SCAN0: Hybrid Meta-GGA in DFT

• SCAN0 is a parameter-free hybrid meta-GGA functional that incorporates 25% Hartree–Fock exchange with SCAN exchange–correlation, derived from the adiabatic connection formalism.
• It improves properties sensitive to nonlocal exchange, notably halving barrier height errors, while exhibiting limitations in atomization energies and strong static-correlation regimes.
• The functional provides a favorable cost–accuracy balance in both molecular energetics and solids, with applications extending from water simulations to high-pressure hydrogen studies.

SCAN0 is a nonempirical hybrid meta-generalized-gradient approximation (meta-GGA) exchange–correlation functional in Kohn–Sham density functional theory, introduced by incorporating the SCAN semilocal functional into the Perdew–Ernzerhof–Burke DFA0 hybrid construction. In the Hui–Chai formulation, SCAN0 is defined by a fixed Hartree–Fock exchange fraction of $a=1/4$, so that

$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$

It occupies the fourth rung of Jacob’s ladder, is free from any fitted parameters, and was designed to improve nonlocal-exchange-dominated properties and self-interaction behavior relative to the parent SCAN semilocal functional while retaining SCAN correlation (Hui et al., 2015).

1. Formal definition and theoretical construction

Hui and Chai write the SCAN0 exchange–correlation energy in the generalized hybrid form

$$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$

with $a=1/n=1/4=0.25$ (Hui et al., 2015). The same structure is also written in later implementations as

$$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$

with $c_x=0.25$ (Lee et al., 2022).

The rationale for $a=1/4$ is based on the adiabatic-connection formalism,

$$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$

together with the DFA0 interpolation model

$$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$

which yields, after integration,

$$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$

The integer $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$0 is taken to be $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$1 because “fourth-order Møller–Plesset perturbation theory (MP4) generally gives good molecular energies,” so the SCAN-based specialization gives the parameter-free SCAN0 hybrid (Hui et al., 2015).

Within a generalized Kohn–Sham description, SCAN0 combines a nonlocal Fock operator with semilocal SCAN exchange and correlation. Kanungo and coauthors write the corresponding hybrid XC operator schematically as

$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$2

with $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$3, emphasizing that comparison to exact multiplicative XC potentials requires inversion of the SCAN0 density to a local effective potential (Kanungo et al., 2021).

2. Benchmark performance in molecular energetics

The original assessment shows that SCAN0 improves some properties substantially relative to SCAN, but not uniformly across all benchmark classes (Hui et al., 2015). On standard molecular test sets, all errors are reported in kcal mol$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$4.

For atomization energies, SCAN0 degrades performance relative to SCAN: on G3/99 atomization energies the mean absolute error rises from $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$5 to $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$6, and on G2-1 ionization, electron-affinity, and proton-affinity subsets the SCAN0 MAEs are $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$7, $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$8, and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$9, compared with $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$0, $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$1, and $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$2 for SCAN (Hui et al., 2015). The paper attributes this deterioration in part to the fact that the semilocal SCAN correlation was tuned to work with SCAN exchange.

For barrier heights, SCAN0 is markedly better than SCAN. The MAE on NHTBH38/04 drops from $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$3 to $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$4, and on HTBH38/04 from $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$5 to $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$6 (Hui et al., 2015). The same study summarizes this as SCAN0 roughly halving the barrier-height MAEs of the parent SCAN functional.

For noncovalent interactions, SCAN0 is slightly worse than SCAN on the S22 and S66 sets, with MAEs increasing from $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$7 to $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$8 and from $$E_{xc}^{\rm SCAN0}=aE_x^{\rm HF}+(1-a)E_x^{\rm SCAN}+E_c^{\rm SCAN},$$9 to $a=1/n=1/4=0.25$0, respectively (Hui et al., 2015). The reported interpretation is that SCAN already captures medium-range dispersion fairly well, so adding a fixed fraction of exact exchange without a long-range dispersion correction does not improve these benchmarks.

