Lecture 0. NC State University

Transcription

1 Chemistry 736 Lecture 0 Overview NC State University

2 Overview of Spectroscopy Electronic states and energies Transitions between states Absorption and emission Electronic spectroscopy Instrumentation

3 Concepts in Spectroscopy Quantum energy Levels Electromagnetic radiation Dipole moment Transition moment Selection rules Experimental techniques Intensities h The origin of spectral lines in molecular spectroscopy is the emission or absorption of a photon when the energy of a molecule changes.

4 The solution to the wave equation for the hydrogen atom gives rise to energy levels that depend on quantum numbers E = R n n 2 R is called the Rydberg constant. R = 13.6 ev (electron volts) R = 109,700 cm -1 (wavenumbers)

5 The hydrogen atom has no nuclear part and the electronic solutions give rise to atomic orbitals s p d These are the angular parts of the wavefunction. The radial part decays exponentially with distance from the nucleus of an atom.

6 Transitions among levels E 1 = -R, E 2 = -R/4 h = E 2 E 1 0 -R/9 -R/4 = E E 2 1 h Energy matching condition Conservation of energy -R

7 Experimental observation of hydrogen atom Hydrogen atom emission is quantized. It occurs at discrete wavelengths (and therefore at discrete energies). The Balmer series results from four visible lines at 410 nm, 434 nm, 496 nm and 656 nm. The relationship between these lines was shown to follow the Rydberg relation.

8 Basic Phenomena Emission spectroscopy - a molecule undergoes a transition from a state of high energy E 1 to a state of lower energy E 2 and emits the excess energy as a photon. Absorption spectroscopy the energy of an incident photon drives a polarization from the molecular ground state to the excited state. An absorbed photon has a frequency given by the Bohr relation: h = E 1 E 2

9 Characteristics of electromagnetic radiation Electromagnetic radiation can be described as a wave with an oscillating electric field. Light can be linearly l polarized along the x, y, or z axes. The electric field vector is to the direction of propagation. E E = electric field B = magnetic field B E = E o cos(2 t)

10 Wave-particle duality We can consider electromagnetic radiation as a particle as well as a wave. In the particle description, the energy of the wave is: E = h This view is essential for spectroscopy, since there must an interaction between the EM radiation and a particle that is typically much smaller than the wavelength of the light (in the wave picture).

11 Characteristics of electromagnetic radiation E Molecule pyridine E = electric field B = magnetic field H H H H N H B E = E o cos(2 t)

12 Definition of the Dipole Moment The dipole moment operator is i = e z r i i where z i e is the electronic charge at a nucleus and r i is a vector from an arbitrary origin. Along the x-direction = e 0 * x dx

13 Examples of ground state dipole moments The ground state dipole moment of hydrogen halides can be calculated from the fractional charges 1 Debye = 3.33 x Cm + - R(pm) (x Cm) HF D 1.9 HCl D HBr D HI D

14 Definition of the transition dipole moment The transition dipole moment results from the interaction of electromagnetic radiation with the molecule l where E = E 0 cos(2 t) and the hamiltonian for interaction is H = x E ox cos (2 t) where x is the transition dipole moment x ge = e g* x dx e 0

15 Selection Rules A transition will be allowed only if the transition dipole moment integral is non-zero. The general rules are: Electronic: l = 1, m = 0 Rotational: J J = 1, M M = 0 Vibrational: v = 1 For mathematical description see the workshop on selection rules.

16 The interaction of electromagnetic radiation with a transition moment The electromagnetic wave has an angular momentum of 1. Therefore, an atom or molecule must have a change of 1 in its orbital angular momentum to conserve this quantity, as shown for the hydrogen atom: Electric vector of radiation l = 0 l = 1

17 Optical electromagnetic radiation permits transitions among electronic states t t = EE t where is the dipole operator and the dot represents the dot product. If the dipole is aligned with the electric vector E(t) then H(t) = - E(t). If they are perpendicular then H(t) = 0. = er where e is the charge on an electron and r is the distance.

18 The Fermi Golden Rule for optical electronic transitions e q E k = 12 6h 2 12 The rate constant is proportional to the square of the matrix element e< 1 q 2 > times a delta function. The delta function is an energy matching function: ( - 12 )=1if = 12 ( - 12 ) = 0 if 12.

19 The Fermi Golden Rule can be used to calculate many types of transitions Transition H(t) dependence 1. Optical transitions Electric field 2. NMR transitions Magnetic field 3. Electron transfer Non-adiabaticity 4. Energy transfer Dipole-dipole 5. Atom transfer Non-adiabaticity 6. Internal conversion Non-adiabaticity 7. Intersystem crossing Spin-orbit coupling

20 Sources of Radiation Nerst filament = infrared Arc lamp (Xe) = UV-vis Tungsten-halogen = visible near-ir Lasers Excimer Ion YAG Ti:sapphire

21 Dispersion is essential A dispersing element separates different frequencies into different spatial directions. A prism separates different frequencies because of the optical beam using the variation of the index of refraction such that high- frequency radiation undergoes a greater deflection than low-frequency radiation. A diffraction grating consists of grooves cut ca. 1 mm apart. Interference from reflected waves gives rise to specific angles of propagation.

22 Detectors Thermistor bolometer, far ir Mercury Cadmium Telluride (MCT), ir Germanium, near ir Silicon, visible Photomultiplier tube. Amplification by dynodes generates current for each photon hit. CCD detector. Array of detectors on a chip. UV coatings, efficiency, ease of use.

23 Absorption Spectrometer Dispersing element is in the spectrograph Sample Spectrograph Detector Light Source Reference Comparison of sample and reference is essential

24 Intensities of Spectral Lines Intensity of absorption for a sample that t has thickness d is given by log I I I0 = cd the molar absorption coefficient is the concentration is the pathlength is d the transmitted intensity is I the incident intensity is I 0

25 I = I 0 10 A A = cdd Beer-Lambert Law A is the absorbance. d is the pathlength. The exponential attenuation ti of the intensity is shown in the Figure. x dx The absorption cross section for an individual molecule is. = h k 12 where k 12 is I 0 I I +di the transition rate constant. d I

26 Theory of Absorption and Emission Absorption - low to high driven by absorption of a photon Stimulated t emission i - high h to low driven by emission of a photon Spontaneous emission - high to low emission independent of photon field Einstein coefficients: B 12 - stimulated absorption B 21 - stimulated emission A 21 - spontaneous emission

27 Spontaneous emission is fluorescence Stimulated t emission i is used for lasers spontaneous stimulated N 1 B 12 N 2 A 21 N 2 B 21