㕘⬎埻柀➇䞼䨞䛂䝁䞁䝢䝳䞊䝔䜱䜽䝇䛻䜘䜛≀㉁䝕䝄䜲䞁䠖」ྜ┦㛵䛸㠀ᖹ⾮䝎䜲䝘䝭䜽䝇䛃2011ᖺ3᭶5᪥䠄ᅵ䠅10:50 – 11:40㻌 ᶡӜབྷᆖᐕᆖ䜘˒ਧ佘63ਧᇔ䝥䝻䝖䞁䞉䝭䝳䞊䜸䞁䛷᥈䜛᪂≀ᛶ䛸㔞Ꮚ䝎䜲䝘䝭䜽䝇◊✲௦⾲⪅ ୰すᐶ䠄኱㜰኱Ꮫ㻌 ᕤ䠅◊✲ศᢸ⪅ ୗྖ㞞❶䠄኱㜰኱Ꮫ䝘䝜䝉䠅ᚋ⸨ⱥ࿴䠄኱㜰኱Ꮫ㻌 ᕤ䠅Markus Wilde(ᮾி኱Ꮫ㻌 ⏕◊䠅
Dino Wilson(኱㜰኱Ꮫ㻌 ᕤ䠅㐃ᦠ◊✲⪅ ⚟㇂ඞஅ(ᮾி኱Ꮫ㻌 ⏕◊)➟஭⚽᫂䠄኱㜰኱Ꮫ㻌 ᕤ䠅Particles in the system

Surface, Subsurface, Bulk, Interface

Solid state physics
Condensed Matter Physics

mass㻌䞉electron㻌

9.10㽢10-31kg

Two kinds of particles㻌㽢 2000䡚200000

䞉nucleus(atom core)ma 㽢1.67㽢10-27 kg
ma : atomic mass46㻌 㻌 㻌78㻌 㻌 㻌PdPt106.42

195.07829㻌 㻌 㻌Cu
63.536

Particles in the system

Surface, Subsurface, Bulk, Interface

electron㻌e-9.1093897㽢10-31kg

1㻌 㻌 㻌
Hydrogen atom,proton㻌 P䠇

HX 1836.14

1.00794

1.672210x10-27kg
Other atom

X 50䡚200

ion core46㻌 㻌 㻌79㻌 㻌 㻌

PdPt

106.42

195.07829㻌 㻌 㻌Cu
63.536

Particles in the system

Surface, Subsurface, Bulk, Interface

electron㻌e-(Anti)Muon 㻌 μ䠇
1.9㽢10-28 kg

9.1093897㽢10-31kg

X 206.7

X 8.882
㻌 P䠇

protonD+H+T+

1.672210x10-27kg

X 50䡚20046㻌 㻌 㻌79㻌 㻌 㻌

Pt
195.078

Pd106.4229㻌 㻌 㻌

Cu63.536

Particles in the system

Surface, Subsurface, Bulk, Interface

electron㻌e-(Anti)Muon 㻌 μ䠇
1.9㽢10-28 kg

9.1093897㽢10-31kg

X 206.7

X 8.882
㻌 P䠇

protonD+H+T+

1.672210x10-27kg

X 50䡚20046㻌 㻌 㻌79㻌 㻌 㻌

Pt
195.078

Pd106.4229㻌 㻌 㻌

Cu63.536≀㉁⎔ቃୗ䛻䛚䛡䜛䝥䝻䝖䞁䞉䝭䝳䞊䜸䞁䛾➨୍ཎ⌮ィ⟬ἲ䛾㛤Ⓨ㻌 䠷୰す㻌 ᐶ䚸Dino Wilson䠹ከయ⣔㔞Ꮚ≧ែィ⟬ᡭἲ䛾㛤Ⓨ 㻌 䠷ᚋ⸨ⱥ࿴䠹㧗ᅽୗ䛻䛚䛡䜛㔠ᒓỈ⣲໬≀䛻䜏䜛Ỉ⣲ຠᯝ 㻌 䠷ୗྖ㞞❶䠹Pd䠄110䠅༢⤖ᬗ⾲㠃䛻䛚䛡䜛Ỉ⣲྾཰䝎䜲䝘䝭䜽䝇䛸ゐ፹཯ᛂᛶ㻌 [Markus Wilde]≀㉁⎔ቃୗ䛻䛚䛡䜛䝥䝻䝖䞁䞉䝭䝳䞊䜸䞁䛾➨୍ཎ⌮ィ⟬ἲ䛾㛤Ⓨ㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ୰す㻌 ᐶ䚸Dino Wilson