Relative to PBE0, SCAN0 has comparable barrier-height performance but much better noncovalent-interaction errors. The reported barrier-height MAEs for SCAN0, $a=1/n=1/4=0.25$1, are comparable to PBE0’s $a=1/n=1/4=0.25$2, whereas SCAN0’s noncovalent MAEs of about $a=1/n=1/4=0.25$3 are much better than PBE0’s roughly $a=1/n=1/4=0.25$4 (Hui et al., 2015).

3. Self-interaction, density quality, and exact-potential analyses

A central motivation for SCAN0 is partial removal of self-interaction error through exact exchange. In the original molecular tests, SCAN0 reduces the spurious binding of He$a=1/n=1/4=0.25$5 and Ar$a=1/n=1/4=0.25$6 relative to SCAN, although it still shows a small derivative discontinuity (Hui et al., 2015). At the same time, SCAN0 fails badly at the dissociation limit of H$a=1/n=1/4=0.25$7, like other single-reference hybrids, showing that the MP4-based argument for $a=1/n=1/4=0.25$8 does not resolve strong static-correlation physics (Hui et al., 2015).

A distinct benchmark for density quality is given by the translationally invariant second cumulant matrix $a=1/n=1/4=0.25$9, whose eigenvalues are the squares of the spatial extents of the electron density along the principal axes. On the Var213 dataset of 213 independent $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$0 components for 100 small molecules, SCAN0 achieves $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$1 a.u., $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$2 a.u., $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$3 a.u., mean signed error $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$4 a.u., and maximum absolute deviation $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$5 a.u. (Hait et al., 2020). In the same benchmark, SCAN has RMSE $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$6 a.u. and B3LYP $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$7 a.u., so SCAN0 is identified there as the best hybrid for second cumulants, although double hybrids still perform better overall (Hait et al., 2020).

The paper on second cumulants also reports that SCAN0 reproduces $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$8 exactly for the H atom, has only about $$E_{xc}^{\rm SCAN0}=E_x^{\rm SCAN}+c_x(E_x^{\rm HF}-E_x^{\rm SCAN})+E_c^{\rm SCAN},$$9 a.u. error for Li and Be, and shows its worst error of about $c_x=0.25$0 a.u. in a spin-polarized halide such as PF. Spin-polarized alkali-metal dimers such as NaLi and Na$c_x=0.25$1 remain difficult, with SCAN0 errors of $c_x=0.25$2–$c_x=0.25$3 a.u. in $c_x=0.25$4 (Hait et al., 2020).

Inverse-DFT studies make a sharper distinction between density accuracy and potential accuracy. For six molecules, Kanungo, Zimmerman, and Gavini report that SCAN0 gives the best overall agreement with the exact XC potential among B3LYP, HSE06, SCAN0, M08-HX, SCAN, PBE, and PW92. The weighted potential and gradient errors $c_x=0.25$5 for SCAN0 are $c_x=0.25$6 for equilibrium H$c_x=0.25$7, $c_x=0.25$8 for compressed H$c_x=0.25$9, $a=1/4$0 for stretched H$a=1/4$1, $a=1/4$2 for LiH, $a=1/4$3 for H$a=1/4$4O, and $a=1/4$5 for ortho-benzyne (Kanungo et al., 2021). These data show both the advantage of SCAN0 relative to common alternatives and the persistence of significant XC-potential errors, especially in strongly correlated situations.

A related open-shell inversion study reports relative density errors of order $a=1/4$6–$a=1/4$7 and $a=1/4$8–$a=1/4$9 for SCAN0 across Li, C, N, O, CN, and CH$$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$0, but potential errors remain substantially larger, with majority-spin $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$1 between $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$2 and $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$3 and $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$4 between $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$5 and $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$6 (Kanungo et al., 2023). That study further states that SCAN0 reproduces intershell structure for all atoms and for both C/N sites in CN, has the correct $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$7 long-range decay, and achieves the lowest potential errors among the five tested functionals B3LYP, SCAN0, SCAN, PBE, and PW92 (Kanungo et al., 2023).

