J Mol Model (2015) 21:253 DOI 10.1007/s00894-015-2795-x
ORIGINAL PAPER
Simultaneous interactions of pyrimidine ring with BeF2 and BF3 in BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes: non-cooperativity Saber Ghafari 1 & Alireza Gholipour 2
Received: 28 February 2015 / Accepted: 23 August 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract We investigated the mutual interplay between beryllium and boron bonds in the BeF2⋅⋅⋅X−Pyr⋅⋅⋅BF3 complexes (X = CN, F, Cl, Br, H, CH3, OH and NH2, where Pyr and ⋅⋅⋅ denote pyrimidine ring and beryllium and boron bonds, respectively) at the M06-2X/aug-cc-pVDZ level of theory. The results indicate that non-cooperative effects are observed when the two kinds of noncovalent interactions beryllium and boron bonds coexist in the complexes. These effects were studied in terms of the energetic and geometric features of the complexes. Atoms in molecules (AIM) and natural bond orbital (NBO) analyses were also performed to unveil the mechanism of these interactions in the title complexes. The electron-withdrawing/donating substituents decrease/increase the magnitude of the binding energies compared to the unsubstituted BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H) complex. The Esynvalues are in agreement with the geometric features of the complexes. The results stress the importance of the mutual effects between noncovalent interactions involving aromatic systems.
Keywords Mutual interplay . Non-cooperative effects . Atoms in molecules . Natural bond orbital
* Alireza Gholipour
[email protected] 1
Young Researchers and Elite Club, Shahreza Branch, Islamic Azad University, Shahreza, Iran
2
Young Researchers and Elite Club, Khoramabad Branch, Islamic Azad University, Khoramabad, Iran
Introduction The boron bond has been recognized as an important type of intermolecular interaction. Phillips and colleagues have investigated the structure, bonding, and energetic properties of the B⋅⋅⋅N interaction [1–4]. Boron trifluoride is a highly toxic, colorless gas, used extensively as a catalyst in organic chemistry. It reacts readily with water, producing hydrogen fluoride and boric acid. Thus, although available commercially at high purity, it is handled more conveniently when dissolved in appropriate solvents [5–8]. Beryllium and its derivatives are used extensively in the chemical industry. Beryllium hydride has attracted considerable interest as a rocket fuel on account of its high heat of combustion. It has also been considered as a moderator for nuclear reactors [8–11]. In this paper, we selected the pyrimidine ring (Pyr) as a remarkable unit to generate both beryllium and boron bonds. The pyrimidine ring is a particular aromatic moiety with two nitrogen atoms that can be considered as an electron donor. Here, we will study the simultaneous interactions of Be⋅⋅⋅N and B⋅⋅⋅N in substituted pyrimidine (BeF2⋅⋅⋅X−Pyr⋅⋅⋅BF3,, X = CN, F, Cl, Br, H, CH3, OH and NH2, where Pyr and ⋅⋅⋅ denote pyrimidine ring and beryllium and boron bonds, respectively) complexes with quantum chemical calculations (see Scheme 1). We wish to analyze the mutual interplay between simultaneous interactions of beryllium and boron bonds for BeF2⋅⋅⋅X −Pyr⋅⋅⋅BF3 complexes using the results of ab initio calculations. Simple models such as BeF2⋅⋅⋅X−Pyr⋅⋅⋅BF3 complexes can be useful to design novel supramolecular systems and drugs, because these interactions play pivotal roles in a wide range of chemical and biological processes. Our aims were to (1) determine the binding energies, structures, and bonding characteristics of these complexes; (2)
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Be…N
B…N
Scheme 1 Molecular model used in the present study. The simultaneous interactions of Be⋅⋅⋅N and B⋅⋅⋅N in a substituted pyrimidine ring. Red sphere CN, F, Cl, Br, H, CH3, OH and NH2 substituents
examine the effect of substituents on the beryllium and boron bonds; and (3) characterize the mutual interplay between the beryllium and boron bonds. We also performed analyses on these complexes with atoms in molecules (AIM) and natural bond orbital (NBO) methodologies. The results reported herein could be useful in crystal engineering and in biological design.
