Chemical bonding in solids. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

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1 Chemical bonding in solids 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

2 BONDING FORCES & ENERGIES 2 Forces acting on atoms depends on their interatomic separation or radius distance between 2 nuclei of 2 atoms 1. Attractive Forces (FA) 2. Repulsive Forces (FR) FN = FA + FR r = intertomic radius Na + Cl - r

3 Na+ Cl- At equilibrium, FN = FA + FR = 0 (no net force) 3 At equilibrium, r = ro equilibrium spacing D C B A Eo = bonding energy of two atoms; E required to separate these two atoms to an infinite separation At equilibrium (at equillibrium spacing): EN = EA + ER is at a min. or EN = Eo

4 Interatomic spacing decreases BONDING FORCES 4 Referring to last Fig. (top): A high interatomic spacing (right side of curve) Little FA No FR ( zero ) B : as interatomic spacing decreases (get closer; move to left part of curve) FA increases FR increases C : interatomic spacing reaches an EQUILIBRIUM (dashed line) r = r0 FN = FA + FR = 0 D : If atoms try to move much closer (r << ro): FR increases dramatically to prevent this.

5 BONDING ENERGIES 5 Referring to Fig. 2.8 (bottom) Energy between 2 atoms also depends on interatomic separation EA = attractive E ER = repulsive E EN = net E = EA + ER As two atoms get closer: EA and ER increase At r = ro EN reaches a minimum (this is Eo) E0 = bonding E of the two atom E0 is the minimum EN E0 is the E required to separate these 2 atoms to infinite separation

6 6 New orbitals are constructed from pre-existing s, p, and d-orbitals = hybrid orbitals 1. Only use valence shell electrons 2. Hybridize the CENTRAL ATOM ONLY (others as needed) 3. The number of hybrid orbitals formed = number of atomic orbitals used

7 7

8 8

9 9 sp 3 hybridization for H 2 O Needed to form 2 sigma bonds and 2 lone pairs

10 10

11 11 BF 3 - trigonal planar according to Valence shell electron pair repulsion (VSEPR) theory (incomplete octet exception)

12 12 Valence shell electron pair repulsion (VSEPR) theory Valence shell electron pair repulsion (VSEPR) theory is a model used, in chemistry, to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms.[1] It is also named Gillespie Nyholm theory after its two main developers. The acronym "VSEPR" is pronounced either "ves-per"[2] or "vuh-seh-per"[3] by some chemists. The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other, and will therefore adopt an arrangement that minimizes this repulsion, thus determining the molecule's geometry. Gillespie has emphasized that the electron-electron repulsion due to the Pauli exclusion principle is more important in determining molecular geometry than the electrostatic repulsion.

13 13 For BF 3, we need 3 hybrid orbitals, so 3 atomic orbitals are required as follows: (s + p + p) = sp 2 Needed to form 3 sigma bonds

14 14

15 BF 3 Molecule 15

16 16 BeH 2 - linear according to VSEPR Theory

17 17

18 BeH 2 Molecule 18 H - 1s orbitals sp hybrids

19 19 PF 5 - trigonal bipyramidal according to VSEPR Theory

20 20 For PF 5, we need 5 hybrid orbitals, so 5 atomic orbitals are required as follows: (s + p + p + p + d) = sp 3 d Needed to form 5 sigma bonds

21 21 SF 6 - octahedral according to VSEPR Theory Lewis Structure Electron Pair Geometry Molecular Geometry

22 22 For SF 6, we need 6 hybrid orbitals, so 6 atomic orbitals are required as follows: (s + p + p + p + d + d) = sp 3 d 2 3 unhybridized d-orbitals Six sp 3 d 2 hybridized orbitals for S-F bonds Isolated S atom Needed to form 6 sigma bonds

23 23 Electron pair arrangement Geometric Figure Example Linear 2 pairs = sp hybrids Trig. Plan. 3 pairs = sp 2 hybrids tetrahedral 4 pairs = sp 3 hybrids

24 24 Electron pair arrangement Geometric Figure Example Trig. Bipyram. 5 pairs = sp 3 d hybrids Octahedral 3 pairs = sp 3 d 2 hybrids

25 25 Sigma ( ) bonds = end-to-end overlap

26 26 Pi ( ) bond = side-by-side overlap

27 What are, and d bonds 27 Bonds Single bond resulting from head to head overlap of atomic orbital Bonds Double and triple bond resulting from lateral or side way overlap of p atomic orbitals d Bond Double, triple and quadruple bond resulting from lateral or side way overlap of d atomic orbitals

