Chemistry 2000 Slide Set 4: Molecular spectroscopy of diatomic molecules Marc R. Roussel January 7, 2020 Marc R. Roussel Spectroscopy of diatomics January 7, 2020 1 / 20
Evidence for MO theory Evidence for MO theory How do we know that MO theory is correct? Equilibrium bond lengths: X-ray or neutron diffraction for solids Rotational (microwave) or vibrational (infrared) spectroscopy for gases Potential energy curve/surface: Vibrational (infrared) spectroscopy Orbital energy diagram: Photoelectron spectroscopy Electronic absorption (UV/visible) spectroscopy Fluorescence spectroscopy Marc R. Roussel Spectroscopy of diatomics January 7, 2020 2 / 20
Effective potential The effective potential 6 4 2 0 V eff -2 -4 -6 0 1 2 3 4 5 6 R The shape of the effective potential implies that a molecule below its dissociation energy vibrates, i.e. a diatomic molecule behaves like two balls connected by a spring. Marc R. Roussel Spectroscopy of diatomics January 7, 2020 3 / 20
Effective potential Quantization of vibrational energy Vibrational energy is quantized, i.e. only certain vibrational energies are allowed: E vibrational levels R Marc R. Roussel Spectroscopy of diatomics January 7, 2020 4 / 20
Effective potential The effective potential: interpretation Nuclear-nuclear repulsion V eff 0 Dissociation energy Long-range attraction due to electron-nucleus interaction Zero-point energy R eq = bond length R Marc R. Roussel Spectroscopy of diatomics January 7, 2020 5 / 20
Infrared spectroscopy Vibrational levels E R Stronger bond ← → narrower potential well ← → larger vibrational spacing Marc R. Roussel Spectroscopy of diatomics January 7, 2020 6 / 20
Infrared spectroscopy Infrared (vibrational) spectroscopy Heteronuclear diatomics can absorb photons to undergo vibrational transitions. Homonuclear diatomics cannot make a vibrational transition by absorbing a single photon. (The basis for this rule will be seen later.) At room temperature, almost all molecules are in the ground vibrational state. By far the most likely process is the absorption of a photon to go from the ground state to the first excited vibrational state. Vibrational energy spacings correspond to the infrared region of the electromagnetic spectrum. Marc R. Roussel Spectroscopy of diatomics January 7, 2020 7 / 20
Infrared spectroscopy Infrared (vibrational) spectroscopy E ∆ E = h ν ∼ infrared vib R Marc R. Roussel Spectroscopy of diatomics January 7, 2020 8 / 20
Infrared spectroscopy Summary of IR spectroscopy IR spectroscopy gives us information about the strength of a chemical bond: Stronger bond ← → higher-energy (shorter wavelength) IR absorption The strength of the bond and spacing between vibrational levels are connected to the shape of the potential energy curve near the equilibrium bond length. Marc R. Roussel Spectroscopy of diatomics January 7, 2020 9 / 20
Units Units in spectroscopy The energy of a photon is given by E = h ν = hc λ SI units of E : Units of ν : Units of λ : Photon energies are sometimes given in electron-volts (eV): 1 eV = 1 . 602 176 634 × 10 − 19 J Marc R. Roussel Spectroscopy of diatomics January 7, 2020 10 / 20
Units Units in spectroscopy Wavenumbers If we define the wavenumber ˜ ν = 1 /λ , E = hc ˜ ν ν is often expressed in cm − 1 . ˜ ν is often casually referred to as a frequency, to which wavenumber is ˜ proportional: ν = c ˜ ν Marc R. Roussel Spectroscopy of diatomics January 7, 2020 11 / 20
