Martinez_Ab_Initio_Spawning - Ab Initio Molecular Dynamics...

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Ab Initio Multiple Spawning Dynamics Todd J. Martínez Department of Chemistry & The Beckman Institute University of Illinois at Urbana-Champaign Ab Initio Molecular Dynamics Terminology Classical No Any DFT Ab initio BOMD Born-Oppenheimer Molecular Dynamics Classical No Any DFT Ab initio Semiempirical Direct Dynamics Classical Yes Gaussian DFT or SCF ADMP Atom-Centered Density Matrix Propagation Classical Yes Plane Wave DFT CPMD Car-Parrinello Molecular Dynamics Dynamics Extended Lagrangian? Electronic Basis Electronic Structure Electronic Basis Sets z Plane waves - Natural for periodic systems Hellman-Feynman Forces are exact Very inefficient for nonperiodic systems (large empty spaces between periodic replicas; in almost all cases, this empty space is filled with basis functions) Obvious, well-defined convergence hierarchy z Gaussian – Periodicity is more difficult to incorporate (but not impossible, e.g. Crystal ) Generally atom-centered (“floating” Gaussians also possible) z Electrons like to be near nuclei! Pulay terms in forces for atom-centered Gaussians Convergence hierarchy more subtle, but now well-understood (Dunning) 2 r e α ikr e Empty space “Pulay” Terms () ;; ˆˆ ˆ ˆ elec el elec elec elec elec elec ele elec el ec elec r ec elec r r c r H rR E rR H r Hr R r R R R R R R H R ψψ = ∂∂ + = + “Hellmann-Feynman Force” “Pulay Force” Pulay force apparently requires derivatives of electronic wavefunctions! Actually, often it does not , but it is always more expensive than HF Force Extended Lagrangian Technique z What is it? Electronic degrees of freedom are propagated under a new Lagrangian, instead of using the variational principle to determine them at each new geometry z Benefits Wavefunction does not need to be converged at each time step z “1” iteration vs. typical 10-15 iterations (apparently) z But , good BOMD codes require < 5 iter b/c geometry change in one time step is small z Disadvantages Need to ensure that the electronic coefficients are always “cold” and nuclei are always “hot” z Energy transfer between ions and “fictitious” degrees of freedom is unphysical Time step needs to be smaller than in BOMD – fictitious degrees of freedom are high-frequency relative to nuclei z Bottom line (according to TJM) EL schemes have ½ time step to save 5 iterations/time step. Works out to a 2.5x speed advantage in favor of EL But need to be careful to maintain adiabatic separation of nuclei and electrons. Both are reasonable and choice depends on taste EL expands dynamic range of frequencies to reduce SCF iterations Electronic Excited States CC H Ph H Ph (CH3)2C C(CH3)2 h ν Ph Ph CH3 CH3 CH3 CH3 + N N N N Mg O R CO2CH3 N Opsin H Chemical Synthesis Energy Conversion Vision
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Light-Driven Molecular Devices F h ν F Switch electron transport on and off Light Mechanical Work Other Applications… Optical Memory Molecular Logic Local control of pH –
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Martinez_Ab_Initio_Spawning - Ab Initio Molecular Dynamics...

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