UNIT-1 MEC PDF

Atomic and Molecular Orbitals Molecular Orbital (MO) The wave function of an electron in The wave function of an electron in a an atom is called atomic orbitals molecule is called molecular orbital Atomic orbitals is mono centric Molecular orbital is polyc...

Atomic and Molecular Orbitals Molecular Orbital (MO) The wave function of an electron in The wave function of an electron in a an atom is called atomic orbitals molecule is called molecular orbital Atomic orbitals is mono centric Molecular orbital is polycentric No bonding and anti-bonding atomic There are bonding anti-bonding orbitals molecular orbitals. It is less stable. It is more stable. It has a simple It has a complex shape. Atomic orbitals are designated as Molecular orbitals designated as s, p, d, f etc., , *, , *, , * Science broadly defined as 'accumulated knowledge, based on observations, suitably tested and verified, and properly or organized and classified'. The first step in the development of any branch of science is to observe the facts or phenomena as they take place in nature or laboratory. An attempt is then made to see if these facts can be put in the form of a general statement or mathematical expression which is known as the law. Therefore, a law is a mathematical statement of the regularity of behavior. The second step consists in seeking an explanation for the experimental facts by reasonable imagination or guess called Hypothesis. For example, Dalton put forward the well-known atomic hypothesis to explain the law of chemical combination. The third step is to put the hypothesis to test. If the assumptions are found correct, the hypothesis is given the status of theory. The actual or direct proof of the theory is impossible. For example, there is hardly any doubt that the kinetic theory of gases is essentially correct but its direct proof has never been fully established. Atoms are the smallest parts of an element that chemically react. In 1808, John Dalton proposed the first atomic theory, i.e., an individual particle of matter is known as an atom. At the end of the 19th century, it was proved experimentally that atoms are divisible and consist of three fundamental particles (electrons, protons and neutrons). This soon led to the questions about the internal arrangement of these fundamental particles (atomic structure). Many atomic models such as J. J. Thomson's model, Rutherford's model, Bohr's model, etc. were suggested from time to time. ELECTROMAGNETIC RADIATIONS In 1864, Clark Maxwell proved that an alternating current of high frequency is capable of radiating continuous energy in the form of waves (electromagnetic waves or electromagnetic radiations). They have both electric and magnetic properties. The radiations such as visible, ultraviolet, infrared, X-rays, etc. are called Electromagnetic Radiations. They consist of electric and magnetic fields Oscillating perpendicular to other and both are perpendicular to the direction of wave propagation. These waves do not require any medium for propagation. Electromagnetic waves travel with the same speed of light (3.0 x 1010 cm/s). All waves have the following five characteristics: (i) Wavelength The distance between two consecutive crests or troughs of the wave is known as wavelength (Fig. 1.1). It is denoted by λ (lambda) expressed in angstrom units (Å). 1 Å = 10−8 cm: 10−10 m (ii) Frequency The number of times a wave passes through a fixed point per unit time is known as frequency. It is denoted by 'υ' (nu) and expressed in cycles per second or hertz (Hz). (iii) Wavenumber The reciprocal of wavelength is called Wave Number. It is denoted by 𝜐̅ and expressed in cm—I (iv) Amplitude The depth of the trough or height of crest is known as amplitude. It is denoted by 'a'. (v) Velocity The distance traveled by a wave in one second is called velocity. It is denoted by 'c' and expressed in m/sec or cm/sec. C = υλ (c: 3.0 x 108 m/sec or 3.0 x 1010 cm/sec) Electromagnetic Spectra The arrangements of various types of electromagnetic radiations in terms of increasing or decreasing wavelengths or frequency is called an electromagnetic spectrum. The spectrum obtained by white light is a continuous spectrum. For example, the visible light is the form of electromagnetic radiation that lies in the wavelength range of 3800—7600 Å. The wavelengths of