Report on a visit to Institut für Optik und Atomare Physik, Technische Universität Berlin through the JSPS Core to Core Program

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1 Report on a visit to Institut für Optik und Atomare Physik, Technische Universität Berlin through the JSPS Core to Core Program Hirokazu Sone Department of Electronic Chemistry, The Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology As part of the JSPS Core to Core program, I studied in Prof. Dr. Otto Dopfer s research group in Institut für Optik und Atomare Physik Technische Universität Berlin for two weeks, from November 1 th to November 14 th, This is report of my stay. Research (a) Aim of this collaboration I am investigating conformational structures of noradrenaline (Fig.1), which is one of typical catecholamine neurotransmitters, with interested in α molecular recognition process through the neurotransmission by using laser β γ desorption supersonic jet laser spectroscopies. To determine the structure of noradrenaline, IR spectroscopy is applied. The IR spectroscopy is useful to determine the geometries of hydrogen bond formation, however, delicate conformational structure, for example, orientations of OH group, are difficult to be determined. Spectral signatures of such subtle structural differences are often found in electronic spectra. Therefore, if we can compare the observed Fig.1 Structure of electronic spectra with theoretical ones, we will obtain more detailed and noradrenaline precise structural information. To simulate the electronic spectra, not only the optimized structures of ground and excited states, but also Franck-Condon (FC) factors, which is square absolute value of overlap integral of vibrational wave functions of ground and excited states, are necessary. Generally, the structural optimization of the electronically excited states is not easy work, however, it has become possible by TURBOMOLE,[1] which is a commercial software for quantum chemical calculations. In our group, the TURBOMOLE has been used for calculations of excited state potential energy surfaces. On the other hand, FC simulation was not possible because such optional calculation is not built in the TURBOMOLE. Recently, a free software, PGOPHER,[2] to calculate the FC factor was developed. In Prof. Dopfer group, simulations of the electronic spectra are carried out by combining TURBOMOLE and the FC simulator, and advantage of this method is demonstrated. Therefore, I decided to learn how to simulate the electronic spectra in this collaboration research in order to utilize it for the structural assignments of noradrenaline.

2 (b) Calculation procedure As mentioned in the introduction, to simulate the electronic spectra, we must obtain the optimized structures and vibrational frequencies and wave functions of electronically ground and excited states at first. In TURBOMOLE, several methods are available for such calculations. In this collaboration study, we used 2 methods, density functional theory (DFT) method and coupled cluster method. The latter one is much more expensive than the former. The accuracy of the calculations will be discussed later. The aim of this collaboration is to learn how to use the FC simulator, so the details of how to use TURBOMOLE is not described in this report. About the details of TURBOMOLE are described elsewhere.[3] Hereafter, the procedure of the simulation of the electronic spectra is overviewed. 1. Calculating optimized structure and its vibrational frequencies of ground state by using Jobex and Numforce script built in TURBOMOLE. 2. Calculating optimized structure and its vibrational frequencies of excited state with outputted coordinate of ground state. Optimized structure and vibrational frequencies are outputted into aoforce.out file. In the next step, we can simulate the FC factors by using PGOPHER with the output files of TURBOMOLE, however, PGOPHER can t import these files directly. PGOPHER can import l-matrix file, for example, Gaussian output file, so aoforce.out files must be converted to such format by using aoforce2g98 script included in TURBOMOLE, which can transform the TURBOMOLE output files to Gaussian format. 3. Typing aoforce2g98 aoforce.out > g98.out, where aoforce.out is a file name of aoforce.out file of ground and excited state, to transform the TURBOMOLE format to l-matrix format. 4. Importing l-matrix file of excited state to PGOPHER by clicking on File Import l-matrix from main menu (Fig. 2). Fig. 2 Import 1-matrix file to PGOPHER Imported data can be checked in View constants as name S0 (Fig. 3). This name is confusing, so this name should be changed.

3 5. Renaming S0 as S1. 6. Checking File Merge and import L-matrix file of ground state by clicking on File Import l-matrix from main menu. In this way, vibrational frequencies and coordinates were imported. To prepare calculation set up, 7. Copy and paste S0 in constants to Fig. 3 Imported file into PGOPHER Lmatriximport Lmatriximport in constants. 8. Clicking Lmatriximport Add new Transition moment in constants (Fig. 4). Then, two popups were shown and chose S1 for Bra and S0 for Ket. After that, <S1 mu S0> was produced in constants. 9. Entering <S1 FCF S0> by right clicking on <S1 mu S0> and selecting Add new Multidimensional FCF. 10. Right Clicking on Dushinsky matrix from <S1 mu S0> produced new window and check Calculate to calculate displacements between excited state and ground state (Fig. 5). Fig. 4 Calculation setup Preparation of simulating FC factor was almost completed. But, here if simulate spectrum button from main window was clicked, simulation would be started and stopped due to the overflow, because vmax which is maximum vibrational quantum number for selected mode is too large at default setting. Thus, Fig. 5 Dushinsky matrix 11. Changing vmax of all modes to Clicking on simulate spectrum button. In this condition, only 0-0 transition is calculated. Line windows is produced by right clicking on this band. Position for this band means different of zero point Fig. 6 Reset vmax of each mode

4 energy between excited and ground state. Band assignment is described at the most right side in Line windows (Fig. 7). 13. Entering the different of zero point energy for S1 origin in constants in order to set relative wavenumber from 0-0 band. 14. Entering some number to vmax of a mode of excited state one-by-one in order to examine that how much this band gives intensity. Fig. 7 Calculated 0-0 transition If vmax is set two or more, overtone transitions are also calculated. It is necessary for simulating combination transitions to set vmax at least two mode. In this simulation, vmax is chosen as mode1=3, mode2=2, mode3=1, mode4=2, mode5=1, mode6=1, mode7=1, mode8=1, mode9=1.

