Tính toán cân bằng lỏng hơi của ar, n2, cl2, CO bằng phương pháp hóa lượng tử và mô phỏng toàn cục monte carlo tt tiếng anh

HUE UNIVERSITY
UNIVERSITY OF SCIENCES

NGUYEN THANH ĐUOC

CACULATION OF THE LIQUID-VAPOR EQUILIBRIA OF Ar,
N2, Cl2, CO USING QUANTUM CHEMICAL METHOD AND
GIBBS ENSEMBLE MONTE CARLO SIMULATION

Major: Theoretical chemistry and Physical chemistry
Code: 944.01.19

SUMMARY PH.D. THESIS IN THEORETICAL CHEMISTRY
AND PHYSICAL CHEMISTRY

HUE, YEAR 2020


The thesis was completed at the Department of Chemistry, University
of Science – Hue University.

Supervisors:

Reviewer 1:
Reviewer 2:
Reviewer 3:

1. Assoc. Prof. Dr. Pham Van Tat
2. Assoc. Prof. Dr. Tran Duong

PREFACE
The study of thermodynamic properties of liquid-vapor equilibria
systems is based on modern quantum chemical calculation combined
with GEMC simulation to calculate thermodynamic data for intentional
substances to have meaning in practice. These data are not only needed
in basic scientific research but also have many practical applications.
Therefore, the study of liquid-vapor equilibria of Ar, N 2, Cl2 and CO
also has a great significance in solving the problems of liquid fuels,
agricultural chemistry, environmental treatment, metallurgy industry,
petrochemical, synthetic materials, pharmaceutical chemistry, food
chemistry and solvents. However, these data are not always fully
measured experimentally, especially when experiments are conducted
in hazardous environments or very complex experiments in practice or
it is almost unable to perform and meet all the requirements necessary
for research and practice. For that reason, I choose the topic:
“Calculation of the liquid-vapor equilibria of Ar, N2, Cl2, CO using
quantum chemical method and Gibbs Ensemble Monte Carlo
simulation”.
Research objectives
To calculate second virial coefficients and determine thermodynamic
values of liquid-vapor equilibria for Ar, N 2, Cl2, CO by quantum
chemical method and Gibbs Ensemble Monte Carlo simulation.
Scientific significance
The thesis offers a new research way- that is to calculate the
thermodynamic values of liquid-vapor equilibria such as critical
pressure, enthalpy, entropy, vapor pressure, vapor density and liquid
density for N2 and CO gases by the theoretical method. In addition, this
method is also used to calculate second virial coefficients for Ar, N 2, Cl2
and CO from the optimal correction parameters of the building potential
function. The advantages of the method used in this thesis are to

overcome the difficulties that the experimental method is difficult to
response in all conditions, and the results obtained from the research
theoretical method also appling the practical needs.
New contributions: Developing new 5-site ab initio intermolecular
interaction potential function and calculating second virial coefficients
to evaluate the potential functions used for GEMC simulation.
1


Chapter 1. OVERVIEW
Introduce the theoretical content used in the study
1.1. The basis of quantum theory.
1.2. The basic sets function
1.3. Intermolecular interaction potential functions
1.4. The equation of state (EOS)
1.5. The second virial coefficients
Expressions for calculating second virial coefficients
B2 (T ) / (cm3mol  1) a  b exp
o

Bcl 
B2 (T ) 

NA
4

2





c/K
T

(1.31)











u




d sin  d  sin  d  exp   k T   1 r dr
0

0

NA



2u d  1 d  2

0




0




B

1

1  exp   u / k T   1  12(k T )
B

2

B

H 0u

2

(1.35)


  drdr d  d 

1

2

1

2

(1.36)

1.6. Ensemble Gibbs Monte Carlo simulation (GEMC)
Antoine equation
B
ln P A 
T C

(1.42)
1.7. Principal component analysis
1.8. Artificial neural network
1.9. The optimization algorithm
1.10. The formula for evaluating errors
Chapter 2. CONTENT AND RESEARCH METHODS
2.1. General diagram of the research process
The work done in this thesis is shown in the following diagram

2

2.2. Data and software
2.3. Ab initio energy calculations
2.4. Constructing molecular interaction potential functions
Ab initio potential function is built according to the following steps

3


Several important functions are built to calculate
5
5 
  ij12  ij6 
q .q 
u (rij )    4 ij  12
 6   f1 (rij ) i j 