28 How do you tell the hybridization of a central atom? 28 Get the Lewis structure of the molecule Look at the number of electron pairs on the central atom. Note: double, triple bonds are counted as single electron pairs. Follow the following chart

29 Kinds of hybrid orbitals 29 Hybrid geometry # of orbital sp linear 2 sp 2 trigonal planar 3 sp 3 tetrahedral 4 sp 3 d trigonal bipyramid 5 sp 3 d 2 octahedral 6

30 Electronegativity Values 30 Table 12.1

31 Molecular Bonds Introduction 31 The bonding mechanisms in a molecule are fundamentally due to electric forces The forces are related to a potential energy function A stable molecule would be expected at a configuration for which the potential energy function has its minimum value

Features of Molecular Bonds 32 The force between atoms is repulsive at very small separation distances This repulsion is partially electrostatic and partially due to the exclusion principle Due to

32 Features of Molecular Bonds 32 The force between atoms is repulsive at very small separation distances This repulsion is partially electrostatic and partially due to the exclusion principle Due to the exclusion principle, some electrons in overlapping shells are forced into higher energy states The energy of the system increases as if a repulsive force existed between the atoms The force between the atoms is attractive at larger distances

33 Potential Energy Function 33 The potential energy for a system of two atoms can be expressed in the form Ur A r B r () n m r is the internuclear separation distance m and n are small integers A is associated with the attractive force B is associated with the repulsive force

34 Potential Energy Function, Graph 34 At large separations, the slope of the curve is positive Corresponds to a net attractive force At the equilibrium separation distance, the attractive and repulsive forces just balance At this point the potential energy is a minimum The slope is zero

35 Bonds in Solids Types 35 Simplified models of bonding in solids include Ionic Covalent Metallic van der Waals Hydrogen

36 Ionic Bonding 36 Ionic bonding occurs when two atoms combine in such a way that one or more outer electrons are transferred from one atom to the other Ionic bonds are fundamentally caused by the Coulomb attraction between oppositely charged ions When an electron makes a transition from the E = 0 to a negative energy state, energy is released The amount of this energy is called the electron affinity of the atom The dissociation energy is the amount of energy needed to break the molecular bonds and produce neutral atoms

37 Ionic Bonding, NaCl Example 37 The graph shows the total energy of the molecule vs the internuclear distance The minimum energy is at the equilibrium separation distance

38 Ionic Bonding 38 The energy of the molecule is lower than the energy of the system of two neutral atoms It is said that it is energetically favorable for the molecule to form The system of two atoms can reduce its energy by transferring electron out of the system and forming a molecule

39 39 Ionic Solids Orderly array of cations and anions Larger ion (usu. anion) determines crystal structure Smaller ion fills in the holes Electroneutrality is maintained Ignore smaller ion to see crystal type NaCl face-centered cubic Cl ions occupy fcc sites Sodium Chloride

40 Ionic Solids 40

41 Ionic Bonding 41 Transfer of electron from electropositive ion to the electronegative ion Coulomb interactions plays an important role Size of the cation reduces and size of anion increases Electro-negativity difference between ions decide the strength of ionic bonding.

42 Halite (NaCl) An example of Ionic Bonding 42

43 Sodium Chloride 45 Cl - ions (green) occupy ccp structure with fcc unit cell Na + ions (gray) occupy octahedral holes e = 2r Cl + 2r Na f > 4r Cl All holes are occupied

44 Zinc Sulfide: ZnS 46 S - ions (yellow) are ccp, occupy fcc sites 4 S - ions/unit cell Zn 2+ ions (purple) occupy 4 of the 8 tetrahedral holes

45 47 Calcium Fluoride: CaF 2 A case where the cation defines the unit cell Ca 2+ ions (purple) occupy fcc sites 4 Ca 2+ ions/unit cell F - ions (yellow) occupy all 8 of the tetrahedral holes 8 F - ions/unit cell

46 Electron Localization Function (ELF) for NaCl 48

47 Properties of Ionic Crystals 49 They form relatively stable, hard crystals They are poor electrical conductors They contain no free electrons Each electron is bound tightly to one of the ions They have high melting points They are transparent to visible radiation, but absorb strongly in the infrared region The shells formed by the electrons are so tightly bound that visible light does not possess sufficient energy to promote electrons to the next allowed shell Infrared is absorbed strongly because the vibrations of the ions have natural resonant frequencies in the low-energy infrared region

48 ZnS CaF 2 50 Ionic solids cations and anions held together with ionic bonds arranged in a crystal lattice that maximizes ion interaction anions are packed close, with the small cations occupying the holes

49 Covalent Bonding 51 A covalent bond between two atoms is one in which electrons supplied by either one or both atoms are shared by the two atoms Covalent bonds can be described in terms of atomic wave functions The example will be two hydrogen atoms forming H 2

50 Molecular Orbital Theory 52 Molecular orbitals are obtained by combining the atomic orbitals on the atoms in the molecule.

