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b/Report/Masterarbeit_Kilian_Seng.tex index ebc018f..b005647 100644 --- a/Report/Masterarbeit_Kilian_Seng.tex +++ b/Report/Masterarbeit_Kilian_Seng.tex @@ -103,6 +103,7 @@ \usepackage{amsfonts} \usepackage{latexsym} \usepackage{amssymb} + \usepackage[section]{placeins} %--- add hyperref %\usepackage[hyphens]{url} @@ -198,9 +199,9 @@ \phantomsection - \addcontentsline{toc}{chapter}{ Inhaltsverzeichnis} \raggedbottom \pagebreak \thispagestyle{empty} - \tableofcontents \raggedbottom \pagebreak \thispagestyle{empty} - + %\addcontentsline{toc}{chapter}{ Inhaltsverzeichnis} \raggedbottom \pagebreak \thispagestyle{empty} + \tableofcontents + \raggedbottom \pagebreak \thispagestyle{empty} \clearpage \phantomsection @@ -220,8 +221,8 @@ \pagenumbering{arabic} %%================================================================================== - \chapter{Abstract} - Cheminformatic has established as a valuable tool in the development and analysis of large chemical networks. Opening the possibility to tackle systemsizes that would not be feasable for a human researcher. The possibilities both for the development of reactions aswell as the the selection and verification of large reaction networks are presented in this thesis. + \chapter*{Abstract} + Cheminformatic has established as a valuable tool in the development and analysis of large chemical networks. Opening the possibility to tackle systemsizes that would not be feasable for a human researcher. The possibilities both for the development of reactions aswell as the the selection and verification of large reaction networks are presented in this thesis. This thesis aims to find sensible synthesis in chemical reaction networks using NMR-spectra and their characteristics. \chapter{Einleitung} Die Chemieinformatik ist ein aufstrebendes Forschungsfeld, das zum Ziel hat die Beschränkungen der Chemischen Industrie mit der Rechenstärke der Informatik anzugehen. So sollen neue Reaktion und Moleküle entwickelt, bestehende Prozesse optimiert und Eigenschaften analysiert werden. Diese Arbeit thematisiert eine Möglichkeit chemische Reaktionen näher zu analysieren und auf Basis dessen einen Prozess zu optimieren. @@ -289,7 +290,7 @@ \end{itemize} Auf dieser Kategorie von Graphen lassen sich drei Unterliegende Graphen Typen definieren. \paragraph{Pushout} - Bei zwei gegebenen Morphismen $g: A \rightarrow C$ und $f: A \rightarrow B$ erzeugen die Morphismen $g': B \rightarrow D$ und $f': C \rightarrow D$ genau dann ein Pushout D von f und g, wenn: + Bei zwei gegebenen Morphismen $g: A \rightarrow C$ und $f: A \rightarrow B$ erzeugen die Morphismen $g': B \rightarrow D$ und $f': C \rightarrow D$ genau dann ein Pushout D von f und g (Abb. \ref{pushout}), wenn: \begin{itemize} \item die Morphismen kommutativ sind: $g' \circ f = f' \circ g$ \item für alle Morphismen Paare $f'': C \rightarrow D''$ und $g'': B \rightarrow D''$ mit $f'' \circ g = g'' \circ f$ genau ein einzigartiger Morphismus $d'': D \rightarrow D''$ existiert, sodass $f'' = d'' \circ f'$ und $g'' = d'' \circ g'$ @@ -300,7 +301,7 @@ \label{pushout} \end{figure} \paragraph{Pullback} - Bei zwei gegebenen Morphismen $g': B \rightarrow D$ und $f': C \rightarrow D$ erzeugen die Morphismen $g: A \rightarrow C$ und $f: A \rightarrow B$ genau dann ein Pulback A von f' und g', wenn: + Bei zwei gegebenen Morphismen $g': B \rightarrow D$ und $f': C \rightarrow D$ erzeugen die Morphismen $g: A \rightarrow C$ und $f: A \rightarrow B$ genau dann ein Pulback A von f' und g' (Abb. \ref{pullback}), wenn: \begin{itemize} \item die morphismen kommutativ sind: $g' \circ f = f' \circ g$ \item für alle Morphismen Paare $f'': A'' \rightarrow B$ und $g'': A'' \rightarrow C$ mit $f' \circ g'' = g'' \circ f''$ genau ein einzigartiger Morphismus $a'': A'' \rightarrow A$ existiert, sodass $f'' = f \circ a''$ und $g'' = g \circ a''$ @@ -418,7 +419,7 @@ Wird dies auf den chemisch gelabelten Graphen angewendet, so stellen die Knotenlabel weiterhin die chemischen Elemente mit etwaigen Ladungen dar, jedoch ist für die Kantenlaben neben den chemischen Bindungen noch ein \textbf{nil} Label nötig, um das entfernen einer Bindung zu beschreiben. Bei einer Graphtransformation müssen weiterhin die Regeln für einen chemisch gelabelten Graphen gewahrt werden. \subsection{Gerichteter Multi Hypergraph}\label{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 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}. + 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}. Da es sich bei den Startkonten und Zielknoten um Multimengen handelt kann eine Kante den gleichen Knoten mehrmals in head und tail haben (Abb. \ref{hypergraphex}). \begin{figure} [h] \includegraphics[width=\textwidth]{hypergraphex.png} \caption{Drei Beispiele für Hyperkanten in Hypergraphen. Die linke Hyperkante beschreibt den Übergang von den Graphen $g_{1}$ und $g_{2}$ zu $g_{3}$. Die mittlere Kante Beschreibt den Übergang von dem Graph $g_{4}$ zu $g_{5}$. Bei einem einfachen Übergang wird eine einfache Kante verwendet. Die rechte Hyperkante beschreibt den Übergang von dem Graphen $g_{6}$ zu $g_{7}$. Es werden zwei Exemplare von $g_{6}$ benötigt, was durch den Doppelten Pfeil dargestellt wird \cite{andersenphd}.} @@ -432,11 +433,11 @@ \end{itemize} Ein Hyperpfad $P$ ist ein minimaler Superpfad. Also gilt: $\forall e \in P: P \setminus {e}$ ist kein Superpfad. \subsection{Zyklen} - Für einen endlichen ungerichteten Graphen $G =(V, E)$ ist ein einfacher Pfad definiert als endliche Sequenz $V_{P} = \langle v_{1}, ... , v_{k} \rangle$ mit $v_{1}, ... , v_{k} \in V$ und $E_{P} = \{(v_{1}, v_{2}), ..., (v_{k-1}, v_{k})\}$ mit $(v_{i}, v_{i+1}) \in E$ mit $i \in {1, ..., k-1}$. Ein solcher Pfad ist ein Zyklus, wenn gilt $(v_{k}, v_{1}) \in E$. Eine Sehne in einem Pfad ist eine Kante $e_{c} \in E$ zwischen zwei Knoten des Pfades $e_{i}, e_{j} \in V_{P}$, welche wiederum nicht Teil des Pfades ist $(_{i}, e_{j}) \notin E_{P}$. Ein sehnen loser Zyklus ist sehnen loser Pfad, bei dem der erste und letzte Knoten über eine Kante verbunden sind. + Für einen endlichen ungerichteten Graphen $G =(V, E)$ ist ein einfacher Pfad definiert als endliche Sequenz $V_{P} = \langle v_{1}, ... , v_{k} \rangle$ mit $v_{1}, ... , v_{k} \in V$ und $E_{P} = \{(v_{1}, v_{2}), ..., (v_{k-1}, v_{k})\}$ mit $(v_{i}, v_{i+1}) \in E$ mit $i \in {1, ..., k-1}$. Ein solcher Pfad ist ein Zyklus, wenn gilt $(v_{k}, v_{1}) \in E$. Eine Sehne in einem Pfad ist eine Kante $e_{c} \in E$ zwischen zwei Knoten des Pfades $e_{i}, e_{j} \in V_{P}$, welche wiederum nicht Teil des Pfades ist $(_{i}, e_{j}) \notin E_{P}$. Ein sehnen loser Zyklus ist sehnen loser Pfad, bei dem der erste und letzte Knoten über eine Kante verbunden sind \cite{chordlesscycle}. \subsection{Integer Linear Programming (ILP)} Ein Lineares Programmier (LP) Problem ist ein mathematisches Problem, bei dem für eine Menge an Variablen $\{x_{1},..., x_{n}\}$ Werte gefunden werden, so dass eine Zielfunktion maximiert oder minimiert wird. Ein LP kann mathematisch als eine Zielfunktion und eine Menge von Bedingungen beschrieben werden: \begin{itemize} - \item $max z = \sum_{j} c_{j} \times x_{j}$ + \item $max \: z = \sum_{j} c_{j} \times x_{j}$ \item Bedingung 1: $\sum_{j} a_{i,j} \times x_{j} \geq b_{i}$ \item Bedingung 2: $0 \leq x_{j}$ \end{itemize} @@ -444,13 +445,13 @@ Bei einem Integer LP Problem ist mindestens eine der Komponenten, meistens die Variable auf Integer also ganzzahlige Werte beschränkt. Es ist möglich, ein Maximierungsproblem in ein Minimierungsproblem zu überführen, indem die Zielfunktion mit einem negativen Wert multipliziert wird. Ebenso können mehrere Zielfunktionen kombiniert werden, indem sie addiert oder subtrahiert werden. Die Kombination aus Multiplikation mit einem großen Faktor und Addition erlaubt es eine primäre Zielfunktion mit einer sekundären oder Tertiären Zielfunktion zu kombinieren. Um das ILP zu lösen, werden alle Variablen und Konstanten auf die gleiche Seite der Gleichung gebracht und Ungleichungen durch positive Konstanten $s$ ausgedrückt: \begin{itemize} - \item $max z - \sum_{j} c_{j} \times x_{j}$ = 0 + \item $max \: z - \sum_{j} c_{j} \times x_{j}$ = 0 \item Bedingung 1: $\sum_{j} a_{i,j} \times x_{j} + s_{i} = b_{i}$ \item Bedingung 2: $0 \leq x_{j}$ \item Bedingung 3: $0 \leq s_{i}$ \end{itemize} - Diese Menge an Gleichungen kann in eine Matrix $\textbf{M}$ überführt werden, bei der die Zeilen die Gleichungen und die Spalten die Variablen $x_{j}, s{i}$ darstellen. - \begin{equation} + Diese Menge an Gleichungen kann in eine Matrix $\textbf{M}$ überführt werden, bei der die Zeilen die Gleichungen und die Spalten die Variablen $x_{j}, s{i}$ darstellen (Gleichung \ref{matrixilp}). + \begin{equation} \label{matrixilp} \begin{bmatrix} z & -c_{1}& ... & -c_{j} & 0 & ... & 0 &| 0\\ 0 & -a_{1,1} & ... & -a_{1,j} & s_{1} & ... & 0 &| b_{1}\\ @@ -466,8 +467,8 @@ s_{i} \end{bmatrix} \end{equation} - Das Lineare Gleichungssystem kann durch das einfache Invertieren der Matrix gelöst werden: - \begin{equation} + Das Lineare Gleichungssystem kann durch das einfache Invertieren der Matrix gelöst werden (Gleichung \ref{matinv}): + \begin{equation}\label{matinv} \textbf{A} \times x = b \iff \textbf{A}^{-1} \times b = x \end{equation} Die daraus resultierende Gleichung ist aber nicht unbedingt Ganzzahlig. Um eine ganzzahlige Optimale Lösung zu finden, wird ein Baum mit der über die Matrixinversion erhaltenen Lösung als Wurzel aufgespannt. @@ -497,19 +498,19 @@ Bei Entscheidung, welcher Knoten als nächstes untersucht wird, können verschiedene Baumsuchalgorithmen verwendet werden \cite{ilp}. \subsection{Petrinetze} Ein Petrinetz ist ein Werkzeug zur Untersuchung der Erfüllbarkeit parallel ablaufender Prozesse \cite{petri1962kommunikation}. Ein Petrinetz besteht aus Knoten und Kanten. Die Knoten lassen sich dabei als Zustände $p$ und Übergänge $t$ unterteilen. Die Zustände werden dabei als Kreise und die Übergänge als Querbalken dargestellt (Abb. \ref{petrinetbase}). - \begin{figure} [h] + \begin{figure} [p] \includegraphics[width=\textwidth]{Petrinet1.png} \caption{Ein einfaches Petrinetz bestehend aus den Zuständen $p_{1}$, $p_{2}$, $p_{3}$, $p_{4}$, $p_{5}$, $p_{6}$, $p_{7}$, dargestellt als Kreise und den Übergängen $t_{1}$, $t_{2}$, $t_{3}$, $t_{4}$, $t_{5}$, $t_{6}$, dargestellt als Querbalken \cite{petrinets}.