FYI

"

(1) Ab initio or first-principles methods have emerged in the last two decades as a powerful tool to probe the properties of matter at the microscopic scale. These approaches are used to derive macroscopic observables under the controlled condition of a “computational experiment,” and with a predictive power rooted in the quantum-mechanical description of interacting atoms and electrons. Density-functional theory (DFT) has become de facto the method of choice for most applications, due to its combination of reasonable scaling with system size and good accuracy in reproducing most ground state properties. Such an electronic-structure approach can then be combined with classical molecular dynamics to provide an accurate description of thermodynamic properties and phase stability, atomic dynamics, and chemical reactions, or as a tool to sample the features of a potential energy surface.

(2) In a molecular-dynamics (MD) simulation the microscopic trajectory of each individual atom in the system is determined by integration of Newton’s equations of motion. In classical MD, the system is considered composed of massive, point-like nuclei, with forces acting between them derived from empirical effective potentials.

(3) Ab initio MD maintains the same assumption of treating atomic nuclei as classical particles; however, the forces acting on them are considered quantum mechanical in nature, and are derived from an electronic-structure calculation. The approximation of treating quantum-mechanically only the electronic subsystem is usually perfectly appropriate, due to the large difference in mass between electrons and nuclei. Nevertheless, nuclear quantum effects can be sometimes relevant, especially for light elements such as hydrogen; classical or ab initio path integral approaches can then be applied, albeit at a higher computational cost. The use of Newton’s equations of motion for the nuclear evolution implies that vibrational degrees of freedom are not quantized, and will follow a Boltzmann statistic. This approximation becomes fully justified only for temperatures comparable with the highest vibrational level in the system considered. " Cited from http://www.fisica.uniud.it/~giannozz/Papers/handbook1.pdf

Classical molecular dynamics

• Interactions are approximated by classical model potentials constructed by comparison with experiment (empirical potentials)

• Leads to simulation of purely classical many-particle problem

• Works well for simple particles (such as noble gases) that interact via isotropic pair potentials

• Poor for covalent atoms (directional bonding) and metals (electrons form Fermi gas)

• Simulations fast, permit large particle numbers

Ab-initio molecular dynamics

• Performs a full quantum calculation of the electronic structure at every time step (for every configuration of the atomic nuclei), ab-initio = from first principles

• Forces are found the dependence of the energy on the particle positions

• Much higher accuracy than classical MD, but much higher numerical effort (restricts number of particles and simulation time)

cited from http://web.mst.edu/~vojtat/class_5403/MolecularDynamics.pdf

The first principle is meta-physical, not physical.

Dear Martin

Could you please explain this more clearly. I could not get the point.

Regards

Ma: i just wanted to point out that the term "first principle" in the context of quantum mechanics should not be taken literally. Nothing is without cause, except the first principle, which is its own cause. The first principle has no attribute (no nature, no dimension). That which is physical cannot be the first principle. "Ab initio" quantum mechanics is a misnomer. "Ab initio" means "from the beginning," but the first cause has no beginning and no end. Note that the first principle can only be approached by negation (via negativa), i.e. by stating what it is not; the more man learns about the phenomenal realm, the longer such a statement will be. Hence, learning about the physical realm (beyond the basic observations of impermanence, incommensurability, etc.) does not bring man any closer to understanding this realms' origin (the first principle/cause). This has been known by man for millennia.