Germylenes: Structures, Electron Affinities, and SingletâTriplet Gaps of

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Germylenes: Structures, Electron Affinities, and Singlet-Triplet Gaps of the Conventional XGeCY3 (X ) H, F, Cl, Br, and I; Y ) F and Cl) Species and the Unexpected Cyclic XGeCY3 (Y ) Br and I) Systems Ashwini Bundhun,† Hassan H. Abdallah,‡ Ponnadurai Ramasami,*,† and Henry F. Schaefer III*,§ Department of Chemistry, UniVersity of Mauritius, Re´duit, Mauritius, School of Chemical Sciences, UniVersiti Sains Malaysia, 11800 Penang, Malaysia, and Center for Computational Quantum Chemistry, UniVersity of Georgia, Athens, Georgia 30602, United States ReceiVed: August 20, 2010; ReVised Manuscript ReceiVed: October 21, 2010

A systematic investigation of the X-Ge-CY3 (X ) H, F, Cl, Br, and I; Y ) F, Cl, Br, and I) species is carried out using density functional theory. The basis sets used for all atoms (except iodine) in this work are of double-ζ plus polarization quality with additional s- and p-type diffuse functions, and denoted DZP++. Vibrational frequency analyses are performed to evaluate zero-point energy corrections and to determine the nature of the stationary points located. Predicted are four different forms of neutral-anion separations: adiabatic electron affinity (EAad), zero-point vibrational energy corrected EAad(ZPVE), vertical electron affinity (EAvert), and vertical detachment energy (VDE). The electronegativity (χ) reactivity descriptor for the halogens (X ) F, Cl, Br, and I) is used as a tool to assess the interrelated properties of these germylenes. The topological position of the halogen atom bound to the divalent germanium center is well correlated with the trend in the electron affinities and singlet-triplet gaps. For the expected XGeCY3 structures (X ) H, F, Cl, Br, and I; Y ) F and Cl), the predicted trend in the electron affinities is well correlated with simpler germylene derivatives (J. Phys. Chem. A 2009, 113, 8080). The predicted EAad(ZPVE) values with the BHLYP functional range from 1.66 eV (FGeCCl3) to 2.20 eV (IGeCF3), while the singlet-triplet splittings range from 1.28 eV (HGeCF3) to 2.22 eV (FGeCCl3). The XGeCY3 (Y ) Br and I) species are most often characterized by three-membered cyclic systems involving the divalent germanium atom, the carbon atom, and a halogen atom. I. Introduction The exploration of divalent germanium compounds has exploded over the past 20 years, yielding many novel chemical species.1-4 The latest progress in this field is particularly impressive.5-8 A remarkable very recent example is the synthesis and characterization of three new thermally stable N-heterocyclic germylenes by West and co-workers.9 Applications of these important chemical species include the manufacture of components of nanomaterials10 and the enablement of precursors11,12 for chemical vapor deposition in the low-temperature synthesis of Ge-rich semiconductors. A surge of germylene theoretical investigations has contributed to the prediction of electron affinities,13-16 geometrical parameters,17-19 dissociation energies,20 singlet-triplet splittings, and other thermodynamic properties.21-24 Density-functional theory (DFT) has been shown to be useful in such predictions. The highly electronegative fluorine atom preferentially favors divalent singlet states. Theoretical studies of the halogensubstituted methylenes/silylenes/germylenes have amply demonstrated singlet electronic ground states.25,26 The substituents,27,28 attached directly to the central divalent atom for the carbene analogues, display linear correlations with vertical and adiabatic singlet-triplet splittings.29 Significantly, the most important factor in determining the energetic favorableness of singlet * To whom correspondence should be addressed: [email protected] (P.R.); [email protected] (H.F.S.). † University of Mauritius. ‡ Universiti Sains Malaysia. § University of Georgia.

silylenes and germylenes is the p-electron donation from the substituent(s) to the formally empty p-orbital of silicon or germanium, respectively. This effect is largest when the substituent is in the position R to the divalent center, while triplet germylenes are forced by electropositive substituents. The study of germylene generation, reactivities, substituent effects, singlet-triplet energy gaps, and relative stabilities (using both experimental and theoretical methods30), is an area of active research. Such studies are inevitably connected with the absolute rate constants of germylene insertion processes.31-33 Notably, it has been observed that there is a strong correlation between singlet-triplet splittings for the divalent reactant species and activation energies. Previous research34 has shed light on the electron affinities and singlet-triplet gaps for the GeX2, GeHX, and XGeMH3 (where X ) H, F, Cl, Br, and I; M ) C, Si, and Ge) species. For the previously studied germylene derivatives, it has been predicted that the BHLYP functional provides the best agreement of the predicted structures with experimental geometrical parameters. The present study aims at providing reliable theoretical predictions for the properties of the tetrahalo systems XGeCY3. In the present research, we investigate the abilities of the germylene species to bind an extra electron, as reflected by the adiabatic electron affinity (EAad), zero-point vibrational corrected electron affinity (EAad(ZPVE)), vertical electron affinity (VEA), and vertical detachment energy VDE. The singlet-triplet splittings (∆ES-T) of this family of germylenes, XGeCY3, are also reported and discussed.

10.1021/jp1078955  2010 American Chemical Society Published on Web 11/22/2010

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II. Theoretical Methods All geometrical parameters are fully optimized using the Gaussian 03 program.35 Three different density functionals, namely, BHLYP, BLYP, and B3LYP, are used here. BHLYP is an HF/DFT hybrid method comprising the Becke (B)36 half and half exchange functional (H)37 and the Lee, Yang, and Parr (LYP)38 nonlocal correlation functional. The B3LYP method combines Becke’s three-parameter exchange functional (B3) with the LYP correlation functional. Finally, BLYP is a pure DFT method, comprised of Becke’s (B) exchange functional plus the LYP correlation. All neutral ground state structures are characterized as minima on the corresponding potential energy surface by performing vibrational frequency analyses. In all cases an extended integration grid (199974) are used, with very tight convergence criteria applied to these calculations. Double-ζ basis sets with polarization and diffuse functions, denoted DZP++, are used for all atoms except iodine, where the 6-311G(d,p) basis set39 is used. The double-ζ basis sets for H, C, and F were constructed by augmenting the HuzinagaDunning-Hay40-42 sets of contracted Gaussian functions, with one set of p polarization functions for each H atom and one set of d polarization functions for each heavy atom (Rp(H) ) 0.75, Rd(C) ) 0.75, Rd(F) ) 1.0). Basis functions for chlorine were obtained from the Ahlrichs standard double-ζ sp set43 with one set of d-like polarization functions (Rd(Cl) ) 0.75). For bromine, the Ahlrichs standard double-ζ spd set was appended with a set of d polarization functions, R ) 0.389. The above basis sets were further augmented with diffuse functions, where each heavy atom received one additional s-type and one additional set of p-type functions. The H atom basis set was appended with one diffuse s function. The diffuse functions were determined in an even-tempered fashion following the prescription of Lee44

Rdiffuse )

(

)