} \label{petrinetbase} \end{figure} In einem Petrinet kann auf jedem Zustand ein Token platziert werden, um ein Gesamtzustand des Systems zu repräsentieren. Ein Übergang kann ausgelöst werden, wenn alle Zustände die auf ihn zeigen mindestens einen Token beinhalten. In dem Beispielgraphen in Abbildung \ref{petrinetmarked} kann nur Übergang $t_{2}$ feuern, da ein Token in $p_{1}$ ist. Bei den Übergängen $t_{3}$ und $t_{5}$ liegt nur ein Token in $p_{5}$ und $p_{7}$, aber keiner in $p_{3}$. - \begin{figure} [h] + \begin{figure} [p] \includegraphics[width=\textwidth]{Petrinetmarked.png} \caption{Ein einfaches Petrinetz bestehend aus den Zuständen $p_{1}$, $p_{2}$, $p_{3}$, $p_{4}$, $p_{5}$, $p_{6}$, $p_{7}$, dargestellt als Kreise und den Übergängen $t_{1}$, $t_{2}$, $t_{3}$, $t_{4}$, $t_{5}$, $t_{6}$, dargestellt als Querbalken. Die Zustände $p_{1}$, $p_{5}$ und $p_{7}$ haben ein Token, weshalb nur Übergang $t_{2}$ ausgelöst werden kann \cite{petrinets}.} \label{petrinetmarked} \end{figure} Nachdem Übergang $t_{2}$ ausgelöst hat, liegt ein neuer Token in $p_{2}$ und $p_{3}$ (Abb. \ref{petrinetmarkedfree}). Der Token in $p_{3}$ ist nötig, damit die Übergänge $t_{3}$ und $t_{5}$ ausgelöst werden können. Ebenso kann ein erneutes Sequenzielles auslösen von $t_{1}$ und $t_{2}$ immer weiter Token in $p_{3}$ erzeugen. Dieser Teil ist also ein Erzeuger. Die erzeugten Token in $p_{3}$ können entweder in $t_{3}$ und $t_{4}$ oder $t_{5}$ und $t_{6}$ verbraucht werden. Die Übergangsequenzen sind also im Konflikt zueinander. - \begin{figure} [h] + \begin{figure} [p] \includegraphics[width=\textwidth]{Petrinetmarkedfree.png} \caption{Ein einfaches Petrinetz bestehend aus den Zuständen $p_{1}$, $p_{2}$, $p_{3}$, $p_{4}$, $p_{5}$, $p_{6}$, $p_{7}$, dargestellt als Kreise und den Übergängen $t_{1}$, $t_{2}$, $t_{3}$, $t_{4}$, $t_{5}$, $t_{6}$, dargestellt als Querbalken. Die Zustände $p_{2}$, $p_{5}$, $p_{7}$ und $p_{3}$ haben ein Token, weshalb die Übergänge $t_{3}$ und $t_{5}$ ausgelöst werden können \cite{petrinets}.} \label{petrinetmarkedfree} @@ -522,7 +523,7 @@ Die im Atomkern befindlichen Neutronen und Protonen können sich in einem von zwei für NMR relevanten Zuständen befinden. Diese Zustände des Kernspins sind die $\alpha$ und $\beta$ 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. \subsection{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] + \begin{table}[h] \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| } @@ -552,7 +553,7 @@ \end{figure} \subsection{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 Spektrometers $\nu_{0}$ geteilt um die chemische Verschiebung $\delta$ in ppm zu erhalten \ref{eqppm}. + 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 Spektrometers $\nu_{0}$ geteilt um die chemische Verschiebung $\delta$ in ppm zu erhalten (Gleichung \ref{eqppm}). \begin{equation} \label{eqppm} \delta[ppm] = \frac{\nu[Hz] - \nu_{TMS}[Hz]}{\nu_{0}[MHz]} \end{equation} @@ -566,8 +567,8 @@ \subsection{Signalintensität} Nachdem wir nun die der Peaks diskutiert haben analysieren wir, was an den ppm-Verschiebungswerten zu sehen ist. Das NMR-Spektrum besteht aus einer berauschten Grundlinie, aus der an manchen Stellen hohe Intensitätswerte hervorstechen. Diese Werte werden Peaks genannt. Sie liegen auf den ppm Werten, die einzelnen Kernen zugeordenet werden können, können aber auch in einem Peakcluster angeordnet sein, welches in Kapitel \ref{chmultiplet} thematisiert wird. Die Peaks selber haben in den aller meisten Fällen eine breite Basis, die mit steigender Intensität immer spitzer zuläuft. Besonders bei sauren Wasserstoffen ist es jedoch möglich, dass der Peak auseinander gezogen wird und nur eine deutlich breitere und niedrigere Gaußglocke zu erkennen ist, die sogar bei manchen Messungen nur als ein anheben der Grundlinie zu erkennen ist. Die Peakhöhe und -breite kann dabei durch äußere Umstände variieren. Um für das Signal trotzdem vergleichbare Werte zu bekommen, wird die Fläche unter den Peaks integriert. Da die Flächen nur relativ zueinander konstante Werte ergeben, wird die kleinste Fläche als 1 definiert. Es wird davon ausgegangen, dass dieser Peak genau einem Wasserstoff im zu untersuchenden Molekül entspricht. Dabei gilt auch, dass die Peaks von chemisch Äquivalenten Kernen an der gleichen Verschiebung auftreten und dadurch überlagern. Die Peakfläche entspricht somit der Anzahl an Kernen, die diese Verschiebung aufweisen. Sollte bei dieser Analyse herauskommen, dass größere Peaks eindeutig Brüche darstellen, wird die kleinste Fläche in ihrem Wert erhöht. Betrachten wir unser vorheriges Beispiel Chlorethan und das zugehörige $^{1}$H-Spektrum. Der kleinere Peak in diesem Beispiel entspricht den chlornahen Wasserstoffen. Setzten wird diesen Peak nun auf 1, würde der Peak der Methylgruppe eine Fläche von etwa 1.5 aufweisen. Die Fläche des kleinsten Peaks wird also auf den nächst Größeren Integer erhöht. Dadurch sind beide Peakflächen mit 2 und 3 ganzzahlig, was auch der tatsächlichen Häufigkeit in Chlorethan entspricht. \subsection{Multiplett Aufspaltung} \label{chmultiplet} - Da das anlegen eines Magnetfeld nur eine Kernspin Konfiguration bevorzugt, jedoch nicht alle Kerne in diese überführt ist immer noch ein Großteil der Kernspins zufällig ausgerichtet. Liegt ein angeregter Kern nun neben anderen nicht angeregten Kernen, so beeinflusst deren Magnetfeld den angeregten Kern. Bei Ausrichtung mit dem Magnetfeld, wird das Signal zu höherer Frequenz und bei entgegengesetzter Ausrichtung zu niedrigere Frequenz verschoben. beide Signale treten nun im Spektrum auf, wobei sie zu dem selben Kern gehören. Sie werden deshalb als ein Peak zusammengefasst. Chemisch Äquivalente Kerne spalten das Multiplett mit gleicher Stärke auf. Dabei kann binomialverteilt jede Kombination an mit und entgegen gerichteten Kernen auftreten \ref{tablepeakheight}. Liegt in der näheren Umgebung ein weiterer nicht zu den anderen benachbarten Kernen chemisch äquivalenter Kern, so kann dieser ebenfalls das Spektrum aufspalten. Da die Frequenz der Aufspaltung verschieden ist, kommt es zu einem kombinierten Multiplett. Zum Beispiel kommt es bei 1,1-Dichlorpropan zu einer Aufspaltung der zentralen 2-Wasserstoffe zu einer Dublett in Quartett Aufspaltung. Die Methylgruppe spaltet dabei in ein Quartett auf und der chlornahe Wasserstoff spaltet dieses Quartett wiederum in ein Dublett auf. Je nach Auspaltungsfrequenz können die beiden Multipletts ineinander verschränkt sein, zwei nebeneinander liegende Quartetts (Quartett in Dublett) oder jedes Signal des Quartetts aufgespalten sein (Dublett in Quartett). Bei Wasserstoff Kernen folgt die Multiplett Zahl der $N+1$-Regel. Bei anderen Kernen kann es aber auch zu einer $2N+1$-Verteilung kommen. Da die Aufspaltung durch Interaktion der Kerne miteinander entsteht und der Interaktionsabstand der Kerne zueinander gleich ist, ist die Aufspaltungsfrequenz gleich groß. Es ist also möglich zwei benachbarte Kerne darüber zu identifizieren, dass der Abstand innerhalb des Multipletts gleich ist. Diese Interaktion ist dabei über bis zu 3 Bindungen gut erkennbar. Bei geminalen, also an den gleichen Kohlenstoff gebundenen Wasserstoffe, können Aufspaltungen von 0 - 18 Hz auftreten und bei vicinalen, also an benachbarte Kohlenstoff gebundene Wasserstoffe, kann diese 6 - 8 Hz sein. - \begin{table}[htb] + Da das anlegen eines Magnetfeld nur eine Kernspin Konfiguration bevorzugt, jedoch nicht alle Kerne in diese überführt ist immer noch ein Großteil der Kernspins zufällig ausgerichtet. Liegt ein angeregter Kern nun neben anderen nicht angeregten Kernen, so beeinflusst deren Magnetfeld den angeregten Kern. Bei Ausrichtung mit dem Magnetfeld, wird das Signal zu höherer Frequenz und bei entgegengesetzter Ausrichtung zu niedrigere Frequenz verschoben. beide Signale treten nun im Spektrum auf, wobei sie zu dem selben Kern gehören. Sie werden deshalb als ein Peak zusammengefasst. Chemisch Äquivalente Kerne spalten das Multiplett mit gleicher Stärke auf. Dabei kann binomialverteilt jede Kombination an mit und entgegen gerichteten Kernen auftreten (Tabelle \ref{tablepeakheight}). Liegt in der näheren Umgebung ein weiterer nicht zu den anderen benachbarten Kernen chemisch äquivalenter Kern, so kann dieser ebenfalls das Spektrum aufspalten. Da die Frequenz der Aufspaltung verschieden ist, kommt es zu einem kombinierten Multiplett. Zum Beispiel kommt es bei 1,1-Dichlorpropan zu einer Aufspaltung der zentralen 2-Wasserstoffe zu einer Dublett in Quartett Aufspaltung. Die Methylgruppe spaltet dabei in ein Quartett auf und der chlornahe Wasserstoff spaltet dieses Quartett wiederum in ein Dublett auf. Je nach Auspaltungsfrequenz können die beiden Multipletts ineinander verschränkt sein, zwei nebeneinander liegende Quartetts (Quartett in Dublett) oder jedes Signal des Quartetts aufgespalten sein (Dublett in Quartett). Bei Wasserstoff Kernen folgt die Multiplett Zahl der $N+1$-Regel. Bei anderen Kernen kann es aber auch zu einer $2N+1$-Verteilung kommen. Da die Aufspaltung durch Interaktion der Kerne miteinander entsteht und der Interaktionsabstand der Kerne zueinander gleich ist, ist die Aufspaltungsfrequenz gleich groß. Es ist also möglich zwei benachbarte Kerne darüber zu identifizieren, dass der Abstand innerhalb des Multipletts gleich ist. Diese Interaktion ist dabei über bis zu 3 Bindungen gut erkennbar. Bei geminalen, also an den gleichen Kohlenstoff gebundenen Wasserstoffe, können Aufspaltungen von 0 - 18 Hz auftreten und bei vicinalen, also an benachbarte Kohlenstoff gebundene Wasserstoffe, kann diese 6 - 8 Hz sein. + \begin{table}[h] \caption{Relative Intensitäten der einzelnen Peaks in den verschiedenen Multipletts, sowie die dafür nötige Anzahl chemisch Äquivalenter benachbarter Wasserstoffe \cite{ocwiley}.