P 和佐田.indd

Size: px
Start display at page:

Download "P 和佐田.indd"

Transcription

1 X Gaussian 03 POP Mulliken natural population analysis r Hartree-Fock 1 1 i n i n i 0, 1, 2

2 2 N 2 N N 3 3 spin spin Mulliken 1955 R. S. Mulliken [1-4] Gaussian 03 Mulliken Mulliken { (r)} { (r)} {C i (r)} 55 {} P density matrix 5 1 Gaussian 03 RHF/STO-3G 1 52 RHF/STO- 3G 2

3 DENSITY MATRIX O 1S S PX PY PZ H 1S H 1S H 1S H 1S Molecular Orbital Coefficients i 4 5 (A1)--O (A1)--O (B2)--O (A1)--O (B1)--O EIGENVALUES O 1S S PX PY PZ H 1S H 1S (A1)--V (B2)--V EIGENVALUES O 1S S PX PY PZ H 1S H 1S P 11 5 {} 6 6 DENSITY MATRIX 1 1 P

4 P 12 DENSITY MATRIX 2 1 P P S 9 S =S 9 RHF/STO-3G STO-3G 3 *** Overlap *** D D D D D D D D D D D D D D D D D D D D D D D D D D D D # IOP(3/33=1) #P RHF/STO-3G POP=FULL GFINPUT IOP(3/33=1) S2S2PX2PY 2PZ S P S P S 1 5 Full Mulliken population analysis Gaussian 03 Full Mulliken population analysis Gaussian 03 4 Full Mulliken population analysis 1 3 P 11 S P 21 S

5 Full Mulliken population analysis: O H H 1S 2S 2PX 2PY 2PZ 1S 1S 1 1 O 1S S PX PY PZ H 1S H 1S O 1S 2 2S 3 2PX 4 2PY 5 2PZ 6 2 H 1S 7 3 H 1S O H H 1S 2S 2PX 2PY 2PZ 1S 1S 8Full Mulliken population analysis N 10 Full Mulliken population analysis Gross orbital populations 5 RHF/STO-3G Gross orbital populations: O 1S S PX PY PZ H 1S H 1S S S Full Mulliken population analysis N10

6 6 Condensed to atoms Condensed to atoms (all electrons): O H H Condensed to atoms Full Mulliken population analysis Condensed to atoms Mulliken Condensed to atoms Mulliken atomic charges 3

7 Mulliken atomic charges: 1 1 O H H Sum of Mulliken charges= q 1 q 2... r 1 r Hartree-Fock Gaussian 03 RHF/STO-3G Standard orientation yz z Debye Charge= electrons Dipole moment (field-independent basis, Debye): X= Y= Z= Tot= Quadrupole moment (field-independent basis, Debye-Ang): XX= YY= ZZ= XY= XZ= YZ= Traceless Quadrupole moment (field-independent basis, Debye-Ang): XX= YY= ZZ= XY= XZ= YZ= Octapole moment (field-independent basis, Debye-Ang**2): XXX= YYY= ZZZ= XYY= XXY= XXZ= XZZ= YZZ= YYZ= XYZ= Hexadecapole moment (field-independent basis, Debye-Ang**3): XXXX= YYYY= ZZZZ= XXXY= XXXZ= YYYX= YYYZ= ZZZX= ZZZY= XXYY= XXZZ= YYZZ= XXYZ= YYXZ= ZZXY= Mulliken Mulliken STO-3G diffuse

8 diffuse Hartree-Fock [5] 1 2 Mulliken B3LYP double-zeta diffuse 631G(d) correlation consistent 1 0 net overlap population Mulliken natural population analysis Mulliken 1980 [6-10]Mulliken natural population analysis natural atomic orbitalnao a.u. O b H b OH c STO-3G 3-21G 6-31G 6-311G 6-31G(d) 6-311G(d,p) 6-31+G(d) G(d,p) G(3df,3pd) 6-31G(d,p) D95 D95* cc-pvdz cc-pvtz aug-cc-pvdz ab3lyp/6-31g(d) OH ÅHOH º b coh net overlap population (Condensed to atoms)

9 (a.u. C b H b CC c CH c STO-3G 3-21G 6-31G 6-311G 6-31G(d) 6-31G(d,p) 6-311G(d,p) 6-31+G(d) G(d,p) G(3df,3pd) D95 D95* cc-pvdz cc-pvtz aug-cc-pvdz ab3lyp/6-31g(d) b c net overlap population (Condensed to atoms) NAO s pd... [9]natural atomic orbital natural natural orbital NAO NAO natural hybrid orbital NHO [10]NHO natural bond orbitalnbonbo [8] #P B3LYP/6-31G(d,p) SCF=TIGHT POP=NBOREAD water 0 1 O H,1,R1 H,1,R1,2,T1 R1= T1= $nbo bndidx $end

10 natural population analysis 9 9 B3LYP/6-31G(d,p) NBO NBO NBO NAO NHO NBO NBO NBO POP=NBOREAD POP=NBO nbo POP=NBOREAD NBO 3.0 Program Manual [11] NBO BNDIND Mulliken NBO [11,12] NATURAL POPULATIONS NAO NAO NAO sp x p y p z... Type (AO) Cor ValRyd NAO NAORydberg NAO Occpancy NAO 02 Energy NAO NAO Summary of Natural Population AnalysisNatural Charge natural charge Total Rydberg NAO Natural Electron Configuration NAO natural electron configuration Wiberg bond index matrix...atom-atom overlap-weighted NAO bond order:mo bond ordernbo [5] Wiberg [13] 1 2 [5,6]Total by atomnao NBO NBO NBO natural Lewis NBO CRBD LPnatural Lewis NBO 1.9e natural Lewis NBO 1 NBO 2 NBO 2 Lewis Lewis

11 (Enter /opt/apl/sp/g03/l607.exe) ******************************Gaussian NBO Version 3.1****************************** N A T U R A L A T O M I C O R B I T A L A N D N A T U R A L B O N D O R B I T A L A N A L Y S I S ******************************Gaussian NBO Version 3.1****************************** /RESON / : Allow strongly delocalized NBO set /BNDIDX / : Print bond indices based on the NAO density matrix Analyzing the SCF density H 3 1S( 0.53) Wiberg bond index matrix in the NAO basis: Atom O H H Job title: water Storage needed: 1243 in NPA, 1525 in NBO ( available) NATURAL POPULATIONS: Natural atomic orbital occupancies NAO Atom No lang Type(AO) Occupancy Energy O 1 S Cor( 1S) O 1 S Val( 2S) O 1 S Ryd( 3S) O 1 S Ryd( 4S) O 1 px Val( 2p) O 1 px Ryd( 3p) O 1 py Val( 2p) O 1 py Ryd( 3p) O 1 pz Val( 2p) O 1 pz Ryd( 3p) O 1 dxy Ryd( 3d) O 1 dxz Ryd( 3d) O 1 dyz Ryd( 3d) O 1 dx2y2 Ryd( 3d) O 1 dz2 Ryd( 3d) H 2 S Val( 1S) H 2 S Ryd( 2S) Wiberg bond index, Totals by atom: Atom O H H Atom-atom overlap-weighted NAO bond order: Atom O H H Atom-atom overlap-weighted NAO bond order, Totals by atom: Atom O H H H 3 S Val( 1S) H 3 S Ryd( 2S) Summary of Natural Population Analysis: Natural Population Natural Atom No Charge Core Valence Rydberg Total O H H ======================================================================= * Total * Natural Population Core ( % of 2) Valence ( % of 8) Natural Minimal Basis ( % of 10) Natural Rydberg Basis ( % of 10) Atom No Natural Electron Configuration O 1 [core]2s( 1.77)2p( 5.15)3d( 0.01) H 2 1S( 0.53) MO bond order: Atom O H H MO atomic valencies: Atom O H H NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) Structure accepted: No low occupancy Lewis orbitals LP LP BD O BD H H