R2 1 R1 + R 2 R2 R3 1

(1)

where R1, R2, and R3 are the three smallest Gaussian orbital exponents of the s- or p-type primitive functions for a given atom (R1 < R2 < R3). Thus Rs(H) ) 0.04415, Rs(C) ) 0.04302, Rp(C) ) 0.03629, Rs(F) ) 0.1049, Rp(F) ) 0.0826, Rs(Cl) ) 0.05048, Rp(Cl) ) 0.05087, Rs(Br) ) 0.0469096, and Rp(Br) ) 0.0465342. The DZP++ basis set for germanium was constructed from the Schafer-Horn-Ahlrichs double-ζ spd set plus a set of five pure d-type polarization functions with Rd(Ge) ) 0.246, and augmented by a set of sp diffuse functions with Rs(Ge) ) 0.024434 and Rp(Ge) ) 0.023059.43 The overall contraction scheme for the basis sets is H(5s1p/3s1p), C(10s6p1d/5s3p1d), F(10s6p1d/5s3p1d), Cl(13s9p1d/7s5p1d), Ge(15s12p6d/9s7p3d), and Br(15s12p6d/9s7p3d). The four forms of the neutral-anion energy difference are evaluated using the following energy differences. Each adiabatic electron affinity is determined by: i. EAad ) E(optimized neutral) - E(optimized anion) The vertical electron affinity by ii. EAvert ) E(optimized neutral) - E(anion at optimized neutral geometry) and the vertical detachment energy of the anion iii. VDE ) E(neutral at optimized anion geometry) E(optimized anion).

Figure 1. Equilibrium geometries for the 1A′ state of HGeCF3, 2A′′ state of the HGeCF3- anion, and 3A′′ state of the HGeCF3.

Additionally, zero-point vibrational energies (ZPVE) are evaluated for each system. The ZPVE corrected adiabatic electron affinities EAad(ZPVE) are reported as follows: iv. EAad(ZPVE) ) [E(optimized neutral) + ZPVEneutral] [E(optimized anion) + ZPVEanion] Each singlet-triplet splitting is predicted as the energy difference between the neutral ground state and the lowest-lying triplet state. III. Results A. HGeCF3 and HGeCF3-. The equilibrium geometries of the 1A′ ground state HGeCF3, the ground state anion 2A′′ HGeCF3- and the 3A′′ triplet state of HGeCF3 are presented in Figure 1. The neutral ground state 1A′ HGeCF3 shows the Ge-H and Ge-C bond lengths to range from 1.577-1.611 Å and 2.064-2.112 Å, respectively, with BHLYP and BLYP as the lower and upper bounds, while the predicted H-Ge-C bond angle varies from 88.9° (BLYP) to 89.4° (BHLYP). The corresponding 2A′′ ground state anion HGeCF3- has predicted bond lengths of 1.602, 1.619, and 1.637 Å and bond angles of

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TABLE 1: Germylene Adiabatic Electron Affinities EAad and Zero-Point Corrected EAad(ZPVE) Values (in parentheses) in eVa HGeCH3b FGeCH3b ClGeCH3b BrGeCH3b IGeCH3b HGeCF3 FGeCF3 ClGeCF3 BrGeCF3 IGeCF3 HGeCCl3 FGeCCl3 ClGeCCl3 BrGeCCl3 IGeCCl3 HGeCBr3 FGeCBr3 ClGeCBr3 BrGeCBr3 IGeCBr3 HGeCI3 FGeCI3 ClGeCI3 BrGeCI3 IGeCI3 a

BH&HLYP

BLYP

B3LYP

0.69 (0.71) 0.64 (0.66) 1.07 (1.09) 1.17 (1.19) 1.33 (1.33) 1.71 (1.74) 1.66 (1.69) 2.00 (2.02) 2.07 (2.08) 2.18 (2.20) 1.67 (1.71) 1.63 (1.66) 1.96 (1.99) 2.03 (2.05) 2.16 (2.18) 1.63 (1.68) 3.21 (3.24) 1.94 (1.96) 2.01 (1.82) 2.13 (2.15) 3.25 (3.26) 3.25 (3.27) 3.40 (3.42) 3.42 (3.45) 3.50 (3.52)

0.72 (0.75) 0.65 (0.67) 1.01 (1.03) 1.09 (1.10) 1.19 (1.20) 1.69 (1.72) 1.59 (1.62) 1.88 (1.90) 1.92 (1.94) 1.99 (2.01) 1.64 (1.71) 1.66 (1.69) 1.87 (1.93) 1.91 (1.95) 1.99 (2.02) 2.94 (2.96) 2.93 (2.96) 3.07 (3.09) 3.09 (3.12) 3.16 (3.18) 2.90 (2.92) 2.92 (2.94) 3.05 (3.06) 3.07 (3.08) 3.11 (3.12)

0.84 (0.86) 0.77 (0.79) 1.17 (1.18) 1.26 (1.27) 1.39 (1.40) 1.83 (1.86) 1.75 (1.78) 2.06 (2.08) 2.11 (2.13) 2.21 (2.23) 1.78 (1.83) 1.77 (1.80) 2.03 (2.06) 2.09 (2.11) 2.18 (2.21) 3.17 (3.20) 3.17 (3.20) 3.31 (3.34) 3.34 (3.37) 3.42 (3.45) 3.20 (3.22) 3.19 (3.21) 3.32 (3.34) 3.35 (3.37) 3.40 (3.42)

The boldface Ge represents the divalent center. b Reference 34.

TABLE 2: Germylene Vertical Electron Affinities (VEA) in eV HGeCF3 FGeCF3 ClGeCF3 BrGeCF3 IGeCF3 HGeCCl3 FGeCCl3 ClGeCCl3 BrGeCCl3 IGeCCl3

BH&HLYP

BLYP

B3LYP

1.61 1.49 1.78 1.85 1.98 1.20 1.24 1.52 1.60 1.74

1.58 1.42 1.67 1.72 1.80 0.94 1.43 1.30 1.40 1.52

1.73 1.58 1.85 1.91 2.01 1.14 1.56 1.53 1.62 1.74

89.8°, 89.6°, and 89.5° (BHLYP, B3LYP, BLYP), respectively. From the singlet to the triplet state, there is a decrease in the Ge-C bond length of 0.042 Å (BHLYP), while the expected45 increase in the bond angle is 26.8°. Relative to the neutral 1A′ ground state HGeCH3,34 the Ge-H bond length for 1A′ HGeCF3 increases by almost 0.012 Å (B3LYP), accompanying a decrease in the H-Ge-C divalent angle by 4.2°. The replacement of hydrogen atoms by fluorine atoms at the carbon center accounts for an increase in the Ge-H bond length of 0.267 Å. The theoretical EAad, EAad(ZPVE), VEA, and VDE results are shown in Tables 1-3. The computed EAad(ZPVE) values range from 1.72 to 1.86 eV in the order BLYP < BHLYP < B3LYP. The EAvert range from 1.58 eV (BLYP) to 1.73 eV (B3LYP), and the VDE range from 1.56 to 1.93 eV. The singlet-triplet splittings for HGeCF3 increase from 1.28 to 1.42 eV in the order BHLYP < B3LYP < BLYP, as found in Table 4. B. FGeCF3 and FGeCF3-. Equilibrium geometries of the 1 A and 1A′ ground states FGeCF3, its corresponding 2A′′ ground state anion FGeCF3-, and the lowest lying triplet 3A′′ state FGeCF3 are presented in Figure 2. Structural changes between the neutral and its corresponding anionic species include an increase in the Ge-F bond length of 0.090 Å, accompanying an increase in the Ge-C bond length of 0.025 Å (BHLYP).

