The Nature of the Interaction of Dimethylselenide with IIIA Group

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The Nature of the Interaction of Dimethylselenide with IIIA Group Element Compounds Timur Ismailovich Madzhidov, and Galina Alekseevna Chmutova J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp312383f • Publication Date (Web): 16 Apr 2013 Downloaded from http://pubs.acs.org on April 24, 2013

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The Journal of Physical Chemistry

The Nature of the Interaction of Dimethylselenide with IIIA Group Element Compounds Timur I. Madzhidov*, Galina A. Chmutova Department of Organic Chemistry, A.M. Butlerov Institute of Chemistry, Kazan Federal University, Kremlyovskaya St. 18. 420008 Kazan Russia [email protected], [email protected] RECEIVED DATE * Corresponding author: Department of Organic Chemistry, A.M. Butlerov Chemical Institute, Kazan Federal University, Kremlyovskaya St. 18, 420008 Kazan, Russia. Tel: 7-843-2337371, 7-904-6627736. Fax: 7-843-2337416. E-mail: [email protected], [email protected].

ABSTRACT: The first systematic theoretical study of the nature of intermolecular bonding of dimethylselenide as donor and IIIA group element halides as acceptors was made with the help of the approach of Quantum Theory of Atoms in Molecules. Density Functional Theory with “old” Sapporo triple-zeta basis sets was used to calculate geometry, thermodynamics and wavefunction of Me2Se…AX3 complexes. The analysis of the electron density distribution and the Laplacian of the electron density allowed us to reveal and explain the tendencies in the influence of central atom (A = B, Al, Ga, In) and halogen (X = F, Cl, Br, I) on the nature of Se…A bonding. Significant changes in properties of the lone pair of selenium upon complexation were described by means of the analysis of the Laplacian of the charge density. Charge transfer characteristics and the contributions to it from electron localization and delocalization were analyzed in terms of localization and delocalization 1 ACS Paragon Plus Environment


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indexes. Common features of the complexation and differences in the nature of bonding were revealed. Performed analysis evidences that gallium and indium halide complexes can be attributed to charge transfer-driven complexes; aluminum halides complexes seem to be mainly of electrostatic nature. The nature of bonding in different boron halides essentially varies; these complexes are stabilized mainly by covalent Se…B interaction. In all the complexes under study covalence of Se…A interaction is rather high.

KEYWORDS: charge-transfer complexes, organoselenium compounds, IIIA group elements, electronic structure, Quantum Theory of Atoms in Molecules, topological analysis, the Laplacian of the charge density distribution, localization and delocalization indices

1. Introduction In the past decades organoselenium chemistry has attracted a great interest of researchers1-3, many of reviews on different aspects of this topic were published recently4-10. Flood of works and data is dedicated to the organoselenium compounds due to their role in biochemical processes5,6,11-14, as well as their direct or indirect usage in preparation of novel organoelement materials such as conductor and semiconductor materials15,16, catalysts17-19, quantum dots20-24, chalcogen-borate glasses25, to name a few. There is no doubt that mainly the activity of organoselenium compounds is tightly connected with their ability to complexation with different kind of acceptors. For example, the role of selenium intramolecular interactions in organic synthesis and biological applications is the subject of recent review4. Some computational works dealing with the nature of bonding with selenium atom were published very recently26-29. Special perspectives are related to the usage of the complexes of organoselenium compounds with III group elements30 in preparation of I-III-IV2 and I-III-IV chalcopyrite semiconductor materials for photoelectric applications. Despite the number of potential applications (especially in electronics31-33), on the whole, coordination chemistry of p block elements is much less thoroughly developed than that of d-elements34,35. Therefore ACS Paragon Plus Environment

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the complexation of organoselenium compounds with different p-acceptors has both great theoretical and practical interest. Quite big experimental material was collected on the complexes of organoselenium compounds with different Lewis acids36-38. However only a little is known about structures of these complexes – X-ray data exist only for a few complexes of such type34,35, quite a few works were performed in a systematic way. The number of thermodynamic data on complexation energy is also limited39-43. Detailed theoretical analysis of the complexes at the modern theoretical level was not performed yet. This encouraged us to make a thorough study of complexes of dimethylselenide (DMSe) with boron, aluminium, gallium and indium halides. This work continues the previous ones on the structure of complexes and the nature of bonding of selenium with different kind of acceptors44,45 using quantum-chemical methods with subsequent analysis within Bader’s Atoms in Molecules theory46. The aims of the study were to show the possibility of correct theoretical description of existing thermodinamic and geometric data on complexes Me2Se...AX3 (A = B, Al, Ga, In; X = F, Cl, Br, I) and to approach the deep understanding of the nature of chemical bond Se - IIIA group element. For the latter task along with local topological characteristics of electron density distribution and redistribution upon complex formation we have used integral characteristics, such as electron localization and delocalization indices, atomic occupancies and others. 2. Computational Details Geometry optimization, frequencies calculation and electronic structure calculations discussed in the paper have been performed with the Gaussian03 program47 within DFT scheme with hybrid PBE1PBE (also known as PBE0) functional48,49 and “old” Sapporo triple-zeta basis sets for all the elements50-58. This level of the calculation was chosen due to a number of reasons. In the previous work59 PBE1PBE functional has shown to provide the best agreement of geometrical data (both bond lengths and angles) of organoselenium molecules with experimental microwave data; our tests have also shown that it gives very reasonable complexation energies and geometries (see below). The results are approximately of the same quality as those achieved by the MP2 method. The choice of the basis was dictated by (i) necessity to use quite precise correlation-consistent full-electronic basis sets for every atoms to perform ACS Paragon Plus Environment

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reasonable AIM calculation, (ii) requirement to reduce basis set superposition error (BSSE) as much as possible (the basis set we have used here returns the least BSSE value), and (iii) desire to use the same basis set for every atom in order to have the ability to compare all types of complexes. BSSE has been taken into account by the well-known Boys-Bernardi a posteriori procedure60. Geometries for the individual selenides and their complexes were fully optimized. Counterpoise corrections to the energy60 and its derivatives61 were taken into account in the process of geometry optimization of molecular complexes. All stationary points were characterized by harmonic analysis as true minima on the potential energy surface. Search for quasi-global minima performed by starting geometry optimization process from a number of initial conformations, which were deemed reasonable from a chemist’s point of view. Hereafter only the most stable conformations are discussed. Complexation energies, ∆E0comp, enthalpies, ∆H298comp, and Gibbs free energies, ∆G298comp, are calculated by addition of the harmonic thermal corrections to electronic energies. All values of thermodynamic parameters of complexes shown in the tables below include BSSE and thermal corrections. Solvent effects were not taken into account. QTAIM analysis were done with AIMAll Professional software62. Integration over atomic basins was performed with different quadratures and integration algorithms that achieve atomic (integrated) Lagrangian values, L(A), smaller than 0.001 a.u. (in atomic units, atomic Lagrangian equal to -1/4 times atomic integral of the Laplacian of the electron density over the atomic basin, L( A) = − 1 4 ∫ ∇ 2 ρ (r )dr ). A

Sum of all atomic Lagrangians does not exceed 0.003 a.u. In ideal case, atomic Lagrangian should be equal to zero, however mentioned values are considered acceptable by the program settings and the integration results are quite reasonable for further analysis. For example, sum of atomic charges are usually not exceed 0.002 a.u. Delocalization indices δ(i,j), a measure of the number of electrons shared by the i and j atoms, and localization index λ(i)63,64, that reflect the number of electrons that belong to the atom i, were obtained during the integration within AIMAll. Finally, the Laplacian of the charge density, ∇2ρ(r), distribution was analyzed through recently implemented algorithm within AIMAll ACS Paragon Plus Environment

