Tools for QM studies of large systems

Transcription

1 Tools for QM studies of large systems Automated, hessian-free saddle point search & characterization QM/MM implementation for zeolites Shaama Mallikarjun Sharada Advisors: Prof. Alexis T Bell, Prof. Martin Head-Gordon

2 Efficient ways to study reaction kinetics Nuclear hessian: 2 nd derivatives of energy, are essential but expensive Characterize stationary points as minima or TS Identify reaction coordinate for TS search Cost: CPU time/10 3 (s) n-butyl lithium oligomers: B3LYP/6-31G Gradient Hessian # atoms Zeolites: large cluster models necessary but prohibitive Pores of molecular dimensions Extended framework favors adsorption and stabilizes TS 1. Methods for automated, hessian-free TS search & characterization 2. Hybrid quantum mechanics/molecular mechanics (QM/MM) Image source: H. B. Schlegel WIREs Comput. Mol. Sci. 1, ,

3 Reactant Product TS Automating the search for transition states Freezing String Method 1 : Andrew Behn, Paul Zimmerman, Shaama M S Hessian-free search 1 /characterization 2 : Shaama M S 3 1 In Q-Chem Coming soon

4 Step 1 Generate TS guess at low cost with minimum user intervention Freezing String Method (FSM) 1,2 Energy Procedure Interpolate create approx. reaction coordinate between innermost images Minimize energy of two nodes closes to userdefined spacing, perpendicular to reaction coordinate Iterate until two ends meet, TS guess is image with max. energy Input parameters in Q-Chem: jobtype fsm $rem Default Function fsm_ngrad 3 max. steps in minimization fsm_nnodes 20 ~ nodes on FSM string fsm_opt_mode 2 1 conjugate gradient minimization 2 quasi-newton minimization 4 (1) Behn et al., J. Chem. Phys., 135, , (2) Sharada et al., J. Chem. Theory. Comput., 8, , 2012.

5 Step 1 FSM costs significantly lower than previous double-ended methods Alanine dipeptide rearrangement 1,2 Earlier methods Goal accurately determine both TS guess & reaction path Strategy string re-optimized & reparameterized at each step vs. Step Cost FSM (20 nodes) 53 TS optimization 52 Total 105 FSM Goal inexpensive TS guess (~ gradients) at cost of reaction path accuracy Strategy one-shot string generation GS growing string method SM string method NEB nudged elastic band Easier to find reaction path once reaction coordinate is exactly known than to simultaneously find both. 5 (1) Behn et al. J. Chem. Theor. Comput. 7, , (2) Peters et al. J. Chem. Phys. 120, , 2004.

6 Reactant Product TS Automating the search for transition states Freezing String Method 1 : Andrew Behn, Paul Zimmerman, Shaama M S Hessian-free search 1 /characterization 2 : Shaama M S 6 1 In Q-Chem Coming soon

7 Step 2 Hessian input to optimization necessary to identify reaction coordinate Q-Chem uses Partitioned-Rational Function Optimization (P-RFO) 1 Reaction coordinate Remaining directions " H % $ ' $ 0 H 22. ' $ ' $... ' $... ' $ ' $ 0... H # nn ' & Diagonalized hessian Maximize energy Minimize energy Alternative to full hessian calculation calculate only the lowest eigenvalue at lower cost than full hessian use this to construct an approximate hessian matrix 7 (1) J. Baker, J. Comput. Chem. 7, , 1986.

8 Step 2 FSM generates good guess to the reaction coordinate Q-Chem uses guess to iteratively calculate lowest hessian eigenvalue x 0 t 1) Calculate lowest eigenvalue/eigenvector (λ, t f ) variationally 1 or with the Davidson method. 2 Cost ~ gradients FSM output Unlike full hessian, cost of constructing approx. hessian is independent of system size 2) Choose the right matrix zero cost H int Diagonal matrix of force constants in delocalized internal coordinates, convert to cartesians. 3) Update the matrix with lowest mode to get approximate hessian zero cost H final = H 1 2 H = B T H int B 3N j=1 (e T j Ht f )(t f e T j + e j t T T f )+ λt f t f 8 (1) Kumeda et al. J. Chem. Phys. Lett. 341, , (2) E. R. Davidson, J. Comput. Phys. 17, 87 94, 1975.

9 Step 2 Davidson method iteratively calculates lowest eigenvalue from FSM guess Subspace b 1, b 2,.. b l Reaction coordinate from FSM Form Hb i b it Hb j = à ij Diagonalize à Residual q ~ Σe i,k (H-λ k I)b i q < ε? Y Stop/ next root N Update the subspace Bias q with preconditioner ξ i = (λ-h ii ) -1 q i Action of hessian on vector required rather than hessian itself Finite differences 2 : H(x 0 )b i g(x +εb ) g(x εb ) 0 i 0 i +O(ε 2 ) 2ε g = E This technique can be applied to characterize stationary points as well! ε = 0.01a o 9 (1) Sharada et al. J. Chem. Phys. 140, , 2014 (2) A. Sawamura, JSIAM Lett. 3, 17 19, 2011.