TABLE 3: Germylene Vertical Detachment Energies (VDE) in eV HGeCF3 FGeCF3 ClGeCF3 BrGeCF3 IGeCF3 HGeCCl3 FGeCCl3 ClGeCCl3 BrGeCCl3 IGeCCl3

BH&HLYP

BLYP

B3LYP

1.81 1.85 2.25 2.31 2.42 1.84 1.86 2.23 2.30 2.41

1.56 1.78 2.11 2.15 2.19 1.97 1.93 2.19 2.22 2.27

1.93 1.94 2.31 2.35 2.43 2.01 1.99 2.31 2.36 2.44

TABLE 4: Germylene Singlet-Triplet Gaps (eV) (kcal mol-1 in parentheses) HGeCH3a FGeCH3a ClGeCH3a BrGeCH3a IGeCH3a HGeCF3 FGeCF3 ClGeCF3 BrGeCF3 IGeCF3 HGeCCl3 FGeCCl3 ClGeCCl3 BrGeCCl3 IGeCCl3 HGeCBr3 FGeCBr3 ClGeCBr3 BrGeCBr3 IGeCBr3 a

BH&HLYP

BLYP

B3LYP

1.14 (26.4) 2.01 (46.4) 1.81 (41.8) 1.74 (40.1) 1.60 (37.0) 1.28 (29.6) 2.18 (50.3) 1.94 (44.7) 1.85 (42.7) 1.69 (39.0) 1.47 (34.0) 2.22 (51.1) 2.12 (48.9) 2.02 (46.5) 1.83 (42.2) 1.54 (35.5) 2.30 (53.0) 2.18 (50.3) 2.07 (47.7) 1.88 (43.3)

1.29 (29.8) 2.09 (48.3) 1.91 (44.0) 1.83 (42.2) 1.70 (39.3) 1.42 (32.8) 2.21 (51.0) 2.00 (46.1) 1.91 (44.1) 1.77 (40.7) 1.63 (37.5) 2.20 (50.7) 2.10 (48.4) 2.02 (46.6) 1.87 (43.2) 1.71 (39.4) 0.65 (15.0) 0.58 (13.4) 0.54 (12.5) 0.46 (10.7)

1.24 (28.5) 2.08 (48.0) 1.89 (43.5) 1.81 (41.7) 1.68 (38.7) 1.37 (31.6) 2.22 (51.2) 2.00 (46.0) 1.91 (44.0) 1.76 (40.5) 1.57 (36.2) 2.23 (51.5) 2.14 (49.3) 2.05 (47.3) 1.88 (43.4) 1.65 (38.0) 2.35 (54.3) 2.21 (50.9) 2.11 (48.7) 1.94 (44.7)

Reference 34.

The C-F bond lying in the Φ(F-Ge-C-F) symmetry (Cs) plane increases in length by 0.023 Å from neutral to anion. This accompanies a decrease in the F-Ge-C bond angle of only 0.5°. From the neutral to the triplet state, the Ge-F and Ge-C bond distances decrease by 0.010 and 0.015 Å, respectively, while the central F-Ge-C bond angle increases by 17.4°. In comparing the triplet 3A′′ states of HGeCF3 and FGeCF3, there is a difference of 0.071 Å in the Ge-C bond distance and in the divalent angle of almost 6.1°. The EAad(ZPVE) is predicted to be 1.62 eV (BLYP) < 1.69 eV (BHLYP) < 1.78 eV (B3LYP). The VEA is slightly lower, ranging from 1.42 to 1.58 eV, with BLYP again as the lowest value, while the VDE predictions are 1.78 eV (BLYP) < 1.85 (BHLYP) < 1.94 (B3LYP). The singlet-triplet splitting is significantly higher compared to the HGeCF3 result, by almost 0.9 eV. The theoretical singlet-triplet gaps are 2.18 eV (BHLYP) < 2.21 eV (BLYP) ∼ 2.22 eV (B3LYP). C. ClGeCF3 and ClGeCF3-. Figure 3 presents the optimized geometries of the 1A′ neutral state of ClGeCF3, the 2A′′ state of the ClGeCF3- anion, and the corresponding 3A′′ state of the ClGeCF3 anion. The 1A′ neutral state of ClGeCF3 has a predicted Ge-Cl bond length ranging from 2.185 to 2.235 Å in the order BHLYP < B3LYP < BLYP. The corresponding divalent angle predictions are 94.5° (BHLYP) < 95.2° (B3LYP) < 96.1° (BLYP). Examining these values reveals that the addition of an extra electron increases the Ge-C bond length by almost 0.017 Å (BHLYP), while the corresponding Cl-Ge-C bond angle increases by only 0.9°. BLYP and BHLYP provide upper

Germylenes


Figure 2. Equilibrium geometries for the 1A/1A′ states of FGeCF3, 2A′′ state of the FGeCF3- anion, and 3A′′ state of the FGeCF3.

and lower signposts, respectively, for all three forms of the neutral anion energy differences. The ClGeCF3 molecule binds an extra electron, with an EAad(ZPVE) of 2.02 eV, VEA of 1.78 eV, and a VDE of 2.25 eV. The difference in electron affinity for ClGeCF3 versus HGeCF3 is 0.28 eV for the EAad(ZPVE), 0.17 eV for the VEA, and 0.44 eV for the VDE. The chlorinated singlet-triplet splitting is lower compared to the valence isoelectronic FGeCF3 species. D. BrGeCF3 and BrGeCF3-. The optimized geometries of the 1A′ state of BrGeCF3, 2A′′ state of the BrGeCF3- anion, and the corresponding lowest lying neutral triplet 3A′′ state are presented in Figure 4. The Ge-Br bond lengths fall in the order 2.335 Å (BHLYP) < 2.358 Å (B3LYP) < 2.387 Å (BLYP). The same order follows for the Ge-C bond distance, from 2.081 to 2.139 Å, and the corresponding Br-Ge-C divalent angle ranges from 95.2° to 96.6°. From Figure 4 the C-F bond lying in the symmetry plane Φ[Br-Ge-C-F] ) 180.0° is slightly longer compared to the other C-F bonds, by about 0.011 Å (B3LYP). The addition of an extra electron to the neutral 1A′ state of the BrGeCF3 molecule causes increases in the Ge-Br and Ge-C bond distances by almost 0.187 and 0.015 Å (BHLYP), respectively. No appreciable differences are observed

in the Br-Ge-C bond angle when comparing the three functionals. From the neutral 1A′ state of BrGeCF3 to the 3A′′ triplet state, there is a significant increase (19.7°) in the divalent angle. The Ge-C bond of the triplet species is slightly shorter compared to its corresponding ground state singlet, by 0.014 Å. E. IGeCF3 and IGeCF3-. Figure 5 (in the Supporting Information) presents the optimized geometries for the 1A′ state of neutral IGeCF3, the 2A′′ state of the anion, and the lowest lying neutral triplet (3A′′) state. The difference in the Ge-I bond length between the neutral and its corresponding anionic species is 0.20 Å, while the decrease in I-Ge-C bond angle is only 1° (BHLYP). For the 3A′′ state no significant changes compared to 1A′ are observed in the geometrical parameters, except for the expected large increase in the divalent angle, by 20.0°. On comparison of the neutral 1A′ ground state IGeCH3 to that of the IGeCF3 molecule, slight changes are observed with respect to the former,34 where the structural parameters are r(Ge-I) ) 2.607 Å, r(Ge-C) ) 1.988 Å, and θ(I-Ge-C) ) 97.5°. For the series of molecules XGeCF3, the divalent angles θ(X-Ge-C) (X ) H, F, Cl, Br, and I) lie in the order 89.4° (H) < 92.7° (F) < 94.5° (Cl) < 95.2° (Br) < 96.1° (I). It may be

