan 15,0 kV/cm.
2. Momen dipol dan polarisabilitas volume klorobenzena
masing-masing adalah 1,57 D dan 1,23.10-23 cm3.
Perkirakan permitivitas relatifnya pada 25 oC, bila
kerapatannya 1,173 g/cm3.
3. Momen dipol dan polarisabilitas volume bromobenzena
masing-masing adalah 5,17.10-30 Cm dan 1,5.10-29 m3.
Perkirakan permitivitas relatifnya pada 25 oC, bila
kerapatannya 1491 kg/m3.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 39
Tugas 3
1. Molekul H2O (μ=1,85 D) mendekati suatu anion. Bagaimana
orientasi molekul H2O yang lebih disukai? Hitung medan listrik
(dalam volt/m) yang dialami oleh anion bila dipol air berjarak :
(a) 1,0 nm, (b) 0,3 nm, dan (c) 30 nm dari ion.
2. Perhitungan orbital molekul dapat digunakan untuk memprediksi
struktur kompleks intermolekul. Ikatan-H antara basa purin
dan pirimidin adalah penyebab struktur double helix DNA.
Anggap bahwa metil-adenin dan metil-timin sebagai model
kedua basa yang dapat membentuk ik-H dalam DNA. Gunakan
software pemodelan molekul dan metoda komputasi untuk: (a).
menghitung muatan atom pada metil-adenin dan metil-timin.
(b). Berdasarkan tabulasi muatan atom, tunjukkan atom-atom
dalam metil-adenin dan metil-timin yang mungkin terlibat dalam
ikatan-H. (c). Gambarkan semua kemungkinan pasangan adenintimin yang dapat diikat ikatan-H, dengan menganggap penataan
linier fragmen A-H...B lebih disukai dalam DNA. (d) Lakukan
optimasi untuk panataan molekul yang lebih tepat. (e)
bandingkan hasil (c) dan (d) dengan DNA yang terjadi secara
alami. (e). Lakukan (a)-(e) untuk pasangan sitosin dan guanin.
Kimia Supramolekul: Sifat-sifat listrik molekul, Dr. Parsaoran Siahaan, September - Oktober 2014, 40
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Pemodelan Pengaruh Ikatan H terhadap Waktu Relaksasi T1 13C