Matrix Infrared Spectroscopic and Theoretical Studies for Products of

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Matrix Infrared Spectroscopic and Theoretical Studies for Products of the Reactions of Pb with Ethane and Halomethanes Han-Gook Cho, and Lester Andrews J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08505 • Publication Date (Web): 24 Oct 2018 Downloaded from http://pubs.acs.org on November 1, 2018

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Matrix Infrared Spectroscopic and Theoretical Studies for the Products of Lead Atom Reactions with Ethane and Halomethanes Han-Gook Choa,b and Lester Andrews*,b aDepartment

of Chemistry, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon,

22012, South Korea bDepartment

of Chemistry, University of Virginia, P. O. Box 400319, Charlottesville, Virginia

22904-4319, United States

S

Supporting Information

ABSTRACT: The insertion products of laser-ablated Pb atom reactions with ethane and mono-, di-, tri-, and tetrahalomethanes in excess argon were prepared and identified from their matrix infrared spectra on the basis of DFT computed frequencies and observed isotopic shifts. Unlike the lighter elements in group 14, the heaviest member lead exists primarily in the oxidation state 2+ using 6p orbitals in reaction products due to relativistic contraction of the 6s orbital. The C-Pb-X (X = H, F, Cl) bond is close to a right angle, indicating that Pb contributes mostly p-character to the C-Pb and Pb-X bonds. The lead reaction product with ethane is CH3CH2-Pb-H. The lower energy product in the CH2FCl reaction is CH2F-PbCl, which is photo-isomerized to CH2Cl-PbF. A lead methylidene (CCl2-PbCl2) was identified only in reactions with CCl4. The relatively small energy difference between the insertion and methylidene products in the tetrachloride system

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allows photochemical conversion from the insertion product to the unusual 3+ Pb oxidation-state methylidene. In this case Pb uses three p orbitals in bonding and C is sp2 hybridized leaving spin paired but not bonding by symmetry single electrons in the C 2p orbital perpendicular to the CCl2 plane and in the Pb 6s orbital. More often lead uses 6p orbitals in bonding due to the high electronic promotion energy for 6s electrons.

INTRODUCTION Previous studies have shown that silicon produces CX2=SiX2 and CX-SiX3 (X = H or halogen) as well as the insertion complexes (CX3-SiX) in direct reactions of Si atoms with methane and halomethanes or C atoms with SiH4.1-6 These products are comparable to the high oxidation-state complexes of transition-metals, which are similarly produced and investigated in a series of recent studies.7,8 They resemble the much larger complexes, and their smaller sizes allow higher level theoretical investigation of their electronic structures and reaction paths. However, unlike transition-metal methylidynes (CX≡MX3),7,8 the Si analogues possess a C-Si single bond due to its sp3 hybridization like C.7 As a result, the Si higher oxidation-state complexes are difficult to produce unless halogenated.3-6 Halogenation generally stabilizes higher oxidation-state products.7,8 Lead, the heaviest group 14 element, has been widely used in human history mainly due to its high malleability, ductility, and corrosion resistance for plumbing, table wares, bullets, printing type, white paints, solders, batteries, and fuel additives.9,10 It shows normally two oxidation states the more common 2+ and the relatively rare 4+ unlike lighter group 14 elements, which usually make four chemical bonds.9-14 The difference is

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attributable to relativistic effects giving stronger contraction of the lead 6s orbital than the 6p orbitals,15 leading to a relatively large difference in the electronegativity of Pb(II) 1.87 and that of Pb(IV) 2.33. This effect is, however, less important in organolead compounds where lead is predominantly tetravalent (e.g. Et4Pb) while few organolead compounds are known to date.11,12 Our previous investigations have shown that CH3-PbH is produced in Pb reactions with CH4 and lead oxides including PbO and linear PbO2 with O2.16,17 In the latter case the strong OPbO band at 765 cm-1 in solid argon is 18 times more intense than the PbO band at 711 cm-1 although the calculated infrared intensities are nearly the same and the insertion reaction requires excited Pb atoms that are produced in the laser ablation experiment.17 Therefore, it is an intriguing question whether or not lead generates high oxidationstate complexes (CX2=PbX2 and CX-PbX3) as well as insertion products (CX3-PbX) in direct reactions with small alkanes and halomethanes like the light group 14 metals and most transition-metals.1-8 In this paper, we report the observation of small molecules produced in direct reactions of laser-ablated Pb atoms with ethane and ten halomethanes. The identified products indicate that electronic promotion needed for formation of more chemical bonds is more difficult than found for the lighter group 14 elements, resulting in a lower preference for higher oxidation-state complexes. These new lead compounds have unique structures reflecting their electronic properties.

EXPERIMENTAL AND COMPUTATIONAL METHODS

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The reactions of laser-ablated Pb atoms (Johnson-Matthey) with a number of small molecules including C2H6, CH3F (Matheson), CD3F, CD2F2. CD2Cl2, CDF3 (synthesized in this lab18,19), CHF3 (PCR Research), CH2F2, CH2FCl, 13CH2Cl2, CF4, CF3Cl, CF2Cl2, CFCl3, (Dupont), CH2Cl2, CCl4 (Fisher), and C2D6, 13CH3F (99% enriched), 13CCl4 (90% enriched) (MSD Isotopes) have been investigated diluted in argon while freezing these reagents on a CsI window at 4 K using a closed-cycle refrigerator (Sumitomo). These methods have been described in more detail earlier.20,21 Reagent gas mixtures were diluted to 0.2–0.7% in argon (Matheson). After reaction, infrared spectra were recorded at a resolution of 0.5 cm–1 using a Nicolet 750 spectrometer with a liquid nitrogen cooled MCT-B detector. Samples were treated by warming and re-cooling (annealing), and irradiated by a mercury arc (175 W, outer globe removed) for 20 min periods also using several optical filters. Density functional theory (DFT) calculations were done using the Gaussian 09 program system,22 the B3LYP density functional,23-24 and the 6-311++G(3df,3pd) basis sets25 for H, C, F, Cl, and the SDD pseudo potential and basis set for Pb26,27 to provide guides for expected vibrational frequencies of reaction products. The optimized geometries were confirmed by vibrational analysis. Additional BPW9128-29 calculations with the same basis sets were performed to compliment the B3LYP results. The vibrational frequencies were calculated analytically, and no scale factor was used in the presentation of calculated frequencies. Zero-point energy is added to the electronic energy in the calculation of energy for a metal complex. NBO analyses30 were also done at the same level of theory for the optimized structures to investigate the bonding properties of several products.

