A theoretical investigation into novel germylenes: effects of nitrogen substitution on stability and multiplicity

Abstract

The effects of substituting nitrogen atoms on the stability of novel singlet (s) and triplet (t) forms of germylenes (1–20) are compared and contrasted, at B3LYP/AUG-cc-pVTZ level of theory. Every one of the 40 new divalents scrutinized appears as a minimum on its energy surface, for showing no negative force constant. Also, every singlet (1_s–20_s) appears more stable than its corresponding triplet (1_t–20_t). The highest stability (ΔE_s-t) is achieved by germylene (11) where all the three nitrogens are bonded to the central boron atom. The E_HOMO slightly decreases when the number of electronegative, σ-acceptor nitrogen atoms increases, and also causes it to be less electron-rich. Germylene 16_s with low stability (ΔE_s–t = 17.19 kcal/mol), bond gap (ΔE_HOMO-LUMO = 57.46 kcal/mol⁻¹), and atomic charge on -G̈e- (+ 0.9012), has high electrophilicity (ω = 3.78 eV) and nucleophilicity (N = 3.87 eV). Germylenes 8_s, 14_s, and 19_s with coordinate covalent bond between nitrogen (N(Y)) and germylene center have low ω and high ΔE_HOMO-LUMO. The purpose of the present work was, therefore, to assess the influence of nitrogen substituents on the stability (ΔΕ_s–t), band gaps (ΔΕ_HOMO–LUMO), N, ω, and heat of hydrogenation (ΔE_H). This investigation is aimed to introduce novel germylenes that can be applied as cumulated multi-dentate NHG̈e ligands.

Introduction

The divalent germylenes, GeR₂, have gained much attention over the last four decades because of their electron-deficient radicals applied in chemical vapor deposition, semiconductor manufacturing, the photonics, and aerospace industries and other roles [1,2,3].

NHGe derivatives with the coordination of electronegative and π-electron-donating heteroatoms have high reactivity [3,4,5,6,7,8,9,10]. The NHGe has a weaker p_π-p_π interaction between nitrogen and germylene center than the corresponding NHC because germanium is less electronegative and larger than carbon. This leads to a reduction in the π electron density on the germylene center which makes the NHGe to be a better π acceptor [11, 12]. In 1982, the first N-heterocyclic germylene with four-membered ring was reported by M. Veith [13]. The systematic theoretical studies employing correlated wave functions on R₂Ge have shown a strong tendency for germylenes to have singlet ground states and a substantial electronic effect of different substituents on the ΔE_s–t of divalent species [14,15,16,17]. The electronegative substituents at germylenes increase the ΔE_s–t gap, whereas the electropositive ones reduce it [18].

Interestingly, many organogermanium compounds have biological activities that have attracted much attention. In addition, Heremann reported saturated and unsaturated five-membered NHGe compounds, [19] which could be used as the original body to prepare the Ge-film by chemical vapor deposition (VCD) [20]. Therefore, the studies on germylenes and germylene reactions have important theoretical as well as practical significance. The aim of our work is to answer the question that arises whether novel singlet and triplet germylenes are researchable and how nitrogen substitutions may influence their stability, multiplicity (singlet (s) vs. triplet (t)), band gap (ΔE_HOMO–LUMO), nucleophilicity (N), and electrophilicity (ω) at B3LYP/AUG-cc-pVTZ//B3LYP/6–311++G** level of theory. In addition, a number of them show prospects of being employed as multi-dentate NHGe ligands.

Computational methods

Our computational study, due to its excellent performance-to-cost ratio as compared with the correlated wave function theory, is confined to B3LYP calculations [21], while some recent reports have questioned the reliability of the most popular density functional, B3LYP [22]. We used B3LYP with the 6–311++G** basis set that is prevalent in many other papers on germylenes [11, 23, 24]. Triplet states were calculated using the unrestricted broken spin-symmetry UB3LYP/6–311++G** method implemented in the GAMESS software package [25, 26]. The vibrational frequency computations are applied to characterize the nature of stationary points, as true minima only real frequency values (with a positive sign) or the transition states only one imaginary frequency value (with a negative sign) is accepted respectively [27, 28]. 

The reactivity parameters are estimated via following the expressions: N = E_HOMO(Nu) − E_HOMO(TCNE);(tetracyanoethylene (TCNE) is preferred as the reference); ω = (μ²/2η), where μ is the chemical potential (μ ≈ (E_HOMO + E_LUMO)/2) and η is chemical hardness (η = E_LUMO − E_HOMO) at the same level of theory [29].

