Halogen-Driven Tunability in Cubic KZnX₃ (X = F–I) Halide Perovskites: A First-Principles Study

Abstract

This paper systematically studied the structural, mechanical, electronic, and optical characteristics of cubic KZnX₃ (X = F, Cl, Br, and I) perovskites through the density functional theory (DFT) in the Quantum Espresso framework. Structural optimization and stability analyses confirm that all compounds crystallize in the cubic Pm-3m phase and are thermodynamically, mechanically, and dynamically stable. Elastic constants indicate that the materials are anisotropic and ductile in nature. Calculations of Debye temperatures show a systematic decrease of 402 K (KZnF₃) to 158 K (KZnI₃), which is related to the increasing mass of halogen and its impact on the rigidity of the lattice. Electronic structure calculations show that all compounds are indirect bandgap semiconductors, with bandgaps systematically decreasing from 4.24 eV (KZnF₃) to 0.86 eV (KZnI₃) at the HSE06 level, enabling tunable semiconducting characteristics for optoelectronic applications. The analysis of the density of states and charge density indicates that the bonding between Zn and X is mixed ionic and covalent and that the bonding between K and X is mostly ionic. Calculations of optical properties show an increase in polarizability, absorption, refractive index and plasmonic response when heavier halogen is used, highlighting the potential of KZnX₃ perovskites for photovoltaic and optoelectronic devices. Overall, halogen substitution in KZnX₃ provides an effective strategy for tailoring electronic and optical properties.

1. Introduction

ABX₃ cubic perovskite crystals, composed of mono- and divalent cations and a monovalent halogen anion (X), have attracted significant attention from both theoretical and experimental perspectives [1,2,3]. This has been driven by the fact that they have a comparatively straightforward crystal structure, are easy to synthesize, allow flexible doping, and comprise a wide variety of physical behavior such as electrical, optical, magnetic, piezoelectric and ferroelectric behavior [4,5,6,7]. Thanks to these characteristics, the halide perovskites have a wide range of practical uses, including a high-performance optical component, birefringence-free lenses, and electronics and magnetism functional materials. More so, they offer useful information regarding geophysical processes, especially in the lower mantle of the Earth, due to their physical characteristics [8,9,10].

Fluoride perovskites are an important subfamily of halide perovskites and have important technical applications in deep-ultraviolet (DUV) optics. Their large band gaps and high optical clarity can be utilized in DUV optoelectronics, scintillators and luminescent applications [11,12,13]. Here, KZnF₃ has been extensively experimentally as well as theoretically investigated in regard to its structural stability and possible application as a radiation detector. Past studies of KZnF₃ have included its synthesis, lattice dynamics, high-pressure phase behavior, elastic properties and optical response and the influences of transition-metal dopants on its crystal field and electronic structure [14,15,16,17,18,19,20,21,22].

Nevertheless, widespread focus has been placed on KZnF₃, and other members of the KZnX₃ (X = F, Cl, Br, and I) family have not been studied in detail, particularly on a first-principles scale. Heavier halogen analogues such as KZnCl₃, KZnBr₃, and KZnI₃ lack any significant theoretical information, even though they could have some technological importance. Specifically, the change in the band gap of the series of halogen, with KZnF₃ having a very large band gap, indicates that the replacement of bigger and less electronegative halogen atoms may cause extensive modifications in the electronic behavior, optical behavior, and thermodynamic behavior. The trends demonstrate a need to understand how to tune the material performance to more practical uses.

Out of these gaps in knowledge, the current work is a systematic and comparative first-principles investigation of the structural, electronic, elastic, optical, phononic, and thermodynamic characteristics of the complete KZnX₃ (X F, Cl, Br, and I) family. The use of KZnF₃ as a reference compound, although an established one, is not novel in our study, as the other halide members have not been investigated previously. We calculate the band structures, density of states, optical functions, phonon dispersions, group velocities, and the thermal parameters of these materials with respect to temperature, providing a full picture in the theoretical perspective of the physical properties of these materials.

This comprehensive study is expected to enrich the fundamental understanding of halide perovskite systems and provide a robust theoretical framework to guide future experimental investigations and potential technological applications. The remainder of this paper is organized as follows: Section 2 describes the computational methodology; Section 3 presents and discusses the structural, elastic, electronic, optical, and thermodynamic properties of KZnX₃ compounds; and Section 4 summarizes the main conclusions of this work.

