利用量子化學計算分子間勢能進行甲烷流體之分子動力學模擬

Abstract

我們使用HF、MP2和DFT來計算甲烷與矽烷雙體作用力，HF會產生純排斥的位能曲線，且基底對HF影響並不大。在MP2的計算中，基底會影響排斥指數項(Repulsion exponent)、平衡鍵長(Equilibrium bond length)、束縛能(Binding energy)與漸進行為(Asymptotic behavior)。比較加了BSSE與未加BSSE的結果，發現加了BSSE的計算其漸進行為會隨著基底增大而逐漸收斂至實驗值，而未加BSSE的計算則不規則的產生位能曲線，顯示BSSE對MP2方法來模擬漸近行為的重要性。我們使用大範圍的exchange-correlation functionals配對的DFT計算，並比較哪種配對較接近MP2結果。 我們接下來將量子化學計算出的位能曲線利用Lennard-Jones potentials fitting出鍵距與束縛能的參數，帶進牛頓方程式，模擬甲烷液體的平衡性質與動態性質並與實驗比較，發現模擬結果與實驗比較已經相當精確，這可說明量子力學對分子間勢能計算相當具精確性。接著利用三種位能模型去模擬甲烷實驗三相圖的氣化曲線與溶化曲線，幫助我們了解氣化曲線與溶化曲線的平衡性質與動態性質。

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order Møller-Plesset (MP2) perturbation theory and the density functional theory (DFT). The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, and compare with MP2 results. Next, we use a curve fitting method to fit the results of quantum chemistry calculation. We can get the force parameters of bond lengths and binding energies and then input them to solve Newton’s equations. To simulate the equilibrium properties and dynamics properties of methane liquid, we perform NVT ensemble molecular dynamics simulations. Our results well reproduce the experimental data. It demonstrates that quantum chemistry calculated intermolecular interaction is very good. Beside we simulate the equilibrium properties and dynamics properties along the vapor-liquid curve and solid-liquid curve in the phase diagram using three potential models.