Molecular Rotations

Molecular Rotations - CH19. Molecular rotations &...

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Unformatted text preview: CH19. Molecular rotations & vibrations +Basics from CH20: General features of spectroscopy 19.1 Experimental techniques Electronic transitions 19.2 Measures of intensity 19.3 Selection rules 19.4 Linewidths Rotational spectroscopy 19.5 The rotational energy levels of molecules 19.6 The populations of rotational states 19.7 Rotational transitions: microwave spectroscopy 19.8 Rotational Raman spectra Vibrational spectra 19.9 The vibrations of molecules 19.10 Vibrational transitions 19.11 Anharmonicity 19.12 Vibrational Raman spectra of diatomic molecules 19.13 The vibrations of polyatomic molecules 19.14 Vibration–rotation spectra 19.15 Vibrational Raman spectra of polyatomic molecules 1 •Spectroscopy is the analysis of the electromagnetic radiation emitted, absorbed, or scattered by molecules. •We can use atomic spectra to obtain detailed information about electronic structure. Atomic spectroscopy Only electronic transitions Molecular spectroscopy Molecule can undergo electronic, vibrational and rotational transitions More complex spectra Series of lines, or sharply defined emission or absorption peaks Spectral analysis leads to properties related to structural parameters and dimensions, shapes, and dipole moments, chemical reactions, chemical mechanisms 2 General features of spectroscopy Relations between frequency , wavelength , and ~ wavenumber (cm-1) c ~ c Bohr frequency condition h | E1 E2 | 3 4 Experimental techniques Dispersion element separates wavelengths spatially as a result of scattering light by fine grooves cut into a coated piece of glass Absorption spectrometer Raman spectrometer 5 Sources of radiation •In emission and chemiluminescence spectroscopy the sample is the source •In absorption and luminescence spectroscopy an external source is required •Continuum sources provide a broad band radiation •Line sources provide very narrow spectral features •Hg or Na lamps used by some instruments •Hollow cathode lamps and electrode discharge lamps •Laser sources are used for a number of spectral methods •Lasers produce spatially narrow (~ 0.01 mm) beams of light with a very narrow bandwidth (~0.01 nm) •Black body radiators - Tungsten lamp 2870oK •Quartz - Iodide - 3600oK more UV & VIS •Discharge Lamps, etc 6 7 8 9 Detector: device that converts radiation into electric current or voltage for appropriate signal processing 10 11 In Chapter 10: Beer-Lambert Law Experimental measurements are usually made in terms of transmittance (T), which is defined as: T = I / Io where I is the light intensity after it passes through the sample and I o is the initial light intensity. The relation between A (Absorbance) and T is: A = -log T = - log (I / I0 )=log (I0 / I ) Then the Beer-Lambert law is A=[J] b c is the molar concentration b is the length is molar absorption coefficient 12 13 14 15 Electronic transitions • Electronic spectra involving transitions of valence electrons in the VIS and UV regions are studied in both absorption/emission. • • One can study emission spectra of solids, liquids, and gases by raising the molecules to an excited electronic states using photons from a high-intensity lamps or a laser and then observe the emission at right angles to the incident beam 16 17 Franck-Condon principle • Because the nuclei are so much more massive than the electrons, an electronic transition takes place very much faster than the nuclei can respond • According to the Franck-Condon principle, the most intense vibronic transition is from the ground vibrational state to the vibrational state lying vertically above it • Transitions to other vibrational levels also occur, but with lower intensity. 18 , 1 19 Electronic spectra of polyatomic molecules • The absorption of a photon can often be traced to the excitation of specific types of e- or to e- that belong to a small group of atoms • Groups with characteristic optical absorptions are called CHROMOPHORES, and their presence often accounts for the colors of substances max ~ max /nm max /cm-1 Group /(L mol-1cm-1) C=O (p*p) 61 000 57 300 37–35 000 60 000 163 174 270–190 167 15 000 5 500 10-20 7 000 C=O (p*n) H2O (p*n) 20 The fates of electronic excites states •A radiative decay process is a process in which a molecule discards its excitation energy as a photon •In a nonradiative decay the excess energy is transferred into the vibration, rotation, translation of the surrounding environment (thermal degradation, excitation energy is converted to heat) 21 Fluorescence and phosphorescence In fluorescence spontaneous emission of radiation occurs within ns after the exciting radiation is extinguished (fast conversion of the absorbed energy into re-emitted energy) In phosphorescence, it may persist much longer (storage if the energy and slow leak ) 22 23 Rotational spectroscopy Very little energy is needed to change the state of