Complex water dynamics in crystalline [Ca(H2O)2](ReO4)2, studied by the vibrational spectroscopy and proton magnetic resonance

Journal Pre-proof Complex water dynamics in crystalline [Ca(H2O)2](ReO4)2, studied by the vibrational spectroscopy and proton magnetic resonance

Joanna Hetmańczyk, Łukasz Hetmańczyk, Paweł Bilski, Asja Kozak PII:

S0022-2860(19)31719-3

DOI:

https://doi.org/10.1016/j.molstruc.2019.127610

Reference:

MOLSTR 127610

To appear in:

Journal of Molecular Structure

Received Date:

26 August 2019

Accepted Date:

17 December 2019

Please cite this article as: Joanna Hetmańczyk, Łukasz Hetmańczyk, Paweł Bilski, Asja Kozak, Complex water dynamics in crystalline [Ca(H2O)2](ReO4)2, studied by the vibrational spectroscopy and proton magnetic resonance, Journal of Molecular Structure (2019), https://doi.org/10.1016/j. molstruc.2019.127610

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

Journal Pre-proof Complex water dynamics in crystalline [Ca(H2O)2](ReO4)2, studied by the vibrational spectroscopy and proton magnetic resonance Joanna Hetmańczyk1, Łukasz Hetmańczyk1, Paweł Bilski2,3, Asja Kozak2 1Jagiellonian

University, Faculty of Chemistry, Gronostajowa 2, 30-387 Kraków,

Poland 2A.

Mickiewicz University, Faculty of Physics, Umultowska 85, 61-614 Poznań,

Poland. 3Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980,

Dubna, Russia

Abstract A 1H nuclear magnetic resonance study of [Ca(H2O)2](ReO4)2 has confirmed the existence of one phase transition at TCh  261.2 K (on heating) and TCc  231.2 K (on cooling), detected earlier by the DSC method. These transitions were reflected by changes in the temperature dependences of second moments of NMR line M2H. The study revealed anisotropic reorientations of whole [Ca(H2O)2]2+ cations, and the reorientations by 180° jumps of H2O ligands. It was found that the phase transition at TC is associated with the reorientation of H2O signed by oxygen O10 in crystal structure in high temperature phase. The oscillations of the cation as a whole unit around the axis crossing Ca and the middle of O9-O10 distance take place in both phases. From the temperature dependence of the full-width at half-maximum values (FWHM) of the bands connected with r(H2O) mode in IR spectra, we can conclude that the reorientational motions of H2O ligands contribute to the phase transition mechanism. The ligands perform fast (R  10‒11 to 10‒13 s) stochastic reorientational motions in the high temperature phase. The estimated mean value of activation energy for the reorientation of the H2O ligands is ca. 11.1 kJmol–1 from Raman spectroscopy (RS) and 11.6 kJmol–1 from infrared spectroscopy, which is consistent with NMR results.



Corresponding author. Tel. +48 12 686 24 31. E-mail address: [email protected], [email protected] (J. Hetmańczyk).

1

Journal Pre-proof The proton-weighted phonon density functions G(ν) obtained at 5 K show some separate peaks characteristic for ordered phase. Additionally, IR, RS and IINS spectra were calculated by the DFT method and an excellent agreement with the experimental data was obtained using CASTEP code.

Keywords: Polymorphism, molecular reorientations; vibrational spectroscopies (IR, RS and IINS); band shape analysis; Solid-state NMR (1H NMR and T1)

2

Journal Pre-proof 1. Introduction Diaquacalcium perrhenate,[Ca(H2O)2](ReO4)2, belongs to a family of coordination compounds which exhibit a polymorphism connected with the occurrence of reorientational motions of the H2O ligands. Similar compounds with the same anion also exhibit an interesting polymorphism [1–3]. At

room

temperature,

(RT)

diaquacalcium

perrhenate

crystallises

in

the

centrosymmetric monoclinic system (space group I2/a, No. = 15) with the unit cell parameters: a = 18.1302(7) Å, b = 7.0722(2) Å, c = 14.1882(5) Å, α = γ = 90o, β = 109,637o and with eight molecules per unit cell (Z = 8) [4]. However, in the literatures one can find that this compound crystallises in noncentrosymmetric monoclinic space group Cc [5] or C2 [6]. The ReO4– anions have a mostly regular tetrahedral geometry with an average Re-O bond length of 1.72 Å. Each calcium atom in this structure is surrounded by eight oxygen atoms with an average Ca-O distance of ~2.46 Å. There are two inequivalent water molecules in asymmetric unit. One (denoted as O9) is bounded to the cation Ca2+ only, whereas the second (denoted as O10) joins two calcium ions making a bridge between them. The polymorphism of the title compound was investigated by the authors by means of differential scanning calorimetry [4]. The measurements were performed in the temperature range of 300–120 K on cooling and heating of the sample at different rates. One reversible phase transition (PT) has been found at: TCh  261.2 K (onset on heating) and TCc  231.2 K (onset on cooling). The thermal hysteresis

of the phase transition temperature TC is equal to ca. 26.1 K and the heat flow anomaly sharpness suggest that the detected phase transition is a first-order type. The value of transition entropy change (S  5.7 Jmol–1K–1) indicates a disordering of the high temperature phase. Xray single crystal and neutron powder diffraction measurements indicate that the crystal space group (I 2/a) is the same for the high and low temperature phases. However, small changes of water molecule orientation and torsion angles are observed in the structure [4]. Vibrational spectroscopy data (IR and RS) registered in paper [4] are in good agreement with the wavenumbers observed in the literature [7–8]. Characteristic changes in band wavenumbers in the FT–IR and Raman spectra were clearly observed. FT-MIR, FT-FIR and RS measurements showed that bands associated with H2O vibrations modes narrow continuously with decreasing temperature. The general aim of the present study is to find connections of the recorded phase transitions with eventual changes of the rate of stochastic reorientational motions of H2O ligands. We have performed temperature dependent infrared (FT–MIR and FT–FIR), Raman 3

Journal Pre-proof (RS), neutron scattering (IINS) measurements and proton magnetic resonance (1H NMR, T1) in order to establish the relationship between the observed phase transition and reorientational motions of the molecular groups. The IR, RS and IINS methods, besides providing information on vibrational dynamics, can also provide information on fast reorientational molecular motions, of course under the condition that their reorientational correlation time R is of an order from 10−11 to 10−13 s. The 1H NMR T1 and M2 methods may inform us about slow τR: 10–4–10–5 s (M2 method): and fast up 10–11 s (T1 method) reorientational molecular motions. The theoretical infrared absorption, Raman spectra as well as phonon distribution function G(ν) were calculated and compared with the appropriate experimental results. The frequency calculations were performed using periodic boundary conditions (CASTEP code).

2. Experimental details The details of sample preparations are given in Ref. [4]. The same sample was employed in investigations performed in this work. Fourier transforms far- and middle-infrared (FT-FIR and FT-MIR) absorption measurements were performed using a Bruker Vertex 70v vacuum Fourier Transform spectrometer. Details of measurements and sample preparation are described in Ref. [4]. Raman light scattering measurements as a function of temperature were performed with a Bruker SENTERRA Raman microscope working in confocal mode. Samples were excited with the 532 nm line. The RS spectra were recorded during cooling of the sample across the temperature range of 295–87 K (steps of 10 K). Temperature measurements were performed using the Linkam FTIR600 Stage System with LNP95. Temperature accuracy was equal to ±0.1 K. The incoherent inelastic/quasielastic neutron scattering spectra and neutron powder diffraction (NPD) patterns were measured using the time-of-flight method on a NERA spectrometer [9] at the high flux pulsed reactor IBR-2 in Dubna (Russia) at temperatures: 5, 200, 250 and 295 K. Experimental details are the same as in our previous paper [10]. Spin-lattice relaxation time T1 of a polycrystalline sample of [Ca(H2O)2](ReO4)2 was measured by a pulse NMR spectrometer working at 25 MHz using the saturation method. The amplitude of magnetization recovery from the moment of saturation was measured on the solidecho slope, so after application of the pulse sequence 90°-τ -90°90° with τ = 20 s.

