Cooperativity in bifurcated lithium-bonded complexes: A DFT study

Accepted Manuscript Cooperativity in bifurcated lithium-bonded complexes: A DFT study Mohammad Solimannejad, Forough Rezaie, Mehdi D. Esrafili PII: DOI: Reference:

S0009-2614(16)30408-0 http://dx.doi.org/10.1016/j.cplett.2016.06.013 CPLETT 33922

To appear in:

Chemical Physics Letters

Received Date: Accepted Date:

17 April 2016 3 June 2016

Please cite this article as: M. Solimannejad, F. Rezaie, M.D. Esrafili, Cooperativity in bifurcated lithium-bonded complexes: A DFT study, Chemical Physics Letters (2016), doi: http://dx.doi.org/10.1016/j.cplett.2016.06.013

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Cooperativity in bifurcated lithium-bonded complexes: A DFT study Mohammad Solimannejad *, Forough Rezaie Department of Chemistry, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran Mehdi D. Esrafili Laboratory of Theoretical Chemistry, Department of Chemistry, University of Maragheh, Maragheh 5513864596, Iran

Abstract Density functional calculations at the B3LYP/6-311++G(d,p) level are performed to analyze intermolecular interactions in complexes connected via bifurcated lithium bonds. Linear (LiN(CHO)2)2-7 clusters are chosen as a model system in the present study. Stabilization energies for these clusters are in the range of -42.59 to -334.05 kcal mol-1. Cooperativity effect based on energy and dipole moment are computed for these clusters. The contraction of Li···O binding distances along with an increase in the magnitude of stabilization energies with the cluster size can be regarded as a signature of cooperative effects in these systems. Key words: bifurcated lithium bond; cooperativity; DFT; QTAIM; MBIE.

*Corresponding Author: Tel: +98-86-34173400; Fax: +98-86-3267345; E-mail address: [email protected] (M. Solimannejad)

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1. Introduction Noncovalent interactions play a vital role in various fields of chemistry and biochemistry. They are responsible for stabilizing many important molecules, for example, DNA and proteins [1,2]. The traditional research for the noncovalent interactions has focused on the more common hydrogen bond interactions, but more recently interest has grown for other types of intermolecular interactions such as lithium bond. In 1959, Shigorin proposed the concept of Li-bonding for the first time [3] and Kollman and colleagues predicted its existence, theoretically [4]. Then, Ault and Pimentel in 1975 [5] provided an experimental evidence for the formation of the LB in X···Li–Y (X = H3N, Me3N, H2O, Me2O; Y = Cl, Br) complexes. As the closest congener of hydrogen, lithium has also been expected to be involved in a three-center interaction in a similar way to hydrogen-bonding. This interaction was named lithium-bonding by analogy with hydrogen-bonding [6-10]. In the theory of noncovalent interactions, the many-body effects are specified as cooperative or anticooperative effects [11]. Cooperativity effect is one significant trait of intermolecular interactions such as Li-bond and other interactions [12-15]. Cooperativity effect was investigated in linear lithium-bonded complexes of (LiCN)n and (LiNC) n (n=2-7) by Solimannejad et al. recently [16]. To the best of our knowledge, no prior theoretical investigations have been reported about cooperativity in bifurcated lithium-bonded (BLB) complexes in the absence of other weak interactions. For this purpose, we have studied molecular geometries, binding energies and cooperativity in linear (LiN(CHO)2)2-7 clusters aggregated via bifurcated LBs (BLBs) interactions for the first time. 2. Computational details All our calculations were performed by GAMESS package [17]. All complexes were fully optimized at the B3LYP/6-311++G(d,p) level. All optimized structures were characterized as potential energy minima by verifying that all vibrational frequencies are real. The stabilization energies were calculated by following equation for all complexes: ∆En = Ecluster - nEmonomer

(1)

where n is number of monomers in the cluster. Ecluster and Emonomer are electronic energy of complexes and energy of the isolated monomer in its minima configuration, respectively. The full counterpoise calculations [18] were carried out for correction of stabilization energies from the inherent BSSE. The cooperative effect (CEn) was obtained for energies of the clusters using the following equations [19]: 2

∆

- ∆

-

(2)

-

where ∆

cluster

is defined as the stabilization energy of clusters, while ∆

dimer

is the

stabilization energy of the dimer (taken as a reference) and n is the number of monomers in the cluster. The above equation is divided by n-2, to take into account additional fragments because the dimer taken as reference. With the monomer taken as a reference, CEn [μ] in terms of dipole moment was calculated using the following equation.

