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Recent developments for the quantum
chemical investigation of molecular
systems with high structural complexity
Stephan Ir...
Group Theme: Quantum Chemistry of Complex Systems
http://qc.chem.nagoya-u.ac.jp
Quantum Chemistry
Statistical Mechanics
Mo...
Density-Functional Tight-Binding (DFTB)
Tight Binding (extended-Huckel-like) method with parameters from DFT
E(NCC-)DFTB
=...
5
ReviewDFTB
Ref.: Oliviera, Seifert, Heine, Duarte, J. Braz. Chem. Soc. 20,
1193-1205 (2009)
...open access
Thomas
Heine
...
6
ReviewDFTB
Density Functional Theory (DFT)
E ré
ë
ù
û= ni
yi
-
1
2
Ñ2
+ vext

r( )+
r

r '( )

r -

r '
ò d3
r' yi
i...
Self-consistent-charge density-functional
tight-binding (SCC-DFTB)
M. Elstner et al., Phys. Rev. B 58 7260 (1998)
E r0 + d...
DFTB and SCC-DFTB methods
 where
 ni and i — occupation and orbital energy ot the ith Kohn-Sham
eigenstate
 Erep — dis...
DFTB method
 Repulsive diatomic potentials replace usual nuclear repulsion
energy
 Reference density r0 is constructed f...
10
 Additional induced-charges term allows for a proper description
of charge-transfer phenomena
 Induced charge qA on ...
14
Traditional DFTB concept: Hamiltonian matrix elements are approximated to
two-center terms. The same types of approxima...
15
LCAO ansatz of wave function
  

 Rri
i c
secular equations
  0
  SHc i
i
variational
principle
...
16
LCAO ansatz of wave function
  

 Rri
i c
secular equations
  0
  SHc i
i
variational
principle
...
17
LCAO ansatz of wave function
  

 Rri
i c
secular equations
  0
  SHc i
i
variational
principle
...
r14
18
LCAO ansatz of wave function
  

 Rri
i c
secular equations
  0
  SHc i
i
variational
princi...
DFTB repulsive potential Erep
Which molecular systems to include?
Development of
(semi-)automatic
fitting:
•Knaup, J. et a...
21/25
New Confining Potentials
Wa
Conventional potential
r0
Woods-Saxon potential
k
R
r
rV 






