Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - Department of Chemistry

Humboldt-Universität zu Berlin | Faculty of Mathematics and Natural Sciences | Department of Chemistry | Studies | Curricula | pc_table | Methods of Statistical Thermodynamics / Basics of Spectroscopy

Methods of Statistical Thermodynamics / Basics of Spectroscopy

Statistical Thermodynamics

Potential Energy Surface: carthesian vs. internal coordinates, connectivity matrix, geometrical vs. structural isomerisation, dissociation. Phase space vs. configuration space. In latter: global vs. local minima, reaction coordinate, transition state. Force field and -constants, normal vibrations, IR spectroscopy. Ensembles: macroscopic material system and its many microscopic realisations under experimental conditions, microcanonical vs. canonical ensemble, demonstration with harmonic oscillator. For the classical canonical ensemble Monte Carlo: Boltzmann-sampling < >T of configuration space, determination of properties, for example <potential energy>T . Metropolis algorithm. For the quantized canonical ensemble Partition function: molecular quantum state as product in case of independent coordinates. Q trans for ideal gas; Qvib (Planck-Einstein function) & choices for zero potential energy; Qrot for spherical rotor; electronic contribution Qel. For system of N independent indistinguishable single particles with Qtotal(1), Fermi-Dirac statistics giving Qtotal(N). From canonical partition function to thermodynamic potentials: Qtotal(β,v,n) → Helmholtz F(T,v,n) and then as usual. Cv of ideal gas, of N space-fixed harmonic oscillators. Chemical applications : chemical potential as f(Q), chemical equilibrium and connection of equilibrium constant Kc(T) with the various Qi/V.

R. W. Kunz: "Molecular Modeling für Anwender", Teubner, 1991;
D. Chandler: "Introduction to Modern Statistical Mechanics", Oxford University Press, 1987;
D. A. McQuarrie: "Statistical Mechanics", University Science Books, 2000;
H. B. Callen: Thermodynamics and an Introduction to Thermostatistics, Wiley 1985;
G. H. Findenegg: "Statistische Thermodynamik", Steinkopff, 1985.

Experimental and theoretical basis of spectroscopy

(i) Processes in the system {material sample + spectrometer}, micro-and macroscopic changes of the sample; continuous and pulse excitation, degrees of freedom of the sample;

(ii) Phenomenological theory of spectrometers, classification with respect to the electromagnetic spectrum, mono- and multichannel and multiplex spectrometers; spectral, time and spatial resolution; (iii) Phenomenological description of reversible and irreversible processes in the system {sample + spectrometer}, flux of entropy, relaxation, fluctuation-dissipation theorem, Nyquist-theorem; (iv) Generation, characteristica and transfer of information, monochannel- and multiplex-spectroscopy; (v) General response of systems, δ-functions, Fourier-analysis; (vi) Handling of Hadamard- and Fouriertransformations, discrete Fourier transformation, transformations of simple mathematical functions; (vii) Convolution/deconvolution, graphical and numeric procedures; examples: monochromators, filter functions; (viii) Spin relaxation as a special case of relaxation, Bloch equations; application of Fourier-transformations in pulse NMR; (ix) Experiments to determine transversal and longitudinal relaxation times, resonance experiments, multidimensional spectroscopy.

P.W. Atkins "Physikalische Chemie", Wiley-VCH, 2002;
P.W. Atkins "Physical Chemistry" , Oxford University Press, 1990;
C. Gerthsen, H. Vogel "Physik", Springer Verlag, 1982;
C. Kittel, H. Krömer "Thermodynamik", Oldenburg-Verlag Münschen, 2000;
H. Günther "NMR spectroscopy", John Wiley and Sons, 1995;
A.G. Marshall, F.R. Verdun "Fourier Transforms in NMR, Optical and Mass Spectrometry", Elsevier, 1990;
A. Abragam "The principles of nuclear Magnetism", Oxford, 1961