Rotational states and rotational transitions of molecules. Microwave spectroscopic methods

Transcription

1 Rotational states and rotational transitions of molecules Microwave spectroscopic methods

2 Consequences of the BO approximation Within the BO approximation, the Schrödinger equation can be solved using an approximation that the electronic, vibrational and rotational degree of freedom can be be separated in molecule. Consequently, the total Hamiltonian can be separated on partial Hamiltonians describing this motions and calculated separately. The wavefunction of the molecule becomes a product of the electronic, vibrational and rotational wavefunctions. The eigenvalue of the Schrödinger equation is a sum of eigenvalues obtained in analysis of the particular motion. A particular electronic state will be always accompanying by a number of vibrational levels and each vibrational level will be always accompnying with a number of rotational levels

3 Convention: term value T(ν)=E el (ν)/hc e.g., -R/n hydrogen atom -R Z 2 /n hydrogenic ions G(ν)=E vib (ν)/hc ν osc /c (v+1/2)---harmonic osc. F(ν)=E rot (ν)/hc BJ(J+1) B=h/(8πcI)---spherical top In general: Energy terms = T+G+F Transitions= (T +G +F )-(T +G +F ) Excited state Ground state + Selection rules!!!

4 Pure rotational molecular spectroscopy Techniques

5 We will consider nonvibrating ground electronic states of molecules, One can also analyse the nonvibrating excited electronic states. In general, the energy level structure of rotating molecule can be complex Since apart to the pure rotation of nuclei one has to consider influence of the orbital angular momentum and spin of electrons the spins of nuclei

6 Spectroscopy from a few MHz (300 m) to several hundred GHz(1mm) The experimental energy range extends from the radiofrequency region, through the microwave region, to the far infrared

7 Relevance and applications Molecules in the gas phase [electron spin resonance studies of liquid phase molecules are also performed in this energy range; the rotational motion is randomized by the frequent collisions and in the solid phase they are suppressed] Isolated or very weakly perturbed molecules [the very strong intermolecular interactions in condensed phase have dominant influence on the spectral characteristics ] Advatages: precised molecular structural parameters narrow natural linewidths e.g., v=10 MHz------Δv~10-9 Hz (in visible ~10 6 Hz) e.g., pressure broadening 1 torr MHz Doppler broadening T~300K khz (vis-uv~2ghz)

8 Molecular structure and intramolecular interactions can be very well studied molecules, radicals, charged molecules very high resolution enables studies of many weak interactions as magnetic interaction between spins of electrons and nuclei physics and molecular properties study of chemical reactions (reactive interactions between molecules) Concentration monitoring Rotational and vibrational energy distribution monitoring (energy transfer in chemical reactions) Micowave spectroscopy is a primary tool for identifying molecules over 200 molecules and radicals in astrophysical environments

9 Experimental method Tunable Microwave source Coaxial cable Or waveguide Absorption cell detector Klystron Backward-wave oscillator (accelerating electrons emit radiation, which is trapped in the cavity and it can be tapped off through an appropriate window;tuning of the frequency can be made by changing the size of cavity mechanically or electrically ) Low pressure cell Vacuum cell molecular Beam; applied external fields Crystal detectors Cristal acts as a rectifier and converts the microwave energy cw to a low frequency current; crystal detector consists of a very fine metal whisker (tungsten) in point contact with a semiconductor (doped silicon Crystal) The cristal is inserted into the waveguide line and the incident power causes a voltage drop across the crystal and the current flows

10 Sources of microwave radiation

11 Direct methods (use properties of stimulated transitions)

12 Molecular beam maser spectroscopy In normal spectroscopy we depend on the ability to measure a net absorption of radiation, whose magnitude depends upon the relative populations of the two energy levels involved in the transition. Here, the population inversion is achieved and stimulated emission measured.

13 Indirect methods Molecular beam deflection techniques: The direction of molecular beams can be controlled by passing them through suitable magnetic or electric fields. Molecules are initially selected at the state of interest and focussing conditions enable to detect them at the detector. The resonant interaction with the microwave field can cause transition to the other state and a field focussing conditions are going to be changed for these molecules. (e.g., see Stark or Zeeman interaction dependance).they will not arrived at the detector. particle counter method Double resonance methods High resolution studies in the excited (electronic vibrational) states. Molecules are excited to the state of oposite parity (+), then radiofrequency can induced transition to rotational level with oposite parity(-). There is no possibilty to emmit radiation from this state back to the ground state. If one monitors a fluorescence from the excited state, one will observe that fluorescence yield will decrease once the microwave transition is induced.

14 Molecular beam magnetic resonance spectrometer If a resonance transition is induced in the homogeneous C field by means of radiofrequency or microwave field, the effective magnetic moment of the molecule is changed. It no longer satisfies the collimating conditions imposed by the B field, and hence misses the stop wire and reaches detector.

15 Molecular beam electric resonance spectrometer The molecular trajectories refer to one or other of two energy levels which can be mixed by an applied electric field to show a second order Stark effect. Molecules in the upper state continues line are focussed by the quadrupole A field, whilst those in the lower state dotted line are removed from the beam.the field can be arranged to deflect upper state molecules from the detector. If radiofrequency transitions are induced in homogeneous field C, the number of lower state molecules increases and this can be deflected onto the detector by the field B. Spectroscopic transitions result in ab increased detector signal.

16 Radioastronomy +internal frequency calibrator e.g., Kitt Peak in Arizona

17 Some microwave spectroscopic detections in laboratory and in interstellar media

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