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EXPERIMENTAL RESULTS AND DISCUSSION The matrix IR spectra, frequency, structure, and energy calculations are reported below for the products of laser ablated lead atom reactions with ethane and ten halomethanes in argon matrixes. The new observed frequencies are listed in Tables 1-4, and the spectral variations upon sample photolysis and annealing as well as the product structures are shown in Figures 1-15. The laser ablation process also provides a plasma plume back along the laser beam, and this radiation is responsible for photodissociation chemistry of the precursor in the condensing matrix sample. This means that common bands will be observed for each precursor regardless of the metal ablated. The new bands reported here are lead dependent and thus not observed with any other laser ablated metal. Pb + C2H6. Shown in Figure 1 are the IR spectra from reactions of laser-ablated Pb atoms with C2H6 and C2D6. In addition laser plume photodissociation of H gives rise to the C2H5 radical (540 cm-1) in all of our metal experiments with ethane.31 The product absorptions marked “i” (i for insertion) were observed in the original deposition spectrum, and they increased on annealing to 20 and 30 K, disappeared on photolysis with λ > 220 nm, and recovered slightly on further annealing to 35 K. The i absorption at 1513.4 cm-1 (with a matrix trapping site absorption at 1508.5 cm-1) shifted to 1086.0 cm-1 (with a site absorption at 1081.5 cm-1) on C2D6 substitution (H/D ratio 1.3936). Annealing to 30 K increased the former band more than the latter band. These bands are near the observed values of 1505.0, 1487.7, and 1472.5 cm-1 for CH3-PbH and 1097.6, 1065.5, and 1055.5 cm-1 for CD3-PbD (H/D ratio 1.3945).16 They may also be compared with 1541.6, 1534.6,

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and 1532.7 cm-1 and 1106.4, 1100.6, and 1099.3 cm-1 (H/D ratio 1.393) observed for the PbH2 and PbD2 molecules.32,33 On the basis of these previous experimental results and B3LYP calculated harmonic values of 1547.7 and 1097.4 cm-1 (H/D ratio 1.410, 2.3 and 1.0% higher, respectively, than the observed frequencies, we assign the i absorptions to the Pb-H stretching mode of CH3CH2-PbH and the Pb-D stretching mode for CD3CD2-PbD. The high H/D ratio 1.3936 is characteristic of the H vibration with a very heavy metal: even the Sn-H vibration for CH3-SnH has a lower H/D ratio 1.3916 indicating more metal involvement with the Sn-H stretching mode than with the Pb-H counterpart.16 The higher difference between harmonic calculated and anharmonic observed frequencies for the Pb-H mode is that the Pb-H value is more anharmonic than the Pb-D vibration. The other vibrational bands of the insertion product are too weak to observe here (Table S1).

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Figure 1. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with C2H6 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% C2H6 in Ar co-deposited for 1 h. (b,c,d,e) after annealing to 20 K, to 30 K, photolysis with λ > 220 nm, and annealing to 35 K, respectively. (f) Pb + 0.5% C2D6 in Ar co-deposited for 1 h. (g-j) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing at 35 K. i stands for insertion product, p for ethane precursor absorption.

The ethylidene, metallacyclopropane, and ethylidyne complexes, which were reported in previous studies of transition-metal reactions with ethane,7,8 were not detected in this study. The Pb insertion complex (singlet electronic state, Pb oxidation state 2+) is

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the most stable among the plausible products from reactions with ethane: CH3CH2-PbH, CH3CH=PbH2, (CH2)2-PbH2 and CH3C-PbH3 are -1.0, +40.1, +190.5, and +380.9 kJ/mol in energy (enthalpy) relative to the calculated energy of the reactants [Pb(3P0) + C2H6]. Evidently C-H bond insertion of ethane by the Pb atom occurred during annealing and the product dissociates during photolysis (> 220 nm) as summarized by reaction (1). Similarly, the previously studied CH3-PbH molecule, which is 7.0 kJ/mol more stable than the reactants, was also produced on annealing and dissociated on photolysis.16

annealing 3

Pb( P0) + C2H6

h

CH3CH2-PbH

(1)

Table 1. Frequencies of Product Absorptions Observed from Reactions of C2H6 and CH3F with Pb in Excess Argona C2H5-PbH 1513.4, 1508.5

C2D5-PbD

CH3-PbF

CD3-PbF

cm–1.

Description

Pb-H str. 493.3, 486.5

440.2

frequencies are in

3-PbF

1086.0, 1081.5 494.0, 487.7

aAll

13CH

493.8, 487.4

Pb-X str.

427.7

C-Pb str.

Stronger absorptions are bold. Description gives major coordinate.

Pb + CH3F. Figure 2 shows the IR spectra from reactions of laser-ablated Pb atoms and methyl fluoride isotopomers, where the product absorptions are marked “i”. Photodissociation of H also gave the CH2F radical (1163 cm-1).34 The new lead dependent product absorptions sharpened in the early process of annealing and slightly increased on

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photolysis. Another product absorption marked “*”, which probably originates from a higher order product, increased further in the process of annealing and photolysis. The i absorption at 487.7 cm-1 (with a matrix site absorption at 494.0 cm-1) shifted to 486.5 cm-1 (with a site absorption at 493.3 cm-1) on deuteration (H/D ratio 1.002) and to 487.4 cm-1 (with a site absorption at 493.8 cm-1) on 13C substitution (12/13 ratio less than 1.001). On the basis of its frequency and small D and 13C isotopic shifts, it is assigned to the strong PbF stretching mode of CH3-PbF. Another i absorption at 440.2 cm-1 shifted to 427.7 cm-1 on 13C

substitution (12/13 ratio 1.029), and its D counterpart was too low in frequency (Table

S2) to observe. The frequency and large isotopic shifts lead us to assign it to the C-Pb stretching mode of the C-F insertion product. Our calculations also indicate that the observed C-F insertion complex is essentially the only stable product among the plausible ones. CH3-PbF, CH2F-PbH, CH2=PbHF, CHPbH2F are -194.0, -10.0, +90.5, and +370.3 kJ/mol in energy relative to the reactants, respectively. The CH3-PbF product absorptions were noticeably stronger than those of CH3-PbH and C2H5-PbH although the computed infrared intensities of the observed Pb-F bands are smaller (1/6) than those of the Pb-H stretching bands (Table S1 and 2), indicating that CH3F is more reactive with Pb than the small alkanes.