4

Journal Pre-proof The proton NMR second moment M2 is obtained by 1H continuous-wave magnetic resonance measurements performed on a homemade instrument operating in the double modulation system. The first derivative of the absorption signal from the r.f. field was recorded upon linear changes in the autodyne generator frequency within a limited range of about 30 MHz. The second moments M2 of the 1H NMR lines were calculated by numerical integration of the spectra of the absorption curve derivatives and corrected for the finite modulated field. The temperature of the sample was controlled by means of a gas-flow cryostat and monitored with a diode DT-470 with a maximum uncertainty of ±1 K. Additionally, in low temperatures the solid-echo method was used to obtain M2. It was measured as a function of temperature range 20–100 K by solid echo obtained using the pulse spectrometer working at frequency 25 MHz. 3. Computational details For the compound [Ca(H2O)2](ReO4)2, the theoretical IR, RS and IINS spectra were computed using density functional perturbation theory (DFPT) method implemented in the CASTEP code [11,12]. The wavenumber calculation was preceded by a geometry optimisation of the experimental structure. The initial structures were constructed from the crystal structure obtained for the high-temperature crystalline phase [4]. Exchange and correlation parts were

approximated using the generalised gradient approximation (GGA) at PBE (Perdew–Burke– Ernzerhof correlation) functional [13,14]. Norm-conserving pseudopotentials were used [15,16] with a plane-wave cut-off energy of 800 eV. The Monkhorst-Pack scheme [17] K-points grid sampling was set at 2× 2× 1 (less than 0.07 Å−1). The convergence threshold for self-consistent iterations was set at 1×10−6 eV/atom. The optimisation parameters were set as follows: energy change: 1×10−5 eV/atom, maximum force: 0.03 eV/Å, maximum stress: 0.05 GPa, and maximum displacement tolerance: 0.1×10−2 Å. Phonon wavenumbers were obtained by diagonalisation of dynamical matrices computed using density functional perturbation theory (DFPT) [12]. The Raman activity tensors were calculated using a hybrid finite displacement/DFPT method [18]. In addition to the direct evaluation of wavenumbers and intensities at zero wave vector, phonon dispersion was also calculated along high symmetry directions throughout the Brillouin zone. Computed Raman activities were transformed into theoretical Raman intensities using the following expression:

5

Journal Pre-proof Ii = 10-12 × (0 - i)4 × (1/i) × RAi ,

(1)

where: Ii is the Raman intensity, RAi is the Raman scattering activities, i is the wavenumber of the normal modes, and 0 denotes the wavenumber of the light of excitation laser (in our measurements 0 = 18797 cm–1) [19]. The theoretical intensities were convoluted with Lorentzian function. The widths of bands in the presented calculated spectra were fitted to the experimental spectra. Intensities of particular transitions in IINS spectra depend on atomic mean-square displacement and can easily be calculated. The aCLIMAX software [20] was used to determine the intensities of transition obtained from the DFPT calculations. Next, these intensities (Dirac delta function) were convoluted with a resolution function characteristic for NERA spectrometer and converted to density of states with the help of the RES program [21]. 4. Results and discussion 4.1. Vibrational analysis The crystal structure of diaquacalcium perrhenate is the same at 295 K and 100 K. The sample crystallises in the centrosymmetric monoclinic system in the space group I 2/a (No. = 15). Hence the mutual exclusion rule causes that bands which are active in the IR are inactive in RS spectroscopy and vice versa. The Ca, Re, O and H atoms occupy 8f Wyckoff positions. For this space group, factor-group analysis predicts the 201 (active optical) +3 (acoustical) phonon modes at the  point [22,23]. Irreducible representations of optical modes is as follows: 51Ag + 50Au + 51Bg + 49Bu. The Ag and Bg modes are Raman active, the Au and Bu modes are infrared active. A factor-group analysis generates 96 internal modes: 24Ag + 24Au + 24Bg + 24Bu; 3 acoustic modes: Au +2Bu; 57 translational: 15Ag + 14Au + 15Bg + 13Bu and 48 rotational modes (including water librations): 12Ag + 12Au + 12Bg + 12Bu. Vibrational FT-IR and RS spectra for [Ca(H2O)2](ReO4)2 were measured as a function of temperature. A detailed description of the vibrational modes in diaquacalcium perrhenate is given in our previous paper [4]. The wavenumber distribution functions G(ν) were calculated in the present paper in the one-phonon-approximation from the time-of-flight IINS spectra [24]. The G(ν) functions of [Ca(H2O)2](ReO4)2 for 5 K and compared with IR and RS spectra in two extreme temperatures in the region 1000–30 cm−1 is shown in Fig. 1. The experimental spectra marked with pink and blue were registered for the high and the low temperature phases, respectively. 6

Journal Pre-proof The most important bands with their tentative assignment are presented in Figures 1 and 3 (will be described later in the text). The G(ν) spectrum obtained for the low temperature phase (5 K) shows some separate peaks characteristic for ordered phase. The G(ν) spectrum obtained at 295 K is very diffused due to a dynamical disorder of H2O molecules connected with their

9.3 K

800

700

(OCaO)

(OReO)

skeletal bending deformations

L(lattice)

r(H2O)

w+r(H2O)

600

500

400

500

400

300

200

100

300

200

100

(OReO)

(b)

t(H2O)

as(ReO)

s(ReO)

900

w(H2O)

295 K

1000

Raman Scattering Intensity

(a)

as(ReO)

w(H2O)

s(ReO)

Absorbance

fast molecular reorientational motions.

295 K 87 K

1000

900

800

700

600 (c)

1000

900

800

700

600

500

400

(OCaO)

w(H2O)

r(H2O)

r(H2O)

w+r(H2O)

t(H2O)

5K

w(H2O)

G()

295 K skeletal bending deformations

300

200

L(lattice)

100

Wavenumber (cm-1) Figure 1. Comparison of the experimental (a) IR, (b) Raman spectra, and (c) phonon density of states spectrum G() (IINS) in the range of 1000–30 cm−1 for [Ca(H2O)2](ReO4)2. Figures 2(a) and 2(b) present the calculated FT-IR and RS spectra compared with the experimental spectra in the lowest temperatures in the wavenumber range (4000–50 cm−1). The bands whose temperature dependencies in the IR and RS spectra are analysed and discussed later in the work are marked in the Figs. 2(a) and (b) as FWHM(T).

7

Journal Pre-proof Optical Vibrational Spectroscopy (a)

Absorbance

**

FT-IR

9.6 K Experimental IR

FWHM (T), (H2O)

** *

CASTEP calculation GGA PBE

Raman Scattering Intensity

4000 3750 3500 3250 3000 2750 2500 2250 2000 1750 1500 1250 1000 750

500

250

0

500

250

0

RS

(b) FWHM (T), s(OH)

87 K Experimental RS

CASTEP calculation GGA PBE

4000 3750 3500 3250 3000 2750 2500 2250 2000 1750 1500 1250 1000 750

Wavenumber (cm-1)

Figure 2. Experimental vibrational (a) IR and (b) RS spectra of [Ca(H2O)2](ReO4)2 in the lowest temperatures compared with calculated ones by DFT methods (* denotes bands of Nujol). The bands which are discussed later are marked as FWHM(T). In the present paper, bands observed in the calculated spectra were assigned based on the CASTEP calculations of phonon eigenvectors and visualisation of individual normal vibrations, and supported by comparing their wavenumbers with the literature data collected for similar complexes[1,2,25]. We have obtained a good agreement between the calculated and experimental IR and RS spectra. The procedure for calculating the theoretical function G(ν) is described in the section III Computational details of this paper. The calculations were performed for a structure determined at room temperature at  point and throughout the whole Brillouine zone (BZ). In Fig. 3, the experimental G() spectra were compared with the calculated and a good agreement was achieved.

