Atomic orbital assignment presentation.pptx

Assignment on atomic orbital
Chemistry presentation on atomic orbital

1. Unit 2 Atomic Orbitals Dr Nazia Tarannum

2. Atomic Orbital Solving the Schrodinger equation gives the energies an electron can have these are its energy levels. For each energy level, the Schrodinger equation also leads to a mathematical expression, called an atomic orbital, describing the probability of finding an electron around the nucleus. An atomic orbital is often thought of as a region of space in which there is a high probability of finding an electron. The energy levels of electrons in the quantum mechanical model are labeled by principal quantum number (n). These are assigned the value n= 1,2,3….

3. For each principle energy level, there may be several orbitals with different shapes and at different energy levels. There energy levels within a principle energy level constitute energy sublevels. Each energy sublevel correspond to an orbital of a different shape, which describes where the electron is likely to be found. Different atomic orbitals are denoted by letters. s orbital are spherical, and p orbital are dumbbell shaped. Because of the spherical shape of an s orbital, the probability of finding an electron at a given distance from the nucleus in an s orbital does not depends on direction. The three kinds of p orbital have different orientations in space.

4. Electron Configuration 1 s 1 row # shell # possibilities are 1-7 7 rows subshell possibilities are s, p, d, or f 4 subshells group # # valence e- possibilities are: s: 1 or 2 p: 1-6 d: 1-10 f: 1-14 Total e- should equal Atomic #

5. Summary of principle energy levels, sublevels and orbitals. Principle energy level Sublevels Type of sublevel n = 1 1 1s (1 orbital) n = 2 2 2s (1 orbital), 2p (3 orbitals) n = 3 3 3s (1 orbital), 3p (3 orbitals), 3d (5 orbitals) n = 4 4 4s (1 orbital), 4p (3 orbitals), 4d (5 orbitals), 4f (7 orbitals) The principle quantum number always equals the number of sublevels within that principle energy level.

6. The maximum number of electrons that can occupy a principle energy level is given by the formula 2n 2 , where n is the principle quantum number. Energy level (n) Maximum of electrons 1 2 2 8 3 18 4 32

7. s orbital p orbital

8. f orbital

9. Aufbau Principle Introduction: The Aufbau principle dictates the manner in which electrons are filled in the atomic orbitals of an atom in its ground state. It states that electrons are filled into atomic orbitals in the increasing order energy level. According to the Aufbau principle, the available atomic orbitals with the lowest energy levels are occupied before those with higher energy levels. The word Aufbau has German roots and can be roughly translated as construct or build up. A diagram illustrating the order in which atomic orbital are filled is provided below.

10. Here, n refers to the principle quantum number and l is the azimuthal quantum number.

11. The Aufbau principle can be used to understand the location of electrons in an atoms and their corresponding energy levels. For example, carbon has 6 electrons and its electronic configuration is 1s 2 2s 2 2p 2 . It is important to note that each orbital can hold a maximum of two electrons (as per the Pauli exclusion principle). Also, the manner in which electrons are filled into orbitals in a single subshell must follow Hund’s rule, i.e. every orbital in a given subshell must be singly occupied by electrons before any two electrons pair up in an orbital.

12. Salient features of the Aufbau principle: According to the Aufbau principle, electrons first occupy those orbitals whose energy is the lowest. This implies that the electrons enter the orbitals having higher energies only when orbitals with lower energies have been completely filled. The order in which the energy of orbitals increases can be determined with the help of the (n+l) rule, where the sum of the principle and azimuthal quantum numbers determines the energy level of the orbital. Lower (n+l) value correspond to lower orbital energies, if two orbitals shere equal (n+l) values, the orbital with the lower n value is said to have lower energy associated with it. The order in which the orbitals are filled with electrons is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on.

13. Bond Length Introduction: Covalent bond is formed between two atoms by the overlapping of atomic orbitals. This overlapping of atomic orbitals take place at certain distances between two atoms. The distance between the centres of two nuclei is known as bond length or bond distance. Bond length Bond length is measured by X-ray diffraction, electron diffraction and by spectroscopic methods. The unit of bond length is Angstrom, Å ( 1 Å = 10 －8 cm ). The bond length ensures the maximum stability of the bond. C-atom C-atom

14. The bond length of some common bonds are given below: Diatomic molecule Bond length Diatomic molecule Bond length C C 1.54 Å O H 0.96 Å C C 1.34 Å C N 1.47 Å C C 1.20 Å C O 1.43 Å C H 1.09 Å C O 1.20 Å N H 1.02 Å C Cl 1.77 Å

