Today’
Today’s talk1

1. Introduction of Multi-Component (MC) method

量子多成分系分子理論の深化と物質デザインへの展開

2. Positronic compound:(B )M C _QM C(A )M C _M O

2.1. MC_MO and MC_QMC methods(D)M C _DFT(C ) A b initio
P IM D2.2. Positronic compounds of nitrile species
Y. Kita, R. Maezono, M. Tachikawa, M. Towler, and R. J. Needs, J. Chem. Phys. 131, 134310 (2009).
M. Tachikawa, Y. Kita, and R. J. Buenker, Phys. Chem. Chem. Phys., 13, 2701 (2011).

「コンピューティクスによる物質デザイン：複合相関と非平衡ダイナミクス」
平成23年度第１回研究会
於 東京大学工学部6号館セミナー室A/D, on 7-8,Oct. 2011

3. Low barrier H-bonding systems:
3.1. Path Integral method
3.2. H/D isotope effect for H3O2- among 50K – 600K
M. Tachikawa and M. Shiga, J. Am. Chem. Soc. 127, 11908-11909 (2005).
K. Suzuki, M. Shiga, and M. Tachikawa, J. Chem. Phys. 129, 144310 (2008).

研究代表者： 立川 仁典
連携研究者： 北幸海(横浜市立大学大学院 生命ナノ)1. Introduction•MultiMulti-Component (MC) system• Electron & Proton– Hydrogen bonding– Proton transfer• Electron & Positron– Positronic compound– PET (Positron Emission Tomography)

3.3. Double proton transfers in Porphycene at 300K
T. Yoshikawa, S. Sugawara, T. Takayanagi, M. Shiga, and M. Tachikawa,Chem. Phys. Lett. 496, 14 (2010).

4. Conclusion

34

2. Introduction: Positron
Positron (e+):

・A positron is an antiparticle of an electron (e-)(charge= +1, mass= 1, spin= 1/2)

for Cancer diagnosis (http://www.shinyokohama.jp/)• However … in the conventional firstfirst-principles calculation,

nuclear quantum effect can not be taken into account directly.

How can we combine quantum effect of both electrons and nuclei?
•MultiMulti-Component (MC) theory
Non-BO(B)MC-QMC(D)MC-DFTGAMESS
Gaussian(C) Ab initio(A)MC-MO
PIMD
BO・A positron was found by C.D.Anderson in 1932.

Application:・Material science:
Band structure and lattice defect ofa metal and semiconductor
・Medical science:
Cancer diagnosis by PET(Positron Emission Tomography)

SPring-8; the synchrotron radiation
facility in Japan

18F-FDG：

2-fluoro-2-deoxy-D-glucose (C6H11O5F)

However, detailed information is still unclear…

cite: http://www.shinyokohama.jp/

52. Introduction: Positronic compounde+(A )M C _M O

6(D )M C _D FT(C ) A b in itio
P IM D• Total Hamiltonian (N electron、1 positron、M fixed nuclei):

When a positron interacts with atom/molecule, they can forma meta-stable “positronic compound” before pair annihilation.
n×e-(B )M C _Q M C

2.Multi2.Multi-Component MO (MC_MO)
NNi 1i 1 j  i

NH tot   h e ( i )   

X-Nuc.

h e (i )  N11
 h p ( p)  riji 1 r pi

1 2 M ZA
i  ,2A 1 riAh p ( p)  

1 2 M ZAp ,
2A 1 r pA

• Total wavefunction:e+ e-Positronic compound:
Nuc.

[X-; e+]tot  C00 e0 0p  CIJ eI Jp Electronic & Positronic Structure ?
 Stable Geometry ??

life-time: 10-7 ~ 10-10 sec.

(n(n-1)×
1)×e-X

Nuc.

IJ

Electrons:+iPositron : f  p   p  pp

Pair annihilation

5(B )M C _Q M C(A )M C _M Of e ie   ie ie

7(D )M C _D FT(C ) A b in itio
P IM Dppp

Nf e  h e   J i  K i   J ppNpNepi

N pp    p C pp

f p  h p   Ji

i

2. HCN with MC_QMC method(B )M C _Q M C(A )M C _M O

[HCN;e+]e--ee--e+e--Nuc.

e--e--Nuc.

e+-Nuc.

