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: Assoc Prof Dr Pham Van Tat 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 Chapter 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 2   c/K T (1.31)        u   d sin  d  sin  d  exp   k T   r dr 0 NA  2u d  d      B 1  exp   u / k T    12(k T ) B B H 0u (1.35)    drdr d  d   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 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 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 Several important functions are built to calculate 5    ij12  ij6  q q  u (rij )    4 ij  12    f1 (rij ) i j    4 rij  rij  i 1 j 1   rij  5  qi q j  Cnij  r u (rij )   Deij e ij ij  f1a (rij )   f (rij )  n 4 o rij  i 1 j 1  n 6,8,10 rij  5  q q  Cnij a r u ( rij )   Deij e ij ij  f1b (rij )   f (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 2.7 Calculating by COSMO model 2.8 Density function theory (DFT) Chapter 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 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 2000 pVDZ pVTZ pV23Z 1500 EH/ mH EH/ mH 2000 1000 pVDZ pVTZ pV23Z 1500 1000 500 500 -500 -1000 -1500 -500 10 Orientation: L EH/ mH EH/ mH Orientation: H 10 r/Å 2000 1500 pVDZ pVTZ pV23Z 1000 500 1500 pVDZ pVTZ pV23Z 1000 500 -500 -1000 -500 -1500 -1000 -1500 -2000 r/Å 2000 -2000 Orientation: T 10 r/Å -2500 Orientation: X 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 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 N-A -2,5481410 3,42178 2,41434 N-M 2,0509010 4,50124 2,17703 A-A -4,8562910 4,30154 3,04527 A-M 2,0083610 4,26305 2,83394 M-M -1,2112810 4,59863 3,12889 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 -100 -100 B2(T)/cm3.mol-1 B2(T)/cm mol -1 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 hệ Cl2 từ phương trình (1.34) so sánh với hàm (2.4)-(a), (2.5)-(b) 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 20 10 -0.010 -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 0.2 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 lỏng–hơi P-x-y hỗn hợp CO (1) 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 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 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 lỏng T-x-y 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 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 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 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 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 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 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 In the future, this research will use the 5-site Lennard-Jones and Morse potential functions to determine the parameter set for virial coefficient calculation and GEMC simulation These parameters are also used for GEMC-NVT or GEMC-NPT simulations to calculate thermodynamic values Then, using the equations of Deiters, Peng-Robinson, RedlichKwong, Redlich-Kwong-Soave and artificial neural networks to evaluate the calculation results for many substances to meet practical needs in research and chemical manufacturing industry LIST OF PUBLICATIONS Nguyen Thanh Đuoc, Nguyen Thi Ai Nhung, Tran Duong, Pham Van Tat, Practical intermolecular potentials and second virial coefficients for energy and environmental researches, Journal of Science and Technology, Vol 52-No.2B, p.233-241, ISSN 0866708X (2014) Nguyen Thanh Đuoc, Nguyen Thi Ai Nhung, Tran Duong, Pham Van Tat, Thermodynamic properties of vapor-liquid equilibria for gases CO and N2 in mixture of greenhouse gases, Journal of Science and Technology, Vol 52-No.4A, p.205-213, ISSN 0866708X (2014) Nguyen Thanh Đuoc, Nguyen Thi Ai Nhung, Tran Duong, Pham Van Tat, Prediction of second virial coefficients of gases chlorine, nitrogen, carbon monoxide and argon using artificial neural network and virial equation of state, Journal of Chemistry, Vol 52– issue 5A, p.208-214, ISSN 08667144 (2014) Nguyen Thanh Đuoc, Nguyen Thi Ai Nhung, Tran Duong, Pham Van Tat, Ab initio Intermolecular Potentials and Calculation of Second Virial Coefficients for The Cl2-Cl2 dimer, Smart Science, Vol.3,No.4,p.193-201, ISSN 2308-047, (2015) Nguyen Thanh Đuoc, Nguyen Thi Ai Nhung, Tran Duong, Pham Nu Ngoc Han, Pham Van Tat, Vapor-liquid equilibria of binary system CO and Cl2 in mixture of greenhouse gases using quantum calculation., Journal of Chemistry, Vol 54 - No.2, p.145-152, DOI: 10.15625/0866-7144.2016-00250, (2016) Nguyen Thanh Đuoc, Tran Duong, Pham Van Tat, Calculation of second virial coefficients of gases Cl2, N2, CO and Ar combing virial equation of state and multivariate model, Journal of Science and Technology - Hue College of Sciences, Vol 13, No.2, p.25-37, ISSN 2354-0842, (2018) 24 Nguyen Thanh Đuoc, Tran Duong, Pham Van Tat, Calculation of virial coefficients and vapor pressure of system CO-CO using ab initio quantum calculation, Journal of Science Hue University: Natural Sciences, Volume 128, No 1A, p.13-25, ISSN 1859-1388, DOI: 10.26459/hueuni-jns.v128i1A.5055, (2019) REFERENCES [1] A K Sum and S I Sandler (2002), “Ab initio pair potentials and phase equilibria predictions of halogenated compounds”, Fluid Phase Equilib., 199:5 – 13 [2] J H Dymond and E B Smith (1980), “The Virial Coefficients of Pure Gases and Mixtures”, Clarendon Press, Oxford [3] K Leonhard and U K Deiters (2002), “Monte Carlo simulations of nitrogen using an ab initio potential, Mol Phys., 100:2571 – 2585 [4] Klamt (1998), “A COSMO and COSMO-RS”, In Encyclopedia of Computational Chemistry; Schleyer, P v R., Ed.; Chichester [5] P E S Wormer (2005), “Second virial coefficients of asymmetric top molecules”, J Phys Chem., 122:184301 – 184307 [6] R Stryjek; J H Vera (1986), “PRSV: An improved Peng– Robinson equation of state for pure compounds and mixtures”, The Canadian Journal of Chemical Engineering, 64 (2): 323–333 [7] D R Lide (2000), “Handbook of Chemistry and Physics”, CRC Press, Raton, 85th edition [8] U K Deiters, ThermoC project homepage: http://thermoc.unikoeln.de/thermoc/start.php 25 ... 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... 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... 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