51 53 Bonding and Anti-bonding Molecular Orbital

52 Basic Rules of Molecular Orbital Theory 54 The MO Theory has five basic rules: The number of molecular orbitals = the number of atomic orbitals combined Of the two MO's, one is a bonding orbital (lower energy) and one is an anti-bonding orbital (higher energy) Electrons enter the lowest orbital available The maximum # of electrons in an orbital is 2 (Pauli Exclusion Principle) Electrons spread out before pairing up (Hund's Rule)

53 Wave Function Two Atoms Far Apart 55 Each atom has a wave function 1 rao ψ1 s() r e 3 πa There is little overlap between the wave functions of the two atoms when they are far away from each other o

54 Combined Wave Functions 56 The wave functions can combine in the various ways shown Ψ s+ + ψ s+ is equivalent to ψ s+ + ψ s - These two possible combinations of wave functions represent two possible states of the two-atom system

55 Splitting of Energy Levels 57 The states are split into two energy levels due to the two ways of combining the wave functions The energy difference is relatively small, so the two states are close together on an energy scale For large values of r, the electron clouds do not overlap and there is no splitting of the energy level

56 Wave Function Covalent Molecule 58 The two atoms are brought close together The wave functions overlap and form the compound wave shown The probability amplitude is larger between the atoms than on either side

57 Sigma Bond Formation by Orbital Overlap 59 Two s orbitals overlap

58 Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals 60 4 C atom orbitals hybridize to form four equivalent sp 3 hybrid atomic orbitals.

59 Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals 61 4 orbitals in Si hybridize to form four equivalent sp 3 hybrid atomic orbitals.

60 Covalent Bonding Features 62 The probability is higher that the electrons associated with the atoms will be located between them This can be modeled as if there were a fixed negative charge between the atoms, exerting attractive Coulomb forces on both nuclei The result is an overall attractive force between the atoms, resulting in the covalent bond

61 Covalent Bonding 63

62 64

63 ELF for Diamond 65

64 Electron Density of Si 66

65 Properties of Solids with Covalent Bonds 67 Properties include Usually very hard Due to the large atomic cohesive energies High bond energies High melting points Good electrical insulators

66 Cohesive Energies for Some Covalent Solids 68

67 69 Metallic Bonding Metal ions are held together by delocalized bonds formed from the atomic orbitals of all the atoms in the lattice. The idea that the molecular orbitals of the band of energy levels are spread or delocalized over the atoms of the piece of metal accounts for bonding in metallic solids.

68 Linear Combination of Atomic Orbitals 70

69 Linear Combination of Atomic Orbitals 71

70 72

71 73 Metallic solids: atoms release their valence electrons, forming cations fixed in a sea of mobile electrons + e - + e - + e - + e - + e - + e - + e e - + e - + e - + e - + e - + e - + e - + e - + e

72 Metallic Solids 74 Metallic bonds are generally weaker than ionic or covalent bonds The outer electrons in the atoms of a metal are relatively free to move through the material The number of such mobile electrons in a metal is large

73 Bonding and Electrical Conductivity in Metals 75 Bonding is strong and non-directional Model for bonding should explain electrical conductivity malleability other properties Models Electron Sea Model Molecular Orbital Model

74 76 Electron sea model for metals Simplest model for Electrical conductivity Malleability

75 Metallic Solids, cont. 79 The metallic structure can be viewed as a sea or gas of nearly free electrons surrounding a lattice of positive ions The bonding mechanism is the attractive force between the entire collection of positive ions and the electron gas

76 Properties of Metallic Solids 80 Light interacts strongly with the free electrons in metals Visible light is absorbed and re-emitted quite close to the surface This accounts for the shiny nature of metal surfaces High electrical conductivity The metallic bond is nondirectional This allows many different types of metal atoms to be dissolved in a host metal in varying amounts The resulting solid solutions, or alloys, may be designed to have particular properties Metals tend to bend when stressed Due to the bonding being between all of the electrons and all of the positive ions

