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Article

Substituent Effects on the Stability of Thallium and Phosphorus Triple Bonds: A Density Functional Study

by
Jia-Syun Lu
1,
Ming-Chung Yang
1 and
Ming-Der Su
1,2,*
1
Department of Applied Chemistry, National Chiayi University, Chiayi 60004, Taiwan
2
Department of Medicinal and Applied Chemistry, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
*
Author to whom correspondence should be addressed.
Molecules 2017, 22(7), 1111; https://doi.org/10.3390/molecules22071111
Submission received: 12 June 2017 / Revised: 29 June 2017 / Accepted: 29 June 2017 / Published: 5 July 2017
(This article belongs to the Section Computational and Theoretical Chemistry)
Browse Figures
Versions Notes

1. Introduction

The preparation and characterization of triply bonded heavier main group element (E14 = Si, Ge, Sn, and Pb) molecules (i.e., RE14≡E14R) is a popular field of study in inorganic chemistry [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. From the valence electron viewpoint, the triply bonded RE13≡E15R compound is isoelectronic to the RE14≡E14R species. However, the former has been the subject of much less study than the latter, in the field of synthetic chemistry. Therefore, the level of understanding of the chemistry of RE13≡E15R is lower than that for group 14 less-coordinate alkyne analogues.
In the group 15 family, phosphorus is more similar to its diagonal relative, carbon, than to nitrogen [42]. Thallium is also known to be monovalent and has an ionic radius that is similar to that of potassium, so it is often presumed to be a pseudo alkali metal [43]. The isolation and characterization of the singly bonded organothallium phosphorus molecule, (Me3SiCH2)3Tl⎼P(SiMe3)3, was experimentally reported about twenty years ago [44]. Two other novel compounds that contain the thallium⎼phosphorus single bond have also been identified [45,46]. If both thallium and phosphorus elements could be stabilized using a single bond to connect them, it might be possible to extend this field to the study of other triply bonded RTl≡PR inorganic molecules. This work reports the first theoretical study of the possible synthesis of the RTl≡PR molecule, which may be isolable as a long-lived compound. The study determines potential inorganic complexes that can stabilize the thallium≡phosphorus triple bond, to demonstrate the theoretical possibility that these unusual acetylene inorganic analogues can be synthesized.

2. Methodology

Using the Gaussian 09 program package [47], all geometries are fully optimized at the M06-2X [48], B3LYP [49,50], and B3PW91 [51,52] levels of theory, in conjunction with the Def2-TZVP [53] and LANL2DZ+dp [54,55,56,57,58] basis sets. These DFT calculations are signified as M06-2X/Def2-TZVP, B3PW91/Def2-TZVP and B3LYP/LANL2DZ+dp, respectively. In order to confirm that the reactants and products have no imaginary frequencies and that the transition states possess only one imaginary frequency, frequency calculations were performed for all structures. Thermodynamic corrections to 298 K, heat capacity corrections and entropy corrections (ΔS) are applied to the three levels of DFT. The relative free energy (ΔG) at 298 K is also computed at the same levels of theory.
Next, (SiiPrDis2)Tl≡P(SiiPrDis2), (Tbt)Tl≡P(Tbt), and (Ar*)Tl≡P(Ar*) are the model reactants for this study. It is known that the B3LYP functional fails to describe non-valent interactions, such as the London dispersion correctly. As a result, for large ligands, calculations were performed using dispersion-corrected M06-2X method [48]. Because of the limitations of the available memory size and CPU time, frequencies are not computed at the dispersion-corrected M06-2X/Def2-TZVP level of theory for the triply bonded R´Tl≡PR´ systems that have bulky ligands (R´), so the zero-point energies and the Gibbs free energies that are derived using the dispersion-corrected M06-2X/Def2-TZVP cannot be used for these systems.