8

Journal Pre-proof Incoherent Inelastic Neutron Scattering (IINS)

800

700

500

(OCaO)

w(H2O)

(OCaO)

w(H2O)

r(H2O)

r(H2O)

r(H2O)

t(H2O)

r(H2O)

w+r(H2O)

600

(OCaO)

900

skeletal bending deformations L(lattice)

w(H2O)

1000

r(H2O)

Castep calculation point

r(H2O)

w(H2O)

Castep calcuation BZ

w(H2O)

Experimental 5 K

w+r(H2O) w+r(H2O) w(H2O) w(H2O) t(H2O) t(H2O)

w(H2O)

G()

w(H2O)

Eksperimental 295 K

400

300

200

100

-1

Wavenumber (cm ) Figure 3. Experimental phonon density of states spectrum G() at two extreme temperatures of [Ca(H2O)2](ReO4)2 and spectra calculated by DFT methods. A detailed description of the librational modes of water molecules in diaquacalcium perrhenate is depicted in Fig. 3. The calculated spectra have not been scaled. A combination of infrared, Raman and incoherent inelastic neutron scattering (IINS) spectroscopies results with periodic density functional theory calculations was used to provide a complete assignment of the vibrational spectra of [Ca(H2O)2](ReO4)2. Calculated and experimental IR, RS and IINS spectra registered for [Ca(H2O)2](ReO4)2 can be divided into a few characteristic ranges of the wavenumbers. The O-H stretching modes (symmetrical and asymmetrical) of the water molecules are observed in the range 3600–3000 cm-1 (see Fig. 2). The calculated symmetric stretching modes have been found to be shifted to lower wavenumbers in respect to the experimental values. The bending δ(HOH) modes were localised in the wavenumbers range from 1680 to1510 cm-1, which can be seen in Figure 2 (IR spectra). In the region of 1050–870 cm‒1 we can observe a very strong band with shoulder bands. These bands can be interpreted as symmetrical and asymmetrical stretching Re–O modes from ReO4- anions mixed with twisting t(H2O) modes of H2O molecules. The calculated modes are shifted towards the lower wavenumbers in relation to the experimental modes (see 9

Journal Pre-proof Figs. 1 and 2). As we can see in Figs. 1 and 3 in the experimental spectra G(), the stretching Re-O modes are not observed. In the wavenumbers region 700–360 cm-1, the bands can be assigned to librational modes of H2O molecules: wagging (out-of-plane bend) w(H2O), rocking (in-plane bend) r(H2O) and twisting t(H2O) modes. Details of the librational bands assignments are presented in Figs. 1 and 3. The Raman spectrum does not contain librational modes of H2O ligands. In the vicinity of 370–320 cm−1 (IR and RS spectra), the bending deformation δ(OReO) modes are observed, whereas they are not observed in the experimental spectra G(). The bands between 310–290 cm−1 are related to bending δ(OCaO) deformation modes. The spectral area below 250 cm−1 is connected mainly with skeletal bending deformations and lattice vibrations.This comparison indicates that there is a good qualitative agreement of the calculated spectrum with the experimental one. 4.2. Molecular motions and phase transition (IR and RS bands shape vs. T) Temperature dependent infrared and Raman measurements for [Ca(H2O)2](ReO4)2 were performed end evaluated in order to investigate the reorientational dynamics of anion and ligands in the high and low-temperature phases. In this part of the manuscript, we will present and discuss the temperature evolution of some Raman and infrared active bands. The band shape analysis can provide some useful information on the dynamics of anion and ligands. Such an evaluation was performed for selected IR and RS bands. The choice of analysed bands was made according to the following criteria. Firstly, the band should not overlap with other peaks (i.e. it should be isolated from others), secondly, it should describe possibly one type of motion, and finally its FWHM (a full half-maximum full-width analysis) should change with temperature. It is worth noticing that this analysis can give information on the molecular reorientational motions only when they occur on a 10–11–10–13 s time scale because the reorientational correlation time R is inversely proportional to the FWHM of the spectral IR and RS bands. The temperature dependence of the FWHM of the bands is determined by the following expression [26–28]: FWHM(T) = (a + bT) + c·exp(-

Ea ), RT

(2)

where: a, b, c and Ea are fitting parameters. Here the Ea is activation energy of the reorientation process. The linear part of equation (2) is associated with the vibrational relaxation, and the 10

Journal Pre-proof exponential term is associated with rotational relaxation and corresponds to the thermal reorientational motions of a diffusion nature. In the present paper, IR and RS data were analysed in more detail in order to shed more light on the reorientational motion of water molecules. The bands which are discussed are visible in Figures 1 and 2. In the wavenumber range 527–371 cm–1, one can see two IR bands; the discussed bands were approximated by two Lorentzian contributions. Figure 4 shows an example of fitting performed at two extreme temperatures (Fig. 4(a) 290 K and Fig. 4(b) 9.3 K).

(a)

experimental points

290 K

Lorentz Peak 1 Lorentz Peak 2 Total fit

Absorbance

FWHM (T)

520

500

480

(b)

460

440

420

400

380

440

420

400

380

9.3 K

Absorbance

FWHM (T)

520

500

480

460

-1

Wavenumber (cm )

Figure 4. Examples of a decomposition of the broad infrared band into two components (Lorentz functions) at two extreme temperatures: (a) 290 K and (b) 9.3 K. Analysis of the temperature dependency of the FWHM was carried out for the band at 501 cm-1. It is associated with librational mode of water molecules r(H2O). 11

Journal Pre-proof Figure 5 depicts the temperature dependences of the FWHM of the infrared bands connected with r mode, located at ca. 501 cm-1. During the cooling of the sample from the room temperature, the FWHM of this band decreases exponentially down to the temperature 225 K. Below TC the changes of FWHM are small and it can be said that this temperature dependency reaches a plateau. This indicates that below phase transition temperature at ~225 K, the reorientational motion of the H2O molecules (most probably about the twofold symmetry axis) is slowed down and is beyond the time scale available for vibrational spectroscopy. Solid lines represent fitting of equation (2) to all experimental points (phase I and II). The fitted parameters are listed in Table 1. The mean value of activation energy Ea(I/II) obtained from the analysis of this band is equal to 11.6 kJmol‒1. 100

IR spectra 90

FWHM(T) = (a + bT) + c·exp(-

Ea ) RT

501 cm-1 r(H2O)

FWHM (cm-1)

80 Ea(I/II)=11.6 kJ mol-1

70

60

50

40

30 0

25

50

75

100

125

150

175

200

225

250

275

300

Temperature (K) Figure 5. Temperature dependence of FWHM of infrared band at 501 cm−1, associated with r(H2O) mode in [Ca(H2O)2](ReO4)2 sample. Solid lines represent fitting of equation (2) to all experimental points (phase I and II).Vertical green lines correspond to the phase transitions identified on the basis of DSC measurements on cooling (solid line) and on heating (broken line).

