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Approximate methods for large molecular systems
Approximate methods for large molecular systems
Marcus Elstner
Physical and Theoretical Chemistry, Technical University of Braunschweig
C60-trimer Si1600 MoS2
4H-SiC-surfacesdefects, doping GaN-devices
Structure-formation, atomic-scale related properties and processes
MotivationMotivation
Si21 a-SiCN-ceramics
Alcohol DeHydrogenase
Photosynthetic Reaction Center
Reactions in biological SystemsReactions in biological Systems
Aquaporin
Photochemistry
bRCatalysis
Proton Transfer
Photochemistry
Electron/Energy Transfer
Need QM description
Computational challangeComputational challange
~ 1.000-10.000 atoms
~ ns molecular dynamics simulation
(MD, umbrella sampling)
- weak bonding forces
- chemical reactions
- treatment of excited states
‚multiscale business‘‚multiscale business‘
CI, MPCASPT2
CI, MPCASPT2
Length scale
predictivity
Continuum electrostatics Continuum electrostatics
Molecular MechanicsMolecular Mechanics
f
s
ps
ns
t i
me
SE-QMapprox-DFT
SE-QMapprox-DFT
HF, DFTHF, DFT
nm
Size problem: Size problem:
number of structures
MD, MC, GA
time scale of processMD, MC -- RP, TST
size of system: number of atoms
ab initio, SE MM
Size problem: QM-Methods Size problem: QM-Methods
Hybride methods: QM/MM, QM/QM
Linear scaling: O(N)
SE/approx. Methods
Semi-empirical /approximate methodsSemi-empirical /approximate methods
approximation, neglect and parametrization of interaction integrals from ab-initio and DFT methods
-HF-based:
CNDO, INDO, MNDO, AM1, PM3, MNDO/d, OM1,OM2
-DFT-based:
SCC-DFTB, DFT- 3center- tight binding (Sankey)
Fireballs --- > Siesta DFT code
~ 1000 atoms, ~ 100 ps MD
Approximate density-functional theory:SCC-DFTB
Self consistent - charge density functional tight-binding
Approximate density-functional theory:SCC-DFTB
Self consistent - charge density functional tight-binding
• Seifert (1980-86): Int. J. Quant Chem., 58, 185 (1996). O-LCAO; 2-center approximation: approximate DFT
http://theory.chm.tu-dresden.de
• Frauenheim et al. (1995): Phys. Rev. B 51, 12947 (1995). efficient parametrization scheme: DFTB
www.bccms.uni-bremen.de • Elstner et al. (1998): Phys. Rev. B 58, 7260 (1998). charge self-consistency: SCC-DFTB www.tu-bs.de/pci
approximate DFT
Extensions and Combinations: Extensions and Combinations:
O(N)-QM/MMdivide+conquer
H. Liu W. YangDuke Univ
QM/MMAMBER: Han, Suhai DKFZ CHARMM: Cui, Karplus; HarvardTINKER: Liu, Yang; Duke CEDAR: Hu, Hermans; NC Univ
DISPERSIONP. Hobza, Prague
TD-DFTB-LR
TD-DFTBR. Allen Texas A&M
SCC-DFTB
SolventCosmo: W. Yang
GB: H. Liu
Electron TransportA. Di Carlo
SCC-DFTB: SCC-DFTB:
available for H C N O S P Zn
(Si, ...)
all parameters calculated from DFT
computational efficiency as NDO-type methods
(solution of gen. eigenvalue problem for valence electrons in minimal basis)
SCC-DFTB: TestsSCC-DFTB: Tests
1) Small molecules: covalent bond
reaction energies for organic molecules
geometries of large set of molecules
vibrational frequencies,
2) non-covalent interactions
H bonding
VdW
3) Large molecules (this makes a difference!)
Peptides
DNA bases
SCC-DFTB: TestsSCC-DFTB: Tests
4) Transition metal complexes
5) Properties
IR, Raman, NMR
excited states with TD-DFT
Transport calculations
SCC-DFTB: Reviews SCC-DFTB: Reviews
1) Application to biological molecules M. Elstner, et al. ,A self-consistent carge density-functional based tight-binding
scheme for large biomolecules, phys. stat. sol. (b) 217 (2000) 357.
