Bridging Quantum Capacitance and Experimental Electrochemical Performance in 2D Materials for Supercapacitors: From Density of States to Device-Level Interpretation

Abstract

Two-dimensional (2D) materials, particularly MXenes and transition metal dichalcogenides (TMDs), have attracted intense interest as supercapacitor electrodes due to their high surface area and tunable electronic structure. However, large discrepancies persist between the quantum capacitance values predicted by density functional theory (DFT) calculations and experimentally measured gravimetric capacitances. In this review, we critically analyze DFT methodologies, surface models, normalization strategies, and electrochemical characterization protocols, and compile an extensive dataset of reported MXene and TMD systems to quantify the degree of experimental–theoretical agreement. We show that MXenes typically achieve less than 20% of their predicted capacitance because of restacking, surface terminations, and limited ion accessibility, whereas TMDs exhibit substantially better correspondence, often approaching or exceeding 70% of theoretical values. These results indicate that the theoretical capacitance predicted by DFT is primarily determined by the electronic structure of the material, which defines the upper limit of charge storage, whereas the experimentally achieved capacitance is largely controlled by morphological factors, surface chemistry, and electrode architecture that limit ion accessibility.

1. Introduction

The rapid advancement of energy storage technologies is crucial for meeting the growing global demand for efficient, reliable, and sustainable power systems [1,2,3]. Among these technologies, supercapacitors have attracted considerable interest owing to their high-power density, fast charge–discharge capability, and long cycling stability [4,5]. Supercapacitors store energy predominantly through interfacial charge accumulation at the electrode–electrolyte interface, which makes their performance conditioned on the electronic structure and surface properties of the electrode materials [6,7].

In this context, the emergence of two-dimensional (2D) materials has opened new opportunities for electrode design, as their nearly atomic thickness, tunable electronic structure, and large theoretical surface area promises enhanced charge storage mechanisms beyond conventional carbon-based materials [8,9]. In low-dimensional systems like the 2D materials, total capacitance is not solely governed by electrical double-layer capacitance (EDLC) but is fundamentally limited by quantum capacitance (C_q), which originates from the finite electronic density of states (DOS) at the Fermi level [10]. This effect becomes particularly significant in 2D materials, including MXenes and transition metal dichalcogenides (TMDs), where electronic confinement and surface chemistry strongly influence charge accumulation [11,12,13]

Despite the growing number of theoretical studies (Density Functional Theory, DFT) reporting large C_q values for these materials, substantial discrepancies persist when compared with experimentally measured capacitances under realistic electrochemical conditions [14,15]. Frequently, this disconnect arises because experimental performance is typically reported in gravimetric terms dependent on microstructure and pore accessibility, whereas theoretical calculations yield intrinsic areal limits based on idealized surfaces, making direct comparison difficult without rigorous normalization protocols [16,17,18,19].

To address this challenge, this review aims to critically bridge the gap between theoretical predictions of C_q and experimental electrochemical data in 2D electrode materials for supercapacitor applications [20]. By systematically analyzing reported DFT methodologies, surface models, and normalization strategies alongside experimental characterization techniques and accessible surface area estimations, we identify the key factors responsible for the observed deviations [21]. Furthermore, this work provides a unified framework for the interpretation of C_q data and proposes practical guidelines to achieve meaningful correlations between computational and experimental results, thereby supporting the rational design of next-generation high-performance supercapacitor electrodes.

2. Theory and Charge Storage Mechanisms

Electrochemical energy storage in supercapacitors is governed by interfacial and bulk processes that enable rapid charge accumulation and release. Unlike batteries, where energy storage relies on diffusion-limited faradaic reactions in the bulk of electrode materials, supercapacitors operate through surface-controlled mechanisms, facilitating high power density and extended cycle life [22,23,24]. Two-dimensional (2D) materials, such as MXenes and TMDs, offer unique physicochemical features, including large specific surface area, tunable electronic structure, and short ion diffusion pathways [25].

2.1. Total Capacitance in Supercapacitor Electrodes

As the electrode accumulates charge, the position of the Fermi level shifts because the number of available electronic states near it is limited. This behavior introduces an additional capacitive response associated with the electronic structure of the electrode material itself. As a result, the capacitance measured experimentally does not originate exclusively from the electrical double layer at the interface, but rather from the combined contribution of the interfacial double-layer capacitance and this intrinsic electronic capacitance of the electrode [26].

In this framework, the electrode–electrolyte interface is represented as a series combination of capacitive elements, reflecting electrochemical and electronic contributions. The experimentally measured capacitance (C_tot) is expressed as:

$${\displaystyle \frac{1}{C_{tot}}}={\displaystyle \frac{1}{C_{el}}}+{\displaystyle \frac{1}{C_{sc}}}$$

(1)

where C_el represents the electrolyte-side capacitance and C_sc denotes the space-charge capacitance within the electrode. The electrolyte capacitance can be further decomposed into the Helmholtz capacitance (C_H) and the diffuse layer capacitance (C_diff):

$${\displaystyle \frac{1}{C_{el}}}={\displaystyle \frac{1}{C_H}}+{\displaystyle \frac{1}{C_{diff}}}$$

(2)

In concentrated electrolytes, C_diff >> C_H; therefore, the diffuse-layer contribution can be neglected, and C_el ≈ C_H. This model accurately describes the capacitance behavior of semiconductor electrodes up to the accumulation regime, where the space-charge capacitance C_sc becomes comparable to or exceeds the C_H.