μ

μ

where μcluster a

- μ

(3)

-

μmonomer are dipole moments of clusters and monomers, respectively.

Many body interaction energy analysis (MBIE) for stabilization energies has been used with the equation (4) [20,21] to evaluate the one-, two-, and higher-body terms. In this equation, ER indicates distortion energy of monomers, and second and third terms are twobody and three-body contributions that were obtained from equations 5, 6, 7, respectively. In equation 5 E(i) is energy of monomer frozen in the geometry of cluster and Em(i) is energy of isolated monomer. The second-order terms, Δ2E(ij), were calculated as the energy difference of the ij dimers minus the sum of the monomers all in the geometry of the complex. The third-order terms were obtained by subtracting, from the energy of each possible ternary complex, the energies of the isolated monomers and the corresponding second-order terms.

∆

∆

∆

∆ (4)

ER(i) = E(i) – Em(i)

(5)

∆2E(ij) = E(ij) – [ E(i) + E(j)]

(6)

∆3E(ijk) = E(ijk) – [ E(i) + E(j) + E(k) ] – ∆2

∆2

∆2E(jk) ]

(7)

The molecular electrostatic potential (MEP) values on the 0.001 au electron density isosurface have been calculated for the isolated monomers and clusters. The quantum theory of atoms in molecules (QTAIM) methodology [22] was used to analyze the electron density of the systems considered at the B3LYP/6-311++G(d,p) 3

computational level. The topological analysis was carried out with the AIMALL program [23]. 3. Results and discussion The optimized structure and BLBs distances of the (LiN(CHO)2)7 cluster, at the B3LYP/6-311++G(d,p) level of theory, are presented in Scheme 1. All of the (LiN(CHO)2)n clusters corresponds to a minimum on the potential surface with C2v symmetry.

Scheme 1. Optimized (LiN(CHO)2)7 cluster at the B3LYP/6-311++G(d,P) level of theory (all intermolecular distances are in Å).

Table 1 presents the calculated BLBs distances for the (LiN(CHO)2)2-7 clusters. One important initial finding is the slight contraction of 35 mÅ in rLi···O binding distances from the dimers to trimers. Non-additive effects also lead to small Li···O contraction for the different clusters. For example, the contraction of Li···O values in (LiN(CHO)2)3-7 are 43, 44, 39,and 14 mÅ larger than Li···O length of dimer. This situation has been reported in linear lithiumbonded clusters of LiCN and LiNC, previously [16]. The average rLi···O lengths estimated from Table 1 are 1.925 Å for trimer, 1.911Å for tetramer, 1.902 Å for pentamer, 1.896 Å for hexamer, and 1.892 Å for heptamer. It is obvious that the contraction in Li···O distances does not enhance remarkably with the cluster size. This situation is similar to halogen bonds and lithium bonds in linear clusters of NCX (X = Cl, and Br) [24] and LiCN (LiNC) [16] that have been reported previously. The observed contraction with the cluster size in the rLi···O binding distances of studied clusters can be interpreted as signature of cooperative effects in these systems. The interaction energy provides a measure of the strength of the BLBs between LiN(CHO)2 monomers in the (LiN(CHO)2)2-7 clusters. Table 2 shows the interaction energies of the studied clusters. Some interesting trends can be found from reported values in Table 2. For instance, the magnitudes of the interaction energies increase with increasing cluster size. Considering the results, it can be seen that (LiN(CHO)2)3 is bound about 53.8 kcalmol-1 more strongly than (LiN(CHO)2)2. The CEn values of studied complexes are enhanced with 4

complex size, too. Based on the magnitude of this contribution, cooperative phenomena play a significant role in the behavior of larger clusters. Good correlation has been established between CEn and complex size for (LiN(CHO)2)3-7 clusters (figure. 1). Red shift of Li-N stretching frequency (ΔʋLi-N) due to formation of clusters in the range of 51-67 cm-1 is reported in Table 2. Red shift of stretching frequency of hydrogen donor is general features of hydrogen-bonded complexes [1]. So, results of present study confirm similarity between HB and LB in this viewpoint. Good linear correlation has been established between the cooperative effect based on stabilization energy (CE n) and stretching frequency shift (cm-1) in (LiN(CHO)2)3-7clusters with a squared correlation coefficient R2 of 0.99 as depicted in figure 2.

