New Algorithms for Conventional and. Jing Kong ( 孔静 ) Q-Chem Inc. Pittsburgh, PA
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1 New Algorithms for Conventional and Nondynamic DFT Jing Kong ( 孔静 ) Q-Chem Inc. Pittsburgh, PA
2 XC Numerical Integration mrxc: multiresolution exchage-correlation Chunming Chang Nick Russ Phys. Rev. A., 84, (2011) J. Chem. Phys., 124, (2006)
3 mrxc: Motivation E E E E ( DFT) ( Coulomb ) (exchange-correlation(xc)) 1ee ee ee Linear-scaling Coloumb: Fast-multipole, l first O(N) for Gaussians J-engine for four index integrals Latest: FTC (Fourier Transform Coulomb) for smooth functions XC: Linear-scaling by design Diagonalization: many flavors of linear-scaling algorithms but little used
4 mrxc: Motivation JCP 122, 2005 Coulomb (Q-Chem 2.1) CPU time in Minutes XC With FTC Diag Atoms G(df)
5 Fast DFT: Why Why bother since DFT is already very fast? Answer: It is still not fast enough for majority of applications.
6 Faster DFT with mrxc DFT exchange-correlation (XC) term: E f( ( r)) dr w f( ) XC i i i F w f ( ), i i i i
7 mrxc: the Grids Problem Even spaced grid, eg e.g. CPMD Efficient for smooth, diffuse functions Cannot handle compact, core functions
8 mrxc: the Grid Problem Atom-centered grid (ACG) Can handle both smooth and compact functions Not as efficient as the even-spaced grid for smooth functions
9 mrxc: the Grid Problem Can we use the two grids in one space? Not really S C f ( ) f ( ) f ( ) But one can still try GAPW: divide the space into regions S C f ( ) f ( ) f ( ) f ( ) Error: 50μH/atom μ or more
10 mrxc: Our Solution Keep the integration formally on ACG grid Smooth part is actually done on cubic grid S F S
11 mrxc: Our Solution F f f
12 mrxc: Basic Formulas Given () i C i ( ) () i Ci ( ) F f () i () i i ( ) C f ( i) i i
13 mrxc: Between Resolutions Added benefit: Smooth part free with FTC for Coulomb! (at least for closed-shell)
14 mrxc: Our Solution What is a smooth function pair? Exponent of limit (interpolated) (exact) threshold
15 mrxc: Gradient Corrected What about GGA? evaluate explicitly ( ) k ( k) ( k, ) k () i ( ) Ci
16 mrxc: Our Solution Details: grid densities: 4 and 6 in bohr -1 Local Interpolation scheme: Cardinal B-spline (PME) Interpolation order: 6
17 mrxc: Example Taxol: a natural cancer drug
18 mrxc: Example Basis sets Number of basis functions Errors (10-6 a.u per atom) Speed-up Speed-up with FTC a 6-31G(df,pd) cc-pvtz
19 Latest Coulomb Method Ewald Screened Coulomb Interaction Chun-Min Chang Yihan Shao J. Chem. Phys, 136, (2012)
20 New: Screened Coulomb Current best Coulomb algorithms FTC for smooth density (O(N 2 ), O(V)) Fast multipoles (CFMM) for well- separated densities s (O(N 2 ), O(V)) J-engine for the rest ((O(N 3 ) - O(N 4 ), O(V 2 ))
21 New: Screened Coulomb New Treat well-sperated densities on the FTC mesh as well
22 New: Ewald Screened Coulomb Based on Ewald method Using a screening Gaussian that is just smooth 1 r ( r) erfc r The screening functions cost little CPU time Replacing CFMM: Smaller separations Reducing the number of explicit AO integrals
23 New: Screened Coulomb Preliminary results Alanine10 with 6-31G* FTC+CFMM+J-engine: 1.8E+9 integrals FTC+J-engine with screening: 3.2E+8 integrals: 5 times less! CPU times: 1.5 to 3 times fast. Other benefit: easier coding of PBC
24 DFT Dispersion Model Adding Dispersion to DFT Zhengting Gan, Emil Proynov, Marek Freindorf, Thomas Furlani Phys. Rev. A, 79, (2009)