In this approach, C_sc is derived assuming that the countercharge compensating for the space charge is localized at the solid surface (x = 0), as shown in Figure 1. The evaluation of C_sc requires solving Poisson’s equation under the appropriate boundary conditions.

$${\displaystyle \frac{d^2\phi }{d{x}^2}}={\displaystyle \frac{1}{ϵ{ϵ}_0}}\rho (x)$$

(3)

with $\phi =0$ and $d\phi /dx=0$ for $x \to \infty$.

The electrostatic potential at surface is given by

$${\phi }_s \mathrm{at} x=0$$

The charge density ρ(x) is controlled by the local potential $\mathrm{\phi }$(x) and we obtain therefore from the identity.

$${\displaystyle \frac{d}{d\phi }}{\left({\displaystyle \frac{d\phi }{dx}}\right)}^2=2{\displaystyle \frac{d^2\phi }{d{x}^2}}=-{\displaystyle \frac{2}{ϵ{ϵ}_0}}\rho \left(\phi \right)$$

(4)

Integrating the Poisson equation, the space charge is defined by according to Gerischer [26]:

$$C_{sc}=\left|{\displaystyle \frac{d{q}_{sc}}{d{\phi }_s}}\right|={\left(2ϵ{ϵ}_0\right)}^{{\displaystyle \frac{1}{2}}}\left|{\displaystyle \frac{d}{d{\phi }_s}}{\left({\int }_{ 0}^{{\phi }_s}\rho \left(\phi \right)d\phi \right)}^{{\displaystyle \frac{1}{2}}}\right|$$

(5)

where C_sc is finally

$$C_{sc}={\displaystyle \frac{2ϵ{ϵ}_0}{2}}{\displaystyle \frac{{\rho }^2\left({\phi }_s\right)}{\left|{\int }_{ 0}^{{\phi }_s}\rho \left(\phi \right)d\phi \right|}}$$

(6)

If the charge density is known as a function of the local potential, the space charge capacity can be calculated.

Gerischer demonstrated that for materials with a low DOS at the Fermi level the applied potential is partially dropped inside the solid, leading to the formation of a space-charge region analogous to that found in semiconductor/electrolyte interfaces. The associated space-charge capacitance is determined by the DOS near the Fermi level and can be directly related to the ability of the electrode to supply or accommodate electronic charge [26].

For a constant DOS N₀ near the Fermi level, the space-charge capacitance is given by:

$$C_{sc}={\left(ϵ{ϵ}_0{e}^2{N}_0\right)}^{{\displaystyle \frac{1}{2}}}$$

(7)

This expression highlights that the capacitance is not governed by classical screening lengths, but rather by quantum-mechanical limitations in the availability of electronic states. In the context of 2D materials, this space-charge capacitance corresponds directly to the quantum capacitance (C_q), which reflects the electronic DOS at the Fermi level:

$$C_q=e^{2}D\left(E_F\right)$$

(8)

Thus, the total capacitance of low-dimensional supercapacitor electrodes must be treated as:

$${\displaystyle \frac{1}{C_{tot}}}={\displaystyle \frac{1}{C_{EDLC}+C_{pseudo}}}+{\displaystyle \frac{1}{C_q}}$$

(9)

2.2. Electric Double-Layer Capacitance and Pseudocapacitance

The total capacitance of a supercapacitor electrode generally arises from two primary contributions: EDLC and pseudocapacitance. EDLC originates from the electrostatic accumulation of ions at the electrode–electrolyte interface through non-faradaic processes, characterized by the absence of charge transfer across the interface. This mechanism is highly reversible and depends intrinsically on the accessible specific surface area (SSA), pore geometry, and the physicochemical properties of the electrolyte [27].

In contrast, pseudocapacitance involves rapid and reversible faradaic reactions occurring at or near the electrode surface. These processes encompass surface redox reactions, electrosorption with partial charge transfer, and intercalation pseudocapacitance (shallow intercalation phenomena). Notably, pseudocapacitive behavior retains the high kinetic advantages of capacitive storage while yielding significantly higher energy densities than pure EDLC-based systems [28].

MXenes and TMDs frequently exhibit a synergistic combination of EDLC and pseudocapacitive contributions. Their atomically thin architectures and high density of chemically active sites promote rapid ion–electron coupling, enabling efficient charge storage even under high-rate operating conditions (high scan rates) [29].

2.3. Charge Storage Mechanisms in MXenes and Transition Metal Dichalcogenides

MXenes (M_n+1X_nT_x) are two-dimensional transition metal carbides and nitrides that exhibit predominantly capacitor-like charge-storage behavior arising from a combination of electrical double-layer capacitance (EDLC), surface redox pseudocapacitance, and rapid intercalation pseudocapacitance within their interlayer structures [30]. The relative contribution of these mechanisms is governed by electrolyte chemistry, ion solvation state, interlayer spacing, and surface terminations [31].

In aqueous electrolytes, charge storage is mainly controlled by surface ion adsorption and fast redox reactions at metal sites and oxygen-containing terminations (–O, –OH), with proton-driven pseudocapacitance dominating in acidic media [32,33]. In non-aqueous and highly concentrated electrolytes, partial or complete cation desolvation enables fast intercalation pseudocapacitance with minimal lattice distortion, allowing high charge-storage rates without diffusion-limited behavior. The exceptional electronic conductivity of MXenes (up to ~15,000 S cm⁻¹), tunable interlayer spacing, and proton transport pathways mediated by confined water collectively support high volumetric capacitance, low resistive losses, and excellent cycling stability. Control of surface terminations and suppression of nanosheet restacking remain critical to maximizing ion accessibility and optimizing the balance between EDLC and pseudocapacitive contributions [31,34,35].

