和佐田P indd

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1 2000 B3LYP/6-31G Gaussian B3LYP/6-31G* Gaussian STO-3G RHF Gaussian RHF/STO-3G B3LYP RHF 6-31G* STO-3G Schrödinger Schrödinger s p d

2 Schrödinger Schrödinger Hohenberg-Kohn Kohn-Sham Kohn-Sham [1-3] Kohn-Sham r 1 r r 1 r r 1 1 r 2 2 r 1, r 2 r 1 1 r 2 2 r 1 2 r 2 1 Pauli 1 r 1 r Slater r 1 r 2 r r rr r 1s r 1 1s r 2 r 1s r

3 4 1 1s 2s r r r r r r r r r r r r 5 Pauli 1s r 1s r 2s r DODS Different Orbital for Different Spin 6 1

4 Slater Slater Gaussian n n 1 Slater n 3 Slater Slater 2n 7 7 n S S DODS S 2 2 spin contamination spin contamination [4] spin contamination spin contamination ESR DODS [1] Gaussian DODS 2 Slater

5 0 1 2 Hartree-Fock Kohn-Sham Hartree-Fock Kohn-Sham V xc Hartree-Fock Hartree-Fock Restricted Hartree-Fock, RHF DODS Hartree-Fock Unrestricted Hartree-Fock, UHF Kohn- Sham UKS Hartree-Fock Kohn-Sham N Hartree-Fock 9 Kohn-Sham 10 r 1 Coulomb Kohn-Sham V xc Kohn- Sham Slater

6 12 Kohn-Sham V xc 13 Hartree-Fock Kohn-Sham { r } i { i } Hartree-Fock 9 Fock { r } i 17 K { r } i {C ji }

7 i C 1i, C 2i,, C ji, C Ki F ij {C ji } C 1i, C 2i,, C ji, C Ki 18 C 1i, C 2i,, C ji, C Ki 16 3 Gaussian [5] GUESS SCF Gaussian 03 Harris DIIS Direct Inversion in the Iterative Subspace extrapolation Hartree-Fock Slater 2 Slater Hartree-Fock Hartree-Fock Hartree-Fock Kohn-Sham Hartree-Fock Hartree-Fock X Local- Spin -Density Approximation, LDA, LSDA LDA Generalized Gradient Approximation, GGA 1990 Becke Hartree-Fock

8 E x E c 21 B3LYP a 0 a x a c 1988 Lee Yang Parr Hartree-Fock Kohn-Sham [3] 2.2

9 1 HOMO-LUMO Hartree-Fock Kohn-Sham 2 UHF spin contamination UKS 3 Kohn-Sham 16 r i { r } i Gauss p x 22 x y, z X, Y, Z 23l m n l m n s p d... l m n Gauss Slater 24 Slater Gauss Hartree-Fock Gauss Slater E xc V xc Gauss

10 Kohn-Sham Slater Gaussian Gauss Hartree-Fock Hartree-Fock Hartree-Fock Hartree-Fock limit Kohn-Sham Kohn-Sham [2] 4 HF Hartree-Fock Schrödinger Hartree-Fock STO-3G B3LYP HF MP2 # RHF RHF HF RHF Hartree-Fock #P ROHF/STO-3G... B3LYP #P ROB3LYP/STO-3G... RO #P HF/STO-3G... UHF UHF UKS UHF UB3LYP HF RHF

11 #P UHF/STO-3G... Kohn-Sham B3LYP [5] Density Functional Method Becke 1988 B Lee Yang Parr LYP

12 #P BLYP/STO-3G SCF SCF Harris GUESS #P B3LYP/STO-3G GUESS=INDO Harris INDO CNDO Hückel SCF SCF #P B3LYP/STO-3G SCF=(MAXCYC=512) DIIS QC Quadratic Convergence ROHF #P B3LYP/STO-3G SCF=(QC,MAXCYC=80) HOMO-LUMO SCF SCF 500 mhartree 0.5 Hartree #P B3LYP/STO-3G SCF=(VSHIFT=500,MAXCYC=256) spin contamination 5 UB3LYP spin contamination { 3 1 2} { } S spin contamination 2 S 2 UHF UKS

13 B3LYP/6-31G* Hartree-Fock Hartree-Fock Kohn-Sham

14 Hartree-Fock post-hartree-fock 6-31G* 1 A. Szabo, N. S. Ostlund "Modern Quantum Chemistr y: Introduction to Advanced Electronic Structure Theory", Dover, 1996,, M. Springborg "Methods of Electronic-Structure Calculations From Molecules to Solids" John Wiley & Sons New York " 12" T. Bally, W. T. Borden, "Reviews in Computational Chemistry", edited by K. B. Lipkowitz D. B. Boyd, Wiley-VCH, New York, vol. 13, Æ. Frisch, M. J. Frisch, G. W. Trucks "Gaussian 03 User's Reference" Gaussian, Inc. 2003

和佐田　裕昭P indd

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