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package. The pictures below were prepared with the help of AIMStudio program of AIMAll Professional software kit. 3. Results und Discussions 3.1 Geometrical Parameters and Energy of Complexation All complexes under study Me2Se – AX3 (A=B, Al, Ga, In; X=F, Cl, Br, I) that are traditionally named “charge-transfer complexes” have principally the same structure. In optimized conformations (Fig. 1) that have Cs symmetry one of A-X bonds lay in symmetry plane bisecting C-Se-C angle and containing central atom A of the acceptor. Here this A-X bond is named “planar” and denoted by subscript “p” and the other two named “non-planar” and denoted by “np” subscript. Geometry of Me2Se molecule changes a little upon complexation (Table S1 in Supplementary data). Some increase in the CSe-C valence angle and decrease of C-Se bond length are among these changes. Changes in the geometry of acceptor molecules are much more significant (Table 1 in the text and Table S1 in Supplementary data). These molecules in the complex are pyramidal; we measured the degree of pyramidality by the value ∆βsum equal to the deviation of the sum of X-A-X angles in AX3 fragment from 360 degrees. Greatest deviations take place in boron complexes, and in them ∆βsum values are the most sensitive to the variations of halogen. Excluding indium complexes, regular variation of halogen lead to the increase of ∆βsum value in the series F < Cl < Br and further change to iodine leads to decrease of pyramidality. The length of A-X bonds increase upon complexation and mainly planar A-X bond elongates to a greater extent than non-planar ones. Calculated length of Se…A bond is shorter than the sum of corresponding van der Waals radii65, that is usual for the majority of complexes of such type36,38. Calculated bond lengths and valence angles in complexes are in good agreement with existing experimental X-ray data30,66,67 (Table S2 in Supplementary data). We should mention that calculated bond lengths are systematically higher than experimental ones. This can be explained by usual overestimation of bond lengths by GGA functionals (and this suggestion is partially supported by underestimation of bond lengths found in case of LDA functionals, that is also known phenomenon). It should also be pointed out that calculated and ACS Paragon Plus Environment

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experimental data refer to different states: quantum-chemical calculations are performed for isolated complexes but experimental data was reported for crystal phase.

Table 1. Energetic and geometric characteristics of the complexes under study Complex Acceptor E0comp

BSSE H298comp

G298comp

l(Se…A) ∆l(AXp)

∆l(AXnp) ∆βsum

I-1 I-2 I-3 I-4 II-1 II-2 II-3 II-4 III-1 III-2 III-3 III-4 IV-1 IV-2 IV-3 IV-4

0.88 0.50 0.43 0.50 1.17 0.53 0.43 0.46 1.10 0.50 0.37 0.42 1.49 0.65 0.51 0.51

3.98 2.49 2.10 -5.31 -16.57 -14.28 -13.86 -13.25 -16.79 -11.37 -10.17 -8.75 -15.30 -13.07 -11.38 -9.58

2.2676 2.0732 2.0956 2.1187 2.5263 2.5300 2.5297 2.5321 2.5279 2.5460 2.5509 2.5591 2.7382 2.7585 2.7672 2.7784

0.0345 0.0154 0.1033 0.0932 0.0238 0.0406 0.0448 0.0499 0.0306 0.0448 0.0483 0.0517 0.0245 0.0345 0.0378 0.0396

BF3 BCl3 BBr3 BI3 AlF3 AlCl3 AlBr3 AlI3 GaF3 GaCl3 GaBr3 GaI3 InF3 InCl3 InBr3 InI3

-6.12 -10.04 -13.86 -17.30 -26.61 -25.03 -24.80 -24.37 -27.72 -23.16 -22.13 -20.89 -27.81 -24.12 -22.79 -21.21

-5.88 -9.88 -13.64 -17.09 -26.35 -24.69 -24.40 -23.96 -27.40 -22.76 -21.69 -20.44 -28.00 -23.63 -22.27 -20.69

0.0383 0.0168 0.0972 0.0917 0.0325 0.0514 0.0559 0.0602 0.0446 0.0585 0.0619 0.0636 0.0446 0.0526 0.0551 0.0556

13.92 14.99 20.47 19.80 10.09 11.57 11.85 11.84 11.87 12.28 12.31 11.95 9.23 9.04 8.89 8.64

Energy quantities (BSSE, ∆E0comp, ∆H298comp, ∆G298comp) in kcal/mol, bond lengths and their changes (l(Se…A), ∆l(AXp), ∆l(AXnp)) in Å, angles (∆βsum) in degrees.

Thermodynamic characteristics of complexation (Table 1) show that complexes under study are much stronger than the ones studied earlier – with methanol44 and di-iodine45. For them both enthalpy of complexation H298comp and Gibbs free energy G298comp are negative (some complexes of boron acceptors such as BF3, BCl3 and BBr3 are the exceptions). Absolute values of calculated complexation enthalpies are less than experimental data (Table S2 in Supplementary data). The latter ones are not numerous41-43, but relative H298comp values are quite reliable.

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Figure 1. Structure of the dimethylselenide-AX3 complexes (A= B, Al, Ga, In; X=F, Cl, Br, I) optimized at the PBE1PBE / Sapporo triple-zeta level. Topological features are shown: bond paths – lines, bond critical points (BCPs) – green points, ring critical points (RCPs) – red points. First of all, weak stability of complexes with boron halides in comparison with other complexes under study is seen. The most surprising remark is that in boron halide complexes I-1 – I-4 enthalpies of complex formation (as well as other thermodynamic characteristics) decrease in the series I-1 (X= F) > I-2 (X= Cl) > I-3 (X= Br) > I-4 (X= I), and the opposite tendency is seen for complexes of other IIIA ACS Paragon Plus Environment

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group elements’ halides. Relatively low variation in values of complexation energy of aluminium halides complexes II-1 – II-4 should be noted. As general tendency one may note the increase in H298comp and G298comp absolute values with shortening of Se…A bond length. This phenomenon is conventional for charge-transfer complexes38. However, we have not found correlation between complexation energy and geometry characteristics of complexation that is general for all complexes under study. In the case of complexes with gallium- and indium-containing acceptors the smaller complexation energy is accompanied by shorter Se…A bond as expected. In the case of aluminium and boron complexes the relation between complexation energy and Se…A length is not so straightforward. In aluminium compounds complexes with smaller (more negative) complexation energy the Se…A distance is usually shorter, the only exception being II-3 complex. However, taking into account slight variations in complexation energy for aluminium compounds’ complexes, we do not consider this case important. We believe that aluminium-containing complexes show approximately the same relation between complexation energy and Se…A distance as in Ga and In-based complexes. In the case of boron halides complexes Se…B length changes unexpectedly – for complexes I-2, I-3 and I-4 it becomes longer (!) together with the increase of complex stability. However, Se…B length reaches maximum for the weakest complex I-1 of dimethylselenide with BF3. 3.2 The electronic structure of the complexes In order to gain deep insight into the nature of intermolecular interactions we used Richard Bader’s Quantum Theory of Atoms in Molecules (QTAIM) as most informative and providing the possibility to analyze different aspects of electron distribution and redistribution at the complex formation. We used two types of characteristics in the study: • Local characteristics, that can be found in given point of space (for example, electron density ρ(r), the Laplacian of the charge density ∇2ρ(r), kinetic G(r) and potential energy densities V(r) and other characteristics at bond critical point (BCP), as well as corresponding properties of the critical points of the Laplacian of the charge density), ACS Paragon Plus Environment