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Figure 2. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CH3F in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CH3F in Ar co-deposited for 1 h. (b-e) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing to 35 K. (f) Pb + 0.5% 13CH3F in Ar co-deposited for 1 h. (g-j) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing at 35 K. (k) Pb + 0.5% CD3F in Ar co-deposited

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for 1 h. (l-o) after annealing to 20 and 32 K, photolysis with λ > 220 nm, and annealing at 35 K. i and * stand for insertion and higher-order products.

Pb + dihalomethanes. Figure 3 shows the product absorptions marked “i” in reactions of Pb with CH2F2, which sharpened in the early stage of annealing and increased with photolysis. They later decreased in annealing to higher temperature (35 K). Deuteration shifted the i absorption at 982.3 cm-1 by 8.1 cm-1 (H/D ratio 1.008) and the i absorption at 492.3 cm-1 (with a site absorption at 498.1 cm-1) only by 0.5 cm-1 (H/D ratio 1.001). On the basis of their frequency and small isotopic shifts, they are assigned to the CF stretching and Pb-F stretching modes of CH2F-PbF. The CHF2 radical was also observed at 1173 cm-1.35 A weaker i absorption at 1192.2 cm-1 is designated for the CH2 twisting mode without observation of its D counterpart. The other absorptions from the products are too weak to observe (Table S12). Another product absorption at 1000.7 cm-1 marked “*”, which increased continuously in annealing and photolysis probably arises from a higher order unknown product. The previous studies have shown that group 3-10 metals, lanthanides, and actinides generated higher oxidation-state complexes (CH2=MX2 and HC≡MHX2) in reactions with dihalomethanes,7,8 and Si also produced CH2=SiX2.4-6 Lead, the heaviest group 14 metal, makes only two bonds in the reaction with CH2F2, generating an insertion product (CH2FPbF). Calculations clearly show that the insertion products is the most stable: CH2F-PbF, CHF2-PbH, CH2=PbF2, CHF=PbHF, and HC-PbHF2 are

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-142.4, -4.6, +31.2, +108.1, and +256.9 kJ/mol relative to Pb(3P0) + CH2F2, respectively. Despite the stability of the metal-halogen bond, the lead methylidene complex (CH2=PbF2) is 173.6 kJ/mol higher energy than CH2F-PbF.

Figure 3. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CH2F2 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CH2F2 in Ar co-deposited for 1 h. (b-e) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing to 35 K. (f) Pb + 0.5% CD2F2 in Ar co-deposited for 1 h. (g-i) after annealing to 20 K, photolysis with λ > 220 nm, and annealing at 35 K. i and * stand for insertion and high-order products. p denotes precursor absorption.

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Table 2. Frequencies of Product Absorptions Observed from Reactions of CH2X2 Molecules with Pb in Excess Argona CH2F-PbF CD2F-PbF CH2F-PbCl CH2Cl-PbF CH2Cl-PbCl

CD2Cl-PbCl

1192.2

2Cl-PbCl

Description CH2 twist

CH2 wag

1192.9 982.3

974.2

498.1, 492.3

497.8, 491.8

aAll

13CH

987.8

621.9

632.1, 626.5 617.5

615.5, 610.7 C-X str.

Pb-X str.

495.0

frequencies are in cm–1. Stronger absorptions are bold. Description gives major coordinate.

Figure 4 illustrates the product absorptions in reaction of Pb with CH2FCl, which are marked “i” and “i’”. The i absorptions also sharpened in the early stage of annealing and slightly decreased on photolysis, whereas, the i’ absorptions sharpened by annealing and increased more than 50% on photolysis. The strong i absorption at 987.8 cm-1 is assigned to the C-F stretching mode of CH2F-PbCl considering the preference of the insertion products in Pb reactions and good correlation with DFT results (strongest band at 972.2 cm-1, Table S4), and the weak i absorption at 1192.9 cm-1 to the CH2 wagging mode. On the other hand, the i’ absorption at 495.0 cm-1 is assigned to the Pb-F stretching mode of CH2Cl-PbF and the one at 621.9 cm-1 to the C-Cl stretching mode on the basis of good correlation with the predicted frequencies (Table S5). The CHFCl free radical absorptions were also observed.36 The two observed products are again the most stable and comparable to each other: CH2F-PbCl, CH2Cl-PbF, CH2=PbFCl, and CH-PbHFCl are computed to be -195.5, -185.9, -24.7, and +82.8 kJ/mol in energy compared to Pb(3P0) + CH2FCl. The stronger i

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absorptions than the i’ absorptions in the original deposition spectrum indicate that C-Cl bond insertion by the Pb atom is preferred due to the weaker bond of the more electron-rich Cl atom. The considerable increase of the i’ absorptions during photolysis suggests photoisomerization of CH2F-PbCl to CH2Cl-PbF. The transition state between the two conformers, which is confirmed by IRC calculation (Figure S1),37 is calculated to be 171.4 and 161.9 kJ/mol higher than the two products, respectively.

hv CH2F-PbCl → CH2Cl-PbF

(2)

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Figure 4. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CH2FCl in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5%

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CH2FCl in Ar co-deposited for 1 h. (b-e) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing to 35 K. i and i’ stand for insertion products. p denotes precursor absorption.