Computational methods The geometries of the BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes depicted in Scheme 1 were optimized using the M06-2X density functional theory (DFT) functional [12, 13] paired with the aug-ccpVDZ basis sets. They were corrected for basis set superposition error (BSSE) using the counterpoise procedure proposed by Boys and Bernardi [14]. Then, calculations were carried out on the BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes to explore the interplay between the two kinds of simultaneous interactions of beryllium and boron bonds. The synergetic energy Esyn was evaluated using Esyn = ΔEComplexes – ΔEBinary complexes. Harmonic vibrational frequencies were computed for all optimized structures to characterize the stationary points. In these cases, the structures do not have an imaginary vibrational frequency. The wave function obtained at the M06-2X/aug-cc-pVDZ computational level was used to analyze the electron density within the atoms in molecules (AIM) methodology, and the orbital interaction within the natural bond orbital (NBO) framework. For this purpose, the AIM2000 program [15] was applied, and existing NBO programs [16] were used. All optimizations were carried out using the GAMESS program [17].
Results and discussion The optimized structures of BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes are depicted in Scheme 1. The results obtained for BeF2⋅⋅⋅X–
Pyr⋅⋅⋅BF3 complexes will be discussed first before comparing them with BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 (X = H) complexes. The total binding energies of BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes (ΔE = EComplexes – ΣEMonomer), calculated at M062X/aug-cc-pVDZ level of theory and corrected BSSE, are summarized in Table 1. The BSSE-corrected binding energies increased from −48.88 to −66.33 kcal mol−1. The list of substituents in Table 1 is given in order of electron withdrawing strength (NH2 < CH3 < OH < H < Br < Cl < F < CN) in terms of the Hammett constants. As can be seen in Table 1, as the substituents become more and more electron-withdrawing in BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes, the binding energies (ΔE) become weaker and weaker. The calculated binding energies for BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 (X = H) is equal to −55.66 kcal mol−1. The highest and lowest binding energies corresponded to BeF2⋅⋅⋅NH2–Pyr⋅⋅⋅BF3 and BeF2⋅⋅⋅CN–Pyr⋅⋅⋅BF3–66.33 and −48.88 kcal mol−1, respectively, among the substituted complexes. On the basis of calculated binding energies, the trend in the strength of the total intermolecular interactions of BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes is NH2 > CH3 > OH > H > Br > Cl > F > CN. The BeF 2 ⋅⋅⋅X-Pyr⋅⋅⋅BF 3 complexes became more destabilized as the electron withdrawing ability of the substituents increased because of the reduced amount of π–electron cloud in the substituted pyrimidine ring (X−Pyr). The electron withdrawing substituents decreased the π–electron cloud by pulling electron density away from the center of the substituted pyrimidine ring, so lone pairs of nitrogen atoms in the pyrimidine ring interact less with the Be and B atoms, leading to a less favorable binding energies compared to the unsubstituted ring BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H) complex. The binding energy was increased compared to the BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H) complex. Positive electrondonating substituents increase the negative charge in the π– electron cloud and thus lead to more favorable electrostatic interactions than unsubstituted complex BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H).
Table 1 Binding (ΔE) and synergetic (Esyn) energies (kcal mol−1). The most important geometrical parameters (in Å) obtained for BeF2⋅⋅⋅XPyr⋅⋅⋅BF3 complexes at M06-2X/aug-cc-pVDZ level of theory X
ΔE
Esyn
σtotal
RBe⋅⋅⋅N
RB⋅⋅⋅N
NH2 CH3 OH H Br Cl F CN
−60.33 −58.73 −56.62 −55.66 −52.61 −52.54 −51.04 −48.88
6.84 6.46 6.44 6.37 5.89 5.86 5.83 5.77
−0.82 −0.25 −0.20 0.00 0.31 0.30 0.49 1.26
1.721 1.736 1.741 1.748 1.753 1.754 1.755 1.760
1.671 1.675 1.678 1.680 1.692 1.692 1.694 1.703
