- H2SO4(H2O)4 - H₂SO₄(H₂O)₄

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported in ICSD database; code 2783

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:	114		P-421c
Lattice parameters (Å):	7.4840	7.4840		6.3490
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	114		P-421c
Lattice parameters (Å):	7.3924	7.3924		5.9960
Angles (°):	90.0	90.0		90.0

Cell contents:

Number of atoms:	38
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

S:	0.0000	0.0000	0.0000
O:	0.1362	0.0921	0.1390
O:	0.0618	0.3496	0.5753
H:	0.0035	0.2651	0.6854
H:	0.1954	0.3533	0.6085
H:	0.0000	0.5000	0.5831
O:	0.9079	0.1362	0.8610
O:	0.6504	0.0618	0.4247
H:	0.7349	0.0035	0.3146
H:	0.6467	0.1954	0.3915
H:	0.5000	0.0000	0.4169
S:	0.5000	0.5000	0.5000
O:	0.3638	0.5921	0.3610
O:	0.4382	0.8496	0.9247
H:	0.4965	0.7651	0.8146
H:	0.3046	0.8533	0.8915
H:	0.5000	0.0000	0.9169
O:	0.8638	0.9079	0.1390
O:	0.9382	0.6504	0.5753
H:	0.9965	0.7349	0.6854
H:	0.8046	0.6467	0.6085
O:	0.4079	0.3638	0.6390
O:	0.1504	0.4382	0.0753
H:	0.2349	0.4965	0.1854
H:	0.1467	0.3046	0.1085
H:	0.0000	0.5000	0.0831
O:	0.5921	0.6362	0.6390
O:	0.8496	0.5618	0.0753
H:	0.7651	0.5035	0.1854
H:	0.8533	0.6954	0.1085
O:	0.0921	0.8638	0.8610
O:	0.3496	0.9382	0.4247
H:	0.2651	0.9965	0.3146
H:	0.3533	0.8046	0.3915
O:	0.6362	0.4079	0.3610
O:	0.5618	0.1504	0.9247
H:	0.5035	0.2349	0.8146
H:	0.6954	0.1467	0.8915

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:	26
k-points
grid:	4 4 4
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
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):

