Interactions ΔEorb Research Articles

Complex Featuring Two Double Dative Bonds Between Carbon(0) and Uranium

Complex Featuring Two Double Dative Bonds Between Carbon(0) and Uranium

Rare-Earth Metal Boroxide with Formal Triple Metal–Oxygen Orbital Interaction: Synthesis from B(C 6 F 5 ) 3 ·H 2 O and Radical-Anion Ligated Rare-Earth Metal Amides

Rare-earth metal boroxides are not only rare and of great synthetic challenge but also important theoretically due to their unrevealed bonding characteristics. In this paper, we report the synthesi...

Berichtigung: Barium as Honorary Transition Metal in Action: Experimental and Theoretical Study of Ba(CO)+ and Ba(CO)−

In this Communication, for the calculations of the anion [Ba(CO)]− neutral Ba and the carbonyl anion CO− were considered as interacting fragments. The choice was made on the basis of the experimental literature values for the electron affinities (EAs) of Ba (0.108 eV, average value of 2P1/2 and 2P3/2)1 and CO (1.37 eV).2 The authors now learned that the experimental value for the EA of CO is incorrect. High-level quantum chemical calculations suggest that CO has a negative EA,3 i.e. the attached electron in CO− is unbound and the anion is a resonance species that may only be observed as metastable resonating species via sophisticated spectroscopy.6 This means that the bonding analysis of the anion [Ba(CO)]− and the calculation of the bond dissociation energy (BDE) must be carried out using the fragments Ba− and neutral CO. The results of the relevant calculations are reported here. The calculated BDE for the reaction [Ba(CO)]− → Ba− + CO at DLPNO-CCSD(T)/def2-QZVPPD using the CCSD/def2-TZVPP optimized geometries is De = 15.6 kcal mol−1, significantly lower than the previous value of 56.1 kcal mol−1 that was obtained with respect to Ba and CO− at the same level of theory. The numerical results of the EDA-NOCV analysis of [Ba(CO)]− using Ba− in the 2D state and CO as fragments are shown in Table 1, together with the previous data using Ba (1S) and CO−(2Π) as fragments. The intrinsic interaction energy with the former fragments ΔEint = −25.6 kcal mol−1 is also significantly lower than the previous value ΔEint = −71.4 kcal mol−1. BaCO− Fragments Ba− (2D) + CO (1Σ+) Ba (1S) + CO− (2Π) ΔEint −25.6 −71.4 ΔEhybrid[a] 4.2 5.8 ΔEPauli 51.0 52.5 ΔEelstat[a] −36.5 (45.2 %) −66.1 (51.0 %) ΔEorb[a] −44.3 (54.8 %) −63.5 (49.0 %) ΔEorb(1)[b] −27.9 (63.0 %) −41.1 (64.7 %) ΔEorb(2)[b] −11.2 (25.3 %) −16.4 (25.8 %) ΔEorb(rest)[b] −5.2 (11.7 %) −6.0 (9.5 %) ΔEprep 1.9 23.2 BDE 23.7 48.2 The partitioning of the orbital term into the most important pairwise interactions gives in both cases two dominant interactions. The largest contribution ΔEorb(1) comes from the donation of the unpaired π electron at Ba− to the LUMO of CO (Figure 1 a). This was also found in the original work as the strongest orbital interaction in the cation Ba(CO)+, where the electronic reference state of Ba+ cation is the excited 2D state that makes it to become a donor Ba+→CO. The deformation density, which is associated with the second strongest orbital interaction shows that ΔEorb(2) comprises two alterations of the electronic charges (Figure 1 b). There is a polarization at barium, where the occupied 6 s AO of Barium mixes with vacant p(σ) and d(σ) orbitals and a concomitant donation from the HOMO of CO into the σ hybrid AO at Ba. Shape of the most important interacting MOs of fragments and plot of the associated deformation densities Δρ of the most important pairwise orbital interactions ΔEorb(1) and ΔEorb(2) BaCO−. The direction of the charge flow is red→blue. Thus, the most important finding in the original work remains the same: The chemical bonds of barium in the carbonyl complexes [Ba(CO)]+ and [Ba(CO)]− use mainly the 5 d AOs as valence orbitals. The use of the (n−1) d functions as genuine valence orbitals not only by barium but also by the lighter alkaline earth atoms calcium and strontium has in the meantime been supported by the experimental observation of the octacarbonyls E(CO)8 (E = Ca, Sr, Ba), which mimic transition metal complexes.7 The authors are grateful to Prof. Peter Schwerdtfeger, who pointed out the error of choosing the wrong interacting fragments for [Ba(CO)]−.