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -586,7 +587,7 @@ \end{center} \end{table} \subsection{Spektrum Analyse} - Im folgenden wird die Analyse eines NMR-Spektrums am Beispiel von 1,1,2-Trichlorpropan erläutert. Nach der Rotationssymmetrie lassen sich alle Wasserstoffe der Methylgruppe aufeinander abbilden. Durch die an der 1-C Position gebundenen Chloratome, gibt es aber keine Symmetrie von den Wasserstoffen der Endpositionen aufeinander. Es gibt also 3 verschiedene Wasserstofftypen. Ebenso lässt sich sagen, dass das Signal für die Methylgruppe mit 3 Wasserstoffen eine gesamtintensität von 3 aufweist. Da die beiden anderen Wasserstofftypen nur jeweils ein Proton umfassen, haben sie eine Intensität von 1. Die H$_{c}$ Methylwassestoffe haben zu dem 2-C H$_{b}$ Wasserstoff einen Abstand von 3 Bindungen. Die beiden Signale spalten einander also jeweils mit der Kopplungskonstante $j_{bc} = 6.8$. Das H$_{c}$-Signal wird dabei als ein Dublett aufgespalten, da nur ein chemisch äquivalenter Kern benachbart ist. Der Wasserstoff der 1-C Position H$_{a}$ und der Wasserstoff der 2-C Position sind zueinander ebenfalls 3 Bindungen entfernt und spalten einander mit der Kopplungskonstante $j_{ab} = 3.6$ auf. Da zu dem H$_{a}$ nur ein chemisch äquivalentes H$_{b}$ benachbart ist, wird das H$_{a}$ Signal zu einem Dublett aufgespalten. Das H$_{b}$ hat sowohl H$_{a}$, als auch 3 H$_{c}$ in seiner Nachbarschaft. Darum wird es von den 3 H$_{c}$ zu einem Quartett und von dem H$_{a}$ zu einem Dublett aufgespalten. Es entsteht ein Dublett in Quartett. Da Chlor elktronenziehend ist, wird mit zunehmender Chlorsubstitution, das Proton immer weiter entschirmt und das Signal erscheint bei höherer Verschiebung. Das H$_{a}$ hat mit zwei benachbarten Chloratomen die größte, H$_{b}$ mit einem benachbarten Chloratom die mittlere und H$_{c}$ mit keinen benachbarten Chloratomen die niedrigste Chemische Verschiebung (Abb. \ref{nmrex}). + Im folgenden wird die Analyse eines NMR-Spektrums am Beispiel von 1,1,2-Trichlorpropan erläutert (Abb. \ref{nmrex}). Nach der Rotationssymmetrie lassen sich alle Wasserstoffe der Methylgruppe aufeinander abbilden. Durch die an der 1-C Position gebundenen Chloratome, gibt es aber keine Symmetrie von den Wasserstoffen der Endpositionen aufeinander. Es gibt also 3 verschiedene Wasserstofftypen. Ebenso lässt sich sagen, dass das Signal für die Methylgruppe mit 3 Wasserstoffen eine gesamtintensität von 3 aufweist. Da die beiden anderen Wasserstofftypen nur jeweils ein Proton umfassen, haben sie eine Intensität von 1. Die H$_{c}$ Methylwassestoffe haben zu dem 2-C H$_{b}$ Wasserstoff einen Abstand von 3 Bindungen. Die beiden Signale spalten einander also jeweils mit der Kopplungskonstante $j_{bc} = 6.8$. Das H$_{c}$-Signal wird dabei als ein Dublett aufgespalten, da nur ein chemisch äquivalenter Kern benachbart ist. Der Wasserstoff der 1-C Position H$_{a}$ und der Wasserstoff der 2-C Position sind zueinander ebenfalls 3 Bindungen entfernt und spalten einander mit der Kopplungskonstante $j_{ab} = 3.6$ auf. Da zu dem H$_{a}$ nur ein chemisch äquivalentes H$_{b}$ benachbart ist, wird das H$_{a}$ Signal zu einem Dublett aufgespalten. Das H$_{b}$ hat sowohl H$_{a}$, als auch 3 H$_{c}$ in seiner Nachbarschaft. Darum wird es von den 3 H$_{c}$ zu einem Quartett und von dem H$_{a}$ zu einem Dublett aufgespalten. Es entsteht ein Dublett in Quartett. Da Chlor elktronenziehend ist, wird mit zunehmender Chlorsubstitution, das Proton immer weiter entschirmt und das Signal erscheint bei höherer Verschiebung. Das H$_{a}$ hat mit zwei benachbarten Chloratomen die größte, H$_{b}$ mit einem benachbarten Chloratom die mittlere und H$_{c}$ mit keinen benachbarten Chloratomen die niedrigste Chemische Verschiebung. \begin{figure} [h] \includegraphics[width=\textwidth]{nmrex.jpg} \caption{$^{1}$H-NMR von 1,1,2-Trichlorpropan. Der Methylwasserstoff (H$_{c}$ rot) hat ein Dublett bei 1.68 ppm mit Intensität 3, der zentrale Wasserstoff (H$_{b}$ grün) hat bei 4.35 ein Dublett in Quartett mit Signalstärke 1 und der Endwasserstoff (H$_{a}$ blau) erzeugt ein Dublett bei 5.96 ppm mit Signalstärke 1 \cite{ocwiley}. } @@ -624,32 +625,32 @@ cyclohexan = smiles ("C1CCCCC1") cyclohexan = Graph.fromGMLString( """ - graph [ - node [ id 0 label "C" ] - node [ id 1 label "H" ] - node [ id 2 label "C" ] - node [ id 3 label "H" ] - node [ id 4 label "C" ] - node [ id 5 label "H" ] - node [ id 6 label "C" ] - node [ id 7 label "H" ] - node [ id 8 label "C" ] - node [ id 9 label "H" ] - node [ id 10 label "C" ] - node [ id 11 label "H" ] - edge [ source 0 target 1 label "-" ] - edge [ source 0 target 2 label "-" ] - edge [ source 2 target 3 label "-" ] - edge [ source 2 target 4 label "-" ] - edge [ source 4 target 5 label "-" ] - edge [ source 4 target 6 label "-" ] - edge [ source 6 target 7 label "-" ] - edge [ source 6 target 8 label "-" ] - edge [ source 8 target 9 label "-" ] - edge [ source 8 target 10 label "-" ] - edge [ source 10 target 11 label "-" ] - edge [ source 10 target 0 label "-" ] - ] + graph [ + node [ id 0 label "C" ] + node [ id 1 label "H" ] + node [ id 2 label "C" ] + node [ id 3 label "H" ] + node [ id 4 label "C" ] + node [ id 5 label "H" ] + node [ id 6 label "C" ] + node [ id 7 label "H" ] + node [ id 8 label "C" ] + node [ id 9 label "H" ] + node [ id 10 label "C" ] + node [ id 11 label "H" ] + edge [ source 0 target 1 label "-" ] + edge [ source 0 target 2 label "-" ] + edge [ source 2 target 3 label "-" ] + edge [ source 2 target 4 label "-" ] + edge [ source 4 target 5 label "-" ] + edge [ source 4 target 6 label "-" ] + edge [ source 6 target 7 label "-" ] + edge [ source 6 target 8 label "-" ] + edge [ source 8 target 9 label "-" ] + edge [ source 8 target 10 label "-" ] + edge [ source 10 target 11 label "-" ] + edge [ source 10 target 0 label "-" ] + ] """ , name = "Cyclohexan) \end{lstlisting} @@ -657,33 +658,33 @@ \begin{lstlisting}[language=Python] cracking = Rule.fromGMLString( """ - rule [ - left [ - edge [ source 1 target 2 label "-" ] - ] - context [ - node [ id 1 label "C" ] - node [ id 2 label "C"] - ] - right [ - node [ id 3 label "H" ] - node [ id 4 label "H" ] - edge [ source 1 target 3 label "-" ] - edge [ source 2 target 4 label "-" ] - ] - ] + rule [ + left [ + edge [ source 1 target 2 label "-" ] + ] + context [ + node [ id 1 label "C" ] + node [ id 2 label "C"] + ] + right [ + node [ id 3 label "H" ] + node [ id 4 label "H" ] + edge [ source 1 target 3 label "-" ] + edge [ source 2 target 4 label "-" ] + ] + ] ) \end{lstlisting} Alle definierten Graphen werden in der Variable inputGraphs und alle definierten Regeln in der Variable inputRules gespeichert. Mit der Variable inputGraphs kann ein Derivationgraph DG erzeugt werden, auf dem die Regeln mit einer Benutzerdefinierten Abfolge angewendet werden können. Die Variable inputRules kann dabei allgemein oder eine spezifische Regel mit ihrem Variablennamen angewendet werden. Es ist ebenfalls möglich nach jeder Regelanwendung eine restriction Funktion aufzurufen, in welcher unerwünschte Eigenschaften der durch die Regeln erzeugten Graphen abgelehnt werden können. \begin{lstlisting}[language=Python] dg = DG(graphDatabase=inputGraphs) - dg.build().execute( - addSubset(inputGraphs) - >> rightPredicate[ - restriction - ]( - repeat(inputRules)) - ) + dg.build().execute( + addSubset(inputGraphs) + >> rightPredicate[ + restriction + ]( + repeat(inputRules)) + ) ) \end{lstlisting} Der durch die Regelanwendung erzeugte Hypergraph kann als über verschiedene print Befehle in einer Latex generierten PDF Datei dargestellt werden. Dafür muss ein FlowPrinter, DGPrinter oder GraphPrinter Objekt erzeugt werden \cite{mod}. @@ -692,13 +693,13 @@ flowPrinter.printUnfiltered = False postSection("Loaded Graphs") for a in inputGraphs: - a.print() + a.print() postSection("Loaded Rules") for a in inputRules: - a.print() + a.print() postSection("Product Graphs") for a in dg.vertices: - a.graph.print() + a.graph.print() \end{lstlisting} M\o{}d wurde verwendet die Einwirkung natürlich auftretenden Reaktionen auf natürliche oder synthetische Moleküle zu untersuchen. \section{networkx} @@ -707,11 +708,11 @@ ORCA ist ein Quantenchemisches Rechnungs Programm auf DFT Basis. Es erlaubt unter anderem Geometrieoptimierung und NMR-Spektren Berechnung von Chemischen Molekülen \cite{ORCA}. Für diese Arbeit wurde ORCA 6.1.1 verwendet. Für die durch das Graptransformationstool generierten Moleküle wurden die Graphen und SMILE Strings bestimmt. Die zugehörigen XYZ Koordinatendateien wurden aus der RDKit Bibliothek über ihren SMILE String bezogen \cite{rdkit} oder mit dem chemischen Zeichenprogramm Avogadro2 \cite{avogadro} gezeichnet. In beiden Fällen wurde die Geometrie mit ORCA mit den der Dichtefunktion PBE, D4 Dispersionskorrektur und dem Basissatz DEF2-SVP optimiert. Anschließend wurden für die optimierte Struktur mit der Dichtefunktion TPSS, dem Basissatz pcSseg-3 und mit autoaux und tightscf die chemischen Verschiebungen berechnet. - \begin{verbatim} + \begin{lstlisting} !PBE D4 DEF2-SVP OPT !TPSS pcSseg-3 autoaux tightscf NMR - \end{verbatim} + \end{lstlisting} Für den Vergleich wurden die selben Berechnungen für TMS durchgeführt. Die Kohlenstoff Verschiebung von TMS lag dabei bei 179.73 ppm. Die Bestimmung chemisch Äquivalenter Kerne wurde von Hand durchgeführt. Für jedes mit dem Graptransformationstool erzeugte Molekül wurde ein $^{13}$C-NMR berechnet. \section{NMR-Vergleich} Um die von dem quatntenchemischen berechneten NMR Spektren zu Vergleichen und ihre Ähnlichkeit zu Quantifizieren wurde die Binning Methode mit anschließender Crosscorrelation angewandt \cite{nmrbin}. Jeder Peak $j$ des Spektrums setzt sich aus seiner Intensität $I_{j}$ und seiner Verschiebung $\nu_{j}$ zusammen. Zuerst wird für ein gegebenes NMR Spektrum der Peak mit der größten chemischen Verschiebung $\nu_{max}$ und der kleinsten chemischen Verschiebung $\nu_{min}$ bestimmt und eine Bingröße $b$ festgelegt. Der größte Wert $\nu_{max}$ wird dabei aufgerundet und um eine Bingröße $b$ erhöht (Gleichung \ref{binupper}). Der kleinste Wert $\nu_{min}$ wird abgerundet und um eine Bingröße $b$ verringert (Gleichung \ref{binlower}). @@ -738,7 +739,7 @@ \begin{equation} \label{overlap} O_{i} = 0.5 \times (I_{i} \times I_{j-1}) + (I_{i} \times I_{j}) + 0.5 \times (I_{i} \times I_{j+1}) : i = j \end{equation} - Der Gesamtüberlapp $O$ ist die Summe aller Teilüberlappe $O_{i}$ (Gelichung \ref{fulloverlap}) + Der Gesamtüberlapp $O$ ist die Summe aller Teilüberlappe $O_{i}$ (Gleichung \ref{fulloverlap}) \begin{equation} \label{fulloverlap} O_{ij} = \sum_{i} O_{i} \end{equation} @@ -842,9 +843,10 @@ \end{figure} \section{NMR: Ein-Molekül-Reaktionen} Für alle Zwischenprodukte wurde mit dem Quantenchemischen Tool ein $^{13}$C-NMR berechnet und ein dazugehöriges Literaturspektrum recherchiert. + \FloatBarrier \subsection{Koffein} Für alle Xanthinringe lässt sich sagen, dass ausschließlich die Protonen der Methygruppen chemisch Äquivalent zueinander sind. In einem $^{13}$C-NMR weisen also alle Kohlenstoffe ein eigenes Signal mit Intensität 1 auf. Die mit dem Quantenchemischen Tool berechneten NMR Spektren wurden den recherchierten Literaturspektren gegenübergestellt (Tabellen \ref{tabelxanthin},\ref{tabel1xanthin},\ref{tabel3xanthin},\ref{tabel7xanthin},\ref{tabel13xanthin},\ref{tabel17xanthin},\ref{tabel37xanthin},\ref{tabel137xanthin}) und ihre Verschiebung zueinander bestimmt. - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Xanthin mit einem Literatur Spektrum \cite{xanthinnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.14 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -861,7 +863,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für 1-Methylxanthin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.39 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -879,7 +881,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für 3-Methylxanthin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.35 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -897,7 +899,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für 7-Methylxanthin mit einem Literatur Spektrum \cite{7xanthinnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.73 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -915,7 +917,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Theophyllin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.61 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -934,7 +936,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Paraxanthin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.19 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -953,7 +955,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Theobromin mit einem Literatur Spektrum \cite{theobrominnoMenmr}. Die Methylsignale (ca. 30 ppm) wurden aus einem anderen Spektrum genommen, da diese Angabe fehlte \cite{theobrominnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.63 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -972,7 +974,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Koffein mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.77 ppm.