S:	3.5325	0.0072	0.0000
	-0.0072	3.5325	0.0000
	0.0000	0.0000	3.2483
Eig. Value:	3.5325	3.5325	3.2483
O:	-1.5846	-0.3084	-0.7391
	-0.3334	-1.6140	-0.2122
	-0.6465	-0.2622	-1.3254
Eig. Value:	-0.7495	-2.3699	-1.4046
O:	-1.4049	0.2039	0.0794
	-0.0068	-1.5620	0.2464
	0.2770	0.2285	-0.8385
Eig. Value:	-1.4523	-1.6427	-0.7104
H:	0.4343	0.3068	-0.2364
	0.4480	0.9204	-0.5900
	-0.3338	-0.4952	0.8685
Eig. Value:	0.2280	1.6237	0.3715
H:	1.5517	0.0959	0.0686
	0.2107	0.2588	0.0512
	-0.1650	0.0292	0.3251
Eig. Value:	1.5712	0.2207	0.3437
H:	0.6285	-0.8565	0.0000
	-0.7355	1.8398	-0.0000
	-0.0000	0.0000	0.3165
Eig. Value:	0.2340	2.2343	0.3165
O:	-1.6140	0.3334	-0.2122
	0.3084	-1.5846	0.7391
	-0.2622	0.6465	-1.3254
Eig. Value:	-2.3699	-1.4046	-0.7495
O:	-1.5620	0.0068	0.2464
	-0.2039	-1.4049	-0.0794
	0.2285	-0.2770	-0.8385
Eig. Value:	-1.6427	-1.4523	-0.7104
H:	0.9204	-0.4480	-0.5900
	-0.3068	0.4343	0.2364
	-0.4952	0.3338	0.8685
Eig. Value:	1.6237	0.2280	0.3715
H:	0.2588	-0.2107	0.0512
	-0.0959	1.5517	-0.0686
	0.0292	0.1650	0.3251
Eig. Value:	0.2207	1.5712	0.3437
H:	1.8398	0.7355	0.0000
	0.8565	0.6285	-0.0000
	-0.0000	0.0000	0.3165
Eig. Value:	2.2343	0.2340	0.3165
S:	3.5325	-0.0072	-0.0000
	0.0072	3.5325	0.0000
	-0.0000	-0.0000	3.2483
Eig. Value:	3.5325	3.5325	3.2483
O:	-1.5846	0.3084	-0.7391
	0.3334	-1.6140	0.2122
	-0.6465	0.2622	-1.3254
Eig. Value:	-0.7495	-2.3699	-1.4046
O:	-1.4049	-0.2039	0.0794
	0.0068	-1.5620	-0.2464
	0.2770	-0.2285	-0.8385
Eig. Value:	-1.4523	-1.6427	-0.7104
H:	0.4343	-0.3068	-0.2364
	-0.4480	0.9204	0.5900
	-0.3338	0.4952	0.8685
Eig. Value:	0.2280	1.6237	0.3715
H:	1.5517	-0.0959	0.0686
	-0.2107	0.2588	-0.0512
	-0.1650	-0.0292	0.3251
Eig. Value:	1.5712	0.2207	0.3437
H:	0.6285	0.8565	-0.0000
	0.7355	1.8398	0.0000
	-0.0000	-0.0000	0.3165
Eig. Value:	0.2340	2.2343	0.3165
O:	-1.5846	-0.3084	0.7391
	-0.3334	-1.6140	0.2122
	0.6465	0.2622	-1.3254
Eig. Value:	-0.7495	-2.3699	-1.4046
O:	-1.4049	0.2039	-0.0794
	-0.0068	-1.5620	-0.2464
	-0.2770	-0.2285	-0.8385
Eig. Value:	-1.4523	-1.6427	-0.7104
