Abstract
藉由數學函數,對於基態CH2的全位能面作一完整性描述. 整個工作分成兩大步驟:首先進行ab initio計算,所採取的方法為CCSD/TZ2P;然後進行數學演算-依據非線性最小平方根法(nonlinear-least-square fitting),以得到函數中參數的最佳值. 至於選擇的數學函數,共有三:Simons-Parr-Finlan(SPF) polynomial, Jensen function, 以及Sorbie-Murrellfunction.基態CH2的電子組態是三重態(triplet state). C-H的平衡鍵長為1.075 Angstrom,H-C-H之間平衡鍵角為133.3度;至於能量則為-39.0828910 hartree. 絕對解離(adiabatic dissociations)的結果為C+H2,CH+H,以及 C+2H. 這些產物也都處於基態的電子組態. 在這裡將不考慮任何位能面交叉(crossing)的現象. 經由理論計算的結果,第一個分解路徑(channel)所需解離能為3.43eV,第二個分解路徑能量需4.74eV,第三個需能量8.43eV.數學演算的結果顯示:SPF polynomial的方均根誤差(Root mean square)為3.930kcal/mol;有93%的點在正負5%的誤差範圍內.Jensen function的方均根誤差為3.745kcal/mol;有74%的點在正負5%的誤差範圍內. 至於 SM function則為4.137kcal/mol,71%的點在正負5%的誤差範圍內. 整體而言,SPF polynomial可以得到較精確的能量值,可是當H-C-H鍵角很小時能量值會出現嚴重的錯誤. 類似的情形也出現於Jensenfunction. 而SM function對於解離區域的現象描述非常正確,符合abinitio的計算結果.The global potential energy surface of ground-state CH2 wasdeduced from high-level ab initio calculations at the CCSD/TZ2Plevel on 2174 points. Parameters of the analytical potentialenergy functions were then fitted by these ab initio results.Three types of analytical functions: Simons-Parr-Finlan(SPF)polynomial, Jensen function and Sorbie-Murrell(SM) function.The equilibrium C-H bond length and H-C-H bond angle of CH2 are1.075 Angstrom and 133.3 degree, respectively, with an energyof -39.0828910 hartree. CH2 correlates with the ground statesof C+H2 and CH+H. The dissociation energies are 3.43eV for thefirst channel and 4.74eV for the second channel. The referencestate is the ground states of three seperate atoms, C+2H, whichis -37.7977887 hartree. The nonlinear-least-squares fitting ofthe parameters of the lobal potential functions was implementedby a modifiedvenberg-Marquardt algorithm with a finite-difference Jacobian.t-mean-square(RMS) error is 3.79 kcal/molfor SPF polynomial,kcal/mol for Jensen function and 4.29 kcal/mol for SM function. The fits of SPF polynomial and Jensenfunction areccurate in the vicinity of ground state while SMfunction givesgood description at the dissociation regions ofCH+H and C+H+H. According to 3-D graphs with fixed C-H bondlength, SPF polyno- mial reports a wrong profile when the H-C-Hbond angle is small and so does Jensen function.