Japan Advanced Institute of Science and Technology,

Ishikawa, Japan.

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Kanazawa

Tokyo

Pseudopotential calculations of Porphyrin Complexes…

FADFT2007@ISSP, Japan.

Ryo Maezono

rmaezono@mac.com

School of Information Science,

JAIST

Research Center for Integrated Science (RCIS)

Japan Advanced Institute of Science and Technology.

- Kiyo TERAKURA organizes new Ab-initio Group…

- Ryo MAEZONO (DMC) @ Informaton Science Dept.

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From this year…

- Taisuke OZAKI (OPEN-MX) ; Order-N method.- Dr. Dam Hieu-Chi as lecturer @ Knowledge Science Dept.- Dr. Jae-Dong Lee as lecturer @ Materials Science Dept.

Diffusion Monte Carlo

most practical implementation of the projection method:

€

Φ =exp −τH[ ]⋅ Ψinit

- Independent from DFT framework.

Fixed node DMC.

projection is limited under assumed fixed node.

(Fermion Sign Problem)

(c.f., Lectures by M. CASULA and J. Kolorenc)

- Can be used as accurate calibrations.

rather than a tool for practical of Materials Science

at THE PRESENT.

Aim

N

N

N

N

TM = Ni, Cu, Zn

TM

Establish procedures for pseudo-pot. QMC calculations.

Porphyrin, Phthalocyanine etc.

- Actively studied in Nano/Bio research field. - Interplay between TM site and Side-chains.

- prepare trial/guiding WF in pseudo-pot. calc.

- Basis set re-optimization.

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suitable for stable DMC accumulation.

Background (1)John TRAIL’s Pseudo potential studies.

- Non-diverging, non-local pseudo potentials.

avoiding eN-cusp. Fock exchange.

- Transition metal ions…s-electrons coexist with d-electrons.→ Difficulty!

John investigated long-range tail.

Asymptotic behavior of orbital functions.

Valence electron but not HOMO

…then wrong behavior…

Trail-Needs （ 2005) , Dolg （ 2005)

Lee-Needs （ 2002)

Ovacharenko-Lester （ 2001)

‘QMC_pp’

J. Trail et.al., JCP 122, 174109 (2005).

Pathology due to Non-locality

€

rcNorm-conserving

Fock non-locality

€

Vlpp r→ ∞( ) ~

Zeffr

€

Zeff +δ l( )

r+η l

Pseudo orb.

AE orbital

John TRAIL investigated …Asymptotic behavior of orbital functions.

Valence electron but not HOMO…then wrong behavior…

J. Trail et.al., JCP 122, 174109 (2005).

→ continuously taken over by outside.Zeff r

‘4s’-orb. of TM ion.3d is HOMO above 4s

N

N

N

N

TM = Ni, Cu, Zn

TM

Interesting test case

Establish procedures for pseudo-pot. calculations.

Porphyrin, Phthalocyanine etc.

- Actively studied in Nano/Bio Science. - Interplay between TM site and Side-chains.

- Generate trial/guiding WF in pseudo-pot. calc. - Basis set re-optimization.

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suitable for stable DMC accumulation.

Gaussian basis set with JRT pseudo.

commonly used in Molecular Science, Bio-molecule bussiness as well.

Conventional pseudo pot. provided with preset basis set.

(such as LANL2DZ etc.)

not fully optimized but well calibrated. ‘This basis set can be reliable upto XXX digit’

→ Basis set optimization by ourselves.

How to setup the basis set for JRT pseudo?

preparation of proper basis set.

(John R. Trail)

Gaussian basis calculation with JRT pseudo.

Lighter Ions.

Practical calculations after JRT2005

I. Gurtubay et.al., JCP 124, 024318 (2006).

→ Basis set optimization manually.

TM Ions.

- Porphyrin calculations.

- See how’s going on TM pseudo by John’s remedy.

The system is too large to be dealt with ‘Billy’.

N

N

N

N

TM = Ni, Cu, Zn

TM

<Aim>

ProcedureLANL1DZ the same core size as JRT pseudo.

N

N

N

N

<Porphin>

Re-optimize H,C,N basis set @ porphin.

TM = Ni, Cu, Zn

TMN

N

N

N

<Porphyrin>Replace TM Pseudo (from LANL to JRT)

QMC_pp(TM)

Re-optimize TM basis set

Structure optimization in B3LYP

H,C,N are treated as AE (6-31G**).

QMC_pp(all)

Replace AE by JRT-Pseudo.

QMC calculations

(hartree)

HFSCF

Variational

-206.4994

B3LYP-212.7404

MP2-210.2612

Non-variational

VMC-210.693(1)

DMC-211.5698(9)

N

N

N

NCu

Cu-Porphyrin [QMC_pp(all)]

Jastrow Functions…

JrR( ) ~F u( )

rR( )+ F χ( )

rR( )+ F f( )

rR( )

<ee> <en> <een>

- Fixed cutoff lengths ; Lu=5.0 a.u./ Lχ=4.0 a.u./ Lf=3.0 a.u./

- N.D.Drummond, M.D.Towler and R.J.Needs; Phys. Rev. B, 70, 235119 (2004)

- Optimization ; Unreweighted SC Variance Minimization. - N.D.Drummond and R.J.Needs; Phys. Rev. B, 72, 085124 (2005)

Tendencies

Absolute values of energy

2 ha. (all) / 4 ha. (TM)B3LYP ＜ DMC ＜ MP2

Energy Diff. ( ‘binding’ )

MP2 ＜ B3LYP ＜ DMC

[TMPo/Atom/Po] [QMCpp(TM)/QMCpp(all)]

€

⊗

MP2 ＜ DMC ＜B3LYP

Only for NiPo,

※ QMC not variational here.

B3LYP, DMC, MP2

Notes

- Atomic calculation of Zn with LANL.

VARMIN (Variance Minimization)

→ Try with latest scheme such as emin/madmin??

Though it is QUITE simple system,

won’t run even with reduced parameters into one.

SummaryReplacing procedure of QMC pseudo potentials

suitable for stable DMC accumulation.

LANL pseudo/basis set … easy to get and calculate in SCF.

No stable DMC

as it is

Stable DMC accumulation.

replace with JRT pseudo re-optimization of basis set

δE~0.001 hartree

High Performance Computing Facilities…

* Cray; T3E,XT3

* SGI; Origin2000,Origin3000,Altix3700,Altix4700

* Clusters; Pentium3,Opteron,Macintosh(Xeon)

* IBM; SP3, p690.

* HP; GS320, ES40, ES45, GS1280

* Hitachi; SR11000

* Fujitsu; PrimePower,PrimeQuest

Architectures

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@JAIST (360 procs) - SGI Altix

Itanium2, 24GB/4cpu

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- Cray XT3Opteron150, 32GB/4cpu

@JAIST (128 procs)

- Hitachi SR11000IBM Power5+, 128GB/16cpu

@Hokkaido Univ. (640 procs)

- Macintosh @JAIST (96 procs, my own!)

Xeon, 16GB/4cpu