Theoretical Prediction of Rare Gas Containing Hydride Cations

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Theoretical Prediction of Rare Gas Containing Hydride Cations: HRgBF (Rg = He, Ar, Kr, and Xe) +

Abhishek Sirohiwal, Debashree Manna, Ayan Ghosh, Thankan Jayasekharan, and Tapan K. Ghanty J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp4064824 • Publication Date (Web): 13 Sep 2013 Downloaded from http://pubs.acs.org on September 19, 2013

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The Journal of Physical Chemistry

Theoretical Prediction of Rare Gas Containing Hydride Cations: HRgBF+ (Rg = He, Ar, Kr, and Xe)

Abhishek Sirohiwal,# Debashree Manna,† Ayan Ghosh,§ Thankan Jayasekharan‡ and Tapan K. Ghanty*,†

#

Indian Institute of Science Education and Research (IISER), Bhopal - 462 023, INDIA. †

Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai - 400 085, INDIA. §

Laser and Plasma Technology Division, Beam Technology Development Group, Bhabha Atomic Research Centre, Mumbai - 400 085, INDIA.

‡

Applied Spectroscopy Division, Physics Group, Bhabha Atomic Research Centre, Mumbai - 400 085, INDIA.

*

Author to whom correspondence should be addressed. Electronic mail: [email protected].

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Abstract: Existence of rare gas containing hydride ions of boron (HRgBF+) has been predicted by using ab initio quantum chemical methods. The HRgBF+ ions are obtained by inserting a Rg atom in between the H and B atoms of HBF+ ion, and the geometries are optimized for minima as well as transition states using second order Møller-Plesset perturbation theory (MP2), density functional theory (DFT), and coupled-cluster theory (CCSD(T)) based techniques. The predicted HRgBF+ ions are found to be metastable, and it exhibits linear structure at the minima and non-linear planar structure at the transition state, corresponding to Cαv and Cs symmetries, respectively. All the predicted HRgBF+ ions show negative binding energies with respect to 2-body dissociation channel leading to global minima (HBF++ Rg) on the singlet potential energy surface. In contrast, the dissociation energies corresponding to another 2-body dissociation channel leading to HRg+ + BF and, two 3-body dissociation channels corresponding to the dissociation into H + Rg + BF+ and H+ + Rg + BF show very high positive energies. Apart from positive dissociation energies the predicted ions show finite barrier heights corresponding to the transition states involving H-Rg-B bending mode leading to the global minima products (HBF+ + Rg). The finite barrier heights in turn would prevent the metastable HRgBF+ species in transforming to global minima products. Structure, harmonic vibrational frequencies, stability, Mulliken and Natural bonding orbital (NBO) charge distribution values for all the species are reported using the MP2 and DFT methods. Furthermore, the intrinsic reaction coordinate analysis confirms that the meta-stable minimum energy structure and the global minimum products are connected through the corresponding transition state for each of the species on the respective singlet potential energy surface. Atoms-in-molecules (AIM) analysis indicates that the HRgBF+ ions are best described as HRg+BF, and are analogous to the isoelectronic HRgCO+ and HRgN2+ ions. The energetic along with charge redistribution and spectroscopic data strongly supports the possible existence of HRgBF+ ions. Hence it might be possible to generate HRgBF+ ions in DC discharge plasma of BF3/H2/Rg mixture at low temperature, and the predicted ions may be characterized using magnetic field modulated infrared laser spectroscopic technique, which has been used earlier to characterize HBF+ ions. Keywords: Rare Gas; Insertion Complex; HBF+, Structure and Energetics; Charge Distributions; ab initio calculations


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1. Introduction The successful identification of HArF1 molecule, associated with H-Ar covalent bonding, by IR spectroscopic method has revolutionized the chemistry of rare gas atoms. After this discovery several novel neutral as well as charged molecules1-14 containing rare gas (Rg) atom are either predicted theoretically and/or observed experimentally. Theoretically these metastable molecular species are investigated by inserting one Rg atom in a thermodynamically stable molecule, and the geometrical parameters are optimized for minimum energy using quantum computational methods. The basic idea is that the chosen stable molecule should provide a better ambient for the Rg atom to redistribute its electron clouds to other atoms within their vicinity, and form novel meta-stable species with binding energies in between pure covalent to van der Waals bonding. The insertion complexes involving noble metal-rare gas atoms have also been investigated theoretically.7,8 However, existence of noble metal-noble gas bonding had been explored earlier.15-17 Very recently, the kinetic stability of the rare gas hydrides has been studied extensively in different molecular environments.18,19 Moreover, the stability of the rare gas hydrocarbons has been explored in an organic liquid-like environment using ab-initio molecular dynamics simulation techniques and it has been accentuated that the rare gas compound may remain stable well above the cryogenic temperature.20 The interaction of a boron (B) atom with a Rg atom is of interest due to the availability of empty 2py and 2pz orbitals of boron. However, very few insertion type molecules that contain both B and Rg atoms, for example, FRgBF2,10, FRgBO21 and FRgBN– 22

are predicted theoretically so far. Since most of the inserted Rg containing molecules are

metastable in nature, they are prepared and characterized experimentally using matrix isolation technique1-6 in cryogenic conditions. Generally, the H-Rg stretch mode vibration is widely used for the unambiguous identification/spectral characterization of these species, however, none of the predicted B and Rg containing molecule has H-Rg moiety to monitor its existence. In the recent past, a new class of boron containing molecular species HBX (X = F, Cl, Br) are prepared23 in supersonic discharge jet source and characterized spectroscopically using laser induced fluorescence (LIF) technique. Further, the HBF+ ion has also been produced in a glow discharge containing mixture of both BF3 and H2 gas, and are spectrally characterized using magnetic modulated IR-laser spectroscopy.24,25 Interestingly HBF+ ion is also isoelectronic to HCO+,

26,27

and N2H+ ions

28-30

(14 electrons), which are important in

atmospheric chemistry. The Rg inserted molecular ions of HCO+, HN2+ and H3O+ are



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investigated31-33 theoretically by us recently. Here we present structure, energetic, and spectroscopic properties of another set of novel interesting cations, viz., HRgBF+.