4 0 rij 
rij 
i 1 j 1 
 rij

5
5 
qi .q j 
Cnij
 r
u (rij )   Deij e ij ij  f1a (rij ) 
 f 2 (rij )


n
4 o rij 
i 1 j 1 
n 6,8,10 rij


5
5 
q .q 
Cnij
a r
u ( rij )   Deij e ij ij  f1b (rij ) 
 f 2 (rij ) i j 
n
4 o rij 
i 1 j 1 
n 6,8,10,12 rij


(2.3)
(2.4)
(2.5)

2.5. Determining the second virial coefficients
The method of calculating the second virial coefficient for Ar, N2, Cl2,
CO is shown in the following diagram

2.6. Perform simulation of liquid vapor equilibria
The process of performing GEMC-NVT simulations is as follows

4


2.7. Calculating by COSMO model
2.8. Density function theory (DFT)
Chapter 3. RESULTS AND DISCUSSION
3.1. Building interaction potential surface
3.1.1. The potential surface of Ar
The ab initio interaction energy of Ar-Ar is calculated by
CCSD(T)/aug-cc-pVmZ (m = 2, 3). Then extrapolate the ab initio
interaction energy to the CCSD(T)/aug-cc-pV23Z basis set. The results
are shown in Figure 3.1

Figure 3.1. Ab initio potential surface of Ar-Ar dimer
3.1.2. Potential energy surfaces of N2
The ab initio interaction energy of N2-N2 is calculated by
CCSD(T)/aug-cc-pVmZ (m = 2, 3, 23) for four special orientations.

5


Orientation L

Orientation H

Orientation X

Orientation T

Figure 3.2. Ab initio potential surface that the special
configuration of N2-N2 dimer

Figure 3.2. Ab initio potential surface that the special orientations of
N2-N2 dimer
3.1.3. Potential energy surfaces of Cl2
The ab initio interaction energy of Cl 2-Cl2 is calculated by
CCSD(T)/aug-cc-pVmZ (m = 2, 3, 23) for four special orientations.

Figure 3.3. Ab initio potential surface of Cl2-Cl2 dimer for L and H
orientations
6


2000

pVDZ
pVTZ
pV23Z

1500

EH/ mH

EH/ mH

2000

1000

pVDZ
pVTZ
pV23Z

1500
1000
500
0

500

-500
-1000

0

-1500
-500

5

6

7

8

9

10

Orientation: L

EH/ mH

EH/ mH

4

5

6

7

Orientation: H

8

9

10

r/Å

2000

1500

pVDZ

pVTZ
pV23Z

1000
500

1500

pVDZ
pVTZ
pV23Z

1000
500
0
-500

0

-1000

-500

-1500

-1000
-1500

-2000

r/Å

2000

-2000
3

4

5

6

7

Orientation: T

8

9

10

r/Å

-2500

3

4

5

6

7

Orientation: X

8

9

10

r/Å

Figure 3.4. Ab initio potential surface of Cl2-Cl2 dimer for T and X
orientations
3.1.4. Potential energy surfaces of CO
The ab initio interaction energy of CO-CO is calculated by
CCSD(T)/aug-cc-pVmZ (m = 2, 3, 23) for four special orientations.

Figure 3.5. Ab initio potential surface of CO-CO dimer for special
orientations

7


Discuss: From the results of calculating the ab initio interaction energy

for Ar, N2, Cl2 and CO, the selection of CCSD(T)/aug-cc-pV23Z
extrapolation basis set to calculate the parameter set of potential
functions (2.3), (2.4 ) and (2.5) are appropriate because this is the basis
set with the ab initio lowest interaction energy.
3.2. Construction of interaction potential function.
3.2.1. Interaction potential of Ar
The ab initio interaction energy of the Ar-Ar dimer is applied to the
potential function (2.3) to determine the two optimal calibration
parameters  and , as shown in Table 3.1.
Table 3.1. Optimize the parameters in equation (2.3) for Ar-Ar dimer;
with the atomic charge of qAr = 0,000
Optimized parameters of Ar-Ar dimer
Ab initio energy
/ Å
/EH
aug-cc-pVDZ
3,64305
192,62175
aug-cc-pVTZ
3,48208
309,77526
aug-cc-pV23Z
3,42641
365,70940
Tham khảo
3,42
372
[7]
3.2.2. Interaction potential of N2
The ab initio interaction energy of the N2-N2 dimer is used to fit

potential functions (2.3) and (2.4) to determine the optimal calibration
parameter set using the non-linear least squares technique, shown in
Table 3.2 and 3.3
Table 3.2. Optimize the parameters of equation (2.3) for the interactions
of N2-N2; atomic charge qN = 0,0; qA/e = -0,0785; qM =
-2qA. EH Hartree energy.
Interactions
 Å
/ Å-1

