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Ab initio electronic structure applications are among the most widely used in High-Performance Computing (HPC), and the eigenvalue problem is often their main computational bottleneck. This article presents our initial efforts in porting these codes to a RISC-V prototype platform leveraging a wide Vector Processing Unit (VPU). Our software tester is based on a mini-app extracted from the ELPA eigensolver library. The user-space Vehave and a RISC-V vector architecture implemented on an FPGA were tested. Metrics from both systems and different vectorisation strategies were extracted, ranging from the most simple and portable one (using autovectorisation and assisting this by fusing loops in the code) to the more complex one (using intrinsics). We observed a progressive reduction in the number of vectorial instructions, executed instructions and computing cycles with the different methodologies, which will lead to a substantial speed-up in the calculations. The obtained outcomes are crucial in advancing the porting of computational materials and molecular science codes to (post)-exascale architectures using RISC-V-based technologies fully developed within the EU. Our evaluation also provides valuable feedback for hardware designers, engineers and compiler developers, making this use case pivotal for co-design efforts., Competing Interests: No competing interests were disclosed., (Copyright: © 2024 Grima Torres R et al.)