  Quantum spin Hall (QSH) insulators have attracted intensive experimental and
theoretical studies due to their beneficial applications in spintronic devices.
Density functional theory (DFT) meets challenges when describing the electronic
structure of QSH materials. Only the Heyd-Scuseria-Ernzerhof (HSE06) with
spin-orbit coupling (SOC) is effective in revealing the band opening in the
typical QSH 1T`-WTe2, but with increased computational demands. Here, using
DFT, Wannier function simulations, the screened hybrid HSE06 functional, and
first-principles-based many body perturbation theory GW, we investigate the
sensitive electronic structure in monolayer 1T`-WTe2, with advanced
meta-generalized gradient (meta-GGA) density functional approximations. The
success of the recent SCAN and r2SCAN meta-GGAs left their predecessor meta-GGA
made very simple (MVS) ignored by the scientific community. Largely unnoticed
were the increased band gaps of MVS compared to any semilocal approximation
including SCAN. We find that the non-empirical MVS approximation yields a
positive fundamental band gap, without any help from exact exchange, Hubbard U,
or SOC correction. We explain the success of the meta-GGA MVS for the band gap
in 1T`-WTe2 by presenting two working mechanisms in meta-GGA approximations.
Besides, we point out the difficulty of using G0W0 for 1T`-WTe2. Although the
single shot GW correction with an MVS reference yields a smaller band gap than
GW with PBE, the G0W0@MVS is still not suitable for simulating 1T`-WTe2, due to
its negative band gap. These DFT and beyond DFT results highlight the
importance of meta-GGAs and novel construction schemes with enhanced kinetic
energy density dependence. The MVS approximation re-appears as an appealing
alternative for accurately describing 1T`-WTe2, paving an efficient way for
exploring other two-dimensional QSH materials in high-throughput calculations.
