Lecture 1 - Bonding and Hybridization

杂化方式及其空间构型Hybridization and Molecular Geometry.Hybridization is a fundamental concept in chemistrythat describes the process by which atomic orbitals combine to form new hybrid orbitals with different shapes and energies. These hybrid orbitals are then used to form covalent bonds with other atoms, and the geometry of the resulting molecule is determined by the spatial arrangement of these hybrid orbitals.The hybridization of an atom is determined by the number and type of atomic orbitals that are involved in the bonding. For example, carbon atoms can hybridize their 2s and three 2p orbitals to form four equivalent sp3 hybrid orbitals. These sp3 hybrid orbitals are tetrahedrally arranged in space, and they can form bonds with up to four other atoms.Other common types of hybridization include sp2hybridization, which results in three equivalent hybrid orbitals that are arranged in a trigonal planar geometry, and sp hybridization, which results in two equivalenthybrid orbitals that are arranged in a linear geometry.The geometry of a molecule is determined by the hybridization of the atoms that are involved in the bonding. For example, a carbon atom that is sp3 hybridized will form four bonds with other atoms, and the resulting moleculewill have a tetrahedral geometry. A carbon atom that is sp2 hybridized will form three bonds with other atoms, and the resulting molecule will have a trigonal planar geometry. A carbon atom that is sp hybridized will form two bonds with other atoms, and the resulting molecule will have a linear geometry.Hybridization is a powerful tool that can be used to predict the geometry of molecules. By understanding the hybridization of the atoms involved in the bonding, it is possible to determine the shape and properties of the molecule.杂化方式及其空间构型。

铟的杂化方式The hybridization of indium (In) atoms in a compound depends on the specific chemical environment and the bonding situation. In general, the hybridization of an atom is determined by the number of electron domains around it, which includes the number of bonding pairs and lone pairs.Indium, being a member of the post-transition metal group, typically exhibits variable oxidation states and can form compounds with a range of hybridization states. For example, in indium(III) compounds, indium often has a d^10 configuration and can form three bonds, which might suggest sp^2 hybridization. However, the actual hybridization can be influenced by factors like the nature of the ligands, the presence of steric hindrance, and the electronic structure of the compound.In some cases, indium may form compounds with four bonds, indicating sp^3 hybridization. This is more common in indium(I) or indium(II) compounds, where the indium atom has a lower oxidation state and can form more bonds.It's important to note that the hybridization of indium is not always straightforward to predict and often requires a detailed understanding of the chemical structure and bonding situation in the specific compound. Therefore, it's generally recommended to consult relevant chemical literature or seek the advice of a chemist when determining the hybridization of indium in a particular compound.。

