Recent Developments in Radiationless Transitions

在本文中,我们将介绍运用第一性原理计算包含非谐效应或势能面锥形交叉情况下内转换速率的最新工作。我们同时计算了包含非谐效应的分子吸收和发射光谱,以检验量子化学方法计算得到势能面的准确性。势能面的锥形交叉对内转换过程的影响是学界广泛关注的焦点。本文将介绍如何在内转换速率计算的过程中考虑势能面锥形交叉的影响,并将之运用于吡嗪分子。本文运用绝热近似理论处理了另外一个重要的无辐射过程,分子的振动驰豫过程,并将这个理论应用于水二聚体和苯胺的振动弛豫速率的计算。In this paper,we introduce recent works on the mathematical treatments and the first-principle calculations concerning the internal conversion rates for the cases with anharmonic potentials,and conical intersecting potentials.The simulations of absorption and emission spectra with anharmonic effects are also presented to check the validity of the potential energy surfaces obtained from the quantum chemical calculations.The effect of conical intersection on internal conversion has attracted considerable attention.In this paper a different approach is proposed and applied to pyrazine.Another important non-radiative process,molecular vibrational relaxation,is also treated by applying the adiabatic approximation to the ab initio anharmonic potential energy surfaces.The vibrational relaxation rates in water dimer and aniline are chosen to demonstrate the calculation

Ab-initio and DFT studies of electronically excited states and chemical reactions of extra large molecular systems(2/3)

在此三年計劃的第二年裡，我們持續地嘗試建立幾種實用與可行的理論計算方法：(1)光 學性質、(2)正則頻率運動模態分析、(3)超大分子系統的電子結構計算。為了完成這些目標， 我們將主要的研究工作集中在以下4 個主題：(a)計算Rhodamine 6G 與1,1’-bi-2-naphthol (BN) 的和周波光譜(sum-frequency generation, SFG)之電子躍遷偶極距導數與永久偶極導數、 (b)distyrylbenzene (DSB)的電子激發態之正則頻率分析、(c) [decaammine(µ-pyrazine)diruthenium]5+ 錯合物分子的拉曼與紅外線光譜研究、以及(d)應用週期 邊界條件(periodic boundary condition)計算方法探討methylnitrene (CH3-N)自由基分子在銅表面 Cu(110)上的幾何結構。這些主題的研究將利用全始算(ab initio)方法(HF, CIS)、密度泛函數理 論(DFT)、以及時間相關密度泛函數理論(TD-DFT)與半經驗(semi-empirical)方法ZINDO/S 。其 中密度泛函數理論的使用將視研究的系統而做不同的泛函數選擇：單分子計算使用B3LYP 方 法，具有週期性邊界的系統使用PBEPBE 與LSDA 方法。特別是，在(b)與(d)的研究裡我們花 費相當大的心血為了能夠符合與解釋實驗上的成果，這些相關的實驗研究是由台灣大學凝態 科學研究中心所執行的。In the second year of the three-year project, have continued to made several attempts to establish a practical and feasible computational approach to calculate (1) optical properties, (2) normal mode analysis, and (3) electronic structures of extra large molecular systems. For this purpose, we have focused on the 4 topics: (a) electronic transition dipole moment derivatives and permanent dipole derivatives calculations for sum-frequency generation (SFG) for Rhodamine 6G and 1,1’-bi-2-naphthol (BN), (b) normal mode analysis of electronically excited states of distyrylbenzene (DSB), and (c) Raman and IR spectra of [decaammine(µ-pyrazine)diruthenium]5+ complex molecule, and (d) geometrical structure of methylnitrene (CH3-N) radicals on Cu(110) surface with periodic boundary condition. These topic are investigated using ab initio methods (HF, CIS), density functional theory DFT (single molecule with B3LYP, periodic boundary systems with PBEPBE, LSDA), time-dependent DFT and semi-empirical ZINDO/S. In particular, we have paid our large efforts to the topic (b) and (d), which are closely related to experimental works done by two researchers in Center for Condensed Matter Sciences (NTU)

