Current Research Projects.

Research in the Ziegler group over the past 25 years has been  concerned with the introduction of  new tools based on computer modelling into the art of designing  catalysts. It is further aimed at  enhancing our understanding of the elementary reaction steps  involved in the catalytic cycles. Catalytic research is an experimental science, and this is not likely to change. However, the rapid developments  in computer technology  combined with significant advances in modelling methodologies have opened up  new avenues in catalytic research. It is the objective of the our research  to explore these possibilities.
The underlying physical theory governing chemistry (and homogenous catalysis) has been known since the formulation of quantum mechanics around 1925. However,  only the emergence over the last decade of high-speed digital computers  has made it possible to apply these laws accurately to complex chemical systems with high accuracy. The field dealing with this subject has become known as computational quantum chemistry. Quantum chemical calculations can analyse all the factors responsible for the shape, colour and smell of molecules  and describe in  details  the way in which they react with each other irrespective of whether the actual reaction takes place in a few femto seconds (10-15 second) or  over thousands of years. We aim at  determining the structure and relative stability of chemical species involved in elementary catalytic processes by quantum chemical calculations. The insight obtained from these calculations should further allow us to propose new catalysts and test their efficiency by computer simulation.
All quantum mechanical calculations and implementations will be based on density fun ctional theory  (DFT). The DFT method is well suited for molecules containing metal atoms, an important component in most catalysts. We have over the past two decades contributed to the development of an extensive program system based on DFT.  The program has been tested on numerous  metal containing molecules,  and extended to include relativistic effects  of importance for atoms at the end of the periodic table. We are currently involved with  the development of  new DFT based methodologies aimed at making the study of chemical processes and particularly catalytic  reaction steps more tractable.
It is our longterm goal to  supply fundamental knowledge about molecular energetics and kinetics, particularly in the field of homogenous catalysis . We hope further to develop a modelling  tool that with the  advent of cheap and powerful workstations will benefit virtually any experimental lab. It is likely that DFT over the next decade will become as indispensable a research tool in  (inorganic ) chemistry as  some of the major  spectroscopic methods employed routinely in  experimental research.

Current interest in theory and applications involves:
 
 

Theory  and implementations

Development and implementation of new density functional methods. Developments, implementations, testing and applications of new energy densities and effective one-electron (Kohn-Sham) potentials. The goal here is to develop new DFT methods that provide more accurate estimates of molecular properties (structures, energies, chemical shifts etc.)

 

Molecular Structures, Force Fields, Activation Energies and Reaction Profiles.  A chemical system is characterized by its potential energy surface. This surface relates positions of the N nuclei to the total energy of all electrons and nuclei at 0° K. It can be calculated by solving the many-electron problem by DFT for each nuclear conformation on the 3N-dimentional surface. Stable chemical species in the system (reactants and products) are characterized as a local energy minimum with positive curvatures (second derivatives with respect to nuclear displacements) whereas a transition state is represented by a local maximum with one negative curvature. A complete reaction path is finally characterized as the steepest descent path connecting the transition state to reactant and product. The ADF program employs energy gradients (energy derivatives with respect to nuclear displacements) in the optimization of structures. We have recently extended this method to include relativistic effects. Work has also been finished on the calculation of force fields (curvatures) by analytical second derivatives [P81,P74] . The energy gradients are also efficient for the optimization of transition state structures [P-120] and the calculated activation barriers are in good agreement with experiment. We have completed work on a minimum energy reaction path (MEP) following method [P107]. The MEP method allow us to follow the reaction from the transition state to product(s) and reactant(s) in a steepest descent path based on mass-weighted coordinates.

Proposed further research. Current approximate  DFT methods are still not capable of describing all parts of the potential energy surface accurately. We plan to improve on this by introducing functionals in which the self-interaction between electrons is fully eliminated, that should help the accuracy in the transition state region. We intend further to introduce functionals that more accurately describe near degeneracy correlation to improve the accuracy in the bond dissociation limit . It is finally required to improve the way in which we navigate on the PES and locate stationary points, especially for transition  states.
 

Direct dynamics. The nuclei above 0° K have kinetic energy in addition to the potential energy and are thus able to move away from the local minima of reactants and products as well as away from  MEP in chemical reactions. This deviation gives rise to the free energy of the system, the property that ultimately determines reaction rates and the relative abundance of reactions and products. An estimate of the free energy can be obtained by dynamics studies.

