Cluster Ions in Vapour over Calcium Dichloride: Theoretical Study of Geometrical Structure and Vibrational Spectra

This work was carried out in collaboration between all authors. Author IM performed computations, wrote the first draft of the manuscript and managed literature searches. Author TPP performed corrections and some selected computations regarding the structure and vibrational spectra. Author AMP performed some selected computations and thermodynamic calculations. All authors analyzed and discussed the results and approved the final manuscript. ABSTRACT Geometrical structure and vibrational spectra for CaCl 3– , Ca 2 Cl 3+ , Ca 3 Cl 5+ , Ca 4 Cl 7+ , and Ca 5 Cl 9+ ions have been studied by employing density functional theory and the second order Møller– Plesset perturbation theory. The equilibrium geometrical structures are as follows: the planar D 3h for CaCl 3– , triple-bridged bipyramid D 3h for Ca 2 Cl 3+ , hexa-bridged bipyramid D 3h for Ca 3 Cl 5+ , polyhedral C 2v for Ca 4 Cl 7+ , and polyhedral D 3h for Ca 5 Cl 9+ . No isomers have been confirmed to exist.


INTRODUCTION
Cluster ions have a potential interest for scientists and researchers owing to the possibilities of designing and fabricating new materials. Due to their size and composition, some cluster ions have unique electronic, optical and magnetic properties [1][2][3]. These species can serve as fundamental building blocks for a new class of materials with desired properties [3,4]. Generally, the cluster ions may be considered as structural elements forming a bridge between the gaseous phase and crystal matter.
Different compounds containing calcium and chlorine have been proved to have many applications ranging from the society to industries [5,6]. Numerous studies on cluster ions have been done by the combination of mass spectrometry and different ionization techniques; such as electron ionization, chemical ionization, field ionization, and others [7][8][9]. Mass spectrometry is a powerful instrumental technique which is used for investigation of inorganic and organic compounds [7]. It is capable of a broad analysis and characterization of molecular and ionic species [10]. For the treatment of the experimental data, the thermodynamic functions of the ions and molecules are required. To calculate the thermodynamic functions, the geometrical parameters and vibrational frequencies are needed, however they are difficult to be measured by available experimental techniques [11]. Quantum mechanical methods now provide reliable data on the structure and properties of the ions.
The aim of the present quantum chemical study is to determine the equilibrium geometrical configuration, geometrical parameters, and normal vibration frequencies of the CaCl 3 − , Ca 2 Cl 3 + , Ca 3 Cl 5 + , Ca 4 Cl 7 + , and Ca 5 Cl 9 + and reveal possible isomers among the alternative structures of the ions.

