Nature of beryllium bonds in view of interacting quantum atoms and natural energy decomposition analysis

Computational and Theoretical Chemistry 1090 (2016) 74–79

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Nature of beryllium bonds in view of interacting quantum atoms and natural energy decomposition analysis K. Eskandari Department of Chemistry, Isfahan University of Technology, Isfahan 84156-83111, Iran

a r t i c l e

i n f o

Article history: Received 23 April 2016 Received in revised form 5 June 2016 Accepted 6 June 2016 Available online 7 June 2016 Keywords: Beryllium bonds Non-covalent Interaction IQA NEDA QTAIM

a b s t r a c t In the light of interacting quantum atoms (IQA) and natural energy decomposition analysis (NEDA) the nature of different types of beryllium bonds is studied. IQA intra-atomic (self) energies indicate that, in most of the traditional beryllium bonds (in which the Lewis base is a lone pair donor), p-Be bonds (Lewis base is an unsaturated molecule) and also the Be–Ng (noble gases) interactions, the beryllium atom is stabilized upon complex formations. According to IQA inter-atomic energy components, the Be


Y bonds (Y is an atom in the Be-bond acceptor that is connected directly to the beryllium atom) have a dominant classical electrostatic character. However, in the IQA partitioning of total inter-molecular interactions, the contributions of non-classical (exchange–correlation) terms are non-negligible. Natural energy decomposition analysis of traditional and p-Be bonds indicate that the attractive interactions come from both the electrical and charge transfer terms. The electrical term in the Be–Ng bonds is negligibly small and the charge transfer is the most dominant contributor in the interaction energy. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction The nature of beryllium bonds has been the subject of a number of recent theoretical and experimental investigations [1–13]. Indeed, a beryllium bond is a non-covalent interaction in which a beryllium atom acts as a strong Lewis acid and interacts with a base. Beryllium bonds share many common characteristics with hydrogen bonds, however, they are in general significantly stronger than conventional hydrogen bonds [1,2]. Similar to hydrogen, the beryllium atom is electropositive and when it is covalently bonded to a more electronegative, its low-lying empty orbitals turning it into a potent electron acceptor. Yáñez and co-workers investigated the interactions between different Lewis bases and some beryllium derivatives, BeX2 , and showed that these interactions have a dominant electrostatic character in addition to some covalent character with a non-negligible charge transfer between interacting molecules [1]. On the other hand, Zhong et al. used SAPT-DFT [14] approach to explore the origin and nature of Be bonds [15]. Their results show that the electrostatic potential is the largest contributor to the binding, with induction and polarization playing important secondary roles. Yáñez et al. studied the so-called p-beryllium bonds between BeX2 and unsaturated compounds (ethylene and acetylene) and

E-mail address: [email protected] http://dx.doi.org/10.1016/j.comptc.2016.06.005 2210-271X/Ó 2016 Elsevier B.V. All rights reserved.

indicated that these complexes are stabilized by a significant charge transfer from pu binding orbitals into the empty p orbitals of Be and rBeH antibonding orbitals [7]. Using localized molecular orbital energy decomposition analysis (LMOEDA) [16] they showed that in the p-beryllium bonds the largest stabilizing contribution comes from the electrostatic term, however, the polarization is also significant. In a different work, Franking and co-workers studied the interactions between noble gases (Ng) and beryllium compounds. They prepared Ng  BeCO3 complexes and identified them via IR spectroscopy [8]. Their EDA of the Ng  Be bonds indicates that the attractive interaction energy comes mainly from orbital interaction (charge transfer and polarization effects). In our pervious work [2], we used quantum theory of atoms in molecules (QTAIM) [17,18] to investigate the nature of beryllium bonds, based on the properties of the electron density and its derivatives. It has been shown that these interactions are very similar to the very strong hydrogen bonds, however, some differences have been also observed. In the current study, to shed more light on the nature of different types of Be bonds, we will use again the real space QTAIM definitions, but our focus will be on the intra and inter-atomic energy terms within the framework of interacting quantum atoms (IQA) [19–21] energy partitioning. In addition, the natural energy decomposition analysis (NEDA) [22] will perform on the chosen beryllium bonded complexes. In this work, three different beryllium interactions are considered; traditional Be

