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Noble Gas Inserted Protonated Silicon Monoxide Cations: HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Pooja Sekhar,†,‡ Ayan Ghosh,§ and Tapan K. Ghanty*,† †

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

§

S Supporting Information *

ABSTRACT: The existence of noble gas containing protonated silicon monoxide complexes have been predicted theoretically through ab initio quantum chemical methods. The predicted HNgOSi+ ions are obtained by insertion of a noble gas atom (Ng = He, Ne, Ar, Kr, and Xe) between the H and O atoms in SiOH+ ion. The structural parameters, energetics, harmonic vibrational frequencies, and charge distributions have been analyzed by optimizing the minima and the transition state structures using second-order Møller− Plesset perturbation theory (MP2), density functional theory (DFT), and coupled-cluster theory (CCSD(T)) based techniques. The predicted HNgOSi+ ions are found to be stable with respect to all possible 2-body and 3-body dissociation channels, except the dissociation path leading to the respective global minimum products. However, these ions are found to be kinetically stable with respect to the global minimum dissociation process as revealed from the finite barrier heights, which in turn can prevent the transformation of these metastable species to the global minimum products. Furthermore, the computed bond lengths, vibrational frequencies, and force constant values suggest that a strong covalent bond exists between the H and Ng atoms in HNgOSi+ ions while the Ng and O atoms share a strong van der Waals kind of interaction. Charge distributions and bonding analysis indicate that HNgOSi+ ions can be best represented as strong complexes between the [HNg]+ ions and OSi molecule. All the computational results suggest that the predicted species, HNgOSi+, may be prepared and characterized by suitable experimental technique at cryogenic temperature. SiH4 and N2O in the same buffer gas.47,48 The significance of this cation was investigated widely by several scientists decades ago. The release of silicon monoxide from SiOH+ in interstellar gas clouds was suggested by Turner and Dalgarno.49,50 The two isomers of protonated silicon monoxide, SiOH + and HSiO+,51−53 are important in processes like deposition of thin Si films, etching technology,54−58 and preparation of ultrapure semiconductor materials in the semiconductor industry.59,60 They are also required for the modeling of bridging and terminal hydroxyls in zeolites61−64 and surface hydroxyls on amorphous silica.65,66 Later on, theoretical studies were carried out to identify the structures and stabilities of various complexes formed by this ion. The study of the cluster growth and that of coexisting isomers of van der Waals complexes like SiOH+−Arn (n = 1− 10) have been studied by Olkhov and co-workers67 using midinfrared photofragmentation spectra. They concluded that SiOH+−Ar dimer exhibits linear (in the minimum energy state) and T-shaped (at the saddle point) geometries, which are attributed to the electron density transfer from the Ar atom to the vacant electrophilic 2pz orbital and the empty 3p orbital, respectively, on the Si atom. They also investigated the ionic hydrogen bonds in SiOH+−X (X = He, Ne, Ar, N2)68 by IR

1. INTRODUCTION Noble gas elements were considered to be chemically inert due to their stable electronic configurations with completely filled s and p valence orbitals. In 1933, Linus Pauling1 predicted the existence of stable molecules by heavier noble gas elements due to their comparatively loosely bound valence electrons. This prediction turned out to be true after the successful synthesis of the first noble gas compound, XePtF6, by Neil Bartlett in 1962.2 The discovery of the first stable molecule of argon, HArF, with strong H−Ar covalent bonding, by Räsänen and co-workers3,4 through IR spectroscopic techniques paved the way for further theoretical prediction of several new noble gas compounds. The successful synthesis of NgBeO and NgBeS by Thompson and Andrews5,6 and Wang and Wang,7 respectively, and the spectroscopic detection of NgMX (M = Cu, Ag, and Au; X = F, Cl, and Br) by Gerry and co-workers8−18 also played significant roles in the advancement of noble gas chemistry. The first bulk compound containing noble gas−noble metal bonding, AuXe42+[Sb2F11−]2,19 has also been reported. Thus, several novel molecules having one or more noble gas atoms have either been observed experimentally or predicted theoretically.20−41 The precursor molecule of our predicted ions, protonated silicon monoxide (SiOH+),42,43 plays a significant role in ionospheric44 and interstellar chemistry.45,46 It was successfully generated by the hollow cathode discharge of (CH3)3SiOH in a mixture of hydrogen and helium and also by the discharge of © 2015 American Chemical Society

Received: September 16, 2015 Revised: October 12, 2015 Published: October 26, 2015 11601

DOI: 10.1021/acs.jpca.5b09018 J. Phys. Chem. A 2015, 119, 11601−11613

Article

The Journal of Physical Chemistry A photodissociation spectroscopy and ab initio calculations. Van der Waals complexes like ArSiF22+ and NeSiF22+ dications with noble gas−silicon interaction were produced by Roithova and Schroder69 through bimolecular collisions of mass-selected SiF3+ species with argon and neon, respectively. Earlier, Cipollini and Grandinetti70 had detected the XeSiF3+ ion in an ion−molecule reaction between the protonated SiF4 and Xe (F3Si−FH+ + Xe → Xe−SiF3+ + HF). Later, Cunje and coworkers71 successfully produced ArSiF3+ and KrSiF3+. Very recently, the stability of noble gas bound SiH3+ and SiX3+ clusters have been studied by Chattaraj and co-workers.72 It has been predicted that heavier noble gas atoms like xenon and radon form stable Ng2SiH3+ clusters by significant electron transfer from these atoms to the electropositive Si center. They also reported the existence of H3SiNgNSi and HSiNgNSi (Ng = Xe and Rn)73 molecules with Si−Ng covalent bond and Ng− N ionic bond. Furthermore, noble gas inserted metastable compounds like FXeSiF and FArSiF3 were theoretically studied by Lundell et al.74 and Cohen et al.75 However, to the best of our knowledge, noble gas inserted SiOH+ complexes have not been reported until now. Recently, stable molecules like FNgBS41 and strong complexes such as HNgCS+39 have been predicted theoretically and compared with the respective valence isoelectronic species, FNgBO25 and HNgCO+.31 The calculated results reveal a significant decrease in the Ng−C bond length in HNgCS+39 as compared to that in HNgCO+31 while there is negligible change in the Ng−B bond strength between FNgBO25 and FNgBS41 molecules. Studies related to these valence isoelectronic molecules, atmospheric importance of protonated silicon monoxide (analogous to HCO+ and HOC+76−78 ions), and the existence of stable HNgCO+31 complexes have motivated us to investigate the change in stability of HOSi+ and HSiO+51−53 on insertion of a noble gas atom. The study of FXeSiF74 and FArSiF375with noble gas−silicon interaction has also encouraged us to investigate the presence of similar interaction in the noble gas inserted protonated silicon monoxide species. Ab initio calculations, ranging from self-consistent field to coupledcluster methods, prove that SiOH+42 is the global minimum on the potential energy surface as compared to HSiO+,51,52 contrary to the valence-isoelectronically analogous HCO+/ HOC+76−78 systems, where HCO+ ion has been found to be more stable than HOC+ ion. Therefore, it is further interesting to investigate the noble gas atom inserted HOSi+ and HSiO+ and compare their structures and properties. In this paper, optimized structures, dissociation energies, vibrational frequencies, charge distributions, and bonding analysis of HNgOSi+ ions have been investigated through quantum computational methods like Møller−Plesset perturbation theory (MP2), density functional theory (DFT), and coupled-cluster theory (CCSD(T)). Moreover, the structure and properties of HNgOSi+ species have been compared to those of HNgSiO+, HNgOC+, and HNgCO+ ions in a systematic and unified manner.

the potential energy surface. We have considered Kr and Xe atoms with 10 and 28 core electrons,83 respectively, by Stuttgart effective core potentials (ECP) along with aug-cc-pVTZ-PP basis sets whereas aug-cc-pVTZ84,85 basis sets have been utilized for the H, He, C, O, Ne, Si, and Ar atoms during B3LYP, MP2, and CCSD(T) calculations. This combination of basis sets has been denoted as AVTZ. For the purpose of comparison, we have also used aug-cc-pVQZ-PP basis set for the Xe atom with 28 core electrons and the aug-cc-pVQZ basis sets for the remaining atoms (represented as AVQZ). Additionally, B3LYP, MP2, and CCSD(T) methods with AVTZ basis sets have been utilized for performing vibrational analysis, Mulliken population analysis, and NBO analysis of HNgOSi+ ions. Intrinsic reaction coordinate (IRC)86 analysis has been performed using second-order Gonzalez−Schlegel algorithms87 with a step size of 0.2 amu1/2 bohr to trace the minimum energy path connecting the metastable species with their global minimum products through the transition state. Atoms-in-molecules (AIM)88−90 analysis has also been performed using the MP2 and B3LYP methods to determine the nature of bonding that exists between the different atoms of HNgOSi+ ion by using AIMPAC88−90 and Multiwfn programs.91 For the purpose of comparison, we have also computed all the parametric values of the optimized structures of HNgSiO+, HNgCO+, and HNgOC+ ions (as reported in the Supporting Information). In this study, all the calculations have been performed through ab initio molecular orbital and density functional based methods using GAMESS92 and MOLPRO 201293 programs.