COMPUTATIONAL DETAILS
The calculations were performed employing the GAMESS (General Atomic and Molecular Electronic Structure System) program [26], Firefly version 8.1.0 [27]. Density functional theory (DFT) with the non-local correlation Becke−Perdew 86 (B3P86) functional [28][29][30] and the second order Møller−Plesset perturbation theory (MP2) were implemented in optimization of geometrical parameters and calculation of vibrational frequencies. Two basis sets were applied: B1 and B2. The basis B1 was the McLean−Chandler basis set 8s4p1d for Ca and 6s5p1d for Cl, incorporated in [26]. More extended basis B2 was the valence correlation consistent cc-PVTZ 6s5p3d1f basis set for Ca and aug-cc-pVTZ 6s5p3d2f for Cl taken from the basis set library EMSL [31][32][33]. The combination of the two methods (DFT and MP2) and two basis sets (B1 and B2) provided the following four theoretical approximations: DFT B1, MP2 B1, DFT B2, and MP2 B2.
All four theoretical methods were used in computation of properties of the diatomic species CaCl, CaCl + , and monomer molecule CaCl 2 to analyze how the basis set and the computational method applied affect the results. To check applicability of the methods used, the calculated equilibrium geometrical parameters and other properties of these species were compared with the available reference data obtained experimentally [12][13][14]16,[36][37][38][39][40][41][42][43][44][45] and theoretic-cally using more advanced CCSD(T) method [17]. The results are presented in Table 1.
The graph for equilibrium internuclear distances R e (Ca-Cl) in CaCl, CaCl + , and CaCl 2 species against the method of determination is shown in Fig. 1. The plot for BaCl from [25] is included for comparison. The trend observed for the CaCl species is alike to that for BaCl that is decreasing of R e values along the plot when proceed from DFT B1 → MP2 B2; but for BaCl the plot is smooth while for CaCl species the plots are zigzag shaped. For all species, the internuclear distances obtained with B2, both DFT and MP2, agree well with the experimental and theoretical reference data available; while the results by the B1 are essentially overrated, particularly it is observed for the diatomic ion CaCl + for which the R e (Ca-Cl) computed with B1 is overrated by 0.12 Å compared to that found with B2. The magnitudes of the dipole moment for CaCl and CaCl + correlate with the equilibrium internuclear distance for the pairs of the data found by DFT B1-DFT B2 or by MP2 B1-MP2 B2: The smaller the distance, the smaller the dipole moment magnitude.
The molecule CaCl 2 was confirmed to be linear, D ∞h , in agreement with literature data [12-14b and 41]. It is worth to mention how the structure changes in series of alkali-earth metal dihalides MX 2 molecules (M = Ca, Sr, Ba; X = F, Cl, Br). Different experimental techniques, such as electric beam deflection and gas-phase electron diffraction study by Klemperer et al. [15] and vibrational spectroscopic studies [14] have been applied to state the shape of MX 2 molecules. Also quantum chemical calculations have been carried out [12,20] and confirmed that the structure of alkali-earth metal dihalides was bent for CaF 2 , SrF 2 , SrCl 2 and barium dihalides but linear for others. The various reasons why some MX 2 are bent while others are linear were analyzed and discussed [19,20]. , and theoretically by CCSD (T) [17]. For the diatomic CaCl molecule, the vibrational frequency computed by DFT B2 is close to the experimental results [37,38] (Table 1) and theoretical value 368 cm -1 [17]. For the diatomic species, CaCl, CaCl + , and BaCl + , the plot of frequencies ω e versus method is given in Fig. 2. This plot correlates in general with that for the internuclear separations in Fig. 1, namely the values of R e decrease from left to right and ω e increase.
In the vibrational spectrum of CaCl 2 molecule ( , ω 2 = 38 cm -1 , ω 3 = 421 cm -1 , obtained by CCSD(T) [17]. As concerns the deformational frequency ω 2 , the contradiction between the theoretical high level computation and experimental results had been discussed already earlier [12]. The problem is common for other alkali-earth dihalides and the contradiction may relate to the shallow bending potential of these molecules as well as matrix effect [12].

Tetraatomic Negative Ion CaCl 3 − and Neutral Species CaCl 3
The geometrical structure of the CaCl 3 − ion was found to be planar of D 3h symmetry. For the neutral CaCl 3 species two configurations were considered, C 2v and D 3h . Among them the former was confirmed to be equilibrium while for the latter, the imaginary frequencies have been revealed and the total energy was higher by 45.7 kJ⋅mol -1 (DFT) and 130 kJ⋅mol -1 (MP2) compared to C 2v structure. The electronic state of the CaCl 3 − ion is 1 A 1 ′, and that of the neutral CaCl 3 is 2 B 2 . The equilibrium geometrical configurations of the CaCl 3 − ion and CaCl 3 neutral species are shown in Fig. 3 and the properties are reported in Table 2. It is seen that the geometrical parameters and vibrational spectra calculated by DFT B2 and MP2 B2 do not contradict each other and the theoretical results [22] obtained through CCSD(T)/6-311+G method.
Vertical detachment energy (VED) has been calculated as the difference between energies of the neutral and ionic species, the structure of the ion being optimized and accepted the same (D 3h ) for the neutral. As is seen the magnitude of VED by MP2 B2 agrees better (than that by DFT B2) with the experimental result [22], being still overrated by ~0.3 eV. Adiabatic electron affinity of the CaCl 3 neutral particle is in good accordance between both methods and theoretical value [22].

