Atomic and molecular structure engineering chemistry notes pdf | B.tech | 1st Chapter
Atomic & Molecular Structure Notes – Concise, downloadable notes for Engineering Chemistry! This atomic and molecular structure engineering chemistry notes PDF covers Molecular Orbital Theory, orbital overlap, bonding and antibonding orbitals, and electron configuration using Aufbau, Hund’s Rule, and Pauli Exclusion. Perfect for quick revision or deep dives into chemical bonding concepts.
Molecular Orbital Theory : atomic and molecular structure engineering chemistry notes pdf
Orbital: An Orbital is a three dimensional space around nucleus where the probability of finding an electron is high. They represent the probability of finding an electron in any one place. They correspond to different energies. So an electron in an orbital has definite energy. Each orbital is denoted by a number and a letter.
The number denotes the energy level of the electron in the orbital. Thus 1 refers to the energy level closest to the nucleus; 2 refers to the next energy level further out, and so on. The letter refers to the shape of the orbital. The letters go in the order s, p, d, f, g, h, i, j, etc.
Atomic Orbitals: Atomic orbitals are regions of space around the nucleus of an atom where an electron is likely to be found. Atomic orbitals allow atoms to make covalent bonds. An atomic orbital can have a maximum of two electrons. Atomic orbitals are labelled as s, p, d, and f sublevels. ( atomic and molecular structure engineering chemistry notes pdf )
s Orbitals: The s orbital is spherical and hold a maximum of two electrons. It has one sub-energy level. The order of size is 1s < 2s < 3s < …, as shown below.
p Orbitals: The p orbital is dumbbell shaped and can hold up to six electrons. It has three sub energy levels. These are given the symbols px, py and pz. The p orbitals at the second energy level are called 2px, 2py and 2pz. There are similar orbitals at subsequent levels: 3px, 3py, 3pz, 4px, 4py, 4pz and so on.
d Orbitals: The d and f orbitals have more complex shapes. The d level has five sub-energy groups and holds up to 10 electrons, The five 3d orbitals are called 3dxy, 3dxz, 3dyz, 3dx² – y², 3dz²
Molecular orbital
(MO: Atoms join to form molecules. When two atoms move closer together to form a molecule, atomic orbitals overlap and combine to become molecular orbitals. Molecular orbitals are regions around molecules where electrons are most likely to be found. The number of newly formed molecular orbitals is equal to the number of combined atomic orbitals. ( atomic and molecular structure engineering chemistry notes pdf )
The molecular orbital surrounds the two nuclei of the atoms, and electrons can move around both nuclei. Similar to atomic orbitals, molecular orbitals maximally contain 2 electrons, which have opposite spins. Molecular orbitals are of two types, bonding molecular orbitals and antibonding molecular orbitals. Bonding molecular orbitals contain electrons in the ground state and antibonding molecular orbitals contain no electrons in the ground state. Electrons may occupy in the antibonding orbitals if the molecule is in the excited state. ( atomic and molecular structure engineering chemistry notes pdf )
1) Each molecular orbital is described by a wave function Ψ, which in turn is associated with a set of quantum number. ( atomic and molecular structure engineering chemistry notes pdf )
2) Electrons fill up these orbitals in the same way as atomic orbitals in accordance to the3 principles (Aufbau, Hunds and Pauli Principle).
3) The Aufbau principle states that orbitals are filled with the lowest energy first. The Pauli exclusion principle states that the maximum number of electrons occupy ingan orbital is two, with opposite spins.
4) Hund’s rule states that when there are several MOs with equal energy, the electrons occupy the MOs one at a time before two occupy the same MO. ( atomic and molecular structure engineering chemistry notes pdf )
Electrons may be considered either of particle or of wave nature. Therefore, an electron in an atom may be described as occupying an atomic orbital, or by a wave function Ψ, which are solution to the Schrodinger wave equation. Wave function is a mathematical function related to probability of finding the particle in a particular region of space. ( atomic and molecular structure engineering chemistry notes pdf )
Electrons in a molecule are said to occupy molecular orbitals. The wave function of a molecular orbital may be obtained by one of two methods:
- 1. Linear Combination of Atomic Orbitals (LCAO)
- 2. United Atom Method.
