COMPUTATIONAL PHYSICAL CHEMISTRY |
GENERAL PERSPECTIVEElectronic structure calculation
Computational physical chemistry aims to achieve for condensed molecular systems (liquids, macromolecules) what quantum chemistry does in the gas phase, namely accurate computation of thermochemical, kinetic and spectroscopic properties. The central quantity in both theory and computation is the potential energy surface (PES). The approach followed in gas-phase quantum chemistry is to map the PES as a function of molecular configuration using a range of electronic structure calculation methods of increasing accuracy. The structure of the PES (often called energy landscape) is the input for the computation of thermochemical, kinetic and spectroscopic properties, which are obtained by perturbation methods using minima and transition states as reference (or, in advanced schemes, the full minimum energy path). So, even though the quantities characterizing reactivity refer to finite temperature and dynamical conditions, the picture sketched by traditional quantum chemistry is in essence static. This is a limitation in some applications. Direct dynamic schemes are the way forward for these problems and the development of these methods is at the frontier of the research in computational chemistry.
Molecular dynamics simulation
Direct dynamics schemes are certainly necessary for the liquid state, which is stabilized by finite temperature dynamical fluctuations. With liquids we enter the realm of statistical mechanics, the other discipline in theoretical chemistry. The computational tool of choice here is molecular dynamics (MD) and Monte Carlo simulation. Application of these methods to chemical reactions has an equally long tradition and has produced a variety of sophisticated methods for the computation of equilibrium constants, rate constants and response properties (susceptibilities). In most of this work the PES is described by a force field. The limitation here, of course, is the difficulty of designing force field models for chemically reactive systems. The challenge of computational condensed phase chemistry is thus to implement these dynamical and statistical methods using the electronic structure based schemes of quantum chemistry for the computation of energies and forces. In practice this means the application of density functional theory (DFT). This defines the focus of the research of the Sprik group. The technique we use is density functional based molecular dynamics simulation (also referred as "ab initio MD" or "Car-Parrinello")
ACID-BASE AND REDOX REACTIONSProton transfer
Exchange of protons and electrons between ions and molecules are two elementary reactions taking a lot of place in physical chemical text books. Both involve transfer of charge, making them extremely sensitive to solvent effects. Moreover, solvent molecules often directly participate as a source of protons and electrons or relay for transfer over long distances. Proton transfer (PT) and electron transfer (ET) reactions therefore seem a good subject for the application of computational schemes in which the solute and solvent are treated at the same level of theory. This is the philosophy of the Car-Parrinello method. Indeed PT is a popular and established topic in Car-Parrinello research which has made significant contributions to the unravelling of the mechanistic detail of PT. Our recent activity in this field has mostly concentrated on the thermochemistry, i.e. computation of pKa's. Hydrogen bonding in aqueous systems can be highly specific and the "democratic" all-atom approach of ab initio MD offers distinct advantages in terms of accuracy and detail of the description of the solvent in the direct vicinity of the solute. However we pay a price in the representation of the long range solvation interactions. Model systems are relatively small and, moreover, periodic, which introduces substantial finite size errors in the estimation of absolute pKa's. Relative pKa' however, can be computed with good accuracy, as shown by the results for the aqueous model systems investigated sofar (see for example the study of the difference in pKa of equatorial and axial OH groups in a simple phosphorane [ JACS 2002] )
Redox half reactions
The study of redox reactions by Car-Parrinello methods is relatively new. It occupies a good part of the research effort in the group. Our methodology is based on the Marcus theory of electron transfer (or the MD implementation developed by Warshel and others). Redox free energies are calculated from the distribution of the values of the vertical (instantaneous) energy gap between the diabatic energy surfaces of reactant and product. For ET these vertical energy gaps correspond to optical charge transfer excitations between donor and acceptor centers, which often can be observed by spectroscopic experiments. For various technical reasons we have first focused on half reactions (R -> O + e-). Instead of reallocating an electron we completely remove it from the system (ionization) or add an extra electron. The vertical energy for such a half reaction corresponds to the difference in total ground state energy of the oxidized (O) and reduced (R) system (the vertical ionization energy) and can be easily computed using variational DFT methods (thus avoiding the problems in DFT related to excited charge transfer states). Similar to our pKa's, free energy changes of half reactions are subject to uncertainties caused by system size effects and periodic boundary conditions. However, also here it is possible to obtain reliable results for relative free energies, which can be equated with the reaction free energies of full redox reactions. The condition is that we compare ion pairs of the same charge (Xn/Xn+1, Yn/Yn+1) giving a full reaction Xn + Yn+1 -> Xn+1+Yn which is "charge symmetric". The long range energies in this special class of reactions cancel out and the reaction free energies can in fact be compared to the redox potentials measured by the electrochemists.