Elstner, et al. An approximate DFT method for QM/MM simulations of biological structures and processes. J. Mol. Struc. (THEOCHEM), 632 (2003) 29.
M. Elstner, The SCC-DFTB method and its application to biological systems, Theoretical Chemistry Accounts, in print 2006.
2) Focus on solids and nanostructures T. Frauenheim, et al., Atomistic Simulations of complex materials: ground and
excited state properties, J. Phys. : Condens. Matter 14 (2002) 3015.
Th. Frauenheim et al. A self-consistent carge density-functional based tight-binding method for predictive materials simulations in physics, chemistry and biology, phys. stat. sol. (b) 217 (2000) 41.
G. Seifert, in: Encyclopedia of Computational Chemistry (Wiley&Sons 2004)
SCC-DFTB Tests 1: Elstner et al., PRB 58 (1998) 7260SCC-DFTB Tests 1: Elstner et al., PRB 58 (1998) 7260
Performance for small organic molecules (mean absolut deviations)
• Reaction energiesa): ~ 5 kcal/mole
• Bond-lenghtsa) : ~ 0.014 A°
• Bond anglesb): ~ 2°
•Vib. Frequenciesc): ~6-7 %
a) J. Andzelm and E. Wimmer, J. Chem. Phys. 96, 1280 1992.b) J. S. Dewar, E. Zoebisch, E. F. Healy, and J. J. P. Stewart, J. Am.Chem. Soc. 107, 3902 1985.c) J. A. Pople, et al., Int. J. Quantum Chem., Quantum Chem. Symp. 15, 2691981.
SCC-DFTB Tests 2: T. Krueger, et al., J.Chem. Phys. 122 (2005) 114110.
SCC-DFTB Tests 2: T. Krueger, et al., J.Chem. Phys. 122 (2005) 114110.
With respect to G2:mean ave. dev.: 4.3 kcal/molemean dev.: 1.5 kcal/mole
SCC-DFTB Tests:SCC-DFTB Tests:
Accuracy for vib. freq., problematic case e.g.:
Special fit for vib. Frequencies:
Mean av. Err.: 59 cm-1 33 cm-1 for CHMalolepsza, Witek & Morokuma: CPL 412 (2005) 237.
Witek & Morokuma, J Comp Chem. 25 (2004) 1858.
H-bonded systems: water H-bonded systems: water
CCSD(T): 5.0 kcal/mole (Klopper et al PCCP 2000 2, 2227)
BLYP: 4.2 kcal/mole
PBE: 5.1 kcal/mole
B3LYP: 4.6 kcal/mole
HF: 3.7 kcal/mole
(from Xu&Goddard, JCPA 2004)
For larger systems:
DFTB: 3.3 kcal/mole
HF: 5.7 kcal/mole @ 6-31G*
B3LYP: 6.8 kcal/mole @ 6-31G* ~2 kcal/mole BSSE (BSIE)
H-bondsHan et al. Int. J. Quant. Chem.,78 (2000) 459.Elstner et al. phys. stat. sol. (b) 217 (2000) 357.Elstner et al. J. Chem. Phys. 114 (2001) 5149.Yang et al., to be published.
H-bondsHan et al. Int. J. Quant. Chem.,78 (2000) 459.Elstner et al. phys. stat. sol. (b) 217 (2000) 357.Elstner et al. J. Chem. Phys. 114 (2001) 5149.Yang et al., to be published.
-~1-2kcal/mole too weak
- relative energies reasonable
- structures well reproduced
Model peptides: N-Acetyl-(L-Ala)n N‘-Methylamide (AAMA) + 4 H2O
H2O-dimer complexes Cs, C2v
NH3-NH3- and NH3-H2O-dimer
Coulomb interaction
Secondary-structure elements for Glycine und Alanine-based polypeptides
Elstner, et al.. Chem. Phys. 256 (2000) 15
Secondary-structure elements for Glycine und Alanine-based polypeptides
Elstner, et al.. Chem. Phys. 256 (2000) 15
N = 1 (6 stable conformers) 310 - helix
stabilization by internal H-bonds
between i and i+3
N
R-helix
between i and i+4
DFTB very good for:
- relative energies
- geometries
- vib. freq. o.k.!
main problem for DFT(B): dispersion!