Transition metal dichalcogenides (TMDs) exhibit a more diverse charge-storage behavior, combining EDLC, surface redox pseudocapacitance, and, in some systems, shallow intercalation pseudocapacitance within van der Waals gaps. Their electrochemical response is highly sensitive to crystalline phase (e.g., metallic 1T versus semiconducting 2H), defect density, and operating potential window. While EDLC contributes to rapid charge accumulation at basal planes and edges, pseudocapacitive surface reactions at defects and catalytically active sites often dominate the total stored charge. Phase engineering toward more conductive polymorphs significantly enhances both electronic transport and active-site density [36,37,38,39].

In layered compounds such as TiS₂, reversible ion intercalation can proceed with capacitor-like kinetics and limited structural distortion, in contrast to deep conversion reactions that occur at low potentials and lead to diffusion-controlled behavior, structural degradation, and poor cycling stability [40,41]. Consequently, optimization strategies for TMD electrodes focus on promoting surface redox activity and shallow intercalation while suppressing bulk conversion processes through defect engineering, morphology control, and integration with conductive matrices.

Overall, both MXenes and TMDs store charge through an interplay of EDLC, surface redox pseudocapacitance, and shallow intercalation mechanisms, with the dominant contribution determined by electronic structure, surface chemistry, and electrolyte conditions. MXenes are typically characterized by highly conductive, surface-controlled pseudocapacitive kinetics, whereas TMDs display a stronger dependence on phase and defect chemistry, which can shift their behavior between capacitive and diffusion-limited regimes. These mechanistic differences motivate the quantitative comparison between experimentally measured and theoretically predicted capacitance trends addressed in the following sections.

2.4. Quantum Capacitance and Electronic Structure Effects

At the nanoscale, particularly for low-dimensional materials, the total capacitance is not solely determined by electrochemical double-layer effects but also by the electronic density of states (DOS) at the Fermi level. This contribution, known as quantum capacitance, becomes significant when the DOS is comparable to or lower than the electrochemical capacitance [10,25,42].

MXenes generally exhibit high quantum capacitance due to their metallic nature and high DOS near the Fermi level, which facilitates efficient charge accommodation. In contrast, semiconducting TMDs may suffer from limited quantum capacitance unless their electronic structure is modified through phase transitions, doping, or hybridization [43,44].

The interplay between quantum capacitance and electrochemical processes is particularly relevant in ultrathin electrodes and solid-state devices, where electronic limitations can dominate overall performance. Understanding and engineering the electronic structure of MXenes and TMDs is therefore crucial for maximizing their charge storage capabilities.

3. Experimental and Theoretical Capacitance Trends in MXenes and TMDs

A diverse array of low-dimensional materials has demonstrated high capacitance, emerging as promising candidates for supercapacitor applications. Among these, MXenes and TMDs have garnered particular attention due to their layered architectures and highly tunable electronic properties. Within both material families, electrochemical performance can be modulated through compositional design, surface functionalization, phase control, and hybridization strategies, resulting in a broad distribution of reported capacitance values.

3.1. MXenes

Experimental investigations of MXene-based electrodes reveal a pronounced dispersion in gravimetric capacitance values, highlighting the critical role played by chemical composition, surface terminations, and hybrid architectures. The following sections analyze the performance based on the primary transition metal. The dataset for these materials is presented in

Table 1. Experimental values for MXenes found in the literature.

Material	Capacitance	SSA	Ref.
	(F g−1)	(m2 g−1)
Cr2C	1456	ND	[45]
Cr2C	91	ND	[46]
Mo2C	276	ND	[47]
Mo2C	1250	ND	[48]
Mo2C	76.44	ND	[49]
Mo2C	1718	ND	[49]
Mo2C	110	ND	[50]
Mo2N	1272.45	ND	[51]
Mo2N	968.74	ND	[51]
Mo2N	687.35	ND	[51]
Mo2N	449.32	ND	[51]
Mo2N	210.6	ND	[52]
Mo2N	158	ND	[53]
Mo2N	203	ND	[53]
Mo2N	171	ND	[53]
MoN/Mo2N	306.7	ND	[54]
Ni-Mo-N/SSM	1020	ND	[55]
MoS2-Mo2N	252.09	ND	[56]
Nb2C	547	ND	[57]
Nb2C	330	ND	[58]
Nb2C/Ti3C2	584	ND	[58]
Nb2C-Pcarbons	465.5	1452.1	[59]
Nb2CT	200	10	[60]
Nb2CT	400	30	[60]
Co-Nb2C	1061	ND	[57]
N-Ti3C2	176	3	[61]
Ti2C	382	ND	[62]
Ti2N/Ti3C2Tx	250.3	ND	[63]
Ti3C2	328	7	[64]
Ti3C2	558.9	47.86	[65]
Ti3C2	357.85	ND	[66]
Ti3C2@Ni3S4	980	21.4	[64]
Ti3C2-PPy	474	ND	[58]
Ti3C2Tx	120	248.76	[67]
Ti3C2Tx	300	ND	[68]
Ti3C2Tx	287.9	ND	[69]
Ti3C2Tx	542	9.887–13.245	[70]
Ti3C2Tx	400.7	33.06	[71]
TiN/Ni	90.18	ND	[72]
V2C	181.1	ND	[73]
V2C	248	ND	[74]
V2C	223.5	ND	[75]
V2C	196.5	ND	[76]
V2C	164	ND	[77]

^ND = not determined.

and

Table 2. Theoretical values for MXenes found in the literature.