Proposed further research.  Knowledge of the MEP in conjunction with the ability to evaluate first and second derivatives analytically gives us sufficient information about the potential energy surface,V, in the vicinity of the reaction coordinate to study dynamics. Thus in this region, we will be able  to formulate a reaction Hamiltonian H=T+V, where T is the kinetic energy operator of the nuclei. The Hamiltonian, H, makes it possible to study reaction dynamics. In such a study we should be able to analyze the coupling of the reaction coordinate with the transverse vibrational modes, and the coupling of the transverse vibrational modes  with each other, as well as transfer of energy between the modes. It would further be possible to formulate a free energy potential surface and discuss  how  far a reaction proceed from the MEP at temperatures above 0° K.  We plan to compare results from our direct dynamic study to those obtained by molecular dynamics calculations based on the Car-Parrinello method discussed next.
 
 

First principle molecular dynamics by the Car-Parrinello method. Expansion of the potential surface around the MEP is conceptually interesting but computationally demanding. Car and Parrinello  (CP) have recently developed a first principle molecular dynamics method in which the expansion is avoided by calculating the required information needed for the molecular dynamics simulation ‘on the run’ as the atoms move. We have been working with the CP based Projector Augmented Wave (PAW) method due to P.E .Blöchl  from IBM Switzerland for the past 5 years, This has lead to  several studies of catalytic processes in a ‘slow growth’ approach [P39,P70,P89]. In the ‘slow growth’ method, a MEP is first determined from a regular 'static' DFT calculation using the ADF program. Next ,the system is 'dragged slowly' along the MEP while CP dynamics is performed along the vibrational modes transverse to the MEP. The 'slow growth' procedure makes it possible to determine the free energy by 'thermodynamic integration' of the mean force on the MEP along the path [P89].  Simulations of our molecular dynamics simulations can be found as Quicktime Movies.

Proposed further research. We plan to explore the ‘slow growth’ CP dynamics procedure as an alternative to the direct dynamics method described above and develop an algorithm that can perform CP dynamics along the MEP without predetermination of MEP by ADF. We will also make use of the CP method in studies of reaction pathways on complex potential surfaces in conjunction with  "bias potential methods"  that allows  for fast exploration  of the PES around a prospective transition state. Other developments will be mentioned below in the next sections.
 
 

Molecular Mechanics Force fields and Combined DFT and MM calculations. Reactivity in metal complexes is determined by the part of the PES that describes ligand-metal bond formation and bond breaking. An example would be the Zr-C linkage emerging in the metallocene complex 1. However, this part of the PES can be influenced by more distant bulky groups (such as R1 and R2 of 1) through steric interactions. These interactions might be costly to describe by DFT or other quantum mechanical (QM) methods if the groups R1 and R2 are large. An expedient solution has been to describe the steric groups by molecular mechanics (MM) and treat 1 by a combined QM/MM method where the total PES is given by ETotal  =  EQM + EQM/MM  + EMM. We can illustrate this merger of MM and DFT  with reference to 1. The term EQM  is the total PES for 1 with the bulky groups P, R1 and R2 replaced by hydrogens. The term EMM is the molecular mechanics energy of R1, R2 and P expressed in terms of a harmonic force fields with force constant derived from experimental or theoretical vibrational frequencies. Finally, EQM/MM represents the nonbonded Coulombic and van der Waals interactions between  atoms on R1, R2 and P  on the one hand and the rest of 1 on the other.

Proposed further research. Combining QM and MM is straight forward and has already been accomplished by other groups  as well. The difficult task involves validation of the method and modifications of the MM force field. We have shown in a previous paper [P-57] that the present MM force fields must be modified  for coordination compounds in order to represent the steric interaction between ligands correctly.
 

Solvation  Simulation.The PES around the metal center is also influenced by solvation  effects. We plan to introduce solvation at two different levels of theory. At the lowest and most practical level use will be made of a continuum model. The essential strategy in all continuum solvation models is to place the solute in a cavity of a dielectric medium. The cavity might be spherical or more realistically follow the shape of the van der Waals surface of the solute. We have already implemented such a continuum scheme in the form of the conductor-like screening model (COSMO) by Klamt   into ADF [P-25].

Proposed further research. On a more sophisticated level, we want to study solvation effects making use of the 'slow growth' procedure and the PAW program. Now, the reaction system will be 'dragged along' the MEP determined from gas phase or  COSMO ADF calculations in the presence of  solvent molecules. The solvent molecules  in the 'slow growth' PAW calculations will either be represented by MM ( van der Waals bodies) or  described purely quantum mechanically. The 'slow growth' solvation model will not be computationally competitive with the COSMO scheme. It will however be able to provide detailed insight into the solvent rearrangements during a chemical reaction. We plan as well to complete the implementation of  the COSMO method into the PAW program.
 