3. RESULTS AND DISCUSSION 3.1. Structural Parameters of HNgOSi+ Species. The species of study, HNgOSi+, exhibits a linear geometry with C∞v symmetry at its minima (Figure 1a) and its transition state

Figure 1. Optimized structures for the (a) linear minima (C∞v symmetry) and (b) planar bent transition states (Cs symmetry) of HNgOSi+ ions (Ng = He, Ne, Ar, Kr, and Xe).

exhibits a planar bent structure with Cs symmetry (Figure 1b) on their respective potential energy surfaces. All the calculated optimized geometrical parameters corresponding to the minima and the transition state structures of HNgOSi+ ions as obtained using all the three methods have been reported in Table 1. The values obtained from different methods like MP2, B3LYP, and CCSD(T) using the AVTZ basis set can be analyzed and compared through this table. Generally, experimental results are found to agree well with the CCSD(T) calculated values rather than the MP2 and DFT computed data. Therefore, CCSD(T) computed values (using AVTZ basis sets) are mentioned throughout this text unless otherwise stated. The H−Ng bond length values of HNgOSi+ ions are found to be 0.751, 0.980, 1.278, 1.423, and 1.615 Å for HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+, respectively. The corresponding DFT computed values are found to be slightly higher than the CCSD(T) values while MP2 values are slightly lower. The H− Ng bond length values in HNgCO+ species have been found to

2. COMPUTATIONAL METHODOLOGY Quantum computational methods like MP2,79 DFT with Becke 3-parameter exchange and Lee−Yang−Parr correlation (B3LYP),80,81 and CCSD(T)82 have been utilized for the optimization of the minima and the transition state geometries of HNgOSi+ molecules. The minimum structure has been optimized using the C∞v point group while the Cs point group has been used for optimizing the transition state geometry on 11602


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Table 1. Optimized Structural Parametersa of HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Species, Calculated Using MP2, B3LYP, and CCSD(T) Methods with AVTZ Basis Sets HHeOSi+ geometrical parameters R(H−Ng)

R(Ng−O)

R(O−Si)

θ(H−Ng−O)

θ(Ng−O−Si)

a

HNeOSi+ b

methods

minima

TS

MP2 B3LYP CCSD(T) MP2 B3LYP CCSD(T) MP2 B3LYP CCSD(T) MP2 B3LYP CCSD(T) MP2 B3LYP CCSD(T)

0.749 0.781 0.751 1.754 1.698 1.747 1.547 1.539 1.541 180.0 180.0 180.0 180.0 180.0 180.0

0.747 0.767 0.749 1.871 1.846 1.860 1.547 1.540 1.541 122.5 113.7 122.3 171.1 169.3 171.2

HArOSi+ b

minima

TS

0.983 1.011 0.980 2.291 2.251 2.282 1.543 1.531 1.536 180.0 180.0 180.0 180.0 180.0 180.0

0.983 1.005 c 2.302 2.285 c 1.543 1.531 c 156.9 144.1 c 177.0 174.8 c

HKrOSi+ b

minima

TS

1.277 1.299 1.278 2.412 2.390 2.419 1.545 1.533 1.538 180.0 180.0 180.0 180.0 180.0 180.0

1.273 1.286 1.274 2.675 2.687 2.674 1.544 1.531 1.537 108.0 106.9 108.2 175.0 174.4 175.1

HXeOSi+ b

minima

TS

1.420 1.444 1.423 2.448 2.430 2.456 1.546 1.535 1.539 180.0 180.0 180.0 180.0 180.0 180.0

1.411 1.426 1.414 2.807 2.824 2.808 1.544 1.531 1.537 101.5 100.5 101.7 175.8 175.3 175.9

minima

TSb

1.608 1.630 1.615 2.549 2.541 2.555 1.547 1.535 1.540 180.0 180.0 180.0 180.0 180.0 180.0

1.595 1.609 1.601 2.981 3.002 2.984 1.544 1.530 1.537 98.3 97.8 98.4 177.3 176.7 177.4

Bond length is in Å, and bond angle θ in degrees. bTransition state. cThe TS of HNeOSi+ could not be optimized by the CCSD(T) method.

Si−O bond length in its precursor molecule SiOH+42 (1.55 Å). Thus, the strong and rigid H−Ng bond and relatively large Ng−O bond in HNgOSi+ ions clearly depict the HNgOSi+ species as complexes of HNg+ ion and OSi molecule. It would be worthwhile to compare the H−Ng and Ng−O bond lengths with respect to the covalent and van der Waals limits, represented as Rcov and RvdW, respectively, as per the study by Gerry and co-workers.14,17 For an X−Y bond, the covalent limit is defined by Rcov = rcov(X) + rcov(Y) and the van der Waals limit by RvdW = rvdW(X) + rvdW(Y), where rcov and rvdW represent the covalent and van der Waals radii, respectively. The standard values of the covalent limit100 for H−Ng bond are 0.59, 0.89, 1.37, 1.47, and 1.71 Å for H−He, H−Ne, H−Ar, H−Kr, and H−Xe, respectively, and the corresponding vdW limits101−103 are 2.63, 2.78, 3.14, 3.27, and 3.48 Å. The calculated Ng−O covalent limits100 are found to be 0.94, 1.24, 1.72, 1.82, and 2.06 Å for He−O, Ne−O, Ar− O, Kr−O, and Xe−O, respectively, and the vdW limits101−103 for the corresponding moiety are 2.93, 3.08, 3.44, 3.57, and 3.78 Å. It is quite evident from the above data that H−Ng bond length values in HNgOSi+ ions are in close proximity with the covalent limits whereas the Ng−O bond length values reside between the covalent and vdW limits. It indicates that a very strong interaction exists between the H and Ng atoms while the Ng and O atoms interact relatively weakly in the [HNg]+OSi complexes. Now we can compare the structural parameters of the transition state geometry with respect to those of minima. The H−Ng bond length is found to contract slightly whereas there is an increase in Ng−O bond length in the transition state as compared to the minima. The computed values further reveal that the expansion and contraction increase along the He−Ar− Kr−Xe series. On the contrary, Si−O bond lengths remain almost the same while going from the minima to the transition state structures. The H−Ng−O bond angle deviates from 180° to 122.3°, 108.2°, 101.7°, and 98.4° in the transition state of HHeOSi+, HArOSi+, HKrOSi+, and HXeOSi+ ions, respectively, whereas there is only a slight decrease in the Ng−O−Si bond angle. As a result, the geometry of HNgOSi+ ions transforms from linear to nonlinear bent structure in going from the minimum to the saddle point.