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• Integral characteristics, which are obtained by integration over a given volume. They can be further divided into: o Atomic characteristics that refer to the properties of a given atom and are found by integration of corresponding operator over given atomic basin (atomic occupancies, atomic dipole moments, atomic kinetic and other energies, localization indexes, to name a few), o Interatomic characteristics that are found by integration of corresponding operator over basins of two separate atoms (delocalization indexes, interatomic coulomb and exchange-correlation energies). Atomic basin is the region of space traversed by the trajectories of gradient of electron density terminating at a given nucleus or attractor (the point that is local maximum electron density). The basin

r is bounded by the surface of zero flux of the electron density ∇ρ (r ) ⋅ n = 0 and contains not more than one nucleus. Nucleus and its atomic basin is considered physical form of existence of atom in the molecule. 3.2.1 Local (topological) parameters of electron density distribution Topological analysis of the electron density – the main tool of QTAIM – searches for critical points of the electron density distribution, where the absolute value of gradient of electron density is equal to zero. Critical points can be divided into some classes (nuclear attractor, bond, ring and cage critical points) according to signs and values of three eigenvalues of the Hessian of the electron density at the given point. The content of topological analysis is presented very simply and understandable in the Bader’s46 and Gillespie-Popelier’s books68. In all the complexes under study bond paths Se…A and bond critical points (BCP) were found to exist (on Fig. 1 they are denoted by dashed line and green points respectively). Some local (topological) properties of these critical points which we deem important for the present paper are collected in Table 2.


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The values of electron density at Se…A bond critical point generally agree with trends in changes of thermodynamic data: the greater the electron density at BCP, the stronger the complex. The only exceptions are aluminium halide complexes, for which changes in electron density at BCPs and in complexation energies are rather small. Contrary to the data reported previously for complexes with different selenides as donors but the same acceptor (methanol or di-iodine)44,45, for complexes under study with one donor and a number of different acceptors we cannot observe general correlation of electron density, potential and kinetic energy densities at the Se…A bond critical point with energetic characteristics of the complexes. However, for hydrogen bonds such type of correlation between complexation energy and ρ(r) in complexes with different donors and acceptors were reported69,70. There is also a well-known Espinosa-Molins-Lecomte equation, relating complexation energy and potential energy density in BCP of hydrogen bonds71. Different types of correlations of electron density at Se…A bond critical point and complexation energy in the complexes together with the results of the analysis of geometric characteristics led us to the conclusion that the nature of bonding of dimethylselenide with IIIA group elements is substantially different. The simplest cases are represented by gallium and indium (GaX3 and InX3) complexes, for which characteristics depend on the electronegativity of substituent X in the expected way. For aluminium compounds for some characteristics one can notice the interplay of several effects influencing geometry, energy and electron distribution in a different manner. The behavior of most characteristics in the case of boron-containing acceptors is much more complicated. Table 2. Local (topological) characteristics* of Se…A intermolecular bond critical points in the complexes under study Complex

Acceptor BCP

ρ(r)

∇2ρ(r)

ε(r)

he(r)

-V(r)/G(r)

I-1

BF3

B…Se

0.0580

-0.0375

0.0109

-0.0255

2.5838

I-2

BCl3

B…Se

0.0949

-0.1431

0.0050

-0.0595

3.5105

I-3

BBr3

B…Se

0.1022

-0.1656

0.0069

-0.0677

3.5741

I-4

BI3

B…Se

0.1061

-0.1729

0.0110

-0.0725

3.6644


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II-1

AlF3

Al…Se

0.0437

0.0891

0.0261

-0.0127

1.3639

II-2

AlCl3

Al…Se

0.0454

0.0813

0.0127

-0.0142

1.4116

II-3

AlBr3

Al…Se

0.0459

0.0788

0.0100

-0.0146

1.4227

II-4

AlI3

Al…Se

0.0460

0.0762

0.0059

-0.0147

1.4349

III-1

GaF3

Ga…Se

0.0604

0.0718

0.0196

-0.0180

1.5000

III-2

GaCl3

Ga…Se

0.0593

0.0656

0.0188

-0.0173

1.5134

III-3

GaBr3

Ga…Se

0.0589

0.0637

0.0177

-0.0170

1.5167

III-4

GaI3

Ga…Se

0.0580

0.0625

0.0157

-0.0163

1.5141

IV-1

InF3

In…Se

0.0490

0.0871

0.0111

-0.0087

1.2852

IV-2

InCl3

In…Se

0.0478

0.0815

0.0216

-0.0084

1.2917

IV-3

InBr3

In…Se

0.0472

0.0792

0.0218

-0.0082

1.2929

IV-4

InI3

In…Se

0.0462

0.0771

0.0218

-0.0078

1.2915

MeOH

H…Se

0.0189

0.0357

0.0019

-0.0009

1.0816

I2

I…Se

0.0372

0.0457

0.0055

-0.0048

1.2963

ρ(r) – electron density, ∇2ρ(r) – the Laplacian of the charge density, ε(r) – ellipticity value, G(r), V(r) and he(r) – kinetic, potential and electronic energy density. All values are in а.u. *

The analysis of local characteristics of Se…A BCPs allows us to characterize in some way the nature of the intermolecular interaction. In the case of BX3 compounds one can see typical covalent interaction, since the Laplacian of the charge density ∇2ρ(r) and consequently Cremer-Kraka electronic energy density he(r)72 at the Se…B bond critical point is negative. This means that the potential contribution sufficiently dominates over the kinetic energy density at the BCP, and the - V(r)/G(r) ratio is bigger than 2. Moreover, electronic density at the BCP in the complexes with boron halides almost reaches (and sometimes even exceeds) the values usual for conventional covalent bonds (about 0.1 a.u.). According to the ranges given by Nakanishi et al.73 (0.1 < ρ(r) < 0.2; -0.4 < ∇2ρ(r) < 0.0; -0.15 < he(r) < -0.04) complexes I-2, I-3 and I-4 can be considered as having weak covalent intermolecular bond. The features of Se…B bonds in the complex with BF3 do not fall into any range in Nakanishi’s scale. Let us remind here that complexation energy is rather low for I-1 despite of its covalent nature seen from topological characteristics.


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Se…Al, Se…Ga and Se…In bonds have positive Laplacian at the BCP and negative electronic energy density. These types of binding (with parameter 0.04 < ρ(r) < 0.06; 0.06 < ∇2ρ(r) < 0.09; -0.02 < he(r) < 0) have been attributed to partially covalent closed-shell interactions74, and according to Grabowski75 they can also be named polar-covalent type. All the Se…A (A = Al, Ga, In) characteristics fall in the range proposed by Nakanishi for charge-transfer molecular complexes. In all complexes of the type Me2Se…AX3 (X= I), as well as in complexes of gallium and indium halides with Х= Br, Cl and even for indium fluoride, intermolecular interactions of H…I, H…Br and H…Cl type were found according to the existence of BCPs and bond paths (Figure 1). According to the data of Table 3 one can conclude that this interactions are weak (electron density at BCP is low). Moreover, this bond critical point is located close to the ring critical point and so the BCPs have large ellipticity. The latter phenomenon gives clear evidence of the fact of closeness of the BCPs to degeneracy, and this point disappear readily during different types of intramolecular motions. So this bond path cannot influence essentially the energetics of complexation.