Dative versus electron-sharing bonding in N-oxides and phosphane oxides R3EO and relative energies of the R2EOR isomers (E = N, P; R = H, F, Cl, Me, Ph). A theoretical study.

Quantum chemical calculations using ab initio methods at the CCSD(T)/def2-TZVPP level and density functional theory using BP86 and M06-2X functionals in conjunction with def2-TZVPP basis sets have been carried out on the title molecules. The calculated energies suggest that the N-oxides R3NO with R = F, Cl are lower in energy than the amine isomers R2NOR, but the latter form is more stable than the N-oxides when R = H, Me, Ph. In contrast, the phosphane oxides R3PO are always more stable than the phosphanyl isomers R2NOR except for the parent system with R = H, where the two isomers are close in energy. The energy decomposition analysis suggests that the best description of the N-O bond in N-oxides R3NO depends on the nature of the substituent R. The halogen systems F3NO and Cl3NO and the triphenyl species Ph3NO possess dative bonds R3N→O, which are enhanced by R3N←O π backdonation. The contribution of the π backdonation is only 10% of the total orbital interactions ΔEorb in Ph3NO, but it amounts to ∼22% of ΔEorb in F3NO and Cl3NO. The N-O bonds H3NO and Me3NO are better described in terms of electron-sharing single bonds between charged fragments R3N+-O-, which are supported by modest R3N+←O- π backdonation that comprise 13-16% of ΔEorb. In contrast, all phosphane oxides R3PO are best depicted with electron-sharing single bonds between charged fragments R3P+-O-, which are significantly supported by R3P+←O- π backdonation contributing 22-32% of ΔEorb.

Energy decomposition analysis

The energy decomposition analysis (EDA) is a powerful method for a quantitative interpretation of chemical bonds in terms of three major components. The instantaneous interaction energy ΔEintbetween two fragments A and B in a molecule A–B is partitioned in three terms, namely (1) the quasiclassical electrostatic interaction ΔEelstatbetween the fragments; (2) the repulsive exchange (Pauli) interaction ΔEPaulibetween electrons of the two fragments having the same spin, and (3) the orbital (covalent) interaction ΔEorbwhich comes from the orbital relaxation and the orbital mixing between the fragments. The latter term can be decomposed into contributions of orbitals with different symmetry which makes it possible to distinguish between σ, π, and δ bonding. After a short introduction into the theoretical background of the EDA we present illustrative examples of main group and transition metal chemistry. The results show that the EDA terms can be interpreted in chemically meaningful way thus providing a bridge between quantum chemical calculations and heuristic bonding models of traditional chemistry. The extension to the EDA–Natural Orbitals for Chemical Valence (NOCV) method makes it possible to breakdown the orbital term ΔEorbinto pairwise orbital contributions of the interacting fragments. The method provides a bridge between MO correlations diagrams and pairwise orbital interactions, which have been shown in the past to correlate with the structures and reactivities of molecules. There is a link between frontier orbital theory and orbital symmetry rules and the quantitative charge‐ and energy partitioning scheme that is provided by the EDA–NOCV terms. The strength of the pairwise orbital interactions can quantitatively be estimated and the associated change in the electronic structure can be visualized by plotting the deformation densities.This article is categorized under:Structure and Mechanism > Molecular StructuresElectronic Structure Theory > Density Functional TheoryComputer and Information Science > Visualization