N-N
6,03880103
3,70241
2,85113
3
N-A
-2,5481410
3,42178
2,41434
3
N-M
2,0509010
4,50124
2,17703
3
A-A
-4,8562910
4,30154
3,04527
3

A-M
2,0083610
4,26305
2,83394
3
M-M
-1,2112810
4,59863
3,12889

8


Table 3.3. Optimize the parameters of equation (2.4) for the interactions
of N2-N2; select ij = 2,0Å-1 to be assumed; qN = 0,0; qA/e = -0,0785; qM =
-2qA; EH Hartree energy.
(C10/ EH)
Å10
Interactions
De/EH
α/ Å-1 β/ Å-1 (C6/ EH) Å6 (C8/ EH) Å8
N-N

8,031×102

N-A

-2,443×104

N-M

9,773×104

3,890 -1,061

2,357×104 -1,968×105 9,897×104

A-A

-3,738×103

2,601 5,701

7,743×103

6,132×103 7,739×103

A-M

2,776×103

2,898 -6,953 -7,366×102

6,722×103 -3,054×104

M-M

-2,535×104

2,544 -2,413 -6,748×102 -5,092×103 2,801×103

3,971 6,479 -1,035×104

3,752 8,308

5,657×104 -3,315×104

7,766×102 -7,083×103 8,569×104

3.2.3. Interaction potential of Cl2
The ab initio interaction energy of the Cl2-Cl2 dimer is used to fit
potential functions (2.4) and (2.5) to determine the optimal calibration
parameter set using the non-linear least squares technique, shown in
Table 3.4 and 3.5
Table 3.4. The optimal parameters of equation (2.4) for Cl 2-Cl2
interactions; select ij = 2,0Å-1 to be assumed. Eigen charge for Cl2
molecules: qCl = 0; qN/e = 0,0783; qM = -2qN; EH Hartree energy.
Interaction

Cl-Cl
Cl-N
Cl-M
N-N
N-M
M-M

De/EH
-1,300.100
-5,649.100
2,780.100
3,192.101

-1,620.101
-4,245.101

a/ Å-1
1,360
1,286
1,070
1,951
1,979
1,096

b/ Å-1
-0,081
-5,149
-2,074
-0,689
-0,342
-1,479

(C6/ EH) Å6 (C8/ EH) Å8 (C10/ EH) Å10
-2,576.100
1,426.101 -3,503.101
-7,132.101
3,761.102 -6,514.102
2
1,090.10
-6,449.102
1,198.103
1,743.102 -9,437.102
1,556.103

2
2
-1,222.10
7,723.10
-1,049.103
-1,278.102
4,217.102 -1,685.103

Table 3.5. The optimal parameters of equation (2.5) for Cl 2-Cl2
interactions; select ij = 2,0Å-1 to be assumed. Eigen charge for Cl2: qCl
= 0; qN/e = 0,0783; qM = -2qN; EH Hartree energy.
Interaction

De/EH

a/ Å-1 b/ Å-1

(C6/ EH) (C8/ EH)
Å8
Å6

(C10/ EH) (C12/ EH)
Å12
Å10

Cl-Cl

3,046.101

2,520 -0,225

5,047.101 -2,794.101

3,642.102 -2,116.102

9


Cl-N

-2,781.101

2,269 -0,043 -1,703.102 3,353.102 -1,500.103 1,537.103

Cl-M

6,524.101

2,938 0,280

1,448.102 -1,240.102

N-N

5,116.101

2,141 -0,255

3,163.102 -2,657.102 -2,259.102 1,404.103

N-M

-4,467.10

1

M-M

-2,554.101

2,852 0,128 -1,909.102 -6,620.102

2,068.103 -2,185.103
5,222.103 -8,645.103

1,981 -0,034 -6,141.101 2,261.103 -1,624.104 2,434.104

3.2.4. Interaction potential of CO
The ab initio interaction energy of the CO-CO dimer is used to fit
potential functions (2.3) and (2.4) to determine the optimal calibration
parameter set using the non-linear least squares technique, shown in
Table 3.6 and 3.7
Table 3.6. Optimize parameters of equation (2.3) for CO-CO; charge of
qN = 0,288; qA/e = -0,288; qM = 2qA; EH Hartree energy.
Interaction
s
O-O
O-A
O-M
O-N

