1. FERENC BILLES STRUCTURAL CHEMISTRY

2. Chapter 1. INTERACTIONS OF ATOMS AND MOLECULES WITH PARTICLES AND EXTERNAL FIELDS

3. Elucidation of the molecular structure

4. Types of properties SystemPropetyExample atomA A: atomic spectrum moleculeΔA, M M: vibrational spectrum molecular ensamble ΔA, ΔM, S S: X-ray diffractogram

5. The model is only an approach to the reality. The experiment disturbs the system. A collision with particles maybe with electrons, atoms, ions, photons, etc. An effect with external fields maybe - effect with external - electric - magnetic -electromagnetic fields. The answer of the system is - the change of its properties - or/and emission of one or more particles. The answer of the particle is - the change of one or more of its properties.

6. Non-central collision types: -elastic, energy change, colliding particle:  remains; -inelastic, the total energy of the colliding particle increases the atom or molecule energy; -partly inelastic. -coherent, coherence remain during the collison; -incoherent, coherence ceasing during the collision or it remains. Coherence: stationary interference in space and time. Coherent waves: constant relative phase.

7. The collision cross-section (  ) characterizes the effectivity of the collision. If N particles impact into a surface of the target with  particle density, the number of the produced reactions (collisions, absorptions, etc.) will be s= .N If the particle stream (particle/cross-section unit) is , and there are n particles on the target surface, s= .n.  Unit of collision cross-section is called barn, 1 barn=10 -28 m 2. The impulse (p) of a photon (velocity v=c) is the impulse of a particle with velocity v < c is p=m.v

8. Elastic scattering

9. Inelastic scattering E 1

10. Induced scattering (coherent).

11. Partially inelastic scattering

12. Induced partially inelastic scattering (coherent)

13. Spontaneous scattering

14. Inelastic scattering with particle change Fig. 1.8 in general: from photon to electron: I: ionization energy, 1a :photon frequency, m e : electron mass, v e : electron velocity

15. Interactions with electric field charge system of charges Q i position vectors r i a charge at the point P position vector R permittivity  potential: Expanding into series around P, second member: dipole moment

17. I II III Next term: quadrupole moment, characterizes asymmetricity of charge distribution example:

18. External electric field acts: Total dipole moment:   polarizability tensor,  hyperpolarizability. distorsion polarization E acts on p: torque orientation polarization Vector of polarization V: volume  o permittivity of vacuum (8.85419 x 10 -12 AsV -1 m -1 ),  e dielectric susceptibility

19. Dielectric induction vector characterizes the surface charge density (weak field) Strong field: D and E not collinear : Relative permittivity (dielectric constant) Molar polarization: characterizes the polarization state of the substance (Clausius and Mosotti): M: molecular mass,  : density More detailed: N A : Avogadro constant (6.0214x10 23 mol -1 ) first term in parenthesis average polarizability for distorsion polarization, second term: orientation polarization,k:Boltzmann constant(1.38066x10 -23 JK -1 ) T: absolute temperature.

20. Interactions with magnetic field Lorentz force, external magnetic field (B) acts on moving (velocity v) charged (Q) particle: B: magnetic induction or magnetic flux density Elementary magnet is a magnetic dipole, m. B acts on m. Electrons have magnetic moment from their nature and from their position (orbit) in the atom or molecule.

21. The magnetic moment of the particle is always coupled with an angular moment. Electron magnetic moment: m s, electron angular moment: spin (s) e: electron charge, m e : electron mass Correspondence principle of quantum mechanics: quantities of classical physics are substituted by operators that act on wavefunctions. For electrons: is the Bohr magneton, h is the Planck constant,is the spin operator. (h-bar)

22. Electron on an atomic orbit: angular moment l, magnetic moment: m. The right side of this equation differs from the similar equation for the electron in the factor 2 for electron spin: The corresponding quantum chemical expression is: The total orbital angular moment L (for some electrons) is coupled to the total orbital magnetic moment M (L and M vector are sums of individual moments): g is the Landé factor

23. Moments for a nucleus Nuclear angular moment: I. Magnetic moment M I, it is not zero if the atomic number is odd ( 1 H) or even with odd mass number ( 13 C). Pay attention! The sign of the right side is positive! g N is the Landé factor of the nucleus,    is the nuclear magneton, m p is the proton mass:

24. Diamagnetism It exists for all molecules independently of other magnetic effects. It is weak, stronger effects cover it. Origin: Changing magnetic flux B induces electric field E, this induces dipole (p  E , E act on p (T=p x E), T is time derivative of angular moment l, this coupled with the magnetic moment m, so The resulted diamagnetic moment is

25. Precession of the magnetic moment According to Larmor's theorem the magnetic dipoles move in a field B and they precess also around the direction of B

26. The direction of B (external field) is per definitionem the z axis. The angular velocity  and B are collinear. For electrons  e and  N are the magnetogyric ratios for electrons and nuclei, respectively. For nuclei

27. Another external magnetic field perpendicular to the first disturbs the stationary state and the magnetic moments change their directions but continue their precession. 1.The second field is an electromagnetic wave, 2.its frequency corresponds to the energy difference of two magnetic levels of the molecule, 3.Magnetic transition moment, not zero:  the system absorbs the wave. The relaxation process of the magnetic moment is observable.  Theoretical basis of NMR (nuclear magnetic resonance), and ESR (electron spin resonance) methods.

