The people involved: Jens Dreyer
Former team members:

International collaboration: Shaul Mukamel, Department of Chemistry, University of Rochester, Rochester, NY, USA

Research topics 1. Ab initio simulation of coherent three-pulse spectroscopies 2. Ab initio simulation of linear and nonlinear spectra of acetic acid dimers

1. Ab initio simulation of coherent three-pulse spectroscopies The molecular structure forms the basis for understanding and predicting chemical, physical and biological properties. Multidimensional femtosecond vibrational spectroscopy is a novel tool with great promise for determining the dynamics of molecular structures such as proteins or hydrogen-bonded systems on ultrafast time scales that are hardly accessed by NMR or X-ray spectroscopy (see Multidimensional Femtosecond Correlation Spectroscopies of Electronic and Vibrational Excitations S. Mukamel Ann. Rev. Phys. Chem. 2000, 51, 691-729). Multidimensional infrared spectroscopy constitutes a three-pulse (four-wave mixing) third-order nonlinear technique that is based on the manipulation and control of multiple quantum coherences to probe coupled vibrational modes. Multidimensional (nD) correlation plots result by displaying the signal with respect to n variables. These may include time intervals between pulses, carrier frequencies, or other pulse parameters like envelopes, polarizations, durations, and even phases. Advantages of multidimensional spectroscopy are: Congested ordinary one-dimensional spectra may be disentangled by spreading the signal into additional dimensions, allowing the time scales of environmental bath interactions to be discerned by lineshape analysis. Newly appearing cross peaks in two-dimensional correlation plots contain direct signatures of intra- or intermolecular interactions that can be converted into structural and dynamical information. Intense tunable 50-100 fs infrared pulses make it possible to monitor structural changes and ultrafast processes such as vibrational energy relaxation and redistribution, charge transfer, conformational fluctuations, and chemical reactions. Properties of potential energy surfaces like diagonal and off-diagonal anharmonicities are measured directly. To analyze multidimensional spectra and to design new experiments theoretical simulations are necessary. The aim of this project is to develep a new methodology which allows to predict multidimensional spectra from first principles. To this end, quantum chemical calculations, e.g. Hartree-Fock or density functional theory, are combined with the simulation of nonlinear response functions. We generate an anharmonic force-field up to fourth-order as well as dipole derivatives to second order for a number of selected local oscillators represented by internal coordinates. Higher-order force constants are calculated by numerical differentiation of second-order (harmonic) force constants. An anharmonic vibrational Hamiltonian is then generated and diagonalized. The representation of the dipole is then transformed into the eigenstate basis, resulting in transition dipole moments between all the eigenstates. Those together with the eigenstate energies are used to calculate nonlinear coherent signals applying the sum over states approach.

Different coherent four-wave mixing techniques are classified by constructing all possible wavevector combinations of the three incoming pulses, which leads to four distinct signal directions that can be measured independently. 2D spectra of multilevel vibrational systems contain a large number of peaks that are likely to overlap. In particular, the usually intense diagonal peaks often obscure the desired cross peaks which carry more detailed structural signatures. We therefore investigate two methods that can be used to simplify the spectra: The superposition of single wavevector spectra, and the use of specific polarization configurations to select desired combinations of tensor components. Both procedures can be applied to control or remove certain groups of peaks from the spectra, that is diagonal peaks, cross peaks or overtone peaks. Initial studies were performed on small molecules, a rhodium-dicarbonyl complex, where extensive experimental data are available for comparison, and a rigid bycyclic dipeptide.

Four distinct signal contributions that can be measured independently.

kI = - k1 + k2 + k3 kII = + k1 - k2 + k3 kIII = + k1 + k2 - k3 kIV = + k1 + k2 + k3

We simulated one- and two-color 2D vibrational spectra, either with all three pulses in resonance with the symmetric and antisymmetric C=O stretching bands (see Figure for a typical photon echo 2D spectrum) or with two resonant with the C=O bands and one tuned to the symmetric and antisymmetric N-H stretching transitions. The one-color experiments reveal information on the coupling of amide I modes, which can be used to monitor the secondary structure of peptides and proteins and follow its fluctuations on ultrafast time scales. The two-color experiments yield the coupling of peptide C=O and N--H bonds, which provides additional insight into structural and dynamical properties.

