Towards gas-phase accuracy for condensed phase problems

Transcription

1 Towards gas-phase accuracy for condensed phase problems Fred Manby Centre for Computational Chemistry, School of Chemistry University of Bristol STC 2006: Quantum Chemistry Methods and Applications Erkner, 3 6 September 2006

2 Outline Molecules Solids Liquids

3 Molecules Gas-phase electronic structure theory Single-reference: MP2, CCSD, CCSD(T), CCSDT, CCSDTQ,... Multireference: CASSCF, CASPT(2), MRCI, MRCC,... Basis set series like (aug-)cc-pvnz Chemical accuracy achievable for gas-phase chemistry: 1 kcal/mol

4 Efficiency and accuracy in single-reference quantum chemistry Local methods Density fitting (Pulay & Saebø, Werner & Schütz, Head-Gordon) (Boys & Shavitt, Whitten, Baerends, Dunlap, Ahlrichs) Explicitly correlated R12 Combinations of these methods (Kutzelnigg, Klopper, Ten-no, Valeev, Manby) (Werner, Manby, Knowles, Schütz) Applications of these methods on enzymes (QM/MM) (Harvey, Manby, Mulholland, Thiel and Werner and coworkers)

5 Electron correlation in solids Periodic DFT Method of increments Stoll Periodic ab initio methods, eg: Periodic Laplace transform MP2 Scuseria et al. Periodic DF-LMP2 in CRYSCOR Pisani, Schütz et al. Finite clusters, possibly embedded

6 A non-embedded extrapolation scheme Consider a block of an NaCl-like crystal, l m n Fixed l, m; as n E lmn = E 0 lm + ne 1 lm Fixed l; as m E k lm = E 0k l + me 1k l As l E jk l = E 0jk + le 1jk

7 A non-embedded extrapolation scheme Putting all this together and assuming symmetry: E lmn = E (l + m + n) E (lm + ln + mn) E lmn E 111 E 111 is the cohesive energy E 011 is the surface energy All this converges amazingly slowly with l, m, n But how quickly do the correlation contributions converge?

8 Convergence of correlation increments in LiH Correlation energies (hartree) (MP2/cc-pVTZ) of LiH blocks -1.2 E lmn n 22n 33n 44n n

9 Hierarchical scheme for correlation in LiH Compute correlation energies of four clusters: E l1 m 1 n 1, E l2 m 2 n 2, E l3 m 3 n 3, E l4 m 4 n 4 Solve four equations of the form E lmn = E (l + m + n) E (lm + ln + mn) E lmn E 111 Equations soluble provided The four clusters do not share an identical side-length No three clusters share any pair of side-lengths

10 Hierarchical scheme for correlation in LiH Our procedure: 1. Choose N 2. Build four largest clusters that satisfy the conditions and lmn N 3. Solve equations for E 000, E 001, E 011, E Check convergence wrt N

11 Hierarchical scheme for cohesive energy of LiH MP2/cc-pVTZ (relative to correlation energy of LiH molecule)

12 Comparison with experimental cohesive energy HF corrected from Dovesi et al. molecular contribution from molecular correlation MP2/cc-pVTZ hierarchical approximation with N = 64 Core 2.2 correction from MP2(full)/cc-pCVTZ CCSD(T) +1.0 correction from CCSD(T)/cc-pVTZ Basis +0.2 correction from MP2/cc-pVQZ Zero point 7.8 DFT calculations Total Expt. 175 (All in millihartree)

13 Summary of LiH work Cohesive energy of LiH from cluster calculations Correlation contribution can be converged sub-millihartree Agreement with experiment essentially perfect No embedding used Surface energies emerge as well (as do vertex and edge energies) Transferability to other solids under investigation (LiF, MgO)

14 Ab initio Monte Carlo simulation of water Standard approaches based on empirical (or ab initio) potentials DFT (Carr-Parinello) not systematically improvable Ab initio electronic structure theory too expensive Two directions for development: Improve accuracy of model potentials Improve efficiency of ab initio methods

15 Possibilities for ab initio simulation Need about 10 5 energy evaluations of a system with about 10 2 atoms Modern ab initio methods very fast: Local methods Density fitting New local methods targeted at fluids being developed (Head-Gordon, Iwata) This work based on a many-body expansion of the binding energy

16 Many-body expansion Binding energy of a liquid (or of any aggregate of monomers) E = [E i E gas i ] + δe ij + δe ijk + i i<j 2-body increments: δe ij = E ij E i E j i<j<k 3-body increments: δe ijk = E ijk δe ij δe ik δe jk E i E j E k Convergence?

17 Truncation in order contribution E/kcal mol 1 1-body body body body body body total Xantheas JCP (1994). Cyclic (H 2 O) 6, MP2/aug-cc-pVDZ, CP

18 Truncation in distance 2-body interactions decay like R 3, but 3-body like R 9 contribution E/millihartree 2-body connected body disconnected body connected body disconnected body total total Our calculations. Cage (H 2 O) 6, MP2/aug-cc-pVDZ

19 Incremental Monte Carlo Use Monte-Carlo moves that adjust one molecule at a time Change in energy involves: one 1-body term about four 2-body terms about a dozen 3-body terms a few extra 2-body terms O(N 0 ) scaling for each MC move BSSE avoided through use of intermolecular LMP2 [Schütz, Rauhut & Werner, JPC (1998)]

20 Classical interactions Long-range 2-body interactions modelled by three terms: Electrostatics modelled by DMA multipoles to quadrupole on every atom Induction modelled by molecule-centred dipoles and polarizabilities Dispersion modelled by simple C 6 /R 6 term Many-body interactions Current approximation: zero But eventually: self-consistent polarizable dipoles

21 IMC simulation of (H 2 O) 6 Frozen monomers, no classical interactions 4000 cycles (=24000 evaluations), T = 100 K, δr tran = 0.1 Å, δθ rot = 3 g OO (r) r / angstrom

22 IMC simluation of (H 2 O) 20 MC setup: steps 6000 T 100 K δr tran 0.1 Å δr int 0.01Å δθ rot 3

23 Subtlety in first peak of g OH r OH / angstrom r = Å r OH / angstrom r 1 = Å, r 2 = Å Klopper et al. PCCP (2000)

24 Comparison with work in Ken Jordan s group Jordan group Manby group 2-body connected MP2 MP2 avoiding BSSE local local 2-body long-range MP2 classical 3-body connected MP2 MP2 3-body long-range MP2 classical 4-body MP2 or classical classical beyond 4-body zero classical

25 Thoughts on water Few (if any) care about (H 2 O) 20 at 100 K But a fully ab initio simulation of liquid water is possible This requires: Periodic boundary conditions Efficiency improvements (better initial guesses, load-balancing) Completion of work on classical models

26 More thoughts on water Advantages of IMC Easy Can introduce hierarchies straightforwardly Perfectly parallel (subject to good load-balancing) All long-range potentials based on ab initio monomer properties No additional work to change from water to something else

27 Conclusions Reproducing gas-phase accuracy for condensed matter is hard Solids: For LiH, the correlation problem can be converged sub-millihartree Surface properties emerge from the cluster hierarchy Liquids: With IMC, ab initio simulation of liquids becomes thinkable But a vast amount remains to be done

28 Acknowledgements Mike Gillan, UCL (LiH) Neil Allan, Bristol (LiH and water) Alisdair Wallis (water) Christopher Woods (water) Jeremy Harvey, Bristol Adrian Mulholland, Bristol