15. Factors affecting bond length: Bond length mainly depends on the following factors described as. ( 1) Bond order: It is observed that as bond order or multiplicity of bond increases, the bond length decreases. Molecules Bond order Bond length C H 3 C H 3 1 1.54 Å C H 2 C H 2 2 1.34 Å C H C H 3 1.20 Å (2) Electronegativity: If an atom is more electronegativite than the other in a diatomic molecule, then the bond length will be comparatively shorter. For example, the bond length of C-F bond is found to be 1.36 Å, whereas it should be 0.77 + 0.64 = 1.41 Å. The greater the difference in electronegativity between the two atoms, the shorter will be the bond length. If the electronegativities of two atoms A and B are X A and X B, then bond length ( r A－B ) is given by r A－B = r A + r B — 0.09 ( X A — X B ) Where r A and r B are the covalent radius of the two atoms.

16. (3) Resonance and delocalisation: Bond length is also affected by resonance. For example, the bond length of each C—C bond in benzene is 1.39 Å which is neither equal to C—C single bond (1.54 Å) nor to C C double bond ( 1.34 Å). It is however, in between them, as benzene occurs in the following two resonance hybrids. (4) Hybridisation: Bond length also depends on the hybridised state of the bonded atoms in a molecule. It is due to the s-character in different types of hybridised orbitals. Molecule Hybridisation of C- atom Percentage of s-character Bond length C H 3 C H 3 sp 3 25 % 1.54 Å C H 2 C H 2 sp 2 50 % 1.34 Å C H C H sp 75 % 1.20 Å So we can say that greater the s-character, smaller will be the orbital, stronger and smaller will be the bond length.

17. Used of bond length determination: A lot of information is furnished from determination of bond length, the important of which are described as follows. Stability of the compound: Bond length determination confirms us about the stability and reactivity of a number of organic compounds. Compounds of normal bond length behave in a normal way. Compounds of shorter or longer bond lengths have abnormal reactivity. It is because such compounds show hybridisation, resonance or have lone pair of electrons. (2) Structure of compound: The determination of bond length gives information about the nature of the compound and the presence of bonds, viz., single, double, triple etc. This helps us in determination of the correct structure of the compound.

18. Valence bond theory

19. Composition and Orientation of Hybrid Orbitals

20. Bent’s Rule Introduction: Bent’s rule states that “More electronegative substituents prefer hybrid orbitals having less s-character and more electropositive substituents prefer hybrid orbitals having more s-character”. This is the reason that in F-C-F s-character is less than 25% while in H-C-H it is more than 25%. It is interesting to note that in the formation of PCl 5 , P-atom exhibits sp 3 d hybridization in which there hybrid orbitals are on the plane and two hybrid orbitals are above and below the plane. In this p z d z 2 form linear hybrid orbitals axially and sp x p y form trigonal equatorial bonds.

21. Evidently P-Cl bonds which are on the axis are lower (i.e., lesser bond energy) than equatorial. But in the case of PCl 3 Cl 2 , it is observed that P-F bonds are on the axis and P-Cl bonds are on the equatorial. This is according to Bent’s rule, because F-atom is more electronegative hence prefer less s-character and is on the axis ( p z d z 2 ) while Cl-being less electronegative prefer more s-character (spxpy). Similarly we can explain the other examples of the type MX 5 (M= P, As, Sb, Bi and X = Cl, Br and I). Thus Bent’s rule is useful tool in inorganic and organic chemistry. It may be used as a supplement to the VSEPR interpretation of the structure of many non-metal fluorides.

22. Valence Shell Electron Pair Repulsion (VSEPR) Theory Introduction: This theory was developed in 1957 by Gillespie and Nyholm. It is based on the effect of electron repulsion on the bond angles. The shape of the molecule or ion depends upon the number of bonding electron pair (bp’s) and non-bonding electron pairs or lone pairs (lp’s) in the central atom. The central atom is oriented in such a way that there is minimum repulsion (maximum stability) between them. The molecule has a definite shape, because there is only one orientation of orbitals corresponding to minimum energy.

23. Gillespie postulated the following rules of VSEPR theory: If the central atom in a molecule is surrounded by only bonding electron pairs (bp’s) and not by non-bonding electron pairs or lone pairs (lp’s), it will have regular geometry or shape. The shape of the molecules with bond angles are given below.

