Accurate Quantum Chemistry for Large Molecules

Transcription

1 Accurate Quantum Chemistry for Large Molecules Fred Manby Centre for Computational Chemistry, School of Chemistry University of Bristol

2 Outline Three problems in quantum chemistry Three solutions

3 Quantum chemistry ĤΨ = EΨ (One possible) hierarchy of methods HF MP2 CCSD CCSD(T) CCSDT FCI (One possible) hierarchy of basis sets VDZ VTZ VQZ V5Z Chemical accuracy a few kj mol 1

4 Benchmarking standard methods Set of simple reactions (from Helgaker, Jørgensen and Olsen) CO 2 + 4H 2 CH 4 + 2H 2 O N 2 + 3H 2 2NH 3 C 2 H 2 + H 2 C 2 H 4 CO + H 2 CH 2 O CH 2 O + 2H 2 CH 4 + H 2 O F 2 + H 2 2HF HCN + 3H 2 CH 4 + NH 3 O 3 + 3H 2 3H 2 O C 2 H 2 + 3H 2 2CH 4 CH 2 + H 2 CH 4 CO + 3H 2 CH 4 + H 2 O 2CH 2 C 2 H 4 HNO + 2H 2 H 2 O + NH 3 Plot normal distributions of errors (in kj mol 1 )

5 CCSD(T) Errors for benchmark reaction energies in kj mol 1 CCSD MP HF VDZ VTZ VQZ V5Z

6 Three problems in quantum chemistry Steep scaling of effort wrt molecular size Steep scaling of effort wrt basis set size Slow convergence wrt basis set size Excited states Quantum dynamics of nuclei Solvation Multireference methods

7 Steep scaling of effort wrt molecular size (H 2 O) n 1500 time/s CCSD(T) CCSD MP2 HF n

8 Steep scaling of effort wrt basis set size H 2 O with MP2/cc-pVnZ 100 time/s 50 0 VDZ VTZ VQZ V5Z V6Z basis set

9 Slow convergence in quantum chemistry error [basis size] 1 time [basis size] 4 0error error time 1/4 time fold improvement in CPU speed gives only one order of magnitude

10 Three problems in quantum chemistry Steep scaling of effort wrt molecular size Steep scaling of effort wrt basis set size Slow convergence wrt basis set size

11 Canonical and local orbitals Indinavir

12 Canonical and local orbitals Indinavir a canonical orbital

13 Canonical and local orbitals Indinavir a local orbital

14 Rapid decay of correlation energy Incremental Correlation Energy [Hartree] kcal/mol bohr Indinavir 1e Interorbital Distance [bohr]

15 Local correlation theories Use localized orbitals Take advantage of the short-ranged nature of correlation Pioneered by Pulay and Saebø Current implementation by Werner and Schütz Achieves linear scaling with respect to system size

16 LMP2/VDZ on (Gly) n : Werner et al. 150 CPU-time / minute standard MP2 local MP n

17 Local coupled cluster (Schütz and Werner) Gly n with LCCSD/VDZ and LCCSD(T)/VDZ (T) CCSD Iteration 7 (~N ) 6 (~N ) CPU time / s LCCSD Iteration (~N) L(T) (~ N) n

18 Three problems in quantum chemistry Steep scaling of effort wrt molecular size local methods Steep scaling of effort wrt basis set size Slow convergence wrt basis set size

19 Density fitting All ab initio quantum chemistry needs 2-electron integrals d r 1 d r 2 ψp( r 1 )ψ q ( r 1 ) 1 ψ r r( r 2 )ψ s ( r 2 ) 12 pq) rs) Idea is to fit these orbital product densities in a set of functions pq) = A D pq A A)

20 Density fitting First used by Boys and Shavitt for H 3 (1959) Used by Baerends and Dunlap in density functional theory (1970s) Recently used in ab initio methods: Ahlrichs, Feyereisen, Komornicki FRM, Knowles, Lloyd PRL (2001); JCP (2001) Werner, FRM, Knowles, JCP (2003) FRM, JCP (2003); Ten-no, FRM, JCP (2003) Schütz, FRM, PCCP (2003) Schütz, Werner, Lindh, FRM, JCP (2004) May, FRM, JCP (2004)

21 Efficiency of density fitting H 2 O with MP2/cc-pVnZ time/s MP2 DF-MP2 0 VDZ VTZ VQZ V5Z V6Z basis set

22 Combining local and density fitting methods Use localized orbitals Werner, FRM, Knowles, JCP (2003) Perform density fitting Fit products of local orbitals in localized fitting expansions ia) A near i,a D ia A A)

23 DF-LMP2 performance Indinavir in cc-pvtz (2008 bf) CPU time/second LMP2 DF-MP2 DF-LMP2 Integrals Transformation Solve Assemble Iteration Total MP Werner, FRM, Knowles, JCP (2003)

