スライド 1

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1 Gaussian の使い方 %chk=default # HF/6-3G** comments H

2 入力ファイル %chk=default チェックポイントファイルの指定 # HF/6-3G** 出力フォーマット (ormal, Print, Terse) Hartree-Fock 法,6-3G** 基底関数 comments コメント電荷スピン多重度 H 元素記号

3 分子構造の情報 XYZ 座標で指定 water molecule 内部参照座標 (Z マトリクス ) で指定 water molecule O H H O H r H r3 r. r3. a3 4.5 a3

4 出力ファイル注意書き開発者 Copright (c) 988,99,99,993,995,998,3,4, Gaussian, Inc. All Rights Reserved. This is the Gaussian(R) 3 program. It is based on the the Gaussian(R) 98 sstem (copright 998, Gaussian, Inc.), the Gaussian(R) 94 sstem (copright 995, Gaussian, Inc.), the Gaussian 9(TM) sstem (copright 99, Gaussian, Inc.), the Gaussian 9(TM) sstem (copright 99, Gaussian, Inc.), the Gaussian 88(TM) sstem (copright 988, Gaussian, Inc.), the Gaussian 86(TM) sstem (copright 986, Carnegie Mellon Universit), and the Gaussian 8(TM) sstem (copright 983, Carnegie Mellon Universit). Gaussian is a federall registered trademark of Gaussian, Inc. This software contains proprietar and confidential information, including trade secrets, belonging to Gaussian, Inc. This software is provided under written license and ma be used, copied, transmitted, or stored onl in accord with that written license. The following legend is applicable onl to US Government contracts under FAR: RESTRICTED RIGHTS LEGED Use, reproduction and disclosure b the US Government is subject to restrictions as set forth in subparagraphs (a) and (c) of the Commercial Computer Software - Restricted Rights clause in FAR Gaussian, Inc. 34 Quinnipiac St., Bldg. 4, Wallingford CT Warning -- This program ma not be used in an manner that competes with the business of Gaussian, Inc. or will provide assistance to an competitor of Gaussian, Inc. The licensee of this program is prohibited from giving an competitor of Gaussian, Inc. access to this program. B using this program, the user acknowledges that Gaussian, Inc. is engaged in the business of creating and licensing software in the field of computational chemistr and represents and warrants to the licensee that it is not a competitor of Gaussian, Inc. and that it will not use this program in an manner prohibited above Cite this work as: Gaussian 3, Revision C., M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomer, Jr., T. Vreven, K.. Kudin, J. C. Burant, J. M. Millam, S. S. Iengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani,. Rega, G. A. Petersson, H. akatsuji, M. Hada, M. Ehara, K. Toota, R. Fukuda, J. Hasegawa, M. Ishida, T. akajima, Y. Honda, O. Kitao, H. akai, M. Klene, X. Li, J. E. Kno, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yaev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Aala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Orti, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskor, I. Komaromi, R. L. Martin, D. J. Fo, T. Keith, M. A. Al-Laham, C. Y. Peng, A. anaakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonale, and J. A. Pople, Gaussian, Inc., Wallingford CT, 4. 入力された情報にもとづく内容 ****************************************** Gaussian 3: IA3W-G3RevC. -Jun-4 6-Apr- ****************************************** %chk=default # HF/6-3G** /38=/; /7=6,8=5,4=/; 3/5=4,6=6,7=,=9,6=,5=,3=/,,3; 4//; 5/5=,3=,38=5/; 6/7=,8=,9=,=,8=/; 99/5=,9=/99; comments Smbolic Z-matri: Charge = Multiplicit = H Input orientation: Center Atomic Atomic Coordinates (Angstroms) umber umber Tpe X Y Z Stoichiometr H() Framework group OH[O(H)] Deg. of freedom Full point group OH Op 48 Largest Abelian subgroup DH Op 8 Largest concise Abelian subgroup C Op Standard orientation: Center Atomic Atomic Coordinates (Angstroms) umber umber Tpe X Y Z

