
==== Front
J Phys Chem A
J Phys Chem A
jx
jpcafh
The Journal of Physical Chemistry. a
1089-5639
1520-5215
American Chemical Society

39159433
10.1021/acs.jpca.4c03220
Article
Comparative Study of Neutral and Cationic Sn2H2: Toward Laboratory Detection of the Cation
https://orcid.org/0009-0006-7268-0844
Biggerstaff Samuel
https://orcid.org/0000-0002-0618-6497
Kitzmiller Nathaniel L.
https://orcid.org/0000-0003-3659-0711
Turney Justin M.
https://orcid.org/0000-0003-0252-2083
Schaefer Henry F. III *
Center for Computational Quantum Chemistry, Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States
* E-mail: ccq@uga.edu.
19 08 2024
29 08 2024
128 34 70907104
15 05 2024
29 07 2024
18 07 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by/4.0/ Permits the broadest form of re-use including for commercial purposes, provided that author attribution and integrity are maintained (https://creativecommons.org/licenses/by/4.0/).

Group 14 M2H2 isomers (M = Si, Ge, Sn, and Pb) have attracted interest due to their radically differing electronic structures from acetylene. To better understand the Sn–H interactions of the neutral and cationic Sn2H2 structures, we present the most rigorous study of these systems to date. CCSD(T)/cc-pwCVTZ harmonic frequencies are presented as the first predictions for the neutral and cationic species to date. CCSDT(Q)/CBS relative energies are reported using the focal point approach, confirming the butterfly isomer as the global minimum on the potential energy surface for both the neutral and cationic species. In all, there exist 7 minima and 15 transition states. NBO analysis is also performed to elucidate the changes in bond order going from neutral to cation across all isomers of Sn2H2. Our results provide insights into the important Sn–H interaction and provide guidance for future work that may detect in the laboratory for the first time.

Basic Energy Sciences 10.13039/100006151 DE-SC0018412 document-id-old-9jp4c03220
document-id-new-14jp4c03220
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Special Issue

Published as part of The Journal of Physical Chemistry Avirtual special issue “Richard J. Saykally Festschrift”.
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pmcIntroduction

Tin is a versatile metal whose chemistry has attracted interest because of its success in a range of applications, such as catalysis and hydrogen energy storage.1−13 Lewis acid zeolite-based catalysts such as Sn-BEA have produced greater than 90% yields in the conversion of certain renewable feedstocks, such as the conversion of triose sugars to lactic acid derivatives.1,2L-Zeolite-supported Pt/Sn catalysts have been shown to be uniquely effective for the dehydrogenation of isobutane, with up to 98% selectivity in the production of isobutene.3 Additionally, Sn-containing materials, such as La2Mg(Ni0.095Sn0.05)9,4 Nd2Sn2O7,5 LmNi4.91Sn0.15,6,7 and LaNi5, making small substitutions of Ni with Sn,8−12 have shown promise as hydrogen storage electrode alloys.

The aforementioned studies involving dehydrogenation catalysis and hydrogen energy storage materials highlight tin’s fascinating chemistry as it interacts with hydrogen. For example, in the production of the Pt/Sn catalyst presented by Cortright,3 hydrogen is introduced to doubly valent SnO to reduce the Sn2+ species to zero valency as Sn is alloyed to Pt. Additionally, the smaller size of the Sn atoms reduces the overall size of the Pt/Sn alloy surface in which Pt can act, decreasing the rate of isomerization and hydrogenolysis reactions and therefore increasing the selectivity of dehydrogenation. Small substitutions of Sn for Ni in LaNi5 increase the hydrogen storage capacity in materials with typically low hydrogen storage density.8−12 Sn-substituted materials have larger unit cell volumes compared to LaNi5,11,12 and the substitution improves stability proportionally for absorption–desorption cycling.12 Even simpler systems like a tin hydride of the form SnHx have recently been found to display potential superconductivity under high pressure.13 Consequently, the study of simple systems containing only tin and hydrogen, that is, tin hydrides, may provide insights into electronic properties governing the broader field of tin chemistry.

Sn2H2 is an electronically interesting example of a tin hydride involved in an important segment of chemical history. The interest in this molecule stems from theoretical research involving the peculiar structure of the valence-isoelectronic Si2H2 molecule. Originally, Si2H2 was expected to exhibit an electronic structure similar to that of acetylene. However, through the inclusion of an effective core potential (ECP), the linear structure was determined to be instead a transition state with two imaginary vibrational frequencies.14 This discovery prompted a surge of research into Si2H2 and other similar molecules.15−21

Unlike acetylene, the global minimum of Si2H2 was not the linear structure, but rather a nonplanar structure with two hydrogen atoms bridging between the two Si atoms, referred to as the butterfly structure.18 Further investigations by Colegrove and Schaefer19 revealed an unprecedented minimum along the potential energy surface: the monobridged structure. This isomer contained one bridging hydrogen with other hydrogen bonded to one of the Si atoms. By further investigating this structure, Grev and Schaefer were able to report the first potential energy surface for the isomerization of Si2H2.20 Over the years of research dedicated to this molecule, the butterfly, monobridged, vinylidene-like, planar, cis, trans, and linear structures were identified as some of the primary stationary points that appeared along the potential energy surface (Figure 1). The butterfly isomer was found to be the global energy minimum; the monobridged, vinylidene-like, and planar trans isomers were found to be local minima, and the planar dibridged, cis, and linear structures were found to be transition states. As theoretical studies continued to investigate Si2H2, the unexpected monobridged structure was experimentally confirmed with microwave spectroscopy.22

Figure 1 Quatlitative structures for the butterfly, monobridged, vinylidene-like, trans, planar dibridged, cis, and perptrans structures of Sn2H2.

At the time, several studies discussed the high sensitivity of the computations in relation to the basis set.18−20 The vibrational frequencies, in particular, were especially susceptible to changes in the method and basis. An example of this is the trans structure. Depending on the basis and level of theory, the trans species was previously reported to have one or two imaginary modes despite being presented as a minimum.

Investigations on Si2H2 continued, and some researchers became interested in other metal hydrides of similar structures. Thus, research appeared which began to explore the potential energy surface of other group 14 hydrides. Ge2H223−26 was investigated thoroughly, and a qualitatively similar potential energy surface was determined. The butterfly was again reported as the global minima, with other stationary points prevalent in Si2H2 also appearing in Ge2H2. Furthermore, the vibrational frequencies were highly sensitive to the basis and level of theory. In the 1990 study by Grev, Deleeuw, and Schaefer,23 the trans structure displayed two imaginary modes. Both imaginary modes, a torsional au mode and a Ge–H stretching bu mode, were determined to be artifacts of the method used (SCF/TZ2P). Experimentally, the butterfly isomer of Ge2H2 was confirmed by Wang and co-workers using matrix isolation.24 Pb2H225−27 was investigated briefly, as well confirming similar electronic structures for the isomers along the potential energy surface, and it was potentially observed by Wang and Andrews27 with the same matrix isolation experiment used to identify the butterfly structure of Ge2H2.

In the unpublished 2010 study of the electronic structure of Sn2H2, geometries have been optimized up to the BP86/QZ4P level of theory with energies calculated at the CCSD(T)/aug-cc-pVQZ level of theory.26 Experimentally, Sn2H2 has been studied by Wang and co-workers, who successfully synthesized and found the vibrational spectra for the neutral form of Sn2H2 using matrix isolation.28 However, Wang and co-workers based their assignments on harmonic modes at the B3LYP/6-311++G**/SDD level of theory, and their assignments in the spectrum for In2H2 have been disputed.29 Furthermore, Nagase et al. reported a potential energy surface for Sn2H2 computed at the MP2/6-311G(2d, 2p) level of theory with zero-point energy corrections (Figure 2).25 This PES demonstrated structures and isomerization pathways qualitatively identical to the potential energy surface of Si2H2, Ge2H2, and Pb2H2, but it is unknown whether the underlying structure of this PES would remain intact under the investigation of higher level computations.

Figure 2 Potential energy surface for Sn2H2 with energies in kcal mol–1 determined by Nagase et al.25 with the MP2/6-311G(2d, 2p) method. Reproduced with permission from [25]. Copyright [2000] [Journal of Organometallic Chemistry].

No experimental or theoretical results on the cation, Sn2H2+, are currently available. It would be fundamentally interesting to observe the resulting structures of a neutral species that already exhibits unusual stationary point geometries when it loses an electron. Given that other group 14 metal hydrides are extremely sensitive to the method and basis, it is imperative to investigate Sn2H2 with the most vigorous methods available. Thus, the present research investigates the electronic properties of Sn2H2 and its cation, Sn2H2+, and we present highly reliable structures and fundamental frequencies using rigorous ab initio methods.

Computational Methods

General Scheme

To account for the neutral and cationic forms of Sn2H2, restricted Hartree–Fock (RHF)30 was used for closed shell Sn2H2, and restricted open-shell Hartree–Fock (ROHF)31 and unrestricted Hartree–Fock (UHF)32 were used to treat open-shell Sn2H2+. ROHF was used in the geometry optimizations, energy calculations, and harmonic vibrational analysis, and UHF was used in the NBO analysis. All basis sets used in this study were downloaded from the Basis Set Exchange.33−35 Geometries, harmonic frequencies, and ionization energies were obtained using CFOUR 2.0.36 Energies were obtained using Molpro,37−39 Psi4,40 and MRCC,41 and the natural bond orders were obtained using NBO 7.0.42 Additionally, energies obtained from Molpro, Psi4, and MRCC were tested against energies obtained from CFOUR to ensure that differences in the software did not affect the results of the study.