Naniwa codes¾ NANIWA is the first principles quantum mechanicalcalculation code for atomic motions near and/or in thematerials. 㻌 㻌䝟䝷䝯䞊䝍䝣䝸䞊䛾⌧ᐇ≀㉁䛾
㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ➨୍ཎ⌮㔞Ꮚ䝅䝭䝳䝺䞊䝅䝵䞁¾ Two kinds of Naniwa codes.
Naniwa-2001 is a quantum mechanical version of thefirst principles molecular dynamics (MD) calculations,for reactions. [Scattering theory]㻌 㻌Naniwa-Static is a nucleus version of the first principlesquantum state calculations.㻌 㻌 㻌 㻌 㻌 㻌Our quantum simulation scheme: Naniwa
Interactions between nucleus is calculated
by DFT based first principle calculations

Potential energy
for nucleus motions: U n (R)Solve the Schrödinger
equation for nucleus
motionWave function for
nucleus motion

Derive thevarious
physicalquantities-Parameters are only
atomic number of elements-No fitting and no artificial procedure

Comparison between our simulation Naniwa-2001
and experimental results

Solve the scattering problem
Transmission㻌 probability
Adsorption, Absorption, desorption…

Rotational energy distributionsof hydrogen molecule desorbing
from Cu(111) surface

with rotational, vibrational excitations

ศᏊᅇ㌿ JศᏊఙ⦰᣺ື ν୪㐍㐠ື 㹩
Our simulation resultssquare䠖 W.A.Dino, et al., PRL  (1997) 286.

Experimental datacircle

䠖H.A.Michelsen et al., J. Chem. Phys. (1993) 8294

No fitting parameters !

Comparison between our simulation Naniwa-2001
and experimental results

Solve the scattering problemTransmission㻌 probability
Adsorption, Absorption, desorption…

Rotational energy
distributions of hydrogenmolecule desorbing fromCu(111) surface

with rotational, vibrational excitations
6D -potential
Energy Surface
V(r,θ,φ,X,Y,Z)

Our simulation resultssquare䠖 W.A.Dino, et al., PRL  (1997) 286.

Experimental datacircle

䠖H.A.Michelsen et al., J. Chem. Phys. (1993) 8294

No fitting parameters !

Comparison between our simulation Naniwa-Staticand experimental results

Calculate the Eigen states
for the atomic motions

3D-potential energy surface :V(x,y,z)Surface-normal vibrationenergy of Hydrogen atomadsorbed on Cu(111) surface
Our simulationresult *135 meVExperimental
data **

129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

ffor EExcited
it d statet t

Electron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci.  (2002) 229.

No fitting parameters !

Comparison between our simulation Naniwa-Staticand experimental results

Calculate the Eigen states
for the atomic motions

Surface-normal vibrationenergy of Hydrogen atom
adsorbed on Cu(111) surface
Our simulation
result *135 meVExperimental
data **

129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

ffor EExcited
it d statet tElectron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci.  (2002) 229.

No fitting parameters !

Surface-normal vibration energy ofHydrogen atom adsorbed on Cu(111)
surfaceOur simulation
result *135 meVExperimental
data **129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

ffor EExcited
it d statet tHarmonic Potential Energy : V(Z)

Comparison between our simulation andexperimental results

normalvibrational excited Wave function

Our simulation results;

Simpleharmonic approximation

Excited state
Ground state
Distance from surface: Z

Electron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci.  (2002) 229.

