Get fractional coordinates from special Wyckoff positions

Question

I'm trying to get the fractional coordinates for $\ce{Mo}$ and $\ce{MoS_2-2H}$ in $\ce{MoS_2-2H}$, where 2H is the phase. $\ce{MoS_2-2H}$ is a bilayer, in which each layer is separated from each other by Van der Waals forces. The $\ce{MoS_2-2H}$ belongs to the space group 194 (table continued, from International Tables of Crystallography pages 600 and 601) and is hexagonal.

As the unit cell contains two layers of $\ce{MoS_2}$, I believe that to find the fractional coordinates of each element, I need $\ce{Mo}$to be in a Wyckoff position with multiplicity 2 and $\ce{S}$ to be in a Wyckoff position with multiplicity 4. The problem is that there are several positions with this type of multiplicity (2a, 2b, 2c and 2d for $\ce{Mo}$; 4e and 4f for $\ce{S}$), but the crystal tends to acquire the most stable Wyckoff positions. How can I know which Wyckoff positions for $\ce{Mo}$ and $\ce{S}$ make the crystal stable?

I a passage in [1] that says it is necessary to calculate the bond length for each of the combinations. Once the bond length is calculated, how do I know which combination for Mo and S is most stable?

References:

1. Newnham, R. E. Structure-Property Relations. 1975. DOI: 10.1007/978-3-642-50017-6.

Answer 1

From that reference, what we got is the bond length from the atomic positions.

One easy way is to look for a CIF file with the crystal information.

From the CIF49801 bellow, we get the following info:

(label type_symbol symmetry_multiplicity Wyckoff_symbol fract_x fract_y fract_z B_iso_or_equiv occupancy)

    Mo1 Mo4+ 2 c 0.3333 0.6667 0.25     . 1.
    S1  S2-  4 f 0.3333 0.6667 0.621(3) . 1.

Whereas from the CIF84180, we get the following info:

    Mo1 Mo4+ 2 d 0.6667 0.3333 0.25     . 1.
    S1  S2-  4 f 0.3333 0.6667 0.120(1) . 1.

The full CIFs were obtained from the ICSD - Inorganic Crystal Structure Database.

CIF49801:

#(C) 2020 by FIZ Karlsruhe - Leibniz Institute for Information Infrastructure.  All rights reserved.
data_49801-ICSD
_database_code_ICSD 49801
_audit_creation_date 1987-01-31
_audit_update_record 2015-02-01
_chemical_name_common 'Molybdenum disulfide'
_chemical_formula_structural 'Mo S2'
_chemical_formula_sum 'Mo1 S2'
_chemical_name_structure_type MoS2(4H)
_chemical_name_mineral ''Molybdenite 2H''
_exptl_crystal_density_diffrn 5.
_citation_title 'On the Structure of Molybdenum Diselenide and Disulfide'
loop_
_citation_id
_citation_journal_full
_citation_year
_citation_journal_volume
_citation_page_first
_citation_page_last
_citation_journal_id_ASTM
primary 'Zeitschrift fuer Anorganische und Allgemeine Chemie (1950) (DE)' 1986
540 15 17 ZAACAB
loop_
_citation_author_citation_id
_citation_author_name
primary 'Bronsema, K.D.'
primary 'de Boer, J.L.'
primary 'Jellinek, F.'
_cell_length_a 3.16021
_cell_length_b 3.16021
_cell_length_c 12.294(4)
_cell_angle_alpha 90.
_cell_angle_beta 90.
_cell_angle_gamma 120.
_cell_volume 106.33
_cell_formula_units_Z 2
_space_group_name_H-M_alt 'P 63/m m c'
_space_group_IT_number 194
loop_
_space_group_symop_id
_space_group_symop_operation_xyz
1 'x, x-y, -z+1/2'
2 '-x+y, y, -z+1/2'
3 '-y, -x, -z+1/2'
4 '-x+y, -x, -z+1/2'
5 '-y, x-y, -z+1/2'
6 'x, y, -z+1/2'
7 '-x, -x+y, z+1/2'
8 'x-y, -y, z+1/2'
9 'y, x, z+1/2'
10 'x-y, x, z+1/2'
11 'y, -x+y, z+1/2'
12 '-x, -y, z+1/2'
13 '-x, -x+y, -z'
14 'x-y, -y, -z'
15 'y, x, -z'
16 'x-y, x, -z'
17 'y, -x+y, -z'
18 '-x, -y, -z'
19 'x, x-y, z'
20 '-x+y, y, z'
21 '-y, -x, z'
22 '-x+y, -x, z'
23 '-y, x-y, z'
24 'x, y, z'
loop_
_atom_type_symbol
_atom_type_oxidation_number
Mo4+ 4
S2- -2
loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_B_iso_or_equiv
_atom_site_occupancy
Mo1 Mo4+ 2 c 0.3333 0.6667 0.25 . 1.
S1 S2- 4 f 0.3333 0.6667 0.621(3) . 1.
#End of TTdata_49801-ICSD