2. Result and Discussion

2.1. Structural and Thermodynamic Stability

Structural properties of the KZnX₃ (X = F, Cl, Br, and I) compounds were studied systematically, where KZnF₃ has been used as the reference parent perovskite compound. KZnF₃ is cubic perovskite with space group Pm-3m (space group 221), with a formula unit per unit cell [23]. In this structure, the Zn atoms are located in the center of the cubical unit cell, the K atoms are on the corners of the unit cell and the halogen atoms are at the face-centered positions. The atom coordinates are K (0, 0, 0), Zn (0.5, 0.5, 0.5) and X (0, 0.5, 0.5), which are located at the 1a, 1b, and 3c Wyckoff sites, respectively.

Figure 1 illustrates the unit-cell structure, while

Table 1. Optimized lattice constants a₀ (Å), the unit-cell volume (V), and formation energy (E_f) (eV/atom) of the KZnX₃ (X = F, Cl, Br, and I) compounds.

Compounds	a (Å)	V (Å3)	Ef	Ref.
KZnF3	4.14, 4.054exp, 4.06exp, 4.129	66.30	−2.812	[13,23,24,25]
	4.12	70.29	−2.758	This study
KZnCl3	4.98	123.57	−2.027	This study
KZnBr3	5.29	148.70	−1.955	This study
KZnI3	5.76	194.44	−1.795	This study

exp—experimentally obtained value.

summarizes the optimized lattice constants, unit-cell volumes, and formation energies of KZnX₃ obtained in this work. The resulting lattice constants are consistent with experimental values as well as with other theoretical values reported in the past. As commonly observed, the GGA approach slightly overestimates or underestimates the lattice parameters; nevertheless, the overall consistency confirms the reliability of the adopted computational methodology.

All KZnX₃ compounds (X = F, Cl, Br, and I) were investigated using the same computational framework, and their optimized structural parameters and formation energies are compiled in Table 1. All the investigated compounds have their optimum lattice constants, unit-cell volumes, and formation energies presented in Table 1. A systematic increase in lattice constants and unit-cell volumes is observed as the halogen is varied from F to Cl, Br, and I, which can be attributed to the increasing ionic radius of the halogen atoms. In contrast, the formation energies decrease progressively along the series, indicating a gradual reduction in thermodynamic stability. For KZnF₃, the calculated structural parameters are in good agreement with the available experimental data, further validating the reliability of our computational approach. KZnF₃, as the parent compound, is therefore used as a reference to analyze and interpret these trends.

Negative formation energies validate that all KZnX₃ (X = F, Cl, Br, and I) compounds are thermodynamically and energetically favorable to prepare. The standard expression was used in computing the enthalpy of formation E_f [26]:

$$E_f={\displaystyle \frac{E_{Total}-\left(n_K{E}_K^{solid}+n_{Zn}{E}_{Zn}^{solid}+n_X{E}_X^{solid}\right)}{n_K+n_{Zn}+n_X}}$$

(1)

where E_Total is the DFT total energy of the unit cell of KZnX₃, and $E_K^{solid}$, $E_{Zn}^{solid}$ and $E_X^{solid}$ are the energies of elemental K, Zn and halogen X in their most stable solid phases. n_K, n_Zn, and n_X denote the number of K, Zn and X atoms in the unit cell, respectively. The calculated formation energies E_f are uniformly negative, indicating that the formation of the KZnX₃ perovskite compounds from their constituent elemental solids is energetically favorable. This thermodynamic behavior suggests that KZnX₃ compounds can be experimentally synthesized under appropriate conditions.

Figure 2 provides the phonon dispersion relations and phonon density of states (PDOS) of the KZnX₃ compounds. Both systems have the typical three acoustic and 12 optical phonon branches of the five atom primitive cell of the cubic perovskite structure. Notably, the existence of any imaginary phonon mode is not present anywhere within the Brillouin zone of any of the halide compositions, and therefore the dynamical stability of the cubic phase is undisputed. KZnF₃ exhibits the highest vibrational frequencies of the series, including optical branches up to approximately 16 THz per the very strong Zn-F interactions and the low mass of fluorine. Varying the halogen atom, F to Cl to Br to I, a systematic phonon softening is evident, manifested by the lowering of the highest optical frequencies (the maximum optical frequencies of KZnCl₃, KZnBr₃, and KZnI₃ being roughly 8, 10 and 8 THz, respectively), and the flattening of the optical modes. This is due to the fact that the ionic radii and atomic masses of the halogen progressively increase, which reduces the rigidity of the bonds and drags the PDOS to the lower frequencies. The PDOS analysis shows that the low-frequency acoustic region is predominantly governed by the heavier K and Zn cations, whereas the high-frequency optical modes are mainly dominated by the halogen (X) atoms. A pronounced overlap between the Zn and X vibrational states in the mid- to high-frequency regions indicates strong covalent Zn–X interactions within the ZnO₆ octahedra. These coupled vibrations play a central role in determining the structural rigidity and lattice stability of the KZnX₃ perovskite framework. In contrast, for KZnI₃, the iodine atom exhibits a dominant contribution in the low-frequency region, reflecting its large atomic mass and the resulting phonon softening effects, which further influence the lattice dynamics and vibrational stability of the system.