Table 3. Topological indices* of weak additional intermolecular bond critical points in the complexes under study Complex

Acceptor BCP

ρ(r)

∇2ρ(r)

he(r)

-V(r)/G(r)

ε(r)

I-4

BI3

H…I

0.0090

0.0264

0.0012

0.7841

1.3671

II-4

AlI3

H…I

0.0066

0.0185

0.0009

0.7474

1.3396

III-2

GaCl3

H…Cl

0.0069

0.0233

0.0013

0.7129

1.6629

III-3

GaBr3

H…Br

0.0068

0.0214

0.0011

0.7336

0.9794

III-4

GaI3

H…I

0.0068

0.0186

0.0009

0.7554

0.6643

IV-1

InF3

H…F

0.0078

0.0295

0.0013

0.7117

0.7804

IV-2

InCl3

H…Cl

0.0062

0.0208

0.0012

0.6847

0.7558

IV-3

InBr3

H…Br

0.0061

0.0187

0.0010

0.7132

0.6172

IV-4

InI3

H…I

0.0060

0.0017

0.0008

0.7425

0.5076

*

Notations as in Table 2. ACS Paragon Plus Environment

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Electron density in A-X BCPs is rather high (0.05-0.1 а.u.). For majority of bonds the Laplacian of the charge density in the BCPs is positive, he(r) is negative in all cases (Table S3 in Supplementary material). These bonds can be attributed to partially covalent bonds (he0) with high degree of ionicity. Only in complexes I-2, I-3 and I-4 the Laplacian in A-X BCPs is negative, thus allowing classifying them as highly covalent. However, both electronic density and electron energy density in AX BCPs in complexes are lesser in complexes than in free АХ3 molecule (Table S3 in Supplementary material). Uniting this data with the discussed later increase of halogen X charge and low changes on A atom these data evidence about increase of ionicity of A-X bonding upon complexation. 3.2.2 Local parameters of the Laplacian of electron density distribution Special attention was paid to the changes in valence shell of selenium atom because lone pairs (LPs) of selenium are mainly responsible for donor ability of dimethylselenide44,45,59. We have analyzed local parameters of the Laplacian of the charge density distribution, since they characterize zones of concentration and depletion of electron density in valence and core electron shells76. Lone pairs can be represented in QTAIM at least in three different ways: • lone pair domain can be represented as the outer charge concentration zone, i.e. the zone, where the Laplacian of the charge density ∇2ρ(r) is negative. The zone is called Valence Shell Charge Concentration (VSCC)77. There are two kinds of VSCC – the one corresponding to bonding electron pair, which is located between two bonded atoms, and the one corresponding to lone pair. • lone pair can be characterized as the most representative point of VSCC domain corresponding to lone pair (see above). This point, named VSCC critical point46,77, is the minimum of the Laplacian of electron density of rank three (it means that the Hessian of the Laplacian of the electron density at the critical point has 3 positive nonzero eigenvalues),


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• lone pair domain can also be represented similar to atomic basins by accumulation basin – the region of space bounded by zero flux surfaces of the Laplacian of the charge density,

[

]

r ∇ ∇ 2 ρ (r ) ⋅ n = 0 and associated to the minima of Laplacian of the charge density78. Here we use only first two definitions. The analysis of the Laplacian of the charge density distribution, similar to the one made in our previous works44,45, allows one to track changes in properties of the lone pairs upon complex formation. One of the selenium lone pairs in isolated dimethylselenide is “transformed” into bonding electron pair between Se and A in Me2Se…AX3 (we call it ex-lone pair or “ex-LP”). Another electron pair VSCC of dimethylselenide is not directly involved into intermolecular interaction (we call it “free-LP”). The changes in local properties of VSCC critical points are collected in Table 4 and the changes in VSCC representing both lone pairs of selenium are shown on Figure 2. Plots of the Laplacian of the charge density show rather pronounced and differing changes in the shape of domain of negative Laplacian (VSCC) near selenium atom in the complexes (in the direction of Se…A bond) compared to isolated dimethylselenide. Since the negative Laplacian zone exhibits the domain where potential (stabilizing) contribution to the electronic energy dominates over kinetic (destabilizing) one, the shape of negative Laplacian can be attributed to the shape of the lone pair. In isolated dimethylselenide molecule VSCC domain corresponding to the lone pairs of selenium is similar in shape to a “cap”. The simplest changes can be seen by the example of gallium and indium-containing complexes. The shape of the “cap” of selenium ex-lone pair in dimethylselenide in complexes III-1 – III4 and IV-1 – IV-4 is somehow stretched in the direction of gallium (indium) atom (Figure 2). The same is true for aluminium halide complexes where ex-lone pair distortion is essentially larger so that the shape of it is rather like a cylinder than a “cap”. Polarizing ability of boron atom is so great that the negative Laplacian domain in all cases is highly distorted and has two points of the Laplacian minima along Se…B line.


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Figure 2. Plots of the Laplacian of the electron density of complex under study in the plane of symmetry (Se…A-Xp plane). Red isolines correspond to the negative Laplacian values, blue ones – to positive, VSCC critical points located in the plane of the picture are marked by yellow dots (the others are not shown), BCPs – by green dots, RCPs are not shown.


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Table 4. Local characteristics* of the VSCC points in the vicinity of Se atom in the complexes and corresponding values for isolated dimethylselenide molecule. k1

k2

k3

∇2ρ(r)

k2/k1

k3/k1

-0.0741

1.236

29.44

0.321 0.357 3.206 0.1282 -0.1140 2.4956

-0.0858

1.113

9.99

3.0871

0.338 0.341 0.845 0.0595 -0.0480 2.5330

-0.0347

1.009

2.50

1.7952

0.523 0.564 2.501 0.1361 -0.1525 2.7412

-0.0895

1.078

4.78

2.7625

0.636 0.640 1.506 0.0953 -0.1503 3.2368

-0.0680

1.005

2.37

1.8098

0.573 0.614 2.193 0.1373 -0.1611 2.8174

-0.0896

1.073

3.83

2.7069

0.692 0.694 1.587 0.1025 -0.1712 3.3169

-0.0753

1.002

2.29

1.8227

0.590 0.628 1.960 0.1372 -0.1630 2.8500

-0.0888

1.065

3.32

2.6652

0.670 0.674 1.551 0.1063 -0.1763 3.2895

-0.0783

1.007

2.32

II-1

1.7754

0.333 0.375 2.992 0.1286 -0.1295 2.5981

-0.0863

1.125

8.98

II-2

1.7776

0.325 0.372 2.950 0.1277 -0.1253 2.5815

-0.0853

1.144

9.07

II-3

1.7792

0.319 0.367 2.914 0.1270 -0.1225 2.5696

-0.0846

1.147

9.12

II-4

1.7807

0.310 0.358 2.879 0.1260 -0.1182 2.5492

-0.0835

1.153

9.28

III-1

1.7795

0.305 0.346 2.944 0.1253 -0.1131 2.5193

-0.0828

1.134

9.64

III-2

1.7793

0.294 0.339 2.935 0.1243 -0.1079 2.4900

-0.0818

1.151

9.98

III-3

1.7803

0.288 0.332 2.905 0.1236 -0.1045 2.4772

-0.0810

1.154

10.11

III-4

1.7809

0.276 0.320 2.880 0.1225 -0.0994 2.4483

-0.0799

1.160

10.44

IV-1

1.7775

0.237 0.276 3.015 0.1208 -0.0959 2.4324

-0.0795

1.165

12.72

IV-2

1.7767

0.231 0.274 3.012 0.1205 -0.0936 2.4147

-0.0791

1.185

13.04

IV-3

1.7767

0.226 0.270 3.001 0.1201 -0.0912 2.4060

-0.0787

1.195

13.28

IV-4

1.7767

0.221 0.264 2.988 0.1195 -0.0884 2.3946

-0.0781

1.195

13.55

Complex

R(CP-Se)

