TTI 2007Tuscany Italy Pseudopotential calculations of Porphyrin Complexes

TTI 2007@Tuscany, Italy. Pseudopotential calculations of Porphyrin Complexes… Kanazawa Ryo Maezono Tokyo rmaezono@mac. com School of Information Science, Japan Advanced Institute of Science and Technology, Kanazawa, Japan.

Aim Porphyrin, Phthalocyanine etc. TM TM = Ni, Cu, Zn - Actively studied in Nano/Bio research field. - Interplay between TM site and Side-chains. Establish procedures for pseudo-pot. QMC calculations. - prepare trial/guiding WF in pseudo-pot. calc. - Basis set re-optimization. suitable for stable DMC accumulation.

People involved… - Mr. Jun Koseki Gaussian SCF calc. / structure optimization. - Prof. Masanori Tachikawa - Ryo MAEZONO. Basis set optimization / QMC calc. - Prof. Richard Needs group QMC code implementation. (CASINO ; QMC code. )

Background (1) John’s Pseudo potential studies. - Non-diverging, non-local pseudo potentials. avoiding e. N-cusp. Fock exchange. Lee-Needs（2002) ‘QMC_pp’ Ovacharenko-Lester（2001) - Transition metal ions… s-electrons coexist with d-electrons. → Difficulty! Valence electron but not HOMO John investigated long-range tail. …then wrong behavior… Asymptotic behavior of orbital functions. Trail-Needs（2005) , Dolg（2005)

Pathology due to Non-locality Fock non-locality Pseudo orb. AE orbital Norm-conserving John investigated … Asymptotic behavior of orbital functions. Valence electron but not HOMO …then wrong behavior… ‘ 4 s’-orb. of TM ion. J. Trail et. al. , JCP 122, 174109 (2005). 3 d is HOMO above 4 s → continuously taken over by outside.

Interesting test case Porphyrin, Phthalocyanine etc. TM TM = Ni, Cu, Zn - Actively studied in Nano/Bio Science. - Interplay between TM site and Side-chains. Establish procedures for pseudo-pot. calculations. suitable for stable DMC accumulation. - Generate trial/guiding WF in pseudo-pot. calc. - Basis set re-optimization.

Gaussian basis set with JRT pseudo. commonly used in Molecular Science, Bio-molecule bussiness as well. preparation of proper basis set. Conventional pseudo pot. provided with preset basis set. (such as LANL 2 DZ etc. ) not fully optimized but well calibrated. ‘This basis set can be reliable upto XXX digit’ How to setup the basis set for JRT pseudo? → Basis set optimization by ourselves. MDT has rich experiences on this. ‘Billy’ utility (his first script with mysterious name)

Gaussian basis calculation with JRT pseudo. Practical calculations after JRT 2005 Lighter Ions. I. Gurtubay et. al. , JCP 124, 024318 (2006). She used ‘Billy’ utility for basis set optimization. TM Ions. <Aim> - Porphyrin calculations. - See how’s going on TM pseudo by John’s remedy. The system is too large to be dealt with ‘Billy’. → Basis set optimization manually. TM TM = Ni, Cu, Zn

Procedure LANL 1 DZ the same core size as JRT pseudo. Structure optimization in B 3 LYP Replace TM Pseudo (from LANL to JRT) Re-optimize TM basis set QMC_pp(TM) <Porphyrin> TM TM = Ni, Cu, Zn H, C, N are treated as AE (6 -31 G**). Replace AE by JRT-Pseudo. QMC_pp(all) Re-optimize H, C, N basis set @ porphin. <Porphin> TM

Basis Set optimization (TM) <Porphyrin> <Ni@Ni. Po> Initial Ni (LANL 1 DZ) -1020. 612 (hartree) s(3), p(2), and d(5) Uncontracted -1020. 970 3*s(1), 2*p(1), and 5*d(1) Optimized -1021. 036 - Gaussian exponents are optimized in HFSCF. - From inner most to outer, d(inner) most effective. (hartree)

Basis Set optimization (C, N, H) <Lighter atoms @ Porphin> Initial -154. 242 (6 -31 G**) (※LANL 1 D 2) Optimized -155. 612 (hartree)

Energy difference “Not depending on Core size ” TM … similar as ‘binding energy’ TM of Ni. Po Initial Optimized -0. 16894 0. 22476 JRT pseudo with LANL 1 DZ (hartree) (c. f. 0. 29691 by AE)

QMC calculations Cu-Porphyrin [QMC_pp(all)] Cu MP 2 -206. 4994 (hartree) -210. 693(1) VMC -211. 5698(9) DMC -210. 2612 B 3 LYP HFSCF -212. 7404 Non-variational Variational

Jastrow Functions… <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 Cu-Porphyrin Cu B 3 LYP MP 2 DMC OPTVMC HFSCF AE 0. 39517 0. 42870 Not. Yet 0. 35248 LANLsmall 0. 28371 0. 18091 Not. Yet 0. 20359 LANLlarge 0. 21771 0. 17061 Unstable 0. 063(2) 0. 19622 QMC_pp(TM) 0. 26160 0. 33397 0. 249(2) 0. 178(2) 0. 29338 QMC_pp(all) 0. 25533 0. 33404 0. 230(1) 0. 170(1) 0. 29309 (hartree) reduced time step, Casula’s scheme, frequent updating.

Tendencies B 3 LYP, DMC, MP 2 Absolute values of energy B 3 LYP＜DMC＜MP 2 [TMPo/Atom/Po] 2 ha. (all) / 4 ha. (TM) [QMCpp(TM)/QMCpp(all)] Energy Diff. ( ‘binding’ ) ※ QMC not variational here. MP 2＜B 3 LYP＜DMC Only for Ni. Po, MP 2＜DMC＜B 3 LYP

Notes - Atomic calculation of Zn with LANL. Though it is QUITE simple system, VARMIN (CASINO ｖ 1. 8. 2) won’t run even with reduced parameters into one. → Try with latest CASINO with emin/madmin? ?

Summary Replacing procedure of QMC pseudo potentials suitable for stable DMC accumulation. LANL pseudo/basis set … easy to get and calculate in SCF. as it is replace with JRT pseudo re-optimization of basis set No stable DMC Stable DMC accumulation. δE~0. 001 hartree

High Performance Computing Facilities… * Hitachi; SR 11000 * Cray; T 3 E, XT 3 * SGI; Origin 2000, Origin 3000, Altix 3700, Altix 4700 * Fujitsu; Prime. Power, Prime. Quest * HP; GS 320, ES 45, GS 1280 * IBM; SP 3, p 690. * Clusters; Pentium 3, Opteron, Macintosh(Xeon)

Architectures - Hitachi SR 11000 @Hokkaido Univ. (640 procs) IBM Power 5+, 128 GB/16 cpu - Macintosh @JAIST (96 procs, my own!) Xeon, 16 GB/4 cpu - SGI Altix @JAIST (360 procs) Itanium 2, 24 GB/4 cpu - Cray XT 3 @JAIST (128 procs) Opteron 150, 32 GB/4 cpu