The nearly flat phonon branches observed between the X and M high-symmetry points indicate low group velocity vibrational modes, which correspond to highly localized lattice vibrations. Physically, this flat dispersion reflects weak interatomic force constants for the corresponding vibrational modes, meaning that these phonons propagate poorly through the lattice and behave more like localized or quasi-localized vibrations rather than extended propagating waves. In perovskite structures, such flat modes are commonly associated with octahedral tilting, bending, and vibrational motions of the ZnX₆ units, as well as vibrations involving the heavier halogen atoms, which naturally lead to reduced phonon dispersion due to their larger mass and weaker restoring forces. These low-dispersion phonon modes contribute to enhanced phonon scattering and reduced thermal transport, which is consistent with the relatively low Debye temperatures and ductile mechanical behavior observed in these compounds. Therefore, the flat region between X and M is a clear signature of localized lattice dynamics and weak phonon propagation, providing microscopic insight into the vibrational, thermal, and mechanical properties of KZnX₃ perovskites. Altogether, the phonon spectra show that the whole KZnX₃ family is dynamically stable and the progressive softening of F to I reflects the inherent mass- and bonding-driven vibrational response of the halide perovskites.

2.2. Elastic Properties

The elastic response of the materials under stress can be used to determine their mechanical stability, inability to be deformed when subjected to stress, and stiffness [27]. Elastic constants characterize the mechanical behaviors of crystalline solids in the ground state, and are of significant use in investigating the structural stability of crystalline solids. The second-order elastic constants of the cubic KZnX₃ (X = F, Cl, Br, and I) compounds were computed with the IR-Elast package and the results are summarized in

Table 2. The calculated elastic constants (C₁₁, C₁₂, and C₄₄) of the KZnX₃ (X = F, Cl, Br, and I) compounds.

Compounds	C11	C12	C44	Ref.
KZnF3	87.11	52.86	49.81	This study
	99.20	38.00	29.10	[25]
	134.80	41.10	41.10	[22]
	111.80	49.80	31.40	[13]
KZnCl3	83.99	21.06	18.45	This study
KZnBr3	41.74	18.24	13.83	This study
KZnI3	42.23	17.98	9.68	This study

.

In the case of cubic crystals, the Born criteria of stability in mechanics are: C₁₁ > 0, C₄₄ > 0, C₁₁ − C₁₂ > 0, and B > 0 [28,29]. These conditions are met in all the calculated elastic constants of KZnX₃, which proves that the compounds are mechanically stable. In the case of KZnF₃, the current elastic constants are well consistent with the previously known theoretical values [22], which also proves the accuracy of our calculations. By employing more elastic parameters, the bulk modulus (B), shear modulus (G), Young’s modulus (Y), Poisson’s ratio (ν), elastic anisotropy factor (A) and Cauchy pressure (Cp) were obtained by using calculated elastic constants.

The quantities that are commonly used to describe the resistance to volume compression, opposition to plastic deformation, and stiffness of a material are the bulk modulus (B), shear modulus (G), and Young’s modulus (Y), respectively [7,30]. The following relation was used to evaluate these parameters using the Voigt–Reuss–Hill approximation [7,8].

$$B=(C_{11}+{2C}_{12})/3$$

(2)

$$G=\frac{1}{2}(G_V+G_R)$$

(3)

$$G_V=\frac{1}{5}(C_{11}-C_{12}+{3C}_{44})$$

(4)

$$G_R={\displaystyle \frac{{5C}_{44}(C_{11}-C_{12})}{{4C}_{44}+3(C_{11}-C_{12})}}$$

(5)

$$Y={\displaystyle \frac{9BG}{3B+G}}$$

(6)

B, G and Y are calculated to obtain the values, as indicated in

Table 3. The calculated elastic modulus (B, Y, and G), the Pugh ratio (B/G), Poisson’s ratio (ν), Cauchy pressure’s (Cp) and the Zener anisotropy factor (A) of the KZnX₃ (X = F, Cl, Br, and I) compounds.

Compounds	B	G	Y	B/G	ν	Cp	A	Ref.
KZnF3	64.27	32.49	83.42	1.98	0.28	3.05	2.91	This study
	58.43	29.70	78.13		0.28			[3]
	70.43	31.20	81.61		0.31			[5]
KZnCl3	42.03	22.88	58.11	1.84	0.27	2.61	0.59	This study
KZnBr3	26.07	12.95	33.34	2.01	0.29	4.41	1.18	This study
KZnI3	26.06	10.59	27.99	2.46	0.32	8.30	0.80	This study

. The order is observed to decline systematically as KZnF₃ > KZnCl₃ > KZnBr₃ > KZnI₃, meaning that KZnF₃ is the most stiff and the least compressible, whereas KZnI₃ is relatively softer and more compressible. This is due to the fact that the ionic radius of the halogen atom is increasing and there is a corresponding decrease in the strength of interatomic bonding between F and I.