Weak product absorptions were observed in reactions of Pb with CH2Cl2 isotopomers as shown in Figure 5. The i absorption at 626.5 cm-1 (with a site absorption at 632.1 cm-1) shifts to 617.5 cm-1 on deuteration (H/D ratio 1.015) and to 610.7 cm-1 (with a site absorption at 615.5 cm-1) on frequency, large

13C

13C

substitution (12/13 ratio 1.026). On the basis of its

shift, and correlation with the predicted value (627.9 cm-1), it is

assigned to the C-Cl stretching mode of CH2Cl-PbCl. The other absorptions are either too weak to observe or out of our observation range (Table S6). The observed product is the most stable: CH2Cl-PbCl, CH2=PbCl2, and CH-PbHCl2 are -225.6, -69.2, and +36.1 kJ/mol in energy relative to the reactants.

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Figure 5. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CH2Cl2 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CH2Cl2 in Ar co-deposited for 1 h. (b-e) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing to 38 K. (f) Pb + 0.5% CD2Cl2 in Ar co-deposited for 1 h. (g-i) after annealing to 20 K, photolysis with λ > 220 nm, and annealing to 35 K. (j) Pb + 0.5%

13CH

2Cl2

in Ar co-

deposited for 1 h. (k-n) As (j) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing to 35 K. i stands for insertion products. p denotes precursor absorption.

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Pb + trihalomethane. Reactions of Pb with fluoroform also generated only insertion product absorptions as shown in Figure 6. The i absorptions increased on both annealing and photolysis. The strongest absorption at 996.9 cm-1 shifts to 938.8 cm-1 on deuteration (H/D ratio 1.062) and is assigned to the CF2 anti-symmetric stretching mode of CHF2-PbF. The C-H bending, CF2 symmetric stretching, and Pb-F stretching bands are observed at 1241.8, 1050.3, and 499.1 cm-1 along with their D counterparts at 1027.1, 1040.8, and 498.9 cm-1 (Tables 3 and S7). These are the strongest bands of the insertion complex and the other ones are too weak to observe. Laser plume photolysis also gave the strong CF3 radical absorption at 1251 cm-1.38 The other plausible products are energetically too high: CHF2-PbF, CF3-PbH, and CH-PbF3 are -115.1, -18.5, and +260.8 kJ/mol in energy compared to the reactants, and the methylidene (CHF-PbF2) is probably not a meaningful energy minimum. Our attempts for geometry optimization of CHF-PbF2 all gave the structure of CHF2-PbF. Similarly, CHCl2PbCl, CCl3-PbH, CH-PbCl3 are -247.4, -37.7, and +49.3 kJ/mol in energy relative to reactants, and geometry optimization of CHCl-PbCl2 ended up with the structure of CHCl2PbCl. Frequencies from the CDF3 reaction are given in Table 3. These results are in contrast to the previous results that the Si + CHX3 reactions primarily produce CH-SiX3 and many transition-metals and actinides formed CH≡MX3.6,39 Clearly, Pb prefers the oxidation state 2+ over higher oxidation states in generation of organolead compounds in direct reactions with halomethanes.

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Figure 6. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CHF3 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CHF3 in Ar co-deposited for 1 h. (b-e) after annealing to 20 and 30 K, photolysis with λ > 220 nm, and annealing to 35 K. (f) Pb + 0.5% CDF3 in Ar co-deposited for 1 h. (g-j) after annealing to 20 and 32 K, photolysis with λ > 220 nm, and annealing to 35 K. i and p stand for insertion product and precursor absorptions.

Table 3. Frequencies of Product Absorptions Observed from Reactions of CHF3 and CDF3 with Pb in Excess Argona CHF2-PbF

CDF2-PbF

Description

1241.8

1027.1, 1025.0

A’ C-H ip bend

1061.7, 1050.3, 1043.9

1045.4, 1040.8

A’ CF2 s str.

998.7, 996.9

938.8

A” CF2 as str.

499.1

498.9

A’ Pb-F str.

aAll

frequencies are in cm–1. Stronger absorptions are bold. Description gives major coordinate.

Pb + tetrahalomethanes. Figure 7 shows the product absorptions in reaction of Pb with CF4. The product absorptions marked “i” increased in annealing to 20 K and following photolysis, and they showed the highest intensity after annealing to 30 K. They later decreased in both the second photolysis and annealing to 35 K. No other set of product absorptions was observed. The strong product absorptions at 1126.8, 1034.9, and 948.4 cm1

are assigned to the CF3 stretching modes of CF3-PbF on the basis of their frequency

correlations with the predicted values (Tables 4 and S8), and the weaker Pb-F stretching band at 518.0 cm-1 to the Pb-F stretching mode. The CF3 radical was also observed but

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weaker than with CHF3 above. The tetrafluoride higher oxidation-state products are again energetically too high in comparison with the observed insertion product; CF3-PbF, CF2PbF2, and CF-PbF3 are -131.2, -71.7, and +223.5 kJ/mol in energy compared to the reactants.

Figure 7. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CF4 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CF4 in Ar co-deposited for 1 h. (b-f) after annealing to 20 K, photolysis with λ > 220 nm, annealing to 30 K, photolysis with λ > 220 nm, and annealing to 35 K. i and p stand for insertion product and precursor absorptions.

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Table 4. Frequencies of Product Absorptions Observed from Reactions of CX4 with Pb in Excess Argona CF3-PbF CF3-PbCl CF2Cl-PbF CF2Cl-PbCl CFCl2-PbCl CCl3-PbCl 1138.2, 1126.8 1037.4, 1034.9 948.4

13CCl

3-PbCl

CCl2-PbCl2

2-PbCl2

Description

1073.8

1063.9

1109.6

1017.1, 1011.5

718.5

694.0

CX3 s str.

1041.5

711.1

685.5

673.2

644.2, 640.9

617.6

CX3 as str.

1004.0

1035.9, 1032.0

1021.9

654.7

628.5

610.6

CX3 as str. 874.7, 872.5. 864.4

518.0

13CCl

847.4, 845.4, 839.5

CX2 as str.

629.4

CX2 bend

477.3

Pb-F str. CX2 wag 598.9, 596.9

aAll

frequencies are in

cm–1.

CX2 scis.

Stronger absorptions are bold. Description gives major coordinate.