ρ(r)

-V(r)/G(r)

DMSe

1.7519

0.108 0.133 3.178 0.1157 -0.0497 2.2010

1.7634

he

“Ex-LPs” I-1

I-2

I-3

I-4

“Free-LPs” I-1

1.7525

0.085 0.118 3.054 0.1133 -0.0366 2.1477

-0.0715

1.385

35.80

I-2

1.7471

0.080 0.108 3.097 0.1141 -0.0334 2.1327

-0.0717

1.345

38.59

I-3

1.7446

0.085 0.107 3.140 0.1147 -0.0341 2.1350

-0.0723

1.254

36.74


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I-4

1.7426

0.091 0.107 3.175 0.1151 -0.0348 2.1375

-0.0728

1.173

34.89

II-1

1.7502

0.089 0.110 3.064 0.1136 -0.0344 2.1385

-0.0714

1.239

34.37

II-2

1.7498

0.088 0.111 3.068 0.1134 -0.0337 2.1351

-0.0714

1.257

34.73

II-3

1.7497

0.088 0.111 3.066 0.1133 -0.0334 2.1302

-0.0713

1.261

34.85

II-4

1.7497

0.088 0.111 3.063 0.1131 -0.0329 2.1320

-0.0712

1.258

34.86

III-1

1.7518

0.084 0.108 3.018 0.1127 -0.0316 2.1260

-0.0706

1.284

35.97

III-2

1.7513

0.084 0.109 3.030 0.1126 -0.0317 2.1242

-0.0707

1.304

36.12

III-3

1.7514

0.084 0.109 3.027 0.1125 -0.0315 2.1260

-0.0706

1.308

36.20

III-4

1.7514

0.084 0.109 3.026 0.1124 -0.0313 2.1244

-0.0705

1.304

36.09

IV-1

1.7528

0.084 0.108 3.006 0.1123 -0.0315 2.1264

-0.0704

1.286

35.79

IV-2

1.7520

0.085 0.111 3.026 0.1125 -0.0321 2.1260

-0.0707

1.306

35.60

IV-3

1.7521

0.085 0.112 3.027 0.1124 -0.0321 2.1294

-0.0707

1.318

35.61

IV-4

1.7521

0.085 0.112 3.027 0.1124 -0.0322 2.1278

-0.0706

1.318

35.61

*

R(CP-Se) is the distance from the selenium nucleus to the VSCC point. kn (n=1-3) – three curvatures of ∇2ρ(r) in VSCC point, other notations are the same as in Table 2. In the case when two ex-LPs of selenium exist, characteristics of the one that is far removed from selenium atom are shown in italics. All values are in a.u.

We would also mention positive Laplacian values (shown by blue isolines) within the basin of aluminium, gallium and indium atoms. Small red shells just around metal nucleus represent core electrons. This means that atoms almost completely loose their valence shell due to ionic character of bonding with halogens and with selenium. It should be noted that in the case of boron halide complexes some part of VSCC domains falls into boron atom basin that shows quite big amount of covalence in its bonding with surrounding atoms (complexes I-2, I-3, I-4). The analysis of the VSCC critical points (Table 4) allows getting more detailed picture of the properties of lone pairs of dimethylselenide upon complexation. The VSCC critical point of ex-lone pair of selenium moves away from selenium atom (increasing R(CP-Se) in comparison with the lone pair in isolated dimethylselenide molecule). Generally, the stronger the complex the greater Se – ex-LP distance. The electron density in the VSCC critical point is greater in more stable complex, despite the ACS Paragon Plus Environment

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fact that usually electron density value decreases very rapidly with the distance from the nucleus. It gives evidence of high concentration of electrons along Se...A line in the complexes under study. The driving force of the rise of local electron occupancy is the greater stabilization of electrons in ex-LP’s VSCC critical point. In boron complexes -V(r) /G(r) ratio decreases in the following halides row: BF3 > BCl3 > BBr3 > BI3, and the opposite trend is observed for aluminium, gallium and indium halides complexes. This ratio is the only value characterizing local electron distribution that fully reflects the trends in complex stability with the same IIIA group element. Among two points of Laplacian minima on Se…B line in boron halide complexes I-1 – I-4 one CP (closest to selenium) is very similar in properties to ex-LPs of selenium in other complexes (with aluminium, gallium and indium). The VSCC critical point that is most distant from selenium atom (properties of which are shown in Table 4 in italics) have smaller electron density ρ(r) (comparing to that of the one closest to selenium) but electrons in it are more stabilized (according to potential/kinetic energy density ratio -V(r)/G(r)). Note that since electron density in this point is lower than in closest to selenium VSCC critical point, the value of electronic energy density he(r)=V(r)+G(r) in the former point is lower than in the latter. This value is less suitable for analysis of electron stabilization in study of local properties of Laplacian of the charge density distribution. In I-1 complex the Laplacian critical point that is the most distant from selenium nucleus is characterized by the smallest electron density and Laplacian values (half the values of those at the closest to selenium VSCC critical point) and the lowest potential/kinetic energy density ratio among boron complexes. This complex is also characterized by smaller stabilization of electrons of closest to selenium ex-LP in comparison with the cases of I-2, I-3 and I-4. It can be concluded that exchange-correlation interactions that are probably mainly responsible for the existence of Laplacian minima are the least significant in this complex. Relative curvatures of the Laplacian of the charge density (k2/k1 and k3/k1) show that Laplacian distribution in the vicinity of the VSCC critical point becomes more spherical: less elliptic in the direction tangent to the direction to the selenium nucleus (k2/k1 becomes closer to 1 in the complex) and more elongated (less oblate) along the direction to the nucleus (k3/k1 decrease). The same is true for ACS Paragon Plus Environment

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highly electrostatic hydrogen bonds44 but di-iodine45 where electrostatics is not so essential and interelectronic repulsion has non-negligible effect. Comparing the values of characteristics of free-lone pair of selenium with corresponding ones of the lone pair in isolated dimethylselenide molecule we can conclude that the free-LP critical point becomes less populated, it is located closer to selenium nucleus, its Laplacian value becomes greater in the complex. Two former features are evidences for the decrease in electron stabilization in the VSCC critical point that is reflected in the decrease of potential/kinetic energy density ratio. Ratios k2/k1 and k3/k1 in free-LPs are greater than in VSCC critical points corresponding to LP of selenium in isolated dimethylselenide molecule and ex-LP of selenium in complexes. This shows that free-lone pair of selenium have tendency to be more contracted in the radial direction and more elongated in tangent direction to nucleus. This statement is supported also by Figure 2. All features of free-LP VSCC were already mentioned in relation to the example of hydrogen-bonded complexes of organoselenium molecules, and seem quite general for complexes where electrostatic component of complexation energy is significant (those that are studied here and hydrogen-bonded complexes44). Moreover, free-LPs in all complexes are much more similar to each other than ex-LPs, since they are quite far from “interaction arena” – Se…A line. These features make this type of critical points less attractive to participation in other intermolecular interactions as we have described previously44 and as it can be expected. 3.2.3 Integral characteristics The unique insight into the chemical changes that occur during the formation of the intermolecular bond is provided by the study of evolution of atomic properties upon complexation. 3.2.3.1 Atomic electron occupancy and charge transfer One of the main effects affecting the complexation and sometimes being its main driving force is сharge transfer from donor to acceptor molecule79-82. All atomic charges under study are so called “Bader charges”, i.e. they were calculated by integration of charge density over atomic basin. Sum of charges over certain fragment represents the growth/decrease of probability of finding electron within the molecular fragment in the complex in 19 ACS Paragon Plus Environment