Material	Quantum Capacitance	Capacitance	Band Gap	SSA	Ref.	Material	Quantum Capacitance	Capacitance	Band Gap	SSA	Ref.
	(μF cm−2)	(F g−1)	(eV)	(m2 g−1)			(μF cm−2)	(F g−1)	(eV)	(m2 g−1)
Cr2C(OH)2	1134.7	7261.9	0	640	[78]	Sc2COS	341.2	0.0	1.48	ND	[79]
Cr2CF2	1443.4	9237.4	1.25	640	[80]	Ag-Sc2CO2	949.2	0.0	0.144	ND	[81]
Cr2CF2	4516.7	28,906.9	1.25	640	[82]	Au-Sc2CO2	1086.5	0.0	0.042	ND	[81]
Hf2C	549.0	2854.8	0	520	[83]	Cu-Sc2CO2	1523.9	0.0	0.589	ND	[81]
Hf2C(OH)2	825.1	4290.6	0	520	[78]	Pd-Sc2CO2	758.5	0.0	0.93	ND	[81]
Hf2CF2	610.9	3176.7	0	520	[82]	Pt-Sc2CO2	828.2	0.0	1.07	ND	[81]
LiXTi1-XN	772.4	0.0	0	ND	[84]	Rh-Sc2CO2	1025.3	0.0	1.71	ND	[81]
Mn2C(OH)2	602.9	0.0	0	ND	[78]	Ta2C(OH)2	715.9	0.0	0	ND	[78]
Mo2C	3244.0	17,841.9	0	550	[85]	Ta2CF2	753.2	0.0	0	ND	[82]
Mo2C(OH)2	1927.5	10,601.0	0.45	550	[78]	Ti2C	246.2	1652.0	half-metal	671	[86]
Mo2CF2	980.5	5392.9	0.27	550	[80]	Ti2C(OH)2	577.9	3877.8	0.3	671	[78]
Mo2CF2	1414.6	7780.3	0.27	550	[82]	Ti2CF2	909.1	6100.1	0	671	[82]
Mo2N	746.7	0.0	0		[87]	Ti3C2	753.7	7386.1	0	980	[88]
Nb2C	1828.4	10,604.7	0	580	[89]	Ti3C2Tx	264.4	2591.2	0	980	[90]
Nb2C	324.1	1879.8	0	580	[10]	Ti3C2Tx	398.8	3908.1	0	980	[90]
Nb2C(OH)2	2061.7	11,958.0	0	580	[78]	Ti3C2Tx	97.5	955.5	0	980	[91]
Nb2CF2	361.2	2094.7	0	580	[80]	V2C	1540.0	9548.1	0.32	620	[78]
Nb2CF2	753.5	4370.3	0	580	[82]	V2C	3010.5	18,665.2	0.32	620	[78]
Nb2N	324.1	0.0	0	ND	[86]	V2C	1041.3	6456.1	0.32	620	[78]
Nb2N	1196.3	0.0	0	ND	[92]	V2C	3465.5	21,486.2	0.32	620	[85]
Nb4N3	174.9	0.0	0	ND	[92]	V2CF2	1517.6	9408.9	0	620	[80]
Sc2C(OH)2	36.0	252.3	0.41	700	[78]	V2CF2	868.1	5382.2	0	620	[82]
Sc2CF2	655.0	4585.0	0.96	700	[93]	W2CF2	1752.7	0.0	0	ND	[82]
Sc2CF2	880.9	6166.3	0.96	700	[82]	Zr2C(OH)2	729.7	3940.6	0.88	540	[78]
Sc2CF2	739.4	5175.7	0.96	700	[94]	Zr2CF2	248.2	1340.5	0.031	540	[80]
Sc2CFN	371.6	0.0	0.9	ND	[79]	Zr2CF2	804.5	4344.3	0.031	540	[82]
Sc2CO2	672.0	0.0	1.85	ND	[81]

^ND = not determined.

and is reviewed in the following sections.

3.1.1. Titanium-Based Systems

As the most extensively explored family, Ti₃C₂-derived materials provide a fundamental benchmark. According to experimental data, Ti₃C₂T_x and Ti₃C₂ generally exhibit specific capacitances ranging from approximately to 120 to 559 F g⁻¹, depending on the processing method and surface area (typically 7–48 m² g⁻¹). Performance can be significantly tuned through hybridization; for instance, the Ti₃C₂@Ni₃S₄ system delivers a high capacitance of 980 F g⁻¹, whereas TiN/Ni composites show more modest values around 90 F g⁻¹.

Theoretically, Ti₃C₂ exhibits a C_q of approximately 754 µF cm⁻². While Ti₂C shows a lower baseline (~246 µF cm⁻²), hydroxyl functionalization (Ti₂C(OH)₂) markedly enhances this to nearly 578 µF cm⁻², and fluoride terminations in Ti₂CF₂ can push theoretical limits to 909 µF cm⁻².

3.1.2. Niobium-Based Systems

Niobium-containing systems demonstrate competitive electrochemical behavior. Experimental values for pure Nb₂C range significantly, with reports spanning from 330 to 547 F g⁻¹. Hybridization strategies have proven highly effective; cobalt-modified Nb₂C achieves exceptional values exceeding 1060 F g⁻¹, and Ni-Mo-N supported stainless steel mesh (a related multi-metallic system) reaches 1020 F g⁻¹.

Theoretically, niobium carbides and nitrides display pronounced sensitivity to surface chemistry. While Nb₂C generally shows high theoretical capacity (~1828 µF cm⁻²), hydroxylated forms (Nb₂C(OH)₂) are predicted to reach as high as 2061 µF cm⁻². Similarly, Nb₂N shows strong potential at 1196 µF cm⁻², whereas Nb₄N₃ exhibits significantly lower intrinsic capacitance near 175 µF cm⁻².

