Interaction of BoronâNitrogen Doped Benzene Isomers with Water

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On the Interaction of Boron-Nitrogen Doped Benzene Isomers with Water Sirous Yourdkhani, Micha# Chojecki, Michal Hapka, and Tatiana Korona J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b05248 • Publication Date (Web): 14 Jul 2016 Downloaded from http://pubs.acs.org on July 17, 2016

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The Journal of Physical Chemistry

On the Interaction of Boron-Nitrogen Doped Benzene Isomers with Water Sirous Yourdkhani,†,‡ Michal Chojecki,‡ Michal Hapka,‡ and Tatiana Korona∗,‡ Department of Chemistry, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran, and Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland E-mail: [email protected]

∗

To whom correspondence should be addressed Department of Chemistry, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran ‡ Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland

†

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Abstract The interaction of 1,2-dihydro-1,2-, 1,3-dihydro-1,3- and 1,4-dihydro-1,4-azaborine isomers with one and two water molecules has been studied using a variety of supermolecular (Møller-Plesset – MP, and coupled cluster – CC) as well as perturbational (symmetry-adapted perturbation theory – SAPT) electron-correlation methods in the complete basis-set limit. It has been found that the water molecule binds to azaborine isomers through O − H · · · π, π−H · · · O, and dihydrogen bonding linkages. The SAPT interaction energy decomposition shows that these complexes are mostly stabilized by dispersion followed closely by induction contributions. Pauli repulsion hinders water molecule to be polarized by azaborine in the O − H · · · π type of complexes. According to the interacting-quantum-atoms analysis, the structures with a primary binding of the O − H · · · π type benefit from an additional stabilization factor resulting from the interaction of the oxygen and the second hydrogen atom of water, i.e. the one which does not point towards the ring, while the interaction of hydrogens from water with azaborines plays a destabilizing role for the π−H · · · O type. The same method states that the intermolecular bindings between azaborines and the water molecule have a multi-centre character with a small bond polarization, and they are classified as closedshell (noncovalent) by quantum theory of atoms-in-molecules analysis at bond critical points. The complexes of azaborines with two water molecules tend to arrange in a circular fashion with a recognizable water dimer attached to the azaborine molecule. A comparison with the CCSD(T) benchmarks shows that the non-additive contribution to the interaction energy of the trimers is negative and with a good accuracy can be accounted for by the MP2 method. A good agreement between Hartree-Fock (HF) and MP2 nonadditive energy, as well as the decomposition of HF nonadditive interaction energies divulge the importance of nonadditive induction energy in the trimers. The interaction energies for the azaborine with one water calculated with the SAPT(DFT), MP2, SCS-MP2, and MP2C methods are in satisfactory agreement with each other. Finally, it has been found that the population analysis from the electron localization function offers the most comprehensive explanation of the orientational preferences of

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the water molecule in the complex.

Introduction Owing to being isoelectronic with the carbon-carbon bond, the boron-nitrogen bond has recently attracted attention of many researchers. 1–4 On the one hand, an equal number of valence electrons in both cases leads to similar properties and reactivity, 4 but on the other hand the polar character of the B-N bond affects characteristics of a system through shifts in the electronic distribution. 5 These shifts may lead to qualitative changes in physicochemical properties, e.g. a formation of a band gap in graphene doped with the B-N moieties or in the BN analogue of graphene, 6–8 which results in a semiconductor character of these materials. This example shows that the investigation of the CC/BN isosterism is quite important for designing new materials and tuning of their properties. 9 Some of these properties can be already studied in a single six-member ring (phenyl) unit, therefore an investigation of benzene analogues with two carbon atoms replaced with one boron and one nitrogen atoms will serve as the simplest representative of the larger B-N doped arenes. Placing one boron and one nitrogen atom at different positions of the benzene ring gives three heterocycle isomers: 1,2-dihydro-1,2-azaborine, 1,3-dihydro-1,3azaborine, and 1,4-dihydro-1,4-azaborine 10,11 (see Figure 1), abbreviated in the following as 1,2-, 1,3- and 1,4-azaborine, respectively. Similarly to arenes, these compounds fulfill usual aromaticity criteria. 2,3,10,12,13 The studies on the delocalization parameter of the three isomers show 2,10 that the aromaticity trend is 1,3-azaborine>1,2-azaborine>1,4-azaborine, and that all azaborines are less aromatic than benzene. 14 On the other hand, their stability is not in line with their aromaticity: 1,2-azaborine is more stable than 1,4-azaborine, and 1,3-azaborine turns out to be the least stable isomer. 15 Recently it has been shown that a lower stability of 1,4-azaborine compared to 1,2-azaborine is due to the exchange repulsion, while the charge separation in the π system due to the arrangement of B and N atoms is

