American Journal of Applied Chemistry
Volume 3, Issue 6, December 2015, Pages: 224-231

Theoretical Study of Structure and Vibrational Spectra of Molecular and Ionic Clusters Existing in Vapour over Rubidium Chloride

Ismail Abubakari1, 2, *, Tatiana Pogrebnaya1, 2, Alexander Pogrebnoi1, 2

1The Nelson Mandela African Institution of Science and Technology (NM–AIST), Arusha, Tanzania

2Dept. of Materials, Energy Science and Engineering, The NM–AIST, Arusha, Tanzania

Email address:

(I. Abubakari)
(T. Pogrebnaya)
(A. Pogrebnoi)
(A. Pogrebnoi)

To cite this article:

Ismail Abubakari, Tatiana Pogrebnaya, Alexander Pogrebnoi. Theoretical Study of Structure and Vibrational Spectra of Molecular and Ionic Clusters Existing in Vapour over Rubidium Chloride. American Journal of Applied Chemistry. Vol. 3, No. 6, 2015, pp. 224-231. doi: 10.11648/j.ajac.20150306.18

Abstract: The geometrical structure and the vibrational spectra of dimer Rb2Cl2, trimer Rb3Cl3, tetramer Rb4Cl4 molecules and heptaatomic Rb4Cl3+, Rb3Cl4 ions were studied. The cluster molecules and ions had been detected in equilibrium vapour over rubidium chloride previously. The quantum chemical calculations by DFT with hybrid functional B3P86 and MP2 methods were performed. The effective core potential with Def2–TZVP (6s4p3d) basis set for rubidium atom and full electron aug–cc–pVTZ (6s5p3d2f) basis set for chlorine atom were used. The equilibrium configuration was confirmed to be rhomb of symmetry D2h for dimer Rb2Cl2, distorted cube (Td) for tetramer Rb4Cl4 and polyhedral (C3v) for heptaatomic ions Rb4Cl3+ and Rb3Cl4. For the trimer molecule Rb3Cl3 two isomers have been revealed: hexagonal (D3h) and butterfly-shaped (C2v), the latter has lower energy and is proved to be predominant in equilibrium vapour in a broad temperature range.

Keywords: Ionic and Molecular Clusters, Rubidium Chloride, Geometrical Structure, Vibrational Spectra, DFT, MP2, Isomers

1. Introduction

Several alkali metals including rubidium may chemically combine with halogen to form different neutral and ionic clusters which exist in vapours [1-10]. These clusters are characterized by different geometrical structures, vibrational spectra, and thermodynamic properties which are mostly depend on the number of atoms composing the species [1]. The formed clusters possess specific electronic, optical, magnetic and structural properties which make them useful in different technical and scientific applications [2,3]. These properties are also strongly depending on size and composition of the clusters. Changing the magnitude and structure of a cluster aggregate allows coming up with new materials of desired properties [11].

To investigate the structure and properties of alkali halide clusters, different experimental techniques e.g. high temperature mass spectrometry [12,13], microwave absorption spectroscopy [14,15] and molecular beam electric resonance [16] and theoretical methods [1,17,21] were employed.

Different molecular and ionic associates were detected in vapour over rubidium chloride; they are dimer, trimer, and tetramer molecules and the ions Rb+(RbCl)n (n = 1–4) [22].

Previously the quantum chemical methods has been used to study tri- and pentaatomic ions Rb2Cl+, RbCl2, Rb3Cl2+, Rb2Cl3 [20]. The ionic clusters were studied by density functional theory (DFT) with the Becke–Lee–Yang–Parr functional (B3LYP5), second order and fourth order Møller–Plesset perturbation theory (MP2 and MP4) using the basis sets aug–cc–pVTZ (5s4p2d1f) for Cl and cc–pVTZ (7s5p4d1f) for Rb [20]. This study aims the investigation of the structure and properties of neutral and heavier ionic clusters of rubidium chloride.