No fitting parameters !

Hamiltonian§ ! 2 · 2 N nc. § ! 2 · 2¨¨ ¸¸i  ¦ ¨¨ ¸¸ I  V ( r , R)
¦2me ¹
2M I ¹i 1©
I 1©
ne

Hme , M I : masses of electron and nucleus I
ne , N nc. : numbers of electron and nucleus
Interactions
N nc. I 1
Z J Z I e2
 Z I e 2 ne i 1 e 2V (r , R) ¦¦ ¦¦ ¦¦i 1 I 1 ri  RIi 1 j 1 r j  ri
I 1 J 1 RJ  RI
ne N nc.

: atomic number of nucleus Ie : elementary charge Particle position vectors

rr1 , r2 , r3 ,, ri ,rne

R

R1 , R2 , R3 ,, RI ,, RNnc.

3( ne  N nc. )Schrödinger equation

H< (r , R)

E< (r , R)

Born-Oppenheimer approximation< n,Z (r , R) \ n; R (r )  IZ;n ( R)\ n; R (r ) : the n-th electron wave functionin the case of the fixed nucleus position R.

IZ ;n ( R) : the Z-th nucleus motion wave functionin the case of the electron state n.

Equation for electron state:ª ne § ! 2 · 2º¸¸i  V (r , R)» \ n; R (r ) U n ( R) \ n; R (r )«¦ ¨¨ ¬ i 1 © 2me ¹¼䞉䞉䞉㻌 (*)

Equation for nucleus motion:ª N nc. § ! 2 · 2º¸¸ I  U n ( R)» IZ ;n ( R)« ¦ ¨¨ ¬ I 1 © 2M I ¹¼

EZ ,nIZ ;n ( R) 䞉䞉䞉㻌 (**)

rr1 , r2 , r3 ,, ri ,rne

RR1 , R2 , R3 ,, RI ,, RNnc.

Equation for electron state:ª ne § ! 2 · 2º¸¸i  V (r , R)» \ n; R (r ) U n ( R) \ n; R (r )«¦ ¨¨ ¬ i 1 © 2me ¹¼

䞉䞉䞉㻌 (*)

For fixed R, we can obtain the eigen energies, U n (R) ,and eigenstates, \ n;R (r ), with the aid of the conventional
first principles (electron states) calculation.

The eigenenergies, U n (R) , as a function of R can beconsider as the adiabatic potential energy surface fornucleus motion.

Equation for nucleus motion:ª N nc. § ! 2 · 2º¸¸ I  U n ( R)» IZ ;n ( R)« ¦ ¨¨ ¬ I 1 © 2M I ¹¼

EZ ,nIZ ;n ( R)䞉䞉䞉㻌 (**)

The eigen energy, EZ ,n , corresponds to the total energy, E, appearedin the Schrödinger equation for total system: H< (r , R) E< (r , R)

quantum numbers: index of quantum state for nucleus motion: index of quantum state for electron system

Isotope㻌㻌 effects

In generally speaking, one believes thatisotope effects appear only in physical phenomena
and the chemical properties are not changed.
㻌㻌㻌Electron density distribution䠖䠖 U n ,Z (r )< n,Z (r , R) \ n; R (r )  IZ;n ( R) ,U n ,Z (r )³³ \³U2n;Rrr1 , r2 , r3 , , ri ,  rne

2(r )  IZ ;n (R ) G (r  r1 )dRdr
2n;R(r )  IZ ;n (R ) dR

From DFT based ab initio electron state calculation→U n;R ( r )¦Mocc."";R(r )䠆Even in the adiabatic approximation, isotope effects appear in the electron states.