The nature of M-PNR2 bonds in the electrophilic phosphinidene complexes [(L)(CO)3M{PNR2}]+ (L = PMe3, PPh3; M = Co, Rh, Ir; R = Me, iPr): Structure, bonding and 31P NMR study

Theoretical insights into the structure and the nature of M-PNR2 bonding in the cationic electrophilic phosphinidene complexes [(L)(CO)3M{PNR2}]+ (M = Co, Rh, Ir; R = iPr, Me; L = PMe3, PPh3) have been investigated at DFT level with emphasis on the density functional BP86, PBE, PW91 and TPSS and dispersion interactions, DFT-D3(BJ). Dispersion corrected functional yields accurate geometries. The geometry optimized with PBE-D3(BJ) functional is in excellent agreement with the experimental geometry of structurally characterized cobalt phosphinidene complex [(PPh3)(CO)3Co{PNiPr2}]+ (IV). The effects of metal atom, trans-influence of phosphine ligands (PMe3, PPh3) and substituent at nitrogen atom of PNR2 ligand on the M-PNR2 bond distances and M-P-N bond angles have been studied. The lengthening of M-PNR2 bonds trans to PMe3 ligand than those trans to PPh3 are due greater trans-influence of the PMe3 ligand. The 31P NMR chemical shifts of phosphinidene and phosphine ligands phosphorus in the complexes I-XII have been calculated out at PBE-D3(BJ)/TZ2P/ZORA with scalar (SC) and spin orbit (SO) relativistic level of theory in solvent chloroform. The computed values of 31P NMR chemical shifts are within the range of experimental values. The Mulliken charge analysis shows that the overall charge flows from phosphinidene ligand to metal fragment. The energy decomposition analysis divulged that the contribution of the electrostatic interaction ΔEelstat in all studied complexes is larger (54.5%–61.3%) than the orbital interactions ΔEorb. The π-bonding contribution is much smaller than the σ-bonding (85.4%–87.0%).

A Comparison of Donor-acceptor Interactions in Borane Complexes of Divalent Tetrylenes(II) and Divalent Tetrylones(0) using Energy Decomposition Analysis Method with Natural Orbital for Chemical Valence Theory

A scheme for chemical bond analysis by combining the energy decomposition analysis (EDA) method with natural orbitals for chemical valence (NOCV) theory has been investigated. Quantum chemical calculations at the BP86/TZ2P+ level of theory are performed for a comparison of chemical bond analysis between tetrylones [BH3-{E(PH3)2}] (B3-EP2) and tetrylenes [(BH3-{NHEMe}] (B3-NHE) (E = C to Pb). The EDA-NOCV results suggest that the B–E bond dissociation energies (BDEs) in tetrylones and tetrylenes decrease from the slighter to the heavier homologs. The decrease in the bond strengths from the lighter to the heavier homologs of B3-EP2 comes mainly from the decrease in the electrostatic attractions ΔEelstat and the orbital interactions ΔEorb, while the decrease in the bond strength from carbene B3-NHC to plumbylene B3-NHPb strongly correlates with the decrease in electrostatic term ΔEelstat.

Effects of density functionals and dispersion interactions on geometries, bond energies and harmonic frequencies of E[tbnd]UX3 (E = N, P, CH; X = H, F, Cl)

