# Comprehensive Density Functional Theory Studies of Vibrational Spectra of Carbonates

^{1}

^{2}

^{3}

^{4}

^{*}

*Nanomaterials*—Recent Advances in Nanofabrication and Nanomanufacturing)

## Abstract

**:**

_{3}, CaCO

_{3}, ZnCO

_{3}, CdCO

_{3}in the structure of calcite; CaMg(CO

_{3})

_{2}, CdMg(CO

_{3})

_{2}, CaMn(CO

_{3})

_{2}, CaZn(CO

_{3})

_{2}in the structure of dolomite; BaMg(CO

_{3})

_{2}in the structure of the norsethite type; and CaCO

_{3}, SrCO

_{3}, BaCO

_{3}, and PbCO

_{3}in the structure of aragonite were calculated. Infrared absorption and Raman spectra were compared with the known experimental data of synthetic and natural crystals. For lattice and intramolecular modes, linear dependences on the radius and mass of the metal cation are established. The obtained dependences have predictive power and can be used to study solid carbonate solutions. For trigonal and orthorhombic carbonates, the linear dependence of wavenumbers on the cation radius R

_{M}(or M–O distance) is established for the infrared in-plane bending mode: 786.2–65.88·R

_{M}and Raman in-plane stretching mode: 768.5–53.24·R

_{M}, with a correlation coefficient of 0.87.

## 1. Introduction

_{3}(M: Ca

^{2+}, Mg

^{2+}, Fe

^{2+}, Zn

^{2+}, Mn

^{2+}, Co

^{2+}, Ni

^{2+}and Cd

^{2+}): calcite (CaCO

_{3}) [29], magnesite (MgCO

_{3}) [30], siderite (FeCO

_{3}) [31], smithsonite (ZnCO

_{3}) [32], hodochrosite (MnCO

_{3}) [33], spherocobaltite (CoCO

_{3}) [34], gaspeite (NiCO

_{3}) [35], and otavite (CdCO

_{3}) [36]. The ability to form isomorphic mixtures is widespread among the minerals of the calcite series [37].

_{3})

_{2}) [38]. Dolomite is structured by natural minerals: minocordite (CaZn(CO

_{3})

_{2}) [39], ankerite (CaFe(CO

_{3})

_{2}) [40], and kutnohorite CaMn(CO

_{3})

_{2}) [41]. Several crystals from the dolomite family were synthesized, including CdMg(CO

_{3})

_{2}, CdMn(CO

_{3})

_{2}, and CdZn(CO

_{3})

_{2}[42], and the structures were identified in [43]. Under ambient conditions, dolomite crystallizes in a rhombohedral structure with the space group R-3 (Z = 2). Its layered structure consists of alternating [CaO

_{6}] and [MgO

_{6}] octahedra separated by nearly flat and parallel carbonate groups. The structure differs from calcite by the absence of a slip plane.

_{3})

_{2}) [44] (Figure 1c). BaMn(CO

_{3})

_{2}does not exist in nature, but it was synthesized in [45]. The norsethite structure is described in c-space group R-3c symmetry with doubled c-axis, which corresponds to different rotations of carbonate groups [46]. As the temperature rises in BaMg(CO

_{3})

_{2}, a phase transition is observed from a phase stable under ambient conditions to a high-temperature structure, which is accompanied by a change in the symmetry R-3c → R-3m. In the R-3m symmetry, the unit cell of BaMg(CO

_{3})

_{2}consists of the [MgO

_{6}] octahedron, [BaO

_{12}] polyhedron, and anions. Octahedra and polyhedra are in alternating layers, they are located exactly one above the other, parallel to the [001] direction and are separated by triangular groups ${\mathrm{CO}}_{3}^{2-}$. Natural isostructural orthorhombic carbonates are aragonite (CaCO

_{3}) (Figure 1d), strontianite (SrCO

_{3}), cerussite (PbCO

_{3}), and witherite (BaCO

_{3}) [47,48], listed in the order of increasing the size of the cation. In a crystal structure with the space group Pmcn (Z = 4), layers of 9-coordinated cations M

^{2+}(M: Ca

^{2+}, Sr

^{2+}, Pb

^{2+}, Ba

^{2+}) in an approximately hexagonal close packing alternate with layers of planar ${\mathrm{CO}}_{3}^{2-}$ groups arranged perpendicular to the c-axis. Like calcites, aragonites form solid solutions [49]. Studies of isostructural orthorhombic carbonates are important for understanding phase transition sequences under pressure and temperature and, therefore, can provide insight into a carbon behavior in the Earth mantle [50,51,52,53].

_{g}(T) symmetry correlate with the distances between the nearest metal and oxygen atoms M–O and the cation ionic radii. Using a graphical approach, the authors developed the spectroscopic Raman model to calculate the ionic radius of a divalent metal cation present in a mineral.

_{0.98}Fe

_{0.02}(CO

_{3})

_{2}was performed [66]. DFT using exchange correlation potentials in the local density approximation (LDA) and generalized gradient approximation (GGA) in the PW basis with TM PP were used here to interpret the obtained results. The Raman and infrared spectra of cerussite were measured and compared with the spectral characteristics of other minerals of the aragonite family [67]. RS and IRS at high temperature in situ were measured for aragonite, strontianite, cerussite, and witherite at atmospheric pressure [68]. Studies for high and medium temperature infrared absorption and Raman spectroscopy on a synthetic strontianite sample led to the construction of a pressure-temperature phase diagram [69]. In addition, here for the first time, the absorption spectra in the far infrared range were measured for the entire family of aragonite-type carbonates.

^{2+}cation type on the shift of positions of the absorption bands of various anhydrous carbonate minerals from the calcite and dolomite families. In this contribution, it is shown that the position of the minima of absorption bands is unique for each chemical composition of carbonates and can be a diagnostic indicator in mineralogy. A selection of the frequencies of intramolecular modes for a large number of carbonates is also found in [71]. In [72], infrared spectra in the wavenumber range of 70–650 cm

^{−1}were presented for 18 common and rare minerals which are quite pure in composition and have a known crystal structure. It is shown that the spectra in the far infrared range of different carbonates from the same structural group have a pronounced similarity, and the observed shifts demonstrate the effect of changing the mass of cations. The vibrational modes of natural minerals—aragonite, calcite, dolomite, magnesite, rhodochrosite, and siderite—that are active in the Raman spectrum were observed, and their pressure and temperature inducing frequency shifts were determined [73].

## 2. Calculation Method

^{−9}a.u. (1 a.u. = 27.21 eV). The vibrational frequencies of the lattice atoms were calculated using the FREQCALC procedure [85,86]. The phonon harmonic frequencies ω

_{p}at the point Г (k = 0, the center of the first Brillouin zone) were obtained from the diagonalization of the mass-weighted Hessian matrix of the second derivatives of energy with respect to atomic displacements u [87,88]:

_{a}and M

_{b}are displaced in the unit cell (index 0) from equilibrium positions along the i- and j-Cartesian directions, respectively. The first order derivatives were calculated analytically, whereas the second order derivatives were obtained numerically. The intensity of IR absorption for the ν-vibration was calculated using the Born effective charge tensor Z*, which characterizes the change in dynamics and the electronic configuration of atom displacement. The relative intensities of the Raman peaks were calculated analytically using the extension scheme of the analytical calculation of IR intensity [89]. The proposed technique was previously used to study the ordinary properties of sulfates [90].

## 3. Crystal Structure

^{6}, and the radius of Mg

^{2+}surrounded by six nearest neighbors is 0.72 Å. Similarly, for calcium: 3p

^{6}, 1.00 Å. In zinc and cadmium, the filled shells are 3d

^{10}and 4d

^{10}, and the radii are 0.74 and 0.95 Å, respectively. In aragonite, each Ca

^{2+}ion is already surrounded by nine oxygen atoms and, therefore, its effective radius is 1.18 Å. In the case of strontium and barium, the radii for the 9-fold environment are 1.31 and 1.47 Å, and for 12—1.44, 1.61 Å. The electronic configuration of lead [Xe] 4f

^{14}5d

^{10}6s

^{2}6p

^{2}distinguishes it from other elements; therefore, the radius of 9-coordinated Pb

^{2+}is 1.35 Å, which is larger than that of strontium, but smaller than that of barium. Transition metals have partially filled 3d shells with the number of electrons from 5 to 8, and decreasing radii for Mn

^{2+}(0.83 Å), Fe

^{2+}(0.78 Å), and Co

^{2+}(0.745 Å). Following [33], we write the chemical formula of an arbitrary solid solution as M1

_{X}

_{1}M2

_{X}

_{2}M3

_{X}

_{3}CO

_{3}, X1 + X2 + X3 = 1. Then, the average radius of the cation is determined as <R

_{M}> = X1·R

_{M1}+ X2·R

_{M2}+ X3·R

_{M3}, where R

_{M1}, R

_{M2}, R

_{M3}are radii of divalent ions M1

^{2+}, M2

^{2+}, M3

^{2+}. For dolomite, the cation radius is 0.86 Å, and for norsethite—1.165 Å. The average atomic mass of metals is calculated in a similar way.

_{0}+ y

_{1}·r, where y

_{0}is the value of the function at r = 0, y

_{1}—derivative of the function y, characterizing the rate of change of the corresponding value. The obtained calculated data y(r

_{i}), I = 1, N are approximated by a linear dependence (fit), and the accuracy of this procedure is controlled by the relation: $K=\sqrt{\sum _{i=1}^{N}{\left({y}_{i}^{fit}-\overline{{y}^{fit}}\right)}^{2}/\sum _{i=1}^{N}{\left({y}_{i}^{data}-\overline{{y}^{data}}\right)}^{2}}$, where the average value $\overline{y}=\frac{1}{N}\sum _{i=1}^{N}{y}_{i}$.