12 Core ( % of 2) Valence Lewis ( % of 8) ================== ============================ Total Lewis ( % of 10) Valence non-lewis ( 0.001% of 10) Rydberg non-lewis ( 0.034% of 10) ================== ============================ Total non-lewis ( 0.035% of 10) (Occupancy) Bond orbital/ Coefficients/ Hybrids ( ) BD ( 1) O 1 - H 2 ( 73.36%) * O 1 s( 22.11%)p 3.52( 77.76%)d 0.01( 0.13%) 1s 2s 3s 4s 2px px dxy ( 26.64%) 3dxz 3dyz * 3dx2y2 3dz2 H 2 s(100.00%) 1s 2s 2py 3py 2pz 3pz ( ) BD ( 1) O 1 - H 3 ( 73.36%) * O 1 s( 22.11%)p 3.52( 77.76%)d 0.01( 0.13%) ( 26.64%) * H 3 s(100.00%) ( ) CR ( 1) O 1 s(100.00%) ( ) LP ( 1) O 1 s( 0.00%)p 1.00( 99.87%)d 0.00( 0.13%) ( ) LP ( 2) O 1 s( 55.90%)p 0.79( 44.02%)d 0.00( 0.07%) ( ) RY*( 1) O 1 s( 99.84%)p 0.00( 0.16%)d 0.00( 0.00%) 7. ( ) RY*( 2) O 1 s(100.00%) 8. ( ) RY*( 3) O 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 9. ( ) RY*( 4) O 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 10. ( ) RY*( 5) O 1 s( 0.01%)p 1.00( 99.99%)d 0.00( 0.00%) 11. ( ) RY*( 6) O 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 12. ( ) RY*( 7) O 1 s( 0.00%)p 1.00( 0.13%)d99.99( 99.87%) 13. ( ) RY*( 8) O 1 s( 0.00%)p 1.00( 0.14%)d99.99( 99.86%) 14. ( ) RY*( 9) O 1 s( 0.04%)p 0.27( 0.01%)d99.99( 99.96%) 15. ( ) RY*(10) O 1 s( 0.00%)p 1.00( 0.16%)d99.99( 99.84%) 16. ( ) RY*( 1) H 2 s(100.00%) ( ) RY*( 1) H 3 s(100.00%) ( ) BD*( 1) O 1 - H 2 ( 26.64%) * O 1 s( 22.11%)p 3.52( 77.76%)d 0.01( 0.13%) ( 73.36%) * H 2 s(100.00%) 19. ( ) BD*( 1) O 1 - H 3 ( 26.64%) * O 1 s( 22.11%)p 3.52( 77.76%)d 0.01( 0.13%) ( 73.36%) * H 3 s(100.00%) hybrid p-character > 25.0% orbital occupancy > 0.10e Line of Centers Hybrid 1 Hybrid NBO Theta Phi Theta Phi Dev Theta Phi Dev ====================================================================================== 1. BD ( 1) O 1 - H BD ( 1) O 1 - H LP ( 1) O LP ( 2) O Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis Threshold for printing: 0.50 kcal/mol E(2) E(j)-E(i) F(i,j) Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u. ============================================================================================ within unit 1 1. BD ( 1) O 1 - H 2 / 17. RY*( 1) H BD ( 1) O 1 - H 3 / 16. RY*( 1) H LP ( 2) O 1 / 16. RY*( 1) H LP ( 2) O 1 / 17. RY*( 1) H Natural Bond Orbitals (Summary): Principal Delocalizations NBO Occupancy Energy (geminal,vicinal,remote) ==================================================================================== Molecular unit 1 (H2O) 1. BD ( 1) O 1 - H (v) 2. BD ( 1) O 1 - H (v) 3. CR ( 1) O LP ( 1) O LP ( 2) O (v),17(v) 6. RY*( 1) O RY*( 2) O RY*( 3) O RY*( 4) O RY*( 5) O RY*( 6) O RY*( 7) O RY*( 8) O RY*( 9) O RY*( 10) O RY*( 1) H RY*( 1) H BD*( 1) O 1 - H BD*( 1) O 1 - H Total Lewis ( %) Valence non-lewis ( %) Rydberg non-lewis ( %) Total unit ( %) Charge unit =2.7 Leave Link 607 at Thu Dec 13 21:11: , MaxMem= cpu: 0.2 x z O H 3 H 2 z z y NHO Directionality and "Bond Bending" (deviations from line of nuclear centers) [Thresholds for printing: angular deviation > 1.0 degree]

13 non-lewis non-lewis NBO 1 NBO Occupancy NBO 02 1 NBO RY* BD* Rydberg * Lewis 1 NBO BD NBO NBO NHO 1 NBO(NBO:1) NHO(NHO:O) NHO(NHO:H2) (NBO:1)0.8565(NHO:O)0.5162(NHO:H2) 20 (NHO:O) sp 3 p sp 3.52 NAO NHO NATURAL POPULATIONS NAO (NHO:O) 21 NAO (NHO:O))0.4696(NAO:2s)0.0241(NAO:3s)0.7059(NAO:2p y )0.0314(NAO:3p y ) (NAO:2p z )0.0023(NAO:3p z )0.0265(NAO:3d yz ) (NAO:3d 2)0.0211(NAO:3d 2) x 2 y z 21 NHO NHO sp n p Theta z Phi x NHO Dev Phi NHO Theta 2.7º Lewis NBO Fock Fock E(2) [6] NBO Lewis NBO NBO* Lewis NBO E(2) 11[8] E(2) 22 * E (2) *

14 22 Lewis E(2) 1 OH(2) 3 H Rydberg 0.52 kcal/mol 22 E(j)-E(i) < ˆF > F(i,j) 3 4 Mulliken natural population analysis B3LYP STO-3G Mulliken [9] Mulliken [5] natural atomic charge OH O H b c STO-3G 3-21G 6-31G 6-311G 6-31G(d) 6-311G(d,p) 6-31+G(d) G(d,p) G(3df,3pd) 6-31G(d,p) D95 D95* cc-pvdz cc-pvtz aug-cc-pvdz ab3lyp/6-31g(d) O-H ÅHOH= º bwiberg c NAO

15 natural atomic charge b c C H CC CH CC CH STO-3G 3-21G 6-31G 6-311G 6-31G(d) 6-31G(d,p) 6-311G(d,p) 6-31+G(d) G(d,p) G(3df,3pd) D95 D95* cc-pvdz cc-pvtz aug-cc-pvdz ab3lyp/6-31g(d) bwiberg c NAO Gaussian 03 Mulliken natural population analysis Mulliken natural population analysis Gaussian 03 Bader Atoms in Molecule [14]