be 0.765, 0.988, 1.281, 1.422, and 1.610 Å along the He−Ne− Ar−Kr−Xe series (Table S1), which are similar to the bond length values of the corresponding moiety in HNgOSi+ species. Thus, the H−Ng bond strength in HNgOSi+ ion is comparable to that in HNgCO+ ion. The H−Ng bond lengths in bare HNg+94−98 and HNgOH2+38 ions have been computed to be 0.776, 0.992, 1.282, 1.416, and 1.607 Å for HHe+, HNe+, HAr+, HKr+, and HXe+ and 0.754, 1.277, 1.425, and 1.609 Å for HHeOH2+, HArOH2+, HKrOH2+, and HXeOH2+, respectively. The similar H−Ng bond lengths in these systems indicate the existence of a strong H−Ng bond in HNgOSi+ ions. It would also be interesting to compare the H−Ng bond length in the present species with that in (RgHRg)+94−98 ion, a linear centrosymmetric complex observed in noble gas matrices. The CCSD(T) values of H−Ng bond lengths are computed to be 1.501, 1.662, and 1.845 Å for ArHAr+, KrHKr+, and XeHXe+ ions, respectively, which are clearly larger than the corresponding values in HNgOSi+ species. Moreover, MP2/AVTZ calculated H−Ng bond lengths in Ng-HOSi+ systems have been reported68 to be 1.880, 1.954, and 2.099 Å, for He-HOSi+, Ne-HOSi+, Ar−HOSi+, respectively, which are quite large as compared to the corresponding MP2 values presented in Table 1 (cf. 0.749, 0.983, and 1.277 Å). All these results further confirm the existence of a strong, short and rigid bond between the H and Ng atoms in HNgOSi+ ions. Now, we can compare the Ng−O bond lengths in HNgOSi+ ions as compared to the same in NgOSi+ and HNgOH2+38,99 systems. The CCSD(T) computed Ng−O bond lengths in HNgOSi+ ions are found to be 1.747, 2.282, 2.419, 2.456, and 2.555 Å along He−Ne−Ar− Kr−Xe series while the corresponding bond lengths have been calculated to be 3.739, 3.687, 2.682, 2.255, and 2.382 Å in HeOSi+, NeOSi+, ArOSi+, KrOSi+, and XeOSi+ (The bent structures of HeOSi+ and NeOSi+ are found to be more stable than their linear structures), respectively, and 1.841, 2.523, 2.583, and 2.714 Å in HNgOH2+38 ions along the He−Ar−Kr− Xe series. In general, the shorter Ng−O bond lengths in HNgOSi+ ions as compared to the other ions clearly reveal a stronger Ng−O bond in the species of our study. The calculated Si−O bond lengths in HNgOSi+ ions have been found to be 1.541, 1.536, 1.538, 1.539, and 1.540 Å along the He−Ne−Ar−Kr−Xe series, which are slightly smaller than the 11603


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Table 2. Energies (in kJ mol−1) of the Various Dissociated Species Relative to the HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Ions, Calculated Using MP2, DFT, and CCSD(T) Methods with AVTZ Basis Sets, and Using CCSD(T) Method with AVQZ Basis Sets (B1) Ng

methods

HNgOSi+

Ng + HOSi+

HNg+ + OSi

H + NgOSi+

H + Ng + OSi+

H+ + Ng + OSi

barrier heighta

He

DFT MP2 CCSD(T) CCSD(T)/B1 DFT MP2 CCSD(T) CCSD(T)/B1 DFT MP2 CCSD(T) CCSD(T)/B1 DFT MP2 CCSD(T) CCSD(T)/B1 DFT MP2 CCSD(T) CCSD(T)/B1

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

−463.7 −466.3 −475.3 −474.6 −507.1 −491.8 −502.7 −503.1 −323.3 −307.5 −315.3 −317.7 −261.0 −248.0 −254.8 −259.8 195.2 −179.3 −183.5 −190.8

171.6 144.8 149.8 150.1 101.8 92.0 95.1 94.9 114.7 107.9 109.5 110.6 123.5 116.9 118.1 118.7 124.5 121.0 122.0 122.6

151.6 189.3 148.8 b 107.7 159.9 118.3 b 257.7 347.3 304.0 b 275.3 317.0 320.1 322.9 274.4 296.4 304.3 307.1

151.8 203.2 150.9 157.3 108.3 177.8 123.5 128.8 292.2 362.1 311.0 314.2 354.4 421.6 371.4 372.1 420.2 490.3 442.7 441.2

364.6 338.6 346.2 347.1 321.1 313.1 318.8 318.5 505.0 497.4 506.2 503.9 567.2 556.9 566.7 561.8 633.0 625.6 637.9 630.9

17.5 7.1 7.1 6.8 1.2 0.2 c c 29.8 23.5 23.2 24.1 44.3 37.1 36.7 37.2 52.7 47.4 47.0 47.7

Ne

Ar

Kr

Xe

a Barrier height corresponding to transition state for the reaction HNgOSi+ → HOSi+ + Ng. bThe geometry of HeOSi+, NeOSi+, and ArOSi+ could not be optimized by the CCSD(T)/AVQZ level of theory. cThe TS of HNeOSi+ could not be optimized by CCSD(T) methods.

It has been found that HNgOSi+ ions are more stable as compared to the isomeric HNgSiO+ species. For the purpose of comparison, the calculated optimized structural parameters of HNgSiO+ ions have been reported in Table S2. The CCSD(T) computed Ng−Si bond lengths (using AVTZ basis sets) in HNgSiO+ ions are found to be 2.861, 3.686, 3.682, 3.620, and 3.709 Å along the series He−Ne−Ar−Kr−Xe. It is also interesting to compare the Ng−Si bond lengths in NgSiH3+ with the corresponding values in HNgSiO+ ions. Thus, the Ng−Si bond lengths calculated using the CCSD(T) method with the def2-QZVPPD basis set are found to be 2.100, 2.295, 2.388, 2.496, 2.644, and 2.706 Å for HeSiH3+, NeSiH3+, ArSiH3+, KrSiH3+, XeSiH3+, and RnSiH3+ respectively.72 Similarly, the Xe−Si bond lengths computed using the MP2 method with the def2-QZVPPD basis set have been found to be 2.588 and 2.653 Å for H3SiXeNSi and HSiXeNSi,73 respectively, while the MP2 calculated Xe−Si bond length in HXeSiO+ is 3.709 Å. Here it may be noted that the Xe−Si bond length in HXeSiO+ ion is larger than that reported for H3SiNgNSi as well as for HSiNgNSi molecule. Similarly, Ng−Si bond lengths in HNgSiO+ species are larger than the corresponding values in NgSiH3+. Larger Ng−Si values in HNgSiO+ ions further reveal that these systems are less stable as compared to our predicted species, HNgOSi+. The computed geometrical parameters for the HNgCO+ ions are also reported in Table S1 for the purpose of comparison. 3.2. Energetics and Kinetic Study. The stability of our predicted species, HNgOSi+, can be determined based on the energies of its various dissociation products obtained using different methods. In order to determine the kinetic and thermodynamic stability of HNgOSi+, the following dissociation channels have been considered: HNgOSi+ → SiOH+ + Ng

HNgOSi+ → HNg + + OSi

(2)

HNgOSi+ → H + NgOSi+

(3)

HNgOSi+ → H + Ng + OSi+

(4)

HNgOSi+ → H+ + Ng + OSi

(5)

−1

The energies in kJ mol corresponding to the three 2-body dissociation (channels 1−3) and two 3-body dissociation (channels 4 and 5) pathways employing the MP2, B3LYP, and CCSD(T) methods (all using AVTZ basis sets) and the CCSD(T) method (using AVQZ basis sets as well) have been reported in Table 2. Since neutral HNg radicals are essentially unbound, we have not considered the dissociation channel, HNgOSi+ → HNg + OSi+. Here, it should be noted that the calculated CCSD(T) T1 diagnostic values for the minima and transition state structures are found to lie below the limiting value of 0.02. This implies that there is no need for multireference methods, and single reference based methods themselves can adequately describe our predicted system. Henceforth, CCSD(T) values of energy computed using AVTZ basis sets are discussed in this paper unless otherwise stated. The computed energy values indicate that the first dissociation channel gives rise to the global minimum products (Ng + SiOH+) whereas the rest of the channels lead to the local minimum products on the potential energy surface. The first channel dissociation energy values calculated using the CCSD(T) method with AVTZ basis sets are −475.3, −502.7, −315.3, −254.8, and −183.5 kJ mol−1 along the series He− Ne−Ar−Kr−Xe, which clearly indicate that HNgOSi+ ions are thermodynamically unstable as compared to the global minimum products. The CCSD(T) computed dissociation energy values for channel 2 are found to be 149.8, 95.1, 109.5, 118.1, and 122.0 kJ mol−1 for HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+, respectively, leading to the respective

(1) 11604


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Figure 2. Minimum energy path for the HNgOSi+ → HOSi+ + Ng reaction (Ng = He, Ne, Ar, Kr, and Xe) using the B3LYP method.

