Research Interests
 

Novel Density Functional Exchange and Correlation Functionals

        Modern density functional theory (DFT) is one of the most popular methods in current computational chemistry1. Its cost effectiveness and accuracy have greatly contributed to its success. In contrast to high level ab initio calculations2, where the electron/electron correlation is calculated by sophisticated and rather time-consuming methods, the DFT calculations provide electron exchange and correlation interactions via approximate functionals. The technical implementation of these functionals can vary, such as by following the conventional molecular orbital3 or fragment-density based approaches4-7. Regardless of how they are implemented, the DFT functionals have been applied with great success in mechanistic organic and organometallic chemistry8-10. However, the accuracy of these calculations is frequently taken for granted without rigorous comparisons to experimental data. In addition, while ab initio methods can provide a theoretically converging series11, improvements in DFT methods can be achieved for limited systems via a semi-empirical parameterization approach. The B3LYP12 hybrid functional is such a successful application, which mixes HF and DF exchange functionals with adjusted DF correlation functional to give the best fit to the 'G2 set'13. This experimental training set contains total wave function properties of mainly organic molecules, such as total energies, internal coordinates and ionization energies.

          Beyond these total energy-based molecular parameters, it is promising to direct attention to wave function based properties, such as spin density, orbital energies and characters. These can be directly probed by physical inorganic techniques14, such as paramagnetic resonance and X-ray absorption spectroscopies. In addition, for inorganic complexes accurate thermochemical data are rarely known. However, in most cases data obtained by absorption spectroscopy in broad energy ranges are available and can provide accurate ground and excited state descriptions. For example, in paramagnetic molecules accurate spin distribution can be obtained from the quantitation of EPR metal hyperfine and ligand superhyperfine coupling constants and g-values using isotopically enriched samples. Using advanced EPR techniques15, such as pulsed ENDOR and ESEEM, the spin distribution on distant atoms coupled into the spin system can also be quantitated, thus giving a complete paramagnetic wave function definition. In addition, using K- and L-edge X-ray absorption spectroscopies16,17, the composition of low-lying, unoccupied orbitals (holes) can be determined for both dia- and paramagnetic compounds in gas, solution or solid phases. Such sources of experimental wave function properties are unique in that they can be compared in the absolute sense without scaling/shifting to computed wave function properties by DFT or ab initio theories. It is notable that the spin density and covalency by definition are not necessarily the same, because spin-polarization can be chemically important. As a first-order approximation (i.e. spin-restricted formalism), spin densities and covalencies can be considered as complementary data to each other.
          The experimental covalencies, as reference points, for a series of chloride and thiolate complexes18-20 are summarized in Table 1. These complexes are important in the definition of ground state bonding of first row transition metal complexes with bioinorganic relevance. As a member of this series, the experimental and computational ground state wave function of D4h [CuCl4]2- has already been compared21. It was found that the most commonly used DFT functionals give a ground state description, which is too covalent. A novel hybrid functional with 38% HF exchange can give the best agreement between calculation and experiment with significant improvements in wave function properties, as well as potential energy surface description. In addition, the mixing of 38% HF exchange improves the excited state description as seen by the good agreement between the calculated and experimental ligand field and ligand-to-metal charge transfer energies.   Table 1: Ground state ligand characters in first-row transition metal chlorides and thiolates
 
average hole covalencies CuII
d9		 NiII
d8		 CoII
d7		 FeII
d6		 FeIII
d5
Cl 3p, %D2d301210917
 D4h43   
S 3p, %D2d383319931
a in distorted trigonal CuII site in plastocyanine
          Without any further adjustment, this spectroscopically calibrated method was successfully applied for bioinorganic systems containing CuII central atoms22. For example, the error between the calculated and experimental excitation energies was reduced to approximately 1500 cm-1 for active site model structures of blue and green cupredoxins and laccases. However, the calculation of the excited state energies and intensities are not as straightforward as for most of the ground state properties. The ground state orbital energy differences can give good starting points for excitation energies. Upon taking into account excited state relaxation effects, calculations with non-aufbau occupations23 are needed for reasonable descriptions or sophisticated time-dependent, post-SCF perturbations24,25 of the ground state electron density. The latter has been found to give accurate excitation energies and intensities for organic molecules26, but has not been tested in detail for transition metal complexes with biological relevance.
          Proposed research: The systematic experimental study of first-row chloride and thiolate complexes will be used to extend the spectroscopic calibration of common density functionals from Cu to other transition metal ions. In addition, high level ab initio calculations will provide independent support, since these calculations can provide a theoretically converging series in solving the Schrödinger equation. They can also be used to validate the employed basis sets, and most importantly, test whether the gas phase calculations can model the experimental conditions. This systematic approach will provide a large theoretical data set by which the results can be generalized beyond the scope of thiolates and chlorides. The difference between the corrected and non-corrected functionals and electron densities will be determined. The aim of this comparision is to provide an analytical form of a correction functional, which can be applied similarly to gradient-corrections as to the improvement of local spin density approximations. Such correction functionals would allow for proper description of the ground state in inorganic complexes/bioinorganic active sites at a reasonable computational cost. These new functionals will be tested for excited state description using various computational approaches, but mostly time-dependent density functional calculations (TDDFT). If needed, methodological or implementational developments of TDDFT will be carried out to improve the excited state descriptions, which can be of great importance for understanding spectral changes in absorption, CD, and MCD spectroscopies. Using ground and excited state wave function properties, a novel family of density functionals can be defined providing recognizable benefits beyond inorganic chemical applications.
 
 

Research questions:

  1. What is the cause of the inaccuracy of ground state bonding description of inorganic complexes in density functional calculations?
  2. What is the general correction functional, other than oxidation- and spin-state dependent Hartree-Fock exchange mixing, to improve density functional theory for transition metal complexes?
  3. How accurate are the TDDFT excited state descriptions and how much improvement is possible?
 
 

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