Cooperativity in Tetrel Bonds

A theoretical study of the cooperativity in linear chains of (H₃SiCN)_<i>n</i> and (H₃SiNC)_<i>n</i> complexes connected by tetrel bonds has been carried out by means of MP2 and CCSD­(T) computational methods. In all cases, a favorable cooperativity is observed, especially in some of the largest linear chains of (H₃SiNC)_<i>n</i>, where the effect is so large that the SiH₃ group is almost equidistant to the two surrounding CN groups and it becomes planar. In addition, the combination of tetrel bonds with other weak interactions (halogen, chalcogen, pnicogen, triel, beryllium, lithium, and hydrogen bond) has been explored using ternary complexes, (H₃SiCN)₂:XY and (H₃SiNC)₂:XY. In all cases, positive cooperativity is obtained, especially in the (H₃SiNC)₂:ClF and (H₃SiNC)₂:SHF ternary complexes, where, respectively, halogen and chalcogen shared complexes are formed

Complexes between Dihydrogen and Amine, Phosphine, and Arsine Derivatives. Hydrogen Bond versus Pnictogen Interaction

A theoretical study of the complexes between dihydrogen, H₂, and a series of amine, phosphine, and arsine derivatives (ZH₃ and ZH₂X, with Z = N, P, or As and X = F, Cl, CN, or CH₃) has been carried out using ab initio methods (MP2/aug-cc-pVTZ). Three energetic minima configurations have been characterized for each case with the H₂ molecule in the proximity of the pnictogen atom (Z). In configuration A, the σ-electrons of H₂ interact with σ-hole region of the pnictogen atom generated by the of X–Z bond. These complexes can be ascribed as pnictogen bonded. In configuration C, the lone electron pair of Z acts as the Lewis base, and H₂ plays the role of the Lewis acid. Finally, configuration B presents a variety of noncovalent interactions depending on the binary complex considered. The atoms-in-molecules theory (AIM), natural bond orbitals (NBO) method as well as the density functional theory–symmetry adapted perturbation theory (DFT-SAPT) approach were used in this study to deepen the nature of the interactions considered

Fostering the Basic Instinct of Boron in Boron–Beryllium Interactions

A set of complexes L₂HB···BeX₂ (L = CNH, CO, CS, N₂, NH₃, NCCH₃, PH₃, PF₃, PMe₃, OH₂; X = H, F) containing a boron–beryllium bond is described at the M06-2X/6-311+G­(3df,2pd)//M062-2X/6-31+G­(d) level of theory. In this quite unusual bond, boron acts as a Lewis base and beryllium as a Lewis acid, reaching binding energies up to −283.3 kJ/mol ((H₂O)₂HB···BeF₂). The stabilization of these complexes is possible thanks to the σ-donor role of the L ligands in the L₂HB···BeX₂ structures and the powerful acceptor nature of beryllium. According to the topology of the density, these B–Be interactions present positive laplacian values and negative energy densities, covering different degrees of electron sharing. ELF calculations allowed measuring the population in the interboundary B–Be region, which varies between 0.20 and 2.05 electrons upon switching from the weakest ((CS)₂HB···BeH₂) to the strongest complex ((H₂O)₂HB···BeF₂). These B–Be interactions can be considered as beryllium bonds in most cases

Ab Initio Study of Ternary Complexes X:(HCNH)⁺:Z with X, Z = NCH, CNH, FH, ClH, and FCl: Diminutive Cooperative Effects on Structures, Binding Energies, and Spin–Spin Coupling Constants Across Hydrogen Bonds

Ab initio calculations have been performed on a series of complexes in which (HCNH)⁺ is the proton donor and CNH, NCH, FH, ClH, and FCl (molecules X and Z) are the proton acceptors in binary complexes X:HCNH⁺ and HCNH⁺:Z, and ternary complexes X:HCNH⁺:Z. These complexes are stabilized by C–H⁺···A and N–H⁺···A hydrogen bonds, where A is the electron-pair donor atom of molecules X and Z. Binding energies of the ternary complexes are less than the sum of the binding energies of the corresponding binary complexes. In general, as the binding energy of the binary complex increases, the diminutive cooperative effect increases. The structures of these complexes, data from the AIM analyses, and coupling constants ¹<i>J</i>(N–H), ^1h<i>J</i>(H–A), and ^2h<i>J</i>(N–A) for the N–H⁺···A hydrogen bonds, and ¹<i>J</i>(C–H), ^1h<i>J</i>(H–A), and ^2h<i>J</i>(C–A) for the C–H⁺···A hydrogen bonds provide convincing evidence of diminutive cooperative effects in these ternary complexes. In particular, the symmetric N···H⁺···N hydrogen bond in HCNH⁺:NCH looses proton-shared character in the ternary complexes X:HCNH⁺:NCH, while the proton-shared character of the C···H⁺···C hydrogen bond in HNC:HCNH⁺ decreases in the ternary complexes HNC:HCNH⁺:Z and eventually becomes a traditional hydrogen bond as the strength of the HCNH⁺···Z interaction increases

