What is LBHB (Low Barrier Hydrogen Bonding) ? 分子性結晶における水素ダイナミクスと同位体効果の起源解明 Yokohama City Univ. (横浜市立大学) Takayoshi Ishimoto (石元孝佳) and Masanori Tachikawa (立川仁典) Nuclear quantum effect on H 3 O 2 - 185 K k-H -D heating cool- ing c (10 -3 emu/mol) T (K) Magnetic susceptibility [2] X-ray structure [2] H D H D D D k-H k-D High temp. Low temp. d OO =2.435 d OH =1.275 d OO =2.501 d OH =1.265 d OO =2.486 d OH =1.233 d OO =2.501 d OH =1.017 center center center off-center • Hamiltonian for Multi-Component system H Ù (e+p) =- 1 2 Ñ 2 i i=1 N å + 1 r ij - Z A r iA A=1 M å i=1 N å j>i N å i=1 N å - 1 2m a Ñ 2 a - 1 r ia + Z A r aA A=1 M å a=1 L å a=1 L å i=1 N å a=1 L å + 1 r ab b>a L å a=1 L å ↑ConvenƟonal DFT ↑Quantum nuclei (Electron: N, Classical nuclei: M, Quantum nuclei: L) ・ Kohn-Sham (KS) eq. for MC_DFT , f p (KS) = h p + J p - J e e M å p N å f e (KS) = h e + J e - J p p M å + V XC(e-e) e N å Electron Quantum nuclei f e, p (KS) f i = e i e, p f i e, p KS operator for MC_DFT Nuclear quantum effect on H 3 (Cat-EDT-TTF) 2 Comparison of the potential energy curves Purely organic single-component conductor composed of only κ-H(D) has recently developed. 3/2 k B T [kcal/mol] 270K 50K 185K 0.15 0.81 0.55 The barrier height of 0.55 kcal/mol corresponds to the thermal energy at 185 K. 1 layer X H-bond intra unit X X X=H:k-Η Χ=D:k-D H 3 (Cat-EDT-TTF) 2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 ΔE (kcal/mol) k OH (Å) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 ΔE (kcal/mol) d OH (Å) 1.31 0.55 conv. DFT 0.42 MC_DFT provides single-well effective PEC for k-H. O1 R O1H R O2H O2 H δ OH = R O1H – R O2H The localization of the deuteron on off-center can be the trigger of the phase transition. MC_DFT provides double-well effective PEC for k-D with the barrier height of 0.55 kcal/mol, which corresponds to the thermal energy at 185 K. MC_DFT κ-D κ-H Conventional DFT provides double-well potential energy curves both for k-H and k-D. • κ-Η(D) has intra-unit hydrogen bond • Molecular arrangement formed “κ-type” Geometry Physical Property • κ-Η has lowest electrical resistivity at room temp. in purely organic single-component conductor. • κ-D has specific temperature dependence in electric resistivity and magnetic susceptibility. The phase transition is found only for κ-D. Nuclear quantum effect decreases the proton-transfer barrier to locate the proton on the center of the H-bond, without dependence on the temperature. ab initio MC_DFT Nuclear quantum effect on PYP Photoactive Yellow Protein (PYP) R OH (Tyr42): 1.02 Å R OH (Glu46): 1.21 Å (para-coumaric acid; chromophore of PYP) H-bonds in PYP LBHB Neutron crystallography demonstrated the formation of LBHB in PYP, which was assumed to play the important role in photosencing process.[4] 1.00 1.05 1.10 1.15 1.20 1.25 gas ONIOM ONIOM/PCM exptl.