5 基底関数について Standard basis: 6-3G(d,p) (5D, 7F) There are 3 smmetr adapted basis functions of AG smmetr. There are smmetr adapted basis functions of BG smmetr. There are smmetr adapted basis functions of BG smmetr. There are smmetr adapted basis functions of B3G smmetr. There are smmetr adapted basis functions of AU smmetr. There are smmetr adapted basis functions of BU smmetr. There are smmetr adapted basis functions of BU smmetr. There are smmetr adapted basis functions of B3U smmetr. Integral buffers will be 644 words long. Raffenetti integral format. Two-electron integral smmetr is turned on. 6 basis functions, 8 primitive gaussians, 6 cartesian basis functions alpha electrons beta electrons nuclear repulsion energ. Hartrees. 6-3G** 基底関数内殻電子軌道は6 個のガウス関数の線形和価電子軌道は3 個 + 個 + 個のガウス関数の線形和 * 印はp 軌道に対してd 型の分極関数を加える (H 以外 ) ** 印はさらにHのs 軌道にもp 型の分極関数を加える Hの場合:s, s, 3s 軌道として3++で3 個の基底関数 5 個の原始ガウス関数 4p, 4p, 4p 軌道として3 個の基底関数 3 個の原始ガウス関数合計 6 個の基底関数 8 個の原始ガウス関数

6 SCF 計算について Atoms= Active= Uniq= SFac=.D+ AtFMM= 6 Big=F One-electron integrals computed using PRISM. Basis= 6 RedAO= T BF= 3 BsUse= 6.D-6 BFU= 3 Harris functional with IECor= 5 diagonalied for initial guess. EpMin=.3D- EpMa= 3.39D+ EpMC= 3.39D+ IAcc= IRadAn= AccDes=.D-6 HarFok: IECor= 5 AccDes=.D-6 IRadAn= IDoV= ScaDFX=.... Initial guess orbital smmetries: Alpha Orbitals: Occupied (AG) スピンの計算値 Virtual (AG) (TU) (TU) (TU) (AG) Beta Orbitals: S s( s ) Virtual (AG) (AG) (TU) (TU) (TU) (AG) The electronic state of the initial guess is -AG..75 <S**> of initial guess=.75 Warning! Cutoffs for single-point calculations used. Requested convergence on RMS densit matri=.d-4 within 8 ccles. Requested convergence on MAX densit matri=.d-. Requested convergence on energ=5.d-5. o special actions if energ rises. Keep R and R integrals in memor in canonical form, Req= SCF Done: E(UHF) = A.U. after 4 ccles Convg =.4D-5 -V/T =. S** =.75 Annihilation of the first spin contaminant: S** before annihilation.75, after.75 SCF で収束したエネルギー ( 解析解は -.5 A.U.)

7 ********************************************************************** Population analsis using the SCF densit. ********************************************************************** 分子軌道係数をつかった解析 Orbital smmetries: Alpha Orbitals: Occupied (AG) Virtual (AG) (TU) (TU) (TU) (AG) Beta Orbitals: Virtual (AG) (AG) (TU) (TU) (TU) (AG) The electronic state is -AG. Alpha occ. eigenvalues Alpha virt. eigenvalues Beta virt. eigenvalues Beta virt. eigenvalues Condensed to atoms (all electrons): H. Mulliken atomic charges: H. Sum of Mulliken charges=. Atomic charges with hdrogens summed into heav atoms: H. Sum of Mulliken charges=. Atomic-Atomic Spin Densities. H. Mulliken atomic spin densities: H. Sum of Mulliken spin densities=. Electronic spatial etent (au): <R**>=.99 Charge=. electrons 軌道エネルギーポピュレーション解析