Photoelectron spectroscopy Photoelectron spectroscopy How do we know that the orbital occupancies predicted by MO theory are correct? Photoelectron spectroscopy is similar in principle to the analysis of the photoelectric effect. An atom or molecule is ionized using a photon of energy h ν . The maximum kinetic energy of the ejected electron is then K max = h ν − I i where I i is the ionization energy of an electron in orbital i . Note: The notation for ionization energy differs from that used in Chem 1000. The ionization energy of an electron in a particular orbital is the negative of its orbital energy ( ε i ). We measure K and calculate the orbital energy of occupied orbitals: − I i = ε i = K max − h ν Marc R. Roussel Spectroscopy of diatomics January 7, 2020 12 / 20
Photoelectron spectroscopy Photoelectron spectroscopy (continued) Removing a valence electron typically requires a photon in the ultraviolet range. Removing a core electron typically requires an x-ray photon. Marc R. Roussel Spectroscopy of diatomics January 7, 2020 13 / 20
Photoelectron spectroscopy Example: Photoelectron spectrum of Ne K /eV 60 50 40 30 20 10 0 0.7 h ν = 60 eV 0.6 2p 0.5 Intensity 0.4 0.3 0.2 2s 0.1 0 0 10 20 30 40 50 60 I /eV Orbital energy level diagram? Rotate clockwise! Marc R. Roussel Spectroscopy of diatomics January 7, 2020 14 / 20
Photoelectron spectroscopy A complication For molecules, the ion formed also has vibrational levels. As a result, the photoelectron spectrum typically has vibrational substructure: E + X 2 e − X 2 R Marc R. Roussel Spectroscopy of diatomics January 7, 2020 15 / 20
Photoelectron spectroscopy Instead of one ionization energy, the photoelectron spectrum gives us a band of several lines corresponding to the ionization of an electron from a particular orbital. + E vib (X 2 ) ∆ Intensity I i "ionization energy": X 2 produced in its vibrational ground state The photoelectron spectrum thus allows us to recover the vibrational spectrum of the ion formed. Marc R. Roussel Spectroscopy of diatomics January 7, 2020 16 / 20
Photoelectron spectroscopy We compare the vibrational spectrum of the molecule to that of the ion. The way in which the vibrational spectrum changed tells us how the potential energy curve changed, and thus how the bonding changed. This can be correlated to the MO diagram: Removing an electron from an orbital not directly involved in bonding (e.g. the 1 π orbital in HF) won’t change the vibrational spectrum much. Removing an electron from a bonding orbital will lead to a weaker bond in the ion, thus to lower vibrational frequencies for the associated normal mode(s) than in the parent molecule. Removing an electron from an antibonding orbital. . . Marc R. Roussel Spectroscopy of diatomics January 7, 2020 17 / 20
Photoelectron spectroscopy Example: UV photoelectron spectrum of N 2 40 3 σ 2150 cm -1 35 30 25 Intensity 20 15 1860 cm -1 10 2 σ * 2390 cm -1 1 π 5 0 15 16 17 18 19 20 I /eV Note: The vibrational “frequency” of N 2 is 2358 cm − 1 . Marc R. Roussel Spectroscopy of diatomics January 7, 2020 18 / 20
Photoelectron spectroscopy Additional hints for interpreting photoelectron spectra Orbitals that are strongly bonding/antibonding will produce a number of lines. (See the 1 π orbital in the photoelectron spectrum of N 2 .) A strictly nonbonding orbital would produce exactly one line. Orbitals that are weakly bonding/antibonding tend to produce a small number of lines, often with the line at lower ionization energy being much more intense. 40 3 σ 2150 cm -1 35 30 25 Intensity 20 15 1860 cm -1 10 2 σ * 2390 cm -1 1 π 5 0 15 16 17 18 19 20 I /eV Marc R. Roussel Spectroscopy of diatomics January 7, 2020 19 / 20
Photoelectron spectroscopy Example: UV photoelectron spectrum of CO 2000 1662 cm -1 1500 Intensity 1636 cm -1 2 σ 1000 1 π 500 0 15 16 17 18 19 20 21 I /eV Note: The vibrational frequency of CO is 2170 cm − 1 . Marc R. Roussel Spectroscopy of diatomics January 7, 2020 20 / 20
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