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Figure 3. Equilibrium geometries for the 1A′ state of ClGeCF3, 2A′′ state of the ClGeCF3- anion, and 3A′′ state of the ClGeCF3.

noted that the three functionals behave similarly, where in most cases the BHLYP functional predicts the shortest bond distances, while the BLYP functional predicts the lowest values for the electron affinities. A different trend is observed for the corresponding triplet species, with the divalent angles falling in the order 110.1° (F) < 113.7° (Cl) < 114.9° (Br) < 116.1° (I) ∼ 116.2° (H). The Ge-C bond distances for the XGeCF3 species (X ) H, F, Cl, Br, and I) are predicted in the order 2.064 Å (H) < 2.078 Å (F) ∼ 2.079 Å (Cl) < 2.081 Å (Br) < 2.083 Å (I). All optimized geometrical parameters of all iodine-containing species are reported in the Supporting Information. F. HGeCCl3 and HGeCCl3-. Turning to the trichloro systems, Figure 6 presents the optimized geometrical parameters for the neutral 1A′′ ground state HGeCCl3, the 2A′′ state of the anion, and the 3A′′ neutral triplet state. The addition of an extra electron produces an increase in the Ge-H bond length of 0.024 Å, with a corresponding decrease in the H-Ge-C bond angle of 1.1°, as well as an increase in the Ge-C bond distances of 0.073 Å (BHLYP). The Ge-C bond length of the 3A′′ triplet state of HGeCCl3 decreases by 0.029 Å from that of the 1A′ ground state HGeCCl3. There is an expected appreciable 3 A′′-1A′′ increase in the H-Ge-C bond angle of 24.1°, together with a decrease in the Ge-H bond length of nearly 0.035 Å. In comparison to the HGeCF3 system, there is no

Figure 4. Equilibrium geometries for the 1A′ state of BrGeCF3, 2A′′ state of the BrGeCF3- anion, and 3A′′ state of the BrGeCF3.

appreciable effect on the Ge-H and Ge-C bond lengths. As observed at the bottom of Figure 6, the -CCl3 moiety, with the BLYP functional, is rotated compared to the other two functionals, accompanying a decrease in the H-Ge-C bond angle by 2.9° compared to the BHLYP functional. The HGeCCl3 electron affinity with ZPVE correction, EAad(ZPVE), falls in the range 1.71 eV (BLYP) to 1.83 eV (B3LYP). The HGeCCl3 VEA decreases by 0.41 eV compared to HGeCF3 and the VDE by 0.07 eV. But in comparison to HGeCH3, the EAad(ZPVE) and VDE increase by 0.62 and 0.17 eV respectively, while the VEA increases by 0.66 eV. G. FGeCCl3 and FGeCCl3-. Figure 7 presents the equilibrium geometries of the neutral ground state 1A′ FGeCCl3, the 2 A′′ ground state anion, and the corresponding neutral 3A′′ state. The 1A′ FGeCCl3 structure has predicted Ge-F bond distances of 1.771 Å (B3LYP) and 1.797 Å (BLYP) and F-Ge-C bond angles in the order 95.7° (BHLYP) < 96.0° (B3LYP) < 97.0° (BLYP), while the 3A′′ triplet state FGeCCl3 is predicted to have

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Figure 6. Equilibrium geometries for the 1A state of HGeCCl3, 2A′′ state of the HGeCCl3-, anion and 3A′′ state of the HGeCCl3.

Ge-F and Ge-C bond distances in the range 1.764 Å (BHLYP) < 1.792 Å (B3LYP) < 1.820 Å (BLYP) and 2.739 Å (BLYP) < 2.843 Å (B3LYP) < 3.100 Å (BHLYP) and bond angles of 89.1°-96.9°. Geometrical changes accompanying the addition of an electron to FGeCCl3 are increases of 0.082 Å and 1.0° in the Ge-F bond length and F-Ge-C bond angle, respectively. The singlet-triplet splitting of 3.57 eV obtained with the BHLYP functional is found to be consistent with the trend observed earlier for the GeHX and XGeCH334 species. Fluorine exerts a marked decrease on the EAad(ZPVE) of FGeCCl3, in almost the same manner as that observed for FGeCF3. The FGeCCl3 electron affinity after ZPVE corrections, EAad(ZPVE), falls in the range from 1.66 eV (BHLYP) to 1.80 eV (B3LYP). The FGeCCl3 VEA decreases by 0.42 eV compared to that for HGeCCl3 and the VDE by 0.26 eV. H. ClGeCCl3 and ClGeCCl3-. The equilibrium geometries for the 1A′ state of the neutral ClGeCCl3, the 2A′′ state of the anion, and the neutral 3A′′ triplet state are displayed in Figure 8. It is observed that the Ge-C bond distance lies in the range 2.071 Å (BHLYP) < 2.092 Å (B3LYP) < 2.116 Å (BLYP). Between the ground-state neutral and the anion there is an increase in the Ge-H bond length of 0.152 Å, with an accompanying slight decrease in the divalent bond angle of 2.3° (B3LYP). The differences in the geometrical parameters between the neutral ground state and the triplet state show a slight

increase in the Ge-Cl bond length by 0.008 Å, with an increase in the bond angle of 12.0° (B3LYP). For ClGeCCl3 the ZPVE corrected adiabatic electron affinity ranges from 1.87 to 1.96 eV in the order BLYP < BHLYP < B3LYP, while the VEA value decreases by 0.44 eV and the VDE value increases by 0.27 eV. I. BrGeCCl3 and BrGeCCl3-. The equilibrium geometries for the 1A state of the neutral, the anion BrGeCCl3-, and the neutral 3A′′ triplet state of BrGeCCl3 are presented in Figure 9. Between the ground state neutral and anion there is a sizable increase in the Ge-Br bond length of 0.166 Å, while the divalent bond angle is predicted to decrease by 2.4°. The equilibrium geometry of the 3A′′ state reveals a tiny increase (relative to X 1A) in the Ge-Br bond length by 0.002 Å, accompanying a large increase in the bond angle of 14.2°. It may be noted that the predicted EAad(ZPVE) ranges from 1.91 to 2.09 eV in the order BLYP < BHLYP < B3LYP. The theoretical value for the singlet-triplet splitting of 46.5 kcal mol-1 with the BHLYP functional is found to be consistent with the trend observed for the simpler germylene derivatives.34 The B3LYP difference in EAad(ZPVE) between BrGeCCl3 and ClGeCCl3 is 0.08 eV. The substitution of the -CH3 group by -CCl3 increases the EAad(ZPVE) and the singlet-triplet gap by 0.89 and 0.11 eV, respectively, with the BHLYP functional.

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Figure 7. Equilibrium geometries for the 1A/1A′ state of FGeCCl3, 2A′′ state of the FGeCCl3- anion, and 3A′′ state of the FGeCCl3.