various waves increase in the following order (Fig). γ-rays < X-rays < UV rays < Visible rays < IR rays Ψ2A+ Ψ2B Ψ2a= (ΨA-ΨB)2 Ψ2a= Ψ2A+ Ψ2B-2ΨAΨB i.e., Ψ2a< Ψ2A+ Ψ2B Types of Combinations of Atomic Orbitals When two atomic orbitals combine along the internuclear axis, the molecular orbitals formed are called and * molecular orbitals and when overlap sideways (lateral), the molecular orbitals formed are known as and * molecular orbitals. As s-orbitals are spherical symmetrical, their wave functions have the same sign in all directions. While in the case of p-orbitals, one lobe is given '+' sign and another lobe as a ‘-’ sign. Combining of positive (+) lobes or negative (-) lobes of two p-orbitals forming bonding molecular orbital and combining Of one '+' ‘lobe’ of one orbital and ‘-’ lobe of Other orbital forms anti- bonding molecular orbital. Positive (+) lobe interaction with positive (+) lobe means the addition of wave functions, while positive (+) lobe interaction with negative (-) lobe subtraction of wave functions. (1) S-S combination of orbitals: On the linear combination of 1s atomic orbitals of two atoms formed two molecular orbitals (Fig. 1.8). Fig. Molecular orbital formation by the combination of 1s atomic orbitals As shown in Fig. 1.8, when the addition of wave functions occur (both wave same sign), 1s molecular orbital is formed while subtraction of wave functions occur (both wave opposite sign), * 1s molecular of is formed. The dotted line between two lobes indicates a nodal orbital where the probability of finding the electron density is zero. Similaraly, the combination of two 2s orbitals forms two molecular orbitals 2s and *2s (2) P-P combination of orbitals: There are two possibilities for the combination of two 'p' orbitals, i.e., either end-to-end combination or a side- by-side combination. (a) End-to-end or axial combination of P-P orbitals: If the Inter nuclear axis is assumed to fall with the x-axis, then the combinations of two px atomic orbitals will yield a bonding or anti-bonding sigma ( ) molecular orbitals Fig. Sigma bond resulting from P-P orbital combination (b) Side by side or lateral combination of P-P orbitals: overlapping of two orbitalssituated perpendicular to the intemuclear axis (Py, Pz) gives rise - bonding molecular orbital and also *-anti- bonding molecular orbital. C) Non-bonding combination of orbitals: When the combination of two atomic orbitals brings no change in overall energy, then the situation is called no- bonding. For example, let us consider a lateral combination of s and p orbitals Fig. Non-Bonding combination of S and P orbitals In this overlap, the stabilization accruing from positive (+) and positive (+) above inter-nuclear axis is destabilized by positive (+) or negative (-) overlap below the inter nuclear axis, thus leading to non-bonding. Similarly, other non-bonding combinations of atomic orbitals are given in Fig. Fig: Some other non-bonding combinations Bond Order of a Molecule The number of covalent bonds between the constituent atoms in a molecule is called its bond order. Bond order is defined as one half of the difference between the number of electrons present in the bonding and the anti-bonding orbitals. Mathematically, Bond order (BO) = 1/2(Number of electrons in bonding orbitals-Number of electrons in anti-bonding orbitals) =1/2(Nb-Na) The bond order provides the following information: l. The value of bond order refers to the existence and stability of the molecule If the value of the bond order is zero or less than zero which indicates the species does not exist or unstable, such as He2. In case the values l, 2 and 3 indicate that the molecule is stable and the two atoms are held together by a single, double and triple bond respectively. +1/2 indicates that species exists but is unstable, such as He2+, H2+ 2. Bond order is inversely proportional to bond length 3. Higher the bond order, the larger is the bond dissociation energy, i.e. bond order is directly proportional to the bond dissociation energy.  