HNeOSi+ could not be optimized using the CCSD(T) method. Moreover, the barrier height corresponding to HHeOSi+ is found to be reasonably small. The MP2 calculated barrier heights are 7.1, 0.2, 23.5, 37.1, and 47.4 kJ mol−1 for HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+, respectively, and the corresponding B3LYP values are 17.5, 1.2, 29.8, 44.3, and 52.7 kJ mol−1. Thus, it is clear that the B3LYP calculated barrier heights have relatively higher values in comparison with those obtained using the other methods. In order to calculate the accurate barrier heights, the zero-point energy corrections must be considered. The zero-point energy (ZPE) corrections calculated using the MP2 method are 5.6, 1.4, 5.0, 5.4, and 5.3 kJ mol−1 along the series He−Ne−Ar−Kr−Xe, respectively, and the corresponding B3LYP values are 6.1, 1.7, 4.7, 5.1, and 5.0 kJ mol−1, respectively. Even though HNgOSi+ ions are thermodynamically unstable with respect to the global minimum products, they are found to be kinetically stable as far as the ZPE corrected barrier heights are concerned for the HArOSi+, HKrOSi+, and HXeOSi+ ions. Therefore, it might be possible to prepare and analyze the predicted species, except HHeOSi+ and HNeOSi+, in cryogenic conditions by employing low temperature matrix isolation techniques. The CCSD(T) computed barrier heights for HHeCO+, HArCO+, HKrCO+, and HXeCO+ ions are 22.7, 10.1, 13.1, and 15.0 kJ mol−1,31 which are comparatively lower than the corresponding values in HNgOSi+ systems, except helium inserted species. These results suggest that HNgOSi+ ions are kinetically more stable than the corresponding HNgCO+ ions and can be more easily detected at cryogenic temperature. Further, we have traced the minimum energy path connecting the predicted metastable species with their global minimum products through the transition state using IRC calculations. These reaction pathways for HNgOSi+ ions, except HNeOSi+, have been shown in Figure 2. It confirms the existence of a transition state connecting our predicted ions

local minimum products on the potential energy surface while the corresponding dissociation energy values for the HNgCO+31 ions are 15.0, −275.2, 28.8, 29.5, and 29.1 kJ mol−1 along the series He−Ne−Ar−Kr−Xe. The higher dissociation energy values for the HNgOSi+ ions as compared to the HNgCO+ ions with respect to this 2-body dissociation channel suggest that the HNg+ and OSi species are bound in a stronger manner in HNgOSi+ ions than the HNg+ and CO species in HNgCO+ ions. The computed energy values for the 2-body dissociation channel 3 have been found to be 148.8, 118.3, 304.0, 320.1, and 304.3 kJ mol−1 along the series He− Ne−Ar−Kr−Xe, which clearly indicate that the predicted HNgOSi+ ion is thermodynamically stable with respect to the corresponding dissociation products. The endothermic nature of the 3-body dissociation channels 4 and 5 illustrates that HNgOSi+ ions are more stable than the dissociation products (H + Ng + OSi+ and H+ + Ng + OSi) by 150.9, 123.5, 311.0, 371.4, 442.7 kJ mol−1 and 346.2, 318.8, 506.2, 566.7, 637.9 kJ mol−1, respectively, for HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+ ions. The corresponding energy values with respect to the dissociation channel 5 for HNgCO+31 ions are 211.5, −51.5, 425.5, 502.5, and 565.7 kJ mol−1 along the series He−Ne−Ar−Kr−Xe. These results also indicate a higher thermodynamic stability of HNgOSi+ ions in comparison with the valence isoelectronic species, HNgCO+. We have also employed the CCSD(T)/AVQZ method to compute all the dissociation energy values, which are found to comply well with that obtained using the AVTZ basis sets. Furthermore, the kinetic stability of the predicted species can be determined by calculating the barrier height for the first dissociation pathway, which has been found to be thermodynamically feasible. The barrier heights computed using the CCSD(T) method with AVTZ basis sets are found to be 7.1, 23.2, 36.7, and 47.0 kJ mol−1 for HHeOSi+, HArOSi+, HKrOSi+, and HXeOSi+, respectively. The transition state of 11605


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the MP2/AVTZ calculated complexation energy values are found to be in the range of 3−26 kJ mol−1 with the largest value for the Xe···HOSi+ complex. The B3LYP/AVTZ calculated values also follow the same trend, though the absolute magnitudes are slightly smaller. 3.3. Harmonic Vibrational Frequency Analysis. One of the best ways to characterize a new molecule is to analyze its ability to reproduce the vibrational frequencies of the predicted systems. The IR frequency values along with their intensities, computed using MP2, B3LYP, and CCSD(T) methods with the AVTZ basis sets, for the minima and the transition state structures of HNgOSi+ ions have been reported in Table 4. It has been observed that the frequencies calculated using the MP2 method are closer to the corresponding CCSD(T) values, and they also nearly resemble the experimental values. Furthermore, the B3LYP computed frequency values are relatively smaller than those obtained by other methods. Therefore, MP2 computed frequencies are discussed in this paper, unless otherwise mentioned. The predicted species, HNgOSi+, exhibits three nondegenerate stretching modes (viz., H−Ng stretch, Ng−O stretch, and O−Si stretch), two doubly degenerate bending modes (viz., H−Ng−O bend and Ng−O−Si bend) at the

with their global minima. Moreover, we have carefully investigated the structures on the actual end-point of the IRC calculations. Indeed, we have found that the global minimum products (Ng and HOSi+) are weakly bonded complexes, Ng··· HOSi+, as obtained from the IRC calculations. Consequently, we have included the Ng···HOSi+ bond length and the complexation energy for each of the complexes in Table 3. Table 3. Calculated Values of H−Ng Bond Length (in Å) and Bond Dissociation Energy (kJ mol−1) for Ng···HOSi+ complexes (Ng = He, Ne, Ar, Kr, and Xe) as Obtained Using B3LYP and MP2 Methods Using AVTZ Basis Sets Re(H−Ng)

De(H−Ng)

species

B3LYP

MP2

B3LYP

MP2

HeHOSi+ NeHOSi+ ArHOSi+ KrHOSi+ XeHOSi+

1.834 1.961 2.180 2.291 2.455

1.882 1.962 2.130 2.236 2.388

2.7 4.7 12.3 16.1 20.7

3.0 6.0 16.1 20.3 26.3

The reported results indicate that the Ng−H bond lengths in Ng···HOSi+ complexes are increased from He to Xe. Similarly,

Table 4. Harmonic Vibrational Frequencies (in cm−1) and Intensitiesa Calculated Using MP2, B3LYPb, and CCSD(T)c Methods with AVTZ Basis Set for HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Ions for the Minima and the Transition States (TS) H−He−O−Si+ normal mode (symmetry) H−Ng stretch

Ng−O stretch

O−Si stretch

H−Ng−O bendd

Ng−O−Si bendd

H−Ng−O−Si torsion

H−Ne−O−Si+

H−Ar−O−Si+

H−Kr−O−Si+

H−Xe−O−Si+

minima

TS

minima

TS

minima

TS

minima

TS

minima

TS

3568.2 (160.7) {3073.6} (243.6) [3546.0] 531.6 (386.6) {587.3} (332.6) [542.6] 1196.7 (825.1) {1194.0} (361.8) [1195.2] 446.8 (37.2) {582.7} (104.6) [463.3] 142.3 (151.3) {147.9} (143.5) [146.4]

3600.4 (581.8) {3268.7} (283.7) [3588.3] 496.6 (328.0) {531.9} (314.8) [508.6] 1171.5 (223.8) {1182.2} (319.9) [1190.2] −619.4 (92.7) {-874.2} (51.4) [−618.3] 143.4 (141.7) {153.3} (130.2) [147.2] 152.8 (240.0) {164.9} (234.2) [156.4]

