YoshiyukiKawazoe

Fundamental Understanding of Materials Properties Based on the Exact Solution of Many Body Coulombic System by Diffusion Quantum 　　　　　Monte Carlo Method: 

Fundamental Understanding of Materials Properties Based on the Exact Solution of Many Body Coulombic System by Diffusion Quantum 　　　　　Monte Carlo Method Yoshiyuki Kawazoe Institute for Materials Research,Tohoku University, Sendai 980-8577, Japan kawazoe@imr.edu http://www-lab.imr.edu/~kawazoe/ CODATA 北京 24th Oct. 2006 Since 1916 http://www.imr.edu/

Slide2: 

Objects of the materials research are many body system via Coulomb interaction Si, steel, DNA all the same！ Described by Schroedinger equation (Dirac eq.) More than 50 years ago, Dirac already said that “All necessary equations are known, only to solve them!” But!!! Many body problem is too much time consuming… difficult to be solved … approximations have applied up to the present! And, many misunderstandings happened!!! Why ab initio simulation can predict new materials?

Slide3: 

Our research area Present standard ～Ｏ（ｎ４） ＣＩ～Ｏ（ｎ12） ～Ｏ（ｎ6） Ab initio calculation has no experimental parameters but a lot of approximations included!

Is LDA good enough?: 

Is LDA good enough?

Cr@Sin clusters: 

Cr@Sin clusters ・n=12 cluster 　　　　GGA and B3PW91→max stable →more accurate method is necessary！

Exact solution of quantum mechanical equation for Coulombic many body system: 

Exact solution of quantum mechanical equation for Coulombic many body system Complete solution with electron exchange-correlation → quantum Monte Carlo method No restriction for functions 　　　　　　　　　　　　→　diffusion QMC : completely numerical solution ; no restrictions

Slide7: 

・Virial theorem：T and V are not independent! 　　　　　General rule for all states in Coulombic system Coulomb force is the result of geometry；three dim. space！ 　　　　　Necessary condition for exact theory T：kinetic energy of electrons V：sum of Vee+VeN+VNN condition for molecular stability

Origin of molecular stability?: 

Origin of molecular stability? Electron clouds overlaps?... No!! e-e interaction Vee is repulsive!... Not possible! Most important interaction to make molecules stable is nucleus-electron VNe attractive force!

Ex.1 How H2 molecule formed from 2H atoms?: 

Ex.1 How H2 molecule formed from 2H atoms? Two models for H2 molecular state HL and MO Heitler-London(HL)model Minimum orbitals MO Independent states Molecular state expressed by 1s orbitals only

Stability condition fulfilled?: 

Stability condition fulfilled? -5.01 -4.22 2.53 1.33 0.5 0.3 HL MO HF DMC -2.48 -2.88 -3.63 -4.75 (eV) condition negative positive negative 2 3.63 4.8(1) -7.27 -9.6(1) 2.0 2.0(1) Only by the 1s orbitals, it is not possible to explain the stability of H2 molecule. Contradict to virial theorem. Expl. -4.75 Stability of materials should be realized by nucleus-electron int. HL and MO give reversed values absolutely

Why molecule is stabilized: Charge density in H2: 

Why molecule is stabilized: Charge density in H2 DMC HF Heitler-London theory (LCAO with 1s atomic orbital) fails! Virial theorem (2T+V=0) should be satisfied! DMC: kinetic energy increases and potential energy more decreases!

Correlation energy in electron system: 

Correlation energy in electron system

Correct explanation of Hund’s multiplicity rule: 

Correct explanation of Hund’s multiplicity rule Electron exchange interaction? At that time, researchers were astonished and tried to explain all of quantum mechanical phenomena by e-exchange. Magnetism＝Heisenberg model? … No!! Exact numerical calculation including all interactions Vee and VeN!

Slide14: 

Diffusion Quantum Monte Carlo (DQMC) method Imaginary-time evolution projector method Electron correlation can be fully taken into account ! Identical with solving the ‘exact’ many-body Schrödinger equation Example 1: New interpretation of Hund’s multiplicity rule for carbon atom -88.253(27) Hongo, Maezono, Yasuhara, Kawazoe Vee for triplet is larger Ven contributes mostly

Correct explanation of Hund’s multiplicity rule: 

Correct explanation of Hund’s multiplicity rule

Absolute value estimation of other physical quantities : 

Absolute value estimation of other physical quantities Electron affinity Ionization potential HOMO-LUMO gap Completed for 3p systems. Computing for transition metals. Extension to crystals

Exact Computation of Electron Affinity by Diffusion QMC Method: 

Exact Computation of Electron Affinity by Diffusion QMC Method Li B C O F Electron affinities of light atoms The electron correlation plays an important role in EAs ! Hongo, Maezono, Yasuhara, Kawazoe

computing cost for ab initio methods: 

computing cost for ab initio methods →complete numerical calculation needed! Ab initio DMS seems to be a better method in future

Slide19: 

V. Kumar, M. Sluiter, J.-Z. Yu, H. Mizuseki, Q. Sun, T. M. Briere, T. Nishimatsu, R. V. Belosludov, A.A. Farajian, J.-T. Wang, Z. Zong, S. Ishii, A. Jain, Q. Wang, G. Zhou, Murgan, C. Majumder, K. Ohno, W. Kohn, S. Louie, H. Yasuhara, B.-L. Gu, P. Jena, Dong, M. Radney, K. Esfarjani, L. Wille, K. Parlinski, S. Tse, S. T. Chui, D.-S. Wang, R.-B. Tao, Z.-Q. Li, Y. Guo, L. Zhou, J. Wu, V. R. Belosludov, Y. C. Bae, A. Taneda, Y. Maruyama, R. Sahara, H.-P. Wang, Z. Tang, T. Ikeshoji, H. Chen, K. Shida, T. Morisato, K. Hongo, H. Kawamura, Khazaei, etc. + Experimentalists: M. Kawasaki, T. Oku, T. Hashizume, T. Kondow, S. Tanemura, K. Sumiyama, T. Sakurai, T. Fukuda, etc. +Companies: Hitachi, Seiko-Epson, NEC-Tokin, New Japan Steel, Codec, Tore-Dawconing, IBM, etc.