Bonding in Homo-Nuclear Diatomic Molecules H2 molecule It is formed by the combination of two 1s atomic orbitals. Molecular orbital configuration of hydrogen molecule = (1s)2 Bond order = ½(2-0) = 1 Thus, the hydrogen atoms in the hydrogen molecule are bonded through a single covalent bond. It is a stable and diamagnetic molecule. Molecular orbital energy-level diagram For H2 molecule 2. Hydrogen molecule ion (H2+): This ion has one hydrogen atom and one H + ion. It contains only one electron. Molecular configuration of H2+ = (1s)1 Bond order = ½ (1-0) = 1/2 From the above data, H2+ ion is weaker than that of hydrogen (H2) molecule. It is unstable and paramagnetic in nature Molecular orbital energy-level diagram For H2+ molecule 3. Helium molecule (He2) The electronic configuration of helium (He) is 1s2. The molecular orbitals of the helium molecule are formed by 1s2 orbitals of two helium atoms. Molecular orbital configuration of He molecule = (1s)2 *(1s)2 Bond order: ½ (2-2) = 0 So that the molecule does not exist Fig. Molecular orbital energy-level diagram for He2 molecule Nitrogen molecule (N2) The electronic configuration of nitrogen is 1s22s22p3. There are five valence electrons in each nitrogen atom. Therefore, the molecular orbitals of nitrogen molecules have ten electrons. Molecular orbital configuration of nitrogen molecule (N2) KK (2s)2 *(2s)2 (2px)2 (2py)2 (2Pz2) Bond order =1/2(8-2) = 3 Nitrogen molecule is diamagnetic because there are no unpaired electrons The molecular orbital energy-level diagram for N2 molecule is presented in Fig. Fig. Molecular orbital energy-level diagram for N 2 molecule 7. Oxygen molecule (O2): The electronic configuration of oxygen atom is 1s22s22p4. There are twelve valence electrons to be accommodated in the molecular orbitals of O2 molecule. Molecular orbital configuration of oxygen molecule (O2) KK (2s)2 *(2s)2 (2Pz2) (2px)2 (2py)2 *(2px)l *(2py)l Bond order= ½[8-4] = 2 The last two molecular orbitals are singly occupied; hence, the molecule is paramagnetic in nature. The molecular orbital energy-level diagram for O2 molecule is shown in Fig. Molecular orbital energy-level diagram for O2 molecule Nitric oxide molecule (NO): The electronic configuration of nitrogen is 1s22s22p3 (five valence electrons) and oxygen is 1s22s22p4 (six valence electrons). It shows that all put together, they have eleven valency electrons. Molecular orbital configuration of nitric oxide molecule (NO)= KK (2s)2 *(2s)2 (2Pz2) (2px)2 (2py)2 *(2px)l Bond order=1/2 (8-3) = 2.5 The presence of one unpaired electron makes the molecule unstable and paramagnetic in nature. The molecular orbital energy-level diagram for NO molecule is shown in Fig. Fig. Molecular orbital energy-level diagram for NO molecule Carbon monooxide molecule (CO): The electronic configuration of Carbon is 1s22s22p2 (four valence electrons) and oxygen is 1s22s22p4 (six valence electrons). It shows that all put together, they have eleven valency electrons. Molecular orbital configuration of Carbon monooxide molecule (CO)= KK (2s)2 *(2s)2 (2Pz2) (2px)2 (2py)2 *(2px) Bond order=1/2 (8-2) = 3 The presence of no unpaired electron makes the molecule stable and diamagnetic in nature. The molecular orbital energy-level diagram for CO molecule is shown in Fig. CRYSTAL FIELD THEORY (CFT) Bethe and Vanvleck proposed Crystal Field Theory (CET) which was later extended by Orgel. This theory is mainly applicable to transition metals. According to this theory, the central metal ion of the complex is regarded as a point charge. Similarly, surrounding ligands are considered as point masses. Bonding between the central metal ion and the surrounding ligands are assumed to be ionic, i.e., bonding between a central metal ion and its ligands simply arises from the purely electrostatic force of attraction (an attraction between a positively charged metal ion and negative charge of the ligand or partial negative charge of ligand). If the ligand is a neutral molecule, the negative end of the dipole is attracted towards the central positive metal ion. The five d-orbitals (dxy, dyz, dzx, dX2-y2 and dz2) in a metal atom or ion have the same energy (degenerate orbitals). This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom or ion. If the negative filed is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the orbitals is changed and results in the splitting of the d-orbitals. The pattern of splitting depends upon the nature of the crystal field. Crystal Filled Splitting in Octahedral Geometry In the octahedral complex, six ligands occupy the six corners of an octahedron. There will be repulsion between the electrons in metal