Geometries and Vibrational Frequencies

Stationary point geometries for the butterfly, monobridged, vinylidene-like, planar, cis, trans, and linear structures of Sn2H2 and Sn2H2+ were fully optimized with coupled cluster, single, double, and perturbative triple excitations, CCSD(T).43−45 The cc-pwCVXZ (X = D, T, and Q) basis sets46,47 (which will be referred to as XZ going forward) were used to describe all atoms. A 28-electron pseudo potential, or effective core potential (ECP), was used to treat Sn atoms for neutral and cation isomers and is designated by “–PP” in the name of the basis set.48 All other electrons, that is, those not included in the ECP, are fully correlated.

Harmonic vibrational frequencies and IR intensities were obtained in CFOUR by using finite differences of analytic gradients at the CCSD(T) level of theory and are reported at the CCSD(T)/TZ level of theory. Once geometries were obtained, center-of-mass dipole moments were recorded from geometry optimizations, and Wiberg bond index49−51 values and natural bond orders were calculated using NBO 7.0.

Energies

Energies of the geometries optimized at the CCSD(T)/QZ level of theory were extrapolated to the complete basis set (CBS) limit using the focal point approach (FPA).52−55 Hartree–Fock (HF) energies were extrapolated using Feller’s three-point formula (1),56 and post-HF energies were estimated using Helgaker’s two-point formula (2):571

2

Post-HF energies were extrapolated to the CBS limit up to the CCSD(T) level of theory. Higher order energy corrections were obtained at the CCSDT and CCSDT(Q) levels of theory with a DZ basis set, and the zero-point vibrational energies (ZPVE) were used for all isomers to correct energies with respect to their ground state vibrations at 0 K. Additionally, the ionization energy of the butterfly minimum was obtained with the EOMIP-CCSD/cc-pwCVQZ-PP method and basis.58

Results and Discussion

Geometries

Twelve stationary points were identified along the potential energy surface for neutral and cationic Sn2H2 with four minima (Figure 3) and eight transition states (Figure 4). Butterfly (C2v, neutral: 1A1, cation: 2A1), monobridged (Cs, neutral: 1A′, cation: 2A″), vinylidene-like (C2v, neutral: 1A, cation: 2B1), and nonplanar trans (C2, neutral: 1A) structures were found to be minima, while planar dibridged (D2h, neutral: 1Ag, cation: 2B1u), monobridged-like, perptrans (C2h, cation: 2Ag), planar trans (C2h, neutral: 1Ag, cation: 2Au), linear (D∞h, neutral: 1Πg, cation: 2Πu), and cis (C2v, neutral: 1A1, cation: 2A1) structures were found to be transition states. With the exception of the trans structures, the geometries of the neutral minima and transition states are in qualitative agreement with previous studies of Sn2H2.25,26,28,59 To differentiate between different trans structures, the molecule with the nearly perpendicular bond angles will be referred to as the perptrans structure, the molecule with a dihedral of 180◦ will be referred to as the planar trans structure, and the molecule with a dihedral of 169.9◦ will be referred to as the nonplanar trans structure. Additionally, three monobridged-like transition states have been investigated. In previous studies, similar monobridged-like structures have been identified for neutral M2H2 (M = Si, Ge, Sn, and Pb) as important transition states linking the monobridged minima to other minima along the potential energy surface.20 However, the monobridged-like transition states in this study have only been optimized to the CCSD(T)/TZ level of theory due to their lower symmetry and computational cost.

Figure 3 Equilibrium geometries predicted at the CCSD(T)/QZ level of theory for the butterfly, monobridged, vinylidene-like, and trans isomers. Bond lengths are in angstroms, and bond angles are in degrees. Values with brackets ([ ]) are associated with the cation species, and those without brackets are associated with the neutral species.

Figure 4 Stationary point geometries predicted for the planar dibridged, MB-TS1, MB-TS2, MB-TS3, trans-ts, perptrans, cis, and linear structures. All geometries are optimized at the CCSD(T)/QZ level of theory, except for the MB-TS structures which are optimized at CCSD(T)/TZ. Bond lengths are in angstroms, and bond angles are in degrees. Values with brackets ([ ]) are associated with the cation species, and those without brackets are associated with the neutral species.

The majority of the structures identified were present in both the neutral and cationic forms, with the exception of the nonplanar trans and perptrans structures. The nonplanar trans structure was found as only a neutral molecule, and the perptrans structure was found only as a cation. Comparing the neutral and cation stationary points, several themes arise. First, the cation Sn–Sn bond is slightly elongated compared to the neutral bond. The largest difference between the bond lengths of the neutral and cation species occurs for the cis isomer (0.212 Å), and the smallest difference is found for the linear isomer (0.057 Å). Second, Sn–H bonds do not change as significantly compared to the difference in Sn–Sn bonds, suggesting that the majority of the lost electron density in the cation is removed from the Sn–Sn bond. Thus, many of the differences in bond angles between neutral and cation molecules arise from the lengthening of the Sn–Sn bond and relatively constant Sn–H bonds. Interestingly, in the butterfly structure, the dihedral angle changes by nearly 10◦, and the molecule becomes closer to the planar dibridged structure as it loses an electron. This effect was observed in Si2H2,60 but not to the same degree as Sn2H2.

Previously, the planar trans structure was identified as a local minimum along the potential energy surface for neutral Sn2H2.25,26,59 However, in this study, the planar trans structure was identified as a transition state, while the nonplanar trans structure was identified as a minimum. Geometrically, the neutral planar and nonplanar trans structures are not too dissimilar, with the greatest differences being their Sn–Sn bond lengths (2.557 and 2.632 Å, respectively) and dihedrals (180◦ and 169.9◦, respectively); however, their bonding structure, as shown later, is quite distinct from one another providing insights into their assignments as a transition state and minimum, respectively. The nonplanar trans structure was found only on the neutral potential energy surface, and no cation equivalent was identified in this study. Similarly, the perptrans transition state was only identified in the cation but does not seem to have a direct connection to the nonplanar trans minimum.

The monobridged-like transition states (MB-TS1 (C1, neutral: 1A, cation: 2A), MB-TS2 (Cs, neutral: 1A′, cation: 2A″), and MT-TS3 (Cs, neutral: 1A′, cation: 2A″)) were investigated as well. MB-TS1 and MB-TS2, which have been previously identified as transition states between the monobridged and butterfly or vinylidene-like minima, respectively, were confirmed in this study.25 MB-TS3 was not observed to be a saddle point between the monobridged and planar trans structure. Since the planar trans structure was identified as a transition state, MB-TS3 cannot directly link the monobridged structure to the planar trans structure as a first-order saddle point. Additionally, the geometries of neutral and cation MB-TS3 vary the most compared to all other structures identified in this research (Figure 5).

Figure 5 Geometries predicted at the CCSD(T)/TZ level of theory for the MB-TS3 (a) neutral and (b) cation structure.

The neutral structure (Figure 5a) looks more similar to the monobridged structure with an A1 bond angle of less than 90◦. In contrast, cation MB-TS3 (Figure 5b) displays a geometry that appears to be more similar to the planar trans structure with an A1 bond angle being greater than 90◦. Scans were performed to identify a transition state between the monobridged minimum and nonplanar trans minimum, but no such saddle points were found in this study.

Relative Energies

Tables 1,2 show the CCSDT(Q)/CBS focal point energies and high-order coupled cluster corrections for the vinylidene-like neutral and cation structures. The remaining focal point tables can be found in Supporting Information. Excluding the planar and nonplanar trans structures, these tables demonstrate our rapid convergence to both the FCI and CBS limits, which validate the rigorous quantum chemistry methods used in this study.

Table 1 Focal Point Analysis Table for the Neutral Vinylidene-Like Isomer Relative to the Neutral Butterfly Isomer in kcal mol–1a,b

vinylidene-like neutral	HF	+δMP2	+δCCSD	+δ(T)	net	
DZ	10.12	+9.24	–3.75	–0.05	[15.57]	
TZ	10.85	+11.07	–5.15	+0.37	[17.14]	
QZ	10.87	+11.35	–5.34	+0.48	[17.35]	
5Z	10.87	+11.36	–5.31	+0.50	[17.43]	
CBS limit	[10.87]	[+11.51]	[−5.45]	[+0.54]	[17.46]	
a HF energies are extrapolated to the CBS limit using a three-point extrapolation formula, and post-HF energies are extrapolated using a two-point extrapolation method. Corrections for CCSDT, CCSDT(Q), and the zero-point vibration energy (ZPVE) are added to obtain the CCSDT(Q)/CBS energy.

b CCSD(T)/CBS + ΔZPVE + ΔT + ΔQ = CCSDT(Q)/CBS = 17.46 – 0.40 – 0.10 – 0.04 = 16.92

Table 2 Focal Point Analysis Table for the Cation Vinylidene-Like Isomer Relative to the Cation Butterfly Isomer in kcal mol–1a,b

vinylidene-like cation	HF	+δMP2	+δCCSD	δ(T)	net	
DZ	3.67	+13.50	–3.24	+1.05	[14.99]	
TZ	5.22	+14.58	–5.03	+1.52	[16.29]	
QZ	5.29	+14.68	–5.30	+1.64	[16.31]	
5Z	5.30	+14.60	–5.28	+1.67	[16.30]	
CBS limit	[5.30]	[+14.75]	[−5.46]	[+1.71]	[16.30]	
a HF energies are extrapolated to the CBS limit using a three-point extrapolation formula, and post-HF energies are extrapolated using a two-point extrapolation method. Corrections for CCSDT, CCSDT(Q), and the zero-point vibration energy (ZPVE) are added to obtain the CCSDT(Q)/CBS energy.

