Integrated Calendar

In large molecular systems (from clusters to nanocrystals and solids) electrons strongly interact with each other and their total wave function is too difficult to understand or describe. The concept of a quasi-particle, going back to Landau, has turned out to be of huge importance. It allows us to understand and intuit about electronic structure and dynamics:
• Electron removal → creation of a positively charged “quasi-hole”.
• Electron insertion → creation of a negatively charged “quasi-electron”.
• Optical excitation → simultaneous creation of a quasi-hole and a quasi-electron. Attractive interaction between the two charges has to be taken into account (Mulliken’s rule).

However, quantitative description of quasi-particles is not an easy task; one method that can do this reasonably accu-rately is called the “GW” method. But GW is an extremely involved and numerically expensive method.
An alternative view, a completely different approach, is to map our real electronic system onto a virtual “non-interacting electron” one. Now, each electron has its own “orbital” and then:
• Electron removal → removal of an electron from an occupied orbital.
• Electron insertion → insertion of an electron into an unoccupied orbital.
• Optical excitation → transition of an electron from an occupied an unoccupied orbital.

Kohn-Sham density functional theories (KS-DFTs) provide such a mapping. Existing applications are numerically much cheaper than GW and supply, as auxiliary quantities, orbitals and orbital energies. Many researchers use these latter quantities in the manner described above. But for both practical and fundamental reasons this procedure often leads to serious errors.
In this talk I discuss the orbitals energies in KS-DFT stressing the fundamental and practical difficulties in viewing them as quasi-particle energies. I then present an approach to DFT we developed, “the optimally tuned range-separated hybrid”, which is better suited for producing orbital energies close to quasiparticle energies. I show this from both the fundamen-tal and practical points of view and I describe additional features of this approach.
Within time limits, I present some triumphs of the method, which succeeds where conventional DFT often fails bitterly. These include: the chemical bond between symmetric bi-radicals, ionization of water clusters, oxidation of aluminum clusters, charge-transfer excitations in molecules and molecular electronics.

Recombination reshuffles genetic material, while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime selection can amplify individual genotypes into large clones. The occurrence of this "clonal condensation" depends, in addition to the ratio of recombination and selection rates, on the heritability of fitness (expected number of offspring). Clonal condensation is an important phenomenon, present in many populations, that has not been captured by traditional population genetics measures (linkage disequilibrium). I hope to convince you that our work provides a qualitative explanation of clonal condensation. In my talk I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy I will derive one of the key quantities of interest: the probability that two individuals are genetically identical. This quantity is the analog of the spin-glass order parameter and it is also closely related to rate of coalescence in population genetics: two individuals that are part of the same clone have a recent common ancestor. Next I will analyze the phase space spanned by time, heritability and the ratio of recombination and selection rates. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe future directions.