Linear Combination of Atomic Orbitals (LCAO)
As per this method the formation of orbitals is because of Linear Combination (addition orsubtraction) of atomic orbitals which combine to form molecule. Consider two atoms A andB which have atomic orbitals described by the wave functions ΨA and ΨB .If electron cloudof these two atoms overlap, then the wave function for the molecule can be obtained bya linear combination of the atomic orbitals ΨA and ΨB i.e. by subtraction or addition of wavefunctions of atomic orbitals
ΨMO= ΨA + ΨB
The above equation forms two molecular orbitals
Bonding Molecular Orbitals
When addition of wave function takes place, the type of molecular orbitals formed are called Bonding Molecular orbitals and is represented by ΨMO = ΨA + ΨB.
They have lower energy than atomic orbitals involved. It is similar to constructive
interference occurring in phase because of which electron probability density increases
resulting in formation of bonding orbital. Molecular orbital formed by addition of
overlapping of two s orbitals shown in Figure 1. It is represented by s.
( atomic and molecular structure engineering chemistry notes pdf )
Anti-Bonding Molecular Orbitals
When molecular orbital is formed by subtraction of wave function, the type of molecular orbitals formed are called Antibonding Molecular Orbitals and is represented by ΨMO = ΨA – ΨB. They have higher energy than atomic orbitals. It is similar to destructive interference occurring out of phase resulting in formation of antibonding orbitals. Molecular Orbital formed by subtraction of overlapping of two s orbitals are shown in figure no. 2. It is represented by σ* (*) is used to represent antibonding molecular orbital) called Sigma Antibonding.
Therefore, Combination of two atomic orbitals results in formation of two molecular orbitals, bonding molecular orbital (BMO) whereas other is anti-bonding molecular orbital (ABMO).
BMO has lower energy and hence greater stability than ABMO. First BMO are filled then ABMO starts filling because BMO has lower energy than that of ABMO.
Formation of molecular orbitals occurs by the combination of atomic orbitals of proportional symmetry and comparable energy. Therefore, a molecular orbital is polycentric and atomic orbital is monocentric. Number of molecular orbitals formed is equal to the number of atomic Orbitals. ( atomic and molecular structure engineering chemistry notes pdf )
Relative Energies of Molecular Orbitals
Bonding Molecular Orbitals (BMO) –Energy of Bonding Molecular Orbitals is less than that of Anti Bonding Molecular Orbitals because the attraction of both the nuclei for both the electron (of the combining atom) is increased.
Anti-Bonding Molecular Orbitals (ABMO)–Energy of Anti Bonding Molecular Orbitals is higher than Bonding Molecular Orbitals because the electrons move away from the nuclei and are in repulsive state.
( atomic and molecular structure engineering chemistry notes pdf )
Energy Level Diagram
The factors upon which relative energies of molecular orbitals depend are:
- Energies of the Atomic orbitals combining to form Molecular Orbitals.
- The extent of overlapping between the atomic orbitals. The greater the overlap, the morethe bonding orbital is lowered and the anti-bonding orbital is raised in energy relative to AOs
1s Atomic Orbitals (AOs) of two atoms form two Molecular Orbitals (MOs) designated as s1s and s *1s.The 2s and 2p orbitals (eight AOs of two atoms) form four bonding MOs and four anti-bonding MOs as:
Bonding MOs: σ 2s, σ 2pz, π 2px, π 2py
Anti – Bonding MO: σ *2s, σ *2pz, π *2px, π *2py
The order of increasing energy of molecular orbitals obtained by combination of 1s, 2s and 2p orbitals of two atoms is → σ1s, σ *1s, σ 2s, σ *2s, σ 2pz, π 2px = π 2py, π *2px= π *2py, σ *2pz (Energy Increases from left to right)
Bond order:
It may be defined as the half of difference between the number of electrons present in the bonding orbitals and the antibonding orbitals that is, Bond order
(B.O.) = (No. of electrons in BMO – No. of electrons in ABMO)/ 2
Those with positive bonding order are considered stable molecule while those with negative bond order or zero bond order are unstable molecule.
