molecular orbital theory
分子轨道理论
才能组成分子轨道
b、d、e符合 a、c不符合
② 能量近似原则 只有能量相近的原子轨道才能组合成有效 的分子轨道
H1S O2P Cl3P Na3S
-1312 (KJ/mol) -1314 (KJ/mol) -1251 (KJ/mol) -496 (KJ/mol)
可以 不行
③ 最大重叠原则
在对称性匹配的条件下，原子轨道的重叠程度越 大，组合成的分子轨道能量降低得越多，形成的 化学键越稳定。
4、分子轨道的几种类型
头碰头形成轨道 、* ，沿键轴（x轴） 方向呈圆柱形对称的重叠
肩并肩形成轨道 、 *，通过键轴的平面 （xz平面、xy平面）呈平面反对称的重叠
2 2
(
2
px
)
2
N2
14e
KK
(
2
s
)
2
(
2s
)
2
2 2
py pz
2 2
(
2
px
)
2
键级为3：二个 键，一个键
抗磁性
问题：N2 + 分子轨道电子排布式如何？ 并比较N2 + 、N2其稳定性。
C2 的分子轨道
2Px*
键级为2
2Py* 2Pz*
2S*
2S
2S
2S
1S*
1S
1S
1S
KK
(
2s
)
2
(
2s
)
2
(
2
px
)
2
2 2
py pz
2 2
关于杂化轨道理论的一些浅显认识【毕业论文,绝对精品】
编号：本科毕业论文（设计）题目：关于杂化轨道理论的一些浅显认识学院化学化工学院专业材料化学学号200840730117姓名指导教师职称副教授完成日期03 -15 摘要杂化轨道理论是大学无机化学、结构化学课程的重要内容是后续元素化合物学习的基础。
本文根据书本上的内容写出了自己对杂化轨道理论的一些理解。
重点介绍了判断中心原子杂化类型的方法，以及杂化的等性与不等性。
并举例说明了杂化轨道理论在解释分子空间构型和物质化学性质的变化上的应用。
分析了杂化轨道理论在其应用方面的优势和局限，浅析了其与价层电子对互斥理论等共价键理论相互依存、相互补充的未来发展方向。
关键词：杂化轨道理论中心原子空间构型价层电子对互斥理论AbstractHybrid orbital theory is an important content of inorganic chemistry and structural chemistry in college text bookand it is the basis for further study of element compounds. According to t the content of text bookthis articlewritten about some understanding of hybrid orbital theory. Focuses on the method to determine the hybrid types ofcentral atomand Equivalent hybridization and inequivalent hybridization. This text illustrates the application ofhybrid orbital theory in the field of explaining the steric configuration of molecule and the change of chemicalproperty. And analyzes the superior and limitations of hybrid orbital theory in the side of its application. And has asimple analysis of the future thrust of Theory of hybrid orbitalcombining with valence-shell electron pairrepulsion theory and other Covalent Bond Theory.key words: Hybrid orbital theory central atom steric configuration valence-shell electron pair repulsiontheory1.前言化学是在原子层次上研究物质变化的一门科学所以了解和掌握原子结构分子结构以及原子间的成键规律对于我们掌握化学反应的本质和规律有着重要意义，而原子轨道的杂化理论则是其中最基本的理论，它能很好的解释分子的几何构型及部分分子的的性质。
吴自玉教授-3-XANES相关知识
其中 dσ 为自旋坐标中的体积元。根据自旋波函数的正交性，这个积分为 零，因此单重态到三重态的跃迁是禁阻的。 而在单重态到单重态或者三重态到三重态的跃迁中，因为
2 α ∫ dσ = 1
所以能够发生跃迁。
Selection Rules
原子中的跃迁定则
偶极近似下的原子跃迁规则：
∆n = 0, ± 1, ± 2, L
MO Theory
Molecular Orbital Theory
Hybridization: Linear Combination of atomic orbitals
H
H
C
H H H-C-H bond angle 109.5°
Tetrahedral geometry
4个碳原子轨道 2s + 2px + 2py + 2pz
A1 A2 E T1 T2
Selection Rules
分子中的跃迁定则
在 Td点群中，偶极算符为 T2对称性。因此只有直乘包含 T2对称性的两个态之间的跃迁才是允许的。 由上表可知，只有以下跃迁是允许的，其它跃迁都是禁 阻的。
A1 ↔ T2
A2 ↔ T1
T1 ↔ T2
E ↔ T1
T1 ↔ T1
E ↔ T2
2
(3 z 2 −zr 2 ) r 2
y y x x x
yz
xz
xy
x2-y2
z2
位于坐标轴之间
沿着坐标轴
在无配位体的情况下，这些 d 轨道是 简并的，即它们具有相同的能量！
Ligand Theory
在八面体配位下，金属 d轨道分裂为两类
eg类：直接指向配 体，与配体的轨道重 迭大，成键轨道和反 键轨道分离大。 t2g类：不直接指向配体，与配体的轨道重迭小，成键 轨道和反键轨道分离小。
什么是分子轨道理论
什么是分子轨道理论
分子轨道理论（Molecular Orbital Theory，简称MO理论）是1932年由美国化学家马利肯（R.S.Mulliken）及德国物理学家洪特（F.Hund）提出的一种描述多原子分子中电子所处状态的方法。
该理论认为原子形成分子后，电子不再属于个别的原子轨道，而是属于整个分子的分子轨道，分子轨道是多中心的。
分子轨道由原子轨道组合而成，形成分子轨道时遵从能量近似原则、对称性一致（匹配）原则、最大重叠原则，即通常说的“成键三原则”。
在分子中电子填充分子轨道的原则也服从能量最低原理、泡利不相容原理和洪特规则。
