1 / 27

Go Large and Go Long?

Go Large and Go Long?. Todd J. Martinez. Extending Quantum Chemistry. Extend accuracy and/or size range of quantum chemistry? Remember the canon!. “Right Answer”. Minimal Basis Set Full CI. Minimal Basis Set/Hartree-Fock. Electron Correlation. Complete Basis Set/Hartree-Fock. Basis set.

Télécharger la présentation

Go Large and Go Long?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  1. Go Large and Go Long? Todd J. Martinez

  2. Extending Quantum Chemistry • Extend accuracy and/or size range of quantum chemistry? • Remember the canon! “Right Answer” Minimal Basis Set Full CI Minimal Basis Set/Hartree-Fock Electron Correlation Complete Basis Set/Hartree-Fock Basis set

  3. Taking the Canon Seriously Can we estimate the exact answer? Hypothesis: One- and Many-particle basis set contributions to energy are additive Implies that electron correlation and the flexibility of the electronic wfn are independent – cannot be true… Examples: Gaussian-2 (G2); Complete Basis Set (CBS) These methods only work well when the SBS is big enough to qualitatively describe correlation, i.e. polarized double-zeta or preferably better Extrapolated Corr/LBS Corr/SBS G2/G3 – Curtiss, et al. J. Phys. Chem. 105 227 (2001) CBS – Montgomery, et al. J. Chem. Phys. 112 6532 (2000) HF/SBS HF/LBS

  4. Beyond the Canon… Can consider a 3-dimensional version of the canon – the new dimension is model size/faithfulness For example, consider the following sequence of models: Should not ask about total energy, but rather about energy differences, e.g. De(OH) in the above examples. Always looking for E anyway – total energies are not experimentally observable for molecules.

  5. Chemical Realism of Model Correlation Basis Set Extending the Canon - IMOMO Canon is now a cube… • Again, assume additivity: Ereal/LBS/CorrEsmall/SBS/HF+ (Esmall/LBS/HF-Esmal/SBS/HF)+ (Esmall/SBS/Corr-Esmall/SBS/HF)+ (Ereal/SBS/HF-Esmall/SBS/HF) • Can be very sensitive to • choice of small model… • Test thoroughly for your problem! Vreven, et al. J. Comp. Chem. 21 1419 (2000)

  6. Multi-Level for Transition States? • Simple variant of previous ideas • Optimize w/low-level method (e.g. HF/3-21G) • Energies w/high-level method (e.g. CCSD/cc-pvtz) • Predict heat of reaction by difference of high-level E • Why not do the same for TS?

  7. Why do Rxns have Barriers? It’s the electrons, … Simple example: H2+HH+H2 “diabats,” often reasonably approximated as harmonic VH H-H VH-H H Adiabatic PES – w/barrier Crudely approx’d as constant

  8. High-Level Low-Level TS moves! Shift and Distort… To see the point, we need to complicate things… Consider XCH3 + Y- X- + H3CY • Correlation and basis set • affect frequency and • relative energy of • diabatic states

  9. Hope springs eternal… • It turns out that the MEP does not change much… • Determine MEP at low-level first • Search along low-level MEP for maximum to get • estimate for high-level barrier height – “IRCMax” High-Level Low-Level Malick, Petersson, and Montgomery, J. Chem. Phys. 108 5704 (1998)

  10. Empirical Valence Bond (EVB) • Parameterize diabats and couplings • One potential energy surface per bonding topology • More potential energy surfaces, but advantage is that • they are simpler than adiabatic surfaces • Possible to incorporate solvent effects • Disadvantages • Diagonalize a matrix to get PES • Number of diabats quickly gets large unless few • reactions are allowed… • Proposed by Warshel and Weiss • Recent applications – Voth, Hammes-Schiffer, others Warshel, et al. – J. Amer. Chem. Soc. 102 6218 (1980) Cuma, et al. J. Phys. Chem. 105 2814 (2001)

  11. Large Molecules Directly… • Is there any way to solve electronic SE for • large molecules w/o additivity approximations? • O(N) Methods • Richard Martin will cover for DFT • Same ideas are applicable in ALL e- structure methods • Generally harder to implement for correlated methods • Available in commercial code (e.g. Qchem) • Pseudospectral Methods • Closely related to FFT methods in DFT

  12. Pseudospectral Methods-Intro Integral Contractions are major bottleneck in Gaussian-based methods N4 work! Try a numerical grid… 2N3 work!