0
)(
R0 = 2.7, ...
Band structure for Se (FCC)
Brillouin zone
22
New Electronic Parameters DFTB Parameterization
Particle swarm optimization (PSO)
New Electronic Parameters DFTB Parameterization
23
1) Particles (=candidate of a solution) are randomly placed initially in a target space.
2) – 3) Position and velocity of ...
Each particle has
randomly generated
parameter sets (r0, a, W)
within some region
Generating one-center
quantities (atomic...
Example: Be, HCP crystal structure
DFTB Parameterization
Total density of states (left) and band structure (right) of
Be (...
DFTB ParameterizationTransferability of optimum parameter sets
for different structures
Artificial crystal structures can...
Correlation of r(orb) vs. atomic diameter
Atomic Number Z
Atomicdiameter[a.u.]
Empirically measured radii
(Slater, J. C., ...
Rocksalt (space group No. 225)
•NaCl
•MgO
•MoC
•AgCl
…
•CsCl
•FeAl
…
B2 (space group No. 221)
Zincblende (space group No. ...
element name
Ga, As hyb-0-2
B, N matsci-0-2
Reference of
previous work :
•d7s1 is used in
POTCAR (DFT)
Further improvemen...
31
•space group No. 229
•1 lattice constant (a)
Transferability checked (single point calculation)
Reference system in PSO...
32
DFTB ParameterizationErepfit
Gaus, M. et al., JPCA, 113, 11866, (2009)
Prof. Henryk
Witek
Dr. Yoshifumi
Nishimura
Chien...
x 1,000,000
Chemistry sans thought
Dr. Matt Addicoat,
(JSPS Postdoc)
Guessing competition:
• What kind of conformations can a
molecule of four different atoms, A, B,
C, D adopt?
Guessing competition:
12 12 6
12 12 2
Guessing competition:
Guessing competition:
• ABCD has a 6 possible structures with
a total of 56 permutations
• ABCDE has 15 possible structure...
• Genetic algorithm
• Simulated annealing
• Monte-Carlo
• Basin hopping
Automated approaches
Wishlist
• No assumed knowledge / limiting
parameters
• Ensemble of structures
• Broad applicability
• level of theory
• c...
Kick
• The original Kick (M. Saunders) took a
geometry (input file) and perturbed it
• The Schaefer version generated
rand...
Kick
• A fragment is supplied as cartesian co-
ordinates which are rotated by a
random angle (Φ,ϑ,Ψ) before being
"kicked"...
(x,y,z)
(0,0,0)
-1
Zeise‟s anion
+ 3 +
- or -
Zeise‟s anion
+ 3 + 2
+ 4
- or -
Zeise‟s anion
Zeise‟s anion
• Pt + 3Cl + C2H4
• 20 jobs, 6 minima
• Pt + 3Cl + 2C + 4H
• 2500 jobs to identify global minimum
• Energies...
1.499
eV
Zeise‟s anion
3.370
eV
3.437
eV
3.553
eV
5.368
eV
... CrazyLego
(made in Nagoya)
J. Comp. Chem. Early View (2013).
DOI: 10.1002/jcc.23420
CrazyLego
• Rather than a box (x,y,z), define a
radius (r)
• Translation (x,y,z) and orientation
(φ,θ,ψ) of new fragment a...
(0,0,0)
r
(0,0,0)
(0,0,0)
([dmim][NO3])2
([emim][NO3])2
M06-2X vs DFTB3-D ([dmim][NO3])2
M06-2X vs DFTB3-D ([emim][NO3])2
M06-2X vs DFTB3-D ([bmim][NO3])2
Global DFTB3-D min. of [emim][NO3]7
(emim+/NO3
-)7
The structures of IL clusters are structurally interesting
J. Comp. Che...
Summary
• DFTB can be used for pre-
scanning configuration space of
complex systems
• MD of complex systems is
possible on...
Acknowledgments
62
From left to right, front row: Tae (Chiang Mai U), Arifin, Akao, Meow (Ubon Ratchathani U), Kato
M, Shi...
Recent developments for the quantum chemical investigation of molecular systems with high structural complexity
Recent developments for the quantum chemical investigation of molecular systems with high structural complexity
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Recent developments for the quantum chemical investigation of molecular systems with high structural complexity

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The structural complexity of molecular clusters increases with size due to the associated, rapidly growing configuration space. Two examples are realized in i) the transition from molecular to bulk systems, and ii) in the subsequent chemical functionalization of nanomaterials. In such systems, traditional quantum chemical approaches of investigations are hampered by the vastly increasing computational cost, even considering ever-growing supercomputer capabilities. Computationally inexpensive, yet accurate schemes such as the density-functional tight-binding (DFTB) method promise here a significant advantage.

We have recently engaged in developing novel methodologies for systems with increasing structural complexity, driven by motivation from experimental studies. In this presentation, we will briefly review a) our advances in the automatic parameterization of DFTB, and b) the Kick-fragment-based “CrazyLego” conformationally aware approach for studying molecular and ionic liquid clusters with increasing size.

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Recent developments for the quantum chemical investigation of molecular systems with high structural complexity

