COMPUTATIONAL PHYSICS

Quantum Chemistry

Dr. C. J. Tymczak
Dr. Nevill Gonzalez Szwacki

Quantum chemistry has been in continued development since before the advent of computers. Using quantum chemical techniques it is possible to calculate the physical and electronic properties of atoms, molecules and bulk materials. There are many different flavors and approximations to quantum chemistry, which attempt to solve the same basic equation, the Many-Body Schrodinger Wave Equation:

where N is the number of particles. There is no known closed form solution to this equation for, which forces us to make approximations. Below is a brief timeline of theoretical developments and approximations of Quantum Chemistry

1927 Thomas-Fermi model--L. H. Thomas and Enrico Fermi
1927 Hartree Theory--D. R. Hartree
1928 Hartree Theory--J. C. Slater and J. A. Gaunt
1930 Hartree-Fock Theory--V. A. Fock
1934 Moller-Plesset Theory---C. Moller and M. S. Plesset
1964 Density Functional Theory--P. Hohenberg and W. Kohn
1965 Kohn-Sham Theory--W. Kohn and L. J. Sham
1993 Hybrid Functionals--A. D. Becke

Most quantum chemical methods solve the Schrodinger Wave Equation by diagonalizing an approximate single particle Hamiltonian matrix. This requires an eigen-solver be employed. Unfortunately, computationally this scales with the cube of the number of atoms, which severely limits its utility. However, for insulating systems this can be avoided using advanced "Linear Scaling" Methods. Linear Scaling methods avoid the cubic scaling by solving for the single particle "Density Matrix" directly. We have been working on these methods for the last ten years at Los Alamos National Laboratory, and recently at Texas Southern University and have developed a general purpose code FreeON.

PRESENTATIONS:

General Decription of FreeON (MondoSCF)

Our Computer Resources

Plasma Simulations

Dr. Daniel Vrinceanu

Ultra cold plasmas (UCP) are obtained from a sample of atoms cooled by standard magneto-optical trap techniques and laser-excited just above the ionization threshold. The excess energy, which can be varied from about 0.1 K to 100 K, is imparted to the free electrons, which quickly leave the plasma. However, the trailing slow ions left behind create a net positive space charge that prevents further ejection of electrons. Therefore only a fraction of the electrons effectively leave the cloud; the value of this fraction depends on the number of atoms ionized. The remaining part of electrons reach a quasi-equilibrium state within a short time, of the order of the electron plasma relaxation time, while the ions barely move, if at all, during this time. Since the most energetic electrons have already left the plasma, the remaining electrons cannot be described by a Maxwell- Boltzmann distribution, which includes electrons with arbitrarily large velocities. On a longer time scale, the cloud expands inducing an adiabatic cooling while the three-body recombination and de-excitation collisions tend to warm up the plasma. The study of UCP’s is important because it opens the exploration of strongly correlated systems, where the potential energy is greater than the kinetic energy. These systems are found in extreme conditions such as the core of Jupiter, the crust of neutron stars and shock waves produced by laser implosion. In contrast, the UCP achieve strong correlations in a very low density and temperature regime, easily accessible by experimentalists thanks to modern atomic and molecular cooling techniques. The initial density profile, energy, and ionization state are accurately known and controllable, and optical probes have proven powerful for obtaining precise measurements of plasma properties. The goal of the proposed research is to develop a scalable parallel tree code, which enables Molecular Dynamics Simulations (MDS) of realistic size and integration time, with direct access to conditions similar to those in experiment. Direct numerical simulation, by calculating each particle’s trajectory according to the interaction with all other particles in the system, provides valuable information on dynamics at the single-particle level, outside the realm of kinetic or hydrodynamic methods. Unfortunately, the wealth of information offered by MDS comes at an extremely high computational cost. A typical UCP experiment employs about 107 particles and follows their dynamics for few hundred microseconds. In contrast, the current most advanced simulations can not use more than tens of thousands of particle, and they can not run for more than few tens of nanoseconds, and that at the price of working with an artificial electron-ion mass ratio. More powerful computers will surely push in the future the frontier of the capabilities of MDS, but in the meanwhile two major difficulties have to be addressed in order to make progress: (i) the limitation in the number of particles, which comes from the O(N2) scaling of the particle- particle force calculation. A scalable parallel tree code can make possible simulations with millions of particles; (ii) the limitation in simulation time, which originates from the fact that the time step should be small enough to follow the motion of the much lighter electrons, even though the ions don’t move much in this time. Better integration schemes and a time multi scale approach, a sort of a tree code in the time domain, can improve the efficiency of simulations, but most probably only by a factor of two or three.

PRESENTATIONS