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K. Eskandari / Computational and Theoretical Chemistry 1090 (2016) 74–79

bonds (between Be and ammonia), p-Be bonds (between Be and unsaturated molecules, ethylene and acetylene) and Ng–Be bonds (between Be and noble gases, Ne and Ar). 2. Theory and computational details The IQA scheme is a real space energy decomposition method which uses second order density matrix to partition the molecular energy into intra- and inter-atomic energy terms:

E¼

X XX Eself ðAÞ þ Eint ðA; BÞ A

ð1Þ

A B–A

in which, Eself ðAÞ is the intra-atomic (self) energy of the atom A and consists of all the monoatomic energy terms; kinetic energy, TðAÞ, nuclear–electron, V ne ðAÞ, and electron–electron interaction, V ee ðAÞ, inside the atomic basin:

Eself ðAÞ ¼ TðAÞ þ V ne ðAÞ þ V ee ðAÞ

ð2Þ

Eint ðA; BÞ is the inter-atomic interaction energy and obtained by collecting all the two-center contributions:

Eint ðA; BÞ ¼ V nn ðA; BÞ þ V en ðA; BÞ þ V ee ðA; BÞ

ð3Þ

here, V nn ðA; BÞ, V en ðA; BÞ and V ee ðA; BÞ are, respectively, nuclear– nuclear, electron nuclear and electron–electron interaction energies. In addition, V ee can be splitted into Columbic, V Cee , and exchange– correlation, V XC ee , terms. Now, Eint ðA; BÞ can be written as:

Eint ðA; BÞ ¼ V cl ðA; BÞ þ V XC ðA; BÞ

ð4Þ

where V cl ðA; BÞ consists of all the classical electrostatic interactions. In the NEDA method the intermolecular interaction energy is portioned into a sum of electrical (EL), core repulsion (CORE) and charge transfer (CT) components:

DE ¼ EL þ CORE þ CT

ð5Þ

Electrical component can be written as a sum of electrostatic (ES), polarization (POL) and self-energy (SE) contributions:

EL ¼ ES þ POL þ SE

ð6Þ

And finally, the core repulsion component is:

CORE ¼ EX þ DEF  SE

ð7Þ

here, EX and DEF are, respectively, the exchange and deformation contributions. The geometry of the molecules presented in this work were fully optimized with MP2/aug-cc-pvTZ level using GAMESS (US) quantum chemistry software [23]. IQA atomic energy terms were evaluated by AIMAll program [24]. This package has been also used to draw molecular graphs of the complexes. HF wavefunctions have used for IQA analyses. For NEDA calculations the NBO 5.0 program [25,26] implemented in the GAMESS was used. 3. Results and discussions 3.1. IQA analysis All the Be bonded complexes studied in this work have been listed in Table 1. The first block indicates traditional Be bonded molecules (CO3 Be


NH3 and X2 Be


NH3 ; X ¼ H; F; Cl and Br) while the second and third blocks correspond to Ng–Be (Ne


BeCO3 and Ar


BeCO3 ) and p-Be (H2 Be and F2 Be with ethylene and acetylene) complexes, respectively. The molecular graphs (MGs) of some of the complexes have been also presented in Fig. 1. Table 1 indicates the virial-based [17,27] atomic energies, DEVB , and also IQA self energies, DEself , of Be atom in these complexes relative to the corresponding values in their isolated optimized monomers.

Table 1 Changes in the virial-based atomic energies (DEVB ), IQA self-energy contributions and variation in the electronic population, DN, of beryllium atomic basin relative to relevant optimized monomers. The relative value for these properties have been defined as DP ¼ PðcomplexÞ  Pðisoleted monomerÞ. All energetic data are in kcal/mol. Complex