  13. Pseudospectral Methods Problem: # grid pts scales w/molecular size, but prefactor is usually very large Pseudospectral Idea – Don’t think of numerical integration, but of transform between spaces Rspectral=physical Qphysical=spectral Q must be R-1… Least-squares fitting matrix

  14. Pseudospectral Performance • PS advantage depends on Ng/N – smaller is better • Not useful for MBS/small molecules • HF and Hybrid DFT, 10x faster/100 atoms • Advantage partly additive w/locality – • local MP230x faster/100 atoms • Only available in commercial • code – Jaguar (Schrödinger) • (accessible at NCSA) Eg where PS-B3LYP optimization and PS-LMP2 energy calculations are possible – active site of cytochrome c oxidase Moore and Martínez, J. Phys. Chem. 104, 2367 (2000)

  15. Quantum Effects • Is there any need for quantum mechanics of nuclei in • large molecules? • Answer not completely known, but certainly yes for: • Tunneling – H+ transfer • Electronic Excited States – Photo-chemistry/biology • Classical mechanics only works with one PES?! What should happen

  16. Traditional Methods Need to solve TDSE for nuclear wavefunction: • Grid methods (Kosloff and Kosloff, J. Comp. Phys. 52 35 1983) • Solve TDSE exactly • Require entire PES at every time step • Only feasible for < 10 degrees of freedom • Mean-Field (Meyer and Miller, J. Chem. Phys. 70 3214 1979) • Classical Mechanics on Averaged PES • Problematic if PES’s are very different E

  17. Spawning Methods • Classical mechanics guides basis set • Adaptively increase basis set when quantum effects occur • Best for t-localized quantum effects • Effort  N Classical Trajectories, • size of N controls accuracy Nuclear wavefunction Electronic state M. Ben-Nun and T. J. Martínez, to appear in Adv. Chem. Phys.

  18. Spawning Application • Transmembrane protein • 248 AA/7 helices • Chromophore: all-trans retinal • 3762 atoms = 11,286 DOF • Light-driven proton pump Light-induced isomerization:

  19. bR Photocycle Can simulate first steps directly 200 fs < 1ps bR568 bR* J625 5 ms 3-5 ps O640 K590 2 ms ms H+ ms 70 ms N520 M412 L550 H+ Initial Geometry of RPSB

  20. Sample Results

  21. Time Scale Problem • Reality check… • We can model the first picosecond… (10-12s) • But the photocycle takes 5ms… (10-3s) • Only 9 orders of magnitude to go?! • Abandon QM for the nuclei and microsecond simulation • is feasible, but still leaves 3 orders of magnitude • What do we do? • Back to the MEP…

  22. Minimum Energy Path (MEP) E† Don’t be deceived! – MEP is usually highly curved What happens if we assume it is straight? MEP

  23. Transition State Theory The canon of rate theories! • Need enough energy to surmount barrier partition functions • For “other” degrees of freedom • For MEP coordinate • TS has finite lifetime

  24. TST II • What is ? Assume it corresponds to oscillator with -1 = TSLifetime • Put it all together…

  25. TST III All we need are: Barrier Height Frequencies at reactant and TS From Quantum Chemistry! What did we assume? Classical mechanics V separable along MEP Not good approx… • > 1 implicates tunneling True if TSLifetime is short Can always write:

  26. Polanyi Rules Vibrational excitation promotes rxn Translational excitation promotes rxn Dynamics Matters!

  27. Corrections to TST • TST almost always within 2 orders of magnitude of • correct rate • Often within factor of 5…. • To do better, need dynamics and tunneling… • Correct TST by doing dynamics around TS? • Avoid rarity of events • Issue is how to sample initial conditions… • Is TS a good idea in the first place? • Hard to find the “right” TS in large molecules • Condensed phase rxns do not have a unique TS • Better to think of ensemble of TS’s • Chandler’s Transition Path Sampling Dellago, et al. J. Chem. Phys. 110 6617 (1999)

More Related