12

Journal Pre-proof Table 1. The fitted parameters: a, b, c and Ea for the temperature dependence of FWHM of the infrared band at 501 cm-1 associated with r(H2O) mode obtained in the temperature range 290–9.3 K for [Ca(H2O)2](ReO4)2. analyzed IR band at ~501 cm-1, r(H2O) mode Fitted parameters

Phase I/II 50.72 ± 1.26

a

(cm-1)

b

(cm-1K-1)

c

(cm-1)

4292.60 ± 315.80

Ea (kJmol-1)

11.60 ± 1.50

0.0246 ± 0.0080

The obtained value is very close to those registered for [Ca(H2O)6]Cl2 (Ea= 11.9 kJmol1)

compound [29]. We observe for both compounds similar behaviour of the water reorientation

dynamics in the PT. In the high-temperature phase, the ligands perform reorientation movements that are inhibited around the PT. The dynamics of ligands was also analysed for Raman spectra. The Raman temperature dependent data were collected within the wavenumber ranges of 3700–3300, 1070–850 and 450–50 cm−1. The most interesting changes can be noticed for the band at 3403 cm-1 (marked in Fig. 2) connected with the symmetric stretching modes (s(OH)). During the cooling of the sample, the intensity changes and narrowing of this band can be noticed in the region of the PT. This band was chosen for further analysis. Figure 6 presents the temperature dependence of the FWHM of the discussed band at ca. 3403 cm–1.

13

Journal Pre-proof 110 100

Raman spectra 3403 cm-1 s(OH)

90

FWHM (cm-1)

80 70 60 50

Ea(I/II) = 11.1 kJ mol-1

40 30 20 10 0 80

100

120

140

160

180

200

220

240

260

280

300

Temperature (K) Figure 6. Temperature dependence of FWHM of Raman band at 3403 cm−1, associated with the stretching vibrations of water molecules, s(OH) mode in [Ca(H2O)2](ReO4)2 sample. Vertical green lines correspond to the phase transitions identified on the basis of DSC measurements on cooling (solid line) and on heating (broken line). During the cooling of the sample from the room temperature, the FWHM of this band decreases exponentially down to the temperature 87 K. The solid line represents fitting of equation (2) to the experimental points registered in temperature range 295–87 K (phase I and II).The fitted parameters are listed in Table 2. The estimated activation energy value for the reorientation of H2O molecules anions is Ea = 11.1 ± 0.4 kJmol‒1. Table 2. The fitted parameters: a, b, c and Ea for the temperature dependence of FWHM of the Raman bands at 3403 cm-1 associated with stretching vibrations of water molecules s(OH) mode obtained in the temperature range 295–87 K for [Ca(H2O)2](ReO4)2. analyzed RS band at ~3403 cm-1, s mode Fitted parameters

Phase I/II

a

(cm-1)

2.47 ± 0.51

b

(cm-1K-1)

0.061 ± 0.009

c

(cm-1)

6570.52 ± 933.04

Ea (kJmol-1)

11.10 ± 0.40 14

Journal Pre-proof 4.3. Hydrogen bonds Figure 7(a) presents the evolution of intensity of peaks associated with hydrogen bonds; these bonds are observed in the spectral range 2250–2000 cm-1 in IR data. Figure 7(b) presents a contour plot of bands connected with hydrogen bonds. In the high temperatures, no bands are observed (or they are very diffused and smeared into background) in the discussed wavenumbers region. As the sample is cooled, the three well separated bands start to appear, and they are visible at the following wavenumbers: 2171, 2128, 2065 cm-1.

(a)

290 K

Absorbance

240 K 220 K

150 K 9.6 K

2250

2200

2150

2100

2050

2000

Temperature (K)

Wavenumber (cm-1) 280 260 240 220 200 180 160 140 120 100 80 60 40 20

Thc

(b)

2250

Tcc

2200

2150

2100

2050

2000

Wavenumber (cm-1)

Figure 7. (a) The evolution of intensity of IR peaks in the spectral range 2250–2000 cm-1, (b) contour plots of MIR spectra in the H-bonding region. 15

Journal Pre-proof The increase of their intensity is well visible in the vicinity of phase transition. Moreover, the first two are symmetric and of the same width, whereas the third is significantly broader and shows some asymmetry. As was shown in Fig. 5, the reorientational dynamic of ligands decreases in the vicinity of phase transition. Such inhibition of this motion makes ideal conditions for the formation of hydrogen bonds. There is a full correspondence between Figs. 7(a) and (b) and 5. The unit cell of [Ca(H2O)2](ReO4)2 contains two independent water molecules, with each of these molecules engaged in the formation of two hydrogen bonds. Two of them are of similar strength (O9-O7 and O10-O6 distances are equal to 2.87 and 2.88 Å, respectively) and two remaining (O9-O2, 2.92 Å and O10-O5, 3.01 Å) are a little bit longer i.e. weaker. 4.4. Experimental spin-lattice relaxation times T1 The T1 relaxation time was measured on cooling from 300 to 140 K, with the accuracy of ±1 K. Because of a very fast increase in the T1 relaxation time with decreasing temperature, no measurements for temperatures lower than 140 K were made. As shown in Figure 8, with temperature increasing from 140 K to 210 K, the relaxation time decreased, reaching the lowtemperature minimum of T1min = 0.35 s at 210 K. With a further increase in temperature, the T1 time starts a relatively fast increase which then slows down. At room temperature T1 ceases to increase and it can be expected that with a further temperature increase it would begin to decrease again down to the high-temperature minimum. Unfortunately, because of the risk of sample damage (evaporation of water from the sample) no measurements were made at higher temperatures. Analysis of the temperature dependence of T1 relaxation time (Fig. 8) did not reveal any discontinuities or other anomalies at the phase transition temperatures identified on the basis of calorimetric measurements (marked in Fig. 8 by vertical green lines) TCh  261.2 K on heating and TCc  231.2 K on cooling. It should be noted that the phase transition observed on cooling occurs at a temperature close to that of T1 minimum (T1 times were also measured on cooling), which can hinder the interpretation of results. Starting from room temperature to about 160 K, the magnetisation recovery can be described by a oneexponential function, however below 160 K a small deviation from the exponential dependence was noted, which increased with decreasing temperature. However, the oneexponential approximation could still be used and the T1 values were calculated

16

Journal Pre-proof assuming this approximation also for temperatures lower than 160 K. The temperature dependence of T1 relaxation time as T1(1/T) is presented in Fig. 8. Temperture (K) 333

286

250

222

200

182

167

154

143

133

5.5

6.0

6.5

7.0

7.5

T1 (s)

10

I 1

II

3.0

3.5

4.0

4.5

5.0

-1

1000/T (K )

Figure 8. Spin-lattice relaxation time T1 as a function of reciprocal temperature for a polycrystalline sample [Ca(H2O)2](ReO4)2. Experimental values are represented by points, while the blue line (the sum of the red and violet lines) is the best approximation with BPP function to the experimental points in the low-temperature phase (below the phase transition). Vertical green lines correspond to the phase transitions identified on the basis of DSC measurements on cooling (solid line) and on heating (broken line). Calculation of activation parameters In order to determine the activation parameters of the relaxation processes, the T1 dependence on 1000/T is described by the BPP formula [30]: 1 𝑇1

(

2

= 3∆𝑀2𝛾2𝐻

𝜏

4𝜏

2 2

1+𝜔 𝜏

)

+ 1 + 4𝜔2𝜏2

(3)

where the correlation time τ is defined by the Arrhenius relation: 𝜏 = 𝜏0exp

𝐸𝑎

( ) 𝑅𝑇

(4)

The best fit, characterised by the correlation coefficient of r2 = 0.9992, of the T1 relaxation time to the experimental values was obtained assuming that the low-temperature minimum corresponds to two different relaxation processes: one of low activation energy and the other of 17

Journal Pre-proof twice higher activation energy. The results of the fit are marked by solid lines in Fig. 8 and the corresponding parameters are given in Table 3. Table 3. Activation parameters of molecular reorientations in [Ca(H2O)2](ReO4)2 obtained from the best fit of the BPP function to the experimental data. Motion type

 (s)

Ea (kJmol‒1)

Δ M2 (G2)

I (violet line)

5.97· 10–12

12.00

0.140

1.46· 10–15

25.82

0.513

II (red line)