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To clarify the substituent effect on these interactions, we considered the relationship between binding energies and Hammett constants. The Hammett constants σpara or σmeta may be useful parameters to describe intermolecular interactions in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes. The linear correlation coefficients of ΔE with σpara or σmeta are equal to 0.91 and 0.92, respectively. On the other hand, it would be more realistic to use σtotal (σtotal = σpara + σmeta) as a new parameter to describe the interactions in these complexes (see Table 1) [18–22]. As can be seen in Fig. 1, there is a good correlation between ΔE and σtotal for BeF2⋅⋅⋅X–Pyr⋅⋅⋅BF3 complexes. The correlation coefficient (R2 =0.93) demonstrates that the electrostatic effect of the substituents is prominent in these complexes. To explore and quantify the effect of the beryllium and boron bonds on each other, binary complexes (dimers) of the BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes were considered. Synergetic energy (Esyn) is a practical parameter for estimating the interplay between noncovalent interactions. The mutual interplay of beryllium and boron bonds can be considered with regard to Bsynergetic energy^ (Esyn = ΔEComplexes−ΔEBinary complexes). These interactions in the complexes should be synergistic when the values of Esyn are negative, while positive Esyn indicates non-cooperative effects in the complexes (see Table 1). The binding energies for BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes calculated at M06-2X/aug-cc-pVDZ level of theory are lower than the sum of the ΔE values of dimers. The values of Esyn range from 5.77 to 6.84 kcal mol−1, and equal 6.37 kcal mol−1 for the unsubstituted case [BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H)]. The magnitude of Esyn increases with electron-donating substituents, but the reverse behavior is observed with the electronwithdrawing substituents. As can be seen in Fig. 2, a satisfactory linear relationship is observed between the ΔE and the Esyn (R2 =0.95). The presence of simultaneous interactions of
Be⋅⋅⋅N and B⋅⋅⋅N interactions in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 leads to positive values of synergetic energy (Esyn). The electron-withdrawing/donating substituents decrease/increase Esyn compared to the BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H) complex, respectively. Comparing Esyn in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes suggests that E s y n is highest in the BeF2⋅⋅⋅NH2-Pyr⋅⋅⋅BF3 complex. The following conclusions can be drawn from the obtained data: the ranking sequence of the synergetic energy is NH2 > CH3 > OH > H > Br > C l > F > CN (see Table 1). The geometry parameters RBe⋅⋅⋅N and RB⋅⋅⋅N are used to indicate the strength of interactions. RBe⋅⋅⋅N and RB⋅⋅⋅N refer to intermolecular distance of Be⋅⋅⋅N and B⋅⋅⋅N interactions in these complexes. Table 1 shows that RBe⋅⋅⋅N and RB⋅⋅⋅N of electron-donating substituents in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes are shorter than the corresponding values in the unsubstituted BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H) complex, in which RBe⋅⋅⋅N and RB⋅⋅⋅N decrease with increasing electron-donating character of the substituents. The RBe⋅⋅⋅N and RB⋅⋅⋅N of BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes decrease with increasing electron-donating character of the substituents. The reverse behavior is observed for electronwithdrawing substituents, and the decrease in the πelectron cloud inside the ring causes the increase in RBe⋅⋅⋅N and RB⋅⋅⋅N. The π-electron cloud is largest/smallest in BeF2⋅⋅⋅CN−Pyr⋅⋅⋅BF3/BeF2⋅⋅⋅NH2−Pyr⋅⋅⋅BF3 complexes. The RBe⋅⋅⋅N values (1.721–1.760 Å) are higher than RB⋅⋅⋅N (1.671–1.703 Å) in the BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes, i.e., boron bonds are stronger than beryllium bonds. It is also worth mentioning that the distances RBe⋅⋅⋅N and RB⋅⋅⋅N of BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes are higher than those of dimers, as shown in Table 2. RBe⋅⋅⋅N and RB⋅⋅⋅N in the dimer are about 1.713–1.740 Å and 1.641–1.672 Å, respectively. The simultaneous presence of beryllium and boron bond interactions weakens each other in the BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes.
2
Fig. 1 Correlation between binding energies (ΔE) and the Hammett constants (σtotal) for BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes
1.5 1
σtotal
R² = 0.931
0.5 0 -0.5 -1 -58
-56
-54
-52
ΔΕ
-50
-48
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4.7
Fig. 2 Correlation between of the binding energies (ΔE) and synergetic energies (Esyn) in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes
R² = 0.958
4.5 4.3
Esyn 4.1 3.9 3.7 3.5 -58
-56
-54
-52
-50
-48