16 [1] R. S. Mulliken, J. Chem. Phys., 23, , 1955 [2] R. S. Mulliken, J. Chem. Phys., 23, , 1955 [3] R. S. Mulliken, J. Chem. Phys., 23, , 1955 [4] R. S. Mulliken, J. Chem. Phys., 23, , 1955 [5] T. Kar, J. G. Ángyán, A. B. Sannigrahi J. Phys. Chem. A, 104, , 2000 [6] F. Weinhold, C. R. Landis Valency and Bonding A Natural Bond Orbital Donor- Acceptor Perspective, Cambridge University Press, Cambridge, 2005 [7] F. Weinhold, Natural bond orbital methods, P. v. R. Schleyer Encyclopedia of Computational Chemistry, Wiley, New York 1998 [8] A. E. Reed, L. A. Curtiss, F. Weinhold Chem. Rev., 88, , 1988 [9] A. E. Reed, R.B. Weinstock, F. Weinhold J. Chem. Phys., 83, , 1985 [10] J. P. Foster, F. Weinhold J. Am. Chem. Soc., 102, , 1980 [11] E. D. Glendening, A. E. Reed, J. E. Carpenter, F. Weinhold NBO 3.0 Program Manual, Gaussian Inc. [12] ~ nbo5/tutorial.html [13] K. B. Wiberg Tetrahedron, 24, , 1968 [14] R. F. W. Bader Atoms in Molecules A Quantum Theory, Oxford University Press, Tronto 1990Gaussian 03 POP AIM

和佐田P indd

和佐田P indd B3LYP/6-31G* Hartree-Fock B3LYP Hartree-Fock 6-31G* Hartree-Fock LCAO Linear Combination of Atomic Orbitals Gauss Gaussian-Type Orbital: GTO Gaussian- Type Function: GTF 2 23 1 1 X, Y, Z x, y, z l m n

More information

和佐田 裕昭P indd

和佐田 裕昭P indd 19 20 Gaussian 20 Gaussian 1998 J. A. Pople Gaussian Windows Macintosh Gaussian 12 [1] 21 HPC2500 Gaussian Gaussian 03 IT Gaussian Gaussian Gaussian 94 5 [2-6] Gaussian 98 1 [7] Gaussian 03 Gaussian 03

More information

(2) N elec = D p,q p,q χ q χ p dr = p,q D p,q S q,p Mulliken PA D Mull p = p = group A D p,p 1 + D p,q S q,p p q p [ r A D Mull p ] group χ p G Mull A

(2) N elec = D p,q p,q χ q χ p dr = p,q D p,q S q,p Mulliken PA D Mull p = p = group A D p,p 1 + D p,q S q,p p q p [ r A D Mull p ] group χ p G Mull A 7 - (Electron-Donor Acceptor) : Charge-Transfer ( CT) ( (Charge-Transfer) - (electron donor-electron acceptor) [1][2][3][4] Van der Waals CT [5] Population Analysis population analysis ( ), observable

More information

和佐田P indd

和佐田P indd 2000 B3LYP/6-31G Gaussian 98 03 B3LYP/6-31G* Gaussian STO-3G RHF Gaussian RHF/STO-3G B3LYP RHF 6-31G* STO-3G Schrödinger Schrödinger s p d Schrödinger Schrödinger Hohenberg-Kohn Kohn-Sham Kohn-Sham [1-3]

More information

Microsoft Excelを用いた分子軌道の描画の実習

Microsoft Excelを用いた分子軌道の描画の実習 J. Comput. Chem. Jpn.,Vol.9, No.4, pp.177 182 (2010) 2010 Society of Computer Chemistry, Japan Microsoft Excel a*, b, c a, 790-8577 2-5 b, 350-0295 1-1 c, 305-8568 1-1-1 *e-mail: nagaoka@ehimegw.dpc.ehime-u.ac.jp

More information

Platypus-QM β ( )

Platypus-QM β ( ) Platypus-QM β (2012.11.12) 1 1 1.1...................................... 1 1.1.1...................................... 1 1.1.2................................... 1 1.1.3..........................................

More information

6

6 000 (N =000) 50 ( N(N ) / = 499500) μm.5 g cm -3.5g cm 3 ( 0 6 µm) 3 / ( g mo ) ( 6.0 0 3 mo ) =.3 0 0 0 5 (0 6 ) 0 6 0 6 ~ 0 000 000 ( 0 6 ) ~ 0 9 q R q, R q q E = 4πε 0 R R (6.) -6 (a) (b) (c) (a) (b)

More information

P 和佐田.indd

P 和佐田.indd Gaussian 03 Q Gaussian 03 [1,2] Q U S 1 2 k B 1.38054 10 23 JK 1 T 1 2 Q el Q trans Q rot Q vib 3 Q Q el Q trans Q rot Q vib 1 24 5 U E el E trans E rot E vib S S el S trans S rot S vib 6 3 4 5 6 R R 1.987

More information

êUìÆã§ñ¬ÅEÉtÉFÉãÉ~ã§ñ¬.pdf

êUìÆã§ñ¬ÅEÉtÉFÉãÉ~ã§ñ¬.pdf SFG SFG SFG Y. R. Shen.17 (p. 17) SFG g ω β αβγ = ( e3 h ) (r γ ) ng n ω ω ng + iγ (r α ) gn ' (r β ) n 'n (r ) (r ) α n 'n β gn ' ng n ' ω ω n 'g iγ n'g ω + ω n 'n iγ nn ' (1-1) Harris (Chem. Phys. Lett.,

More information

Microsoft PowerPoint - 基礎化学4revPart2 [互換モード]

Microsoft PowerPoint - 基礎化学4revPart2 [互換モード] 化学結合と分 の形 Part 2 軌道を使った考え方を学ぶ 3 原 価結合法 (V 法 ) 共有結合の本質は軌道の重なり軌道を意識した結合を簡単に理解する 共有結合の本質は軌道の重なり 原子価結合法 (V 法 ) Valance ond Method 原子価結合法 V 法で用いる原子価軌道とその重なり方 原子価軌道 Valence Orbital 軌道の重なり方から見た共有結合の種類 原子価結合法

More information

Gaussian & WebMO II. 構造の入力 (4) New Job メニューの Create New Job をクリックすると, 分子編集用の Editor が現れる ログアウトは右上端の Logout をクリックする

Gaussian & WebMO II. 構造の入力 (4) New Job メニューの Create New Job をクリックすると, 分子編集用の Editor が現れる ログアウトは右上端の Logout をクリックする Gaussian & WebMO 2015-1 Gaussian および WebMO による分子軌道計算 Gaussian は世界で最も広く使用されている量子化学計算プログラムである ここでは, Gaussian の入力ファイルと出力ファイルの扱いを容易にするため,Web ベースの計算支援プログラム WebMO を併用して計算を行う方法を説明する Windows 用の市販プログラムである Chem3D,GaussView

More information

2.4 ( ) ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) Minoru TANAKA (Osaka Univ.) I(2011), Sec p. 1/30

2.4 ( ) ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) Minoru TANAKA (Osaka Univ.) I(2011), Sec p. 1/30 2.4 ( ) 2.4.1 ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) I(2011), Sec. 2. 4 p. 1/30 (2) Γ f dr lim f i r i. r i 0 i f i i f r i i i+1 (1) n i r i (3) F dr = lim F i n i r i. Γ r i 0 i n i

More information

.....Z...^.[.......\..

