The Born-Oppenheimer electronic wavefunction Φ BO R (r) picks up a topological phase factor ±1, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R-space. We show that this topological quantity reverts to a geometric quantity e iγ if the geometric phase γ = Im ΦR|∇µΦR · dRµ is evaluated with the conditional electronic wavefunction ΦR(r) from the exact electron-nuclear factorization ΦR(r)χ(R) instead of the adiabatic function Φ BO R (r). A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wavefunction.

We present the derivation of an ab initio and parameter-free effective electron-electron interaction that goes beyond the screened random phase approximation and accounts for superconducting pairing driven by spin fluctuations. The construction is based on many-body perturbation theory and relies on the approximation of the exchange-correlation part of the electronic self-energy within time-dependent density functional theory. This effective interaction is included in an exchange-correlation kernel for superconducting density functional theory in order to achieve a completely parameter free superconducting gap equation. First results from applying the new functional to a simplified two-band electron gas model are consistent with experiments.

0 0 2 . Inset (bottom-right corner): the imaginary part of u v. 2 New J. Phys. 16 (2014) 119601 J A Berger et al New J. Phys. 16 (2014) 119601 J A Berger et al 0 1 1 1 . Inset: the screened interaction Γ u v GW as a function of the interaction y v [ ] 0 0 2 . AbstractIn this work we determine the one-body Greenʼs function as solution of a set of functional integro-differential equations, which relate the one-particle Greenʼs function to its functional derivative with respect to an external potential. In the same spirit as Lani et al (2012 New J. Phys. 14 013056), we do this in a onepoint model, where the equations become ordinary differential equations (DEs) and, hence, solvable with standard techniques. This allows us to analyze several aspects of these DEs as well as of standard methods for determining the onebody Greenʼs function that are important for real systems. In particular: (i) we present a strategy to determine the physical solution among the many mathematical solutions; (ii) we assess the accuracy of an approximate DE related to the GW +cumulant method by comparing it to the exact physical solution and to standard approximations such as GW ; (iii) we show that the solution of the Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. approximate DE can be improved by combining it with a screened interaction in the random-phase approximation. (iv) We demonstrate that by iterating the GW Dyson equation one does not always converge to a GW solution and we discuss which iterative scheme is the most suitable to avoid such errors.

We show that the equations underlying the GW approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact, find the correct solution. These theorems are general enough to cover a large class of similar algorithms. An efficient algorithm for including self-consistent vertex corrections well beyond GW is also described and further used in numerical validation of the two theorems.

We present ab initio calculations of the electronic and transport properties of one-dimensional π -conjugated stacks of guanine-and melanin-based molecules. The electron and hole bandwidths are found to be very large for these organic materials (up to 2 eV), and the effective masses of the charge carriers are rather small. Since these material parameters basically determine the intermolecular charge-transport properties, we predict highly ordered self-assembled one-dimensional stacks of such biological molecules to be promising candidates for applications in organic electronics.