2. Computational Methodology In this work, all the calculations have been performed using GAMESS34 and MOLPRO 201235 program codes. MP236, DFT along with hybrid exchange correlation energy functional B3LYP37-38, and the CCSD(T)39 methods are employed to optimize the geometrical structures of HRgBF+ ions in their minima as well as transition states. We have employed energy adjusted Stuttgart effective core potentials40 and the corresponding (6s6p1d1f)/ [4s4p1d1f] basis sets for Kr and Xe atoms. For the remaining atoms, 6-311+ +G(2d,2p) basis sets have been used in MP2 and DFT methods. On the other hand, aug-ccpVTZ basis sets have been used for the latter atoms in CCSD(T) calculations. The geometry optimization have been performed at MP2, DFT and CCSD(T) levels of theory based on analytical and numerical gradients for C4v and Cs symmetries, corresponding to the linear minima and planar transition states, respectively. The stability of the predicted ionic species is determined by computing the energy differences between the predicted ions and the possible unimolecular dissociation channels. The harmonic infrared frequencies are also computed using the MP2, DFT and CCSD(T) methods in order to characterize the nature of the stationary points on the respective potential energy surfaces. Atoms-in-molecules (AIM)41 approach has been used to compute the topological properties of the predicted ions as well as to evaluate the nature of the bonding exists among the constituent atoms. Further, we have applied intrinsic reaction coordinate42 methods coupled with second order Gonzalez-Schlegel algorithms43 with a step size of 0.05 amu1/2 bohr in order to trace out the minimum energy path that connect the local and the global minima through the transition state.

3. Results and Discussions A. Structural parameters of HRgBF+ species The Rg inserted HBF+ ions (HRgBF+) show true minima on the singlet potential surface by MP2, DFT, and CCSD(T) methods, and exhibit linear structure (C∞V symmetry) at the minima position and nonlinear planar structure (Cs symmetry) at the transition state. The optimized structures at both minima and transition states are shown in Figure 1. Table 1 lists all the structural parameters of the HRgBF+ ions (except HNeBF+ ion) for both minima and transition states. Here it may be noted that the neon atom is very prompt in the formation of


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van der Waals complex ion (NeHBF+) with HBF+ rather than the inserted type ion (HNeBF+). It is well known that polraizable tendency of an atom increases with increase in size of the atom. Thus, down the group, the condensable ability of the rare gases increases in the order He < Ne < Ar < Kr < Xe due to increase in the extent of polarization. It is also known that in comparison to He and Ne, other rare gases (Ar, Kr and Xe) show more condensation effect. However, as far as chemical reactivity is concerned, Ne is less reactive than He, and this aspect has been discussed recently by Grandinetti.44 The size of a Ne atom is larger than that of a He atom; however, due to the presence of p orbitals, extent of attractive electrostatic interactions is likely to be smaller for a Ne atom while interacting with other atoms. Again, orbital repulsion may be higher because of the same reason. Consequently, it is unlikely for a Ne atom to form HNeBF+ complex. Therefore, the results of HNeBF+ ion will not be discussed in this paper. In general, the CCSD(T) computed results are quite accurate in predicting experimentally determined parameters of many systems, thus the results obtained with CCSD(T) method will be discussed in more details rather than DFT and MP2 methods. The computed H-Rg bond lengths are 0.771, 1.286, 1.422, 1.620 Å for HHeBF+, HArBF+, HKrBF+, and HXeBF+, respectively, and these values are found to be very close to the corresponding MP2 calculated values. However, DFT calculated bond length values deviate considerably from the corresponding CCSD(T) values. Protonated rare gas ions (RgH+) are fundamental species in rare gas chemistry, and have been investigated extensively both theoretically as well as experimentally.45-49 In fact, hydrohelium cation (HeH+) is an important ion in astrochemistry, which was first observed in mass spectrometry50. In its singlet ground state (X1Σ) its bond length is 0.77 Å, which is similar to the bond length of HHe+ in HHeBF+ ion. The CCSD(T) computed bond lengths of bare HHe+, HAr+, HKr+, and HXe+ ions, are 0.776, 1.282, 1.416, 1.607 Å, respectively, and are comparable to the bond lengths of the corresponding moiety in the HRgBF+ ions. In this context, it is important to compare the HRg+ bond length values of other two isoelectronic molecular cations viz., HRgCO+ and HRgN2+.31,32 The CCSD(T) computed bond length values of HRg+ moiety in HRgCO+ are 0.764, 1.281, 1.417, and 1.610 Å corresponding to HHe+, HAr+, HKr+, and HXe+ moiety. Similarly the computed bond lengths of HRg+ in HRgN2+ are 0.765, 1.280, 1.416, and 1.607 Å, respectively, for HHe+, HAr+, HKr+, and HXe+ moiety. These results indicate that in all the three systems the bond lengths of HRg+ moiety are very similar, and the molecular ions can be best described as HRg+ X where X = CO, N2, and BF. The next



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bond length value of importance in HRgBF+ cation is Rg-B, and the CCSD(T) computed values are 2.240, 2.943, 2.980 and 3.090 Å corresponding to He-B, Ar-B, Kr-B, and Xe-B bonds, respectively. In general, CCSD(T) calculated Rg-B bond length values are found to be closer to the corresponding MP2 calculated values, and differ from the respective DFT values. It is also of interest to compare the Rg-X bond lengths in HRgCO+, HRgN2+ and HRgBF+ ions. The CCSD(T) bond lengths of Rg-C in HRgCO+ ions are 2.221, 2.911, 3.068 and 3.124 Å along the series He-Ar-Kr-Xe, respectively, while Rg-N bond lengths in HRgN2+ are 2.138, 2.841, 2.922 and 3.093 Å along the series He-Ar-Kr-Xe, respectively. As discussed above, the Rg-B bond length values are slightly larger than the Rg-C and Rg-N bond lengths in the respective systems along the He-Ar-Kr-Xe series. This implies that even though empty low-lying 2p orbitals of B are available for bonding with a Rg atom, it is not evident from the calculated trend in the Rg-B bond length values. Due to the larger atomic size of B as compared to that of C or N, the Rg-B bond length values are larger. The B-F bond length value is ~1.25 Å and is similar for all the HRgBF+ systems considered here. B. Energetics of HRgBF+ Ions In order to determine the stability of the predicted HRgBF+ cations we have computed the energetics of the most probable unimolecular dissociation channels and the obtained energies for all the channels are listed in Table 2. The possible dissociation channels considered for the HRgBF+ ions are

HRgBF+ →

HBF+ + Rg

(1)

HRg+ + BF

(2)

H + Rg + BF+

(3)

H+ + Rg + BF

(4)