O-C
A-A
A-M
A-N
A-C
M-M
M-N
M-C
N-N
N-C
C-C

 Å
4,01587
5,44554
1,30102
1,99607
6,84265
1,42979
2,65758
9,50862
4,94311
1,29411
7,18785
1,15666
1,12357
9,54075
2,62695



8,30828103
-7,92058103
-7,41641103
-6,74762103
-1,03540103
2,35691103
7,74247103
-7,36597103
7,76582103
-1,09881103
-1,26157103
-5,09211103
5,65726103
-1,96816103
6,13199103

/ Å-1
1,23734
8,59447
1,17546
1,91608
9,45690
4,46329
3,91091
3,61241
3,30443
4,49248
4,42874
4,20080
4,71344

1,57037
1,82830

Bảng 3.7. Optimize parameters of equation (2.4) for the interactions of
CO-CO; select ij = 2,0Å-1 to be assumed; EH Hartree energy.
Interactions
De/EH
O-O
1,023×101
O-A
2,680×100
O-M
-8,881×10-1
O-N
-2,131×101
O-C
1,251×101

(C10/ EH)
α/ Å-1 β/ Å-1 (C6/ EH) Å6 (C8/ EH) Å8
Å10
1,832 10,523 4,785×102 -2,591×103 4,945×103
1,473 -2,100 6,559×101 -2,799×102 9,257×102
1,497 5,168 -1,609×102 1,497×103 -4,236×103
2,533 0,403 8,781×102 -2,752×103 1,201×103
1,670 1,675 -3,830×102 4,268×103 -1,087×104

10

A-A
A-M
A-N
A-C
M-M
M-N
M-C
N-N
N-C
C-C

-3,407×100
-3,103×10-1
2,458×104
3,503×100
3,660×101
-1,214×103
1,635×103
-1,877×101
-2,468×101
7,176×100

1,709
1,381
5,415
2,591
1,901
3,850
3,391
1,917

1,772
2,067

2,697
0,953
0,210
0,485
2,906
1,335
1,618
0,308
3,222
2,088

6,326×102
-2,332×102
-1,227×103
8,651×102
-2,142×103
3,851×102
4,852×102
3,153×103
-2,679×101
-1,447×103

7,776×103 -3,481×104
-2,804×102 3,090×103
6,422×103 -1,170×104
-1,369×104 4,118×104
6,111×103 -1,087×103

2,335×103 -1,118×104
-4,577×103 1,154×104
-1,606×104 2,806×104
-6,220×102 1,312×103
1,564×104 -4,352×103

Discuss: The ab initio interaction energy uses to fit of potential
functions (2.3), (2.4) and (2.5) to determine the optimal calibration
parameter set that give good results after fitting ab initio energy by the
Genetic algorithm and the Levenberg-Marquardt algorithm. Therefore,
the potential functions (2.3), (2.4) and (2.5) built in this study are
reliable with the private parameters set for specific substances.
3.3. The second virial coefficients
3.3.1. Determine the second virial coefficient from the potential
function and the state equation (EOS)
3.3.1.1. The second virial coefficient of Ar
The second virial coefficient B2(T) of Ar-Ar is calculated from the
parameter set obtained by the potential function (2.3) and is calculated
using the EOS (1.31). All of these values are shown in Figure 3.6

Figure 3.6. The second virial coefficient of argon.
3.3.1.2. The second virial coefficient of N2
11


The second virial coefficient B2(T) of N2-N2 is calculated by equation
(1.35) and (1.36) from the parameter set of potential functions (2.3),
(2.4) and the state equation, shown in Figure 3.7

Figure 3.7. The second virial coefficient of N2-N2 dimer

3.3.1.3. The second virial coefficient of Cl2
The second virial coefficient B2(T) of Cl2-Cl2 is calculated from the
parameter set of potential functions (2.4), (2.5) and D-EOS equation,
shown in Figure 3.8
100

100

0

-100

-100

B2(T)/cm3.mol-1

3

B2(T)/cm .mol

-1

0

----aug-cc-pVDZ
aug-cc-pVDZ
aug-cc-pVTZ
…..aug-cc-pVTZ
aug-cc-pV23Z
 aug-cc-pV23Z

Deiters EOS
○D-EOS
Exp.
 TN

-200
-300
-400
-500

----aug-cc-pVDZ
aug-cc-pVDZ
…..aug-cc-pVTZ
aug-cc-pVTZ
 aug-cc-pV23Z
aug-cc-pV23Z
○D-EOS
Deiters EOS
 TN Exp.

