和佐田P indd

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1 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 X, Y, Z x, y, z l m n s p d f Slater Slater-Type Orbital: STO Slater-Type Function: STF 2 2 Gauss 1 STO-1G

2 波動関数 (a.u. 3/2 ) 波動関数 (a.u. 3/2 ) STO-3G STO-3Gの原始 GTF STO-1G の厳密解 r (a.u.) 動径 r (a.u.) Gauss Gauss Contracted GTF: CGTF 1 CGTF GTF Gauss primitive GTF CGTF 2 LCAO CGTF 2 2s 2p p x p y p z 1 CGTF 2 p p x p y p z shell p p-shell shell s p sp-shell Gaussian STO-3G LANL2MB STO-3G Slater 3 GTF CGTF STO

3 1RHF/STO-3G 合計 7 個の基底関数 Minimal Basis Sets O 2s 2p 5 個の基底関数 H 1 個の基底関数 = 7 2RHF/3-21G 合計 13 個の基底関数 Split Valence Basis Sets O 9 個の基底関数 H 2 個の基底関数 2s' 2p' ' 2s 2p C 1 + C 2 = = 13 3RHF/6-31G(d) 合計 19 個の基底関数 Polarized Basis Sets O 15 個の基底関数 H 2 個の基底関数 2s' 2p' d ' 2s 2p C 1 + C 2 = = 19 4RHF/6-311G(d,p) 合計 31 個の基底関数 O 19 個の基底関数 H 6 個の基底関数 2s" 2p" d " p 2s' 2p' ' 2s 2p 5RHF/6-311+G(d,p) 合計 35 個の基底関数 Diffuse Basis Sets O 23 個の基底関数 H 6 個の基底関数 2s''' 2p''' d " p 2s" 2p" ' 2s' 2p' 2s 2p C 1 + C = 35 6RHF/6-311+G(2d,p) 合計 41 個の基底関数 O 29 個の基底関数 H 6 個の基底関数 2s''' 2p''' d' 2s" 2s' 2s 2p" d 2p' 2p " p ' = 41 7RHF/ G(3df,3pd) 合計 80 個の基底関数 O 42 個の基底関数 H 19 個の基底関数 f d" p" d 2s''' 2p''' d' " p' 2s" 2p" d " p 2s' 2p' ' 2s 2p = = = 80 CGTF CGTF GTF G 2s 2p 2s' 2p' 6-31G 6 GTF 1 CGTF 3 GTF CGTF GTF Pople GTF GTF 3 STO-3G 3 3 GTF G GTF 3-21G Gaussian D95 Huzinaga-Dunning D95 full double-zeta double-zeta full

4 split-valence Pople 2p G(d) 6-31G* 2p 6 d d 5 6 d 10 f 6-311G(d,p) 6-311G** s p 6-31G 6-311G * * 3-21G* 3-21G * shell G(2d,p) diffuse d d' d-shell Rydberg diffuse G(d,p) 2s 2p sp-shell s s' s'' p p' p'' 12 s''' p''' diffuse 2diffuse G 3df,3dp 2 diffuse Gaussian diffuse 6-311G(d',p) 6-311G(3df',3dp') '

5 6-31G 6-311G 4p 5 diffuse d f d d xy d yz d zx d x 2 d y 2 d z 2 6 f 10 d d x 2 d y 2 d z 2 d x 2 y d 2 x 2 2 2z 2 x 2 y y 2 z 2 expr 2 3s f 7 f 3 4p d 5 d 6 Cartesian d Gaussian 6-31G Cartesian d d 3 d Cartesian d Z-Matrix orientation: Center Atomic Atomic Coordinates (Angstroms) Number Number Type X Y Z : Rotational constants (GHZ): General basis read from cards: (5D, 7F) Centers: LANL2MB Centers: 1 44 S Exponent= D+04 Coefficients= D-03 : Exponent= D+01 Coefficients= D-03 Integral buffers will be words long. Raffenetti 2 integral format. Two-electron integral symmetry is turned off. 318 basis functions, 1446 primitive gaussians, 322 cartesian basis functions 215 alpha electrons 209 beta electrons nuclear repulsion energy Hartrees. :

6 [1,2] 4 HF STO-3G CISD CISD(T) CCSD CCSD(T) RHF/3-21G CISD/STO-3G MPn CI CCSD post-hartree-fock Rydberg diffuse 1 Hartree-Fock Hartree-Fock DZP Hartree-Fock 0.02 Å [1-3] post-scf [3] d [4] FSO HF/4-31G S-O 0.22 Å F-O 0.10 Å 0.04 Å [1-4] [5] Cu Cu 3 4 [Cu H 2 O 3 ] [Cu H 2 O 4 ] Cu [Cu H 2 O 2 ] H 2 O [Cu H 2 O 2 ] 2H 2 O s p [1] double-zeta