Variational Monte Carlo [VMC] method:•Energy is obtained by using Metropolis sampling.
•Parameters in trial WF can be optimized under variational principles

Diffusion Monte Carlo [DMC] method：•Projection to ground state by using imaginary-time dependent
Schrödinger equation(D )M C _D FT(C ) A b in itio
P IM D

Dr. Kita(B) MC_QMC (Jastrow factor)

f p  h p   J p  K p    J i

 ie    e C e ii

PAHCN= EHCN – E[HCN;e+]Np

f e  h e   J i  K i    J p

Configuration
Interaction

IJ

Trial Wave function ΨT：

NeHartree-FockCIJ eI Jp• Fock equations:

2. Multi Component QMC (MC_QMC)(A) MC_MOe0 0p

DMC

MC_MO(HF) -92.90074 (hartree)[ e-/e+= 6-311++G(2d,2p)/[15s15p6d2f] ]VMC-93.2591(5) [4]DMC-93.39830(8) [4]HF
VMC

Numerical
accurateenergy !

Positron affinity (meV)[4] Y. Kita, R. Maezono, M. Tachikawa, M. Towler,
and R. J. Needs, J. Chem. Phys. 131, 134310 (2009).

HF+2.0
VMC -0.1(9)DMC +37.8(48)2. PAs of nitrile species

2. Experimental PA values !

PAexptl=180 meV

PA=135 meV(4.23D)HCNHCCCN

PA=155 meV(4.36D)

e+CH3CH2CCNPropionitrile

PA(CH3CN)=180 meV•Path Integral procedure– (N )-body quantumNPˆ 2Hˆ   I  V 0  R 1  R N ,I 1

2M I(B )M C _Q M C– (N × P )-body classical  ˆˆZ  Tr eH  Tr eH / P

P

M. Tachikawa, Y. Kita, and R. J. Buenker, Phys. Chem. Chem. Phys., 13, 2701 (2011).

3.1. ab initio PIMD simulation•Path Integral procedure– (N )-body quantumNPˆ 2Hˆ   I  V 0  R 1  R N ,I 1

2M IP1NκVeff   I (RI(s)  RI(s1) )2  V0 R1(s) RN(s) ,Ps1  I 1 2  ˆ

← Partition function2 PκI  M I   

HN(=2)  P(=8)

Figure 2. Schematic illustration of quantum H2 molecule with 8 (P) beads.

ˆZ  Tr eH  Tr eH / POH



PV 0 : PotentialP1NκVeff   I (RI(s)  RI(s1) )2  V0 R1(s) RN(s) ,Ps1  I 1 2Full quantum treatment !!

12(D )M C _D FT(C ) A b in itio
P IM D•Potentialab initio MO← Partition function

N(1)
( 2)
( P)  lim  dRI dRI dRI  exp Veff P
 I 1
(B )M C _Q M C(A )M C _M O・Marx and Parrinello (1994)
・Cheng, Barnett, and Landman (1995)
・Schulte, Bohm, and Ramirez (1996)• Kitamura, Tsuneyuki, Ogitsu, and Miyake(2000)– (N × P )-body classical

N(1)
( 2)
( P)  lim  dRI dRI dRI  exp Veff P I 1N=211(D )M C _D FT(C ) A b in itio
P IM D・Marx and Parrinello (1994)
・Cheng, Barnett, and Landman (1995)
・Schulte, Bohm, and Ramirez (1996)• Kitamura, Tsuneyuki, Ogitsu, and Miyake(2000)

V 0 : Potential(Private communication)

The PA values are strongly correlated with the dipole moments.
9(A )M C _M O

PAexptl=235 meV

Positron (e+) adsorption

PA (Positron Affinity)=E(X)-E([X;e+])3.1. ab initio PIMD simulation

PA=164 meV(4.35D)CH2CHCN

acetonitrile(D )M C _D FT(C ) A b in itio
P IM D

PA=87 meV(4.12D)

CH3CN

PA=38 meV(3.29D)J. R. Danielson, J. J. Gosselin, and C. M. Surko,Phys. Rev. Lett. 104, 233201 (2010).