4.5. Experimental Proton Continuous Wave The values of the second moment of NMR line, M2 for a polycrystalline sample of [Ca(H2O)2](ReO4)2 were measured as a function of temperature on a continuous wave (c.w.) spectrometer working at 30 MHz. The measurements, similarly as those of T1, were carried out on cooling in a wide temperature range 300–20 K, with the accuracy of ± 1K. The derivatives of the continuous wave spectra (henceforth referred to as NMR lines) have a rather complex structure because of the overlapping of the two Pake’s doublets coming from two inequivalent water molecules present in each cation [Ca(H2O)2]2+. The second moment M2 of these lines was determined by multiple accumulation of each measurement. The results are shown in Figure 9, where also the phase transition temperatures are marked TCc  231.2 K on cooling and TCh  261.2 K on heating. A further description of this dependence refers to the direction of

increasing temperatures as subsequent molecular reorientations appear on heating. In the range 20–80 K, the second moment M2 is practically unchanged and equal to 26.4 G2. This fragment is referred to as the plateau I –rigid. Above 80 K the value of M2 decreases to reach at 100 K the values of 25.4 G2 unchanged up to 143 K; this fragment is called plateau II. Starting from 143K, the value of M2 decreases to 233 K at which it reaches plateau III of 21.2 G2. With a further temperature increase, M2 slightly decreases to reach another plateau (plateau IV) of M2 = 20.5 G2 in the range 273–283 K, then M2 decreases to 19.9 G2 at 300 K. Between 223 and 233 K there is a small, although visible, jumpwise change in M2, which is typical for a phase transition. Taking into account the fact that the second moment values were measured on cooling and that the phase transition temperature detected by DSC on cooling was

18

Journal Pre-proof TCc  231.2 K , this jumpwise change in M2 confirms the presence of a phase transition at this

temperature. 28 27

26.4 G2 26

25.4 G2

M2 (G2)

25 24 23 22

21.2 G2

21

20.5 G2

20 19 18 0

20

40

60

80

100 120 140 160 180 200 220 240 260 280 300 320

Temperature (K)

Figure 9. The values of M2 of NMR line as a function of temperature for a polycrystalline sample of [Ca(H2O)2](ReO4)2. The vertical green lines denote the phase transitions detected by DSC method on cooling (solid line) and on heating (broken line). The above results permit estimation of the activation energies of molecular reorientations whose onset on the temperature scale is manifested as a decrease in M2 after each subsequent plateau [31]: Ea  0.155  T (kJ mol1 )

(5)

Table 4 presents the activation energies of subsequent molecular reorientations. Table 4. Experimental activation energy values Ea obtained from c.w. NMR measurements

number of plateau

Ea (kJmol‒1)

I rigid

12.5–14

II

23

III

41

IV

45

19

Journal Pre-proof Calculations and interpretation Interpretation of the experimental M2 temperature dependence requires the calculation of its value for a rigid lattice and for the assumed models of molecular reorientations in order to compare them with the values of particular plateaus. The second moment value (M2 total) is composed of two components: the value calculated for a single molecule (M2 intra) and for molecules interacting in the crystal lattice (M2 inter) [32]: 𝑀2 𝑡𝑜𝑡𝑎𝑙 = 𝑀2 𝑖𝑛𝑡𝑟𝑎 + 𝑀2 𝑖𝑛𝑡𝑒𝑟

(6)

Denoting the second moment of a rigid lattice as M2 rigid, the subsequently appearing reorientations give the subsequent plateau values M2: (7)

𝑀2 = 𝜌 ∙ 𝑀2 𝑟𝑖𝑔𝑖𝑑 where ρ < 1

The models of reorientations were chosen on the basis of calculated approximated energy of the crystal lattice UL (electrostatic interactions were omitted) corresponding to the rotation or oscillation of the water molecule containing O9 or O10 oxygen atoms (notation assumed after Ref. [4]). Rigid lattice For powdered sample of [Ca(H2O)2](ReO4)2, the second moment 𝑀2 𝑖𝑛𝑡𝑟𝑎 𝑟𝑖𝑔𝑖𝑑 for the vector joining a spin I at site j with another one (of the same nuclear spin I and gyromagnetic coefficient γI) at site k is calculated from the formula: 3

ℎ2

1

𝑁

= 5𝛾2𝐼 4𝜋2𝐼(𝐼 + 1)𝑁∑𝑗,𝑘𝑟𝑗𝑘―6 𝑀𝑟𝑖𝑔𝑖𝑑 2

(8)

where N is the number of nuclear spins in a given molecule [32]. The total value M2 total rigid is obtained from the above formula taking into account only k > j and N equal to the number of all spins in selected elementary cells. In this study, one elementary cell was considered, localised at the origin of the system of coordinates, surrounded on each side with 3 layers of elementary cells (i.e. 27 cells containing N spins I). If a given sample contains other nuclear spins (denoted as S), they need to be taken into account because they increase the second moment value by [32]: (𝐼 ― 𝑆) = 4/15𝛾2𝑆 𝑀𝑟𝑖𝑔𝑖𝑑 2

2

(2𝜋ℎ ) 𝑆(𝑆 + 1)𝑁1 ∑𝑃𝑗,𝑘𝑟𝑗,𝑙―6

(9)

20

Journal Pre-proof The studied compound [Ca(H2O)2](ReO4)2 contains also the nuclei of rhenium 185Re and 187Re, however their contribution to the final M2 is insignificant because of the large distances of the rhenium nuclei from the water molecules. Moreover, the nuclei of 17O occur in a very small amount and, in the temperature range considered, the dipolar interaction in the system 17O –1H can be neglected. Rotating parts of molecules A description of rotating molecules requires definition of the axis of rotation. When the rotating internuclear vector is perpendicular to this axis, then 𝜌𝑟𝑜𝑡 𝑗,𝑘 = ¼. In the calculations performed in this study, the coefficient ρ was calculated for the arbitrary angles 𝜃𝑗𝑘 made by the 𝑟𝑗𝑘 vector with the rotation axis from the following formula [33]: 2 𝜌𝑟𝑜𝑡 𝑗,𝑘 = 1/4(1 ― 3𝑐𝑜𝑠 𝜃𝑗𝑘)

2

(10)

If a molecule contains more than one rotating fragment then, even when calculating only the intramolecular part of the second moment, the method of Monte-Carlo simulations proposed for the second moment calculations by R. Goc is used [34–35].

Oscillating parts of molecules For the oscillating molecule, the coefficient 𝜌𝑜𝑠𝑐 for a single part of the molecule performing oscillations by the angle α with respect to the oscillation axis is calculated from the formula: 3

2 2 2 4 𝜌𝑜𝑠𝑐 𝑗,𝑘 =1 ― 4[(1 ― 𝐽0(𝛼))sin 2𝜑𝑗𝑘 + (1 ― 𝐽0(2𝛼))sin 2𝜑𝑗𝑘 ]

(11)

where 𝐽0 is the Bessel function and 𝜑𝑗𝑘 is the angle made by the oscillation axis and the vector 𝑟𝑗𝑘 (analogously as 𝜃𝑗𝑘 in the formula for 𝜌𝑟𝑜𝑡 𝑗,𝑘 ). Similarly as for the calculations of the intramolecular interaction component of M2, the calculations of the intermolecular component 𝑀2 𝑖𝑛𝑡𝑒𝑟 were made using the Monte-Carlo method. Results of calculations for the rigid lattice The theoretical value of M2 were calculated assuming the structural data for [Ca(H2O)2](ReO4)2 published in 2018 by J. Hetmańczyk et al. [4]. The M2 value calculated for 21