b CCSD(T)/CBS + ΔZPVE + ΔT + ΔQ = CCSDT(Q)/CBS = 16.30 – 0.08 + 0.16 – 0.13 = 16.25

The butterfly isomer was found to lie lowest in energy, followed by the monobridged, vinylidene-like, and trans isomer, as seen in Table 3. Energies for the monobridged-like transition states are given in Table 4. The order of energies did not differ between those of the cation and the neutral species. Additionally, there is no clear trend as to whether removing an electron from the system increases or decreases the relative energies. The planar dibridged transition state demonstrates the largest relative energy difference between the neutral and cation structure. The neutral planar dibridged structure lies 5.83 kcal mol–1 above the butterfly isomer, and the cation lies 1.66 kcal mol–1 above the butterfly isomer. When considering the change in the geometry, this energy difference appears reasonable. The planar dibridged structure acts as a transition state for the inversion of the butterfly structure. In the neutral form, the butterfly isomer lies farther away in its geometry from the planar isomer compared to its cationic counterpart. Therefore, the inversion barrier for the cation species is smaller, because its minimum lies closer to the geometry of the planar transition state. Additionally, the ionization energy of the butterfly global minimum was calculated to be 7.27 eV, a smaller ionization energy than that of C2H2 (11.49 eV).61

Table 3 Relative Energies at the CCSDT(Q)/CBS Approximation for the Butterfly, Planar, Monobridged, Vinylidene-Like, Perptrans, Cis, and Linear Isomers Given in kcal mol–1

 	neutral	cation	
butterfly	0.00	0.00	
planar	5.83	1.66	
monobridged	11.79	13.84	
vinylidene-like	16.92	16.25	
perptrans	- - -	25.32	
planar trans	22.82	25.38	
nonplanar trans	24.56	- - -	
cis	28.56	27.53	
linear	58.74	67.91	

Table 4 Relative Energies at the CCSD(T)/cc-pwCVTZ Level of Theory with ZPVE Corrections for the Monobridged Transition States Relative to the Butterfly Isomer Given in kcal mol–1

 	neutral	cation	
MB-TS1	13.56	14.71	
MB-TS2	19.01	20.22	
MB-TS3	23.84	26.10	

Across the majority of the focal point approximations, there is exceptional convergence toward the CCSDT(Q)/CBS limit. The relatively small high-order energy corrections of the focal point approach suggest that stationary points are sufficiently described by a single-reference determinant. As the methods increase in the excitation level, the high-order coupled cluster corrections converge rapidly with the largest correction for CCSDT being −0.52 kcal mol–1 in the cation linear transition state and the largest correction for CCSDT(Q) being +0.81 kcal mol–1 in the neutral nonplanar trans minimum. The neutral nonplanar trans minimum seems to be particularly sensitive to the level of theory and basis set. In the focal point table for the nonplanar trans minimum (Table 5), the HF/CBS energy is initially less than the HF/CBS energy of the neutral planar trans structure (Table 6); however, as the level of theory increases to CCSD(T), the energy of the nonplanar trans minimum becomes greater than that of the neutral trans structure. The swap in energy orderings also occurs when moving from the DZ to TZ basis. Additionally, both structures seem to be sensitive to the energy method and basis set, given their relatively large CCSDT and CCSDT(Q) correction. The corresponding planar trans cation (Table 7) has high-order energy corrections that are somewhat large compared to the rest of the structures but not to the degree of the neutral trans structures.

Table 5 Focal Point Analysis Table for the Neutral Nonplanar Trans Structure Relative to the Neutral Butterfly Isomer in kcal mol–1ab

nonplanar trans neutral	HF	+δMP2	+δCCSD	+δ(T)	net	
DZ	26.87	+1.08	–2.44	–2.87	[22.63]	
TZ	27.36	+2.52	–2.80	–2.66	[24.42]	
QZ	27.41	+2.86	–2.77	–2.68	[24.83]	
5Z	24.43	+2.91	–2.69	–2.69	[24.96]	
CBS limit	[27.43]	[+3.08]	[−2.74]	[−2.69]	[25.11]	
a HF energies are extrapolated to the CBS limit using a three-point extrapolation formula, and post-HF energies are extrapolated using a two-point extrapolation method. Corrections for CCSDT, CCSDT(Q), and thezero-point vibration energy (ZPVE) are added to obtain the CCSDT(Q)/CBS energy.

b CCSD(T)/CBS + ΔZPVE + ΔT + ΔQ = CCSDT(Q)/CBS = 25.11 – 1.25 – 0.11 + 0.81 = 24.56

Table 6 Focal Point Analysis Table for the Neutral Planar Trans Structure Relative to the Neutral Butterfly Isomer in kcal mol–1ab

planar trans neutral	HF	+δMP2	+δCCSD	+δ(T)	net	
DZ	28.03	–3.43	+1.05	–2.52	[23.13]	
TZ	28.31	–2.23	+0.49	–2.35	[24.23]	
QZ	28.36	–2.06	+0.52	–2.37	[24.45]	
5Z	28.37	–2.02	+0.59	–2.38	[24.56]	
CBS limit	[28.38]	[−1.93]	[+0.54]	[−2.38]	[24.60]	
a HF energies are extrapolated to the CBS limit using a three-point extrapolation formula, and post-HF energies are extrapolated using a two-point extrapolation method. Corrections for CCSDT, CCSDT(Q), and the zero-point vibration energy (ZPVE) are added to obtain the CCSDT(Q)/CBS energy.

b CCSD(T)/CBS + ΔZPVE + ΔT + ΔQ = CCSDT(Q)/CBS = 24.60 – 1.30 + 0.02 – 0.51 = 22.82

Table 7 Focal Point Analysis Table for the Cation Planar Trans Structure Relative to the Cation Butterfly Isomer in kcal mol–1ab

planar trans cation	HF	+δMP2	+δCCSD	+δ(T)	net	
DZ	24.39	+4.27	–1.18	–1.28	[26.20]	
TZ	25.53	+4.98	–2.28	–1.05	[27.18]	
QZ	25.51	+5.05	–2.36	–1.03	[27.18]	
5Z	25.52	+5.00	–2.29	–1.03	[27.20]	
CBS limit	[25.52]	[+5.10]	[−2.41]	[−1.00]	[27.20]	
a HF energies are extrapolated to the CBS Limit using a three-point extrapolation formula, and post-HF energies are extrapolated using a two-point extrapolation method. Corrections for CCSDT, CCSDT(Q), and the zero-point vibration energy (ZPVE) are added to obtain the CCSDT(Q)/CBS energy.

b CCSD(T)/CBS + ΔZPVE + ΔT + ΔQ = CCSDT(Q)/CBS = 27.20 – 1.39 – 0.17 – 0.26 = 25.38

Potential Energy Surface

Contrary to the work of Nagase et al., we found that the potential energy surface differs from that of other M2H2 (M = Si, Ge, or Pb) molecules (Figure 6). The primary difference is centered around the geometry of the nonplanar trans minimum. In the other M2H2 molecules, the trans minimum has a planar structure; however, we found that the trans minimum for Sn2H2 is nonplanar, therefore, changing the connectivity of minima and transition states.

Figure 6 Potential energy surface for Sn2H2 with energies in kcal mol–1 calculated at the CCSDT(Q)/CBS limit with FPA with the exception of the MB-TS1, MB-TS2, and MB-TS3 structures, which were calculated at CCSD(T)/TZ with harmonic zero-point vibrational corrections. Energies without brackets represent neutral structures, and those with brackets ([ ]) represent cation structures.

Butterfly, monobridged, vinylidene-like, MB-TS1, and MB-TS2 remain qualitatively similar, with MB-TS1 bridging the monobridged and butterfly structures and MB-TS2 bridging the monobridged and vinylidene-like structures. MB-TS3, however, contains two imaginary modes and thus is not a first-order saddle point between two minima. Originally, MB-TS3 was thought to bridge the monobridged and planar trans minima, but due to the nonplanarity of the trans minimum, MB-TS3 no longer connects these structures. A saddle point between the nonplanar trans structure was investigated, but no such transition states were identified.

The planar trans structure was identified as a transition state in this study. The H-wagging motion of its imaginary mode seems to suggest that the structure would be connected to the nonplanar trans minimum, but the focal point analysis showed that the nonplanar trans minimum lies higher in energy than the planar trans transition state. Upon further investigation, the planar trans structure was found to connect to the butterfly structure with an intrinsic reaction path computation. Additionally, the planar dibridged, perptrans, and cis transition states were seen here to connect to the butterfly minimum.

Vibrational Frequencies

The predicted CCSD(T)/TZ harmonic vibrational frequencies are presented in Tables 8–10. The majority of the infrared intensities are significantly small, but all cation minima contain at least one bright enough mode to be observed via infrared spectroscopy. The symmetric Sn–H stretch (1044 cm–1, b1) is the brightest mode for the butterfly structure. There has been no experimental analysis to date for the cation Sn2H2+, so there is no ability to compare our predicted modes to experiment. However, it is important to note that the ordering of modes is synonymous with that of the neutral species with relative intensities that match well.

