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Variationally optimized basis set for biological molecules
Hiori Kino
Contents•Final target•Status of the openmx program•Purpose of this research•optimized basis set•applications and transferability
•simplified (optimized) PAO•transferability
understanding the functions of biochemical enzymes and related materials with thousands of atoms microscopically
--- drug design in a computer
To avoid this enzyme reaction
Coating the target molecule
burying the reaction center of the enzyme
One of the policy to find a drug:
To find a molecule which fits and is bound strongly
Find stable atomic structure
Final target
Netropsin attached atthe minor groove.
Cisplatin connected to guanine base molecules
Anticancer drugs --- e.g. bind strongly to DNA in order to prevent replication of DNA
Daunomycin inserted into the base molecules
Target:Examples(1)
XK263, HIV protease inhibitor
XK263 is bound strongly with the reaction center of the HIV protease→ prevent its action as an enzyme
Target:Examples(2)
Status of the OpenMX program
Linear combination of PseudoAtomicOrbitalPseudopotentials: TM, Schroedinger, dirac/scalar relativistic, partial core correctionsXC-functional: LDA, PBEorbital optimizationMPI- parallelizedstable order(N)
Download from http://staff.aist.go.jp/t-ozaki/
Purpose of this research
A number of order(N) programs
But, how accurate is linear combination of (pseudo)atomic orbitals?More basis set → more accurate, but heavy calculation
smaller basis set=more efficient and better accurary
Optimized basis set(1)
r
V(r)
r
V(r)Confinement potential
(Basis set for order(N)-LCAO must be compact.)
Atomic orbital
(primitive) Pseodoatomic orbital
rc
Its eigenfunction of pseudopotential with confimentment potential.
is calculated for an atom.
r
V(r)
(primitive) Pseodoatomic orbital
rc
Optimized basis set(2)wavefunction of a molecule
If rc is infinite and if infinite number of PAO is used → the same accuracy as plane wave calculations.
However, it is an expensive calculation, finite rc and finite number of PAO want to be used
Optimized basis set(3)
construct an optimized PAO depending on the environment from primitive PAOs
(energy minimization)
n=0n=1n=2n=3n=4...
n*=0n*=1
some atomsome L
H
n=0…4
H
n=0,1
Orbital optimization --- optimize the coefficient of linear combination
'
,',,';*,,*,,,n
LnatomprinLnatonLnatomopt
Applications to simple molecules and transferability
Target: DNA, RNA, proteinatoms: H,C,N,O,P, counter metallic cation
Is it possible to categorize environment?How to get good and small basis set?
cytosine
Many carbon atoms.Environment of each atom is different.
Simplified orbital(1)1. Calculate many molecules and optimize orbitals
proteinGGGGAGGVGGLGGIGGPGGFGGMGGWGGCGDKGDRGDHGEKGGNGGSGGTFGYG
RNA,RNAB-AB-GB-CB-TB-UA-ATA-GCB-AU(B-C)2Na
SaccaridearabinoseD-GlicoD-GluAcfructosefucoseglucoseribose
LipidDPPColeic acid
Acidcitric acidlactic acid
OthersAMPADPATP
Atomic positions are optimized using amber98 or mm3 force field
Simplified orbital(2)
C,O,N,S,P: s,p --- 2 optimized orbitals from 5 primitive orbitals d --- 1 optimized orbitals from 5 primitive orbitals( corresponding to double zeta plus polarized )
H: s --- 2 optimized orbitals from 5 primitive orbitals p --- 1 optimized orbitals from 5 primitive orbitals( corresponding to double zeta plus polarized )
s52p52d51
s52p51
Simplified orbital(3)
21
2222
22221
ddD
drrrRrRd
drrRRd
priopt
priopt
Effective charge (ESP charge) has ambiguities.