(B )M C _Q M C(A )M C _M OO2

 PκI  M I   

H

H

Path integral for nucleus

Ab initio MO for electron•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).

3.1. ab initio PIMD simulation(B )M C _Q M C(D )M C _D FT(C ) A b in itio
P IM D(A )M C _M O

•Nuclear quantum effect in LBHB system

The nuclear quantum effect of proton (or deuteron) is very important inmany fields, especially in the case of Low Barrier Hydrogen Bonding(LBHB) systems with large anharmonicity.

• Hydrogen ion clusters of H2n+1+ • Zundel structure of H3O2H5+

Hydroxyl ion transfer in aqueous solution

H7+

J. Am. Chem. Soc.,
127, 11908-11909 (2005).
J. Chem. Phys.,
129, 144310 (2008).

Comp. Theor. Chem. in press (2011)• Zundel structure of N2H7+

14

3.2. H3O2- anion by ab initio MO•Optimized structure
ROO
r1Quantum
H3O2-(300K)

Quantum
D3O2-(300K)

r2[H2O … OH-]

・ROO= 2.491 Å・r1,r2 = 1.095, 1.398 Å・OH* = 0.303 Å

ChemPhysChem (Communication),9, 383-387 (2008)• Porphycene

Double well potential (74cm-1)→ Shared proton can have
have two positions on either oxygen side

Chem. Phys. Lett. 496, 14 (2010).

•Hydrogen adsorption
on carbon• Gly･(H2O)n clusters
Chem. Phys., 365, 60-68 (2009).

Theor. Chem.Acc., in press (2011)

We focus on the H/D isotope effect for H3O2- by Path Integral (PI) simulation.

3.2. H3O2- anion by PIMD(B )M C _Q M C(A )M C _M O

15(D )M C _D FT(C ) A b in itio
P IM D→ TwoTwo-dimensional distribution for ROO andantianti-symmetric stretching coordinate of OH* = (r1-r2)

3.2. Isotope effect on H3O2-(B )M C _Q M C(A )M C _M O

16(D )M C _D FT(C ) A b in itio
P IM D

Path integral molecular dynamics (PIMD) method (2005)[1] [300K, MP2]

H3O2H3O2D3O2OH*<ROO>=2.498Å>=2.498Å

××

ROO(Å)MEP×

(Å)

(Å)

OH* = r1-r2

D3O2-MEP×

ROO(Å)<ROO>=2.504Å>=2.504Å•The OO distance of D3O2- is slightly longer than that of H3O2-> Ubbelohde effect (lattice expansion of crystals)•Seeing the MEP (minimum energy path), the ROO of double
minima region is longer than that of single minimum region.
[1] M. Tachikawa and M. Shiga, J. Am. Chem. Soc. 127, 11908-11909 (2005).

•H3O2- has a symmetric structure, while D3O2- has an asymmetric structure.
•Average OO bond length of D3O2- isslightly longer than that of H3O2-.

H*ROO

2.498 (Å)

D*

<ROO

2.504 (Å)[1] M. Tachikawa and M. Shiga, J. Am. Chem. Soc. 127, 11908-11909 (2005).

Quantum Monte Carlo (QMC) method (2005)[2] [0K, CCSD(T)]• Both H3O2- and D3O2- species have symmetric structures.
• Average OO bond length of D3O2- isslightly shorter than that of H3O2-.

H*D*ROO

ROO

2.497 (Å)>

2.492 (Å)[2] A. B. McCoy, X. Huang, S. Carter, and J. M. Bowman, J. Chem. Phys., 123, 064317 (2005).

Why have we obtained such different results?
We have carried out PI simulation at various temperatures.