The Cauchy pressure Cp = C₁₂ − C₄₄, Pugh ratio B/G and Poisson ratio (ν) were used to analyze the ductile or brittle nature of the materials. When the Cauchy pressure value is positive (negative), it shows ductile (brittle) behavior. Moreover, the Poisson ratio, which is more than 0.26, and the Pugh ratio, which is more than 1.75, are typical of ductile materials [31,32,33,34]. Table 3 illustrates that all KZnX₃ compounds are ductile, all of them have positive Cauchy pressure, the Poisson ratio value is more than 0.26, and the B/G ratio value is more than 1.75. KZnI₃ has the best values of B/G and the Poisson ratio, which means that it has a relatively high ductility. The Zener anisotropy factor (A) was used to determine the elastic anisotropy that greatly determines the formation of cracks and mechanical reliability [11]:

$$A={\displaystyle \frac{{2C}_{44}}{{3C}_{11}-C_{12}}}$$

(7)

An elastic material that is isotropic has A = 1, and non-unity values denote elastic anisotropy. The results of the calculations of the anisotropy factors of all the KZnX₃ shows that they are not equal to one (Table 3), which shows that the compounds have anisotropic elastic behavior.

2.3. Debye Temperature

The Debye temperature (θ_D) is one of the key physical quantities, which characterizes the vibrational properties of the lattice and determine the temperature dependence of the heat capacity of solids. Its value gives valuable information on the interatomic bonding strength, rigidity of the lattice and thermal behavior. Several theoretical approaches have been developed to estimate (θ_D), among which mechanical models based on elastic constants are widely employed due to their reliability and simplicity. In the present system, (θ_D) is evaluated using the classical relation. In this system, the determination of θ_D is possible with the help of the classical relation [35]:

$${\Theta }_D={\displaystyle \frac{h}{k_B}}[(\frac{3\mathrm{n}}{4\mathrm{\pi }}){\mathrm{N}}_{\mathrm{A}}\mathsf{\rho }/\mathrm{M}]V_m$$

(8)

with h being the constant of Planck, k_B being the constant of Boltzmann, n being the number of atoms per unit formula, N_A being the number of Avogadro, rho being the density, M being the molecular mass per unit formula and V_m being the average velocity of sound. The longitudinal and transverse sound velocities are used to get the average sound velocity as [36]:

$$V_m=[\frac{1}{3}(\frac{1}{v_l^3}+\frac{2}{v_t^3}){]}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$

(9)

The bulk modulus (B) and shear modulus (G) are used to obtain the longitudinal (V_l) and transverse (V_t) wave velocities by the following equations [37]:

$$V_l=\left[\right(3B+4G)/3\rho {]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(10)

$$\mathrm{and} V_t=[G/\rho {]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(11)

According to Table 4, KZnF₃ has the highest longitudinal (2655.58 ms⁻¹), transverse (1459.31 ms⁻¹), and average (1626.69 ms⁻¹) sound velocities, making its Debye temperature the largest (401.76 K). This number is well consistent with the theoretical and experimental values of the Debye temperature already found in the literature, proving the consistency of the current calculations.

A systematic decrease in V_l, V_t, and V_m is observed from KZnF₃ to KZnI₃, leading to a corresponding reduction in θ_D from 401.76 K to 157.52 K. This trend can be attributed to the increasing atomic mass of the halogen element, which weakens the lattice stiffness and lowers the characteristic vibrational frequencies.

Other significant values of the Debye model can be obtained by θ_D, including the Debye temperature of acoustic phonons [38,39] and the Debye frequency, which is the highest frequency of vibrational movement of atoms in thermal excitation [40,41]. The sound velocities and Debye temperature were calculated and are summarized in Table 4. As far as we know, there is no theoretical or experimental information about the Debye temperatures of KZnCl₃, KZnBr₃, and KZnI₃. Thus, the current findings give practical predictions that can be considered as reference data in experimental and theoretical studies in the future.

Table 4. Calculated density (ρ), longitudinal (V_l), transverse (V_t), and average (V_m) sound velocities, Debye temperature (θ_D), and melting temperature (T_m) of the KZnX₃ (X = F, Cl, Br, and I) compounds. Available theoretical and experimental values are included for comparison.