.....Z...^.[.......\.. 15 10 16 42 55 55 56 60 62 199310 1995 134 10 8 15 1 13 1311 a s d f 141412 2 g h j 376104 3 104102 232 4 5 51 30 53 27 36 6 Y 7 8 9 10 8686 86 11 1310 15 12 Z 13 14 15 16 102193 23 1712 60 27 17 18 Z

More information

目次 Gaussian 利用の手引き 1 1. はじめに 利用できるバージョン 概要 マニュアル 2 2. TSUBAME での利用方法 Gaussian の実行 2 (1) TSUBAMEにログイン 2 (2) バージョンの切り替え 2 (3) イン

目次 Gaussian 利用の手引き 1 1. はじめに 利用できるバージョン 概要 マニュアル 2 2. TSUBAME での利用方法 Gaussian の実行 2 (1) TSUBAMEにログイン 2 (2) バージョンの切り替え 2 (3) イン Gaussian 利用の手引 東京工業大学学術国際情報センター 2017.04 version 1.10 目次 Gaussian 利用の手引き 1 1. はじめに 1 1.1 利用できるバージョン 1 1.2 概要 1 1.3 マニュアル 2 2. TSUBAME での利用方法 2 2.1 Gaussian の実行 2 (1) TSUBAMEにログイン 2 (2) バージョンの切り替え 2 (3)

More information

http://www1.doshisha.ac.jp/ bukka/qc.html 1. 107 2. 116 3. 1 119 4. 2 126 5. 132 6. 136 7. 1 140 8. 146 9. 2 150 10. 153 11. 157 12. π Hückel 159 13. 163 A-1. Laguerre 165 A-2. Hermite 167 A-3. 170 A-4.

More information

光学

光学 Control of Refractive Indices of Optical Polymers: Theoretical Prediction and Molecular Design Method Shinji ANDO The fundamental theory and a method to predict the refractive indices and dispersions of

More information

* 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) *

* 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) * * 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) *1 2004 1 1 ( ) ( ) 1.1 140 MeV 1.2 ( ) ( ) 1.3 2.6 10 8 s 7.6 10 17 s? Λ 2.5 10 10 s 6 10 24 s 1.4 ( m

More information

05松山巌様.indd

05松山巌様.indd 2011 pp. 65 96 2002 2 2012 1 18 65 2011 1 5 1 2 3 4 5 2002 9 1 2 3 4 5 1 2 66 3 4 5 5 1 4 1 4 1 2 3 4 5 6 5 1 8 7 5 1 4 67 2011 21 4 3 1 7 1 1 1 1 2 2 3 3 4 2 2 / 3 68 1 1 1 2 2 2 32 3 3 4 4 2 /fa/ 2/f/

More information

2

2 D 1 2 3 XX XY ( ) 4 5 GID ( ) ( ) ( ) ( ) WHO( ) ( ) ( ) WHO ( ) WHO ( ) 6 7 8 9 X Y XX XY XO XXY XXXY Y Y SRY Y SRY X XX XY SRY XY XX Y Y X Y Y DNA DNA 10 XY XY 11 12 13 F M T 14 U H R 15 K N F 16 M T

More information

D:/cssj/jcs/v7n2/a5tex/TX2.dvi

D:/cssj/jcs/v7n2/a5tex/TX2.dvi J. Chem. Software, Vol. 7, No. 2, p. 87 98 (2001) *,, 338-8570 255 *e-mail: tokita@apc.saitama-u.ac.jp (Received: September 13, 2000; Accepted for publication: September 27, 2000; Published on Web: November

More information

SiC SiC QMAS(Quantum MAterials Simulator) VASP(Vienna Ab-initio Simulation Package) SiC 3C, 4H, 6H-SiC EV VASP VASP 3C, 4H, 6H-SiC (0001) (11 20) (1 1

SiC SiC QMAS(Quantum MAterials Simulator) VASP(Vienna Ab-initio Simulation Package) SiC 3C, 4H, 6H-SiC EV VASP VASP 3C, 4H, 6H-SiC (0001) (11 20) (1 1 QMAS SiC 7661 24 2 28 SiC SiC QMAS(Quantum MAterials Simulator) VASP(Vienna Ab-initio Simulation Package) SiC 3C, 4H, 6H-SiC EV VASP VASP 3C, 4H, 6H-SiC (0001) (11 20) (1 100) MedeA SiC QMAS - C Si (0001)

More information

Microsoft Word - abstract-example.doc

Microsoft Word - abstract-example.doc シュレーディンガー方程式の FC 法 ( 自由完員関数法 による解法 I. 収束性の高い方法の検討 石川敦之 黒川悠索 中辻博 ( 量子化学研究協会 JST-CREST a.ishikawa@qcri.or.jp 近年 Schrödinger 方程式及び Dirac 方程式の一般的解法として Free-complement(FC 法が我々の グループにより提案された この方法論は g H E n n

More information

4/15 No.

4/15 No. 4/15 No. 1 4/15 No. 4/15 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = m ψ(r,t)+v(r)ψ(r,t) ψ(r,t) = ϕ(r)e iωt ψ(r,t) Wave function steady state m ϕ(r)+v(r)ϕ(r) = εϕ(r) Eigenvalue problem

More information

座標変換におけるテンソル成分の変換行列

座標変換におけるテンソル成分の変換行列 座標変換におけるテンソル成分の変換行列 座標変換におけるテンソル成分の変換関係は 次元数によらず階数によって定義される変換行列で整理することができる 位置ベクトルの変換行列を D としてそれを示そう D の行列式を ( = D ) とするとき 鏡映や回映といった pseudo rotation に対しては = -1 である が問題になる基底は 対称操作に含まれる pseudo rotation に依存する

More information

Molecule tomic rbital bridied tomic rbital Valence Shell Electron Pair Repulsion Rule Molecular rbital 2 1+ + 1+ 1+ 1+ 2 9+ + 9+ 9+ 9+ 2 1+ 1+ 1s 1s 2 9+ 9+ 2p 2p 9+ () 2 (2p ) 2 (2p ) 2 (2p ) 1 Energ

More information

大規模共有メモリーシステムでのGAMESSの利点

大規模共有メモリーシステムでのGAMESSの利点 Technical white paper GAMESS GAMESS Gordon Group *1 Gaussian Gaussian1 Xeon E7 8 80 2013 4 GAMESS 1 RHF ROHF UHF GVB MCSCF SCF Energy CDFpEP CDFpEP CDFpEP CD-pEP CDFpEP SCF Gradient CDFpEP CDFpEP CDFpEP

More information

1) K. J. Laidler, "Reaction Kinetics", Vol. II, Pergamon Press, New York (1963) Chap. 1 ; P. G. Ashmore, "Catalysis and Inhibition of Chemical Reactio

1) K. J. Laidler, Reaction Kinetics, Vol. II, Pergamon Press, New York (1963) Chap. 1 ; P. G. Ashmore, Catalysis and Inhibition of Chemical Reactio 1) K. J. Laidler, "Reaction Kinetics", Vol. II, Pergamon Press, New York (1963) Chap. 1 ; P. G. Ashmore, "Catalysis and Inhibition of Chemical Reactions", Butterworths, London (1963) Chap. 7, p. 185. 2)

More information

untitled

untitled 9 9. 9. 9. (FEM, nite element method) 4 9.. (element) (mesh discretization) DT LOK DT M([ ],[ ] )=[ ] DIMENSION M(,NF) DT M/,4,5,,5,,,5,6,,6,,,6,7, 4,8,9, 4,9,5,.../ DIMENSION M(4,NF) DO I=,IF- DO J=,JF

More information

PDF用 レポート:中国保険市場の現状と展望.PDF

PDF用 レポート:中国保険市場の現状と展望.PDF 1 INDEX 2 4 9 13 24 29 2 3 4 1000 900 800 700 600 500 400 300 200 100 0 90 91 92 93 94 95 96 97 98 99 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 100% 50% 0% 89 90 91 92 93 94 95 96 97 98 99 5 6 7 8 9

More information

磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論

磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論 email: takahash@sci.u-hyogo.ac.jp April 30, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 260 Today s Lecture: Itinerant Magnetism 60 / 260 Multiplets of Single Atom System HC HSO : L = i l i, S = i s i, J = L +