Similarly, in the Pb + CF3Cl reaction the CF3-PbCl, CF2Cl-PbF, CF-PbF2Cl, and CCl-PbF3 products are -213.8, -154.3, +133.5, and +188.5 kJ/mol in energy relative to the reactants. Geometry optimization of CF2-PbFCl and CFCl-PbF2 lead to the structure of CF2Cl-PbF. The product absorptions of the Pb + CF3Cl reaction shown in Figure 8 increased in the early stage of annealing and photolysis, and they were grouped into two sets marked “i” and “i’” on the basis of correlation with the predicted frequencies of the expected insertion products. The i absorptions at 1073.8, 1041.5, and 1004.0 cm-1 are assigned to the CF3 stretching modes of CF3-PbCl (Tables 4 and S9). The i’ absorptions at 1063.9, 1032.0, and 711.1 cm-1 are designated for the CF2Cl stretching modes of CF2Cl-

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PbF and those at 629.4 and 477.3 cm-1 to the CF2 bending and Pb-F stretching modes (Tables 4 and S10).

Figure 8. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CF3Cl in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CF3Cl in Ar co-deposited for 1 h. (b-f) after annealing to 20 K, photolysis with λ > 220 nm, annealing to 30 K, photolysis with λ > 220 nm, and annealing to 35 K. i and i’ stand for insertion products, and p for precursor absorptions.

Figure 9 shows the Pb + CF2Cl2 product spectra, where the product absorptions marked “i” emerged in annealing and disappeared on photolysis. The i absorptions at 1109.6, and 1021.9 cm-1 are assigned to the symmetric and anti-symmetric C-F2 stretching

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modes of CF2Cl-PbCl, and the ones at 685.5 and 598.9 cm-1 to the C-Cl stretching and CF2 scissoring modes on the basis of correlation with the predicted frequencies. The observed bands are the strongest ones for the insertion complex (Table S11). The CF2Cl radical was also observed.40 CF2Cl-PbCl, CFCl2-PbF, CF-PbFCl2, and CCl-PbF2Cl are -232.8, -176.6, +48.2, and +100.3 kJ/mol higher in energy relative to the reactants, respectively. Geometry optimization of the plausible methylidenes leads the structures of the insertion products: CF2-PbCl2 to CF2Cl-PbCl while CFCl-PbFCl and CCl2-PbF2 to CFCl2-PbF.

Figure 9. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CF2Cl2 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CF2Cl2 in Ar co-deposited for 1 h. (b-f) after annealing to 20 K, photolysis with λ > 220 nm,

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annealing to 30 K, photolysis with λ > 220 nm, and annealing to 35 K. i and p stand for insertion product and precursor absorptions.

The product absorptions in reaction of Pb with CFCl3 are shown in Figure 10, which emerged on annealing and almost disappeared and re-emerged on subsequent annealing. The i absorption at 1017.1 cm-1 is assigned to the C-F stretching mode of CFCl2-PbCl, and those at 673.2 and 654.7 cm-1 to the symmetric and anti-symmetric C-Cl2 stretching modes. CFCl2-PbCl, CCl3-PbF, CF-PbCl3, and CCl-PbFCl2 are -250.4, -202.0, -31.3, and +19.4 kJ/mol in energy against the reactants. CCl3-PbF, which is energetically comparable to CFCl2-PbCl, was not detected probably because three electron-rich Cl atoms react with the metal atom faster than a single F. The plausible methylidenes (CFCl-PbCl2 and CCl2-PbFCl) converge to CFCl2-PbCl and CCl3-PbF during geometry optimization.

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Figure 10. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CFCl3 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CFCl3 in Ar co-deposited for 1 h. (b-f) after annealing to 20 and 30 K, photolysis with λ > 220 nm, annealing to 30 and 35 K. i and p stand for insertion product and precursor absorptions.

Figures 11 and 12 show product absorptions marked i and m in reactions of Pb with CCl4 and 13CCl4 and their variations following annealing and full arc photolysis. In addition several other common bands for transient intermediates were also observed with other metals.41 The CCl3 radical absorption at 898.0 and its 13CCl3 counterpart at 869.0 cm-1 gave the very strong bands labeled r (for radical) on the left side in the two figures. These bands

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were first observed in this laboratory, and they revealed splittings at 895.5 and 866.5 cm1for

mixed 35,37Cl isotopic components.42 The i absorptions observed on sample deposition increased on annealing and

decreased on photolysis, and showed the same behavior with a second annealing and photolysis in this experiment. On the other hand, the m absorptions were not observed on sample deposition, but they appeared on first annealing to 20 K, increased slightly on photolysis and decreased on annealing to 30 K, but they almost doubled on another full arc photolysis followed by a slight decrease on annealing to 35 K. This behavior suggests that the product responsible for the i absorptions converts to the m absorptions on uv photolysis. It is also notable that unlike the other Pb systems described above, the computed tetrachloro insertion and methylidene complexes are energetically close: CCl3-PbCl, CCl2PbCl2, and CCl-PbCl3 are 266.6, 237.3, and 54.2 kJ/mol lower energy and more stable than [Pb(3P0) + CCl4], which provides a good chance to observe both the insertion product (CCl3-PbCl) and a slightly higher energy lead methylidene (CCl2-PbCl2). Since both product absorptions increased substantially on the initial annealing to 20 K, these highly exothermic reactions (3 and 4) appear to proceed without activation energy. It is interesting to note that the union of CCl2 and PbCl2 is exothermic by 47.7 kJ/mol, reaction (5), but this is not the reaction path here. Photochemical reaction (6) is also expected to contribute.

