P 和佐田.indd
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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
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