Quantum-chemical calculations have been performed to evaluate the geometries, bonding nature and harmonic frequencies of the compounds [EUX3] at DFT, DFT-D3, DFT-D3(BJ) and DFT-dDSc levels using different density functionals BP86, BLYP, PBE, revPBE, PW91, TPSS and M06-L. The stretching frequency of UN bond in [NUF3] calculated with DFT/BLYP closely resembles with the experimental value. The performance of different density functionals for accurate UN vibrational frequencies follows the order BLYP>revPBE>BP86>PW91>TPSS>PBE>M06-L. The BLYP functional gives accurate value of the UE bond distances. The uranium atom in the studied compounds [EUX3] is positively charged. Upon going from [EUF3] to [EUCl3], the partial Hirshfeld charge on uranium atom decreases because of the lower electronegativity of chlorine compared to flourine. The Gopinathan–Jug bond order for UE bonds ranges from 2.90 to 3.29. The UE bond dissociation energies vary with different density functionals as M06-L<TPSS<BLYP<revPBE<BP86<PBE≈PW91. The orbital interactions ΔEorb, in all studied compounds [EUX3] are larger than the electrostatic interaction ΔEelstat, which means the UN bonds in these compound have greater degree of covalent character (in the range 63.8–77.2%). The UE σ-bonding interaction is the dominant bonding interaction in the nitride and methylidyne complexes while it is weaker in [PUX3]. The dispersion energy contributions to the total bond dissociation energies are rather small. Compared to the Grimme’s D3(BJ) corrections, the Corminboeuf’s dispersion corrections are larger with metaGGA functionals (TPSS, M06-L) while smaller with GGA functionals.

Insights into the nature of ME bonds in [(PMe3)4ME(Mes)]+ (M = Mo, W) and [(PMe3)5WE(Mes)]+: a dispersion-corrected DFT study

Structures and bonding energy analysis of terminal cationic metal–ylidyne complexes [(PMe3)4ME(Mes)]+ (M = Mo, W) and [(PMe3)5WE(Mes)]+ (E = Si, Ge, Sn, Pb) were investigated by DFT, DFT-D3 and DFT-D3(BJ) methods using BP86, PBE and PW91 functionals. The Nalewajski–Mrozek (N–M) bond orders and Pauling bond orders show that the M–E bonds in the studied cationic complexes are essentially ME triple bonds. Atomic orbital populations reveal that the out-of-plane π-bonding in all complexes is stronger than the in-plane π-bonding. The bonding of the M–E σ-bond is quite strong, as is the total M–E π-bond strength, and increases upon going from molybdenum to tungsten. The contribution of the orbital interactions ΔEorb is significantly larger (58–63%) than the electrostatic contributions ΔEelstat in all the complexes studied. The absolute values of the bond dissociation energies decrease in the order Si > Ge > Sn > Pb. The D3-dispersion energies with zero-damping are in the range 13.0–17.9 kcal mol−1 (BP86), 7.1–10.6 kcal mol−1 (PBE) and 7.7–10.6 kcal mol−1 (PW91), which are smaller than the corresponding DFT-D3(BJ) energies of 21.0–24.6 kcal mol−1 (BP86), 9.9–13.6 kcal mol−1 (PBE) and 10.6–13.6 kcal mol−1 (PW91). The percentage dispersion-corrections to the bond dissociation energies increase as E becomes heavier. The effects of relativistic core contractions in heavier nuclei, i.e. tungsten and lead, are also evaluated.

Structure and Bonding Analysis of the Cationic Electrophilic Phosphinidene Complexes of Iron, Ruthenium, and Osmium [(η5-C5Me5)(CO)2M{PNiPr2}]+, [(η5-C5H5)(CO)2M{PNR2}]+ (R = Me, iPr), and [(η5-C5H5)(PMe3)2M{PNMe2}]+ (M = Fe, Ru, Os)

Quantum-chemical DFT calculations for the electronic, molecular structure and M-PNR(2) bonding analyses of the experimentally known cationic electrophilic phosphinidene complexes [(η(5)-C(5)Me(5))(CO)(2)M{PN(i)Pr(2)}](+) and of the model complexes [(η(5)-C(5)H(5))(CO)(2)M{PNR(2)}](+) (R = (i)Pr, Me) and [(η(5)-C(5)H(5))(PMe(3))(2)M{PNMe(2)}](+) were carried out using BP86/TZ2P/ZORA level of theory. The calculated geometrical parameters of the studied complexes are in good agreement with the reported experimental values. The short M-P bond distances and calculated Pauling bond orders (range of 1.23-1.68), suggest the presence of M-P multiple bond characters. The Hirshfeld charge analysis shows that the overall charge flows from phosphinidene ligand to metal fragment. The M-P σ-bonding orbitals are well-occupied (>1.80e). The energy decomposition analysis revealed that the contribution of the electrostatic interaction ΔE(elstat) is, in all studied complexes, significantly larger (55.2-62.6%) than the orbital interactions ΔE(orb). The orbital interactions between metal and PNR(2) in [(η(5)-C(5)H(5))(L)(2)M{PNR(2)}](+) arise mainly from M ← PNR(2) σ-donation. The π-bonding contribution (19-36%) is much smaller than the σ-bonding. The interaction energies, as well as bond dissociation energies, depend on the auxiliary ligand framework around the metal and decrease in the order (η(5)-C(5)H(5)) > (η(5)-C(5)Me(5)) and CO > PMe(3). Upon substitution of R = (i)Pr with smaller group R = Me, the M-PNR(2) bond strength slightly decreases.