8 多極子モーメント分子軌道係数をつかった解析 Dipole moment (field-independent basis, Debe): X=. Y=. Z=. Tot=. Quadrupole moment (field-independent basis, Debe-Ang): XX= -.34 YY= -.34 ZZ= -.34 XY=. XZ=. YZ=. Traceless Quadrupole moment (field-independent basis, Debe-Ang): XX=. YY=. ZZ=. XY=. XZ=. YZ=. Octapole moment (field-independent basis, Debe-Ang**): XXX=. YYY=. ZZZ=. XYY=. XXY=. XXZ=. XZZ=. YZZ=. YYZ=. XYZ=. Headecapole moment (field-independent basis, Debe-Ang**3): XXXX= YYYY= ZZZZ= XXXY=. XXXZ=. YYYX=. YYYZ=. ZZZX=. ZZZY=. XXYY= XXZZ= YYZZ= XXYZ=. YYXZ=. ZZXY=. -=.D+ E-= D- KE= D- Smmetr AG KE= D- Smmetr BG KE=.D+ Smmetr BG KE=.D+ Smmetr B3G KE=.D+ Smmetr AU KE=.D+ Smmetr BU KE=.D+ Smmetr BU KE=.D+ Smmetr B3U KE=.D+ エネルギーの内訳

9 分子軌道係数をつかった解析 Isotropic Fermi Contact Couplings Atom a.u. MegaHert Gauss (-4) cm- H() Center ---- Spin Dipole Couplings XX-RR 3YY-RR 3ZZ-RR Atom XY XZ YZ Atom Anisotropic Spin Dipole Couplings in Principal Ais Sstem Atom a.u. MegaHert Gauss (-4) cm- Aes Baa H() Bbb Bcc

10 計算結果のまとめ UPC-UK SP UHF 6-3G(d,p) H() PCUSER 6-Apr- # HF/6-3 G** comments, H Version=IA3W-G3RevC. State=-AG HF= S=.75 S-=. SA=.75 RMSD=.4e-6 Dipole=.,.,. PG=OH [O( 今日の格言 Age does not diminish the etreme disappointment of having a scoop of ice cream fall from the cone. -- Jim Fiebig Job cpu time: das hours minutes 3. seconds. File lengths (MBtes): RWF= Int= DE= Chk= 3 Scr= ormal termination of Gaussian 3 at Thu Oct 4 9:9:45 3.

11 いろいろなキーワード # HF/STO-3G opt=-matri gfprint pop=full 構造を最適化する (Z マトリクスの変数を使う ) 分子軌道の係数を書き出す GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad Bern optimiation. Initialiation pass ! Initial Parameters!! (Angstroms and Degrees)! ! ame Value Derivative information (Atomic Units)! ! r. estimate DE/DX!! r3. estimate DE/DX!! a3 4.5 estimate DE/DX! Trust Radius=3.D- FncErr=.D-7 GrdErr=.D-7 umber of steps in this run= maimum allowed number of steps=. GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

12 force displacement Variable Old X -DE/DX Delta X Delta X Delta X ew X (Linear) (Quad) (Total) r r a Item Value Threshold Converged? Maimum Force.3.45 YES RMS Force.3.3 YES Maimum Displacement.43.8 YES RMS Displacement.. YES Predicted change in Energ= D-8 Optimiation completed. -- Stationar point found ! Optimied Parameters!! (Angstroms and Degrees)! ! ame Value Derivative information (Atomic Units)! ! r DE/DX =.!! r DE/DX =.!! a3.83 -DE/DX =.! GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad 最適化された Z マトリクス変数収束判定条件が満たされた

13 分子軌道係数密度行列 Molecular Orbital Coefficients (A)--O (A)--O (B)--O (A)--O (B)--O EIGEVALUES O S S PX PY PZ H S H S (A)--V (B)--V EIGEVALUES O S S PX.. 4 PY PZ H S H S DESITY MATRIX O S.787 S PX... 4 PY PZ H S H S H S H S