3. General Considerations

Two interaction models that describe the chemical bonding of the triply bonded RTl≡PR, which serve as a basis for discussion, are given in this section. For convenience, the RTl≡PR molecule is divided into two fragments: Tl⎼R and P⎼R. On the basis of theoretical results (see below), three computational methods (M06-2X/Def2-TZVP, B3PW91/Def2-TZVP and B3LYP/LANL2DZ+dp) all indicate that the Tl⎼R and P⎼R fragments are respectively calculated to be in the singlet ground state and the triplet ground state.
In model [I], electron promotion energy (ΔE1) forces the P⎼R moiety from the triplet ground state to the singlet excited state, so the electronic structure of RTl≡PR can be described in terms of the dimerization of singlet Tl⎼R and singlet P⎼R fragments, as shown in Figure 1. From the chemical bonding viewpoint, model [I] shows that the Tl≡P triple bond consists of one σ⎼donation of Tl→P and two π⎼donations of Tl←P. In model [II], the electron advancement energy (ΔE2) promotes the Tl⎼R unit from the singlet ground state to the triplet excited state. Accordingly, the bonding structure of RTl≡PR can also be represented as the dimerization of triplet Tl⎼R and triplet P⎼R fragments, as shown in Figure 1. From the bonding structure viewpoint, model [II] shows that the Tl≡P triple bond is composed of one Tl←P π⎼bond, one regular σ⎼bond and one π⎼bond.
It is schematically shown in Figure 1 that the formation of the triply bonded RTl≡PR molecule can be regarded as either [Tl⎼R]1 + [P⎼R]1 → [RTl≡PR]1 (model [I]) or [Tl⎼R]3 + [P⎼R]3 → [RTl≡PR]1 (model [II]). It is worthy of note that since the lone pair of phosphorus has significant amount of s character, this could reduce the bonding overlaps between Tl and P elements (see the black lines in model [I] and model [II] in Figure 1). As a consequence, the Tl≡P triple bond should be very weak, which is in contrast to the traditional triple bond of acetylene. This prediction is confirmed in the following section. Both models are used in this study clearly show that the Tl≡P triple bond is mostly attributed to electron donation from the lone pair of P to the empty p-orbital of Tl.
This bonding analysis is used to interpret the bonding properties of the triply bonded RTl≡PR molecule in the next section.