24 DF-LMP2/VDZ on (Gly) n CPU-time / minute LMP2 DF-MP2 DF-LMP n

25 DF-LMP2 accuracy Comparison of MP2 and DF-LMP2 reaction energies (kcal/mol) VTZ VQZ MP2 DF-LMP2 MP2 DF-LMP2 I II III I HF + 2-butene 2-fluorobutane II III THF + 2 H 2 O 2 γ-butyrolactone + 3 H 2 O

26 Other DF-local theories DF-HF Polly, Werner, FRM, Knowles, Mol. Phys. in press (2004) Needed since the DF-LMP2 program was so fast DF-LCCSD(T) Schütz and FRM, PCCP (2003) In progress, but indicates 100-fold improvement in speed over LCCSD(T) DF-LMP2 gradients Schütz, Werner, Lindh, FRM, JCP (2004)

27 Three problems in quantum chemistry Steep scaling of effort wrt molecular size local methods Steep scaling of effort wrt basis set size density fitting Slow convergence wrt basis set size

28 The origin of slow convergence Ĥ only has terms like 1/r 12 and /r 12 blows up when electrons coalesce ĤΨ(r 12)/Ψ(r 12 ) = E does not Cancellation of divergence must be from KE Ψ(r 12 ) = 1 r 12 for small r r 12 = 1 r 12

29 Slow convergence in the helium atom

30 Slow convergence Orbital expansions are not very good for describing correlation Orbitals expanded about nuclei, not about other electrons Simple solution: include terms that depend on r 12 in the wavefunction

31 Explicitly correlated theories Hylleraas pioneering calculations on helium log(error) orbital-based wavefunctions Hylleraas wavefunctions number of terms

32 DF-MP2-R12 theory Based on MP2-R12 theory (Kutzelnigg, Klopper et al.) Uses density fitting FRM, JCP (2004) Uses an optimal correlation factor Andy May, FRM, JCP (2004) Local versions under development (FRM and H-J Werner)

33 Benchmarking explicitly correlated theories 1 CO + SO 3 CO 2 + SO 2 2 C 2 H 2 + H 2 O CH 3 CHO 3 CO + Cl 2 COCl 2 4 furan + H 2 S thiophene + H 2 O 5 CO + CH 3 OH HCOOCH 3 6 CO + NH 3 HCONH 2 7 CO + H 2 O CO 2 + H 2 8 CS H 2 O CO H 2 S 9 H 2 CCO + HCHO C 2 H 4 O + CO 10 H 2 O 2 + H 2 2 H 2 O 11 C 2 H 2 + H 2 C 2 H 4 12 C 2 H 4 + H 2 C 2 H 6 13 HCHO + H 2 CH 3 OH 14 C 2 H 6 + H 2 2 CH 4 15 CO + H 2 HCHO 16 CH H 2 O 2 CO H 2 O 17 NH H 2 O 2 HNO H 2 O 18 CO + H 2 O 2 CO 2 + H 2 O 19 SO 2 + H 2 O 2 SO 3 + H 2 O 20 HNCO + NH 3 NH 2 CONH 2

34 Benchmarking explicitly correlated theories CCSD(T) correlation energy contributions relative to AVQZ+R12 4 Energy difference (kcal/mol) AVTZ AVQZ AVTZ+R Reaction number

35 Three problems in quantum chemistry... and three solutions Steep scaling of effort wrt molecular size local methods Steep scaling of effort wrt basis set size density fitting Slow convergence wrt basis set size explicit correlation

36 Some applications DNA intercalators: J Platts (Cardiff) PHBH enzyme: W Thiel (Mülheim), R Mata, H-J Werner (Stuttgart) Gas-phase conformation of enkephalins: J Hirst (Nottingham) Chorismate mutase: Fred Claeyssens, AJM, JNH

37 Chorismate mutase Protein bulk treated by molecular mechanics (QM/MM) Calculations by Fred Claeyssens

38 Chorismate mutase energy / kcal mol HF MP2 CCSD(T) reaction coordinate / angstrom

39 Future work Method development Correlated alternatives to Hartree-Fock theory Optimal control, interaction of light and matter (with GGBK) Quantum mechanics of light nuclei Combined molecular mechanics and quantum mechanics (with JNH, AJM) Applications High-level quantum chemistry of enzymes (with AJM, JNH) Quantum chemistry at interfaces (with NLA, JPR)

40 Conclusions Chemical accuracy can now be achieved for large molecules New methods combine three key developments Local description of correlation Density fitting Explicit correlation Methods available in Molpro quantum chemistry package Distributed to 300 research groups across the world

41 Acknowledgements Hans-Joachim Werner (Stuttgart) Martin Schütz (Regensburg) Ricardo Mata (Stuttgart) Peter Knowles (Cardiff) Andrew May (Bristol) Seiichiro Ten-no (Nagoya) Fred Claeyssens (Bristol) Jeremy Harvey (Bristol) Adrian Mulholland (Bristol)