DEVB

DT

DV ee

DV en

DEself

DN

H2 Be


NH3 HFBe


NH3 F2 Be


NH3 HClBe


NH3 Cl2 Be


NH3 HBrBe


NH3 Br2 Be


NH3 CO3 Be


NH3

32.49 5.91 34.76 3.66 14.31 2.05 7.15 45.20

34.10 6.40 35.07 4.53 14.75 2.20 7.07 45.01

15.69 12.38 1.68 13.37 2.57 14.72 14.83 6.94

27.09 33.86 50.98 35.29 9.22 38.97 50.33 142.47

8.69 27.88 17.59 26.45 2.95 26.44 28.44 104.40

0.005 0.022 0.027 0.021 0.002 0.022 0.025 0.053

Ne


BeCO3 Ar


BeCO3

24.66 24.78

24.94 29.23

24.11 37.32

79.86 106.13

30.80 39.58

0.033 0.046

13.61 17.03 14.59 19.99

14.32 17.11 14.97 20.00

25.96 0.44 28.15 2.71

28.24 9.47 30.68 16.88

16.59 7.19 17.51 5.82

0.023 0.005 0.023 0.001

H2 Be


C2 H4 F2 Be


C2 H4 H2 Be


C2 H2 F2 Be


C2 H2

The relative values of all the contributions in the IQA self-energies have been also collected in the Table 1. All of the relative values have been defined as DP ¼ PðcomplexÞ  Pðisoleted monomerÞ, in which P refers to the atomic properties. It has been previously shown that in the traditional Be-bonded complexes the absolute value of virial-based atomic energy of the beryllium atom decreases (i.e. EVB ðBeÞ becomes less negative and DEVB ðBeÞ is positive) upon complex formation, comparable to the hydrogen atom in the hydrogen bonded complexes [2]. Similar results have been observed for most of the traditional Be bonds of this work (Table 1). CO3 Be


NH3 and Br2 Be


NH3 are the only exceptions in which DEVB ðBeÞ is negative and the beryllium atom is stabilized upon complex formation. In addition, in the p-Be bonded systems, similar to general trends in the traditional Be bonds, the Be atom is destabilized when the complex is formed. A different situation is found for Ng–Be complexes; the kinetic energy and hence the absolute value of virial-based energy of beryllium increases upon complex formation. On the other hand, from the IQA self-energy point of view, there is distinction between beryllium bonds and hydrogen bonds; as indicated in Table 1, in most of the complexes the beryllium atom is stabilized upon complex formation, unlike to hydrogen atom in the hydrogen bonded complexes [20]. In the traditional Be bonds (with the exception of H2 Be


NH3 and F2 Be


NH3 complexes) the absolute values of beryllium self-energy increase (DEself ðBeÞ is negative) during complex formation. In these complexes, the formation of beryllium bond is accompanied by two stabilizing changes: a decrease in the Be kinetic energy and an increase in the absolute value of nuclear–electron attraction. The destabilizing effect arising from electron–electron repulsion is small and is overwhelmed by the other two contributions. In the CO3 Be


NH3 and Br2 Be


NH3 systems, in which DTðBeÞ is positive (destabilizing effect), V ne ðBeÞ is the main stabilizing contributor, however, it is large enough to compensate for all destabilizing terms. In the H2 Be


NH3 and F2 Be


NH3 complexes DEself ðBeÞ is positive. Here, the negative values of DTðBeÞ are canceled out by two destabilizing effects: increase in the electron–electron repulsion and decrease in the absolute value of nuclear–electron attraction. During formation of p-Be and Ng–Be complexes the beryllium atom experiences an increase in its absolute value of self-energy (Eself ðBeÞ becomes more negative). In the p-Be bonds of BeH2 , the beryllium atom suffers an increase in electron–electron repulsion (mirrored in the positive values of DV ee ) and absolute values of nuclear–electron attraction (DV ne is negative) and a decrease in kinetic energy. The substitution of hydrogens of BeH2 by fluorine

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K. Eskandari / Computational and Theoretical Chemistry 1090 (2016) 74–79

Fig. 1. Molecular graphs of beryllium bonded complexes. Top: traditional Be bonds (H2 Be


NH3 and F2 Be


NH3 ), Middle: Ng–Be bonds (CO3 Be


Ne and CO3 Be


Ar), Bottom: p-Be bonds (H2 Be


C2 H4 and F2 Be


C2 H2 ). Red, green and purple dots are bond critical points, ring critical points and nonnuclear attractors (NNAs), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