Pb + CCl4 → CCl3-PbCl

[∆E = −266.6 kJ/mol]

(3)

Pb + CCl4 → CCl2-PbCl2

[∆E = −237.3 kJ/mol]

(4)

CCl2 + PbCl2 → CCl2-PbCl2

[∆E = −47.7 kJ/mol]

(5)

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 > 220 nm CCl3-PbCl

CCl2-PbCl2

(6)

The i absorptions at 718.5, 716.2 , 640.9, and 628.5 cm-1 shifted to 694.0, not resolved, 617.6, and 610.6 cm-1 on

13C

substitution (12/13 ratios 1.0353, 1.0377, and

1.0293), and they are assigned to the CCl3 stretching modes of CCl3-PbCl (Tables 4 and S13). The 716.2 cm-1 band, marked with two down lines in Figure 11, defines a splitting of 2.3 cm-1, which is due to a mixed 35,37-chlorine isotopic modification that falls below the intense peak for the all 35-chlorine product. A similar splitting of 2.5 cm-1 was observed for the higher frequency, intense CCl3 radical absorption, and a smaller 2.0 cm-1 splitting was found for the intense 745.7cm-1 band for isolated CCl2.43

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Figure 11. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with CCl4 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% CCl4 in Ar co-deposited for 1 h. (b-f) after annealing to 20 K, photolysis with λ > 220 nm, annealing to 30 K, photolysis with λ > 220 nm and annealing to 35 K. i, m and * stand for insertion, methylidene, and high-order product absorptions. p denotes precursor absorption.

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Figure 12. IR spectra in the product absorption regions for laser-ablated Pb atoms co-deposited with 13CCl4 in excess argon at 4 K and their variation on annealing and photolysis. (a) Pb + 0.5% 13CCl 4

in Ar co-deposited for 1 h. (b,c,d,e,f) after annealing to 20 K, photolysis with λ > 220 nm,

annealing to 30 K, photolysis with λ > 220 nm, and annealing to 35 K, respectively. i, m and * stand for insertion, methylidene, and higher-order product absorptions. p denotes

13CCl 4

precursor

absorption.

These absorptions are lower than the isolated CCl3 radical at 898.0, 895.5 cm-1 in solid argon (chlorine isotopic splitting) with

13CCl 3

at 869.0, 866.5 cm-1 (12/13 ratio

1.0334), which suggests a transfer of charge from the PbCl subunit to the CCl3 group. Mulliken charges (Supporting Information) reveal a negative 0.24 charge on the CCl3 group and a positive 0.24 charge on the PbCl unit, and Natural charges give a larger 0.69 charge

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separation. The observed frequencies are lower than the B3LYP values by 1, 15 and 26 wavenumbers, which are reasonable for such a metal bearing molecule. The BPW91 frequencies are even lower which is expected. The m absorptions at 874.7 and 872.5 cm-1 (chlorine isotopic splitting) exhibit 13C counterparts at 847.4 and 845.4 cm-1(13C shift 27.3 cm-1 and 12/13 ratio 1.0322). This band is assigned to the strongest anti-symmetric CCl2 stretching mode of CCl2-PbCl2 on the basis of its relatively high frequency and correlation with the predicted frequency and isotopic shift (866.8 and 27.6 cm-1). The 872.5 cm-1 band beside the stronger 874.7 cm-1 band is due to the 35Cl37Cl splitting from the stronger 35Cl2 band. The same pattern has been observed for the CCl2 intermediate at 745.7 and 743.7 for this species with two equivalent Cl atoms.43 Unfortunately the next strong CCl2 symmetric stretching band expected at ~780 cm-1 is weaker and covered by precursor absorption, and the other ones are too weak to observe. In contrast to the insertion (ClPb-CCl3) product’s CCl3 absorptions falling 179 cm-1 below those for the isolated CCl3 radical, the CCl2 antisymmetric C-Cl absorptions for the methylidene are 129 cm-1 higher than those for the isolated CCl2 intermediate in the direction of the 1195.4 cm-1 value for the CCl2+ cation.44 This suggests that the CCl2 subunit in the methylidene is positively charged, which is supported by the +0.25 Mulliken and +0.11 Natural charge calculations for the CCl2 subunit (Supporting Information). As described above, unlike most transition metal systems, the plausible lead methylidenes in reactions with small alkanes and halomethanes are generally too high energetically to be produced or are not meaningful minima. In contrast the observed CCl2-

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PbCl2 is reasonably stable (only 29.3 kJ/mol higher energy than CCl3-PbCl), which allows observation in the direct reaction of Pb with CCl4 (reaction 4). This is probably the first experimental observation of a lead methylidene complex although the C—Pb bond is longer than that in the insertion product (Figure 15). This new lead bearing molecule is a methylidene in formula, but it does not contain the double bond usually associated with methylidenes.8 The sharp new 864.4 and 839.5 cm-1bands for 12C and 13C counterparts remain to be assigned (12/13 frequency ratio 1.02966). These bands observed on deposition decrease on annealing and increase on uv photolysis, which are appropriate for a reactive species. The latter band is sharp and reveals a 37Cl counterpart at 833.5 cm-1 and the weaker former band exhibits a 37Cl counterpart at 858.4 cm-1, and these relative intensities are near the 3/1 ratio for chlorine isotopes in natural abundance for a single Cl bearing species. These 6.0 cm-1 35Cl-37Cl

splittings match those computed for the diatomic molecule and reported for the

gaseous CCl radical from high-resolution FTIR measurements (866.1 and 860.1 cm-1). The above lower 12/13 frequency ratio and shift are appropriate for the diatomic molecule as verified by a hand calculation. Our measurements define a very small 1.7 cm-1 argon matrix shift for the CCl radical.45,46 Matrix site-split bands at 870, 866 and 864 cm-1 have been assigned to the argon matrix isolated CCl radical.47 Structures and Bonding. Figure 13 shows the structures of the most plausible products in reactions of ethane and methyl fluoride. The C-Pb-H and C-Pb-F bond angles of the insertion complexes (C2H5-PbH and CH3-PbF) are near right angles (92.1 and 93.1°), indicating that the Pb atom uses mostly p-orbitals for these bonds, and the two 6s electrons

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remain a lone pair in this ground singlet electronic state. The NBO calculations also show that Pb contributes 94% p- and 6% s-characters to both of the C-Pb and Pb-F bonds of CH3PbF and 81% p- and 19% s-characters to the C-Pb bond of C2H5-PbH and 94% p- and 6% s-characters to the Pb-H bond. 30 The PbH2 moiety of the metallacyclopropane [(CH2)2-PbH2], which is a common product in transition-metal reactions,7,8 is weakly bound to the ethylene moiety. The two CPb bond lengths are 2.912 and 3.027 Å, whereas the C-C bond length is 1.340 Å, which is comparable to that (1.325 Å) for ethylene. The H-Pb-H angle is 92.1°. On the other hand, the Pb atom in the ethylidyne (CH3C-PbH3) shows sp3 hybridization making four chemical bonds. CH3C-PbH3 has a triplet ground state unlike other lead complexes examined in this study. The NBO results indicate that Pb contributes 77% p- and 23% s-characters to the CPb bond, 75% p- and 25% s-characters to the two out-of-plane Pb-H bonds and 74% p- and 26% s-character to the in-plane Pb-H bond. The bent C-C-Pb molecular skeleton (142.0°) indicates that the unpaired electrons reside on the carbon atom bonded to Pb (Mulliken spin density 1.91),22 contributes 57% p- and 43% s-characters to the C-C bond and 61% p- and 39% s-characters to the C-Pb bond.