More information

42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =

42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 = 3 3.1 3.1.1 kg m s J = kg m 2 s 2 MeV MeV [1] 1MeV=1 6 ev = 1.62 176 462 (63) 1 13 J (3.1) [1] 1MeV/c 2 =1.782 661 731 (7) 1 3 kg (3.2) c =1 MeV (atomic mass unit) 12 C u = 1 12 M(12 C) (3.3) 41 42 3 u

More information

スライド 1

スライド 1 Gaussian の使い方 %chk=default # HF/6-3G** comments H 入力ファイル %chk=default チェックポイントファイルの指定 # HF/6-3G** 出力フォーマット (ormal, Print, Terse) Hartree-Fock 法,6-3G** 基底関数 comments コメント 電荷 スピン多重度 H 元素記号 分子構造の情報 XYZ 座標で指定

More information

untitled

untitled 1 Hitomi s English Tests 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 2 0 0 1 1 0 0 0 0 0 1 1 1 1 0 3 1 1 0 0 0 0 1 0 1 0 1 0 1 1 4 1 1 0 1 0 1 1 1 1 0 0 0 1 1 5 1 1 0 1 1 1 1 0 0 1 0

More information

応力とひずみ.ppt

応力とひずみ.ppt in yukawa@numse.nagoya-u.ac.jp 2 3 4 5 x 2 6 Continuum) 7 8 9 F F 10 F L L F L 1 L F L F L F 11 F L F F L F L L L 1 L 2 12 F L F! A A! S! = F S 13 F L L F F n = F " cos# F t = F " sin# S $ = S cos# S S

More information

02-量子力学の復習

02-量子力学の復習 4/17 No. 1 4/17 No. 2 4/17 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = 2 2m 2 ψ(r,t)+v(r)ψ(r,t) ψ(r,t) Wave function ψ(r,t) = ϕ(r)e iωt steady state 2 2m 2 ϕ(r)+v(r)ϕ(r) = εϕ(r)

More information

PowerPoint プレゼンテーション

PowerPoint プレゼンテーション ガウシアンと群論 ( 名古屋工業大学 ) 川崎晋司 ガウシアンの特徴非経験的分子軌道計算 分子のシュレディンガー方程式をどう解くか HΨ = EΨ 電子だけでなく原子核も入る もちろん複数 一電子波動関数の形にして解こう = 分子軌道法 例えばハートリー法では多電子波動関数 Ψを一電子波動関数 φの積で近似 Ψ r 1, r, = ϕ r 1 ϕ r しかし この近似ではパウリの原理 ( 電子の入れ替えに反対称

More information

1 1.1,,,.. (, ),..,. (Fig. 1.1). Macro theory (e.g. Continuum mechanics) Consideration under the simple concept (e.g. ionic radius, bond valence) Stru

1 1.1,,,.. (, ),..,. (Fig. 1.1). Macro theory (e.g. Continuum mechanics) Consideration under the simple concept (e.g. ionic radius, bond valence) Stru 1. 1-1. 1-. 1-3.. MD -1. -. -3. MD 1 1 1.1,,,.. (, ),..,. (Fig. 1.1). Macro theory (e.g. Continuum mechanics) Consideration under the simple concept (e.g. ionic radius, bond valence) Structural relaxation

More information

k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i σ ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m σ A σ σ σ σ f i x

k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i σ ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m σ A σ σ σ σ f i x k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m A f i x i B e e e e 0 e* e e (2.1) e (b) A e = 0 B = 0 (c) (2.1) (d) e

More information

3 filename=quantum-3dim110705a.tex ,2 [1],[2],[3] [3] U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h

3 filename=quantum-3dim110705a.tex ,2 [1],[2],[3] [3] U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h filename=quantum-dim110705a.tex 1 1. 1, [1],[],[]. 1980 []..1 U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h i z (.1) Ĥ ( ) Ĥ = h m x + y + + U(x, y, z; t) (.) z (U(x, y, z; t)) (U(x,

More information

II 1 3 2 5 3 7 4 8 5 11 6 13 7 16 8 18 2 1 1. x 2 + xy x y (1 lim (x,y (1,1 x 1 x 3 + y 3 (2 lim (x,y (, x 2 + y 2 x 2 (3 lim (x,y (, x 2 + y 2 xy (4 lim (x,y (, x 2 + y 2 x y (5 lim (x,y (, x + y x 3y

More information

96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A

96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A 7 Lorentz 7.1 Ampère I 1 I 2 I 2 I 1 L I 1 I 2 21 12 L r 21 = 12 = µ 0 2π I 1 I 2 r L. (7.1) 7.1 µ 0 =4π 10 7 N A 2 (7.2) magnetic permiability I 1 I 2 I 1 I 2 12 21 12 21 7.1: 1m 95 96 7 1m =2 10 7 N

More information

1 2 LDA Local Density Approximation 2 LDA 1 LDA LDA N N N H = N [ 2 j + V ion (r j ) ] + 1 e 2 2 r j r k j j k (3) V ion V ion (r) = I Z I e 2 r

1 2 LDA Local Density Approximation 2 LDA 1 LDA LDA N N N H = N [ 2 j + V ion (r j ) ] + 1 e 2 2 r j r k j j k (3) V ion V ion (r) = I Z I e 2 r 11 March 2005 1 [ { } ] 3 1/3 2 + V ion (r) + V H (r) 3α 4π ρ σ(r) ϕ iσ (r) = ε iσ ϕ iσ (r) (1) KS Kohn-Sham [ 2 + V ion (r) + V H (r) + V σ xc(r) ] ϕ iσ (r) = ε iσ ϕ iσ (r) (2) 1 2 1 2 2 1 1 2 LDA Local

More information

Microsoft PowerPoint - 基礎化学4revPart1b [互換モード]

Microsoft PowerPoint - 基礎化学4revPart1b [互換モード] 化学結合と分 の形 なぜ原 と原 はつながるのかなぜ分 はきまった形をしているのか化学結合の本質を理解しよう 分子の形と電子状態には強い相関がある! 原子 分子 基礎化学 ( 化学結合論 構造化学 量子化学 ) 電子配置分子の形強い相関関係 ( 電子状態 ) ( 立体構造 ) 分子の性質 ( 反応性 物性 ) 先端化学 ( 分子設計 機能化学 ) 機能 分子の形と電子配置の基礎的理解 基礎 ( 簡単

More information

COGNACのコンセプト \(COarse Grained molecular dynamics program developed by NAgoya Cooperation\)

COGNACのコンセプト \(COarse Grained molecular dynamics program developed by NAgoya Cooperation\) COGNAC (COarse-Grained molecular dynamics program by NAgoya Cooperation) ( ), 0 sec -3 msec -6 sec -9 nsec -12 psec -15 fsec GOURMET SUSHI PASTA COGNAC MUFFIN -15-12 -9-6 -3 0 fm pm nm m mm m United atom

More information

40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x,

40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x, 9.. x + y + 0. x,y, x,y, x r cos θ y r sin θ xy x y x,y 0,0 4. x, y 0, 0, r 0. xy x + y r 0 r cos θ sin θ r cos θ sin θ θ 4 y mx x, y 0, 0 x 0. x,y 0,0 x x + y x 0 x x + mx + m m x r cos θ 5 x, y 0, 0,

More information

P 和佐田.indd

P 和佐田.indd B3LYP/6-31G* X HGS MOL-TALOU [1] 1 2-4 II CS Chem Office [2] Molecular Dynamics 1 ChemDraw 2 3 Chem 3D 4 Gaussian Input X 28 27 12 13 26 11 29 14 10 15 25 2 9 27 2 21 7 3 43 7 3 5 Cu 41 Cu 4 10 22 28 H

More information

PDF

PDF 1 1 1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5 1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV

More information

高密度荷電粒子ビームの自己組織化と安定性

高密度荷電粒子ビームの自己組織化と安定性 1885 2014 1-11 1 1 Hiromi Okamoto Graduate School of Advanced Sciences ofmatter, Hiroshima University ( ( ) $)$ ( ) ( ) [1],, $*1$ 2 ( $m,$ q) $*1$ ; $\kappa_{x}$ $\kappa_{y}$ 2 $H_{t}=c\sqrt{(p-qA)^{2}+m^{2}c^{2}}+q\Phi$

More information

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b) 2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................