10 Reactant Product TS Automating the search for transition states Freezing String Method 1 : Andrew Behn, Paul Zimmerman, Shaama M S Hessian-free search 1 /characterization 2 : Shaama M S 10 1 In Q-Chem Coming soon

11 Sample file: qchem/samples/fsmsilane.in Step 3 FSM + TS optimization input file FSM $molecule 0 1 <reactant XYZ> **** <product XYZ> $end $rem jobtype fsm fsm_ngrad 3 fsm_nnode 18 method b3lyp basis 6-31g symmetry false sym_ignore true TS $rem jobtype ts scf_guess read geom_opt_hessian read geom_opt_print 4 max_scf_cycles 250 geom_opt_max_cycles 1000 method b3lyp basis 6-31g geom_opt_dmax 100 symmetry false sym_ignore true $end $molecule read $end Read in approx. hessian from FSM Small step (dmax) recommended Read in TS guess from FSM 11

12 Step 3 P-RFO performs remarkably well even with an approximate hessian input Penalty due to approx. hessian < full hessian cost for large systems Cost (# of gradients) Exact - TS cost Exact - Hessian cost Approx. - TS cost Approx. - Hessian cost Alanine dipeptide rearrangement Ireland Claisen rearrangement Cellotriose dehydration 22 atoms 56 atoms 66 atoms 12 All calculations: B3LYP/6-31G

13 Reactant Product TS Automating the search for transition states Freezing String Method 1 : Andrew Behn, Paul Zimmerman, Shaama M S Hessian-free search 1 /characterization 2 : Shaama M S 13 1 In Q-Chem Coming soon

14 Step 4 Finite difference Davidson method can be applied post-optimization Subspace guesses obtained from eigenvectors of P-RFO updated hessian 1 Characterization time (min) Exact hessian Davidson method Characterization time (min) Exact hessian Davidson method Oligomer size (# atoms) Oligomer size (# atoms) Minima (Lowest eigenvalue) TS (Lowest 2 eigenvalues) n-butyl lithium oligomers 2 : B3LYP/6-31G 14 (1) Sharada et al., J Chem. Phys. 140, , (2) Margl, P. Can. J. Chem. 87, , 2009.

15 Step 4 Also useful when analytical hessians unavailable or when metal atoms present CH 3 F optimization with MP2/6-311G(d,p) Davidson method ~ 7.5 times faster than calculating full finite difference hessian will only scale better with increasing system size Bromo- and methoxy- derivatives of Co-diaryldithiolene for electrocatalytic proton reduction 1 CPU time (hr) Exact hessian Davidson method Br-TS OMe-TS 15 (1) Letko et al., J Am. Chem. Soc. 136, , BP86/6-31+G**

16 Summary Procedure for hessian-free, automated TS search and characterization Reactant Product TS FSM gradients Finite difference Davidson gradients P-RFO gradients Finite difference Davidson 2-30 gradients Computationally efficient procedure to study large systems, metalcontaining complexes or when analytical hessians are not available 16

17 QM/MM implementation for zeolites MM parameter optimization: Paul Zimmerman, Yi-Pei Li Q-Chem developers: Paul Zimmerman, Joe Gomes 17

18 Zeolites are aluminosilicates with pores of molecular dimensions Si O H Al Active site Framework Si substituted with Al, and proton compensates for charge imbalance Uses Fuel and petrochemical production Monomolecular reactions Probe activity/selectivity trends Computational study Challenges Active site location difficult to determine from experiments Extended pore environment must be included for accurate description Low cost High accuracy 18

19 QM/MM can approximately describe extended framework with little added cost Cluster: MM (force fields) Non-reactive, rigid Parameters adapted from CHARMM Si and O parameters modified to reproduce pure QM results 1,2 within error ~ 10 kj/mol Atom Q ε (kcal/mol) R (Å) Si O Active region: QM (DFT) Electrostatically embedded substrate + active site (5 tetrahedral atoms) Non-bonding interactions with MM Computational time limited by QM size only 19 (1) Zimmerman et al. J. Chem. Theory Comput., 7, , (2) Li et al (in progress)

20 Sample file: qchem/samples/qmmm_zeo-force.qcin QM/MM input file components $molecule: Tinker XYZ format Fixed atoms (MM)... H Al O Force field parameters $force_field_params NumAtomTypes 130 AtomType AtomType AtomType AtomType AtomType AtomType AtomType AtomType AtomType $end Lennardcharge Jones Additional $rem variables qm_mm_interface zeolite force_field charmm27 user_connect true qmmm_print true qm_mm true qmmm_full_hessian false aimd_fixed_atoms 807 geom_opt_coords 0 Framework Si & O Substrate (CHARMM) $opt FIXED 21 XYZ ENDFIXED $end QM atom indices $qm_atoms $end Recommended level of theory: ωb97x-d 1,2 /6-311G** Non-bonding interactions significant in zeolites TS stabilized by electrostatic interactions with framework 20 Chai & Head-Gordon: (1) J. Chem. Phys., 128, , 2008 (2) Phys. Chem. Chem. Phys., , 2008

21 QM/MM is an efficient approach to study adsorption & catalytic properties of zeolites Benefits over small cluster models accurately captures non-bonding interactions between substrate and framework allows us to analyze trends in activation energies with respect to active site location type of extended environment (channel/intersection/cage) both within a zeolite as well as across frameworks Drawbacks and future work activation entropies for dehydrogenation calculated using simple harmonic approximation are lower than experiment develop approaches that take into account the extended environment in entropy calculation as well 21