  1. 1. Recent developments for the quantum chemical investigation of molecular systems with high structural complexity Stephan Irle WPI-Institute of Transformative Bio-Molecules & Department of Chemistry, Graduate School of Science Nagoya University Nagoya, Japan APCTCC-6 Gyeongju, Korea, July 10-13, 2013
  2. 2. Group Theme: Quantum Chemistry of Complex Systems http://qc.chem.nagoya-u.ac.jp Quantum Chemistry Statistical Mechanics Molecular Dynamics Method Development DFTB, RISM, GA , Stochastic Search … Yi = cn i jn n å Theoretical Spectroscopy (UV/Vis, IR, Raman) Nanomaterials Self-assembly, reactions, properties 2 Biosystems Reactions and ligand-protein interaction Solution Chemistry Solvation, electron AD AD A - D +
  3. 3. Density-Functional Tight-Binding (DFTB) Tight Binding (extended-Huckel-like) method with parameters from DFT E(NCC-)DFTB = niei i valence orbitals å + 1 2 EAB rep A¹B atoms å E(SCC-)DFTB = E(NCC-)DFTB + 1 2 gABDqA A,B atoms å DqB ES( pin-polarized)DFTB = E(SCC-)DFTB + 1 2 pAl pAl'WAll' l'ÎA å lÎA å A atoms å Marcus Elstner Christof Köhler Helmut Eschrig Gotthard Seifert Thomas Frauenheim 4 Method Development: Fast QM Fast QM Method: Approximate DFT Eschrig, Seifert (1980‟s): • 2-center approximation • Minimum basis set No integrals, DFTB is roughly 1000 times faster than DFT! Foulke, Haydock (1989): Introduction
  4. 4. 5 ReviewDFTB Ref.: Oliviera, Seifert, Heine, Duarte, J. Braz. Chem. Soc. 20, 1193-1205 (2009) ...open access Thomas Heine Helio Duarte
  5. 5. 6 ReviewDFTB Density Functional Theory (DFT) E ré ë ù û= ni yi - 1 2 Ñ2 + vext  r( )+ r  r '( )  r -  r ' ò d3 r' yi i=1 M å + Exc ré ë ù û- 1 2 r  r( )r  r '( )  r -  r ' d3 ròò d3 r'+ 1 2 Za Zb  Ra -  Rba,b=1 a¹b N å = ni ei i=1 M å + Erep at convergence: Various criteria for convergence possible: • Electron density • Potential • Orbitals • Energy • Combinations of above quantities Walter Kohn/John A. Pople 1998
  6. 6. Self-consistent-charge density-functional tight-binding (SCC-DFTB) M. Elstner et al., Phys. Rev. B 58 7260 (1998) E r0 + dr[ ]= ni fi ˆH r0[ ] fi i valence orbitals å 1    + ni fi ˆH r0[ ] fi i core orbitals å 2    + + Exc r0[ ] 3   - 1 2 r0VH r0[ ] R3 ò 4    - r0Vxc r0[ ] R3 ò 5    + Enucl 6  + + 1 2 drVH dr[ ] R3 ò 7    + 1 2 ¶2 Exc ¶dr2 r0 dr2 R3 òò 8    +o 3( ) Second order Taylor-expansion of DFT energy in terms of reference density r0 and charge fluctuation r (rr0 + r) yields: Density-functional tight-binding (DFTB) method is derived from terms 1-6 SCC-DFTB method is derived from terms 1-8 Phys. Rev. B, 39, 12520 (1989) Foulkes + Haydock Ansatz ReviewDFTB 7
  7. 7. DFTB and SCC-DFTB methods  where  ni and i — occupation and orbital energy ot the ith Kohn-Sham eigenstate  Erep — distance-dependent diatomic repulsive potentials  qA — induced charge on atom A  AB — distance-dependent charge-charge interaction functional; obtained from chemical hardness (IP – EA) EDFTB = niei i valence orbitals å term1   + 1 2 Erep AB A¹B atoms å terms 2-6    ESCC-DFTB = niei i valence orbitals å term1   + 1 2 gABDqADqB A,B atoms å terms 7-8    + 1 2 Erep AB A¹B atoms å terms 2-6    ReviewDFTB 8
  8. 8. DFTB method  Repulsive diatomic potentials replace usual nuclear repulsion energy  Reference density r0 is constructed from atomic densities  Kohn-Sham eigenstates i are expanded in Slater basis of valence pseudoatomic orbitals i  The DFTB energy is obtained by solving a generalized DFTB eigenvalue problem with H0 computed by atomic and diatomic DFT r0 = r0 A A atoms å fi = cmicm m AO å H0 C = SCe with Smn = cm cn Hmn 0 = cm ˆH r0 M ,r0 N [ ] cn ReviewDFTB 9