2IZ ;n (R )  broad, delocalized㻌 D+ 㻌 э H + э μ䠇

2Hydrogen isotopes on㻌 Pd(111) surface
㻌 μ, H, D㻌 㻌 㻌 㻌Pd atom㻌 㻌 㻌 㻌(111) surface㻌 㻌 㻌 㻌face center cubic (FCC)㻌 㻌 㻌 㻌
lattice constant:

3.99Å (calc.) ,3.89Å㻌 (exp.)㻌㻌㻌㻌㻌㻌㻌㻌

Adsorbed state of hydrogen atom on Pd(111)
Wave functions of hydrogen motionGround state
on fcc hollow site

Surface normal vibration
excited state
on fcc hollow site

Energy difference (excitaion energy) is 134 meV(Experimental data: 124 meV)H. Conrad, et al, J. Vac. Sci. Technol. A5, 452 (1987).

Localized States on surface & in subsurface@ local potential minimum

fcc hollow

1st OH

2nd TH1㻌 μ㻌 㻌 㻌 H㻌 㻌 㻌 D 㻌 㻌

Eigen energy (eV)-2.0-2.2-2.4

-2.6

-2.8

-3.0

1/9

12㉁㔞

㻌 μ㻌 㻌 㻌 H㻌 㻌 㻌 D 㻌 㻌-2.5

-1.9

1-2.0

Eigen energy (eV)-2.6

21-2.2-2.4
2-2.6-2.8
121-3.0
2-2.8-2.2

1/9

12㉁㔞

㻌μ㻌 㻌 㻌-2.9H㻌

㻌㻌D㻌 μ㻌 㻌 㻌 H㻌 㻌 㻌 D 㻌 㻌

Eigen energy (eV)-2.0㻌 μ㻌 㻌-2.2-2.4-2.6

㻌 H㻌 㻌-2.8-3.0

1/9

12㉁㔞

㻌 μ+ on Pd(111) surface㻌 㻌-1.9

1

Eigen energy (eV)

1+-+-

1fcc

1hcp
-2.2

(Anti) muon㻌㻌 μ䠇
Particle statistics

Fermionic

Mass:㻌 㻌 㻌 㻌 㻌 㻌 mμ105.658369(9) MeV/c2

Electric charge:

eSpin:

1⁄

Mean lifetime :㻌 τ

2.19703(4)×10−6 sec

Antimuon catches an electron, and forms
the hydrogen like atom.
μ+䠇e−Muonium
Its reduced mass and magnetic
moment is different from ahydrogen atom.

2

Isotope of hydrogenmμ 䡚0.113mp
䡚206.7meμ䠇㻌 Antimuon 㻌 -------> positron 㻌 䠇㻌 Antimuon neutrino 㻌 䠇㻌 electron neutrinoLife time:τ

positron emission

Muon spin spectroscopy䠖μSR

Spin:1⁄------->
2

The primary decay mode of a pion is a purely
leptonic decay into a muon and a muon neutrino.
And the muon is 100% spin polarized

Gyromagnetic ratio 䠖135.53 MHz/T

precession movement in
the magnetic moment
sensitive magnetic measurement

μSR 㻌 time spectrum.
e+ detector

e+Fouriertransformation

In the material
Muon plays as the small-mass proton with acommunication function.
We can detect the quantum behaviors ofHydrogen-like particles in material.