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responsible for the lowest stability of the 1,3-azaborine. 14 Properties of the azaborine isomers have attracted a lot of attention, while intermolecular complexes with azaborines as constituent molecules remain to a large extent unexplored. Although general preferences for their interaction patterns can be inferred from aromaticity of these molecules (e.g. it has been shown that azaborines participate in the electrophilic substitution reaction 16 ), the polarity of azaborines can also play an important role in the reactivity and complexation patterns, e.g. two 1,4-azaborine molecules were shown to bind through the dihydrogen bond. 17 Since azaborine isomers can be regarded as building blocks of the BN-doped nanographenes, 18 an investigation of their complexes with water, which is a medium or a pollutant in many processes, 19 is of a great importance. 20 Therefore, we decided to study the energy-optimized structures of azaborines with one or two water molecules with the help of symmetry-adapted perturbation theory 21 (SAPT), Møller-Plesset theory to the second (MP2) and third (MP3) order, as well as MP2 coupled 22 (MP2C), spin-component-scaled MP2 23 (SCS-MP2), and coupled cluster (CC) singles and doubles with the perturbative inclusion of triple excitations – CCSD(T) 24 methods. The SAPT approach was also used for analysing of the physical origin of the interaction through its energy partitioning into physically sound components. A more detailed insight into the nature of the interactions within the azaborine-water complexes is performed with several specialized models, like Pendas’ interacting-quantum-atoms scheme 25 (IQA) and Bader’s quantum theory of atoms in molecules 26 (QTAIM). Threebody interactions of azaborine and two water molecules are investigated with the MP2, MP2+SDFT, 27 MP3, and CCSD(T) methods. Additionally, the electron localization function (ELF) method, 28 QTAIM and bond descriptors are utilized to predict the preferable binding sites of azaborines interacting with water.

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Methods Overview The main quantity describing the intermolecular interaction is the interaction energy, defined for a complex of n molecules as a difference between the electronic energy of the complex and the sum of energies of the constituent molecules, what for the case of the dimer AB and the trimer ABC leads to definitions

Eint (AB) = EAB − (EA + EB ), Eint (ABC) = EABC − (EA + EB + EC ),

(1)

where the geometries of the molecules A, B, and C are the same as in the respective complex. The interaction energies can be calculated either with the supermolecular or with the perturbational approach. The supermolecular method is based on the straightforward application of Equation (1) with the energies obtained at a selected level, like MP2 or CCSD(T). In the SAPT perturbational approach the interaction energy of the dimer AB is obtained directly, as a sum of the electrostatic, induction, and dispersion energies together with their exchange counterparts. Also an estimation of higher-order induction terms, the so-called delta Hartree-Fock (HF) term, 29 is included, leading to the following working formula, (1)

(1)

(2)

(2)

(2)

(2)

Eint (AB) = Eelst + Eexch + Eind + Eexch−ind + Edisp + Eexch−disp + δEHF .

(2)

Throughout this work the SAPT(DFT) approach 30,31 have been used, where the intramonomer electron correlation is treated at the density-functional theory (DFT) and the time-dependent (TD) DFT levels. Commonly used supermolecular methods often show some drawbacks, when used for the intermolecular complexes. In particular, the MP2 method overestimates the stabilization of the complex, if it is composed of monomers containing conjugated bonds. 32 The rescaling of the spin-parallel and antiparallel components of the MP2 correlation energy (SCS-MP2)

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leads to a better agreement of the resulting correlation energy with the CCSD(T) benchmark and is usually beneficial for the interaction energies, too. Another remedy to the MP2 supermolecular energy deficiencies is the recently proposed MP2C method of Heßelmann, 22 which is based on the MP2 interaction energy decomposition proposed by Chalasi´ nski and Szcz¸e´sniak. 33 In the MP2C the uncoupled HF (UCHF) dispersion energy is replaced with a more accurate coupled Kohn-Sham (CKS) counterpart, (2)

(2)

EMP2C = EMP2 int int − Edisp (UCHF) + Edisp (CKS).

(3)

The physical insight into the nature of the trimer interaction energy is provided by first expressing it as a sum of two-body (additive) and three-body (nonadditive) terms,

Eint (ABC) = Eint [2, 3] + Eint [3, 3],

(4)

and analysing these two components separately. The additive energy is composed of the dimer interaction energies,

Eint [2, 3] = Eint (AB) + Eint (BC) + Eint (CA),

(5)

and the nonadditive energy is defined as the remaining part of the total trimer interaction energy,

Eint [3, 3] = Eint (ABC) − Eint [2, 3],

(6)

The nonadditive part of the MP2 interaction energy does not contain the potentially signif(3)

icant third-order dispersion energy, Edisp [3, 3], which first appears at the MP3 level. 33,34 In order to correct for this shortcoming, Podeszwa and Szalewicz 27 proposed to obtain Eint [3, 3] (3)

as a sum of EMP2 int [3, 3] and Edisp (CKS)[3, 3] terms, what leads to a hybrid approach denoted

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as MP2+SDFT. The additive part can still be calculated at the SAPT level, so the final formula for the trimer interaction energy utilized in this paper is given as, Ehybrid = ESAPT (AB) + ESAPT (BC) + ESAPT (CA) + Ehybrid [3, 3], int int int int int (3)

Ehybrid [3, 3] = EMP2 int [3, 3] + Edisp (CKS)[3, 3]. int

(7)

We have also obtained the trimer interaction energy in a supermolecular way with the MP3 and CCSD(T) methods for a comparison with the MP2+SDFT approach. Finally, we present a decomposition of the nonadditive HF energy into the Heitler-London exchange and the deformation energy. 35 The three-body Heitler-London exchange energy, ǫHL exch [3,3], is obtained at the HF level of theory as the zeroth iteration of the three-body Pauli-blockade selfconsistent field (SCF) equations. 36 The deformation energy is then obtained as the difference HF HL EHF def = Eint [3, 3] − ǫexch [3, 3].