4. Results and Discussion

4.1. Small Ligands on Substituted RTl≡PR

The effect of small substituents on the stability of the triply bonded RTl≡PR species is discussed from the kinetic and the thermodynamic viewpoints. Five small substituents (R = H, F, OH, CH3 and SiH3) are used for the RTl≡PR model molecule. The important geometrical parameters for the RTl≡PR compounds are calculated at the three computational methods (M06-2X/Def2-TZVP, B3PW91/Def2-TZVP and B3LYP/LANL2DZ+dp) and the results are listed in Table 1. The Cartesian coordinates for the triply bonded minima are given in the Supplementary Information.
There are four noteworthy features of Table 1:
(1) The central Tl≡P triple bond distances (Å) for R = F, OH, H, CH3 and SiH3 are respectively estimated to be 2.313⎼2.422 Å, 2.336⎼2.443 Å and 2.331⎼2.480 Å, at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP and B3LYP/LANL2DZ+dp levels of theory. As mentioned in the Introduction, neither experimental nor theoretical results for the triply bonded RTl≡PR species are available to allow a definitive comparison. However, to the author’s best knowledge, there are only a few published reports concerning the singly bonded R3Tl⎼PR3 molecules and these report the Tl⎼P bond length to be 2.922 Å [44], 3.246–3.301 Å [45] and 3.032–3.168 Å [46]. These single bond distances are all longer than the sum of the covalent radii (i.e., 2.62 Å) [62] for the Tl and P elements.
(2) The three DFT calculations shown in Table 1 demonstrate that the R⎼Tl and R⎼P components have a singlet and triplet ground state, respectively. The three DFT computational results also show that the singlet-triplet energy differences (ΔEST) for R⎼Tl and R⎼P fragments are estimated to be at least +67 and −15 kcal/mol, respectively. These energy values strongly suggest that model [I], which is shown in Figure 1, is superior to model [II] in describing the bonding characters of triply bonded RTl≡PR molecules that feature small substituents (R). Model [I] shows that the bonding structure of the triple bond in RTl≡PR can be represented as Tl Molecules 22 01111 i001P. It must be noted that the fact that the lone pair of phosphorus has s character and the valence p orbital of phosphorus is much smaller than that of thallium means that both factors can vigorously affect the bonding overlaps between phosphorus and thallium atoms. Therefore, it is anticipated that the triple bond in these RTl≡PR species is very weak. This prediction is confirmed by the three DFT calculations shown in Table 1. All of the values for the Wiberg bond index (WBI) [59,60,61] are a little bit higher than 1.0, rather than 2.0. That is to say, regardless of whether small electropositive or small electronegative groups are attached, the RTl≡PR systems possess a quite weak Tl≡P triple bond.
(3) As already shown, model [I] describes the bonding characters in triply bonded RTl≡PR compounds that feature small substituents better than model [II]. This, in turn, strongly implies that an acute bond angle ∠Tl⎼P⎼R (close to 90°) and a linear bond angle ∠R⎼Tl⎼P (close to 180°) is favored in the triply bonded RTl≡PR molecule, which is verified by the three DFT calculations as shown in Table 1. The nearly perpendicular angle on the P center can also be attributed to the “orbital non-hybridization effect” [63,64,65,66] and the “inert s-pair effect” [63,64,65,66] as discussed previously.
(4) The binding energies (BE) that are required to cleave the central Tl≡P bond, which leads to one R⎼Tl and one R⎼P fragment in the singlet ground state and in the triplet ground state, respectively, are summarized in Table 1. The calculated BE values (kcal/mol) for the RTl≡PR molecules are in the range of 67–96, 67–96 and 68–93, at the M06-2X, B3PW91 and B3LYP levels of theory, respectively. This data confirms that the central thallium and phosphorus atoms in the substituted RTl≡PR compounds are strongly bonded.
Considering the stability of RTl≡PR, the theoretical results for the potential energy surfaces of the model molecule, RTlPR (R = F, OH, H, CH3 and SiH3), are described in Figure 2. This figure shows a number of stationary points exist, including local minima that correspond to RTl≡PR, R2Tl=P, Tl=PR2 and the transition states that connect them. The three DFT computational results show that all of the triply bonded RTl≡PR compounds that feature small substituents immediately transfer to the corresponding doubly bonded species via facile 1,2-migration reactions. In other words, the theoretical evidence shows that triply bonded RTl≡PR species that feature small ligands are both kinetically and thermodynamically unstable, regardless of whether they are electronegative or electropositive, so it is unlikely that they could be prepared or synthesized in a laboratory.

