P 和佐田.indd

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1 force 0 m 1 m 2 k (1) (2) 1 2

2 R R e 0 4 (3) 3 dv/dx 0 x (3) (4) 4 (4) (1) k N 3N x y z 3N 6 3N 5 3N 3N 3N (Hessian) 0 1 (2)

3 V 二次の鞍点始状態 ( エネルギー極小点 ) 遷移状態 ( 鞍点 ) 遷移状態終状態 ( エネルギー極小点 ) Gaussian FREQ 2 B3LYP/6-31G(d)

4 FREQ INT=(GRID=UltraFine) B3LYP 1 INT integral integral [1] a low frequencies (cm 1 ) (cm 1 ) fine ultrafine fine ultrafine fine ultrafine R(2-1) R(3-1) R(4-2) R(5-2) R(6-2) T(3-1-2) T(4-2-1) T(5-2-1) T(6-2-1) D( ) D( ) D( ) Energy a R Å T D %MEM Link0

5 Gaussian freqmem hpc% freqmem Usage: freqmem number-of-atoms number-of-basis-functions rhf/uhf conventional/direct sp/spd/spdf hpc% freqmem rhf direct spd RHF direct frequencies with spd functions: One pass requires megawords. freqmem freqmem 200 s p d 2000 RHF RB3LYP conventional direct direct 2.4GW 1 word = 8 byte 18.8 GB 2 Gaussian Low frequencies Low frequencies Low frequencies Low frequencies cm 1 FREQ RAMAN VCD Thermochemistry q Q K 1 atm U E C V S [2]

6 水分子は 3 原子から成る自由度は 3 3 2=6 x H O 1 H 2 z Z 行列指定による上の図の座標系振動解析計算に使用される座標系対称性に従って変換されている上の図の座標系とは異なる E el ( 電子エネルギー ) 単位は a.u. 1 a.u. = (kcal mol 1 ) 6 個の 0 に近い振動数低い振動数がよく一致している基準振動のモードを示す三つの固有ベクトル T(K) P(atm) } 原子量分子量回転対称数 (1) (2) (2) = (1)+PV = (1)+RT (3) (3) = (2) TS (6) (4) (5) 内部エネルギー定容比熱エントロピー (E el )... (S el )... (E trans )... (S trans )... (E rot )... (S rot )... (E vib )... (S vib )... 分配関数波数 (cm 1 ) 赤外吸収強度同じ零点振動エネルギー計算された基準振動と吸収強度から赤外線吸収スペクトルの概形を棒グラフで表示 ( 省略 ) 構造最適化が終了していることを再確認 } (4) = E el +(1) (5) = E el +(2) (6) = E el +(3) E trans +E rot +E vib

7 [3 4] Gaussian [5] Zero-point correction a.u. E(RB+HF-LYP) B3LYP E el a.u. 1 a.u.= kcal/mol cal force Maximum Displacement NO Gaussian Gaussian [6] 調和振動子ポテンシャルエネルギー 0 原子間距離 Morse ポテンシャル 4 Gaussian 03

8 %CHK=H2O.chk #P B3LYP/6-31G(d) GEOM=CHECKPOINT FREQ=(READFC,READISOTOPES) water molecule : Harmonic Frequency 0 1 温度 (K) 圧力 (atm) スケーリングファクター酸素の質量数デフォルト値を変更しない場合であっても 1 スケーリングファクター以外は省略できない水素の質量数 1 } Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mdyne/a), and normal coordinates: A1 Frequencies A B 波数は変化しない Red. masses Frc consts IR Inten Atom AN X Y Z X Y Z X Y Z Thermochemistry Temperature Kelvin. Pressure Atm. Thermochemistry will use frequencies scaled by スケーリングファクターの変更 Atom 1 has atomic number 8 and mass Atom 2 has atomic number 1 and mass Atom 3 has atomic number 1 and mass } 各同位体の正確な質量が設定される Molecular mass: amu. Principal axes and moments of inertia in atomic units: EIGENVALUES X Y Z This molecule is an asymmetric top. Rotational symmetry number 2. Rotational temperatures (Kelvin) Rotational constants (GHZ): Zero-point vibrational energy (Joules/Mol) (Kcal/Mol) Vibrational temperatures: (Kelvin) Zero-point correction= (Hartree/Particle) Thermal correction to Energy= Thermal correction to Enthalpy= Thermal correction to Gibbs Free Energy= Sum of electronic and zero-point Energies= Sum of electronic and thermal Energies= } 変更 Sum of electronic and thermal Enthalpies= Sum of electronic and thermal Free Energies= E (Thermal) CV S KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin Total Electronic Translational Rotational Vibrational Q Log10(Q) Ln(Q) Total Bot D Total V= D Vib (Bot) D Vib (V=0) D Electronic D Translational D Rotational D 振動に関する熱力学的諸量のみが変更される [1,7,8]