2. Ab initio simulation of linear and nonlinear spectra of acetic acid dimers Carboxylic acids are important model systems displaying key features of hydrogen-bonded systems in nature. They represent a structural motif of cooperative hydrogen bonds in proteins containing aspartic or glutamic acid and mimic multiple hydrogen bonds in acid base pairs. Acetic acid predominantly forms cyclic C2h-symmetric dimers with two hydrogen bonds in the gas phase as well as in nonpolar solution.

Vibrational spectra provide information about local properties of hydrogen bonded groups. The lineshapes of the high-frequency O-H stretching mode of OH groups involved in the hydrogen bonds are often very complex and highly congested reflecting the complicated underlying microscopic interactions, and consequently, the dynamics and line broadening mechanisms of hydrogen bonds. Only recently high-resolution infrared (IR) spectra of acetic acid dimer became available from supersonic jet Fourier transform spectroscopy measured in the group of Martin Suhm. These cold gas phase spectra uncover much of the vibrational fine structure and can thus serve as a reference for zero temperature gas phase calculations to analyze the O-H stretching mode IR spectra.

To reach a quantitative understanding of the spectra we performed density functional theory calculations of the linear O-H stretching mode IR spectra taking the following spectral broadening mechanisms into account: (1) anharmonic coupling between the high-frequency O-H stretching vibration and low-frequency modes, (2) Fermi resonance coupling between the v=1 state of the O-H stretching mode and combination tones of fingerprint modes, and (3) a combination of (1) and (2). From a comparison of calculated and experimental spectra one can conclude that only the combined mechanism accounts for the full spectral width and substructure. We identify 2 Raman active low-frequency modes, the in-plane bending and stretching inter-dimer hydrogen bond modes, and combination states of the C-O stretching, out-of-plane methyl group deformation, in-plane O-H deformation and the C=O stretching IR and Raman active modes to explain the lineshape of the O-H stretching IR absorption spectram in (CH3-COOH)2. The same conclusion holds for the spectrum of (CD3-COOH)2, except that combination bands of the methyl group deformation mode are missing. Only a few peaks of minor intensity observed in the gas phase IR spectrum are not accounted for by the present calculations. Thus, it is demonstrated that both anharmonic coupling to low-frequency modes as well as Fermi resonance coupling with fingerprint modes are essential mechanisms underlying the lineshape of the O-H stretching IR absorption band in acetic acid dimers.

These studies were extended to simulations of the 2D IR spectra to investigate the multidimensional signatures of the respective coupling mechanisms. Coherent 2D IR spectra were predicted for all 3 coupling mechanisms (homogeneous line width = 1 cm-1, vibrational temperature 0 K). Spectra including the R3 diagram only resemble conditions, where the excited vibrational state has decayed already. a. Anharmonic coupling b. Fermi resonance coupling to fingerprint combination modes c. Combined mechanism In going from anharmonic coupling of the O-H stretching mode to low-frequency modes (3 modes) to Fermi resonance coupling with fingerprint mode combination tones (9 modes) to a combined mechanism (11 modes) the number of individual 2D peaks grows considerably and the complexity of the vibrational signatures increases substantially.

Introduction of homogeneous broadening (36 cm-1) causes many individual peaks to overlap to a single vibrational feature. This spectrum, calculated for ground state absorption only (R3 feynman pathways), may be compared to the experimental 2D IR spectrum measured at a population relaxation time of T=400 fs, at which the excited vibration state of the O-H stretching mode has decayed already. Thus, the spectra contain only diagonal and cross peaks. The most striking diagonal and cross peaks are observed for the most intense bands in the linear spectrum. From the good agreement with experimental results it is concluded that Fermi resonances dominate the T=400 fs experimental 2D spectrum. Low-frequency progressions make a minor contribution to the 2D spectra because of their substantially smaller transition dipoles.

Publications on ab initio simulations of linear and nonlinear spectra of acetic acid dimers