  9. 9. 10  Additional induced-charges term allows for a proper description of charge-transfer phenomena  Induced charge qA on atom A is determined from Mulliken population analysis  Kohn-Sham eigenenergies are obtained from a generalized, self-consistent SCC-DFTB eigenvalue problem SCC-DFTB method (I) ReviewDFTB
  10. 10. 14 Traditional DFTB concept: Hamiltonian matrix elements are approximated to two-center terms. The same types of approximations are done to Erep. From Elstner et al., PRB 1998           0 0 (Density superposition) (Potential superposition) eff eff A B eff eff A eff B V V V V V r r r r r r     A B D C A B D C Situation I Situation II Both approximations are justified by the screening argument: Far away, neutral atoms have no Coulomb contribution. Approximations in the DFTB Hamiltonian ReviewDFTB
  11. 11. 15 LCAO ansatz of wave function      Rri i c secular equations   0   SHc i i variational principle pseudoatomic orbital Example: X4: Atom 1 – 4 are the same atom & have only s shell 1 4 2 3 r12 r23 r14 r34 r13 r24 How to construct? two-center approximation nearest neighbor off-diagonal elements only (minimum basis set) Hamiltonian Overlap pre-computed parameter •Reference Hamiltonian H0 •Overlap integral Sμν SCC-DFTB HamiltonianDFTB
  12. 12. 16 LCAO ansatz of wave function      Rri i c secular equations   0   SHc i i variational principle pseudoatomic orbital H11 H22 H33 H44 Atom 1 – 4 are the same atom & have only s shell Diagonal term Orbital energy of neutral free atom (DFT calculation) 1 4 2 3 r12 r23 r14 r34 r13 r24 Hamiltonian Overlap       qH 2 1 Charge-charge interaction function Induced charge SCC-DFTB HamiltonianDFTB
  13. 13. 17 LCAO ansatz of wave function      Rri i c secular equations   0   SHc i i variational principle pseudoatomic orbital H11 H22 H33 H41 H44 Atom 1 – 4 are the same atom & have only s shell 1 4 2 3 r12 r23 r14 r34 r13 r24 r14 Two-center integral       qSHH 2 10 Charge-charge interaction function Induced charge Hamiltonian Overlap Lookup tabulated H0 and S at distance r SCC-DFTB HamiltonianDFTB
  14. 14. r14 18 LCAO ansatz of wave function      Rri i c secular equations   0   SHc i i variational principle pseudoatomic orbital H11 H22 H33 H41 H43 H44 Atom 1 – 4 are the same atom & have only s shell 1 4 2 3 r12 r23 r34 r13 r24 r34 Two-center integral       qSHH 2 10 Charge-charge interaction function Induced charge Hamiltonian Overlap Repeat for all off-diagonal terms Lookup tabulated H0 and S at distance r SCC-DFTB HamiltonianDFTB
  15. 15. DFTB repulsive potential Erep Which molecular systems to include? Development of (semi-)automatic fitting: •Knaup, J. et al., JPCA, 111, 5637, (2007) •Gaus, M. et al., JPCA, 113, 11866, (2009) •Bodrog Z. et al., JCTC, 7, 2654, (2011) 19 Repulsive PotentialsDFTB
  16. 16. 21/25 New Confining Potentials Wa Conventional potential r0 Woods-Saxon potential k R r rV        0 )( R0 = 2.7, k=2 )}(exp{1 )( 0rra W rV   r0 = 3.0, a = 3.0, W = 3.0 Typically, electron density contracts under covalent bond formation. In standard ab initio methods, this problem can be remedied by including more basis functions. DFTB uses minimal valence basis set: the confining potential is adopted to mimic contraction • •+ • • 1s σ1s H H H2 Δρ = ρ – Σa ρa H2 difference density 1s Henryk Witek New Electronic Parameters DFTB Parameterization 21
