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The splitting of quasi-Fermi levels (QFLs) represents a key concept utilizedto describe finite-bias operations of semiconductor devices, but itsatomic-scale characterization remains a significant challenge. Herein, thenon-equilibrium QFL or electrochemical potential profiles withinsingle-molecule junctions obtained from the newly developed first-principlesmulti-space constrained-search density functional formalism are presented.Benchmarking the standard non-equilibrium Green's function calculation results,it is first established that algorithmically the notion of separateelectrode-originated nonlocal QFLs should be maintained within the channelregion during self-consistent finite-bias electronic structure calculations.For the insulating hexandithiolate junction, the QFL profiles exhibitdiscontinuities at the left and right electrode interfaces and across themolecule the accompanying electrostatic potential drops linearly and Landauerresidual-resistivity dipoles are uniformly distributed. For the conductinghexatrienedithiolate junction, on the other hand, the electrode QFLs penetrateinto the channel region and produce split QFLs. With the highest occupiedmolecular orbital entering the bias window and becoming a good transportchannel, the split QFLs are also accompanied by the nonlinear electrostaticpotential drop and asymmetric Landauer residua-resistivity dipole formation.Our findings underscore the importance of the first-principles extraction ofQFLs in nanoscale junctions and point to a new direction for the computationaldesign of next-generation electronic, optoelectronic, and electrochemicaldevices.

Quasi-Fermi level splitting in nanoscale junctions from $\textit{ab initio}$