More information

( ) ( ) Modified on 2009/05/24, 2008/09/17, 15, 12, 11, 10, 09 Created on 2008/07/02 1 1) ( ) ( ) (exgen Excel VBA ) 2)3) 1.1 ( ) ( ) : : (1) ( ) ( )

( ) ( ) Modified on 2009/05/24, 2008/09/17, 15, 12, 11, 10, 09 Created on 2008/07/02 1 1) ( ) ( ) (exgen Excel VBA ) 2)3) 1.1 ( ) ( ) : : (1) ( ) ( ) () ( ) Modified on 2009/05/24, 2008/09/17, 15, 12, 11, 10, 09 Created on 2008/07/02 1 1) () ( ) (exgen Excel VBA ) 2)3) 1.1 ( ) () : : (1) ( ) ( ) (2) / (1) (= ) (2) (= () =) 4)5) () ( ) () (=) (1) : (

More information

,

, 2002 9710178 15 2 6 , 1 1 15 2 6 Mopac2000lite, Gaussian Moapc2000lite Gaussian98 2 1 1 1.1... 1 1.2... 2 1.3... 2 1.3.1... 2 1.3.2... 4 1.3.3... 5 1.4... 6 1.4.1 Mopac (5,5)... 6 1.4.2 Gaussian (3,3)...

More information

, = = 7 6 = 42, =

, = = 7 6 = 42, = http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8

More information

1 VisBAR edu H 2 O.....

1 VisBAR edu H 2 O..... VisBAR edu v1.03 ( ) 25 4 22 1 VisBAR edu 1 1.1....................................................... 1 1.2.................................................. 2 2 3 2.1 H 2 O.........................................

More information

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, 変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +

More information

1: (Emmy Noether; ) (Feynman) [3] [4] {C i } A {C i } (A A )C i = 0 [5] 2

1: (Emmy Noether; ) (Feynman) [3] [4] {C i } A {C i } (A A )C i = 0 [5] 2 2003 1 1 (Emmy Noether 1) [1] [2] [ (Paul Gordan Clebsch-Gordan ] 1915 habilitation habilitation außerordentlicher Professor Außerordentlich(=extraordinary) 1 1: (Emmy Noether; 1882-1935) (Feynman) [3]

More information

68 JAXA-RR r v m Ó e ε 0 E = - Ó/ r f f 0 f 1 f = f 0 + f 1 x k f 1 = f k e ikx Ó = Ó k e ikx Ó k 3

68 JAXA-RR r v m Ó e ε 0 E = - Ó/ r f f 0 f 1 f = f 0 + f 1 x k f 1 = f k e ikx Ó = Ó k e ikx Ó k 3 67 1 Landau Damping and RF Current Drive Kazuya UEHARA* 1 Abstract The current drive due to the rf travelling wave has been available to sustain the plasma current of tokamaks aiming the stational operation.

More information

untitled

untitled (a) (b) (c) (d) (e) (f) (g) (f) (a), (b) 1 He Gleiter 1) 5-25 nm 1/2 Hall-Petch 10 nm Hall-Petch 2) 3) 4) 2 mm 5000% 5) 1(e) 20 µm Pd, Zr 1(f) Fe 6) 10 nm 2 8) Al-- 1,500 MPa 9) 2 Fe 73.5 Si 13.5 B 9 Nb

More information

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11

More information

ML λ λ 1 λ 1.1 λ λ λ e (λ ) ::= x ( ) λx.e (λ ) e 1 e 2 ( ) ML λx.e Objective Caml fun x -> e x e let 1

ML λ λ 1 λ 1.1 λ λ λ e (λ ) ::= x ( ) λx.e (λ ) e 1 e 2 ( ) ML λx.e Objective Caml fun x -> e x e let 1 2005 sumii@ecei.tohoku.ac.jp 2005 6 24 ML λ λ 1 λ 1.1 λ λ λ e (λ ) ::= x ( ) λx.e (λ ) e 1 e 2 ( ) ML λx.e Objective Caml fun x -> e x e let 1 let λ 1 let x = e1 in e2 (λx.e 2 )e 1 e 1 x e 2 λ 3 λx.(λy.e)

More information

SPring-8_seminar_

SPring-8_seminar_ X 21 SPring-8 XAFS 2016 (= ) X PC cluster Synchrotron TEM-EELS XAFS / EELS HΨ k = E k Ψ k XANES/ELNES DFT ( + ) () WIEN2k, Elk, OLCAO () CASTEP, QUANTUM ESPRESSO FEFF, GNXAS, etc. Bethe-Salpeter (BSE)

More information

橡卒論.PDF

橡卒論.PDF 1329 1 1 2 2 2.1 2 2.1.1 1 2 2.1.2 2 4 2.1.3 3 6 2.2 8 2.2.1 8 2.2.2 12 2.3Booth 13 3 16 3.1 16 3.1.1Robertson 16 3.1.2Booth 18 3.2 19 3.2.1 19 3.2.2Wallace tree 21 3.3 25 3.4 27 3.4.1 4 27 3.4.22 Booth

More information

φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1)

φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1) φ 4 Minimal subtraction scheme 2-loop ε 28 University of Tokyo Atsuo Kuniba version 2/Apr/28 Formulas Γ n + ɛ = n n! ɛ + ψn + + Oɛ n =,, 2, ψn + = + 2 + + γ, 2 n ψ = γ =.5772... Euler const, log + ax x

More information

eaxys Prize lub Symposium in Japan, March 28, 2014 Profile JSPS Stephan

eaxys Prize lub Symposium in Japan, March 28, 2014 Profile JSPS Stephan 16:00- - 2 2 Access to a Stable 2 2 4-Membered ing with on-kekulé nglet Biradical haracter from a Disilyne Dr. Katsuhiko Takeuchi 2007 3 2009 3 2012 3 2012 4 2012 4 (JSPS ) 2013 8 eaxys Prize lub Symposium

More information

エネルギー分解における分子の安定化要因の特定法の提案

エネルギー分解における分子の安定化要因の特定法の提案 エネルギー分解における分子の安定化要因の特定法の提案 A Theoretical Proposal of a Controlling Factor for the Stabilization of Molecules by Energy Decomposition Analysis 奥山倫弘 Michihiro OKUYAMA 要旨分子内でどのようにして結合が組み換わるのか, また, この組み換えにより生じる分子の安定化要因を明らかにする事は,

More information

46 12 3 1 ATP ( ) ATP ~P 1~P hyd Gº 1 1 1950 ~P hyd Gº Hansia et al. Biophys Chem 119: 127, 2006 ~P hyd Gº 1? ATP hyd Gº ATP ATP ATP ~P ε ~P George [BBA 223: 1, 1970] ~P 2) hyd Gº 1. ph Mg 2+ 2. 1 2 2