Deviation index
Simplified orbital(4)Carbon orbitals
cationic
anionic
neutral
center: center of mass, radii: standard deviations
(Deviations of s orbitals are almost the same)
Simplified orbital(6) # dE(primitive) dE(simiplied)
proteinGGG 24 0.0155 0.0006GAG 27 0.016 0.0022GVG 33 0.0131 0.0006GLG 36 0.0136 0.0005DNA,RNAB- Ade 31 0.0134 0.0025B- Cyt 29 0.0123 0.0001A- GpC 61 0.0133 0.0015Saccaridearabinose 37 0.015 0.0019D-Gluc 57 0.0132 0.0006lipidDP 104 0.0088 0.001PC 28 0.0111 0.0009
a.u./atom
Transferability(1): H2Or(OH) angle dipole mement
p-SV 1.121 98.4 2.348p-DV 1.025 102.7 2.471p-DVP 1.008 105.3 1.913so-DVP 0.982 105.6 2.001fo-DVP 0.973 104.7 1.736full 0.965 104.5 1.77full-H4.5-O5.0 0.965 104.5 1.77full-H5.0-O5.0 0.968 104.6 1.92full-H5.5-O5.0 0.977 104.9 1.78
exp 0.957 104.5 1.855
BLYP/ PW 0.973 104.4 1.81LDA/ PW 0.973 104.6 1.8
PW91PW91 0.955 104 2.245
PW theory: Sprik, J. Chem. Phys. 105, 1142 (1996).PW91PW91: Gaussian03, 6-311+G(d,p)
200Ry, XC=PBE
Comment: Small dipole moment is due to finite truncation of PAO
H4.5-O4.5 full=s5p5(d5)
Transferability(2):H2O dimer
R(OO) r(OH) OHO dipolep-SV 2.9121.142,1.119,1.118 180.3 4.09p-DV 2.871.032,1.022,1.023 181.2 2.12p-DVZ 2.8481.020,1.005,1.007 177.4 3.499so-DVZ 2.90.989,0.980,0.982 177.4 2.99fo-DVZ 2.9680.981,0.970,0.970 178.5 2.63full 2.9850.973,0.964,0.064 179.3 2.719
PW/ LDA 2.7 169PW/ Becke88 3.02 177PW/ Becke88+Perdew86 2.95 177PW/ BLYP 2.95 173PW/ B3LYP 2.94 0.975 2.15exp. 2.98 174 2.6
PW/… Sprik, J. Chem. Phys. 105, 1142(1996).PW/B3LYP: P.L. Silverstrelli amd M. Parrinello, J. Chem. Phys. 111, 3572(1999)
H4.5, O4.5, s52p52d51 for O, s52p51 for H, 200Ry, PBE
so-DVZ gives good results for internal bonds,but it gives shorter bond length for hydrogen bonds.(more d orbitals are necessary for O.)
Transferability(3): acetic dimerC=O C-O O-H O=C-O O…O O…H O-H…O
p-SV 1.404 1.423 1.272 126 2.635 1.369 173p-DV 1.311 1.383 1.111 124.5 2.632 1.521 179.6p-DVP 1.306 1.372 1.116 125.5 2.626 1.51 179.5so-DVP 1.261 1.331 1.069 125.7 2.57 1.502 177.4fo-DVP 1.254 1.329 1.064 125.9 2.568 1.504 177.2full 1.197 1.276 1.022 123.5 2.625 1.603 178.1
exp 1.217 1.32 1.033 126.2 2.696
Aquino 1.244 1.331 1.026 2.65Turi 1.217 1.32 1.033 126.2 2.696
H4.5 O4.5, 160Ry
A.J.A. Aquino, et al., J. Phys. Chem. A (2002), 106, 1862. BLYP?/ SVP+sp?L. Turi, J. Phys. Chem. (1996) 100, 11285. MP2/D95++(d,p)
A problem: so gives shorter length for O…O
O
O OO
H
H
Transferability(4): carboplatinpSZ pDZ pDZP so fo
Pt-N1 2.086 2.092 2.07 2.047 2.032Pt-O1 2.031 2.025 2.012 2.02 2.001C1-C3 1.601 1.567 1.561 1.562 1.567C5-O1 1.435 1.374 1.365 1.345 1.347C5-O2 1.335 1.262 1.257 1.231 1.215N1-H3 1.147-1.150 1.063-1.065 1.058-1.060 1.025-1.027 1.035-1.036C1-H1 1.209 1.129 1.129 1.103 1.094O1-Pt-N1 87.2 87.2 87.6 88.3 89.1O1-Pt-O1' 86.2 86.4 87 86.6 87.7N1-Pt-N1' 98.8 98.7 97.2 96.6 93.9C5-C3-C5' 103 105 105.5 106.9 108.6
theo1 exp1 exp2Pt-N1 2.06 2.021 2.01Pt-O1 1.98 2.025 2.029C1-C3 1.56 1.56 1.552C5-O1 1.34 1.293 1.284C5-O2 1.23 1.229 1.217N1-H3 1.025-1.03 0.93-1.07 - - -C1-H1 1.095 1.09 - - -O1-Pt-N1 80 87.1 88.2O1-Pt-O1' 96.5 90.5 88.9N1-Pt-N1' 104 95.5 93.6C5-C3-C5' 115 107.6 107.4
theo1 BLYP-XC, CPMD, E. Tornaghi, et al., Chem. Phys. Lett. 246 (1995) 469.
H4.5, O4.5, 160Ry
Transferability(5)
CH4, C2H6, C4H4, C2H2, benzene, N2, NH3, HCN, O2, CH3OH, formaldhyde, formie acid, formamide, NO2, PH3, H2S2, H2SO4, thioformamide, Glycine, CH3F, cisplatin, ...
Transferability(6):problems
BE(kcal/ mol)p-SV -10.1p-DV -9.65p-DVP -9.99so-DVP -8.85full - 7.5
exp -4.5~-5.5
PW/ LDA -5.49PW/ BLYP -4.3
Binding energy is 2 times as large as those of exp. and PW theory.~SIESTA gives similar result to openMX.
H2O, H4.5 O4.5
PW: Sprik, J. Chem. Phys. 105, 1142 (1996).
about 2 times as large as those of exp. and PW theory in the cases of acetic dimer and GpC(DNA) ~SIESTA gives the result similar to exp and PW theories in GpC.
D. Sanchez-Portal, et al.,Int. J. Quant. Chem.65, 453 (1997).
M. Machado, P. Ordejon, condmat/9908022.