and

CIF84180:

#(C) 2020 by FIZ Karlsruhe - Leibniz Institute for Information Infrastructure.  All rights reserved.
data_84180-ICSD
_database_code_ICSD 84180
_audit_creation_date 1999-01-19
_audit_update_record 2013-02-01
_chemical_name_common 'Molybdenum(IV) sulfide - 2H'
_chemical_formula_structural 'Mo S2'
_chemical_formula_sum 'Mo1 S2'
_chemical_name_structure_type MoS2(4H)
_chemical_name_mineral ''Molybdenite 2H''
_exptl_crystal_density_diffrn 5.
_citation_title

;
Characteristics of the crystal structure, electrophysical properties, and
model of the valence band spectrum of laminar compounds of molybdenum
disulfide type
;
loop_
_citation_id
_citation_journal_full
_citation_year
_citation_journal_volume
_citation_page_first
_citation_page_last
_citation_journal_id_ASTM
primary 'Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy' 1983 19 1060
1065 IVNMAW
loop_
_citation_author_citation_id
_citation_author_name
primary 'Kalikhman, V.L.'
_cell_length_a 3.16
_cell_length_b 3.16
_cell_length_c 12.29
_cell_angle_alpha 90.
_cell_angle_beta 90.
_cell_angle_gamma 120.
_cell_volume 106.28
_cell_formula_units_Z 2
_space_group_name_H-M_alt 'P 63/m m c'
_space_group_IT_number 194
loop_
_space_group_symop_id
_space_group_symop_operation_xyz
1 'x, x-y, -z+1/2'
2 '-x+y, y, -z+1/2'
3 '-y, -x, -z+1/2'
4 '-x+y, -x, -z+1/2'
5 '-y, x-y, -z+1/2'
6 'x, y, -z+1/2'
7 '-x, -x+y, z+1/2'
8 'x-y, -y, z+1/2'
9 'y, x, z+1/2'
10 'x-y, x, z+1/2'
11 'y, -x+y, z+1/2'
12 '-x, -y, z+1/2'
13 '-x, -x+y, -z'
14 'x-y, -y, -z'
15 'y, x, -z'
16 'x-y, x, -z'
17 'y, -x+y, -z'
18 '-x, -y, -z'
19 'x, x-y, z'
20 '-x+y, y, z'
21 '-y, -x, z'
22 '-x+y, -x, z'
23 '-y, x-y, z'
24 'x, y, z'
loop_
_atom_type_symbol
_atom_type_oxidation_number
Mo4+ 4
S2- -2
loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_B_iso_or_equiv
_atom_site_occupancy
Mo1 Mo4+ 2 d 0.6667 0.3333 0.25 . 1.
S1 S2- 4 f 0.3333 0.6667 0.120(1) . 1.
#End of TTdata_84180-ICSD