K. Shimomura et al., Phys. Rev. Lett. 89 (2002) 255051.

Bulk ZnO

Bulk ZnO௒ᚋ䛾᪉㔪ᚑ᮶ἲ㻌 䞉⾲㠃⣔㻌 㻌 Pd(111)䠗μ䠇䛾ⴭ䛧䛔ྠ఩యຠᯝ䛾ㄪᰝ㻌 㻌 Pd(110)䠗ᐇ㦂䛷ぢฟ䛥䜜䛯᪂䛧䛔྾╔≧ែ䛾ྠᐃ䚸㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 PES䛾ぢ┤䛧䛸䝎䜲䝘䝭䜽䝇䛾ゎᯒ㻌 䞉䝞䝹䜽⣔䚸䠗᪤Ꮡ㻌 μSRᐇ㦂㻌 ZnO㻌 䛷☜ㄆ㻌 㻌 㻌 㻌 㻌 㻌 㻌 →㻌 䝞䝹䜽ෆ㻌 Ỉ⣲䞉䝭䝳䞊䜸䞁䛾≧ែᡭἲ㛤Ⓨ㻌 㻌 㻌 㻌 㻌 㻌 㻌㻌 㻌 䞉㧗㏿໬䝁䞊䝕䞁䜾㻌 㻌 䞉ỗ⏝ᛶ䛾ྥୖ㻌 䞉ከ⢏Ꮚ⣔䜈䛾ᣑᙇ㻌 㻌 㻌ከయ⣔㔞Ꮚ≧ែィ⟬ᡭἲ䛾㛤Ⓨᚋ⸨ⱥ࿴䝥䝻䝖䞁䞉䝭䝳䞊䜸䞁䛷᥈䜛᪂≀ᛶ䛸㔞Ꮚ䝎䜲䝘䝭䜽䝇㻌㻌䞊㻌ከయ⣔㔞Ꮚ≧ែィ⟬ᡭἲ䛾㛤Ⓨ㻌䞊㻌኱㜰኱Ꮫ䞉኱Ꮫ㝔ᕤᏛ◊✲⛉㻌 ⢭ᐦ⛉Ꮫ䞉ᛂ⏝≀⌮Ꮫᑓᨷᚋ⸨ⱥ࿴◊✲༠ຊ㻌 ኱㜰኱Ꮫ䞉኱Ꮫ㝔ᕤᏛ◊✲⛉㻌 ᗈ℩႐ஂ἞䚸ྂᇛோᚿ
2011.0335

ᮏᖺᗘ䛾ྲྀ䜚⤌䜏

Direct Energy Minimization (DEM) methodኚศཎ⌮䜢⏝䛔䛶඲䜶䝛䝹䜼䞊 E*<³ (r1 , r2 ,, rN ) Hˆ <(r1 , r2 ,, rN )d:³ < (r , r ,, r )<(r , r ,, r )d:*12N

12N䛜᭱ᑠ䛸䛺䜛䜘䛖䛻Ἴື㛵ᩘ㻌<㻌 (㻌r1 ,㻌r2㻌,㻌 㻌, r㻌N )㻌 䛾᭦᪂䜢⧞䜚㏉䛩䚹

Path-Integral Renormalization Group (PIRG) method⹫᫬㛫Ⓨᒎ䛾⧞䜚㏉䛧䛻䜘䜚Ἴື㛵ᩘ㻌 <㻌 (㻌r1㻌, r㻌2 ,㻌㻌 ,㻌rN㻌) 㻌 䜢ᇶᗏ≧ែ䜈䛸ᑟ䛟䚹㻌Krylov subspace expansion (KSE) methodἼື㛵ᩘ䛾䜽䝸䝻䝣㒊ศ✵㛫ᒎ㛤䛻䜘䜚ᇶᗏ≧ែ䜢ồ䜑䜛䚹< ri | c1H<0 ri  c2 H 2 <0 ri    cn H n <0 ri

Natural Orbital (NO) methodኚศཎ⌮䜢⏝䛔䛶Ἴື㛵ᩘ䛸㟁Ꮚ༨᭷ᩘ䜢஺஫䛻᭦᪂䛧䚸䛭䛾⧞䜚㏉䛧䛻䜘䜚ᇶᗏ≧ែ䜈䛸ᑟ䛟䚹
36

DEM (Direct Energy Minimization) ἲ䛾ᴫせSD #1SD #2SD #L&1 &1 &1&1&2 &2 &2&2&L &L &L&L
< r1 , r2 , , rN { C1 I1 I2 I3  IN  C2 I1 I2 I3  IN    CL I1 I2 I3  IN

Ii

A( new)(r ) C< r1 , r2 ,, rN

NC

I( old ) A( old )Ai( new)(r)  ¦ CP [ P (r)P 1Ncಶ䛾ಟṇ㛵ᩘNC  L{ ¦C j ) jj 1EIi

< Hˆ << <A( new)(r ) CwEwC *jI0( old ) A( old )AiHC ESC
Nc +Lḟ䛾୍⯡໬ᅛ᭷್᪉⛬ᘧNC(r)  ¦ CP [ P (r)P 137