Energy decomposition analysis

AbstractThe energy decomposition analysis (EDA) is a powerful method for a quantitative interpretation of chemical bonds in terms of three major expressions. The instantaneous interaction energy ΔEintbetween two fragments A and B in a molecule A–B is partitioned in three terms, namely, (1) the quasiclassical electrostatic interaction ΔEelstatbetween the fragments, (2) the repulsive exchange (Pauli) interaction ΔEPaulibetween electrons of the two fragments having the same spin, and (3) the orbital (covalent) interaction ΔEorb, which comes from the orbital relaxation and the orbital mixing between the fragments. The latter term can be decomposed into contributions of orbitals with different symmetry, which makes it possible to distinguish betweenσ, π, andδbonding. After a short introduction into the theoretical background of the EDA, we present illustrative examples of main group and transition metal chemistry. The results show that the EDA terms can be interpreted in a chemically meaningful way, thus providing a bridge between quantum chemical calculations and heuristic bonding models of traditional chemistry. © 2011 John Wiley &amp; Sons, Ltd.This article is categorized under:Structure and Mechanism &gt; Molecular Structures

Syntheses and Crystal Structures of [Hg{C(PPh3)2}2][Hg2I6] and [Cu{C(PPh3)2}2]I and Comparative Theoretical Study of Carbene Complexes [M(NHC)2] with Carbone Complexes [M{C(PH3)2}2] (M = Cu+, Ag+, Au+, Zn2+, Cd2+, Hg2+)

The synthesis and X-ray structure analysis of the carbodiphosphorane (CDP) complexes [Hg{C(PPh3)2}2][Hg2I6] and [Cu{C(PPh3)2}2]I are reported. The cations [Hg{C(PPh3)2}2]2+ and [Cu{C(PPh3)2}2]+ have approximately linearly coordinated metal atoms. Quantum chemical calculations of model compounds bearing N-heterocyclic carbene (NHC) ligands, [M(NHC)2] and [M{C(PH3)2}2] (M = Cu+, Ag+, Au+, Zn2+, Cd2+, Hg2+), have been carried out at the BP86/TZ2P level. The metal–ligand bonds are very strong, and the bond dissociation energies exhibit a V-shaped trend for first-, second-, and third-row transition metals: Ag+ < Cu+ < Au+ and Cd2+ < Zn2+ < Hg2+. The investigation of the bonding situation in the complexes using an energy decomposition analysis shows that the metal–ligand bonding comes mainly from electrostatic attraction. Inspection of the orbital interactions shows that the Mq←(NHC)2 and Mq←{C(PH3)2}2 σ donation provides between 65 and 75% of the total orbital interactions ΔEorb. The contribution of the Mq→(NHC)2 and Mq→{C(PH3)2}2 π back-donation is very weak. The nature and strength of the donor–acceptor bonds of the two-electron donor ligand NHC and the four-electron donor ligand CDP with the group 11 and group 12 metal cations are very similar.