Characterizing Complexes with Pnicogen Bonds Involving sp² Hybridized Phosphorus Atoms: (H₂CPX)₂ with X = F, Cl, OH, CN, NC, CCH, H, CH₃, and BH₂

Ab initio MP2/aug′-cc-pVTZ searches of the potential surfaces of (H₂CPX)₂ complexes, with X = F, Cl, OH, CN, NC, CCH, H, CH₃, and BH₂, have been carried out to identify and characterize the properties of complexes with P···P pnicogen bonds. All (H₂CPX)₂ form equilibrium conformation A dimers with <i>C</i>_2<i>h</i> symmetry in which A–P···P–A approaches a linear alignment, with A the atom of X directly bonded to P. Conformation A dimers containing the more electronegative substituents are stabilized by a P···P pnicogen bond, have shorter P–P distances, and have binding energies which correlate with the P–P distance. Dimers stabilized by a P···P pnicogen bond and two P···H_b interactions consist of those with the more electropositive substituents, have shorter P–H_b distances, and have binding energies which are too high for their P–P distances. Conformation A complexes with P···H_b interactions in addition to the P···P bond are more stable than the corresponding (PH₂X)₂ complexes, while with only one exception, complexes stabilized by only a P···P bond are less stable than the corresponding (PH₂X)₂ complexes. In the region of the potential surfaces with C–P···P–C approaching linearity (conformation B), the only planar equilibrium complex is (H₂CPOH)₂, which is stabilized primarily by two O–H···P hydrogen bonds. The remaining (H₂CPX)₂ complexes are not stabilized by pnicogen bonds, but by π interactions between the two H₂CPX monomers which are in parallel planes. When A–P···P–C approaches linearity, two types of equilibrium structures with P···P bonds exist. Of the conformation C dimers, (H₂CPOH)₂ is planar and the most stable, with a P···P pnicogen bond and an O–H···P hydrogen bond. (H₂CPH)₂ and (H₂CPCH₃)₂ are also planar, and stabilized by a P···P pnicogen bond and a P···H_b interaction. The absence of a P···H_b interaction results in nonplanar C′ conformations with structures in which the monomers essentially retain their symmetry plane, but the plane of one molecule is rotated about the P···P bond relative to the other. C and C′ dimers are less stable than the corresponding A dimers, except for (H₂CPCH₃)₂. ³¹P chemical shielding patterns are consistent with the changing nature of the interactions which stabilize (H₂CPX)₂ complexes. EOM-CCSD ³¹P–³¹P spin–spin coupling constants increase quadratically as the P–P distance decreases

Pnicogen-Bonded Cyclic Trimers (PH₂X)₃ with X = F, Cl, OH, NC, CN, CH₃, H, and BH₂

Ab initio MP2/aug’-cc-pVTZ calculations have been carried out to determine the structures and binding energies of cyclic trimers (PH₂X)₃ with X = F, Cl, OH, NC, CN, CH₃, H, and BH₂. Except for [PH₂(CH₃)]₃, these complexes have <i>C</i>_3<i>h</i> symmetry and binding energies between −17 and −63 kJ mol^–1. Many-body interaction energy analyses indicate that the two-body terms are dominant, accounting for 97–103% of the total binding energy. Except for the trimer [PH₂(OH)]₃, the three-body terms are stabilizing. Charge transfer from the lone pair on one P atom to an antibonding σ* orbital of the P atom adjacent to the lone pair plays a very significant role in stabilization. The charge-transfer energies correlate linearly with the trimer binding energies. NBO, AIM, and ELF analyses have been used to characterize bonds, lone pairs, and the degree of covalency of the P···P pnicogen bonds. The NMR properties of chemical shielding and ³¹P–³¹P coupling constants have also been evaluated. Although the ³¹P chemical shieldings in the five most strongly bound trimers increase relative to the corresponding isolated monomers, there is no correlation between the chemical shieldings and the charges on the P atoms. EOM-CCSD ³¹P–³¹P spin–spin coupling constants computed for four (PH₂X)₃ trimers fit nicely onto a plot of ^1pJ­(P–P) versus the P–P distance for (PH₂X)₂ dimers. A coupling constant versus distance plot for the four trimers has a second-order trendline which has been used to predict the values of ^1pJ­(P–P) for the remaining trimers