H:	0.4343	0.3068	0.2364
	0.4480	0.9204	0.5900
	0.3338	0.4952	0.8685
Eig. Value:	0.2280	1.6237	0.3715
H:	1.5517	0.0959	-0.0686
	0.2107	0.2588	-0.0512
	0.1650	-0.0292	0.3251
Eig. Value:	1.5712	0.2207	0.3437
O:	-1.6140	-0.3334	0.2122
	-0.3084	-1.5846	0.7391
	0.2622	0.6465	-1.3254
Eig. Value:	-2.3699	-1.4046	-0.7495
O:	-1.5620	-0.0068	-0.2464
	0.2039	-1.4049	-0.0794
	-0.2285	-0.2770	-0.8385
Eig. Value:	-1.6427	-1.4523	-0.7104
H:	0.9204	0.4480	0.5900
	0.3068	0.4343	0.2364
	0.4952	0.3338	0.8685
Eig. Value:	1.6237	0.2280	0.3715
H:	0.2588	0.2107	-0.0512
	0.0959	1.5517	-0.0686
	-0.0292	0.1650	0.3251
Eig. Value:	0.2207	1.5712	0.3437
H:	1.8398	-0.7355	-0.0000
	-0.8565	0.6285	-0.0000
	-0.0000	0.0000	0.3165
Eig. Value:	2.2343	0.2340	0.3165
O:	-1.6140	-0.3334	-0.2122
	-0.3084	-1.5846	-0.7391
	-0.2622	-0.6465	-1.3254
Eig. Value:	-2.3699	-1.4046	-0.7495
O:	-1.5620	-0.0068	0.2464
	0.2039	-1.4049	0.0794
	0.2285	0.2770	-0.8385
Eig. Value:	-1.6427	-1.4523	-0.7104
H:	0.9204	0.4480	-0.5900
	0.3068	0.4343	-0.2364
	-0.4952	-0.3338	0.8685
Eig. Value:	1.6237	0.2280	0.3715
H:	0.2588	0.2107	0.0512
	0.0959	1.5517	0.0686
	0.0292	-0.1650	0.3251
Eig. Value:	0.2207	1.5712	0.3437
O:	-1.6140	0.3334	0.2122
	0.3084	-1.5846	-0.7391
	0.2622	-0.6465	-1.3254
Eig. Value:	-2.3699	-1.4046	-0.7495
O:	-1.5620	0.0068	-0.2464
	-0.2039	-1.4049	0.0794
	-0.2285	0.2770	-0.8385
Eig. Value:	-1.6427	-1.4523	-0.7104
H:	0.9204	-0.4480	0.5900
	-0.3068	0.4343	-0.2364
	0.4952	-0.3338	0.8685
Eig. Value:	1.6237	0.2280	0.3715
H:	0.2588	-0.2107	-0.0512
	-0.0959	1.5517	0.0686
	-0.0292	-0.1650	0.3251
Eig. Value:	0.2207	1.5712	0.3437
O:	-1.5846	0.3084	0.7391
	0.3334	-1.6140	-0.2122
	0.6465	-0.2622	-1.3254
Eig. Value:	-0.7495	-2.3699	-1.4046
O:	-1.4049	-0.2039	-0.0794
	0.0068	-1.5620	0.2464
	-0.2770	0.2285	-0.8385
Eig. Value:	-1.4523	-1.6427	-0.7104
H:	0.4343	-0.3068	0.2364
	-0.4480	0.9204	-0.5900
	0.3338	-0.4952	0.8685
Eig. Value:	0.2280	1.6237	0.3715
H:	1.5517	-0.0959	-0.0686
	-0.2107	0.2588	0.0512
	0.1650	0.0292	0.3251
Eig. Value:	1.5712	0.2207	0.3437

