1. Why do molecules form? Molecular bonds Rotations Vibrations Spectra Complex planar molecules Molecules CHAPTER 9 Molecules Johannes Diderik van der Waals (1837 – 1923) “Life... is a relationship between molecules.” Linus Pauling Remember: homework due this Wednesday by 2:30pm in room 144

2. Molecules are combinations of atoms. When more than one atom is involved, the potential and the wave function are functions of way more than one position (a position vector for each nucleus and electron): Solving the Schrodinger Equation in this case is even harder than for multi-electron atoms. Serious approximation methods are required. This is called Chemistry! Electrons’ positionsNuclei positions

3. Molecular Bonding and Spectra The only force that binds atoms together in molecules is the Coulomb force. But aren’t most atoms electrically neutral? Yes! Indeed, there is no attraction between spherically symmetrical molecules—the positive and negative charges both behave like point sources and so their fields cancel out perfectly! So how do molecules form? Nucleus Electron cloud Nucleus Electron cloud

4. Why Molecules Form Most atoms are not spherically symmetrical. For example, these two “atoms” attract each other: +  +  The combination of attractive and repulsive forces creates a stable molecular structure. Force is related to the potential energy surface, F = −dV/dr, where r is the position. Atom #1Atom #1Atom #2Atom #2 This is because the distance between opposite charges is less than that between charges of the same sign.

5. Charge is distributed very unevenly in most atoms. The probability density for the hydrogen atom for three different electron states.

6. Closed shells of electrons are very stable. Ionization energy (eV) Atomic number (Z) Noble gases (difficult to remove an electron) Atoms with closed shells (noble gases) don’t form molecules.

7. Atoms like closed electron shells. Atoms with closed shells (noble gases) also have the smallest atomic radii. Atomic number (Z) Atomic radius (nm) But add an extra electron, and it’s weakly bound and far away.

8. An extra electron or two outside a closed shell are very easy to liberate. Atoms with one or two (or even more) extra electrons will give them up to another atom that requires one or two to close a shell. Atoms with extra electrons are said to be electropositive. Those in need of electrons are electronegative.

9. Ionic Bonds An electropositive atom gives up an electron to an electronegative one. Example: Sodium (1s 2 2s 2 2p 6 3s 1 ) readily gives up its 3s electron to become Na +, while chlorine (1s 2 2s 2 2p 6 3s 2 3p 5 ) easily gains an electron to become Cl −.

10. Covalent Bonds Two electronegative atoms share one or more electrons. Example: Diatomic molecules formed by the combination of two identical electronegative atoms tend to be covalent. Larger molecules are formed with covalent bonds. Diamond

11. Van der Waals bonds A weak bond found mostly in liquids and solids at low temperature. Example: 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.

12. Hydrogen Bonds If a hydrogen atom is covalently bonded to an electronegative atom, the H can simultaneously bond essentially covalently to another molecule. The hydrogen bond (5 to 30 kJ/mole) is stronger than a van der Waals bond, but weaker than covalent or ionic bonds.

13. Metallic Bonds In metals, in which electrons are very weakly bound, valence electrons are essentially free and may be shared by a number of atoms. The Drude model for a metal: a free-electron gas!

14. Molecular Potential Energy Curve The potential depends on the charge distributions of the atoms involved, but there is always an equilibrium separation between two atoms in a molecule. The energy required to separate the two atoms completely is the binding energy, roughly equal to the depth of the potential well. Vibrations are excited thermally, that is, by collisions with other molecules, or by light, creating superpositions of ground plus an excited state(s).

15. An approximation of the force felt by 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. One example is the Lennard-Jones potential in which n = 12 and m = 6. Molecular Potential The shape of the curve depends on the parameters A, B, n, and m.

16. Vibrational Motion: A Simple Harmonic Oscillator The Schrödinger Equation can be separated into equations for the positions of the electrons and those of the nuclei. The simple harmonic oscillator accurately describes the nuclear positions of a diatomic molecule, as well as more complex molecules.

17. The energy levels are those of a quantum- mechanical oscillator. Vibrational States n is called the vibrational quantum number. Don’t confuse it for n, the principal quantum number of the electronic state. Vibrational-transition selection rule:  n = ±1 The only spectral line is  ! However, deviations from a perfect parabolic potential allow other transitions (~2 , ~3 , …), called overtones, but they’re much weaker.

18. Vibrational Frequencies for Various Bonds Different bonds have different vibrational frequencies (which are also affected by other nearby atoms). Notice that bonds containing Hydrogen vibrate faster because H is lighter. Wavenumber (cm -1 ) ← Higher energy (frequency)

19. Water’s Vibrations