"Investigation of the elastic properties of zinc sulfide Material Using Quantum-
Chemical Programs"

Abstract:

Purpose of the research work: Determining the elastic properties of a material through quantum
chemical modeling. The relevance of applying quantum chemical modeling as an alternative to the
experimental method in the era of technology, in which various new materials are being developed in
the 21st century, is increasing every year (Bauer et al., 2020). Of course, in laboratories, the
importance of an empirical method of research carried out by human hands is not excluded. However,
with the development of technology, the use of various applications in research has a number of
advantages. One of them is the ability to quickly study the physical and chemical properties of
materials and achieve results with high accuracy, creating various extreme situations (high
temperature, pressure, etc.). In addition, another advantage of using such programs is economically
less costly and safe in the study of radioactive elements. The object of the study was ZnS (zinc
sulfide), depending on the variety of physical properties and variability of the state of the
environment. Studying the properties of selected object -zinc sulfide- using a quantum chemical
program, we found a change in its physical properties at extreme pressure. We have seen that a brittle
material with high hardness can now be used to create a wide range of applied tools, forming a strong
crystal. At the same time, we observed a change in the electrical conductivity of the object. Change
in electrical conductivity properties, practical coincidence with the theoretically provided physical
properties of the object, showed the reliability of the research work.

 

Introduction:

Today, zinc sulfide (ZnS) is widely used in high-tech industries such as electronics, photonics, sensors
and quantum devices, so it is necessary to take into account the mechanical characteristics of the
material to increase the efficiency and strength of the ZnS material devices used. ZnS is a compound
with high transparency and semiconductor properties in a wide range of wavelengths, therefore it is
an object of interest in the creation of new optoelectronic devices. ZnS belongs to the class of simple
binary compounds, depending on the type of bond and in composition to the class of sulfides. This
compound was formed in two main crystalline structures - cubic (sphalerite) and hexagonal
(wurtzite), that is, a class of ionic crystals. The elastic properties of the class of sulfides depend on
their crystal structure, interatomic bonds and internal symmetry, therefore, knowledge of these
properties allows optimizing materials for various industrial and technological applications, and
therefore various studies are carried out in the world of science. In research methods, one of the
scientists resorts to experiments, and the other works in non-empirical directions.

 

Literature Review:

The continuous development of new functional materials in the 21st century necessitates efficient and

accurate methods for investigating their structural, electronic, and mechanical properties. Quantum-
chemical modeling, particularly based on Density Functional Theory (DFT) and Hartree-Fock (HF)

approximations, has become a powerful alternative to experimental techniques, offering predictive

insights into material behavior under varying physical conditions. The foundations of quantum-
mechanical modeling of solids are illustrated in the early works by Catti, Valerio, and Dovesi (1995),

who conducted theoretical studies on the structural and magnetic properties of hematite (α-Fe2O3)
using periodic HF (Hartree-Fock ) methods. These studies demonstrated the applicability of quantum
mechanical approaches to complex oxide systems and laid the groundwork for further applications to
semiconductors and sulfides. Lichanot et al. (1993) further applied Hartree-Fock calculations to study
the elastic properties of Li2S and Na2S, highlighting the capability of ab initio methods in capturing
interatomic forces and lattice dynamics in binary ionic crystals. Their methodology is relevant to
current research on ZnS due to the similar sulfide nature and the emphasis on elastic behavior. In the
context of zinc sulfide (ZnS), numerous studies have explored its tunable electronic properties.
Homann et al. (2006) investigated the composition-dependent band gap in mixed crystals of ZnSxSe1−x

3 through a combination of experimental and theoretical methods, revealing how quantum-chemical
modeling can complement empirical data to predict optical and electronic behavior. Maslyuk et al.
(2006) also employed quantum mechanical approaches to study surface adsorption processes, further
demonstrating the versatility of such tools in describing surface reactivity and interaction in inorganic
systems like MgSO4·H2O. Historical insights into the physical properties of ZnS can be traced back
to Davis and Lind (1967), who examined the properties of mixed CdS-ZnS crystals. Their early
empirical observations serve as a benchmark for validating modern theoretical predictions derived
from DFT and HF computations. The CRYSTAL program, used in this research (CRYSTAL23
version), has been extensively validated for calculating electronic structures and elastic constants
using Gaussian-type orbitals in periodic systems. Its basis set library enables precise simulations of
lattice and band structure properties, which is particularly useful for materials like ZnS with cubic
and hexagonal polymorphs. Additionally, more recent reviews emphasize the future potential of
integrating quantum computing into quantum-chemical modeling. Bauer et al. (2020) discussed how
quantum algorithms can be applied to solve problems in quantum chemistry and materials science,
pointing to the next frontier in computational modeling where even more accurate simulations of
large systems may become feasible. Supporting this transition, comprehensive databases and
theoretical reviews, such as those found in (Fang et al., 2010) and (Davis & Lind, 1968) have
consolidated decades of work on DFT modeling for solid-state materials, providing a foundational
framework for the ongoing research on ZnS.