J. IGeCCl3 and IGeCCl3-. The optimized geometries of the A ground state neutral IGeCCl3, the 2A′′ state of the anion, and the 3A′′ triplet state are presented in Figure 10 (Supporting Information). The geometries of the neutral ground state 1A IGeCCl3 show the Ge-I bond length and X-Ge-C bond angle ranging from 2.568 to 2.623 Å and 101.1-102.3° respectively. The Ge-C bond length falls in the range 2.078-2.123 Å in the order BHLYP < B3LYP < BLYP. The addition of an extra electron to the neutral 1A IGeCCl3 species reveals an increase in the Ge-I bond distance by 0.179 Å, while the Ge-C bond distance increases by 0.04 Å, and the divalent bond angle decreases slightly by 2.5°. The predicted EAad(ZPVE) ranges from 2.02 to 2.18 eV, with the BLYP and BHLYP functional as lower and upper limits. It should be noted that though the 6-311G(d,p) basis sets is used for the iodine atom, this does not influence the relative trends for the geometrical parameters and energy separations of IGeCCl3. The iodo substituents decrease the VEA and VDE by 0.24 and 1.01 eV, respectively, compared to IGeCF3.34 From Table 1, it is seen that there is a difference in the EAad(ZPVE) of only 0.13 eV between BrGeCCl3 and IGeCCl3. The energy splittings obtained with all three functionals, from Table 4, are found to be consistent with the trends previously observed for the simpler germylene derivatives.34 1

K. XGeCBr3 and XGeCI3- (X ) H, F, Cl, Br, and I). Unlike the XGeCF3 and XGeCCl3 (X ) H, F, Cl, Br, and I) molecules, the heavier XGeCBr3 and XGeCI3 (X ) H, F, Cl, Br, and I) molecules converged to unexpected structures (Supporting Information), using the same DFT functionals, namely, BHLYP, BLYP, and B3LYP. For the bromine and iodine substituents at the carbon center, it is observed that in some cases the expected structures collapse to three-membered cyclic systems with the formation of weak bonds involving the divalent germanium center, the carbon atom, and one of the bromine atoms. These unconventional structures are included in Figures 11-20 (see Figures 15-20 in the Supporting Information). In some cases, the molecules are optimized to yield structures where the carbon moiety is rotated or one of the halogen atoms is completely bonded to the divalent germanium center. Following the (3n - 6) rule for the number of fundamentals in these polyatomic molecules, 12 real vibrational frequencies are found in all cases. To ensure these atypical structures are not due the level of computations and basis sets, optimization at the Hartree-Fock level of theory was also carried out. Further, investigating these molecules using the LAN2L2DZ/ECP42,54,55 basis sets for the bromine and iodine with the different functionals, the same effects are observed.

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Figure 8. Equilibrium geometries for the 1A state of ClGeCCl3, 2A′′ state of the ClGeCCl3- anion, and 3A′′ state of the ClGeCCl3.

Figure 9. Equilibrium geometries for the 1A state of BrGeCCl3, 2A′′ state of the BrGeCCl3- anion, and 3A′′ state of the BrGeCCl3.

Interestingly, a wealth of unusual structures has been reported for the digermanium fluorides.56 Although these tribromo- and triiodo-substituted species show different trends in their geometrical parameters, their zero-point corrected electron affinities for the XGeCBr3 and XGeCI3 (X ) H, F, Cl, Br, and I) molecules are included in Table 1. It is noted that all EAad and EAad(ZPVE) are larger than those for the XGeCF3 and XGeCCl3 molecules (X ) H, F, Cl, Br, and I). Exceptions are for the computed zero-point corrected electron affinities values of (1.68 eV) HGeCBr3 and ClGeCBr3 (1.96 eV) which are irregularly predicted by the BHLYP functional. Furthermore, the computed zero-point corrected electron affinities are relatively larger for the XGeCI3 molecules, which increase from 3.26 eV (HGeCI3) to 3.52 eV (IGeCI3).

can be used as a noteworthy reactivity descriptor, qualitatively defined by Pauling.46 The standard Pauling electronegativities lie in the order F(3.98) > Cl(3.16) > Br(2.96) > I(2.66) > C(2.55) > H(2.20) > Ge(2.01). In extending the electronegativities of atoms to functional groups, Geerlings and co-workers47 have suggested χCH3 ) 5.72, χCF3 ) 6.28, χCCl3 ) 5.63, χCBr3 ) 5.49, χCI3 ) 5.33. We expect to observe similar trends in the geometrical parameters, electron affinities, and singlet-triplet splittings for the X-Ge-CY3 systems. We also expect, as a function of the halogen atom, the X-Ge-CY3 systems should display trends in geometrical parameters, electron affinities, and singlet-triplet gaps, compared to the GeHX and XGeCH3 systems.34 Halogen substitution appears to increase the favorability of the singlet states, and the magnitude of this stabilization follows the electronegativity. Previous computational results for the simpler XGeCH3 species (X ) H, F, Cl, Br, and I)34 are used here for comparison purposes. It is observed that the bond angles for all molecules in their singlet neutral ground states lie in the range 89.1-102.3°. The lone pair on the germanium atom causes a larger repulsion compared to the analogous repulsion of the bonding pair of

IV. Discussion (i). Structural Parameters. The predicted structural parameters show that the Ge-X, Ge-C, and C-Y bond distances lengthen in going from H f F f Cl f Br f I. These expected trends are due to the change in atomic sizes and electronegativities (χ) of the halogen substituent. The electronegativity (χ)

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Figure 11. Equilibrium geometries for the 1A state of HGeCBr3, 2A/2A′′ state of the HGeCBr3- anion, and 3A/3A′′ state of the HGeCBr3.

electrons; hence the ideal angle of 120° is decreased significantly. This lone pair “occupies” a large space and consequently results in divalent angles less than 120°. The values of the divalent angles in the series X-Ge-CY3 (X ) H, F, Cl, Br, and I; Y ) F and Cl), with respect to substituent X, show a larger effect compared to varying the halide substituent on the -CY3 moiety. While fixing either the Ge-X bond or the -CY3 moiety, the divalent bond angles fall in the order F < Cl < Br < I. From HGeCH3 f HGeCF3, one sees a decrease in the divalent angle by nearly 4.5°, where the electronegativity of the fluoro substituents should in principle cause a decrease in the divalent angle. However, the same effect is not observed in going from HGeCF3 f FGeCF3. On the contrary, the divalent angle is increased by 3.3° (BHLYP). The large electronegativity of the fluoro substituent gives rise to strong Coulombic repulsion, acting against the decrease in the bond angle. In going from the singlet ground state to the lowest lying triplet state, similar trends in the change of the structural parameters are predicted. The importance of the ligand-ligand interactions is also one of the factors driving the increase in the bond angles, which depend on the electronegativity of the ligand, independently of the size of the halogen. Comparing the geometrical parameters of the lowest singlet and triplet states of the same molecule, the most noticeable

difference is that the bond angles of the triplet states are larger by 10-20°, for all XGeCF3 and XGeCCl3 (X ) H, F, Cl, Br, and I). In the singlet state the HOMO is of a′ symmetry, corresponding to the lone pair of electrons lying in the molecular plane. Consequently, in the triplet state an electron is moved to an orbital of a′′ symmetry, in a simple picture an out-of-plane atomic p orbital of the divalent germanium atom. As a result, of the valence shell electrons in the molecular plane, only one electron remains at the germanium center, leading to a large decrease in the repulsion, opening the bond angle in the triplet states. Another remarkable difference between the neutral ground and the lowest lying triplet states is that the Ge-X bond length is shorter in the triplet state. Analysis of the geometrical parameters reveals a regular trend, similar to the GeHX (X ) H, F, Cl, Br, and I) series34 with respect to the substituent electronegativity. To study the influence of a given halide substituent on the bond length, r, it is useful to plot the values of the Ge-C bond distance for fixed -CF3 in the series XGeCY3 (X ) H, F, Cl, Br, and I) as a function of the Pauling electronegativity of the second substituent X. Similarly, in keeping the r(Ge-X) bond distance fixed, the trend in the Ge-C bond elongation can be analyzed. The decreases in the repulsive interaction of the ligands from the singlet to the triplet state are illustrated in the trends shown in the Ge-X bond length along

