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Dft Study of Titanium Cubane and Molybdenum Sulphide Compounds UNIVERSITAT 2004 ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS José Gracia Budría Departament de Química Física i Inorgànica DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS José Gracia Budría Memoria presentada para optar al título de Doctor en Química UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 El Dr. Josep Maria Poblet Rius, catedrático de Química Física del departamento de Química Física i Inorgànica de la Universitat Rovira i Virgili; y el Dr. José Pedro Sarasa Solano, profesor titular de Química Física del Departamento de Química Física y Orgánica de la Universidad de Zaragoza CERTIFICAN: Que la presente Memoria titulada: “DFT Study of Titanium Cubane and Molybdenum Sulphide Compounds” ha sido realizada en el departamento de Química Física i Inorgànica de la Universitat Rovira i Virgili, por el licenciado en Ciencias Químicas D. José Gracia Budría, bajo nuestra dirección y autorizamos su presentación para obtener el grado de doctor. Tarragona, 25 de marzo de 2004 Dr. Josep Maria Poblet Rius Dr. José Pedro Sarasa Solano III UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS José Gracia Budría Tesis Doctoral. Tarragona, 2004 UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 Quiero expresar mi agradecimiento: A todos los miembros del departamento de Química Física i Inorgánica por mantener siempre sus puertas abiertas. A Jose Ortiz y a Joan Iglesias por su dedicación, trabajo y consejos desde el servicio informático. A Esther Bordas, Jesús Cabrero, Josep Maria Campanera, Daniel Curulla, Elias Daura, Isabel Gómez, Nuria Queralt, Susana Romo, Engelbert Sans y Ana Valcárcel como compañeros y amigos. A Alfredo Gil y Xavier López que empezaron remando conmigo en este viaje y espero que los lleve a buen puerto. A Francisco Ample, más que darle las gracias, forma parte de uno de los apartados que más interés me ha despertado, como colaborador y autor de las pequeñas partes de programación de esta tesis, y por compartir sus ideas y pensamientos durante todo este tiempo. Al grupo de Química Inorgánica de la Universidad de Alcalá dirigido por el Dr. Mena y también en especial al Dr. Avelino Martín, como colaboradores en los análisis teóricos realizados y autores de todo el trabajo experimental en lo relacionado con los compuestos cubánicos de titanio. Al catedrático Josep Maria Poblet codirector de esta tesis y una de las personas más razonables que he conocido. Al Dr. Pedro Sarasa codirector de esta tesis, un ejemplo a seguir, al que ha sido desde antes de acabar la licenciatura mi profesor y amigo. Por último a mi familia y amigos que siempre han formado y formarán la mitad de mi vida que se mantiene en contacto con el mundo real. En especial a Raquel porque toda historia tiene dos partes, una que se ve y otra que se siente, y no hay nada más importante que poder sentir. VII UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 PRÓLOGO El extraordinario desarrollo experimentado por la química computacional en las últimas décadas ha motivado un progresivo incremento en el número de estudios basados en un análisis teórico de los sistemas. El optimismo presente no es en vano, sino fruto una creciente experiencia y de la validación de los métodos empleados. A pesar del claro progreso y de las óptimas perspectivas futuras, no se debe olvidar la complejidad de los sistemas reales. En mi opinión, hay que tratar de evitar la sensación de que un estudio computacional ahorra tiempo y dinero a la ciencia. La posibilidad de un estudio simultaneo y conjunto entre el trabajo experimental en el laboratorio y el análisis teórico es un triunfo presente para química computacional. No obstante, la especial complicación de muchos sistemas reales los hace todavía inabordables computacionalmente en su totalidad. Nos vemos obligados a trabajar con sistemas modelo que nos apartan en cierta medida de la realidad. Estos sistemas modelo pueden reproducir fielmente los sistemas reales, pero se pasa a estar a expensas de poder reproducir los valores experimentales para estar completamente seguro de que