Table 8 Harmonic Vibrational Frequencies in cm–1, Intensities in km mol–1, and Relative Intensities for the Butterfly, Monobirdged, Vinylidene-Like, and Nonplanar Trans Minima Are Given at the CCSD(T)/TZ Level of Theorya

 	description	neutral	cation	
butterfly	sym Sn–H–Sn str. ω1 (a1)	1332.7	(18.2, 4.4)	1333.8	(5.4, 1.1)	
H wag ω2 (a1)	669.4	(45.5, 10.9)	594.7	(14.1, 2.7)	
Sn–Sn str. ω3 (a1)	193.6	(0.8, 0.2)	130.8	(0.0, 0.0)	
anti-sym. Sn–H str. ω4 (a2)	957.5	(0.0, 0.0)	1028.5	(0.0, 0.0)	
sym. Sn–H str. ω5 (b1)	1043.9	(417.9, 100.0)	1115.5	(517.9, 100.0)	
anti-sym Sn–H–Sn str. ω6 (b2)	1244.5	(76.9, 4.4)	1194.8	(75.7, 14.6)	
monobridged	H2 str. ω1 (a′)	1840.8	(185.0, 100.0)	1878.4	(25.8, 18.3)	
H1 str. ω2 (a′)	1325.8	(121.0, 65.4)	1292.1	(47.6, 33.9)	
H1 bend ω3 (a′)	950.8	(137.1, 74.1)	921.4	(140.6, 100.0)	
H2 bend ω4 (a′)	414.1	(0.5, 0.3)	409.2	(0.3, 0.2)	
Sn–Sn str. ω5 (a′)	207.2	(3.1, 1.7)	173.8	(6.3, 4.5)	
H wag ω6 (a″)	133.9	(25.7, 13.9)	102.2	(3.0, 2.1)	
vinylidene-like	sym Sn–H str. ω1 (a1)	1898.1	(137.1, 100.0)	1941.3	(23.8, 40.3)	
H scissor ω2 (a1)	696.3	(92.5, 67.5)	688.9	(59.0, 100.0)	
Sn–Sn str. ω3 (a1)	205.1	(3.3, 2.4)	167.0	(0.4, 0.8)	
H wag ω4 (b1)	236.1	(0.4, 0.3)	319.7	(4.4, 7.5)	
anti-sym Sn–H str. ω5 (b2)	1912.7	(136.7, 99.6)	1967.7	(40.3, 68.2)	
H rock ω6 (b2)	195.4	(19.1, 13.9)	219.8	(9.1, 15.5)	
nonplanar trans	sym Sn–H str. (a)	1810.9	(1.37, 0.4)	- - -	- - - - - -	
sym Sn–Sn–H bend (a)	407.1	(2.46, 0.7)	- - -	- - - - - -	
H wag (a)	352.8	(0.11, 0.0)	- - -	- - - - - -	
Sn–Sn str. (a)	159.0	(0.11, 0.0)	- - -	- - - - - -	
anti-sym Sn–H str. (b)	1821.1	(379.1, 100.0)	- - -	- - - - - -	
anti-sym Sn–Sn–H bend (b)	191.2	(11.3, 3.0)	- - -	- - - - - -	
a Bolded values indicate intensities greater than 400 km mol–1.

Table 9 Harmonic Vibrational Frequencies in cm–1, Intensities in km mol–1, and Relative Intensities for the Planar, Linear, Cis, Perptrans, and Trans Transition States Are Given at the CCSD(T)/TZ Level of Theorya

 	description	neutral	cation	
planar dibridged	sym Sn–H–Sn str. ω1 (ag)	1405.8	(0.0, 0.0)	1361.0	(0.0, 0.0)	
Sn–Sn str. ω2 (ag)	180.8	(0.0, 0.0)	176.4	(0.0, 0.0)	
Anti-sym Sn–H str. ω3 (b1g)	1359.2	(0.0, 0.0)	1266.2	(0.0, 0.0)	
anti-sym Sn–H–Sn str. ω4 (b2u)	1184.8	(81.2 13.0)	1112.0	(70.0, 9.2)	
sym Sn–H str. ω5 ()	1340.0	(625.5, 100.0)	1297.6	(757.9, 100.0)	
H wag ω5 (b1u)	437.7i	(10.7, 1.7)	312.9i	(2.9, 0.4)	
linear	sym Sn–H str. ω1 ()	2038.6	(0.0, 0.0)	2031.5	(0.0, 0.0)	
Sn–Sn str. ω2 ()	287.3	(0.0, 0.0)	283.6	(0.0, 0.0)	
anti-sym Sn–H str. ω3 ()	2047.1	(0.2, 1.9)	2050.0	(105.1, 100.0)	
sym Sn–Sn–H bend ω4 (πu)	341.2	(9.6, 100.0)	314.6	(16.6, 15.8)	
sym Sn–Sn–H bend ω5 (πu)	341.2	(9.6, 100.0)	314.6	(16.6, 15.8)	
anti-sym Sn–Sn–H bend ω6 (πg)	844.3i	(0.0, 0.0)	921.7i	(0.0, 0.0)	
anti-sym Sn–Sn–H bend ω7 (πg)	844.3i	(0.0, 0.0)	921.7i	(0.0, 0.0)	
cis	sym. Sn–H str. ω1 (a1)	1751.0	(547.0, 100.0)	1806.9	(330.6, 100.0)	
sym. Sn–Sn–H bend ω2 (a1)	363.4	(9.8, 1.8)	301.9	(0.0, 0.0)	
Sn–Sn str. ω3 (a1)	195.0	(0.8, 0.2)	99.0	(0.0, 0.0)	
anti-sym Sn–H str. ω4 (b2)	1716.1	(459.8, 84.1)	19.1	(0.1, 0.0)	
anti-sym Sn–Sn–H bend ω5 (b2)	459.3	(49.9, 9.1)	1792.6	(30.8, 9.3)	
H scissor ω6 (a2)	494.5i	(0.0, 0.0)	281.7i	(0.0, 0.0)	
perptrans	sym Sn–H str. ω1 (ag)	- - -	- - - - - -	1812.9	(0.0, 0.0)	
sym Sn–Sn–H str. ω2 (ag)	- - -	- - - - - -	449.5	(0.0, 0.0)	
Sn–Sn str. ω3 (au)	- - -	- - - - - -	106.9	(0.0, 0.0)	
anti-sym Sn–H str. ω4 (bu)	- - -	- - - - - -	1821.5	(319.2, 100.0)	
anti-sym Sn–Sn–H bend ω5 (bu)	- - -	- - - - - -	235.9	(0.9, 0.3)	
H wag ω6 (ag)	- - -	- - - - - -	283.3i	(0.8, 0.2)	
planar trans	sym Sn–H str. ω1 (ag)	1827.6	(0.0, 0.0)	1841.6	(0.0, 0.0)	
sym Sn–Sn–H bend ω2 (ag)	479.8	(0.0, 0.0)	476.1	(0.0, 0.0)	
Sn–Sn str. ω3 (ag)	208.2	(0.0, 0.0)	152.4	(0.0, 0.0)	
anti-sym Sn–H str. ω4 (bu)	1840.3	(326.4, 100.0)	1850.6	(98.4, 100.0)	
anti-sym Sn–Sn–H bend ω5 (bu)	154.9	(14.1, 4.3)	123.7	(30.5, 31.0)	
H wag ω6 (au)	277.8i	(120.3, 37.0)	236.9i	(16.6, 16.9)	
a Bolded values indicate intensities greater than 400 km mol–1.

Table 10 Harmonic Vibrational Frequencies in cm–1, Intensities in km mol–1, and Relative Intensities for the MB-TS1, MB-TS2, and MB-TS3 Transition States Are Given at the CCSD(T)/TZ Level of Theory

 	description	neutral	cation	
MB-TS1	Sn2–H2 str. ω1 (a)	1784.7	(195.7, 100.0)	1817.8	(78.4, 34.7)	
Sn1–H1 str. ω2 (a)	1269.7	(127.3, 65.0)	1312.4	(166.1, 73.5)	
Sn2–H1 str. ω3 (a)	900.5	(151.4, 77.4)	849.1	(226.1, 100.0)	
H scissor ω4 (a)	578.6	(25.6, 13.1)	574.4	(7.8, 3.4)	
Sn–Sn str. ω5 (a)	210.9	(0.5, 0.3)	154.4	(0.2, 0.1)	
H wag ω6 (a)	191.9i	(19.6, 10.0)	128.7i	(12.6, 5.6)	
MB-TS2	Sn2–H2 str. ω1 (a′)	1934.4	(18.7, 44.1)	1952.4	(17.5, 29.9)	
Sn2–H1 str. ω2 (a′)	1753.5	(42.4, 100.0)	1719.4	(58.6, 100.0)	
H scissor ω3 (a′)	665.0	(41.3, 97.4)	646.4	(41.9, 71.5)	
Sn–Sn str. ω4 (a′)	239.9	(2.1, 5.0)	192.9	(1.7, 2.9)	
H wag ω5 (a″)	281.5	(0.4, 1.0)	220.9	(0.0, 0.0)	
H rock ω6 (a′)	263.9i	(2.0, 4.7)	327.5i	(2.5, 4.3)	
MB-TS3	Sn2–H2 str. ω1 (a′)	1825.9	(221.8, 100)	1871.4	(50.3, 100)	
Sn1–H1 str. ω2 (a′)	1730.6	(167.5, 75.5)	1847.3	(33.7, 67.0)	
H rock ω3 (a′)	486.8	(16.0, 7.2)	477.4	(0.4, 0.8)	
Sn–Sn str. ω4 (a′)	202.5	(0.2, 0.1)	170.7	(0.7, 1.4)	
H scissor ω5 (a′)	203.8i	(5.0, 2.3)	109.5i	(19.0, 37.8)	
H wag ω6 (a″)	76.0i	(26.2, 11.8)	189.6i	(11.0, 21.9)	

With the exception of the trans structures, the identification of minima and transition states agrees with previous studies of similar M2H2 molecules including Sn2H2. However, the planar trans structure was found to be a transition state with an imaginary mode, while the nonplanar trans structure was found to be a minima. This diverges from previous studies which identified the planar trans structure as the minima.18,19,23 The imaginary mode in the planar trans structure (228i cm–1, au) is a H-wagging mode indicating that the nearby minima are most likely not planar. Manually searching the potential energy surface at the CCSD(T)/DZ and CCSD(T)/TZ levels of theory revealed a slight decrease in energy, leading to the discovery of the nonplanar trans structure. However, FPA determined that these minima lie 1.74 kcal mol–1 higher in energy than the planar trans structure. The harmonic vibrational frequencies of the nonplanar trans structure do not contain any imaginary modes, suggesting that this structure does exist as a minimum. Further attempts at finding minima connecting to the planar trans transition state identified the butterfly as the corresponding minimum in both directions of the planar trans structure’s imaginary mode.