25 Nondyanmic Correlation RI-B05: Self Consistent stent Calculation of Nondynamic Correlation Emil Proynov Yihan Shao J Chem Phys (2012) J. Chem. Phys. 136, (2012) Chem. Phys. Lett. 493, 381 (2010)
26 Nondynamic Correlation Problem: DFT becomes less accurate as the bond is stretched. t Example: the dissociation of H2 molecule: GGA(BPW91): +45 kcal/mol l HF: +178 kcal/mol H-H H.H
27 B05: introduction B05 is an empirical model (JCP 122, (2005)) The delocalization of exact exchange is measured by the effective normalization The total normalization of the XC hole should be 1 f N N eff eff (1 X ( r)) X ( r) opp 1 HF HF E ND fu X fux d 2 r
28 B05: XC Hole
29 B05: XC Hole eff N X 1 2
30 B05: XC Hole + = h h h hx C X Correlation h XC
31 B05: Introduction E E a E a E a E a E HF opp opp par par opp opp par par XC X ND ND ND ND DC DC DC DC opp par opp par a 0.514, a 0.651, a 1.075, a ND ND DC DC
32 B05: Challenges Problems with B05: Nonsmooth energy surface. Nonlinear equation at every point. HF Exchange potential at every point (O(N 5 ) scaling). No apparent SCF solution.
33 B05: Challenges Becke: A longer-term objective is full self- consistency. Because the present formalism involves exact-exchange energy density in a very complicated way, this will be technically challenging.
34 B05: RI-SCF Solution Our solution: Smoothen the energy surface. Analytic interpolation of the hole function. RI approximation for real-space HF exchange: O(N 3 ) scaling, 6 times slower than a regular DFT. SCF solution.
35 DFT for nondynamical correlation MAEs for Atomization Energy for 39 Molecules (kcal/mol) B3LYP M06 RI-B MAEs of Barrier Heights for 10 Reactions (kcal/mol) M06 RI-B
36 DFT for nondynamical correlation Lastest: Implementation of MCY and PSTS MAEs for Atomization Energy for 39 Molecules (kcal/mol) PSTS MCY2 RI-B
37 RI-B05: NO Dimer NO dimer, a difficult case O O N Long distance between the two N s Ns Very weakly bound ~3kcal/mol Experiment: East, JCP, 109, 2185 (1998). Many MRCI/CCSD studies from 1994 to 2008 N
38 RI-B05: NO Dimer Questions for DFT: Is the ground state singlet or triplet? How long is the N-N bond? The direction and magnitude of the dipole moment? How is the dissociation energy?
39 RI-B05: NO Dimer Basis: G3Large Grid: (100,302) Restricted for singlet
40 RI-B05: NO Dimer Is ground-state singlet or triplet? Energy difference between singlet and triplet in kcal/mol (Singlet calculated with restricted determinant) HF B3LYP M06-2X MRCI PSTS* MCY2* RI-B05 S-T * Experimental geometry
41 RI-B05: NO Dimer How long is the N-N bond? N-N distance in Å HF BLYP B3LYP M06-2X MRCI RI-B05 Exp N-N
42 RI-B05: NO Dimer Dipole moment HF BP B3LYP M06-2X CASPT2/ RI-B05 Exp MRCI NO Dimer ?0.171
43 RI-B05: NO Dimer Is the dimer stable? Dissociation energy in kcal/mol HF B3LYP M06-2X MRCI PSTS* MCY2* RI-B05 D e * Experimental geometry
44 RI-B05: Summary Summary about RI-B05: Conceptually simple. Only 4 parameters close to the ideal. Based on HF reference. Promising in overcoming previous DFT failures.
45 RI-B05: Future Implementation of analytic gradient Further improve the model Studies of tough systems NO dimer, C2, CH2, etc Develop a qualitative physical picture
46 Research at Q-Chem Inc. Funded by Small Business Research Grants from NIH
47 People Current: Yihan Shao Emil Proynov Zhengting Gan Nick Russ Chunmin Chang Marek Freindorf Marysue Griffin Hilary Pople Jaime Martell Past: Shawn T. PSC Holger Julish Prakashan UCLA Weimin ScottTrade
48 Thank you! The End
49 People
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