  Designing efficient, metal free, and in-expensive catalyst for
electrochemical hydrogen evolution reaction (HER) is crucial for large scale
clean and green energy production. Recently synthesized 1D Biphenylene
nanoribbons (BPRs) display few exciting properties originating from the unique
co-existence of 4, 6 and 8 coordinated carbon rings. Here, we present a first
principles calculation of the electronic structure and electrocatalytic
activity of various sized N-BPRs (N indicates the width). The electrocatalytic
performance is evaluated based on several descriptors including electronic
property, carrier mobility, Gibbs free energy ($\Delta$G$_{HER}$), exchange
current density etc. The electronic properties are crucially sensitive to the
width (N) of BPRs transiting it from semiconducting to metallic nature at N=18.
The p$_z$ orbitals of C-atoms from the central tetragonal rings are mainly
responsible for the decrease in band gap with increasing width. The room
temperature electron mobility is found to be as high as $\sim6.3\times$10$^4$
cm$^2$V$^{-1}$s$^{-1}$, while hole mobility is relatively lower in magnitude.
Gibbs free energy also depends sensitively on the width of BPRs as evident from
the p-band center analysis. We propose 15-BPR as the most promising candidate
for electrocatalytic activity with extremely small overpotential
($\approx$0.005 V) and a high exchange current density, much better than the
state-of-the-art Pt(111). A close inspection of the elementary reactions of HER
(Volmer, Heyrovsky and Tafel) confirms Volmer-Tafel mechanism to be most
dominant on 15-BPR with Tafel as the rate-determining step with a barrier of
0.56 eV. The present study provides a deeper insight into the excellent HER
catalytic activity of a newly synthesized BPR which is inexpensive and is
expected to hasten experimental validation towards H$_2$ production.
