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(5)Nitrogen orbitals

cationicneutral

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

Simplified orbital(7)

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.

Summary

•Good and efficient(small) optimized DVP basis set and high transferability for intramolecular parameters

•insufficient DVP for hydrogen bond•too large binding energy for hydrogen bond