Pnicogen-Bonded Complexes H_<i>n</i>F_5–<i>n</i>P:N-Base, for <i>n</i> = 0–5

Ab initio MP2/aug′-cc-pVTZ calculations have been carried out on the pnicogen-bonded complexes H_<i>n</i>F_5–<i>n</i>P:N-base, for <i>n</i> = 0–5 and nitrogen bases NC^–, NCLi, NP, NCH, and NCF. The structures of these complexes have either <i>C</i>_4<i>v</i> or <i>C</i>_2<i>v</i> symmetry with one exception. P–N distances and interaction energies vary dramatically in these complexes, while F_ax–P–F_eq angles in complexes with PF₅ vary from 91° at short P–N distances to 100° at long distances. The value of this angle approaches the F_ax–P–F_eq angle of 102° computed for the Berry pseudorotation transition structure which interconverts axial and equatorial F atoms of PF₅. The computed distances and F_ax–P–F_eq angles in complexes F₅P:N-base are consistent with experimental CSD data. For a fixed acid, interaction energies decrease in the order NC^– > NCLi > NP > NCH > NCF. In contrast, for a fixed base, there is no single pattern for the variations in distances and interaction energies as a function of the acid. This suggests that there are multiple factors that influence these properties. The dominant factor appears to be the number of F atoms in equatorial positions, and then a linear F_ax–P···N rather than H_ax–P···N alignment. The acids may be grouped into pairs (PF₅, PHF₄) with four equatorial F atoms, then (PH₄F, PH₂F₃) with F_ax–P···N linear, and then (PH₃F₂ and PH₅) with H_ax–P···N linear. The electron-donating ability of the base is also a factor in determining the structures and interaction energies of these complexes. Charge transfer from the N lone pair to the σ* P–A_ax orbital stabilizes H_<i>n</i>F_5–<i>n</i>P:N-base complexes, with A_ax either F_ax or H_ax. The total charge-transfer energies correlate with the interaction energies of these complexes. Spin–spin coupling constants ^1p<i>J</i>(P–N) for (PF₅, PHF₄) complexes with nitrogen bases are negative with the strongest bases NC^– and NCLi but positive for the remaining bases. Complexes of (PH₄F, PH₂F₃) with these same two strong bases and H₄FP:NP have positive ^1p<i>J</i>(P–N) values but negative values for the remaining bases. (PH₅, PH₃F₂) have negative values of ^1p<i>J</i>(P–N) only for complexes with NC^–. Values of ¹<i>J</i>(P–F_ax) and ¹<i>J</i>(P–H_ax) correlate with the P–F_ax and P–H_ax distances, respectively

P···N Pnicogen Bonds in Cationic Complexes of F₄P⁺ and F₃HP⁺ with Nitrogen Bases

Ab initio MP2/aug’-cc-pVTZ calculations have been carried out on cationic pnicogen-bonded complexes F₄P⁺:N-base and F₃HP⁺:N-base, with linear F_ax–P···N and H_ax-P···N, respectively. The bases include the sp³-hybridized nitrogen bases NH₃, NClH₂, NFH₂, NCl₂H, NCl₃, NFCl₂, NF₂H, NF₂Cl, and NF₃, and the sp bases NCNH₂, NCCH₃, NP, NCOH, NCCl, NCH, NCF, NCCN, and N₂. The binding energies of these complexes span a wide range, from −15 to −180 kJ mol^–1, as do the P–N distances, which vary from 1.89 to 3.11 Å. There is a gap in the P–N distances between 2.25 and 2.53 Å in which no complexes are found. Thus, the equilibrium complexes may be classified as inner or outer complexes based on the value of the P–N distance. Inner complexes have P···N bonds with varying degrees of covalent character, whereas outer complexes are stabilized by intermolecular P···N bonds with little or no covalency. Charge-transfer stabilizes these pnicogen-bonded complexes. For complexes F₄P⁺:N-base, the dominant charge-transfer interaction is from the lone pair on N to the σ*P–F_ax orbital. In addition, there are three other charge-transfer interactions from the lone pair on N to the σ*P–F_eq orbitals, which taken together, are more stabilizing than the interaction involving σ*P–F_ax. In contrast, the dominant charge-transfer interaction for complexes F₃HP⁺:N-base is from the lone pair on N to the σ*P–F_eq orbitals. Computed EOM-CCSD Fermi-contact terms are excellent approximations to the total spin–spin coupling constants ^1p<i>J</i>(P–N) and ¹<i>J</i>(P–H_ax), but are poor approximations to ¹<i>J</i>(P–F_ax). ^1p<i>J</i>(P–N) values increase with decreasing P–N distance, approach a maximum, and then decrease and change sign as the P–N distance further decreases and the pnicogen bond acquires increased covalency. ¹<i>J</i>(P–F_ax) values for F₄P⁺:N-base complexes increase with decreasing distance. Although the P–H_ax distance changes very little in complexes F₃HP⁺:N-base, patterns exist which suggest that changes in ¹<i>J</i>(P–H_ax) reflect the hybridization of the nitrogen base and whether the complex is an inner or outer complex

