- NAHCOLITE - NaHCO₃

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 AMCSD

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:	14		P2_1/a
Lattice parameters (Å):	15.1920	5.6290		3.7067
Angles (°):	90.0	104.5		90.0

Symmetry (theoretical):

Space group:	14		P2_1/a
Lattice parameters (Å):	13.9538	5.1174		3.1309
Angles (°):	90.0	103.3		90.0

Cell contents:

Number of atoms:	24
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.1678	0.0302	0.2806
C:	0.1270	0.5381	0.8642
H:	0.0058	0.7100	0.5122
O:	0.2069	0.5673	0.1328
O:	0.0781	0.7519	0.7071
O:	0.0898	0.3168	0.7385
Na:	0.3322	0.5302	0.7194
C:	0.3730	0.0381	0.1358
H:	0.4942	0.2100	0.4878
O:	0.2931	0.0673	0.8672
O:	0.4219	0.2519	0.2929
O:	0.4102	0.8168	0.2615
Na:	0.8322	0.9698	0.7194
C:	0.8730	0.4619	0.1358
H:	0.9942	0.2900	0.4878
O:	0.7931	0.4327	0.8672
O:	0.9219	0.2481	0.2929
O:	0.9102	0.6832	0.2615
Na:	0.6678	0.4698	0.2806
C:	0.6270	0.9619	0.8642
H:	0.5058	0.7900	0.5122
O:	0.7069	0.9327	0.1328
O:	0.5781	0.7481	0.7071
O:	0.5898	0.1832	0.7385

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:	1 4 6
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:
Na:	sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
C:	carbon, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
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

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:	1.0842	0.0365	0.0044
	-0.0338	1.2081	0.0035
	0.0242	0.0374	1.0326
Eig. Value:	1.0875	1.2106	1.0268
C:	1.8541	0.0851	1.2411
	0.0155	2.1991	0.0516
	1.2219	0.1040	1.9025
Eig. Value:	0.6464	2.1903	3.1190
H:	1.4808	0.2115	0.7780
	0.1536	0.3068	0.1042
	0.8137	0.1590	0.9514
Eig. Value:	2.0833	0.2783	0.3774
O:	-1.5980	-0.1223	-0.7105
	-0.1241	-0.8582	-0.1087
	-0.7683	-0.1143	-1.5325
Eig. Value:	-2.3241	-0.8408	-0.8238
O:	-1.4452	0.3014	-0.7187
	0.2465	-1.2997	0.2695
	-0.7005	0.2731	-1.1943
Eig. Value:	-2.2037	-1.1380	-0.5975
O:	-1.3759	-0.4783	-0.5944
	-0.2974	-1.5561	-0.3324
	-0.5910	-0.4306	-1.1598