4. Performance in solids and extreme-pressure hydrogen

In a benchmark of band gaps for 25 simple solids near the basis-set limit, SCAN0 is one of the top-performing global hybrids. Using the occ-RI-K algorithm within the Gaussian-planewave density-fitting framework, SCAN0 yields an RMSD of $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$8 eV and a mean signed deviation of $$E_{xc}[\rho]=\int_0^1 E_{xc,\alpha}[\rho]\,d\alpha,$$9 eV, tying PBE0 and revPBE0 at $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$0 eV and outperforming B3LYP at $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$1 eV and B97-3 at $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$2 eV (Lee et al., 2022). The same study reports maximum positive and negative errors of $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$3 eV for BAs and $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$4 eV for LiF, respectively, and identifies the fixed 25% exact-exchange fraction as a near-optimal balance for small- and medium-gap solids (Lee et al., 2022).

The implementation details in that work are specific: exact exchange is evaluated through occ-RI-K, the GPW fitting uses $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$5 eV, GTH-PBE norm-conserving pseudopotentials and the uncontracted def2-QZVP-GTH basis are employed, Brillouin-zone integration uses a $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$6 Monkhorst–Pack mesh, and a Madelung constant correction is applied for the Coulomb singularity in exact exchange (Lee et al., 2022). These details matter because the authors attribute residual basis-set incompleteness errors of about $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$7 eV and finite-size or $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$8-mesh residuals below $$E_{xc,\alpha}^{\rm DFA0} =E_{xc,\alpha}^{\rm DFA} +\bigl(E_x^{\rm HF}-E_x^{\rm DFA}\bigr)(1-\alpha)^{n-1},$$9 eV to the computational setup rather than to the functional itself (Lee et al., 2022).

A different solid-state application concerns high-pressure hydrogen between 400 and 700 GPa. In that study, SCAN0 is used as a nonempirical meta-GGA hybrid with

$$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$0

and is evaluated as single points on RSCAN geometries in VASP 6.4.2 (Racioppi et al., 2 Oct 2025). The reported molecular-to-atomic transition pressures are about $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$1 GPa for PBE, about $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$2 GPa for RSCAN, and about $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$3 GPa for SCAN0 by extrapolation (Racioppi et al., 2 Oct 2025).

More specifically, the SCAN0 sequence reported for hydrogen is: C2/c lowest at $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$4 GPa with band gap $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$5 eV; C2/c $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$6 Cmca-12 near $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$7 GPa; Cmca-12 $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$8 Cmca-4 near $$E_{xc}^{\rm DFA0} =\frac{1}{n}E_x^{\rm HF}+\Bigl(1-\frac{1}{n}\Bigr)E_x^{\rm DFA}+E_c^{\rm DFA}.$$9 GPa; and a molecular $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$00 atomic transition only at extrapolated pressures $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$01 GPa (Racioppi et al., 2 Oct 2025). The same work concludes that PBE artificially weakens intramolecular H–H bonds and enhances intermolecular interactions through charge delocalization, whereas meta-GGA descriptions preserve a more localized molecular character (Racioppi et al., 2 Oct 2025). For phonons, only PBE and RSCAN are directly computed; the paper states that SCAN0, being even “stiffer” than RSCAN around equilibrium, is expected to yield similarly stable phonons (Racioppi et al., 2 Oct 2025).

5. Water studies and nomenclature variation

The label “SCAN0” is not used uniformly across the provided literature. In the Hui–Chai formulation and in the solid-state studies above, SCAN0 contains $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$02 exact exchange (Hui et al., 2015, Lee et al., 2022, Racioppi et al., 2 Oct 2025). By contrast, the water studies by Zhang and collaborators define a functional they call SCAN0 as

$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$03

with $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$04 (Zhang et al., 2021). This indicates a nomenclature inconsistency rather than a single universally standardized parameterization.

In large-scale simulations of liquid water, the 10% exact-exchange SCAN0 of Zhang et al. is combined with DeePMD-kit and Deep Wannier models. The final neural-network potential is trained on $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$05 SCAN0-DFT snapshots, and production simulations are carried out for $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$06 H$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$07O molecules in both classical DPMD and quantum PI-DPMD (Zhang et al., 2021). Relative to SCAN, that work reports a softer hydrogen-bond network and improved agreement with experiment for many structural, dynamical, dielectric, and electronic observables. Examples include density changes from $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$08 g cm$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$09 with SCAN to $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$10 g cm$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$11 in classical SCAN0 DPMD and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$12 g cm$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$13 in quantum SCAN0 PI-DPMD, versus $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$14 experimentally, and dielectric constants of $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$15 classically and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$16 quantum-mechanically versus $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$17 experimentally (Zhang et al., 2021).

