From 29c93204c71d1b6439a80485d42f6c37666b8a8e Mon Sep 17 00:00:00 2001 From: kilian Date: Wed, 30 Sep 2026 14:27:49 +0200 Subject: [PATCH] Dateien nach "Report" hochladen --- Report/Masterthesis.tex | 72 +++++++++++++++++++++++++++++++++++++--- Report/nmrdevice.jpg | Bin 0 -> 2030641 bytes Report/refs.bib | 7 ++++ 3 files changed, 74 insertions(+), 5 deletions(-) create mode 100644 Report/nmrdevice.jpg diff --git a/Report/Masterthesis.tex b/Report/Masterthesis.tex index 6968005..92a263f 100644 --- a/Report/Masterthesis.tex +++ b/Report/Masterthesis.tex @@ -28,15 +28,77 @@ \end{equation} \subsubsection{Das chemische Molekül als nicht einzigartig gelabelter Graph} - Ein chemisches Molekül bestehend aus kovalenten Bindungen kann dabei als ein ungerichteter Graph betrachtet werden. Dabei können die Kanten nach den Bindungstypen: einfach, doppelt, dreifach, vierfach und aromatisch gelabelt werden. Die Knoten können nach dem Elementtyp und mit der Elementarladung (-7 bis +7) gelabelt werden. Im Gegensatz zu einem gelabelten Graphen sind diese Label aber nicht einzigartig. Es ist möglich das Kantenlabel Beispielsweise einer Doppelbindung durch zwei Einfachbindungen zwischen den selben Knoten zu ersetzten. Diese Darstellung kann aber keine aromatischen Bindungen repräsentieren. Etwaige sterische Informationen sind dabei mit einem Graphen nicht darstellbar. + Ein chemisches Molekül bestehend aus kovalenten Bindungen kann dabei als ein ungerichteter Graph betrachtet werden. Dabei können die Kanten nach den Bindungstypen: einfach, doppelt, dreifach, vierfach und aromatisch gelabelt werden. Die Knoten können nach dem Elementtyp und mit der Elementarladung gelabelt werden. Im Gegensatz zu einem gelabelten Graphen sind diese Label aber nicht einzigartig. Es ist möglich das Kantenlabel Beispielsweise einer Doppelbindung durch zwei Einfachbindungen zwischen den selben Knoten zu ersetzten. Diese Darstellung kann aber keine aromatischen Bindungen repräsentieren. Etwaige sterische Informationen sind dabei mit einem Graphen nicht darstellbar. \subsubsection{Morphismen} + \subsubsection{Zyklen} \subsubsection{Graphtransformation} \subsubsection{Gerichteter Multi Hypergraph} - Ein gerichteter Multi Hypergraph $\mathcal{H} = (V,E)$ ist ein Tupel. Dabei ist $V$ eine Menge von Knoten und $E$ eine Menge von gerichteten Hyperkanten. Eine Hyperkante $e \in E$ ist selber ein Tupel $ e = (U, W)$ aus der Multimenge von Startknoten (tail) $U$ und einer Multimenge von Zielknoten (head) $W$. Beide Multimengen enthalten ausschließlich Knoten und sind daher Teilmengen der Menge von Knoten $U,W \subseteq V$ \cite{andersenhyperflow}. - \subsubsection{Zyklen} - \subsection{NMR} - + Ein gerichteter Multi Hypergraph $\mathcal{H} = (V,E)$ ist ein Tupel. Dabei ist $V$ eine Menge von Knoten und $E$ eine Menge von gerichteten Hyperkanten. Eine Hyperkante $e \in E$ ist selber ein Tupel $ e = (U, W)$ aus einer Multimenge von Startknoten (tail) $U$ und einer Multimenge von Zielknoten (head) $W$. Beide Multimengen enthalten ausschließlich Knoten und sind daher Teilmengen der Menge von Knoten $U,W \subseteq V$ \cite{andersenhyperflow}. + + \subsection{NMR-Spektroskopie} + \subsubsection{Spektren} + Um die im Hypergraphen entwickelten organischen Moleküle zu untersuchen eignet sich NMR-Spectroskopie. Spektroskopie (lat. Erscheinung, Sichtbarwerden) befasst sich mit der + Darstellung realer Eigenschaften durch eine Auftragung einer kontinuierlichen oder kleinschrittig gestaffelten Größe gegen die Intensität. In der organischen Chemie werden vor allem vier Spektroskopie Typen verwendet. Als kleinschrittig gestaffeltes Spektrum die Massenspektroskopie, bei der ein Molekül in kleinere geladene Fragmente geteilt wird. Diese Fragmente können über ein ganzzahliges Masse-Ladungs-Verhältnis und ihre Häufigkeit Charakterisiert werden. Zerstörungsfrei hingegen sind die kontinuierlichen, auf elektromagnetischen Wellen basierenden Absorptions- oder Resonanzspektren. Die