Germylenes


Figure 12. Equilibrium geometries for the 1A state of FGeCBr3, 2A/2A′′ state of the FGeCBr3- anion, and 3A/3A′′ state of the FGeCBr3.

the series, shown in Figure 21. It is observed that the Ge-C bond length increases monotonically. Additionally, for FGeCF3 and FGeCCl3 species, the symmetry of the neutral ground states depends on the theoretical level. These structural changes may be related to the decreasing electron density around the divalent germanium center in the molecular plane from the singlet state to its corresponding triplet species. The ligand gets closer to the germanium atom and achieves a better screening of the bonding electrons. Comparing the triplet bond angle of these germanium derivatives for GeXY and XGeCH334 (X; Y ) H, F, Cl, Br, and I) the agreement is acceptable. Comparison with experimental bond angles is not possible, since no literature results are available, except the experimentally determined r(Ge-C) ) 1.95-2.00 Å48 of organogermanium derivatives. Halogen-containing groups retaining this trend are noted, with the -CF3 group considered the most electronegative, followed by -CCl3. Hence it may inferred that the -CH3 group is even less electronegative than -CCl3 and -CCBr3, in line with chemical perceptions, but not

consistent with the predicted electronegativities reported by Giju et al.47 for χCH3 ) 5.72. (ii). Electron Affinities. For X ) F, Cl, Br, and I, the electron affinities increase in the series XGeCF3 and XGeCCl3, showing that electron withdrawal is only one of the important effects. For X ) F, with fluorine directly attached to the divalent germanium center, while keeping the -CF3 moiety fixed, we observe a decrease in the electron affinities from HGeCF3 f FGeCF3 and HGeCCl3 f FGeCCl3. This gives an indication that the effect of π-donation from the lone pairs of electrons predominates. Taking into account the previously reported EAad(ZPVE) values,34 the trend is GeF2 (0.87 eV) < GeHF (0.98 eV) < HGeCF3 (1.71 eV). Since χCF3 ) 6.28 > χCH3 ) 5.72 > χF ) 3.98,47 it is expected that the EAad(ZPVE) for the HGeCF3 species would be smaller than the reported value 0.87 eV. This shows that there is a shielding effect from the -CY3 moiety, which acts against the decrease in the electron affinities. For X ) F (χF ) 3.98), accompanying a shortening of the Ge-F bond, the lone pair of the fluorine substituent crowds into the

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Figure 13. Equilibrium geometries for the 1A state of ClGeCBr3, 2A/2A′′ state of the ClGeCBr3- anion, and 3A/3A′′ state of the ClGeCBr3.

germanium π-orbital. This rationalizes the difference in the electron affinities between the HGeCF3 f FGeCF3 and HGeCCl3 f FGeCCl3 molecules. The lowest electron affinities are also correlated with the Ge-F bond distance, which is likely to reflect the ionic character and, hence, increase the positive charge in the divalent germanium center. The presence of conjugation by the heteroatom lone pair provides strong π donor character. The electronegative substituent withdraws electron density from the germanium center, increasing the “positive charge” which in turn makes the germanium a better π-acceptor and enhances π-donation from the halide substituent. It is observed that the contribution of the shortening of the Ge-F bond is related to the predicted electron affinity decrease with respect to the Cl/ Br/I substituents. There is a linear correlation between the Pauling electronegativities of the halogens with the energy differences between the neutral and the corresponding anionic species, as depicted in Figure 22. This correlation can be explained as a result of the decreasing order of back-donation: I < Br < Cl. As seen from the predicted EAad(ZPVE) values from Table 1, the inductive effect in the presence of the -CF3 moiety in HGeCF3 is more pronounced. The nominal “charge” on the divalent germanium center is found to be more positive in the case where X ) F for the

XGeCF3 and XGeCCl3 species. Hence the presence of a strongly electron withdrawing atom being directly attached to the germanium atom reduces the 4s and 4p populations. The 4p contribution to the σ Ge-F bond is higher in the singlet state than the corresponding triplet state. In contrast, for the lowest lying triplet state, the 4s contribution of the germanium atom is less, confirming the antibonding character of the σ orbitals in the halo-substituted organogermylene. It is predicted that the spn hybridization is reduced from F f Cl f Br f I. Therefore, stabilization of the σ nonbonding orbital by electron-withdrawing substituents such as halogens increases the 4s character of the germanium atom. The decrease in the electron affinity in the case of the fluoro substituent reveals that there is greater π-donation compared to the other halogen substituents. This π-donation is also affected by the smaller size of the fluorine atom. The increase in the partial charge on the divalent germanium center with fluoro substitution may be correlated with the polarity of the σ Ge-F bond and interelectron repulsion between the negatively charge halogen substituents. The σ Ge-F bond is more polarized than the Ge-Cl/Ge-Br/Ge-I bonds and hence results in the less effective donor ability of the nonbonding electron pairs on the Cl/Br/I substituents. Hence, there should not be a large difference in the electron withdrawing abilities

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Figure 14. Equilibrium geometries for the 1A state of BrGeCBr3, 2A/2A′′ state of the BrGeCBr3- anion, and 3A/3A′′ state of the BrGeCBr3.

Figure 21. Ge-X and Ge-C bond lengths (Å) (B3LYP) as a function of halogen substituent.

of the σ Ge-F, Ge-Cl, Ge-Br, and Ge-I bonds. Irrespective of the order of the halogen electronegativities, which decrease down the column, the electron affinities increase in the opposite order. Hence, the electronegativities of the halogen substituents are not the sole factor in determining the ability of these species to accept an additional electron. This electron capturing ability

is most probably dependent on the halogen substituent, the electron density at the divalent center, and the interelectron repulsion. (iii). Singlet-Triplet Splittings. Table 4 reports the singlet-triplet splittings for all molecules studied in this research. The trend is appreciable; the largest singlet-triplet

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Figure 22. Adiabatic electron affinities (eV) (B3LYP) vs halogen substituents. The GeHX and XGeCH3 are from ref 34.