Linear Trigonal Tetrahedral TrigonalOctahedralBipyramidallinear LinearTrigonal planar Trigonal planar(AB3)Bent(AB E)TetrahedralBent (AB 2E 2)Tetrahedral (AB )Pyramidal (AB E)Trigonal BipyramidalTrigonal Bipyramidal(AB 5)Unsymmetrical Tetrahedron (AB 4E)T-shaped (AB 3E 2)Linear (AB 2E 3)Square planar(AB4E 2 )Octahedral(AB6)Squarepyramidal(AB5E)1.Determine the Lewis structure2.Determine the number of electron pairs (orclouds) around the CENTRAL ATOM –multiple bonds count as ONE CLOUD (seenext slide).3.Find out the appropriate VSEPR geometryfor the specified number of electron pairs,both bonding and lone pairs.e the positions of atoms to establishthe resulting molecular geometry.Multiple Bonds and Molecular GeometryMultiple bonds count as one -e.g. 4 bonding pairs aroundC, but trigonal planarinstead of tetrahedral.cysteineHF electron rich regionelectron poorregionGG10.2Cl2CONH3H2OThese types of molecules, where C = central atom and T = terminal atoms of the same type, are never polar.End to end overlap = sigma (109.5 o Lewis Structure Electron pairsaround CFig. 10.7Fig. 10.8BF3-trigonal planar according to VSEPR Theory (incomplete octet exception)Isolated S atom(upgraded –more will be added)1. Hybrid orbitals get 1 electron for a V-bond, 2 electrons for a lone pair.2. Remaining electrons go into unhybridized orbitals= S bondsDOUBLE BONDS: Ethylene, CH2CH2 Lewis Structure:sp2hybridization on each C atom -sp2hybrids and unhybridized p-orbitalV bond = end-to-end overlap of the sp 2hybridized orbitals••••••••••1 electron from the sp 2hybrid on C, the other from the hydrogen 1s orbital••S bond = side-by-side overlap of theunhybridized p-orbitalsElectron from the unhybridizedp-orbital on the C atomSigma (V) Bonding in EthylenePi (S) Bonding in EthyleneDOUBLE BONDS : Formaldehyde, CH 2O Lewis Structure:Apply VSEPR Theory and Determine HybridizationHC = O H ••••sp2 120 osp2hybridization on C -sp 2hybridization on O -Sigma (V ) Bonding in Formaldehyde••••••••••••sp hybrids and unhybridized p-orbitalsSigma (V) Bonding in AcetyleneUnhybridized p-orbitalsPi (S) Bonding in AcetyleneExplain the Bonding Using Valence Bond Theory CO2Sigma Bonding in CO2Pi Bonding in CO2Molecular Orbitals-Preliminary Ideas Don’t forget that electrons behave like WAVES, and there are WAVE FUNCTIONS (\)that describe the electron position in space = ATOMIC ORBITALS (\2)e'Waves (electrons) can interfere with each other, either CONSTRUCTIVELY or DESTRUCTIVELYSigma bond formation involving p-orbitalsV*2pV2pPi bond formation involving p-orbitalsS2pS*2pS2pPrinciples of Molecular Orbital Theory1. The total number of molecular orbitals= total number of atomic orbitals contributed by the bonding atoms2. Bonding MO’s are lower in energy (more stable) than antibonding MO’s3. Electrons occupy molecular orbitals following the Pauli Exclusion Principle (spins pair up) and Hund’s Rule (remain unpaired as long as an empty orbital isavailable of the same energy)Energy Levels of Molecular Orbitals for Homonuclear Diatomics -H 2, O 2, etcMolecular orbitalsAtomic orbitals Atomicorbitals 2p 2p 2s 2s1s1s V 1s V *1sV 2sV *2sS 2p V 2pS *2p V *2pMolecular Orbital Electron Configurations e.g. O 2Bond OrderOrder = ½[# electrons bonding MO’s -# electrons antibonding MO’s]1. The greater the bond order, the more stable the molecule2. A high bond order means higher bond energies and shorter bond lengths.3. Fractional bond orders are possibleV 1s V *1s1s 1sH 2+V 1sV *1s 1s 1s H 2Bond order =Bond order =sp2hybridization of theterminal oxygens-Sigma Bonding in O3Explain using Valence Bond TheoryPi Bonding in O 3Combine 3 p-orbitals = 3 molecular orbitalsPi Bonding in O 3Antibonding S orbital Nonbonding S orbital••••Bonding S orbitalBenzene -C6H6orbitals into molecular orbitals.。

硼氢化钠的杂化方式英文回答：To answer the question about the hybridization of sodium borohydride, I would like to start by explaining what hybridization is. In chemistry, hybridization refers to the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals have different shapes and energies compared to the original atomic orbitals. Hybridization is important in understanding the bonding and molecular geometry of compounds.Now, let's talk about the hybridization of sodium borohydride (NaBH4). Sodium borohydride is an inorganic compound that is commonly used as a reducing agent in organic synthesis. It consists of a sodium cation (Na+) and a borohydride anion (BH4-).The borohydride anion is formed by the hybridization of the boron atom's 2s orbital and three of its 2p orbitals.This hybridization results in the formation of four sp3 hybrid orbitals. Each of these hybrid orbitals overlaps with a hydrogen 1s orbital to form four sigma bonds between boron and hydrogen.To illustrate this, let's consider the Lewis structure of sodium borohydride. The boron atom is at the center, surrounded by four hydrogen atoms. Each hydrogen atom is connected to the boron atom by a single bond. The boron atom also has a lone pair of electrons, making the borohydride anion negatively charged.In summary, the hybridization of sodium borohydride involves the mixing of the boron atom's 2s and 2p orbitals to form four sp3 hybrid orbitals. These hybrid orbitals then overlap with the hydrogen 1s orbitals to form four sigma bonds. This hybridization allows sodium borohydride to act as a reducing agent in various chemical reactions.中文回答：关于硼氢化钠的杂化方式，我想先解释一下什么是杂化。

