Research in our group is dedicated to the understanding of chemical and biophysical problems with the help of contemporary quantum chemical methods. Besides using available methods for ground and excited state calculations, we are developing methods for the calculation of excited states of large molecules. Currently we are pursuing the following research projects in our group:
Development of quantum chemical methods for the calculation of excited states of large molecules
Figure 1: Basic structure of the ADC working equations
The ADC scheme of the polarization propagator provides numerical equations to compute excitation energies of molecular systems.
Based on perturbation theory, one can derive ADC-schemes of different order. For example, ADC(2) is an ab initio method that is related to CIS(D) or CC2, which describes charge-transfer states, doubly excited states, and Rydberg states in principle physically correct.
However, ADC(2) is computationally expensive and its effort scales like O(N5) as its strict variant or as O(N6) in its extended formulation.
ADC combines CI with perturbation theory and bears the advantages to be hermitian and size extensive.
Like in CI, the excitation energies Ωn and transition vectors Yn are obtained by diagonalization of the matrix representation of the shifted Hamiltonian M=(H-1E0).
Loosely speaking, ADC(2) can be seen as an "MP2 for excited states".
In our group, we develop efficient ADC codes that allow for the treatment of medium-sized and large closed- and open shell molecular systems.
In this context we have recently implemented a local version as well as an unrestricted formulation of the ADC(2)-scheme in Q-Chem.
Besides the simple computation of excitation energies, we also exploit the so-called intermediate state representation (ISR) approach, to compute excited state dipole moments, excited state absorption and two-photon absorption probabilities.
For more information on our recent work on ADC, please consult Jan Henrik's and Michael's papers:
- J. H. Starcke, M. Wormit, J. Schirmer and A. Dreuw, Chem. Phys. 2006, 329, 39.
- J. H. Starcke, M. Wormit and A. Dreuw, JCP 2009, 130, 024104.
- J. H. Starcke, M. Wormit and A. Dreuw, JCP 2009, 131, 144311.
Figure 2: Time-dependent Kohn-Sham equation
The time-dependent Kohn-Sham equation is the time-dependent analog of the standard time-independent Kohn-Sham equation widely used to compute ground state properties. In analogy to the derivation of the latter, for the derivation of the td-KS equation a mapping between time-dependent densities and wavefunctions needs to be established, as well as a variational principle must be given. Despite the lack of a valid variational principle, td-KS is a formally exact theory, and once the exact time-dependent Schrödinger equation has been solved to obtain the exact electron density trajectory, td-KS can be employed to exactly reproduce the time evolution of the electron density of the interacting system. However, owing to the lack of a formally exact variational principle, td-KS cannot predict the time evolution, even if the exact time-dependent exchange-correlation potential functional would be known, one still would need the exact density trajectory to construct the xc-potential from the potential functional. Caught your interest? Then read this:
Figure 3: Linear-response TDDFT equations to compute excitation energies.
Linear-response TDDFT is currently one of the most prominent approaches to compute excitation energies and excited state properties of large molecular systems. Despite its success for local excited states well below the ionization potential, TDDFT exhibits substantial failures for charge-transfer states. We have recently shown that this failure can be corrected by inclusion of long-range Hartree-Fock exchange in the exchange-correlation functional. Thus we are developing new long-range corrected functionals for the improved treatment of CT excited states within TDDFT. For more details, check out the following papers:
- A. Dreuw, J. L. Weisman and M. Head-Gordon, JCP 2003, 119, 2943.
- A. Dreuw and M. Head-Gordon, JACS 2004, 126, 4007.
- A. Dreuw and M. Head-Gordon, Chem. Rev. 2005, 105, 4009.
- A. Dreuw, J. Plötner, M. Wormit, M. Head-Gordon A. D. Dutoi, Z. Phys. Chem. 2009, accepted for publication.
Energy and electron transfer in pigment protein complexes
Application of theoretical and computational methods to pigment protein complexes allows for a detailed investigation of their function resulting in deeper insight into the underlying molecular mechanisms. Since such protein complexes are much too large to be treated quantum mechanically as a whole, one needs to establish a theoretical methodology to tackle individual pigments or a few pigments quantum chemically, to gain insight into their individual properties and interactions to be able to extrapolate on the function of the full pigment protein. As illustrated in Figure 1, an experimentally determined crystal structure serves as input to derive molecular models for the pigments of interest. The latter is then subjected to approximate quantum chemical calculations. Together with experimental data, it is then very often possible to gain detailed insight into possible energy and electron transfer processes. A photo-protection mechanism, the so-called non-photochemical quenching, may serve as an illustrative example for our research in that area.