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -994,9 +996,10 @@ \end{table} \newline Die Methylwasserstoff lassen sich dabei den Signalen um ca. 30 ppm zuordnen, wobei das 1-Methyl Signal mit 28.6 bis 30.18 bei dem mit dem Quantenchemischen Tool berechneten und 26.7 bis 27.7 in den experimentellen Spektren den niedrigsten Wert aufweist. Die mittlere Verschiebung weißt das 3-Methylsignal mit 31.0 bis 32.1 bei dem mit dem Quantenchemischen Tool berechneten und 28.8 bis 29.7 in den experimentellen Spektren auf. Die größte Verschiebung ist dem 7-Methylsignal mit 36.7 bis 36.9 bei dem mit dem Quantenchemischen Tool berechneten und 32.9 bis 33.9 in den experimentellen Spektren zuzuordnen. Die Signale des Purinrings sind für den größten Teil konstant über alle Moleküle, wobei Xanthin mit 151.03 bei dem mit dem Quantenchemischen Tool berechneten, zu 140.5 im Experiment eine besonders große Differenz aufweist. Die größten Unterschiede sind über alle Xanthine bei dem Kohlenstoff neben dem 7-Stickstoff. Über alle Moleküle gemittelt lässt sich bestimmen, dass die mit dem Quantenchemischen Tool berechneten Spektren im Durchschnitt um 2.5 ppm nach oben verschoben sind. + \FloatBarrier \subsection{Vanillin und 3,4-Dihydroxyaldehyd} Für 3-hydroxylierte Zwischenprodukte gilt, dass keine Kerne chemisch Äquivalent zueinander sind. Wenn nicht oder nur in der 4-Position hydroxyliert ist, sind jeweils die im Phenylrest gegenüberliegenden Wasserstoffe und Kohlenstoff zueinander chemisch Äquivalent. In einem $^{13}$C-NMR weisen also alle Kohlenstoffe in 3-hydroxilierten Moleküle ein eigenes Signal mit Intensität 1 auf. In nicht oder 4-hydroxylierten Molekülen verschmelzen jeweils zwei Signale zu insgesamt zwei Signalen mit Intensität 2. Die mit dem Quantenchemischen Tool berechneten NMR Spektren wurden den recherchierten Literaturspektren gegenübergestellt (Tabellen \ref{tabelzimt},\ref{tabelmcoum},\ref{tabelpcoum},\ref{tabelald},\ref{tabelcafac},\ref{tabel3ald},\ref{tabel4ald},\ref{tabel34ald}) und ihre Verschiebung zueinander bestimmt. - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Zimtsäure mit einem Literatur Spektrum \cite{cinamnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 4.02 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1015,7 +1018,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für m-Coumarsäure mit einem Literatur Spektrum \cite{mcoumnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.53 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1036,7 +1039,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für p-Coumarsäure mit einem Literatur Spektrum \cite{pcoumnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 4.71 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1055,7 +1058,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Benzaldehyd mit einem Literatur Spektrum \cite{aldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 4.80 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1072,7 +1075,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für Kaffesäure mit einem Literatur Spektrum \cite{caffacdnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.18 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1087,13 +1090,13 @@ 1 & 116.4 & 116.16 & -0.24 \\ 1 & 141.5 & 149.28 & 7.78 \\ 1 & 114.6 & 110.95 & -3.65 \\ - 1 & 176.2 & 171.66 & -4.549 \\ + 1 & 176.2 & 171.66 & -4.55 \\ & & & 2.18 \\ \hline \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für 3-Hydroxybenzaldehyd mit einem Literatur Spektrum \cite{mhydaldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.83 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1112,7 +1115,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für 4-Hydroxybenzaldehyd mit einem Literatur Spektrum \cite{phydaldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.35 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1129,7 +1132,7 @@ \end{tabular} \end{center} \end{table} - \begin{table}[htb] + \begin{table}[p] \caption{Vergleich des mit dem Quantenchemischen Tool berechneten Spektrum für 3,4-Dihydroxybenzaldehyd mit einem Literatur Spektrum \cite{mphydaldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt -3.81 ppm.} \begin{center} \begin{tabular}{ |c|c|c|c| } @@ -1155,9 +1158,10 @@ \begin{equation} \label{binsize} b \in \{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0\} \end{equation} + \FloatBarrier \subsection{Koffein} Den Erwartungen entsprechend weißt das mit dem Quantenchemischen Tool berechnete Spektrum von 7-Methylxanthin eine hohe Ähnlichkeit zu dem experimentellen Spektrum von 7-Methylxanthin auf. Das Spektrum von Paraxanthin ist jedoch noch etwas ähnlicher. Die Spektren von Theobromin haben im Vergleich dazu die größten Übereinstimmungen, wobei Koffein am zweit ähnlichsten ist. Allgemein scheint eine Identifikation des 7-Methylrest gut zu funktionieren, jedoch keine einfache Unterscheidung der Restlichen Methylgruppen möglich zu sein. Da in allen Molekülen das Xanthin-Grundgerüst vorliegt und die Addition einer Methylgruppe dieses nicht zu sehr verändert, haben alle Moleküle eine signifikante Ähnlichkeit zueinander (Tabelle \ref{nmrsimcoff}). - \begin{table}[htb] + \begin{table}[h!] \caption{Resultierende normalisierte Wahrscheinlichkeiten beim Vergleich aller Zwischenprodukte der Koffeinsynthese, sowie Xanthin und Koffein mit den natürlichen Zwischenprodukten 7-Methyxanthin und Theobromin.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -1176,9 +1180,10 @@ \end{tabular} \end{center} \end{table} + \FloatBarrier \subsection{Vanillin und 3,4-Dihydroxyaldehyd} Bei der Vanillin Synthese liegen die chemischen Verschiebungen des Grundgerüsts weiter auseinander, weshalb manche Moleküle, wie 3-Hydroxybenzaldehyd nur eine sehr geringe Ähnlichkeit zu den natürlich Zwischenprodukten aufweisen. p-Coumarsäure hat die größte Ähnlichkeit zu sowohl seinem eigenen experimentellen Spektrum, sowie zu dem von 4-Hydoxybenzaldehyd. Die zweitgrößte Ähnlichkeit zu dem experimentellen Spektrum von p-Coumarsäure hat Kaffeesäure. Bei dem experimentellen Spektrum von 4-Hydroxybenzaldehyd hat das richtige Molekül die zweit größte Ähnlichkeit. Kaffesäure hat eine genauso große Ähnlichkeit zu p-Coumarsäure wie 4-Hydroxybenzaldehyd (Tabelle \ref{nmrsimvani}). Im Vergleich zu den Xanthinen sind die Abweichungen der berechneten zu den experimentellen Spektren bei den Vanillevorprodukten deutlich weniger Konstant. So hat Kaffesäure mit 2.35 ppm die geringste Abweichung zwischen beiden zugehörigen Spektren. Trotzdem ist die Verschiebung beider Spektren nicht konstant und die Varianz der Werte ist deutlich größer als bei den Spektren der Xanthine, weshalb die nicht normalisierte Crosskorrelation allgemein geringer ausfällt. Das berechnete Spektrum von Kaffesäure hat dabei mit vielen Peaks eine Distanz unter 1.0 ppm zu Peaks in dem Literaturspektrum von p-Coumarsäure, weshalb der Überlapp größer als erwartet ausfällt. Die berechneten Spektren von p-Coumarsäure und 4-Hydroxybenzaldehyd haben weniger überlappende Spektren mit beiden Literaturspektren. Die Überlappenden Peaks sind aber die Spektren überlappen dabei jedoch mit den Peaks mit Intensität 2. Das berechnete Spektrum von p-Coumarsäure überlappt dabei mit beiden Intensität 2 Peaks im Literaturspektrum von 4-Hydroxybenzaldehyd. Da die Überlappenden Intensitäten multipliziert werden, wird dieser Überlapp stärker gewichtet. Allgemein haben alle para-hydroxylierten Phenylgruppen größeren Überlapp mit der p-Coumarsäure. Bei 4-Hydroxybenzaldehyd scheint der Überlapp größer bei Molekülen ohne meta-Hydroxygruppe zu sein. - \begin{table}[htb] + \begin{table}[h!] \caption{Resultierende normalisierte Wahrscheinlichkeiten beim Vergleich aller Zwischenprodukte der Vanillesynthese mit den natürlichen Zwischenprodukten p-Coumarsäure und 4-Hydroxybenzaldehyd.