Journal Pre-proof this structure for the rigid lattice in low-temperature phase was M2 total rigid = 34.4 G2, so much higher than the experimental value of 26.4 G2 recorded at 20 K. It is known that the second moment value depends directly on the O-H distances. According to Ref. [4], in the studied compound this distance was 0.85 Å. In a similar compound [Mn(H2O)2](ReO4)2, it was 0.998 Å as reported in Ref. [1], while in [Sr(H2O)2](ReO4)2 it was 0.989 Å [36], so in the compound studied [Ca(H2O)2](ReO4)2 it is the shortest. Taking into account the fact that the positions of hydrogen atoms in this compound were established on the basis of XDR results, it seemed justified to assume a longer O-H distance of 0.885 Å (maintaining the directions of the bonds). The second moment of NMR line was calculated for the low- and high-temperature crystal phases of [Ca(H2O)2](ReO4)2, and the results presented in Table 5 were compared with those obtained for the O-H reported in paper [4]. Table 5. Calculated NMR second moment M2 rigid (G2) for rigid lattice in two temperature phases

low temperature 0.885

high temperature

O-H (Å)

0.85

0.85

0.885

intra (G2)

33.39

26.25

32.69

25.89

inter (G2) total (G2)

1.01 34.40

1.02 27.27

1.07 33.76

1.13 27.02

The second moment values M2 total rigid simulated assuming the O-H distance of 0.885 Å are in good agreement with the experimental M2 corresponding to the “plateau I-rigid”, equal to 26.4 G2. It should be noted that the differences in M2 total rigid values obtained for the low- and high-temperatures phases are smaller than 1%, and the intermolecular contribution to the total M2 value is only of about 4%. Reorientations related to transition from plateau I to plateau II At first we assumed that the second moment M2 decrease by 1.0 G2 (from the value for the rigid lattice 26.4 G2 to 25.4 G2) was related to the onset of reorientation of one or two water molecules. However, the simulation of M2 changes showed that such reorientations are related to a much smaller change in M2. The change in the second moment, ΔM2, calculated as a function of the reorientation angle of the protons of the water molecule containing oxygen atom O9 was of 0.698 G2 for the reorientation by 180° (defined as the water molecule flip). Thus, it is suggested that the greater change in M2 observed in the experiment can be related to the 22

Journal Pre-proof rotation of the water molecule containing oxygen atom O10, or to the onset of an additional oscillation by a certain angle α of the molecule skeleton with respect to an additional axis between the two water molecules, as indicated by the earlier measurements of T1 relaxation time. In order to propose the possible models of reorientations, we calculated the energy of crystal lattice related to the rotation of the O9 water molecule with respect to the axis Ca-O9 and that related to the rotation of the O10 water molecule with respect to the axis Ca-O10. The results are presented in Figures 10(a) and (b), respectively. As follows from the results, the former type motion is related to a much lower change in Ea (Fig. 10(a)) and the activation energy of this reorientation is close to 14 kJmol–1. This value corresponds to the experimentally observed change in M2 from the plateau I-rigid to II plateau (Table 4). The onset of the reorientation of the O10 water molecule would need the activation energy of 75 kJmol–1 (Fig. 10(b)), which means that such a reorientation is impossible in low temperatures. To sum up, the transition from plateau I to plateau II is related to the onset of the O9 water molecule flips around 180° and the onset of libration of the whole cation around the small constant angle.

20

18

(a)

(b)

reorientation of water molecule containing O9

100

reorientation of water molecule containing O10

16 80

Energy (kJ/mol)

Energy (kJ/mol)

14

12

10

8

60

40 6

4

20

2

0

0 0

50

100

150

200

250 o

Angle ( )

300

350

400

0

50

100

150

200

250

300

350

400

o

Angle ( )

Figure 10. Crystal lattice energy (the Coulomb term omitted) for reorientation (a) of water molecule containing O9 and that (b) of water molecule containing O10. 23

Journal Pre-proof

Reorientations corresponding to M2 change from plateaus II and III The experimentally observed M2 change from the value of plateau II of 25.4 G2 to that of plateau III of 21.2 G2 (near the phase transition) suggests its origin is related to the oscillations of the molecule skeleton by a certain angle, the more so that the change is continuous and takes place over a wide range of temperatures 140–233 K. This suggestion is supported by the fact that the activation energy of such an oscillation determined from M2 and T1 measurements was 23 and 26 kJmol–1, respectively. The change in the crystal lattice energy caused by reorientation of the water molecule containing O9 and oscillations of the cation [Ca(H2O)2]2+ by a certain angle was calculated. From among the many proposed axes of the cation oscillations, only for one was the second moment value close to the experimental value. It was the axis passing through the Ca atom and the centre of mass between O9 and O10, henceforth referred to as the axis Ca-O9-10. The simulated M2 values and the lattice energy values corresponding to the above reorientations are given in Figures 11(a) and (b), respectively. 100

M2 total (O9+[Ca(H2O)2]2+]

(a)

M2 total (O9+O10+[Ca(H2O)2]2+]

90 80 70

M2 (G2)

60 50 40 30 20 10 0 -60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

o

angle ( )

Figure 11. (a) Simulated M2 values corresponding to reorientations of O9 water and oscillations of the cation [Ca(H2O)2]2+ around the additional axis Ca–O9-10 as a function of the oscillation angle (red circles). The simulated M2 values corresponding to reorientations of both water 24

Journal Pre-proof molecules (O9 and O10) and oscillations of the cation [Ca(H2O)2]2+ around the additional axis Ca–O9-10 (black crosses). 100

(b)

90

Energy (kJ/mol)

80 70 60 50 40 30 20 10 0 -80

-40

0

40

80

120

160

200

240

280

320

360

400

o

Angle ( )

Figure 11. (b) Crystal lattice energy related to reorientation of O9 water molecule and oscillations of the cation [Ca(H2O)2]2+ around the additional axis Ca–O9-10 as a function of the angle of oscillations. In order to explain the jumpwise changes in M2 for the oscillation angles 30–70° and in the vicinity of 150°, we should refer to the plot of the crystal lattice energy as a function of the cation oscillation angle (Fig. 11(b)). The oscillations at these angles correspond to the energies greater than 100 kJmol–1. The energy value closely depends on the equilibrium between the negative Van der Waals potential and the positive Lenard-Jones potential, while these potentials are determined by the atom-atom distances. When atoms are too close to each other as a result of oscillations, the intermolecular part of the second moment increases. That is why the simulation of M2 as a function of the angle of oscillations of a chosen molecule fragment should give a plot similar to that obtained for the atom-atom potential as a function of the same angle. In the oscillation angle range 0–360° there are two energy minima; the first one at -8° and the second one at 171°, and the latter is sharper than the former. Taking into account the experimental values of activation energies Ea given in Table 3, it is possible to identify the range of oscillation angles corresponding to the energies: - the first minimum corresponds to the oscillation angles from -30 to +10°, - the second minimum corresponds to the oscillation angles from +161 to +175°. 25

Journal Pre-proof The second minimum cannot be reached because of the activation energy barrier separating these two minima of over 100 kJmol–1. Plateau III Plateau III corresponding to M2 = 21.2 G2 starts in the vicinity of the phase transition related to the onset of the O10 water molecule reorientation. The phase transition is manifested as a jumpwise change in M2 by M2 close to 0.5 G2. The value of M2 remains constant in the temperature range 233–263 K, then the angle of the cation oscillations increases with increasing temperature and the value of M2 decreases to 19.9 G2 at 300 K. This value corresponds to the cation oscillation angle of -40° (Fig. 11a). Correlation times On the basis of the data from Table 3 it was possible to establish the dependence of correlation times on reciprocal temperature for the O9 water molecule reorientation (black line) and for oscillations of the cation [Ca(H2O)2]2+ (orange line), see Figure 12. The correlation times describing the two types of motion overlap [37]. This result suggests that in the studied crystal, prior to the phase transition, a resonance of the frequencies of both types of motion takes place, which may be driving the transition from the low-temperature phase to the hightemperature one, similarly as noted for a similar compound [Mg(H2O)6](BF4)2 [38]. In the latter compound a resonance was observed between the frequencies of the motions of the cation and anion, while in the compound we studied there is a resonance between the motions taking place only in the cation. Figure 12 presents the correlation time describing the reorientations of O10 water (green line). The correlation time shortening at about 300 K and a little below was interpreted as being caused by an additional motion, most probably by the flip of O10 water with the relaxation time 𝑇1_O10. The relaxation time can be described by the formula: 1 𝑇1_𝑒𝑥𝑝