Magnetic Behavior: If all the molecular orbitals in species are spin paired, the substance is diamagnetic. But if one or more molecular orbitals are singly occupied it is paramagnetic.
Molecular orbital energy level diagram of Nitrogen molecule (N2): The electronic configuration of nitrogen atom is 1s2 2s2 2p 1 2 1 2p 1 and N molecule has 14 electrons. The Molecular orbital diagram is shown in Fig. 3 The molecular orbital electronic configuration of the molecule is:
Molecular orbital energy level diagram of Oxygen molecule (O2)
Oxygen atom has electronic configuration of is 1s2 2s1 2px 2y 2pz Therefore, 2 1 1 oxygenmolecule has 16 electrons. In the formation of molecular orbitals, the electrons in the inner shells are expressed as KK denoting (σ1s) 2(σ*1s) 2. The remaining 12 electrons are filled in molecular orbitals as shown in figure 4 For O2 σ1s, σ 1s, σ 2s, σ 2s, σ 2pz, [π2px = π2py], [π2px= π2py], σ *2pz
Valence bond theory
Valence bond theory explains the geometry of the complex compound using the concept of hybridization. This theory is a chemical bonding theory that explains the bonding between two atoms is caused by the overlap of half-filled atomic orbitals. The two atoms share each other’s unpaired electron to form a filled orbital to form a hybrid orbital and bond together.
According to this theory, a covalent bond is formed between the two atoms by the overlap of half filled valence atomic orbitals of each atom containing one unpaired electron. Based on the pattern of overlapping, there are two types of covalent bonds: sigma bond and a pi bond. The covalent bond formed by sidewise overlapping of atomic orbitals is known as pi bond whereas the bond formed by overlapping of atomic orbital along the inter nucleus axis is known as a sigma bond.
According to VBT theory, a coordination entity is formed as a result of coordinate covalent bond formation by electron pairs from ligands (Lewis bases) through overlap of appropriate atomic orbitals (usually hybrid orbitals) of the metal (Lewis acid) and ligand. A coordination entity is composed of central atom, usually that of metal. ( atomic and molecular structure engineering chemistry notes pdf )
Limitation of the VBT:
- Fail to explain the colour & characteristics of absorption spectra of complex compounds.
- Orbital contribution and temperature dependency on magnetic moment of coordination complex are not properly explained by VBT. ( atomic and molecular structure engineering chemistry notes pdf )
- It is not helpful to predict the mystery of formation of outer or inner orbital coordination complex.
- VBT fails to predict any distortion in the shapes of the coordination complexes from regular geometry.
Crystal Field Theory:
Coordination compounds /Complex compounds
They are molecular compounds which retain their identities even when dissolved in water and their properties are completely different from those constituents. Ex. [K4Fe(CN)6] is a complex compound. Compounds containing complex ions are called complex compounds .These complex ions have coordinate bonds in their structure and known as coordinate ions and the compounds are called coordinate compounds. ( atomic and molecular structure engineering chemistry notes pdf )
Central ion : The cation to which one or more neutral molecules or anions are attached is called central ion
Ligands: Any atom or ion or molecule which is capable of donating a pair of electrons to the central metal atom are called ligands. The particular atom which donates pair of electrons is called a donor atom. Ex.Donor atoms-N ,O,S and halogens
Unidentate ligands: The ligands containing one donor atom is called unidentate ligand. Ex.F-, Cl-, Br-, I-, CN-.
Bidentate ligands:.The ligands which contains two donor atoms are called bidentate ligands. Ex.Ethylene diammine.
Coordination Number
The total number of ligands attached to the central atom is called coordination number Ex.[Ag(NH3)2]2+ / CN-2 ; [Cu(H2O)4]2+ / CN-4 Crystal field theory is very much different from valence bond theory.
According to valence bond theory, bonding between the metal ion and the ligands is purely covalent, while according to crystal field theory, the interaction between the metal ion and ligands, is purely electrostatic, i.e metal-ligand bonds are 100% ionic. Crystal field theory (CFT) describes the breaking of orbital degeneracy in transition metal complexes due to the presence of ligands.
