Advanced methods of molecular dynamics 1.Monte Carlo methods 2.Free energy calculations 3.Ab initio molecular dynamics 4.Quantum molecular dynamics 5.Trajectory.

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Presentation transcript:

Advanced methods of molecular dynamics 1.Monte Carlo methods 2.Free energy calculations 3.Ab initio molecular dynamics 4.Quantum molecular dynamics 5.Trajectory analysis

When classical mechanics is not adequate? A “quantum measure“ of an object with mass m And kinetic energy E is its de Broglie wave length: = 2  ћ/p = 2  ћ/(2mE) 1/2 Shall d be the characteristic dimension of the system, then: << d classical mechanics,  d quantum mechanics.

of selected objects 1. A student running “classic” late for class: m = 70 kg, v = 5 m/s ~ m 2. Valence electron: quantum m = 9x kg, E = 1 eV ~ m e-e- 3. Vibrating neon atom: semi-quantum m = 2x kg, E = 0.01 eV ~ m Ne

Particle – wave dualism Wave character of quantum objects: double slit experiment - difraction R. Kosloff et al., HU Jerusalem

Even classical objects can exhibit wave behavior R. Kosloff et al., HU Jerusalem

Quantum motions of atoms and molecules 1. Zero point vibrations – energy cannot decrease below h  /2 2. Tunneling – under a barrier between two wells (also above the barrier reflection) 3. Energy transfer via quantum resonances, interferences

Quantum interactions 1. With electrons: Non-adiabatic interactions – avoided crossings, conical intersections,… 2. With photons: electronic/vibrational/rotational photoexcitations - spectroscopy, control of reactions by optical pulses, …

Quantum vs classical mechanics Comparison between a quantum and classical ball elastic vibrations (elasticaly bouncing from the floor) M. Reed, Yale University

Time-dependent vs time-independent Classical mechanics: time-dependent (dynamical Newton equations) Quantum mechanics: time-independent: H  =E  time-dependent: ih  /  t =H  Stationary bound and Scattering states  j, E j ; time-indep. Hamiltonian Dynamical evolution, non- Stationary response  (t); also for a time-dep. Hamiltonian For time-indep. Hamiltonian (in principle) equivalent:  (t) =  j  j exp[(-i/h)E j t]