h2o中心原子杂化方式In the molecule H2O, the central atom is oxygen (O). To understand the hybridization of the central atom in H2O, we need to consider its electronic configuration and the concept of hybrid orbitals. The electronic configuration of oxygen is 1s2 2s2 2p4, with six valence electrons.In H2O, two hydrogen atoms are bonded to the central oxygen atom. Each hydrogen atom contributes one electron, resulting in a total of eight electrons around the oxygen atom. To achieve a stable electronic configuration, oxygen needs two more electrons.To form bonds, the valence electrons of oxygen undergo hybridization. Hybridization is the process of mixing atomic orbitals to form new hybrid orbitals that are suitable for bonding. In the case of H2O, oxygen undergoes sp3 hybridization.In sp3 hybridization, one 2s orbital and three 2porbitals of oxygen combine to form four new hybrid orbitals called sp3 orbitals. These orbitals are arranged in a tetrahedral geometry around the oxygen atom.The four sp3 orbitals are oriented in space in a way that minimizes electron-electron repulsion. Three of these orbitals form sigma bonds with the hydrogen atoms, while the fourth orbital contains a lone pair of electrons. The sigma bonds are formed by overlapping the sp3 orbitals with the 1s orbitals of the hydrogen atoms.The resulting molecule, H2O, has a bent or V-shaped structure. The bond angle between the two hydrogen atoms is approximately 104.5 degrees. This bond angle is slightly less than the ideal tetrahedral angle of 109.5 degrees due to the presence of the lone pair on the oxygen atom, which creates additional repulsion.From a molecular geometry perspective, thehybridization of the central atom in H2O leads to a bent or V-shaped structure. This is because the repulsion between the lone pair and the bonding pairs of electrons pushes thehydrogen atoms closer together, resulting in a smaller bond angle.From a chemical bonding perspective, the sp3 hybridization of oxygen allows for the formation of sigma bonds with the hydrogen atoms, enabling the molecule to achieve a stable electronic configuration. The hybrid orbitals provide the necessary spatial orientation for bonding, ensuring that the molecule is stable and has the desired geometry.Overall, the hybridization of the central atom in H2Ois a crucial factor in determining the molecule's structure and properties. The sp3 hybridization of oxygen allows for the formation of strong sigma bonds with the hydrogen atoms, resulting in a bent molecular geometry. Understanding the hybridization of central atoms in molecules is essentialfor predicting their shapes and understanding theirchemical behavior.。

分波态密度pdos解析实例English Answer:Introduction.The partial density of states (PDOS) is a valuable tool for understanding the electronic structure of materials. It provides insight into the distribution of electron states over different energy levels and atomic orbitals. In this article, we will provide a detailed explanation of PDOS and discuss its applications in materials science.Definition and Calculation.The partial density of states is defined as the contribution of a specific atomic orbital or set oforbitals to the total electronic density of states (DOS). It is calculated by projecting the DOS onto the wavefunctions of the desired orbitals. This can be done using various computational methods, such as the densityfunctional theory (DFT).Interpretation.The PDOS provides valuable information about the electronic structure of materials. The peaks in the PDOS indicate the energy levels at which electrons are mostlikely to be found. The height of the peaks corresponds to the number of states available at those energy levels. By analyzing the PDOS, researchers can gain insights into the bonding, hybridization, and other electronic properties of materials.Applications.The PDOS has numerous applications in materials science, including:Understanding bonding: The PDOS can reveal the natureof chemical bonds in materials. For example, a high PDOS at low energies indicates strong bonding, while a low PDOS indicates weak bonding.Identifying electronic transitions: The PDOS can be used to identify the energy levels involved in electronic transitions. This information is essential forunderstanding the optical and electrical properties of materials.Designing new materials: The PDOS can guide the design of new materials with desired electronic properties. By manipulating the PDOS, researchers can tailor thematerials' bandgap, conductivity, and other characteristics.Conclusion.The partial density of states is a powerful tool for understanding the electronic structure of materials. It provides detailed information about the distribution of electron states, bonding, and other electronic properties. The PDOS has numerous applications in materials science, including understanding bonding, identifying electronic transitions, and designing new materials.Chinese Answer:导言。