4.2. Large Ligands on Substituted R′Tl≡PR′

As previously mentioned, in order to stabilize R′Tl≡PR′ from the kinetic viewpoint, three types of large substituents (R´) are used in this study. These are SiMe(SitBu3)2, SiiPrDis2, Tbt (=C6H2-2,4,6-(CH(SiMe3)2)3), and Ar* (=C6H3-2,6-(C6H2-2,4,6-i-Pr3)2) [67,68], as shown in Figure 3. The geometrical structures of R′Tl≡PR′ are optimized at the dispersion-corrected M06-2X/Def2-TZVP [53] level of theory. Their important calculated parameters are listed in Table 2.
Five important conclusions can be drawn from these theoretical results:
(i) The results presented in Table 2 predict that the Tl≡P triple bond lengths (Å) are about 2.386 Å, 2.384 Å, 2.385 Å, and 2.336 Å, for (SiMe(SitBu3)2)Tl≡P(SiMe(SitBu3)2), (SiiPrDis2)Tl≡P(SiiPrDis2), (Tbt)Tl≡P(Tbt), and (Ar*)Tl≡P(Ar*), respectively. These theoretically estimated values are shorter than the experimentally reported Tl⎼P single bond distance, as mentioned previously [44,45,46]. Similarly to the case for small substituents, the DFT optimized results show that all of the triply bonded R′Tl≡PR′ molecules that feature bulky ligands studied adopt a bent structure, as shown in Table 2.
(ii) If the R´Tl≡PR´ compound is cut in half, the Tl⎼R´ and P⎼R′ two fragments are obtained. The DFT results shown in Table 2 demonstrate that the ΔEST for the Tl⎼R′ unit is greater than 30 kcal/mol and the modulus of ΔEST for the P⎼R′ moiety is greater than 37 kcal/mol. That is to say, the promotion energy from the singlet ground state to the triplet excited for Tl⎼R′ is smaller than the energy that is required for promotion from that for Tl⎼R (Table 1). The bonding model that is shown in Figure 1 shows that model [II] can be used to interpret the bonding character in triply bonded R′Tl≡PR′ molecules that feature bulky ligands, R′. Namely, the bonding structure of the triple bond in R′Tl≡PR′ is best described as Tl Molecules 22 01111 i002P. In this model, the electrons that are donated from the lone pair of phosphorus have s character, as shown in Figure 1. Moreover, the size of 2p orbital of P is also much smaller than the 6p orbital of Tl. These two factors combined produce a weak Tl≡P triple bond in the R′Tl≡PR′ species. Supporting theoretical evidence in Table 2 shows that the WBI for R′Tl≡PR′ is 2.21, 2.37, 2.13, and 2.20 for R = SiMe(SitBu3)2, SiiPrDis2, Tbt, and Ar*, respectively. These WBI values are much smaller than the value for acetylene (2.99).
(iii) In order to determine the effect of bulky substituents on the stability of triply bonded R′Tl≡PR′ compounds, the dispersion-corrected M06-2X/Def2-TZVP level of theory is used to determine the potential energy surfaces for the isomerization reaction. As shown in Table 2, the triply bonded R′Tl≡PR′ molecules have values that are at least 87 (ΔH1) and 71 (ΔH2) kcal/mol lower than that for the corresponding doubly bonded isomers. Therefore, the theoretical results show that a triply bonded R′Tl≡PR′ compound that features bulky substituents is more stable than its corresponding doubly bonded R′2Tl=P: and: Tl=PR′2 isomers, from the kinetic viewpoint.
(iv) In order to verify the conclusion from point (ii), “charge decomposition analysis” (CDA), reported by Dapprich and Frenking [69] is used in the present study. For instance, the computational results concerning (SiMe(SitBu3)2)Tl≡P(SiMe(SitBu3)2) based on the dispersion-corrected M06-2X/Def2-TZVP method are collected in Table 3. As seen in the X column, the biggest contribution from R′⎼Tl to R′⎼P is No.227 (HOMO⎼1) orbital. However, the largest contribution from R′⎼P to R′⎼Tl is No.228 (HOMO) orbital. As a result, the net electron transfer (−0.213) is from R′⎼P to R′⎼Tl, which is shown in the (X – Y) column. Namely, the R′⎼P unit donates more electrons to the R′⎼Tl unit. The theoretical evidence is in good agreement with the valence-electron bonding model (Figure 1; model [II]) as stated earlier. Consequently, the bonding nature of R′Tl≡PR′ can be considered as R′Tl Molecules 22 01111 i002PR′.
(v) The NBO [59,60,61] and NRT [70,71,72] are also used to determine the bonding properties of the electronic structures of the R′Tl≡PR′ molecules, as shown in Table 4. This table clearly shows that the major bonding character between Tl and P comes from electron donation from 2p(P) to 6p(Tl), which is denoted as 6p(Tl) ← 2p(P). In the (SiMe(SitBu3)2)Tl≡P(SiMe(SitBu3)2) molecule, for instance, the dispersion-corrected M06-2X/Def2-TZVP calculations show that the Tl≡P π bonding occurs as follows: π⊥ (Tl≡P) = 0.3114(sp4.77)Tl + 0.9503(sp1.42)P. That is, a polarized π⊥ bond exists between Tl and P, which arises from the donation of the P lone pair to the empty Tl p orbital. As seen in Table 4, the Tl≡P π⊥ bonding orbitals comprise 9.7% natural Tl orbitals and 90% natural P orbitals (Figure 5). The similar theoretical results can also be found in the Tl≡P π‖ bonding orbitals as already represented in Table 4.