From the energy diagram it can be inferred that the predicted ions can undergo two 2-body dissociation channel as well as two 3-body dissociation channels. The channel (1) represents the global minima while channels (2), (3), and (4) correspond to the local minima on the potential energy surface. The predicted ions are found to be higher in energy (174-495 kJmol1

) with respect to the dissociated products corresponding to the channel (1), which clearly

indicate that the dissociation process is exothermic and these ions are meta-stable in nature. However, corresponding to the dissociation channel (2), the energies of the HRgBF+ ions are lower than that of the dissociated products (HRg+ + BF) and the dissociation energies are in the range of 51-74 kJmol-1. It indicates that the channel (2) is a local minimum in the same potential energy surface. Similarly the computed energies show positive dissociation energies 6 ACS Paragon Plus Environment

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for other two 3-body dissociation channels (channel (3) and (4)), except for the channel (3) in case of HHeBF+ in MP2. The CCSD(T) computed energy values for channel (3) are 25.8, 203.3, 281.9 and 346.9 kJmol-1 for HHeBF+, HArBF+, HKrBF+, and HXeBF+ respectively. The dissociation energy values obtained for channel (4) are 270.1, 447.6, 526.1 and 591.1 kJmol-1 for HHeBF+, HArBF+, HKrBF+, and HXeBF+ respectively. Now it is interesting to compare the dissociation/binding energies of the channel (2) of the present ions with that of the other isoelectronic system such as HRgCO+ and HRgN2+ ions, which are reported recently. The dissociation energies correspond to channel (2) for HRgCO+ are 15.0, 28.8, 29.5 and 29.1 kJmol-1 for He-Ar-Kr-Xe series. Similar dissociation energy values for HRgN2+ ions are 31.4, 21.2, 21.8 and 21.1 kJmol-1 for He-Ar-Kr-Xe series while these are 73.6, 50.9, 53.2 and 54.6 kJmol-1 for HHeBF+, HArBF+, HKrBF+, and HXeBF+ respectively. It indicates the existence of stronger binding between the HRg+ moiety and BF in HRgBF+ than HRg+ and CO in HRgCO+, and HRg+ and N2 in HRgN2+. In spite of having stronger interaction between the HRg+ fragment and BF in HRgBF+, larger Rg-B bond length values are clearly due to larger size of the B atom. Since the predicted ions are metastable in nature, now it is important to know the barrier heights corresponding to the transition states of the ions dissociating into the global minima products. The CCSD(T) computed barrier heights corresponding to the saddle points are 15.5, 21.0, and 26.7 kJmol-1 for HArBF+, HKrBF+, and HXeBF+ respectively. However, for the HHeBF+ ion barrier height could not be calculated due to convergence problem in the transition state geometry at the CCSD(T) level of theory. The calculated DFT(MP2) barrier heights are found to be 38.6 (11.6), 28.5 (16.7), 35.2 (22.1) and 35.2 (25.6) kJmol-1, for the HHeBF+, HArBF+, HKrBF+, and HXeBF+ series, respectively. All these calculated values indicate that barrier heights may be sufficient for experimental identification of these meta-stable species. The intrinsic reaction coordinates (IRC) connecting the meta-stable minima and the global minima product through transition state are computed, and the reaction path ways are shown in Figure 2. Thus the energy diagram data analysis indicates that the HRgBF+ cations are unstable with respect to the channel (1), however, they are stable with respect to other dissociation channels. Thus, it may be possible to prepare and characterize these systems by employing suitable experimental conditions along with low temperature matrix isolation technique.1-6 Zero-point energy correction is another important parameter to be considered for determining an accurate barrier height value. Therefore, we have evaluated the zero-point energy corrected barrier heights and the corresponding values are found to be 35.2 (6.2), 24.2 (12.1), 30.5 (17.3) and 30.5 (20.8) kJ mol-1 as calculated using DFT (MP2). These results imply that although the 7 ACS Paragon Plus Environment


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predicted HRgBF+ species are found to be thermodynamically unstable; however, as saddle point is found for each of these species and the barrier height (the energy difference between the HRgBF+ species and the corresponding transition state) is calculated to be rather high, these species are kinetically stable and might be observed experimentally at cryogenic conditions, similar to other rare gas hydrides detected experimentally. Since the present systems are cationic in nature, it might be possible to prepare these through electron bombardment of gaseous mixtures of boron, fluorine, hydrogen containing precursors and rare gas at cryogenic conditions. Subsequently, these can be characterized using Fouriertransform infrared spectroscopy. C. Charge Distributions and Bonding Analysis of HRgBF+ Ions The electronic charge density distributions in molecules provide valuable information about the nature of the bond exist between the constituent atoms in a molecule. The partial atomic charges computed by Mulliken population analysis using MP2 and DFT methods for the HRgBF+ ions are reported in Table 3. The partial atomic charges obtained for HRgBF+ ions by both MP2 and DFT methods are quite comparable, however, the atomic charges obtained by MP2 method will be discussed. The atomic charge on H (qH), B (qB) and F (qF) on bare HBF+ ion is 0.173, 0.507 and 0.320 respectively. The insertion of rare gas atom into the HBF+ ion redistributes its original charges and the qH value varies from 0.173 to 0.597, 0.370, 0.255 and 0.164 for HHeBF+, HArBF+, HKrBF+ and HXeBF+, respectively. The charge on the Rg atom is found to be 0.314, 0.645, 0.689 and 0.816 along the series He-Ar-Kr-Xe, respectively. The charges acquired by the Rg atoms are comparable except for helium atom in the HRgBF+ ions. The qB value changes from 0.507 to 0.228, 0.059, 0.041 and 0.084 while the charge on F atom varies from 0.320 to -0.140, -0.075, 0.013, -0.064 along the series HeAr-Kr-Xe. The combined charges of H and Rg atoms in the HRgBF+ ions are 0.911, 1.015, 0.944, 0.980, respectively, along the series He-Ar-Kr-Xe. This indicates that maximum amount of the positive charge is concentrated on the HRg moiety of HRgBF+ ions. The charge distribution data indicates that substantial amount of charge distribution has taken place after the insertion of a Rg atom in HBF+ ion, and the HRgBF+ ion can be described as (HRg)+ BF. Similar charge redistributions have also been noted in the MP2 method. At the transition state the qH value slightly increases from its minima along the He-Ar-Kr-Xe series. The qRg and qB values values are found to decrease and increase, respectively. The charge on the F atom shows more negative value as compared to its charge in the minima state.