_{M}obeys the linear dependence V/Z(Å

^{3}) = 25.22 + 31.54·R

_{M}with a correlation coefficient of 0.936. The large slope of this dependence of 31.54 Å

^{2}indicates that the replacement of the cation is of great importance for carbonates. The indicated dependence with the experimental values of volumes has the form V/Z(Å

^{3}) = 22.48 + 36.2482·R

_{M}(Å

^{3}) with the coefficient K = 0.945. For each individual lattice type, the correlation coefficient is much better: for calcite and aragonite, 0.995, and for dolomite, 0.969. The linear dependence is explained by the fact that the cell volume is weakly related to the structure symmetry but is determined by the stacking of layers of polyhedrons, which depends on the ionic radii of the substitutional atoms. According to Vegard’s law, the unit cell parameters change linearly depending on the composition, and for trigonal crystals, it can be written as: a(Å) = 4.008 + 0.959·R

_{M}(0.941), c(Å) = 11.772 + 4.917·R

_{M}(0.88). Hereinafter, the coefficient K is indicated in brackets. The linear dependence for all carbonates is fulfilled for the average distance between metal M and oxygen O: R

_{M–O}(Å) = 1.374 + 1.02·R

_{M}(0.985) with high accuracy.

## 4. Vibrational Spectra

_{tot}= A

_{1g}(R) + 3A

_{1u}+ 3A

_{2g}+ 3A

_{2u}(IR) + 4E

_{g}(R) + 6E

_{u}(IR). A

_{1g}and 4E

_{g}modes are active in Raman spectra (R), 3A

_{2u}and 5E

_{u}modes are active in infrared (IR), A

_{1u}and 3A

_{2g}modes are spectroscopically inactive, and 1A

_{2u}and 1E

_{u}modes are acoustic. Nine translational modes will refer to the symmetry A

_{2g}+ A

_{1u}+ A

_{2u}+ E

_{g}+ 2E

_{u}, six librational modes to A

_{2g}+ A

_{2u}+ E

_{g}+ E

_{u}, and twelve internal vibrations to A

_{1g}+ A

_{2g}+ A

_{1u}+ A

_{2u}+ 2E

_{g}+ 2E

_{u}. Modes of the A

_{2u}symmetry have polarization

**E**||

**z**and modes of E

_{u}symmetry have

**E**⏊

**z**polarization. Internal vibrations of E

_{u}symmetry are of the ν

_{4}type (in-plane bending), A

_{2u}modes are of the ν

_{2}type (out-of plane bending), and E

_{u}symmetry are of the ν

_{3}type of symmetric stretching. In the Raman spectrum, the ν

_{4}(in-plane asymmetric stretching) mode has E

_{g}symmetry, the ν

_{1}symmetric stretch mode has A

_{1g}symmetry, and a ν

_{3}asymmetric stretch type has E

_{g}symmetry.

_{tot}= 4A

_{g}(R) + 6A

_{u}(IR) + 4E

_{g}(R) + 6E

_{u}(IR). Nine translational modes refer to symmetry A

_{g}+ 2A

_{u}+ E

_{g}+ 2E

_{u}, six rotational modes refer to A

_{g}+ A

_{u}+ E

_{g}+ E

_{u}, and 12 internal modes refer to 2A

_{g}+ 2A

_{u}+ 2E

_{g}+ 2E

_{u}. For the norsethite type structure with the space group R-3m, the expansion of the vibrational representation is: Г

_{tot}= 3A

_{1g}(R) + 2A

_{1u}+A

_{2g}+ 5A

_{2u}(IR) + 4E

_{g}(R) + 6E

_{u}(IR). For the aragonite orthorhombic structure, the symmetry of the carbonate group decreases to C

_{s}. There will be 60 vibrational modes in total, where 1B

_{1u}+ 1B

_{2u}+ 1B

_{3u}are acoustic. The vibrational representation is decomposed into irreducible representations as Γ

_{tot}= 9A

_{g}+ 6B

_{1g}(R) + 9B

_{2g}(R) + 6B

_{3g}(R) + 6A

_{u}+ 9B

_{1u}(IR) + 6B

_{2u}(IR) + 9B

_{3u}(IR). The B

_{2u}symmetry modes have polarizations

**E**||

**x**(

**a**), B

_{3u}—

**E**||

**y**(

**b**), B

_{1u}—

**E**||

**z**(

**c**). There will be 24 internal modes, eight of the ν

_{4}and ν

_{3}types, and four of the ν

_{2}and ν

_{1}types. The available experimental and theoretical data on vibration spectra of the carbonates under consideration are summarized in Supplementary Materials [92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110].

## 5. Optical Spectra of Crystals with a Calcite Structure

_{3}, the most intense mode (5132 km/mol) in IRS corresponds to the internal vibration ν

_{3}of E

_{u}symmetry with the wavenumber of 1424 cm

^{−1}. Taking its intensity as 100%, for the ν

_{2}vibration with a wavenumber of 874 cm

^{−1}, we obtained 4%, and for the ν

_{4}(746 cm

^{−1}) mode, even less—0.9%. In calcite, the wavenumbers corresponding to the vibrations ν

_{3}, ν

_{2}, and ν

_{4}are 1400, 875, and 712 cm

^{−1}, and their intensities are 5447 km/mol (100%), 3%, and 0.5%, which practically do not differ from magnesite. For ZnCO

_{3}and CdCO

_{3}, the structures of the spectra in the high-frequency region remain similar to magnesite. Thus, for internal modes, there is a linear correlation between the change in the wavenumber and the radius of the cation R

_{M}. For ν

_{4}, it can be written in the form: ω

_{E}

_{u}(cm

^{−1}) = 812.9 − 98.7·R

_{M}(0.958), and with a smaller K coefficient for ν

_{3}: ω

_{E}

_{u}(cm

^{−1}) = 1546.9 − 154.8·R

_{M}(0.854). A good correlation (K = 0.96) for the calculated intensity is observed for the ν

_{3}vibrations, where it increases with rise of atomic mass as: I(km/mol) = 4948 + 14 M, and, for the ν

_{2}mode, it decreases with increasing radius: I(km/mol) = 478 − 326 R

_{M}.

_{3}, the most intense ones are the E

_{u}symmetry modes with wavenumbers of 344 cm

^{−1}(25%), 301 cm

^{−1}(2%), and A

_{2u}symmetry modes at 351 cm

^{−1}(4%), 242 cm

^{−1}(5%). For CaCO

_{3}, the lattice modes are shifted to the low-wavenumber region, and their intensities decrease. In the region of lattice vibrations of ZnCO

_{3}, the most intense modes will be E

_{u}symmetry with wavenumbers of 287 cm

^{−1}, 212 cm

^{−1}, and only then with A

_{2u}symmetry: 348 cm

^{−1}, 176 cm

^{−1}. In CdCO

_{3}, this trend continues. Thus, for translation modes of E

_{u}symmetry, a dependence on the cation mass is observed: ω(cm

^{−1}) = 306.0 − 1.37·M (0.915). For the rest of the lattice modes, the best linear dependence was established for the cation radius: for rotational ones: ω

_{Eu}(cm

^{−1}) = 466.5 − 353.1·R

_{M}(0.91), ω

_{A}

_{2u}(cm

^{−1}) = 463.2 − 348.5·R

_{M}(0.884, and for translational modes: ω

_{A}

_{2u}(cm

^{−1}) = 484.7 − 186.3·R

_{M}(0.991).

_{1}type, and falls on 1099 cm

^{−1}in MgCO

_{3}, and 1087 cm

^{−1}in calcite. This mode has a significant polarization dependence [89]: the xx and yy components are ten times larger than the zz component. Internal vibrations of ν

_{4}type also have a noticeable intensity: for magnesite—with a wavenumber of 737 cm

^{−1}, for calcite—711 cm

^{−1}, and also for ν

_{3}type: 1444 cm

^{−1}and 1433 cm

^{−1}, respectively. In carbonates of relatively heavy metals zinc and cadmium, the positions of the maxima of the ν

_{4}and ν

_{1}bands are practically preserved (ω

_{E}

_{g}(cm

^{−1}) = 783.3 − 72.9·R

_{M}(0.906), ω

_{A1g}(cm

^{−1}) = 1138.0 − 49.2·R

_{M}(0.906)), whereas for the ν

_{3}region the changes are significant. This is due to the fact that the intensity of this mode increases linearly with an increase in the atomic mass of the metal cation: I

_{ν3}(%) = −29.9 + 1.1·M (0.987). For CdCO

_{3}, the ν

_{3}vibration becomes the most intense in RS and has pronounced xz and yz polarizations.

_{g}symmetry, and its wavenumbers in MgCO

_{3}are 323 cm

^{−1}(intensity 11%), ZnCO

_{3}310 cm

^{−1}(15%), CdCO

_{3}258 cm

^{−1}(23%), and CaCO

_{3}275 cm

^{−1}(18%). Thus, for the lattice translational vibration, there is a linear dependence of the form ω(cm

^{−1}) = 361.0 − 210.6·R

_{M}(0.992), and for rotational, ω(cm

^{−1}) = 449.0 − 185.5·R

_{M}(0.912). Since there is a good linear relationship between R

_{M–O}and the radius of the R

_{M}cation, the above formulas can easily be rewritten for distances as well. The above formulas allow predicting the wavenumber values for other carbonates; thus, for the lattice modes E

_{g}(T), E

_{g}(L), internal ν

_{4}and ν

_{1}, the wavenumbers predicted by the formulas for MnCO

_{3}are 186, 296, 723, and 1097 cm

^{−1}, and for CoCO

_{3}, they are 204, 311, 729, and 1101 cm

^{−1}. The experimental values for rhodochrosite are 184, 290, 719, and 1086 cm

^{−1}[62]; for spherocobaltite, they are 194, 302, 725, and 1090 cm

^{−1}[34].