More information

β

β β 01 7 1 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 18 s s s d 10 s p s p s p 3 s p 4 s p 5 s p 6 1 1H He 1.01 4.00 3Li 4Be 5B 6C 7N 8O 9F 10Ne 6.94 9.01 10.81 1.01 14.01 16.00 19.00 0.18 3 11Na 1Mg 13Al 14Si

More information

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0,

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0, .1.1 Y K L Y = K 1 3 L 3 L K K (K + ) 1 1 3 L 3 K 3 L 3 K 0 (K + K) 1 3 L 3 K 1 3 L 3 lim K 0 K = L (K + K) 1 3 K 1 3 3 lim K 0 K = 1 3 K 3 L 3 z = f(x, y) x y z x-y-z.1 z = e x +xy y 3 x-y ( ) z 0 f(x,

More information

1: Sheldon L. Glashow (Ouroboros) [1] 1 v(r) u(r, r ) ( e 2 / r r ) H 2 [2] H = ( dr ψ σ + (r) 1 2 ) σ 2m r 2 + v(r) µ ψ σ (r) + 1 dr dr ψ σ + (r)ψ +

1: Sheldon L. Glashow (Ouroboros) [1] 1 v(r) u(r, r ) ( e 2 / r r ) H 2 [2] H = ( dr ψ σ + (r) 1 2 ) σ 2m r 2 + v(r) µ ψ σ (r) + 1 dr dr ψ σ + (r)ψ + 1 1.1 21 11 22 10 33 cm 10 29 cm 60 6 8 10 12 cm 1cm 1 1.2 2 1 1 1: Sheldon L. Glashow (Ouroboros) [1] 1 v(r) u(r, r ) ( e 2 / r r ) H 2 [2] H = ( dr ψ σ + (r) 1 2 ) σ 2m r 2 + v(r) µ ψ σ (r) + 1 dr dr

More information

講 座 熱電研究のための第一原理計算入門 第1回 密度汎関数法による第一原理バンド計算 桂 1 はじめに ゆかり 東京大学 2 密度汎関数理論 第一原理 first-principles バンド計算とは 結晶構造 Schrödinger 方程式は 量子力学を司る基本方程式で 以外の経験的パラメータや

講 座 熱電研究のための第一原理計算入門 第1回 密度汎関数法による第一原理バンド計算 桂 1 はじめに ゆかり 東京大学 2 密度汎関数理論 第一原理 first-principles バンド計算とは 結晶構造 Schrödinger 方程式は 量子力学を司る基本方程式で 以外の経験的パラメータや 講 座 熱電研究のための第一原理計算入門 第1回 密度汎関数法による第一原理バンド計算 桂 1 はじめに ゆかり 東京大学 2 密度汎関数理論 第一原理 first-principles バンド計算とは 結晶構造 Schrödinger 方程式は 量子力学を司る基本方程式で 以外の経験的パラメータや任意パラメータを使わず 基 ある 定常状態において電子 i の状態を定義する波動 本的な物理方程式のみを用いて行う電子状態計算であ

More information

A_chapter3.dvi

A_chapter3.dvi : a b c d 2: x x y y 3: x y w 3.. 3.2 2. 3.3 3. 3.4 (x, y,, w) = (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, ) xȳw (,,, )xȳw (,,, ) xyw, F F = xy w x w xy w xy w

More information

untitled

untitled 24 2016 2015 8 26,,,,,,,,,,,, D.,,, L.,,, E.,,,,,, 1 1,,,,, 2,,, 7 1 2, 3 4 5 6 7 Contribution No.: CB 15-1 20 40,,,,,,,, 3,,,,, 10,,,,,,, 2, 3 5, 7 ,,, 2,, 3,, 4,,,,,,,,,,,,, 4,,,,,,,,, 1, 50, 1, 50 50,

More information

Microsoft PowerPoint - 20120608_BO_Sapporo.ppt

Microsoft PowerPoint - 20120608_BO_Sapporo.ppt 2012 年 6 月 8 日 2012/06/08 環 境 物 質 科 学 基 礎 論 I 1 環 境 物 質 科 学 基 礎 論 I(Course in Materials Science I) 化 学 結 合 電 子 構 造 原 子 軌 道 分 子 軌 道 結 晶 構 造 Chemical Bonding, Electronic Structure, Atomic Orbital, Molecular

More information

The Phase Behavior of Monooleoylglycerol-Water Systems Mivoshi Oil & Fat Co.. Ltd. Faculty of Science and Technology, Science University of Tokyo Inst

The Phase Behavior of Monooleoylglycerol-Water Systems Mivoshi Oil & Fat Co.. Ltd. Faculty of Science and Technology, Science University of Tokyo Inst The Phase Behavior of Monooleoylglycerol-Water Systems Mivoshi Oil & Fat Co.. Ltd. Faculty of Science and Technology, Science University of Tokyo Institute of Colloid and Interface Science, Science University

More information

Fig. 3. Morse curves for the ground ( a ) and excited state ( b ) of a diatomic molecule2) Fig. 2. The various modes of energy dissipation from electr

Fig. 3. Morse curves for the ground ( a ) and excited state ( b ) of a diatomic molecule2) Fig. 2. The various modes of energy dissipation from electr Color and Constitution of Organic Colorants, and Some Approach to New Chromophore Masaru MATSUOKA Fig. 3. Morse curves for the ground ( a ) and excited state ( b ) of a diatomic molecule2) Fig. 2. The

More information

平成 30 年度 ( 第 40 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 30 ~8 年月 72 月日開催 30 日 [6] 1 4 A 1 A 2 A 3 l P 3 P 2 P 1 B 1 B 2 B 3 m 1 l 3 A 1, A 2, A 3 m 3 B 1,

平成 30 年度 ( 第 40 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 30 ~8 年月 72 月日開催 30 日 [6] 1 4 A 1 A 2 A 3 l P 3 P 2 P 1 B 1 B 2 B 3 m 1 l 3 A 1, A 2, A 3 m 3 B 1, [6] 1 4 A 1 A 2 A 3 l P 3 P 2 P 1 B 1 B 2 B 3 m 1 l 3 A 1, A 2, A 3 m 3 B 1, B 2, B 3 A i 1 B i+1 A i+1 B i 1 P i i = 1, 2, 3 3 3 P 1, P 2, P 3 1 *1 19 3 27 B 2 P m l (*) l P P l m m 1 P l m + m *1 A N

More information

(4) P θ P 3 P O O = θ OP = a n P n OP n = a n {a n } a = θ, a n = a n (n ) {a n } θ a n = ( ) n θ P n O = a a + a 3 + ( ) n a n a a + a 3 + ( ) n a n

(4) P θ P 3 P O O = θ OP = a n P n OP n = a n {a n } a = θ, a n = a n (n ) {a n } θ a n = ( ) n θ P n O = a a + a 3 + ( ) n a n a a + a 3 + ( ) n a n 3 () 3,,C = a, C = a, C = b, C = θ(0 < θ < π) cos θ = a + (a) b (a) = 5a b 4a b = 5a 4a cos θ b = a 5 4 cos θ a ( b > 0) C C l = a + a + a 5 4 cos θ = a(3 + 5 4 cos θ) C a l = 3 + 5 4 cos θ < cos θ < 4

More information

CMP Technical Report No. 4 Department of Computational Nanomaterials Design ISIR, Osaka University 2 2................................. 2.2......................... 2 3 3 3................................