The same liquid-water study reports weaker hydrogen bonding under exact exchange, with the average number of H-bonds per molecule decreasing from $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$18 in SCAN to $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$19 in SCAN0 and to $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$20 after including nuclear quantum effects. It also gives diffusion coefficients of $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$21 Å$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$22/ps for D$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$23O and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$24 Å$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$25/ps for H$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$26O under SCAN0, compared with experimental values of $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$27 and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$28, and rotational correlation times of $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$29 ps for D$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$30O and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$31 ps for H$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$32O, with SCAN reported at $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$33 ps (Zhang et al., 2021).

Later melting studies, again using a 10% exact-exchange functional labeled SCAN0 and Deep Potential models, emphasize remaining deficiencies. One assessment reports for SCAN0: classical melting temperature $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$34 K, quantum melting temperature $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$35 K, nuclear-quantum shift $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$36 K, coexistence densities $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$37 g cm$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$38 and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$39 g cm$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$40, density discontinuity $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$41 g cm$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$42, and temperature of maximum density $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$43 K (Li et al., 30 Dec 2025). A related account adds a D$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$44O melting point of $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$45 K and an isotope shift of about $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$46 K, while stressing that all DFT-based models, including SCAN0, predict a spurious stabilization of ice by nuclear quantum effects and overestimate hydrogen-bond strength (Li et al., 30 Dec 2025). Thus, within the water literature, the exact-exchange admixture softens liquid structure relative to SCAN, yet the underlying functional still produces elevated melting temperatures and an excessive separation between the density maximum and melting point (Li et al., 30 Dec 2025, Li et al., 30 Dec 2025).

6. Relation to SCAN-based double hybrids, strengths, and limitations

SCAN0 is one member of a broader SCAN-based hierarchy that also includes SCAN0-DH, SCAN-QIDH, and SCAN0-2. These double-hybrid functionals are constructed by inserting SCAN into existing hybrid and double-hybrid models and are likewise free from fitted parameters (Hui et al., 2015). In direct comparisons, all three double hybrids outperform SCAN0 for noncovalent interactions and self-interaction tests, with SCAN0-2 including about $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$47 Hartree–Fock exchange and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$48 second-order Møller–Plesset correlation and achieving about $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$49 kcal mol$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$50 on S22 and $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$51 kcal mol$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$52 on S66, together with near-CCSD(T) quality for He$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$53 and Ar$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$54 (Hui et al., 2015).

The principal strengths of SCAN0, as stated in the original work, are its nonempirical character, the adiabatic-connection derivation of the mixing fraction, improved exchange relative to SCAN, better barrier heights, improved treatment of self-interaction, and a computational profile comparable to other widely used fourth-rung hybrids such as PBE0 (Hui et al., 2015). The second-cumulant benchmark adds that SCAN0 reduces the positive bias of SCAN to essentially zero and offers a favorable cost–accuracy balance for routine geometry- and density-sensitive applications (Hait et al., 2020).

Its limitations are equally explicit. Correlation remains purely semilocal, so there is no long-range dispersion correction and van der Waals interactions are underbound at large distances (Hui et al., 2015). Atomization energies worsen relative to SCAN, static correlation remains problematic, and H$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$55 dissociation exhibits catastrophic breakdown in the dissociation limit (Hui et al., 2015). Exact-potential studies further show that even when density errors are only of order $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$56–$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$57, the model XC-potential errors remain of order $$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$58–$$E_{xc}^{\rm SCAN0}=\frac{1}{4}E_x^{\rm HF}+\frac{3}{4}E_x^{\rm SCAN}+E_c^{\rm SCAN}.$$59 (Kanungo et al., 2021, Kanungo et al., 2023). In that sense, SCAN0 is best understood not as a universal remedy, but as a rigorously derived, parameter-free hybrid that materially improves several exchange-sensitive observables while preserving the characteristic limitations of semilocal-correlation hybrids (Hui et al., 2015).