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.2975	0.0000	0.0000
	0.0000	2.2975	0.0000
	0.0000	0.0000	2.1051
Eig. Value:	2.2975	2.2975	2.1051
Refractive index (N):	1.5158	0.0000	0.0000
	0.0000	1.5158	0.0000
	0.0000	0.0000	1.4509
Eig. Value:	1.5158	1.5158	1.4509
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	34	34	34	34
5	34	34	34	34
6	69	69	69	69	4.969e+37 0.0	6.832e+37 0.0	1.180e+38 0.1
7	69	69	69	69	4.970e+37 0.0	6.833e+37 0.0	1.180e+38 0.1
8	69	70	70	69	3.583e+38 0.2	2.687e+38 0.1	6.270e+38 0.3
9	95	95	95	95	8.989e+38 0.5	1.236e+39 0.6	2.135e+39 1.1
10	95	95	95	95	8.990e+38 0.5	1.236e+39 0.6	2.135e+39 1.1
11	101	101	101	101	1.284e+37 0.0	1.766e+37 0.0	3.051e+37 0.0
12	101	101	101	101	1.284e+37 0.0	1.766e+37 0.0	3.050e+37 0.0
13	124	124	124	124	2.602e+38 0.1	3.578e+38 0.2	6.180e+38 0.3
14	124	126	126	124	2.602e+38 0.1	3.578e+38 0.2	6.180e+38 0.3
15	138	138	138	138	1.207e+38 0.1	2.612e+37 0.0	1.469e+38 0.1
16	141	141	141	141
17	160	160	160	160	1.296e+40 6.7	6.722e+37 0.0	1.302e+40 6.8
18	180	180	180	184
19	184	184	184	184	2.291e+39 1.2	3.151e+39 1.6	5.442e+39 2.8
20	184	184	184	187	2.291e+39 1.2	3.151e+39 1.6	5.442e+39 2.8
21	191	191	191	191	1.810e+38 0.1	1.358e+38 0.1	3.168e+38 0.2
22	213	213	213	213	4.072e+37 0.0	5.599e+37 0.0	9.671e+37 0.1
23	213	237	237	213	4.071e+37 0.0	5.598e+37 0.0	9.670e+37 0.1
24	244	244	244	244	3.537e+38 0.2	4.863e+38 0.3	8.400e+38 0.4
25	244	249	249	244	3.537e+38 0.2	4.863e+38 0.3	8.400e+38 0.4
26	250	250	250	250	3.508e+39 1.8	2.631e+39 1.4	6.139e+39 3.2
27	262	262	262	262
28	267	267	267	283	1.355e+39 0.7	1.864e+39 1.0	3.219e+39 1.7
29	286	286	286	286	3.775e+38 0.2	3.646e+37 0.0	4.139e+38 0.2
30	309	309	309	309	5.906e+38 0.3	8.121e+38 0.4	1.403e+39 0.7
31	309	310	310	309	5.906e+38 0.3	8.121e+38 0.4	1.403e+39 0.7
32	310	338	338	310
33	438	438	438	438
34	441	441	441	441	4.193e+39 2.2	3.092e+39 1.6	7.284e+39 3.8
35	488	488	488	488	4.709e+38 0.2	6.475e+38 0.3	1.118e+39 0.6
36	491	491	491	491	8.784e+39 4.6	6.588e+39 3.4	1.537e+40 8.0
37	583	583	583	583	3.018e+39 1.6	2.263e+39 1.2	5.281e+39 2.7
38	584	584	584	584	1.590e+39 0.8	2.187e+39 1.1	3.777e+39 2.0
39	584	586	586	584	1.590e+39 0.8	2.187e+39 1.1	3.777e+39 2.0
40	586	591	591	586	2.903e+39 1.5	3.991e+39 2.1	6.894e+39 3.6
41	620	620	620	620	1.052e+40 5.5	5.106e+38 0.3	1.103e+40 5.7
42	620	620	620	620	2.117e+39 1.1	2.911e+39 1.5	5.029e+39 2.6
43	620	625	625	620	2.117e+39 1.1	2.911e+39 1.5	5.029e+39 2.6
44	625	630	630	625
45	630	632	632	632	2.694e+37 0.0	3.704e+37 0.0	6.399e+37 0.0
46	632	636	636	634	2.277e+38 0.1	1.707e+38 0.1	3.984e+38 0.2
47	695	695	695	695	2.133e+38 0.1	2.933e+38 0.2	5.065e+38 0.3
48	695	696	696	695	2.133e+38 0.1	2.933e+38 0.2	5.065e+38 0.3
49	696	706	706	696
50	714	714	714	714	2.124e+36 0.0	1.593e+36 0.0	3.717e+36 0.0
51	724	724	724	724	2.542e+39 1.3	1.190e+38 0.1	2.661e+39 1.4
52	727	727	727	727	1.368e+38 0.1	1.881e+38 0.1	3.249e+38 0.2
53	727	732	732	727	1.368e+38 0.1	1.881e+38 0.1	3.249e+38 0.2
54	744	744	744	746	3.124e+37 0.0	4.296e+37 0.0	7.420e+37 0.0
55	779	779	779	779	4.009e+38 0.2	5.512e+38 0.3	9.521e+38 0.5
56	779	780	780	779	4.009e+38 0.2	5.512e+38 0.3	9.521e+38 0.5
57	798	798	798	798	4.173e+38 0.2	5.738e+38 0.3	9.910e+38 0.5
58	798	798	798	798	4.173e+38 0.2	5.738e+38 0.3	9.910e+38 0.5
59	812	812	812	812
