| Summary: | 碩士 === 國立臺灣大學 === 化學工程學研究所 === 105 === The two-phase thermodynamic (2PT) method is a method which extracts the atomic data (position and velocity) and systematic data (density and classical energy) from molecular dynamic (MD) simulation to determine thermodynamic properties rapidly and accurately, especially absolute entropy and free energy. In 2PT method, it assumes that atoms in a system are all in vibrational motion and the vibrational density of state (DOS) is determined by the Fourier transform of the velocity autocorrelation (VAC) function. With another assumption, considering the vibrational motion is harmonic, the quantum statistic can be applied to calculate the entropy and free energy. According to the fact that low frequency vibration is usually anharmonic, the DOS is decomposed to a gas-like (non-harmonic) and a solid-like (harmonic) component by a fluidicity parameter in 2PT method. The partition function applied to the gas-like component is hard sphere/rigid rotor statistics so that the 2PT method can be extended to gas and liquid system from a short (within 20 ps) MD simulation. The thermodynamics properties calculated by 2PT method always give high accuracy for pure fluids, as well as mixtures. Despite of its success, recently Desjarlais noted that 2PT method always overestimate the entropy of liquid metals. That is to say, predicting the thermodynamic properties of conformational complex molecules by 2PT method still has a development space. In the first part in this research, a further work following the suggestion proposed by Desjarlais in gas-like DOS, we propose a new approach to determine the fluidicity which can be easily implemented in a computer code. The application of this new approach to Lennard-Jones fluids, water and common organic fluids provides an information that the entropy determined from using the Gaussian memory function for the gas-like component (denoted as 2PT-GMF) is always lower than that determined from that using delta memory function (denoted as 2PT-δMF). In Lennard-Jones cases the 2PT-GMF method (with an absolute average relative error of 1 % compared to the results from MBWR EOS) is usually more accurate 2PT-δMF (AARD = 2 %) in the liquid and supercritical regions; whereas, in other phases, the 2PT-GMF method does not provide better approach than 2PT-δMF. Moreover, in water and common organic fluids cases, we find the results from 2PT-GMF method are similar to those from 2PT-δMF (within 1% relative difference).
In the second part, considering the conformation of molecules, the anharmonic effects from torsions play an important role in vibrational mode. In 2PT method, the atomic velocity in Cartesian coordinates is used to construct the vibrational DOS so that the anharmonic effects may be ignored. In this work, we will develop the 2PT method taking torsions into account. After constructing the DOS based on internal coordinates, the 2PT method decomposes the DOS into a gas-like (free rotation) and a solid-like (harmonic vibration) component. The thermodynamic properties associated with each component of DOS can be obtained by a suitable quantum statistics. In this part of thesis, we examine the vibrational energy and entropy of ethane over a wide range of temperatures (200 K to 1000 K) and compare our results to the theoretical model proposed by Pitzer and Gwinn and the revised form proposed by McClurg et al. We find that the 2PT method gives higher value of energy and entropy at high temperature region, which means the 2PT model can include more anharmonic effects.
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