四面體雙聚體分子之量子化學計算與分子動力學模擬

Abstract

本論文主要探討四面體雙聚體分子之量子化學計算與分子動力學模擬探討熱力學性質。我們從最簡單的四面體甲烷分子開始研究並推廣到矽烷與四氯化碳分子。我們首先準確的架構並計算出12個不同方位的能量曲線，探討方位、中間氫原子數目對能量關係、吸引力、斥力、剛體與非剛體對能量造成的影響。 在量子計算方面主要使用的方法有Hartree-Fock (HF)、Density Function Theory (DFT)、Second-order Møller-Plesset Perturbation Theory (MP2) 與Single-point Coupled Cluster with Single and Double and Perturbative Triple Excitations CCSD(T) 等計算方法。基底方面使用Pople的方法從小的基底到6-311++G (3df, 3pd)，並使用Dunning的基底 [cc-pVXZ 與aug-cc-pVXZ，其中 X = D、T、Q、5] 進行一連串完整的計算並探討能量收斂狀況。計算時中心原子距離從3.0 Å到9.0 Å，並使用四種近似法 (Extrapolation methods) 與完整基底極限展開法 (Complete Basis set limit) 得到鍵結最低能量極限值，與目前光譜實驗量測所可以測得的容許差值約在0.03 kcal/mol之內。 而在分子動力學模擬方面主要是利用Lennard-Jones (L-J) potential function 去做擬合並建構力場，先分別探討4-site與5-site的影響。4-site需要決定四個擬合參數16條方程式，5-site需要決定六個擬合參數25條方程式。利用得到的擬合參數去模擬在不同溫度、密度與壓力下Radial Distribution Function (RDF) 的平衡性質並探討溫度效應與實驗值做比較。而動態性質方面主要是研究沿著汽化線做Velocity Autocorrelation Function (VAF) 的模擬，求得擴散係數 (Diffusion Coefficient) 並與文獻上既有的實驗值做比較。最後做 X-ray散射 與Neutron散射模擬研究皆與真實文獻上實驗吻合。由上述結果可知，就我們目前所做的量子化學勢能曲線 (Potential Energy Surface) 理論計算結果與所得到的5-site理論擬合參數值皆可精準與實驗相驗證。

In this study, intermolecular interaction energy data for the tetrahedral molecule dimers have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of tetrahedral molecule properties. The full potential curves of the tetrahedral molecule dimers at 12 symmetric conformations were calculated by the supermolecule counterpoise-corrected Hartree-Fock (HF), Density Function Theory (DFT), second-order Møller-Plesset (MP2) perturbation theory and single-point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople’s medium size basis sets [up to 6-311++G (3df, 3pd)] and Dunning’s correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q, 5). For each conformer, the intermolecular carbon–carbon separation was sampled in a step 0.1 Å for a range of 3.0 ~ 9.0 Å. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well-established analytical extrapolation schemes and while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (~0.03 kcal/mol). A 4-site and 5-site potential models were used to fit the ab initio potential data. We performed molecular dynamics simulations using the ab initio force field and compared the simulation results to experiments. Quantitative agreements for the atomwise radial distribution functions, the self-diffusion coefficients, and the X-ray and Neutron diffraction scattering functions over a wide range of experimental conditions can be obtained, thus validating the ab initio force field without using experimental data a priori.