以上信息仅供参考，建议查阅化学专业书籍文献或咨询化学专业人士获取更全面更准确的信息。
《结构化学》教学大纲(英文版)
‘Structural Chemistry ’Course SyllabusCourse Code：09040001Course Category：Major BasicMajors：ChemistrySemester：SpringTotal Hours：54 Hours Credit：3Lecture Hours：54 HoursTextbooks：《Structural Chemistry》孙墨珑编著，东北林业大学出版社。
I.Introduction to Structural ChemistryThe major targets this course includes the followings: (1) to introduce the material structure of the basic concepts, basic theory, and basic methods for learning “Structural Chemistry”; (2) to explore the relationship between the microstructures and properties of atoms, molecules, and crystals; (3) to systematically clarify the essence of the periodic law of elements; (4) to deeply and qualitatively clarify the essence of the chemical bonds. This course introduces the basic principles of quantum mechanics and their applications in simple systems, structure of atoms, molecules, and crystals, symmetry of molecular orbitals, molecular orbital theory, and ligand field theory, etc. After learning this course, the students should be able to analyze and solve the basic chemistry problems from the point of view of quantum mechanics.II.Table of contentsSection I (Chapter 1) Basic knowledge of quantum mechanics1.1 Failures of classical mechanics1）Black-body radiation & Planck’s solution;2）Ph otoelectric effect & Einstein’s theory;3）Hydrogen spectrum & Bohr’s model.1.2Characteristics of the motion of microscopic particles1)Wave-particle duality;2)Uncertainty principle.1.3The basic postulates of quantum mechanics1)Postulate 1: wavefunction;2)Postulate 2: Hermitian operators;3)Postulate 3: Schrödinger equation;4)Postulate 4: linearity and superposition;5)Postulate 5: Pauli exclusion principle.1.4Applications of quantum mechanics in simple cases1)Free particle in one-dimensional (1D) box;2)Applications of the 1D-box model in simple chemical systems;3)Free particle in two-dimensional (2D) & three-dimensional (3D) box;4)Tunneling & scanning tunneling microscopy (STM).Section II (Chapter 2) Structures and properties of atoms2.1 One-electron atom: H atom1)The Schrödinger equation of H atoms;2)Solution of the Schrödinger equation of H atom.2.2Quantum numbers1)Principle quantum number, n;2)Angular momentum quantum number, l;3)Magnetic quantum number, m;4)Zeeman effect.2.3Wavefunction and electron cloud1)Radial distribution;2)Angular distribution;3)Spatial distribution.2.4 Structure of multi-electron atoms1)The Schrödinger equation of multi-electron atoms•Self-consistent field method;•Central field approximation.2)The building-up principles and electron configuration of multi-electron atoms•Pauli exclusion principle;•Principle of minimum energy;Hund’s rule.2.5Electron spin and Pauli exclusion principle2.6Atomic spectroscopy1)Orbital-spin coupling;2)Spectroscopic terms & term symbol;3)Derivation of atomic term.4)Hund’s rule on the spectroscopic terms;2.7Atomic properties1)Energy of ionization;2)Electron