1

1

1

= 𝑇1_𝑂9 + 𝑇1_𝑜𝑠𝑐 + 𝑇1_𝑂10

(12)

from which the value of 𝑇1_O10 was found. On the basis of the BPP formula, the corresponding correlation time was calculated. The calculation was performed in the low-temperature approximation, assuming ∆𝑀2_O10 = 0.232 G2, obtained from the Monte Carlo simulations for rotation of the O10 water molecule. The activation energy Ea = 41 kJ mol–1 was taken from the

26

Journal Pre-proof results of the calculations collected in Table 4, and using the Arrhenius formula the preexponential factor was determined as 𝜏0 = 1.19 ∙ 10 ―13𝑠. Temperature (K) 333

250

200

167

143

125

111

100

91

83

1 0.1

 (water with O10) 2+

 ([Ca(H2O)2] )

0.01

 (water with O9)  (for T1min)

0.001

 (for c.w. line)

Thc = 231.2 K

 (s)

1E-4

Tcc = 261.2 K

1E-5 1E-6 1E-7 1E-8 1E-9 1E-10 1E-11 3

4

5

6

7

8

1000/T (K-1)

9

10

11

12

Figure 12. Correlation times versus reciprocal temperature for reorientation of water molecules and oscillation of the cation [Ca(H2O)2]2+. Red lines correspond to the correlation times calculated from the NMR linewidths for temperatures at which M2 started to decrease, while the blue line indicates the correlation time at the temperature of T1 minimum for measurements at 25 MHz.

5. Conclusions 1. Vibrational–reorientational dynamics of H2O ligands in the high- and low-temperature phases of [Ca(H2O)2](ReO4)2 were investigated by Fourier transform middle and far-infrared spectroscopy (FT-MIR and FT-FIR), Raman Spectroscopy (RS) and incoherent inelastic neutron scattering (IINS) methods. The experimental spectra were compared with the calculated ones and a good agreement was achieved. A combination of infrared, Raman and incoherent inelastic neutron scattering (IINS) spectroscopies results with periodic density functional theory calculations was used to provide a complete assignment of the vibrational spectra of [Ca(H2O)2](ReO4)2.

27

Journal Pre-proof 2. Temperature dependence of the FWHM of r(H2O) band at ca. 501 cm-1 in the infrared spectra suggests that the observed phase transition is associated with a change of the H2O reorientational dynamics. The ligands perform fast (R  10‒11 to 10‒13 s) stochastic reorientational motions in the high temperature phase. The estimated mean value of activation energy for the reorientation of the H2O ligands is ca. 11.1 kJmol–1 from Raman spectroscopy and 11.6 kJmol-1 from Infrared spectroscopy. Below PT, the reorientational correlation time R for these molecular groups becomes significantly longer (R > 10–10 s). 3. The proton-weighted phonon density functions G(ν) obtained at temperatures 5 K show some separate peaks characteristic for ordered phase. The G(ν) spectra obtained at 295 K are very diffused because of a dynamical disorder of H2O molecules connected with their fast molecular reorientational motions. 4. Measurements of M2 on the sample cooling confirmed the occurrence of a phase transition detected by the calorimetric studies. The activation parameters and changes in M2 (M2) suggested that the phase transition was related to the onset of reorientation of the O10 water molecule. 5. The value of pre-exponential factor (𝜏0) implies that the activation parameters of the reorientation I and (Table 3) describe mainly the motion of the O9 water molecule, whereas reorientation II can be associated with the oscillations of an entire [Ca(H2O)2]2+ cation around the axis Ca-O9-10. 6. The activation energies of the subsequent relaxation processes (Tables 3 and 4) obtained by the two different experimental methods in the low-temperature phase are in a very good agreement. The activation energy Ea determined from T1 measurements for the reorientation of the O9 water molecule (12.0 kJmol–1) is in a good agreement with the Ea value obtained from the FTIR study (11.6 kJmol–1) and Raman spectroscopy (11.1 kJmol–1).

ACKNOWLEDGMENTS The infrared absorption (FT-MIR) research was carried out with equipment purchased thanks to the financial support of the European Regional Development Fund within the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/08). 28

Journal Pre-proof

REFERENCES [1] J. Hetmańczyk, Ł. Hetmańczyk, A. Migdał-Mikuli, Edward Mikuli, Crystal structure, solidsolid phase transition and thermal properties of [Mn(H2O)2](ReO4)2, J. Coord. Chem. 70 (2017) 1190–1206. https://doi.org/10.1080/00958972.2017.1301439. [2] J. Hetmańczyk, Ł. Hetmańczyk, Vibrational and reorientational dynamics and thermal properties in [Mg(H2O)4](ReO4)2 supported by periodic DFT study, Vib. Spectrosc. 94 (2018) 49–60. https://doi.org/10.1016/j.vibspec.2017.12.002. [3] Ł. Hetmańczyk, J. Hetmańczyk, Phase transition, thermal dissociation and dynamics of NH3 ligands

in

[Cd(NH3)4](ReO4)2,

Spectrochim

Acta

A.

164

(2016)

24–32.

https://doi.org/10.1016/j.saa.2016.03.045. [4] J. Hetmańczyk, Ł. Hetmańczyk, W. Nitek, Crystal structure, phase transitions and vibrations of H2O molecules in [Ca(H2O)2](ReO4)2, J. Therm. Anal. Calorim. 131 (2018) 479–489. https://doi.org/10.1007/s10973-017-6494-y. [5] R.G. Matveeva, V.V. Ilyukhin, M.B. Varfolomeev, N.V. Belov, Crystal structure of calcium perrhenate dihydrate Ca(ReO4)2·2H2O, Soviet Physics – Doklady. 252 (1980) 92–102. [6] J.P. Picard, J.P. Besse, R. Chevalier, M. Gasperin, Structure cristalline de Ca(ReO4)2·2H2O, J Solid State Chem. 69 (1987) 380–384. https://doi.org/10.1016/0022-4596(87)90097-1. [7] H.D. Lutz, Bonding and structure of water molecules in solid hydrates. Correlation of spectroscopic and structural data, Solid Materials. Structure and Bonding 69 (1988) 97–125. https://doi.org/10.1007/3-540-18790-1_3. [8] K. Nakamoto, Infrared and Raman spectra of inorganic and coordination compounds, 5th ed. New York: Wiley-Interscience Publication (1997). [9] I. Natkaniec, D. Chudoba, Ł. Hetmańczyk, V.Yu. Kazimirov, J. Krawczyk, I.L. Sashin, S. Zalewski, Parameters of the NERA spectrometer for cold and thermal moderators of the IBR-2 pulsed reactor, J. Phys.: Conference Series. 554 (2014) 012002. https://doi.org/10.1088/17426596/554/1/012002. [10] J. Hetmańczyk, Ł. Hetmańczyk, A. Migdał-Mikuli, E. Mikuli, M. Florek-Wojciechowska, H. Harańczyk, Vibrations and reorientations of H2O molecules in [Sr(H2O)6]Cl2 studied by Raman light scattering, incoherent inelastic neutron scattering and proton magnetic resonance, Spectrochim. Acta A. 124 (2014) 429–440. https://doi.org/10.1016/j.saa.2014.01.054.

29

Journal Pre-proof [11] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, First

principles

methods

using

CASTEP,

Z.

Kristallogr.