77 ELF for Na Metal 81 Electrons moved from ions and distributed uniformly in the interstitial regions. The electrons in the interstitial regions move freely around the crystal. Good conductors and ductile

78 82

79 Another Carbon Example -- Buckyballs 83 Carbon can form many different structures The large hollow structure is called buckminsterfullerene Also known as a buckyball

80 84

81 85

82 Types of Covalent Bonds 86 Polar Covalent Bond e - are shared unequally asymmetrical e - density results in partial charges (dipole) d + d -

83 Types of Covalent Bonds 87 Nonpolar Covalent Bond e - are shared equally symmetrical e - density usually identical atoms

84 Polar and Nonpolar Bonds 88 AlP (polar) NaCl (ionic) Al (metallic) elf=0.5

85 Degree of Covalency From ELF 89

86 Charge Density Distribution in TiC Mixed iono-covalent bonding 90 Depleted Charge at Ti site indicate the electron transfer from Ti to C ionic bonding Finite charge in between atoms and their nonspherical distribiution show the covalent bonding.

87 Diamond (covalent) Charge transfer plot 91 NaCl (ionic) Nb ( metallic)

88 Van der Waals Bonding 92 Two neutral molecules are attracted to each other by weak electrostatic forces called van der Waals forces Atoms that do not form ionic or covalent bonds are also attracted to each other by van der Waals forces The van der Waals force is due to the fact that the molecule has a charge distribution with positive and negative centers at different positions in the molecule As a result of this charge distribution, the molecule may act as an electric dipole Because of the dipole electric fields, two molecules can interact such that there is an attractive force between them Remember, this occurs even though the molecules are electrically neutral

89 Types of Van der Waals Forces 93 Dipole-dipole force An interaction between two molecules each having a permanent electric dipole moment Dipole-induced dipole force A polar molecule having a permanent dipole moment induces a dipole moment in a nonpolar molecule

90 Types of Van der Waals Forces, cont. 94 Dispersion force An attractive force occurs between two nonpolar molecules The interaction results from the fact that, although the average dipole moment of a nonpolar molecule is zero, the average of the square of the dipole moment is nonzero because of charge fluctuations The two nonpolar molecules tend to have dipole moments that are correlated in time so as to produce van der Waals forces

91 95

92 Vander Waals Bonds Even in Solids 96

93 Hydrogen Bonding 97 In addition to covalent bonds, a hydrogen atom in a molecule can also form a hydrogen bond Using water (H 2 O) as an example There are two covalent bonds in the molecule The electrons from the hydrogen atoms are more likely to be found near the oxygen atom than the hydrogen atoms This leaves essentially bare protons at the positions of the hydrogen atoms The negative end of another molecule can come very close to the proton This bond is strong enough to form a solid crystalline structure

94 Hydrogen Bonding (Final) 98 The hydrogen bond is relatively weak compared with other electrical bonds Hydrogen bonding is a critical mechanism for the linking of biological molecules and polymers DNA is an example

95 If ΔEN is: Bond type is: < 0.4 Nonpolar covalent 0.4 < Δ EN < 1.7 Polar covalent > 1.7 Ionic 99 Given: Electronegativities of these elements H = 2.2 C = 2.55 N = 3.04 O = 3.44 F = 3.98 Na = 0.93 K = 0.82 P = 2.19 S = 2.58 Cl = 3.16 Determine bond type for the following bonds: H H H O H C Na Cl C Cl F F K F H N Take the absolute value of the difference!

96 Intermolecular Forces (IMF) 10 0 Attractive forces between molecules. Much weaker than chemical bonds within molecules. a.k.a. van der Waals forces

97 Types of IMF 10 1 London dispersion forces Exist in all atoms and molecules (temporary dipoles) Attraction between two instantaneous dipoles Weakest Larger the molecule, larger the dispersion force.

98 Types of IMF 10 2 London Dispersion Forces

Types of IMF 10 3 -Dipole-Dipole forces -Attraction between two permanent

99 Types of IMF Dipole-Dipole forces -Attraction between two permanent dipoles -Polar molecules -Medium strength -Stronger when molecules are closer together

100 Types of IMF 10 4 Dipole-Dipole Forces d- d+

101 Types of IMF 10 5 Hydrogen bonding Special kind of dipole-dipole Occurs between molecules that have an H bonded to either O, N, or F. Extremely polar bonds Strongest Not chemical bonding

102 Types of IMF 10 6 Hydrogen Bonding (ice)

103 Types of IMF The hydrogen bonds in water explain its relatively high boiling point, considering that it is a small molecule. The H-bonds hold the water molecules together as a liquid, so you have to heat it a lot before it will change to a gas. Compare boiling points of these molecules: Molecule IMF (s) present Molar Mass (g/mol) Boiling Point ( o C) CH London Disp. HCl London Disp. Dipole-Dipole H 2 O London Disp./Dipole Dipole/Hydrogen Bonding 107

104 Covalent bonding 10 8 Elemental semiconductors of Si, Ge and diamond are bonded by this mechanism and these are purely covalent. The bonding is due to the sharing of electrons. Covalently bonded solids are hard, high melting points, and insoluble in all ordinary solids. Compound semiconductors exhibit a mixture of both ionic and covalent bonding.

