"The project will develop new methods for calculating nonlinear spectroscopic properties, both in the electronic as well as in the vibrational domain. The methods will be used to study molecular interactions at interfaces, allowing for a direct comparison of experimental observations with theoretical calculations. In order to explore different ways of modeling surface and interface interactions, we will develop three different ab initio methods for calculating these nonlinear molecular properties: 1) Multiscale methods, in which the interface region is partitioned into three different layers. The part involving interface-absorbed molecules will be described by quantum-chemical methods, the closest surrounding part of the system where specific interactions are important will be described by classical, polarizable force fields, and the long-range electrostatic interactions will be described by a polarizable continuum. 2) Periodic-boundary conditions: We will extend a response theory framework recently developed in our group to describe periodic systems using Gaussian basis sets. This will be achieved by deriving the necessary formulas, and interface our response framework to existing periodic-boundary codes. 3) Time-domain methods: Starting from the equation of motion for the reduced single-electron density matrix, we will propagate the electron density and the classical nuclei in time in order to model time-resolved vibrational spectroscopies.The novelty of the project is in its focus on nonlinear molecular properties, both electronic and vibrational, and the development of computational models for surfaces and interfaces that may help rationalize experimental observations of interface phenomena and molecular adsorption at interfaces. In the application of the methods developed, particular attention will be given to nonlinear electronic and vibrational spectroscopies that selectively probe surfaces and interfaces in a non-invasive manner, such as SFG."