 

Research Method:​ 

In work, we used the CRYSTAL23 software package to find out how the elastic properties of zinc
sulfide change under increased pressure. This package of programs is based on the functional theory
of density (FPG).In the study, 5 different density functional methods, B3LYP, B3PW, HSE06, PBE
and PWGGA were calculated. First step, using five TFT methods, we determined the parameters of
the cubic crystal grid. The parameters of the grid (a, b, c) with the transmission of Å in angstrom are
the same for all functions, equal to 3.83251875 Å. This indicates the fluidity of the structure under
consideration, taking into account that all grid sites are the same. Total energy values in units of
Energy (Etot * 10 ^ 3 Hartree), Hartree vary slightly depending on functionality.These minor
deviations are due to the difference in the applied exchange-correlation functions affecting the
modeling of electron interactions. Knowing this value, we can investigate the conductivity of the
electric current of a substance,which is very important when studying the electronic structure. In 2
nd step, performed optimization in the calculation of grid parameters, especially in DFT (density theory)
methods to achieve the best configuration of a molecule or crystal grid with minimum energy. This
allows us to find the most stable geometry of the system, at which the energy of the potential surface
reaches a minimum. This is very important for accurate modeling of the properties of molecules or
materials. Correct geometry affects the computation of properties such as spectra, reactions, and
interactions. Incorrect geometry can lead to incorrect results. Thus, optimization is an important step
in TFT (DFT) calculations and other quantum chemistry methods that ensure the accuracy and
reliability of the results. The next step in investigating the physical properties of ZnS was the effect
of high pressure on the crystal network. Taken elasticity coefficients C11, C12, C44 results describe
longitudinal, transverse elongation and displacement, respectively. The correctness of the obtained
values of elastic constants can be checked by fulfilling the following conditions. C44 is a shear
modulus that describes how a material responds to in-plane shear loads (eg, in the xy plane). This is
important for the analysis of the deformation of materials under the influence of shear.To evaluate the
mechanical behavior of the ZnS crystal under varying pressure conditions, we calculated several key
elastic parameters, including the bulk modulus (B), shear modulus (G), and Young’s modulus (E). To
observe how the crystal volume changes with pressure, the relative length (da/a) and volume (dV/V)
was plotted against the corresponding pressure values. From this graph, the gradient of the curve
was used to estimate the shear modulus (G), which describes the material’s ability to resist shape
changes under shear stress. In addition, Young’s modulus (E) was calculated to assess the material's

4 stiffness under uniaxial tension or compression. This parameter helps characterize the extent to which
the material deforms linearly under stress. Together, the analysis of these three module allows us to
assess how the internal bonding forces and crystal structure respond to increasing external
pressure. Monitoring the variation of these parameters provides insights into the elastic
strengthening or softening of the material, and helps determine its suitability for use in high-pressure
environments.

 

Conclusion:

In this work, the elastic properties of ZnS material were studied using the B3LYP, B3PW, HSE06,
LDA, PBE, PBESOL, PWGGA, SC pseudopotentials within the density functional theory (DFT)
framework using the CRYSTAL23 quantum software package. The results obtained during the
calculation of the structure of the ZnS system coincide with the values given in experimental and
theoretical studies and prove that the basic assumptions are correctly chosen. It was also found that
there is a strong coupling between the S-3p and Zn-4s/4d orbitals, which dominate the electronic
structure in the compounds. The values of elastic constants (C11, C12, C44), bulk modulus, Young's
modulus, shear modulus and crystal lattice parameters were calculated using the Voigt-Royce Hill
approximation. The results showed that cubic ZnS has a high bulk modulus, which indicates its good
resistance to deformation. According to the calculation results, ZnS is determined as an elastic
material. The value of Poisson's ratio V obtained in our calculations varies from 0.284 to 0.321, which
proves that the proportion of ionic bonds in the interatomic bonding for these compounds is high.
When calculating the density of states of the system using the B3LYP method to determine its
electronic structure, an analysis of its composition revealed that zinc sulfide is a semiconductor, but
becomes a dielectric with increasing pressure. This property indicates its potential for widespread use
in the fields of electronics (computer components), energy, and telecommunications (fiber optics).

​

References :

Bauer, B., Bravyi, S., Motta, M., & Chan, G. K. (2020). Quantum algorithms for quantum
chemistry and quantum Materials science. Chemical Reviews, 120(22), 12685–12717.
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Catti, M., Valerio, G., & Dovesi, R. (1995). Theoretical study of electronic, magnetic, and structural
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https://doi.org/10.1103/physrevb.51.7441

Davis, E. A., & Lind, E. L. (1967). Physical properties of mixed crystals of CdS and ZnS. Journal
of Physics and Chemistry of Solids, 28(7), 1365–1375.

Fang, X., Zhai, T., Gautam, U. K., Li, L., Wu, L., Bando, Y., & Golberg, D. (2011). ZnS
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Homann, T., Hotje, U., Binnewies, M., Börger, A., Becker, K., & Bredow, T. (2005). Composition-
dependent band gap in ZnSxSe1−x: a combined experimental and theoretical study. Solid

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Lichanot, A., Aprà, E., & Dovesi, R. (1993). Quantum Mechnical Hartree‐Fock study of the elastic
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