## 6. Vibrational Spectra of Crystals with a Dolomite Structure

_{3})

_{2}, the most intense mode (5318 km/mol, 100%) is the ν

_{3}mode at 1416 cm

^{−1}. The internal vibration ν

_{2}with a wavenumber of 877 cm

^{−1}has an intensity of 3.5%, and for vibration ν

_{4}at 727 cm

^{−1}, the intensity is close to 1%. Unlike calcite, the vibration ν

_{1}of the A

_{u}symmetry is allowed by symmetry; however, its intensity is practically zero. The most intense (19%) in the region of lattice vibrations is the E

_{u}symmetry mode with a wavenumber of 337 cm

^{−1}. Modes of the same symmetry, but with a much lower intensity, appear at 257 (2.5%) and 167 cm

^{−1}(4%).

_{3})

_{2}, the most intense (5788 km/mol, 100%) vibration will be ν

_{3}with a wavenumber of 1407 cm

^{−1}, and for lattice vibration with a wavenumber of 338 cm

^{−1}, the intensity is 16%. A similar picture is observed in CaZn(CO

_{3})

_{2}, where the intensity of the ν

_{3}vibration is 5928 km/mol (100%), and the intensities of two lattice vibrations with wavenumbers of 290 and 310 cm

^{−1}are 11% and 3.5%, respectively. The situation is different in CaMn(CO

_{3})

_{2}, where the intensity of the ν

_{3}mode is much lower—1121 km/mol (100%), and against its background, the relative intensities of other ν

_{2}and ν

_{4}vibrations increased to 22 and 6%, respectively.

_{1}symmetric vibration with a wavenumber of 1097 cm

^{−1}. Its full intensity is taken as 100%. Then, the intensities of the ν

_{4}, ν

_{2}, and ν

_{3}modes will be 15%, 0.2% and 9%, respectively. In the region of lattice vibrations, the most intense are the E

_{g}symmetry modes with wavenumbers of 296 cm

^{−1}(13%) and 175 cm

^{−1}(3%). In CdMg(CO

_{3})

_{2}, the ν

_{1}mode does not change in wavenumber and remains most intense. The wavenumber of the ν

_{3}mode decreases, but its intensity sharply increases to 49%. In CaMn(CO

_{3})

_{2}, the intensity of the ν

_{3}mode becomes maximum (taken as 100%), while for the ν

_{1}vibration it is only 15%. Thus, as for IRS, the binary carbonate CaMn(CO

_{3})

_{2}differs from other crystalline dolomites in the parameters of its vibrational spectra.

_{3})

_{2}crystal (Figure 4) in the region of intramolecular vibrations, the most intense (5194 km/mol) vibration will be ν

_{3}with a wavenumber of 1439 cm

^{−1}. Against this background, the ν

_{2}vibration with a wavenumber of 878 cm

^{−1}and the intensity of 3% is almost imperceptible, moreover, the ν

_{4}vibrations (694 cm

^{−1}, 0.5%) and ν

_{1}allowed here (1125 cm

^{−1}, 0.2%) practically do not appear. In the region of lattice vibrations, vibrations of E

_{u}symmetry with wavenumbers of 315, 200, and 106 cm

^{−1}stand out in intensity, while less intense vibrations of A

_{2u}symmetry have wavenumbers of 347 and 115 cm

^{−1}. The first of these less intense vibrations corresponds to the displacements of magnesium atoms in antiphase with the anions, and the second corresponds to the displacements of barium atoms. Magnesium atoms are also involved in the formation of this mode, and they shift synchronously with the anion. In RS of BaMg(CO

_{3})

_{2}, vibrations of anion atoms will also dominate: ν

_{1}with a wavenumber of 1126 cm

^{−1}(its intensity is taken as 100%), ν

_{2}of the same symmetry and intensity of 3%, as well as doubly degenerated ν

_{4}(697 cm

^{−1}) and ν

_{3}(1444 cm

^{−1}) with intensities of 21% and 3%, respectively. For lattice vibrations, the A

_{1g}symmetry mode with a wavenumber of 284 cm

^{−1}and E

_{g}symmetry modes with wavenumbers of 108 and 254 cm

^{−1}will be noticeable, of which the first is rotational, and the second is translational vibration.

_{Eu}(cm

^{−1}) = 379.0 − 244.3·R

_{M}(0.794); for RS, ω

_{Eg}(cm

^{−1}) = 367.3 − 216.2·R

_{M}(0.896), and ω

_{Eg}(cm

^{−1}) = 413.1 − 39.6·R

_{M}(0.813). Using the first formula, we obtain for ankerite (CaFe(CO

_{3})

_{2}) 164 cm

^{−1}(in experiment, 166 cm

^{−1}[72]), kutnogorite Ca

_{0.78}Mn

_{1.13}(CO

_{3})

_{2}159 cm

^{−}

^{1}(153 cm

^{−}

^{1}). For lattice vibrations active in RS, the formulas give estimated values for rhodochrosite (MnCO

_{3}) 188, 297 cm

^{−}

^{1}. The experimental values are 185 and 290 cm

^{−}

^{1}[73].

## 7. Vibrational Spectra of Crystals with Aragonite Structure

_{1}–ν

_{4}wavenumbers in four carbonates is, according to [68], 1.5% for IRS; 0.8% for RS; for IRS [55]—2.0%, and for RS [57]—0.9%.

_{3}type with the B

_{2u}, B

_{3u}symmetry, wavenumbers of 1448 and 1480 cm

^{−1}and intensities of 4523 and 4727 km/mol. In Figure 4, they correspond to a broad intense band with the maximum at 1462 cm

^{−1}(1461 cm

^{−1}in [68]). For convenience of comparison, the intensity of vibration of B

_{3u}symmetry is taken as 100%. In SrCO

_{3}, the maximum intensity of the B

_{3u}mode at 4757 km/mol is taken as 100%, in BaCO

_{3}, the B

_{2u}symmetry modes at 4953 km/mol, and in PbCO

_{3}: 6241 km/mol. Thus, the intensity ν

_{3}increases with the atomic mass of the metal, and the position of the maximum in the series changes according to the law: ω(cm

^{−1}) = 1480.2 − 0.365·M (cm

^{−1}) with a correlation coefficient of 0.991.

_{1}type will be active due to the modes of symmetry B

_{3u}, B

_{1u}. In the spectrum shown in Figure 4, they correspond to a weak (0.2%) band with a maximum at 1090 cm

^{−1}, the wavenumber of which shifts towards lower values with increasing atomic mass: ω(cm

^{−1}) = 1090.6 − 0.127·M. The intensity of vibrations of the ν

_{2}type of B

_{1u}symmetry is much higher than that of ν

_{1}vibrations, it decreases with an increase in the atomic mass of the metal, and its wavenumber practically does not change: ω(cm

^{−1}) = 893.3 − 0.065·M. In the experimental spectra, this dependence has the form: ω(cm

^{−1}) = 866.2 − 0.123·M. Vibrations of the ν

_{4}type in CaCO

_{3}and SrCO

_{3}correspond to the modes of symmetries B

_{3u}, B

_{2u}with distances between wavenumbers of 13 and 6 cm

^{−1}. In BaCO

_{3}and PbCO

_{3}, the distances between wavenumbers decrease to 2 and 3 cm

^{−1}. This behavior of vibrational modes of the ν

_{4}type is consistent with experimental data [68], where it was found that two peaks are observed in aragonite (CaCO

_{3}) and strontianite (SrCO

_{3}), and only one for cerussite (PbCO

_{3}) and witherite (BaCO

_{3}). There is a good ordinary dependence of the peak position on the atomic mass of the metal: in the experiment it is ω(cm

^{−1}) = 707.5 − 0.128·M, and in the calculation: ω(cm

^{−1}) = 715.4 − 0.119·M, with the correlation coefficients 0.944 and 0.977, respectively.

_{3}), ν

_{1}vibration of A

_{g}symmetry with a wavenumber of 1078 cm

^{−1}is the most intense (taken as 100%). Vibrations ν

_{4}of the A

_{g}and B

_{1g}symmetries with intensities of 9% each are also noticeable, which form the maximum in the spectrum shown in Figure 5 at 702 cm

^{−1}. In BaCO

_{3}, the ν

_{1}vibration maximum shifts to 696 cm

^{−1}, and its intensity increases. In addition, the width of this peak increases. Oscillations of the ν

_{3}type in CaCO

_{3}have B

_{3g}(1465 cm

^{−1}) and B

_{2g}(1595 cm

^{−1}) symmetries, and an intensity of 5%. In SrCO

_{3}, these are vibrations at wavenumbers of 1450 and 1565 cm

^{−1}with intensities of 4%. In BaCO

_{3}, they shift to lower values of 1429 and 1528 cm

^{−1}, and the intensities increase to 9 and 13%. Oscillations of the B

_{2g}symmetry correspond to the displacements of atoms to the C–O bonds along the b axis, whereas B

_{3g}—along the a axis, perpendicular to the layers of anions and cations.

_{3}differs from the spectra of other carbonates with the aragonite structure. Here, the most intense (taken as 100%) is the vibration of the ν

_{3}type of B

_{2g}symmetry with a wavenumber of 1486 cm

^{−1}[68]. Three other vibrations of this type have B

_{3g}, A

_{g}, B

_{1g}symmetries, similar wavenumbers of 1394, 1383 and 1380 cm

^{−1}and intensities of 50%, 16%, and 25%, respectively. They form a second maximum in RS at 1388 cm

^{−1}. The ν

_{1}-type vibration with a wavenumber of 1067 cm

^{−1}has an intensity of 61%. Modes of the same A

_{g}symmetry are also dominant in the formation of the ν

_{2}band, the position of which in aragonites obeys the law: ω(cm

^{−1}) = 895.6 − 0.117·M with a high correlation coefficient of 0.977.