2. Methodology

The density functional theory (DFT) with hybrid functional the Becke–Perdew correlation B3P86 [23-26] and second order Møller–Plesset perturbation theory (MP2) implemented into PC GAMESS (General Atomic and Molecular Electronic Structure System) program [27] and Firefly version 8.1.0 [28] were used for calculation of geometrical parameters and frequencies of normal vibrations. The visualization of the geometrical structure, specification of parameters, and assignment of vibrational modes in infrared spectra was done using the Chemcraft software [29] and MacMolPlt program [30]. The effective core potentials with Def2–TZVP (6s4p3d) basis set for Rb atom [31,32] and full electron aug–cc–pVTZ basis set for Cl (6s5p3d2f) atom [32,33] were applied in this study. The basis sets were taken from the EMSL (The Environmental Molecular Sciences Laboratory, GAMESS US) Basis Set Exchange version 1.2.2 library [34,35].

The Openthermo software [36] was used in calculation of the thermodynamic properties including energies rE and enthalpies r(0) of the reactions which were calculated through the following equations:

rE = Ei prod – ∑Ei reactant          (1)

Δr(0) = ∆rE + ∆rε               (2)

rε = 1/2hc(∑ωi prod – ∑ωi reactant)        (3)

where ∑Ei prod, ∑Ei reactant are the sums of the total energies of the products and reactants respectively,rε is the zero point vibration energy correction, ∑ωi prod and ∑ωi reactant are the sums of the vibration frequencies of the products and reactants respectively.

3. Results and Discussion

3.1. Monomer RbCl and dimer Rb2Cl2

The properties of the diatomic RbCl and dimer Rb2Cl2 molecules was computed using three different DFT hybrid functionals, B3LYP5, B3P86 and B3PW91 and Møller–Plesset perturbation theory (MP2) for the purpose of choosing the appropriate method to be implemented in this study and estimation of uncertainties in theoretical values. The results for diatomic molecule RbCl together with the available experimental data are shown in Table 1.

Table 1. Properties of the monomer molecule RbCl.

Notes: Here and hereafter, Re is the equilibrium internuclear distance (), E is the total electron energy (au), ωe is the fundamental frequency (cm–1), μe is the dipole moment (D), IEvert and IEad are the ionization energies, vertical and adiabatic, respectively (eV), EA is the electron affinity (eV).

As is seen the calculated internuclear distance (Re) using three DFT hybrid functionals were overrated by 0.07–0.09 when compared with the reference data and that of MP2 was overrated by 0.07 . Considering both DFT and MP2 methods, the results obtained show very little variation whereas DFT/B3P86 and MP2 give the best results regarding to the reference. The calculated values of frequency were underrated by 6–9 cm–1 (2.7–3.9%) for DFT methods while MP2 result coincides with the experimental value [38]. The results for dipole moment (μe), show high deviation from reference data for the case of MP2, overrated by 0.88 D; and overrated by 0.41–0.47 D for the DFT methods.

The adiabatic ionization energy (IEad) was obtained as the energy difference of the RbCl+ ion and neutral molecule where the internuclear separation Re(Rb-Cl) was optimized both for neutral and ionic species and vertical ionization energy (IEvert) was obtained as the energy difference of the RbCl+ ion and neutral molecule where the internuclear separation Re(Rb-Cl) was optimized in neutral molecule only and accepted the same for the ion. Electron affinities (EA) were obtained by determining the energy difference between neutral molecule and negatively charged ion. The results obtained for IE and EA using both DFT and MP2 methods agree well with the reference. As the optimization procedure by MP2 was not implemented for the species with multiplicity more than 1 in the software [27,28], the IEad by MP2 method was not calculated in this study.