24. If the central atom, in a molecule, is surrounded by both bp’s and lp’s, it will have distorted or irregular geometry or shape. Because, the lp’s repel adjacent electron pairs more strongly than bonding electron pairs. The repulsion increases as: (bp – bp) ˂ (bp – lp) ˂ (lp – lp) Due to this reason the bond angle decreases in the order of CH 4 (109.5˚) > NH 3 (107.8˚) > H 2 O (105.5˚) And the number of lp’s increases as: CH 4 (0) ˂ NH 3 (1) ˂ H 2 O (2)

25. Repulsion between bp of electrons is greater if the bp electron is near the central atom. Example H 2 O (105.5˚) > H 2 S (92.5˚) > H 2 Se (91.0˚) > H 2 Te (89.5˚) If the electronegativity of the central atom decreases bond angles decreases because bp of electrons shift away from the central atom. Example PI 3 (102˚) > PBr 3 (101.5˚) > PCl 3 (1 00˚) Although the multiple bonds do not effect the geometry of the molecules but the bond angle involving single bonds are generally smaller than those of multiple bonds.

26. Application of VSEPR Theory:

27. VSEPR shape (SF 4 )

28. VSEPR shape (ClF 3 )

29. VSEPR shape ( I 3 - )

30. Molecular Orbital Theory Introduction: Hund and Milliken have developed an approach to bond formation which is based upon the effects of the various electron field upon each other and which employs molecular orbital rather than atomic orbitals. Each such orbital characterizing the molecule as a whole is described by a definite combination of quantum numbers and possesses a relative energy value. According to the theory the atomic orbitals combine and form a resultant orbital known as the molecular orbital in which the identity of both the atomic orbitals is lost. All the electrons pertaining to both the atoms are considered to be moving along the entire molecule under the influence of all the nuclei.

31. This may be illustrated by the figure depicted here. Formation of AB molecule by valence bond method and molecular orbital method

32. Basic principle of Molecular Orbital Theory ( MOT): When nuclei of two come close to each other, their atomic orbitals interact resulting in the formation of molecular orbital. In a molecule atomic orbitals of atoms lose their identity after the formation of molecular orbitals. Each molecular orbitals may be describe by the wave function Ψ , which is known as molecular orbitals wave function. Ψ 2 represent the probability density or electron density. Each molecular orbitals wave function Ψ is associated with a set of quantum number which represents the energy and shape of the occupied molecular orbitals. Each electron in a molecular orbitals belongs to all nuclei presented in the molecular structure. Each electron moving in the molecular orbitals is having clockwise or anticlockwise (i.e. ± ½ ).

33. Central themes of molecular orbital (MO) theory A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals. Atomic wave functions are summed to obtain molecular wave functions. If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei). If wave functions cancel each other, an antibonding MO is formed (a node of zero electron density occurs between the nuclei).

34. Contours and energies of the bonding and antibonding molecular orbitals in H 2

35. Number of AOs combined = number of MOs produced Bonding MO: lower in energy than isolated atoms Antibonding MO: higher in energy than isolated atoms To form MOs, AOs must have similar energy and orientation Sigma (s) and pi (p) bonds are denoted as before; a star (asterisk) is used to denote antibonding MOs. Bond order = Higher bond order = stronger bond (no. of e - in bonding MOs) - (no. of e - in antibonding MOs) 2

36. Now, the bond order of a molecule is determined by the formula which is as follows: N atom orbital N atom orbital Molecular orbital diagram of N 2 (Homonuclear diatomic molecule): Bond order = (no. of e - in bonding MOs) - (no. of e - in antibonding MOs) 2 = 10 - 4 2 = 6 1s 1s 2s 2s 2p 2p Magnetic properties = Diamagnetic

37. Molecular orbital diagram of O 2 Bond order = 8 - 4 2 = 2 Magnetic properties = Paramagnetic (Two unpaired electrons)

38. Molecular orbital diagram of B 2 Bond order = 4 - 2 2 = 1 Magnetic properties = Paramagnetic (Two unpaired electrons)

39. Molecular orbital diagram of F 2 Bond order = 8 - 6 2 = 1 Magnetic properties = Diamagnetic

40. Bond order = 8 - 2 2 = 3 Magnetic properties = Diamagnetic Molecular orbital diagram of CO (Heteronuclear diatomic molecule)

41. Molecular orbital diagram of NO Bond order = 8 - 3 2 = 2.5 Magnetic properties = Paramagnetic (One unpaired electrons)

42. Bond order = 9 - 4 2 = 2.5 Magnetic properties = Paramagnetic (One unpaired electrons) Molecular orbital diagram of N 2 + (Ion diatomic molecule):

43. Molecular orbital diagram of O 2 + Bond order = 8 - 3 2 = 2.5 Magnetic properties = Paramagnetic (One unpaired electrons)