Static response theory. Catalytic studies are often initiated by identifying the involved species by spectroscopic fingerprint methods. We have in a parallel effort developed methods that can calculate spectrocopic parameters from first principle based on DFT. A large number of spectroscopic parameters can be expressed in terms of analytical second order energy derivatives: El,n =d2E/dldn, where l and n are external pertubations and E the total energy. Examples are ESR and NMR  shielding tensors (l = magnetic field, n = nuclear or electron magnetic dipole moment) or ESR and NMR  spin-spin  coupling constants (l;n = nuclear or electron magnetic dipole moments; force constants ( l, n = nuclear displacements); absorption intensities (l = electric or magnetic field, n = nuclear displacement or photon ). We are in the process of implementing a general program for the calculation of such properties based on double perturbation  theory and DFT. Magnetic and electric  properties

 Of special importance has been our work on NMR chemical shifts[P-110,P-48,P-36] and spin-spin coupling [P-28,P-10,P-19] and ESR g-tensors [P-73,P-1; P-17; P-37]. Response properties
Further proposed research. We plan to improve our NMR/ESR program in several ways. First, the approximate functionals currently in use have poor asymptotic properties near the nuclei and at the tail of the molecular density. An efford will be made to adopt functionals with better asymptotic properties. Next, the present functionals depend only on the electron density, not the current density. It will be explored whether functionals depending on current densities as well provide better NMR/ESR parameters. NMR/ESR parameters are dependent on the environment (solvent or host lattice) as well as changes in geometry due to thermal motion. We contemplate to introduce ESR/NMR calculations into the PAW program. In such a development both the impact on ESR/NMR parameters from fluxional behaviour, thermal motion and environment could be simulated and studied.
 

Time and frequency dependent  response theory. Time dependent DFT can be used to calculate  polarization and magnetization of a molecule due to a time dependent external electric of magnetic field with a certain frequency.  The theory makes it further possible to determine (excitation) energies and intensities (oscillatory strengths) of electronic transitions. More recently work has been directed towards circular dichroism (CD), vibronic curcular dichroism (VCD) and magnetic circular dichroism (MCD).

 

Excited state dynamics. We plan with the help of  time-dependent DFT to extend our first principle molecular dynamics studies to include excited states.

Catalysis is the gentle art of triggering desirable chemical reactions without forceful means such as high pressures or excessive heat. Its practical use has changed the world around us by facilitating the production of an ever increasing variety of synthetic materials. Catalysts are also used to increase the efficiency in fuel consumption and reduce the expulsion of pollutants. Other catalysts are employed by nature  to convert  nitrogen , oxygen and carbon dioxide from the atmosphere into chemicals  vital to the eco-system of our planet.
         The way in which reactions are triggered by catalysts is often not  known in details, because catalytic processes by virtue are fast , and thus difficult to follow even by sophisticated detection  methods. It is in general agreed that a catalytic process is characterised by a chain of chemical events (or elementary reaction steps) where the catalyst is consumed at the beginning of the chain and regenerated at the end. The chain is  referred to as the catalytic cycle.We intend in our computational studies to analyze catalytic processes of petrochemical pharmaceutical , biological or photonic importance, with the ultimate aim of designing better catalysts.
 

 Polymerization Catalysis. Olefin polymerization stitches together monomers with a carbon-carbon double bond to form long chains of hydrocarbons (plastics). The polymerization can involve polar or non-polar monomers and result in both linear and branched polymers. We plan to extend our already well established research program in olefin homo-polymerization [P-24] by coordination complexes to co-polymerization between polar and non-polar monomers. The study will analyze how steric (QM/MM) and electronic factors on the catalyst can influence the tolerance of polar groups and the length of the polymer from  smaller units (alpha-olefins, detergents, fragrance, lubricants) to large linear or branched polymers. It will further analyze the relation between the structure of the catalyst and the topology of the resulting polymer in terms of branching. We intend also to extend our study from coordination polymerization to ring-opening, radical and cationic polymerization, where transition metal centers also play a prominent role. The scope will further be extended from olefins to other organic and inorganic monomers, including transition metal complexes. We have in addition the potential to use our spectroscopic program to scan the novel polymers for optical properties of interest for the electronic industry. For a cool website about polymers click here

 

Enantioselective Catalysis. The cosmetic, agrochemical and pharmaceutical industries make extensive use of enantiomerically pure compounds. These compounds can be synthesized by the aid of transition metal complexes where the steric bulk of the ligands exerts enantioselectivity on the reactivity of the metal center. Our QM/MM scheme is well suited for such studies and we anticipate to investigate the enantioselective hydroxylation, cyclopropanation, hydrogenation, hydroboration, and hydrosilation of olefins. The more long-term goal will be to find strategies for the enantioselective addition of sigma-bonds to prochiral substrates. Considerations will also be given to designing catalysts for enantioselective co-polymerization.