(8)

The EHF def term corresponds to the induction nonadditive effect and results from the distortion of HF orbitals of one monomer in the field of the other two monomers. It is also referred to as the SCF-deformation nonadditivity. (It should be noted parenthetically that the “deformation energy” term utilized here denotes the energetic effect of the electronic wave function distortion under the influence of another monomer for fixed nuclei positions, while the same term is frequently used to describe the destabilization of the monomer in the complex caused by the geometry change with respect to the free monomer.) In the IQA scheme, the total electronic energy is divided into intra-basin (monoatomic) and inter-basin (two-body) contributions. The intra-basin contributions define the atomic net energy or atomic self-energy, while the inter-basin contributions present the pairwise

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additive interaction energy between two atoms,

E=

X

AA (TA + EAA en + Eee ) +

A

X

AB AB AB (EAB nn + Een + Ene + Eee ) =

A>B

X A

EA self +

X

EAB int ,

(9)

A>B

where “ee”, “en” denote the electron-electron, electron-nucleus contributions etc. The EAB ee energy can be further divided into the Coulomb and exchange-correlation parts (EAB C and EAB XC , respectively) based on the decomposition of the two-electron reduced density (2-RD) into Coulombic and exchange-correlation components. Therefore, the inter-basin interaction energy can be described as a sum of two components: the EAB XC energy, which existence can be traced back to the antisymmetry of the wave function, and the remaining electrostatic term, resulting from “classical” Coulombic interaction. This decomposition is utilized in the analysis of the interactions at the level of single atoms and functional groups. In particular, AB the relative importance of EAB XC and ECl in the total interaction energy serves as a tool for a

bond classification.

Computational Details The local minima on the potential energy surface (PES) of the azaborine-water(s) complexes were found at the MP2 level in the aug-cc-pVTZ basis set 37 (aug-cc-pVXZ will be abbreviated as aXZ in the following). The harmonic frequency analysis confirmed that the optimized structures are indeed minima. For dimers (azaborine plus one water) the optimization was also performed by means of the B3LYP 38–40 functional and its D3 Grimme 41 version, denoted as B3LYP-D3, in order to assess their accuracy with respect to the MP2 approach. The CCSD(T), MP2, MP3, and SCS-MP2 supermolecular interaction energies were calculated for the optimized geometries in a full basis set of the complex, in order to account for the basis-set superposition error (BSSE). 42 The second-order dispersion terms needed in the MP2C model were obtained with the EXX functional. 43 8


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The PBE0 functional 44,45 corrected for the long-range behavior according to the recipe of Gr¨ uning et al. 46 was used in SAPT(DFT) dimer calculations. The energy of the highest occupied molecular orbital (HOMO) of the monomers, required for the asymptotic correction (AC), was calculated for geometries of isolated monomers using the PBE0 functional and the same basis set as in the corresponding SAPT(DFT) calculations. Vertical ionization potentials (IPs) of the monomers were provided as a difference of the unrestricted KS energy for the cation and the restricted KS for the neutral monomers with the same PBE0 functional and the large aQZ basis set. 37 Several studies have shown that the SAPT(PBE0AC) provide interaction energies which are close to CCSD(T) 47,48 and SAPT(CCSD). 49 The exchange terms in SAPT(DFT) were calculated within the so-called S2 approximation. In addition, since the calculations of the small coupled exchange-dispersion term is time-demanding, this component was estimated from the uncoupled KS exchange-dispersion term as discussed in Refs. 48,50,51 All SAPT(DFT) calculations (also for a dimer in a trimer) were carried out in a dimer basis set. In the long-range corrected SAPT (LRC-SAPT) calculations, the HJS functional composed of the PBE correlation and the short-range exchange ωPBE based on Henderson, Janesko, and Scuseria approach was used. 52 For every complex the range-separation parameter, ω, was tuned using the IP-tuning procedure, i.e., by minimizing the difference between the negative of the HOMO energy and the vertical IP. 53 The dipole and quadrupole moments of the azaborines and of the benzene molecule (the latter optimized at the same level as azaborines), were obtained within the CC singles and doubles model based on the expectation-value formula (the XCCSD(3) model, see Ref. 54 ). The static dipole polarizabilities were calculated likewise on the XCCSD level 55 (which is the same level as used in the SAPT(CCSD) method). The coordinate origin and the axis orientation were selected according to the charge centroids. The density fitting (DF) 56 (also known as resolution-of-identity (RI)) approach for twoelectron repulsion integrals was used in supermolecular HF and MP2, and in SAPT(DFT) 47

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calculations. For the aXZ (X=T,Q) orbital basis set, 37 the corresponding JKFIT 57 and MP2FIT 58 auxiliary basis set 59 were utilized. No DF was utilized for the XCCSD, MP3, CCSD(T), and LRC-SAPT methods. The LRC-SAPT calculations were performed in the aTZ basis set. The correlated part of the supermolecular interaction energies, the SAPT dispersion energy, damped with the exchange-dispersion energy, and the third-order nonadditive part of the dispersion energy were extrapolated to a complete basis set limit (CBS). 60,61 To get more insight into the nonadditivity issues, the MP3 and CCSD(T) supermolecular interaction energies were obtained for the trimers, too. These calculations were also performed in the full-complex basis set in order to reduce the BSSE. 42,62 We have previously shown 63 that when a valence-valence basis is utilized, it is safer to exclude core electrons from the correlation treatment. Therefore, 1s orbitals of B, C, N, and O atoms were frozen in all post-HF calculations. The one-electron reduced densities (1-RDs) obtained using the MP2 method in the aTZ basis were utilized for topological analyses of the ELF and the QTAIM. The ELF population study and the electron density difference maps (EDD) were calculated using the Multiwfn 64 program, while the AIM charges were obtained using the AIMAll 65 program. The QTAIM topological analysis and IQA calculations were performed for the M06-2X 66 /aTZ 1-RDs with the AIMAll 65 program (the selection of the functional results from the IQA limitations, as implemented in AIMAll). Geometry optimizations were performed using the turbomole program 67,68 (version 7.0.1). The supermolecular CCSD(T), SCS-MP2, MP2C, and MPn interaction energies, SAPT(DFT), and first- and second-order properties calculations were performed with the developer version of molpro. 69,70 The MP2 and M06-2X 1-RDs as well as B3LYP and B3LYP-D3 interaction energies were obtained by gaussian09 (revision E.01). 71