Gaussian DEM௨ୗ䛾䜘䛖䛺䜺䜴䝇ᇶᗏ㛵ᩘ䜢ᑟධ䛩䜛䚹M¦ D F (r)Ii (r)
AAi ,mmNprim¦d eF m (r)p 1ྠ᫬䛻௨ୗ䛾䜘䛖䛺⾲⌧䜢⏝䛔䜛䛸䚸(r) 

2m, pm 1

ABI

D p r  R C

N

AB(S )

1
JI

B
J

J1(r) N

AB(S )
J1

M
BJ,u

D

1JIu(r) u1

M
B
I,u

Du(r)

N~
DIB,u

AB 1B(S)D¦
JIJ ,uu1J 1䝝䝭䝹䝖䝙䜰䞁䛾⾜ิせ⣲䛿䚸ୗグ䛾䜘䛖䛻⾲䜟䛥䜜䜛䚹< Hˆ 0 <LL¦¦ SA 1B 1
LĤ I§ M M A* ~ B· AB§ 1·*¨'DDdr
F(r)
V(r)
F(r)
¨¸ q ¸¸ G J I J I¦
patom¨ ¦¦ I , p I ,q ³
© 2
¹I 1 © p q¹NABL

1 MAX MAX AB N N M M M M A* B A* BSDi, p Di,q DI,r DI,s2 A1 B1I1 i1 p1 q1 r1 s1L

dr dr' i (r) i (r)

1r r'

L

1 MAX MAX AB N N M M M M A* B A* B
SDi, p DI,q DI,r Di,s2 A1 B1I1 i1 p1 q1 r1 s1ィ⟬㔞҃ L2N2M4

dr dr' i (r) I (r)

L䠖SDᩘ
N䠖㟁Ꮚᩘ
M䠖ᇶᗏᩘ

I(r') I (r')

1r r'I(r') i (r') ABi I

Gaussian DEM 䛻䛚䛡䜛ィ⟬䛾ὶ䜜ึᮇタᐃ

Slater⾜ิᘧ䛾ᩘ㻌 Lಟṇ㛵ᩘ䛾ᩘ Nc
䜺䜴䝇ᇶᗏ䝉䝑䝖(6-31G, 6-31G** ,…)Hartree-Fock ᪉⛬ᘧ䜢ゎ䛟(L-1) ಶ䛾ึᮇSlater ⾜ิᘧ䜢సᡂ䛩䜉䛶䛾䠍㟁ᏊἼື㛵ᩘ䛾᭦᪂
DEM
processno䜶䝛䝹䜼䞊཰᮰䠛
yesENDಟṇ㛵ᩘ䛾ಶᩘNc䛾ຠᯝBe (iterlimitfinal=20)
N=46-31G*-14.560
0510