To reach more accurate energetic data, single point calculations are accomplished B3LYP/AUG-cc-pVTZ (correlation consistent polarized valence triple zeta) based on the B3LYP/6–311++G**geometries [30].

Results and discussion

We have compared and contrasted novel singlet (s) and triplet (t) germylenes (1_s–20_s vs. 1_t–20_t) with regard to their geometrical parameters (Table 1); second-order perturbation stabilization energies (E⁽²⁾) (Table 2); occupancy numbers (Table 3); relative stability (ΔΕ_s-t = Ε_t−E_s) and ΔE_H (Table 4); the frontier molecular orbital energies (HOMO and LUMO) for singlet germylenes along with their band gaps (ΔΕ_HOMO–LUMO) (Table 5) at B3LYP/AUG-cc-pVTZ//B3LYP/6–311++G** level of theory.

Table 1 Optimized bond length (Å), carbenic angle (∠ZG̈eV/deg), and dihedral angle (∠G̈eVBZ/deg) for novel singlet (1_s–20_s) and triplet (1_t–20_t) germylenes, at B3LYP/6–311++G** level

Table 2 Calculated second-order perturbation stabilization energies (E⁽²⁾), for the intermolecular interactions (donor/acceptor NBO) of singlet (1_s–20_s) germylenes, at the B3LYP/6–311++G** level of theory

Table 3 Calculated occupancy number of LP_G̈e, π_{(N-G̈e) or (G̈e-N)}, σ_(G̈e-B), LP_N(V,W,X,Y,Z) using NBO analysis, and the ESP diagrams for singlet germylenes, at the B3LYP/6–311++G** level of theory

Table 4 Singlet–triplet energy gaps (ΔE_s–t, kcal mol⁻¹), heats of hydrogenation (ΔE_H, kcal/mol⁻¹), along with dipole moments (D), and the smallest calculated vibrational frequencies (υ_min, cm⁻¹) of our germylenes, at B3LYP/AUG-cc-pVTZ level of theory

Table 5 NBO charges on -G̈e- and B atoms for singlet (1_s–20_s) and triplet (1_t–20_t) germylenes, at B3LYP/6–311++G** level of theory

The range of bond angle ∠ZG̈eV for our germylenes is from 67.29° to 83.78°. The singlet state of our germylenes has longer bond angle (∠ZG̈eV) than their corresponding triplets. The optimized bond lengths for (Z-G̈e or G̈e-V) 1_s–20_s vs. 1_t–20_t vary in a range of 1.93 to 2.82 Å. The Z-G̈e or G̈e-V bond lengths of our singlet germylenes, except 18_s, depend on the π-bonds and π-donor interactions (LP_N → LP^*_G̈e) nature of the nitrogen adjacent to germylene center. For instance, the G̈e–C bond lengths in germylene 6_s with G̈e=N bond and 2_s with high LP_N(Z)→LP^*_G̈e interaction (E⁽²⁾ = 13.65 kcal/mol⁻¹) are 0.03 Å and 0.08 Å longer than G̈e–N bond lengths, respectively (Tables 1 and 2).

Germylenes 6_s, 8_s, 14_s, and 19_s have coordinate covalent bonds between nitrogen and boron or germylene atoms. They do not show any occupancy number for a lone pair on nitrogen at situation V or Y but display occupancy number for π_(N(V)-B) or σ_(G̈e-N(Y)) bonds (Table 3).

Our germylenes have singlet ground state, so every triplet germylene (1_t–20_t) appears at a higher level of energy than its corresponding singlet (1_s–20_s). For instance, 1_s appears at almost 26.52 kcal/mol⁻¹ lower in energy than its corresponding 1_t. Our highest and lowest stable germylenes are 11 (ΔE_s–t = 34.27 kcal/mol⁻¹) and 15 (ΔE_s–t = 14.87 kcal/mol⁻¹), respectively. The overall stability order of our germylenes based on their ΔE_s-t values is 11 > 7 > 5 > 4 > 18 > 9 > 20 > 3 > 2 > 1 > 14 > 17 > 12 > 8 > 6 > 19 > 10 > 13 > 16 > 15. This stability can be related to our imposed structures. Germylene 18_s have high stability (ΔE_s–t = 32.29 kcal/mol⁻¹), vibrational frequencies (υ_min = 220.60 cm⁻¹), and dipole moment (D = 3.71). Interestingly, germylene 16_s with low stability (ΔE_s–t = 17.19 kcal/mol⁻¹) has high dipole moment (D = 3.80) (Table 4).