-200
-300
-400
-500

-600

-600

-700

-700

-800
100

a)

200

300

400

500

600

700

800

-800

900

100

T/K

200

b)

300

400

500

600

700

800

900

T/K

Hình 3.13. Hệ số virial của hệ Cl2 từ phương trình (1.34) được so sánh
với các hàm thế (2.4)-(a), (2.5)-(b) và dữ liệu thực nghiệm.

Figure 3.8. The second virial coefficient of Cl2 from D-EOS equation is
compared with equation (2.4)-a, (2.5)-b and experimental data.
3.3.1.4. The second virial coefficient of CO

12

The second virial coefficient B2(T) of CO-CO is calculated from the
parameter set of potential functions (2.3), (2.4) and the state equation,
shown in Figure 3.9.

Figure 3.9. The second virial coefficient of CO-CO dimer
Discuss: The parameter sets calculated from potential functions (2.3),
(2.4) and (2.5) used to calculate the second virial coefficients for the
substances all give good results with the experimental data. In addition,
when using state equations to evaluate the results of calculating the
second virial coefficients from potential functions (2.3), (2.4) and (2.5),
we find that the result of the second virial coefficient calculated are not
much different from each other and with experimental data.
3.3.2. Determination of second virial coefficients from artificial
neural networks
The second virial coefficients can also be calculated from artificial
neural networks by I(5)-HL(6)-O(3) type for Ar, N 2, Cl2 and CO. The
results obtained from artificial neural networks, state equations and
experimental data are shown in Figure 3.10

13


Figure 3.10. The second virial coefficients for gases
a) Argon; b) Nitrogen; c) Carbon monoxide; d) Chlorine
Finally, we find that the results of calculating the second virial
coefficient B2(T) of argon, nitrogen, chlorine and carbon monoxide by
three methods are ab initio interaction potential, state equation and
artificial neural network results are consistent with experimental data.
3.4. Thermodynamic properties of the studied substances
3.4.1. GEMC simulation

3.4.1.1. Properties of fluid structures
- Nitrogen liquid

14


b)

a)

Figure 3.11. Dependence of the distribution functions g(rN-N) and g(rM-M)
on temperature during GEMC-NVT simulation on N2
- Carbon monoxide liquid

b)

a)

d)

c)

Figure 3.12. Dependence of the distribution functions g(rC-C), g(rO-O), g(rCO) and g(rM-M) on temperature during GEMC-NVT simulation on CO
3.4.1.2. Diagram of liquid - vapor equilibria
- Nitrogen liquid
15


Figure 3.13. Diagram of liquid-vapor equilibria of nitrogen
The results of the calculation from GEMC-NVT simulation using the

parameter set of potential functions (2.3), (2.4) and the state equation of
thermodynamic values such as vapor pressure (Pv), vapor density (v),
liquid density (L), enthalpy (Hv), entropy (Sv), critical temperature
(Tc) and critical density (c) of N2 are shown in Tables 3.8, 3.9 and 3.12.
Table 3.8. Thermodynamic values of nitrogen from GEMC-NVT using
potential functions (2.4) and experimental data (Exp)
T/K

P v/
bar

Exp

V /
Exp
g.cm-3

L/
g.cm-3

Exp

Hv/
J.mol-1

Exp

Sv/
J/mol.K

Exp

6059

5819,6

86,557

83,137

70

0,349 0,39 0,0028 0,002

0,8420

0,840

80

1,001 1,37 0,0062 0,006

0,7925

0,796 5662

5464,9

70,775

68,311

90

2,532 3,61 0,0140 0,015

0,7416

0,746

4943

5039,6

54,922

55,996

100 5,810 7,79 0,0309 0,032

0,6889

0,688

3861

4498,4

38,610

44,984

110 12,316 14,67 0,0658 0,062

0,6301

0,620

3195

3762,8

29,045

34,207

120 24,452 25,13 0,1348 0,124

0,5144

0,525

2590

2607,9

21,583

21,733

Table 3.9. Thermodynamic values of nitrogen using state equation and
experimental data (Exp)
T/K
70

