Long-range excitations in time-dependent density functional theory

Adiabatic time-dependent density functional theory fails for excitations of a heteroatomic molecule composed of two open-shell fragments at large separation. Strong frequency-dependence of the exchange-correlation kernel is necessary for both local and charge-transfer excitations. The root of this is static correlation created by the step in the exact Kohn-Sham ground-state potential between the two fragments. An approximate non-empirical kernel is derived for excited molecular dissociation curves at large separation. Our result is also relevant for the usual local and semi-local approximations for the ground-state potential, as static correlation there arises from the coalescence of the highest occupied and lowest unoccupied orbital energies as the molecule dissociates.Comment: 7 pages, 2 figure

Effect of many modes on self-polarization and photochemical suppression in cavities

The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born–Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born–Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He$^+$ scattering.Comment: 5 pages, 2 figures, J. Chem. Phys. accepte

Moral Hazard and Peer Monitoring in a Laboratory Microfinance Experiment

Most problems with formal sector credit lending to the poor in developing countries can be attributed to the lack of information and inadequate collateral. One common feature of successful credit mechanisms is group-lending, where the loan is advanced to an individual if he/she is a part of a group and members of the borrowing group can monitor each other. Since group members have better information about each other compared to lenders, peer monitoring is often less expensive than lender monitoring. Theoretically this leads to greater monitoring and greater rates of loan repayments. This paper reports the results from a laboratory experiment of group lending in the presence of moral hazard and (costly) peer monitoring. We compare peer monitoring treatments when credit is provided to members of the group sequentially and simultaneously, and individual lending with lender monitoring. The results depend on the relative cost of monitoring by the peer vis-à-vis the lender. In the more typical case where the cost of peer monitoring is lower than the cost of lender monitoring, our results suggest that peer monitoring results in higher loan frequencies, higher monitoring and higher repayment rates compared to lender monitoring. In the absence of monitoring cost differences, performance is mostly similar across group and individual lending schemes, although loan frequencies and monitoring rates are sometimes modestly greater with group lending. Within group lending, although the dynamic incentives provided by sequential leading generate the greatest equilibrium surplus, simultaneous group leading provides equivalent empirical performance.Group Lending, Monitoring, Moral Hazard, Laboratory Experiment, Loans, Development

Magnetic properties of doped GdI2

Motivated by the recent experimental studies on layered ferromagnetic metallic system GdI2 and its doped variant GdI2Hx we develop a model to understand their ground state magnetic phase diagram. Based on first principle electronic structure calculations we write down a phenomenological model and solve it under certain approximations to obtain the ground state energy. In the process we work out the phase diagram of the correlated double exchange model on a triangular lattice for the specific band structure at hand.Comment: 13 pages, 5 figures, corrected typo

Velocity altiude range and path of an aircraft performing optimal turn: Complete analytical solution

Werner Grimm and Markus Hans established two kinds of optimal turn rate viz., accelerating control and decelerating control for an aircraft to obtain a specified heading and speed in a minimum time. Either of the two controls or both with transition of one control to the other are required to use for this purpose. Unlike in the previous papers in the present feature the velocity, range, altitude and interestingly  curvilinear path acquired by the aircraft in an arbitrary time in course of either optimal turning are determined in closed form. A change of the boundary condition to simplify the optimization technique is also suggested. Finally a few numerical examples are cited