9 FREQ ReadFC H2O.chk ReadIsotopes GEOM=CHECKPOINT K 1 atm B3LYP/ 6-31G(d) [1] (2) 1

10 S N 2 (5) CH 3 Cl + Cl * CH 3 Cl * + Cl (5) %NPROC=8 %chk=sn2.chk #P RHF/6-31+G(d) 6D OPT=Z-MATRIX Chloromethane + Chloride ion SN2, TS C Cl 1 R1 H 1 R H 1 R H 1 R Cl 1 R R1 1.8 R Link1-- %chk= SN2.chk #P RHF/6-31+G(d) 6D FREQ GEOM=ALLCHECKPOINT 3 4 6

11 (D 3h ) 6 Z Z 6 OPT=TS OPT=TS (6) CH 3 Cl + F CH 3 F + Cl (6) C F Z OPT=ModRedundant Z [2,3] Z OPT=ModRedundant a Z Cl C F 3.0 Å 2.5 Å OPT=ModRedundant b " F" 1 C 6 F 3.0 Å 2.5 Å F 202

12 Z 行列作成時にはXを原子の番号付けに組み入れる C F 距離を3.0 Åに固定始状態の構造最適化の第一段階 X 3.0 Å 計算時には X は原子の番号付けからはずす 3 4 a %NPROC=8 %CHK=SN2.chk #P RHF/6-31+G(d) 6D OPT=MODREDUNDANT b Chloromethane + fluoride C Cl H H H F F C F 距離を2.5 Åに変更して固定 } C F 距離を 3.0 Å に固定したときの最適化構造の座標 %NPROC=8 %CHK=SN2.chk #P RHF/6-31+G(d) 6D OPT=(MODREDUNDANT,READFC) GEOM=CHECKPOINT GUESS=CHECKPOINT c Chloromethane + fluoride C F 距離を 2.3 Å に変更して固定したまま構造最適化 %NPROC=8 %CHK=SN2_TS.chk SN2.chkのコピー構造最適化回数を10 回に制限 #P RHF/6-31+G(d) 6D OPT=(TS,NOEIGENTEST,CALCFC,MODREDUNDANT,MAXCYC=10) GEOM=CHECKPOINT GUESS=CHECKPOINT Chloromethane + fluoride A 固定を解除構造最適化の最初の一回だけ振動解析計算を行う ( 毎回行うには CALCALL を指定するが非常に時間がかかる ) d %NPROC=8 %CHK=SN2_TS.chk #P RHF/6-31+G(d) 6D OPT=(TS,MODREDUNDANT,NOEIG,READFC,MAXCYC=10) e Chloromethane + fluoride -1 1 C Cl H H H F H 力の定数の推測値をチェックポイントファイルから読み込む C F 距離についてのヘス行列要素に負の曲率を指定してポテンシャル面が上に凸であるとする

13 Berny optimization. Initialization pass ! Initial Parameters!! (Angstroms and Degrees)! ! Name Definition Value Derivative Info.! ! R1 R(1,2) estimate D2E/DX2!! R4 R(1,5) estimate D2E/DX2!! R5 R(1,6) 2.3 Frozen!! R6 R(3,6) estimate D2E/DX2!! A10 L(2,1,6,-3,-1) estimate D2E/DX2!! A11 L(2,1,6,-2,-2) estimate D2E/DX2! C F force E x de/dx E c C F 7b F 2 force a b c d C Cl C F a b (Å) force (a.u.) (Å) force (a.u.) (a.u.) (kcal/mol) c d C F C F force 2.1 Å force

14 C Cl OPT=TS OPT=TS d e d CalcFC e ReadFC MaxCyc OPT NoEig NoEigenTest Standard orientation: Center Atomic Atomic Coordinates (Angstroms) Number Number Type X Y Z Low frequencies Low frequencies ****** 1 imaginary frequencies (negative Signs) ****** Diagonal vibrational polarizability: Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mdyne/a), and normal coordinates: A A A Frequencies