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comparison with that in the isolated molecule. This probability can be considered as the number of electrons transferred from one fragment to another with the boundary between fragments defined as zero-flux surface. Hereafter we use not entirely exact phrase “number of transferred electrons” in this meaning. The value of transferred charge (CT) was calculated as deviation of the sum of atomic charges constituting the fragment AX3 or Me2Se in the complex from zero. Table 5. QTAIM atomic charges (q) in isolated molecules (denoted by subscript “isol”) and in complexes, and the value of transferred charge (CT). Complex

q(Se)

q(Seisol)

q(A)

q(Аisol)

q(Xp)

q(Xnp)

q(Xisol)

CT

I-1

0.2572

0.1811

2.3757

2.4924

-0.8618

-0.8606

-0.8301

0.2097

I-2

0.3198

0.1811

1.7910

2.0316

-0.7014

-0.7005

-0.6769

0.3134

I-3

0.3158

0.1811

1.3476

1.6048

-0.5558

-0.5516

-0.5344

0.3127

I-4

0.3023

0.1811

0.6177

0.5294

-0.3046

-0.3018

-0.1760

0.2909

II-1

0.0752

0.1811

2.5608

2.6018

-0.8860

-0.8851

-0.8669

0.1092

II-2

0.0625

0.1811

2.4091

2.4242

-0.8281

-0.8286

-0.8076

0.0773

II-3

0.0573

0.1811

2.3191

2.3182

-0.7949

-0.7959

-0.7722

0.0682

II-4

0.0463

0.1811

2.1855

2.1566

-0.7436

-0.7454

-0.7184

0.0493

III-1

0.2076

0.1811

2.0028

2.1230

-0.7577

-0.7483

-0.7076

0.2524

III-2

0.2196

0.1811

1.6221

1.6785

-0.6254

-0.6186

-0.5595

0.2422

III-3

0.2229

0.1811

1.4306

1.4578

-0.5598

-0.5536

-0.4857

0.2367

III-4

0.2226

0.1811

1.1769

1.1592

-0.4699

-0.4653

-0.3861

0.2243

IV-1

0.1812

0.1811

2.0438

2.1508

-0.7684

-0.7529

-0.7170

0.2304

IV-2

0.1911

0.1811

1.7082

1.7578

-0.6475

-0.6376

-0.5857

0.2145

IV-3

0.1934

0.1811

1.5451

1.5645

-0.5899

-0.5807

-0.5219

0.2062

IV-4

0.1952

0.1811

1.3297

1.3165

-0.5129

-0.5053

-0.4384

0.1938

All values are in a.u.


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Figure 3. The influence of complexation on atomic occupancies: changes in (a) atomic occupancies, (b) atomic localization ∆λ, (c) intra-fragment localization ∆λintra, (d) inter-fragment delocalization δinter upon complex formation. For simplicity only most important atoms that are most affected by complexation are shown (Se, A and X of AX3 molecule), values for halogen atom are averaged over all three atoms present in a complex. The data shown in Tables 5 and Figure 3a demonstrate the existence of significant changes in atomic occupancies. These changes take place both in donor and acceptor molecules. Charges on selenium and A atoms of acceptor are always positive, halogens have negative charges. In boron, gallium and indium complexes the electron occupancy of selenium atom decreases in comparison with free dimethylselenide molecule and increases in aluminium complexes (Table 5). The value of transferred charge is the greatest in boron complexes and the lowest in aluminium complexes. In all complexes polarization of DMSe molecule by the acceptor takes place, resulting in the decrease of electron occupancy of methyl groups (sum of occupancies of constituting atoms) in the series B > Al > Ga > In. For example, sum of ACS Paragon Plus Environment

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hydrogens and carbon charges of methyl group is equal to -0.003, 0.007, 0.011, 0.012 а.u. for chlorides and in isolated DMSe is -0.089 а.u. Molecules of boron, gallium and indium halides have the ability to effectively accept electron density so that the transferred charge is rather great. Therefore selenium atom and the whole donor molecule loose electrons. The ability of aluminium halogenides to withdraw electrons is not so pronounced. Therefore, rather high polarization of DMSe molecule is not accompanied by significant transfer of electrons to acceptor molecule, and electronic occupancy of selenium atom increases upon complexation. The increase of charges on halogen atom of halide molecules approaches maximum in iodides. Charges on “planar” halogens generally grow to a greater extent than on “non-planar” ones. In all cases rather large amount of electron charge is transferred to halogen atoms. In the case of I-1 – I-4 complexes, boron atom withdraws much bigger amount of electron density than halogens, though it is not true for Me2Se…BI3 complex (I-4) where electron occupancy of boron atom decreases upon complexation. In the case of Al, Ga and In halides complexes the increase of atomic weight of halogen leads to gradual decrease of electron occupancy of metal atom (see Figure 3a) and increase of occupancy of a halogen. Excluding I-1 complex, the value of transferred charge decreases in the following element halides series: F > Cl > Br > I (BF3 molecule as it was usually pointed out have unconventional properties). Excluding complexes I-2 and I-3, one can note the influence of the halogen on the ability of acceptor molecule to withdraw electrons. Generally, when passing from fluorides to iodides the occupancy change of atom A decreases significantly from positive to negative value (Fig. 3a). At the same time the amount of electron density accepted by the halogen atom upon complexation increases from fluorides to iodides. Therefore fluorides enhance the ability of the central atom to accept electrons in the complex, however fluorine atom itself accepts the least number of electrons among halogens. This behavior becomes weaker down the halogen group. Atom A of iodides AI3 looses the electrons upon complexation but iodine atom withdraws the biggest amount of electrons. This fact can be explained as follows: fluorine atom as the strongest acceptor withdraws the greatest amount of electrons in isolated ACS Paragon Plus Environment

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molecules of halides, thus allowing the central atom to accept more electrons in a complex, and from the other side, the ability of halogen to accept electrons upon complexation is lowered. Since electronegativity of the halogen decreases and its radii increases down the group, the number of electrons accepted by central atom decreases and the number of electrons transferred to halogen atom increases. The only exception is boron halides, since boron atom itself has high acceptor ability in the complex. 3.2.3.2 The localization (LI) and delocalization (DI) indexes Deeper insight into electron redistribution is provided by the localization (λ(i)) and delocalization (δ(i,j)) indexes63,64. The first of them characterizes the number of electrons localized within atomic basin i and the second one – the number of electrons, shared by the basins of a pair of atoms i and j. With the use of localization and delocalization indexes atomic occupancy can be represented as

λ (i) + 1 2 ∑ δ (i, j ) = N (i) , where N(i) is a total electronic occupancy of the basin of atom i. Using this j ≠i

equation charge transfer value can be decomposed into three terms: (i) the change of atomic localization of the electrons after complex formation, denoted here as ∆λ, (ii) the change of delocalization indexes between atoms constituting the fragment (intra-fragment delocalization), ∆δintra, that mainly reflects weakening or strengthening of the bonds forming molecular fragment upon complexation (however there is also some effect from electron delocalization between formally unbound atoms), (iii) inter-fragment delocalization term, δinter, which shows the number of electrons becoming shared by different fragments in the complex. Alternatively, by summing first two terms one gets changes in intra-fragment localization of electrons of the atom, ∆λintra, including not only changes in localization of electrons within the atom, but also changes in delocalization within the fragment. The number of electrons transferred from/to the fragment F can be written as: ACS Paragon Plus Environment