5. Conclusions

In summary, the theoretical observations strongly support the idea that both electronic and steric effects determine the relative stability of molecules that contain a Tl≡P triple bond, as well as its corresponding doubly bonded isomers. The simple bonding models schematically illustrated in Figure 1 show that model [I], whose bonding character is symbolized by Tl Molecules 22 01111 i001P, better interprets the triple bond in RTl≡PR species that feature small substituents. Model [II], whose bonding property is typified as Tl Molecules 22 01111 i002P, better describes the triple bond in R′Tl≡PR′ molecules that feature bulky ligands (Figure 6). However, regardless of whether the substituents in triply bonded RTl≡PR compound are large or small, their Tl≡P triple bonds are quite weak. Two effects can explain these phenomena. The different sizes of the p orbitals in the Tl and P elements mean that their overlapping populations are pretty small and the lone pair of the phosphorus atom has significant amount of s character, which results in poor overlaps between thallium and phosphorus. It is hoped that the results of experimental synthesis and structural characterization will confirm these predictions.

Supplementary Materials

Supplementary materials are available online. The CDA and NRT results concerning the (SiiPrDis2)Tl≡P(SiiPrDis2), (Tbt)Tl≡P(Tbt), and (Ar*)Tl≡P(Ar*) molecules are collected in the Supporting Information.

Acknowledgments

The authors are grateful to the National Center for High-Performance Computing of Taiwan for generous amounts of computing time, and the Ministry of Science and Technology of Taiwan for the financial support. Special thanks are also due to reviewers for very help suggestions and comments.

Author Contributions

Jia-Syun Lu and Ming-Chung Yang performed the theoretical calculations; Ming-Der Su wrote the paper.

Conflicts of Interest

The authors declare no conflict of interest.

