- NaHSO4(H2SO4)2 - NaHSO₄(H₂SO₄)₂

Theoretical atomic positions and lattice parameters at experimental volum from ICSD database; code 78764

Crystal Structure

Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.

Symmetry (experimental):

Space group:	2		P-1
Lattice parameters (Å):	5.0840	8.7460		11.7650
Angles (°):	68.86	88.44		88.97

Symmetry (theoretical):

Space group:	2		P-1
Lattice parameters (Å):	5.0366	9.0821		11.6358
Angles (°):	66.43	88.60		89.16

Cell contents:

Number of atoms:	42
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.8884	0.4658	0.3565
S:	0.1802	0.1924	0.2166
S:	0.3629	0.2374	0.5482
S:	0.3661	0.6303	0.1304
O:	0.1230	0.2289	0.0827
O:	0.0269	0.2919	0.2623
O:	0.1464	0.0189	0.2904
O:	0.4770	0.2191	0.2212
O:	0.5745	0.2773	0.4575
O:	0.1735	0.3622	0.5377
O:	0.4699	0.1794	0.6812
O:	0.2214	0.0931	0.5416
O:	0.5613	0.5056	0.1917
O:	0.1624	0.6544	0.2083
O:	0.5097	0.7887	0.0634
O:	0.2501	0.5862	0.0284
H:	0.5184	0.3367	0.2094
H:	0.6258	0.0997	0.6953
H:	0.0739	0.0468	0.6088
H:	0.6616	0.7828	0.0027
H:	0.0948	0.6628	0.9806
Na:	0.1116	0.5342	0.6435
S:	0.8198	0.8076	0.7834
S:	0.6371	0.7626	0.4518
S:	0.6339	0.3697	0.8696
O:	0.8770	0.7711	0.9173
O:	0.9731	0.7081	0.7377
O:	0.8536	0.9811	0.7096
O:	0.5230	0.7809	0.7788
O:	0.4255	0.7227	0.5425
O:	0.8265	0.6378	0.4623
O:	0.5301	0.8206	0.3188
O:	0.7786	0.9069	0.4584
O:	0.4387	0.4944	0.8083
O:	0.8376	0.3456	0.7917
O:	0.4903	0.2113	0.9366
O:	0.7499	0.4138	0.9716
H:	0.4816	0.6633	0.7906
H:	0.3742	0.9003	0.3047
H:	0.9261	0.9532	0.3912
H:	0.3384	0.2172	0.9973
H:	0.9052	0.3372	0.0194

Atom type

We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.

Visualization of the crystal structure:

You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crystallographic axis.
Please note that the structure is represented using the primitive cell, and not the conventional one.

Parameters of the Calculation

All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.

Number of electronic bands:	96
k-points
grid:	4 4 2
number of shifts:	1
shifts:	0.5 0.5 0.5
Kinetic energy cut-off:	40 Ha [=1088.464 eV ]
eXchange-Correlation functional:	LDA pw90

Pseudopotentials:
H:	hydrogen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
O:	oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
Na:	sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
S:	sulphur, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local

Dielectric Properties

We define:

The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.

Born effective charges (Z):

