In the search for obtaining electronic devices at ever smaller length scales, electronic components utilizing molecules as building blocks has become an topic of interest. In contrast to traditional macroscopic solid-state devices, molecules exhibit a plethora of fascinating and potentially useful phenomena in addition to the small-size advantage. In particular, an interesting feature is whether transport across a molecule can be initiated by absorption of light, so-called photoactivated transport. Theoretically, we can get information on how the distribution of electrons in molecules behave by finding an (approximate) solution, called the wave function, to the electronic Schrödinger equation for the molecule. Usually, we consider molecules or molecular systems with a fixed number of electrons, i.e., what we call electron conserving systems. The primary objective of this project is to develop a theoretical framework, using wave functions, to describe properties of molecules which are involved in electron transport. This requires going beyond standard electron conserving wave functions to consider wave functions where the number of electrons is not fixed. The developed theory will be able to also describe molecules which are photoexcited, i.e., which have absorbed energy in the form of light. The developments in the project will be aimed at applications to molecules involved in electron transport, and specfically how to use light to control such processes.
The overarching goal of the proposed project is establish a grand-canonical wave function based molecular electronic-structure theory for molecules with fluctuating number of electrons. Although the term grand-canonical is used, it is not considered in connection to equilibrium situations in statistical mechanics, but rather a formal device to achieve electron number fluctuations. The proposed grand-canonical framework will be achieved by exponential unitary transformations of a electron number conserving reference wave function. The parametrization allows for net flow of charge while still being unitary. The introduced parametrization through a unitary transformation preserves its analogy with standard electronic-structure methods of number conserving wave functions, and enables extension to the well-established framework of response theory. The approach proposed in the project will have significance for several areas of application, but in this three-year project I will focus on establishing the framework with applications to molecules involved in electron transport processes. A major theoretical challenge for transport across molecules is the comprehensive treatment of the interaction between the molecule and light. The description and prediction of photoinduced transport processes will enable a new playground for photoactivated control of transport properties through molecules. Hence, these processes serve as suitable and timely driving forces for the initial developments of the grand-canonical wave function proposed in this project.