atoms has two opposite effects: while makes DV ne positive, moderates destabilizing role of V ee . Nevertheless, the change in beryllium kinetic energy is adequate to make DEself ðBeÞ negative. In the Ng–Be interactions both the kinetic energy and electron– electron repulsion play destabilizing roles, however, those are compensated by a considerable stabilizing effect of nuclear– electron attraction. To rationalize the origin of beryllium self-energy changes, several factors must be considered: charge transfer, changes in interatomic surfaces and electronic reorganization within the atomic basins [19]. When the changes in the shape of density or atomic basins are small, there is a simple relation between charge transfer and variations in the intra-atomic energy components; an electron increase induces an increase in kinetic energy, electron– electron repulsion and nuclear–electron attraction (which becomes more negative). The variations of the electron population of beryllium basins have been gathered in the last column of Table 1. The beryllium atom, in most of the systems, gains charge

upon formation of the complex. The changes in the intra-atomic energy terms indicate that the charge transfer is not the only factor that governs the beryllium self-energy. The deformation of atomic basins and density reorganization affect the intra-atomic terms. It is not surprising, if one takes into account that the geometry of Be containing units and hence, the shape of atomic basin and density of beryllium, in the complex deviate largely from those in the chosen references (i.e. their isolated optimized monomers). Now, let us focus on the Be bond (Be


YÞ interaction, itself. Here Y is an atom in the Be-bond acceptor that is connected directly (usually with a bond path) to the beryllium atom (i.e., nitrogen atom, Neon or Argon atoms, and p system in the traditional, Ng–Be and p-Be complexes, respectively). Table 2 collects all the inter-atomic energy components of Be


Y pair. Classical part of the interactions has been also listed in the Table. In the traditional Be bonds, there is a stabilizing interaction between beryllium and Y (nitrogen) atom. Indeed a large amount (more than 95%) of this attractive interaction comes from classical

77

K. Eskandari / Computational and Theoretical Chemistry 1090 (2016) 74–79 Table 2 IQA interatomic contribution in the Be


Y interactions. Delocalization index is denoted by dðBe; YÞ. All energetic data are expressed in atomic units. %XC