3.1.3. Molybdenum-Based Systems in MXenes

Molybdenum-based Mxenes exhibit the most significant dispersion in electrochemical performance across the dataset. Experimental values for Mo₂C span exceptionally wide range, from as low as 76.4 F g⁻¹ to a remarkable 1718 F g⁻¹. Similarly, Mo₂N samples show substantial variation, with values clustered between roughly 158 and 1272 F g⁻¹. This variability suggests that synthesis conditions and phase purity are decisive factors for Mo-based materials.

Theoretically, Mo₂C stands out as a high-performance candidate, with calculations predicting values up to 3244 µF cm⁻² for bare surface and 1927 µF cm⁻² for hydroxyl-terminated variants.

3.1.4. Vanadium, Chromium, and Emerging Candidates

Other transition metals present striking contrasts between theoretical potential and experimental realization.

• Vanadium: Experimental V₂C consistently operates between 164 and 284 F g⁻¹. However, theoretical models suggest a much higher ceiling, with certain V₂C configurations predicted to reach phenomenal C_q values between 3010 and 3465 µF cm⁻².
• Chromium: Cr₂C shows immense experimental variability, with reported values ranging from 91 F g⁻¹ to 1456 F g⁻¹. Theoretically, Chromium fluorides (Cr₂CF₂) exhibit the highest predicted values in the dataset, reaching an extraordinary 4516 µF cm⁻².

Scandium and other scandium-based variants show promise in simulations, with Cu-doped Sc₂CO₂ reaching ~1524 µF cm⁻². Conversely, Zirconium (Zr₂CF₂) and Hafnium (Hf₂CF₂)-based MXenes fall within a more moderate theoretical range of 248–804 µF cm⁻²

3.2. Transition Metal Dichalcogenides

Similar to MXenes, the electrochemical behavior of TMDs is heavily dependent on the metal center, the chalcogen, and the crystalline phase. The following sections analyze these trends based on the primary transition metal. The dataset for these materials is summarized in

Table 3. Experimental values for TMDs found in the literature.

Material	Capacitance	SSA	Ref.	Material	Capacitance	SSA	Ref.
	(F g−1)	(m2 g−1)			(F g−1)	(m2 g−1)
1T-MoS2	266.5	28.9	[95]	VS2	106	ND	[96]
1T-MoS2	170.4	28.9	[95]	VS2	349	ND	[97]
2H-MoS2	139.3	57.1	[95]	VS2	235	ND	[98]
2H-MoS2	93.6	57.1	[95]	VS2	155	ND	[99]
MoS2	402	7.56	[40]	VS2	180	ND	[100]
MoS2	11.6	2.9	[95]	VS2	139	ND	[101]
MoS2	48	8.0	[102]	VS2	120	ND	[101]
MoS2/GO	248	98	[102]	VS2	54	ND	[101]
MoS2/GO	180	49	[102]	WS2	130	14.0	[103]
MoS2/GO	210	32	[102]	WS2	40	22.7	[104]
MoSe2	394	330	[105]	WS2/PANI	560	35	[103]
MoSe2/rGO	169.3	ND	[106]	WS2/PANI	464	ND	[107]
2H-MoSe2	4.1	4.603	[108]	WS2/PPy	400	23	[103]
TiO2/TiS2	49.5	32.21	[41]	WS2/ZIF-8	437.6	535	[109]
TiS2	480	9.6	[40]	WSe2	618.75	ND	[110]
TiS2/MoS2	709	13.1	[40]

^ND = not determined.

and

Table 4. Theoretical values for TMDs found in the literature.

Material	Quantum Capacitance	Capacitance	Band Gap	SSA	Ref
	(μF cm−2)	(F g−1)	(eV)	(m2 g−1)
CoS2	420	1270.50	1.06	295–310	[111]
FeS2	923.73	2794.28	0.73	295–310	[43]
1T’-MoS2	395	1362.75	0.00	345.00	[112]
1T-MoS2	321	1123.50	0.00	350.00	[112]
1T-MoS2	1718.06	6013.21	0.00	350.00	[113]
2H-MoS2	1615.14	5329.96	1.8	330.00	[114]
2H-MoS2	100	330.00	1.9	330.00	[111]
MoS2	943.75	3114.38	0.00	330.00	[43]
MoS2	200	660.00	0.00	330.00	[115]
MoS2/G	346.99	1145.07	0.3	330.00	[116]
MoSe2	78	346.32	1.34	444	[44]
2H-MoSe2	91	404.04	1.5	444	[44]
Ni3S2	780	0.00	1.08	ND	[111]
TaS2	1111.29	0.00	ND	ND	[43]
TaS2	151	0.00	0.6	ND	[117]
TaSe2	103	0.00	0.78	ND	[117]
TiS2	131.41	0.00	ND	ND	[43]
VS2	20.19	72.68	1.2	360.00	[118]
VS2 Svac.	35.61	128.20	1.20	360.00	[118]
VS2 Vvac.	21.75	78.30	1.20	360.00	[118]
As-VS2	31.24	112.46	1.20	360.00	[119]
WS2	116	290.00	1.8	250.00	[117]
WSe2	152	0.00	1.57	ND	[117]
WSe2/G	838.24	0.00	1.2	ND	[120]
ZrS2	142	0.00	1.68	ND	[117]
ZrSe2	127	0.00	1.2	ND	[117]

^ND = not determined.

and discussed in the subsequent sections.