3063.3 (730.7) {2539.7} (437.0) [3094.3] 222.0 (48.2) {236.0} (54.5) [233.1] 1179.9 (110.8) {1212.3} (178.4) [1204.6] 131.1 (354.7) {205.3} (276.2) [130.06] 98.3 (0.1) {101.4} (43.5) [99.0]

3069.2 (763.4) {2643.8} (317.0) e 2221.0 (57.4) {234.9} (60.7) e 1179.7 (109.0) {1212.3} (165.3) e −159.0 (255.8) {-254.9} (202.1) e 105.8 (86.6) {112.3} (165.2) e 109.1 (153.8) {113.3} (73.2) e

2775.3 (227.8) {2553.6} (0.5) [2759.9] 198.5 (143.7) {206.4} (47.1) [199.3] 1173.3 (181.6) {1202.0} (265.6) [1196.6] 412.9 (86.0) {446.1} (77.5) [407.9] 104.0 (41.1) {101.0} (42.3) [106.5]

2812.6 (513.0) {2695.9} (444.7) [2801.8] 160.6 (29.4) {158.8} (30.1) [162.6] 1171.9 (106.0) {1209.0} (156.6) [1196.1] −327.7 (96.4) {-348.4} (81.2) [−328.6] 96.5 (30.0) {106.5} (31.5) [100.3] 97.5 (52.2) {93.9} (57.6) [99.3]

2547.0 (77.2) {2360.1} (1.2) [2511.4] 178.3 (29.8) {184.6} (29.7) [178.0] 1170.6 (225.2) {1197.2} (306.8) [1193.1] 442.4 (86.5) {462.2} (79.8) [437.7] 103.4 (31.5) {100.0} (33.8) [106.0]

2598.2 (413.3) {2483.6} (276.2) [2571.4] 130.2 (14.1) {127.5} (18.3) [132.5] 1169.9 (107.4) {1208.4} (160.4) [1194.9] −306.3 (93.8) {-315.9} (98.9) [−294.5] 93.0 (15.2) {101.3} (29.9) [101.1] 93.1 (34.2) {88.7} (38.0) [95.6]

2323.0 (12.3) {2179.2} (5.2) [2271.3] 167.7 (27.9) {171.1} (25.8) [166.9] 1167.1 (265.8) {1192.2} (339.1) [1187.9] 428.8 (54.1) {435.9} (52.2) [424.6] 103.5 (26.0) {97.8} (27.0) [105.6]

2377.7 (200.3) {2275.7} (155.8) [2330.8] 111.9 (10.8) {108.9} (12.0) [113.2] 1167.4 (111.1) {1207.8} (168.2) [1193.0] −274.9 (31.6) {-287.3} (67.8) [−276.6] 88.3 (22.9) {91.7} (26.6) [91.5] 89.1 (17.8) {83.2} (25.7) [90.6]

a Corresponding IR intensity values calculated using B3LYP and MP2 methods are given within the parentheses (in km mol−1). bThe B3LYP calculated values are given within the curly brackets. cThe CCSD(T) calculated values are given within the square brackets. dFor minima the modes are doubly degenerate. eThe TS of HNeOSi+ could not be optimized by the CCSD(T) method.

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Table 5. MP2 and B3LYPa Calculated Values of the Harmonic Vibrational Frequencies (in cm−1) and Intrinsic Force Constants in Parentheses (in N m−1) Corresponding to Individual Internal Coordinates of HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Ions internal coordinate H−Ng stretch Ng−O stretch O−Si stretch H−Ng−O bend Ng−O−Si bend a

HHeOSi+

HNeOSi+

HArOSi+

HKrOSi+

HXeOSi+

3559.0 (600.8) [3061.2] (444.5) 629.9 (74.9) [691.3] (90.1) 1156.0 (801.3) [1169.8] (820.5) 469.0 [585.3] 134.7 [137.0]

3063.0 (530.4) [2540.4] (364.8) 275.3 (39.7) [277.8] (40.3) 1169.4 (820.0) [1201.9] (866.1) 128.2 [206.0] 102.3 [100.0]

2775.6 (446.2) [2554.1] (377.9) 252.3 (42.9) [255.3] (43.9) 1162.3 (809.9) [1191.5] (851.3) 412.6 [446.0] 105.0 [101.6]

2547.2 (380.7) [2360.4] (327.0) 241.4 (46.1) [243.6] (47.0) 1158.6 (804.9) [1186.1] (843.5) 442.0 [461.8] 105.2 [101.7]

2323.2 (318.1) [2179.3] (279.9) 232.6 (45.5) [229.7] (44.4) 1155.6 (800.7) [1182.1] (837.8) 428.0 [435.2] 106.5 [100.9]

The B3LYP calculated values are given within the square brackets.

ions. The corresponding values for HHeCO+, HNeCO+, HArCO+, HKrCO+, and HXeCO+ ions are 3399.2, 2977.5, 2755.1, 2547.4, and 2337.4 cm−1, respectively, as listed in Tables S4 and S5. The relatively high H−Ng stretch values in HNgOSi+ species as compared to the other ions clearly indicate the presence of a strong and rigid H−Ng bond. Harmonic vibrational frequency values for the HNgOSi+ and HNgSiO+ species are compared in Tables S6 and S7. It would also be worthwhile to understand the coupling that exists between the different vibrational modes in this metastable species. Therefore, we have partitioned the normal modes of vibrational frequency into the individual internal coordinates using the Boatz and Gordon methodology.104 The individual internal coordinate vibrational frequencies of HNgOSi+ ions, as calculated using the MP2 and B3LYP methods, have been reported in Table 5. The internal coordinate frequency values of H−Ng bond suggest that the coupling of H−Ng stretching mode with the other modes is almost negligible. The MP2 calculated normal mode Ng−O stretch vibrational frequencies in HNgOSi+ ions range from 167.7 to 531.6 cm−1 while its internal coordinate frequencies lie in a range of 232.6−629.9 cm−1 along the series Xe−Kr−Ar−Ne−He. These results suggest that the Ng−O stretch is coupled to the other modes in a stronger manner in HNgOSi+ ions. The force constant (k) values computed using the MP2 method for the H−Ng stretch and Ng−O stretch in HNgOSi+ ions are 600.8, 530.4, 446.2, 380.7, and 318.1 N m−1 and 74.9, 39.7, 42.8, 46.1, and 45.5 N m−1 along the series He−Ne−Ar− Kr−Xe. The high force constant values of H−Ng bond indicate that a strong and rigid bond exists between the H and Ng atoms in HNgOSi+ ions. Thus, the computed frequency values have been observed to agree well with the structural parameters. 3.4. Charge Distribution Analysis of HNgOSi+ Species. In order to determine the nature of bonding that exists between the atoms or fragments in a neutral or ionic species, it is essential to know the partial atomic charges present on each atom constituting the molecule/ion. The atomic charges computed by Mulliken population analysis using the B3LYP and MP2 methods have been reported in Table 6. However, in most of the cases, the charges calculated by both the methods are found to be equivalent. Here, the B3LYP calculated atomic charges are discussed further unless otherwise mentioned. Now we can compare the atomic charges of SiOH+ ion as reported in Table S8 before and after the insertion of a noble gas atom. The partial charge on the H atom is changed from 0.383 in SiOH+ to 0.485, 0.526, 0.268, 0.155, and −0.015 in