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Sample Availability: Not available.
Molecules 22 01111 g001 550
Figure 1. The interaction models, [I] and [II], for the triply bonded RTl≡PR molecule.
Figure 1. The interaction models, [I] and [II], for the triply bonded RTl≡PR molecule.
Molecules 22 01111 g001
Molecules 22 01111 g002 550
Figure 2. The Relative Gibbs free energy surfaces for RTl≡PR (R = F, OH, H, CH3 and SiH3). These energies are in kcal/mol and are calculated at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 1.
Figure 2. The Relative Gibbs free energy surfaces for RTl≡PR (R = F, OH, H, CH3 and SiH3). These energies are in kcal/mol and are calculated at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 1.
Molecules 22 01111 g002
Molecules 22 01111 g003 550
Figure 3. Four bulky groups. For details, see references [66,67].
Figure 3. Four bulky groups. For details, see references [66,67].
Molecules 22 01111 g003
Molecules 22 01111 g004 550
Figure 4. The potential energy surface for the 1,2-migration reaction of the R′Tl≡PR′ molecules with balky groups (R′).
Figure 4. The potential energy surface for the 1,2-migration reaction of the R′Tl≡PR′ molecules with balky groups (R′).
Molecules 22 01111 g004
Molecules 22 01111 g005a 550Molecules 22 01111 g005b 550
Figure 5. The natural Tl≡P π bonding orbitals ((a) and (b)) for (SiMe(SitBu3)2)Tl≡P(SiMe(SitBu3)2). For comparison, see also Figure 3.
Figure 5. The natural Tl≡P π bonding orbitals ((a) and (b)) for (SiMe(SitBu3)2)Tl≡P(SiMe(SitBu3)2). For comparison, see also Figure 3.
Molecules 22 01111 g005aMolecules 22 01111 g005b
Molecules 22 01111 g006 550
Figure 6. The predicted geometrical structure based on the present theoretical calculations.
Figure 6. The predicted geometrical structure based on the present theoretical calculations.
Molecules 22 01111 g006
Table
Table 1. The important geometrical parameters, the natural charge densities (QTl and QP), the binding energies (BE), the HOMO-LUMO energy gaps and the Wiberg Bond Index (WBI) for RTl≡PR using the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round brackets) and B3LYP/LANL2DZ+dp (in square brackets) levels of theory.
Table 1. The important geometrical parameters, the natural charge densities (QTl and QP), the binding energies (BE), the HOMO-LUMO energy gaps and the Wiberg Bond Index (WBI) for RTl≡PR using the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round brackets) and B3LYP/LANL2DZ+dp (in square brackets) levels of theory.
RFOHHCH3SiH3
Tl≡P (Å)2.4222.4372.3202.3392.313
(2.425)(2.443)(2.327)(2.349)(2.336)
[2.455][2.480][2.331][2.360][2.337]
R-P-Tl (°)179.7179.1179.1175.2174.6
(179.7)(176.5)(178.5)(174.5)(175.7)
[178.5][177.9][178.2][171.3][179.1]
P-Tl-R (°)94.6398.9286.51100.494.76
(96.59)(101.5)(86.82)(102.2)(92.71)
[94.22][100.1][86.36][102.6][90.78]
R-P-Tl-R (°)180.0179.4179.1178.0177.0
(180.0)(178.8)(179.2)(178.8)(179.1)
[180.0][179.2][179.8][179.9][179.4]
QP (1)0.160.076−0.63−0.37−0.83
(0.17)(0.13)(−0.60)(−0.33)(−0.72)
[0.096][0.021][−0.62][−0.39][−0.76]
QTl (2)1.191.141.121.070.82
(1.11)(1.03)(0.87)(0.99)(0.75)
[1.25][1.17][0.99][1.13][0.89]
ΔEST for Tl⎼R (kcal/mol) (3)102.183.5784.8566.8275.96
(103.7)(80.69)(85.69)(67.38)(77.63)
[102.2][83.15][83.05][67.94][74.40]
ΔEST for P⎼R (kcal/mol) (4)−28.91−17.53−30.75−26.43−15.84
(−33.35)(−21.29)(−35.49)(−30.26)(−18.68)
[−31.76][−20.24][−33.16][−29.21][−14.46]
HOMO—LUMO (kcal/mol)184.1167.6210.6151.2142.1
(131.6)(118.1)(212.0)(149.3)(145.1)
[182.5][169.1][215.4][146.5][148.5]
