- Zn-oxalate - Zn(COO)₂

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/c
Lattice parameters (Å):		angstroms
Angles (°):	s

Symmetry (theoretical):

Space group:	14		P2_1/c
Lattice parameters (Å):	0.5292	0.5292		0.5292
Angles (°):	90	114.46		90

Cell contents:

Number of atoms:	14
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Zn:	0.0000	1.0000	0.0000
C:	0.0912	0.1203	0.5461
O:	0.1811	0.2050	0.3816
O:	0.1371	0.2168	0.7774
Zn:	0.5000	0.5000	0.5000
C:	0.4088	0.6203	0.9539
O:	0.3189	0.7050	0.1184
O:	0.3629	0.7168	0.7226
C:	0.9088	0.8797	0.4539
O:	0.8189	0.7950	0.6184
O:	0.8629	0.7832	0.2226
C:	0.5912	0.3797	0.0461
O:	0.6811	0.2950	0.8816
O:	0.6371	0.2832	0.2774

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:	6 6 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:
Zn:	zinc, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local
C:	carbon, 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):

Zn:	2.4567	-0.3322	-0.3531
	-0.3564	2.1308	-0.0415
	-0.4942	0.1133	2.7674
Eig. Value:	2.3754	1.8602	3.1193
C:	1.3825	0.0099	-0.7046
	0.0166	1.1617	-0.0803
	-0.6404	0.0366	2.6161
Eig. Value:	1.0867	1.1615	2.9122
O:	-1.5608	-0.5839	0.4386
	-0.4633	-1.0821	-0.0617
	0.7088	0.1384	-1.8335
Eig. Value:	-2.3922	-0.6655	-1.4186
O:	-1.0501	-0.0583	0.4426
	-0.2214	-1.1450	-0.2860
	0.1787	-0.5638	-2.1663
Eig. Value:	-0.7641	-1.2304	-2.3669
Zn:	2.4567	0.3322	-0.3531
	0.3564	2.1308	0.0415
	-0.4942	-0.1133	2.7674
Eig. Value:	2.3754	1.8602	3.1193
C:	1.3825	-0.0099	-0.7046
	-0.0166	1.1617	0.0803
	-0.6404	-0.0366	2.6161
Eig. Value:	1.0867	1.1615	2.9122
O:	-1.5608	0.5839	0.4386
	0.4633	-1.0821	0.0617
	0.7088	-0.1384	-1.8335
Eig. Value:	-2.3922	-0.6655	-1.4186
O:	-1.0501	0.0583	0.4426
	0.2214	-1.1450	0.2860
	0.1787	0.5638	-2.1663
Eig. Value:	-0.7641	-1.2304	-2.3669
C:	1.3825	0.0099	-0.7046
	0.0166	1.1617	-0.0803
	-0.6404	0.0366	2.6161
Eig. Value:	1.0867	1.1615	2.9122
O:	-1.5608	-0.5839	0.4386
	-0.4633	-1.0821	-0.0617
	0.7088	0.1384	-1.8335
Eig. Value:	-2.3922	-0.6655	-1.4186
O:	-1.0501	-0.0583	0.4426
	-0.2215	-1.1450	-0.2860
	0.1787	-0.5638	-2.1663
Eig. Value:	-0.7641	-1.2304	-2.3669
C:	1.3825	-0.0099	-0.7046
	-0.0166	1.1617	0.0803
	-0.6404	-0.0366	2.6161
Eig. Value:	1.0867	1.1615	2.9122
O:	-1.5608	0.5839	0.4386
	0.4633	-1.0821	0.0617
	0.7088	-0.1384	-1.8335
Eig. Value:	-2.3922	-0.6655	-1.4186
O:	-1.0501	0.0583	0.4426
	0.2214	-1.1450	0.2860
	0.1787	0.5638	-2.1663
Eig. Value:	-0.7641	-1.2304	-2.3669

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	3.1717	0.0000	0.0000
	0.0000	3.0888	0.0000
	0.0000	0.0000	3.7965
Eig. Value:	3.1717	3.0888	3.7965
Refractive index (N):	1.7809	0.0000	0.0000
	0.0000	1.7575	0.0000
	0.0000	0.0000	1.9485
Eig. Value:	1.7809	1.7575	1.9485
Ɛ₀:	11.9454	-0.0000	1.3764
	-0.0000	8.4067	0.0001
	1.3764	0.0001	8.0436
Eig. Value:	12.3820	8.4067	7.6070

Single Crystal Raman spectra

Single crystal 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.

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.

Horizontal:

Xmin:
Xmax:

Vertical:

Ymin:
Ymax:

Choose the orientation of the crystal with respect to the reference system:

Rotation around X axis:
Rotation around Z axis:
Rotation around Y axis:

- Zn-oxalate - Zn(COO)2