Pv/
bar

Exp

V/
Exp
g.cm-3

0,385 0,39 0,0019 0,002

L /
g.cm-3

Exp

Hv/
J.mol-1

Exp

Sv/
J.mol-1K-1

Exp

0,8385

0,840

5828,7

5819,6

83,2671

83,137

16


80

1,369 1,37 0,0061 0,006

0,7939

0,796 5481,5

5464,9

68,5188

68,311

90

3,605 3,61 0,0151 0,015

0,7450

0,746

5056,1

5039,6

56,1789

55,996

100 7,783 7,79 0,0320 0,032

0,6894

0,688

4509,4

4498,4

45,0940

44,984

110 14,658 14,67 0,0626 0,062

0,6215

0,620

3762,8

3762,8

34,2073

34,207

120 25,106 25,13 0,1251 0,124

0,5234

0,525

2578,4

2607,9

21,4867

21,733

- Carbon monoxide liquid

Figure 3.14. Diagram of liquid - vapor equilibria of carbon monoxide
The results of the calculation from GEMC-NVT simulation using the
parameter set of potential functions (2.3), (2.4) and the state equation of
thermodynamic values such as vapor pressure (Pv), vapor density (v),
liquid density (L), enthalpy (Hv), entropy (Sv), critical temperature
(Tc) and critical density ( c) of CO are shown in Tables 3.10, 3.11 and
3.12.
Table 3.10. Thermodynamic values of CO from GEMC-NVT using
potential functions (2.4) and experimental data (Exp)
T/K

Pv/
bar

Exp

V/
Exp
g.cm-3

L/
g.cm-3

Exp

Hv/
J.mol-1

Exp

Sv/
J.mol-1K-1

5836,918

6038

72,961

80 1,021 0,811

0,006 0,005

0,792

0,791

85 1,631 1,013

0,010 0,008

0,766

0,769 5601,989

5719

65,906

90 2,536 2,026

0,017 0,014

0,740

0,754

5378,592

5298

59,762

100 5,726 6,079

0,040 0,037

0,687

0,700

4812,418

4965

48,124

110 11,960 10,132 0,087 0,082

0,625

0,653

3859,594

4304

35,087

17


120 23,430 20,264 0,180 0,116

0,515

0,566

2280,411

3741

19,003

Table 3.11. Thermodynamic values of CO using state equation and
experimental data (Exp)
T/K

Pv/
bar

Exp

V /
Exp
g.cm-3

L/
g.cm-3

Exp

Hv/
J.mol-1

Exp

Sv/
J.mol-1K-1

6076,216

6038

75,953

80 0,837 0,811

0,004 0,005

0,800

0,791

85 1,461 1,013

0,006 0,008

0,778

0,769 5879,080

5719

69,166

90 2,385 2,026

0,010 0,014

0,755

0,754

5298

62,935

100 5,444 6,079

5664,150

0,021 0,037

0,705

0,700

5160,500

4965

51,605

110 10,666 10,132 0,042 0,082

0,647

0,653

4512,000

4304

41,018

120 18,765 20,264 0,079 0,116

0,575

0,566

3610,600

3741

30,088

Table 3.12. Critical properties of nitrogen and carbon monoxide
resulting from the GEMC-NVT simulation results using potential
equations Eq (2.3) and Eq (2.4); EOS-PR: Peng-Robinson equation of
state; Exp.: experimental values
Nitrogen
Carbon monoxide
Method
Method
c/
c/
Tc/ K
ref.
Tc/ K
Ref.
g.cm-3
g.cm-3
Eq (2.3)
Eq (2.4)
EOS-PR
Exp.

132,876

124,432
126,143
126,200

0,3284
this work
0,3125
0,3233
[92]
0,3140
[8]

Eq (2.3)
Eq (2.4)
EOS-PR
Exp.

137,961
124,386
131,634
131,910

0,333
this work
0,321
0,324
[92]
0,3010
[8]

Discuss: The calculation results from the above process is then put into
the GEMC-NVT simulation. After simulation, we obtained a diagram of
the properties of the liquid structure and the liquid-vapor equilibrium
diagram of N2 and CO. In addition, thermodynamic values such as
vapor pressure (Pv), vapor density (v), liquid density (L), enthalpy
(Hv), entropy (Sv), critical temperature (Tc) and critical density (c) of
N2 and CO calculated by GEMC-NVT simulation process and by state
equation. The results of calculating the thermodynamic values obtained
by GEMC-NVT simulation and by the state equation are very good with
experimental data.
3.4.2. COSMO model
3.4.2.1. Calculation of liquid - vapor equilibria
- Carbon monoxide liquid

18


The average charge density values surrounding the molecule are
characterized by the value m received from the COSMO calculation
results using Gaussian03TM. The surface of the charge around the CO
molecule is described in Figure 3.15.