minimum energy state, and additionally one torsional vibration mode (H−Ng−O−Si) at its transition state. A gradual decrease in the vibrational frequency of the H−Ng bond has been observed from 3568.2 to 2323.0 cm−1 along the series He− Ne−Ar−Kr−Xe in HNgOSi+ ions. The Ng−O stretch frequency values range from 167.7 to 531.6 cm−1 where the He−O bond possesses the maximum value. However, the H− Ng stretch frequency values exhibit a slight increase in the transition state while the Ng−O stretch frequencies decrease considerably in the transition state. These results are in good agreement with the change in H−Ng (decrease) and Ng−O (increase) bond lengths from minima to the transition state. The O−Si stretch frequencies have been observed from 1167.1 cm−1 in HXeOSi+ to 1196.7 cm−1 in HHeOSi+. These values are found to remain almost the same for all these ions irrespective of the noble gas atom inserted. The frequency values of H−Ng−O bending mode in the minimum energy structures are 466.8, 131.3, 412.9, 442.4, and 428.8 cm−1 for HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+ ions, respectively. This doubly degenerate bending mode possesses negative frequency values in the transition state since it dissociates to form the global minimum products. The doubly degenerate Ng−O−Si bending mode exhibits frequency values of 142.3, 98.3, 104.0, 103.4, and 103.5 cm−1 along the series He−Ne−Ar−Kr−Xe. The higher values of the doubly degenerate H−Ng−O bending mode as compared to the corresponding Ng−O−Si bending modes in HNgOSi+ ions suggest that it may be difficult to break the H−Ng−O bond to give rise to the global minimum products (Ng + HOSi+). The H−Ng−O−Si torsional mode frequency values are found to be 152.8, 109.1, 97.5, 93.1, and 89.1 cm−1 for the transition state structures of HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+ ions, respectively. The IR frequency values of the precursor ion, SiOH+, corresponding to the H−O stretch, O−Si stretch, and H−O−Si bend are 3803.1, 1120.4, and 336.8 cm−1, respectively, as reported in Table S3. Thus, the corresponding values of HNgOSi+ ions show considerable deviation from those of its precursor ion. This difference can be attributed to the formation of new chemical bonds between the atoms during the insertion of a noble gas atom into SiOH+ ion. It would be interesting to compare the H−Ng stretching vibrational frequencies in HNgOSi+ ions with those in the bare HNg+ ions. The vibrational frequency values of the H−Ng stretching mode in bare HNg+ ions are 3259, 2930, 2652, 2574, and 2340 cm−1 along the series He−Ne−Ar−Kr−Xe, which are slightly smaller as compared to the corresponding values in HNgOSi+ 11607


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HNgOSi+ ions along the He−Ne−Ar−Kr−Xe series. It is quite interesting to note that q(H) values in bare HNg+ ions are 0.641, 0.666, 0.405, 0.319, and 0.218 for HHe+, HNe+, HAr+, HKr+, and HXe+ species, respectively, which are relatively higher than the corresponding values in HNgOSi+ ions. The charge on the O atom deviates from −0.423 in SiOH+ to −0.517, −0.612, −0.492, −0.473, and −0.484 in HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+, respectively. The charge on the Si atom is decreased from 1.040 in SiOH+ to 0.672, 0.668, 0.552, 0.572, and 0.567 along the series He−Ne− Ar−Kr−Xe in HNgOSi+ species. The noble gas atoms He, Ne, Ar, Kr, and Xe have acquired charges of 0.360, 0.419, 0.672, 0.746, and 0.932, respectively, after their insertion into SiOH+ ion. These results suggest that there is maximum charge redistribution in HXeOSi+ ion due to the more polarizable nature of xenon as compared to the other noble gas atoms. At this stage, we can compare the cumulative charges of the HNg+ fragments in HNgOSi+ ions with those in the bare HNg+ ions. The cumulative charges on HHe+, HNe+, HAr+, HKr+, and HXe+ fragments in HNgOSi+ ions are 0.845, 0.945, 0.940, 0.901, and 0.917, respectively, while unit positive charge resides on the bare HNg+ ions. This further proves that there is significant redistribution of charges after the insertion of a Ng atom in SiOH+ ion. This may be accounted due to the charge transfer from the H−Ng fragment to the Si−O+ moeity in HNgOSi+ ions. In the transition state, there is considerable increase in the q(H) values while the atomic charge of Ng decreases slightly from that in the minima. It has been found that the q(O) value in HNgOSi+ ions tends to become more negative in the transition state as compared to that in its minimum energy state. However, q(Si) values remain almost the same as those in the minima. Thus, there is an increase in the charge separation while going from the minimum to the transition state of HNgOSi+ ions. It is well-known that Mulliken population analysis has a huge dependence on the chosen basis set. Therefore, to acquire more accurate results, we have also carried out natural bond orbital (NBO) analysis for the minimum energy structures using MOLPRO program. The atomic charges calculated by NBO analysis using both MP2 and B3LYP methods have also been reported in Table 6. Through the NBO and Mulliken analysis, we can conclude that the H−Ng bond is covalent in nature while the Ng−O bond exhibits considerable ionic character. Thus, HNgOSi+ ion can be represented as a complex of [HNg]+ ion and OSi molecule. 3.5. Analysis of Topological Properties of HNgOSi+ Species. It would be better to perform the atoms-in-molecules (AIM) analysis developed by Bader88−90 for a clear understanding of the nature of bonding that exists between the constituent atoms. For this purpose, the electron density [ρ], the Laplacian of the electron density [∇2ρ], and the local energy density [Ed] for H−Ng, Ng−O, and O−Si bonds at their respective bond critical point (BCP) in HNgOSi+ ions have been calculated using the MP2 and DFT methods by the AIMPAC program,88 and the computed values have been reported in Table 7. The MP2 calculated BCP electron density values for the H−Ng bond are 0.255, 0.227, 0.241, 0.209, and 0.169 e a0−3 in HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+ ions, respectively. Large negative values of the ∇2ρ and the high ρ values at BCP suggest strong covalent nature of the H−Ng bond in HNgOSi+ ions whereas low electron density [ρ < 0.1] values and positive values of ∇2ρ for the Ng−O bond

a

q(Si)

q(O)

q(Ng)

The B3LYP calculated values are given in the parentheses. bThe Mulliken and NBO charges are calculated using GAMESS and MOLPRO programs, respectively. cTransition state.

0.182 (0.175) 0.771 (0.761) −1.307 (−1.342) 1.354 (1.407) 0.050 (0.081) 0.902 (0.884) −0.435 (−0.503) 0.483 (0.538) 0.535 (0.485) 0.368 (0.360) −0.510 (−0.517) 0.607 (0.672) q(H)

0.600 (0.574) 0.348 (0.350) −0.563 (−0.615) 0.614 (0.691)

0.638 (0.587) 0.300 (0.311) −1.310 (−1.326) 1.371 (1.428)

0.554 (0.526) 0.424 (0.419) −0.535 (−0.612) 0.556 (0.668)

0.613 (0.631) 0.369 (0.321) −0.539 (−0.614) 0.557 (0.662)

0.757 (0.736) 0.230 (0.236) −1.283 (−1.323) 1.286 (1.352)

0.317 (0.268) 0.655 (0.672) −0.458 (−0.492) 0.487 (0.552)

0.376 (0.344) 0.613 (0.639) −0.496 (−0.555) 0.506 (0.572)

0.437 (0.418) 0.536 (0.532) −1.293 (−1.328) 1.320 (1.379)

0.174 (0.155) 0.767 (0.746) −0.455 (−0.473) 0.515 (0.572)

0.263 (0.254) 0.707 (0.713) −0.454 (−0.507) 0.485 (0.540)

0.325 (0.307) 0.635 (0.631) −1.299 (−1.334) 1.339 (1.396)

−0.068 (−0.015) 1.025 (0.932) −0.471 (−0.484) 0.514 (0.567)

min TSc

Mulliken min min min min min min atom charge

Mulliken

TSc

NBO

min

Mulliken

TSc

NBO

min

Mulliken

TSc

NBO

min

Mulliken

TSc

NBO

H−Xe−O−Si+ H−Kr−O−Si+ H−Ar−O−Si+ H−Ne−O−Si+ H−He−O−Si+

Table 6. MP2 and B3LYPa Calculated Values of the Mullikenb and NBOb Charges in HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Ions Using AVTZ Basis Sets

NBO


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Table 7. Bond Critical Point Electron Density (ρ in ea0−3), Laplacian (∇2ρ in ea0−5), Local Electron Density (Ed in au), and Ratio of Local Electron Kinetic Energy Density and Electron Density (G/ρ in au) of HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Ions Calculated Using MP2 and B3LYPa Methods with AVTZ Basis Sets bond H−He−O−Si+ H−Ne−O−Si+ H−Ar−O−Si+ H−Kr−O−Si+ H−Xe−O−Si+ a

H−Ng

Ng−O

ρ

2

∇ρ

Ed

G/ρ

0.255 (0.246) 0.227 (0.218) 0.241 (0.232) 0.209 (0.200) 0.169 (0.162)

−3.173 (−2.127) −2.923 (−2.009) −1.119 (−0.903) −0.633 (−0.542) −0.333 (−0.299)