D05b C1-P-2004.21 J. Dreyer Hydrogen-bonded acetic acid dimers: Anharmonic coupling and linear infrared spectra studied with density functional theory J. Chem. Phys. 122 (2005) 184306/1-10 Download PDF/PS-File or URL: C1-P-2004.21   D05a C1-P-2004.22 J. Dreyer Density functional theory simulations of two-dimensional infrared spectra for hydrogen-bonded acetic acid dimers Int. J. Quant. Chem. 104 (2005) 782-193 Download PDF/PS-File or URL: C1-P-2004.22   NBC05 C1-P-2004.17 N. Huse, B. D. Bruner, M. L. Cowan, J. Dreyer, E. T. J. Nibbering, R. J. D. Miller, T. Elsaesser Anharmonic couplings underlying the ultrafast vibrational dynamics of hydrogen bonds in liquids Phys. Rev. Lett. 95 (2005) 147402/1-4 Download PDF/PS-File or URL: C1-P-2004.17   HBC05 C1-P-2004.12 N. Huse, B. D. Bruner, M. L. Cowan, J. Dreyer, E. T. J. Nibbering, T. Elsaesser, R. J. D. Miller Heterodyne 2D-IR photon echo spectroscopy of multi-level OH stretching coherences in hydrogen bonds in: Ultrafast Phenomena XIV, T. Kobayashi, T. Okada, T. Kobayashi, K. A. Nelson, S. D. Silvestri eds. (Springer Verlag Berlin 2005) pp. 407-409   Download PDF/PS-File or URL: C1-P-2004.12 HHD04 C1-P-2004.2  K. Heyne, N. Huse, J. Dreyer, E. T. J. Nibbering, T. Elsaesser, S. Mukamel Coherent low-frequency motions of hydrogen bonded acetic acid dimers in the liquid phase J. Chem. Phys. 121 (2004) 902-913 Download PDF/PS-File or URL: C1-P-2004.2   HHD03 C1-P-2002.17 N. Huse, K. Heyne, J. Dreyer, E. T. J. Nibbering, T. Elsaesser Vibrational multi-level quantum coherence due to anharmonic couplings in intermolecular hydrogen bonds Phys. Rev. Lett. 91 (2003) 197401/1-4 Download PDF/PS-File or URL: C1-P-2002.17

Publications on ab initio simulations of nonlinear response

DMMb03 C1-P-2003.03 J. Dreyer, A. M. Moran and S. Mukamel Tensor components in three pulse vibrational echoes of a rigid dipeptide Bull. Korean Chem. Soc. 24 (2003) 1091-6 Download PDF/PS-File or URL: C1-P-2003.03   DMM03a C1-P-2003.01 J. Dreyer, A. M. Moran and S. Mukamel  Coherent three-pulse spectroscopy of coupled vibrations in a rigid dipeptide: Density functional theory simulations J. Phys. Chem. B 107 (2003) 5967-5985 Download PDF/PS-File or URL: C1-P-2003.01   MDM03b C1-P-2002.20 A. A. Moran, S.-M. Park, J. Dreyer and S. Mukamel  Linear and nonlinear infrared signatures of local ?- and 310-helical structures in alanine polypeptides J. Chem. Phys 118 (2003) 3651-3659 Download PDF/PS-File or URL: C1-P-2002.20   MDM03a C1-P-2002.19  A. A. Moran, J. Dreyer and S. Mukamel  Ab initio simulation of the two-dimensional vibrational spectrum of dicarbonylacetylacetonato rhodium(I) J. Chem. Phys 118 (2003) 1347-1355 Download PDF/PS-File or URL: C1-P-2002.19

Publications on excited-state structures and intramolecular charge transfer

NDr01 C1-P-2000.13 E. T. J. Nibbering and J. Dreyer Femtosecond chemical events of intramolecular charge transfer and intermolecular hydrogen bond breaking after electronic excitation: structural dynamics in the condensed phase in Femtochemistry, F. C. de Schryver, S. de Feyter, and G. Schweitzer, Eds., (Wiley-VCH, Weinheim, Germany, 2001) pp. 345-66   DKu00 C1-P-2000.01 A. Kummrow, J. Dreyer, C. Chudoba, J. Stenger, E. T. J. Nibbering and T. Elsaesser Ultrafast charge transfer studied by femtosecond IR-spectroscopy and ab initio calculations J. Chin. Chem. Soc. 47 (2000), 721-728 Download PDF/PS-File or URL: C1-P-2000.01   DKu00 C1-P-1999.07 J. Dreyer and A. Kummrow  Shedding light on excited state structures by theoretical analysis of femtosecond transient infrared spectra: Intramolecular charge transfer in 4-(dimethylamino) benzonitrile J. Am. Chem. Soc. 122 (2000) 2577-2585 Download PDF/PS-File or URL: C1-P-1999.07   CKD99 C1-P-1999.02 C. Chudoba, A. Kummrow, J. Dreyer, J. Stenger, E. T. J. Nibbering, T. Elsaesser and K. Zachariasse  Excited state structure of 4-dimethylamino-benzonitrile studied by femtosecond mid-infrared spectroscopy and ab-initio calculations Chem. Phys. Lett. 309 (1999) 357-363 Download PDF/PS-File or URL: C1-P-1999.02