Structure and Bonding Energy Analysis of Cationic Metal–Ylyne Complexes of Molybdenum and Tungsten, [(MeCN)(PMe3)4M≡EMes]+ (M = Mo, W; E = Si, Ge, Sn, Pb): A Theoretical Study

The molecular and electronic structures and bonding analysis of terminal cationic metal-ylyne complexes (MeCN)(PMe(3))(4)M≡EMes](+) (M = Mo, W; E = Si, Ge, Sn, Pb) were investigated using DFT/BP86/TZ2P/ZORA level of theory. The calculated geometrical parameters for the model complexes are in good agreement with the reported experimental values. The M-E σ-bonding orbitals are slightly polarized toward E except in the complex [(MeCN)(PMe(3))(4)W(SnMes)](+), where the M-E σ-bonding orbital is slightly polarized toward the W atom. The M-E π-bonding orbitals are highly polarized toward the metal atom. In all complexes, the π-bonding contribution to the total M≡EMes bond is greater than that of the σ-bonding contribution and increases upon going from M = Mo to W. The values of orbital interaction ΔE(orb) are significantly larger in all studied complexes I-VIII than the electrostatic interaction ΔE(elstat). The absolute values of the interaction energy, as well as the bond dissociation energy, decrease in the order Si > Ge > Sn > Pb, and the tungsten complexes have stronger bonding than the molybdenum complexes.

Multiple Boron−Boron Bonds in Neutral Molecules: An Insight from the Extended Transition State Method and the Natural Orbitals for Chemical Valence Scheme

We have analyzed the character of B═B and B≡B bonds in the neutral molecules of general form: LHB═BHL (2-L) and LB≡BL (3-L), for various ancillary ligands L attached to the boron center, based on a recently developed method that combines the extended transition state scheme with the theory of natural orbitals for chemical valence (ETS-NOCV). In the case of molecules with the B═B bond, 2-L, we have included L = PMe(3), PF(3), PCl(3), PH(3), C(3)H(4)N(2)═C(NHCH)(2), whereas for molecules containing the B≡B connection, 3-L, the following ligands were considered L = CO, PMe(3), PCl(3), (Me(2)NCH(2)CH(2)O)(2)Ge. The results led us to conclude that use of phosphorus ligands leads to strengthening of the B═B bond by 6.4 kcal/mol (for 2-PMe(3)), by 4.4 (for 2-PF(3)) and by 9.2 (for 2-PH(3)), when compared to a molecule developed on the experimental basis, 2-C(3)H(4)N(2) (ΔE(total) = -118.3 kcal/mol). The ETS scheme has shown that all contributions, that is, (i) orbital interaction ΔE(orb), (ii) Pauli repulsion ΔE(Pauli), and (iii) electrostatic stabilization ΔE(elstat), are important in determining the trend in the B═B bond energies, ΔE(total). ETS-NOCV results revealed that both σ(B═B) and π(B═B) contributions are responsible for the changes in ΔE(orb) values. All considered molecules of the type LB≡BL, 3-L, exhibit a stronger B≡B bond when compared to a double B═B connection in 2-L (|ΔE(total)| is lower by 11.8-42.5 kcal/mol, depending on the molecule). The main reason is a lower Pauli repulsion contribution noted for 3-CO, 3-PMe(3), and 3-PCl(3) molecules. In addition, in the case of 3-PMe(3) and 3-PCl(3), the orbital interaction term is more stabilizing; however, the effect is less pronounced compared to the drop in the Pauli repulsion term. In all of the systems with double and triple boron-boron bonds, the electronic factor (ΔE(orb)) dominates over the electrostatic contribution (ΔE(elstat)). Finally, the strongest B≡B connection was found for 3-Ge [L = (Me(2)NCH(2)CH(2)O)(2)Ge], predominantly as a result of the strongest σ- and π-contributions, despite the highest destabilization originating from the sizable bulkiness of the germanium-containing ligand. The data on energetic stability of multiple boron-boron bonds (relatively high values of bond dissociation energies |ΔE(total)|), suggest that it should be possible to isolate experimentally the novel proposed systems with double B═B bonds, 2-PMe(3), 2-PF(3), 2-PCl(3), and 2-PH(3), and those with triple B≡B connections, 3-PMe(3), 3-Ge, and 3-PCl(3).