Compounds	ρ (kg/m3)	Vl (m/s)	Vt (m/s)	Vm (m/s)	θD (K)	Tm (K)	Ref.
KZnF3	3814.08	2655.58	1459.31	1626.69	401.76	1067.86	This study
	3752	5110	2811	3134	384.2	-	[25]
	4024exp	-	-	-	437	-	[42]
KZnCl3	2823.71	2530.15	1421.00	1581.27	323.58	1049.41	This study
KZnBr3	3843.03	1679.03	917.84	1023.52	196.91	799.73	This study
KZnI3	4142.88	1557.12	799.40	895.33	157.52	802.58	This study

exp—experimentally obtained value.

Table 4. Calculated density (ρ), longitudinal (V_l), transverse (V_t), and average (V_m) sound velocities, Debye temperature (θ_D), and melting temperature (T_m) of the KZnX₃ (X = F, Cl, Br, and I) compounds. Available theoretical and experimental values are included for comparison.

Compounds	ρ (kg/m3)	Vl (m/s)	Vt (m/s)	Vm (m/s)	θD (K)	Tm (K)	Ref.
KZnF3	3814.08	2655.58	1459.31	1626.69	401.76	1067.86	This study
	3752	5110	2811	3134	384.2	-	[25]
	4024exp	-	-	-	437	-	[42]
KZnCl3	2823.71	2530.15	1421.00	1581.27	323.58	1049.41	This study
KZnBr3	3843.03	1679.03	917.84	1023.52	196.91	799.73	This study
KZnI3	4142.88	1557.12	799.40	895.33	157.52	802.58	This study

exp—experimentally obtained value.

2.4. Electronic Properties

In this section, we explore the electronic characteristics of KZnF₃ in terms of the calculated energy band structures, density of states, and charge distribution. Figure 3 shows the electronic band structures of the cubic KZnX₃ (X = F, Cl, Br, and I) along high-symmetry directions in the Brillouin zone, calculated using either the GGA-PBE or HSE06 exchange-correlation functional. The zero of energy is defined as the valence band maximum (VBM). The HSE06 band gap values for all investigated compounds are summarized in

Table 5. Calculated bandgap values of the KZnX₃ (X = F, Cl, Br, and I) compounds.

Compounds	KZnF3	KZnCl3	KZnBr3	KZnI3
GGA PBE	3.902 This study Experimental: 3.700, 3.664, 3.680 [13,22,25]	1.626	0.610	0.362
HSE06	4.241	2.257	1.111	0.860
Nature	Indirect	Indirect	Indirect	Indirect

.

In the case of KZnF₃, the VBM is at the R point, and the conduction band minimum (CBM) is at the Γ point, which is an indirect R-G band gap. The band gap of KZnF₃ has been calculated as 3.902 eV in GGA-PBE and is found to be 4.241 eV in HSE06 functional. Figure 3a indicates that the HSE06 band structure has a distinct and broad band gap indicating the indirect wide-band-gap characteristic of the insulator/semiconductor KZnF₃. Our predicted values are in agreement with previously reported theoretical and experimental values of the band gap of KZnF₃, which was reported as listed in Table 5. Indeed, the HSE06 formalism does produce systematically larger band gaps than GGA-PBE, as its treatment of exchange interactions is better.

In the rest of the halide compounds KZnCl₃, KZnBr₃, and KZnI₃, the values of the valence band maximum (VBM) and conduction band minimum (CBM) are observed to be at other k-points, and hence, at other k-points are indirectly semiconducting. The indirect band gap in KZnCl₃ [Figure 3b] is much smaller than in KZnF₃, which is calculated to be 1.626 eV (GGA-PBE) and 2.257 eV (HSE06). An additional reduction in the band gap is seen in KZnBr₃ [Figure 3c], where the band gap reduces to 0.610 eV (GGA-PBE) and 1.111 eV (HSE06). Lastly, KZnI₃ [Figure 3d] is the narrowest gap indirect semiconductor with GGA-PBE and HSE06 indirect band gap values of 0.362 eV and 0.860 eV, respectively. As far as we know, there is no prior theoretical and experimental band gap data in the literature on KZnCl₃, KZnBr₃ and KZnI₃ that can be used as a reference in other works. The current results have been a valuable source of information for future research.