 

Bio-inspired Catalysis. Metalloenzynes are used by nature to oxidize hydrocarbons via the controlled transfer of an oxygen atom from the metal center to a carbon atom. The oxidation often involves the breakage  (activation) of a carbon-hydrogen bond, a process that has been difficult to achieve by man-made transition metal complexes. Metalloenzymes can be considered as metal complexes with extra large ligands and a very fluxional conformation. This makes them prime candidates for our CP molecular dynamics method augmented with MM (see section 2c and 2d). We want to study oxidation and carbonylation of alkanes (especially methane), alcohols and aldehydes by metalloenzymes. Of key interest will be to establish whether the C-H bond is activated by hydrogen abstraction or oxidative addition, and how this preference depends on natures choice of metal and ligand environment. We will also study how metalloenzymes convert dinitrogen into ammonia and water into oxygen and hydrogen. Nature has had considerable time to develop optimal enzymes. However it has been restricted to metals found 'in abundance'. We are not bound by this restriction and can explore the optimal metal/ligand combination for C-H bond activation and other useful catalytic transformations conducted by metalloenzymes. In our search for bio-inspired catalysts that out-perform nature, we hope to be able to design robust and efficient catalyst that might activate the C-H bond of methane and turn this abundant substance into more valuable chemicals. Aim will also be taken at the design of catalysts that can split water into hydrogen and oxygen.

 

Heterogeneous Catalysis. The catalysts describe so far are dispersed in solvent as a homogeneous solution. In heterogeneous catalysis the catalysts are dispersed on 2D surfaces or in porous 3-D solids such as Zeolites. In some instances metal sites on surfaces or acid/base sites in porous material might in addition directly exhibit catalytic activity. Heterogeneous catalysts are used extensively in petrochemical conversion, upgrading and cleaning processes. Our QM/MM and CP-MD methodologies are ideally suited to treat these extended systems. The experience from recent work with heterogeneous polymerization catalysts dispersed on a magnesium chloride surface has encouraged us to build up a strong research program in this field within the next two years.

Individual projects
 

The research carried out within this project is wide in scope and involves a large number of researchers. Broadly speaking, the work can be described as the development of static and dynamic density functional theory for the application to chemical problems, in particular to systems within the realm of inorganic chemistry. Currently, the project can be divided into nine subgroups dealing with the following topics:

(SG1) Olefin polymerizations with early transition metals: (Tomasi) This project deals with the computational modeling of the homo- and copolymerization of alpha-olefins by modern homogeneous metallocene catalysts that are based on early transition metals; a highly valuable process of the chemical industry. The focus of our proposed research is twofold: (1st) on the deeper understanding of the work principles of established catalysts and (2nd) on the computer-based rational design of catalysts having catalytic abilities that exceed what is already reported. Our investigations are conducted in close collaboration with experimental partners. The enhanced insight into the work principles of established catalysts revealed from the computational exploration will bring us to the position to propose modifications of the catalysts' structure towards the rational design of new catalysts having more desirable properties. The improved catalysts will be then probed by our experimental collaborators. The present project represents front line research in catalysis and polymer science.

(SG2) C-H Activation: (Zhu) This project explores an important chemical reaction: the direct oxidation of methane to methanol by platinum complexes. The understanding of its mechanism, acquired from detailed studies of all reaction steps, together with further ongoing systematic studies on the role of the ligands, will help designing improved, more efficient catalysts for this reaction. Methane is the most abundant and cheapest hydrocarbon source in the world and methanol is an important chemical material used in every field in chemistry.  Success of this project can improve not only the efficiency of methanol production but also save energy and money.

(SG3) Biological: (Hernandez) The research of this subgroup focuses on achieving a better understanding of the reaction mechanisms of metalloenzymes.. These enzymes constitute about 40% of the known enzymes and are known to play a crucial role in many metabolic processes. Theoretical methods are powerful tools in the study of enzymatic catalysis because they provide invaluable information not only on the structure of the native enzyme but also on the structures of the complexes formed at the active site. These data often are inaccessible to the usual experimental techniques, like X-ray crystallography or NMR.