verbreitetsten Resonanzspektren sind dabei UV/Vis und Infrarot. Die verwendeten Elektromagnetische Strahlung ist dabei im UV/Vis (200 - 800 nm) und Infrarot (800 nm - 1 mm). Die meist verbreitetste Spektroskopie hingegen ist die Kern-Magnet-Resonanz-Spektroskopie (Nucleus-Magnetic-Resonance, kurz NMR-Spektroskopie). UV-Resonanzspektroskopie ist möglich, wobei die Menge von Molekülen, die dafür verwendbar sind, sehr gering ist. Die elektromagnetischen Wellen für NMR sind im Radiowellenbereich (über 100 mm) \cite{ocwiley}. + \subsubsection{Kernspin} + Die im Atomkern befindlichen Neutronen und Protonen können sich in einem von zwei für NMR relevanten Zuständen befinden. Dem Kernspin in $\alpha$ oder $\beta$ Konfiguration. Dieser Kernspin ist keine Visuelle Rotation, hat aber die Eigenschaft, wie Ladung in Bewegung, ein Magnetfeld zu erzeugen. Die verschiedenen Zustände unterscheiden sich dabei in der theoretischen Drehrichtung und damit auch in der Richtung des induzierten Magnetfeldes. Unter normalen Umständen treten beide Konfigurationen im Verhältnis 1:1 auf. Durch das induzierte Magnetfeld kann ein entgegen gerichtetes, externes Magnetfeld diese Konfiguration energetisch hindern. Dadurch befinden sich deutlich weniger Kerne in diesem Zustand. Die Temperatur der Teilchen erlaubt jedoch einen Wechsel Abhängig vom Energieunterschied. Es ist ebenfalls möglich diesen Konfigurationswechsel durch Radiowellen einer zu dem Kern gehörigen Charakteristischen Wellenlänge zu erzwingen, wobei die Rückänderung der Konfiguration, auch Relaxation genannt, nach kurzer Zeit eintritt. Diese Relaxation emittiert dabei eine für den Kern charakteristische Wellenlänge. Sowohl die absorbierte, als auch die emittiert Wellenlänge hängen von der Energiedifferenz der beiden Konfigurationen ab, welche wiederum von der Umgebung des Kerns, aber auch von dem angelegten Magnetfeld abhängen. Die Frequenz der Strahlung ist dabei linear proportional zur Stärke des Magnetfeld \cite{ocwiley}. + \subsubsection{NMR aktive Kerne} + Da für NMR-Spektren der Kernspin nötig ist, kann es nur für Spektren verwendet werden, die Kernresonanz aufweisen. Das sind alle Kerne, die keine gerade Menge von Protonen und gerade Menge von Neutronen haben. Für die organische Chemie besonders wichtige Kerne sind in Tabelle \ref{tabelleisotope} aufgeführt. Für Wasserstoff ist dabei $^{1}$H besonders gut geeignet. Es tritt mit hoher Häufigkeit von 99,985 $\%$ auf und hat mit einer ungefähren Resonanzfrequenz von 300 MHz eine deutlich verschiedene Frequenz zu dem mit 0.015 $\%$ sehr seltenen $^{2}$H (D Deuterium), welches bei etwa 45.7 MHz resoniert. Bei Stickstoff bietet sich das Isotop $^{14}$N ebenso gut wie Deuterium an. Für Kohlenstoff ist $^{12}$C mit relativer Häufigkeit von 98,89 $\%$ nicht geeignet, da es 6 Neutronen und 6 Protonen hat und darum nicht NMR aktiv ist. Darum wird das deutlich seltenere $^{13}$C für NMR Spektren verwendet. Für Sauerstoff ist $^{17}$O die einzige Option, wobei die relative Häufigkeit mit 0.037 $\%$ noch geringer ist. + \begin{table}[htb] + \caption{Tabelle der chemischen Isotope, der in der organischen Chemie relevanten Elemente, mit natürlicher Relativer Häufigkeit und ob sie NMR aktiv sind \cite{ocwiley}.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabelleisotope} + Isotop N & Protonen/Neutronen & NMR-Aktivität & Natürliche Häufigkeit in $\%$ \\ + \hline + $^{1}$H & 1/0 & Ja & 99.985 \\ + $^{2}$H (D) & 1/1 & Ja & 0.0015 \\ + $^{3}$H (T) & 1/2 & Ja & 0 \\ + $^{12}$C & 6/6 & Nein & 98.89 \\ + $^{13}$C & 6/7 & Ja & 1.11 \\ + $^{14}$N & 7/7 & Ja & 99.63 \\ + $^{15}$N & 7/8 & Ja & 0.37 \\ + $^{16}$O & 8/8 & Nein & 99.759 \\ + $^{17}$O & 8/9 & Ja & 0.037 \\ + $^{18}$O & 8/10 & Nein & 0.037 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \subsubsection{NMR-Spektrometer} + Um ein NMR Spektrum aufzunehmen, werden wenige Milligramm der zu untersuchenden Probe in 0.3 bis 0.5 mL Lösungsmittel aufgelöst. Das Lösungsmittel