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Discussion Orientations of the water molecule toward azaborine isomers The azaborine isomers are polar molecules with the dipole moments ranging from 0.8 to 1.6 a.u., which result from different electronegativities of boron and nitrogen (see Table 1). The orientations of dipole moments of the all three azaborines are depicted in Figure 1 together with axes orientation and numbering of carbon atoms, utilized later in the analysis of the dimer and trimer structures. The presence of the dipole moment makes these molecules qualitatively different from the isoelectronic benzene, which is characterized by a nonvanishing quadrupole moment (also shown in this table for a comparison). The structures corresponding to the local minima of the azaborine-water species obtained at the MP2/aTZ level of theory are depicted in Figure 2 together with selected geometrical parameters of the complexes. The B3LYP/aTZ and B3LYP-D3/aTZ optimized structures can be found in Figures SF1 and SF2 of the supporting information. As can be seen from Figure 2, the interaction of azaborine isomers with a water molecule leads to five, four, and three distinguishable orientations for 1,2-azaborine, 1,3-azaborine, and 1,4-azaborine, respectively. In spite of intensive trials no more minima on the potential energy surface have been found. The minima can be divided into three categories, denoted in the following as n-H(N), n-Cm, and cyclic 2-H(N)H(B) or n-H(Cm)H(B), where n corresponds to 1,n-azaborine, m is the number of the carbon atom, which is the closest to the water molecule, and H(X) denotes a hydrogen atom bound to an atom X. Out of these structures the n-Cm ones are similar to the benzene-water minimum known from the literature, 72 while the n-H(N) and cyclic minima are specific to azaborines. It should be mentioned that in the work of Al-Hamdani et al., 73 on the effect of the exact exchange in the DFT functionals on the orientations of water with respect to 1,2-azaborine, similar water· · · 1,2-azaborine structures were reported. In the 2-H(N), 3-H(N), and 4-H(N) structures the water molecule forms a hydrogen bond

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through its oxygen atom to the hydrogen linked to the nitrogen of azaborine. Since the nitrogen atom is a part of the ring, one effectively has a multicenter donor of a proton forming a hydrogen bond with water, i.e. a bond of the π−H · · · O type. 74 The observed elongation of the N–H bond of about 0.005 ˚ A is typical for the covalent bond involved and weakened by the hydrogen bond. It should be noted, however, that the oxygen atom from H2 O is located approximately in the same plane as the azaborine ring, what means that there is no direct interaction between the oxygen atom and the cloud of the π electrons from the ring. The 2-H(N)H(B), 3-H(C4)H(B), and 4-H(C2)H(B) structures are peculiar in a sense that in the same interaction region one hydrogen atom (this linked to the carbon or nitrogen atom) plays a role of the Lewis acid, while another hydrogen atom (connected to boron) becomes the Lewis base. As a result, the interaction of water with azaborine occurs through two types of intermolecular bondings: the C–H· · · O hydrogen bond, 74 where carbon acts as the hydrogen donor, and the H· · · H dihydrogen bond. 75,76 Also in this case the elongation of the covalent C–H or O–H bonds is typical for a bond involved in the hydrogen bond interaction. However, because of the simultaneous interaction with two centres, the C–H· · · O angle is different from 180◦ , which is a typical feature of the hydrogen bond. Similarly to the n-H(N) structures, H2 O is placed approximately in the same plane as the azaborine ring, which prevents a direct interaction of the water molecule and the π electrons. This is in contrast to the n-Cm type, where the water molecule resides above the ring and one from two O–H bonds points with its hydrogen end approximately towards one carbon atom (Cm). (This hydrogen atom will be denoted as H1w in the following, while another hydrogen atom from the water – as H2w .) The n-Cm type encompasses the 2-C2, 2-C3, 2-C4, 3-C3, 3-C4, and 4-C2 structures. It should be noted that the adopted naming convention involves some simplifications, since none of the angles O–H1w · · · Cm is close to 180◦ : they vary from about 140◦ to 170◦ depending on the structure. Especially for the cases: 2-C2, 2-C3, and 3-C4 the names should be rather 2-C2/C3, 2-C3/C2, and 3-C4/C3, since the hydrogen atom points

