## 1 Introduction  
Molecular physics applications in ultrafast science are rapidly developing in multiple areas of spectroscopy and X-ray diffraction. Here, we consider the application of ultrafast techniques to single crystal studies, with the aim to interpret and exploit the structural sensitivity of the information obtained from photoinduced dynamics. Practical approaches for quantitative analysis of ultrafast processes in crystals combine the areas of crystal optics, X-ray crystallography, and non-linear optical excitation theory. The basis for this approach is formed by the electric field decomposition in the presence of birefringence, and the resulting linear combination of the separate field-dipole interactions for the orthogonal modes that solve Maxwell's equations in anisotropic media. In the area of ultrafast spectroscopy, two-dimensional electronic spectroscopy (2 DES) is a powerful technique that provides ultrafast dynamics information [1, 2]. The methodology, analysis, and theory of 2 DES [3] is highly advanced and has shown many fascinating examples and results for complex materials, including photosynthesis [4, 5], solid state physics, and solar cell science [6]. Two-dimensional electronic spectroscopy measurements intrinsically have ultrafast time resolution and can be applied to a multitude of molecular processes for isolated pigments, as well as structures and aggregates with weak or strong coupling. There are very similar considerations for two-dimensional infrared spectroscopy of oriented single crystals and other four-wave mixing techniques such as time-domain impulsive Raman spectroscopy. There are many different types of ultrafast and non-linear spectroscopy experiments. Experimentally, ultrafast spectroscopy typically uses femtosecond optical pulses that are resonant with electronic and/or vibrational transitions and create and interrogate coherences and populations in molecular systems. Recently, the theoretical framework was shown for two-dimensional spectroscopy measurements of oriented single crystals [7]. This is a unique application, where the non-linear spectroscopy measurement is sensitive to explicit molecular structure, crystal symmetry, crystal orientation, and polarisation of the incident field. The third-order response of molecular crystals is generally different from that of isotropic solutions. Depending on the crystal symmetry, the interesting case arises where selected Feynman pathways that contribute to the overall third-order response become symmetry-disallowed, whereas the allowed pathways are weighted via the symmetry progressions of the four-point correlation functions for each individual coherence. An analytical calculation of the resulting four-point correlation functions was shown, from the initial result of using crystal classes or reduced point-group symmetries, to include all point-group symmetries following definition of additional zero-valued tensor elements [7]. The method therefore adheres to Neumann's Principle, which states that the symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal [8]. The theory was shown and demonstrated for selected polarisation conditions that correspond to the principal directions of refractive indices. Here, we provide a set of tools to model the electric field decomposition and associated dipole projections in a more generalised approach to extend such measurements to include all crystal orientations and polarisation directions, excluding the isotropic directions of the optic axes. We emphasise that serial femtosecond crystallography (SFX), which is an emerging technique at X-ray free-electron laser facilities (XFELs) [9; 10; 11], could benefit from the consideration of this orientation-sensitive information that arises from crystal photoexcitation. Using pump-probe techniques, femtosecond time resolution has been achieved for X-ray crystallography of macromolecules.