Iyengar_ADMP - Atom-centered Density Matrix Atom-centered...

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Srinivasan S. Iyengar Department of Chemistry and Department of Physics, Indiana University Atom-centered Density Matrix Atom-centered Density Matrix Propagation (ADMP): Theory and Propagation (ADMP): Theory and Applications Applications
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Iyengar Group, Indiana University Brief discussion of ab initio molecular dynamics Atom-centered Density Matrix Propagation (ADMP) Nut-n-bolts issues Some Results: Novel findings for protonated water clusters QM/MM generalizations: ion channels Gas phase reaction dynamics Outline Outline
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Iyengar Group, Indiana University Molecular dynamics on a single potential surface Molecular dynamics on a single potential surface Parameterized force fields (e.g. AMBER, CHARMM) Energy, forces: parameters obtained from experiment Molecular motion: Newton’s laws Works for large systems But hard to parameterize bond-breaking/formation ( chemical reactions ) Issues with polarization/charge transfer/dynamical effects Born-Oppenheimer (BO) Dynamics Solve electronic Schrödinger eqn (DFT/HF/post-HF) for each nuclear structure Nuclei propagated using gradients of energy (forces) Works for bond-breaking but computationally expensive Large reactive, polarizable systems : Something like BO, but preferably less expensive.
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Iyengar Group, Indiana University Circumvent Computational Bottleneck of BO Avoid repeated SCF: electronic structure, not converged, but propagated “Simultaneous” propagation of electronic structure and nuclei: adjustment of time-scales Car-Parrinello (CP) method Orbitals expanded in plane waves Occupied orbital coefficients propagated O(N 3 ) computational scaling (traditionally) O(N) with more recent Wannier representations (?) Atom-centered Density Matrix Propagation (ADMP) Atom-centered Gaussian basis functions Electronic Density Matrix propagated Asymptotic linear-scaling with system size Allows the use of accurate hybrid density functionals suitable for clusters CP: R. Car, M. Parrinello, Phys. Rev. Lett. 55 (22), 2471 (1985). ADMP: Schlegel, et al. JCP , 114 , 9758 (2001). Iyengar, et al. JCP , 115 ,10291 (2001). Iyengar et al. Israel J. Chem. 7 , 191, (2002). Schlegel et al. JCP 114, 8694 (2002). Iyengar and Frisch JCP 121 , 5061 (2004). References… Extended Lagrangian dynamics Extended Lagrangian dynamics
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Iyengar Group, Indiana University Atom-centered Density Matrix Propagation (ADMP) Atom-centered Density Matrix Propagation (ADMP) Construct a classical phase-space {{R,V,M},{P,W, μ }} The Lagrangian (= Kinetic minus Potential energy) Nuclear KE [ ] MV V Tr 2 1 T = L “Fictitious” KE of P ( 29 [ ] 2 1/4 1/4 μ Tr 2 1 + Energy functional P) E(R, - Lagrangian Constraint for N-representability of P : Idempotency and Particle number ( 29 [ ] P P Λ Tr 2 - - P : represented using atom-centered gaussian basis sets i i occ N i = = 1 P : matrix density particle single of Definition
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This note was uploaded on 12/07/2011 for the course CHEM 350 taught by Professor Duanejohnson during the Summer '06 term at University of Illinois, Urbana Champaign.

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Iyengar_ADMP - Atom-centered Density Matrix Atom-centered...

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