3.2.1. Molybdenum-Based Systems in TMDs

Molybdenum dichalcogenides are the most extensively studied family, displaying a critical dependence on phase engineering. Experimental reports indicate that metallic 1T-MoS₂ nanosheets deliver specific capacitance values as high as 266.5 F g⁻¹ (28.9 m² g⁻¹), significantly outperforming the semiconducting 2H phase, which exhibits approximately 139 F g⁻¹ despite having nearly double the surface area (57.1 m² g⁻¹). This behavior is consistent with theoretical predictions, where 1T-MoS₂ achieves an exceptional C_q of 1718 µF cm⁻², compared to the lower baseline of pristine MoS₂ (~944 µF cm⁻²) and MoS₂/graphene composites (~347 µF cm⁻²).

Hybridization further modulates performance. MoS₂/GO composites reach values of 248 F g⁻¹, whereas pristine commercial MoS₂ yields only 11.6 F g⁻¹. In selenide systems, MoSe₂ supported activated carbon achieves 394 F g⁻¹, while the 2H-MoSe² phase shows negligible capacity (4.1 F g⁻¹), reinforcing the dominance of electronic structure over simple surface metrics.

3.2.2. Tungsten-Based Systems

Tungsten sulfides and selenides generally require composite engineering to unlock their potential. Pristine WS₂ typically display low experimental capacitance (~40–130 F g⁻¹) and low theoretical C_q values (~116 µF cm⁻²). However, combining WS₂ with conductive polymers like polyaniline (PANI) dramatically increases capacitance to 560 F g⁻¹. Similarly, WS₂/ZIF-8 hybrids reach 437.6 F g⁻¹, leveraging the high surface area of the MOF structure (~535 m² g⁻¹).

Notably, tungsten selenide (WSe₂) exhibits striking contrast: while pristine WSe₂ has a low theoretical C_q (~152 µF cm⁻²), graphene hybridization is predicted to boost this to 838 µF cm⁻². Experimentally, specific WSe₂ formulations have been reported to achieve values as high as 618.75 F g⁻¹, suggesting significant room for optimization.

3.2.3. Titanium, Vanadium, and Tantalum-Based Systems

Titanium, Vanadium, and Tantalum-based TMDS present a complex landscape where experimental results often diverge from theoretical baselines.

• Titanium: TiS₂ demonstrates robust experimental performance, with pure TiS₂ reaching 480 F g⁻¹ and TiS₂/MoS₂ hybrids achieving 709 F g⁻¹. This occurs despite a relatively low theoretical C_q of ~131 µF cm⁻².
• Vanadium: Pristine VS₂ is particularly intriguing. Theoretical calculations predict a minimal electronic contribution (~20 µF cm⁻²); however, experimental data reveals a wide capacitance range from 54 to 349 F g⁻¹, indicating that extrinsic factors or pseudocapacitive mechanisms may play a larger role than intrinsic C_q suggests.
• Tantalum: Theoretical models for Tantalum sulfides show immense variability, with TaS₂ predictions ranging from 151 up to 1111 µF cm⁻² depending on the simulation parameters, while TaSe₂ remains lower at ~103 µF cm⁻².

3.2.4. Other Metal Sulfides

Beyond the primary layered TMDs, other transition metal sulfides display high theoretical potential consistent with their high density of states. FeS₂ (~924 µF cm⁻²), Ni₃S₂ (~780 µF cm⁻²), and CoS₂ (~420 µF cm⁻²) all exhibit substantial intrinsic capacitance, positioning them as competitive candidates for hybrid electrode designs.

4. Comparison

To provide a representative comparison between theoretical predictions and experimentally achievable performance, some selected MXenes and TMDs are presented in

Table 5. Electronic characteristics and comparison of theoretical, experimental, and projected capacitances of selected MXenes.

Material	Theoretical (µF cm−2)	Projected (F g−1)	Experimental (F g−1)	Electronic Behavior	Ref.
Ti2C	246.2	1652	382	Half-metal	[62,86]
Ti3C2	753.7	7386.2	414	Metallic	[64,65]
Ti3C2Tx	253.6	2485	312.25	Metallic	[67,68]
Cr2C	2364.9	15,135	773	Metallic	[45,46]
Mo2C	3244	17,842	686	Metallic	[47,48]
Nb2C	1076	6242	438	Metallic	[57,58]

and

Table 6. Electronic characteristics and comparison of theoretical, experimental, and projected capacitances of selected TMDs.

Material	Theoretical (µF cm−2)	Projected (F g−1)	Experimental (F g−1)	Band Gap (eV)	Ref.
MoSe2	78	346	394	1.50	[44,105]
1T-MoS2	571	2831	154	Metallic	[112,113]
MoS2/G	347	1145	212	0.3	[102,116]
TiS2	131	1420	480	0.2	[40,43]
VS2	20.19	72.68	150	1.2	[101,118]
TiS2/MoS2	131	1420	709	Metallic	[40,43]

, respectively. These materials were chosen based on the availability of both DFT derived quantum capacitance values and reliable experimental gravimetric capacitances.

First-principles calculations typically report capacitance in areal units (µF cm⁻²), obtained from the quantum capacitance (see Equation (8)) which reflects the electronic charge storage capability per unit surface area. To enable comparison with experimental data, these values must be converted into gravimetric capacitance (F g⁻¹) using the specific surface area (SSA):

$$C \left(\mathrm{F} {\mathrm{g}}^{-1}\right) = C_q \left(\mathrm{\mu }\mathrm{F} \mathrm{c}{\mathrm{m}}^{-2}\right) \ast SSA\left({\mathrm{m}}^2 {\mathrm{g}}^{-1}\right) \ast {10}^{-2}$$

(10)

Thus, the theoretical gravimetric capacitance implicitly assumes an ideal, fully accessible surface area, typically corresponding to perfectly exfoliated monolayers. This assumption explains the extremely high average theoretical values reported for MXenes such as Cr₂C (15,135 F g⁻¹) and Mo₂C (17,842 F g⁻¹) in Table 5, which are two orders of magnitude larger than their experimental counterparts.