affinity;3)Electronegativity.Section III (Chapters 3-6) Structures and properties of molecules Chapter 3 Geometric structure of molecules─Molecular symmetry & symmetry point group3.1Symmetry elements and symmetry operations1)Symmetry elements and symmetry operations;2)Combination rules of symmetry elements;3.2Point groups & symmetry classification of molecules3.3Point groups & groups multiplication3.4Applications of molecular symmetry1)Chirality & optical activity;2)Polarity & dipole moment.Chapter 4 S tructure of biatomic molecules (X2 & XY)4.1 Linear variation method and structure of H2+ ion1) Shrödinger equation of H2+ ion;2) Linear variation method;3) Treatment of H2+ ion using linear variation method;4) Solutions of H2+ ion.4.2 Molecular orbital theory and diatomic molecules1) Molecular orbital theory;2) Structure of homonuclear diatomic molecules (X2);3) Structure of heteronuclear diatomic molecules (XY).4.3 Valence bond (VB) theory and H2 moleculeChapter 5 Structure of polyatomic molecules (A)5.1 Structure of Methane (CH4)1) Delocalized molecular orbitals of methane (CH4);2) Localized molecular orbitals of methane (CH4).5.2 Molecular orbital hybridization1) Theory of molecular orbital hybridization;2) Construction of hybrid orbitals;3) Structure of AB n molecules;4) Molecular stereochemistry: valence shell electron-pair repulsion (VSEPR)model.5.3 Delocalized molecular orbital theory─Hückel molecular orbital (HMO) theory1) HMO method & conjugated systems;2) HMO treatment for butadiene;3) HMO treatment for cyclic conjugated polyene (C n H n);4) Molecular diagrams;5) Delocalized π bonds.5.4 Structure of electron deficient molecules5.5 Symmetry of molecular orbitals and symmetry rules for molecular reactions5.6 Molecular spectroscopy1)Infrared absorption spectroscopy: molecular vibrations;2)Raman scattering spectroscopy: molecular vibrations;3)Fluorescence spectroscopy: electronic transitions;4)NMR spectroscopy: nuclear magnetic resonances.Chapter 6 Structure of polyatomic molecules (B), coordination compounds 6.1 Crystal field theory6.2 CO and N2 coordination complexes6.3 Organic metal complexes1) Zeise’s salts;2) Sandwich complexes.6.4 Clusters1) Transition-metal cluster compounds2) Carbon clusters and nanotubesSection IV (Chapters 7-9) Structure of crystalsChapter 7 Basics of crystallography7.1 Periodicity and lattices of crystal structure1) Characteristics of crystal structure;2) Lattices and unit cells;3) Bravais lattices and unit cells of crystals;4) Real crystals & crystal defects.7.2 Symmetry in crystal structure1) Symmetry elements and symmetry operations;2) Point groups (32) and space groups (230).7.3 X-Ray diffraction of crystals1) X-ray diffraction of crystals•Laue equation;•Bragg’s law;•Reciprocal lattice.2) Instrumentation of X-ray diffraction;3) Applications of X-Ray diffraction•Single crystal diffraction: crystal structure determination;•Powder diffraction: qualitative & quantitative analysis of