Influence of Substituent Effects on the Formation of P···Cl Pnicogen Bonds or Halogen Bonds

Ab initio MP2/aug′-cc-pVTZ calculations have been carried out in search of equilibrium structures with P···Cl pnicogen bonds or halogen bonds on the potential energy surfaces H₂FP:ClY for Y = F, NC, Cl, CN, CCH, CH₃, and H. Three different types of halogen-bonded complexes with traditional, chlorine-shared, and ion-pair bonds have been identified. Two different pnicogen-bonded complexes have also been found on these surfaces. The most electronegative substituents F and NC form only halogen-bonded complexes, while the most electropositive substituents CH₃ and H form only pnicogen-bonded complexes. The halogen-bonded complexes involving the less electronegative groups Cl and CN are more stable than the corresponding pnicogen-bonded complexes, while the pnicogen-bonded complexes with CCH are more stable than the corresponding halogen-bonded complex. Traditional halogen-bonded complexes are stabilized by charge transfer from the P lone pair to the Cl–A σ* orbital, where A is the atom of Y directly bonded to Cl. Charge transfer from the Cl lone pair to the P–F σ* orbital stabilizes pnicogen-bonded complexes. As a result, the H₂FP unit becomes positively charged in halogen-bonded complexes and negatively charged in pnicogen-bonded complexes. Spin–spin coupling constants ^1X<i>J</i>(P–Cl) for complexes with traditional halogen bonds increase with decreasing P–Cl distance, reach a maximum value for complexes with chlorine-shared halogen bonds, and then decrease and change sign when the bond is an ion-pair bond. ^1p<i>J</i>(P–Cl) coupling constants across pnicogen bonds tend to increase with decreasing P–Cl distance

Properties of Cationic Pnicogen-Bonded Complexes F_4–<i>n</i>H_<i>n</i>P⁺:N-Base with F–P···N Linear and <i>n</i> = 0–3

Ab initio MP2/aug′-cc-pVTZ calculations were performed to investigate the pnicogen-bonded complexes F_4–<i>n</i>H_<i>n</i>P⁺:N-base, for <i>n</i> = 0–3, each with a linear or nearly linear F–P···N alignment. The nitrogen bases include the sp³ bases NH₃, NClH₂, NFH₂, NCl₂H, NCl₃, NFCl₂, NF₂H, NF₂Cl, and NF₃ and the sp bases NCNH₂, NCCH₃, NP, NCOH, NCCl, NCH, NCF, NCCN, and N₂. The binding energies vary between −20 and −180 kJ·mol^–1, while the P–N distances vary from 1.89 to 3.01 Å. In each series of complexes, binding energies decrease exponentially as the P–N distance increases, provided that complexes with sp³ and sp hybridized bases are treated separately. Different patterns are observed for the change in the binding energies of complexes with a particular base as the number of F atoms in the acid changes. Thus, the particular acid–base pair is a factor in determining the binding energies of these complexes. Three different charge-transfer interactions stabilize these complexes. These arise from the nitrogen lone pair to the σ*P–F_ax, σ*P–F_eq, and σ*P–H_eq orbitals. The dominant single charge-transfer energy in all complexes is N_lp → σ*P–F_ax. However, since there are three N_lp → σ*P–F_eq charge-transfer interactions in complexes with F₄P⁺ and two in complexes with F₃HP⁺, the sum of the N_lp → σ*P–F_eq charge-transfer energies is greater than the N_lp → σ*P–F_ax charge-transfer energies in the former complexes, and similar to the N_lp → σ*P–F_ax energies in the latter. The total charge-transfer energies of all complexes decrease exponentially as the P–N distance increases. Coupling constants ^1p<i>J</i>(P–N) across the pnicogen bond vary with the P–N distance, but different patterns are observed for complexes with F₄P⁺ and complexes of the sp³ bases with F₃HP⁺. These initially increase as the P–N distance decreases, reach a maximum, and then decrease with decreasing P–N distance as the P···N bond acquires increased covalent character. For the remaining complexes, ^1p<i>J</i>(P–N) increases with decreasing P–N distance. Complexation increases the P–F_ax distance and ¹<i>J</i>(P–F_ax) relative to the corresponding isolated ion. ¹<i>J</i>(P–F_ax) correlates quadratically with the P–N distance