} \begin{center} \begin{tabular}{ |c|c|c| } @@ -1197,7 +1202,7 @@ \end{tabular} \end{center} \end{table} - + \FloatBarrier \section{ILP: Ein-Molekül-Reaktionen} Der Hypergraph der komplett explorierten Synthese wurde an Gurobi übergeben und um eine Kante die in das Ausgangsprodukt hineinfließt und aus dem Zielmolekül herausfließt erweitert. Die Wahrscheinlichkeiten wurden als konstante Werte $p_{i,e}$ den Kanten $e$ des Hypergraphen zugeordnet. Die Kante 4 von Zimtsäure zu Benzaldehyd hat also die Wahrscheinlichkeit $p_{1,4} = 0.09$ das diese Reaktion dem ersten Referenzspektrum mit p-Coumarsöure entspricht. Die Wahrscheinlichkeit wurde der Kante zugeordnet, welche in den Knoten fließt. Für jede Kante werden vier ganzzahlige Variablen $x_{e}$, $b_{e}$, $n_{1,e}$ und $n_{2,e}$ definiert. Die Variable $b_{e}$ ist dabei eine Wahrheitsvariable, die definiert ob eine Kante verwendet wird. Die Variable $x_{e}$ beschreibt wie oft die selbe Kante verwendet wird. Die Variablen $n_{1,e}$ und $n_{2,e}$ sind ebenfalls Wahrheitsvariablen und legen fest, welche zwei Reaktionen den Referenz NMR-Spektren entsprechen und deswegen zu der Zielfunktion da zuzählen. Dabei ist $n_{1,e}$ die Zuordnungsvariable zu dem ersten Referenz NMR-Spektrum mit 7-Methylxanthin oder p-Coumarsäure und $n_{2,e}$ die Zuordnungsvariable zu dem zweiten Referenz NMR-Spektrum mit 3,7-Methylxanthin oder 4-Hydroxybenzaldehyd. @@ -1213,13 +1218,14 @@ \item $\sum_{e} n_{1,e} = 1$ \item $\sum_{e} n_{2,e} = 1$ \end{itemize} - Unter diesen Beschränkungen soll ein Pfad durch den Hypergraphen bestimmt werden, welcher ein geordnetes Paar von Molekülen auswählt, welche zusammen die größte Wahrscheinlichkeit aufweisen und zusammen alle Zwischenprodukte der Synthese darstellen. Die ausgehenden Kanten sind nicht in die Zielfunktion eingeflossen (Gleichung \ref{objective}). + Unter diesen Beschränkungen soll ein Pfad durch den Hypergraphen bestimmt werden, welcher ein geordnetes Paar von Molekülen auswählt. Dieses Paar von Molekülen soll alle Zwischenprodukte der Synthese beinhalten und addiert die größte Wahrscheinlichkeit aufweisen. Die ausgehenden Kanten sind nicht in die Zielfunktion eingeflossen (Gleichung \ref{objective}). \begin{equation} \label{objective} max Obj = \sum_{e} 1000 \times (p_{1,e} \times n_{1,e} + p_{2,e} \times n_{2,e}) \newline - \frac{x_{e}}{ max(p_{1,e}, p_{2,e})} \end{equation} + \FloatBarrier \subsubsection{Koffein} Der Hypergraph für die Koffeinsynthese wird in Tabelle \ref{hypergraphcaffsynth} dargestellt. - \begin{table} + \begin{table}[h!] \caption{Der für die Koffeinsynthese definierte Hypergraph in Gurobi mit den für jede Kante definierten Wahrscheinlichkeiten.} \begin{center} \scriptsize @@ -1246,7 +1252,7 @@ \end{center} \end{table} Die beste gefundene Lösung ist für die Kanten 1, 4, 10, 13 und 14 jeweils ein flow $x_{e} = 1$ und alle anderen Kanten ein flow $x_{e} = 0$ (Tabelle \ref{ilpsolcaff}). Dies entspricht der natürlich auftretenden Lösung. - \begin{table} + \begin{table}[h!] \caption{Lösung von Gurobi für die Koffeinsynthese.} \begin{center} \scriptsize @@ -1272,9 +1278,10 @@ \end{tabular} \end{center} \end{table} + \FloatBarrier \subsection{Vanillin und 3,4-Dihydroxyaldehyd} - Der Hypergraph für die Vanillinsynthese wird in Tabelle \ref{hypergraphcaffsynth} dargestellt. - \begin{table} + Der Hypergraph für die Vanillinsynthese wird in Tabelle \ref{hypergraphvanilsynth} dargestellt. + \begin{table}[h!] \caption{Der für die Vanillinsynthese definierte Hypergraph in Gurobi mit den für jede Kante definierten Wahrscheinlichkeiten.} \begin{center} \scriptsize @@ -1301,7 +1308,7 @@ \end{center} \end{table} Die beste gefundene Lösung ist für die Kanten 1, 2, 6, 13 und 14 jeweils ein flow $x_{e} = 1$ und alle anderen Kanten ein flow $x_{e} = 0$ (Tabelle \ref{ilpsolvan}). Dies entspricht der natürlich auftretenden Lösung. - \begin{table} + \begin{table}[h!] \caption{Lösung von Gurobi für die Vanillinsynthese.} \begin{center} \scriptsize @@ -1328,15 +1335,16 @@ \end{center} \end{table} Dabei ist jedoch anzumerken, dass die Lösung des ILP für das erste Moleküle 4-Hydroxybenzaldehyd und für das zweite Molekül p-Coumarsäure gewählt hat. Die Zuordnung erfolgte also genau anders herum. Zudem ist davon auszugehen, dass die zweitbeste Lösung genau den selben Wert Zielwert aufweist. + \FloatBarrier \section{Fazit: Ein-Molekül-Reaktionen} Bei den bisher betrachteten Ein-Molekül-Reaktionen wurde immer nur ein festgelegtes Startmolekül in das System gegeben. Dieses Startmolekül wurde nach Transformationsregeln variiert, wobei jedoch nach dem natürlichen Vorbild auch genau ein Zielmolekül synthetisiert werden sollte. In dem Koffein Beispiel gab es dabei keine Enantiomere oder E/Z-Isomere. In dem Vanille Beispiel gab es keine Enatiomere. Es gab mit Zimtsäure, Coumarsäure und Kaffesäure zwar E/Z-Isomere, welche aber durch die natürliche Vorgabe von E-Zimtsäure bereits vorgegeben waren. Außerdem entstand keine neue Doppelbindung mit einem E/Z-Isomer durch Graphtransformation. Der Schluss von dem Graphen auf eine Geometrie war deswegen immer eindeutig. \newline Die Berechnung der NMR Spektren war trotzdem fehleranfällig. Dabei konnten bestimmte Molekülveränderungen besser in dem NMR-Berechnungstool abgebildet werden. Eine Methylierung erzeugte dabei nur eine geringe Veränderung im Xanthingrundgerüst, weshalb die Zuordnung vor allem in dem Signal der Methylgruppe lag. Die Hydroxylierung und Oxidierung zum Aldehyd resultierten in deutlichen Veränderungen der Phenylgruppe, weshalb das Grundgerüst selber verändert wurde. \newline Für die Synthesen waren immer genau drei Reaktionen nötig, welche mittels des ILP nur bezüglich ihrer Reihenfolge variiert werden konnte. Das Problem ließe sich daher ebenfalls durch die einfache Addition zweier Moleküle entlang eines ausgewählten Pfades lösen. Der Raum möglicher Lösungen ist mit 6 pro Hypergraph stark begrenzt. Trotzdem eigneten sich beide Beispiele mit der natürlich auftretenden Selektivität der Reihenfolge, der guten Differenzierbarkeit der NMR-Spektren und Kompaktheit der Synthese als Graphtransformationsregeln als Demonstration des Konzeptes. Es ist anzumerken, dass die erwartete Synthese über die Auswahl der Referenzspektren festgelegt wurde. Diese Synthese wurde über NMR-Spektren abstrahiert. Es lässt sich so sagen, dass die NMR-Spektren in dieser Analyse die Struktur hinreichend Codieren, aber nicht eine Unbekannte Synthese vollständig hergeleitet wurde. \newline Für ausgewählte Literaturspektren von nicht in der natürlichen Synthese erwarteten Molekülen wurden ebenfalls die Crossskorrelationen mit den berechneten Spektren ermittelt. Dabei konnte ebenfalls eine erhöhte Korrelation mit dem zugehörigen berechneten Spektrum bestimmt werden. Das ILP konnte dabei den neuen Syntheseplan ebenfalls zuverlässig zuordnen. Die Auswahl eines Syntheseplans basierend auf der Ähnlichkeit von NMR-Spektren ist daher gerechtfertigt und stellt eine Verbesserung gegenüber der Auswahl ohne selbige dar. \section{Multi-Molekül-Reaktionen} - Um die Grenzen der Möglichkeiten des ILP weiter auszureizen werden im Folgenden Reaktionen, die ebenfalls mit einfachen Reaktionsregeln ein hochvernetztes Reaktionsnetzwerk erzeugen betrachtet. + Die bisherigen Ein-Molekül-Reaktionen lassen sich durch ein ILP lösen, erfordern die Verwendung jedoch nicht. Um die Grenzen des ILP weiter auszureizen, wird ein komplexerer Hypergraph entwickelt. Dieser Hypergraph wird mit wenigen, einfachen Transformationsregeln und mit einem Ausgangsmolekül erzeugt. Das Ziel ist ein hochvernetztes Reaktionsnetzwerk. \section{Olefin Metathese und Diels Alder} Die zwei Reaktionen Olefin Metathese in Kombination mit der Diels-Alder-Reaktion erlaubt mit dem richtigen Ausgangsmolekülen die Entwicklung eines hochvernetzten Reaktionsnetzerks und unterliegenden Hypergraphen. \subsection{Olefin Metathese} Die Olefin Metathese ist eine vergleichbar neuere Reaktion \cite{olefinmetathese}. Mit meistens einem organischen Ruthenium-Katalysator werden dabei die Reste zweier Doppelbindungen rekombiniert. Dar Ruthenium-Katalysator hat dabei eine offene Bindungsstelle an die eine Hälfte der C-C-Doppelbundung als Carben bindet (A und E). Eine Olefin (B und F) bindet an diesen Komplex (C und G). Aus diesem Komplex wird ein Olefin abgespalten, welches entweder das eingehende Olefin ist oder eine beliebige Kombination beider Olefine (D) (Abb. \ref{olefinmetathese}). - \begin{figure} [h] + \begin{figure} [h!] \includegraphics[width=\textwidth]{olefinmetathese.png} \caption{Katalysezyklus der Olefinmetathese \cite{olefinmetathese}. } \label{olefinmetathese} @@ -1344,10 +1352,12 @@ In der Forschung wurde dieser Katalytische Prozess zu immer gezielteren Ausbeuten durch spezialisierte Katalysatoren weiterentwickelt. Dabei wurde neben der generellen Selektivität der Produkte auch eine gezielte Selektivität hin zu E-Isomeren erzielt. Für die Anwendung auf ein Reaktionsnetzwerk ist eine Produktspezialisierung jedoch weniger interessant. Die E/Z-Selektivität ist dabei insbesondere im Hinblick auf den chemischen Molekül als Graphen nicht umsetzbar, wenngleich sie bei der Geometirerealisierung berücksichtigt werden kann. Die Möglichkeiten der Olefinmetathese sind jedoch begrenzt, wenn es um die Queervernetzung geht. Bei einer Olefin Metathese bleibt die Gesamtzahl an Einfach und Doppelbindungen gleich. \subsection{Diels Alder} Die Diels Alder Reaktion ist eine ohne Katalysator natürlich auftretende Reaktion, bei der zwei Doppelbindungen enthaltenden Moleküle verbunden werden. Dabei wird eine Vinylgruppe und zwei mit einer Einfachbindung verbundenen Vinylgruppen zu einem Cyclohexen Ring (Abb. \ref{dielsalder}). Wenn diese Bedingungen in einer Lösung vorhanden sind, kommt es zu dieser Kombination, mit nur geringer Rückreaktion \cite{dielsalder}. - \begin{figure} [h] - \includegraphics[width=\textwidth]{dielsalder.png} - \caption{Die Diels Alder Reaktion \cite{dielsalder}. } - \label{dielsalder} + \begin{figure} [h!] + \begin{center} + \includegraphics[width=0.6\textwidth]{dielsalder.png} + \caption{Die Diels Alder Reaktion \cite{dielsalder}. } + \label{dielsalder} + \end{center} \end{figure} Die Diels Alder Reaktion ist einfach und sorgt dafür, dass Doppelbindungen zu Einfachbindungen werden. In der Kombination mit der Olefin Metathese sollten so viele verschiedene Produkte möglich werden. \subsection{Butadien} @@ -1356,19 +1366,19 @@ Bei der Definition der Transformationsregeln für Multi-Molekül-Reaktionen müssen auf der linken und rechten Seite, sowie im Kontext die gleichen Atome vorliegen. Bei den meisten mehrstufigen, chemischen Synthesen wird ein Zentrales Molekül betrachtet. Es kommt zwar vor, dass für eine Reaktion zwei Moleküle zusammen geführt werden, aber Teile des Moleküls, die in Reaktionen abgespalten werden, werden in der Restlichen Synthese nicht weiter erwähnt. Bei einem Multi Molekül sollen diese abgespaltenen Moleküle potenziell wieder miteinander Reagieren. Es ist also wichtig, dass eine Transformationsregel in hinsicht auf Multi-Molekül-Reaktionen, alle Teile vollständig weiterführt. \subsection{Olefin Metathese und Diels Alder} In dem Graptransformationstool wurde mit dem Molekül Butadien (Abb. \ref{butadienmod}) gestartet. Auf dieses wurden wiederholt die Olefin Metathese (Abb. \ref{olmetmod}) und die Diels Alder Reaktion (Abb. \ref{dialdmod}) angewendet. - \begin{figure} [h] + \begin{figure} [p] \begin{center} \includegraphics[width=0.5\textwidth]{butadienmod.png} \caption{Butadien in dem Graptransformationstool.} \label{butadienmod} \end{center} \end{figure} - \begin{figure} [h] + \begin{figure} [p] \includegraphics[width=\textwidth]{olmetmod.png} \caption{Olefin Metathese in dem Graptransformationstool.