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It is well known that the Mulliken population analysis provides qualitative information about the electronic charge distribution within the system. However, the basis set dependence of Mulliken charges is well known in the literature. Accordingly, we have performed NBO analysis for obtaining the partial atomic charges in the HRgBF+ ions using DFT and MP2 methods with 6-311G++(2d,2p), cc-pVTZ and aug-cc-pVTZ basis sets in MOLPRO program, and reported the results in Table 4. For the purpose of comparison we have also calculated the Mulliken charges as well. From the values reported in the Table it is clear that the Mulliken charges differ noticeably while calculating from one basis set to other. On the other hand, NBO charges remain almost the same with change in basis sets. Significant differences in the calculated charge values have been observed for the atomic charges on the B and F atoms in the HRgBF+ ions using two different analysis schemes, viz. Mulliken and NBO. In the NBO analysis it has been found that the BF fragment is significantly ionic in nature with considerable charge separation, while charge redistribution is found to be rather small in the Mulliken analysis. In fact, atomic charges calculated using NBO method clearly indicates that the nature of bonding for the B-F bond is ionic. Nevertheless, both Mulliken and NBO charges clearly indicate that the HRgBF+ ion exist as a complex of HRg+ and BF species. For a better quantification of charge transfer characteristics, and to evaluate the nature of bonds in a molecule, atoms-in-molecules (AIM)41 approach, which has been developed by Bader is highly successful and often used. The AIM calculations have been performed using MP2 and DFT (B3LYP) methods and 6-311++G(2d,2p) basis sets along with Stuttgart valence basis sets (with ECP). AIM approach is based on the topology of the electron density, and a bond path is defined as the line along which the electron density is the maximum with respect to a neighboring line. A critical point is a point where gradient of the electron density is zero, and (3,-1) critical point is defined where two of the eigenvalues of the hessian matrix are negative, and refereed as bond critical point. AIM approach allows one to locate and distinguish various types of interactions that exist between the constituent atoms in a molecule. We have applied AIM method to compute the topological parameters and analyzed the chemical bonds that exist between different atoms in HRgBF+ ions, and the obtained results are reported in Table 5. The important quantities required for the analysis of a chemical bond are the electron density (ρ) and its Laplacian (∇2ρ) at the bond critical points (BCPs) of the molecules. In general, shared type of interactions resulting covalent bond, show ∇2ρ < 0 while non-shared type of interactions leading to ionic, hydrogen, and vdW 9 ACS Paragon Plus Environment


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bonds show ∇2ρ > 0 values. The predicted HRgBF+ ions show high negative value at BCPs corresponding to the H-Rg bonds, indicating the existence of a strong covalent character in these bonds. The covalent nature of the H-Rg bonds is further supported by the observation of high BCP electron density values for these bonds. In contrast to H-Rg bonds, the Rg-B bonds show low positive values for ∇2ρ as well as low ρ values. A high positive value of ∇2ρ for the B-F bond implies that this bond is intact and only a small perturbation occurred during the formation of HRgBF+ ions. Moreover, ionic nature of the B-F Bond can be inferred from a high positive value of ∇2ρ, which is also supported by the calculated NBO charge values as discussed above. AIM also offers the computation of local electron density and is defined as Ed(r) = G(r) + V(r), where G(r) and V(r) correspond to local kinetic and potential energy densities, respectively. The sign of Ed(r) indicates whether accumulated charge at a given point, r, is stabilizing [Ed(r) < 0] or destabilizing [Ed(r) >0]. A negative value of Ed(r) suggests that V(r) dominates over G(r) and the electron density accumulates in the bond region. The computed Ed(r) values for the H-Rg bonds are -0.680, -0.269, and -0.410 in HHeBF+, HArBF+, and HKrBF+ ions respectively, which indicate that H-Rg bonds are stabilizing with respect to the accumulation of electron density at the bond region, leading to covalent nature of the H-Rg bonds. The Ed(r) values of Rg-B bonds are -0.0006, 0.0008, 0.0005, and -0.0001 for HHeBF+, HArBF+, HKrBF+, and HXeBF+ ions, respectively. Further, the computed Ed(r) values of the B-F bonds in all the predicted systems show high negative values, suggesting that the bonds are stabilizing in nature when electron density accumulates in the bond region. From the computed BCP properties, it is evident that the H-Rg bonds show high degree of covalency. The degree of covalency is more for H-He and H-Kr bonds than that for the H-Ar and H-Xe bonds in the predicted ions. On the other hand, all the calculated BCP values for the Rg-B bond indicate that ion-dipole interaction plays a major role in the Rg-B bonding with a strong ionic character. The above computed properties suggest that the HRgBF+ species may be represented as a strong van der Waals complex between the (HRg)+ and BF fragments. D. Harmonic Vibrational Frequencies of HRgBF+ Ions In addition to the energetic and geometrical parameters, another property of interest, which is experimentally observable, is vibrational spectrum of a molecular species. Therefore, we have computed the harmonic vibrational modes and their corresponding IR frequencies for the HRgBF+ ions. The computed IR frequencies along with their intensities for the respective 10 ACS Paragon Plus Environment

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modes are given in Table 6. Here we have discussed the vibrational frequency details as obtained using MP2 method, unless otherwise mentioned. The normal modes of the predicted ions are assigned to their respective stretching, bending, and torsional vibrations, and the ions show three stretches, two doubly degenerate bends, and one torsional mode of vibrations at the minima position. The H-Rg stretching frequency values are found to be in the range, 3486-2266 cm-1 along the He-Ar-Kr-Xe series, i.e., H-He stretch shows the highest frequency value. The Rg-B stretching frequency values are found to be in the range of 74-348 cm-1 with Xe-B bond has the lowest frequency value of 74 cm-1 and the He-B bond with the highest value (348 cm-1). The B-F stretch frequency values are 1583, 1527, 1533, 1531 cm-1, respectively for He-Ar-Kr-Xe containing ions. The B-F stretching frequency value almost remains the same except for the He containing ion. In the computed IR spectrum the H-Rg stretch shows higher frequency value and is also associated with the highest intensity value among all the normal modes present in the HRgBF+ ions. Now, it is interesting to compare these values with that of the corresponding H-Rg stretch frequency values of isoelectronic counterpart such as HRgCO+