^{−1}, formed by the B

_{3u}symmetry mode with an intensity of 13%, and the main maximum with an intensity of 23% at 194 cm

^{−1}(B

_{2u}symmetry). For SrCO

_{3}, four peaks are observed at 129, 175, 192 and 215 cm

^{−1}with intensities of 3, 18, 15 and 9%, while in BaCO

_{3}the intense band is at 157 cm

^{−1}(B

_{1u}and B

_{3u}) with a low-wavenumber band at 146 cm

^{−1}, and high-wavenumber at 171 cm

^{−1}shoulders. In PbCO

_{3}, the main features of the spectrum are shifted to the low-wavenumber region. There are two main peaks at 82 cm

^{−}

^{1}with an intensity of 17%, and a peak at 103 cm

^{−}

^{1}and an intensity of 18%. This structure of the IRS in the lattice region is consistent with the results of measurements [72], where it was found that the broad band at 263 cm

^{−}

^{1}in the structure of aragonite shifts to longer wavelengths with an increase in the atomic number of the metal: up to 227 cm

^{−}

^{1}in strontianite, then up to 205 cm

^{−}

^{1}in witherite, and, finally, up to 136 cm

^{−}

^{1}in cerussite.

^{−1}, 209 cm

^{−1}and 250, 276 cm

^{−1}. There is a good agreement between the calculated and experimental data [68]. In SrCO

_{3}, there are two intense bands with maxima at 150 and 191 cm

^{−1}, formed by the modes of symmetries B

_{3g}, B

_{2g}, and a weak band at 252 cm

^{−1}. In the BaCO

_{3}spectrum, the maximum of the first band is at 153 cm

^{−1}, the second at 181 cm

^{−1}with a shoulder at 198 cm

^{−1}, and the third at 237 cm

^{−1}. The second maximum is formed by modes with B

_{2g}symmetry with pronounced yz polarization. The spectrum of PbCO

_{3}contains a large number of bands of low intensity, not exceeding 6%.

_{4}, ν

_{1}, ν

_{3}) vibrations active in RS for carbonates with the aragonite structure, obtained from experimental data [68] and theoretical calculations using the B3LYP method are summarized in Table 2. In the calculations, each type of vibration was determined as the average of the individual modes, which are shown in Table S9. For lattice vibrations, similar linear dependences are also obtained, as recorded in Table S10.

_{3}) X1 (SrCO

_{3}) X2 (BaCO

_{3}) X3 solid solutions were measured. Thus, in the spectrum of the composition 0.34:0.33:0.33, wavenumbers of 1452, 1086, 711, 273, 192, 155 cm

^{−1}were observed. Calculation according to the formulas of Tables S8 and S9 gives: 1466, 1077, 703, 262, 183, and 158 cm

^{−1}, that is, the root mean square deviation of the calculated and experimentally determined wavenumbers is about 2.7%.

## 8. Conclusions

_{3}, CaCO

_{3}, ZnCO

_{3}, CdCO

_{3}in the structure of calcite, CaMg(CO

_{3})

_{2}, CdMg(CO

_{3})

_{2}, CaMn(CO

_{3})

_{2}, CaZn(CO

_{3})

_{2}—in the structure of dolomite, BaMg(CO

_{3})

_{2}—in the structure of the norsethite type, CaCO

_{3}, SrCO

_{3}, BaCO

_{3}, PbCO

_{3}—in the structure of aragonite. The analysis of the calculated results and their comparison with the available experimental data shows that the wavenumbers and intensities of individual vibrational modes obey the ordinary laws. For the calcite family, the intramolecular modes of the ν

_{2}and ν

_{3}types that are active in IRS correlate with the cation radius ω(cm

^{−1}) = 812.9 − 98.7·R

_{M,}and ω(cm

^{−1}) = 1546.9 − 154.8·R

_{M}with correlation coefficients of 0.958 and 0.854. Vibration of the ν

_{4}type is active in RS, where the dependence of its wavenumber on the radius of the metal cation has the form ω(cm

^{−1}) = 783.3 − 72.9·R

_{M}, and for the most intense ν

_{1}: ω(cm

^{−1}) = 1138.0 −42.9·R

_{M,}with coefficients of correlation 0.906. For the entire class of trigonal crystals (calcite, dolomite, norsethite), the dependence of low- wavenumber lattice vibrations has the form for E

_{u}symmetry: E

_{u}: ω(cm

^{−1}) =379.0 − 243.3·R

_{M,}and E

_{g}: ω(cm

^{−1}) = 367.3 − 216.2·R

_{M}, ω(cm

^{−1}) = 413.1 − 139.6·R

_{M}. For carbonates with aragonite structure for the calculated wavenumbers ν

_{4}, ν

_{2}, ν

_{1}, ν

_{3}, linear dependences with high correlation coefficients are obtained for the atomic mass: ω(cm

^{−1}) = 714.3 − 0.128·M; ω(cm

^{−1}) = 895.6 − 0.117·M; ω(cm

^{−1}) = 1087.1 − 0.116·M; ω(cm

^{−1}) = 1619.0 − 0.638·M, and for IRS: ω(cm

^{−1}) = 715.4 −−0.119·M’; ω(cm

^{−1}) = 893.3 − 0.065·M; ω(cm

^{−1}) = 1090.6 − 0.127·M; ω(cm

^{−1}) = 1480.2 − 0.365·M. For trigonal and orthorhombic carbonates, linear dependences of metal substitution were established for the radius of the RM cation (the distance between the metal and oxygen R

_{M–O}) only for the infrared in-plane bending mode ν

_{4}: ω(cm

^{−1}) = 786.2 − 65.88·R

_{M}(ω(cm

^{−1}) = 881.0 − 67.13·R

_{M–O}), and Raman in-plane asymmetric stretching mode ν

_{4}: ω(cm

^{−1}) = 768.5 − 53.24·R

_{M}(ω(cm

^{−1}) = 844.2 − 53.83·R

_{M–O}), with a correlation coefficient of 0.87 (0.91). For the rest of the modes, it was not possible to obtain linear dependences with high correlation coefficients.

## Supplementary Materials

^{−1}) of lattice, translational (T), rotational (L) and internal mode vibrations active in IR spectra (IR), obtained in this work by the B3LYP method, measured experimentally (Exp.) and calculated (Theor.) for carbonates with calcite structure, Table S2: Wavenumbers (cm

^{−1}) of lattice, translational (T), rotational (L), and internal modes vibrations active in the Raman spectra, obtained in this work by the B3LYP method, measured experimentally [Exp] and calculated [Theor] in the works of other authors for carbonates with calcite structure, Table S3: Wavenumbers (cm

^{−1}) of lattice and internal modes vibrations active in the IR spectra, obtained in this work by the B3LYP method, measured experimentally [Exp.] and calculated [Theor.] in the works of other authors for carbonates with dolomite and norsethite structure, Table S4: Wavenumbers (cm

^{−1}) of lattice and internal modes vibrations active in Raman spectra, obtained in this work by the B3LYP method, measured experimentally [Exp.] and calculated [Theor.] in the works of other authors for carbonates with dolomite and norsethite structure, Table S5: Wavenumbers (cm

^{−1}) of internal modes v

_{1}, v

_{2}, v

_{3}, v

_{4}vibrations active in infrared spectra (IRS) calculated by the B3LYP method, measured experimentally [Exp.] and calculated [Theor.] in the works of other authors for crystals with aragonite structure, Table S6: Wavenumbers (cm

^{−1}) of internal modes v

_{1}, v

_{2}, v

_{3}, v

_{4}vibrations active in the Raman spectra, calculated by the B3LYP method, measured experimentally [Exp.] and calculated [Theor.] in the works of other authors for crystals with aragonite structure, Table S7: Wavenumbers (cm

^{−1}) of lattice vibrations, active in infrared (IR) spectra, calculated by the B3LYP method, measured experimentally [Exp.] and calculated [Theor.] in the works of other authors for crystals with aragonite structure, Table S8: Wavanumbers (cm

^{−1}) of lattice vibrations active in the Raman spectra, calculated by the B3LYP method, experimentally measured [Exp.] and calculated [Theor.] in the works of other authors for crystals with aragonite structure, Table S9: Values of the coefficients ω

_{0}(сm

^{−1}), ω

_{1}(сm

^{−1}/a.m.u.) of linear interpolation of frequencies ω = ω

_{0}+ ω

_{1}·М (сm

^{−1}) by the atomic mass of the metal M intramolecular (ν

_{4}, ν

_{2}, ν

_{1}, ν

_{3}) modes, active in the Raman and infrared spectra absorption (IR) of carbonates with aragonite structure, obtained from theoretical calculations by the B3LYP method. The correlation coefficient K is shown in parentheses. Table S10: Values of the coefficients ω

