简单回顾量子化学

简单回顾 量子化学

第一章 • 从经典力学到量子力学；物质波 • 量子力学的基本假定和薛定谔方程 • 简单体系的精确计算 • 双态系统；一维势箱；线性谐振子； • 刚性转子 • 四氢原子和类氢离子

第二章 • 定态微扰法；变分法 • 应用于解氦原子基态 • 多电子原子： • 单电子近似，自旋和泡利原理 • Slater 行列式 • 分子体系的自洽场方法 • 三大近似； Hartree-Fock 方程公式推导（变分方法） • Hartree-Fock方程的局限性；组态相关 • Hartree-Fock-Roothaan 方程基组

第三章计算方法 一 Hartree-Fock-Roothaan 方程基组二密度泛函（DFT）方法 Kohn-Sham 方程交换相关势三半经验方法四固体计算方法初步平面波，倒空间五几种常见的优化方法；分子动力学

掌握了量化，计算模拟还需要什么？ 1。对研究体系有深刻的理解，一定要有需要回答的问题以及先验的猜测。 2。选择合适的理论计算方法量化精度级别，计算方法，热力学，动力学 3。恒心，好奇心

Au/TiOx/Mo{112} Chen, Goodman, Science (2004) 306, 252

Au/TiOx/Mo{112} TiOx/Mo{112} Au/TiOx/Mo{112} ‘1-ML’ Au/TiOx/Mo{112} ‘2-ML’

CO oxidation Superior reactivity at a particular coverage Reaction occurs on Au ? Why ? Nano-effect Can we use theoretical modelling to verify the experiment? Structures DFT + thermodynamics

Difficulties for theoretical modelling SIESTA 1. System is very large and is metallic (8x2), not linear-scaling 2. Temperature and pressure are important Combine with thermodynamics DFT is zero-temperature technique 3. Chemical composition (atomic number) is unknown TiOx/Mo{112} TRY ! !! Measure stability Try structure

For example:

Compute the chemical potential of O By using the experimental data (DHO2 and SO2) in the literatures, mO2 (T, p) can be calculated. Liu, Jenkins, King J. Am. Chem. Soc., 126, (2004) 10746

(i) Determine the chemical potential of O in the gas phase at the (T,p) m(O)= -3.13 +1/2Etot(O2) (1) (ii) Determine the upper-limit of the chemical potential of Ti DG= 1/2Etot(Ti2O3) + 1/2m(O)-Etot(TiO2) (2) TiO2 is more stable at the (T,p) than Ti2O3 • (iii) Finally, work out the DGf of the reaction, • Mo{112}+ nTiO2 (bulk)+ n(x-2)/2 O2(g)→nTiOx/Mo{112} • DGf= 1/n (Etot(nTiOx/Mo{112})-Etot(Mo{112}) - nEtot(TiO2) - n(x-2) m(O) ) (3)

Calculated free energetics (DGf, unit: eV) and periodicity of selected TiOx films on Mo{112} at 1400 K, pO2=1x10-8 torr .

97.9 meV (Ti-O-Ti mode) 82.9 meV (Ti-O-Ti mode) Exp. 84 meV 81.1 meV (Ti-O-Mo mode)

p(8x2)

reconstruction No reconstruction Unreconstructed TiO3 Au Condensed TiO3 Au Unreconstructed TiO3 Mo{112} Mo{112} EAu = -qTiDGf -qTirecDGfrec+ ∫EaddiffdqAu ≈ - qTiDGf -qTirecDGfrec + ∑ Eadquasi-diffDqAu (4)

TiO3 phase interfaces Au Au phases p(1x3) p(1x1) Reconstruction model (d’) (d) (g) (h) Au b.TiO3 Au Mo p(8x2) (e) (f)

Plot of EAu (eV) against Au coverage (ML), showing the energy gain of Au growth on the unreconstructed and reconstructed TiO3/Mo{112}

CO+O2 reaction at the interface Ea < 0.1 eV CO+O2 transition states at the (1x1) interface (left) and the (1x3) interface (right). CO adsorption energy Activity difference at RT 0.57 eV 0.80 eV

Seeing is not believing ? Expt. Theory (1x1) Au 1 layer Au/TiOx/Mo 2-layer Au domains + (1x1) TiO3 domain Reaction site Au/oxide interface Au Au/TiOx/Mo catalyst (Au+TiO3)/Mo 2layer Au most active activity 3-layer Au most active Liu, Phys. Rev. B 73, 233410 (2006)

简单回顾 量子化学