Csatolások az elektron és magmozgás között, energiafelületek kereszteződése

1. Csatolások az elektron és magmozgás között, energiafelületek kereszteződése • A rögzitett mag közelités (kb. az adiabatikus közelités) • A Born-Huang Hamilton operátor (egzakt) • Csatolások azonos szimmetriájú elektronikus hf.-ek között: Elkerült kereszteződések • Az alábbi 2x2-es mátrix sajaértékei xfüggvényében, x=0..1 Avoided crossing (elkerült kereszteződés) Selected Chapters Budapest Fall 2011

2. Kónikus (kúpos) kereszteződések(Conical Intersections) Kétatomos molekuláknál a potenciálgörbék metszésének a feltétele az, hogy H11=H22és H12=H21=0. Egy változó (R) csak az egyik feltételt tudja kielégiteni, kivéve, ha a két állapot szimmetriája különbözik ( J. von Neumann and E. Wigner, Phys.Z.1929, 30,467). Elterjedt a tévhit, hogy azonos szimmetriájú potenciálfelültek nem kereszteződnek. Ez azonban nem igaz, sőt a gerjesztett elektron állapotoknak az alapállapotba való sugárzásnélküli visszatérésének a fő mechnizmusa a fekületek kereszteződése. Ha két magkordináta van, akkor még meg lehet jeleniteni. N-2 dimenziós objektum Selected Chapters Budapest Fall 2011

3. How do conical intersections controlphotostability and photochemical reactivity? Dihydroazulene (DHA) Vinylheptafulvene(VHF) Photochromism DihydroazuleneVinylheptafulvene Martial Boggio-Pasqua, M. J. Bearpark, P. A. Hunt, G. Groenhof, M. Bouxin-Cademartory, B. Hess, S. P. de Visser, H. J. C. Berendsen, M. Olivucci, A. E. Mark, and M. A. Robb Selected Chapters Budapest Fall 2011

4. Dihydroazulene (DHA)/ Vinylheptafulvene(VHF) Photochromism Selected Chapters Budapest Fall 2011

5. Cyclohexane conformational dynamics • 48 natural internal coordinates: • 18 stretchings • 64=24 CH2 deformations (scissor, rock, wag, twist) • 3 ring deformations • 3 ring torsions: boat, twist-boat and chair (b, t, c) • Chair is absolute min, c=2.4 rad • Twist-boat/boat pseudorotational pathway:b=Acos(2), t=Asin(2) =pseudorotational angle • Boat: =0o, 30o, 60o,… Twist-boat: =15o, 45o, 75o,... Selected Chapters Budapest Fall 2011

6. T=600K, 24.1 ps, start at opt. twist-boat Selected Chapters Budapest Fall 2011

7. T=800K, 24.1 ps, start at optimized boat Selected Chapters Budapest Fall 2011

8. An example - trioxane skeleton compounds • An example: trioxane is stable relative to three formaldehyde molecules. Its concerted decomposition is an exceptionally clean thermal reaction (H. K. Aldridge and M. C. Lin, Int. J. Chem. Kinet,1991, 23, 947) with a barrier of 51 kcal/mol. , and so is C3O3Cl6 relative to phosgene. Can these molecules (or the partially substituted trioxanes) be kinetically stable? • In contrast, C3O6 is unstable relative to 3 CO2 molecules Selected Chapters Budapest Fall 2011

9. Dissociation of C3O6 -energies (red= kinetic, green=potential) Selected Chapters Budapest Fall 2011

10. Methods for ab initio classical dynamics simulations (Density Functional Theory is considered ab initio) • Born-Oppenheimer: The electronic wave function is optimized for the current position of the nuclei • The Car-Parinello method: The wave function is not fully optimized, just kicked in the right direction in every stepThis is less accurate but less expensive than B-O; in dynamics, the accuracy of individual points is less important Selected Chapters Budapest Fall 2011

11. Fock matrix dynamics • In a dynamical simulation, the Fock matrix elements are analytical functions of time, because they are analytical functions nuclear coordinates, and the nuclear coordinates are analytical functions of time (we exclude the rigid body approximation) • Therefore, we can extrapolate from previous steps, using either a polynomial approximation, or a Fourier-type extrapolation • The current method is directly applicable only to SCF (Hartree-Fock and DFT) wavefunctions Selected Chapters Budapest Fall 2011

12. exact Some difficulties: Energy hysteresis • The simplest version of Fock matrix extrapolation is zeroth order: use simply the Fock matrix from the previous step • Surprisingly, this procedure leads to an violation of the energy conservation • The reason is the SCF is always converged to finite accuracy • Consider a case where the SCF iteration undershoots: Selected Chapters Budapest Fall 2011

13. Small but systematic errors hysteresis • SCF always lags slightly behind, and the forces have a slight error in the direction of the previous step • Consider an oscillator: SCF force (blue) true force (red) velocity 0 SCF error in the forces adds to the energy. In the return phase, the sign is the same: systematic. If the SCF overshoots, the system loses energy Selected Chapters Budapest Fall 2011

14. Energy conservation for butadiene Green: SCF is always started with an extended Hückel guess; Red: SCF started with the previous converged wavefunction (loose SCF threshold 10-4) Selected Chapters Budapest Fall 2011

15. Fluorid ion vizben (27 viz molekula) Selected Chapters Budapest Fall 2011

16. Jodid vizben Selected Chapters Budapest Fall 2011

17. Selected Chapters Budapest Fall 2011

18. The end Tinky Selected Chapters Budapest Fall 2011