60	835	835	835	844	4.147e+37 0.0	5.703e+37 0.0	9.850e+37 0.1
61	844	844	844	849
62	851	851	851	851	1.289e+38 0.1	2.184e+36 0.0	1.311e+38 0.1
63	879	879	879	879	1.345e+39 0.7	1.849e+39 1.0	3.194e+39 1.7
64	879	880	880	879	1.345e+39 0.7	1.849e+39 1.0	3.194e+39 1.7
65	890	890	890	890	6.786e+38 0.4	9.331e+38 0.5	1.612e+39 0.8
66	890	891	891	890	6.787e+38 0.4	9.332e+38 0.5	1.612e+39 0.8
67	953	953	953	955	7.511e+36 0.0	1.033e+37 0.0	1.784e+37 0.0
68	955	955	955	955	4.211e+39 2.2	5.790e+39 3.0	1.000e+40 5.2
69	955	964	964	964	4.211e+39 2.2	5.790e+39 3.0	1.000e+40 5.2
70	964	970	970	971	2.359e+40 12.3	7.901e+37 0.0	2.367e+40 12.3
71	971	971	971	971
72	974	974	974	974	3.811e+37 0.0	2.858e+37 0.0	6.668e+37 0.0
73	984	984	984	984
74	993	993	993	993	6.234e+40 32.4	1.052e+38 0.1	6.244e+40 32.5
75	1073	1073	1073	1083	6.139e+38 0.3	8.441e+38 0.4	1.458e+39 0.8
76	1083	1083	1083	1083	1.702e+37 0.0	2.341e+37 0.0	4.043e+37 0.0
77	1083	1086	1086	1090	1.702e+37 0.0	2.340e+37 0.0	4.042e+37 0.0
78	1090	1090	1090	1090	2.206e+38 0.1	3.033e+38 0.2	5.239e+38 0.3
79	1090	1097	1097	1097	2.206e+38 0.1	3.033e+38 0.2	5.239e+38 0.3
80	1097	1252	1252	1115	4.392e+37 0.0	3.294e+37 0.0	7.685e+37 0.0
81	1263	1263	1263	1263	2.905e+39 1.5	9.060e+37 0.0	2.995e+39 1.6
82	1265	1265	1265	1314	3.069e+38 0.2	4.220e+38 0.2	7.289e+38 0.4
83	1320	1320	1320	1320	3.219e+38 0.2	4.427e+38 0.2	7.646e+38 0.4
84	1320	1339	1339	1320	3.219e+38 0.2	4.427e+38 0.2	7.646e+38 0.4
85	1339	1339	1339	1339
86	1339	1400	1400	1339	1.433e+38 0.1	1.075e+38 0.1	2.508e+38 0.1
87	1621	1621	1621	1621	1.027e+39 0.5	1.412e+39 0.7	2.438e+39 1.3
88	1621	1626	1626	1621	1.027e+39 0.5	1.412e+39 0.7	2.438e+39 1.3
89	1634	1634	1634	1634	6.717e+38 0.3	2.597e+38 0.1	9.314e+38 0.5
90	1658	1658	1658	1658	3.446e+38 0.2	4.739e+38 0.2	8.185e+38 0.4
91	1658	1658	1658	1658	3.446e+38 0.2	4.739e+38 0.2	8.185e+38 0.4
92	1658	1672	1672	1658	3.850e+38 0.2	2.888e+38 0.2	6.738e+38 0.4
93	1672	1701	1701	1677	3.452e+38 0.2	4.747e+38 0.2	8.199e+38 0.4
94	1701	1701	1701	1701
95	1708	1708	1708	1708	3.847e+36 0.0	5.290e+36 0.0	9.137e+36 0.0
96	1708	1715	1715	1708	3.847e+36 0.0	5.290e+36 0.0	9.136e+36 0.0
97	1722	1722	1722	1722	1.778e+37 0.0	2.445e+37 0.0	4.223e+37 0.0
98	1722	1732	1732	1722	1.778e+37 0.0	2.445e+37 0.0	4.224e+37 0.0
99	2899	2899	2899	2899	1.264e+40 6.6	9.468e+39 4.9	2.210e+40 11.5
100	2901	2901	2901	2901	9.709e+39 5.1	1.335e+40 6.9	2.306e+40 12.0
101	2901	2902	2902	2901	9.709e+39 5.1	1.335e+40 6.9	2.306e+40 12.0
102	2902	2960	2960	2902	4.649e+40 24.2	3.487e+40 18.1	8.136e+40 42.3
103	2984	2984	2984	2984	7.553e+37 0.0	1.038e+38 0.1	1.794e+38 0.1
104	2984	2986	2986	2984	7.552e+37 0.0	1.038e+38 0.1	1.794e+38 0.1
105	2986	2989	2989	3010	1.837e+39 1.0	2.526e+39 1.3	4.363e+39 2.3
106	3010	3010	3010	3010	8.764e+39 4.6	1.205e+40 6.3	2.081e+40 10.8
107	3010	3013	3013	3013	8.764e+39 4.6	1.205e+40 6.3	2.081e+40 10.8
108	3013	3028	3028	3015
109	3041	3041	3041	3041	5.264e+39 2.7	7.238e+39 3.8	1.250e+40 6.5
110	3041	3052	3052	3041	5.264e+39 2.7	7.238e+39 3.8	1.250e+40 6.5
111	3052	3073	3073	3052	2.832e+39 1.5	2.124e+39 1.1	4.956e+39 2.6
112	3073	3126	3126	3126	9.571e+39 5.0	1.316e+40 6.8	2.273e+40 11.8
113	3126	3132	3132	3139	1.905e+41 99.1	1.737e+39 0.9	1.922e+41 100.0
114	3158	3158	3158	3158

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.