el sistema esta correctamente enmarcado. Nuestro planteamiento para esta memoria implicó desde un principio un trabajo de colaboración conjunta con un grupo experimental, corroborando las suposiciones experimentales y siempre como apoyo a las posibles dudas o sombras que no se pudiesen aclarar fácilmente sin el necesario análisis teórico. En la estructuración de esta tesis se ha intentado presentar lo que ha sido nuestra forma de trabajar durante estos cuatro años, o lo que debería haber sido. La mayoría de los distintos apartados empiezan por un resumen de los datos experimentales de que disponíamos antes de empezar los cálculos; apoyándonos en estos datos, se modelizaban aquellos sistemas que más interés, o dudas, despertaban tanto a nivel experimental como teórico, para así completar su estudio. Evidentemente la química teórica tiene la ventaja de poder proponer sistemas todavía no sintetizados, y ese podía ser uno de nuestros grandes objetivos, ir más allá de las personas que trabajan en el laboratorio. No obstante, ese no ha sido el objetivo de este trabajo. Prácticamente todos los resultados presentados aquí se basan en sistemas sintetizados, o no IX UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 observados, pero de los cuales su síntesis ha sido probada de forma infructuosa, e igualmente se puede estudiar el motivo. Evidentemente, esto supone que sabemos que nos estamos dejando muchos posibles compuestos por tratar. El resultado del trabajo se presenta realmente fructífero. Por un lado se es capaz de reproducir los sistemas, obteniendo los datos experimentales y partir de ahí aportar otros nuevos. El aporte de información extra es evidentemente bidireccional y nos ayuda a conocer lo que podemos o no tratar. Como ejemplo diré nuestra grata sorpresa en la reproducción de espectros RMN, lo cual nos ha llevado a intentar abrir nuevas vías de trabajo en este campo debido a los buenos resultados obtenidos. El trabajo multidisciplinar ayuda tanto a ver tus posibilidades como las del resto de grupos implicados, de tal forma que a mí me resulta difícil pensar en otra forma de trabajar más efectiva. Esto significa a su vez, que todavía nos que da mucho trabajo por hacer, los avances no han sido pocos y en muchos casos nos permiten discutir sobre la veracidad de los datos experimentales. No obstante, todavía queda lejos la irrefutabilidad de los datos teóricos. Tratar de que un estudio teórico sea un paso preliminar obligatorio al trabajo en el laboratorio constituye para mí el objetivo ideal y la evolución más lógica de nuestro trabajo. Tarragona, Marzo 2004 J. Gracia X UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 TABLE OF CONTENTS 1 Introduction and scope . 1 1.1 Introduction . 2 1.1.1 Computational details . 4 1.2 Cubic aggregates . 4 1.2.1 Bonding considerations . 6 1.2.2 Metal element . 9 1.2.3 Incomplete cubane structures . 12 1.3 Molybdenum catalysts . 16 1.4 Scope of the work . 21 Density functional methods. 2 . 31 The calculation of NMR shielding tensors 2.1 Introduction . 32 2.2 Electron correlation and DFT . 35 2.2.1 Comparing methods . 38 2.2.1.1 Models based on Hartree method . 38 2.2.1.2 DFT based methods . 41 2.2.2 Comparative table . 48 2.3 The NMR spin Hamiltonian . 49 2.3.1 Shielding tensor . 49 Spin-Hamiltonian parameters as energy 2.3.2 . 51 derivates 2.3.3 The molecular electronic Hamiltonian . 53 2.3.4 Interaction terms . 54 2.3.5 Physical contributions . 57 XI UNIVERSITAT ROVIRA I VIRGILI DFT STUDY OF TITANIUM CUBANE AND MOLYBDENUM SULPHIDE COMPOUNDS. Autor: José Manuel Gracia Budria ISBN: 978-84-690-6751-2 / DL: T.1196-2007 2.3.6 Relativistic effects . 59 Variational perturbation theory for the calculation of 2.4 . 62 NMR parameters Density functional calculations of NMR chemical 2.5 . 66 shifts 2.5.1 ZORA relativistic approximation . 66 2.5.2 Calculation of NMR parameters . 69 2.5.3 DFT shielding tensor . 71 2.5.3.1 The Gauge-Origin problem . 79 2.5.3.2 Frozen core approximation . 80 Review of the factors to take into account in the 2.6 calculation of shielding tensors from approximate . 82 wave functions 2.6.1 XC functionals .
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