d-orbitals and the electrons of the ligands. However, not all the d-electrons will be affected equally. Those in the dX2-y2 and dz2and orbitals (eg orbitals) which are directed along the x, y and z axes will be repelled more than those in the dxy, dyz and dzx orbitals (t2g orbitals) which are directed between these axes. Hence, under the influence of the approaching ligands, the electrons in the orbitals dX2-y2 and dz2 and exist in the higher energy levels compared to dxy, dyz and dzx. This splitting of the degenerate levels due to the presence of a definite geometry is known as Crystal Field Splitting. The difference between the eg and t2g orbitals is designated by ∆o (subscript 'o' denotes an octahedral environment) or 10Dq. This is called crystal field stabilization energy (CFSE). The two eg orbitals are raised by 3/5 ∆o or 0.6 ∆o or 6Dq and three orbitals are lowered by 2/5 ∆o or 0.4 ∆o or 4Dq. in octahedral field. The splitting of the d-orbitals in an octahedral field is given in Fig. Fig. Splitting old-orbitals in an octahedral field Crystal Field Splitting in Tetrahedral Geometry In a tetrahedral complex, the splitting is the reverse of octahedral splitting. The direction of approach of the four ligands does not coincide exactly with the eg or t2g orbitals. Now, the approach of ligands raises the energy for both eg and t2g sets of orbitals. However, the energy of t2g sets of orbitals is raised maximum, since they are closest to the ligands. Therefore, crystal splitting is opposite of that takes place in octahedral complexes. For the same metal, same ligands and metal-ligand distance, the relation between tetrahedral splitting energy (∆t) and octahedral splitting energy (∆o) is ∆t = 2/3 x 2/3 = 4/9 ∆o Thus, the tetrahedral splitting (∆t) is always much smaller than the octahedral splitting (∆o). The splitting of the d-orbitals is given in Fig. in a tetrahedral field. Fig. Splitting old-orbitals in a tetrahedral field The orbital splitting energies are not sufficiently large for force paring and therefore, low spin configurations are rarely observed in tetrahedral complexes. Pi molecular orbitals of Butadiene  Butadiene is a conjugated diene consisting of two adjacent pi-bonds and comprised of 4 p-orbitals and 4 pi-electrons. To draw the molecular orbital diagram of butadiene, start by drawing 4 p-orbitals all aligned with the same phase. This has zero nodes and is the lowest energy pi-orbital (π1 ) As the number of nodes in an orbital increases, so does its energy. The highest-energy molecular orbital has three nodes and has all p-orbitals with opposite phases (π4) Intermediate orbitals (π2 ) and (π3 ) have one and two nodes, respectively. Once the molecular orbital diagram is built, the next step is to add the 4 pi-electrons. This will fill up the lowest-energy orbital (π1 ) and the second-lowest-energy orbital (π2 ) The highest-occupied molecular orbital (HOMO) of butadiene is the highest-energy orbital that contains pi-electrons. This is π2 The lowest-unoccupied molecular orbital (LUMO) of butadiene is the lowest-energy orbital that has zero pi-electrons. This is π3 Pi molecular orbitals of Benzene  A molecular orbital description of benzene provides a more satisfying and more general treatment of "aromaticity". We know that benzene has a planar hexagonal structure in which all the carbon atoms are sp2 hybridized, and all the carbon-carbon bonds are equal in length. As shown below, the remaining cyclic array of six p-orbitals ( one on each carbon) overlap to generate six molecular orbitals, three bonding and three antibonding. The plus and minus signs shown in the diagram do not represent electrostatic charge, but refer to phase signs in the equations that describe these orbitals (in the diagram the phases are also color coded). When the phases correspond, the orbitals overlap to generate a common region of like phase, with those orbitals having the greatest overlap (e.g. π1) being lowest in energy. The remaining carbon valence electrons then occupy these molecular orbitals in pairs, resulting in a fully occupied (6 electrons) set of bonding molecular orbitals. It is this completely filled set of bonding orbitals, or closed shell, that gives the benzene ring its thermodynamic and chemical stability, just as a filled valence shell octet confers stability on the inert gases.