Figure 23. Graph of singlet-triplet splittings (eV) (B3LYP) vs halogen substituents. The GeHX and XGeCH3 results are from ref 34.

gap appears where the fluoro substituent is directly attached to the divalent germanium center and the splitting decreases as one approaches iodine. Hydrogen is less electronegative than iodine, resulting in the lowest singlet-triplet gap for X ) H. The presence of a strongly electronegative substituent stabilizes the 1A′ singlet state, and the 3A′′ state energy lies higher by 1.37 eV (HGeCF3) to 2.23 eV (FGeCCl3). Hence the presence of three halogen substituents favors the singlet states. There are two germylene orbitals whose occupancy determines whether a structure is a ground singlet state. In the lowest singlet state, the a′ symmetry molecular orbital is the HOMO, a σ-type nonbonding orbital having contributions from the in-plane p orbitals of the divalent germanium center and from the in-plane p orbitals of the substituent X ) F, Cl, Br, and I. Considering the effect of electronegativity and the size of the halo substituents this is reflected on the HOMO energy. In the case of the most electronegative ligand, χF ) 3.98, the participation of the germanium s orbital to the bonding will be large, decreasing the energy of the a′ orbital. This leads to an increase in the HOMO-LUMO gap (EH-L), favoring the singlet state. The a′′ orbital is the LUMO in the singlet but becomes the SOMO for the corresponding triplet species, as one of the electron occupies the a′′ orbital. The p-type nonbonding orbital consists of the germanium out-of-plane p orbital and the out-of-plane p orbitals of the ligand. In the case of the highly electronegative ligand fluorine, this will be a strong antibonding orbital and hence higher in energy. This fluorination results in the highest value of the EH-L and, consequently, is reflected in the predicted singlet-triplet splittings. Figure 23 summarizes the singlet-triplet splittings (electronvolts) as a function of halogen substituent. With a decrease (F f I) in the electronegativity of the halides, the contribution of the germylene 4s orbital to the a′ HOMO

Bundhun et al. decreases, raising the energy of this orbital. In the triplet species, with a decrease in the electronegativity and an increase in the size of the halides, the energy of the out-of-plane p orbital increases. The overlap of the latter orbitals with the germanium 4p orbital decreases and hence diminishes the antibonding character of the a′′ orbital, lowering the energy of that orbital. Thus, in going down the halogen group, the a′ and a′′ orbital energy separation tends to decrease. The observed relationship between charge and electronegativity permits singlet-triplet gaps to be qualitatively predicted. The Mulliken atomic charge on the divalent germanium center is significantly more positive than that at the adjacent carbon center. The charges on the germanium atom for the XGeCF3 (X ) H, F, Cl, Br, and I) species fall in the order +0.37e (H) ∼ +0.37e (I) < +0.47e (Cl) ∼ +0.47e (Br) < +0.71e (F), while the charges on the carbon center for the -CF3 group lie in the order +0.28e (F) < +0.29e (H) ∼ +0.29e (I) < +0.30e (Cl) ∼ +0.30e (Br). Analyzing the charge present on the germanium center for the XGeCCl3 (X ) H, F, Cl, Br, and I) species, the same trend is observed but with a slightly higher positive charge compared to the XGeCF3 analogues, except for the carbon center, which follows a different trend. The charges on the germanium atom for the XGeCCl3 molecules are as follows: +0.41e (H) < +0.45e (I) < +0.54e (Cl) < +0.55e (Br) < +0.83e (F), while for the carbon the charges are all negative: -0.63e (F) < -0.54e (H) < -0.52e (Br) < -0.51e (Cl) < -0.49e (I). Considering the carbon center to be more electronegative, this indicates that chlorine, bromine, and iodine are σ and π donors in -CY3. As expected for the -CF3 moiety, in the presence of a strongly electron-withdrawing fluoro substituent, the 2s and 2p populations on the carbon center are smallest.49 It is known that the σ orbitals of the carbon-halogen bonds have some antibonding character. The 2s carbon contribution to the spn hybridization strongly decreases in going from fluorine toward iodine substitution, when the halogen is directly attached to the divalent germanium center. The trend in the singlet-triplet gaps of these organogermanium species is similar to those reported for simple carbene,50 silylene, and germylene derivatives.51,52 The predicted singlet-triplet separations can be rationalized in terms of the charge on the divalent germanium and the π-donation from the halogen substituent to which Ge is directly attached. Hence, the net charge, σ-donation, and π-back-bonding act synergistically for the understanding of singlet-triplet splittings. The trend in the partial charges of the central atom for a given halogen is not regular. The divalent germanium center always carries a positive partial charge, which decreases from fluorine toward iodine. Fluorine has a stabilizing effect due to its facility in π-donation; the π and σ effects could lead to an even more positive charge on the carbon atom. This shows that the π-donation from the halogen leads to more favorable bonding. The quest for new germylenes, employing relatively bulky groups such as -CY3 (Y ) F, Cl, Br, and I) (or more realistically -Si(SiR3)3) may enlarge the divalent angle in a way to make the triplet lower in energy than its corresponding singlet state.53 As the divalent angle approaches 120°, the singlet-triplet splitting decreases to 10-20 kcal mol-1. The energy of the inplane nonbonding orbital of the divalent center is influenced by the electronegativity of the attached substituent. A nearly linear correlation is found between the singlet-triplet splitting and the EH-L of the corresponding singlet states. Apparently, electronegative substituents (X ) F, Cl, Br, and I) favor the singlet states, while the EH-L is increased with the lowering of the energy of the HOMO. The highest EH-L is found for F,

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J. Phys. Chem. A, Vol. 114, No. 50, 2010 13211 of the halogen substituents F > Cl > Br, the acceptor abilities of the σ*(C-Y) orbitals increase in the order σ*(C-F) < σ*(C-Cl) < σ*(C-Br). These results are intriguing in light of the higher donor abilities of the σC-Cl and σC-Br bond. Thus the order of the acceptor ability toward the C-F orbital is C-Br > C-Cl, while the order of acceptor abilities toward the C-Cl orbital is C-Br > C-F. With respect to the carbon-halogen bond, the hyperconjugative interactions are lower, because the carbon-halogen bonds are weaker donors than C-H bonds. Though the difference in the acceptor ability of the σ*(C-Cl) and σ*(C-Br) bonds is not very large, it is susceptible to the nature of X substitution. The C-F bonds are more polarized toward the halogen than C-Cl/C-Br bonds. Furthermore, for XGeCBr3 and certain XGeCI3, the structures of the anions and low-lying triplet structures are strongly affected by the functional. V. Conclusions

Figure 24. Schematic representation of the energy levels of the σ and σ* orbitals of the carbon-halogen bonds.

while the lowest values are encountered for bromine and iodine. In contrast, when X is attached to the divalent germanium centers, the highest relative EH-L is encountered. Such a trend is at variance with the electronegativity trend F < Cl < Br. This is consistent with the partial charges on the carbon atom which follow the electronegativity trend of the halogens, Y ) F, Cl, Br, and I. Also, germanium has a positive charge, while carbon is negative, which is consistent with the trend observed for the simple germylenes HGeCH3 f IGeCH3, in the order -0.60 (F) < -0.59 (H) < -0.57 (Cl) < -0.55 (Br) < -0.53 (I).34 The trend of carbon charges follows the electropositivity of the halogens X ) F < Cl < Br < I. Some minor back-bonding between germanium and chlorine or bromine is indicated by hybridization. The Ge-X bond lengths are necessarily proportional to the halogen size X ) F < Cl < Br < I, where X is directly attached to the divalent germanium center. Similarly, the retro electronegativity trend (I > Br > Cl > F) is observed for the X-Ge-C bond angles in the triplet states. (iv). The Surprising XGeCBr3 and XGeCI3 (X ) H, F, Cl, Br, and I) Germylenes. A plausible explanation for the atypical characteristics of these species is that the carbon-halogen bonds are σ acceptors; hence hyperconjugative effects are particularly sensitive to changes in substituent effects. The σ*C-F bonds have higher acceptor abilities, while the anomeric effect predominates for the bromo and iodo substituents. The anomeric effect contributes to the electronic and steric factors. Thus we see the acceptor ability of the carbon-halogen bonds, where the substituents X ) F, Cl, and Br are closely associated with their electronegativity. Another factor that contributes may be reflected by the carbon-halogen bond strengths of carbonbromine and carbon-iodine. The relative levels of the σ and σ* energy levels can be represented qualitatively in Figure 24. The σ energy levels increase from σ(C-F) < σ(C-Cl) < σ(C-Br) < σ(C-I), whereas the σ* energy levels decrease from σ*(C-F) > σ*(C-Cl) > σ*(C-Br) > σ*(C-I). This implies that the σ(C-Y) f σ*(C-Y) energy separation of the -CY3 fragment becomes smaller as one proceeds along the series from fluorine to iodine. Even with a decrease in the electronegativity

