Computational Methods for Electronic Structure

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The long-range goal of this research is to develop theoretical and computational methods to predict accuratelythe properties of many-electron systems and then to apply the methods to important condensed mattersystems. The focus of this research is primarily on the development and application of quantumMonte Carlo (QMC) methods. However, part of the research attempts to tie these approaches to othertheoretical 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 futurethere will be development of QMC methods, with emphasis upon more accurate wave functions, improvedboundary 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 temperatureand pressure. Although there have been numerous previous QMC and DFT simulations, the CEIMCmethod removes most of their limitations. The connection between the insulator-metallic transition, theatomic 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-existentor unreliable. A further challenge is the microscopic simulation of water from first principles, which isabsolutely 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 simulateelectrons and their spin states in real nanostructure devices, potentially more accurately and efficientlythan with existing grid-based approaches. The entire device can be simulated by coupling tworandom walks-one to solve the electrostatic equations in a complicated structure and another for the Nbodyquantum equation for the electrons.The computational complexity of the simulation of the basic equations of matter (onclassical not quantum computers) is a very important and fundamental issue. The challenge is to solveaccurately problems with many interacting particles, including strongly interacting systems and cooperativephenomena. QMC methods have made it possible to compute the thermodynamic properties of bosonicsystems, including superfuidity. However, the fermion sign problem is a critical issue limitingpresent work, and steps toward solving or minimizing the sign problem are among the outstanding challengesin computational science. In addition, development of new computational approaches frequentlyleads to new theoretical understanding as well as algorithms useful in other disciplines.The development of these computational quantum methods will have a qualitative impactupon the course of many fields of science including physics, materials science, chemistry and evenbiology, 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 andsolutions; and properties of nanoscale systems. The research is carried out primarily by graduate studentsand postdocs who often go later to industry, thus transferring the latest computational methods. Algorithmsand software developed as a result of the research will be made available to the general researchcommunity through the Materials Computation Center and used in undergraduate courses, graduatecourses, and summer schools at the University of Illinois and elsewhere.