_{0}(сm

^{−1}), ω

_{1}(сm

^{−1}/a.m.u.) of linear interpolation of wavenumbers ω = ω

_{0}+ ω

_{1}·М (сm

^{−1}) by the atomic mass of the metal M of lattice vibrations active in the Raman spectra of carbonates with aragonite structure obtained from theoretical calculations by the B3LYP method. The correlation coefficient K is shown in parentheses.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Liu, Y.; Shen, Y.; Zhao, S.; Luo, J. Structure-property relationship in nonlinear optical materials with p-conjugated CO
_{3}triangles. Coord. Chem. Rev.**2020**, 407, 213152. [Google Scholar] [CrossRef] - Hazen, R.M.; Downs, R.T.; Jones, A.P.; Kah, L. Carbon Mineralogy and Crystal Chemistry. Rev. Mineral. Geochem.
**2013**, 75, 7–46. [Google Scholar] [CrossRef] - Miller, K.G.; Kominz, M.A.; Browning, J.V.; Wright, J.D.; Mountain, G.S.; Katz, M.E.; Sugarman, P.J.; Cramer, B.S.; Christie-Blick, N.; Pekar, S.F. The Phanerozoic Record of Global Sea-Level Change. Science
**2005**, 310, 1293–1298. [Google Scholar] [CrossRef][Green Version] - Dupraz, C.; Reid, R.P.; Braissant, O.; Decho, A.W.; Norman, R.S.; Visscher, P.T. Processes of carbonate precipitation in modern microbial mats. Earth-Sci. Rev.
**2009**, 96, 141–162. [Google Scholar] [CrossRef] - Litasov, K.D.; Goncharov, A.F.; Hemley, R.J. Crossover from melting to dissociation of CO
_{2}under pressure: Implications for the lower mantle. Earth Planet. Sci. Lett.**2011**, 309, 318–323. [Google Scholar] [CrossRef] - Litasov, K.D.; Shatskiy, A.; Ohtani, E.; Yaxley, G.M. Solidus of alkaline carbonatite in the deep mantie. Geology
**2013**, 41, 79–82. [Google Scholar] [CrossRef] - Montañez, I.P.; McElwain, J.C.; Poulsen, C.J.; White, J.D.; DiMichele, W.A.; Wilson, J.P.; Griggs, G.; Hren, M.T. Climate, pCO
_{2}and terrestrial carbon cycle linkages during late Palaeozoic glacial–interglacial cycles. Nat. Geosci.**2016**, 9, 824–828. [Google Scholar] [CrossRef] - Sieber, M.J.; Wilke, F.; Koch-Müller, M. Partition coefficients of trace elements between carbonates and melt and suprasolidus phase relation of Ca-Mg-carbonates at 6 GPa. Am. Mineral.
**2020**, 105, 922–931. [Google Scholar] [CrossRef] - Xie, M.; Yang, L.; Ji, Y.; Wang, Z.; Ren, X.; Liu, Z.; Asiri, A.M.; Xiong, X.; Sun, X. An amorphous Co-carbonate-hydroxide nanowire array for efficient and durable oxygen evolution reaction in carbonate electrolytes. Nanoscale
**2017**, 9, 16612–16615. [Google Scholar] [CrossRef] - Sobhani-Nasab, A.; Pourmohamadian, H.; Rahimi-Nasrabadi, M.; Sheikhzadeh, G.A.; Tabrizi, H.B. Evaluation of the thermal properties of SrCO
_{3}-microencapsulated palmitic acid composites as thermal energy storage materials. J. Therm. Anal. Calorim.**2020**, 140, 2123–2130. [Google Scholar] [CrossRef] - De Beauvoir, T.H.; Sangregorio, A.; Cornu, I.; Josse, M. Synthesis, sintering by Cool-SPS and characterization of A
_{2}Cu(CO_{3})_{2}(A = K, Na): Evidence for multiferroic and magnetoelectric cupricarbonates. Dalton Trans.**2020**, 49, 7820–7828. [Google Scholar] [CrossRef] [PubMed] - Lee, J.; Ryu, K.H.; Ha, H.Y.; Jung, K.-D.; Lee, J.H. Techno-economic and environmental evaluation of nano calcium carbonate production utilizing the steel slag. J. CO2 Util.
**2020**, 37, 113–121. [Google Scholar] [CrossRef] - Mazhar, S.F.B.; Meyer, H.J.; Samuels, T.; Sharonov, M.; Shi, L.; Alfano, R.R. Exploration of the competition between O- and E-wave induced stimulated Raman and supercontinuum in calcite under ultrafast laser excitation. Appl. Opt.
**2020**, 59, 5252–5257. [Google Scholar] [CrossRef] [PubMed] - Karuppaiah, M.; Akilan, R.; Sakthivel, P.; Asaithambi, S.; Shankar, R.; Yuvakkumar, R.; Hayakawa, Y.; Ravi, G. Synthesis of self-essembled micro/nano structured manganese carbonate for high performance, long lifespan asymmetric supercapacitors and investigation of atomic-level intercalation properties of OH
^{−}ions via first principle calculation. J. Energy Storage**2020**, 27, 101138. [Google Scholar] [CrossRef] - Assaedi, H.; Alomayri, T.; Kaze, C.R.; Jindal, B.B.; Subaer, S.; Shaikh, F.; Alraddadi, S. Characterization and properties of geopolymer nanocomposites with different contents of nano-CaCO
_{3}. Constr. Build. Mater.**2020**, 252, 119137. [Google Scholar] [CrossRef] - Atuchin, V.V.; Kesler, V.G.; Kokh, A.E.; Pokrovsky, L.D. X-ray photoelectron spectroscopy study of b-BaB
_{2}O_{4}optical surface. Appl. Surf. Sci.**2004**, 223, 352–360. [Google Scholar] [CrossRef] - Ramana, C.V.; Vemuri, R.S.; Kaichev, V.V.; Kochubey, V.A.; Saraev, A.A.; Atuchin, V.V. X-ray photoelectron spectroscopy depth profiling of La
_{2}O_{3}/Si thin films deposited by reactive magnetron sputtering. ACS Appl. Mater. Interfaces**2011**, 3, 4370–4373. [Google Scholar] [CrossRef] - Atuchin, V.V.; Molokeev, M.S.; Yurkin, G.Y.; Gavrilova, T.A.; Kesler, V.G.; Laptash, N.M.; Flerov, I.N.; Patrin, G.S. Synthesis, Structural, Magnetic, and Electronic Properties of Cubic CsMnMoO
_{3}F_{3}Oxyfluoride. J. Phys. Chem. C**2012**, 116, 10162–10170. [Google Scholar] [CrossRef] - Rubio, E.J.; Atuchin, V.V.; Kruchinin, V.N.; Pokrovsky, L.D.; Prosvirin, I.P.; Ramana, C.V. Electronic Structure and Optical Quality of Nanocrystalline Y
_{2}O_{3}Film Surfaces and Interfaces on Silicon. J. Phys. Chem. C**2014**, 118, 13644–13651. [Google Scholar] [CrossRef] - Atuchin, V.V.; Vinnik, D.; Gavrilova, T.A.; Gudkova, S.; Isaenko, L.I.; Jiang, X.; Pokrovsky, L.D.; Prosvirin, I.P.; Mashkovtseva, L.S.; Lin, Z. Flux Crystal Growth and the Electronic Structure of BaFe
_{12}O_{19}Hexaferrite. J. Phys. Chem. C**2016**, 120, 5114–5123. [Google Scholar] [CrossRef] - Kang, L.; Lin, Z.; Qin, J.; Chen, C. Two novel nonlinear optical carbonates in the dee-ultraviolet region: KBeCO
_{3}F and RbAlCO_{3}F_{2}. Sci. Rep.**2013**, 3, 1366. [Google Scholar] [CrossRef] [PubMed][Green Version] - Than, T.T.; Young, J.; Rondinelli, J.M.; Halasyamani, P.S. Mixed-metal carbonate fluorides as deep-ultraviolet non-linear optical materials. J. Am. Chem. Soc.
**2017**, 139, 1285–1295. [Google Scholar] - Zhang, X.; Wu, H.; Cheng, S.; Han, G.; Yang, Z.; Pan, S. K
_{9}[B_{4}O_{5}(OH)_{4}]_{3}(CO_{3})X×7H_{2}O (X = Cl, Br): Synthesis, characterizations, and theoretical studies of noncentrosymmetric halogen borate-carbonates with short UV cutoff edges. Inorg. Chem.**2019**, 58, 6974–6982. [Google Scholar] [CrossRef] [PubMed] - Peng, G.; Lin, C.S.; Yang, Y.; Zhao, D.; Lin, Z.; Ye, N.; Huang, J.S. Y
_{2}(CO_{3})_{3}×H_{2}O and (NH_{4})_{2}Ca_{2}Y_{4}(CO_{3})_{9}×H_{2}O: Partial aviovalent cation substitution enabling evolution from centrosymmetry to noncentrosymmetry for nonlinear optical response. Chem. Mater.**2019**, 31, 52–56. [Google Scholar] [CrossRef] - Chen, K.; Peng, G.; Lin, C.; Luo, M.; Fan, H.; Yang, S.; Ye, N. NaPb
_{2}(CO_{3})_{2}F_{2}(OH)_{1−x}(0 < x ≤ 1): A new member of alkali-lead carbonate fluoride system with large birefringence. J. Solid State Chem.**2020**, 288, 121407. [Google Scholar] [CrossRef] - Zou, G.; Ok, K.M. Novel ultraviolet (UV) nonlinear optical (NLO) materials discovered by chemical substitution-oriented design. Chem. Sci.
**2020**, 11, 5404–5409. [Google Scholar] [CrossRef] - Gong, P.; Liu, X.; Kang, L.; Lin, Z. Inorganic planar p-conjugated groups in nonlinear optical crystals: Review and outlook. Inorg. Chem. Front.
**2020**, 7, 839–952. [Google Scholar] [CrossRef] - Dorfman, S.M.; Badro, J.; Nabiei, F.; Prakapenka, V.B.; Cantoni, M.; Gillet, P. Carbonate stability in the reduced lower mantle. Earth Planet. Sci. Lett.
**2018**, 489, 84–91. [Google Scholar] [CrossRef] - Zolotoyabko, E.; Caspi, E.N.; Fieramosca, J.S.; Von Dreele, R.B.; Marin, F.; Mor, G.; Addadi, L.; Weiner, S.; Politi, Y. Differences between Bond Lengths in Biogenic and Geological Calcite. Cryst. Growth Des.
**2010**, 10, 1207–1214. [Google Scholar] [CrossRef] - Liang, W.; Li, Z.; Yin, Y.; Li, R.; Chen, L.; He, Y.; Dong, H.; Dai, L.; Li, H. Single crystal growth, characterization and high-pressure Raman spectroscopy of impurity-free magnesite (MgCO
_{3}). Phys. Chem. Miner.**2018**, 45, 423–434. [Google Scholar] [CrossRef] - Liang, W.; Yin, Y.; Li, Z.; Li, R.; Li, L.; He, Y.; Dong, H.; Li, Z.; Yan, S.; Zhai, S.; et al. Single crystal growth, crystalline structure investigation and high-pressure behavior of impurity-free siderite (FeCO
_{3}). Phys. Chem. Miner.**2018**, 45, 831–842. [Google Scholar] [CrossRef] - Gao, J.; Zhu, F.; Lai, X.-J.; Huang, R.; Qin, S.; Chen, D.; Liu, J.; Zheng, L.-R.; Wu, X. Compressibility of a natural smithsonite ZnCO
_{3}up to 50 GPa. High Press. Res.**2014**, 34, 89–99. [Google Scholar] [CrossRef] - Liang, W.; Li, L.; Li, R.; Yin, Y.; Li, Z.; Liu, X.; Shan, S.; He, Y.; Meng, Y.; Li, Z.; et al. Crystal structure of impurity-free rhodochrosite (MnCO