ΔE Atoms in molecules The topological analysis of electron charge density (ρ) was performed by the AIM method on the obtained wave functions at M06-2X/aug-cc-pVDZ level of theory. One way of characterizing the non covalent interactions is AIM analysis that interprets these interactions in term of critical points (CPs). Scheme 2 illustrates the positions of bond critical points (BCPs) and ring critical points (RCPs) as well as bond paths connecting CPs. Scheme 2 presents a typical molecular graph of the BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes considered in this study. The topological properties of ρ calculated at the BCPs of the intermolecular beryllium and boron bonds may be treated as a measure of their strength. It is worth noting that the values of the electron density calculated at the BCPs of Be⋅⋅⋅N and B⋅⋅⋅N interactions are lower for electron-withdrawing substituents than those of other substituents. The electron-withdrawing substituents in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes pull the lone pair of nitrogen atoms of pyrimidine inside the ring and decrease the electron Table 2 Binding energies (ΔE) (kcal mol−1) and most important geometrical parameters (in Å) obtained for BeF 2⋅⋅⋅X-Pyr and XPyr⋅⋅⋅BF3 dimers at M06-2X/aug-cc-pVDZ level of theory X
ΔE X-Pyr⋅⋅⋅BeF2
ΔE X-Pyr⋅⋅⋅BF3
RBe⋅⋅⋅N
RB⋅⋅⋅N
NH2 CH3 OH H Br Cl F CN
−38.17 −37.29 −35.92 −36.52 −34.20 −34.24 −34.42 −32.44
−28.99 −27.89 −26.22 −26.87 −24.16 −24.27 −24.36 −22.21
1.713 1.722 1.721 1.728 1.735 1.734 1.735 1.740
1.641 1.643 1.650 1.652 1.665 1.668 1.669 1.672
density of Be⋅⋅⋅N and B⋅⋅⋅N interactions. On the other hand, complexes containing electron-donating substituents exhibit higher ρBCPs values than other substituents (see Table 2). The minimum/maximum values of electron density for the beryllium and boron bonds were observed for the BeF2⋅⋅⋅CN −Pyr⋅⋅⋅BF3/BeF2⋅⋅⋅NH2−Pyr⋅⋅⋅BF3 complexes compared to other complexes. The change in Be⋅⋅⋅N and B⋅⋅⋅N bond lengths confirms the electron density (ρ) data [18–21], the electron density calculated at the BCPs of Be⋅⋅⋅N (5.75–6.57 in e a0−3) are less than BCPs of B⋅⋅⋅N (9.91–10.67 in e a0−3) in the BeF2⋅⋅⋅XPyr⋅⋅⋅BF3 complexes (see Table 3).
Natural bond orbitals For a better understanding of the substituent effect on beryllium and boron bonds in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes, NBO
Be…N
B…N
Scheme 2 Typical molecular graphs for BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3complexes. Red spheres Bond critical points, yellow spheres ring critical points
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Table 3 Electron densities-ρ (in e a0−3) at Be⋅⋅⋅N and B⋅⋅⋅N interactions, E(2) from natural bond orbital (NBO) analysis corresponds to nN→σ*Be-F and nN→σ*B-F interactions in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes calculated at M06-2X/aug-cc-pVDZ level of theory X
ρBCPBe…N
ρBCPB…N
nN→σ*Be-F
nN→σ*B-F
NH2 CH3 OH H Br Cl F CN
6.57 6.21 6.12 6.06 5.94 5.93 5.92 5.75
10.67 10.65 10.59 10.51 10.20 10.19 10.15 9.91
2.98 2.87 2.76 2.71 2.54 2.45 2.43 2.29
4.82 4.73 4.63 4.50 4.43 4.32 4.21 4.11
Molecular electrostatic potential The electrostatic potential V®) that is created in the space around a molecule by its nuclei and electrons is given by following equation: VðrÞ ¼
M X A¼1
analysis was carried out at M06-2X/aug-cc-pVDZ level of theory. Herein, the nN→σ*Be-F and nN→σ*B-F interactions energies can be considered as a measure of the strength of the beryllium and boron bonds, respectively. The nN→σ*Be(2) F and nN→σ*B-F interaction energy (E ) as a local descriptor is also related to the charge transferred in the beryllium and boron bond interaction. These interactions are due to a large degree of charge transfer from the N lone pairs to the sigma anti-bonding orbital of the BeF and BF. The E(2) values of these interactions can be used as an index to predict the strength of the beryllium and boron bonds, and play an important role in the stabilization of the Be⋅⋅⋅N and B⋅⋅⋅N interactions in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes. Table 3 suggests that the electron-donating substituents increase the electron density on the nitrogen atom of the pyrimidine ring and increase its inclination towards polarization of Be⋅⋅⋅N and B⋅⋅⋅N interactions by increasing the E(2) of nN→σ*Be-F and nN→σ*B-F interactions. For beryllium and boron bonds, the maximum/minimum values of E (2) were observed for BeF2⋅⋅⋅NH2−Pyr⋅⋅⋅BF3/ BeF2⋅⋅⋅CN−Pyr⋅⋅⋅BF3 complexes compared to other complexes. For all substituents, the E(2) values of nN→σ*B-F (4.11– 4.82 a.u.) is higher than the E(2) values of nN→σ*Be-F (2.29– 2.98 a.u.) values, means that the orbital interactions of B⋅⋅⋅N are stronger than those of Be⋅⋅⋅N interactions. This shows that the orbital interactions play an important role in the formation of beryllium and boron bonds.