selbst sollte dabei möglichst wenig der zu untersuchenden Kerne enthalten. Bei Wasserstoff wir zum Beispiel ein Deuteriertes Lösungsmittel verwendet. Die Lösung wird in ein elektrisch induziertes Magnetfeld eingebracht \ref{nmrdevice}. Ein Radiofrequenzpulsgenerator sendet einen kurzen Impuls an Radiowellen in die Probe, der das gesamte zu untersuchende Spektrum umfasst. Diese Radiowellen treffen auf die Röhre, wobei ein überwiegender Teil nicht absorbiert wird. Die absorbierten Radiowellen regen die Kernspins an, welche nach einander relaxieren. Die dabei emittierten Radiowellen werden in alle Richtungen abgestrahlt und von einem Radiofrequenzdetektor gemessen. Dieser ist orthogonal zum Radiofrequenzpulsgenerator positioniert, damit möglichst keine der durchgehenden Strahlung direkt auf den Detektor trifft. Der Radiofrequenzdetektor misst eine gedämpfte Schwingung mit verschiedenen Frequenzen. Diese Frequenzen können mit der Fouriertransformation von einem zeitabhängigen Oszillationsspektrum zu einem frequenzabhängigen Peakspektrum umgerechnet werden. + \begin{figure} [h] + \includegraphics[width=\textwidth]{nmrdevice.jpg} + \caption{Schematischer Aufbau eines NMR-Spektrometers \cite{ocwiley}. } + \label{nmrdevice} + \end{figure} + \subsubsection{Chemische Verschiebung} + Da die Rotation des geladenen Atomkerns ein Magnetfeld induziert liegt nahe, dass die Bewegung von Elektronen ebenfalls zu einer solchen Induktion führt. Dieses ist nach der Lenz'schen Regel dem induzierenden Magnetfeld entgegen gerichtet. Dadurch lässt sich sagen, dass bei Kernen mit hoher umliegender Elektronen dichte ein schwächeres effektives Feld anliegt. Um diesen Kern anzuregen, wird eine geringere Frequenz benötigt. + Da diese Frequenz zwar für den Kern charakteristisch ist, aber mit dem angelegten Magnetfeld variiert, wird ein interner Standard verwendet. Für Wasserstoff und Kohlenstoff Spektren ist dieser Tetramethylsilan (TMS (CH$_{3}$)$_{4}$Si). Die Frequenz $\nu$ wird daher als Differenz zu der Frequenz dieses Internen Standard $\nu_{TMS}$ betrachtet. Da aber die Differenz eines Kerns zum internen Standard proportional zur Feldstärke zunimmt, wird die Differenz durch die Frequenz des internen Standard $\nu_{TMS}$ geteilt um die chemische Verschiebung $\delta$ in ppm zu erhalten \ref{eqppm}. + \begin{equation} \label{eqppm} + \delta[ppm] = \frac{\nu[Hz] - \nu_{TMS}[Hz]}{\nu_{TMS}[MHz]} + \end{equation} + Kerne, bei denen die gleiche Elektronendichte vorliegt, haben das gleich starke effektive Magnetfeld, absorbieren die gleiche Wellenlänge und ihre Peaks liegen somit im entstehenden Spektrum bei der gleichen ppm Zahl. Sie werden darum als chemisch Äquivalent bezeichnet. Um zu bestimmen, ob zwei Kerne in einem Molekül chemisch Äquivalent zueinander sind, müssen beide Kerne durch Symmetrieoperationen, wie Rotationen um Einfachbindungen oder Spiegelungen aufeinander abzubilden sein. + \subsubsection{Multiplett Aufspaltung} + \begin{table}[htb] + \caption{Table of relative peak intensity in multiplets, by number of neighboring chemically equivalent hydrogen cores \cite{ocwiley}.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tablepeakheight} + equivalent hydrogen N & multiplet name & relative intensity \\ + \hline + 0 & singlet (s) & 1 \\ + 1 & duplet (d) & 1 : 1 \\ + 2 & triplet (t) & 1 : 2 : 1 \\ + 3 & quartet (q) & 1 : 3 : 3 : 1 \\ + 4 & quintet (quin) & 1 : 4 : 6 : 4 : 1 \\ + 5 & sextet & 1 : 5 : 10 : 10 : 5 : 1 \\ + 6 & septet & 1 : 6 : 15 : 20 : 15 : 6 : 1 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \section{Methoden} \subsection{M\o{}d} \subsection{ORCA} diff --git a/Report/nmrdevice.jpg b/Report/nmrdevice.jpg new file mode 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Peter, C. Vollhardt, Neil E. Schore}, + title = {Organische Chemie}, + publisher = {Wiley-VCH}, + year = {2020}, + isbn = {978-3-527-34582-3}, +} \ No newline at end of file

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