  17. 17. Band structure for Se (FCC) Brillouin zone 22 New Electronic Parameters DFTB Parameterization
  18. 18. Particle swarm optimization (PSO) New Electronic Parameters DFTB Parameterization 23
  19. 19. 1) Particles (=candidate of a solution) are randomly placed initially in a target space. 2) – 3) Position and velocity of particles are updated based on the exchange of information between particles and particles try to find the best solution. 4) Particles converges to the place which gives the best solution after a number of iterations. • • • • • • • • •• • • •• •• • • •• • •• ••• • • • • •• •••••••• particle 1) 4) 2) 3) Particle Swarm Optimization DFTB Parameterization 24
  20. 20. Each particle has randomly generated parameter sets (r0, a, W) within some region Generating one-center quantities (atomic orbitals, densities, etc.) “onecent” Computing two-center overlap and Hamiltonian integrals for wide range of interatomic distances “twocent” “DFTB+” Calculating DFTB band structure Update the parameter sets of each particle Memorizing the best fitness value and parameter sets Evaluating “fitness value” (Difference DFTB – DFT band structure using specified fitness points) “VASP” DFTB Parameterization orbital a [2.5, 3.5] W [0.1, 0.5] r0 [3.5, 6.5] density a [2.5, 3.5] W [0.5, 2.0] r0 [6.0, 10.0] Particle Swarm Optimization 25
  21. 21. Example: Be, HCP crystal structure DFTB Parameterization Total density of states (left) and band structure (right) of Be (hcp) crystral structure 2.286 3.584 •Experimental lattice constants •Fermi energy is shifted to 0 eV 26 Electronic Parameters
  22. 22. DFTB ParameterizationTransferability of optimum parameter sets for different structures Artificial crystal structures can be reproduced well e.g. : Si, parameters were optimized with bcc only W (orb) 3.33938 a (orb) 4.52314 r (orb) 4.22512 W (dens) 1.68162 a (dens) 2.55174 r (dens) 9.96376 εs -0.39735 εp -0.14998 εd 0.21210 3s23p23d0 bcc 3.081 fcc 3.868 scl 2.532 diamond 5.431 Parameter sets: Lattice constants:bcc fcc scl diamond Expt. 27
  23. 23. Correlation of r(orb) vs. atomic diameter Atomic Number Z Atomicdiameter[a.u.] Empirically measured radii (Slater, J. C., J. Chem. Phys., 41, 3199-3204, (1964).) Calculated radii with minimal- basis set SCF functions (Clementi, E. et al., J. Chem. Phys., 47, 1300-1307, (1967).) Expected value using relativistic Dirac-Fock calculations (Desclaux, J. P., Atomic Data and Nuclear Data Tables, 12, 311-406, (1973).) This work r(orb) In particular for main group elements, there seems to be a correlation between r(orb) and atomic diameter. 28 DFTB ParameterizationElectronic Parameters
  24. 24. Rocksalt (space group No. 225) •NaCl •MgO •MoC •AgCl … •CsCl •FeAl … B2 (space group No. 221) Zincblende (space group No. 216) •SiC •CuCl •ZnS •GaAs … Others •Wurtzite (BeO, AlO, ZnO, GaN, …) •Hexagonal (BN, WC) •Rhombohedral (ABCABC stacking sequence, BN)  more than 100 pairs tested 29 DFTB ParameterizationBinary Systems
  25. 25. element name Ga, As hyb-0-2 B, N matsci-0-2 Reference of previous work : •d7s1 is used in POTCAR (DFT) Further improvement can be performed for specific purpose but this preliminary sets will work as good starting points 30 DFTB ParameterizationBinary Systems