30

and HRgN2+

31

ions reported using DFT. The H-Rg frequency

+

values of HRgCO ions are 3005, 2535, 2405, 2270 cm-1 for He-Ar-Kr-Xe containing ions respectively. The H-Rg frequency values are 3177, 2585, 2449, 2241 cm-1 respectively for He-Ar-Kr-Xe containing ions in HRgN2+ while the corresponding frequency values are 2308, 2262, 2196, 2065 cm-1 in HRgBF+ ions with the same DFT level of theory. It is clear that the H-Rg frequency values in HRgBF+ are less than that in other families of ions; however it is distinct for their experimental observations. The MP2 calculated IR frequency values of bare HBF+ ions are 2912, 1643, and 787 cm-1 corresponding to H-B stretch, B-F stretch, and HBF degenerate bends respectively. It is important to note that after the insertion of Rg atoms into the HBF+ ion, frequency values are changed significantly. The distinct vibrational features of the HRgBF+ ions can be used to characterize these ions in IR spectroscopic methods. Since these ions are metastable, it is of interest to know the various couplings operating among different vibrational modes. Therefore the normal coordinate frequencies are partitioned into individual internal coordinates using Boatz and Gordon approach51 and the results are listed in Table 7. Individual coordinate analysis indicates negligible coupling in H-Rg stretching frequencies while Rg-B stretching modes are highly coupled with other modes. The computed force constant (k) values corresponding to the H-Rg stretching are 499, 392, 366, and 303 Nm-1 for H-He, H-Ar, H-Kr, and H-Xe bonds, respectively. The data indicate an increase in k value along the series, He-Ar-Kr. However, k values of H-He and H-Xe bonds are very close to 11 ACS Paragon Plus Environment


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Page 12 of 28

each other. Thus the spectroscopic data along with energetic and charge distribution data strongly support a possibility on the existence of HRgBF+ ions. Now it is interesting to compare the stretching frequency of the isolated BF molecule with that of the B-F stretching frequency in HRgBF+ ions. The MP2 calculated B-F stretching frequency value has been found to be 1398 cm-1 in the BF molecule, as compared to the corresponding values of 1583, 1527, 1533, and 1531 cm-1 in the HHeBF+, HArBF+, HKrBF+ and HXeBF+ ions, respectively. Thus, it is clear that there is a blue shift from the bare B-F stretching frequency value to the corresponding values for the HRgBF+ ions. This type of blue shifting has been found for other rare gas compounds, denoted here as Rg-AB for the purpose of explanation (e.g., Rg-AuF, Rg-BeS etc).52,53 Here A-B stretching frequency is blue-shifted as compared to that in the isolated AB molecule, and it has been rationalized in terms of the interaction strength of the Rg atom with the A atom. In a similar way, in the present work, the Rg-B interaction is found to be strongest in the HHeBF+ ion with an interaction energy of 75.6 kJ/mol at the MP2 level, as compared to the corresponding values of 53.0, 55.1, 53.2 kJ/mol in HArBF+, HKrBF+ and HXeBF+ ions. Exactly a similar trend is observed in the calculated Rg-B stretching frequency values, where He-B frequency value is found to be the maximum, as reported in Tables 6 and 7. Consequently, the maximum B-F stretching frequency value of 1583 cm-1 in HHeBF+ ion can be rationalized from the maximum amount of Rg-B interaction in the HHeBF+ ion.

In addition to the MP2 calculated frequency values, we have also included the DFT and CCSD(T) calculated frequencies in Table 6. Here it may be noted that ab initio based methods such as MP2 and CCSD(T) computed frequency values are closer to the experimental ones in the case of rare gas hydride systems.

6,54-56

Similar to the HRgOH2+

systems,32 the DFT calculated values corresponding to the H-Rg stretching mode are found to be smaller as compared to the corresponding MP2 and CCSD(T) calculated values. Nevertheless, it is important to note that the characterization of meta-stable rare gas compounds through IR spectroscopy is possible only in rare gas matrix. On the other hand, the computational results are, in general, obtained using gas phase calculations within harmonic approximation.


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4. Conclusion In summary, in the present work we have predicted the probable existence of novel meta-stable cationic species, HRgBF+ using quantum chemical methods, viz., MP2, DFT and CCSD(T). Structure, harmonic vibrational frequencies, energetics and charge distribution data are reported for the minima and the transition state structures. The predicted ions exhibit linear (Cαv) structure at minima and non-linear planar structure (Cs) at the transition states. The predicted ions show negative binding energies (unstable) with respect to global minima (HBF+ + Rg), while positive binding energies (stable) with respect to another 2 body dissociation channel (HRg+ + BF) and all other possible unimolecular dissociation channels. However, the HRgBF+ ions show reasonably good barrier heights for their respective transition states, which would prevent their transformation to the global minimum products, HBF+ + Rg. The intrinsic reaction coordinate analysis further confirms that the predicted ions are metastable in nature and are connected to the global minima through the HRgB bending modes. In addition to the energetic parameters, charge redistribution data along with spectroscopic properties strongly support the possibility of formation of HRgBF+ ions. The calculated bond length and charge distribution values further imply that these ions can be better represented as [HRg]+[BF]. All the calculated results reported in this work indicate that it may be possible to prepare HRgBF+ ions in DC discharge plasma of BF3/H2/Rg mixture at low temperature, and can be characterized using IR spectroscopic method.

ACNOWLEDGMENTS The authors would like to thank Computer Division, BARC for providing computational facilities and support. It is pleasure to thank Dr. A. K. Nayak, Dr. A. K. Das, Dr. N. K. Sahoo and Dr. S. K. Ghosh for their continuous help and encouragements. We would also like to thank Dr. L. M. Gantayet and B. N. Jagatap for their kind interest and support. A. Sirohiwal gratefully acknowledges the support from NIUS (HBCSE-TIFR, Mumbai).

REFRENCES 1. Khriachtchev, L.; Pettersson, M.; Runeberg, N.; Lundell, J.; Räsänen, M. A Stable Argon Compound. Nature (London) 2000, 406, 874-876.