Na:	1.2047	0.0013	-0.0264
	-0.0985	1.1394	0.0743
	-0.0446	-0.0152	1.2006
Eig. Value:	1.2634	1.1122	1.1690
S:	2.8108	0.0163	0.0844
	0.4043	3.3208	-0.5352
	0.0028	-0.4331	3.8940
Eig. Value:	2.6902	3.1622	4.1733
S:	3.2086	0.1993	0.3197
	-0.0541	3.2256	-0.1959
	-0.0682	-0.2066	3.2453
Eig. Value:	3.2776	2.9561	3.4457
S:	3.1018	0.4872	-0.0320
	-0.2793	3.0680	-0.1859
	0.0257	-0.0685	3.3624
Eig. Value:	3.1615	2.9557	3.4150
O:	-1.4010	0.3091	-0.2055
	0.1177	-0.7777	0.0500
	-0.2612	-0.1397	-2.4973
Eig. Value:	-1.4266	-0.7045	-2.5449
O:	-1.0753	0.4564	0.1830
	0.2474	-1.3293	-0.1441
	0.1549	-0.1954	-1.0181
Eig. Value:	-0.8154	-1.6631	-0.9442
O:	-1.2141	0.1508	0.2602
	-0.0154	-1.8945	0.8897
	0.1839	1.0018	-1.5287
Eig. Value:	-1.2927	-2.6804	-0.6641
O:	-1.6365	-0.4757	0.0468
	-0.6071	-1.4079	0.1254
	0.0848	0.2509	-0.7604
Eig. Value:	-2.0972	-1.0087	-0.6989
O:	-1.2718	-0.0250	0.3414
	-0.0154	-0.7769	0.0774
	0.5223	0.0599	-1.3218
Eig. Value:	-0.8746	-0.7624	-1.7336
O:	-1.2268	0.4201	-0.0763
	0.5463	-1.5105	0.0454
	-0.0684	0.1133	-0.8559
Eig. Value:	-0.8693	-1.8833	-0.8405
O:	-1.2608	0.3052	-0.6939
	0.3947	-0.9767	0.1660
	-0.6946	0.2483	-1.5737
Eig. Value:	-0.9423	-0.6247	-2.2442
O:	-1.3638	-0.6541	0.3195
	-0.7602	-1.4500	0.3089
	0.3519	0.1842	-0.9689
Eig. Value:	-0.6677	-2.2470	-0.8681
O:	-1.1523	0.1074	-0.2298
	0.4560	-1.6786	0.4191
	-0.3568	0.5074	-1.0804
Eig. Value:	-1.0497	-2.0928	-0.7687
O:	-1.1811	0.1356	0.3354
	0.2802	-0.9021	-0.2158
	0.3958	-0.2184	-1.1600
Eig. Value:	-1.6560	-0.7785	-0.8087
O:	-1.3570	-0.3733	0.7288
	-0.2913	-1.0568	0.3501
	0.7581	0.2262	-1.3451
Eig. Value:	-2.2552	-0.8987	-0.6049
O:	-1.4025	-0.1078	-0.7255
	-0.0613	-0.8864	-0.2019
	-0.8063	-0.1287	-1.5664
Eig. Value:	-0.7005	-0.8770	-2.2780
H:	0.4775	0.3929	-0.0672
	0.2293	1.6752	-0.1816
	-0.0745	-0.3861	0.4637
Eig. Value:	0.4025	1.8145	0.3994
H:	1.0914	-0.6952	0.2099
	-0.7437	1.0618	-0.1922
	0.5359	-0.4656	0.4199
Eig. Value:	1.9566	0.3629	0.2535
H:	1.1468	0.1828	-0.7215
	0.5501	0.4291	-0.5439
	-0.6784	-0.1867	0.9972
Eig. Value:	1.9514	0.2483	0.3734
H:	1.1180	-0.3111	-0.7391
	-0.0788	0.3330	0.0796
	-0.8988	0.3758	1.1499
Eig. Value:	0.3238	0.2706	2.0065
H:	1.3833	-0.5220	0.6881
	-0.2209	0.3947	-0.1895
	0.9358	-0.5239	0.9437
Eig. Value:	2.1537	0.2169	0.3511