} \label{olmetmod} \end{figure} - \begin{figure} [h] + \begin{figure} [p] \includegraphics[width=\textwidth]{dialmod.png} \caption{Diels Alder Reaktion in dem Graptransformationstool.} \label{dialdmod} @@ -1399,7 +1409,7 @@ \item 1,4,4a,8a-Tetrahydronaphthalin: C1CC2C=CC=CC2CC=1 \end{itemize} Wenn die Startmoleküle mit einem generischen Olekinmetathese Katalysator zum reagieren gebracht wird ist zu erwarten, dass alle Moleküle in verschiedenen Enantiomeren und E/Z-Isomeren synthetisiert werden würden. Daher ist es ohne das tatsächliche durchführen dieses Experiments schwierig einen Reaktionspfad herauszusuchen, der von dem ILP bestätigt werden soll. Es wurde sich für die Synthese von Benzol entschieden, da die hohe Symmetrie im Vergleich zu den anderen Spektren zu einem sehr markanten Spektrum führt (Abb. \ref{benzsynthmod}). - \begin{figure} [h] + \begin{figure} [p] \includegraphics[width=\textwidth]{benzsynthmod.png} \caption{Benzolsynthese in dem Graptransformationstool. Erst Olefin Metathese von zwei Butadien zu Hexatrien und Ethylen. Dann Olefin Metathese von Hexatrien und Butdien zu Ethylen und Octatetraen. Zuletzt eine Ringschluss Olefin Metathese von Octatetraen zu Bensol und Ethylen.} \label{benzsynthmod} @@ -1417,8 +1427,8 @@ \item Octatetraen und Ethylen \item Benzol und Ethylen \end{itemize} - Für den Vergleich der NMR Spektren wurden die Bingrößen $b$ (Gleichung \ref{binsize}) verwendet. Der Ähnlichkeitsindex wurde als Mittelwert des Ähnlichkeitsindex für alle Bingrößen genommen. Die finale Wahrscheinlichkeit entspricht dem Ähnlichkeitsindex normalisiert für jedes Referenzspektrum. - \begin{table} + Für den Vergleich der NMR Spektren wurden die Bingrößen $b$ (Gleichung \ref{binsize}) verwendet. Der Ähnlichkeitsindex wurde als Mittelwert des Ähnlichkeitsindex für alle Bingrößen genommen. Die finale Wahrscheinlichkeit entspricht dem Ähnlichkeitsindex normalisiert für jedes Referenzspektrum (Tabelle \ref{nmrsimbenz}). + \begin{table} [h!] \caption{Resultierende Wahrscheinlichkeiten für den Vergleich aller aus Butadien Entwickelten Moleküle mit Hexatrien und Ethylen, Octatetraen und Ethylen und Benzol und Etylen.} \begin{center} \scriptsize @@ -1519,8 +1529,8 @@ \begin{equation} \label{objspectrd} \sum_{e} x_{e} \end{equation} - Für die Lösung des ILP wurden die beiden besten Lösungen bestimmt. - \begin{table} + Durch das ILP wurden die beiden besten Lösungen bestimmt. + \begin{table}[h!] \caption{Lösung 1 für die Knotenauswahl beim ILP vom Butadien Beispiel mit $z = 3$.} \begin{center} \scriptsize @@ -1538,7 +1548,7 @@ \end{tabular} \end{center} \end{table} - \begin{table} + \begin{table}[h!] \caption{Lösung 2 für die Knotenauswahl beim ILP vom Butadien Beispiel mit $z = 4$.} \begin{center} \scriptsize @@ -1556,13 +1566,15 @@ \end{tabular} \end{center} \end{table} - Beide Lösungen die aus der Auswahl der besten Knoten resultieren ergeben chemisch Sinn. Die erste Lösung (Tabelle \ref{ilpspec1}) ist die erwartete Lösung. Die zweite Lösung (Tabelle \ref{ilpspec2}) verwendet viele der gleichen Kanten, aber Produziert mit Kante 18, Octatetraen aus zwei Hexatrien. Diese Variation ist ebenfalls erwartbar. + Beide Lösungen die aus der Auswahl der besten Knoten resultieren ergeben chemisch Sinn. Die erste Lösung (Tabelle \ref{ilpspec1}) ist die erwartete Lösung. Die zweite Lösung (Tabelle \ref{ilpspec2}) verwendet viele der gleichen Kanten, aber produziert mit Kante 18, Octatetraen aus zwei Hexatrien. Diese Variation ist ebenfalls erwartbar. \section{Petrinetz Zertifikat: Multi-Molekül-Reaktionen} Durch den einfachen Optimierungsprozess des ILP wird die Zielfunktion maximiert und eine Menge an Kanten zurückgegeben. Diese Kanten haben keine Reihenfolge oder Zusammenhang abseits der Definition des ILP. Darum kommt es oft vor, dass die Reaktionen in Sequenz ein Molekül für eine Reaktion benötigen, welches erst durch eine andere Reaktion erzeugt wird. Beide Reaktioen ließen sich so nur chemisch Durchführen, wenn die jeweils andere zuvor stattgefunden hat. Um solche Lösungen des ILP Problems auszuschließen wurde für jede Lösung ein Petrinetzzertifikat erstellt. \subsection{Petrinetz Zertifikat: Olefin Metathes und Diels Alder} \subsubsection{Produkt} - Nach der Untersuchung mit einem Petrinetz basierend auf dem Hypergraphen konnte nur eine Lösung zertifiziert werden (Tabelle \ref{ilpprodzert}) - \begin{table} + Die 10 Lösungen, welche durch die Bestimmung der Kantenwahrscheinlichkeit als Produkt beider Produkte erhalten wurden, wurden mit einem Petrinetz, basierend auf dem Hypergraphen, auf Erfüllbarkeit untersucht. + Dabei wurden zu Beginn drei Token in Butadien angenommen. + Nach der Untersuchung mit einem Petrinetz konnte nur eine Lösung zertifiziert werden (Tabelle \ref{ilpprodzert}). Dabei wird wie erwartet Hexatrien erzeugt. Aus Hexatrien erfolgt die Synthese von 3,5-Divinyl-Cyclohex-1-en. Es findet keine weitere Reaktion statt. + \begin{table}[h!] \caption{Lösung 10 für die Kantenwahrscheinlichkeit als Produkt beim ILP vom Butadien Beispiel mit $z = 197.08$.} \begin{center} \scriptsize @@ -1579,9 +1591,12 @@ \end{tabular} \end{center} \end{table} + \newline Diese Lösung entspricht nicht der erwarteten Synthese von Benzol aus Butadien (Abb. \ref{benzsynthmod}). \subsubsection{Durchschnitt} - \begin{table} + Die 10 Lösungen, welche durch die Bestimmung der Kantenwahrscheinlichkeit als Durchschnitt beider Produkte erhalten wurden, wurden mit einem Petrinetz, basierend auf dem Hypergraphen, auf Erfüllbarkeit untersucht. Dabei wurden zu Beginn drei Token in Butadien angenommen. + Nach der Untersuchung mit einem Petrinetz konnte nur eine Lösung zertifiziert werden (Tabelle \ref{ilpavgzert}). + \begin{table}[h!] \caption{Lösung 5 für die Kantenwahrscheinlichkeit als Durchschnitt beim ILP vom Butadien Beispiel mit $z = 798.54$.} \begin{center} \scriptsize @@ -1599,6 +1614,7 @@ \end{tabular} \end{center} \end{table} + \newline Diese Lösung entspricht der erwarteten Synthese von Benzol aus Butadien (Abb. \ref{benzsynthmod}). \subsubsection{Knoten Auswahl} Beide Lösungen der Knotenauswahlmethode erfüllen ein Petrinetzzertifikat. @@ -1608,7 +1624,7 @@ \chapter{Zusammenfassung und Ausblick} In dieser Masterarbeit wurde die Möglichkeit untersucht die Syntheseplanung und -analyse mittels NMR-Spektren zu automatisieren. Dabei wurden die charakteristischen Verschiebungen in $^{13}$C-NMR-Spektren verwendet, um die Wahrscheinlichkeit einzelner Moleküle und Reaktionen zu bestimmen. Diese Wahrscheinlichkeiten wurden über eine ILP-Berechnung optimiert. Noch öfter als $^{13}$C-NMR-Spektren in der organischen Chemie sind die $^{1}$H-NMR-Spektren. Diese haben zu den charakteristischen Verschiebungen noch zusätzliche Informationen durch Multiplettaufspaltungen. Da Wasserstoff im Gegensatz zu Kohlenstoffen als Protonen abgespalten werden können, kommt es vor allem bei Wasserstoff-Stickstoff und Wasserstoff-Sauerstoff Bindungen zu großen Schwankungen in der chemischen Verschiebung. Hinzu kommt, dass da Quantenchemischen Tool in der Berechnung der $^{1}$H-NMR-Spektren deutlich inkonstanter von den experimentellen Spektren abweicht. Zudem kommt es bei der Berechnung der Peakintensitäten und Aufspaltung zu größeren Fehlern, weshalb es für die verwendete Analyse nicht geeignet ist. Die Crosskorrelation bietet eine sehr einfache Methode zum Vergleich von NMR-Spektren. Da jedoch bei den $^{1}$H-NMR-Spektren die Multiplettaufspaltung oft mehr Informationen enthält, als nur Intensität und chemische Verschiebung, geht bei der Analyse eine zentrale Komponente verloren. Beim Vergleich zwischen Spektren der gleichen Substanz, ist die Crosskorrelation auch bei $^{1}$H-NMR-Spektren geeignet, da nur leichte Verschiebungen der Peaks zu erwarten sind. Wenn jedoch zwei verschiedene Substanzen verglichen werden, kann die Verschiebung schon größer sein, weshalb die Ähnlichkeit gering ist, auch wenn die Spektren als Ganzes betrachtet ähnlich sind. Für eine solche Analyse könnte ein Machine Learning Model trainiert werden \cite{nmrsimml}, welches diese Details berücksichtigt. Zum Training dieses Models müssten jedoch deutlich mehr Beispiele verwendet werden und der NMR-Vergleich müsste eine deutlich zentralere Rolle in dieser Arbeit einnehmen. Mehr Beispiele können zudem verwendet werden um den Schweratomeffekt in der NMR-Berechnung zu Quantifizieren, sowie allgemeine Fehler in der Verschiebung zu ermitteln und so den idealen Verschiebungswert zu ermitteln. Die Kombination beider Ein-Molekül-Reaktionen legt jedoch nahe, dass dieser Fehler nicht durch eine Verschiebung mit einer Konstante zu beschreiben ist. Die Lösungen des ILP erfüllen die Erwartungen. In der NMR-Spektroskopie ist es auch möglich zwei Substanzen in einem NMR-Spektrum abzubilden. Dabei kann der Vergleich der Intensität der zugeordneten Peaks bestimmt werden, welches Stoffmengenverhältnis beide Substanzen zueinander haben \cite{nmrquant}. Es ist also möglich anstelle von mehreren NMR-Spektren für eine Synthese, nur ein gemeinsames NMR-Spektrum zu bestimmen und auf Basis dieses Spektrums neben den vorliegenden Substanzen, auch deren relative Stoffmenge zu bestimmen. Sowohl die natürlichen Synthesen im Organismus, als auch die Olefin Metathese und Diels Alder Reaktion für Butadien, eignen sich als Reaktion in einem Topf. Dadurch könnten die Startmoleküle mit den Enzymen und Katalysatoren in eine Lösung gebracht werden und nach einer festen Zeit NMR-Spektren aufgenommen werden. Basierend auf diesen Spektren könnten die relativen Stoffmengen und basierend auf diesen die Gleichgewichtskonstanten für diese Reaktionen bestimmt werden. Zudem erlaubt eine solche Analyse die Bestimmung von Nebenprodukten, welche in dem bisherigen Ansatz nicht definiert wurden. Die bisherige Untersuchung eignet sich trotzdem als eine Demonstration der möglichen Kombination beider bisher getrennter Felder. - \chapter{Danksagung} + \chapter*{Danksagung} Ich möchte die Gelegenheit nutzen, mich herzlichst bei dem Arbeitskreis Chemieinformatik zu bedanken. Besonderer Dank gilt Daniel Merkle, der mcih sowohl tatkräftig bei dem Inhaltlichen unterstützt hat als auch durch seine große Begeisterung eine konstante Quelle der Motivation war. Ebenso danke ich Yuri Kolcak, Addie Jordon und Cassandra König für die beratende Expertise zu theoretischen und inhaltlichen Fragen. Auch Marcel Friedrichs hat mir besonders bei technischen Problemen unterstützt. Zuletzt danke ich Verena Uhlig und Nicole Schellenberg, für die organisatorischen Unterstützung und das sie Daniel erinnert haben, wenn meine Fragen in den vielen Aufgaben etwas untergegangen sind. %%================================================================================== \addcontentsline{toc}{chapter}{Quellenverzeichnis} @@ -1633,7 +1649,7 @@ \vspace{1.2cm} \onehalfspacing - \section{Eigenständigkeitserklärung} + \section*{Eigenständigkeitserklärung} Hiermit versichere ich, dass ich die vorliegende Arbeit selbstständig angefertigt und keine anderen als die angegebenen Hilfsmittel benutzt habe. Alle Stellen, die dem Wortlaut oder dem Sinn nach anderen Werken entnommen sind, habe ich in jedem einzelnen Fall unter genauer diff --git a/Report/refs.bib b/Report/refs.bib index da19859..ef1d85f 100644 --- a/Report/refs.bib +++ b/Report/refs.bib @@ -10,7 +10,7 @@ type = {journal Article} } @article{DFTORCA, - author = {Neese, Frank and Wennmohs, Frank and Becker, Ute and Riplinger, Christoph}, + author = {Neese, F. and Wennmohs, F. and Becker, U. and Riplinger, C.