28. Paramagnetism The magnetic dipole density of a molecule depends on the sum of elementary magnetic moments. The vector of magnetization shows the strength of magnetization, M is proportional (in the case of weak fields) to the magnetic field strength H  0 : permeability of vacuum, (1.25664x10 -6 VsA -1 m -1 ),  m : magnetic susceptibility, The magnetic field strength is determined by B and not by H:  magnetic permeability weak field, linear:

29.  r is the relative permeability Stronger field: B and H are not parallel,  r is a tensor. Very strong field ferromagnetism: rr mm the substance is <1<0Diamagnetic (Bi) >1>0Paramagnetic(W) >>1>>0Ferromagnetic(Fe) In the case of ferromagnetic substances: magnetization curve, a hysteresis curve. Its area (curve integral) is proportional to the power of magnetization. Curie's law: A>0 and B are constants At temperture T: ferromagnetism  paramagnetism (Curie point)

30. Hysteresis curve: good magnetic tape, diskette or pendrive need a magnet with large magnetization area.

31. Interactions with electromagnetic waves Wave: disturbance, periodic in time and space, propagates energy in space and time. Electromagnetic wave (  ) propagates E perpendicular to H, both perpendicular to direction of propagation (transversal wave). E perturbs atom or molecule energy E j to higher level E i : Absorption of photon is possible (inelastic collision). Light absorption depends on 1. the probability of absorption 2. the relative population of the excited state 3. the average lifetime of the excited state

32. 1. The probability (a) of the process must be larger than zero: t: time, t p : time of process (absorption), and is the operator of perturbation, Potential energy operator: multiplication with potential energy (U).  p: change in the dipole moment during the perturbation.

33. The expression for K ij The integral in this equation is called transition moment of the process: P 2 is the transition probability. 2. The effect of population According to Boltzmann's distribution law N number of atoms (population) in the energy level (i or j). The process is drived by (N j -N i )/N j.

34. Frequency dependence of populations at 298K /Hz N i /N j 10 8 (1-2)x10 -5 10 0.99 10 12 0.85 10 13 0.30 10 14 10 -7 The data follow the exponential law.

35. 3.The average lifetime of the excited state. This is the average time of existance of a particle in its excited state. Long: the saturation of the excited state is easy Short: its saturation is is difficult. Type of the excited state Average lifetimes (s) rotational10 -10 – 10 -11 vibrational10 -7 – 10 -8 electronic (singlet)10 -5 - 10 -6 electronic (triplet)10 -2 - 10

36. The electromagnetic spectrum

37. Spectrometers used in optical spectroscopy 1.Dispersive spectrometer Sample: IR after the light source, UV-VIS: after the monchromator The grating resolves the spectrum. Two beams.The sample beam (S) is related to the reference beam (R). Half phase S, half phase R. The electronics balances them and amplifies the signal.

38. 2. Fourier Transform spectrometer

39. Interferograms

40. One-beam spectra

41. Double-beam spectra

42. Incident light (rates) 1.reflects on the sample surface, reflectivity  2.absorbs by the sample, absorptivity  3.transmits the sample, transmittivity  A spectrum consists of either of lines or bands A spectral line is the signal of one transition. A spectral band originates from - the same transition of several molecules with somewhat different chemical environment; - frequencies of several transitions are very close, the spectrometer cannot resolve the lines.

43. L inewidth The natural linewidth is determined by Heisenberg's uncertainty law: Energy uncertainty:  E=h. , Time uncertainty:  t= , average lifetime of excited state The natural linewidth:

44. Doppler effect (gas phase) An atom or a molecule nears to the detector with velocity v and emits light with frequency 0 (wavelength ). The observed frequency increases by v/. If the particle moves away from the detector, the frequency decreases by v/. Since =c/ o (c is the velocity of light in vacuum)

45. The velocity distribution in a gas follows Boltzmann's law, the spectral line gets a well-defined profile. Line broadening

46. Theoretically the change in the nuclear spin influences the electronic energy levels of the atom.. Practically, however, since this effect is very small its influence is practically unobservable. Instrument effect The measuring instrument influences the line profile, too. It has a transition function, that modifies the input signal to the output one. The result: the instrument broadens the lines and bands. Effect of nuclear spin

47. The spectrum The intensity of experimental spectra is measured as transmittance of the sample (often %): or as absorbance I is the transmitted light intensity, I o is the incident one. The intensity of the reflected light is measured as reflectance: I r is the intensity of the reflected light, r is called reflectivity.

48. The independent variable of the spectra is either frequency, or wavenumber or wavelength.

49. 0 is the nominal frequency of the band, FWHH is the full width at half hight. Characteristic data of a band