Pentaatomic Positive Ion Ca 2 Cl 3 +
Several shapes, such as linear, kite-shaped, and bipyramidal have been considered. The first two structures were found to be nonequilibrium due to the appearance of imaginary frequencies. Only the bipyramidal configuration of the D 3h symmetry was confirmed to be the equilibrium structure for the Ca 2 Cl 3 + , in which the calcium atoms were in the vertices of the bipyramid and the chlorine atoms in the horizontal plane (Fig.  4). The parameters obtained by DFT B2 and MP2 B2 method for the Ca 2 Cl 3 + ion of D 3h symmetry are given in Table 3.
The geometrical parameters and vibration frequencies obtained by the DFT and MP2 methods are close to each other, respectively. Note, that the vibrational spectrum of the Ca 2 Cl 3 + ion does not contain low frequencies. Thus the structure of this ion is compact and rigid. The most intensive bands are ω 3 (A 2 ′′) = 284 cm −1 and ω 4 (E′) = 304 cm −1 (MP2 B2), which correspond to antisymmetrical stretching Ca-Cl vibrations; the mode ω 5 (E′) = 122 cm −1 is bending Cl-Ca-Cl vibration.
If compare the parameters of the Ca 2 Cl 3 + ion with those of the similar Ba 2 Cl 3 + ion studied previously [25], then for the latter the bipyramidal configuration (D 3h ) was found to be equilibrium as well and no other isomers were revealed.
It is also worth to compare the bipyramidal configuration of the Ca 2 Cl 3 + ion to that of the neutral dimer molecule Ca 2 Cl 4 . The same theoretical approaches, DFT B2 and MP2 B2, were applied to compute the molecular parameters of the dimeric molecule Ca 2 Cl 4 . Two isomeric configurations were proved to exist: the planar cyclic configuration of D 2h symmetry, and bipyramid with a Cl-atom-tail of C 3v symmetry (Figs. 5a and 5b). The calculated molecular parameters are displayed in Table 4. The ion Ca 2 Cl 3 + , compared to dimer molecule Ca 2 Cl 4 of C 3v symmetry, looks more compact and stable, as far as detachment of the terminal loose Cl atom from the neutral dimer favours the stabilization of the ion. For the planar shape of Ca 2 Cl 4 molecule, low deformational frequencies are found, ω 8 = 20 cm −1 (DFT B2) and 24 cm −1 (MP2 B2), ω 10 = 40 cm −1 (DFT B2) and 41 cm −1 (MP2 B2) which correspond to the bending mode of the terminal Ca-Cl bonds. In the bipyramidal configuration (C 3v ) the lowest frequency, ω 8 = 50 cm −1 (DFT B2 and MP2 B2), corresponds to the bending of the Cl-tail fragment. Thus the bipyramidal structure looks as compact and more rigid compared to the planar one. It has lower energy than planar configuration, by 4 kJ⋅mol −1 (DFT B2) and 22 kJ⋅mol −1 (MP2 B2). Worth to mention that when computed with the McLean−Chandler basis set, the opposite result has been obtained that is the bipyramidal structure corresponds to higher energy, by 10 kJ⋅mol −1 (DFT B1) and 13 kJ⋅mol −1 (MP2 B1), than the planar one. According to the theoretical study [12b, 12c], the structure of D 2h symmetry was more stable by 2.5 kJ⋅mol −1 , and that of C 3v was found to be nonequilibrium due to imaginary frequencies. We do not consider these results to be dramatically controversial but they show that these two structures are comparable by energy and isomers may coexist in equilibrium vapour.

Octaatomic Positive Ion Ca 3 Cl 5 +
Two possible configurations of the ions were considered; bipyramidal of D 3h symmetry and C 2v symmetry, in the latter two Ca 2 Cl 2 cyclic fragments are located in the mutually perpendicular planes (Fig. 6). The two-cycled configuration was found of higher energy, by 193 kJ⋅mol −1 compared to bipyramidal, and several very low frequencies relating to the bending modes were revealed in the range between 7 and 40 cm −1 . This structure is not considered further and only the bipyramidal one has been examined.

Fig. 3. The geometrical structure for (a) CaCl 3 of D 3h symmetry; (b) CaCl 3 of C 2v symmetry
The parameters of the ion Ca 3 Cl 5 + (D 3h ) are reported in Table 5. There are two kinds of equilibrium internuclear distances Ca-Cl: R e (Ca-Cl v ) and R e (Ca-Cl h ) where Cl v and Cl h denote the chlorine atoms in the vertex and horizontal plane of the bipyramid, respectively. The basis of the bipyramid is hexagon formed by three Ca and three Cl atoms. The internuclear separation between two Cl h atoms (5.182 Å, MP2 B2) is much larger than that between two Cl v ,