Na:	1.2047	0.0013	-0.0264
	-0.0985	1.1394	0.0743
	-0.0446	-0.0152	1.2006
Eig. Value:	1.2634	1.1122	1.1690
S:	2.8108	0.0163	0.0844
	0.4043	3.3208	-0.5352
	0.0028	-0.4331	3.8940
Eig. Value:	2.6902	3.1622	4.1733
S:	3.2086	0.1993	0.3197
	-0.0541	3.2256	-0.1959
	-0.0682	-0.2066	3.2453
Eig. Value:	3.2776	2.9561	3.4457
S:	3.1018	0.4872	-0.0320
	-0.2793	3.0680	-0.1859
	0.0257	-0.0685	3.3624
Eig. Value:	3.1615	2.9557	3.4150
O:	-1.4010	0.3091	-0.2055
	0.1177	-0.7777	0.0500
	-0.2612	-0.1397	-2.4973
Eig. Value:	-1.4266	-0.7045	-2.5449
O:	-1.0753	0.4564	0.1830
	0.2474	-1.3293	-0.1441
	0.1549	-0.1954	-1.0181
Eig. Value:	-0.8154	-1.6631	-0.9442
O:	-1.2141	0.1508	0.2602
	-0.0154	-1.8945	0.8897
	0.1839	1.0018	-1.5287
Eig. Value:	-1.2927	-2.6804	-0.6641
O:	-1.6365	-0.4757	0.0468
	-0.6071	-1.4079	0.1254
	0.0848	0.2509	-0.7604
Eig. Value:	-2.0972	-1.0087	-0.6989
O:	-1.2718	-0.0250	0.3414
	-0.0154	-0.7769	0.0774
	0.5223	0.0599	-1.3218
Eig. Value:	-0.8746	-0.7624	-1.7336
O:	-1.2268	0.4201	-0.0763
	0.5463	-1.5105	0.0454
	-0.0684	0.1133	-0.8559
Eig. Value:	-0.8693	-1.8833	-0.8405
O:	-1.2608	0.3052	-0.6939
	0.3947	-0.9767	0.1660
	-0.6946	0.2483	-1.5737
Eig. Value:	-0.9423	-0.6247	-2.2442
O:	-1.3638	-0.6541	0.3195
	-0.7602	-1.4500	0.3089
	0.3519	0.1842	-0.9689
Eig. Value:	-0.6677	-2.2470	-0.8681
O:	-1.1523	0.1074	-0.2298
	0.4560	-1.6786	0.4191
	-0.3568	0.5074	-1.0804
Eig. Value:	-1.0497	-2.0928	-0.7687
O:	-1.1811	0.1356	0.3354
	0.2802	-0.9021	-0.2158
	0.3958	-0.2184	-1.1600
Eig. Value:	-1.6560	-0.7785	-0.8087
O:	-1.3570	-0.3733	0.7288
	-0.2913	-1.0568	0.3501
	0.7581	0.2262	-1.3451
Eig. Value:	-2.2552	-0.8987	-0.6049
O:	-1.4025	-0.1078	-0.7255
	-0.0613	-0.8864	-0.2019
	-0.8063	-0.1287	-1.5664
Eig. Value:	-0.7005	-0.8770	-2.2780
H:	0.4775	0.3929	-0.0672
	0.2293	1.6752	-0.1816
	-0.0745	-0.3861	0.4637
Eig. Value:	0.4025	1.8145	0.3994
H:	1.0914	-0.6952	0.2099
	-0.7437	1.0618	-0.1922
	0.5359	-0.4656	0.4199
Eig. Value:	1.9566	0.3629	0.2535
H:	1.1468	0.1828	-0.7215
	0.5501	0.4291	-0.5439
	-0.6784	-0.1867	0.9972
Eig. Value:	1.9514	0.2483	0.3734
H:	1.1180	-0.3111	-0.7391
	-0.0788	0.3330	0.0796
	-0.8988	0.3758	1.1499
Eig. Value:	0.3238	0.2706	2.0065
H:	1.3833	-0.5220	0.6881
	-0.2209	0.3947	-0.1895
	0.9358	-0.5239	0.9437
Eig. Value:	2.1537	0.2169	0.3511