}, title = {The ORCA quantum chemistry program package}, journal = {The Journal of Chemical Physics}, volume = {152}, @@ -27,7 +27,7 @@ @book{bender2006foundations, title={Foundations of Combinatorics with Applications}, - author={Bender, Edward A. and Williamson, S. Gill}, + author={Bender, E. A. and Williamson, S. G.}, year={2006}, publisher={Dover Publications}, address={Mineola, NY}, @@ -39,7 +39,7 @@ @book{Graphtheory, title = {Graphentheorie : eine anwendungsorientierte Einführung}, series = {Mathematik-Studienhilfen}, - author = {Tittmann, Peter}, + author = {Tittmann, P.}, address = {München}, publisher = {Hanser}, year = {2019}, @@ -48,7 +48,7 @@ url = {https://www.hanser-elibrary.com/doi/book/10.3139/9783446465039}, } @article{andersenhyperflow, - author = {Andersen, Jakob L. and Flamm, Christoph and Merkle, Daniel and Stadler, Peter F.}, + author = {Andersen, J. L. and Flamm, C. and Merkle, D. and Stadler, P. F.}, title = {Chemical Transformation Motifs—Modelling Pathways as Integer Hyperflows}, year = {2019}, issue_date = {March-April 2019}, @@ -66,7 +66,7 @@ numpages = {14} } @book{ocwiley, - author = {K. Peter, C. Vollhardt, Neil E. Schore}, + author = {Peter, K. and Vollhardt, C. and Schore, N. E. }, title = {Organische Chemie}, publisher = {Wiley-VCH}, year = {2020}, @@ -74,7 +74,7 @@ } @phdthesis{andersenphd, title = {Analysis of Generative Chemistries}, - author = { Jakob Lykke Andersen }, + author = {Andersen, J. L. }, year = 2015, month = {September}, address = {Leipzig, DE}, @@ -84,12 +84,12 @@ } @book{equilibrium, title={Principles of organic synthesis}, - author={Norman, Richard OC}, + author={Norman, R. OC}, year={2017}, publisher={Routledge} } @article{lewisrep, - author = {Packer, John E. and Woodgate, Sheila D.}, + author = {Packer, J. E. and Woodgate, S. D.}, title = {Lewis structures, formal charge, and oxidation numbers: A more user-friendly approach}, journal = {Journal of Chemical Education}, volume = {68}, @@ -104,7 +104,7 @@ eprint = {https://pubs.acs.org/jceda8/article-pdf/68/6/456/416109/ed068p456.pdf}, } @article{hypergraphpath, - author = {Krieger, Spencer and Kececioglu, John}, + author = {Krieger, S. and Kececioglu, J.}, title ={Shortest Hyperpaths in Directed Hypergraphs for Reaction Pathway Inference}, journal = {Journal of Computational Biology}, @@ -132,7 +132,7 @@ abstract = { Signaling and metabolic pathways, which consist of chains of reactions that produce target molecules from source compounds, are cornerstones of cellular biology. Properly modeling the reaction networks that represent such pathways requires directed hypergraphs, where each molecule or compound maps to a vertex, and each reaction maps to a hyperedge directed from its set of input reactants to its set of output products. Inferring the most likely series of reactions that produces a given set of targets from a given set of sources, where for each reaction its reactants are produced by prior reactions in the series, corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete.We give the first exact algorithm for general shortest hyperpaths that can find provably optimal solutions for large, real-world, reaction networks. In particular, we derive a novel graph-theoretic characterization of hyperpaths, which we leverage in a new integer linear programming formulation of shortest hyperpaths that for the first time handles cycles, and develop a cutting-plane algorithm that can solve this integer linear program to optimality in practice. Through comprehensive experiments over all of the thousands of instances from the standard Reactome and NCI-PID reaction databases, we demonstrate that our cutting-plane algorithm quickly finds an optimal hyperpath—inferring the most likely pathway—with a median running time of under 10 seconds, and a maximum time of less than 30 minutes, even on instances with thousands of reactions. We also explore for the first time how well hyperpaths infer true pathways, and show that shortest hyperpaths accurately recover known pathways, typically with very high precision and recall.Source code implementing our cutting-plane algorithm for shortest hyperpaths is available free for research use in a new tool called Mmunin. } } @ARTICLE{chordlesscycle, - author = {{Silva Dias}, Elis{\^a}ngela and {Castonguay}, Diane and {Longo}, Humberto and {Abdala Rfaei Jradi}, Walid}, + author = {{Silva Dias}, E. and {Castonguay}, D. and {Longo}, H. and {Abdala Rfaei Jradi}, W.}, title = "{Efficient Enumeration of Chordless Cycles}", journal = {arXiv e-prints}, keywords = {Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics}, @@ -148,7 +148,7 @@ adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @inbook{ilp, - author = {Chen, Der-San and Batson, Robert G. and Dang, Yu}, + author = {Chen, D.-S. and Batson, R. G. and Dang, Y.}, publisher = {John Wiley and Sons, Ltd}, isbn = {9781118166000}, title = {Linear Programming—Fundamentals}, @@ -160,7 +160,7 @@ keywords = {traveling salesman problem, Hamiltonian paths, machine sequencing problems, vehicle Routing, genome sequencing}, } @article{petrinets, - author = {Peterson, James L.}, + author = {Peterson, J. L.}, title = {Petri Nets}, year = {1977}, issue_date = {Sept. 1977}, @@ -177,7 +177,7 @@ numpages = {30} } @phdthesis{petri1962kommunikation, - author = {Petri, Carl Adam}, + author = {Petri, C. A.}, title = {Kommunikation mit Automaten}, school = {Technische Universit{"a}t Darmstadt}, year = {1962}, @@ -199,7 +199,7 @@ } @misc{mod, title={A Software Package for Chemically Inspired Graph Transformation}, - author={Jakob L. Andersen and Christoph Flamm and Daniel Merkle and Peter F. Stadler}, + author={J. L. Andersen and C. Flamm and D. Merkle and P. F. Stadler}, year={2016}, eprint={1603.02481}, archivePrefix={arXiv}, @@ -236,7 +236,7 @@ the field of computational networks.}, added-at = {2008-09-24T13:11:32.000+0200}, address = {Pasadena, CA USA}, - author = {Hagberg, Aric A. and Schult, Daniel A. and Swart, Pieter J.}, + author = {Hagberg, A. A. and Schult, D. A. and Swart, P. J.}, biburl = {https://www.bibsonomy.org/bibtex/272096c6553d7057409fe78ca698eb332/mschuber}, booktitle = {Proceedings of the 7th Python in Science Conference}, editor = {Varoquaux, Ga\"el and Vaught, Travis and Millman, Jarrod}, @@ -251,7 +251,7 @@ } @article{rdkit, added-at = {2017-04-11T06:11:47.000+0200}, - author = {Landrum, Greg}, + author = {Landrum, G.}, biburl = {https://www.bibsonomy.org/bibtex/28d01fceeccd6bf2486e47d7c4207b108/salotz}, description = {Release 2016_09_4 (Q3 2016) Release · rdkit/rdkit}, interhash = {ee9a4ddeff3121aa622cf35709fa6e21}, @@ -263,12 +263,12 @@ year = 2016 } @article{avogadro, - author={Hanwell, Marcus D. - and Curtis, Donald E. - and Lonie, David C. - and Vandermeersch, Tim - and Zurek, Eva - and Hutchison, Geoffrey R.}, + author={Hanwell, M. D. + and Curtis, D. E. + and Lonie, D. C. + and Vandermeersch, T. + and Zurek, E. + and Hutchison, G. R.}, title={Avogadro: an advanced semantic chemical editor, visualization, and analysis platform}, journal={Journal of Cheminformatics}, year={2012}, @@ -292,7 +292,7 @@ issn = {0169-7439}, doi = {https://doi.org/10.1016/j.chemolab.2005.10.002}, url = {https://www.sciencedirect.com/science/article/pii/S0169743905001620}, - author = {Lorant Bodis and Alfred Ross and Ernö Pretsch}, + author = {L. Bodis and A. Ross and E. Pretsch}, keywords = {Spectra comparison, NMR spectra, Quality control}, abstract = {A new method is described for calculating the similarity degree of two spectra. Its performance is optimized with similar, computer-generated 1H NMR spectra. The method is compared with a recently proposed local cross-correlation method. Using a test set, its power to discriminate between related and unrelated 1H NMR spectra is better than with the cross-correlation method. Better results are also obtained when comparing measured spectra of a database with the corresponding estimated ones or with estimated spectra of randomly assigned structures. Although, so far, it has only been tested with 1H NMR spectra, due to the generality of the approach, the novel procedure can be applied to comparing other spectra or patterns as well.} } @@ -303,7 +303,7 @@ url = {https://www.gurobi.com} } @Article{caffeinesynth, - AUTHOR = {Lin, Zhipeng and Wei, Jian and Hu, Yongqiang and Pi, Dujuan and Jiang, Mingguo and Lang, Tao}, + AUTHOR = {Lin, Z. and Wei, J. and Hu, Y. and Pi, D. and Jiang, M. and Lang, T.}, TITLE = {Caffeine Synthesis and Its Mechanism and Application by Microbial Degradation, A Review}, JOURNAL = {Foods}, VOLUME = {12}, @@ -317,7 +317,7 @@ DOI = {10.3390/foods12142721} } @Article{vanillinesynth, - AUTHOR = {Tazon, Arnold William and Awwad, Fatima and Meddeb-Mouelhi, Fatma and Desgagné-Penix, Isabel}, + AUTHOR = {Tazon, A. W. and Awwad, F. and Meddeb-Mouelhi, F. and Desgagné-Penix, I.}, TITLE = {Biotechnological Advances in Vanillin Production: From Natural Vanilla to Metabolic Engineering Platforms}, JOURNAL = {BioChem}, VOLUME = {4}, @@ -330,7 +330,7 @@ DOI = {10.3390/biochem4040017} } @article{xanthinnmr, - author = {Benoit, Robert L. and Fréchette, Monique}, + author = {Benoit, R. L. and Fréchette, M.}, title = {Protonation of hypoxanthine, guanine, xanthine, and caffeine}, journal = {Canadian Journal of Chemistry}, volume = {63}, @@ -348,7 +348,7 @@ abstract = { The protonation equilibria of three hydroxypurines, hypoxanthine, guanine, and xanthine, and of related caffeine have been studied by 1H and 13C nmr and uv spectroscopies in aqueous sulfuric or perchloric acids. The results have been interpreted on the basis of the excess acidity method. The values and the protonation sites are discussed and comparisons are made with results of recent theoretical calculations. } } @article{manyxanthinesnmr, - author = {Mueller, Christa E. and Shi, Dan and Manning, Malcolm, Jr. and Daly, John W.