CFT qualitatively describes the strength of the metal-ligand bonds. Based on the strength of the metal-ligand bonds, the energy of the system is altered. This may lead to a change in magnetic properties as well as color. This theory was developed by Hans Bethe and John Hasbrouck van Vleck.
Crystal Field Theory was developed to describe important properties of complexes (magnetism, absorption spectra, oxidation states, coordination,).are repelled by the lone pairs of the ligands. This repulsion will raise the energy level of the d orbitals. ( atomic and molecular structure engineering chemistry notes pdf )
All the ligands approaching the energy of each orbital will increase by the same amount. In other words, they will remain degenerate. Since d-orbitals differ in their orientation, those orbitals lying in the direction of the ligands is raised to a larger extent than the others.
So, five degenerate d-orbitals will split into two sets, having different amount of energies. This splitting of five degenerate d-orbitals of the metal ion under the influence of approaching ligands, into two sets of orbitals having different energies is called as Crystal- field splitting. ( atomic and molecular structure engineering chemistry notes pdf )
This splitting is affected by the following factors
- Nature of the ligands. The stronger the ligand, the greater is the splitting.
- Oxidation state of the central metal ion. A higher oxidation state leads to larger splitting.
- Size of d orbitals (i.e., transition series).
- Geometry of the complex. ( atomic and molecular structure engineering chemistry notes pdf )
- Nature of the metal ion6. Arrangement of the ligands around the metal ion.
Crystal Field Splitting in Octahedral Complexes
The octahedral arrangement of six ligands surrounding the central metal ion is as shown in the figure.
In an octahedral complex, the metal ion is at the centre and the ligands are at the six corners. In the figure, the directions x, y and z point to the three adjacent corners of the octahedran. The lobes of the eg orbitals (dx2-y2 and dz2) point along the x, y and z axis while the lobes of the t2g orbitals (dxy, dzx and dyz)point in between the axes. ( atomic and molecular structure engineering chemistry notes pdf )
As a result, the approach of six ligands along the x, y z, -x,-y and –z directions will increase the energy of dx2-y2 and dz2 orbitals (which point towards the ligands) much more than that it increases the energy of dxy, dzx and dyz orbitals ( which point in between the metal-legand bond axis). The approach of the ligands is considered as a two step process. ( atomic and molecular structure engineering chemistry notes pdf )
In the first step, it is assumed that the ligands approach the metal ion spherically, i.e. at an equal distance from each of the d-orbitals. At this stage all the d- orbitals are raised in energy by the same amount (The fived-orbitals remain degenerate0.In the second step the spherical field changes to octahedral field leading to splitting oforbitals
The energy difference between t2g and eg orbitals is known as crystal field splitting and it is denoted by the symbol Δo or 10Dq Thus, under the influence of an octahedral field, the d orbitals split into triply degenerate orbitals with less energy and another as doubly degenerate orbitals with higher energy. The main energy level between these two sets of orbitals is taken as zero, which is called bari centre. The splitting between these two orbitals is called crystal field splitting. The magnitude of stabilization will be 0.4 Δo and the magnitude of destabilization will be 0.6 Δo. ( atomic and molecular structure engineering chemistry notes pdf )
Crystal Field Spillting in Tetrahedral Complexes
The tetrahedral arrangement of four ligands surrounding the metal ions is as shown in the figure.
A regular tetrahedron is a cube. One atom is at the centre of the cube, and four of the eight corners of the cube are occupied by ligands. The directions x, y and z point to the face centres. The dx2-y2 and dz2 orbitals point along the x, y and z directions and dxy, dzx and dyz orbitals point in between x, y and z directions. ( atomic and molecular structure engineering chemistry notes pdf )
The direction of approach of ligands does not coincide exactly with either the e or t2 orbitals. The t2 orbitals are pointing close to the direction in which the e orbitals are lying in between the ligands. As a result, the energy of t2 orbitals increases compared to the energy of e orbitals.
Thus, d orbitals again split into two sets- triply degenerate t2 of higher energy and Fig: Splitting of d-orbitals in an octahedral complex Crystal Field Splitting in Tetrahedral Complexes: The tetrahedral arrangement of four ligands surrounding the metal ions is as shown in the figure. ( atomic and molecular structure engineering chemistry notes pdf )