_{3}) and thermal expansion properties. Phys. Chem. Miner.**2020**, 47, 1–11. [Google Scholar] [CrossRef] - Chariton, S.; Cerantola, V.; Ismailova, L.; Bykova, E.; Bykov, M.; Kupenko, I.; McCammon, C.; Dubrovinsky, L.S. The high-pressure behavior of spherocobaltite (CoCO
_{3}): A single crystal Raman spectroscopy and XRD study. Phys. Chem. Miner.**2018**, 45, 59–68. [Google Scholar] [CrossRef] - Reddy, B.J.; Frost, R.L. Electronic and vibrational spectra of gaspeite. Neues Jahrb. Mineral. Mon.
**2004**, 525–536. [Google Scholar] [CrossRef] - Liu, L.G.; Lin, C.C. A Calcite → aragonite-type phase transition in CdCO
_{3}. Am. Mineral.**1997**, 82, 643–646. [Google Scholar] [CrossRef] - Liu, Z.T.Y.; Burton, B.P.; Khare, S.V.; Sarin, P. First-principles phase diagram calculations for the carbonate quasibinary systems CaCO
_{3}-ZnCO_{3}, CdCO_{3}-ZnCO_{3}, CaCO_{3}-CdCO_{3}and MgCO_{3}-ZnCO_{3}. Chem. Geol.**2016**, 443, 137–145. [Google Scholar] [CrossRef][Green Version] - Zucchini, A.; Comodi, P.; Nazzareni, S.; Hanfland, M. The effect of cation ordering and temperature on the high-pressure behaviour of dolomite. Phys. Chem. Miner.
**2014**, 41, 783–793. [Google Scholar] [CrossRef] - Garavelli, C.G.; Vurro, F.; Fioravanti, G.C. Minrecordite, a new mineral from Tsumeb. Mineral. Rec.
**1982**, 13, 131–136. [Google Scholar] - Chai, L.; Navrotsky, A. Synthesis, characterization, and energetics of solid solution along the dolomite-ankerite join, and implications for the stability of ordered CaFe(CO
_{3})_{2}. Am. Mineral.**1996**, 81, 1141–1147. [Google Scholar] [CrossRef] - Frondel, C.; Bauer, C.L.H. Kutnahorite: A manganese dolomite, CaMn(CO
_{3})_{2}. Am. Mineral.**1955**, 40, 748–760. [Google Scholar] - Tareen, J.A.K.; Fazeli, A.R.; Basavalingu, B.; Bhandige, G.T. Decarbonation curves and associated thermodynamic data for synthetic Cd-dolomites CdMg(CO
_{3})_{2}, CdMn(CO_{3})_{2}and CdZn(CO_{3})_{2}. J. Therm. Anal.**1995**, 44, 937–954. [Google Scholar] [CrossRef] - Bromiley, F.A.; Ballaran, T.B.; Langenhorst, F.; Seifert, F. Order and miscibility in the otavite-magnesite solid solution. Am. Mineral.
**2007**, 92, 829–836. [Google Scholar] [CrossRef] - Effenberger, H.; Zemann, J. Single crystal X-ray investigation of norsethite, BaMg(CO
_{3})_{2}: One more mineral with an aplanar carbonate group. Z. Krist.**1985**, 171, 275–280. [Google Scholar] [CrossRef] - Liang, W.; Li, L.; Yin, Y.; Li, R.; Li, Z.; Liu, X.; Zhao, C.; Yang, S.; Meng, Y.; Li, Z.; et al. Crystal structure of norsethite-type BaMn(CO
_{3})_{2}and its pressure-induced transition investigated by Raman spectroscopy. Phys. Chem. Miner.**2019**, 46, 771–781. [Google Scholar] [CrossRef] - Pippinger, T.; Miletich, R.; Effenberger, H.; Hofer, G.; Lotti, P.; Merlini, M. High-pressure polymorphism and structural transitions of norsethite, BaMg(CO
_{3})_{2}. Phys. Chem. Miner.**2014**, 41, 737–755. [Google Scholar] [CrossRef] - Antao, S.M.; Hassan, I. The orthorhombic structure of CaCO
_{3}, SrCO_{3}, PbCO_{3}and BaCO_{3}: Linear structure trends. Can. Mineral.**2009**, 47, 1245–1255. [Google Scholar] [CrossRef] - Ye, Y.; Smyth, J.R.; Boni, P. Crystal structure and thermal expansion of aragonite-group carbonates by single-crystal X-ray diffraction. Am. Mineral.
**2012**, 97, 707–712. [Google Scholar] [CrossRef] - Kaabar, W.; Bott, S.; Devonshire, R. Raman spectroscopic study of mixed carbonate materials. Spectrochim. Acta A
**2011**, 78, 136–141. [Google Scholar] [CrossRef] - Litasov, K.; Shatskiy, A.; Gavryushkin, P.N.; Bekhtenova, A.; Dorogokupets, P.I.; Danilov, B.S.; Higo, Y.; Akilbekov, A.T.; Inerbaev, T.M. P-V-T equation of state of CaCO
_{3}aragonite to 29 GPa and 1673 K: In situ X-ray diffraction study. Phys. Earth Planet. Inter.**2017**, 265, 82–91. [Google Scholar] [CrossRef] - Lobanov, S.S.; Dong, X.; Martirosyan, N.S.; Samtsevich, A.I.; Stevanovic, V.; Gavryushkin, P.N.; Litasov, K.D.; Greenberg, E.; Prakapenka, V.B.; Oganov, A.R.; et al. Raman spectroscopy and x-ray diffraction of sp3CaCO3 at lower mantle pressures. Phys. Rev. B
**2017**, 96, 104101. [Google Scholar] [CrossRef][Green Version] - Smith, D.; Lawler, K.V.; Martinez-Canales, M.; Daykin, A.W.; Fussell, Z.; Smith, G.A.; Childs, C.; Smith, J.S.; Pickard, C.J.; Salamat, A. Postaragonite phases of CaCO
_{3}at lower mantle pressures. Phys. Rev. Mater.**2018**, 2, 013605. [Google Scholar] [CrossRef] - Zhang, Z.; Mao, Z.; Liu, X.; Zhang, Y.; Brodholt, J.P. Stability and Reactions of CaCO
_{3}polymorphs in the Earth’s Deep Mantle. J. Geophys. Res. Solid Earth**2018**, 123, 6491–6500. [Google Scholar] [CrossRef][Green Version] - Zhu, Y.; Li, Y.; Ding, H.; Lu, A.; Li, Y.; Wang, C. Infrared emission properties of a kind of natural carbonate: Interpretation from mineralogical analysis. Phys. Chem. Miner.
**2020**, 47, 1–15. [Google Scholar] [CrossRef] - Weir, C.E.; Lippincott, E.R. Infrared studies of aragonite, calcite, and vaterite type structures in the borates, carbonates, and nitrates. J. Res. Natl. Bur. Stand. Sect. A Phys. Chem.
**1961**, 65, 173–180. [Google Scholar] [CrossRef] - Bischoff, W.D.; Sharma, S.K.; Mackenzie, F.T. Carbonate ion disorder in synthetic and biogenic magnesian calcites—A Raman spectral study. Am. Mineral.
**1985**, 70, 581–589. [Google Scholar] - Lin, C.-C.; Liu, L.-G. Post-aragonite phase transitions in strontianite and cerussite—A high pressure Raman spectroscopic study. J. Phys. Chem. Solids
**1997**, 58, 977–987. [Google Scholar] [CrossRef] - Valenzano, L.; Noël, Y.; Orlando, R.; Zicovich-Wilson, C.M.; Ferrero, M.; Dovesi, R. Ab initio vibrational spectra and dielectric properties of carbonates: Magnesite, calcite and dolomite. Theor. Chem. Acc.
**2007**, 117, 991–1000. [Google Scholar] [CrossRef] - Kalinin, N.V.; Saleev, V.A. Ab initio modeling of Raman and infrared spectra of calcite. Comput. Opt.
**2018**, 42, 263–266. [Google Scholar] [CrossRef] - Sun, J.; Wu, Z.; Cheng, H.; Zhang, Z.; Frost, R.L. A Raman spectroscopic comparison of calcite and dolomite. Spectrochim. Acta Part A Mol. Biomol. Spectrosc.
**2014**, 117, 158–162. [Google Scholar] [CrossRef][Green Version] - Perrin, J.; Vielzeuf, D.; Laporte, D.; Ricolleau, A.; Rossman, G.R.; Floquet, N. Raman characterization of synthetic magnesian calcites. Am. Mineral.
**2016**, 101, 2525–2538. [Google Scholar] [CrossRef] - Liu, J.; Caracas, R.; Fan, D.; Bobocioiu, E.; Zhang, D.; Mao, W.L. High-pressure compressibility and vibrational properties of (Ca,Mn)CO
_{3}. Am. Mineral.**2016**, 101, 2723–2730. [Google Scholar] [CrossRef] - Minch, R.; Seoung, D.-H.; Ehm, L.; Winkler, B.; Knorr, K.; Peters, L.; Borkowski, L.; Parise, J.B.; Lee, Y.; Dubrovinsky, L.S.; et al. High-pressure behavior of otavite (CdCO
_{3}). J. Alloy Compd.**2010**, 508, 251–257. [Google Scholar] [CrossRef] - Dufresne, W.J.; Rufledt, C.J.; Marshall, C.P. Raman spectroscopy of the eight natural carbonate minerals of calcite structure. J. Raman Spectrosc.
**2018**, 49, 1999–2007. [Google Scholar] [CrossRef] - Efthimiopoulos, I.; Germer, M.; Jahn, S.; Harms, M.; Reichmann, H.J.; Speziale, S.; Schade, U.; Sieber, M.; Koch-Müller, M. Effects of hydrostaticity on the structural stability of carbonates at lower mantle pressures: The case study of dolomite. High Press. Res.
**2018**, 39, 36–49. [Google Scholar] [CrossRef][Green Version] - Efthimiopoulos, I.; Jahn, S.; Kuras, A.; Schade, U.; Koch-Müller, M. Combined high-pressure and high-temperature vibrational studies of dolomite: Phase diagram and evidence of a new distorted modification. Phys. Chem. Miner.
**2017**, 44, 465–476. [Google Scholar] [CrossRef] - Martens, W.N.; Rintoul, L.; Kloprogge, J.T.; Frost, R.L. Single crystal raman spectroscopy of cerussite. Am. Mineral.
**2004**, 89, 352–358. [Google Scholar] [CrossRef][Green Version] - Wang, X.; Ye, Y.; Wu, X.; Smyth, J.R.; Yang, Y.; Zhang, Z.; Wang, Z. High-temperature Raman and FTIR study of aragonite-group carbonates. Phys. Chem. Miner.
**2018**, 46, 51–62. [Google Scholar] [CrossRef] - Efthimiopoulos, I.; Müller, J.; Winkler, B.; Otzen, C.; Harms, M.; Schade, U.; Koch-Müller, M. Vibrational response of strontianite at high pressures and high temperatures and construction of P–T phase diagram. Phys. Chem. Miner.
**2019**, 46, 27–35. [Google Scholar] [CrossRef] - Lane, M.D.; Christensen, P.R. Thermal infrared emission spectroscopy of anhydrous carbonates. J. Geophys. Res.
**1997**, 102, 25581–25592. [Google Scholar] [CrossRef] - Deines, P. Carbon isotope effects in carbonate systems. Geochim. Cosmochim. Acta
**2004**, 68, 2659–2679. [Google Scholar] [CrossRef] - Brusentsova, T.N.; Peale, R.E.; Maukonen, D.; Harlow, G.E.; Boesenberg, J.S.; Ebel, D.; Prêt, D.; Sammartino, S.; Beaufort, D.; Fialin, M.; et al. Far infrared spectroscopy of carbonate minerals. Am. Mineral.