V cl

5.659 5.589 5.470 5.743 5.712 5.789 5.846 5.892

0.029 0.031 0.025 0.035 0.031 0.036 0.039 0.041

0.705 0.695 0.731 0.717 0.767 0.724 0.749 0.759

96.0 95.8 96.6 95.3 96.1 95.2 95.1 94.9

4.0 4.2 3.4 4.7 3.9 4.8 4.9 5.1

0.12 0.11 0.10 0.13 0.12 0.13 0.14 0.15

6.510 10.194

6.547 10.262

0.012 0.020

0.029 0.052

70.1 72.6

29.9 27.4

0.05 0.08

6.165 6.166 12.330

3.399 3.400 6.799

3.559 3.559 7.118

0.012 0.012 0.024

0.117 0.117 0.234

90.6 90.6 90.6

9.4 9.4 9.4

0.05 0.05 0.10

5.356 5.356 10.713

5.551 5.551 11.102

2.981 2.981 5.962

3.090 3.089 6.179

0.006 0.006 0.011

0.086 0.086 0.172

93.8 93.8 93.8

6.2 6.2 6.2

0.03 0.03 0.06

0.057 0.058 0.197 0.312

6.170 6.170 0.000 12.340

6.274 6.275 0.000 12.549

3.560 3.560 0.460 7.579

3.620 3.620 0.265 7.505

0.013 0.013 0.002 0.028

0.044 0.044 0.195 0.283

76.8 76.9 99.1 90.9

23.2 23.1 0.9 9.1

0.06 0.06 0.01 0.13

0.014 0.014 0.270 0.241

5.574 5.573 0.000 11.147

5.529 5.529 0.000 11.058

3.096 3.096 0.604 6.796

3.071 3.071 0.336 6.478

0.006 0.006 0.002 0.013

0.020 0.020 0.268 0.229

139.3 139.4 99.4 94.7

39.3 39.4 0.6 5.3

0.03 0.03 0.01 0.07

Y

Eint

V nn

V en

V ne

H2 Be


NH3 HFBe


NH3 F2 Be


NH3 HClBe


NH3 Cl2 Be


NH3 HBrBe


NH3 Br2 Be


NH3 CO3 Be


NH3

N N N N N N N N

0.735 0.725 0.757 0.753 0.798 0.760 0.788 0.800

8.300 8.277 8.322 8.411 8.491 8.442 8.535 8.685

9.937 9.877 9.947 10.078 10.227 10.130 10.273 10.430

4.727 4.683 4.576 4.793 4.742 4.825 4.857 4.906

Ne


BeCO3 Ar


BeCO3

Ne Ar

0.041 0.072

11.622 18.077

11.688 18.197

H2 Be


C2 H4

C C Total

0.129 0.129 0.258

5.889 5.889 11.778

F2 Be


C2 H4

C C Total

0.092 0.092 0.184

H2 Be


C2 H2

C C NNA Total

F2 Be


C2 H2

C C NNA Total

interactions. About 4–5% of interactions corresponds to the nonclassical component, V XC , coming from about 0.1 pairs of electrons, dðBe; YÞ, shared between Be and N basins. In the Ng–Be interactions, there is again an attractive interaction between beryllium and noble gas atoms, however, these interactions are significantly weaker than that’s of traditional Be bonds. For instance, Eint ðBe; NeÞ in the Ne


BeCO3 complex is about 20 times weaker than Eint ðBe; NÞ in the traditional Be bonded CO3 Be


NH3 complex. This reduction is mainly due to the decrease in the jV cl j of the Ng–Be pair. Although in the traditional Be bonds, the attractive V en ðBe; YÞ term is considerably greater than the repulsive V nn ðBe; YÞ component, they almost cancel each other in the Ng–Be pair. This reduces the contribution of the classical term in the Eint ðBe; NgÞ to about 70%. In the p-Be complexes, one deals with different topological features. As indicated in Fig. 1 (and showed, at different level of theories, by Yáñez and coworkers [7]), in the H2 Be


C2 H4 complex the beryllium atom is connected to C2 H4 via three bond paths; two between Be atom and the carbons of ethylene and the third one between the beryllium atom and the C—C bond critical point (BCP). In F2 Be


C2 H4 , the bond paths between the beryllium and carbons are disappeared and instead, two bond paths between carbons and fluorine atoms are observed. The Be atom is connected only to the BCP of C—C bond. The molecular graphs of H2 Be


C2 H2 and F2 Be


C2 H2 are more complicated. At MP2/aug-cc-pvTZ level, a nonnuclear attractor (NNA) is located in the middle of CC bond of acetylene, which is connected to the beryllium through a bond path (Fig. 1). Indeed, the existence or absence of this NNA in the molecular graph of C2 H2 depends strongly on the method and basis set used [28,29]. For example, the results obtained at the MP2/6-311++G(d,p) level exhibits no NNA in the molecular graph of acetylene. Here, the bond paths connect the beryllium atom to carbons and also the BCP of CC bond. In the IQA analysis of p-Be bonds, the interactions between beryllium and both carbon atoms (and also NNA, in the case of acetylene) have been considered (Table 2). In the H2 Be


C2 H4 complex, there are two attractive interactions between the beryllium and carbon atoms. These interactions are stronger (more

V Cee

%cl

V XC ee

Complex

dðBe; YÞ

negative) than Ng


Be interactions, but considerably weaker than traditional Be


N bonds. Less than 10% of each Be


C interaction corresponds to the nonclassical V XC ðBe; CÞ term coming from delocalization of about 0.05 pair of electrons. Replacement of hydrogens in the BeH2 by fluorine reduces the absolute values of both classical and nonclassical components and hence the total interatomic interaction energy between the beryllium and carbon atoms. As stated, the molecular graphs of H2 Be


C2 H2 and F2 Be


C2 H2 are affected by a NNA in the acetylene. Accordingly, in the interatomic IQA analysis the interactions between this NNA and the beryllium atom should also be considered. Interestingly, in these complexes the attractive Be


NNA interactions are mainly responsible for the formation of p-Be bonds. These interactions are mainly electrostatic in nature and controlled by difference between V Cee ðBe; NNAÞ and V ne ðBe; NNAÞ classical terms. Indeed, since there is no nucleus in the basin of NNA, the V nn ðBe; NNAÞ and V en ðBe; NNAÞ terms are zero (note that V en ðBe; NNAÞ refers to the interaction between electrons of beryllium and nucleus of NNA). In addition, due to small amounts of electron delocalization between Be and NNA basins, the nonclassical part of electron–electron interaction, V XC ee ðBe; NNAÞ, is negligibly small. In the H2 Be


C2 H2 complex, the p-Be bond is strengthened by secondary interactions between beryllium and the carbons of C—C bond. But it is not the case for BeF2