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.2097	0.0000	0.0000
	0.0000	2.1629	0.0000
	0.0000	0.0000	2.2083
Eig. Value:	2.2097	2.1629	2.2083
Refractive index (N):	1.4865	0.0000	0.0000
	0.0000	1.4707	0.0000
	0.0000	0.0000	1.4860
Eig. Value:	1.4865	1.4707	1.4860
Ɛ₀:	0.0000	0.0000	0.0000
	0.0000	0.0000	0.0000
	0.0000	0.0000	0.0000
Eig. Value:	0.0000	0.0000	0.0000

Powder Raman

Powder Raman spectrum

The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm^-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.

Choose the polarization of the lasers.

I ∥

I ⊥

I Total

Horizontal:

Xmin:
Xmax:

Vertical:

Ymin:
Ymax:

Data about the phonon modes

Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.

1	0	0	0	0
2	0	0	0	0
3	0	0	0	0
4	51	51	51	51	5.144e+38 0.7	4.961e+38 0.7	1.011e+39 1.4
5	53	53	53	53	8.448e+38 1.1	8.293e+38 1.1	1.674e+39 2.3
6	63	63	63	63	5.784e+38 0.8	3.687e+38 0.5	9.471e+38 1.3
7	64	64	64	64
8	65	65	65	65	1.166e+39 1.6	1.087e+39 1.5	2.253e+39 3.0
9	70	70	70	70
10	73	73	73	73	1.147e+39 1.5	9.581e+38 1.3	2.105e+39 2.8
11	78	78	78	78
12	83	83	83	83	5.500e+38 0.7	3.851e+38 0.5	9.351e+38 1.3
13	89	89	89	89	1.259e+39 1.7	1.133e+39 1.5	2.393e+39 3.2
14	90	90	90	90	1.639e+39 2.2	7.801e+38 1.1	2.419e+39 3.3
15	92	93	92	92
16	96	96	96	96	2.089e+38 0.3	2.924e+38 0.4	5.013e+38 0.7
17	98	98	98	99
18	100	100	100	100
19	106	107	106	106
20	109	109	109	109	3.308e+39 4.5	2.023e+39 2.7	5.331e+39 7.2
21	113	113	113	113	7.638e+38 1.0	7.490e+38 1.0	1.513e+39 2.0
22	116	116	116	116
23	120	120	120	120	4.754e+38 0.6	3.842e+38 0.5	8.597e+38 1.2
24	123	123	123	124
25	126	126	126	126	8.157e+38 1.1	7.417e+38 1.0	1.557e+39 2.1
26	133	135	133	134
27	139	139	139	139	1.365e+38 0.2	1.534e+38 0.2	2.899e+38 0.4
28	140	145	140	148
29	164	164	164	164	2.190e+38 0.3	2.398e+38 0.3	4.589e+38 0.6
30	168	169	177	169
31	179	180	180	180
32	180	181	180	182	4.400e+38 0.6	1.693e+38 0.2	6.093e+38 0.8
33	184	187	189	196
34	196	196	196	196	6.187e+38 0.8	9.578e+38 1.3	1.576e+39 2.1
35	206	206	206	206	5.471e+38 0.7	7.862e+38 1.1	1.333e+39 1.8
36	208	210	210	209
37	223	223	223	223	1.036e+39 1.4	1.178e+39 1.6	2.215e+39 3.0
38	227	232	229	227
39	232	242	232	232	7.611e+38 1.0	9.462e+38 1.3	1.707e+39 2.3
40	242	242	242	242	3.376e+38 0.5	2.572e+38 0.3	5.947e+38 0.8
41	242	250	243	245
42	257	261	266	262
43	387	387	387	388
44	388	388	388	389	1.853e+39 2.5	1.764e+39 2.4	3.617e+39 4.9
45	394	394	394	394	3.227e+39 4.4	2.210e+39 3.0	5.437e+39 7.3
46	394	394	394	395
47	402	402	402	402	1.674e+39 2.3	1.646e+39 2.2	3.320e+39 4.5
48	405	406	407	408
49	438	438	439	439
50	439	439	440	441	6.193e+39 8.4	9.794e+39 13.2	1.599e+40 21.6
51	442	442	442	442	6.408e+39 8.7	6.960e+39 9.4	1.337e+40 18.1
52	448	448	449	448
53	454	455	454	457
54	476	476	476	476	6.819e+39 9.2	7.533e+39 10.2	1.435e+40 19.4
55	536	536	536	537
56	537	537	537	538	3.962e+39 5.4	5.696e+39 7.7	9.659e+39 13.0
57	538	540	540	540
58	540	542	542	541	2.055e+39 2.8	2.906e+39 3.9	4.962e+39 6.7
59	543	544	544	544
60	544	544	544	545	3.967e+39 5.4	4.672e+39 6.3	8.639e+39 11.7
61	547	548	549	549
62	551	551	551	551	4.336e+39 5.9	2.200e+39 3.0	6.535e+39 8.8
63	553	553	553	553	5.027e+39 6.8	8.241e+39 11.1	1.327e+40 17.9
64	556	559	557	559
65	559	559	559	560	1.490e+39 2.0	1.469e+39 2.0	2.958e+39 4.0
66	564	567	565	565