**2010**, 95, 1515–1522. [Google Scholar] [CrossRef] - Farsang, S.; Facq, S.; Redfern, S.A.T. Raman modes of carbonate minerals as pressure and temperature gauges up to 6 GPa and 500 °C. Am. Mineral.
**2018**, 103, 1988–1998. [Google Scholar] [CrossRef] - Erba, A.; Baima, J.; Bush, I.; Orlando, R.; Dovesi, R. Large-Scale Condensed Matter DFT Simulations: Performance and Capabilities of the CRYSTAL Code. J. Chem. Theory Comput.
**2017**, 13, 5019–5027. [Google Scholar] [CrossRef] [PubMed] - Dovesi, R.; Erba, A.; Orlando, R.; Zicovich-Wilson, C.M.; Civalleri, B.; Maschio, L.; Rérat, M.; Casassa, S.; Baima, J.; Salustro, S.; et al. Quantum-mechanical condensed matter simulations with CRYSTAL. Wiley Interdiscip. Rev. Comput. Mol. Sci.
**2018**, 8, e1360. [Google Scholar] [CrossRef] - Becke, A.D. Density functional thermochemistry. III. The role of exact exchange. J. Chem. Phys.
**1993**, 98, 5648–5652. [Google Scholar] [CrossRef][Green Version] - Lee, C.; Yang, W.; Parr, R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B
**1988**, 37, 785–789. [Google Scholar] [CrossRef][Green Version] - Valenzano, L.; Torres, F.J.; Doll, K.; Pascale, F.; Zicovich-Wilson, C.M.; Dovesi, R. Ab InitioStudy of the Vibrational Spectrum and Related Properties of Crystalline Compounds; the Case of CaCO
_{3}Calcite. Z. Phys. Chem.**2006**, 220, 893–912. [Google Scholar] [CrossRef] - Peintinger, M.F.; Oliveira, D.V.; Bredow, T. Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations. J. Comput. Chem.
**2013**, 34, 451–459. [Google Scholar] [CrossRef] - Laun, J.; Oliveira, D.V.; Bredow, T. Consistent gaussian basis sets of double- and triple-zeta valence with polarization quality of the fifth period for solid-state calculations. J. Comput. Chem.
**2018**, 39, 1285–1290. [Google Scholar] [CrossRef] - Piskunov, S.; Heifets, E.; Eglitis, R.; Borstel, G. Bulk properties and electronic structure of SrTiO
_{3}, BaTiO_{3}, PbTiO_{3}perovskites: An ab initio HF/DFT study. Comput. Mater. Sci.**2004**, 29, 165–178. [Google Scholar] [CrossRef] - Evarestov, R.; Kotomin, E.A.; Mastrikov, Y.; Gryaznov, D.; Heifets, E.; Maier, J. Comparative density-functional LCAO and plane-wave calculations ofLaMnO3surfaces. Phys. Rev. B
**2005**, 72, 214411. [Google Scholar] [CrossRef][Green Version] - Sophia, G.; Baranek, P.; Sarrazin, C.; Rérat, M.; Dovesi, R. First-principles study of the mechanisms of the pressure-induced dielectric anomalies in ferroelectric perovskites. Phase Transit.
**2013**, 86, 1069–1084. [Google Scholar] [CrossRef] - Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188. [Google Scholar] [CrossRef] - Pascale, F.; Zicovich-Wilson, C.M.; Gejo, F.L.; Civalleri, B.; Orlando, R.; Dovesi, R. The calculation of the vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code. J. Comput. Chem.
**2004**, 25, 888–897. [Google Scholar] [CrossRef] [PubMed] - Zicovich-Wilson, C.M.; Pascale, F.; Roetti, C.; Saunders, V.R.; Orlando, R.; Dovesi, R. Calculation of the vibration frequencies of alpha-quartz: The effect of Hamiltonian and basis set. J. Comput. Chem.
**2004**, 25, 1873–1881. [Google Scholar] [CrossRef] [PubMed] - Carteret, C.; De La Pierre, M.; Dossot, M.; Pascale, F.; Erba, A.; Dovesi, R. The vibrational spectrum of CaCO
_{3}aragonite: A combined experimental and quantum-mechanical investigation. J. Chem. Phys.**2013**, 138, 014201. [Google Scholar] [CrossRef][Green Version] - Baima, J.; Ferrabone, M.; Orlando, R.; Erba, A.; Dovesi, R. Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations. Phys. Chem. Miner.
**2016**, 43, 137–149. [Google Scholar] [CrossRef][Green Version] - Maschio, L.; Kirtman, B.; Rérat, M.; Orlando, R.; Dovesi, R. Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method in an atomic orbital basis. II. Validation and comparison with experiments. J. Chem. Phys.
**2013**, 139, 164102. [Google Scholar] [CrossRef][Green Version] - Korabel’Nikov, D.; Zhuravlev, Y.N. Structural, elastic, electronic and vibrational properties of a series of sulfates from first principles calculations. J. Phys. Chem. Solids
**2018**, 119, 114–121. [Google Scholar] [CrossRef] - Shannon, R.D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. Sect. A
**1976**, 32, 751–767. [Google Scholar] [CrossRef] - Grzechnik, A.; Simon, P.; Gillet, P.; McMillan, P. An infrared study of MgCO
_{3}at high pressure. Phys. B Condens. Matter**1999**, 262, 67–73. [Google Scholar] [CrossRef] - Clark, S.J.; Jouanna, P.; Haines, J.; Mainprice, D. Calculation of infrared and Raman vibration modes of magnesite at high pressure by density-functional perturbation theory and comparison with experiments. Phys. Chem. Miner.
**2010**, 38, 193–202. [Google Scholar] [CrossRef] - Yao, C.; Wu, Z.; Zou, F.; Sun, W. Thermodynamic and Elastic Properties of Magnesite at Mantle Conditions: First-Principles Calculations. Geochem. Geophys. Geosyst.
**2018**, 19, 2719–2731. [Google Scholar] [CrossRef] - Gillet, P.; Biellmann, C.; Reynard, B.; McMillan, P. Raman spectroscopic studies of carbonates part I: High-pressure and high-temperature behaviour of calcite, magnesite, dolomite and aragonite. Phys. Chem. Miner.
**1993**, 20, 1–18. [Google Scholar] [CrossRef] - Schauble, E.A.; Ghosh, P.; Eiler, J.M. Preferential formation of 13C–18O bonds in carbonate minerals, estimated using first-principles lattice dynamics. Geochim. Cosmochim. Acta
**2006**, 70, 2510–2529. [Google Scholar] [CrossRef] - De La Pierre, M.; Carteret, C.; Maschio, L.; André, E.; Orlando, R.; Dovesi, R. The Raman spectrum of CaCO3polymorphs calcite and aragonite: A combined experimental and computational study. J. Chem. Phys.
**2014**, 140, 164509. [Google Scholar] [CrossRef][Green Version] - Spivak, A.V.; Solopova, N.; Cerantola, V.; Bykova, E.; Zakharchenko, E.; Dubrovinsky, L.S.; Litvin, Y. Raman study of MgCO
_{3}–FeCO_{3}carbonate solid solution at high pressures up to 55 GPa. Phys. Chem. Miner.**2014**, 41, 633–638. [Google Scholar] [CrossRef] - Siva, T.; Muralidharan, S.; Sathiyanarayanan, S.; Manikandan, E.; Jayachandran, M. Enhanced Polymer Induced Precipitation of Polymorphous in Calcium Carbonate: Calcite Aragonite Vaterite Phases. J. Inorg. Organomet. Polym. Mater.
**2017**, 27, 770–778. [Google Scholar] [CrossRef] - Farfan, G.A.; Boulard, E.; Wang, S.; Mao, W.L. Bonding and electronic changes in rhodochrosite at high pressure. Am. Mineral.
**2013**, 98, 1817–1823. [Google Scholar] [CrossRef] - Zhao, C.; Li, H.; Jiangb, J.; He, Y.; Liang, W. Phase Transition and vibration properties of MnCO
_{3}at high pressure and high-temperature by Raman spectroscopy. High Press. Res.**2018**, 38, 212–223. [Google Scholar] [CrossRef] - Böttcher, M.E.; Gehlken, P.-L.; Skogby, H.; Reutel, C. The vibrational spectra of BaMg(CO
_{3})_{2}(norsethite). Miner. Mag.**1997**, 61, 249–256. [Google Scholar] [CrossRef] - Chaney, J.; Santillán, J.D.; Knittle, E.; Williams, Q. A high-pressure infrared and Raman spectroscopic study of BaCO
_{3}: The aragonite, trigonal and Pmmn structures. Phys. Chem. Miner.**2015**, 42, 83–93. [Google Scholar] [CrossRef] - Brooker, M.H.; Sunder, S.; Taylor, P.; Lopata, V.J. Infrared and Raman spectra and X-ray diffraction studies of solid lead(II) carbonates. Can. J. Chem.
**1982**, 61, 494–502. [Google Scholar] [CrossRef] - Catalli, K.; Santillán, J.; Williams, Q. A high pressure infrared spectroscopic study of PbCO
_{3}-cerussite: Constraints on the structure of the post-aragonite phase. Phys. Chem. Miner.**2005**, 32, 412–417. [Google Scholar] [CrossRef] - Frech, R.; Wang, E.C.; Bates, J.B. The i.r. and Raman spectra of CaCO
_{3}(aragonite). Spectrochim. Acta Part A Mol. Spectrosc.**1980**, 36, 915–919. [Google Scholar] [CrossRef] - Bayarjargal, L.; Fruhner, C.-J.; Schrodt, N.; Winkler, B. CaCO
_{3}phase diagram studied with Raman spectroscopy at pressures up to 50 GPa and high temperatures and DFT modeling. Phys. Earth Planet. Inter.**2018**, 281, 31–45. [Google Scholar] [CrossRef] - Biedermann, N.; Speziale, S.; Winkler, B.; Reichmann, H.J.; Koch-Müller, M.; Heide, G. High-pressure phase behavior of SrCO
_{3}: An experimental and computational Raman scattering study. Phys. Chem. Miner.**2017**, 44, 335–343. [Google Scholar] [CrossRef][Green Version] - Minch, R.; Dubrovinsky, L.S.; Kurnosov, A.; Ehm, L.; Knorr, K.; Depmeier, W. Raman spectroscopic study of PbCO
_{3}at high pressures and temperatures. Phys. Chem. Miner.**2010**, 37, 45–56. [Google Scholar] [CrossRef] - Alía, J.M.; de Mera, Y.D.; Edwards, H.G.M.; Martín, P.G.; Andres, S.L. FT-Raman and infrared spectroscopic study of aragonite-strontianite (CaxSr
_{1−x}CO_{3}) solid solution. Spectrochim. Acta Part A Mol. Biomol. Spectrosc.**1997**, 53, 2347–2362. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Fragments of the crystal structures of (