7 6-31G* 6-31 G* 4-31G 6-31G CI [3] Basis Set Superposition Error: BSSE BSSE A B AB A B A B B A A B BSSE diffuse BSSE BSSE kcal/mol kcal/mol van der Waals BSSE van der Waals BSSE triple-zeta diffuse [2,6] HF 2 H 2 O G(d,p) Hartree-Fock MP2 BLYP [6] ccpvxz HF/cc-pVDZ 6-31G(d,p) cc-pvtz van der Waals Hartree-Fock post-scf MP2/d-aug-cc-pVDZ diffuse

8 diffuse [2] STO-3G 6-31G(d,p) 4 O O H H H H STO-3G 6-31G(d,p) STO-3G OH Mulliken population analysis Gaussian Hartree-Fock Mulliken population analysis Mulliken population diffuse Mulliken population 6-31G* diffuse diffuse

9 Gaussian Gaussian 03 [7] G(d,p) B3LYP #p B3LYP/6-31G d,p... d f 5D 6D 7F 10F d #p B3LYP/6-31G d,p 5D... double-zeta BSSE diffuse ExtraBasis #P B3LYP 6-31G EXTRABASIS 5D tetraaquacopper(ii) 2 2 Cu O H O 0 D [Cu H 2 O 4 ] G 0.8 d

10 3 #P B3LYP GEN 5D tetraaquacopper(ii) 2 2 Cu O H Cu G P P O H G* O H 6-31G* Cu 6-311G Wachters 4p [8] 6-31G* t- STO-3G Z

11 X 5 diffuse 6-31 G(d) 6-31G(d) BSSE GTO 3 d i i N f [9] 4 GFINPUT IOP 3/24 10 [9,10] [9,11] O 0 0 shell s p d... sp N f 1.0 O s 5 1 GTF GTF i d i 5 5 2s 3 s 2p 5 p

12 # RHF GEN Water 0 1 O H 1 R1 H 1 R1 2 T1 R T O 0 S D D D D D D D D D D+00 S D D D D D D+00 P D D D D D D D D D D+00 H 0 S E E E E E E E E E E-02 diffuse diffuse ECP diffuse [12,13] CEP-121G diffuse diffuse even-tempered [2] I I

13 #P B3LYP CEP-121G GFINPUT I, CEP-121G -1 1 I Gaussian : Standard basis: CEP-121G(6D, 10F) Basis set in the form of general basis input: 1 0 SP D D D D D D D D D D D D+00 SP D D D+01 : B3LYP #P B3LYP CEP-121G EXTRABASIS GFINPUT I, CEP-121G -1 1 I I 0 SP a.u x y y x x

14 x / l 4 [2] 4 ave r max Gaussian 03 diffuse diffuse [ 1 ] A. Szabo and N. S. Ostlund "Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory", Dover, ,, 1987 [ 2 ] T. Helgaker, P. Jørgensen, and J. Olsen "Molecular Electronic-Structure Theory", John Wiley & Sons Ltd., New York [ 3 ] S. Iwata "Reliability of Ab Initio Calculations" in K. Ohno and K. Morokuma, ed. "Physical Science Data 12 Quantum Chemistry Literature Data Base", Elsevier, Tokyo 1982 [ 4 ] 1983 [3] 7 5

15 [ 5 ] C. W. Bauschlicher, Jr., S. R. Langhoff and H. Partridge J. Chem. Phys. 94, [ 6 ] N. R. Kestner and J. E. Combariza "Reviews in Computational Chemistry", 13, [ 7 ] Æ. Frisch, M. J. Frisch and G. W. Trucks "Gaussian 03 User's Reference" Gaussian, Inc [ 8 ] A. J. H. Wachters J. Chem. Phys. 52, [ 9 ] Basis Set Order Form [10] H. Tatewaki and T. Koga. J. Chem. Phys. 104, [11] H. Yamamoto, and O. Matsuoka Bulletin of the University of Electro-Communications, 5-1, [12] S. Huzinaga, ed. "Physical Science Data 16 Gaussian Basis Sets for Molecular Calculations", Elsevier, Tokyo 1984 [13] A. W. Ehlers, M. Böhme, S. Dapprich, A. Gobbi, A. Höllwarth, V. Jonas, K. F. Köhler, R. Stegmann, A. Veldkamp and G. Frenking Chem. Phys. Lett

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