3.2. H3O2- anion by PIMD
2D distribution with respect to OH* and ROO [3]1.2

H3O2-T 3O 2-ROO(H) = 2.484 (Å)

ROO(T) = 2.477 (Å)

r1

0.6
0.0-0.6-1.2

OH* (Å)

600 K 1.2
0.6

2.2

2.52.8

ROO(H) = 2.529 (Å)

2.2

2.5

2.8

-0.6
-1.2
2.5

ROO (Å)

2.8

2.2

2.5

ROO (Å)2.56• At 50K, average OO bondlength of T3O2- is shorter thanthat of H3O2- due to theanharmonicity of the potential,
which is a similar result ofQMC [2].

Fig. OO stretching modeby harmonic approximation ‡0->1 excitation Temperature(cm-1)
(K)

2.52
2.50

2.46

0

100

200300400

19401

T 3O 2 -245343

500

600

Temperature (K)Potential surface of Porphycene molecule0.0

4.4464279

3.3. Porphycene by PIMD

● trans, ■ cis× TS, ＋ SS

1.1

323

D 3O 2-•The contribution of vibrational excitation energies of OO stretching modefor T3O2- and D3O2- are smaller than that for H3O2-, which is very important.
•Coupling of ROO and OH* is indispensable.

PM6-SRP(kcal/mol)

4.4

H3O2-

‡ CCSD( T ) / aug-cc-pVTZ

Fig. 7. Temperature dependence of ROO .

Double proton transfer in Porphycene molecule

5.5

OO
Gauss_view

2.48

2.8

3.3. Porphycene by PIMDHDTClassicaleq

2.54[2] A. B. McCoy, X. Huang, S. Carter, and J. M. Bowman, J. Chem. Phys., 123, 064317 (2005).
[3] K. Suzuki, M. Shiga, and M. Tachikawa, J. Chem. Phys., 129, 144310 (2008).

0.0

3.2. Temperature dependence of <ROO>

OH* = r1- r2r2

•At 600K, average OO bondlength of T3O2- is longer thanthat of H3O2-,
which is a similar result of ourprevious PIMD [1].

ROO(T) = 2.551 (Å)

0.0

2.2ROO(D )M C _D FT(C ) A b in itio
P IM D R OO  (Å)

OH* (Å)

50 K(B )M C _Q M C(A )M C _M O

concerted pathstepwise path

20

21

3.3. Porphycene by PIMD
Double proton transfer in Porphycene molecule

3.3. Application (near future)
Hydrogen storage in nano-space

22

Aqueous solution of NMA(methylacetamide, CH3-NH-CO-CH3)
NMA molecule•16 beads, 500,000 steps

PIMD results：
results：
・concerted path (300K)
・cis structure appears (500K)

Hydrogen storage
in Zeolite-Templated Carbon (ZTC)

Low-barrier hydrogen bond inphotoactive yellow protein (PYP)

Classical results：
results：・stepwise path
PIMD

Classical[4] T. Yoshikawa, S. Sugawara, T. Takayanagi, M. Shiga,and M. Tachikawa, Chem. Phys. Lett. 496, 14 (2010).

4. Summary•Development of MultiMulti-Component molecular theory:– Multi component molecular orbital (MC_MO)
from HartreeHartree-Fock (HF) to Configuration Interaction (CI)– Multi component quantum Monte Carlo (MC_QMC)– Ab initio path integral simulation(B )M C _QM C(A )M C _M O(D)M C _DFT(C ) A b initio
P IM D•Application to HH-bonded systems & positronic molecules:molecules:– Positronic nitrile species with MC_QMC and MC_MO•

We have obtained 135 meV as PA(CH3CN), which is 75% of therecent experimental value of 180 meV.

– Low barrier HH-bonded (LBHB) systems with PIMD
•Temperature dependency of the H/D/T isotope effects on H3O2-.

•Double proton transfer in Porphycene molecule.

T.Kyotani, U. Ngashima,
H. Ogawa et al,

S. Yamaguchi, H. Kamikubo, K. Kurihara, R. Kuroki, N. Niimura, N.
Shimizu, Y. Yamazaki, and M. Kataoka, PNAS, 106, 440-444 (2009).