crystalline materialsChapter 8 Crystalline solids, I: metals and alloys8.1 Close Packing of Spheres1) Close packing of identical spheres;2) Packing density;3) Interstices.8.2 Structures and Properties of Pure Metals8.3 Structures and Properties of AlloyChapter 9 Crystalline solids, II: ionic crystals9.1 Packing of Ions;9.2 Crystal Structure of Some Typical Ionic Compounds9.3 Trend of Variation of Ionic Radii9.4 Pauling Rule of Ionic Crystal Structure9.5 Crystals of Functional Materials1) Nonlinear optical materials;2) Magnetic materials;3) Conductive polymers;4) Semiconductors: band gap and photocatalysisIII.Table of ScheduleReferences[1] 王荣顺主编，东北师范大学等，《结构化学》，高等教育出版社，2003年。
共价键理论
共价键理论
一个原子含有几个未成对电子，就可以和几个自旋量 子数不同的电子配对成键，或者说，原子能形成共价键的数 目是受原子中未成对电子数目限制的，这就是共价键的饱和 性。例如，H原子只有一个未成对电子，它只能形成H2而不 能形成H3；N原子有三个未成对电子，N和H只能形成NH3， 而不能形成NH4。由此可知，一些元素的原子（如N、O、F 等）的共价键数等于其原子的未成对电子数。
共价键理论
图2-7 CH4分子的形成
共价键理论
C原子的1个s轨道与3个p轨道经杂化形成4个sp3杂化轨道 ，每一个sp3新轨道一端膨胀一端缩小，C原子和H原子成键时 从较大的一端进行轨道重叠，4个sp3杂化轨道间的夹角为 109.5°。可见，原子轨道杂化的原因是杂化后轨道形状发生改 变(一端显得突出而肥大)，便于最大重叠；轨道方向改变，使 成键电子距离最远，斥力最小，能量降低。总之，杂化后能 增大轨道重叠区域，增强成键能力，使分子更稳定。
共价键理论
(2)π键。 原子轨道以“肩并肩”的方式 发生重叠，轨道重叠部分对通过
一个键轴的平面具有能面反对称性，这 种键称为π键，如pzpz、pypy轨道重叠形成π 键，如图2-5(b)所示。
共价键理论
图2-5 σ键和π键形成示意图
共价键理论
有些分子中既有σ键， 也有π键。例如，N2分子的 结构中有一个σ键和两个π键。 N原子的电子层结 ，而pypy、pz-pz分别沿y轴和z轴 相互平行或以“肩并肩”的 方式重叠形成π键，如图2-6 所示。
含有配位键的化合物称为配位化合物，这类化合物将在以后 的章节中讨论。
第四章 休克尔(Hückel) 分子轨道理论
第四章
<0
相邻C间交换积分为
相间C间交换积分为0
各C原子参与共轭前2p轨道能量均为， 相邻的2p轨道间交盖引起的能量下降值为， 相邻的2p轨道间的重叠近似为0。 对共轭分子体系，在σ-π分离和π电子近似下， 应用线性变分法，能量对变分系数求一阶导数，则 可得 n 个线性方程（久期方程）。
第四章
0
目录 18/93
量子化学
属于E值对应的一套系数c1 , c2 ,…, c k， 波函数Ψ
第四章
c11 c 2 2 c k k c i i
i 1
k
归一化条件：
E有k个根E0, E1,…,Ek-1, E0为基态，其它为激发态。 所有分子轨道理论都基于变分方法而进行。
2/93
量子化学 4.1 变分法
第四章
设体系哈密顿算符 的本征值按大小次序排列为： E0≤E1≤E2≤…Ei≤… 等号表示有简并态情形。 设属于每个本征值的本征函数分别为： 0 , 1 , 2 , …,i ,… 则存在 的系列本征方程：
3/93
量子化学
第四章
根据厄米算符本征函数的性质， i , i 0 , 1, 2
i 1, 2 , , k
其中：
H ij i H j d
* S ij i j d
18
*
上式中E 代替了 ，因为求解上述方程可以得到E的 一组解，其中最小的一个就是体系基态能量的近似值。
16/93
量子化学
为0，称此行列式为久期行列式。
第四章
ci 不全为零的条件是它们的系数构成的行列式
此，一个不太理想的 可能给出了较好的E0近似
分子轨道理论
* 2px
2px
2p ？
2py
2pz
* 2 s
2p
N2的键级=（10-4）/2=3
2s
2s
1*s
2s
1s AO
1s
1s AO
MO
同核与异核双原子的分子轨道符号的关系
1s
1
Байду номын сангаас
1*s
2
2s
3
* 2 s
2p
5
2p
1
* 2 p
* 2 p
3s
7
* * 2 py 2pz 2py 2pz
2p
* 2 s
2px
2p
O2的键级=（10-6）/2=2
2s
2s
1*s
2s
1s AO
1s
1s AO
MO
N2分子轨道能级图
* * 2 py 2pz
N2分子轨道表示式
* 2 2 * 2 2 2 2 （1s )2(1 ) （ ) ( ) （ ） （ ） ( ) s 2s 2s 2py 2pz 2 px
MO c11 c2 2 MO
*
c11 - c2 2
成键原则 能量相近原则 决定成键效率 决定能否成键
分子轨道电子排布遵循原则 能量最低原理 Pauli不相容原理 Hund法则
最大重叠原则
对称性匹配原则
处理分子轨道方法
1. 弄清分子轨道的数目和能级高低 2. 由原子价电子算出可用来填充的分子轨道的电子数 3. 按规则将电子填入分子轨道
分子轨道类型
分子轨道表示式
根据分子轨道能级高低及轨道电子数，将分子轨道从 低能级到高能级的每个能级用括号括起来，右上角注 明轨道电子数。如，H2的分子轨道表达式 （1s )2
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
(10 electrons) (9 electrons) (10 electrons) (12 electrons) (10 electrons)
Notice – different elements can have the same number of el Theory
Orbital Mixing
When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must:
1s22s1 or, "1s two, 2s one".