For the dimer molecule Rb2Cl2, a planar cyclic structure of D2h symmetry (Fig. 1a) was confirmed to be equilibrium, while linear one (C∞v) was found to be a saddle point on the potential energy surface. The calculated properties; internuclear distance, valence angle, vibrational spectra and enthalpy of the dissociation reaction are presented in Table 2. As seen the calculated values of internuclear distance are overrated by 0.04–0.09 compared with literature data [45] and the values of enthalpy of dissociation reaction are in agreement with the reference data [22,46].

The absence of low frequencies in the vibrational spectra of Rb2Cl2 indicates the rigidity of the structure; the lowest frequency being about 50 cm–1.

In the IR spectrum, three vibrational modes ω4, ω5, and ω6 have nonzero intensities but due to overlapping of ω5 and ω6 only two peaks could be seen which are asymmetrical stretching 171 cm–1 and wagging 52 cm–1 (MP2).

Based on results for the RbCl and Rb2Cl2 molecules, it is worth to mention that the data obtained by MP2 and DFT/B3P86 hybrid functional agree better with the available literature data therefore these two methods were chosen for further computations of heavier molecular and ionic clusters.

Table 2. Properties of the dimer molecule, Rb2Cl2.

Notes: aThe MP2 calculation. Here and hereafter, αe is the valence angle (deg). rE and rH°(0) are the energy and enthalpy of the dissociation reaction Rb2Cl22RbCl (kJ mol-1), Ii are the infrared intensities (D2×amu–1×2). The reducible vibration representation reduces to Γ = 2Ag + B1g + B1u + B2u + B3u.

3.2. Trimers Rb3Cl3 and tetramer Rb4Cl4

For the trimer molecule Rb3Cl3, three possible geometrical configurations were considered; linear of D∞h symmetry, hexagonal of D3h symmetry and butterfly-shaped of C2v symmetry. The linear configuration was found to be unstable due to presence of imaginary frequencies but the rest two configurations, (Figs. 1b and 1c) were confirmed to be equilibrium. The results are shown in Table 3.

Table 3. Properties of trimer Rb3Cl3 molecule, hexagonal (D3h) and butterfly-shaped (C2v) .

Notes: rEiso = E(C2v)–E(D3h) is the relative energy of the butterfly-shaped isomer regarding the hexagonal one (kJ mol-1). The reducible vibration representations for Rb3F3 of D3h and C2v symmetry reduces to Γ =  and Γ = 6A1 + A2 + B1 + 4B2 respectively. For the C2v butterfly-shaped isomer, the values given in parentheses near the frequencies are infrared intensities (D2amu-1Å-2).

For the hexagonal isomer (D3h), one internuclear distance Re(Rb–Cl) and one valence angle αe(Rb–Cl–Rb) or βe(Cl–Rb–Cl) are needed to describe the structure; for the butterfly-shaped isomer (C2v), four internuclear distances Re1, Re2, Re3, Re4 and two valence angles αe(Rb2–Cl5–Rb3) and βe(Cl4–Rb1–Cl6) are used for the description. The butterfly-shaped configuration has lower energy, by 2.6 kJ mol–1 (DFT) and 10.0 kJ mol–1 (MP2), than hexagonal one.

The relative concentration of isomers p(C2v)/p(D3h) have been estimated using the same procedure as it was described previously [21]. The enthalpy of the isomerization and relative energy of isomers rEiso (MP2) for the isomerization reaction Rb3Cl3 (D3h) Rb3Cl3 (C2v) was calculated using Eqs. (2) and (3).

The values of p(C2v)/p(D3h) were obtained for the temperature range between 700-2000 K; the plot is shown in Fig. 2. As is seen the butterfly-shaped isomer is more abundant than hexagonal one and the concentration of the former decreases with temperature increase.

Figure 1. Equilibrium geometric structures of molecules: (a) Rb2Cl2 (D2h); (b) Rb3Cl3 (D3h); (c) Rb3Cl3 (C2v); (d) Rb4Cl4 (Td).