67	567	567	567	567	5.563e+39 7.5	4.275e+39 5.8	9.838e+39 13.3
68	569	571	569	570
69	576	578	578	576
70	578	580	580	578	5.118e+39 6.9	4.308e+39 5.8	9.426e+39 12.7
71	600	610	600	600
72	610	611	610	610	3.519e+39 4.8	5.530e+39 7.5	9.049e+39 12.2
73	816	817	816	818
74	818	818	818	823	7.081e+38 1.0	1.220e+38 0.2	8.301e+38 1.1
75	836	839	837	837
76	839	841	839	839	3.135e+38 0.4	2.116e+38 0.3	5.250e+38 0.7
77	886	891	887	886
78	898	898	898	898
79	898	898	898	898	1.415e+40 19.1	4.189e+38 0.6	1.456e+40 19.7
80	904	904	904	904	2.001e+39 2.7	2.321e+38 0.3	2.233e+39 3.0
81	908	908	908	908	5.588e+39 7.5	3.277e+38 0.4	5.916e+39 8.0
82	914	914	914	915
83	915	916	917	917
84	917	917	919	919	1.300e+40 17.6	3.729e+38 0.5	1.337e+40 18.1
85	935	938	935	935
86	942	942	942	942	5.853e+40 79.1	4.057e+38 0.5	5.894e+40 79.6
87	957	957	957	957	4.883e+40 66.0	9.321e+38 1.3	4.976e+40 67.2
88	972	974	974	974
89	974	983	977	981
90	984	984	984	984	1.987e+39 2.7	7.782e+38 1.1	2.765e+39 3.7
91	990	997	993	991
92	1003	1003	1003	1003	5.891e+39 8.0	5.333e+38 0.7	6.424e+39 8.7
93	1015	1015	1015	1015	1.426e+39 1.9	3.820e+38 0.5	1.808e+39 2.4
94	1029	1041	1032	1029
95	1043	1043	1072	1072
96	1072	1072	1084	1116	1.009e+40 13.6	4.073e+39 5.5	1.416e+40 19.1
97	1148	1148	1148	1148	8.829e+39 11.9	1.858e+39 2.5	1.069e+40 14.4
98	1150	1151	1154	1169
99	1170	1170	1179	1173
100	1184	1184	1184	1184	1.329e+40 18.0	1.630e+39 2.2	1.492e+40 20.2
101	1228	1229	1228	1229
102	1234	1234	1234	1234	4.175e+39 5.6	2.832e+39 3.8	7.007e+39 9.5
103	1236	1236	1236	1236	1.001e+39 1.4	1.169e+39 1.6	2.170e+39 2.9
104	1239	1249	1239	1242
105	1267	1267	1268	1268
106	1270	1270	1270	1270	1.585e+39 2.1	7.530e+38 1.0	2.338e+39 3.2
107	1275	1275	1275	1275	1.029e+39 1.4	6.991e+38 0.9	1.728e+39 2.3
108	1277	1277	1277	1277
109	1300	1300	1300	1300
110	1300	1308	1308	1300	4.870e+39 6.6	2.474e+39 3.3	7.345e+39 9.9
111	1319	1319	1319	1319	2.329e+39 3.1	1.778e+39 2.4	4.107e+39 5.5
112	1319	1320	1321	1319
113	1341	1341	1341	1341	1.807e+39 2.4	1.134e+39 1.5	2.940e+39 4.0
114	1343	1347	1350	1349
115	1350	1358	1362	1358
116	1362	1362	1368	1362	2.303e+38 0.3	3.710e+38 0.5	6.013e+38 0.8
117	2272	2278	2275	2272
118	2278	2340	2278	2278	3.098e+40 41.9	4.304e+40 58.1	7.403e+40 100.0
119	2417	2417	2417	2417	5.322e+40 71.9	6.916e+39 9.3	6.013e+40 81.2
120	2489	2492	2545	2495
121	2558	2559	2559	2559
122	2559	2581	2567	2560	2.839e+40 38.3	4.491e+40 60.7	7.329e+40 99.0
123	2581	2596	2588	2596
124	2596	2644	2596	2666	1.229e+40 16.6	1.599e+40 21.6	2.828e+40 38.2
125	2788	2788	2788	2788	5.552e+40 75.0	5.360e+39 7.2	6.088e+40 82.2
126	2810	2811	2831	2821

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥

I Total

You can define the size of the supercell for the visualization of the vibration.

Normalized

Raw

Options for intensity.

Single Crystal Raman spectra

Single crystal Raman spectrum

The Raman measurements performed on single crystals employ polarized lasers and allow for the selection of specific elements of the individual Raman tensors of the Raman-active modes.

By convention, in the following we assume a measurement as X(XZ)Z, i.e. incident laser polarized along the X axis, emergent light polarized along the Z axis. If the crystal is aligned with the xyz reference frame, we sample the α_xz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.