jh200004-NAH

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)

Abstract

Nuclear Quantum Effect (NQE), such as zero-point vibrational energy, tunneling, and its H/D isotope effect, is quite important in various systems fromsmall molecules to material or biochemical complex species. Especially, in the case of “Low Barrier Hydrogen Bonding (LBHB) systems”, NQE of proton (or deuteron) isindispensable. To elucidate such hydrogen-functional mechanism, we will develop some ab initio approaches for multi-component systems including both electrons andnuclei quantum-mechanically: (I) Multi-component density functional theory (MC_DFT) and (II) ab initio path integral molecular dynamics (PIMD) methods.

What is LBHB (Low Barrier Hydrogen Bonding) ?
WeakMediumStrong<44 - 15

15 - 40

C-H……O

O-H….OHB Strength(kcal/mol)
Example(X-HA)

Where is LBHB?

•Zundel structure of H3O2-•HB patterns by Jefferey [1]Hydroxyl ion transfer in aqueous solution•H3(Cat-EDT-TTF)2•PYP (Photo Yellow Protein)

The phase transition isfound only for κ-D

The formation of LBHB is foundin PYP by neutron crystallography

DE=0.2 kcal/mol(Low barrier height)•HB ferroelectric materials（Ionic HB）
O-H…OF-H-F-

LBHB
Longer(RXA)

LongerTc(H) = 371K
Tc(D) = 516K

Shorter？？

[1] G. A. Jefferey, An Introduction to Hydrogen Bonding, (Oxford University Press 1997).

ab initio MC_DFT

ab initio PIMD–(N )-bodyPˆquantumHˆ = å+ V R  R ,2MN01N

V0 : PotentialI  ˆˆZ = Tr e -H = Tr e - H / P← Partition function

N(1)( 2)(P)  lim   dRI dRI  dRI  exp- Veff P 
 I =1
P1
 N κI (s )Veff = å å (RI - RI( s+1) )2 + V0 R1(s ) RN(s ) ,Ps =1  I =1 2
NN NL11 N M Z
1 2 N L 1 L M ZA L L 1
H (e+ p) = -å Ñi2 + å å - å å A -åÑa - åå + åå + åå2rr
2m
i=1i=1 j>i ij
i=1 A=1 iAaa=1i=1 a=1 ria
a=1 A=1 raA
a=1 b>a rabÙ

N(=2)  P(=8)

 PκI = M I   

↑Conven onal DFT

2Ab initio MO for electron

Nuclear quantum effect on H3O2dOH* (Å)

H3O2-1.2

ROO

ROO(T) = 2.477 (Å)

0.6
0.0

-0.6
-1.2

dOH* (Å)

600 K 1.2
0.6

2.2

2.5

2.8

2.2

ROO(H) = 2.529 (Å)

2.5

2.8

ROO(T) = 2.551 (Å)

0.0-0.6
-1.2
2.2

2.5

ROO (Å)r1T3O2-(H) = 2.484 (Å)

2.8

2.2

2.52.8ROO (Å)

Electrone, p e, pfe,(KS)p f i = e i fi

dOH* = r1- r2r2

X

X=H：k-Η
Χ=D：k-D

1 layer•At 600K, average OO bond length ofT3O2- is longer than that of H3O2-,
which is a similar result of our previous
PIMD.

dOO=2.435
dOH=1.275

k-D

Our HFCC using PIMD qualitatively reproduced experimental HFCC.

H

dOO=2.486
dOH=1.233

ΔE (kcal/mol)

MC_DFT
HDConv. DFT

Z = H (PA) or null (DA)ZROH (Tyr42): 1.02 ÅROH(Glu46): 1.21 Å1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

[Å]

MC_DFT

1.10
1.05
DAgasPADAPAONIOMDAPA

ONIOM/PCM

k-H

pe

-0.10

0.00

0.10

exptl.[4]The significant elongationof OH bond is possible when
Arg52 is deprotonated.

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

0.20

0.30

0.2

0.3

1.31

κ-D
0.55

-0.3

-0.2

-0.1

270K
3/2 kBT 0.81
[kcal/mol]

0dOH (Å)

0.1

185K

heating -D

Doff-centerD

 Purely organic single-component conductor
composed of only κ-H(D) has recently developed.
 The phase transition is found only for κ-D.
Geometry• κ-Η(D) has intra-unit hydrogen bond
• Molecular arrangement formed “κ-type”
Physical Property• κ-Η has lowest electrical resistivity at room
temp. in purely organic single-componentconductor.
• κ-D has specific temperature dependence inelectric resistivity and magnetic susceptibility.

δOH = RO1H – RO2H

O1

HO2
RO2H

 Conventional DFT provides double-well potential energy curves both fork-H and k-D.

0.42-0.20

185 KcoolingRO1HkOH (Å)

1.15

1.00

dOO=2.501
dOH=1.017

κ-H

1.20

H

(para-coumaric acid;chromophore of PYP)

centerD

dOO=2.501
dOH=1.265-0.30

ΔE (kcal/mol)

H

H

LBHB

■ OH bond lengths of Glu46

ROH

H

Arg52

centerComparison of the potential energy curves

Nuclear quantum effect on PYP

H-bonds in PYP

M

T (K)

Low temp.

centerH

conv. DFTDD

H-bondintra unit

D[5]HHNf p(KS) = hp + å J p - å J e

Magnetic susceptibility[2]X

improvement

DHp

Quantum nuclei

X-ray structure[2]

k-H

1.25e

H3(Cat-EDT-TTF)2High temp.

・Muoniated acetone radical (Mu-ACE) Neutron crystallographydemonstrated the formation ofLBHB in PYP, which wasassumed to play the importantrole in photosencing process.[4]MX• At 50K, average OO bond length ofT3O2- is shorter than that of H3O2- due tothe anharmonicity of the potential,
which is a similar result of QMC.

Photoactive Yellow Protein (PYP)

Nfe(KS) = he + å J e - å J p + VXC(e-e) ,Nuclear quantum effect on H3(Cat-EDT-TTF)2

ROO・2D distribution with respect to dOH* and ROO [3]50 K↑Quantum nuclei

・ Kohn-Sham (KS) eq. for MC_DFT KS operator for MC_DFT•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).

Path integral for nucleus

Full quantum
treatment !!

(Electron: N, Classical nuclei: M, Quantum nuclei: L)•Potential: ab initio MO–(N × P )-body classicalP• Hamiltonian for Multi-Component system

・Marx and Parrinello (1994)
・Cheng, Barnett, and Landman (1995)
・Schulte, Bohm, and Ramirez (1996)• Kitamura, Tsuneyuki, Ogitsu, and Miyake (2000)

2I

I =1Tc(H) = -Tc(D) = 85K

The Tc increases (more than100K) by deuteration!

c (10-3 emu/mol)Geometric
Isotope Effect

50K

0.55 0.15

 MC_DFT provides single-well effective PEC for k-H.
 Nuclear quantum effect decreases the proton-transfer barrier to locate
the proton on the center of the H-bond, without dependence on thetemperature.
 MC_DFT provides double-well effective PEC for k-D with the barrier heightof 0.55 kcal/mol, which corresponds to the thermal energy at 185 K.
 The barrier height of 0.55 kcal/mol corresponds to the thermal energy at185 K.

The localization of the deuteron on off-center can be
the trigger of the phase transition.

[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).