For most structures, there is excellent convergence between different basis set sizes; however, the cis cation is an exception to this observation. With the TZ basis set in Table 9, the cis cation contains a very low lying mode (19.1 cm–1). When the harmonic frequency calculations of different basis sets are compared, this mode becomes an imaginary mode as the basis set size increases (Table 11). Such a sensitivity to the basis set is a characteristic which has been shown for other isomers, particularly for the trans structure in Si2H2.18−20 In contrast, this low lying mode and convergence toward two imaginary modes are not observed in the neutral form of the cis structure. Instead, the neutral molecule shows excellent convergence toward its identity as a first-order saddle point.

Table 11 Harmonic Vibrational Frequencies in cm–1 for the Cis Cation Transition State Are Given at the CCSD(T)/DZ, CCSD(T)/TZ, and CCSD(T)/QZ Level of Theory

 	description	DZ	TZ	QZ	
cis	sym. Sn–H str. ω1 (a1)	1805.9	1806.9	1809.8	
sym. Sn–Sn–H bend ω2 (a1)	300.9	301.9	300.2	
Sn–Sn str. ω3 (a1)	95.1	99.0	99.6	
anti-sym Sn–H str. ω4 (b2)	76.1	19.1	74.4i	
anti-sym Sn–Sn–H bend ω5 (b2)	1792.4	1792.6	1795.2	
H scissor ω6 (a2)	266.2i	281.7i	286.4i	

Additionally, three monobridged transition states were evaluated because of their importance to the potential energy surface of Sn2H2 (Table 10). MB-TS1 and MB-TS2 were transition states, which agreed with the previous studies on similar molecules. MB-TS1 bridges the monobridged and butterfly minima, and MB-TS2 bridges the monobridged and vinylidene-like minima. MB-TS3, however, does not agree with previous research, where the structure now displays two imaginary modes. In smaller M2H2 molecules, a structure similar to MB-TS3 would bridge the monobridged and the trans minima, but the nonplanarity of the trans minimum does not allow for this pathway, and MB-TS3 does not appear as a first-order saddle point.

In the experimental analysis of the neutral species by Andrews and co-workers,28 they identified two peaks in their infrared spectrum that were associated with the butterfly structure of Sn2H2. They used the B3LYP/6-311++G**/SDD level of theory to assist in elucidating the nature of the vibrations. The first of these peaks was in a bright mode (913 cm–1). Wang and co-workers assigned this mode to an antisymmetric Sn–H–Sn stretch (970 cm–1, b2). Our analysis, however, predicts the b2 mode to lie higher in frequency (1237 cm–1) and to have a lower relative intensity (9.7). However, the symmetric Sn–H stretching mode (1044 cm–1, b1) lies closer in frequency to the observed vibration and has a greater relative intensity (100.0). The second peak identified was a much weaker vibration (1118 cm–1) which was assigned as the antisymmetric Sn–H–Sn stretching mode (1176 cm–1, b1). In contrast, our analysis identified the second antisymmetric mode (958 cm–1, a2) as having different symmetry and not being IR visible. The presence of two antisymmetric Sn–H–Sn stretching modes with different symmetries suggests a misprint in Wang and co-workers original paper, and according to the results of the present study, it would appear that the first brighter mode is the symmetric Sn–H stretching mode (1044 cm–1, b1) with an intensity of 418 km mol–1, and the second, weaker mode is the antisymmetric Sn–H–Sn streching mode (1244.5 cm–1, b2) with an intensity of 77 km mol–1.

NBO

Natural bond order (NBO) analysis was used to determine the orbitals, natural bond orders, and Wiberg bond index values for neutral and cation molecules (Table 12). Among each of the isomers, the cation Sn–Sn bond order decreases by roughly 0.5, further demonstrating that the electron lost in the cation is mostly being removed from the Sn–Sn bond. The Sn–H bond orders did not change significantly, where the largest difference using the Wiberg bond index was 0.09 in the Sn–H interaction in the cis isomer and the largest difference using natural bond orders was 0.23 in the planar trans structure. In the linear isomer, there was a H–H interaction with a 0.11 Wiberg bond index value, but this was not seen for the natural bond orders.

Table 12 Wiberg Bond Index Values Obtained from NBO 7.0 for the Butterfly, Monobridged, Vinylidene-Like, Nonplanar Trans, Planar Dibridged, MB-TS1, MB-TS2, MB-TS3, Planar Trans, Pertrans, Cis, and Linear Structures Which Were Optimized to the CCSD(T)/QZ Level of Theory

 	 	Wiberg	NBO	
 	 	neutral	cation	neutral	cation	
butterfly	Sn–Sn	1.11	0.64	1.27	0.62	
Sn–H	0.35	0.38	0.43	0.46	
H–H	0.00	0.00	0.00	0.00	
monobridged	Sn–Sn	1.82	1.13	2.05	1.50	
Sn1–H1	0.40	0.38	0.39	0.43	
Sn2–H1	0.52	0.48	0.47	0.45	
Sn2–H2	0.89	0.89	0.91	0.87	
H–H	0.00	0.00	0.06	0.00	
vinylidene-like	Sn–Sn	1.85	1.15	1.99	1.38	
Sn–H	0.92	0.91	0.96	0.93	
H–H	0.01	0.01	0.00	0.00	
nonplanar trans	Sn–Sn	2.17	- - -	2.18	- - -	
Sn–H	0.88	- - -	0.97	- - -	
H–H	0.00	- - -	0.00	- - -	
planar dibridged	Sn–Sn	1.25	0.72	1.27	0.62	
Sn–H	0.42	0.38	0.43	0.46	
H–H	0.05	0.04	0.00	0.00	
MB-1	Sn–Sn	1.29	0.89	1.96	1.27	
Sn1–H1	0.48	0.48	0.47	0.48	
Sn1–H2	0.04	0.04	0.00	0.00	
Sn2–H2	0.89	0.89	0.86	0.92	
Sn2–H1	0.40	0.34	0.41	0.43	
H1–H2	0.00	0.00	0.00	0.00	
MB-2	Sn–Sn	1.85	1.14	2.00	1.44	
Sn1–H1	0.06	0.06	0.00	0.00	
Sn1–H2	0.05	0.05	0.00	0.00	
Sn2–H2	0.91	0.92	0.95	0.93	
Sn2–H1	0.88	0.86	0.94	0.91	
H1–H2	0.00	0.00	0.00	0.00	
MB-3	Sn–Sn	1.84	1.33	1.90	1.48	
Sn1–H1	0.84	0.87	0.90	0.89	
Sn1–H2	0.05	0.05	0.00	0.00	
Sn2–H2	0.86	0.87	0.95	0.94	
Sn2–H1	0.08	0.06	0.00	0.00	
H1–H2	0.00	0.00	0.00	0.00	
planar trans	Sn–Sn	2.15	1.43	2.50	1.76	
Sn–H	0.88	0.87	0.75	0.98	
H–H	0.00	0.00	0.00	0.00	
perptrans	Sn–Sn	- - -	0.66	- - -	0.97	
Sn–H	- - -	0.84	- - -	0.99	
H–H	- - -	0.00	- - -	0.00	
cis	Sn–Sn	0.99	0.58	0.96	0.97	
Sn–H	0.93	0.84	0.98	0.98	
H–H	0.03	0.00	0.02	0.00	
linear	Sn–Sn	2.95	2.41	2.90	2.35	
Sn–H	0.98	0.94	0.95	0.93	
H–H	0.11	0.01	0.00	0.00	

The changes in the bond orders of the isomers between their neutral and cation forms may be correlated with the changes in geometries. As an electron is removed from each neutral structure, the Sn–Sn bond length increases and the bond order decreases, supporting the argument that the majority of the electron that is lost from the neutral species is removed from the vicinity of the Sn–Sn bond. This trend can also be observed in the comparison of the neutral and cation species of Si2H2.60

Additionally, the orbitals of the neutral and cationic species of Sn2H2 were investigated. All HOMO, LUMO, SOMO, bonding, and important interaction orbitals are shown in Supporting Information. Overall, the NBO orbital analysis agrees with the research of Frenking and co-workers59 for the neutral species, with the exception of the trans and monobridged structures. In the butterfly structure (Figure 7), there are a Sn–Sn single bond (Figure 7a), two Sn–H single bonds Figure 7b,c, two donor–acceptor bonds formed between an empty π orbital (Figure 7d,e), and a Sn–H bond on an adjacent Sn atom. This donor–acceptor interaction gives a notably large stabilizing second-order perturbation energy of 161 kcal mol–1 and 67 kcal mol–1 in the neutral and cationic species, respectively, resulting in the two bridging hydrogens. This is responsible for the unusual nonplanar butterfly structure where the hydrogens are tilted toward the adjacent Sn atom. The other Sn2H2 structures behave as discovered in the analysis of Lein et al.,59 except for the trans and monobridged structures.