BE (kcal/mol) (5)95.5883.5784.8566.8275.96
(95.74)(82.10)(85.69)(67.38)(77.63)
[93.43][83.15][83.05][67.94][74.40]
WBI (6)1.1591.1621.4561.3821.404
(1.194)(1.197)(1.491)(1.415)(1.417)
[1.191][1.178][1.475][1.403][1.372]
(1) The natural charge density on the central phosphorus atom; (2) The natural charge density on the central thallium atom; (3) ΔEST (kcal mol−1) = E(triplet state for R⎼Tl) – E(singlet state for R⎼Tl); (4) ΔEST (kcal mol−1) = E(triplet state for R⎼P) – E(singlet state for R⎼P); (5) BE (kcal mol−1) = E(singlet state for R⎼Tl) + E(triplet state for R⎼P) – E(singlet for RTl≡PR); (6) The Wiberg bond index (WBI) for the Tl≡P bond: see reference [59,60,61].
Table
Table 2. The Bond Lengths (Å), Bond Angels (°), Singlet—Triplet Energy Splitting (ΔEST), Natural Charge Densities (QTl and QP), Binding Energies (BE), the HOMO-LUMO Energy Gaps, the Wiberg bond index (WBI), and Some Reaction Enthalpies for R′Tl≡PR′ at the dispersion-corrected M06-2X/Def2-TZVP Level of Theory. See also Figure 4.
Table 2. The Bond Lengths (Å), Bond Angels (°), Singlet—Triplet Energy Splitting (ΔEST), Natural Charge Densities (QTl and QP), Binding Energies (BE), the HOMO-LUMO Energy Gaps, the Wiberg bond index (WBI), and Some Reaction Enthalpies for R′Tl≡PR′ at the dispersion-corrected M06-2X/Def2-TZVP Level of Theory. See also Figure 4.
R′SiMe(SitBu3)2SiiPrDis2TbtAr*
Tl≡P (Å)2.3862.3842.3852.336
∠R′–Tl–P (°)166.9166.4168.9161.2
∠Tl–P–R′ (°)122.3113.7116.2115.6
∠R′–Tl–P–R′ (°)171.4179.5173.9174.4
QTl (1)0.9750.7391.1661.218
QP (2)−0.860−0.826−0.344−0.257
ΔEST for Tl—R′ (kcal/mol) (3)35.9135.5231.2730.24
ΔEST for P—R′ (kcal/mol) (4)−43.10−37.47−39.74−40.52
HOMO—LUMO (kcal/mol)71.2727.2158.0539.34
BE (kcal/mol) (5)80.2485.4362.5167.89
ΔH1 (kcal/mol) (6)91.3490.4989.2287.11
ΔH2 (kcal/mol) (6)73.9872.8371.2774.01
WBI (7)2.1162.2732.1272.201
(1) The natural charge density on the central thallium atom; (2) The natural charge density on the central phosphorus atom; (3) ΔEST (kcal mol−1) = E(triplet state for R′⎼Tl) – E(singlet state for R′⎼Tl); (4) ΔEST (kcal mol−1) = E(triplet state for R′⎼P) – E(singlet state for R′⎼P); (5) BE (kcal mol−1) = E(triplet state for R′⎼Tl) + E(singlet state for R′⎼P) – E(singlet for R′Tl≡PR′); (6) See Figure 4; (7) The Wiberg bond index (WBI) for the Tl≡P bond: see reference [59,60,61].
Table
Table 3. The charge decomposition analysis (CDA) (a) for R′Tl≡PR′ (R′ = SiMe(SitBu3)2) system based on M06-2X orbitals, where the X term indicates the number of electrons donated from R′⎼Tl fragment to R′⎼P fragment, the Y term indicates the number of electrons back donated from R′⎼P fragment to R′⎼Tl fragment and the Q term indicates the number of electrons involved in repulsive polarization. Significant X and Y terms are bolded for easier comparison. (a),(b)
Table 3. The charge decomposition analysis (CDA) (a) for R′Tl≡PR′ (R′ = SiMe(SitBu3)2) system based on M06-2X orbitals, where the X term indicates the number of electrons donated from R′⎼Tl fragment to R′⎼P fragment, the Y term indicates the number of electrons back donated from R′⎼P fragment to R′⎼Tl fragment and the Q term indicates the number of electrons involved in repulsive polarization. Significant X and Y terms are bolded for easier comparison. (a),(b)
OrbitalOccupancyXYX – YQ
2182.0000000.0007570.0005860.000171−0.002462
2192.0000000.0010360.0005220.000513−0.004450
2202.0000000.0009320.0005390.000394−0.006342
2212.0000000.0000260.004350−0.004325−0.002504
2222.0000000.001151−0.0001640.001315−0.001354
2232.0000000.0000810.003145−0.003064−0.001960