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approximately to the halfway between respective two carbon atoms. However, the QTAIM study of the charge densities shows the line paths H1w · · · Cm for all the n-Cm structures, therefore the selection of the naming convention can be justified by Bader’s theory. In all the n-Cm structures the O–H bond of water pointing to azaborine is elongated by 0.003–0.005 ˚ A. Bearing in mind that the carbon atoms form the aromatic ring, the intermolecular contact types in the n-Cm structures can be classified as a hydrogen bonding with a multicenter proton acceptor, i.e. O − H· · ·π. 77 A comparison of the orientations of the n-Cm structures with the orientation of water over benzene or aromatic rings of some amino acids 78 reveals that the π-system in the azaborine isomers is concentrated mostly around carbon atoms, while nitrogen and boron atoms have a lesser contribution to the π system, e.g. no structures analogous to the n-Cm type with the H–O bond pointing toward the B or N were found, even for the most plausible case of 1,2-azaborine, where these two atoms are direct neighbours. There is also no local minima with a direct interaction between oxygen and the electropositive boron atom. Additionally, an examination of the present minima reveals that there is no structure with the O−H1w bond pointing towards C1, as well as no structure with this bond pointing toward C2 in 1,3-azaborine. In the next section we will look for the explanation of the existence or nonexistence of the above-mentioned structures using quantum mechanical methods based on the analysis of various molecular properties. It is interesting to investigate whether the MP2/aTZ optimized local minima can be reproduced by a less-expensive method(s), like B3LYP or B3LYP-D3. The comparison of the B3LYP- and the MP2-optimized structures reveals that the cases: 2-C3, 2-H(N)H(B), and 3-C4 are missing in the former approach (see Figure SF1 of the Supporting Information). Additionally, instead of the 2-C3 structure, the B3LYP method provides the second 2-C4 structure (named 2-C4′ ), where the O–H2w bond points out of the ring plane. If the 2-C4′ geometry is used as a starting point for the MP2 or B3LYP-D3 optimization, the 2-C3 case is obtained instead. On the other hand, if the structures are common for B3LYP and MP2, the geometrical parameters (bond distances and angles) are quite similar for both cases. A

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systematic difference is that the bond distances in the B3LYP structures are, on average, 0.1 ˚ A larger than the MP2 ones. The lack of some minima on the B3LYP/aTZ PES raises the question to what extent the addition of the dispersion correction to B3LYP may cure this situation. It turns out that indeed there is a generally good agreement between the MP2 and B3LYP-D3 local minima (see Figure SF2 in the Supporting Information). The only notable difference occurs for the 2-C4 structure, as the most similar 2-C2C4 structure from B3LYP-D3 should be rather regarded as a hybrid between the 2-C2 and 2-C4 MP2 local minima. The reoptimization of the 2-C2C4 structure by MP2 turns it into 2-C2. The B3LYP-D3 interaction energies show a satisfactory agreement with other correlated methods utilized in this study, while the B3LYP interaction energies are from 3.6 to 8.1 kJ/mol smaller in absolute value than the CCSD(T) values. The differences between the B3LYP and B3LYP-D3 local minima and interaction energies, as well as a better agreement of B3LYP-D3 with MP2, can be therefore attributed to the inclusion of the long-range dispersion effect through the D3 correction.

Analysis of dimer structures Global monomer properties and atomic charges There exist several approaches, which allow for an explanation of the directionality of the intermolecular interactions. The simplest one is based on deriving possible relative orientations of two molecules from the analysis of molecular properties like multipole moments and polarizabilities. Multipole moments govern the behavior of the long-range electrostatic energy, while polarizabilities show the ability of a molecular electronic cloud to deform as a response to the electric field caused by permanent multipole moments of another molecule. 79 These properties, calculated at the CCSD level, are listed in Table 1. The quantitative change between azaborines and benzene is the emergence of the dipole moment, which vary substantially with the position of the boron and nitrogen in the ring. However, already the components of the quadrupole moment are quite similar for the azaborines and the benzene 14


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molecules. The replacement of two carbon atoms by a boron and nitrogen atoms leads to a minor increase of the average polarizability and to the removal of the αxx = αyy identity for azaborines. According to the simplest dipole-dipole interaction picture the most favourable structure would involve a direct interaction between the oxygen of the water and the boron, i.e. it is exactly one from the “missing” cases mentioned above. On the other hand, the n-Cm type could be qualitatively explained as the interaction of the azaborine quadrupole moment with the dipole and quadrupole moments of water. The anisotropy of the dipole polarizability can be used to rationalize possible orientations of the n-H(N) and cyclic structures, since a larger contribution of the induction energy is expected in these cases because of about twofold decrease of the polarizability in a direction perpendicular to the ring. However, these global molecular properties alone do not carry enough information to explain details of the azaborine-water interactions. For this purpose one has to utilize a more detailed analysis of the wave function and/or the electron density. The examination of a full 1-RD is a cumbersome task, therefore several methodologies were invented to simplify this issue. These approaches usually operate with some physically meaningful, although not necessarily well-defined quantities, like atomic net charges in molecules or local energies and multipole moments. Nonetheless, attributing properties to single atoms or functional groups seems to be the only reasonable way to see the coarseness of molecules involved in the interaction. Atomic charges analyzed here were usually defined with the help of QTAIM, although other definitions are also available in the literature. The examination of data listed in Table 2 reveals that the AIM charge of the C1 atom for all the three azaborine isomers is positive, while it is negative for all other carbon atoms (C2, C3, and C4). The effective net positive charge explains why the C1 atom does not bind noncovalently to the H1w atom, which has a partial positive charge as well. The sign of the C1 charge can be explained as a result of the binding of C1 to the electronegative nitrogen atom. However, the AIM charges do not clarify the absence of the binding between

