Molecular bonding

1. Molecular bonding

2. Molecular Bonding and Spectra The Coulomb force is the only one to bind atoms. The combination of attractive and repulsive forces creates a stable molecular structure. Force is related to potential energy F = −dV / dr, where r is the distance separation. it is useful to look at molecular binding using potential energy V Negative slope (dV / dr < 0) with repulsive force Positive slope (dV / dr > 0) with attractive force

3. Molecular Bonding and Spectra • Eq. 10.1 provides a stable equilibrium for total energy E < 0. The shape of the curve depends on the parameters A, B, n, and m. Also n > m. An approximation of the potential of one atom in the vicinity of another atom is where A and B are positive constants. Because of the complicated shielding effects of the various electron shells, n and m are not equal to 1.

4. Molecular Bonding and Spectra Vibrations are excited thermally, so the exact level of E depends on temperature. Once a pair of atoms is joined, then: One would have to supply energy to raise the total energy of the system to zero in order to separate the molecule into two neutral atoms. The corresponding value of rat the minimum value is an equilibrium separation. The amount of energy to separate the two atoms completely is the binding energy which is roughly equal to the depth of the potential well.

5. Molecular Bonds Ionic bonds: • The simplest bonding mechanisms. • Ex: Sodium (1s22s22p63s1) readily gives up its 3s electron to become Na+, while chlorine (1s22s22p63s23p5) readily gains an electron to become Cl−. That forms the NaCl molecule. Covalent bonds: • The atoms are not as easily ionized. • Ex: Diatomic molecules (H2, N2, O2) formed by the combination of two identical atoms tend to be covalent. These are referred to as homopolar molecules. • Larger molecules are formed with covalent bonds.

6. Molecular Bonds Van der Waals bond: Weak bond found mostly in liquids and solids at low temperature Ex: In graphite, the van der Waals bond holds together adjacent sheets of carbon atoms. As a result, one layer of atoms slides over the next layer with little friction. The graphite in a pencil slides easily over paper. Hydrogen bond: Holds many organic molecules together Metallic bond: Free valence electrons may be shared by a number of atoms.

7. Ionic bonding NaCl Must be added electro negative electron affinity=3 eV Formation of releases 3.8eV In Na the 3s electron is weakly bound When Cl atom captures an electron Add to the system

8. Potential energy of and When Na+ and Cl- are brought together a molecule is formed • As these ions are brought together closer than 0.4 nm the attraction increases • At very close distances, a repulsive force acts between them due to Pauli Exclusion Principle (electron clouds start overlapping) Assume separation of Na+ and Cl- is 0.4 nm 0.4 nm 0.4 nm This energy is emitted

9. Covalent Bonding or homopolar bonding Responsible for formation of stable diatomic molecules The two electrons are shared Solve Schrodinger’s equation and make us of the Pauli Exclusion Principle Interaction of proton P1 with each electron Interaction of proton P2 with each electron Interaction between the two electrons Interaction between the two protons

10. Plots of wave function and of two electrons when they are apart 0.1 nm =twice Bohr radius • Spins anti-parallel • Spins parallel Probability of Electron Location

11. Total potential energy versus r for two hydrogen atoms Note: If there was not an exchange term VE, there would be no difference between the two potential curves.

12. Exchange energy and the Pauli exclusion principle Pauli Exclusion Principle: There are two possible wave functions symmetric Wave function antisymmetric Probability Distribution Exchange Term Total wave function for Fermions is antisymmetric: (both electrons are between the nuclei) { antisymmetric }

13. Hybrid covalent bonds Four covalent bond of molecule: the hybrid (mixed) orbitals are represented by Or other combinations by subtracting rather than adding the mixture of one 2s and three 2p orbitals to give four hybrids Each C----H bond consists of an overlapping 1s orbital from hydrogen and an sp3 hybrid orbital from carbon. Theses orbitals have two lobes and only the longer ones are depicted.

14. Probability density

15. Van der Waals bonds The van der Waals forces for bonding arises when an electrically neutral molecule has centers of positive and negative charge which do not coincide Dipole-dipole force Dipole-induced force Dispersion force All types fall off with 1/r^6

16. Hydrogen bond Hydrogen bond is a misnomer. It is not a bond but a particular strong dipole-dipole attraction between polar molecules that occurs when a hydrogen atom bound to a highly negative atom such as N, O, or F and experiences attraction to some other nearby electronegative atom. The two negative fluorine ions are bound by the positively charged proton between them Very weak bond energy = 0.1 eV

17. Hydrogen bond A hydrogen atom attached to a relatively electronegative atom is a hydrogen bond donor. The hydrogen bond (5 to 30 kJ/mole) is stronger than a van der Waals interaction, but weaker than covalent or ionic bonds. This type of bond occurs in both inorganic molecules such as water and organic molecules like DNA and proteins. Model of hydrogen bonds between molecules of water

18. Bonding in complex molecules (a) And (b): Formation of a sigma bond in from the overlap of the orbitals on adjacent N atoms. (c) Formation of a pi bond by overlap of the orbitals on adjacent N atoms. A similar bond is formed by overlap of the orbitals.

19. Fermions versus bosons

20. Symmetry of Boson wave function Bosons have integer spin S=0,1,2… Fermionshave half integer spin S=1/2,3/2… Bosons are not subject to Pauli principle. Fermions obey the Pauli principle. Exchange by particles which are identical does not change their probability distribution. Solutions of this equation are: symmetric antisymmetric Bosons Fermions a,b corresponds to particle in different states a,b corresponds to particle in different states Assume a=b Two fermions cannot occupy the same state Two bosons have a nonzero probability occupying the same state

21. Bose-Einstein condensation in gases 2001 Nobel Prize Wieman Cornell Ketterle The transitions from a broad velocity distribution to an extremely narrow one signifies Bose-Einstein condensation Rb, Na atoms Two horizontal axes represent velocity components in x and y Vertical axis represents number of atoms having those having velocities Field of view 200um by 270um