Figure 2. Temperature dependence of relative amount of the C2v isomer regarding to D3h isomer of trimer Rb3Cl3 molecule.

The IR spectra of both isomers of Rb3Cl3 molecule are shown in Fig. 3. The most intensive bands correspond to the stretching vibration modes and bending modes have lower intensities.

When comparing the properties of Rb3Cl3 with Rb3F3 molecule, a similarity may be noted: the same two isomers were revealed for Rb3F3 [21] and the butterfly-shaped isomer was predominant in that case as well.

For the tetramer molecule Rb4Cl4, the geometrical configuration considered was cube with Td symmetry (Fig. 1d) and it was confirmed to be equilibrium. The geometrical parameters and vibrational frequencies of the tetramer molecule are presented in Table 4.



Figure 3. Theoretical IR spectra of the trimer Rb3Cl3 molecule calculated by MP2 method: (a) hexagonal isomer (D3h); (b) butterfly-shaped isomer (C2v).

Table 4. Properties of tetramer molecule Rb4Cl4, cube of Td symmetry.

Notes: The reducible vibration representation reduces to Γ = 2A1 + 2E + T1 + 3T2

One internuclear distance Re(Rb–Cl) and one valence angle αe(Rb–Cl–Rb) or βe(Cl–Rb–Cl) are needed to describe the structure. In the IR spectrum, three vibrational modes are active but only one peak could be observed ω6 (T2) which is assigned to asymmetrical stretching Rb–Cl vibration; other two modes have low intensities.

3.3. Heptaatomic Ions Rb4Cl3+ and Rb3Cl4–

For heptaatomic ions Rb4Cl3+ and Rb3Cl4two alternative structures were considered, polyhedral of C3v symmetry and two-cycled with mutually perpendicular planes of D2d symmetry (Fig. 4); only polyhedral structure of symmetry C3v was confirmed to be equilibrium. The results for both positive and negative ions are presented in Table 5. The polyhedral structure is described by two internuclear distances Re1 and Re2 and three valence angles, αe(Rb2–Cl5–Rb3), βe(Rb1–Cl4–Rb3) and γe(Cl4–Rb2–Cl7). Compared to the D2d structure, the polyhedral configurations possesses lower energy with the energy drop of 87 kJ mol–1 and 83 kJ mol–1 for Rb4Cl3+ and Rb3Cl4 respectively, according to MP2 results.

Table 5. Properties of the heptaatomic ions Rb4Cl3+ and Rb3Cl4 (C3v).

Notes: γe is the valence angle (deg). The reducible vibration representations reduce to Γ = 4A1 + A2 + 5E for both Rb4Cl3+ and Rb3Cl4

Figure 4. Geometric structures of heptaatomic ions: polyhedral of D3h symmetry (a) Rb4Cl3+ (b) Rb3Cl4: two cycled with the mutually perpendicular planes of D2d symmetry (c) Rb4Cl3+ (d) Rb3Cl4.

As is seen in Table 5 the respective geometrical parameters and vibrational frequencies of the positive and negative ions are close to each other. The IR spectra are shown in Fig. 5. In both spectra, the stretching vibrational modes have higher intensities than bending modes.



Figure 5. Theoretical IR spectra of heptaatomic ions (C3v) calculated by MP2 method: (a) Rb4Cl3+; (b) Rb3Cl4.

4. Conclusion

The properties of the trimer and tetramer molecules and heptaatomic ionic clusters have been investigated theoretically using DFT/B3P86 and MP2 methods. The corresponding parameters of the species calculated by two methods are generally in a good accordance to each other; while the internuclear distances Rb–Cl found with DFT/B3P86 are longer by 0.02–0.04 than those found with MP2 method. Among the species considered, for the Rb3Cl3 molecule two isomers, hexagonal C3v and butterfly-shaped C2v, were proved to exist; the latter was evaluated to be more abundant in vapour. When compare the Rb3Cl3 with Rb3F3 studied previously, alike features may be noted (including the existence of two isomers). The results obtained for the heptaatomic ions show similarities between the respective properties of positive and negative ions.