  26. 26. 31 •space group No. 229 •1 lattice constant (a) Transferability checked (single point calculation) Reference system in PSO Experimental lattice constants available a 31 DFTB ParameterizationBCC elements Prof. Henryk Witek Dr. Yoshifumi Nishimura Chien-Pin Chou
  27. 27. 32 DFTB ParameterizationErepfit Gaus, M. et al., JPCA, 113, 11866, (2009) Prof. Henryk Witek Dr. Yoshifumi Nishimura Chien-Pin Chou
  28. 28. x 1,000,000 Chemistry sans thought Dr. Matt Addicoat, (JSPS Postdoc)
  29. 29. Guessing competition: • What kind of conformations can a molecule of four different atoms, A, B, C, D adopt?
  30. 30. Guessing competition:
  31. 31. 12 12 6 12 12 2 Guessing competition:
  32. 32. Guessing competition: • ABCD has a 6 possible structures with a total of 56 permutations • ABCDE has 15 possible structures with a total of 577 permutations
  33. 33. • Genetic algorithm • Simulated annealing • Monte-Carlo • Basin hopping Automated approaches
  34. 34. Wishlist • No assumed knowledge / limiting parameters • Ensemble of structures • Broad applicability • level of theory • computational chemistry "backend" • Least amount of human work possible
  35. 35. Kick • The original Kick (M. Saunders) took a geometry (input file) and perturbed it • The Schaefer version generated random co-ordinates within a box of pre-set size • Adelaide (Addicoat/Metha) Version works on the same principle as Schaefer version • Adds the capability to recognise
  36. 36. Kick • A fragment is supplied as cartesian co- ordinates which are rotated by a random angle (Φ,ϑ,Ψ) before being "kicked" • Geometry optimisation, parsing and resubmission of unique geometries (frequency, higher level E) automatic.
  37. 37. (x,y,z) (0,0,0)
  38. 38. -1 Zeise‟s anion
  39. 39. + 3 + - or - Zeise‟s anion
  40. 40. + 3 + 2 + 4 - or - Zeise‟s anion
  41. 41. Zeise‟s anion • Pt + 3Cl + C2H4 • 20 jobs, 6 minima • Pt + 3Cl + 2C + 4H • 2500 jobs to identify global minimum • Energies up to 12 eV from lowest energy minimum • Includes many dissociated minima • 9000 jobs to locate all possible substitutions of ethylene
  42. 42. 1.499 eV Zeise‟s anion 3.370 eV 3.437 eV 3.553 eV 5.368 eV
  43. 43. ... CrazyLego (made in Nagoya) J. Comp. Chem. Early View (2013). DOI: 10.1002/jcc.23420
  44. 44. CrazyLego • Rather than a box (x,y,z), define a radius (r) • Translation (x,y,z) and orientation (φ,θ,ψ) of new fragment are still chosen randomly • Can „backtrack‟ and place new fragment near old fragment • The „key atom‟ in each fragment is its centroid • A fragment location is rejected if it violates minimum distance constraint
  45. 45. (0,0,0) r
  46. 46. (0,0,0)
  47. 47. (0,0,0)
  48. 48. ([dmim][NO3])2
  49. 49. ([emim][NO3])2
  50. 50. M06-2X vs DFTB3-D ([dmim][NO3])2
  51. 51. M06-2X vs DFTB3-D ([emim][NO3])2
  52. 52. M06-2X vs DFTB3-D ([bmim][NO3])2
  53. 53. Global DFTB3-D min. of [emim][NO3]7 (emim+/NO3 -)7 The structures of IL clusters are structurally interesting J. Comp. Chem. Early View (2013). DOI: 10.1002/jcc.23420
  54. 54. Summary • DFTB can be used for pre- scanning configuration space of complex systems • MD of complex systems is possible on nanosecond timescale
  55. 55. Acknowledgments 62 From left to right, front row: Tae (Chiang Mai U), Arifin, Akao, Meow (Ubon Ratchathani U), Kato M, Shibata, Usui; back row: Siva, Tim, Nishimoto, SI, Yokogawa, Baba, Anupriya, Hiro, Noguchi Dr. Matt Addicoat, (JSPS Postdoc) Dr. Yoshifumi Nishimura Thank you for your attention!

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