第一原理計算酸醇酯水四成分具反應性系統汽液相平衡

Abstract

具化學反應性系統（如酯化反應）之汽液相平衡資料，大多數依靠實驗量測取得，然實驗由於過於耗費人力、金錢及時間，所以本研究致力於建立一套預測模型，能夠在不使用任何實驗數據的情況下，提供可靠的反應及相平衡資料，本研究分為兩部分，第一部分為使用第一原理計算化學反應平衡常數，第二部分為使用液相模型及狀態方程式搭配上計算的反應平衡常數計算四成分汽液反應平衡。 本研究中，我們使用密度泛函理論計算參與反應物質的自由能，並藉此計算化學反應平衡常數。我們一共測試三種密度泛函模型（B3LYP、wB97X及wB97XD）並搭配四種基組（6-31g(d,p)、6-31+g(d,p)、6-311+g(d,p)、6-311+g(3d2f,2pd)）。我們將計算結果與透過實驗生成熱所計算出的反應平衡常數進行比較，發現以wB97X及wB97XD搭配6-311+g(d,p)或6-311+g(3d2f,2pd)結果較好，其反應自由能誤差大概在0.5 kcal/mol左右，小於化學精準度的誤差1 kcal/mol。 在含酸-醇-酯-水四成分系統的相平衡計算，我們使用Hayden O’Connell狀態方程式描述各成分的逸壓係數，活性係數部分則比較兩種預測型液相模型，包括COSMO-SAC及官能基法modified-UNIFAC，搭配純物質蒸氣壓計算各成分的逸度。我們測試十種四成分系統，溫度範圍由303.15 K至404.687 K、壓力由3.2 kPa至109.65 kPa，共663個數據點。結果發現兩種液相模型的表現各有優劣，以wB97XD/6-311+g(d,p)及HOC分別搭配COSMO-SAC及modified-UNIFAC的情況下，其誤差分別是壓力百分誤差8.69%及6.02%、溫度誤差3.04度及4.82度、汽相酸類莫爾誤差2.83%及1.97%、醇類3.61%及4.84%及酯類5.12%及4.27%、反應進度3.56%及2.68%。

A chemical reaction of the system (such as esterification) of the vapor-liquid equilibrium data almost rely on experimental measurements. The experiment spend too much time and money, so we are effort to establish a theoretical model to provide reliable data of chemical reaction and vapor-liquid equilibrium data. The study have the two parts, the first part is to use first-principles calculations to calculate chemical reaction equilibrium constant, the second part is to use liquid model and state equation with the equilibrium constants to calculate data of four components of vapor-liquid equilibrium with reaction. In this study, we use the density functional theory calculations to get the free energy of each component, and to calculate the equilibrium constant of chemical reactions. We test three kinds of functional (such as B3LYP, wB97X, wB97XD) and four kinds of basis set (such as 6-31g(d,p), 6-31+g(d,p), 6-311+g(d,p), 6-311+g(3d2f,2pd)). We compare the chemical reaction constants from calculated and experiments and found wB97X and wB97XD with 6-311+g(d,p) and 6-311+g(3d2f,2pd) are better results, and the reaction free energy probably in error 0.5 kcal/mol, less than chemical accuracy 1kcal/mol. In the phase and reaction equilibrium of the acid-alcohol-ester-water system, we use Hayden O'Connell state equation describes the fugacity coefficient of the components, then compare the two predictive activity coefficient models, including COSMO-SAC and functional group method modified-UNIFAC. We test ten kinds of four component system, the temperature range from 303.15 K to 404.687 K, pressure from the 3.2 kPa to 109.65 kPa, and 663 data points. It’s found that the performance of two liquid models have the advantages and disadvantages, and the best choice is using wB97XD/6-311+g(d,p) and HOC respectively with the case COSMO-SAC and modified-UNIFAC. The errors are pressure percentage 6.02% and 8.69%, temperature error 3.04 degrees and 4.82 degrees, vapor phase error of acid (2.83% and 1.97 %), alcohol (3.61% and 4.84%), esters(5.12% and 4.27%), and reaction extension(3.56% and 2.68%).