(SG4) Fischer-Tropsch synthesis: (Lo) The Fischer-Tropsch synthesis provides a way for transforming coal into hydrocarbons. It has therefore huge industrial significance. This project focuses on the synthesis of saturated and unsaturated hydrocarbons from syngas made up of CO and H2. In particular, the studies are performed on the formation of C1 and C2 units on the surfaces of iron and iron-alloys with low Miller indices. Structures of surface species and transition states are determined by density functional theory, and the kinetic behaviors are studied using the kinetic Monte Carlo method. The ultimate goal of this project is to help developing more active and selective catalysts, based on the acquired knowledge at the microscopic level.

(SG5) Manganese complexes for alkene epoxidation with H2O2: (Haras) Within this project, we attempt to propose the optimum structure of a recently discovered Manganese catalyst, to obtain useful reactivities in specific cases. The prototype manganese complex provided by our experimental partner needs first to be tested in the epoxidation of cyclohexene to explain mechanistic aspects of the process and to verify correlation between theoretical and experimental data. To reach the ultimate goal of developing an optimized catalyst, a large number of possible reaction channels with different possible candidates have to be studied. In order to get a realistic picture, all the calculations will be done at the DFT level using the ADF package with unrestricted treatment and inclusion of solvent effects.
 

(SG 6) TD-DFT: (Seth, Peralta, Fan,Minkov, Krykunov) Magnetic circular dichroism (MCD) is a nice compliment to standard electronic spectroscopy in that it can provide additional information about the geometry, magnetic properties and electronic structure of the molecule of interest. In this project we are interested in developing methodologies for calculating MCD spectra using time dependent density functional theory (TDDFT). TDDFT has the virtue of being applicable to systems of quite large size while still being reasonably accurate. In our previous work we have focused on more classical MCD spectroscopy where the influence of spin-orbit coupling has been neglected. It has been found that the effects of spin-orbit coupling can be significant in some cases. Our present work therefore looks to extend previous methodology to include spin-orbit coupling and thereby allow important systems such as open-shell metalloenzymes or chiral transition metal complexes to be treated. The importance of this work is self-evident as it expands the range of properties that can be calculated theoretically for chemically realistic systems.
 

(SG 7) Solid-oxide fuel cells: (Knapp, Galea, Vartak) The project is of a high industrial interest as it examines different processes that take place on SOFC anode materials and stability of the anodes with respect to sulfur and carbon deposition. Utilizing plane-wave gradient corrected periodic DFT calculations, in connection with the Projector-Augmented-Wave (PAW) method, the research considers the adsorption and dissociation of the anode fuel and a typical sulfur species (e.g. hydrogen sulfide) on numerous metal/alloy surfaces. By studying the mechanistic processes involved during these reactions, one should be able to understand and ultimately overcome the disadvantages currently associated with SOFC anode materials saving thus energy and money.

(SG 8) Ab Initio Molecular Dynamics: (Jechow) Traditionally, chemical reaction processes have been modeled by static (zero temperature) methods. However, recent studies have shown that such methods cannot correctly treat some important problems. Such problems can be treated by a dynamic (finite temperature) method. This project aims to extend the applicability of quantum mechanical dynamical approaches (ab initio molecular dynamics) and to study systems where these approaches have not traditionally been applied. In the near future, research effort within this project will be put on the role of entropy in determining the reaction profile of a given process. Molecular dynamic simulations using the Projector Augmented Wave (PAW) program written by Blöchl will be performed on test reactions such as the benzyl isocyanide isomerization and the ene reaction between singlet oxygen and simple alkenes.

(SG9) Development of energy gradients in solid state theory: (Kadantsev) The objective of this project is to develop a new computational framework that will allow one to deal with problems of chemical adsorption on surfaces in an efficient and practical way. This research is important because 90% of catalytic reactions take place on the surfaces. The established technique to study adsorption is the so-called “plane wave/supercell” approach. The problem with this technique is that most of the computational effort is wasted on chemically uninteresting vacuum regions. Localized in real space basis sets such as linear combinations of atomic orbitals (LCAO) are more appropriate to tackle the adsorption problems. The ADF code implemented in our group is unique in its usage of localized in real space Slater type orbitals (STOs) as the basis set functions. At the moment, ADF is capable of only calculating energies of periodic systems. Implementation of energy gradients for periodic systems in ADF will allow one to calculate the “special points” on the potential energy surface. One then can deduce all the kinetic data for the reaction at hand. A possible application of the energy gradients for the periodic systems is the study of the reactions, which take place on the anode of the fuel. Once the energy gradients are implemented, other enhancements to the periodic ADF program can be considered.