In order to better understand the electronic structure, the total and partial density of states (TDOS and PDOS) were studied in the HSE06 approximation (Figure 4). The presence of halogen p states with substantial contributions of Zn-d states in all compounds implies intense p-d orbital hybridization at all their valence bands below the Fermi level (E = 0 eV). The contribution of the K states is mainly negligible around the Fermi level, which proves the ionic nature of K and its insignificant role in the electronic transportation. The valence band of KZnF₃ comprises predominantly F-p with a Zn-d contribution, but the conduction band is predominantly formed with Zn-s and Zn-d contributions, as expected of a wide-band-gap insulator. In the case of KZnCl₃, the Cl-p states become closer to the Fermi level, pushing the broadening of the valence band and narrowing the band gap. This is more dominant at KZnBr₃, where Br-p states dominate over Zn-d states, as it further reduces the band gap. KZnI₃ has I-p states at the lowest point of the valence band nearest to the Fermi level, so the band gap in the series is the smallest.

The bonding behavior can be further explained by charge density analysis (Figure 5). In the case of KZnF₃, Zn displays a directional charge density to F atoms, which implies that Zn and F atoms are partly covalently bonded, and K displays an almost spherical charge distribution, which confirms the existence of ionic K-F interactions. The same behavior is observed in KZnCl₃, which exhibits a little lower Zn-Cl covalency, but in KZnBr₃, the Zn-Br charge density is further delocalized, and hence weaker covalency is shown. This is the most delocalized in KZnI₃, showing that the covalency is not strong at all. In all the halides, the K-X bonds are mostly ionic. Therefore, X-Zn bonds have a mixed ionic–covalent nature that gradually decreases from F to I, and KX bonds are mostly ionic.

The tunable electronic structure and bonding characteristics of the KZnX₃ series enable their optoelectronic properties to be tailored for photovoltaic applications. KZnF₃, characterized by predominantly ionic K–F interactions and a wide band gap, is well suited for use as a transparent conducting layer or electron transport material. KZnCl₃ and KZnBr₃, with higher Zn-X covalency and p-d hybridization, are good candidates as active absorbers of visible and near-infrared light, respectively. The delocalized KZnI₃ has delocalized Zn-I states, allowing it to absorb lower-energy photons, which is beneficial to tandem or broad-spectrum solar cell applications. The KZnX₃-based halogenation is a viable approach to design the electronic structure and optimize the materials towards high-performance optoelectronic and solar energy devices.

2.5. Optical Properties

The optical behavior of materials is determined by their electronic structure and interaction with incident photons and gives important information about their appropriation in optoelectronics [43]. The optical performances of cubic KZnX₃ (X = F, Cl, Br, and I) compounds are organized and studied in the photon energy of 0–15 eV. The complex dielectric function is also used to obtain the frequency-dependent optical parameters.

$$\epsilon \left(\omega \right)={\epsilon }_1\left(\omega \right)+i{\epsilon }_2\left(\omega \right)$$

(12)

where ε₁(ω) and ε₂(ω) denote the real and imaginary components, respectively.

2.5.1. Dielectric Function

The polarization response of the material is described by the real part of the dielectric function, ε₁(ω). As shown in Figure 6a, the static dielectric constant ε₁(0) is lowest for KZnF₃ and increases progressively for KZnCl₃, KZnBr₃, and KZnI₃, indicating enhanced polarizability with increasing halogen atomic size. As the photon energy increases, ε₁(ω) increases and peaks of about 3.11 at 5.62 eV for KZnF₃, 5.02 at 4.63 eV for KZnCl₃, 4.82 at 4.22 eV for KZnBr₃, and 5.05 at 3.91 eV for KZnI₃ are found, due to the strong interband electronic transitions. At stronger energies, ε₁(ω) is smaller and oscillatory. Interestingly, at the energies of 9–12 eV, ε₁(ω) has a negative value at KZnCl₃, KZnBr₃, and KZnI₃, suggesting a plasma-like response, but KZnF₃ is largely positive.

The imaginary component, ε₂(ω), is the optical absorption caused by interband transitions, and it is presented in Figure 6b. The optical band gap of the compounds is reflected on the absorption onset. KZnF₃ has a higher threshold energy of approximately 5.10 eV, which is in line with its broader band gap, with KZnCl₃, KZnBr₃ and KZnI₃ having lower threshold energies of approximately 0.5–1.5 eV, which is the narrowing of the band gap as the halogen atomic number increases. Peaks of ε₂(ω) are pronounced at 12.91 eV (2.1), 8.09 eV (4.97), 7.93 eV (5.03), and 7.33 eV (6.45) of KZnF₃, KZnCl₃, KZnBr₃ and KZnI₃, respectively. The series at KZnI₃ has the highest intensity of absorption, which is a sign of greater absorption of ultraviolet light.

