Japan Advanced Institute of Science and Technology,

Kanazawa, Japan.

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Kanazawa

Tokyo

Pseudopotential calculations of Porphyrin Complexes…

TTI2007@Tuscany, Italy.

Ryo Maezono

rmaezono@mac.com

School of Information Science,

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.

People involved…

- Mr. Jun Koseki

QMC code implementation.

- Prof. Richard Needs group

(CASINO ; QMC code.)

- Prof. Masanori Tachikawa

- Ryo MAEZONO.QuickTime˛ Ç∆TIFFÅià≥èkǻǵÅj êLí£ÉvÉçÉOÉâÉÄǙDZÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

Gaussian SCF calc./ structure optimization.

Basis set optimization / QMC calc.

Background (1)

John’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’

Pathology due to Non-locality

€

rcNorm-conserving

Fock non-locality

€

Vlpp r→ ∞( ) ~

Zeffr

€

Zeff +δ l( )

r+η l

Pseudo orb.

AE orbital

John 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.

MDT has rich experiences on this.

‘Billy’ utility (his first script with mysterious name)

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.

Gaussian basis calculation with JRT pseudo.

Lighter Ions.

Practical calculations after JRT2005

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

She used ‘Billy’ utility for basis set optimization.

→ 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.

TM

Basis Set optimization (TM)

<Ni@NiPo

>

Initial -1020.612(LANL1DZ)

- From inner most to outer, d(inner) most effective.

-1021.036Optimized (hartree)

- Gaussian exponents are optimized in HFSCF.

N

N

N

N

<Porphyrin>

Ni

s(3), p(2), and d(5)

-1020.970Uncontracted 3*s(1), 2*p(1), and 5*d(1)

(hartree)

Basis Set optimization (C, N, H)

<Lighter atoms @ Porphin>

Initial -154.242(6-31G**)

-155.612Optimized (hartree)

(※LANL1D2)

N

N

N

N

Energy difference“Not depending on Core size ”

€

ΔE

N

N

N

N

-0.16894

0.22476Optimized

JRT pseudoInitial with LANL1DZ

(c.f. 0.29691 by AE)

of NiPo

€

ΔE

(hartree)

TM

TM… similar as ‘binding energy’

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)

Energy differences

N

N

N

NCu

Cu-Porphyrin

Cu

0.39517

0.28371

0.21771

0.26160

AE

LANLsmall

LANLlarge

QMC_pp(TM)

0.42870

0.18091

0.17061

0.33397

0.25533 0.33404QMC_pp(all)

NotYet

NotYet

Unstable

0.249(2)

NotYet

NotYet

0.063(2)

0.178(2)

0.230(1) 0.170(1)

0.35248

0.20359

0.19622

0.29338

0.29309

B3LYP MP2 DMC OPTVMC HFSCF

(hartree)

reduced time step, Casula’s scheme, frequent updating.

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 (CASINO ｖ 1.8.2)

→ Try with latest CASINO with 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