As shown in Table 5, pristine MXenes (Ti₂C, Ti₃C₂, Cr₂C, Mo₂C, Nb₂C) exhibit very large theoretical capacitances, exceeding 6000–17,000 F g⁻¹ after surface-area normalization. These values originate from their metallic or half-metal electronic structures, characterized by a high density of transition metal d states at the Fermi level and, consequently, large quantum capacitance.

However, the experimentally measured capacitances remain in the range of 300–800 F g⁻¹, even for top-performing systems such as Mo₂C (686 F g⁻¹) and Cr₂C (773 F g⁻¹). Functionalized materials, such as Ti₃C₂T_x, further exhibit reduced experimental values due to surface termination disorder, partial oxidation, and severe restacking effects, which drastically lower the effective ion-accessible surface area.

The representative transition metal dichalcogenides summarized in Table 6 illustrate the comparatively strong consistency between theoretical predictions and experimentally achievable capacitance for this class of materials. In general, TMDs display moderate theoretical capacitances, typically below 3000 F g⁻¹. Their electronic structures range from semiconducting systems (MoSe₂, VS₂) to metallic ones (1T-MoS₂, TiS₂, and TiS₂ /MoS₂).

As shown in Table 6, semiconducting compounds such as MoSe₂ (band gap ≈ 1.5 eV) and VS₂ (≈1.2 eV) exhibit moderate theoretical gravimetric capacitances (346 and 72.7 F g⁻¹, respectively), yet experimentally reach 394 and 150 F g⁻¹, respectively, in some cases exceeding their surface-area-normalized theoretical estimates. This behavior reflects the strong sensitivity of gravimetric capacitance to the real accessible surface area and electrode morphology, which are often underestimated or idealized in first-principles models.

Metallic or quasi-metallic TMDs show higher theoretical limits. For instance, 1T-MoS₂ exhibits a theoretical capacitance of 2831 F g⁻¹; however, the experimentally reported value (154 F g⁻¹) remains substantially lower, highlighting that metallic electronic character alone does not warranty efficient utilization of quantum capacitance. In contrast, layered sulfides such as TiS₂ (band gap ≈ 0.2 eV) achieve a favorable balance, combining a moderate theoretical value (1420 F g⁻¹) with a high experimental capacitance of approximately 480 F g⁻¹.

Figure 2 compares the reported theoretical and experimental gravimetric capacitance values for MXene-based electrodes. Data were averaged from multiple independent literature sources due to the substantial dispersion observed in reported results. Given this variability and the heterogeneous experimental conditions across studies, standard deviations are omitted, and only mean values are presented for clarity.

Theoretical predictions suggest exceptionally high capacitance values, frequently exceeding 10,000 F g⁻¹, highlighting the potential of MXenes as electrode materials from an electronic structure perspective. Conversely, experimentally measured capacitances for the same materials rarely exceed 500 F g⁻¹, revealing a significant discrepancy between computational predictions and practical electrochemical performance.

Figure 3 presents a similar analysis for TMDS, processed using the same methodology. In this case, theoretical capacitance values are significantly lower than those predicted for MXenes, and a markedly improved agreement with experimental measurements is observed. Notably, several materials, including WSe₂, WS₂, and VS₂, exhibit experimental capacitances that closely match, or in some instances slightly exceed, their corresponding theoretical values.

To quantitatively assess the alignment between theory and experiment, the ratio of experimental to theoretical capacitance (C_exp/C_theor) was calculated for all materials where both datasets were available. These ratios are summarized in Figure 4 and Figure 5 for MXenes and TMDs, respectively.

For MXenes, the ratio remains consistently below 0.2, indicating that approximately 20% or less of the theoretically predicted capacitance is experimentally achieved. In contrast, TMD-based electrodes display ratios closer to unity, reflecting substantially better correspondence between computed C_q and measured electrochemical performance. In several cases, experimental capacitance surpasses theoretical estimates.

Collectively, the data presented in Table 6 and Figure 3 and Figure 5, supported by statistical analysis, indicate that TMDs exhibit greater predictability and reproducibility than MXenes. Notably, the consistently higher C_exp/C_theo ratios observed for TMDs are mainly related to structural and electrochemical factors that enable a more efficient use of their intrinsic electronic properties. While theoretical capacitance derived from electronic-structure calculations reflects the density of states available for charge storage, the experimentally accessible capacitance is strongly influenced by structural and electrochemical factors such as ion transport pathways, interlayer accessibility, and surface chemistry. Unlike MXenes, which often experience restacking and surface terminations (–O, –OH, –F) that partially block ion-accessible sites, layered TMDs typically maintain more stable interlayer spacing and can support ion intercalation or surface redox processes. These features improve electrolyte penetration and enable a larger fraction of the theoretically predicted capacitance to be realized experimentally.

This alignment is attributed to the superior chemical stability, lower oxidation sensitivity, and enhanced preservation of two-dimensional morphology in TMDs, which reduce the discrepancy between theoretical assumptions and experimentally accessible surface area. Consequently, despite their lower theoretical capacitance, TMDs currently constitute a more reliable platform for the rational design of high-performance two-dimensional supercapacitor electrodes.

Figure 6 compares the capacitance of MXenes and TMDs collected in this review as a function of their electronic band gap. MXenes (Figure 6a) cluster almost exclusively in the metallic or near-zero band gap region, consistently exhibiting high theoretical and experimental capacitance values, typically exceeding 10³ F g⁻¹. In contrast, TMDs (Figure 6b) span a broader electronic spectrum, ranging from metallic and semi-metallic systems (e.g., Ni₃S₂, TiS₂, and 1T-MoS₂) to wide-band-gap semiconductors such as 2H-MoS₂ and WSe₂.