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31. Jayasekharan, T.; Ghanty, T. K. Theoretical Prediction of HRgCO+ Ion (Rg=He, Ne, Ar, Kr, and Xe) J. Chem. Phys. 2008, 129, 184302. 32. Jayasekharan, T.; Ghanty, T. K. Theoretical Investigation of Rare Gas Hydride Cations : HRgN2+ (Rg=He, Ar, Kr, and Xe). J. Chem. Phys. 2012, 136, 164312. 33. Ghosh, A.; Manna, D.; Ghanty, T. K. Theoretical Prediction of Rare Gas Inserted Hydronium Ions: HRgOH2+. J. Chem. Phys. 2013, 138, 194308. 34. Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. J.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347-1363. 35. Werner, H. -J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. et. al. MOLPRO, Version 2012.1, a Package of ab initio Programs. 2012, see http://www.molpro.net. 36. Frisch, M. J.; Head-Gordon, M.; Pople, J. A. A Direct MP2 Gradient Method. Chem. Phys. Lett. 1990, 166, 275-280. 37. Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. 38. Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. 39. Hampel, C.; Peterson, K.; Werner, H.-J. A Comparison of the Efficiency and Accuracy of the Quadratic Configuration Interaction (QCISD), Coupled Cluster (CCSD) and Brueckner Couple Cluster (BCCD) Methods. Chem. Phys. Lett. 1992, 190, 1-12. 40. Andrae, D.; Haussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-adjusted ab initio Pseudopotentials for the Second and Third Row Transition Elements. Theor. Chim. Acta 1990, 77, 123-141. 41. Bader, R. F. W. Atoms in Molecules-A Quantum Theory (Oxford University Press, Oxford, 1990); Biegler-könig, F. W.; Bader, R. F. W.; Tang, T. H. Calculation of the Average Properties of Atoms in Molecules. II. J. Comput. Chem. 1982, 3, 317-328. 42. Baldridge, K. K.; Gordon, M. S.; Steckler, R.; Truhlar, D. G. Ab initio Reaction Paths and Direct Dynamics Calculations. J. Phys. Chem. 1989, 93, 5107-5119. 43. Gonzalez, C.; Schlegel, H. B. Reaction Path Following in Mass-weighted Internal Coordinates. J. Phys. Chem. 1990, 94, 5523-5527. 44. Grandinetti, F. Neon behind the signs. Nature Chemistry, 2013, 5, 438-438.


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45. Lundell, J. Density Functional Approach on Ground State RgH+ and RgHRg+(Rg = Ar, Kr, Xe) ions. J. Mol. Struct. 1995, 355, 291-297. 46. Fridgen, T. D.; Parnis, J. M. Electron Bombardment Matrix Isolation of Rg/Rg′/Methanol

Mixtures

(Rg= Ar,

Characterization of the Proton-bound

Kr,

Xe):

Fourier-Transform

Infrared

Dimmers Kr2H+, Xe2H+, (ArHKr)+ and

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FIGURE CATIONS

Figure 1.

Minimum Energy (C4v-symmetry) and transition state (Cs-Symmetry)

Structures of HRgBF+ ions

(Rg = He, Ar, Kr, Xe).

Figure 2. Minimum Energy Path for HRgBF+  HBF+ + Rg Reaction (Rg = He, Ar, Kr, Xe)


Page 19 of 28

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Figure 1. (Color online) Minimum Energy (C4v-symmetry) and transition state (CsSymmetry) Structures of HRgBF+ ions

(Rg = He, Ar, Kr, Xe).



50

50

HHeBF+

Relative Energy (kJ/mol)


0 -50 -100 -150 -200 -250

Transition state of HHeBF+ (35.2 kJ/mol)

-300 -350 -400

+

He + HBF (~ -516.94 kJ/mol)

-450 -500

HArBF+

0 -50 -100

Transition state of HArBF+ (24.2 kJ/mol)

-150 -200 -250 -300

Ar + HBF+ ( ~ -362.4 kJ/mol)

-350 -400

-550 -2

0

2

4

6

-6

0


HKrBF+

-50 -100

Transition state of HKrBF+ (30.5 kJ/mol)

-150 -200 -250

Kr + HBF+ ( ~ -312.23 kJ/mol)

-300 -350 -8

-6

-4

-2

0

2

4

6

-2

0

2

4

6

8

Reaction Coordinate, bohr amu

Reaction coordinate, bohr amu

0

-4

1/2

1/2


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Page 20 of 28

HXeBF+

-50 Transition state of HXeBF+ (30.57 kJ/mol)

-100 -150 -200 -250

Xe + HBF+ (~ -258.1 kJ/mol)

-300

8

-10

1/2

-8

-6

-4

-2

0

2

4

6

8 1/2



Figure 2. Minimum Energy Path for HRgBF+  HBF+ + Rg Reaction (Rg = He, Ar, Kr, Xe)


Page 21 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 1. Optimized Geometrical Parametersa of HRgBF+ (Rg = He, Ar, Kr, and Xe) by MP2, DFT and CCSD(T) Methods. Geometrical Methods Parameters MP2 R(H-Rg) DFT CCSD(T)

R(Rg-B)

MP2 DFT CCSD(T)

HHeBF+ Minima TSb 0.768 0.757 0.837 0.771 ----c 0.771 d 0.776 0.764e 0.765f

HArBF+ Minima TSb 1.285 1.277 1.323 1.291 1.278 1.286 1.282d 1.281e 1.280f

HKrBF+ Minima TSb 1.424 1.412 1.463 1.428 1.413 1.422 1.416d 1.417e 1.416f

HXeBF+ Minima TSb 1.621 1.606 1.649 1.616 1.604 1.620 1.607d 1.610e 1.607f

2.258 2.135 2.240 2.221g 2.138h

2.941 2.841 2.943 2.911g 2.841h

2.984 2.902 2.980 3.068g 2.922h

3.135 3.081 3.090 3.124g 3.093h

2.534 2.536 ----c

3.353 3.359 3.318

3.524 3.559 3.487

3.788 3.837 3.730

MP2 1.242 1.245 1.247 1.252 1.246 1.252 1.246 1.253 DFT 1.234 1.241 1.241 1.248 1.240 1.249 1.241 1.250 c CCSD(T) 1.249 ---1.253 1.256 1.252 1.258 1.251 1.260 MP2 180 116.2 180 107.4 180 103.7 180 101.4 θ (H-Rg-B) DFT 180 108.0 180 104.5 180 101.2 180 101.0 CCSD(T) 180 ----c 180 107.5 180 103.2 180 101.1 MP2 180 173.5 180 176.9 180 177.3 180 178.2 θ (Rg-B-F) DFT 180 172.0 180 176.2 180 176.8 180 178.0 CCSD(T) 180 ----c 180 179.0 180 177.8 180 178.8 a b c + Bond length is in Å, and bond angle θ in degree; Transition state; CCSD(T) for the TS of HHeBF is not converged properly; R(B-F)

