## 2 Methodology
### Calculation of Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR) Properties  
Nuclear magnetic resonance (NMR) spectroscopy has been long investigated to provide the atomic-scale and element-specific detailed information about the structure, disorder and dynamics of materials [84]. In photosynthetic antenna complexes, solid-state NMR has significantly assisted in providing a mechanistic and electronic perspective of the pigment-protein and pigment-pigment interactions by resolving their atomic details [85]. Several structures of the photosynthetic membrane proteins have been resolved in the past decades using high resolution crystallography. However, in depth details of the structure-function interactions of photosynthetic membrane proteins still remain to be elucidated, which can be resolved using the solid-state NMR [85]. NMR spectra of quadrupolar nuclei are often challenging due to the associated anisotropic (or orientation-dependent) interactions, including chemical shift anisotropy and dipolar coupling. Notably, solid-state NMR spectroscopy of quadrupolar nuclei has been widely used in diverse problems related to chemistry, biology, geology, and materials science. Thus, it becomes extremely crucial to develop the methods for studying these nuclei to exploit their site-specific and atomic-scale structural information using NMR spectroscopy [84]. The NMR and NQR spectra for a BChl monomer taken from the FMO complex can be easily computed utilizing the computational approaches [86], whereby the chemical shifts that represent the change of resonance frequency of nucleus relative to a given standard are generally measured. This chemical shift of a nucleus that plays a vital role in the structural characterization of molecules is related to the shielding tensors as [86]:  
\[\delta=1\sigma_{iso}-\sigma, \tag{1}\]  
where \(\sigma\) is the shielding tensor which describes the magnetic polarizability of an atomic nucleus under study, 1 is the unit matrix and \(\sigma_{iso}\) is the isotropic value or trace of the shielding tensor of the standard reference used in the NMR experiments. Mathematically, the shielding tensor (also known as absolute chemical shift) is defined by the following relation [86]:  
\[\sigma_{\alpha\beta}=\left(\frac{\partial^{2}E}{\partial\mu_{a}\partial B_{ \beta}}\right), \tag{2}\]  
where \(\alpha,\beta=1\), 2, 3 are the tensor indices, \(E\) is the total electronic energy of the molecule, \(B\) is the external magnetic field and \(\mu\) is the magnetic moment of the nucleus of interest. In calculating the chemical shift, the difference between the measured shielding tensor and the shielding tensor of the reference system is obtained. The tetra methyl saline (TMS) has been taken as a reference system (see, e.g., [86]). Furthermore, the value of the isotropic shielding coefficient can be computed by averaging the three principal components of shielding tensor obtained from the shielding tensor matrix, i.e., \(\sigma_{iso}=\left(\sigma_{11}+\sigma_{22}+\sigma_{33}\right)/3\). Moreover, another quantity that describes the electronic structure properties of the system is known as the nuclear quadruple interaction. Calculations of the quadruple interaction properties such as the asymmetry parameter and quadruple frequency for the nuclei \({}^{14}N\) and \({}^{25}Mg\) available in each BChl of FMO complex can also be done.