Despite this distinct electronic differentiation, no direct correlation between band gap magnitude and capacitance is observed within either material class. Several semiconducting TMDs achieve capacitance values comparable to, or exceeding, those of their metallic counterparts, whereas certain metallic MXenes exhibit moderate experimental performance despite high theoretical limits. This behavior suggests that while the band gap determines the upper bound of C_q by influencing the density of states at the Fermi level, it does not solely dictate the experimentally accessible gravimetric capacitance.

The discrepancies between theoretical and experimental capacitance values originate from both computational idealizations and experimental constraints. DFT calculations are commonly performed on defect-free, fully accessible monolayers and frequently neglect electrolyte screening and solvation effects. Experimentally, restacking, agglomeration, incomplete exfoliation, and structural defects introduce deviations, while variations in electrochemical techniques and testing protocols introduce additional dispersion in reported values. Moreover, faradaic contributions, surface redox processes, and composites which are not captured by conventional quantum capacitance models, may explain cases where experimental capacitance exceeds theoretical predictions in some TMD systems. Together, these factors highlight the need for improved theoretical descriptions and consistent experimental normalization prior to quantitative comparison.

5. Outlook and Perspectives

The systematic comparison between theoretical and experimental capacitance values for MXenes and TMDs demonstrates that current DFT–based predictions consistently overestimate practical electrochemical performance, with experimental values reaching on average only ~10–20% of the theoretical limit for MXenes and ~70% for TMDs. This discrepancy highlights the need for methodological refinement on both the computational and experimental approaches to enable a reliable and meaningful interpretation of quantum capacitance in realistic supercapacitor electrodes.

From a theoretical perspective, several aspects are critical for improving predictive capability. First, realistic surface area modeling is essential, as deviations between theoretical and experimental specific surface areas constitute the dominant source of error when converting areal quantum capacitance into gravimetric values. Whenever possible, experimentally measured BET or electrochemically active surface areas should be incorporated, and aggregation or restacking penalties should be applied to idealized models. Second, electrolyte effects, including ion–surface interactions, solvation, and dielectric screening, should be explicitly considered through implicit or explicit solvent models and constant-potential approaches. Third, defects, surface terminations, and structural disorder, particularly relevant for MXenes, must be included to accurately capture the electronic density of states near the Fermi level.

Importantly, the common assumption that the quantum (space-charge) capacitance C_q is much smaller than the Helmholtz capacitance C_H and thus that C_tot ≈ C_H is not universally valid. For highly metallic MXenes, reported C_q values can approach or exceed several tens of mF cm⁻², becoming comparable to C_H. In this regime, the total capacitance is no longer governed solely by the electronic structure of the electrode but becomes strongly dependent on electrolyte properties such as ion size, solvation shell, concentration, and dielectric constant. Future theoretical treatments should therefore explicitly account for both contributions in the series capacitance framework to avoid systematic overestimation.

On the experimental side, reliable validation of theoretical predictions requires standardized and comprehensive characterization. Systematic reporting of surface area, controlled morphology to minimize restacking and oxidation (especially for MXenes), standardized electrochemical testing protocols, and detailed structural and chemical analyses (XRD, SEM/TEM, XPS) are necessary to ensure meaningful comparison across studies.

From a materials design perspective, pristine MXenes such as Mo₂C and Cr₂C remain attractive for applications targeting maximum achievable capacitance, provided that advanced synthesis and stabilization strategies are available. In contrast, TMDs such as TiS₂, MoS₂, and VS₂ offer lower theoretical maximum capacitance but significantly better experimental–theoretical consistency, making them more suitable for reliable and scalable implementations. Hybrid MXene-TMD architectures represent a promising compromise, combining high electronic density of states with improved structural stability and ion accessibility.

Overall, bridging quantum capacitance theory with experimental electrochemical performance requires a shift from idealized, material-centric modeling toward integrated system-level descriptions in which electrode electronic structure, accessible surface area, and electrolyte properties are treated on equal footing. Multiscale approaches combining DFT, molecular dynamics, and data-driven correction schemes, together with standardized experimental methodologies, will be essential to establish quantum capacitance as a quantitatively reliable design parameter for next-generation supercapacitor electrodes.

6. Conclusions

This review systematically evaluates the relationship between C_q predicted via first-principles calculations and experimentally measured electrochemical capacitance of MXenes and TMDs. The analysis reveals a pronounced systematic discrepancy in MXenes, which typically realize less than 20% of their theoretical capacitance. This shortfall is primarily attributed to layer restacking, surface terminations, oxidation, and limited ion-accessible surface area. In contrast, TMDs exhibit superior alignment between theoretical predictions and experimental results, frequently reaching 50–100% of calculated values. This performance is attributed to their enhanced chemical stability and better preservation of two-dimensional morphology during electrode processing.

These findings demonstrate that while metallic electronic character and a high density of states are prerequisites for large C_q, they are insufficient to guarantee high gravimetric capacitance in practical devices. Instead, experimentally accessible performance is ultimately governed by morphology, surface chemistry, and electrode architecture. Consequently, accurate comparison between theory and experimental necessitates rigorous surface area normalization and realistic structural modeling.

Future advancements will depend on improving computational–experimental consistency and developing hybrid material strategies that integrate the high intrinsic electronic capacitance of MXenes with the structural robustness of TMDs for scalable, high-performance supercapacitor electrodes.