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Rocket clouds

1. Rotational

1.1. Raman

1.1.1. Polarizability isotropic anisotropic

1.1.2. Raman Shift Energy Level v=2B(2J+3) First separation: 6B, other: 4B

1.1.3. Intensity anti-stokes lower lower no. of molecules present in lower energy state before irradiation

1.2. Microwave

1.2.1. Intensity Transition Probability Population Pj Jmax=[(kT/2hB)^0.5]-0.5

1.2.2. Energy Level Energy Level (Linear and spherical) B=ħ/4πI Ej=hBJ(J+1) vj=2B(J+1) equally spaced = 2B Energy Level (Symmetric) Ej,k=hBJ(J+1)+h(A-B)K^2

1.3. Rigid Rotor

1.3.1. Linear diatomic I=μR^2 triatomic I=2mr^2

1.3.2. Symmetric

1.3.3. Asymmetric

1.3.4. Spherical

1.4. Non- Rigid Rotor

1.4.1. Centrifugal distortion Increases I and decreases B Ej=hBJ(J+1)-hDJ^2 (J+1)^2 D ̃=(4B ̃^3)/v ̃^2

1.5. Orientation in space: Mj (Linear)

1.5.1. 2J+1 orientations with respect to an external axis 2J+1 degenerate states at J level Stark effect: measure permanent dipole moment

2. Vibrational

2.1. IR

2.1.1. Degrees of freedom (normal modes) Linear 3N-5 as only 2 rotational non linear 3N-6

2.2. Raman

2.2.1. Exclusion rule

2.3. Vibrations of molecules

2.3.1. Symmetrical stretching

2.3.2. Asymmetrical stretching

2.3.3. Scissoring (Bending)

2.3.4. Rocking

2.3.5. Wagging

2.3.6. Twisting

2.4. Harmonic oscillator

2.4.1. V(x)=0.5kx^2

2.4.2. Ev=(v+0.5)hv

2.4.3. Energy Level equally spaced: hv v=1/2π(k/µ)^1/2

2.4.4. limitations no dissociation of molecule

2.5. Anharmonicity

2.5.1. Energy Level Ev=(v+0.5)hv-(v+0.5)^2 hv xe (anharmonicity constant)

2.5.2. Intensity overtone (+T) --> (-Intensity) hotband weaker than fundamental (+T) --> (+hot band) but (-fundamental)

2.5.3. overtones first overtone: v=0 to v=2 second overtone: v=0 to v=3

2.5.4. hot band first hot band: v=1 to v=2 second hot band: v=2 to v=3

3. Vibro-rotational

3.1. Raman

3.1.1. OQS branch O: J=-2; Q: J=0 always allowed; S: J=+2

3.2. IR

3.2.1. Energy Level Evj=(v+0.5)hv+hBJ(J+1) vR=v+2B(J+1) vP=v-2BJ

3.2.2. PQR branch P: J=-1; Q: J=0; R: J=+1 Q found in polyatomic molecules, except NO

3.3. real spectrum

3.3.1. R converge; P diverge

3.3.2. anharmonicity

3.3.3. centrifugal distortion Bj=Bo-DJ(J+1)

4. UV-Vis

4.1. types of electronic transitions

4.1.1. organic

4.1.2. Inorganic transition between d orbitals

4.2. Vibrational fine structure

4.2.1. Resolving fine structure state: gas phase Temp: low T Solvent: apolar

4.2.2. Franck-Condon Principle intensity vibration state vertically above; Largest overlap between vibrational wavefunctions

4.2.3. Number of bands relative position of the potential E curve Horizontal Displacement and its direction steepness of the curve

4.3. Rotational structure

4.3.1. bond length greater than ground state: R lines converge shorter than ground state: P lines converge

4.4. Jablonski diagram

4.4.1. singlet Fluorescence S to S*

4.4.2. triplet Phosphorescence S to T (intersystem crossing)

5. Photoelectron

5.1. Ionization Energy

5.1.1. Ekin=hv-Ii

5.2. XPS

5.2.1. Photoelectron spectrum electron from σ bond fine structure: vibrational excitation electron from lp lack of vibrational structure slight change of equilibrium bond length

5.3. Peak broadening

5.3.1. Instrumental

5.3.2. Physical Lifetime Collisional deactivation Spontaneous emission Doppler To minimize: low pressure approaching: λ compressed; receding: λ expanded Temp dependent