**a**) CaCO

_{3}(calcite), (

**b**) CaMg(CO

_{3})

_{2}(dolomite), (

**c**) BaMg(CO

_{3})

_{2}(norsethite) and (

**d**) CaCO

_{3}(aragonite) The unit cells are outlined. Lone atoms, excepting those in the unit cells, are omitted for clarity.

**Figure 2.**Calculated infrared spectra (IR) (top) and spectra of Raman light scattering (bottom) of intramolecular ν1, ν2, ν3, ν4, and lattice vibrations of magnesium (red, squares), calcium (black, circles), zinc (blue, triangles), and cadmium (lilac, rhombuses) carbonates with a calcite structure. For comparison, the experimental spectra of calcite are given [68].

**Figure 3.**Calculated infrared spectra (IR) (top) and Raman spectra (bottom) of intramolecular ν1, ν2, ν3, ν4, and lattice vibrations of double calcium-magnesium (black, squares), cadmium-magnesium (red, circles), calcium-manganese (blue, triangles), and calcium-zinc carbonates (lilac, rhombuses) with a dolomite structure.

**Figure 4.**Calculated infrared spectrum (IR) (top) and Raman spectrum (bottom) of intramolecular ν1, ν2, ν3, ν4, and lattice vibrations of double barium-magnesium carbonate in a norsesite-type structure. The solid line is the Gaussian broadening of the frequencies of long-wave oscillations (squares).

**Figure 5.**Calculated infrared spectra (IR) (top) and Raman spectra (bottom) of intramolecular ν1, ν2, ν3, ν4, and lattice vibrations of calcium (black, squares), strontium (red, circles), barium (blue, triangles), lead carbonates (lilac, rhombuses) with aragonite structure. For comparison, the experimental spectra of aragonite and cerussite are given [68] (Reproduced with permission from [68]; Copyright Springer Nature, 2020).

**Table 1.**Calculated lattice constants a, b, c, unit cell volume V, and average distances between the atoms of metal M and oxygen O (R

_{M–O}) and carbon C and oxygen (R

_{C–O}).

Carbonate | a, Å | b, Å | c, Å | V, Å^{3} | R_{M–O}, Å | R_{C–O}, Å |
---|---|---|---|---|---|---|

MgCO_{3} | 4.6624 | 4.6624 | 15.1891 | 285.9527 | 2.1229 | 1.2857 |

CaCO_{3}_C | 5.0385 | 5.0385 | 17.3168 | 380.7118 | 2.3905 | 1.2878 |

ZnCO_{3} | 4.7094 | 4.7094 | 15.1297 | 290.5952 | 2.1344 | 1.2973 |

CdCO_{3} | 4.9819 | 4.9819 | 16.6163 | 357.1529 | 2.3312 | 1.2874 |

CaMg(CO_{3})_{2} | 4.8382 | 4.8382 | 16.2563 | 329.5605 | 2.2571 | 1.2865 |

CdMg(CO_{3})_{2} | 4.8140 | 4.8140 | 15.8629 | 318.3695 | 2.2253 | 1.2862 |

CaMn(CO_{3})_{2} | 4.8295 | 4.8295 | 15.8159 | 319.4686 | 2.2302 | 1.2874 |

CaZn(CO_{3})_{2} | 4.8558 | 4.8558 | 16.2964 | 332.7782 | 2.2648 | 1.2866 |

BaMg(CO_{3})_{2} | 5.0637 | 5.0637 | 17.0662 | 378.9683 | 2.6811 | 1.2846 |

CaCO_{3}_A | 5.0020 | 8.0175 | 5.8581 | 234.9323 | 2.5604 | 1.2857 |

SrCO_{3} | 5.1469 | 8.4418 | 6.1947 | 269.1522 | 2.6838 | 1.2884 |

BaCO_{3} | 5.3665 | 8.9327 | 6.6847 | 320.4459 | 2.8567 | 1.2910 |

PbCO_{3} | 5.2453 | 8.5723 | 6.3725 | 286.5319 | 2.7451 | 1.2897 |

**Table 2.**Linear interpolation coefficients of the wavenumbers of intramolecular (ν

_{4}, ν

_{1}, ν

_{3}) vibrations of the M cation mass for carbonates with aragonite structure, active in RS, obtained from experimental data [68] and theoretical calculations by the B3LYP method. The correlation coefficient is shown in brackets.

Method | ν_{4} | ν_{1} | ν_{3} | v_{3} |
---|---|---|---|---|

Experiment [68] | 713.2 − 0.173·M (0.986) | 1090.1 − 0.17·M (0.919) | 1495.3 − 0.588·M (0.989) | 1597.2 − 0.582·M (0.99) |

B3LYP | 714.3 − 0.128·M (0.933) | 1087.059 − 0.116·M (0.894) | 1486.0 − 0.426·M (0.992) | 1619.0 − 0.638·M (0.998) |

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Zhuravlev, Y.N.; Atuchin, V.V. Comprehensive Density Functional Theory Studies of Vibrational Spectra of Carbonates. *Nanomaterials* **2020**, *10*, 2275.
https://doi.org/10.3390/nano10112275

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Zhuravlev YN, Atuchin VV. Comprehensive Density Functional Theory Studies of Vibrational Spectra of Carbonates. *Nanomaterials*. 2020; 10(11):2275.
https://doi.org/10.3390/nano10112275

**Chicago/Turabian Style**

Zhuravlev, Yurii N., and Victor V. Atuchin. 2020. "Comprehensive Density Functional Theory Studies of Vibrational Spectra of Carbonates" *Nanomaterials* 10, no. 11: 2275.
https://doi.org/10.3390/nano10112275