Table 3 presents the results for the dipole moment (μ), the increase in the dipole moments upon complexation (∆μ) as well as the CEn based on the dipole moment CEn (μ) for the (LiN(CHO)2)2-7 clusters. ∆μ is defined as the difference between the dipole moment of complexes and monomers. The CEn (μ) values are calculated using Eq. (3). CEn (μ) of complexes is enhanced with the complex size. This trend can be interpreted with the cooperativity effects observed in studied clusters. The electrostatic potentials at the 0.001 electrons/Bohr3 isodensity surfaces of LiN(CHO)2 monomer and complexes have been analyzed by means of the WFA surface analysis suite [25,26]. Table 4 gives the magnitudes of the most positive (VS,max) and most negative electrostatic potentials (V S,

min

) on the surface of these complexes. The VS,max in

(LiN(CHO)2)2-7 complexes is more positive than that in the LiN(CHO)2 isolated monomer. This indicates that the Li atom in the (LiN(CHO)2)2-7 complexes is a stronger electron acceptor than that of free LiN(CHO)2 molecule. Moreover, VS,max of the studied complexes are enhanced with complex size. On the other hand, VS,min on the O atoms becomes more negative in these complexes with an increase of monomers in the clusters. This is also in agreement with the cooperative effects as discussed above. In figure. 3, the plot of cooperativity parameter based on stabilization energy (CEn) versus the product of VS,max and VS,min is depicted. The correlation is good, with a squared correlation coefficient R2 of 0.95 for (LiN(CHO)2)3-7clusters. Table 5 lists the variations in electron density and the corresponding Laplacian values at bond critical points (BCPs) located between the LiN(CHO) 2 molecules in the clusters. It has been manifested in numerous studies that the QTAIM analysis gives valuable information about the strength and origin of the interactions [25]. From Table 5, it is seen that the electron 5

densities at the Li···O BCPs of the (LiN(CHO)2)2-7 clusters are in a range of 0.0209–0.0346 au. An enhancement in electron density and Laplacian of electron density is observed for these clusters with cooperativity. These results demonstrate that the BLBs is gradually become stronger with the increase of the (LiN(CHO)2)2-7 monomers. In the next step, the MBIE analysis has been carried out for the calculation of distortion energy, two-body, three-body and higher terms and results are listed in Table 6. According to these results, two-body interactions have a greater contribution than three-body and higher-body terms. These evidences show that two-body interactions have more contribution in the stability of the investigated BLB clusters. The MBIE of the title clusters also show that the sum of the three-body and higherbody terms is negative, which indicates a favorable cooperativity in these systems (Table 6). The sum of the distortion energy of the monomers is small compared to the binding energy of the studied series. The two-body term is the dominant attractive term representing more than 88% of the attractive terms in studied clusters. The ratio of third-order term to the secondbody terms is decreased as the size of the cluster increases. CEn seems to be saturated with the cluster size, n=7. However, 3-body terms (Table 6) represent 6.2% in comparison to the sum of 2-body terms for the cluster size n=3 and increase up to 13.1% for the cluster size n=7. It seems that the incremental contribution of three body terms is stabilized for clusters with n=5, 6, and 7 to about 9.4 - 10 kcal/mol. This can be linked with different contributions from terminal monomers and from increasing number of "inner" monomers of the cluster which tend to be stabilized.

4. Conclusion In this work, we have performed a systematic computational investigation of the intermolecular BLBs in the linear (LiN(CHO) 2)2-7 clusters. Our results indicated that magnitudes of the interaction energies increase with increasing the cluster size. The contraction of Li···O binding lengths with cluster size can be regarded as a signature of cooperative effects in these systems. In addition, the increase of electron density at the Li···O BCP interactions can be interpreted with cooperativity effect in the studied clusters. These findings may help for a better understanding of the cooperative role of BLBs in molecular recognition and crystal engineering.