}, + author = {Mueller, C. E. and Shi, D. and Manning, M., Jr. and Daly, J. W.}, title = {Synthesis of paraxanthine analogs (1,7-disubstituted xanthines) and other xanthines unsubstituted at the 3-position: structure-activity relationships at adenosine receptors}, journal = {Journal of Medicinal Chemistry}, volume = {36}, @@ -362,7 +362,7 @@ eprint = {https://pubs.acs.org/jmcmar/article-pdf/36/22/3341/7236147/jm00074a015.pdf}, } @article{7xanthinnmr, - author = {Jayantha, Bhagya and Zhang, Shuyuan and Summers, Ryan M. and Mendis, Gamini P. and Jayakody, Lahiru N.}, + author = {Jayantha, B. and Zhang, S. and Summers, R. M. and Mendis, G. P. and Jayakody, L. N.}, title = {Engineered Pseudomonas putida monoculture system for green synthesis of 7-methylxanthine}, journal = {Green Chemistry}, volume = {27}, @@ -377,7 +377,7 @@ eprint = {https://pubs.rsc.org/gc/article-pdf/27/37/11365/10400487/d5gc02883c.pdf}, } @article{theobrominnoMenmr, - author = {Bouzková, Kateřina and Babinský, Martin and Novosadová, Lucie and Marek, Radek}, + author = {Bouzková, K. and Babinský, M. and Novosadová, L. and Marek, R.}, title = {Intermolecular Interactions in Crystalline Theobromine as Reflected in Electron Deformation Density and 13C NMR Chemical Shift Tensors}, @@ -426,7 +426,7 @@ eprint = {https://pubs.acs.org/jctcce/article-pdf/9/6/2629/8808212/ct400209b.pdf}, } @article{theobrominnmr, - author = {Thevis, Mario and Opfermann, Georg and Krug, Oliver and Schänzer, Wilhelm}, + author = {Thevis, M. and Opfermann, G. and Krug, O. and Schänzer, W.}, title = {Electrospray ionization mass spectrometric characterization and quantitation of xanthine derivatives using isotopically labelled analogues: an application for equine doping control analysis}, journal = {Rapid Communications in Mass Spectrometry}, volume = {18}, @@ -448,12 +448,12 @@ issn = {1386-1425}, doi = {https://doi.org/10.1016/S1386-1425(00)00401-7}, url = {https://www.sciencedirect.com/science/article/pii/S1386142500004017}, - author = {Kazuhiko Hanai and Akio Kuwae and Takatomo Takai and Hitoshi Senda and Ko-Ki Kunimoto}, + author = {K. Hanai and A. Kuwae and T. Takai and H. Senda and K.-K. Kunimoto}, keywords = {-Cinnamic acid, -Cinnamic acid, Polymorphism, IR/Raman spectra, NMR spectra}, abstract = {The IR and Raman spectra of the two polymorphic forms (58°- and 68°-forms) of cis-cinnamic acid were measured, and the spectral differences discussed on the basis of the crystal structures of the two forms. The IR bands related to the COOH group differ in the frequencies and band shape, reflecting differences in the hydrogen bonding between the two modifications. These spectra were compared with those of trans-cinnamic acid. The IR, Raman, and NMR spectra of the isotopic compounds, including the deuterated and 13C analogs of the cis and trans acids, were also recorded in the solid state and in solution to confirm the spectral assignments.} } @article{mcoumnmr, - author = {Nakazawa, Takahiro and Ohsawa, Keisuke}, + author = {Nakazawa, T. and Ohsawa, K.}, title = {Metabolism of Rosmarinic Acid in Rats}, journal = {Journal of Natural Products}, volume = {61}, @@ -475,7 +475,7 @@ eprint = {https://pubs.acs.org/jnprdf/article-pdf/61/8/993/13045095/np980072s.pdf}, } @article{pcoumnmr, - author = {Świsłocka, Renata and Kowczyk-Sadowy, Małgorzata and Kalinowska, Monika and Lewandowski, Włodzimierz}, + author = {Świsłocka, R. and Kowczyk-Sadowy, M. and Kalinowska, M. and Lewandowski, W.}, title = {Spectroscopic (FT-IR, FT-Raman, 1H and 13C NMR) and theoretical studies of p-coumaric acid and alkali metal p-coumarates}, journal = {Journal of Spectroscopy}, volume = {27}, @@ -489,7 +489,7 @@ year = {2012} } @article{aldhnmr, - author = {Kuan, Fu-Hua and Inoue, Yoshio and Chûjô, Riichiro}, + author = {Kuan, F.-H. and Inoue, Y. and Chûjô, R.}, title = {Structure and molecular dynamics of solid-state inclusion complexes of cyclodextrin and permethylated cyclodextrin with benzaldehyde studied by high-resolution CP/MAS13C NMR}, journal = {Journal of inclusion phenomena}, volume = {4}, @@ -501,7 +501,7 @@ year = {1986} } @Article{caffacdnmr, - AUTHOR = {Yu, Jiahui and Xie, Jingchen and Sun, Miao and Xiong, Suhui and Xu, Chunfang and Zhang, Zhimin and Li, Minjie and Li, Chun and Lin, Limei}, + AUTHOR = {Yu, J. and Xie, J. and Sun, M. and Xiong, S. and Xu, Ch. and Zhang, Z. and Li, M. and Li, C. and Lin, L.}, TITLE = {Plant-Derived Caffeic Acid and Its Derivatives: An Overview of Their NMR Data and Biosynthetic Pathways}, JOURNAL = {Molecules}, VOLUME = {29}, @@ -529,7 +529,7 @@ year = {2006} } @article{phydaldhnmr, - author = {Jha, Anjali and Kumar, B.Rajesh and Kumar Ch, RaviShankar}, + author = {Jha, A. and Kumar, B.R. and Kumar Ch, R.}, title = {Synthesized Novel Schiff Base of 4-Hydroxybenzaldehyde with Anilines for Optoelectronic Applications}, journal = {SSRN Preprint Server}, @@ -540,7 +540,7 @@ year = {2024} } @article{mphydaldhnmr, - author = {Nova Syafni and Deddi Putra and Dayar Arbain}, + author = {N. Syafni and D. Putra and D. Arbain}, title = {3,4-DIHYDROXYBENZOIC ACID AND 3,4-DIHYDROXYBENZALDEHYDE FROM THE FERN Trichomanes chinense L.; ISOLATION, ANTIMICROBIAL AND ANTIOXIDANT PROPERTIES}, journal = {Indonesian Journal of Chemistry}, volume = {12}, @@ -552,7 +552,7 @@ url = {https://journal.ugm.ac.id/ijc/article/view/21342} } @article{heavyateff1, - author = {Lodewyk, Michael W. and Siebert, Matthew R. and Tantillo, Dean J.}, + author = {Lodewyk, M. W. and Siebert, M. R. and Tantillo, D. J.}, title = {Computational Prediction of 1H and 13C Chemical Shifts: A Useful Tool for Natural Product, Mechanistic, and Synthetic Organic Chemistry}, journal = {Chemical Reviews}, volume = {112}, @@ -566,7 +566,7 @@ eprint = {https://pubs.acs.org/chreay/article-pdf/112/3/1839/8644981/cr200106v.pdf}, } @article{heavyatef2, - author = {Jonas, Eric and Kuhn, Stefan and Schlörer, Nils}, + author = {Jonas, E. and Kuhn, S. and Schlörer, N.}, title = {Prediction of chemical shift in NMR: A review}, journal = {Magnetic Resonance in Chemistry}, volume = {60}, @@ -580,7 +580,7 @@ year = {2022} } @article{nmrbinsize, - author = {Schripsema, Jan}, + author = {Schripsema, J.}, title = {Similarity and differential NMR spectroscopy in metabolomics: application to the analysis of vegetable oils with 1H and 13C NMR}, journal = {Metabolomics}, volume = {15}, @@ -591,7 +591,7 @@ year = {2019} } @article{olefinmetathese, - author = {Connon, Stephen J. and Blechert, Siegfried}, + author = {Connon, S. J. and Blechert, S.}, title = {Recent Developments in Olefin Cross-Metathesis}, journal = {Angewandte Chemie International Edition}, volume = {42}, @@ -605,7 +605,7 @@ year = {2003} } @article{dielsalder, - author = {Sauer, Jürgen and Wiest, Hubert and Mielert, Albrecht}, + author = {Sauer, J. and Wiest, H. and Mielert, A.}, title = {Eine Studie der DIELS-ALDER-Reaktion, I. Die Reaktivität von Dienophilen gegenüber Cyclopentadien und 9.10-Dimethyl-anthracen}, journal = {Chemische Berichte}, volume = {97}, @@ -618,7 +618,7 @@ year = {1964} } @article{ringstrain, - author = {Wiberg, Kenneth B.}, + author = {Wiberg, K. B.}, title = {The Concept of Strain in Organic Chemistry}, journal = {Angewandte Chemie International Edition in English}, volume = {25}, @@ -640,12 +640,12 @@ issn = {0098-1354}, doi = {https://doi.org/10.1016/j.compchemeng.2016.04.019}, url = {https://www.sciencedirect.com/science/article/pii/S0098135416301156}, - author = {Willis, Mark J. and von Stosch, Moritz }, + author = {Willis, M. J. and von Stosch, M. }, keywords = {Chemical reaction network, Structural optimization, Kinetic fitting, Mixed-integer-linear programming}, abstract = {The manual determination of chemical reaction networks (CRN) and reaction rate equations is cumbersome and becomes workload prohibitive for large systems. In this paper, a framework is developed that allows an almost entirely automated recovery of sets of reactions comprising a CRN using experimental data. A global CRN structure is used describing all feasible chemical reactions between chemical species, i.e. a superstructure. Network search within this superstructure using mixed integer linear programming (MILP) is designed to promote sparse connectivity and can integrate known structural properties using linear constraints. The identification procedure is successfully demonstrated using simulated noisy data for linear CRNs comprising two to seven species (modelling networks that can comprise up to forty two reactions) and for batch operation of the nonlinear Van de Vusse reaction. A further case study using real experimental data from a biodiesel reaction is also provided.} } @article{nmrsimml, - author = {Rowlands, J. Benji and Jonsson, Lina and Goodman, Jonathan M. and Howe, Peter W. A. and Czechtizky, Werngard and Leek, Tomas and Lewis, Richard J.}, + author = {Rowlands, J. B. and Jonsson, L. and Goodman, J. M. and Howe, P. W. A. and Czechtizky, W. and Leek, T. and Lewis, R. J.}, title = {Towards automatically verifying chemical structures: the powerful combination of 1H NMR and IR spectroscopy}, journal = {Chemical Science}, volume = {16}, @@ -668,7 +668,7 @@ issn = {0165-9936}, doi = {https://doi.org/10.1016/j.trac.2012.02.007}, url = {https://www.sciencedirect.com/science/article/pii/S0165993612000702}, - author = {Santosh Kumar Bharti and Raja Roy}, + author = {S. K. Bharti and R. Roy}, keywords = {Calibration-curve method, Electronic referencing, Metabolomics, NMR spectroscopy, Nuclear magnetic resonance (NMR), Pharmaceutical analysis, Quantitative NMR (qNMR), Referencing technique, Standard-addition method, Validation}, abstract = {This review illustrates the need to use nuclear magnetic resonance (NMR) spectroscopy for the quantitative analysis of small molecules in their crude forms and in mixtures. We provide the basic concepts of quantitative NMR (qNMR), a brief description of important acquisition and processing parameters responsible for obtaining high-quality, reproducible NMR spectra in order to maximize accuracy, and the latest referencing techniques used for quantitative analysis. We also describe methods that are used for quantitative analysis including calibration-curve and standard-addition methods. Further, we briefly address validation of qNMR spectroscopy and its major applications in various scientific disciplines.} }

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