15 Red. masses Frc consts IR Inten Atom AN X Y Z X Y Z X Y Z A A A i cm 1 8 MOLCAT Cl F S N Gaussian intrinsic reaction coordinate: IRC 0 [9] IRC SN2_RHF_For.chk SN2_RHF_Rev.chk

16 %NPROC=8 %CHK=SN2_RHF_For.chk #P RHF/6-31+G(d) 6D IRC=(READCARTESIANFC,FORWARD,MAXPOINTS=20,STEPSIZE=20) GEOM=CHECKPOINT GUESS=CHECKPOINT Chloromethane + fluoride: FORWARD -1 1 %NPROC=8 %CHK=SN2_RHF_Rev.chk #P RHF/6-31+G(d) 6D IRC=(READCARTESIANFC,REVERSE,MAXPOINTS=50,STEPSIZE=20) GEOM=CHECKPOINT GUESS=CHECKPOINT Chloromethane + fluoride: REVERSE -1 1 IRC ReadCartesianFC Forward Reverse MaxPoints IRC StepSize IRC StepSize IRC IRC %NPROC=8 %CHK=SN2_RHF_Rev.chk #P RHF/6-31+G(d) 6D IRC=(RESTART,FORWARD,MAXPOINTS=50,STEPSIZE=20) GEOM=CHECKPOINT GUESS=CHECKPOINT Chloromethane + fluoride: REVERSE -1 1 IRC=RESTART MaxPoints 20 30

17 %CHK=SN2_RHF_For.chk Default route: MAXDISK=40GB #P RHF/6-31+G(d) 6D IRC=(READCARTESIANFC,FORWARD,MAXPOINTS=20,STEPSIZE =20) GEOM=CHECKPOINT GUESS=CHECKPOINT Chloromethane + fluoride: FORWARD Redundant internal coordinates taken from checkpoint file: SN2_RHF_For.chk Charge = -1 Multiplicity = 1 C,0, , , Cl,0, , , H,0, , , 遷移状態の構造 H,0, , , H,0, , , F,0, , , IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC Z-MATRIX (ANGSTROMS AND DEGREES) CD Cent Atom N1 Length/X N2 Alpha/Y N3 Beta/Z J C Cl H H H F : Item Value Threshold Pt 1 Converged? Maximum Force YES RMS Force YES Maximum Displacement YES RMS Displacement YES Predicted change in energy= d-06 Optimization completed. -- Optimized point # 1 Found ! Optimized Parameters!! (Angstroms and Degrees)! ! Name Value Derivative information (Atomic Units)! ! X DE/DX = !! Y DE/DX = 0.0!! X DE/DX = 0.0!! Z DE/DX = 0.0! RADIUS OF CURVATURE = NET REACTION COORDINATE UP TO THIS POINT = # OF POINTS ALONG THE PATH = 1 # OF STEPS = 3 Calculating another point on the path Stepping into the G*F direction 以下二点目以降の探索 IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC : 一点目の探索 ( 最適化が終了 ) 一点目の探索 ( 終状態の方向 ) xyz 座標系による構造最適化 Optimization completed. -- Optimized point # 20 Found ! Optimized Parameters!! (Angstroms and Degrees)! 20 点目の構造最適化が終了 ! Name Value Derivative information (Atomic Units)! ! X DE/DX = ! :! Z DE/DX = ! RADIUS OF CURVATURE = NET REACTION COORDINATE UP TO THIS POINT = # OF POINTS ALONG THE PATH = 20 # OF STEPS = IRC の各点での構造 Summary of reaction path following: とエネルギー (Int. Coord: Angstroms, and Degrees) ENERGY RX.COORD X1 Y1 Z1 遷移状態 X2 Y2 Z2 X3 Y3 : Total number of gradient calculations: 42 Total number of points: 20 Average number of gradient calculations: IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC-IRC

18 [1] J. B. Foresman, Æleen Frisch " " Gaussian Inc., Pittsburgh, Pennsylvania, USA 1998 [2] " Gaussian94 " Vol. 29 No (1998) [3] " 12" 2004 [4] J. H. Knox " " (1974) [5] "Thermochemistr y in Gaussian" [6] "Vibrational Analysis in Gaussian" [7] A. P. Scott and L. Radom J. Phys. Chem. 100, (1996) [8] P. Sinha, S. E. Boesch, C. Gu, R. A. Wheeler, and A. K. Wilson J. Phys. Chem. 108, 9213 (2004) [9] (1983)

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