The electrostatic potential (ESP) map is related to the electronic density and is considered a fundamental determinant of atomic and molecular properties [31]. Therefore, ESP has largely been used as a molecular descriptor of the chemical reactivity, which takes part in both electrophilic and nucleophilic reactions. For investigation, ESP surfaces are plotted over the optimized electronic structures of our germylenes using density functional B3LYP method with 6–311++G** basis set because the computationally or experimentally observed ESP surface directly provides information about the electrophilic (electronegative charge region) and nucleophilic (most positive charge region) regions (Table 3). The ESP map shows that the negative potential sites are on nitrogen atoms. The red and blue regions indicate the lowest and highest electrostatic potential energy values, respectively [31].

Germylene 5_s with two nitrogens adjacent to its germylene center has more positive atomic charges on -G̈e- (+ 1.1876) and B (+ 0.8576) than 2_s which has one nitrogen (-G̈e- = + 1.0487 and B = + 0.7724). Also, germylene 11_s with three nitrogens adjacent to its boron has high positive atomic charge on its B (+ 0.9043) than 1_s which has no nitrogen (B = + 0.5960). The atomic charges of the singlet germylene centers are significantly high positive compared to their corresponding triplets (Figure 1). Germylene 5_s with the lowest vibrational frequencies (υ_min = 24.12 cm⁻¹) has high positive atomic charge on the B (+ 0.8576) and -G̈e- (1.1876) (Tables 4 and 5).

Fig. 1

Schematic E_HOMO, E_LUMO (eV), and ΔE_HOMO-LUMO (kcal/mol⁻¹) for singlet silylenes at the B3LYP/6311++G** level of theory. IsoValue = 0.02 and the density = 0.0004

The crucial factor for stability of germylenes is nucleophilicity index, N, which was introduced by Domingo et al. [29] The nucleophilicity of our germylenes is decreased when their energy of the highest occupied molecular orbital (E_HOMO) is decreased [32]. For instance, germylene 10_s has the highest nucleophilicity (3.98 eV) and E_HOMO (− 5.48 eV) (Table 5).

As E_HOMO slightly decreased, the number of σ-acceptor nitrogen atoms increased, also caused less electron-rich. For example, germylene 19_s with four nitrogens has lower E_HOMO (− 6.09 kcal/mol⁻¹) than 2_s (− 5.73 kcal/mol⁻¹) which has one nitrogen (Table 6). Germylene 11 with high stability (34.27 kcal/mol⁻¹) and ω (3.56 eV) has the lowest N (2.98 eV) (Tables 5, 6, and Figure 1).

Table 6 Frontier molecular orbital energies (E_HOMO/eV and E_LUMO/eV), along with their ΔE_HOMO–LUMO (kcal/mol⁻¹), nucleophilicity (N), and global electrophilicity (ω) for the singlet (s) germylenes (1_s–20_s), at B3LYP/6–311++G**

Germylenes 1_s, 3_s, 10_s, and 16_s regardless of LP_G̈e → σ^* interactions have high N because they do not have any nitrogen adjacent to the germylene center. Germylene 2_s despite nitrogen adjacent to the germylene center has high N (3.72 eV) for high LP_N(Z) → LP^*_G̈e interaction (E⁽²⁾ = 13.65 kcal/mol⁻¹). Two factors that have an effect on our ω and ΔE_HOMO-LUMO are σ-bond (σ_(G̈e-N(Y))) and LP_{N(W or Y)} → LP^*_G̈e interactions. Hence, germylenes 8_s, 14_s, and 19_s with σ-bond between nitrogen (N(Y)) and germylene center have low ω and high ΔE_HOMO-LUMO. This σ-bond arose from a tendency of nonbonding electrons of nitrogen to empty p orbital of the germylene center. Also, germylene 18_s with LP_N(Y) → LP^*_G̈e (E⁽²⁾ = 47.25 kcal/mol⁻¹) and 20_s with LP_N(W) → LP^*_G̈e (E⁽²⁾ = 42.73 kcal/mol⁻¹) interaction have low ω and high ΔE_HOMO-LUMO.

Germylene 20_s despite LP_N(W) → LP^*_G̈e (E⁽²⁾ = 42.73 kcal/mol⁻¹) interaction has similar ω with 3_s which do not have any LP_N(Z) and LP_N(V) → LP^*_G̈e interactions (Tables 2 and 6).

Recently, we have reached novel borastannylenes that have similar structures with our germylenes, but they have different properties at geometrical parameters, stability (ΔΕ_s-t), the heat of hydrogenation (ΔE_H), nucleophilicity (N), and electrophilicity (ω). Such various properties have attributed to the effect of our imposed topology and LP_N(V) interactions [33].