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    ∆N ( F ) = ∑ ∆λ (i ) + 1 ∑ ∑ ∆δ (i, j ) + 1 ∑ ∑ δ (i, j ) = ∑ ∆λintra (i) + 1 ∑ δ (i, j )  2 2 2 i∈F j∈F B∉F i∈F  j∉X  i∈F  betweeni∈Fdifferent  fragments within fragment F

[

]

∆N ( F ) = ∑ ∆λintra (i ) + 1 ∆δ inter (i ) = ∆λintra ( F ) + 1 δ inter 2 2 i∈F Electron localization changes in the atom i, ∆λ(i), can be both positive and negative. Intra-fragment delocalization changes of atom the A within the fragment F, ∆δ intra (i ) = ∑ ∆δ (i, j ) , are equal to the sum j∈ F

of changes in pair delocalization within the fragment and are usually negative. It means that the number of electrons shared by two atoms (corresponding mainly to bonds) belonging to the fragment, decreases upon complexation. This is true both for donors (because they lose electrons) and acceptors (because bonds in them become weaker).1 Intra-fragment localization at atom i ∆λintra(i) = ∆λ(i) + ½∆δintra(i) is generally negative with a few exceptions (e.g. I-1 complex). Inter-fragment delocalization at atom i

δ inter (i ) = ∑ δ (i, j ) can be only positive. Thus atomic charge changes upon complexation are controlled j∉ F

by the competition between intra-fragment localization (how effectively atom participates in localization of electrons at its basin and on “bonds” with other atoms within the fragment) and inter-fragment delocalization (how effectively this atom shares electrons with atoms of the neighboring fragment). The localization and delocalization indexes calculated for the studied complexes are shown in Table 6 and on Figure 3. These data show that in all cases selenium atom loses rather large amount of localized electrons (large value of ∆λ, Fig. 3b) causing the decrease of intra-fragment localization (∆λ(Se) and ∆λintra(Se) are similar, see Fig. 3b and 3c). This statement is also valid for the whole dimethylselenide molecule (∆λ(DMSe) is 1.5-3 times greater than ∆δintra(DMSe), Table 6). Weakening of intra-fragment electron localization at selenium atom is accompanied by the increase of their participation in interfragment delocalizations. About 40% of all inter-fragment delocalization involve selenium atom, 20% acceptor’s complexation centre A and about 30% - halogen atoms. Thus, five atoms (Se, A, three

1

The summation in ∆δintra runs over all pairs of atoms within the fragment, bonded and non-bonded. For convenience hereafter we assume that ∆δintra reflects the changes in the number of electrons localized at bonds of the fragment keeping in mind that word “bond” refers to any two atoms within the fragment. 24 ACS Paragon Plus Environment

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halogen atoms) of thirteen account for more than 90% of overall delocalization. Moreover, Se…A delocalization index contributes 25-55% to the sum of delocalization indexes (inter-fragment delocalization). The reason of different behavior of selenium atom in AlX3 and GaX3 (InX3) complexes mentioned in Section 3.2.3.1 is that selenium atom in aluminium compounds’ complexes lose two times less localized electrons than in gallium (indium) ones, but participation of selenium atom in interfragment delocalization in both types of complexes is approximately the same.

Table 6. QTAIM value of the localization and delocalization characteristics of complexes: intrafragment changes in atomic localization (∆λ), intra-fragment delocalization (∆δintra), inter-fragment delocalization (δinter) and the contribution to the latter from selenium-atom A interaction. Complex

∆λ(DMSe)

∆λ(AX3)

∆δintra(DMSe) ∆δintra(AX3)

δinter

δ(Se…A)

I-1

-0.4258

-0.0437

-0.1657

-0.1289

0.7660

0.2122

I-2

-0.6834

-0.0089

-0.2849

-0.3356

1.3123

0.4695

I-3

-0.7239

0.0238

-0.3159

-0.4389

1.4560

0.5644

I-4

-0.7542

0.3231

-0.3477

-0.8429

1.6258

0.6670

II-1

-0.2213

-0.0595

-0.1725

-0.1410

0.5963

0.1722

II-2

-0.2716

-0.0681

-0.2049

-0.2535

0.8008

0.2067

II-3

-0.2885

-0.0622

-0.2181

-0.3089

0.8812

0.2264

II-4

-0.3088

-0.0578

-0.2343

-0.3867

0.9911

0.2517

III-1

-0.4442

0.1428

-0.2065

-0.2920

0.8006

0.4325

III-2

-0.4909

0.1715

-0.2322

-0.4140

0.9664

0.4520

III-3

-0.5128

0.1826

-0.2374

-0.4607

1.0303

0.4665

III-4

-0.5332

0.1821

-0.2507

-0.5185

1.1224

0.4855

IV-1

-0.4009

0.1319

-0.1550

-0.3074

0.7687

0.4347

IV-2

-0.4286

0.1602

-0.1632

-0.3658

0.7701

0.4351

IV-3

-0.4394

0.1662

-0.1679

-0.4080

0.8896

0.4392

IV-4

-0.4520

0.1629

-0.1763

-0.4448

0.9071

0.4468

All values are in a.u.


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For the acceptor molecule as a whole intra-atomic localization either decreases or increases, but anyway it generally has rather small effect on the charge transfer value (Table 6). Intra-fragment delocalization occurring due to the weakening of intra-acceptors binding decreases and exceeds atomic localization, thus as a whole intra-fragment localization changes are negative (Fig. 3c). Increase of electron occupancy of acceptor molecule is the consequence of electron sharing by donor and acceptor δinter (Table 6). This picture is rather common for complexes where charge transfer has non-negligible effect (for example, the same picture can be seen in complexes of DMSe with methanol and di-iodine – see Tables S4 and S5 in Supplementary data). Acceptor molecule in the complexes of aluminium and gallium (indium) behaves in a very different way (Table 6): aluminium halides molecules lose electrons both localized on acceptor’s atoms (∆λ) and delocalized on bonds (∆δintra), gallium (indium) halides are characterized by the increase of atomic localization (due to the increase of halogen atoms localization – Fig. 3b). Complexation center of acceptor molecule, A, can lose and withdraw electrons depending on halogen atom: greater electronegativity of the halogen results in greater electron localization on atom A, however the effect is small (Fig. 3b). Boron halides are strongly different from the other IIIA element halides: localization of electrons at boron atom in I-1, I-2 and I-3 complexes increases (Fig. 3b); however, this effect is accompanied by the decrease in atomic localization of halogen (Fig. 3b), and in complexes I-1, I-2 the effect is so large that the overall atomic localization at acceptor molecule decreases (Table 6), in I-3 complex overall atomic localization is positive but small. Boron iodide complex I-4 is completely different from other boron halide complexes, since localization at boron atom decreases and that of iodine atom increases. The nature of charge-transfer in this complex looks similar to that in gallium iodide complex III-4 (and indium iodide complex IV-4). However, charge transfer features (localization and delocalization effects) of mentioned boron complex are greater than in the case of corresponding gallium (indium) complexes.

