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FERENC BILLES STRUCTURAL CHEMISTRY. Chapter 1. INTERACTIONS OF ATOMS AND MOLECULES WITH PARTICLES AND EXTERNAL FIELDS. Elucidation of the molecular structure. Types of properties. The model is only an approach to the reality. The experiment disturbs the system.
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FERENC BILLES STRUCTURAL CHEMISTRY
Chapter 1. INTERACTIONS OF ATOMS AND MOLECULES WITH PARTICLES AND EXTERNAL FIELDS
The model is only an approach to the reality. The experiment disturbs the system. Acollision with particles maybe with electrons, atoms, ions, photons, etc. An effect with external fields maybe - effect with external - electric - magnetic -electromagnetic fields. The answerof the systemis - the change of its properties - or/and emission of one or more particles. The answer of the particleis - the change of one or more of its properties.
Non-central collision types: • elastic, energy change, colliding particle: l 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.
The collisioncross-section(s) characterizes the effectivity of the collision. If N particles impact into a surface of the target with r particle density, the number of the produced reactions (collisions, absorptions, etc.) will be s=s.r.N If the particle stream (particle/cross-section unit) is F, and there are nparticles on the target surface, s=s.n.F Unit of collision cross-section is called barn, 1 barn=10-28 m2. The impulse (p) of a photon(velocity v=c) is the impulse of a particlewith velocity v < c is p=m.v
Inelastic scattering with particle change Fig. 1.8 in general: from photon to electron: I: ionization energy, n1a:photon frequency, me: electron mass, ve: electron velocity
Interactions with electric field charge system of charges Qi position vectors ri position vector R a charge at the point P permittivitye potential: Expanding into series around P, second member: dipole moment
Next term:quadrupole moment, characterizes asymmetricity of charge distribution example: I II III
External electric field acts: distorsion polarization Total dipole moment: apolarizability tensor, bhyperpolarizability. E acts on p: torque orientation polarization Vector of polarization V: volume eopermittivity of vacuum(8.85419 x 10-12 AsV-1m-1), cedielectric susceptibility
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: molecularmass, r: density More detailed: NA: Avogadro constant (6.0214x1023mol-1) first term in parenthesisaverage polarizability for distorsion polarization, second term: orientation polarization,k:Boltzmann constant(1.38066x10-23JK-1) T: absolute temperature.
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 .
The magnetic moment of the particle is always coupled with an angular moment. Electronmagneticmoment: ms, electronangularmoment: spin (s) e: electron charge, me: electron mass Correspondence principle of quantum mechanics: quantities of classical physics are substituted by operators that act on wavefunctions. For electrons: (h-bar) is the Bohr magneton, h is the Planck constant, is the spin operator.
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 totalorbital magnetic moment M (L and M vector are sums of individual moments): g is the Landé factor
Moments for a nucleus Nuclear angular moment: I. Magnetic moment MI, it is not zeroif the atomic number is odd (1H) or even with odd mass number (13C). Pay attention! The sign of the right side is positive! gN is the Landé factor of the nucleus, mNis the nuclear magneton, mp is the proton mass:
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=aE), 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
Precession of the magnetic moment According to Larmor's theorem the magnetic dipoles move in a field Band they precess also around the direction of B
The direction of B(external field) is per definitionemthez axis. The angular velocity and B are collinear. For electrons For nuclei ge and gN are the magnetogyric ratios for electrons and nuclei, respectively.
Another external magnetic field perpendicular to the firstdisturbsthe stationary state and the magnetic momentschangetheir directionsbut continue their precession. • The second field is an electromagnetic wave, • its frequency corresponds to the energy difference of two magnetic levelsof the molecule, • Magnetic transition moment, not zero: • 4 the system absorbs the wave. • The relaxation process of the magnetic moment is observable. • 4Theoretical basisof • NMR(nuclear magnetic resonance), and • ESR (electron spin resonance) methods.
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 strengthH m0:permeability of vacuum,(1.25664x10-6 VsA-1m-1), cm:magnetic susceptibility, The magnetic field strength is determined by B and not by H: m: magnetic permeability weak field, linear:
mr is the relative permeability Stronger field: B and H are not parallel, mr is a tensor. Very strong field ferromagnetism: In the case of ferromagnetic substances: magnetization curve, ahysteresis 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 4 paramagnetism (Curie point)
Hysteresis curve: good magnetic tape, diskette or pendrive need a magnet with large magnetization area.
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 todirection of propagation (transversal wave). E perturbs atom or molecule energy Ej to higher level Ei: Absorptionof 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
1. The probability(a)of the process must be larger than zero: t: time, tp: time of process (absorption), and is the operator of perturbation, Potential energy operator: multiplication with potential energy (U). Dp: change in the dipole moment during the perturbation.
The expression for Kij The integral in this equation is called transitionmoment of the process: P2 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 (Nj-Ni)/Nj.
Frequency dependence of populations at 298K The data follow the exponential law.
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.
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.
Incident light (rates) • reflects on the sample surface, reflectivity r • absorbs by the sample, absorptivity • transmits the sample, transmittivityt Aspectrum consists of either of lines or bands A spectral line is the signal of one transition. • Aspectral bandoriginates 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.
Linewidth The natural linewidth is determined by Heisenberg's uncertainty law: Energy uncertainty:E=h., Time uncertainty: t=, average lifetime of excited state Thenatural linewidth:
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 frequencyincreases by v/. If the particle moves away from the detector, the frequency decreasesby v/. Since=c/o (c is the velocity of light in vacuum)
Line broadening The velocity distribution in a gas follows Boltzmann's law, the spectral line gets a well-defined profile.
Effect of nuclear spin 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 theinput signalto the output one. The result: the instrument broadens the lines and bands.
The spectrum The intensity of experimental spectra is measured as transmittanceof the sample (often %): or as absorbance I is the transmitted light intensity, Io is the incident one. The intensity of the reflected light is measured as reflectance: Ir is the intensity of the reflected light, r is called reflectivity.
The independent variable of the spectra is either frequency, or wavenumber or wavelength.
Characteristic data of a band n0 is the nominal frequencyof the band, FWHH is the full width at half hight.