In fact, we have introduced 4,6-diaza-7-boratricyclo[1.1.1.0^1,7.0^7,3.0^7,5]hexa-2-stannylene (10_s) with high stability and N that can be applied as accumulated multi-dentate ligands. But, for this purpose, we found that singlet 5-aza-7-boratricyclo[1.1.1.0^1,7.0^7,3.0^7,5]hexa-2-germylene (4_s) and 1,3-diraaza-7-boratricyclo[1.1.1.0^1,7.0^7,3.0^7,5]hexa-2-germylene (5_s) are suitable.

The heats of hydrogenation for our germylene were calculated at B3LYP/AUG-cc-pVTZ level. The calculated heat of hydrogenation [33] is a thermodynamic method to estimate the relative stability of germylenes. For instance, germylene 18_s with high stability (ΔE_s–t = 32.29 kcal/mol⁻¹) has low heat of hydrogenation (ΔE_{H =} − 3.87 kcal/mol⁻¹). Also, germylene 16_s with low stability (ΔE_s–t = 17.19 kcal/mol⁻¹) has the highest heat of hydrogenation (ΔE_H = − 20.88 kcal/mol⁻¹). Our triplet germylenes have higher heats of hydrogenation than their corresponding singlets. For instance, the heat of hydrogenation 2_s and 2_t are − 18.19 and + 12.98 kcal/mol⁻¹, respectively (Table 4). 

We have employed the NBO analysis to stress the roles of intermolecular orbital interactions through second-order perturbation theory. The NBO analysis provides significant evidence for the nature of our hydrogenated germylenes. The nonbonding electrons at the nitrogen appear to have a tendency to make a coordinate covalent bond with the empty p orbital of boron atom. This is demonstrated by hydrogenated germylenes 2′_s, 6′_s, 8′_s, 12′_s, 13′_s, 14′_s, and 18′_s, for showing π_(N-B) occupancy number. Interestingly, hydrogenated germylenes with the nitrogen attached to boron have π_(N-B) or LP_N → LP^*_B interactions. For example, hydrogenated germylenes 2′_s with π_(N-B) and 4′_s with high LP_N(X) → LP^*_B interactions (E⁽²⁾ = 11.64 kcal/mol⁻¹) have one nitrogen attached to boron. Hydrogenated germylene 20′_s has the lowest ΔE_H (− 1.79 kcal/mol⁻¹) for LP_N(W) → LP^*_B interaction. This interaction has caused to decrease in the stability of 20′_s (Tables 7 and 8).

Table 7 Calculated occupancy number of LPπ_(N-B), and LP_{N(V, W, X, Y, Z)} using NBO analysis for singlet hydrogenated germylenes, at the B3LYP/6–311++G** level of theory

Table 8 Calculated second-order perturbation stabilization energies (E⁽²⁾), for the intermolecular interactions (donor/acceptor NBO) of hydrogenated germylenes, at the B3LYP/6–311++G** level of theory

Conclusions

In this research, we have studied thermodynamical and geometrical parameters for investigation of the effects of nitrogen substitution on the stability, multiplicity, and reactivity of novel singlet and triplet germylenes (1_s–20_s and 1_t–20_t, respectively), all of which appear as minima on their potential energy surfaces at B3LYP/AUG-cc-pVTZ//B3LYP/6-311G** level of theory. The germylene 11 with the enormous steric strain for their cubic structure has the highest stability (ΔE_s-t = 34.27 kcal/mol⁻¹). The E_HOMO slightly decreases when the number of electronegative, σ-acceptor nitrogen atoms increases, also causes it to be less electron-rich. We have employed the NBO analysis to stress the roles of intermolecular orbital interactions through second-order perturbation theory. The NBO analysis provides significant evidences for the nature of our germylenes. Based on the following arguments, two factors that have the effect on our ω and ΔE_HOMO-LUMO are σ-bond (σ_(G̈e-N(Y))) and LP_{N(W or Y)} → LP^*_G̈e interactions. Germylenes 8_s, 14_s, and 19_s with σ-bond between nitrogen (N(Y)) and germylene center have low ω and high ΔE_HOMO-LUMO. Germylenes 18_s and 20_s with LP_{N(W or Y)} → LP^*_G̈e interactions have low ω and high ΔE_HOMO-LUMO. The nucleophilicity index, N, is a crucial factor for showing the aptitude of our germylenes for coordination to transition metal complexes. So, we introduce germylenes 4_s and 5_s with high stability (ΔE_s-t = 32.95 and 33.60 kcal/mol⁻¹, respectively) and N (3.49 and 3.45 eV) that can be applied as multi-dentate ligands.