AM1, PM3, MNDO quite bad
OM2 much improved (JCC 22 (2001) 509)
Glycine and Alanine based polypeptides in vacuo Elstner et al., Chem. Phys. 256 (2000) 15
Elstner et al. Chem. Phys. 263 (2001) 203 Bohr et al., Chem. Phys. 246 (1999) 13
Glycine and Alanine based polypeptides in vacuo Elstner et al., Chem. Phys. 256 (2000) 15
Elstner et al. Chem. Phys. 263 (2001) 203 Bohr et al., Chem. Phys. 246 (1999) 13
N = 1 (6 stable conformers)
N
Relative energies, structures and vibrational properties: N=1-8
2 R P
(6-31G*)
C7
eq C5ext C7
ax
MP4-BSSE
MP2
B3LYP
SCC-DFTB
E relative energies (kcal/mole)
MP4-BSSE: Beachy et al, BSSE corrected at MP2 level
Ace-Ala-Nme
Strength of SCC-DFTBStrength of SCC-DFTB
DNA:
A. V. Shiskin, et al., Int. J. Mol. Sci. 4 (2003) 537.
O. V. Shishkin, et al., J. Mol. Struc. (THEOCHEM) 625 (2003) 295.
Structure of large molecules
- dynamics
- relative energies
Problems: Problems:
same Problems as DFT
additional Problems:
- except for geometries, in general lower accuracy than DFT
- slight overbinding (probably too low reaction barriers?!)
- too weak Pauli repulsion
- H-bonding (will be improved)
- hypervalent species, e.g. HPO4 or sulfur compounds
- transition metals: probably good geometries, ... ?
- molecular polarizability (minimal basis method!)
SCC-DFTB vs. NDDO (MNDO, AM1, PM3)SCC-DFTB vs. NDDO (MNDO, AM1, PM3)
DFTB:
energetics of ONCH ok, S, P problematic
very good for structures of larger Molecules
vibrational frequencies mostly sufficient (less accurate than DFT)
NDDO:
very good for energetics of ONCH (and others, even better than DFT)
structures of larger Molecules often problematic !!!
do NOT suffer from DFT problems e.g. excited states
Mix of DFTB and NDDO to combine strengths of both worlds
DFT Problems: DFT Problems:
(1) Ex: Self interaction error. J- Ex = 0 !: Band gaps, barriers
(2) Ex: wrong asymptotic form; - HOMO << Ip: virtual KS orbitals
(3) Ex: ‚somehow too local‘; overpolarizability, CT excitations
(4) Ec: ‚too local‘: Dispersion forces missing
(5) Ec: even much more ‚too local‘: isomerization reactions
(6) Multi-reference problem
(1) –(3) of course related, cure: exact exchange!
DFT Problems: (very) selective publications DFT Problems: (very) selective publications
(1) Ex: PRB 23 (1981) 5048, JCP 109 (1998) 2604
(2) Ex: JCP 113 (2000) 8918, Mol. Phys. 97 (1999) 859.
(3) Ex: JPCA 104 (2000) 4755, JCP 119 (2003) 2943.
(4) Ec: JCP 114 (2001) 5149
(5) Ec: Angew. Chem. Int. Ed. 2006, 45, 4460 –4464
(6) Koch, Wolfram / Holthausen, Max C.A Chemist's Guide to Density Functional Theory, Wiley
Problems of DFT-GGAProblems of DFT-GGA
- overbinding of small molecules: CO... B3LYP, rev-PBE 10 kcal
- transition metals: B3LYP, PB86 ..., spin states, energetics 10-20 kcal
- vib. Freqencies:
- conjugate systems: GGAs overpolarize PA‘s of respective proton donors 10 kcal
- H-bonds: ok with DFT, HF (cancellation of errors), water structure?
- proton transfer (PT) barriers: GGA< B3LYP < MP2< CCSD 2-4 kcal with B3LYP!
Solution1: don‘t worry or don‘t care different functionals VERY different accuracy
Solution2: use something else
-VdW- problem (dispersion) complete failure
‚Solution‘: empirical dispersion for GGAs
-excited states within TD-DFT: ionic, CT states, double excitations, Rydberg states
Solution: exact exchange or CI-based methods