jh210006-NAH

大規模電子状態シミュレーションを用いた結晶系における水素量子効果の研究

Yokohama City Univ. （横浜市立大学）
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) ?
•Zundel structure of H3O2-•HB patterns by Jefferey [1]WeakMedium

Strong<44 - 15

15 - 40

C-H……O

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

Hydroxyl ion transfer in aqueous solution

Where is LBHB?

•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

Geometric
Isotope EffectLonger(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  ˆˆ

Z = 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 N
L
11 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 H3O2OH* (Å)

1.2

H3O2-T3O2-ROO(H) = 2.484 (Å)

ROO(T) = 2.477 (Å)

0.6
0.0

-0.6-1.2

OH* (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)

2.8

2.2

2.5

2.8

ROO (Å)Electrone, p e, pfe,(KS)p f i = e i fiNM

epfe(KS) = he + å J e - å J p + VXC(e-e) ,Quantum nuclei

NMpef p(KS) = hp + å J p - å J e

CPLB method
ROO

・2D distribution with respect to OH* 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 quantumtreatment !!

(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!

r1

OH* = r1- r2r2

• 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 previous
PIMD.

Combined Plane wave and Localized Basis-sets method is using MC_DFT
at the cluster model around H/D.
ECPLB, surface = EPlane wave, surface− EPlane wave, cluster+ EMC_DFT, cluster

Plane wave, cluster

Plane wave, surface• H/D atom adsorption on Pd(111) surface

・Muoniated acetone radical (Mu-ACE)

improvement

rH-surface=0.800 Å >rD-surface=0.785 ÅEads(H)=2.683 eV <Eads(D)=2.698 eV

MC_DFT, cluster

Adsorption distance rH-surface is longer than of rD-surface.
Although no direct observations of this geometricaldifference surface have been reported, this result
expects due to the anharmonicity of the potential.
Adsorption energy Eads(H) is lower than Eads(D), which
result corresponds to the experimentally trend.[6][5]Our HFCC using PIMD qualitatively reproduced experimental HFCC.

•CH4/CD4 molecular adsorption on Rh(111) surface

Nuclear quantum effect on PYP

H-bonds in PYP

HHDHHHDD

HD

Conv. DFT

1.20
1.15
1.10
1.05

HArg52Z = H (PA) or null (DA)H

LBHB

MC_DFT

1.25

ROH Neutron crystallographydemonstrated the formation ofLBHB in PYP, which wasassumed to play the importantrole in photosencing process.[4]rD-C=1.113 Å>
rH-surface =2.071 Å < rD-surface=2.107 ÅEads(CH4)=0.399 eV > Eads(CD4)=0.330 eV
rH-C=1.119 Å■ OH bond lengths of Glu46[Å]

Photoactive Yellow Protein (PYP)

Z(para-coumaric acid;
chromophore of PYP)

ROH (Tyr42): 1.02 Å
ROH(Glu46): 1.21 Å

1.00

DAgasPADAPAONIOMDAPA

ONIOM/PCM

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

Adsorption energy Eads(CH4) is higher than Eads(CD4)due to the anharmonicity of the potential, which issimilar trend as observed C6H12/C6D12 adsorption.[7]0.002-0.003 ÅAdsorption distance rH-surface rad(C6H12) > rad(C6D12)
0.084 eVis shorter than rD-surface. AndE (C H ) < Eads(C6D12)
bond length rH-C is longer ads 6 12than rD-C. which is alsosimilar trend as C6H12/C6D12[7]Rh(111)
adsorption.
These results suggest CD4 has a weaker interaction
with the Rh(111) surface than CH4.

Our CPLB method is expected to be an effective tool for analysing H/D on metal surfaces.

[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). [6] Y. Jin, et al., J. Alloys
Compd., 340, 207 (2002). [7] T. Koitaya, et al., J. Chem. Phys., 136, 214705 (2012).