More information

  

   i 36 38 42 44 45 Al 47 SEM EPMATEMXRFXRD EPMA ( 50A EPMA-8705 EPMA1500) 14 30 60 EPMA EPMA Al Al i EPMA 14 ii iii iv v vi Incidence electrons Photon X-ray Secondary electron Backscattered electron Specimen

More information

1

1 4 Nano Device Technologies From New Functions of Extreme Substances to Telecommunication Technologies 4-1 Controlling Intermolecular Interactions using Nano- Structural Molecules OTOMO Akira, YOKOYAMA

More information

EQUIVALENT TRANSFORMATION TECHNIQUE FOR ISLANDING DETECTION METHODS OF SYNCHRONOUS GENERATOR -REACTIVE POWER PERTURBATION METHODS USING AVR OR SVC- Ju

EQUIVALENT TRANSFORMATION TECHNIQUE FOR ISLANDING DETECTION METHODS OF SYNCHRONOUS GENERATOR -REACTIVE POWER PERTURBATION METHODS USING AVR OR SVC- Ju EQUIVALENT TRANSFORMATION TECHNIQUE FOR ISLANDING DETECTION METHODS OF SYNCHRONOUS GENERATOR -REACTIVE POWER PERTURBATION METHODS USING AVR OR SVC- Jun Motohashi, Member, Takashi Ichinose, Member (Tokyo

More information

TM-m30 詳細取扱説明書

TM-m30 詳細取扱説明書 M00094100 Rev. A Seiko Epson Corporation 2015. All rights reserved. 2 3 4 5 6 Bluetooth 7 Bluetooth 8 1 9 Bluetooth 10 1 11 1 2 6 5 4 3 7 12 1 13 14 ONF 1 N O O N O N N N O F N N F N N N N N N F F O O

More information

<90AD8DF489C88A D322E696E6462>

<90AD8DF489C88A D322E696E6462> Graduate School of Policy and Management, Doshisha University 27 2011 11 2011 2011 10 2013 1950 1 1953 12 atoms for peace 2 3 1948 1960 1956 4 1958 1 1955 2 1957 IAEA International Atomic Energy Agency

More information

Fig. 1 KAMOME50-2 Table 1 Principal dimensions Fig.2 Configuration of the hydrofoils (Endurance and sprint foil) Fig. 3 Schematic view of the vortex l

Fig. 1 KAMOME50-2 Table 1 Principal dimensions Fig.2 Configuration of the hydrofoils (Endurance and sprint foil) Fig. 3 Schematic view of the vortex l A study on the simulation of the motion of personal full-submerged hydrofoil craft by Yutaka Terao, Member Summary A new energy utilization project developed by Tokai University was started in 1991. It

More information

q quark L left-handed lepton. λ Gell-Mann SU(3), a = 8 σ Pauli, i =, 2, 3 U() T a T i 2 Ỹ = 60 traceless tr Ỹ 2 = 2 notation. 2 off-diagonal matrices

q quark L left-handed lepton. λ Gell-Mann SU(3), a = 8 σ Pauli, i =, 2, 3 U() T a T i 2 Ỹ = 60 traceless tr Ỹ 2 = 2 notation. 2 off-diagonal matrices Grand Unification M.Dine, Supersymmetry And String Theory: Beyond the Standard Model 6 2009 2 24 by Standard Model Coupling constant θ-parameter 8 Charge quantization. hypercharge charge Gauge group. simple

More information

TM-m30 詳細取扱説明書

TM-m30 詳細取扱説明書 M00094106 Rev. G Seiko Epson Corporation 2015-2018. All rights reserved. 2 3 4 5 6 7 8 Bluetooth 9 ... 71 10 1 11 Bluetooth 12 1 13 1 2 6 5 4 3 7 14 1 1 2 3 4 5 15 16 ONF 1 N O O N O N N N O F N N F N

More information

Int Int 29 print Int fmt tostring 2 2 [19] ML ML [19] ML Emacs Standard ML M M ::= x c λx.m M M let x = M in M end (M) x c λx.

Int Int 29 print Int fmt tostring 2 2 [19] ML ML [19] ML Emacs Standard ML M M ::= x c λx.m M M let x = M in M end (M) x c λx. 1, 2 1 m110057@shibaura-it.ac.jp 2 sasano@sic.shibaura-it.ac.jp Eclipse Visual Studio ML Standard ML Emacs 1 ( IDE ) IDE C C++ Java IDE IDE IDE IDE Eclipse Java IDE Java Standard ML 1 print (Int. 1 Int

More information

原子・分子架橋系の量子輸送の理論 現状と展望

原子・分子架橋系の量子輸送の理論 現状と展望 1cm 10 21 1 m 1nm 10 9 1 10-4 N Maxwell DFT E.Tsuchida and M.Tsukada Phys.Rev.B52(1995)5573-5578 Phys.Rev.B54(1996)7602-7605 J.Phys.Soc.Jpn.67(1998)3844-3858 Chem.Phys.Lett.311(1999)236-240 N.Watanabe

More information

TM-m30 詳細取扱説明書

TM-m30 詳細取扱説明書 M00094101 Rev. B Seiko Epson Corporation 2015-2016. All rights reserved. 2 3 4 5 6 7 8 Bluetooth 9 Bluetooth 10 1 11 Bluetooth 12 1 13 1 2 6 5 4 3 7 14 1 1 2 3 4 5 15 16 ONF 1 N O O N O N N N O F N N F

More information

1 158 14 2 8 00225 2 1.... 3 1.1... 4 1.2... 5 2.... 6 2.1...7 2.2... 8 3.... 9 3.1... 10 3.2... 16 4.... 17 4.1... 18 4.2... 20 4.3... 22 5.... 23 5.1... 24 5.2... 28 5.3... 34 5.4... 37 5.5... 39 6....

More information

平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2

平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2 3 90 2006 1. V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2 = xz y 2 = 0} V (x,y) n = 1 n = 2 (x,y) V n = 1 n = 2 (3/5,4/5),(5/13,12/13)... n 3 V (0,±1),(±1,0) ( ) n 3 x n + y n = z n,

More information

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h 0 g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h 0 g(a + h) g(a) h g(x) a A = g (a) = f x (a, b) 5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h 0 f(a + h, b) f(a, b) h............................................................... ( ) f(x, y) (a, b) x A (a, b) x

More information

スライド 1

スライド 1 Magnetic Properties of Dangling Bond Networks on Hydrogenated Si(111) Surfaces [PRL, 90, 026803 (2003)] Design of newtwork topology makes it magent Curvature-Induced Metallization of Double-walled Semiconducting

More information

1 FMO RHF MP2 MP2 RI MP2 RHF RHF 2

1 FMO RHF MP2 MP2 RI MP2 RHF RHF 2 1 2 3 1 1 FMO RHF MP2 MP2 RI MP2 RHF RHF 2 2 2011.01 2010.10 2010.04 2010.02 RHF 2009.04 RI MP2 2008.10 RHF 2008.07 FMO RHF MP2 MP2 3 3 PAICS Teoretical study of the prion protein based on the fragment

More information

輻射の量子論、選択則、禁制線、許容線

輻射の量子論、選択則、禁制線、許容線 Radiative Processes in Astrophysics 005/8/1 http://wwwxray.ess.sci.osaka- u.ac.jp/~hayasida Semi-Classical Theory of Radiative Transitions r r 1/ 4 H = ( cp ea) m c + + eφ nonrelativistic limit, Coulomb

More information

EGunGPU

EGunGPU Super Computing in Accelerator simulations - Electron Gun simulation using GPGPU - K. Ohmi, KEK-Accel Accelerator Physics seminar 2009.11.19 Super computers in KEK HITACHI SR11000 POWER5 16 24GB 16 134GFlops,

More information