Theoretical study for the electronic structure and dynamics of large systems

此計畫用密度泛函理論(DFT)完成 Rhodamine 6G (Rhd6G)和Distyrylbenzene (DSB)的基態結構之研究。在Rhd6G 方面， 我們也獲得振動模態及分析之。以這些計 算結果為基礎，以計算doubly-resonant infrared-visible (IR-VIS) sum-frequency generation (SFG)。 為了比較，我們也用DFT 的結果計算IR 光譜。我們的計算顯示與觀 測數據有很好的一致性。在DSB 方面，我 們完成DFT 計算以研究三種異構物的基態 結構。以這些結果為基礎，我們以ZINDO/S 完成半經驗分子軌域計算以獲得可能的電 子激發態。在第一個允許的電子躍遷裡我 們預測反-反激發態為最低能量，順-反為次 低而順-順為最高。In this project, density functional theory (DFT) calculations are performed to investigate ground state structure of Rhodamine 6G (Rhd6G) and Distyrylbenzene (DSB). For Rhd6G, we also carried out normal mode analysis and obtained normal modes. Based on these calculated results, doubly-resonant infrared-visible (IR-VIS) sum-frequency generation (SFG) is calculated. For comparison, we also calculated IR spectra using the DFT results. Our calculations show a good agreement with the observed data. For DSB, we performed DFT calculations to investigate ground state structures for three isomers. Based on the results, we carried out semi-empirical molecular orbital calculations using ZINDO/S to obtain possible electronic excitations. We predicted that trans-trans excitation exhibits the lowest, cis-trans the next lowerst, and cis-cis the highest for the first allowed electronic optical transition

Ab-initio and DFT studies of electronically excited states and chemical reactions of extra large molecular systems

在三年計劃的第一年裡，我們嘗試建立以下幾個實用與可行性的計算方法：(1)電性與磁 性性質的計算，(2)正規模態分析，(3)超大分子系統的電子結構計算。為了達到這些目的，我 們將研究專注於以下4 個主題：(a)在sum-frequency generation （SFG ）中磁性對旋光性分子 的影響，(b) [decaammine(µ-pyrazine)diruthenium]5+ 錯合物的正規振動模態分析，(c) CH3-N + 陽 離子自由基吸附在Cu(110)表面上的電子結構。這些主題的研究利用全始算(ab initio)方法、密 度泛函理論(DFT)方法、以及半經驗方法中的ZINDO/S 來完成。In the first year of the three-year project, we have made several attempts to establish a practical and feasible computational approach to calculate (1) electric and magnetic properties, (2) normal mode analysis, and (3) electronic structures of extra large molecular systems. For this purpose, we have focused on the three topics: (a) the magnetic effect of chiral molecules on sum-frequency generation (SFG), (b) normal mode analysis of [decaammine(μ -pyrazine)diruthenium]5+ complex compounds, and (c) electronic structure of methylnitrene (CH3-N + ) cation radical on Cu(110) surface. These topic are investigated using ab initio methods, density functional theory DFT) and semi-empirical ZINDO/S

Theoretical study for the electronic structure,dynamics,and dynamics of large systems

在此計畫中我們替某一個環境之下的分子的displaced-distorted harmonic potential surface 發展一個核關聯函數，並且論證這個核關聯函數的應用。因此，利用ab initio 計算可以得到pyridine 的 1 Ａ1 , 1 B1 , 1 B2 singlet state 的3 個簡諧位能表面。這些狀態 的幾何最佳化和力場計算是使用complete-active-space self-consisted-field (CASSCF) 理論方法。激發態的振動頻率由正則模式分析(normal mode analysis)被位能分佈的 基底所指定。In this project, we develop a nuclear correlation function for displaced-distorted harmonic potential surfaces of a molecule in the presence of its environment and demonstrate applications of this nuclear correlation function. To this end, three harmonic potential-energy surfaces of 1 A1, 1 B1, and 1 B2 singlet states of pyridine is obtained using ab initio calculations. Geometric optimizations and force field calculations of these states are determined with the complete-active-space self-consisted- field (CASSCF) theoretical method. Vibrational frequencies of excited states are assigned on the basis of potential energy distribution from normal mode analysis