220

(2005)

567–570.

https://doi.org/10.1524/zkri.220.5.567.65075. [12] K. Refson, S.J. Clark, P.R. Tulip, Variational density-functional perturbation theory for dielectrics

and

lattice

dynamics,

Phys.

Rev.

B

73

(2006)

155114

https://doi.org/10.1103/PhysRevB.73.155114. [13] J.P. Perdew, K. Burke and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77 (1996) 3865-3868. https://doi.org/10.1103/PhysRevLett.77.3865. [14] Y. Zhang and W. Wang, Comment on “Generalized Gradient Approximation Made Simple”, Phys. Rev. Lett. 80 (1998) 890. https://doi.org/10.1103/PhysRevLett.80.890. [15] A.M. Rappe, K. M. Rabe, E. Kaxiras, and J. D. Joannopoulos, Optimized pseudopotentials, Phys. Rev. B 41 (1990) 1227–1230. https://doi.org/10.1103/PhysRevB.41.1227. [16] M.H. Lee, PhD thesis, Cambridge 1995. http://boson4.phys.tku.edu.tw/qc/my_thesis/index.htm. [17] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B13 (1976) 5188–5192. https://doi.org/10.1103/PhysRevB.13.5188. [18] V. Milman, A. Perlov, K. Refson, S.J. Clark, J. Gavartin, B. Winkler, Structural, electronic and vibrational properties of tetragonal zirconia under pressure: a density functional theory study, J. Phys.: Condens. Matter 21 (2009) 485404. https://doi.org/10.1088/09538984/21/48/485404. [19] D. Michalska, R. Wysokinski, The prediction of Raman spectra of platinum(II) anticancer drugs

by

density

functional

theory,

Chem.

Phys.

Lett.

403

(2005)

211–217.

https://doi.org/10.1016/j.cplett.2004.12.096. [20] A.J. Ramirez-Cuesta, aCLIMAX 4.0.1, The new version of the software for analyzing and interpreting

INS

spectra,

Comput.

Phys.

Comm.

157

(2004)

226–238.

https://doi.org/10.1016/S0010-4655(03)00520-4. [21] W.J. Kazimirov, I. Natkaniec, Programme for Calculation of the Resolution Function of NERA-PR and KDSOG-M Inelastic Neutron Scattering Inverse Geometry spectrometers, Preprint P14-2003–48 JINR, Dubna (2003). [22] M.I. Aroyo, J.M. Perez-Mato, D. Orobengoa, E. Tasci, G. de la Flor, A. Kirov, Crystallography online: Bilbao Crystallographic Server, Bulg. Chem. Commun. 43(2) (2011). 183–197.

30

Journal Pre-proof [23] M.I. Aroyo, J.M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov and H. Wondratschek, Bilbao Crystallographic Server: I. Databases and crystallographic computing programs, Z. Krist. 221 (2006) 15–27. https://doi.org/10.1524/zkri.2006.221.1.15. [24] S.W. Lovesey, Theory of Neutron Scattering from Condensed Matter, Clarendon Press, Oxford (1984). [25] J. Hetmańczyk, Ł. Hetmańczyk, Dynamics of H2O ligands and ReO4− anions at the phase transition in [Mn(H2O)2](ReO4)2 studied by complementary spectroscopic methods, J. Raman Spectrosc. 49, (2018) 298–311. https://doi.org/10.1002/jrs.5281. [26] C. Carabatos-Nédelec, P. Becker, Order–disorder and structural phase transitions in solid‐state materials by Raman scattering analysis, J. Raman Spectrosc. 28 (1997) 663–671. [27] P. da R. Andrade, A.D. Pasad Rao, R.S. Katiyar, S.P.S. Porto, Analysis of the relationship between temperature dependence of the libration mode and dielectric relaxation in NaNO2, Solid St. Commun. 12 (1973) 847–851. https://doi.org/10.1016/0038-1098(73)90092-6. [28] P. da R. Andrade, S.P.S. Porto, On linewidth of phonons associated to a disorder mechanism, Solid St. Commun. 13 (1973) 1249–1254. https://doi.org/10.1016/00381098(73)90574–7. [29] J. Hetmańczyk, Ł. Hetmańczyk, A. Migdał-Mikuli, Edward Mikuli, Vibrational and reorientational dynamics, crystal structure and solid–solid phase transition studies in [Ca(H2O)6]Cl2 supported by theoretical (DFT) calculations, J. Raman Spectrosc. 47 (2016) 591– 601. https://doi.org/10.1002/jrs.4863. [30] S. Albert and H.S. Gutowsky, Nuclear relaxation and spin exchange in ammonium hexafluorophosphate

(NH4PF6),

J.

Chem.

Phys.

59

(1973)

3585–3594.

https://doi.org/10.1063/1.1680522. [31] J.S. Waugh and E.I. Fedin, Determination of hindered rotation barriers in solids, Sov. Phys. Solid States 4 (1963) 1633–1636. [32] J.H. van Vleck, The Dipolar Broadening of Magnetic Resonance Lines in Crystals, Phys. Rev. 74 (1948) 1168–1183. https://doi.org/10.1103/PhysRev.74.1168. [33] R. Andrew, Molecular Motion in Certain Solid Hydrocarbons, J. Chem. Phys. 18 (1950) 607–618. https://doi.org/10.1063/1.1747709. [34] R. Goc, Computer calculation of the Van Vleck second moment for materials with internal rotation

of

spin

groups,

Comput.

Phys.

Commun.

162

(2004)

102–112.

https://doi.org/10.1016/j.cpc.2004.06.071.

31

Journal Pre-proof [35] R. Goc, A. Pajzderska, and J. Wąsicki, Second Moment Simulations for Different Models of Rotations and Oscillations in Polycrystalline Thiourea Pyridinium Nitrate Inclusion Compound and its Two Perdeuterated Analogues, Z. Naturforsch., A 60 (2005) 177–182. [36] T. Todorov, O. Angelova and J. Macicek, The Covert Water in the Structure of Sr(ReO4)2∙2H2O: a Revision of the Sesquihydrate Model, Acta Cryst C52 (1996) 1319–1323. https://doi.org/10.1107/S0108270195016362. [37] M. Grottel, A. Kozak, A. E. Kozioł, and Z. Pająk, An X-ray and NMR study of structure and ion motions in C(NH2)3PF6, J. Phys.: Condens. Matter 1 (1989) 7069–7083. https://doi.org/10.1088/0953-8984/1/39/019. [38] E. Mikuli, J. Hetmańczyk, B. Grad, A. Kozak, J. W. Wąsicki, P. Bilski, K. HołdernaNatkaniec, and W. Medycki, The relationship between reorientational molecular motions and phase transitions in [Mg(H2O)6](BF4)2, studied with the use of 1H and 19F NMR and FT-MIR, J. Chem. Phys. 142 (2015) 064507. https://doi.org/10.1063/1.4907372.

32

Journal Pre-proof

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Joanna Hetmańczyk: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Writing - Original Draft, Writing - Review & Editing, Visualization, Supervision, Project administration, Funding acquisition. Łukasz Hetmańczyk: Methodology, Formal analysis, Investigation, Writing - Original Draft, Writing - Review & Editing, Visualization. Paweł Bilski: Methodology, Formal analysis, Investigation, Writing - Original Draft, Writing - Review & Editing, Visualization. Asja Kozak: Methodology,Formal analysis, Investigation, Writing - Original Draft, Writing - Review & Editing, Visualization.

Journal Pre-proof Highlights     

Polymorphism of crystalline [Ca(H2O)2](ReO4)2 studied by solid state NMR. Reorientational motion of H2O investigated by IR and RS band shape analysis. Dynamics of H2O ligands is disturbed in the phase transition. Calculated FT-IR, Raman and neutron spectra compared with experimental results. Two kinds of not equivalent water molecules in the lattice [Ca(H2O)2](ReO4)2.