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Figure 13. The B3LYP structures of the most plausible (insertion and methylidene) products from reactions of Pb with C2H6 and CH3F. The 6-311++G(3df,3pd) basis sets are used for C, H, and F and the SDD pseudopotential and basis set for Pb. The bond lengths and angles are in Å and degrees.

Evidently Pb also promotes a 6s electron for the higher energy CH2=PbHF and CHPbH2F molecules: NBO indicates that the natural bond orders of the C-Pb bonds in these two complexes are 1.97 and 0.94.30 The group 4-6 metal and actinide methylidenes show agostic distortion, which results from coordination of C-H bonding electrons to the empty d-orbitals.48-50 The CH2 moiety of the Pb methylidene (CH2=PbHF) does not reveal noticeable computed distortion as shown in Figure 13: thus the d-orbitals of a main group metal are more difficult to access than those of a transition-metal. The shorter C-Pb bond (2.074 Å) is also indicative of a multiple bond. The longer C-Pb bond and bent HCPb

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moiety (103.4°) of the methylidyne also show that the C-Pb bond is a single bond and the carbon atom provides mostly p-character to the bonds (C contributes 80% p- and 19% scharacters to the C-H bond and 88% p- and 12% s-characters to the C-Pb bond). The promotion energy from s2p2 to sp3 for Pb is substantial (calculated to be 620 kJ/mol in comparison with 452, 436, 531, 454, 2.5, and 53 kJ/mol for C, Si, Ge, Sn, Ti, and Zr, respectively), leading to high energies for the lead carbyne complexes (e.g. CH-PbH2F is 564 kJ/mol higher in energy than CH3-PbF). This contrasts the previously studied transition-metal high oxidation-state analogues, where the metal atom hybridizes including d-orbitals to form a triple bond with the neighboring C atom and three bonds with H, halogen, or other ligands.7,8 These chemical bonds stabilize the metal complexes with C-M multiple bonds particularly in the heavy metal systems. In this main group metal system, the energetically high d-orbitals cannot be utilized and the promotion energy from s2p2 to sp3 is also high due to the relativistic effect (stronger contraction of the lead 6s orbital than the 6p orbitals).15 The B3LYP structures of plausible products in reactions of Pb with di- and trihalomethanes are shown in Figure 14. The C-Pb-X bond angles of the insertion products are again close to right angles, showing that Pb uses two p-orbitals to form the C-Pb and Pb-X bonds. The Cl-C-Pb moiety of CH2Cl-PbF is considerably bent (96.2°), showing substantial electronic contribution of Cl bonded to C to Pb. Strong interactions between the Cl and metal center in small metal complexes (often the H-C-M angles smaller than 90°) were previously observed in many transition-metal analogues.7,8 The unusual dihedral angle [Φ(ClCPbF) = 104.8°] probably originates from electron donation to the empty p-orbital

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after forming the C-Pb and Pb-F bonds with two p-electrons. NBO30 analysis estimates the interaction energy between the Cl atom bonded to C and the empty p-orbital of Pb atom to be 25 kJ/mol. The heavy group 4 metal prefers to use its p-orbitals for not only bonding but also intra-molecular electronic interaction.

Figure 14. The B3LYP structures of the most plausible products from reactions of Pb with CH2F2, CH2FCl, and CHF3. The 6-311++G(3df,3pd) basis sets are used for C, H, F and Cl

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and the SDD pseudopotential and basis set for Pb. The bond lengths and angles are in Å and degrees.

The methylidenes (CH2=PbF2 and CH2=PbFCl) are somewhat nonplanar (Φ(HCPbH) = 60.2 and 53.9°). Carbon provides 70% p- and 30% s-characters to the two CH bonds of CH2=PbF2 and 80% p- and 20% s-characters to the two C-Pb bonds (natural CPb bond order 1.57). Similarly, C contributes 70% p- and 30% s-characters to the two C-H bonds of CH2=PbFCl and 70% p- and 30% s-characters to a C-Pb bond and 89% p- and 10% s-characters to the other C-Pb bond (natural C-Pb bond order30 1.58). In the methylidynes, C gives high p-character to the C-H and C-Pb bonds, 80 and 92% in CH-PbHF2 and 81 and 95% in CH-PbF3, respectively. The high p-characters in the bonds lead to the highly bent H-C-Pb moiety (99.9 and 99.5°), and consequently the lone pair electrons on C have high (73 and 77%) s-characters. Clearly the C-Pb bonds are single bonds (natural bond orders30 both 0.93), and Pb basically formulates sp3 hybridization, contributing 69 and 68% p-characters to the C-Pb and Pb-H bonds of CH-PbHF2 and 81% to the both Pb-F bonds. Likewise, Pb provides 69 and 76% p-characters to the C-Pb and three Pb-F bonds of CH-PbF3. Figure 15 shows the B3LYP structures of the plausible products in reactions of Pb with tetrahalomethanes. The structures of the insertion products are similar to those described above, and the Cl atoms bonded to C in CF2Cl-PbF and CF2Cl-PbCl are also bent toward Pb. In contrast, the tetrahalomethylidenes (CX2-PbX2 with the unusual lead oxidation state 3+) have Cs structures, where Pb is at the apex of the pyramidal structure