1520

2530

3540

䜶䝛䝹䜼䞊㻌
energy (a.u.) (a.u.)-14.570

Nc=2-14.580

Nc=4-14.590

6-31G**
ξ2**

Nc=8

ξ4**
ξ8**

Nc=10-14.600

ξ10**-14.610

CCSD(T)-14.620

Iteration᭦᪂ᩘ40䠄ィ⟬౛䠅Ⅳ⣲ཎᏊ㻌 䠉䠒㟁Ꮚ⣔䞊
6-31G-37.670
0200

400

600

800

1000

1200

1400

1600

-37.680-37.700

energy (a.u.)䜶䝛䝹䜼䞊㻌 (a.u.)-37.690-37.710-37.720┦㛵䜶䝛䝹䜼䞊

-37.730-37.740

CID-37.750-37.760

CISD

Number of Slater Determinant

Slater ⾜ิᘧ䛾ᩘCIἲ䜘䜚䜒ᑡ䛺䛔SD䛾ᩘ䛷䚸䜘䜚ṇ☜䛺┦㛵䜶䝛䝹䜼䞊䜢ィ⟬䛷䛝䜛䛣䛸䛜䜟䛛䛳䛯䚹41௒ᚋ䛾ィ⏬
¾ ࿘ᮇቃ⏺᮲௳䛾ᑟධ䠄ᅛయ⾲㠃䜈䛾㐺⏝䠅¾ 㟁Ꮚ䞉䝥䝻䝖䞁䞉䝭䝳䞊䜸䞁⣔㔞Ꮚ≧ែ䝅䝭䝳䝺䞊䝅䝵䞁䝥䝻䜾䝷䝮䜈䛾Ⓨᒎ¾ ☢ሙୗ䛷䛾䝅䝭䝳䝺䞊䝅䝵䞁䝥䝻䜾䝷䝮㛤Ⓨ42㧗ᅽୗ䛻䛚䛡䜛㔠ᒓỈ⣲໬≀䛻䜏䜛Ỉ⣲ຠᯝୗྖ㞞❶㔠ᒓỈ໬≀䛾㉸ఏᑟ
¾ Ashcroft䛾ண– H-rich䛺㔠ᒓྜ㔠䛿㧗䛔㉸ఏᑟ㌿⛣ ᗘ䜢ᣢ䛴ྍ⬟ᛶ䛜䛒䜛䠊– 㧗ᅽ䛻䛩䜛䛣䛸䛷SiH4䛺䛹ศᏊᛶ䛾䜒䛾䜒㟁Ꮚⓗ┦஫స⏝䛜ᙉ䜑䜙䜜䛶㔠ᒓ໬䛩䜛䠊– 㧗ᅽ䛻䛩䜛䛣䛸䛷㟁Ꮚྠኈ䛾᩺ຊ䜽䞊䝻䞁┦஫స⏝䜢㉺䛘䛶㟁Ꮚ᱁Ꮚ┦஫స⏝䛜ᙉ䜑䜙䜜䠈㉸ఏᑟ≧ែ䛜ᐇ⌧䛩䜛ྍ⬟ᛶ䛜䛒䜛䠊ඛ⾜◊✲౛¾ H-rich䛺໬ྜ≀䛾䜋䛖䛜䠈㧗䛔Tc䛾ྍ⬟ᛶ䛜ᣦ᦬䛥䜜䛶䛔䜛䠊¾ ᇶᮏⓗ䛻Allen-Dynes䛾ᘧ䜢⏝䛔䛯ண 䠊

MH4MH3The prediction from first-principles,
Kim et al., PNAS 107,2793(2010).

¾ ᚲ䛪䛧䜒ᐇ㦂䛷䛿⌮ㄽண᝿䛾䜘䛖䛻䛿ほ 䛥䜜䛶䛔䛺䛔䠊䠄౛䠖AlH3)

Goncharenko et al., PRL 100, 045504(2008).䠄ᐇ㦂䜒⾜䛔䠈㉸ఏᑟ䛻䛿䛺䜙䛺䛔䛣䛸䜢☜ㄆ䠊䠅௒ᚋ䛾ィ⏬
¾ ⯆࿡῝䛔㟁Ꮚ≧ែ䜔≀ᛶ䜢ᣢ䛳䛯H-rich䛺≀㉁䛾
᥈⣴ཬ䜃Ỉ⣲䛜ᘬ䛝㉳䛣䛩≉␗䛺≀ᛶ䜢ㄪ䜉䜛䠊¾ ≉䛻䠈㧗ᅽୗ䛷ぢ䜙䜜䜛≀ᛶ䠈䛒䜛䛔䛿㧗ᅽ䛷ྜᡂ䛥䜜䜛≀㉁䛻ὀ┠䛩䜛䠊Pd䠄110䠅༢⤖ᬗ⾲㠃䛻䛚䛡䜛Ỉ⣲྾཰䝎䜲䝘䝭䜽䝇䛸ゐ፹཯ᛂᛶ
Markus Wilde