由耦合簇理論計算建立用於電荷自洽密度泛函緊束縛法參數化程序的位能函式庫

Abstract

電荷自洽密度泛函緊束縛法(以下簡稱SCC-DFTB)是量子化學領域中一種強大的半經驗方法，可應用於大尺度的化學分子系統的計算。但是SCC-DFTB仍然存在一些應用上的限制，第一個是以目前的SCC-DFTB參數組無法同時得到精確的能量、平衡結構和振動頻率，這是由於目前該方法在參數化程序中使用太少的參考位能面來擬合參數；第二個限制則是來自目前的SCC-DFTB參數組只能應用在少部分特定元素的計算。為了克服這些限制，在參數化的程序中必須使用多樣化的參考位能面來擬合各種元素間不同的鍵結狀態。在我們快速的參數化程序中，大多數高階的精確量子化學方法都因為太過於昂貴而不適用於產生這些參考位能面，因此，我們建構出一種類力場的位能函數，利用四階泰勒近似來展開這些位能函數。藉由精確的耦合簇理論計算，我們的位能函數不僅提供精確的位能面，並且節省了許多計算的時間。我們建構的位能函式庫總共包含了74種常見化學分子的位能函數，這些分子不但包含了週期表中前三週期的元素，並且存在這些元素之間最典型的鍵結狀態。在建構位能函式庫的過程中，我們設計了驗證程序來評估其精確性；在擬合函數的程序中，我們將每個位能函數的均方根誤差值控制在小於10-4 a.u.；另外我們也將這些位能函數實作到可被Gaussian09程式調用的外部程式當中，並進行結構優化和振動頻率計算。對於所有選定的化學分子，我們的位能函數可以得到和耦合簇理論計算(CCSD(T)/cc-pVTZ)幾乎相同的平衡結構和振動頻率，而且振動頻率的誤差皆小於10cm-1。

The SCC-DFTB method is a powerful semi-empirical method of quantum chemistry, which is able to treat huge molecular systems. However, SCC-DFTB has certain limitations, which diminish its strength for particular chemical applications. The first limitation concerns the fact that accurate energies, equilibrium geometries, and vibrational frequencies cannot be obtained with the existing parameter sets simultaneously. In the current parameterization of SCC-DFTB, insufficient number of reference potential energy surfaces were used for determination of the parameters. The second limitation comes from the fact that the current SCC-DFTB parameter sets are available only for few selected elements. To overcome those limitations, numerous reference potential energy surfaces representing various bonding mechanisms between atoms are required in the parameterization process. For generating reference potential energy surfaces usable in a fast parameterization process, most of high-level accurate quantum chemical methods are too expensive to be employed. Therefore, we construct a collection of force-field like potential energy functions on the 4-th order Taylor approximation to expand those functions. Generated by accurate Coupled cluster calculations, our potential energy function not only provide us with accurate potential energy surfaces but also allow for substantial savings in the computational time. The final library of potential energy functions were determined for 74 common molecules containing the elements of the first, second, and third row of the periodic table of elements. The list of these molecules attempts to represent the most typical bonding situations between these elements. We conclude the derivation of the library of potential energy functions by presenting a verification algorithm designed to validate the accuracy of our library. In the fitting process, we are able to control the RMS error to be less than 10-4 a.u. in all the studied cases. We have also implemented each of potential energy function as an external program, which can be invoked from the Gaussian09 program, for performing geometry optimization and calculating vibrational frequencies. In all of studied cases, our library of potential energy functions can reproduce the equilibrium geometry and vibrational frequencies giving results almost identical with those from the CCSD(T)/cc-pVTZ calculation. For all the calculated vibrational frequencies, the error to CCSD(T) is smaller than 10 cm-1.