−0.806 (−0.552) −0.774 (−0.547) −0.326 (−0.269) −0.204 (−0.177) −0.140 (−0.124)

0.050 (0.081) 0.191 (0.206) 0.193 (0.185) 0.218 (0.208) 0.338 (0.305)

O−Si

ρ

2

∇ρ

Ed

G/ρ

0.055 (0.067) 0.023 (0.026) 0.035 (0.037) 0.039 (0.041) 0.039 (0.040)

0.272 (2.910) 1.605 (0.174) 0.158 (0.158) 0.153 (0.153) 0.132 (0.131)

0.002 (0.000) 0.008 (0.009) 0.002 (0.002) 0.000 (0.001) −0.002 (−0.001)

1.201 (1.097) 1.376 (1.300) 1.070 (0.993) 0.982 (0.917) 0.890 (0.846)

ρ

2

∇ρ

Ed

G/ρ

0.169 (0.175) 0.172 (0.181) 0.171 (0.179) 0.170 (0.178) 0.169 (0.177)

1.406 (1.386) 1.435 (1.443) 1.421 (1.427) 1.413 (1.418) 1.406 (1.412)

−0.074 (−0.080) −0.077 (−0.085) −0.075 (−0.084) −0.074 (−0.083) −0.074 (−0.082)

2.513 (2.438) 2.525 (2.468) 2.520 (2.461) 2.517 (2.457) 2.514 (2.454)

The B3LYP calculated values are given in the parentheses.

the critical points corresponding to their local energy density (denoted as HCP) and tabulated the values of ρ(r) and Ed(r)/ ρ(r) for the H−Ng and Ng−O bonds at the corresponding HCPs for the HNgOSi+ species in Table 8. Negative value of

indicate an ionic or van der Waals kind of interaction between the Ng and O atoms in HNgOSi+ ions. It is also important to compute the local energy density [Ed(r)] defined as Ed(r) = G(r) + V(r), where G(r) and V(r) denote the local kinetic energy and potential energy densities, respectively. A negative value of Ed(r) implies that V(r) dominates over G(r) resulting in the accumulation of electron density at BCP while positive values for Ed(r) are destabilizing. The BCP Ed values calculated by the MP2 method for the H− Ng bond are −0.806, −0.774, −0.326, −0.204, and −0.140 au along the series He−Ne−Ar−Kr−Xe whereas the corresponding values for the Ng−O bond are 0.002, 0.008, 0.002, 0.0, and −0.002 for HHeOSi+, HNeOSi+, HArOSi+, HKrOSi+, and HXeOSi+, respectively. These results suggest the existence of a stable H−Ng covalent bond while Ng and O atoms exhibit a van der Waals kind of interaction in HNgOSi+ ions. However, a small negative Ed value and less positive ∇2ρ values for the Xe− O bond in the HXeOSi+ ion reveal that it may be slightly covalent in nature. Furthermore, negative values of Ed for the O−Si bond in HNgOSi+ ions suggest that they are partially covalent in nature. Recently, Boggs and co-workers105 classified covalent bonds into four types: Type A, Type B, Type C, and Type D based on the values of G(r)/ρ(r). A strong “Type A” covalent bond is marked by ∇2ρ < 0, ρ(r) ≥ 0.1, and Ed(r) < 0 at BCP. Since the H−Ng bond in the HNgOSi + ions satisfies all these requirements, it is identified as a “Type A” covalent bond. If ρ(r) ≥ 0.1 and Ed(r) < 0 at BCP, then the corresponding bond is regarded as a “Type B” covalent bond. Thus, the O−Si bond in HNgOSi+ species is considered as a “Type B” covalent bond. Moreover, a “Type C” covalent bond with partial covalent character has G(r)/ρ(r) < 1 along with Ed(r) < 0 at BCP while “Type D” is identified by G(r)/ρ(r) < 1 and |Ed(r)| < 0.005. The computed results reveal that the Ng−O bond is not covalent. However, there exists a strong van der Waals interaction between the Ng and O atoms in HNgOSi+ ions. Thus, the computed AIM values also confirm the existence of the predicted species as [HNg]+[OSi] complex. Apart from the electron density based topological analyses, the distribution of local energy density has been found to provide valuable information in predicting the covalent and noncovalent regions in a molecular system. Very recently, it has been shown to be highly successful in rationalizing the bonding situations in various noble gas species as reported by Grandinetti and co-workers.106 Accordingly, we have calculated

Table 8. Various Topological Properties at the Local Energy Density Critical Points [(3,+1)HCP] for the HNgOSi+ (Ng = He, Ne, Ar, Kr, and Xe) Ions Calculated Using MP2 Method with AVTZ Basis Sets H−Ng Bond bonds

RH−Nga

R(H)b

R(Ng)b

Edc

ρd

−Ed/ρ

H−He H−Ne H−Ar H−Kr H−Xe

0.749 0.983 1.277 1.420 1.608

0.285 0.321 0.379 0.421 0.584

0.464 0.663 0.898 0.998 1.024 Ng−O Bond

−0.424 −0.345 −0.246 −0.197 −0.139

0.323 0.325 0.251 0.211 0.170

1.315 1.064 0.980 0.936 0.819

bonds

RNg−Oa

R(Ng)b

R(O)b

Ed c

ρd

−Ed/ρ

He−O Ne−O Ar−O Kr−O Xe−O

1.754 2.291 2.412 2.448 2.549

0.605 0.876 1.210 1.271 1.387

1.149 1.415 1.202 1.177 1.162

0.006 0.016 0.002 0.000 −0.002

0.060 0.039 0.035 0.039 0.040

−0.095 −0.415 −0.062 −0.009 0.043

a

MP2 calculated optimized bond length (Å) with aug-cc-pVTZ-PP basis set. bDistance (Å) of the HCP from the atom in parentheses. c Energy density (hartree a0−3) at the HCP. dElectron density (e a0−3) at the HCP.

Ed(r)/ρ(r) at HCP, referred to as bond degree (BD),107,106 has been shown to be a useful index in determining the covalent nature of a chemical bond. The BD parameter for the H−Ng bond decreases from 1.315 to 0.819 in going from HHeOSi+ to HXeOSi+ species, which is consistent with the calculated BCP quantities as reported in Table 7. Moreover, high positive values of BD for the H−Ng bond clearly indicate their covalent nature. On the other hand, small negative values of the BD parameter for the Ng−O bond imply that this bond is not only weak but also noncovalent in nature, although a small amount of covalency exists for the Xe−O bond, which shows a small positive BD value. Apart from the BD values, distances of the critical point from each atom constituting either the H−Ng or Ng−O bonds are also included in the same table, which show definite trends in going from He to Xe containing species. 11609


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The Journal of Physical Chemistry A 3.6. Comparison of the Relative Stabilities of HNgOSi+ and HNgSiO+ Species vis-à-vis HNgOC+ and HNgCO+ Ions. It would be interesting to compare the energy differences between the isomeric set of ions, HNgOSi+ and HNgSiO+. Accordingly, we have also optimized the structures of all the HNgSiO+ ions, and the energy differences calculated by the CCSD(T) method are found to be 158.7, 110.1, 122.0, 128.3, and 130.6 kJ mol−1 along the series He−Ne−Ar−Kr−Xe, as reported in Table 9. Here it may be noted that the energy gap