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the C2 atom of the 1,3-azaborine molecule and H2 O – the net charge in this case is of the same sign and the same order of magnitude as for the C2 and C3 atoms for 1,2-azaborine, for which the corresponding minimum structures do exist. We have checked that other definitions of atomic charges (see the Supporting Information) also do not provide an answer to the question of orientational preferences of water interacting with 1,3-azaborine. It seems therefore that the mechanisms behind the absent 3-C2 structure are too subtle to be derived from the analysis of the monomer charge density. IQA model of interacting molecules Opposite to the net atomic charges analysis, the IQA method focuses on atom pairs XY, for which it provides the energy characteristics of the binding pattern between atoms X and Y. The resulting quantities are usually called interaction energies, EXY int (they should not be confused with the intermolecular interaction energies defined through Equation (1)). As usual, negative values of such interaction energies indicate that atoms attract each other, although it does not necessarily mean that a regular bond between these two atoms is formed in the QTAIM theory sense. Therefore, the IQA method can be used for an analysis of the existing structures, but cannot explain why some structures are not formed at all. However, one of our goals is to explain why the structures 2-C1, 3-C1, 4-C1, and 2-C3 do not appear. To this end, one H1w C1 H1w C2 can examine the Eint and Eint energies for the existing n-Cm structures. It turns out

that these energies are always positive and large (they are always larger than 100 kJ/mol) w Cm indicating a strong repulsion, while the EH1 energies for Cm connected to boron are of int

the same order of magnitude, but negative. A detailed comparison of these two energy values shows that for the existing n-Cm structures the repulsive contribution from the H1w · C1 pair is effectively damped by the attractive contributions resulting from the interaction of H1w with other carbon atoms (see Table 4 and the Supporting Information). Therefore, we attribute the absence of the n-C1 structures to the strong repulsion between the C1 and H1w

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atoms, which is not counterbalanced by the attraction of the latter atom to the remaining ring members. Therefore, the absence of the n-C1 structures and the existence of structures where water is connected to the carbon close to boron can be explained by the values of the atom-atom IQA energies. It is less clear why for the case of carbons connected to other carbons (C2 w Cm of about −30 kJ/mol) the and C3 in 1,2-azaborine and C2 in 1,3-azaborine with EH1 int

2-C2 and 2-C3 structures do exist, whereas the hypothetical 3-C2 structure cannot be found H1w C2 in spite of an intensive search of the PES. The Eint energies for the existing structures

of 1,3-azaborine with water are of the same order of magnitude as for complexes with 1,2azaborine. It can be only argued that in the 2-C2 and 3-C3 structures a weak attraction between the H1w atom and both C2 and C3 atoms adds up, which is apparently enough to form these two minima on the PES, while for the 3-C2 case only one carbon atom (C2) would take part in this type of interaction. Actually, a similar argument can be applied for the analysis of the AIM charges. A full list of the pair energies is available in the Supporting Information. ELF search for the binding sites of azaborines A more advanced reactivity analysis is provided by the electron localization function (ELF) method. 80 It is argued in the literature that the localization of an electron determines reactive sites of a molecule 81 and that the ELF gives a local indication of the Pauli repulsion strength. 82 The ELF is a function of spatial coordinates of a single electron and can be analyzed in an analogous way as the charge density. In particular, the three-dimensional (3D) space around a molecule can be divided into basins separated by zero-flux surfaces (see Figure 3 for a partition of 1,3-azaborine, analogous ELF partitions of 1,2-azaborine and 1,4-azaborine can be found in the Supporting Information). The integration of the ELF over basins V(X,Y), where X and Y are neighbour atoms, gives the valence-electron population in ¯ the basin (N(X, Y)), which can be further divided into contributions from individual atoms

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¯ ¯ X and Y (N(X) and N(Y)) via a partition of the space into Bader atoms. An examination of Figure 3 reveals the ELF basins which can be attributed to covalent bonds, but there is no significant visual difference between various basins containing carbon atoms. Recognizable variations in the basin sizes can be found for boron- and nitrogencontaining basins (which are larger and smaller, respectively, than the corresponding carbon basins). These changes are in line with the electronegativity of these three atom types. However, notable differences appear after the electron populations determined from ELF are partitioned into contributions from individual atoms. In particular, the summed atomic contributions, listed in Table 2, yield numbers, which are significantly less than four (the number of valence electrons for carbon) for C1 in all three azaborines, approximately four for C2 (n = 2, 3) and for C3 in 1,2-azaborine, whilst they are larger than four for other cases: C2 (n = 4), C3 (n = 3), and C4 (n = 2, 3). Therefore, the ELF analysis provides us with the valence electron population at a particular carbon atom, which can be then compared with the number of valence electrons for C. If it is less than four, the hydrogen bonding cannot be created, while the population larger than four favours such an interaction. This explains the absence of some structures discussed above in a straightforward way. Let us turn our attention to the population on hydrogen atoms. An examination of the partition of the protonated V(B, H) basin shows that the hydrogen linked to boron is effectively negative (it is populated by more than one electron), while the hydrogen participating in the V(N, H) basin is effectively positive (it is populated with less than one electron). These differences explain opposite roles of these two hydrogens and their participation in either hydrogen, or dihydrogen bondings. It should be noted that the ELF electron population on the hydrogen atoms connected to the Cm atoms is also smaller than one, but always larger than 0.95, therefore the hydrogen atom connected to carbon has only a small depletion of the negative charge. A different character of the C1 atom for three azaborines and for the C2 atom for 1,3-

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azaborine can be also recognized from an analysis of the Laplacian of the charge density (see the contour map of the Laplacian of the charge density of 1,3-azaborine in Figure 3, and analogous maps in the Supporting information for two remaining azaborines). The C1 atom and the C2 atom of 1,3-azaborine are encompassed by disconnected regions of the ∇2 ρ < 0 charge concentration. 26 These are exactly the same atoms, for which a direct C· · · H–O contact cannot be found, as already established by the ELF populations. Therefore, the ELF and QTAIM analyses are the two tools which proved to be the most fruitful in explaining the orientational preferences of the water-azaborine complexes.