Eig. Value:	-1.1513	-2.2782	-0.6623
Na:	1.0842	-0.0365	0.0044
	0.0338	1.2081	-0.0035
	0.0242	-0.0374	1.0326
Eig. Value:	1.0875	1.2106	1.0268
C:	1.8541	-0.0851	1.2411
	-0.0155	2.1991	-0.0516
	1.2219	-0.1040	1.9025
Eig. Value:	0.6464	2.1903	3.1190
H:	1.4808	-0.2115	0.7780
	-0.1536	0.3068	-0.1042
	0.8137	-0.1590	0.9514
Eig. Value:	2.0833	0.2783	0.3774
O:	-1.5980	0.1223	-0.7105
	0.1241	-0.8582	0.1087
	-0.7683	0.1143	-1.5325
Eig. Value:	-2.3241	-0.8408	-0.8238
O:	-1.4452	-0.3014	-0.7187
	-0.2465	-1.2997	-0.2695
	-0.7005	-0.2731	-1.1943
Eig. Value:	-2.2037	-1.1380	-0.5975
O:	-1.3759	0.4783	-0.5944
	0.2974	-1.5561	0.3324
	-0.5910	0.4306	-1.1598
Eig. Value:	-1.1513	-2.2782	-0.6623
Na:	1.0842	0.0365	0.0044
	-0.0338	1.2081	0.0035
	0.0242	0.0374	1.0326
Eig. Value:	1.0875	1.2106	1.0268
C:	1.8541	0.0851	1.2411
	0.0155	2.1991	0.0516
	1.2219	0.1040	1.9025
Eig. Value:	0.6464	2.1903	3.1190
H:	1.4808	0.2115	0.7780
	0.1536	0.3068	0.1042
	0.8137	0.1590	0.9514
Eig. Value:	2.0833	0.2783	0.3774
O:	-1.5980	-0.1223	-0.7105
	-0.1241	-0.8582	-0.1087
	-0.7683	-0.1143	-1.5325
Eig. Value:	-2.3241	-0.8408	-0.8238
O:	-1.4452	0.3014	-0.7187
	0.2465	-1.2997	0.2695
	-0.7005	0.2731	-1.1943
Eig. Value:	-2.2037	-1.1380	-0.5975
O:	-1.3759	-0.4783	-0.5944
	-0.2974	-1.5561	-0.3324
	-0.5910	-0.4306	-1.1598
Eig. Value:	-1.1513	-2.2782	-0.6623
Na:	1.0842	-0.0365	0.0044
	0.0338	1.2081	-0.0035
	0.0242	-0.0374	1.0326
Eig. Value:	1.0875	1.2106	1.0268
C:	1.8541	-0.0851	1.2411
	-0.0155	2.1991	-0.0516
	1.2219	-0.1040	1.9025
Eig. Value:	0.6464	2.1903	3.1190
H:	1.4808	-0.2115	0.7780
	-0.1536	0.3068	-0.1042
	0.8137	-0.1590	0.9514
Eig. Value:	2.0833	0.2783	0.3774
O:	-1.5980	0.1223	-0.7105
	0.1241	-0.8582	0.1087
	-0.7683	0.1143	-1.5325
Eig. Value:	-2.3241	-0.8408	-0.8238
O:	-1.4452	-0.3014	-0.7187
	-0.2465	-1.2997	-0.2695
	-0.7005	-0.2731	-1.1943
Eig. Value:	-2.2037	-1.1380	-0.5975
O:	-1.3759	0.4783	-0.5944
	0.2974	-1.5561	0.3324
	-0.5910	0.4306	-1.1598
Eig. Value:	-1.1513	-2.2782	-0.6623