2.5.2. Absorption Coefficient

Figure 6c shows the optical absorption coefficient, α(ω), versus the photon energy. All the compounds display a low photon energy and, in this regime, there is no absorption, which implies that the material is optically transparent. The absorption edge moves systematically to the lower energies of KZnF₃ to KZnI₃ in a progressive narrowing of the band gap as the atomic number of the halogen atom increases. The latest absorption onset and weakest absorption intensity of KZnF₃ is observed with the highest values below a specific band gap of approximately 0.9 × 10⁶ cm⁻¹. By contrast, KZnCl₃ and KZnBr₃ have lower absorption edges and the largest absorption coefficients, at 1.68 × 10⁶ cm⁻¹ and 1.58 × 10⁶ cm⁻¹, respectively, in the ultraviolet. KZnI₃ exhibits a lower maximum absorption of about 1.55 × 10⁶ cm⁻¹ and it has a stronger absorption at lower photon energies. As the photon energy increases, α(ω) increases rapidly due to intense interband electronic transitions. At higher photon energies, the absorption coefficient displays oscillatory behavior, originating from complex high-energy electronic transitions. For KZnF₃, the optical absorption starts at a slightly higher energy than the HSE06 bandgap because the first electronic transition has a low probability. Stronger, dipole-allowed transitions appear at higher photon energies, which is why the absorption edge is shifted. Since all KZnX₃ compounds have cubic symmetry (Pm-3m), their optical response is isotropic, so no polarization dependence is expected.

2.5.3. Optical Conductivity

Figure 6d gives the photon-energy-dependent optical conductivity σ(ω). At low photon energies (0–3 eV), all the compounds exhibit negligible conductivity, showing low electronic transition. As the photon energy increases, σ(ω) rises rapidly due to the interband transitions and goes almost in step with the pattern of the absorption spectra. The highest conductivity peak for KZnF₃ is 3.28 at 12.88 eV and 5.46 at 11.79 eV for KZnCl₃, 4.91 at 8.50 eV for KZnBr₃, and 6.14 at 7.82 eV for KZnI₃. KZnI₃ has the greatest conductivity peak at lower energies, but KZnF₃ has the lowest conductivity peak at higher energies. Above these maxima, oscillations are produced by high-energy electronic transitions.

2.5.4. Refractive Index

The essential optical parameter is the refractive index that describes the dispersion and uptake of photons that encounter the material. Past studies have shown that denser materials are likely to have higher values of refractive index [44]. The value of the refractive index against the photon energy of the KZnX₃ compounds under study is shown in Figure 6e. The trends of the dielectric function ε(ω) are closely reflected in the refractive index spectra, thus displaying the close connection between the two optical characteristics. At the static limit (n(0)), KZnF₃, KZnCl₃, KZnBr₃ and KZnI₃ are found to have values of the refractive index of 1.50, 2.00, 1.96 and 2.08, respectively. n(ω) increases slowly with the photon energy, with the highest values of 1.77 at 5.61 eV (KZnF₃), 2.25 at 4.64 eV (KZnCl₃), 2.22 at 4.26 eV (KZnBr₃), and 2.47 at 7.13 eV (KZnI₃). It is known that these maxima are due to strong interband electronic transitions and the maxima are well added to the sharp features of the dielectric function.

2.5.5. Extinction Coefficient

An optical response that is evidently halogen-dependent with increasing photon energy is observed in the extinction coefficient k(ω). KZnF₃ has the lowest absorption and k(ω) remains low throughout most of the energy range, representing a broader band gap. KZnCl₃ and KZnBr₃, on the other hand, show a moderate absorption behavior, with a slow onset and strong peaks in the middle of the energy range. KZnI₃ exhibits the greatest absorption of all the compounds, an earlier onset, and larger peak intensities associated with better optical transitions because of heavier halogen ions.

2.5.6. Reflectivity

The reflectivity R(ω), which characterizes a material’s ability to reflect incident electromagnetic radiation, is presented in Figure 6g. At the static limit, the reflectivity of KZnF₃, KZnCl₃, KZnBr₃, and KZnI₃ are approximately 0.04, 0.10, 0.11, and 0.12, respectively, which decrease in order of the atomic number of halogens. The highest reflectivity is approximately 0.11 at 11.89 eV in KZnF₃, 0.31 at 12.24 eV in KZnCl₃, 0.30 at 11.47 eV in KZnBr₃ and 0.38 at 9.85 eV in KZnI₃, which implies that the optical response of iodide-based compounds is stronger.

2.5.7. Energy-Loss Function

The energy-loss L(ω) is a description of the energy loss of fast electrons passing through the material. The L(ω) for all compounds is almost zero at low photon energy and tends to increase considerably at high photon energy. KZnF₃ has the lowest maximum loss (0.41), with KZnCl₃ and KZnBr₃ having intermediate peaks of 0.92 and 0.93, respectively. The maximum energy-loss peak of KZnI₃ is the highest, and it peaks strongly at approximately 1.9 around 15 eV, which means that heavier halogen ions have more plasmonic excitations.