/chm1045/notes/Struct/EConfig/Struct08.htm
Electronic Configurations – Box Diagram
/chm1045/notes/Struct/EConfig/Struct08.htm
The lowest level (K), can contain 2 electrons. The next level (L) can contain 8 electrons. The next level (M) can contain 8 electrons.
/ronutt/che115/AO.htm
Atomic Subshells (cont’d)
D Orbitals: The d subshell is divided into 5 orbitals (dxy, dxz, dyz, dz2 and dx2-y2). These orbitals have a very complex shape and are higher in energy than the s and p orbitals.
Electron Configuration
Two ways to remember the order of electrons
/wiki/Image:Electron_orbitals.svg
Valence Electrons
The valence electrons are the electrons in the last shell or energy level of an atom.
Lithium Electronic Configuration
The arrows indicate the value of the magnetic spin (ms) quantum number (up for +1/2 and down for -1/2) The occupation of the orbitals would be written in the following way:
The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.
Electronic Configuration
Electronic configurations can also be written in a short hand which references the last completed orbital shell (i.e. all orbitals with the same principle quantum number 'n' have been filled)
The electronic configuration of Na can be written as [Ne]3s1 The electronic configuration of Li can be written as [He]2s1
The electrons in the stable (Noble gas) configuration are termed the core electrons The electrons in the outer shell (beyond the stable core) are called the valence electrons
All chemistry is done at the electronic level (that is why electrons are very important). Electronic configuration is the arrangement of electrons in an atom. These electrons fill the atomic orbitals Atomic orbitals are arrange by energy level (n), subshells (l), orbital (ml) and spin (ms) - in order:
Atomic Subshells
These are some examples of atomic orbitals:
S subshell: (Spherical shape) There is one S orbital in an s subshell. The electrons can be located anywhere within the sphere centered at the atom’s nucleus.
/ronutt/che115/AO.htm
P Orbitals: (Shaped like two balloons tied together) There are 3 orbitals in a p subshell that are denoted as px, py, and pz orbitals. These are higher in energy than the corresponding s orbitals.
Electronic Configuration
Every element is different.
The number of protons determines the identity of the element. The number of electrons determines the charge. The number of neutrons determines the isotope.
Carbon - 1s22s22p2 - four valence electrons
Examples of Electronic Configuration
Ne 1s2 2s2 2p6 F 1s2 2s2 2p5 F- 1s2 2s2 2p6 Mg 1s2 2s2 2p6 3s2 Mg2+ 1s2 2s2 2p6
The two electrons in Helium represent the complete filling of the first electronic shell. Thus, the electrons in He are in a very stable configuration For Boron (5 electrons) the 5th electron must be placed in a 2p orbital because the 2s orbital is filled. Because the 2p orbitals are equal energy, it doesn't matter which 2p orbital is filled.
Forming a Covalent Bond
Molecules can form bonds by sharing electron
Two shared electrons form a single bond
Atoms can share one, two or three pairs of electrons
Have similar energy levels. Overlap well. Be close together. This is and example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons.
Molecular Orbital Theory
Luis Bonilla Abel Perez University of Texas at El Paso Molecular Electronics, Chem 5369
Atomic Orbitals
Heisenberg Uncertainty Principle states that it is impossible to define what time and where an electron is and where is it going next. This makes it impossible to know exactly where an electron is traveling in an atom. Since it is impossible to know where an electron is at a certain time, a series of calculations are used to approximate the volume and time in which the electron can be located. These regions are called Atomic Orbitals. These are also known as the quantum states of the electrons. Only two electrons can occupy one orbital and they must have different spin states, ½ spin and – ½ spin (easily visualized as opposite spin states). Orbitals are grouped into subshells. This field of study is called quantum mechanics.