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] Kohn-Sham r 1 r 2 1 2 r 1 r 2 1 1 2 2 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 2 2 2 2 3 3 Slater r 1 r 2 r r rr r 1s r 1 1s r 2 r 1s r
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
Slater Slater Gaussian n n 1 Slater n 3 Slater Slater 2n 7 7 n S S 2 8 8 DODS S 2 2 spin contamination spin contamination [4] spin contamination spin contamination ESR DODS [1] Gaussian DODS 2 Slater
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 11 12 11
12 Kohn-Sham V xc 13 Hartree-Fock Kohn-Sham 9 10 14 15 16 14 15 16 { r } i { i } Hartree-Fock 9 Fock { r } i 17 K { r } i 17 9 10 {C ji } 18 18 19
20 9 10 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
E x E c 21 B3LYP a 0 a x a c 1988 Lee Yang Parr Hartree-Fock Kohn-Sham [3] 2.2
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 0 1 2... Gauss 23 24 Slater 24 Slater Gauss Hartree-Fock Gauss Slater E xc V xc Gauss
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
#P UHF/STO-3G... Kohn-Sham B3LYP [5] Density Functional Method Becke 1988 B Lee Yang Parr LYP
#P BLYP/STO-3G SCF SCF Harris GUESS #P B3LYP/STO-3G GUESS=INDO Harris INDO CNDO Hückel SCF SCF 64 512 #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} { 3 1 2 1} S 2 2 2.0339 spin contamination 2 S 2 UHF UKS
B3LYP/6-31G* Hartree-Fock Hartree-Fock Kohn-Sham
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,, 1987 2 M. Springborg "Methods of Electronic-Structure Calculations From Molecules to Solids" John Wiley & Sons New York 2000 3 " 12" 2004 4 T. Bally, W. T. Borden, "Reviews in Computational Chemistry", edited by K. B. Lipkowitz D. B. Boyd, Wiley-VCH, New York, vol. 13, 1-97 1999 5 Æ. Frisch, M. J. Frisch, G. W. Trucks "Gaussian 03 User's Reference" Gaussian, Inc. 2003