ZA − jr−RA j
Z
ρðr0 Þ 0 dr jr0 −rj
Where M is total number of nuclei in the molecule, ZA defines the charge of the nucleus located at RA and ρ®) is the electron density at location r. The sign of V®) at any point depends on whether the effects of the nuclei or the electrons are dominant there. The molecular electrostatic potential (MEP) on the electron density isosurface of 0.001 electrons Bohr−3 was obtained and depicted using the surface analysis suite program. Politzer et al. [23] showed that the Hellmann-Feynman theorem provides a straightforward interpretation of noncovalent bonding in terms of Coulombic interactions. These authors demonstrated that the formation and properties of σ-hole complexes can be explained in a very satisfactory and straightforward mathematical modeling in terms of electrostatics/polarization plus dispersion, xchange, Pauli repulsion, orbitals, etc. [23]. Among the electronic properties of these molecules, the MEP was chosen to find those regions where electron rich moieties can interact. The surface MEP of BeF2, BF3 and substituted pyrimidines ring were computed on the 0.001 a.u. contour of the electronic density. Scheme 3 shows the overall patterns of surface electrostatic potential maps for BeF2, BF3 and the substituted pyrimidines. Note the negative and positive regions are blue and red, respectively. Table 4 lists the most positive surface electrostatic potentials (VS,max) in the BeF2, BF3 and the substituted pyrimidines monomers, and the most negative values of the MEP (VS,min) for the lone-pair of nitrogen atoms in substituted pyrimidines. Of primary interest are the locations of the most negative and the most positive VS, the VS,min and VS,max, which are relevant to the approach of electrophiles and nucleophiles, respectively. The positive region can interact with an electronegative atom/group, thereby giving rise to a directional interaction.
Scheme 3 Overall patterns of surface molecular electrostatic potential (MEP) maps for BeF2, BF3 and the substituted pyrimidines
BeF2
BF3
Substituted pyrimidines
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Table 4 Maximum (VS,max) and minimum (VS,min) electrostatic potentials (kcal mol−1) on the 0.001 au electron density isosurface of the isolated monomers at M06-2x/aug-cc-pVDZ
VS,max VS,min X NH2 CH3 OH H Br Cl F CN
BeF2 39.868 VS,min X-Pyr −25.93 −25.87 −25.81 −25.75 −25.64 −25.43 −25.27 −25.13
BF3 42.469 VS,max X-Pyr⋅⋅⋅BeF2 30.548 31.274 32.132 32.879 33.989 33.111 33.274 34.435
References 1.
Pyrimidine −24.874 VS,max X-Pyr⋅⋅⋅BF3 37.469 40.221 41.123 41.321 41.333 42.900 42.123 42.456
2.
3.
4.
5. 6.
7.
Conclusions Results from quantum computations are beginning to paint a more complete picture of how substituents affect binding energies. These interactions are somewhat affected by the nature of substituents attached to the pyrimidine ring in BeF2⋅⋅⋅XPyr⋅⋅⋅BF3 complexes, while strong correlations were found between the binding energies and Hammett electronic parameters σtotal of substituents. The electron-withdrawing/donating substituents decrease/ increase the magnitude of the binding energies compared to the unsubstituted BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 (X = H) complex. The main reason for different behavior between electron withdrawing and donating substituents is the decrease/increase of the π electron cloud. The total binding energies in BeF2⋅⋅⋅X-Pyr⋅⋅⋅BF3 complexes were lower than the sum of ΔE values of dimer complexes for both electron-donating and electron-withdrawing substituents, so that the values of Esyn are positive while positive Esyn indicates non-cooperative effects in the BeF2⋅⋅⋅XPyr⋅⋅⋅BF3 complexes. The change in Be⋅⋅⋅N and B⋅⋅⋅N bond length confirms the electron density (ρ) data; these increases were accompanied by a reduction in the RBe⋅⋅⋅N and RB⋅⋅⋅N bond length. Also, the results obtained by AIM analysis demonstrate that the B⋅⋅⋅N interaction is stronger than Be⋅⋅⋅N interactions in BeF2⋅⋅⋅XPyr⋅⋅⋅BF3 complexes. NBO analysis showed that, in BeF 2 ⋅⋅⋅X-Pyr⋅⋅⋅BF 3 complexes, there is significant charge transfer from lone electron pairs (the nitrogen atoms of the pyrimidine ring) to the BeF and BF antibonding orbitals. The magnitude of the E(2) of nN→σ*B-F interaction in BeF2⋅⋅⋅XPyr⋅⋅⋅BF3 complexes was observed to be higher than those of nN→σ*Be-F interactions.
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