Concluding Remarks


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Complexes of dimethylselenide (as a donor) with compounds of IIIA group elements (as an acceptor) have been studied by DFT and analyzed in the framework of Quantum Theory of Atoms in Molecules. Calculated geometrical parameters and thermodynamic characteristics are in good agreement with experimental data which are however not numerous. Quantum-chemical data testifies that complexes under study have greater stability in comparison with di-iodine and methanol complexes studied previously. Thermodynamic stability of boron halide complexes increases in the series fluoride < chloride < bromide < iodide, but in the complexes of other IIIA elements (aluminum, gallium, indium) halides the stability changes oppositely. Aluminum halides form the complexes with DMSe, which are of approximately the same stability. The analysis of local characteristics of electron density distribution (so-called topological analysis) and of the Laplacian of the charge density distribution allows us to conclude that Me2Se…AX3 (A=B, Al, Ga, In; X=F, Cl, Br, I) molecular complexes are generally similar to charge-transfer systems. However, the details of electron distribution in these two types of systems (local and integral characteristics) are quite different. According to topological analysis, selenium-boron bond can be attributed as having covalent nature, but bonds with aluminum, gallium and indium may be considered partially covalent. Only one lone pair of selenium participates in complexation process. Critical point of the domain of the lone pair VSCC shifts closer to the acceptor complexation center A, electron density at this point increases, and electrons become more stabilized in comparison with isolated molecule. The properties of another lone pair of selenium change to a much lesser extent. Analysis of localization and delocalization of electrons during complex formation provides the possibility of deeper understanding of the nature of bonding. There are common trends for all complexes under study and the ones that are not considered here (e.g., hydrogen-bonded complexes and iodine complexes). Complex formation leads to lesser localization of electrons on the fragments of any type. However, for donors the decrease in localization comes from the release of electrons from the atoms (the main effect) and bonds (intra-fragment delocalization which is almost two times less significant). For acceptor molecule intra-fragment localization changes are caused mainly (and in some cases ACS Paragon Plus Environment

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exclusively) by the decrease in the number of electrons delocalized on atomic pairs (mainly on bonds) within the fragment. The electrons “released” due to changes in localization upon complexation are involved in delocalization between atoms of different fragments. Since the decrease in electron localization over donor molecule is more significant than over the acceptor one, the former totally loses electrons while the latter accepts them. This process results in conventional charge transfer. Some discrepancies between the properties of complexes under study allow us to make several conclusions about the difference in the nature of bonding. We can distinguish three limiting types of bonding in molecular complexes: • Charge transfer-driven complexes, which are classic Mulliken complexes, stabilized by the transfer of the electron density from one fragment to another. Charge transfer in this type of complexes mostly involves formally unbound atoms of different fragments. For these complexes covalence of interactions between bonded atoms is weak, sometimes it is even hard to decide what atoms are bonded (for example, complexes of tetracyanoethylene). • Covalence-driven complexes, which are stabilized by covalent interaction between atoms that are considered as bonded in the complex. • Electrostatics-driven complexes, which are stabilized by electrostatic attraction of different molecules. We realize that such classification is to a much extent arbitrary; as it often happens that most of the complexes belong simultaneously to a number of classes in greater or lesser extent. Complexes under study can be divided into three groups according to the peculiarities of bonding: boron halides complexes (however, they can also be further divided), aluminum halides complexes and the united group of gallium and indium halide complexes. In our opinion, the latter type of complexes represents the simplest case. The group to which gallium (indium) halide complexes belong is characterized by rather large charge transfer value, most of the charge being transferred to halogen atom.


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There is rather high delocalization index in Se…Ga and Se…In bonds, which is about 50% of total inter-fragment delocalization. In these complexes donor molecule is weakly polarized, the properties of the lone pair of selenium change insignificantly. These complexes are very similar to the complexes of di-iodine molecule I2 studied previously45, and this allows us to call them charge transfer-driven complexes with high degree of covalence. In aluminum compound complexes the value of charge transfer is rather low (less than 0.1 ē similar to the H-bonded complexes44). There is no significant increase of localization of electrons on any atom of the acceptor. Se…Al delocalization index is rather low compared to Se…Ga, Se…In and Se…B ones and similar to the value for Se…I complex45. These complexes seem to be of high electrostatics-driven nature (also with quite high level of covalence). Contrary to other complexes of IIIA group halides high covalence of Se…B bond is the common feature of boron halide complexes, and the Laplacian of electron charge density analysis evidences high polarization of electron shells of selenium caused by acceptor molecule. However, the nature of bonding varies in different boron complexes. From localization/delocalization point of view complex I-1 with hard Lewis acid (BF3) seems to be a electrostatics-driven complex: it is characterized by relatively low Se…B delocalization, relatively low value of the transferred charge being accompanied by the high degree (about 50%) of electron transfer to fluorine atoms. Soft Lewis acid – BI3 – behaves similar to gallium (indium) complexes, and seems to be of high charge transfer-driven nature. Other boron compounds’ complexes I-2 and I-3 differ from the mentioned ones: they are characterized by sufficient increase of occupation of boron atom, relatively low charge transfer to halogens (like in electrostaticsdriven complexes), high delocalization indexes on Se…B bond. All these features are conventional for the formation of polar covalent bond. Therefore I-2 and I-3 (and to a lesser extent I-1, since it has similar features though they are less pronounced) can not be attributed to conventional charge-transfer complexes but have a lot in common with covalently-bound compounds. We wanted to give more deep insight into factors controlling thermodynamics and other characteristics of complexes using IQA analysis83,84, however, the accuracy of integration appropriate


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for the serious discussion was not achieved in the calculations with available programs (AIMAll62, Promolden84,85).

Acknowledgments. Authors acknowledge Dr. Todd A. Keith for kindly putting at our disposal AIMAll Professional package, Prof. A. Martin Pendas for Promolden package and both of them for continuous communication during our research. Dr. M.Yu. Balakina, Dr. O.D. Fominykh and Dr. O.N. Kataeva are gratefully acknowledged for valuable discussion during the work on this paper and preparation of the manuscript. Part of the work was made in the Laboratory of Chemoinformatics in the University of Strasbourg and Prof. A. Varnek is highly acknowledged for valuable discussions during it. The work was supported by Russian Federal Program “Scientific and scientific-pedagogical personnel of innovative Russia” (№ P1349, 11th of June of 2010). Authors want to express thanks to Reviewer for valuable comments and discussion.

Supporting Information Available: compilation of data on the geometry of complexes, comparison of theoretical and experimental data, topological properties of A-X bonds and contribution to charge transfer value in DMSe…MeOH and DMSe…I2. This information is available free of charge via the Internet at http://pubs.acs.org.

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Structure of the dimethylselenide-AX3 complexes (A= B, Al, Ga, In; X=F, Cl, Br, I) optimized at the PBE1PBE / Sapporo triple-zeta level. Topological features are shown: bond paths – lines, bond critical points (BCPs) – green points, ring critical points (RCPs) – red points. 180x175mm (300 x 300 DPI)


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Plots of the Laplacian of the electron density of complex under study in the plane of symmetry (Se…A-Xp plane). Red isolines correspond to the negative Laplacian values, blue ones – to positive, VSCC critical points located in the plane of the picture are marked by yellow dots (the others are not shown), BCPs – by green dots, RCPs are not shown. 180x177mm (300 x 300 DPI)



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The influence of complexation on atomic occupancies: changes in (a) atomic occupancies, (b) atomic localization ∆λ, (c) intra-fragment localization ∆λintra, (d) inter-fragment delocalization δinter upon complex formation. For simplicity only most important atoms that are most affected by complexation are shown (Se, A and X of AX3 molecule), values for halogen atom are averaged over all three atoms present in a complex. 180x112mm (300 x 300 DPI)


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The Nature of the Interaction of Dimethylselenide with IIIA Group

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