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.4459	0.0000	0.3668
	0.0000	2.3353	0.0000
	0.3668	0.0000	2.3961
Eig. Value:	2.7886	2.3353	2.0533
Refractive index (N):	1.5639	-0.0000	0.6056
	-0.0000	1.5282	-0.0000
	0.6056	-0.0000	1.5479
Eig. Value:	1.6699	1.5282	1.4329
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	ac	0	0	0	0
2	ac	0	0	0	0
3	ac	0	0	0	0
4	Ag	35	35	35	35	2.500e+39 3.5	2.026e+39 2.8	4.526e+39 6.4
5	Bg	56	56	56	56	2.014e+37 0.0	3.397e+37 0.0	5.411e+37 0.1
6	Bu	89	89	89	89
7	Au	94	94	94	94
8	Bg	105	105	105	105	1.111e+40 15.6	1.814e+40 25.5	2.925e+40 41.1
9	Ag	109	109	109	109	5.662e+38 0.8	3.944e+38 0.6	9.606e+38 1.3
10	Au	122	122	126	122
11	Ag	126	126	127	126	4.025e+38 0.6	3.077e+37 0.0	4.333e+38 0.6
12	Ag	132	132	132	132	9.799e+38 1.4	8.019e+38 1.1	1.782e+39 2.5
13	Bg	134	134	134	134	5.930e+39 8.3	9.459e+39 13.3	1.539e+40 21.6
14	Bu	138	138	138	138
15	Ag	139	139	139	139	6.395e+37 0.1	4.808e+37 0.1	1.120e+38 0.2
16	Ag	139	139	141	139	1.429e+39 2.0	1.074e+39 1.5	2.504e+39 3.5
17	Au	149	149	150	149
18	Bg	150	150	151	150	2.779e+38 0.4	3.154e+38 0.4	5.933e+38 0.8
19	Bu	159	177	159	164
20	Bg	182	182	182	182	5.299e+37 0.1	5.890e+37 0.1	1.119e+38 0.2
21	Au	187	187	187	187
22	Bg	187	187	191	187	5.388e+38 0.8	6.122e+38 0.9	1.151e+39 1.6
23	Bu	191	204	210	192
24	Ag	210	210	211	210	1.547e+39 2.2	9.188e+38 1.3	2.466e+39 3.5
25	Bu	211	213	213	213
26	Au	213	218	228	214
27	Au	230	230	235	230
28	Ag	235	235	240	235	9.539e+39 13.4	6.818e+39 9.6	1.636e+40 23.0
29	Bg	240	240	249	240	1.999e+38 0.3	2.671e+38 0.4	4.670e+38 0.7
30	Bu	249	256	256	256
31	Ag	256	256	256	256	1.884e+39 2.6	1.815e+39 2.6	3.699e+39 5.2
32	Ag	256	281	264	277	3.104e+39 4.4	2.181e+39 3.1	5.285e+39 7.4
33	Ag	299	299	299	299	4.361e+38 0.6	4.260e+38 0.6	8.620e+38 1.2
34	Bg	328	328	328	328	1.051e+39 1.5	1.119e+39 1.6	2.170e+39 3.0
35	Au	333	333	333	333
36	Bu	339	348	339	348
37	Ag	634	634	634	634	1.111e+40 15.6	8.767e+39 12.3	1.988e+40 27.9
38	Bg	638	638	638	638	1.026e+39 1.4	1.095e+39 1.5	2.121e+39 3.0
39	Ag	685	685	685	685	6.850e+39 9.6	1.538e+39 2.2	8.388e+39 11.8
40	Bg	688	688	688	688	1.092e+39 1.5	1.199e+39 1.7	2.291e+39 3.2
41	Au	698	698	698	698
42	Bu	698	700	698	698
43	Bu	737	748	737	746
44	Au	749	749	749	749
45	Ag	802	802	802	802
46	Ag	802	802	802	802	3.595e+39 5.1	2.332e+39 3.3	5.927e+39 8.3
47	Bg	802	802	802	802	5.784e+37 0.1	9.715e+37 0.1	1.550e+38 0.2
48	Au	802	806	803	817
49	Bu	1051	1052	1051	1052
50	Au	1053	1053	1055	1053
51	Bg	1082	1082	1082	1082	2.184e+36 0.0	2.327e+36 0.0	4.511e+36 0.0
52	Ag	1082	1082	1082	1082	5.569e+40 78.3	2.717e+39 3.8	5.840e+40 82.1
53	Ag	1084	1084	1084	1084	1.348e+40 18.9	9.904e+38 1.4	1.447e+40 20.3
54	Ag	1084	1084	1084	1084	1.827e+40 25.7	1.535e+39 2.2	1.980e+40 27.8
55	Bu	1133	1134	1133	1134
56	Au	1134	1136	1134	1148
57	Bg	1223	1223	1223	1223	5.201e+38 0.7	6.041e+38 0.8	1.124e+39 1.6
58	Ag	1223	1223	1223	1223	5.025e+40 70.6	2.091e+40 29.4	7.116e+40 100.0
59	Bu	1435	1435	1435	1435
60	Au	1436	1436	1445	1436
61	Bu	1456	1489	1456	1488
62	Au	1492	1492	1536	1492
63	Ag	1536	1536	1540	1536	2.964e+39 4.2	1.594e+38 0.2	3.124e+39 4.4
64	Bg	1540	1540	1552	1540
65	Bu	1600	1687	1600	1682
66	Au	1687	1687	1699	1687
67	Ag	1699	1699	1714	1699	3.285e+39 4.6	1.726e+39 2.4	5.011e+39 7.0
68	Bg	1718	1718	1718	1718	7.619e+38 1.1	8.299e+38 1.2	1.592e+39 2.2
69	Bg	2028	2028	2028	2028	3.508e+40 49.3	1.937e+40 27.2	5.445e+40 76.5
70	Bg	2028	2028	2028	2028	3.449e+40 48.5	1.712e+40 24.1	5.161e+40 72.5
71	Bu	2250	2452	2250	2353
72	Au	2503	2503	2506	2503

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