5 (c) Results and Discussion Fig.2a shows resonance enhanced multi-photon ionization (REMPI) spectra, i.e. electronic spectrum, of noradrenaline. From our experimental results, it was found that noradrenaline has 3 conformers in gas phase. In this collaboration study, we simulated the electronic spectrum of the main conformer only. Thus, to compare the simulated spectrum with the observed one, the electronic transitions of the main conformer are painted. Horizontal axis represents relative wavenumber, and 0 cm -1 corresponds to 0-0 transition of the main conformer. Tentative assignments of progressions are also shown in the figure. The frequency of the lowest energy band observed in the spectrum is cm -1, which is denoted by mode 1. A band observed at cm -1 is assigned to 2 quanta of mode 1. Other bands are assigned to mode 2 (59 cm -1 ), mode 3 (117 cm -1 ), mode 4 (135 cm -1 ), mode 5 (149 cm -1 ) and combination of them and mode 1, which are listed in Table I. The most intensity band is assigned to 4 1. Spectral feature of this spectrum is that almost no bands are observed at higher energy region than 4 1 (135 cm -1 ). Such spectral pattern is not normal. This unusual pattern may be explained by FC factor or some excited state dynamics, which will be discussed later. Calculated vibrational frequencies below 300 cm -1 are shown in Table II and Table III with assignments. Vibrational frequencies calculated by TD-B3LYP are higher than the corresponding frequencies by CC2. The simulated spectra of CC2 and B3LYP/TD-B3LYP are shown in Fig. 8b and 8c. As can be seen in the figure, the simulated spectrum by CC2 level shows a quite good agreement with experimental spectrum in below 140 cm -1 region. In this simulation, the most intense band is predicted to 138 cm -1, however, in higher energy region than this band, a lot of intense bands are predicted. This disagreement suggests a possibility of opening some non-radiative channels, such like internal conversion to S 0 state or intersystem crossing, at higher energy region than 140 cm -1. To confirm the excited state dynamics, the potential energy surface should be calculated by TURBOMOLE, which is a future issue. On the other hand, the simulated spectrum of B3LYP/TD-B3LYP level looks not to reproduce the experimental one at a glance. However, the FC pattern is similar to that by CC2 calculation. Difference point from CC2 is frequencies. Actually, by linear scaling, this spectrum becomes to give a good agreement with experimental spectra (Fig 8d). Because B3LYP/TD-B3LYP level calculation is much more economic than CC2 calculation, the B3LYP/TD-B3LYP with linear scaling may be an alternate method for the expensive CC2 calculation, which will be important for calculations of larger system. How to determine the scaling factor is a future issue. (d) Future work Through this work, it was found that FC simulation could be powerful tool to assign structure from electronic spectra. In order to complete the conformational assignment of noradrenaline in gas

6 phase, the FC factor of other conformations should be calculated, which is now in progress. Fig.8 Experimental and calculated spectra of noradrenaline, a) REMPI spectrum, b) FC simulation by CC2 and c) FC simulation by B3LYP/TD-B3LYP. d) FC simulation by B3LYP/TD-B3LYP scaled by Horizontal axis is relative wavenumber from 0-0 transition of main conformer.

7 Summary I accomplished my objective that is to understand how to calculate the FC simulation. However, I regret that I could not communicate with students of Prof. Dopfer laboratory so much, because of lack of ability of English conversation. Needless to say, all students are German and are not native English speaker, thus the situation is not so different from me. Probably, the stomach for having a communication with them is matter, and I did not have so much, which is necessary to be seriously regretted. If I have the similar chance, I want to have conversations positively. Acknowledgements I would like to express my deep appreciation to Dr. Alexander Patzer in Institut für Optik und Atomare Physik Technische Universität Berlin who gave me a lecture that how to simulate the FC factor and I thank Dr. Shun-ichi Ishiuchi who supported me during staying in Berlin, and Prof. Otto Dopfer for his kindness and Prof. M. Fujii in Tokyo Institute of Technology and all the staff who assisted with this program. Table I Calculated and observed frequencies (cm -1 ) and assignments. B3LYP/TD-DFT CC2 Experimental frequency assignment frequency assignment frequency assignment N.A N.A

8 Table II Calculated vibrational frequencies by RI-CC2 below 9 mode mode S0 S1 assignments torsion(β-γ) α-β-γ bending(out-of-plane) torsion(α-β) β-o-h bending(out-of-plane) α-β-γ bending(out-of-plane) H-N-H bending(in-plane) C ring -O free -H bending(out-of-plane) C ring -O free -H bending(in-plane) H-N-H bending(out-of-plane) Table III Calculated vibrational frequencies by B3LYP / TD-B3LYP below 9 mode mode S0 S1 assignments torsion(β-γ) α-β-γ bending(out-of-plane) torsion(α-β) β-o-h bending(out-of-plane) α-β-γ bending(out-of-plane) H-N-H bending(in-plane) C ring -O free -H bending(out-of-plane) C ring -O free -H bending(in-plane) H-N-H bending(out-of-plane) References [1] TURBOMOLE V , a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, , TURBOMOLE GmbH, since 2007; available from [2] Western, C. M. A Program for Simulating Rotational Structure, University of Bristol, [3]