C2 H2 , in which the Be


C interactions are repulsive. It is also worth noting that when the IQA calculations for F2 Be


C2 H2 complex were repeated with MP2/6-311++G(d,p) wavefunction (which creates a molecular graph with no NNA in the acetylene) the Be


C interactions play stabilizing role and provide the bonding glue between BeF2 and C2 H2 . In the pervious paragraphs, we focused merely on the Be bond, i.e. the interaction between beryllium and Y atoms. Although it contains some useful information, does not provide a complete picture. Indeed, the picture of bonding might be affected by the secondary interactions, which occurs between other atoms of Be-bond donor (BeD) and Be-bond acceptor (BeA) fragments. Table 3 gathers the total intermolecular energies between BeD

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K. Eskandari / Computational and Theoretical Chemistry 1090 (2016) 74–79

Table 3 Intermolecular IQA contributions (between all atoms of BeD and BeA fragments) in the beryllium bonded complexes. All energetic data are in atomic units. Complex

Eint ðBeD; BeAÞ

V cl ðBeD; BeAÞ

V XC ðBeD; BeAÞ

%cl

%XC

H2 Be


NH3 F2 Be


NH3

0.178 0.171

0.103 0.104

0.076 0.068

57.6 60.4

42.4 39.6

Ne


BeCO3 Ar


BeCO3

0.042 0.072

0.016 0.031

0.026 0.041

39.0 43.4

61.0 56.6

H2 Be


C2 H4 H2 Be


C2 H2

0.151 0.167

0.052 0.061

0.099 0.106

34.3 36.4

65.7 63.7

and BeA, obtained by adding all the inter-fragment IQA interaction terms. The contributions of classical and nonclassical terms in the total intermolecular interaction have been also indicated in Table 3. It seems that the secondary interactions increase the weight of nonclassical component in the formation of complexes. In the traditional Be-bonded complexes about 40% of interaction corresponds to exchange–correlation term (recall that more than 95% of Be


N bonds results from classical interactions). The changes in Ng–Be and p-Be complexes are more dramatic; the nonclassical component becomes the main factor for the formation of these complexes, when the secondary interactions are considered. 3.2. NEDA analysis To gain a better understanding of distinctions between different types of beryllium bonds in terms of intermolecular components, we applied NEDA scheme on some selected complexes. Table 4 compares the contributions of NEDA energy terms for Be-bonded complexes. In the traditional Be bonds, the electrical (EL) is the most dominant contribution to the interaction energy followed by charge transfer (CT) contribution. These attractive interactions are enough to overcome the strong CORE repulsion between the monomers. The classic electrostatic, ES, interaction is the greatest contributor to the EL, with POL playing a secondary role. For instance, in the H2 Be


NH3 complex, the EL interaction stabilizes the dimer by 65.47 kcal=mol, which about 87% (57.36 kcal=mol) of it comes from the classical electrostatic term. Indeed, large positive natural charge of Be and also the dipole–dipole interaction are responsible for this strong ES interaction. The BeH2 molecule is linear and does not have a permanent dipole moment. However, when this molecule interacts with a Lewis base, departs significantly from linearity (see Fig. 1) and acquires an induced dipole moment. The perturbed monomer density yields a dipole moment of 3.2 Debye for BeH2 subunit in the H2 Be


NH3 complex. This induced dipole moment interacts with the lone pair on the nitro-

Table 4 NEDA components (in kcal/mol), natural charges of beryllium, q, and dipole moments,