Figure 7 Natural bonding orbitals obtained from NBO analysis of the CCSD(T)/QZ geometries of the butterfly cation and neutral minima: (a) Sn–Sn bonding orbital with primarily π character (HOMO/SOMO). (b,c) Degenerate Sn–H bonding orbitals. (d,e) Degenerate lowest unoccupied molecular orbitals (LUMO). Orbitals (b,d) and orbitals (c,e) have second-order perturbation interaction energies of 161 kcal mol–1 and 67 kcal mol–1 in the neutral and cation, respectively. The cation and neutral are represented in one image as their orbitals are qualitatively similar.

Unlike Lein et al.,59 this study found that the trans minima are not planar, containing a small torsion (τ = 169.9°). A planar trans structure does exist, but it was found to be a transition state according to its harmonic vibrational analysis. Beginning with the planar transition state, NBO analysis suggests that there are three bonding (Figure 8a–c) orbitals with no donor–acceptor-type interactions and a natural bond order of 2.50 in the neutral species indicating that resonance has a noteworthy impact on bonding. The neutral species contains two pairs of interacting orbitals: Figure 8c–f (103 kcal mol–1) and Figure 8d–g (87 kcal mol–1), and the HOMO (Figure 8e) has no strong interactions.

Figure 8 Natural bonding orbitals obtained from NBO analysis of the CCSD(T)/QZ geometry of the neutral planar trans transition state: (a,b) degenerate Sn–H bonding orbitals. (c) Sn–Sn bonding orbital with primarily σ character. (d) Sn–Sn bonding orbital with primarily π character. (e) HOMO Sn–Sn bonding orbital with primarily π character. (f) LUMO. (g) Important bonding interaction orbital. Orbitals (c,f) have a second-order perturbation interaction energy of 103 kcal mol–1, and orbitals (d,g) have a second-order perturbation interaction energy of 87 kcal mol–1.

Unlike other Sn2H2 structures which have similar natural bonding orbitals between the neutral and cation, the planar trans cation has qualitatively different orbitals compared to its neutral counterpart (Figure 9). The cation contains two Sn–H single bonding orbitals (Figure 9c,d), no Sn–Sn bonding orbitals with the σ character, and only one Sn–Sn bonding orbital with the π character (Figure 9e). Additionally, the interacting orbitals differ with two pairs of degenerate interacting orbitals increasing the overall bond order: Figure 9a–g and Figure 9b–h (45.60 kcal mol–1), and the HOMO (Figure 9f) has no strong interactions. The cation planar trans structure fits the qualitative picture presented by Lein et al.59

Figure 9 Natural bonding orbitals obtained from NBO analysis of the CCSD(T)/QZ geometry of the cation planar trans transition state: (a,b) degenerate Sn lone pair orbitals. (c,d) Degenerate Sn–H bonding orbitals. (e) HOMO Sn–Sn bonding orbital with primarily π character. (f) LUMO. (g,h) Important bonding interaction orbitals. Orbitals (a,g) and orbitals (b,h) have a second-order perturbation interaction energy of 46 kcal mol–1.

The lack of a planar trans minimum in Sn2H2 instigated a search for a minimum of a similar geometry: the nonplanar trans minimum (Figure 10). In this structure, there is only one bonding orbital between the Sn atoms (Figure 10e) and there are two Sn–H single bonding orbitals (Figure 10c,d) and two donor–acceptor interactions between a lone pair and an empty π orbital on adjacent Sn atoms with a second-order perturbation energy of 93 kcal mol–1: Figure 10a–f and Figure 10b–g. The bonding of the trans minima in this study is more similar to Lein et al.59 description of the planar trans structure and is qualitatively similar to the planar trans cation in its orbital construction.

Figure 10 Natural bonding orbitals obtained from NBO analysis of the CCSD(T)/QZ geometry of the neutral nonplanar trans minimum: (a,b) degenerate Sn lone pair orbitals. (c,d) Degenerate Sn–H bonding orbitals. (e) HOMO Sn–Sn bonding orbital with primarily π character. (f) LUMO. (g,h) Important bonding interaction orbitals. Orbitals (a,g) and orbitals (b,h) have a second-order perturbation interaction energy of 93 kcal mol–1.

The nonplanar geometry of the trans minima can also be partially explained by the NBO analysis. Figure 10 shows the bonding orbital as well as the four orbitals involved in the donor–acceptor interactions. Figure 10e shows the natural bonding orbital between the Sn atoms; Figure 10a,b shows the lone pairs, while Figure 10f,g shows the lone valence natural bond orbitals. The natural bonding orbital in Figure 10e contains an electron density that is primarily on one side of the molecule. Through Coloumbic repulsion, this seems to shift the lone pair orbitals slightly to the side, breaking the plane of the molecule.

For the monobridged structure, Lein et al.59 suggested that there was a donor–acceptor interaction between a lone pair on a Sn atom and a empty valence orbital on the adjacent Sn atom. However, the NBO analysis shows two Sn–H bonds (Figure 11a,b) and two bonding orbitals between the Sn atoms (Figure 11c,d). There is not a lone pair with significant interactions with any other orbitals, but one of the Sn–H bonds interacts with a lone valence orbital in the adjacent Sn atom, leading to the bridging hydrogen: Figure 11a–e. The HOMO (Figure 11f) has no strong interactions.

Figure 11 Natural bonding orbitals obtained from NBO analysis of the CCSD(T)/QZ geometry of the neutral and cation monobridged minimum: (a) Sn-bridging H-bonding orbital. (b) Sn-terminal H-bonding orbital. (c) Sn–Sn bonding orbital with the σ character. (d) HOMO/SOMO Sn–Sn bonding orbital with primarily π character. (e) Unoccupied interacting orbital. (f) LUMO. Orbitals (a,e) have second-order perturbation interaction energies of 160 kcal mol–1 and 73 kcal mol–1 for the neutral and cation, respectively. The cation and neutral are represented in one image as their orbitals are qualitatively similar.

Further NBO analysis demonstrates that the lost electron between the neutral and cationic structures always originates from the Sn–Sn bond. In each neutral molecule, the HOMO is always a Sn–Sn bonding orbital of either σ or π character, and when molecules lose an electron, the singly occupied molecular orbital is always the same HOMO Sn–Sn bonding orbital. Additionally, for all molecules which contain a donor–acceptor interaction, the second-order perturbation energy of the cation is much smaller than that of the neutral form. The strength of the donor–acceptor interactions decreases as an electron leaves the system, partially destabilizing the molecules.

Dipole Moments and Partial Charges

Center-of-mass dipole moments and partial charges were calculated for each molecule based on the QZ geometry with the exception of the monobridged transition states, which were only optimized with the TZ basis set. Partial charges, calculated from NBO analysis, are given in Table 13, dipole moments for the minima are presented in Figure 12, and dipole moments of transition states are included in Supporting Information.

Table 13 Partial Charges from NBO Analyses of the Butterfly, Monobridged, Vinylidene-Like, Nonplanar Trans, Planar Dibridged, MB-TS1, MB-TS2, MB-TS3, Planar Trans, Perptrans, Cis, and Linear Structures along the Sn2H2 Potential Energy Surface Calculated from CCSD(T)/QZ Geometries for All Structures except MB-TS1, MB-TS2, and MB-TS3 Which Are Calculated from CCSD(T)/TZ Geometries

structure	 	neutral	cation	structure	 	neutral	cation	
butterfly	Sn1	+0.36	+0.93	monobridged	Sn1	+0.29	+0.83	
Sn2	+0.36	+0.93	Sn2	+0.24	+0.75	
H1	–0.36	–0.43	H1	–0.30	–0.38	
H2	–0.36	–0.43	H2	–0.22	–0.20	
vinylidene-like	Sn1	+0.20	+0.69	nonplanar trans	Sn1	+0.28	 	
Sn2	+0.23	+0.69	Sn2	+0.28	 	
H1	–0.22	–0.19	H1	–0.28	 	
H2	–0.22	–0.19	H2	–0.28	 	
planar dibridged	Sn1	+0.36	+0.96	MB-TS1	Sn1	+0.45	+0.97	
Sn2	+0.36	+0.96	Sn2	+0.18	+0.72	
H1	–0.36	–0.46	H1	–0.36	–0.43	
H2	–0.36	–0.46	H2	–0.26	–0.27	
MB-TS2	Sn1	+0.28	+0.77	MB-TS3	Sn1	+0.21	+0.81	
Sn2	+0.16	+0.66	Sn2	+0.36	+0.73	
H1	–0.25	–0.28	H1	–0.29	–0.28	
H2	–0.19	–0.16	H2	–0.27	–0.25	
planar trans	Sn1	+0.27	+0.76	perptrans	Sn1	 	+0.87	
Sn2	+0.27	+0.76	Sn2	 	+0.87	
H1	–0.27	–0.26	H1	 	–0.37	
H2	–0.27	–0.26	H2	 	–0.37	
cis	Sn1	+0.37	+0.89	linear	Sn1	+0.11	+0.57	
Sn2	+0.37	+0.89	Sn2	+0.11	+0.57	
H1	–0.37	–0.39	H1	–0.11	–0.07	
H2	–0.37	–0.39	H2	–0.11	–0.07	

Figure 12 Relative center-of-mass dipole moments for the butterfly neutral, butterfly cation, monobridged neutral, monobridged cation, vinylidene-like neutral, vinylidene-like cation, and nonplanar trans neutral calculated from CCSD(T)/QZ geometries.

