Created: May 08, 2020
Modified: May 16, 2020
Modified: May 16, 2020
molecular dynamics
This page is from my personal notes, and has not been specifically reviewed for public consumption. It might be incomplete, wrong, outdated, or stupid. Caveat lector.- Stack:
- goal: sample from conformations of arbitrary hydrocarbons (or whatever).
- simpler goal: sample from conformations of ethane.
- simpler goal: understand how to represent molecular configurations
- new subgoal: A quantum mechanical description of molecules
- new subgoal: what is the Schrodinger equation and how can we use it to derive the dynamics of a hydrogen atom?
- new subgoal: A quantum mechanical description of molecules
- simpler goal: understand how to represent molecular configurations
- simpler goal: sample from conformations of ethane.
- All dynamics in quantum physics are determined by the Schrodinger equation. This just says that the state evolves according to the gradient of the Hamiltonian (?). NO: it says that the wavefunction evolves according to the gradient. What is the wavefunction? It is a function of system state (positions--and momenta???--of particles) to a real-valued 'density'.
- Q: What is the wavefunction a function of?
- Q: How is a Hamiltonian defined on wave functions?
- for intuition, this is like having dynamics on distribution-space.
- This is what we want: we represent a distribution somehow (eg by building up a model from smaller pieces). Then we define a Hamiltonian on the parameters of this distribution.
- For example, we could represent a distribution over the locations of electrons in an orbital as some kind of squashed Gaussian-like thing (imagine the shape of a p orbital, or an sp3 hybridized orbital), maybe parameterized by the distance of the center of mass from the nucleus. (bad example bnut whatever)
- The Born-Oppenheimer approximation is to assume that the Hamiltonian of a molecule factors into an electron term (electron dynamics given fixed nuclii) and a nucleus term (nuclei given fixed electrons).
- The Eckhart conditions let us further divide the motion of the nuclei into vibrational (intre-atom) and
- Eventually: density functional theory.
- (and then do better!)