Authors’ Contributions

All authors participate well in all steps including computation, data analysis and manuscript preparation towards production of this work.


The authors are very thankful to the Tanzania Commission for Science and Technology (COSTECH) through The Nelson Mandela African Institution of science and Technology for supporting and sponsoring this research work.


Tables A1 to A5 contain the thermodynamic functions of the ionic and molecular clusters; trimer Rb3F3, tetramer Rb4Cl4, and heptaatomic Rb4Cl3+ and Rb3Cl4. The tables include absolute temperature T in K, molar heat capacity cp°, Gibbs reduced free energy Φ°, and entropy S° which are given in J mol–1 K–1, and enthalpy increment H°(T)–H°(0) in kJ mol–1.

Table A1. Thermodynamic functions of the Rb3Cl3, C2v.isomer.

T cp° H°(T)–H°(0) Φ°
298.15 130.24 514.540 33.025 403.718
700 132.51 626.923 85.999 504.067
800 132.64 644.626 99.257 520.555
900 132.71 660.253 112.524 535.226
1000 132.78 674.239 125.799 548.440
1100 132.82 686.896 139.079 560.461
1200 132.86 698.455 152.363 571.486
1300 132.89 709.090 165.649 581.668
1400 132.91 718.938 178.939 591.124
1500 132.93 728.108 192.230 599.955

Table A2. Thermodynamic functions of the Rb3Cl3, D3h isomer.

T cp° H°(T)–H°(0) Φ°
298.15 130.23 516.663 33.245 405.102
700 132.51 629.039 86.216 505.873
800 132.63 646.742 99.474 522.400
900 132.70 662.368 112.741 537.100
1000 132.76 676.355 126.016 550.339
1100 132.84 689.012 139.296 562.379
1200 132.83 700.570 152.579 573.421
1300 132.81 711.205 165.866 583.616
1400 132.89 721.053 179.155 593.085
1500 132.92 730.223 192.446 601.926

Table A3. Thermodynamic functions of the Rb4Cl4, Td isomer.

T cp° H°(T)–H°(0) Φ°
298.15 178.92 570.693 43.797 423.724
700 182.18 725.158 116.611 558.571
800 182.35 749.497 134.838 580.950
900 182.47 770.982 153.079 600.894
1000 182.56 790.212 171.331 618.881
1100 182.63 807.615 189.590 635.260
1200 182.67 823.507 207.854 650.295
1300 182.69 838.129 226.123 664.188
1400 182.74 851.670 244.394 677.103
1500 182.75 864.278 262.669 689.165

Table A4. Thermodynamic functions of the Rb4Cl3+, C3v isomer.

T cp° H°(T)–H°(0) Φ°
298.15 154.80 556.647 38.787 426.489
700 157.39 690.161 101.719 544.848
800 157.52 711.187 117.465 564.356
900 157.64 729.746 133.222 581.722
1000 157.70 746.357 148.988 597.369
1100 157.73 761.388 164.759 611.607
1200 157.77 775.115 180.534 624.670
1300 157.82 787.745 196.313 636.735
1400 157.73 799.440 212.095 647.944
1500 157.77 810.330 227.878 658.411

Table A5. Thermodynamic functions of the Rb3Cl4, C3v isomer.

T cp° H°(T)–H°(0) Φ°
298.15 154.92 546.945 38.729 416.983
700 157.42 680.513 101.683 535.252
800 157.54 701.542 117.431 554.753
900 431.62 720.103 133.190 572.114
1000 157.70 736.715 148.957 587.758
1100 157.77 751.748 164.729 601.994
1200 157.79 765.475 180.506 615.053
1300 157.80 778.106 196.286 627.117
1400 157.84 789.802 212.068 638.325
1500 157.92 800.692 227.852 648.791


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