6

References: [1]

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Table 1. Binding distances (r, Å) in the (LiN(CHO)2)2-7 clusters. n

r12

r23

r34

r45

r56

2

1.954

3

1.930

1.920

4

1.924

1.896

1.912

5

1.922

1.890

1.887

1.908

6

1.921

1.887

1.881

1.883

1.907

7

1.921

1.886

1.878

1.877

1.882

r67

ravr

1.925 1.911

8

1.902 1.896 1.907

1.892

Table 2. Calculated stabilization energies (corrected with BSSE), cooperative effect (CE n) (kcal mol-1) and stretching frequency shift (cm-1) of clusters.

n

∆En

BSSE

∆En+BSSE

CEn

ΔʋLi-N

1

-

-

-

-

-

2

-43.57

0.98

-42.59

-

-51.37

3

-98.38

1.98

-96.40

-11.22

-60.68

4

-157.04

2.97

-154.06

-13.15

-63.83

5

-217.35

3.98

-213.37

-14.34

-65.22

6

-278.46

4.98

-273.48

-15.13

-66.33

7

-340.03

5.98

-334.05

-15.70

-66.88

9

Table 3. a

a

p

μ, D by ,

p

ha

cooperative effect (CEn μ , Debye) for each complex.

n

μ

∆μ

CEn μ

1

4.61

-

-

2

11

1.78

1.78

3

17.81

3.97

1.99

4

24.73

6.28

2.09

5

31.71

8.65

2.16

6

38.72

11.05

2.21

7

45.75

13.47

2.24

10

∆μ, D by

a

Table 4.

The most positive (VS,max, kcal mol-1) and most negative (VS,min, kcal mol-1)

electrostatic potentials in the monomer and the corresponding clusters. n

VS,max

VS,min

1

207.3

-70.8

2

235.6

-94.5

3

246.8

-104.3

4

252.4

-109.3

5

255.5

-112.3

6

257.6

-114.2

7

260.6

-119.3

11

Table 5. Calculated changes of QTAIM parameters (in au) for the studied clusters calculated at the B3LYP level. (

and

).

n 2 2.655

1.918

3 2.946

2.165

2.878

2.095

4 3.022

2.230

3.194

2.365

2.935

2.140

5 3.052

2.255

3.283

2.442

3.264

2.422

2.958

2.159

6 3.065

2.267

3.321

2.475

3.354

2.499

3.295

2.447

2.971 2.169

7 3.153

2.336

3.406

2.551

3.464

2.601

3.458

2.595

3.381 2.522

12

3.049 2.231

Table 6. Sum of the MBIE energy terms (kcal mol-1) of the (LiN(CHO)2)2-7 clusters. ∑∆2E(i,j)

∑∆3E(i,j,k)

cluster

∑

(LiN(CHO)2)2

1.82

-45.39

(LiN(CHO)2)3

5.05

-97.39

-6.03

(LiN(CHO)2)4

8.83

-151.33

-14.03

-0.51

(LiN(CHO)2)5

12.88

-206.06

-22.10

-1.21

(LiN(CHO)2)6

17.02

-261.12

-32.11

-2.14

(LiN(CHO)2)7

21.30

-316.50

-41.57

-4.16

R(i)

13

Higher terms

CEn (kcal mol-1)

-18 -16 -14 -12 -10 -8 -6 -4 -2 0

CEn = -5.29ln(n) - 5.6224 R² = 0.9866

0

1

2

3

4

5

6

7

8

n Figure. 1 Correlation between the cooperative effect based on stabilization energy and complex size for (LiN(CHO)2)3-7clusters.

CEn (kcal mol-1)

-16

-15 -14 -13 CEn = 0.7169ΔʋLi-N+ 32.394 R² = 0.9935

-12 -11

-10 -60

-62

-64

-66

-68

ΔʋLi-N Figure. 2 Correlation between the cooperative effect based on stabilization energy (CE n) and stretching frequency shift (cm-1) in (LiN(CHO)2)3-7clusters.

14

Vs,max.Vs,min

Vs,max.Vs,min= 1093.9CEn - 13291 R² = 0.9566

-33000 -31000 -29000 -27000 -25000 -23000 -21000 -19000 -9

-11

-13 -15 -1 CEn (kcal mol )

-17

Figure. 3 Correlation between the cooperative effect based on stabilization energy (CEn) and the magnitude product of most positive and negative electrostatic potentials, V S, 2

(kcal/mol) in(LiN(CHO)2)3-7clusters.

15

min

VS,

max

Graphical Abstract

Schematic presentation of optimized (LiN(CHO)2)7 cluster. (intermolecular distances are in Å).

16

Highlights 

Cooperative effect in bifurcated lithium-bonded complexes is presented.



The magnitude of cooperativity is increased with the cluster size.



Contraction of Li···O distances is signature of cooperativity in studied clusters.

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