14 分子軌道の可視化

15 基準振動解析 %chk=default チェックポイントファイルの指定 # HF/6-3G** Opt Freq 最適化の後基準振動解析を行う water molecule コメント電荷スピン多重度 O 構造情報 H r H r3 a3 r. r3. a3 4.5 重要基準振動解析は最適化された座標で行わないと意味がない

16 Freq ルーチンでは何を計算しているか D: 入力座標系での動力学行列 W: 質量荷重座標 W は直交しているが, 縮退した 6 個の固有ベクトルとの関係は分からない T: 分子の自由並進ベクトルの組 (,, ) R: 分子の自由回転ベクトルの組 (,, ) ] 6 [3 / / / R T C W DW X M W KM M D ) ( sin sin ) (cos ) (cos sin ) (cos sin sin ) (cos sin ) (cos ) (cos sin sin ) (cos ) (cos sin ) (cos sin sin ) (cos sin ) (cos ) (cos sin, i i i a a r R T Inside Gaussian ()

17 慣性主軸系での動力学行列を解く P M U Inside Gaussian () Q / t t P P C MC t C U PU / DW W t Q DQ D t Q W L / / X M W M QL ~ t t t M X X L Q M QL ~ ~ / ~ t ~ X XM, X X t Q, Q Q D L L, [(3 [(3 t L L [3 6] [66] [3 3] 6) (3 6) (3 6)] 6)] P: 荷重変位行列 Γ - : 慣性負荷行列 ( 対称 ) U:Γ - を対角化するユニタリ行列 γ: 慣性負荷の主値 ( 対角 ) Q: 規格直交化された荷重変位行列 Q : PUγ / に直交するように (Schmidt 直交化によって ) つくった行列 D : 慣性主軸系での動力学行列 L:D を対角化するユニタリ行列 X: 座標変位ベクトル M~ - : 換算質量行列 X~: 規格化された座標変位ベクトル

18 二原子分子の場合 * ) ( m X L K D R w w w w K K K K Dw D: 動力学行列 ( 任意座標系 ) R: 慣性主軸系での固有ベクトル ( 純並進を軸に一致させた ) L: D の部分行列 [ ] の固有ベクトル X: 質量荷重の逆変換 X の規格化定数の二乗を換算質量 m* と定義 Inside Gaussian (3)

19 基準振動ベクトル Full mass-weighted force constant matri: Low frequencies Low frequencies Diagonal vibrational polariabilit: Diagonal vibrational hperpolariabilit: Harmonic frequencies (cm**-), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolariation ratios for plane and unpolaried incident light, reduced masses (AMU), force constants (mdne/a), and normal coordinates: 3 A A B Frequencies Reduced masses Force constants IR Intensities Raman Activities Depol. (Plane) Depol. (Unpol) Coord Atom Element: 低振動数の解 ( 負値かに近ければよい ) 振動数 ( 大きめにでる非調和項を入れると改善される ) モード質量とモード剛性 IR とラマンの強度原子の座標変位

20 熱力学諸量 () Thermochemistr Temperature 98.5 Kelvin. Pressure. Atm. Atom has atomic number 8 and mass Atom has atomic number and mass.783 Atom 3 has atomic number and mass.783 Molecular mass: 8.56 amu. Principal aes and moments of inertia in atomic units: 3 EIGEVALUES X... Y... Z... This molecule is an asmmetric top. Rotational smmetr number. Rotational temperatures (Kelvin) Rotational constants (GHZ): Zero-point vibrational energ (Joules/Mol) (Kcal/Mol) Vibrational temperatures: (Kelvin) 温度圧力同位体は指定可能慣性モーメントの主値と慣性主軸回転温度回転定数零点エネルギー振動温度