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Figure 4: Workflow of a quantum chemical investigation of a complex pigment protein like the major Light Harvesting Complex 2 (LH2) of purple bacteria (upper left corner).
NPQ is a fundamental photosynthetic mechanism, by which plants protect themselves against over-excitation of the photosynthetic apparatus and concomitant formation of dangerous byproducts like triplet states and singlet oxygen, which can lead to substantial oxidative damage of the cells and in the worst case to cell death. Although NPQ is very well studied empirically, a detailed molecular mechanism is not yet known neither is the precise location of NPQ in the plant photosynthetic apparatus. Using the above described theoretical methodology, we were able to investigate the possibility of excess energy quenching through the formation of a chlorophyll-carotenoid quenching complex. We could demonstrate that in such complexes, quenching of chlorophyll fluorescence is possible via electron transfer quenching and the subsequent formation of a carotenoid radical cation. Inspired by our theoretical prediction, a corresponding experiment has been performed and the carotenoid radical cation has indeed been detected in intact thylakoids when NPQ is active. For more infos on that subject, please read Michael's recent works:
- A. Dreuw, G. R. Fleming and M. Head-Gordon, JPCB 2003, 107, 6500.
- A. Dreuw, G. R. Fleming and M. Head-Gordon, Biochem. Soc. Trans. 2005, 33, 858.
- M. Wormit and A. Dreuw, JPCB 2006, 110, 24200.
- M. Wormit and A. Dreuw, PCCP 2007, 9, 2917.
- A. Dreuw and M. Wormit, J. Inorg. Biochem. 2008, 102, 458.
- M. Wormit, P. H. P. Harbach, J. M. Mewes, S. Amarie, J. Wachtveitl and A. Dreuw, BBA Bioenergetics 2009, 1787, 738.
Figure 5: β-Carotene and Lutein.
Carotenoids are ubiquitous natural pigments occurring in all living organisms. They act as protecting agents against oxidative stress, by quenching free radicals, singlet oxygen or excess excitation energy as in NPQ mentioned above. Due to their importance, much effort has been undertaken to study their excited state properties. Today it is well known, that carotenoids and conjugated polyene chains in general posses a low-lying doubly excited state, which is optically one-photon forbidden and theoretically very difficult to describe. Moreover, the observation of carotenoid radical cations during NPQ has triggered interest also in the spectroscopic properties of carotenoid radical cations. Recently, we have addressed the excited states properties of the so-called xanthophylls carotenoids lutein, zeaxanthin and violaxanthin, as well as those of their radical cations. Our recent work on carotenoids and their radical cations can be read in:
- A. Dreuw, JPCA 2006, 110, 4592.
- S. Amarie, K. Afrete, J. H. Starcke, A. Dreuw and J. Wachtveitl, JPCB 2008, 112, 14011.
- A. Dreuw, J. H. Starcke and J. Wachtveitl, Chem. Phys. 2009, submitted for publication
Photo-initiated processes in medium-sized organic molecules
Many organic pigments exhibit a surprisingly reach photochemistry, and in most cases, photo-initiated reactions cannot be understood with "standard" chemical intuition. The latter originates from experimental laboratory research which is almost exclusively performed in the electronic ground state. Thus chemical knowledge corresponds to ground state knowledge. However, the deposition of the energy of one photon onto one molecule can induce reactions which are not possible otherwise. A famous example is the cis-trans isomerization of a double bond, which is thermally almost impossible, photochemically induced, however, it occurs practically instantaneously on a sub-picosecond timescale. Such fast isomerization processes are often exploited in photoswitches like azobenzene for example. Since photo-induced processes can usually not be predicted based on the molecular structure alone in most organic and inorganic molecules, a deeper understanding of photo-processes always requires thorough quantum chemical investigation. Three proto-typical examples of our research in this area are given below.
Figure 6: Pigment Yellow 101.
The organic pigment P.Y. 101 is well known since more than 100 years.
It is a yellow fluorescent and very photostable pigment.
Though widely used as colorant, the details of its photochemistry have not been studied yet.
In recent studies, we could show that P.Y.101 ows its fluorescence to intramolecular hydrogen bonds that prevent low-lying nπ* states from efficient fluorescence quenching.
Moreover, we could identify an intramolecular excited-state proton-transfer pathway as well as isomerization pathways that all correspond to non-destructive de-activation channels of P.Y.101 explaining its photostability.