Redox potential calculations
This approach was applied to the transition metal aqua ion reactions Ag2+ + Cu 1+ → Ag1+ + Cu 2+ [JACS 2003] and MnO41- + RuO42- → MnO42-+ RuO41- [JCP 2005] with good results. Even better results (accuracies of 100 meV or less) were obtained for two well-known redox active organo sulfur compounds (TTF, TTH) in acetonitrile [JPCB 2005] and simple quinones in methanol and acetonitrile solution (Angew. Chem. in press). We emphasize that the computed redox potentials are directly compared to experimental standard potentials referring to ideal solutes. The good agreement (for the charge symmetric reactions we have studied sofar) suggests that a half reaction scheme, inspite of dealing with periodic models with a net charge, may make it easier to extrapolate to infinite dilution[CPC05]. This may very well turn out to be the main advantage of the half reaction scheme. More work is under way to prove this important point. In addition to the problem of long range effects we are also looking into the statistical mechanics of our approach, in particular the use of Marcus theory. Two ion pairs were singled out. The first is the Ru2+/Ru3+ half reaction [TCA 2005]. Both oxidation states form very similar hexahydrates and the redox reaction is considered as a perfect example of an outer sphere electron transfer process for which Marcus theory was designed. The other system is the Ag1+/Ag2+ couple. Oxidation of the d10 mono-cation induces a change of coordination and can therefore be expected to show non-linear behaviour violating the assumptions made in Marcus theory (JCP in press).
Electron transfer and kinetics
The Marcus scheme based on vertical energy gap time series gives access to reorganization and activation free energies, which can be used to analyze and understand the mechanism driving the kinetics (which is why this theory is so powerful). The information on kinetics derived from half reactions is of course only qualitative. We are therefore currently extending our methodology to full ET reactions involving both donor and acceptor. This will require us to confront several of the flaws in the DFT implementation used in ab initio MD. This not only includes the problem of charge transfer excitations, circumvented in the restriction to half reactions, but also self interaction errors in the determination of the ground state of molecular radicals (a version of the infamous H2+ problem, which leads to overstabilization of singly occupied delocalized states). We have made a promising beginning with mending some of the self interaction errors in a successful simulation of the solvation of the hydroxyl radical in water, which avoids the formation of spurious hemi bonds between the OH radical and H2O molecules [PCCP 2005]. More work is however necessary, in particular the application to the electronic states of two mixed valence metal centers.
VIBRATIONAL AND ELECTRONIC SPECTROSCOPYIn parallel with the project on solution chemistry we are carrying out calculations of spectroscopic properties of molecules and coordination complexes in solution. This involves currently the computation of infrared spectra (IR) exploiting the progress that has been made in the theory of electronic polarization of extended periodic systems. Combining this method with time dependent density functional theory (TDDFT) techniques we also compute electronic absorption spectra in solution. We were able to reproduce with reasonable accuracy the IR spectrum of aqueous uracil [JPCB 2003] and NMA [JCTC 2005] and assign and interpret the spectra in terms of molecular vibrations. The TDDFT computations include the absorption spectrum of aqueous acetone [JCP 2003] and some of the aqueous transition metal ions used as model in the redox studies, namely Ag+, Cu+[JCP 2004] and Ru2+[JPCB 2005]. These computations were meant mainly as a test of the performance of TDDFT for spectra in molecular liquids computed the Car-Parrinello way, that is treating solute and solvent at the same level of theory. The results confirmed that TDDFT can give a reliable representation of valence excitations in solution validating at the same time the underlying structure of one-electron orbitals which is welcome support for the redox potential calculations. The TDDFT calculations, however, also clearly exposed the problems encountered for excitations to delocalized (conduction) states and solute-solvent charge transfer excitations.
DIRECTIONS AND OUTLOOKMany redox reactions of interest are coupled to transfer of protons to the solvent or other solutes. This holds in particular for molecules of main group elements. Extending our methods to proton coupled electron transfer is therefore a priority in current research. We will start again with half reactions. Consistent treatment of long range effects in the redox and acid-base step is now critical. Of particular interest are reactions which effectively add or remove hydrogen atoms leaving the charge to the system the same. Generalization of the diabatic energy gap scheme for the computation of free energies to full ET reactions is another priority as is the relaxation of the constraint of charge symmetry. Together these developments will open up a whole class of redox reactions of importance in biochemistry. The target model systems will be initially some of the cofactors in enzymatic reactions, which are still relatively small. We are also continuing the development of self interaction correction schemes for molecular radicals. The aim is here is the study of the chemistry of radiation dammage. The long term objective is to move on to some of redox processes in the chain of reactions involved in respiration and photosynthesis. This will require the use of hybrid methods such as QM/MM.
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