Molecular modeling of asymmetric induction in heterogeneously catalyzed hydrogenation of the C=O bond

Modifiering av metallytor med starkt adsorberade kirala organiska molekyler är eventuellt den mest relevanta teknik man vet i dag för att skapa kirala ytor. Den kan utnyttjas i katalytisk produktion av enantiomeriskt rena kirala föreningar som behövs t.ex. som läkemedel och aromkemikalier. Trots många fördelar av asymmetrisk heterogen katalys jämfört med andra sätt för att få kirala föreningar, har den ändå inte blivit ett allmänt verktyg för storskaliga tillämpningar. Detta beror t.ex. på brist på djupare kunskaper i katalytiska reaktionsmekanismer och ursprunget för asymmetrisk induktion. I denna studie användes molekylmodelleringstekniker för att studera asymmetriska, heterogena katalytiska system, speciellt hydrering av prokirala karbonylföreningar till motsvarande kirala alkoholer på cinchona-alkaloidmodifierade Pt-katalysatorer. 1-Fenyl-1,2-propandion (PPD) och några andra föreningar, som innehåller en prokiral C=O-grupp, användes som reaktanter. Konformationer av reaktanter och cinchona-alkaloider (som kallas modifierare) samt vätebundna 1:1-komplex mellan dem studerades i gas- och lösningsfas med metoder som baserar sig på vågfunktionsteori och täthetsfunktionalteori (DFT). För beräkningen av protonaffiniteter användes också högst noggranna kombinationsmetoder såsom G2(MP2). Den relativa populationen av modifierarnas konformationer varierade som funktion av modifieraren, dess protonering och lösningsmedlet. Flera reaktant–modifierareinteraktionsgeometrier beaktades. Slutsatserna på riktning av stereoselektivitet baserade sig på den relativa termodynamiska stabiliteten av de diastereomeriska reaktant–modifierare-komplexen samt energierna hos π- och π*-orbitalerna i den reaktiva karbonylgruppen. Adsorption och reaktioner på Pt(111)-ytan betraktades med DFT. Regioselektivitet i hydreringen av PPD och 2,3-hexandion kunde förklaras med molekyl–yta-interaktioner. Storleken och formen av klustret använt för att beskriva Pt-ytan inverkade inte bara på adsorptionsenergierna utan också på de relativa stabiliteterna av olika adsorptionsstrukturer av en molekyl. Populationerna av modifierarnas konformationer i gas- och lösningsfas korrelerade inte med populationerna på Pt-ytan eller med enantioselektiviteten i hydreringen av PPD på Pt–cinchona-katalysatorer. Vissa modifierares konformationer och reaktant–modifierare-interaktionsgeometrier var stabila bara på metallytan. Teoretiskt beräknade potentialenergiprofiler för hydrering av kirala α-hydroxiketoner på Pt implicerade preferens för parvis additionsmekanism för väte och selektiviteter i harmoni med experimenten. De uppnådda resultaten ökar uppfattningen om kirala heterogena katalytiska system och kunde därför utnyttjas i utvecklingen av nya, mera aktiva och selektiva kirala katalysatorer.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Isentropic Exergy and Pressure of the Shock Wave Caused by the Explosion of a Pressure Vessel

An accidental burst of a pressure vessel is an uncontrollable and explosion-like batch process. In this study it is called an explosion. The destructive effectof a pressure vessel explosion is relative to the amount of energy released in it. However, in the field of pressure vessel safety, a mutual understanding concerning the definition of explosion energy has not yet been achieved. In this study the definition of isentropic exergy is presented. Isentropic exergy is the greatest possible destructive energy which can be obtained from a pressure vessel explosion when its state changes in an isentropic way from the initial to the final state. Finally, after the change process, the gas has similar pressure and flow velocity as the environment. Isentropic exergy differs from common exergy inthat the process is assumed to be isentropic and the final gas temperature usually differs from the ambient temperature. The explosion process is so fast that there is no time for the significant heat exchange needed for the common exergy.Therefore an explosion is better characterized by isentropic exergy. Isentropicexergy is a characteristic of a pressure vessel and it is simple to calculate. Isentropic exergy can be defined also for any thermodynamic system, such as the shock wave system developing around an exploding pressure vessel. At the beginning of the explosion process the shock wave system has the same isentropic exergyas the pressure vessel. When the system expands to the environment, its isentropic exergy decreases because of the increase of entropy in the shock wave. The shock wave system contains the pressure vessel gas and a growing amount of ambient gas. The destructive effect of the shock wave on the ambient structures decreases when its distance from the starting point increases. This arises firstly from the fact that the shock wave system is distributed to a larger space. Secondly, the increase of entropy in the shock waves reduces the amount of isentropic exergy. Equations concerning the change of isentropic exergy in shock waves are derived. By means of isentropic exergy and the known flow theories, equations illustrating the pressure of the shock wave as a function of distance are derived. Amethod is proposed as an application of the equations. The method is applicablefor all shapes of pressure vessels in general use, such as spheres, cylinders and tubes. The results of this method are compared to measurements made by various researchers and to accident reports on pressure vessel explosions. The test measurements are found to be analogous with the proposed method and the findings in the accident reports are not controversial to it.