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Transcript
CHAPTER 9 Molecules Why do molecules form? Molecular bonds Rotations Vibrations Spectra Complex planar 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 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): V V (r1 , r2 ,..., rN ; r1, r2,..., rM ) (r1 , r2 ,..., rN ; r1, r2,..., rM , t ) Electrons’ positions Solving the Schrodinger Equation in this case is even harder than for multi-electron atoms. Serious approximation methods are required. This is called Chemistry! Nuclei positions Molecular Bonding and Spectra Nucleus The only force that binds atoms together in molecules is the Coulomb force. Nucleus E 0 Electron cloud Electron cloud 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? Why Molecules Form Most atoms are not spherically symmetrical. For example, these two “atoms” attract each other: Atom #1 Atom #2 + + - This is because the distance between opposite charges is less than that between charges of the same sign. 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. Charge is distributed very unevenly in most atoms. The probability density for the hydrogen atom for three different electron states. Closed shells of electrons are very stable. Atoms with closed shells (noble gases) don’t form molecules. Ionization energy (eV) Noble gases (difficult to remove an electron) Atomic number (Z) Atoms with closed shells (noble gases) also have the smallest atomic radii. Atomic radius (nm) Atoms like closed electron shells. Atomic number (Z) But add an extra electron, and it’s weakly bound and far away. 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. Ionic Bonds An electropositive atom gives up an electron to an electronegative one. Example: Sodium (1s22s22p63s1) readily gives up its 3s electron to become Na+, while chlorine (1s22s22p63s23p5) easily gains an electron to become Cl−. 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 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! 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). Molecular Potential An approximation of the force felt by one atom in the vicinity of another atom is: A B V n- m r r 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. The shape of the curve depends on the parameters A, B, n, and m. 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. Vibrational States The energy levels are those of a quantummechanical oscillator. Evibr (n 1 2) 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: Dn = ±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. Vibrational Frequencies for Various Bonds Different bonds have different vibrational frequencies (which are also affected by other nearby atoms). ← Higher energy (frequency) Wavenumber (cm-1) Notice that bonds containing Hydrogen vibrate faster because H is lighter. Water’s Vibrations