rotation of a molecule, and the electromagnetic radiation emitted or absorbed lies in the microwave region, with wavelengths of the order of 0.1–1 cm and frequencies close to 10 GHz. Moment of inertia, I mi ri i 2 24 25 26 Rotational energy (use rigid rotor model) Examples: HCl, CO2, linear C2H2 27 Classification of rotors 28 K- quantum number K=0 means all the angular momentum arises from the rotation about the principal axis K is close to J is used to signify a component on the principal axis (axis of the molecule) 29 Centrifugal distortion F ( J ) BJ ( J 1) DJ J 2 ( J 1) 2 4B3 DJ ~ 2 30 31 ∆K=0 32 Rotational transitions When a rigid molecule changes its rotational quantum number from J to J + 1 in an absorption, the change in rotational energy of the molecule is The energies of these transitions are 2hB, 4hB, 6hB, …. The frequency of the radiation absorbed in a transition starting from the level J is therefore 33 34 Vibrational spectra measurements IR spectroscopy measures the wavelength and intensity of the absorption of infrared light by a sample Gas-phase IR spectrum of formaldehyde, H2-C=O 35 Vibrational spectra calculations ● Normal mode analysis (NMA) was first applied to proteins in 1980s NMA has direct connection to the experimental techniques of infrared and Raman spectroscopy Problem: These experiments are not able to measure directly the lowest frequency modes of motion Theory can help: NMA is harmonic approximation ! NMA provides visual model which characterizes the available types of motion in terms of frequency, atomic amplitudes, and directions of motion ● ● ● 36 What are normal modes? Simple harmonic motion: Amplitude, A. The amplitude of the oscillation is the maximum distance that the oscillating object moves away from the equilibrium position. Frequency, f. The frequency of the oscillation is the number of oscillations per second. Period, T. The period is the time for the oscillator to complete one cycle. f=1/T 37 What are normal modes? Tacoma Narrows Bridge collapsed in 1940 38 What are normal modes? Musical instruments are based on some sort of harmonic oscillator 39 Normal modes Water molecule (3N-6) CH2Cl2 asymmetric stretch symmetric stretch in plane bending or scissoring out-of-plane bending or wagging out-of plane bending or twisting out-of-plane bending 40 or rocking Normal Mode Analysis Potential energy V is a complicated function of the Cartesian coordinates of the atoms Potential V expressed as a power series in the displacements coordinates q mx x i i i ie V V qi 0 i V qi qi 1 2 i j V q i q j ... qi q j 2 fij force constant matrix qi j f ij q j 0, i 1, ...3 N second-order differential equations DIAGONALIZATION (linear algebra) Results: frequencies and normal mode vectors 41 Vibrational motions in proteins dihedral angles bond angle bending bond stretching hydrogen vibrations domain motions Collective motion Local motion 42 2D pump-probe spectroscopy 1. Intense PUMP PULSE with frequency pump excites a particular vibrational mode 2. PROBING PULSE is used to investigate the response of the molecule at a different frequency probe 43 3D pump-probe spectroscopy Fluctuations of the conformation can be investigated by introducing a third dimension: TIME-DELAY. Fluctuations of the conformation lead to fluctuations in the coupling strengths, which induce the transfer of vibrational excitations between the coupled modes 44 (vibrational transitions 100 fs) MD simulations vs. experiment Example from my research project Metropolis sampling, 100 trajectories, J=0 Experiment Classical MD spectra show the strong activity in the range 600-1900 cm-1, similar to the experimental measurements J. Phys. Chem. A 108 (2004) 900 Science 299 (2003) 1375 45 Normal modes of H5O2+ (cm-1) Example from my research project 46 Vibrational transitions The specific selection rule for vibrational transitions is Δν = ±1 47 CO2 molecule H2O molecule Nonlinear molecules: Number of vibrational modes = 3N − 6 Linear molecules: Number of vibrational modes = 3N − 5 48 Anharmonicity •Where xe is the anharmonicity constant. •Anharmonicity also accounts for the appearance of additional weak absorption lines called overtones corresponding to the transitions with Δv = +2, +3, …. •Overtones in a vibrational spectrum can appear in the nearinfrared region and overtone spectroscopy is a technique used by analytical chemists in the characterization of food. 49 Vibrational-rotational spectra Example: (linear molecule) When the vibrational transition v + 1 ← v occurs, J changes by ±1 and in some cases by 0 (when ∆J = 0 is allowed). The absorptions then fall into three groups called branches of the spectrum. The P branch consists of all transitions with ∆J = −1. The Q branch consists of all lines with ∆J = 0. The R branch consists of lines with ∆J = +1: 50 Table of key equations 51 ...
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Molecular Rotations - CH19. Molecular rotations &...

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