Figure 3.15. Correlation on the surface of the charge m with the ab
initio energy. Symbol: : ab initio energy; : charge density m (e/Å2)
The vapor pressure curve of the CO-CO is shown in Figure 3.16b.
14

40

12

Pv/bar

P()Ai,(Å 2)

30
10
8
6

20

10
4
2
0
-0.010

0

-0.005

0.000

0.005

0.010

60

80

100

120

140

T/K

Mật độ điện tích bề mặt, m (e/Å 2)

a)

b)

Figure 3.16. a) The surface of the charge and b) The CO-CO vapor pressure
is determined from the COSMO calculation. Symbols: □: experimental data;
: state equation; ─: CCSD (T)/aug-cc-pVQZ calculated.

From Figure 3.16b we determine the critical temperature of the CO
system is TC = 132,91 K, the critical vapor pressure PC = 34,990 bar,
from equation (1.42) with the coefficients defined above, the pressure
the critical vapor rate of the system is determined PC = 33,8262; relative
error ARE,% = 3,3261%.
19


3.4.2.2. Phase diagram of liquid - vapor equilibrium
- Diagram of liquid equilibria at liquid-vapor at isothermal

conditions P-x-y
The density of the shielding surface area surrounding the molecule is
generated from the DFT VWN-BP/DNP energy calculation. Sigma
values of single-molecule are obtained from surface charge densities, as
depicted in Figure 3.17.

Figure 3.17. Sigma values for single CO and Cl2 molecules are
determined from COSMO calculations
The liquid-vapor equilibria diagram based on COSMO-SAC model of
CO(1) -Cl2(2) at 300K to 450K temperature is shown in Figure 3.18.
100

y1-300K
x1-350K
y1-350K
x1-400K

60

y1-400K
x1-450K

40

x2-300K
y2-300K
x2-350K

80

Ptot (M Pa)

80

Ptot (M Pa)

100

x1-300K

y2-350K
x2-400K
y2-400K

60

x2-450K
y2-450K

40

y1-450K

20

20

0

0

0.0

0.2

0.4

0.6

0.8

1.0

0.0

x1, y1 (mol)

0.2

0.4

0.6

0.8

1.0

x2, y2(mol)

Hình 3.24. Giản đồ cân bằng lỏng–hơi P-x-y của hỗn hợp CO (1) và Cl2 (2)

Figure 3.18. Diagram P-x-y liquid-vapor equilibria of CO(1) and Cl2(2)
COSMO-SAC model calculations have improved the efficiency of the
difference in liquid and vapor content when temperature increases. This
20


method is capable of calculating for most systems with the highest
accuracy. The results seem to be consistent with the NRTL and Wilson
methods, whose activity coefficients are calculated shown in the
following table
NRTL
RMS

Wilson

MRDp,
%
4,12

0,012

MDy

RMS

0,011

0,010

MRDp

,%
4,013

COSMO-SAC
MDy

RMS

0,015

0,002

MRDp,
%
5,735

MDy
0,013

- Diagram liquid component, vapor component x – y
To see the difference between the liquid component x and the vapor
component y, the diagram x-y is built based on calculations from the
activity coefficient. The liquid phase components x 1 and y1 of the first
component CO and x2 and y2 of the second component Cl2 at
temperatures 300K to 450K.
1.0

1.0

0.8

0.8

y2(mol)

y1 (m ol)

x2-y2(300K)

0.6

x1-y1 (300K)

0.4

x2-y2(350K)
x2-y2(400K)
x2-y2(450K)

0.6

0.4

x1-y1 (350K)
x1-y1 (400K)

0.2

0.2

x1-y1 (450K)

0.0

0.0
0.0

0.2

0.4

0.6

0.8

1.0

x1 (mol)

0.0

0.2

0.4

0.6

0.8

1.0

x2 (mol)

Hình 3.25. Giản đồ x–y xây dựng từ hệ số hoạt độ ở điều kiện đẳng nhiệt

Figure 3.19. The diagram of x-y from activity coefficient isothermal
- Diagram of liquid-vapor equilibria at constant pressure conditions
T-x-y
The COSMO-SAC method is also used to calculate the liquid equilibria
for the second order CO(1)-Cl2(2) system under constant pressure
conditions.

