Day 2 :
Pascal Institute of Physics, France
Keynote: Quantum Monte Carlo: The application to chemically accurate reaction activation barrier evaluation on metal catalysts
Time : 10:00-10:45
Philip E Hoggan, admitted to Trinity College, Cambridge in 1978, aged 17 on his entrance examination results. After his BA in Chemistry and Mathematics, he obtained a scholarship and completed the MA in Theoretical Chemistry in 1983. He went to Nancy, France where he obtained his PhD in 1987 (age 26). In France, it was then possible to continue and obtain a DSc by research, which he defended in public (fall 1991). This was the sesame to forming his own group, which was initially an integrated theme with an FTIR catalytic intermediate group in Caen, France. The STOP Slater Type Orbital Package was software developed also in this period 1992-1998. Having already passed the National Qualification for Professors in 1993, Philip E Hoggan finally obtained the chair for theoretical chemistry in Blaise Pascal University in 1998. Since 2005, solid surfaces, metal catalysts, and semiconductors. These, he and his number of first principles methods, including Quantum Monte Carlo which is the method of choice for the catalytic work. He has a half-a-dozen international conferences, in Cambridge, Buenos Aires, two locations in Turkey as in France. He speaks 5 languages fluently.
To introduce the Quantum Monte Carlo approach (QMC), recap first quantum mechanics, structure, and properties. The time-dependent or stationary Schrödinger equation is used. There is currently also a hive of research activity in developing the related approaches for and heterogeneous systems. Most methods are ‘deterministic’, is a unique valid solution which in a few ‘toy’ cases, such as the H2 molecule or the uniform electron gas model of metals, can be obtained analytically. Arbitrary accuracy for any system must then be ab initio full configuration interaction (full CI). This gives electron correlation and properties. These reference calculations are often approximated. QMC provides a stochastic first principles ‘solution’ of the Schrödinger equation. To obtain precise results, stepwise in Diffusion Monte Carlo (DMC). DMC can be made CI, with explicit and is accessible for larger and more complex systems. It is reputed to give the ‘correct’ answer, albeit cited with standard error. Heterogeneous systems include molecule-metal surface reactions. This theoretical prediction of catalytic activation barriers uses QMC. The QMC methodology has been used for increasingly large molecules for 30 years and 15 years for solid fermion systems. The QMC random error for such systems can be made small by long simulations and averaging techniques but any systematic contribution must be removed with the help of benchmarks compared to reliable molecular beam experiment. The breakthrough regarding QMC metal surface reaction activation barriers presented here we have shown energy values to chemical accuracy, as compared to the molecular beam results for bond dissociation of hydrogen at Cu(111) and Pt(111). These values are poorly estimated by other first principles methods, yet QMC is very satisfactory. Secondly, reactions used in an involve a key bond-dissociation step, the validated QMC approach can be extended. Recently, we have been involved in the ‘hot-topic’ of the water-gas shift reaction. This is carbon-monoxide reacting (conditions at a Pt(111) surface) to yield hydrogen as a and carbon-dioxide burned to recover water, so removal of carbon-dioxide is the only issue and it can be accomplished by dissolution. The forward reaction removes the toxic effluent, carbon-monoxide. This so-called ‘water-gas’ equilibrium can go thermodynamically ‘uphill’ i.e. towards hydrogen, suitable catalyst. Barrier heights are less than 20 kcal/mol. Yields are excellent since a catalytic process is selective.
Kyushu University, Japan
Keynote: Rabi model and spin-boson model
Time : 11:00-11:45
Fumio Hiroshima has completed his PhD in the year 1996 from Hokkaido University. He is the Professor of Kyushu Univeristy and investigates quantum field theory from purely mathematical point of view and stochastic analysis. He has published more than 65 papers in reputed journals and books.
The so-called quantum Rabi model and spin-boson model are discussed by path measures in this talk. The quantum Rabi model describes a linear interaction between a two-level atom and one-mode photon. The Hamiltonian of the Rabi model can be realized as a self-adjoint operator acting in a Hilbert space. The spectrum of the self-adjoint operator H can be studied by a path measure. H has purely discrete spectrum and each discrete spectrum can be regarded as a function of a coupling constant. Our problem is as follows. (i) Are there any crossings among them? (ii) If so, how do they take place? We can conjecture that the ground state energy of H has no crossing. In this talk, we prove this fact by a functional-integral method. As a corollary, we conclude that the ground state energy of H is simple (i.e., the ground state is unique). On the other hand, spin-boson model describes a linear interaction between a two-level atom and a scalar quantum field. Then spin-boson model seems to be an infinite freedom version of the Rabi model. We consider localization properties of the ground state of the spin-boson model by the functional-integral method.