Energetics of azaborine complexes with one water molecule The CBS-extrapolated (aTZ→aQZ) interaction energies from SAPT(DFT), MP2, SCS-MP2 and MP2C, and SAPT(DFT) components are listed in Table 3. As can be seen from this table, all four methods predict similar interaction energies. Especially SAPT(DFT), MP2C, and SCS-MP2 are quite close to each other. The MP2 interaction energy lies about 2 kJ/mol below SAPT(DFT), what is less than 10% difference in comparison to the total interaction energy. The order of the total stabilization energies (electronic plus zero-point energy (ZPE), the latter with unscaled harmonic frequencies) is the same as for the interaction energies, since in all cases the zero-point energy difference between the dimer and monomers is similar and amounts to about 13–14 kJ/mol. In the case of the 1,2-azaborine complexes, the absolute value of Eint becomes smaller in the sequence 2-H(N)H(B)≈2-H(N)>2-C2≈2-C3≈2-C4. For the 1,3- and 1,4-azaborine complexes, the energetic sequences are 3-H(N)≈3-C3>3-C4>3-H(C4)H(B) and 4-H(N)>4-C2>4-H(C2)H(B), respectively. Additionally, from 1,2-azaborine to 1,4-azaborine, the energy difference between the most and the least favourable structure increases from about 6 kJ/mol through 10 kJ/mol up to 12.5 kJ/mol. This means a much lower probability for the complex resting in the highest local minimum at a room temperature for the latter cases. 19



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The most stable structures for all the azaborine isomers are those involving the hydrogen atom connected to nitrogen, i.e. two structures of 1,2-azaborine: 2-H(N)H(B) and 2-H(N), plus 3-H(N) and 4-H(N) for remaining azaborine isomers. The negative of the CBSinterpolated SAPT(DFT) interaction energies are as large as 20, 26 and 28 kJ/mol for 1,2-, 1,3-, and 1,4-azaborine, respectively. All the remaining interaction energy values are significantly smaller than 20 kJ/mol in absolute value. Among these four cases the n-H(N) minima represent typical hydrogen-bonded structures with the N–H· · · Ow angle equal to 180◦ . These structures can be distinguished from other types by the negative value of the (1)

(1)

total first-order contribution E(1) = Eelst + Eexch . In all other cases the first-order exchange of the undistorted monomers’ electron clouds outweighs electrostatics, and the E(1) term is strongly repulsive. However, even for the nitrogen-hydrogen structures the first-order contribution does not exceed −3 kJ/mol, therefore the stability of the complexes at the minimum cannot be explained solely in terms of the unperturbed electron-cloud interaction. On the other hand, the asymptotic behavior of the interaction energy should be governed by the electrostatics in these cases, since both the molecules possess the permanent dipoles (see Table 1). Indeed, if water and 1,2-azaborine are separated, the electrostatic contribution becomes a dominant part of the total interaction energy (see the figure in the Supporting Information, where both molecules are being separated starting from the 2-H(N) minimum structure). However, in the vicinity of the minimum the main stabilization factor turns out to be dispersion with a non-negligible contribution from the induction. It should be noted (2)

that the Eind term is large in the absolute value, but it is quenched to a large extent by its exchange counterpart. As a result, only about 40% of the induction contributes to the stabilization of the complex for the hydrogen-bonded structures. Additionally it can be noted that also the δEHF term, which approximately corresponds to a higher-order induction and exchange-induction, is negative for all the structures. The 2-H(N)H(B), 3-H(C4)H(B), and 4-H(C2)H(B) complexes constitute the so-called hydrogen-dihydrogen bonded complexes. 83 These structures have an identical dihydrogen

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bond H(B)· · · H1w , while they differ by a hydrogen bond. In the 2-H(N)H(B) structure the nitrogen atom acts as the hydrogen donor, while in the two latter structures these are the carbon atoms which provide the hydrogen atom to the hydrogen bond. The SAPT interaction energies decrease in the absolute value as the separation of the boron and nitrogen increases in the ring, revealing the importance of the nitrogen atom as a very effective water attractor. The SAPT decomposition shows that the second-order induction energy, which describes the polarization of azaborine through water and vice versa, follows the same pattern as the total interaction energy. The significant contribution of the induction energy in the total SAPT energy indicates a large role of the polarization in the interactions under study, what leads to the deformation of monomers’ charge density in the complexes. 84 In the present case one expects a noticeable polarization in both directions, since both the molecules have permanent dipoles with appreciable polarizabilities (see Table 1). This deformation can be seen from Figure 4 with the aid of the EDD maps for the 1,2-azaborine complexes (similar EDD maps for 1,3- and 1,4-azaborine complexes are shown in the Supporting Information). The maps reveal that the rings for the 2-C2, 2-C3, and 2-C4 structures are polarized towards the water molecule, while the polarization of the oxygen of the water molecule towards the azaborine can be seen in 2-H(N). In the 2-H(N)H(B) structure, similarly to the 2-H(N) complex, the Ow atom is polarized towards the ring, while the hydrogen atom linked to boron is polarized towards the water molecule, which shows a mutual polarization in contrast to the one-direction polarization in 2-Cm. It should be noted that the SAPT method provides a quantitative insight into the one-direction polarization. For in(2)

stance, in the 2-C2 complex, the Eind (azaborine→water) is equal to −2.3 kJ/mol, while (2)