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produced by the C-Pb and two Pb-X bonds. The CCl2-PbCl2 molecule has a 1A’ground electronic state. NBO30 analysis shows that Pb contributes mostly p-character to the bonds, 99 and 97% p-characters to the C-Pb and two Pb-Cl bonds of CCl2-PbCl2 and 56 and 96% p-characters to the C-Pb and two Pb-F bonds of CF2-PbF2. NBO analysis also indicates that the Pb-X bonds donate electron density to the C-Pb bond, making the C-Pb-X angle smaller than 90° (Figure 15). The 620 kJ/mol computed s to p promotion energy for Pb is provided here by the formation of two Pb-Cl bonds at 301 kJ/mol each taken from the diatomic molecule, and the C-Pb bond at 240 kJ/mol taken from Pb(CH3)4. 51 This Pb-Cl bond energy is in excellent agreement with the CCSD(T)/ATZ Average Bond Energy value (309 kJ/mol) computed for PbCl2.52 The bonding in Cl2C--PbCl2 is due to a fortunate and unusual relationship between the atomic orbitals. The 114.1° Cl-C-Cl and two 122.8° Cl-C-Pb angles characterize sp2 hybridization with an almost planar Cl2C-Pb subunit, and the remaining C 2p pi orbital contains a single electron. After promotion of one 6s electron, the Pb 6s orbital also contains a single electron. Thus we have spin paired but not bonding single electrons in C 2p and Pb 6s orbitals. Structures of the unobserved tetrahalomethylidynes are similar to those of less halogenated analogues in Figures 13 and 14, and Pb involves sp3 hybridization. For example, Pb contributes 68, 78, 77, and 77% p-characters and 32, 22, 23, and 23% scharacters to the C-Pb and three Pb-Cl bonds of CCl-PbCl3, and the C-Pb bond is a single bond (natural bond order 0.76). However, this higher energy product is not observed.

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Figure 15. The B3LYP structures of the most plausible products from reactions of Pb with CF4, CF2Cl2, CFCl3 and CCl4. The 6-311++G(3df,3pd) basis sets are used for C, F and Cl

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and the SDD pseudopotential and basis set for Pb. The bond lengths and angles are in Å and degrees.

The results of similar calculations for PbO and OPbO are also of interest here.17 The ground 1∑ state for PbO has a 1.906 Ằ B3LYP bond length while 1∑g OPbO bonds are slightly longer at 1.910 Å. The natural charge for Pb in the diatomic is 1.20 and for the triatomic is 2.14 while the Mulliken charges are +0.65 and +0.98 e-, respectively. The PbO diatomic exhibits two electron pair pi bonds that are 11.7% Pb and 88.3% O made up of p orbitals in both cases and a third sigma orbital with two electrons that is 16.6% Pb using 12.4% s and 87.1% p atomic orbitals and 83.4% O using 18.7% s and 81.2% p atomic orbitals. The OPbO triatomic has two electron pair pi bonds using p orbitals that are 5.64% Pb and 94.4% O and two sigma orbitals with 1.85 occupancy that are 32.3% Pb with 50.0 % s and p character and 67.7% O with 5.0% s and 94.8% p character. These NBO results suggest that the two lead oxide molecules contain Pb(III) and Pb(IV). Probably the strong PbO multiple bonds make sp hybridization of Pb possible. This bond energy is enough to compensate the s-to-p promotion energy of Pb.

CONCLUSIONS Pb, the heaviest of group 14 metals, generates

insertion products (CCl3-PbCl

oxidation state 2+) in reactions with ethane and halomethanes, which were identified from the matrix IR spectra on the basis of correlation with B3LYP computed values and observed isotopic shifts. The C-Pb-X (X = H, F or Cl) moiety of each product is highly

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bent (close to right angle), showing that Pb uses two p-orbitals to form the C-Pb and Pb-X bonds. NBO30 calculations also indicate that Pb contributes mostly p-character to the bonds. The Pb methylidenes, on the other hand, were not detected in most systems due to their higher energies. These complexes may contain a C-Pb double bonds and require energetic electronic promotion of Pb. A lead methylidene was observed only in reactions with carbon tetrachloride, where the carbene is relatively close in energy to the insertion product unlike the other systems investigated in this work. This singlet ground state methylidene (CCl2-PbCl2 with unusual Pb oxidation state 3+) is generated in reactions with carbon tetrachloride, and it is probably the first lead methylidene to be formed and investigated. Unlike those in the other systems, the tetrachloro methylidene exhibits a unique singlet state structure, where the Pb atom is at the apex of the pyramid defined with the C-Pb and two Pb-Cl bonds. NBO results show that Pb contributes mostly p-character to these three chemical bonds, and the CCl2 structure is sp2 hybridized. Remaining are unusual spin paired but not bonding by symmetry single electrons in the carbon 2p pi orbital and in the lead 6s orbital. The energetically even higher lead methylidynes were not observed in this study in contrast to the previously observed Si analogues in reactions with tri- and tetrahalomethanes.6 Parallel to the C and Si analogues, the heavy group 14 metal forms sp3 hybridization to make the four chemical bonds needed to produce the high oxidation-state complexes. As a result, the Pb methylidynes have a C-M single bond, in contrast to the CM triple bonds of the transition-metal analogues via hybridization including d-orbitals.7,8

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Moreover, the high promotion energy from s2p2 to sp3 for this heavy metal prevents lead carbyne complexes from being formed.

ASSOCIATED CONTENT Supporting Information Tables S1-S14 of calculated vibrational frequencies, intensities and Cartesian coordinates of the observed products, Figure S1 showing interconversion between CH2F-PbCl and CH2Cl-PbF, and Mulliken and natural charges for CCl3-PbCl and CCl2-PbCl2.This material is available free of charge from the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *L. A.: e-mail, [email protected]; tel, 434-924-3513. ORCID Han-Gook Cho: 0000-0003-0579-376X Lester Andrews: 0000-0001-6306-0340 Notes The authors declare no competing financial interests.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support from the Korea Research Foundation (KRF) funded by Korean government grant (NRF-2018R1D1A1B07043787) and the KISTI supercomputing center, and retirement funds from the T.I.A.A. for L. A.

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