If you want to know more about P.Y. 101, have a look at Jürgen's work:
- A. Dreuw, J. Plötner, L. Lorenz, J. Wachtveitl, J. E. Djanhan, J. Brüning, T. Metz, M. Bolte and M. U. Schmidt, Angew. Chemie Int. Ed. Engl. 2005, 44, 7783
- J. Plötner and A. Dreuw, PCCP 2006, 8, 1197
- J. Plötner and A. Dreuw, Chem. Phys. 2008, 347, 472
Figure 7:Computed Z/E isomerization pathway of HTI.
The molecular photo-switch hemithioindigo hemistilbene (HTI) can be selectively photo-isomerized from the Z-isomer into the E-isomer and vice versa.
We could demonstrate that two Z and E-isomers exist in the electronic ground state as well as on the S1 surface.
The S1 isomers are separated by small energy barriers along the dihedral twisting coordinate, but also a conical intersection with the electronic ground state is present at about 90° twisting angle.
Comparison with previously published experimental data reveals that most excited molecules, however, do not isomerize, but instead relax to the equilibrium structure of the Z-isomer on the S1 surface and return back into the ground state via regular fluorescence.
Only a small fraction of the excited state population decays via the identified conical intersection and forms ground state E-isomers.
This explains the comparably long lifetime of 38 ps of the excited HTI molecules and the observed low quantum yield of photo-switching. For more details please read Jürgen's latest paper:
Figure 8: Upon excitation of DMABME*2H2O with a
blue photon, the water dimer is evaporated a TICT state can be
formed and red-shifted fluoescence can be observed.
In recent experiments it could be shown that at least two water
molecules are required in complexes with 4-(dimethylamino)benzoic acid methyl ester (DMABME) for
anomalous red-shifted fluorescence to occur in the gas phase.
Based on our theoretical investigation, the two experimentally
observed isoenergetic isomers could be assigned to complexes
in which a water dimer is hydrogen-bonded
either to the carbonyl oxygen of the ester function or to the amino
Surprisingly, our computed
IR spectra revealed that the N-bonded isomer is responsible for the
observed red-shifted fluorescence.
For an explanation, we went further and investigated the mechanism of twisted intramolecular
charge-transfer (TICT) formation and energy
dissipation in detail.
In general, for red-shifted fluorescence to occur, the N-bonded complexes
must be able to dissipate energy, which in the gas phase can only
happen non-radiatively via fragmentation.
We could demonstrate that only the N-bonded isomer photo-dissociates
rapidly enough into free DMABME and a water dimer as a result of the immediate repulsion between the
amino nitrogen and the water dimer in the TICT state.
The O-bonded isomer, on the contrary, stays intact because the hydrogen bond is
strengthened by the additional electrostatic attraction in the ICT
state. Furthermore, we have suggested an experiment to further
corroborate our proposed mechanism. For more check out this paper:
Catalytic role of Calixhydroquinone nanotubes in acetone-water proton exchange
Figure 9: Proposed reaction mechanism of acetone-water proton exchange catalyzed by Calixhydroquinone nanotubes
Usually, the proton exchange between water and acetone does not take
place in neutral aqueous solution. However, it has been recently
observed experimentally that Calixhydroquinone nanotubes possess
the unique property to indeed catalyze this proton exchange. We
studied the mechanism of the catalysis and could exclude that
concerted proton transfer occurs. Instead, stepwise proton
transfer via ionic intermediates created by predissociation of CHQ
OH-groups is the most likely mechanism. We could demsonstrate that the presence of charged species, protonated
acetone or deprotonated hydroquinone, leads to a substantial decrease
of the proton transfer energy barrier and to calculated reaction rates
that provide an explanation for the experimentally observed proton
exchange. Furthermore, our quantum chemical investigation demonstrates
that the catalytic activity of CHQ aggregates is not based on a
reduction of the energy barrier connected with proton transfer but on
the desolvation of acetone and prevention of solvent water cluster
formation. Please see Maxim's work for more details:
Structure of adenine-water complexes
Recently, femtosecond multiphoton ionization detected infrared spectra of jet-cooled monohydrates of adenine and 9-methyladenine were detected in the group of Prof. Brutschy. By quantum chemical vibrational analysis and comparison with available literature data we were able to identify two isomers of adenine hydrate with the water molecule hydrogen-bonded to either the amino or the N9-H group. These two hydrates revealed different fragmentation patterns in the ion depletion spectra, indicating an isomer specific intermolecular dynamics. This different behaviour is discussed in terms of competing electronically excited state relaxation and dissociation processes. For more details please read Yevgeniy's paper: