## 1 Introduction  
The potential of nanoparticle hyperthermia therapy to treat cancerous cells has been widely investigated in the last decade [1; 2; 3; 4; 5; 6]. The advantage of this approach is that particles can be conjugated to specific antibodies or targeting ligands which, in turn, penetrate leaky tumor blood vessels to selectively target cancerous cells [7; 8; 9]. Gold nanoparticles (GNPs) are good candidates for hyperthermia treatment because of their strong optical resonant absorption of near infrared (NIR) light in the so-called optical therapeutic window. When used in tandem, these two phenomena result in a relatively non-invasive method of selectively heating tumors while sparing healthy cells [10; 11; 12; 13]. While there are possible strategies for hyperthermia therapy without gold nanoparticles [14; 15], the design freedom afforded by bespoke particle morphology and the resultant control over optical makes GNPs worthy of further investigation and optimization for this application. As the human skin tissues only weakly absorb light with wavelengths between 700 nm to 900 nm, NIR light optically penetrates biological tissues and reaches GNPs injected inside superficial tumors [16; 17; 18]. As the peak of this resonance, absorption can be tuned depending on the size and shape of GNPs [19], different types of GNPs including nanospheres, nanoshells and nanorods have been explored [6; 10; 20; 21; 22; 23]. According to [PERSON], et al. [24], the calculated surface plasmonic resonance (SPR) absorption efficiency of gold nanorods was much higher than that of nanospheres and nanoshells. Additionally, the SPR of nanorods could be highly controllable by modifying their aspect ratio (AR defined as the ratio of the length to width of the rod, although high AR particles may be difficult to produce). [PERSON], et al. [25] explained that due to the complicated structure of nanoshells, manufacturing nanorods is easier than producing nanoshells. However, the effects of nanorod orientation and possible electromagnetic interaction between the closely spaced nanorods on the plasmonic absorption have not been quantitatively studied. [PERSON], et al. [26], [PERSON], et al. [27] and [PERSON], et al. [28] have shown that the volume fraction of the solution can result in preferred orientation or self-assemblies of gold nanorods (GNR) but the previous studies did not analyze the effect of aggregation on the plasmonic resonance of GNR solutions. [PERSON] and [PERSON] [29] found that the aggregation of gold nanorods caused a significant shift of the SPR wavelength of gold nanorod but this study did not present the effect of GNR aggregation on its absorption efficiency, the critical aspect of the hyperthermia. Most existing investigations [26; 27; 28] examined the extinction spectra of GNRs and GNR solutions in isolation, but few reported the actual heat generation capability of these solutions to estimate a real potential for their intended application [30; 31; 32; 33; 34]. To fill this knowledge gap, the current study presents the absorption efficiency spectra and the plasmonic absorption resonance of GNR aggregations along with the corresponding effect of these aggregations on heat generation in GNR solutions of various concentrations. Clustering alone can shift the wavelength of the SPR from 700 nm to 1000 nm [35]. Since the heating ability of GNRs depends on their optical properties [36], and particle aggregation changes these properties, the heat generation potential of GNRs solutions can be significantly impacted by aggregates and self-assemblies [37; 38]. Therefore, it is important to study both the optical properties of non-uniformly dispersed GNR solutions along with their resulting temperature increase. The present paper investigates this computationally and experimentally. The discrete dipole approximation (DDA) was used to calculate the optical properties of a single GNR and for GNR dimers with various gaps within the assemblies.