Sn atoms are found to be positively partially charged, while the H atoms are negatively partially charged in all neutral and cation structures. As the neutral structures lose an electron, partial charges shift more dramatically on Sn atoms compared to those on H atoms. Partial charges on Sn atoms shift as much as 0.6 in the case of the butterfly minimum, while the partial charge of H atoms changes by 0.1 at most in the case of the planar dibridged transition state. Among the minima, the butterfly structure demonstrates the most dramatic change in the partial charges between the neutral and cation forms.

The dipole moments of the minima reveal that losing an electron from the molecule typically decreases the overall dipole moment (Figure 12). The butterfly’s dipole moment nearly disappears, decreasing from −0.86 to −0.02 D; the monobridged dipole moment decreases from 0.52 to 0.17 D; the vinylidene-like dipole moment increases slightly from 0.84 to 0.91 D. The increases in the dipole moment can also be observed from the partial charges, where the vinylidene-like minimum is the only minimum whose partial charge on both H atoms becomes more positive.

Conclusions

The geometries, relative energies, vibrational frequencies, and bond orders have been presented for many structures of Sn2H2 and Sn2H2+ in this study. The geometries for the butterfly, monobridged, vinylidene-like, nonplanar trans, planar dibridged, perptrans, planar trans, cis, and linear were found using the CCSD(T) method with a cc-pwCVQZ-PP basis set having a 28-electron effective core potential. Additionally, three monobridged-like transition states have been identified using the CCSD(T) method with a cc-pwCVTZ-PP basis set. The butterfly isomer lies lowest in energy on the potential energy surfaces of both the neutral and cation species of Sn2H2. Energy minima stationary points present in other group 14 metal hydrides, M2H2 (M = Si, Ge, Sn, and Pb) were confirmed, such as the monobridged, vinylidene-like, and planar trans isomers, but the planar trans isomer was identified to be a transition state disagreeing with former research. Instead, through rigorous coupled cluster calculations, a newly identified nonplanar trans minimum was determined to lie along the potential energy surface, revealing a PES of Sn2H2 differing from the one provided by Nagase et al.25 Focal point analysis provided energies approaching the FCI and CBS with a rapid convergence. Harmonic vibrational frequencies were also obtained with the CCSD(T) method with a cc-pwVCTZ-PP basis set. Our neutral species predictions were compared to the experimental assignments of Wang and co-workers,28 and some discrepancies were found.

Furthermore, the neutral and cation structures were examined closely to identify differences between their electronic structures and to provide theoretical data to assist in the detection of the cation. The primary geometric differences were related to the Sn–Sn bonds, where bond lengths and bond orders changed the most in geometry and electron occupation. The bond lengths typically increased in the cation, and bond orders decreased by roughly 0.5 among all structures. The changing geometries and differences in electronic occupation indicate that the lost electron in the Sn2H2 cation originates from the Sn–Sn bond. Additionally, harmonic vibrational analysis of the cation revealed vibrational modes and intensities, which may assist in the laboratory detection of the cation. Generally, our analysis of the neutral and cation Sn2H2 highlights the importance of studying the electronic structure with rigorous, high-level theory.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.4c03220.Cartesian coordinates, numeric center-of-mass dipole moments, focal point approach tables, and natural bond orbitals (PDF)

Supplementary Material

jp4c03220_si_001.pdf

The authors declare no competing financial interest.

Acknowledgments

This research was supported by the U.S. Department of Energy, Basic Energy Sciences, Division of Chemistry, Computational and Theoretical Chemistry (CTC) Program, under contract DE-SC0018412.
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References

