Computational Methods for Electronic Structure

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The long-range goal of this research is to develop theoretical and computational methods to predict accurately the properties of many-electron systems and then to apply the methods to important condensed matter systems. The focus of this research is primarily on the development and application of quantum Monte Carlo (QMC) methods. However, part of the research attempts to tie these approaches to other theoretical issues such as the fundamental distinction between metals and insulators in terms of the manybodyelectron wave function. QMC can provide very accurate results for electronic systems: the most well-known example is the homogenous electron gas where QMC has provided the benchmark upon which are based most density functional (DFT) calculations. DFT-based methods are the only current method feasible for accurate large-scale simulations of realistic systems; however, even the improved functionals have well-known defects. The past few years have seen substantial progress in coupling the simulation of ions at a finite temperature with QMC simulation of the electrons (the CEIMC method). In addition to being more accurate, in cases where other averaging must be performed, the QMC approach can be as efficient as DFT- based approaches. Applications to extended systems of hydrogen are now in production. In the near future there will be development of QMC methods, with emphasis upon more accurate wave functions, improved boundary conditions, and new methods able to use much larger computational facilities efficiently. The research will enable applications to elements with core electrons using more accurate pseudopotentials. Methods to calculate electronic forces will enable dynamical calculations of ionic systems. Applications of the methods will include hydrogen throughout the whole phase diagram of temperature and pressure. Although there have been numerous previous QMC and DFT simulations, the CEIMC method removes most of their limitations. The connection between the insulator-metallic transition, the atomic molecular-transition and temperature and zero point effects is still lacking in current approaches. The simulations should clarify the situation, especially under conditions where experiment is non-existent or unreliable. A further challenge is the microscopic simulation of water from first principles, which is absolutely fundamental to many scientific questions and which appears to be within reach of QMC simulation. The power of this approach can be applied to other problems, for example, new methods to simulate electrons and their spin states in real nanostructure devices, potentially more accurately and efficiently than with existing grid-based approaches. The entire device can be simulated by coupling two random walks-one to solve the electrostatic equations in a complicated structure and another for the Nbody quantum equation for the electrons. The computational complexity of the simulation of the basic equations of matter (on classical not quantum computers) is a very important and fundamental issue. The challenge is to solve accurately problems with many interacting particles, including strongly interacting systems and cooperative phenomena. QMC methods have made it possible to compute the thermodynamic properties of bosonic systems, including superfuidity. However, the fermion sign problem is a critical issue limiting present work, and steps toward solving or minimizing the sign problem are among the outstanding challenges in computational science. In addition, development of new computational approaches frequently leads to new theoretical understanding as well as algorithms useful in other disciplines. The development of these computational quantum methods will have a qualitative impact upon the course of many fields of science including physics, materials science, chemistry and even biology, by enabling much more accurate, and potentially faster, simulation of a broad range of systems. The calculations will resolve questions about the properties of hydrogen at high temperatures and pressures, the basis of models for the formation of Jovian planets; the microscopic properties of water and solutions; and properties of nanoscale systems. The research is carried out primarily by graduate students and postdocs who often go later to industry, thus transferring the latest computational methods. Algorithms and software developed as a result of the research will be made available to the general research community through the Materials Computation Center and used in undergraduate courses, graduate courses, and summer schools at the University of Illinois and elsewhere.