Crystal structure and elastic and phonon properties of realgar versus pressure

Realgar, α-As₄S₄ (space group P2₁/n), is one of the best-known arsenic sulfide minerals because of its extended use in the past as a red pigment and its employment in modern times for advanced optical and electronic technological applications. From a geological perspective, the main realgar deposits are hydrothermal and epithermal, but it is also a relevant phase found between the upper mantle and Earth's crust and therefore one of the main sources of arsenic. Despite this widespread use and interest, few experimental and theoretical studies have been focused on the characterization of the structural, elastic and vibrational properties of realgar, especially their variation with pressure. Some quantities, such as the cohesive energy between the As₄S₄ units and the elastic moduli, have never been reported in the scientific literature. The present work deals with a density functional theory investigation of the cited properties of realgar using the recently proposed PBEh-3c method, which was devised in particular to deal with crystalline solids characterized by weak van der Waals interactions. This approach is validated against the available crystal-chemical, mechanical and spectroscopic data from previous studies, finding a generally good agreement. The equation-of-state parameters of the energy versus unit-cell volume data were V₀ = 767.13 (9) ų, B₀ = 15.73 (8) GPa and B′ = 9.1 (2), with the bulk modulus value (B₀) in good agreement with the value obtained from the elastic tensor analysis (B = 16.1 GPa). The cohesive energy was found to be about 146.1 kJ mol^–1, a value that follows the typical ones of organic crystals. The present work provides new insights into this peculiar mineral that, from a mineralogical point of view, could be considered a prototype of a heterodesmic structure made by inorganic molecular clusters.

Computing details

(realgar_00)

Crystal data

As16S16	c = 6.4508 (1) Å
Mr = 1711.71	β = 105.7711 (1)°
Monoclinic, P21/n	V = 768.73 Å^3
a = 9.2467 (1) Å	Dx = 0 Mg m^−3
b = 13.3918 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1202	0.0198	0.7625
As2	0.4294	0.8609	0.8702
As3	0.3218	0.8754	0.1924
As4	0.0438	0.8365	0.7212
S1	0.3467	0.0052	0.7020
S2	0.2113	0.0261	0.1202
S3	0.2472	0.7703	0.6523
S4	0.1086	0.7896	0.0659

(realgar_01)

Crystal data

As16S16	c = 6.1997 (1) Å
Mr = 1711.71	β = 106.0193 (1)°
Monoclinic, P21/n	V = 675.94 Å^3
a = 8.9463 (1) Å	Dx = 0 Mg m^−3
b = 12.6791 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1088	0.0253	0.7562
As2	0.4342	0.8649	0.8616
As3	0.3278	0.8754	0.1977
As4	0.0392	0.8323	0.7133
S1	0.3407	0.0151	0.6848
S2	0.2084	0.0329	0.1262
S3	0.2492	0.7663	0.6374
S4	0.1118	0.7808	0.0698

(realgar_02)

Crystal data

As16S16	c = 6.2785 (1) Å
Mr = 1711.71	β = 106.1564 (1)°
Monoclinic, P21/n	V = 703.02 Å^3
a = 9.0565 (1) Å	Dx = 0 Mg m^−3
b = 12.8723 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1123	0.0247	0.7576
As2	0.4314	0.8635	0.8621
As3	0.3256	0.8746	0.1940
As4	0.0395	0.8344	0.7124
S1	0.3420	0.0129	0.6898
S2	0.2094	0.0306	0.1245
S3	0.2468	0.7680	0.6382
S4	0.1100	0.7830	0.0650

(realgar_03)

Crystal data

As16S16	c = 6.3494 (1) Å
Mr = 1711.71	β = 105.9769 (1)°
Monoclinic, P21/n	V = 730.05 Å^3
a = 9.1443 (1) Å	Dx = 0 Mg m^−3
b = 13.0792 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1157	0.0227	0.7596
As2	0.4304	0.8624	0.8650
As3	0.3240	0.8749	0.1932
As4	0.0414	0.8352	0.7160
S1	0.3438	0.0098	0.6947
S2	0.2102	0.0287	0.1226
S3	0.2469	0.7688	0.6438
S4	0.1096	0.7857	0.0654

(realgar_04)

Crystal data

As16S16	c = 6.4220 (1) Å
Mr = 1711.71	β = 105.8238 (1)°
Monoclinic, P21/n	V = 757.76 Å^3
a = 9.2207 (1) Å	Dx = 0 Mg m^−3
b = 13.3008 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1190	0.0206	0.7617
As2	0.4296	0.8613	0.8686
As3	0.3224	0.8752	0.1926
As4	0.0432	0.8361	0.7197
S1	0.3459	0.0065	0.6999
S2	0.2109	0.0268	0.1209
S3	0.2471	0.7698	0.6499
S4	0.1090	0.7885	0.0658

(realgar_05)

Crystal data

As16S16	c = 6.4965 (1) Å
Mr = 1711.71	β = 105.6973 (1)°
Monoclinic, P21/n	V = 786.14 Å^3
a = 9.2824 (1) Å	Dx = 0 Mg m^−3
b = 13.5414 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1221	0.0184	0.7639
As2	0.4291	0.8603	0.8728
As3	0.3208	0.8757	0.1922
As4	0.0447	0.8372	0.7235
S1	0.3481	0.0032	0.7053
S2	0.2117	0.0249	0.1192
S3	0.2474	0.7710	0.6563
S4	0.1080	0.7915	0.0661

(realgar_06)

Crystal data

As16S16	c = 6.5723 (1) Å
Mr = 1711.71	β = 105.6052 (1)°
Monoclinic, P21/n	V = 815.17 Å^3
a = 9.3263 (1) Å	Dx = 0 Mg m^−3
b = 13.8080 (1) Å	T = 0 K

Data collection

h = →	l = →
k = →

Special details

Refinement. This is a realgar alpha-As4S4 crystal model belonging to the P2_1/n space group, calculated with periodic boundary conditions, using the Density Functional Theory and PBEh-3c hybryd functional, which includes both the DFT-D3 correction for long-range interactions and a geometrical counterpoise correction to remove the basis set superposition error (BSSE). Gaussian-type Orbitals (GTO) basis set have been used for each atom in the unit cell.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
As1	0.1248	0.0161	0.7662
As2	0.4290	0.8596	0.8774
As3	0.3194	0.8763	0.1921
As4	0.0458	0.8384	0.7272
S1	0.3504	0.9998	0.7109
S2	0.2124	0.0229	0.1175
S3	0.2478	0.7725	0.6631
S4	0.1068	0.7947	0.0666