Undecaatomic Positive Ion Ca 4 Cl 7 +
The properties of Ca 4 Cl 7 + were computed by DFT and MP2 methods with McLean-Chandler basis set (B1). Two configurations of the ion were considered, the polyhedron of C 2v symmetry and chain with three cycles lying in mutually perpendicular planes of C 2v symmetry. The latter configuration, with energy higher than the former by 210 kJ⋅mol −1 (DFT) and 234 kJ⋅mol −1 (MP2), appeared to be nonequilibrium as associated with imaginary frequencies. The polyhedron of C 2v symmetry was confirmed to be equilibrium (Fig. 7).
This structure may be considered as composed of the Ca 2 Cl 3 + bipyramidal moiety and two CaCl 2 molecules attached. The Ca atoms of CaCl 2 molecules link to the Cl atoms of the base of the Ca 2 Cl 3 + bipyramid and Cl atoms are attached to the vertex Ca atoms of the bipyramid. Two Ca atoms and three Cl atoms lie in one plane forming a pentagonal ring. The attachment of two CaCl 2 molecules results in a distortion the original bipyramid Ca 2 Cl 3 + , and the Ca v -Cl h internuclear separations become nonequivalent as well as valence angles Cl h -Ca v -Cl h . The dipole moment of the ion Ca 4 Cl 7 + appears due to both the attachment of CaCl 2 molecules and distortion of the bipyramidal Ca 2 Cl 3 + fragment and directs along the C 2 axis (axis z in Fig. 7). The parameters of the Ca 4 Cl 7 + ion are given in Table  6. There are six types of equilibrium internuclear distances obtained, The theoretical IR spectrum is presented in Fig.  8. As is seen, the most intensive bands are observed for ω 1 , ω 4 , ω 15 , ω 16 , ω 19 , ω 22 , and ω 24 frequencies. The modes ω 1 (A 1 ) = 267 cm −1 , ω 15 (B 1 )= 297 cm −1 , and ω 16 (B 1 ) = 263 cm −1 correspond to the stretching vibrations of the attached CaCl 2 molecules and bipyramidal fragment Ca 2 Cl 3 + ; ω 19 (B 1 ) = 160 cm −1 is assigned to the bending mode of Ca-Cl bonds formed between Ca atoms in the CaCl 2 molecules attached and Cl atoms in the Ca 2 Cl 3 + bipyramid. The highest intensity band ω 22 (B 2 ) = 332 cm −1 relates to the stretching vibration of CaCl 2 moieties. Overlapping of two bands ω 4 (A 1 ) and ω 24 (B 2 ) gives the peak at 215 cm −1 , which is stretching vibration of atoms in the pentagonal ring, and the stretching of the bipyramidal moiety.

3.6Tetradecanatomic Positive Ion Ca 5 Cl 9 +
Opposite to the ionic clusters considered above, the tetradecanatomic Ca 5 Cl 9 + ion was not detected experimentally. Nevertheless the formation of this ion is feasible. The properties of Ca 5 Cl 9 + were computed by DFT B1 method only.
Two configurations of the ion were considered, the polyhedron of D 3h symmetry and the chain structure composed of four cycles in mutually perpendicular planes, C 2v symmetry. The latter configuration, with energy higher by 255 kJ⋅mol −1 than the former, appeared to be nonequilibrium as associated with imaginary frequencies. The polyhedral structure of the D 3h symmetry was confirmed to be equilibrium (Fig. 8). The parameters are given in Table 6.    + possesses a perfect and compact structure and looks like a sandwich of two slightly nonplanar CaCl 3 fragments on the top and bottom and Ca 3 Cl 3 hexagon between. In the CaCl 3 fragments, the internuclear distance Ca-Cl is 2.755 Å.

CONCLUSION
The cluster ions CaCl + , CaCl 3 -, Ca 2 Cl 3 + , Ca 3 Cl 5 + , and Ca 4 Cl 7 + have been detected earlier in the equilibrium vapour by high temperature mass spectrometry technique. The formation of the heavier cluster Ca 5 Cl 9 + was predicted. The geometrical structure and vibrational spectra of the ions were determined using the DFT and MP2 methods. The structures of the positive ions were designed through the consequent attachment of CaCl 2 molecule to CaCl + ion. Alternative configurations were considered but no isomers revealed. The equilibrium geometrical structures of the ions Ca 2 Cl 3 + , Ca 3 Cl 5 + , and Ca 5 Cl 9 + confirmed to be compact and rigid of a perfect shape and high symmetry. The equilibrium structure of the ion Ca 4 Cl 7 + is of lower symmetry, and therefore lower stability of the ion regarding dissociation with CaCl 2 molecule elimination may be expected.