CCSD(T) computed H-Rg bond lengths in bare dHRg+ ions, eHRgCO+ ions and fHRgN2+ ions; CCSD(T) calculated gRg-C bond lengths in HRgCO+ ions and hRg-N bond lengths in HRgN2+ ions respectively;



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Table 2. Energies (in kJmol-1) of the Various Dissociated Species Relative to the HRgBF+ (Rg = He, Ar, Kr, and Xe) Ions, Calculated Using MP2, DFT and CCSD(T) Methods. Rg = He

Rg = Ar

Rg = Kr

Rg = Xe

Molecular Species

MP2

DFT

CCSD(T)

MP2

DFT

CCSD(T)

MP2

DFT

CCSD(T)

MP2

DFT

CCSD(T)

HRgBF+

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Rg + HBF+

-511.5

-475.8

-495.0

-345.5

-326.8

-317.5

-279.2

-267.4

-239.0

-220.0

-209.2

-173.9

HRg+ +BF

75.6

105.2

73.6

53.0

63.8

50.9

55.1

65.8

53.2

54.5

60.7

54.6

H + Rg +BF+

-13.9

46.3

25.8

152.0

195.2

203.3

218.4

254.6

281.9

277.5

312.8

346.9

H+ + Rg + BF

269.6

299.1

270.1

435.5

448.1

447.6

501.8

507.5

526.1

561.0

565.8

591.1

11.6

38.6

---b

16.7

28.5

15.5

22.1

35.2

21.0

25.6

35.2

26.7

Barrier Height corresponding to TSa (HRgBF+ →HBF+ + Rg) a

Transition state; bCCSD(T) for the TS of HHeBF+ is not converged properly.


Page 23 of 28

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Table 3. MP2 (DFT) Calculated Values of the Mulliken Charges in HRgBF+ (Rg = He, Ar, Kr and Xe) Ions using 6-311++G(2d,2p) Basis Sets with GAMESS Program. H-He-B-F+ Atom

Minima

H-Ar-B-F+ TSa

Minima

H-Kr-B-F+

TSa

Minima

TSa

H-Xe-B-F+ Minima

TSa

charge q(H)

q(Rg)

q(B)

q(F)

a

0.597

0.623

0.370

0.383

0.255

0.305

0.164

0.197

(0.527)

(0.635)

(0.342)

(0.388)

(0.231)

(0.306)

(0.158)

(0.211)

0.314

0.357

0.645

0.610

0.689

0.686

0.816

0.796

(0.246)

(0.345)

(0.607)

(0.596)

(0.645)

(0.681)

(0.764)

(0.781)

0.228

0.159

0.059

0.148

0.041

0.199

0.084

0.191

(0.309)

(0.167)

(0.079)

(0.149)

(0.043)

(0.218)

(0.121)

(0.201)

-0.140

-0.140

-0.075

-0.143

0.013

-0.191

-0.064

-0.185

(-0.084)

(-0.147)

(-0.031)

(-0.134)

(0.079)

(-0.205)

(-0.043)

(-0.192)

Transition state



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Table 4. MP2 and DFT Calculated Values of the Mulliken and NBO Charges in HRgBF+ (Rg = He, Ar, Kr and Xe) Ions using 6311++G(2d,2p), cc-pVTZ and aug-cc-pVTZ Basis Sets with MOLPRO Program.

Atom charge 6-311G++(2d,2p) q(H) MP2 DFT q(Rg) MP2 DFT q(B) MP2 DFT q(F) MP2 DFT cc-pVTZ q(H) MP2 DFT q(Rg) MP2 DFT q(B) MP2 DFT q(F) MP2 DFT aug-cc-pVTZ q(H) MP2 DFT q(Rg) MP2 DFT q(B) MP2 DFT q(F) MP2 DFT

H-He-B-F+ Mulliken NBO

H-Ar-B-F+ Mulliken NBO

H-Kr-B-F+ Mulliken NBO

H-Xe-B-F+ Mulliken NBO

0.597 0.528 0.314 0.247 0.246 0.345 -0.159 -0.120

0.647 0.541 0.265 0.231 0.553 0.691 -0.466 -0.464

0.360 0.334 0.594 0.544 0.203 0.247 -0.157 -0.127

0.443 0.407 0.505 0.463 0.525 0.602 -0.475 -0.474

0.260 0.236 0.690 0.648 0.197 0.233 -0.148 -0.118

0.320 0.291 0.611 0.565 0.540 0.614 -0.472 -0.471

0.154 0.145 0.795 0.748 0.197 0.228 -0.148 -0.121

0.173 0.176 0.742 0.678 0.555 0.581 -0.471 -0.437

0.565 0.485 0.350 0.296 0.012 0.141 0.071 0.076

0.650 0.544 0.263 0.229 0.549 0.683 -0.464 -0.458

0.326 0.292 0.613 0.567 0.002 0.087 0.058 0.052

0.445 0.411 0.505 0.464 0.531 0.605 -0.482 -0.481

0.227 0.210 0.705 0.647 -0.003 0.077 0.070 0.063

0.319 0.292 0.609 0.561 0.550 0.625 -0.479 -0.478

0.133 0.129 0.816 0.760 -0.032 0.034 0.082 0.075

0.177 0.180 0.734 0.668 0.566 0.594 -0.478 -0.444

0.583 0.533 0.305 0.215 0.134 0.326 -0.023 -0.075

0.647 0.539 0.262 0.230 0.564 0.697 -0.474 -0.466

0.342 0.279 0.613 0.585 0.066 0.223 -0.022 -0.088

0.444 0.406 0.501 0.465 0.545 0.618 -0.491 -0.489

0.232 0.217 0.741 0.683 -0.059 0.066 0.085 0.032

0.318 0.290 0.611 0.566 0.558 0.629 -0.488 -0.486

0.042 0.041 0.983 0.914 -0.036 0.111 0.010 -0.067

0.173 0.179 0.742 0.675 0.572 0.593 -0.488 -0.450


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 5. Bond Critical Point Electron Density (ρ), it’s Laplacian (∇2ρ) and the Local Electron Eensity (Ed(r)) of HRgBF+ (Rg = He, Ar, Kr and Xe) Ions Calculated using MP2 (DFT)Method.