The structural parameters, four different neutral-anion energy differences (namely, EAad, EAad(ZPVE), VEA, and VDE), plus the singlet-triplet gaps of the smaller XGeCY3 (X ) H, F, Cl, Br, and I; Y ) F and Cl) systems have been investigated. It has been observed that these structures are conventional when the halogens attached to the carbon center are fluorine or chlorine substituents, but this is not the case for bromine and iodine. For the tribromo germylene derivatives an unexpected three-membered cyclic system is observed, while for the triiodo germylenes, in some cases, one of the halogen atoms from the carbon center is bonded to the divalent center. It is also observed that the breaking of the carbon-halogen bond increases with decreasing halide electronegativity. All halogens stabilize the trihalo-substituted germylenes relative to GeHX and HGeCH3, since carbon is a strong π acceptor in the -CY3 substituent and a σ acceptor with -CCl3, -CBr3, and -CI3. The ability to bind an extra electron by the XGeCY3 (X ) H, F, Cl, Br, and I; Y ) F and Cl) molecules has been predicted. It is observed that a related trend in the predicted electron affinities and singlet-triplet gaps is followed compared to the simple GeHX and XGeCH3 species. The BHLYP functional which incorporates the largest fraction of the Hartree-Fock method37 provides the best agreement for the predicted structures and electron affinities of simpler germylenes34 compared to experimental values. Hence, the BHLYP functional provides the most appropriate values for these systems in the absence of experimental data. Acknowledgment. The authors thank the reviewers for their helpful comments on the manuscript. The research has been supported by the Mauritius Tertiary Education Commission (TEC) and the U.S. National Science Foundation. A.B. acknowledges the use of facilities at the School of Chemical Sciences, Universiti Sains Malaysia, Penang, Malaysia, and the Center for Computational Quantum Chemistry (CCQC) at the University of Georgia. Supporting Information Available: Equilibrium geometries for the 1A′ state of IGeCF3, 2A″ state of the IGeCF3- anion, and 3A′′ state of the IGeCF3 (Figure 5); for the 1A state of IGeCCl3, 2A′′ state of the IGeCCl3- anion, and 3A′′ state of the IGeCCl3 (Figure 10); for the 1A state of IGeCBr3, 2A/2A′′ state of the IGeCBr3- anion, and 3A′′ state of the IGeCBr3 (Figure 15); for the 1A state of HGeCI3, 2A state of the HGeCIr3- anion, and 3A state of the HGeCI3 (Figure 16); for the 1A state of FGeCI3, 2A state of the FGeCI3- anion, and 3A state of the FGeCI3 (Figure 17); for the 1A state of ClGeCI3, 2A state of

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the ClGeCI3- anion, and 3A state of the ClGeCI3 (Figure 18); for the 1A state of BrGeCI3, 2A state of the BrGeCI3- anion, and 3A/3A′′ state of the BrGeCI3 (Figure 19); for the 1A state of IGeCI3, 2A/2A′′ state of the IGeCI3- anion, and 3A state of the IGeCI3 (Figure 20). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Wang, X.; Zhu, Z.; Peng, Y.; Lei, H.; Fettinger, J. C.; Power, P. P. J. Am. Chem. Soc. 2009, 131, 6912. (2) Walker, R. H.; Miller, K. A.; Scott, S. L.; Cygan, Z. T.; Bartolin, J. M.; Kampf, J. W.; Holl, M. M. B. Organometallics 2009, 28, 2744. (3) Jana, A.; Schulzke, C.; Roesky, H. W. J. Am. Chem. Soc. 2009, 131, 4600. (4) Ullah, F.; Kindermann, M. K.; Jones, P. G.; Heinicke, J. Organometallics 2009, 28, 2441. (5) Jana, A.; Sarish, S. P.; Roesky, H. W.; Schulzke, C.; Do¨ring, A.; John, M. Organometallics 2009, 28, 2563. (6) Hayes, P. G.; Gribble, C. W.; Waterman, R.; Tilley, T. D. J. Am. Chem. Soc. 2009, 131, 4606. (7) Jana, A.; Objartel, I.; Roesky, H. W.; Stalke, D. Inorg. Chem. 2009, 48, 798. (8) Jaque, P.; Toro-Labbe´, A.; Geerlings, P.; Proft, F. D. J. Phys. Chem. A 2009, 113, 332. (9) Tomasik, A. C.; Hill, N. J.; West, R. J. Organomet. Chem. 2009, 694, 2122. (10) Timoshkin, A. Y.; Schaefer, H. F. J. Phys. Chem. C 2008, 112, 13816. (11) Chizmeshya, A. V. G.; Ritter, C. J.; Hu, C.; Tice, J. B.; Tolle, J.; Nieman, R. A.; Tsong, I. S. T.; Kouvetakis, J. J. Am. Chem. Soc. 2006, 128, 6919. (12) Mui, C.; Han, J. H.; Wang, G. T.; Musgrave, C. B.; Bent, S. F. J. Am. Chem. Soc. 2002, 124, 4027. (13) Gopakumar, G.; Ngan, V. T.; Lievens, P.; Nguyen, M. T. J. Phys. Chem. A 2008, 112, 12187. (14) Larkin, J. D.; Bock, C. W.; Schaefer, H. F. J. Phys. Chem. A 2005, 109, 10100. (15) Yang, J.; Bai, X.; Li, C.; Xu, W. J. Phys. Chem. A 2005, 109, 5717. (16) Pak, C.; Rienstra-Kiracofe, J. C.; Schaefer, H. F. J. Phys. Chem. A 2000, 104, 11232. (17) Antoniotti, P.; Borocci, S.; Grandinetti, F. J. Phys. Chem. A 2006, 110, 9429. (18) Li, X.; Kiran, B.; Wang, L.-S. J. Phys. Chem. A 2005, 109, 4366. (19) Li, Q.; Li, G.; Xu, W.; Xie, Y.; Schaefer, H. F. J. Chem. Phys. 1999, 111, 7945. (20) Li, Q.; Li, G.; Xu, W.; Xie, Y.; Schaefer, H. F. Phys. Chem. Chem. Phys. 2002, 3, 179. (21) Xu, W.; Yang, J.; Xiao, W. J. Phys. Chem. A 2004, 108, 11345. (22) Li, C. P.; Li, X. J.; Yang, J. C. J. Phys. Chem. A 2006, 110, 12026. (23) Nam, P.-C.; Nguyen, M. T.; Chandra, A. K. J. Phys. Chem. A 2006, 110, 4509. (24) Ignacio, E. W.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 7439. (25) Szabados, A.; Hargittai, M. J. Phys. Chem. A 2003, 107, 4314. (26) Drake, S. A.; Standard, J. M.; Quandt, R. W. J. Phys. Chem. A 2002, 106, 1357. (27) Irikura, K. K.; Goddard, W. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1992, 114, 48.

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