21


240

240

220

220
200

T (K )

T (K )

200
180

x1(0.02MPa)
y1(0.02MPa)
x1(0.04MPa)
y1(0.04MPa)
x1(0.06MPa)
y1(0.06MPa)
x1(0.08MPa)
y1(0.08MPa)
x1(0.09MPa)
y1(0.09MPa)

160
140
120
100
0.0

0.2

180
x2(0.02MPa)
y2(0.02MPa)
x2(0.04MPa)
y2(0.04MPa)
x2(0.06MPa)
y2(0.06MPa)
x2(0.08MPa)
y2(0.08MPa)
x2(0.09MPa)
y2(0.09MPa)

160
140
120
0.4

0.6

0.8

100

1.0

0.0

x1, y1 (mol)

0.2

0.4

0.6

0.8

1.0

x2, y2 (mol)

Hình 3.26. Giản đồ cân bằng lỏng hơi T-x-y của hệ bậc hai CO (1)-Cl2( 2)

Figure 3.20. Diagram T-x-y liquid-vapor equilibrium of CO(1)Cl2(2)
The difference between the pressure levels is also described in Figure
3.21, and the changes in the liquid and x components of CO and Cl 2 are
not significantly different, these components are close to each other.
1.0

1.0

0.8

0.8

y2 (m o l)

y1 (m o l)

x2-y2(0.01MPa)

0.6

x1-y1(0.01MPa)

0.4

x2-y2(0.03MPa)
x2-y2(0.05MPa)
x2-y2(0.07MPa)
x2-y2(0.09MPa)

0.6

0.4

x1-y1(0.03MPa)
x1-y1(0.05MPa)

0.2

0.2

x1-y1(0.07MPa)
x1-y1(0.09MPa)

0.0

0.0
0.0

0.2

0.4

0.6

0.8

1.0

x1 (mol)

0.0

0.2

0.4

0.6

0.8

1.0

x2 (mol)

Hình 3.27. Giản đồ x – y xây dựng từ hệ số hoạt độ ở các điều kiện đẳng áp

Figure 3.21. The diagram x-y from the activity coefficients at constant
Discuss: The value of the calculation results is indicated in the RMS
error, the relative deviation MRDp and MDy. From this we conclude that
the differences between the models are not significant. The liquid-vapor
equilibrium of the binary CO(1)-Cl2(2) created by COSMO-SAC model
is well suited to experimental data and to Wilson and NRTL models.
CONCLUSIONS
The thesis has achieved the following objectives
1. About ab initio interactive energy
- Building a dimer structure for research substances Ar, N 2, Cl2 and CO.
-Calculating ab initio interactive energy of four special configuration
for Ar, N2, Cl2 and CO gases.

22


2. About the ab initio potential function
- Developing a new 5-site Lennard-Jones potential function (2.3) to
determine the ,  parameters for argon and the , ,  parameter sets
for nitrogen and carbon monoxide.
- Developing and determining set of parameters for the 5-site Morse
potential function (2.4) for N 2, Cl2, CO and the 5-site Morse potential
function (2.5) for the Cl2 system.
3. About calculating second virial coefficients
- Developing new 5-site Morse interaction potential functions (2.4) and
(2.5) to calculate second virial coefficients for N2, Cl2, CO.
- The results using equations (1.31), (1.32) and (1.34) to calculate the
second virial coefficients for argon, nitrogen, chlorine and carbon
monoxide are all in accordance with the new development potential
equations and experimental values.
- The results using the neural network I(5)-HL(6)-O(3) model to
calculate the second virial coefficient for argon, nitrogen, chlorine and
carbon monoxide are consistent with the state equations and
experimental values.
4. About liquid-vapor equilibrium
- Building the structural properties and the liquid-vapor equilibria
diagram for nitrogen and carbon monoxide.
- Results of using GEMC-NVT simulation and COSMO model to
calculate thermodynamic values such as vapor pressure (P v), critical
pressure (Pc), critical temperature (Tc), vapor density (v), liquid density
(L), enthalpy (Hv), entropy (Sv) and critical density (c) of nitrogen
and carbon monoxide are all consistent with experimental values.
ORIENTATIONS

23