105 Ionic bonding 10 9 Ionic bonding is due to the electrostatic force of attraction between positively and negatively charged ions (between 1A and 7A). This process leads to electron transfer and formation of charged ions; a positively charged ion for the atom that has lost the electron and a negatively charged ion for the atom that has gained an electron. All ionic compounds are crystalline solids at room temperature. NaCl and CsCl are typical examples of ionic bonding. Ionic crystals are hard, high melting point, brittle and can be dissolved in ordinary liquids.

106 Ionic bonding 11 0 The metallic elements have only up to the valence electrons in their outer shell will lose their electrons and become positive ions, whereas electronegative elements tend to acquire additional electrons to complete their octed and become negative ions, or anions. Na Cl

107 Comparison of Ionic and Covalent Bonding 11 1

108 Potential energy diagram for molecules This typical curve has a minimum at equilibrium distance R 0 R > R 0 ; the potential increases gradually, approaching 0 as R the force is attractive V(R) 0 R0 Repulsive 11 2 R R < R 0 ; the potential increases very rapidly, approaching at small radius. the force is repulsive r R Attractive

109 Metallic bonding 11 3 Valance electrons are relatively loosely bound to the nucleus and therefore they move freely through the metal and they are spread out among the atoms in the form of a low-density electron cloud. A metallic bond result from the sharing of a variable number of electrons by a variable number of atoms. A metal may be described as a cloud of free electrons Therefore, metals have high electrical and thermal conductivity

110 Metallic bonding 11 4 All valence electrons in a metal combine to form a sea of electrons that move freely between the atom cores. The more electrons, the stronger the attraction. This means the melting and boiling points are higher, and the metal is stronger and harder. The positively charged cores are held together by these negatively charged electrons. The free electrons act as the bond (or as a glue ) between the positively charged ions. This type of bonding is nondirectional and is rather insensitive to structure. As a result we have a high ductility of metals - the bonds do not break when atoms are rearranged metals can experience a significant degree of plastic deformation.

111 van der Waals bonding 11 5 It is the weakest bonding mechanism. It occurs between neutral atoms and molecules. The explanation of these weak forces of attraction is that there are natural fluctuation in the electron density of all molecules and these cause small temporary dipoles within the molecules. It is these temporary dipoles that attract one molecule to another. They are as called van der Waals' forces. Such a weak bonding results low melting and boiling points and little mechanical strength.

112 van der Waals bonding 11 6 The dipoles can be formed as a result of unbalanced distribution of electrons in asymmetrical molecules. This is caused by the instantaneous location of a few more electrons on one side of the nucleus than on the other. symmetric asymmetric Therefore atoms or molecules containing dipoles are attracted to each other by electrostatic forces.

113 Compound with Semiconductivit y from metallic constituents (Cs 2 Pt) 117

114 118 Charge Density Distribution in KGaH

115 119 Allotropes of Carbon Diamond Hardest known substance C atoms have tetrahedral geometry, sp 3 hybridization Does not conduct electricity. Graphite Soft, used as lubricant C atoms have trigonal planar geometry, sp 2 hybridized Conducts electricity due to presence of extended bonding system. Others Amorphous carbon Buckminsterfullerene

116 Delocalized Electrons in Graphite 120 n p orbitals on n carbon atoms n overlapping molecular orbitals

117 MOs in Diamond and Graphite 121 Diamond (an insulator) Graphite (a conductor)

118 122 Quartz SiO 2 network of SiO 4 tetrahedra Si is sp 3, bonds to O. high m.p. (1600 o C) Contrast to CO 2 CO 2 is a gaseous molecule C is sp, and bonds to oxygen. the p orbitals on Si do not overlap readily with those on oxygen.

Chemical bonding in solids from ab-initio Calculations

Chemical bonding in solids from ab-initio Calculations 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India & Center for Materials Science and Nanotechnology, University