3. Methods and Materials

The calculation in the present research was carried out in the context of density functional theory (DFT) by the Quantum Espresso (QE) package [45]. Norm-conserving/ultrasoft PAW [46] pseudopotentials were taken from a well-established and validated pseudopotential library (e.g., the PSLibrary provided with Quantum ESPRESSO), with explicit treatment of the valence electrons for K (3s²3p⁶4s¹), Zn (3d¹⁰4s²), and halogen atoms X = F, Cl, Br, and I (ns²np⁵) ensuring computational reproducibility, reliability, and accuracy of the results for KZnX₃ halide perovskites. The Generalized Gradient Approximation (GGA) in the Perdew–Burke–Ernzerhof functional (PBE) form of the exchange–correlation functional was used with ultrasoft pseudopotentials for structural optimization, mechanical analysis, and the evaluation of electronic and thermal properties [47]. Convergence tests indicated that a 60 Ry plane-wave cutoff energy and 10 × 10 × 8 Monkhorst–Pack k-point grid give well converged results, with the overall energies being 10⁻⁶ Ry. To obtain a more accurate description of the exchange–correlation effects, particularly for electronic and optical properties, the hybrid Heyd–Scuseria–Ernzerhof functional (HSE06) was also applied using norm-conserving pseudopotentials [48]. The energy strain method of the thermos-pw package [49,50] was used to estimate the elastic constants. The thermodynamic and dynamical stability of KZnX₃ were studied by the finite-displacement method of the Phonopy code [51,52]. Further, the frequency of phonons, matrices of the force constant and fine-scale vibrational features were calculated with density functional perturbation theory (DFPT) [53]. For these phonon calculations, a 2 × 2 × 2 supercell was constructed, and a reduced k-point grid of 4 × 4 × 4 together with a plane-wave cutoff energy of 40 Ry was employed to ensure computational efficiency while maintaining sufficient accuracy for lattice dynamical properties. In addition, the frequency-dependent optical properties, including the dielectric function, absorption coefficient, and optical conductivity, were calculated within the independent-particle approximation using the Kubo–Greenwood formalism as implemented in Quantum ESPRESSO.

4. Conclusions

In this study, a comprehensive first-principles investigation of the structural, mechanical, electronic, thermal, and optical properties of cubic perovskite KZnX₃ (X = F, Cl, Br, and I) compounds has been carried out using density functional theory. These materials are of considerable interest due to their tunable physical properties and potential applicability in future optoelectronic and energy-related technologies, highlighting the importance of reliable theoretical predictions to guide experimental efforts. The structural analysis indicates that all the KZnX₃ compounds crystallize in the cubic Pm-3m perovskite structure and have negative formation energy, and thus they are thermodynamically stable. The computed elastic constants and mechanical parameters obtained show that all compositions pass the Born stability criteria. Ductility indicators, including the Pugh ratio, Cauchy pressure, and Poisson’s ratio, consistently reveal a ductile nature across the series, with KZnI₃ exhibiting the highest ductility. Furthermore, deviations of the Zener anisotropy factor from unity indicate elastic anisotropy in all compounds. KZnF₃ has the highest Debye temperature among the analyzed materials, and these are the first reported Debye temperatures of KZnCl₃, KZnBr₃, and KZnI₃. Electronic band structure calculations of all KZnX₃ compounds show them to be indirect-band-gap semiconductors. The density of states and charge density studies have shown that the X-p and Zn-d states are the main contributors to the valence bands, and the Zn state is the main contributor to the conduction bands, together with potassium, which also makes a minimal contribution near the Fermi level, although, as it is known, its role is mainly ionic in nature. The Zn–X bonds exhibit a mixed ionic–covalent character, being strongest for F and weakest for I. Optical property analysis reveals a systematic enhancement in optical response from KZnF₃ to KZnI₃, manifested by an increasing dielectric constant, refractive index, absorption coefficient, and optical conductivity. While KZnF₃ remains transparent in the visible region, KZnCl₃, KZnBr₃, and KZnI₃ exhibit strong absorption at lower photon energies, making them promising candidates for optoelectronic and photovoltaic applications. It should be noted that in perovskites containing heavier halogens such as Br and I, relativistic effects, particularly spin–orbit coupling (SOC), can influence the electronic band structure and modify the band gap. Although SOC was not included in the present calculations, its consideration in future studies may provide a more accurate description of the electronic properties. Additionally, the use of heavier halogens may raise potential environmental and toxicity concerns; therefore, further studies on environmental safety and material stability are desirable for practical applications.

Overall, the results presented in this work provide valuable theoretical insight and are expected to stimulate further experimental investigations of KZnX₃ perovskite materials.