We introduce a computationally efficient method to calculate the quasiparticle band structure of general van der Waals (vdW) heterostructures. A layer-projected scissors (LAPS) operator, which depends on the one-body density matrix, is added to the density functional theory Hamiltonian. The LAPS operator corrects the band edges of the individual layers for self-energy effects (both intralayer and interlayer) and unphysical strain fields stemming from the use of model supercells. The LAPS operator is treated self-consistently whereby charge redistribution and interlayer hybridization occurring in response to the band energy corrections are properly accounted for. We present several examples illustrating both the qualitative and quantitative performance of the method, including ${\mathrm{MoS}}_2$ films with up to 20 layers, bilayer ${\mathrm{MoS}}_2$ in an electric field, lattice-matched ${\mathrm{MoS}}_2\text{/}{\mathrm{WS}}_2$ and ${\mathrm{MoSe}}_2\text{/}{\mathrm{WSe}}_2$ bilayers, and ${\mathrm{MoSe}}_2\text{/}{\mathrm{WS}}_2$ moiré structures. Our work opens the way for predictive modeling of electronic, optical, and topological properties of experimentally relevant vdW materials, including twisted homobilayers and incommensurate heterostructures.

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• Band gap
• 2-dimensional systems
• Band structure methods
• Density functional calculations
• Electronic structure
• GW method