[4] DA PA DA PA DA PA ■ OH bond lengths of Glu46 R OH [Å] Conv. DFT DD HH HD DH MC_DFT Arg52 H H H H Z Z = H (PA) or null (DA) ab initio PIMD The significant elongation of OH bond is possible when Arg52 is deprotonated. –(N )-body quantum Potential V R R V M P H N N I I I : , 2 ˆ ˆ 0 1 0 1 2 + = å = ・Marx and Parrinello (1994) ・Cheng, Barnett, and Landman (1995) ・Schulte, Bohm, and Ramirez (1996) • Kitamura, Tsuneyuki, Ogitsu, and Miyake (2000) eff N I P I I I P P P H H V dR dR dR e Tr e Tr Z - = = = - - exp lim 1 ) ( ) 2 ( ) 1 ( / ˆ ˆ 2 1 ) ( ) ( 1 0 2 ) 1 ( ) ( 1 , 1 ) ( 2 = + - = åå = + = P M R R V P R R V I I P s s N s s I s I N I I eff κ κ –(N × P )-body classical •Potential: ab initio MO Path integral for nucleus Ab initio MO for electron Full quantum treatment !! ← Partition function •M. Shiga, M. Tachikawa, and S. Miura, J. Chem. Phys. 115, 9149 (2001). •M. Tachikawa and M. Shiga, J. Am. Chem. Soc. 127, 11908 (2005). N(=2) P(=8) [1] G. A. Jefferey, An Introduction to Hydrogen Bonding, (Oxford University Press 1997). Weak Medium Strong Geometric Isotope Effect (R XA ) HB Strength (kcal/mol) < 4 4 - 15 C-H……O O-H….O F-H-F - O-H…O - 15 - 40 Example (X-HA) Longer Shorter Longer LBHB (Ionic HB) ?? •HB ferroelectric materials The Tc increases (more than 100K) by deuteration! Tc(H) = -- Tc(D) = 85K Tc(H) = 371K Tc(D) = 516K •H 3 (Cat-EDT-TTF) 2 The phase transition is found only for κ-D •Zundel structure of H 3 O 2 - Hydroxyl ion transfer in aqueous solution DE=0.2 kcal/mol (Low barrier height) Where is LBHB? The formation of LBHB is found in PYP by neutron crystallography •PYP (Photo Yellow Protein) ・2D distribution with respect to d OH* and R OO [3] -0.6 -1.2 1.2 0.6 0.0 2.2 2.5 2.8 d OH* (Å) ROO (H) = 2.484 (Å) ROO (T) = 2.477 (Å) ROO (Å) ROO (H) = 2.529 (Å) ROO (T) = 2.551 (Å) -0.6 -1.2 1.2 0.6 0.0 50 K 600 K 2.2 2.5 2.8 H 3 O 2 - T 3 O 2 - • At 50K, average OO bond length of T 3 O 2 - is shorter than that of H 3 O 2 - due to the anharmonicity of the potential, which is a similar result of QMC. •At 600K, average OO bond length of T 3 O 2 - is longer than that of H 3 O 2 - , which is a similar result of our previous PIMD. d OH* (Å) 2.2 2.5 2.8 2.2 2.5 2.8 ROO (Å) r 1 r 2 d OH* = r 1 -r 2 ROO •HB patterns by Jefferey [1] Abstract Nuclear Quantum Effect (NQE), such as zero-point vibrational energy, tunneling, and its H/D isotope effect, is quite important in various systems from small molecules to material or biochemical complex species. Especially, in the case of “Low Barrier Hydrogen Bonding (LBHB) systems”, NQE of proton (or deuteron) is indispensable. To elucidate such hydrogen-functional mechanism, we will develop some ab initio approaches for multi-component systems including both electrons and nuclei quantum-mechanically: (I) Multi-component density functional theory (MC_DFT) and (II) ab initio path integral molecular dynamics (PIMD) methods. improvement ・Muoniated acetone radical (Mu-ACE) Our HFCC using PIMD qualitatively reproduced experimental HFCC. [1] T. Isono, H. Kamo, A. Ueda, K. Takahashi, A. Nakao, R. Kumai, H. Nakao, K. Kobayashi, Y. Murakami and H. Mori, Nat. Commun. 2013, 4, 1344 [2] A. Ueda, S. Yamada, T. Isono, H. Kamo, A.Nakao, R. Kumai, H. Nakao, Y. Murakami, . Yamamoto, Y. Nishio and Hatsumi Mori, J. Am. Chem. Soc. 2014, 136, 12184–12192 [3] T. Udagawa, M. Tachikawa, J. Chem. Phys., 2006, 125, 244105 [4] S. Yamaguchi, H. Kamikubo, et al., Proc. Natl. Acad. Sci., 106, 440 (2009). [5] R. M. Macrae et al., Physica B, 326 81 (2003). [5] jh200004-NAH