21 熱力学諸量 () Zero-point correction=.386 (Hartree/Particle) Thermal correction to Energ=.59 Thermal correction to Enthalp=.6865 Thermal correction to Gibbs Free Energ=.559 Sum of electronic and ero-point Energies= Sum of electronic and thermal Energies= 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 Log(Q) Ln(Q) Total Bot.9489D Total V=.654D Vib (Bot).4479D Vib (V=).D Electronic.D+.. Translational.343D Rotational.4484D = 5. J K - mol - ( 実験値 ( 水蒸気 ) 8.8 J K - mol - ) =.47 J K - mol - = 3R/

22 励起状態の計算 %chk=default チェックポイントファイルの指定 # B3LYP/6-3G** TD=(states=5) 時間依存 DFT water molecule コメント電荷スピン多重度 O 構造情報 H r H r3 a3 r. r3. a3 4.5

23 通常の DFT 計算の結果 Initial guess orbital smmetries: Occupied (A) (A) (B) (A) (B) Virtual (A) (B) (B) (A) (B) (A) (B) (A) (A) (A) (B) (B) (B) (A) (A) (B) (B) (A) (A) (A) (B) (B) (A) (B) (A) The electronic state of the initial guess is -A. Requested convergence on RMS densit matri=.d-8 within 8 ccles. Requested convergence on MAX densit matri=.d-6. Requested convergence on energ=.d-6. o special actions if energ rises. Keep R integrals in memor in canonical form, Req= Integral accurac reduced to.d-5 until final iterations. Initial convergence to.d-5 achieved. Increase integral accurac. SCF Done: E(RB+HF-LYP) = A.U. after 9 ccles Convg =.94D-8 -V/T =.8 S** =. EpMin=.3D- EpMa= 8.59D+3 EpMC=.3D+3 IAcc= IRadAn=.D-6 HarFok: IECor= 5 AccDes=.D-6 IRadAn= IDoV= ScaDFX=.... Range of M.O.s used for correlation: 3 Basis= 3 AE= 5 BE= 5 FC= FV= ROrb= 9 OA= 4 OB= 4 VA= 5 VB= 5 R, R, and R3 integrals will be kept in memor, Req= Orbital smmetries: Occupied (A) (A) (B) (A) (B) Virtual (A) (B) (B) (A) (A) (B) (B) (A) (A) (A) (B) (B) (B) (A) (A) (B) (B) (A) (A) (A) (B) (B) (A) (B) (A) AccDes=

24 励起状態の計算結果 initial guesses have been made. Convergence on wavefunction:. Iteration Dimension Mult CISAX will form AO SS matrices at one time. Iteration Dimension 3 Mult 3 Iteration 3 Dimension 4 Mult 4 Iteration 4 Dimension 44 Mult 44 *********************************************************************** Ecited states from <AA,BB:AA,BB> singles matri: *********************************************************************** Ground to ecited state Transition electric dipole moments (Au): state X Y Z Osc Ground to ecited state transition velocit dipole Moments (Au): state X Y Z Osc

25 Ground to ecited state transition magnetic dipole Moments (Au): state X Y Z < del b> * <b rdel > (Au), Rotator Strengths (R) in cgs (**-4 erg-esu-cm/gauss) state X Y Z R(velocit) < r b> * <b rdel > (Au), Rotator Strengths (R) in cgs (**-4 erg-esu-cm/gauss) state X Y Z R(length) < del b> * <b r > (Au) state X Y Z Osc.(frdel) Ground to ecited state transition densities written to RWF 633

26 励起配置吸収波長振動子強度など Ecitation energies and oscillator strengths: Ecited State : Singlet-B ev nm f= > This state for optimiation and/or second-order correction. Coping the ecited state densit for this state as the -particle RhoCI densit. Ecited State : Singlet-A 9.46 ev nm f=. 5 -> 7.7 Ecited State 3: Singlet-A 9.74 ev 7.8 nm f= > Ecited State 4: Singlet-B.669 ev 6.73 nm f= > Ecited State 5: Singlet-B.9866 ev nm f=.5 3 ->

P 和佐田.indd

P 和佐田.indd force 0 m 1 m 2 k (1) (2) 1 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) 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)