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 H3O2-

185 Kk-H

-D

heating

cool-ing

c (1

0-3

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.

dOO=2.435dOH=1.275

dOO=2.501dOH=1.265

dOO=2.486dOH=1.233

dOO=2.501dOH=1.017

center

center

center

off-center

• Hamiltonian for Multi-Component system

HÙ

(e+p) = -1

2Ñ2i

i=1

N

å + 1rij- ZA

riAA=1

M

åi=1

N

åj>i

N

åi=1

N

å - 12ma

Ñ2a -1

ria+ ZA

raAA=1

M

åa=1

L

åa=1

L

åi=1

N

åa=1

L

å + 1rabb>a

L

åa=1

L

å↑Conven onal DFT ↑Quantum nuclei

(Electron: N, Classical nuclei: M, Quantum nuclei: L)

・ Kohn-Sham (KS) eq. for MC_DFT

, fp(KS) = hp + J p - Je

e

M

åp

N

åfe(KS) = he + Je - Jpp

M

å +VXC(e-e)e

N

åElectron Quantum nuclei

fe, p(KS)fi =ei

e, pfie,p

KS operator for MC_DFT

Nuclear quantum effect on H3(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 kBT [kcal/mol]

270K 50K185K

0.150.81 0.55

The barrier height of 0.55 kcal/mol corresponds to the thermal energy at 185 K.

1 layer

XH-bond intra unit

X

X

X=H：k-ΗΧ=D：k-D

H3(Cat-EDT-TTF)2

0.00.20.40.60.81.01.21.4

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30

ΔE(k

cal/

mol

)

kOH (Å)

0.00.20.40.60.81.01.21.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

ΔE(k

cal/

mol

)

dOH (Å)

1.31

0.55

conv. DFT

0.42MC_DFT provides single-well effective PEC for k-H.

O1

RO1H RO2H

O2HδOH = RO1H – RO2H

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 PYPPhotoactive Yellow Protein (PYP)

ROH (Tyr42): 1.02 ÅROH(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 PADA PA

■ OH bond lengths of Glu46

RO

H

[Å

]

Conv. DFTDDHH HDDH

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 PotentialVRRV

M

PH N

N

I I

I :,2

ˆˆ

0101

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

PIII

P

PPHH

VdRdRdR

eTreTrZ

-

==

=

--

explim1

)()2()1(

/ˆˆ

2

1

)()(10

2)1()(

1

,1

)(2

=

+-=å å=

+

=

P

MRRVP

RRV IIP

s

sN

ssI

sI

N

I

Ieff 　κ

κ

–(N × P )-body classical •Potential: ab initio MO

Path integral for nucleus

Ab initio MO for electronFull 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

(RXA)

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 ShorterLonger

LBHB

（Ionic HB）

？？

•HB ferroelectric materials

The Tc increases (more than 100K) by deuteration!

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

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

•H3(Cat-EDT-TTF)2

The phase transition is found only for κ-D

•Zundel structure of H3O2-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 dOH* and ROO [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

H3O2- T3O2-

• 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.

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

d OH

* (Å

)

2.2 2.5 2.8 2.2 2.5 2.8

ROO (Å)

r1 r2dOH* = r1- r2

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 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.

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