gen of ammonia. The contributions of self-polarization effects are small and POL + SE is about 8.12 kcal=mol. The complex is also significantly stabilized by CT term (49.65 kcal=mol), arising from electron transfer from the lone pair of NH3 toward the empty p orbital of beryllium and the rBeH antibonding orbital [1]. Successive substitution of BeH2 hydrogens by halogens leads to stronger traditional beryllium bonds. Substituting hydrogens by one or two halogens leads to more positive Be charges, larger induced dipole moments of BeD subunit, and hence stronger ES component. Self-polarization effects are similarly enhanced with these substitutions. Charge transfer also increases as the hydrogens are substituted by chlorine or bromine; however, it decreases in the mono and disubstituted fluoro-derivatives. In all of these complexes the EL is the most dominant contributor. In the p-Be bonds, the largest contribution corresponds to the CT term; however, the EL contribution is still important and necessary for overcoming the CORE repulsion. In these complexes the self-polarization term is very small and electrical term comes mainly from classical electrostatic interactions. Substituting of hydrogens of BeH2 by two fluorine atoms strengthens the complex. Indeed, this substitution weakens both CT and EL attractive terms, meanwhile diminishes the core repulsion component. The later is larger and hence the complexes exhibit stronger beryllium bonds. In contrast to the traditional and p-Be bonded complexes, in the Ng–Be systems the ES and POL + SE contributions (and hence, the EL term) are negligibly small. It is not surprising, if one takes into account that the natural charges and induced dipole moments of Ne and Ar are almost zero. Consequently, the charge transfer is essentially responsible for formation of Ng–Be complexes. 4. Conclusions In the current work, we used IQA and NEDA schemes to investigate the nature of different types of beryllium bonds. Conventional QTAIM (virial-based) energy partitioning indicates that, in contrast to Be–Ng bonds, the stability of beryllium atom decreases during the formation of p-Be bonds and most of the traditional Be bonds. However, from the IQA self-energy point of view the behavior of beryllium is different; upon formation of most of the Be-bonded complexes the absolute value of beryllium self-energy increases (becomes more negative). Inter-atomic IQA analysis suggests that the attractions between Be


Y pair comes mainly from classical electrostatic contributions, however, the influences of other inter-fragment interactions increase the impact of non-classical (exchange–correlation) terms in the total intermolecular interaction. According to NEDA, the electrical and charge transfer terms are responsible for formation of traditional and p-Be

l, of BeD and BeA species (Debye) in different types of Be-bonded complexes.

Complex

CT

ES

POL

EX

DEF

SE

EL

CORE

DEint

q (Be)

l (BeD)

l (BeA)

H2 Be


NH3 HFBe


NH3 F2 Be


NH3 HClBe


NH3 Cl2 Be


NH3 HBrBe


NH3 Br2 Be


NH3 CO3 Be


NH3

49.65 47.67 44.87 55.92 61.14 57.85 62.73 73.19

57.36 58.79 58.77 65.05 69.29 67.03 73.12 66.2

18.51 21.63 22.11 27.15 37.08 30.24 43.95 27.39

11.17 9.41 7.48 11.43 11.56 12.18 13.12 5.96

107.11 105.3 93.53 124.4 137.77 131.53 151.73 112.4

10.39 11.98 11.82 15.2 20.41 16.99 24.4 14.52

65.47 68.43 69.06 76.99 85.95 80.28 92.67 79.07

85.55 83.9 74.23 97.77 105.81 102.37 114.21 91.92

29.58 32.2 39.71 35.13 41.28 35.76 41.18 60.34

1.3 1.5 1.7 1.4 1.5 1.4 1.4 1.7

3.2 3.6 3.8 4.0 4.1 4.3 4.2 9.6

2.1 2.1 2.0 2.2 2.3 2.3 2.4 2.1

Ne


BeCO3 Ar


BeCO3

26.66 47.16

0.73 0.76

2.73 0.74

1.68 2.63

28.56 43.67

1.36 0.32

2.1 1.18

25.51 40.72

3.25 7.62

1.7 1.7

7.8 8.2

0 0

H2 Be


C2 H4 F2 Be


C2 H4 H2 Be


C2 H2 F2 Be


C2 H2

55.43 26.63 62.54 25.26

35.4 21.69 40.09 24.87

0.71 6.15 3.49 9.77

9.76 4.64 11.32 5.64

94.1 48.87 106.17 52.56

0.89 3.35 2.32 5.22

35.22 24.5 41.27 29.42

83.45 40.89 92.54 41.71

7.21 10.23 11.27 12.98

1.3 1.8 1.3 1.8

3.3 2.9 3.4 2.8

0.1 0.1 0.3 0.1

K. Eskandari / Computational and Theoretical Chemistry 1090 (2016) 74–79

complexes. In the Be–Ng complexes the electrical term is negligibly small and the charge transfer is the most dominant contributor in the interaction energy.

Acknowledgments The author gratefully acknowledges the Sheikh Bahaei National High-Performance Computing Center (SBNHPCC) for providing free access to its computational facilities. SBNHPCC is supported by scientific and technological department of presidential office and Isfahan University of Technology (IUT).

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