2242.0000000.0000370.002403−0.002366−0.000054
2252.0000000.0017770.029263−0.027486−0.030329
2262.0000000.0004770.013735−0.013259−0.007124
2272.0000000.0084450.068258−0.059813−0.018272
HOMO2282.000000−0.0053390.003033−0.008432−0.004437
LUMO2290.0000000.0000000.0000000.0000000.000000
2300.0000000.0000000.0000000.0000000.000000
sum 456.0000000.0288530.241774−0.212922−0.107250
(a) For clearness, only list the X, Y, and Q terms for HOMO (No.228) ⎼10 ~ LUMO+2. (b) Summation of contributions from all unoccupied and occupied orbitals.
Table
Table 4. The natural bond orbital (NBO) and the natural resonance theory (NRT) analysis for R′Tl≡PR′ molecules that feature ligands (R′ = SiMe(SitBu3)2, SiiPrDis2, Tbt, and Ar*) at the dispersion-corrected M06-2X/Def2-TZVP level of theory (1,2).
Table 4. The natural bond orbital (NBO) and the natural resonance theory (NRT) analysis for R′Tl≡PR′ molecules that feature ligands (R′ = SiMe(SitBu3)2, SiiPrDis2, Tbt, and Ar*) at the dispersion-corrected M06-2X/Def2-TZVP level of theory (1,2).
R′Tl≡PR′WBINBO AnalysisNRT Analysis
OccupancyHybridizationPolarizationTotal/Covalent/IonicResonance Weight
R′ = SiMe(SitBu3)22.11σ = 2.21σ : 0.5116 Tl (sp1.27) + 0.8592 P (sp2.07)26.18% (Tl)2.22/1.55/0.67Tl⎼P: 23.17%
Tl=P: 66.87%
Tl≡P: 9.94%
73.82% (P)
π⊥ = 1.84π⊥: 0.3114 Tl (sp4.77) + 0.9503 P (sp1.42)9.70% (Tl)
90.30% (P)
π‖ = 1.92π‖: 0.6833 Tl (sp99.87) + 0.7556 P (sp99.99)5.69% (Tl)
94.31% (P)
R′ = SiiPrDis22.37σ = 1.83σ : 0.6422 Tl (sp0.86) + 0.7665 P (sp20.18)41.24% (Tl)2.59/0.83/1.76Tl⎼P: 17.35%
Tl=P: 71.14%
Tl≡P: 11.51%
58.76% (P)
π⊥ = 1.92π⊥: 0.4064 Tl (sp99.99) + 0.9137 P (sp44.72)16.51% (Tl)
83.49% (P)
π‖ = 1.93π‖: 0.4551 Tl (sp99.99) + 0.8997 P (sp94.99)14.79% (Tl)
85.21% (P)
R′ = Tbt2.13σ = 1.77σ : 0.6888 Tl (sp0.94) + 0.7249 P (sp38.46)47.45% (Tl)2.08/1.59/0.49Tl⎼P: 27.42%
Tl=P: 63.76%
Tl≡P: 8.82%
52.55% (P)
π⊥ = 1.94π⊥: 0.4133 Tl (sp35.51) + 0.9244 P (sp87.83)23.43% (Tl)
82.74% (P)
π‖ = 1.90π‖: 0.4118 Tl (sp99.89) + 0.9077 P (sp99.99)17.28% (Tl)
82.72% (P)
R′ = Ar*2.20σ = 1.96σ: 0.7362 Tl (sp0.04) + 0.6767 P (sp64.96)54.20% (Tl)2.17/1.66/0.51Tl⎼P: 19.82%
Tl=P: 71.69%
Tl≡P: 8.49%
45.80% (P)
π⊥ = 1.77π⊥: 0.3177 Tl (sp99.99) + 0.9482 P (sp99.99)10.09% (Tl)
89.91% (P)
π‖ = 1.92π‖: 0.4083 Tl (sp99.99) + 0.9128 P (sp99.99)16.67% (Tl)
83.33% (P)
(1) The value of the Wiberg bond index (WBI) for the Tl–P bond and the occupancy of the corresponding σ and π bonding NBO (see reference [59,60,61]). (2) NRT; see reference [70,71,72].

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Lu, J.-S.; Yang, M.-C.; Su, M.-D. Substituent Effects on the Stability of Thallium and Phosphorus Triple Bonds: A Density Functional Study. Molecules 2017, 22, 1111. https://doi.org/10.3390/molecules22071111

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Lu J-S, Yang M-C, Su M-D. Substituent Effects on the Stability of Thallium and Phosphorus Triple Bonds: A Density Functional Study. Molecules. 2017; 22(7):1111. https://doi.org/10.3390/molecules22071111

Chicago/Turabian Style

Lu, Jia-Syun, Ming-Chung Yang, and Ming-Der Su. 2017. "Substituent Effects on the Stability of Thallium and Phosphorus Triple Bonds: A Density Functional Study" Molecules 22, no. 7: 1111. https://doi.org/10.3390/molecules22071111

APA Style

Lu, J.-S., Yang, M.-C., & Su, M.-D. (2017). Substituent Effects on the Stability of Thallium and Phosphorus Triple Bonds: A Density Functional Study. Molecules, 22(7), 1111. https://doi.org/10.3390/molecules22071111

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