Dapsens Y. ; Mondelli P. ; Pérez-Ramírez C. J. Design of Lewis-acid centres in zeolitic matrices for the conversion of renewables. Chem. Soc. Rev. 2015, 44 , 7025–7043. 10.1039/C5CS00028A.25917850
Osmundsen C. M. ; Holm M. S. ; Dahl S. ; Taarning E. Tin-containing silicates: structure–activity relations. Proc. R. Soc. 2012, 468 , 2000–2016. 10.1098/rspa.2012.0047.
Cortright R. D. ; Hill J. M. ; Dumesic J. A. Selective dehydrogenation of isobutane over supported Pt/Sn catalysts. Catal. Today 2000, 55 , 213–223. 10.1016/S0920-5861(99)00249-7.
Liao B. ; Lei Y. Q. ; Chen L. X. ; Lu G. L. ; Pan H. G. ; Wang Q. D. A study on the structure and electrochemical properties of La2Mg(Ni0.95M0.05)9 (M = Co, Mn, Fe, Al, Cu, Sn) hydrogen storage electrode alloys. J. Alloys Compd. 2004, 376 , 186–195. 10.1016/j.jallcom.2003.12.011.
Zinatloo-Ajabshir S. ; Morassaei M. S. ; Amiri O. ; Salavati-Niasari M. ; Foong L. K. Nd2Sn2O7 nanostructures: Green synthesis and characterization using date palm extract, a potential electrochemical hydrogen storage material. Ceram. Int. 2020, 46 , 17186–17196. 10.1016/j.ceramint.2020.03.014.
Anbarasu S. ; Muthukumar P. ; Mishra S. C. Thermal modeling of LmNi4.91Sn0.15 based solid state hydrogen storage device with embedded cooling tubes. Int. J. Hydrogen Energy 2014, 39 , 15549–15562. 10.1016/j.ijhydene.2014.07.088.
Linder M. ; Mertz R. ; Laurien E. Experimental analysis of fast metal hydride reaction bed dynamics. Int. J. Hydrogen Energy 2010, 35 , 8755–8761. 10.1016/j.ijhydene.2010.05.023.
Ratnakumar B. V. ; Witham C. ; Bowman R. C. ; Hightower A. ; Fultz B. Electrochemical Studies on LaNi5 - x Sn x Metal Hydride Alloys. J. Electrochem. Soc. 1996, 143 , 2578–2584. 10.1149/1.1837050.
Todorova S. ; Abrashev B. ; Rangelova V. ; Mihaylov L. ; Vassileva E. ; Petrov K. ; Spassov T. Hydrogen Gas Phase and Electrochemical Hydriding of LaNi5-xMx (M = Sn, Co, Al) Alloys. Materials 2021, 14 , 14 10.3390/ma14010014.
Deng H. ; Zhuang Y. ; Liu J. ; Guo J. ; Lu J. ; Yan J. Electrochemical performance of LaNi5–xSnx alloys. J. Alloys Compd. 2004, 376 , 211–214. 10.1016/j.jallcom.2003.12.026.
Iosub V. ; Latroche M. ; Joubert J. ; Percheron-Guegan A. Optimisation of MmNi5-xSnx (Mm = La, Ce, Nd and Pr, 0.27. Int. J. Hydrogen Energy 2006, 31 , 101–108. 10.1016/j.ijhydene.2005.02.004.
Borzone E. M. ; Blanco M. V. ; Baruj A. ; Meyer G. O. Stability of LaNi5-xSnx cycled in hydrogen. Int. J. Hydrogen Energy 2014, 39 , 8791–8796. 10.1016/j.ijhydene.2013.12.031.
Hong F. ; Shan P. F. ; Yang L. X. ; Yue B. B. ; Yang P. T. ; Liu Z. Y. ; Sun J. P. ; Dai J. H. ; Yu H. ; Yin Y. Y. ; et al. Possible superconductivity at 70 K in tin hydride SnHx under high pressure. Mater. Today Phys. 2022, 22 , 100596 10.1016/j.mtphys.2021.100596.
Obara S. ; Kitaura K. ; Morokuma K. A comparative study ofab-initio effective core potential and all-electron calculations for molecular structures and transition states. Theor. Chim. Acta 1981, 60 , 227 10.1007/BF00553746.
Snyder L. C. ; Wasserman Z. Molecular orbital calculation of the bond lengths and photoelectron spectrum of disilane. Chem. Phys. Lett. 1977, 51 , 349–351. 10.1016/0009-2614(77)80418-1.
Snyder L. C. ; Wasserman Z. R. ; Moskowitz J. W. Stability and bonding of disilyne and its isomers: A generalized valence bond-effective potential study. Int. J. Quantum Chem. 1982, 21 , 565–579. 10.1002/qua.560210305.
Kawai F. ; Noro T. ; Murakami A. ; Ohno K. Comparison of the equilibrium geometry of acetylene (C2H2disilyne (Si2H2. Chem. Phys. Lett. 1982, 92 , 479 10.1016/0009-2614(82)87044-9.
Lischka H. ; Koehler H. J. Ab initio investigation on the lowest singlet and triplet state of disilyne (Si2H2). J. Am. Chem. Soc. 1983, 105 , 6646–6649. 10.1021/ja00360a016.
Colegrove B. T. ; Schaefer H. F. Disilyne (Si2H2) revisited. J. Phys. Chem. 1990, 94 , 5593–5602. 10.1021/j100377a036.
Grev R. S. ; Schaefer H. F. The remarkable monobridged structure of Si2H2. J. Chem. Phys. 1992, 97 , 7990–7998. 10.1063/1.463422.
Hühn M. ; Amos R. D. ; Kobayashi R. ; Handy N. C. Structure and properties of disilyne. J. Chem. Phys. 1993, 98 , 7107–7112. 10.1063/1.464754.
Cordonnier M. ; Bogey M. ; Demuynck C. ; Destombes J.-L. Nonclassical structures in silicon-containing molecules: The monobridged isomer of Si2H2. J. Chem. Phys. 1992, 97 , 7984–7989. 10.1063/1.463421.
Grev R. S. ; Deleeuw B. J. ; Schaefer H. F. Germanium-germanium multiple bonds: The singlet electronic ground state of Ge2H2. Chem. Phys. Lett. 1990, 165 , 257–264. 10.1016/0009-2614(90)85439-J.
Wang X. ; Andrews L. ; Kushto G. P. Infrared Spectra of the Novel Ge2H2 and Ge2H4 Species and the Reactive GeH1,2,3 Intermediates in Solid Neon, Deuterium and Argon. J. Phys. Chem. A 2002, 106 , 5809–5816. 10.1021/jp020219v.
Nagase S. ; Kobayashi K. ; Takagi N. Triple bonds between heavier Group 14 elements. A theoretical approach. J. Organomet. Chem. 2000, 611 , 264–271. 10.1016/S0022-328X(00)00489-7.
Shimizu T. Theoretical Investigations of the Acetylene Analogues of Group 14 Elements E 2 × 2; Philipps-Universität Marburg, 2010.
Wang X. ; Andrews L. Infrared Spectra of Group 14 Hydrides in Solid Hydrogen: Experimental Observation of PbH4, Pb2H2, and Pb2H4. J. Am. Chem. Soc. 2003, 125 , 6581–6587. 10.1021/ja029862l.12785799
Wang X. ; Andrews L. ; Chertihin G. V. ; Souter P. F. Infrared Spectra of the Novel Sn2H2 Species and the Reactive SnH1,2,3 and PbH1,2,3 Intermediates in Solid Neon, Deuterium, and Argon. J. Phys. Chem. A 2002, 106 , 6302–6308. 10.1021/jp025763i.
Mull H. F. ; Franke P. R. ; Sargent C. ; Douberly G. E. ; Turney J. M. ; Schaefer H. F. III Four isomers of In2H2: A careful comparison between theory and experiment. Mol. Phys. 2021, 119 , e1979675 10.1080/00268976.2021.1979675.
Roothaan C. C. J. New Developments in Molecular Orbital Theory. Rev. Mod. Phys. 1951, 23 , 69–89. 10.1103/RevModPhys.23.69.
Roothaan C. C. J. Self-Consistent Field Theory for Open Shells of Electronic Systems. Rev. Mod. Phys. 1960, 32 , 179–185. 10.1103/RevModPhys.32.179.
Pople J. A. ; Nesbet R. K. Self-Consistent Orbitals for Radicals. J. Chem. Phys. 2004, 22 , 571–572. 10.1063/1.1740120.
Pritchard B. P. ; Altarawy D. ; Didier B. ; Gibson T. D. ; Windus T. L. New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community. J. Chem. Inf. Model 2019, 59 , 4814–4820. 10.1021/acs.jcim.9b00725.31600445
Schuchardt K. L. ; Didier B. T. ; Elsethagen T. ; Sun L. ; Gurumoorthi V. ; Chase J. ; Li J. ; Windus T. L. Basis Set Exchange: A Community Database for Computational Sciences. J. Chem. Inf. Model 2007, 47 , 1045–1052. 10.1021/ci600510j.17428029
Feller D. The role of databases in support of computational chemistry calculations. J. Comput. Chem. 1996, 17 , 1571–1586. 10.1002/(SICI)1096-987X(199610)17:13<1571:AID-JCC9>3.0.CO;2-P.
Stanton J. F. ; Gauss J. ; Cheng L. ; Harding M. E. ; Matthews D. A. ; Szalay P. G. CFOUR, Coupled-Cluster techniques for Computational Chemistry, a quantum-chemical program package. http://www.cfour.de.
Werner H.-J. ; Knowles P. J. ; Knizia G. ; Manby F. R. ; Schütz M. Molpro: A general-purpose quantum chemistry program package. WIREs Comput. Mol. Sci. 2012, 2 , 242–253. 10.1002/wcms.82.
Werner H.-J. ; Knowles P. J. ; Manby F. R. ; Black J. A. ; Doll K. ; Heßelmann A. ; Kats D. ; Köhn A. ; Korona T. ; Kreplin D. A. ; et al. The Molpro quantum chemistry package. J. Chem. Phys. 2020, 152 , 144107 10.1063/5.0005081.32295355
Werner H.-J. ; Knowles P. J. ; Celani P. ; Györffy W. ; Hesselmann A. ; Kats D. ; Knizia G. ; Köhn A. ; Korona T. ; Kreplin D. MOLPRO, version 2023, a package of ab initio programs, https://www.molpro.net accessed August 1, 2022.
Smith D. G. ; Burns L. A. ; Simmonett A. C. ; Parrish R. M. ; Schieber M. C. ; Galvelis R. ; Kraus P. ; Kruse H. ; Di Remigio R. ; Alenaizan A. ; et al. PSI4 1.4: Open-source software for high-throughput quantum chemistry. J. Chem. Phys. 2020, 152 , 184108 10.1063/5.0006002.32414239
Kállay M. ; Nagy P. R. ; Mester D. ; Rolik Z. ; Samu G. ; Csontos J. ; Csóka J. ; Szabó P. B. ; GyeviNagy L. ; Hégely B. ; et al. The MRCC program system: Accurate quantum chemistry from water to proteins. J. Chem. Phys. 2020, 152 , 074107 10.1063/1.5142048.32087669
Glendening E. D. ; Badenhoop J. K. ; Reed A. E. ; Carpenter J. E. ; Bohmann J. A. ; Morales C. M. ; Karafiloglou P. ; Landis C. R. ; Weinhold F. Nature Bond Articles, https://nbo7.chem.wisc.edu/index.htm accessed July 11, 2023.
Čížek J. On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods. J. Chem. Phys. 1966, 45 , 4256–4266. 10.1063/1.1727484.
Purvis G. D. III ; Bartlett R. J. A full coupled-cluster singles and doubles model: The inclusion of disconnected triples. J. Chem. Phys. 1982, 76 , 1910–1918. 10.1063/1.443164.
Raghavachari K. ; Trucks G. W. ; Pople J. A. ; Head-Gordon M. A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 1989, 157 , 479–483. 10.1016/S0009-2614(89)87395-6.
Peterson K. A. Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13–15 elements. J. Chem. Phys. 2003, 119 , 11099–11112. 10.1063/1.1622923.
Dunning T. H. Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90 (2 ), 1007–1023. 10.1063/1.456153.
Metz B. ; Stoll H. ; Dolg M. Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-d main group elements: Application to PbH and PbO. J. Chem. Phys. 2000, 113 , 2563–2569. 10.1063/1.1305880.
Wiberg K. B. Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 1968, 24 , 1083–1096. 10.1016/0040-4020(68)88057-3.
Harper L. K. ; Shoaf A. L. ; Bayse C. A. Predicting Trigger Bonds in Explosive Materials through Wiberg Bond Index Analysis. ChemPhyschem 2015, 16 , 3886–3892. 10.1002/cphc.201500773.26458868
Mayer I. Bond order and valence indices: A personal account. J. Comput. Chem. 2007, 28 , 204–221. 10.1002/jcc.20494.17066501
Császár A. G. ; Tarczay G. ; Leininger M. L. ; Polyansky O. L. ; Tennyson J. ; Allen W. D. Spectroscopy from Space, Springer Science & Business Media; Kluwer, Dordrecht, The Netherlands, 2001. pp 317.
Császár A. G. ; Allen W. D. ; Schaefer H. F. III In pursuit of the ab initio limit for conformational energy prototypes. J. Chem. Phys. 1998, 108 , 9751–9764. 10.1063/1.476449.
East A. L. L. ; Allen W. D. The heat of formation of NCO. J. Chem. Phys. 1993, 99 , 4638–4650. 10.1063/1.466062.
Gonzales J. M. ; Allen W. D. ; Schaefer H. F. Model Identity SN2 Reactions CH3X + X- (X = F, Cl, CN, OH, SH, NH2, PH2): Marcus Theory Analyzed. J. Phys. Chem. A 2005, 109 , 10613–10628. 10.1021/jp054734f.16834318
Feller D. ; Peterson K. A. ; Crawford T. D. Sources of error in electronic structure calculations on small chemical systems. J. Chem. Phys. 2006, 124 , 054107 10.1063/1.2137323.16468851
Helgaker T. ; Klopper W. ; Koch H. ; Noga J. Basis-set convergence of correlated calculations on water. J. Chem. Phys. 1997, 106 , 9639–9646. 10.1063/1.473863.
Stanton J. F. ; Gauss J. Analytic energy derivatives for ionized states described by the equation-of-motion coupled cluster method. J. Chem. Phys. 1994, 101 , 8938 10.1063/1.468022.
Lein M. ; Krapp A. ; Frenking G. Why Do the Heavy-Atom Analogues of Acetylene E2H2 (E = Si-Pb) Exhibit Unusual Structures?. J. Am. Chem. Soc. 2005, 127 , 6290–6299. 10.1021/ja042295c.15853336
Schueller K. M. ; Mull H. F. ; Turney J. T. ; Schaefer H. F. III Butterfly, Vinylidene-Like, Monobridged and Trans Structures of Si2H2+: Comparison to the Well-Characterized Neutral Si2H2. Isr. J. Chem. 2023, 63 , e202300033 10.1002/ijch.202300033.
Dutta A. K. ; Vaval N. ; Pal S. EOMIP-CCSD(2)*: An Efficient Method for the Calculation of Ionization Potentials. J. Chem. Theory Comput. 2015, 11 , 2461 10.1021/ct500927h.26575546