H-He-B-F+ Bond

H-Rg

Rg-B

B-F

H-Ar-B-F+

H-Kr-B-F+

H-Xe-B-F+

ρ

∇2ρ

Ed

ρ

∇2ρ

Ed

ρ

∇2ρ

Ed

ρ

∇2ρ

Ed

(ea0-3)

(ea0-5)

(au)

(ea0-3)

(ea0-5)

(au)

(ea0-3)

(ea0-5)

(au)

(ea0-3)

(ea0-5)

(au)

0.235

-2.667

-0.680

0.230

-0.896

-0.269

0.246

-1.069

-0.410

…

…

…

(0.210)

(-1.562)

(-0.419)

(0.212)

(-0.657)

(-0.207)

(0.242)

(-1.160)

(-0.418)

(0.150)

(-0.382)

(-0.141)

0.027

0.064

-0.0006

0.018

0.047

0.0008

0.020

0.048

0.0005

0.020

0.041

-0.0001

(0.035)

(0.062)

(-0.001)

(0.028)

(0.045)

(0.0001)

(0.024)

(0.047)

(0.0002)

(0.022)

(0.040)

(-0.0004)

0.254

1.697

-0.214

0.249

1.659

-0.207

0.250

1.664

-0.209

0.250

1.664

-0.208

(0.264)

(1.660)

(-0.231)

(0.259)

(1.610)

(-0.223)

(0.259)

(1.612)

(-0.224)

(0.258)

(1.607)

(-0.223)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

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Table 6. Harmonic Vibrational Frequencies (in cm-1) Calculated using MP2, {DFT}, and [CCSD(T)] Methods for HRgBF+ (Rg = He, Ar, Kr and Xe) Ions for the minima and the transition states (TS). Corresponding IR Intensity Values Calculated using DFT and MP2 Methods are Given within the Parentheses (in km mol-1). H-He-B-F+ Normal mode

Minima

H-Ar-B-F+ TS

Minima

H-Kr-B-F+ TS

Minima

H-Xe-B-F+ TS

Minima

TS

(symmetry) H-Rg stretch

B-F stretch

Rg-B stretch

H-Rg-B bendb

Rg-B-F bendb

3239.9 (21.89) {2307.7} (664.7) [3164.2] 1583.3 (99.2) {1582.4} (145.2) [1559.8] 347.9 (278.7) {401.9} (231.9) [354.9] 538.1 (184.2) {712.1} (153.2) [526.4]

3485.6 (781.97) {3304.5} (692.1) [---]a 1543 (111.9) {1541} (112.7) [---]a 310.9 (215.1) {314.3} (191.2) [---]a -640.1 (108.46) {1212.1} (27.6) [---]a

2600.5 (147.8) {2262.3} (97.3) [2673.1] 1527.2 (131.1) {1539.9} (153.4) [1520.8] 140.7 (24.7) {157.2} (27.7) [139.8] 370.5 (115.5) {444.1} (107.3) [350.11]

2686.2 (531.2) {2572.9} (415.2) [2762.90] 1497 (142.3) {1494.5} (148.8) [1495.09] 104.3 (14.4) {103.2} (13.3) [109.88] -248.2 (102.9) {-283.4} (82.4) [-241.19]

2496.7 (42.2) {2195.8} (75.5) [2481.5] 1533.1 (127.2) {1544.0} (146.1) [1528.1] 127.3 (15.1) {142.1} (15.4) [126.8] 377.2 (81.2) {440.1} (74.9) [369]

204.7 (35.56) {196.6} (18.1) [202.2] -

2596 (398) {2460.0} (344.9) [2577.45] 1490.6 (144.3) {1486.4} (144.4) [1484.55] 85.9 (5.4) {81.8} (5.3) [89.56] -223.8 (71.1) {-242.3} (60.4) [-214.98]

190.9 (32.76) 158.4 (7.5) 130.8 (5.7) 156.9 (3.9) 124.4 (4.8) {188.9} (27.3) {149.7} (3.0) {126.8} (7.6) {147.8} (1.2) {118.7} (4.5) a [---] [149.4] [122.86] [147.8] [121.08] 195.4 (64.24) 131.3 (5.7) 125 (3.4) H-Rg-B-F b {193.5} (71.9) {123.3} (6.1) {115.8} (3.7) torsion a [---] [122.42] [119.56] a CCSD(T) for the TS of HHeBF+ is not converged properly; bFor minima the modes are doubly degenerate. 26 ACS Paragon Plus Environment

2266.3 (5.5) {2065.4} (57.5) [2221.8] 1531 (131.1) {1538.3}(151.2) [1530.22] 117.3 (13.03) {125.8} (11.9) [120.6] 362.6 (40.2) {393.8} (36.5) [366.6]

2354.7 (233.9) {2259.2}(210.4) [2316.28] 1481.4 (150.1) {1476.4}(145.8) [1475.60] 73.6 (2.8) {68.2} (2.9) [76.13] -190.8 (40) {-206.5} (40.5) [-194.91]

150.4 (2) {138.1} (0.6) [141.1] -

113.6 (3) {104.3} (2.9) [109.25] 114.2 (2) {103.4} (2.1) [107.87]

Page 27 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 7. MP2 [DFT] Calculated Values of the Harmonic Vibrational frequencies (in cm-1) and (Intrinsic Force Constants in N/m) Corresponding to Individual Internal Coordinates of HRgBF+ (Rg = He,Ar, Kr and Xe) Ions.

Internal coordinate

HHeBF+

HArBF+

HKrBF+

HXeBF+

H-Rg stretch

3243.4 (499.0)

2601.2 (391.9)

2497.0 (365.9)

2266.5 (302.6)

[2310.5] (253.2)

[2263.4] (296.7)

[2196.3] (283.0)

[2065.6] (251.4)

1547.1 (982.8)

1516.6 (944.5)

1521.7 (950.9)

1520.8 (949.8)

[1563.8] (1004.3)

[1527.6] (958.3)

[1531.2] (962.9)

[1526.6] (957.1)

386.4 (25.8)

220.6 (24.8)

221.4 (28.2)

215.9 (27.9)

[455.3] (35.9)

[239.7] (29.2)

[239.2] (32.8)

[224.7] (30.2)

536.0

367.6

373.9

358.5

[708.3]

[441.2]

[436.5]

[389.5]

209.8

165.2

164.8

160.1

[210.1]

[158.0]

[158.1]

[149.9]

B-F stretch

Rg-B stretch

H-Rg-B bend

Rg-B-F bend



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TOC GRAPHICS

Rg = He, Ar, Kr and Xe


Page 28 of 28

Theoretical Prediction of Rare Gas Containing Hydride Cations

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