decides the stability of HNgOSi+/HNgSiO+ ions has been found to be the H−Ng bond characteristics. The H−Ng bond length values are found to have slight differences in HNgOSi+/ HNgSiO+ species resulting in higher stretching frequencies for the corresponding moiety in HNgOSi+ ions as compared to that in HNgSiO+ ions, as reported in Tables S6 and S7. On the contrary, the strength of the C−O bond contributes more to the stability of HNgCO+ species as compared to that of HNgOC+ ions. The triple bonded C−O bond lengths in HNgCO+ are found to be slightly smaller than those in HNgOC+ ions, which leads to an observable increase in C−O stretching frequency in HNgCO+ ions as compared to that in HNgOC+ ions. Moreover, these differences in H−Ng and C−O frequency values in HNgOSi+−HNgSiO+ and HNgCO+− HNgOC+ pairs, respectively, are found to decrease along the series He−Ne−Ar−Kr−Xe. These H−Ng and C−O frequency values clearly reveal that helium inserted species possess extreme values, with HHeOSi+ and HHeCO+ ions being the most stable ones, while the HHeSiO+ and HHeOC+ are the least stable among the helium inserted species considered here. This may be the probable reason for higher energy gap values for the HHeOSi+−HHeSiO+ and HHeCO+−HHeOC+ pairs. Apart from the frequencies of H−Ng and C−O stretchings, frequency values corresponding to the Ng−O−Si bending mode are found to be higher by an amount of 52−74 cm−1 than the Ng−Si−O bending mode values. Also, Ng−C−O bending mode frequency values are found to be higher by an amount of 55−81 cm−1 than the Ng−O−C frequency values. While going from helium to xenon, the trend in the variation in the energy difference between the HNgOSi+ and HNgSiO+ ions is found to follow the trend of the H−Ng−O bending mode frequencies. In a similar way, the trend in the H−Ng−C bending mode frequencies is shown to follow the energy difference trend in HNgCO+ and HNgOC+ ions. Thus, both the higher stability of HNgCO+ and HNgOSi+ ions and the trend in the relative energy difference of the two isomers, viz., HNgOX+ and HNgXO+ ions (X = C and Si), are consistent with the calculated vibrational frequency values. From the calculated values of the energy differences of various species discussed here, it is clear that the insertion of a Ng atom into the HOSi+−HSiO+ and HOC+−HCO+ ions decreases the energy difference between HNgOSi+ and HNgSiO+, and HNgOC+ and HNgCO+ pairs by an amount of ∼140−150 kJ mol−1 (Table 9). Preference of a Ng atom toward H−C bond in HCO+ (as compared to H−O bond in HOC+) and H−O bond in HOSi+ (as compared to H−Si bond in HSiO+) can be attributed to a higher q(H) value in HCO+ and HOSi+ as compared to that in HOC+ and HSiO+ species, respectively (Table S8). A higher q(H) value in HOSi+ and HCO+ as compared to that in HSiO+ and HOC+, respectively, facilitates the formation of the covalently bonded HNg+ ion in these species. Consequently, HNgOSi+ and HNgCO+ ions are stabilized more as compared to the HNgSiO+ and HNgOC+ ions, respectively. For the purpose of comparison the charge distributions in HNgOX+ and HNgXO+ ions (X = C and Si) are reported in Tables S10 and S11.

Table 9. Comparison between HNgOSi+ and HNgSiO+ as Well as HNgCO+ and HNgOC+ Ions in Terms of Their Energy Gap (in kJ mol−1) Calculated Using MP2, B3LYP, and CCSD(T) Methods with AVTZ Basis Sets energy gap species

MP2

B3LYP

CCSD(T)

HOSi+/HSiO+ HHeOSi+/HHeSiO+ HNeOSi+/HNeSiO+ HArOSi+/HArSiO+ HKrOSi+/HKrSiO+ HXeOSi+/HXeSiO+ HCO+/HOC+ HHeCO+/HHeOC+ HNeCO+/HNeOC+ HArCO+/HArOC+ HKrCO+/HKrOC+ HXeCO+/HXeOC+

248.3 152.9 106.2 118.9 125.2 127.6 193.5 21.4 13.0 15.4 17.3 18.0

278.9 157.5 108.8 124.9 130.5 131.9 162.2 19.7 9.1 11.3 13.7 13.8

269.3 158.7 110.1 122.0 128.3 130.6 165.4 13.4 7.4 9.3 11.1 11.8

between the HNgOSi+ and HNgSiO+ ions are lower than that between the isomeric protonated silicon monoxide species (269.3 kJ mol−1). It indicates that the insertion of a noble gas atom into HOSi+ and HSiO+ ion pair decreases the energy difference between them. Furthermore, the dissociation energy values of HNgSiO+ ions as reported in Table S9 suggest that they are more stable than the 2-body dissociation products (HNg + OSi+) and the 3-body dissociation products (H + Ng + OSi+ and H+ + Ng + OSi), except HHeSiO+. For the purpose of comparison, we have also computed the energy gaps between the analogous isomeric set of ions, HNgOC+ and HNgCO+, as listed in Table 9, and all the parametric values of their optimized structures have been reported in Table S1. The CCSD(T) computed energy difference values between the HNgCO+ and HNgOC+ ions have been found to be 13.4, 7.4, 9.3, 11.1, and 11.8 kJ mol−1, respectively, along the series He−Ne−Ar−Kr−Xe. These computed energy differences are found to be much smaller as compared to the same for the HCO+ and HOC+ pair (165.4 kJ mol−1). It is quite interesting to note that both sets of isomeric species (HNgOSi+−HNgSiO+ and HNgCO+−HNgOC+) follow the same trend of considerable decrease in energy gap values on insertion of a Ng atom into HXO+ and HOX+ pair (X = C and Si). It is also important to note that the stability order of the parent ions, viz., a higher stability of HCO+ and HOSi+ ions as compared to that of the HOC+ and HSiO+ ions, respectively, is maintained even after the insertion of a Ng atom. It is to be noted that the energy gap value is found to be the maximum for the helium inserted ions in both HNgOSi+− HNgSiO+ and HNgCO+−HNgOC+ pairs. The reason may be attributed to three factors: vibrational frequencies, bond lengths, and charge distribution. The dominating factor that

4. CONCLUSION In a nutshell, we have predicted theoretically the existence of a unique series of noble gas inserted cationic species, HNgOSi+, through the analysis of structural parameters, energetics, vibrational frequencies, and charge distributions of its minima and transition state structures by employing MP2, DFT, and 11610


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encouragements. P.S. gratefully acknowledges the support of NIUS (HBCSE−TIFR, Mumbai).

CCSD(T) methods with various basis sets. These results suggest that the precursor SiOH+ ion provides an ambient environment for a noble gas atom to redistribute its electron clouds to all the atoms within their vicinity leading to a stable species. It was found that HNgOSi+ ion exhibits a linear geometry with C∞v symmetry in the minimum energy state, and its transition state exhibits a nonlinear planar bent structure with Cs symmetry. The computed energy values show that the predicted species is thermodynamically unstable with respect to the global minimum products (Ng + SiOH+) on their respective potential energy surfaces. However, the high barrier height values corresponding to the transition state connecting the HNgOSi+ ions (except HNeOSi+) with their respective global minima ensure the kinetic stability of the predicted species. The positive dissociation energies corresponding to the rest of the 2-body and 3-body dissociation channels reveal the thermodynamic stability of HNgOSi+ ions with respect to these dissociation products. The intrinsic reaction coordinate (IRC) analysis confirms the metastable nature of our predicted ions by tracing out the minimum energy path that connects these ions with their global minima through a transition state. The calculated bond lengths, energetics, vibrational frequencies, and force constants suggest the existence of a strong and rigid H− Ng bond and strong van der Waals kind of interaction between the Ng and O atoms in HNgOSi+ complexes. Furthermore, Mulliken population, NBO, and AIM analysis also indicate that the predicted species should be viewed as a strong complex involving HNg+ ion and OSi molecule. Thermodynamic stability with respect to four dissociation channels and the kinetic stability with respect to the global minimum products suggest that it may be possible to prepare and detect HNgOSi+ ions experimentally, except HHeOSi+ and HNeOSi+, whose barrier heights are found to be rather low. Thus, it may be possible to prepare and characterize HNgOSi+ species by employing suitable experimental techniques at cryogenic temperature. It would be interesting to search for ionic complexes in the triplet state, similar to the neutral noble gas compounds predicted by us recently.108

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b09018. Structural parameters, charge distributions, harmonic vibrational frequencies, and relative energies (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Tel: (+)91-22-25595089. Fax: (+)91-22-25505151. E-mail: [email protected]. Present Address ‡

P.S.: Indian Institute of Science Education and Research Thiruvananthapuram, CET Campus, Computer Science Building, Sreekaryam, Thiruvananthapuram 695016, India. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the Computer Division, BARC, for providing computational facilities and support. We would like to thank Dr. A. K. Nayak, Dr. K. Dasgupta, and Dr. B. N. Jagatap for their kind interest and continuous 11611


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