(2)

Eind (water→azaborine) = −6.2 kJ/mol. The Eexch−ind (azaborine→water) term amounts to 2.1 kJ/mol and almost completely cancels with the corresponding induction term, so the exchange repulsion prevents water to be polarized by azaborine. Analogous SAPT-based analysis of the preferred direction of the polarization can be performed for other cases (see

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the Supporting Information). The remaining second-order SAPT contribution is the dispersion energy. As can be seen from Table 3, only 15% of dispersion is cancelled by the exchange-dispersion term. It is also (2)

(2)

evident from Figure 5 that in some cases the net dispersion contribution, i.e., Edisp +Eexch−disp , is even larger in the absolute value than the total interaction energies. We can, therefore, conclude that in spite of the presence of a highly polar water moiety, the main stabilization factor is again dispersion with a considerable contribution from the induction energy. The same quantitative interpretation of the intermolecular interactions holds for both PBE0AC and HJS as base SAPT(DFT) xc functionals. For all the azaborine complexes LRCSAPT consequently predicts a bit more attractive interaction energies compared with the PBE0AC results with differences in the 0.15–0.74 kJ/mol range. For a detailed comparison of SAPT energy contributions from both functionals see the Supporting Information.

QTAIM and IQA analyses The IQA method is a tool which enables a localized description of the intra- and intermolecular interactions. In the present case one can divide water-azaborine interactions into two categories: a primary interaction, which is defined as the interaction of the azaborine molecule with atom(s) of water involved in the noncovalent bond, and a secondary interaction, which involves the interaction with the remaining water atom(s). Then, in the n-Cm complexes, the interaction of H1w with azaborine is primary while the interaction with the remaining water atoms, i.e Ow and H2w is secondary. In the n-H(N) complexes the interaction of Ow with azaborine is primary, while the interaction of the hydrogen atoms of water with azaborine is secondary. Similarly, in the cyclic complexes the interaction of Ow and H1w with azaborine is primary and this of H2w – secondary. The IQA energy data divided into primary and secondary interactions, and into the classical and exchange-correlation parts are shown in Table 4 and Figure 6. One can see that the total classical interaction contribution (Etot Cl ) to the total IQA inter-basin interaction energy 22


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(Etot int ) plays a stabilizing role for all the complexes. The stabilization role of the exchangecorrelation (Etot XC ) contribution always outweighs the classical contribution. In some cases, even up to 90% of the Etot int energy is composed of the nonclassical term. The relatively small contribution of the Coulombic classical term to the IQA interaction energy indicates that the effective polarization of a binding between azaborine and water is small. As expected, the absolute value of Etot is about one order of magnitude smaller than for chemical bonds. It is also interesting to consider the nature of the water-azaborine interactions from the QTAIM point of view. The bond paths of the hydrogen and dihydrogen bondings are depicted in Figure 7 for the 1,2-azaborine complexes (analogous molecular graphs of 1,3- and 1,4-azaborine complexes, as well as data for bond critical points – BCPs – can be found in the Supporting Information). First of all, one can see that indeed the 2-Cm structures are characterized by the bond paths directed towards the corresponding Cm atom, in agreement with the adopted naming convention. Positive values of the Laplacian of the charge density and of the total electron energy density indicate the closed-shell nature of the respective atom-atom binding. Another quantity listed in Table 4, which is used to analyze the electron sharing is a delocalization index 85 (δ), defined as an averaged exchange-correlation density between two atomic basins (note that EXC is directly related to δ 86 ). The δ AB index is a measure of the number of electron pairs shared between the A and B basins and, therefore, a measure of the bond order. A comparison of delocalization indices from Table 4 with the literature 87 shows that the present values are of the same order of magnitude as for indices characteristic for strong hydrogen bonds. This finding is in agreement with the geometry changes of the O–H bond, which is also typical for a bond involved in the hydrogen bonding. It should be also noted that the interactions under study are in principle multi-centered. The multi-centre character 88 is indicated by both the magnitude of the delocalization index and a dominant contribution of the exchange-correlation energy for the primary interaction.

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Complexes of azaborines with two water molecules Two water molecules can arrange themselves around an azaborine molecule in several ways. The search of the potential energy surface at the MP2/aTZ level resulted in structures depicted in Figure 8, and pair SAPT(DFT) and nonadditive MP2+SDFT energies for these structures are listed in Table 5. The first and second water molecules are denoted as “w1” and “w2” in this table and hereafter. An examination of Figure 8 reveals that three-body systems can be viewed in most cases as a water dimer interacting with azaborine through both water molecules, i.e. as a cyclic trimer. The two exceptions are complexes denoted as 2-C2:H(N)H(B) and 4-H(C2)H(B):H(N), which are of the w1· · · azaborine· · · w2 type. The preference of cyclic orientations is reflected in their larger stabilization as compared to the (3-C4:H(N)) is 28 kJ/mol larger (in the absolute value) than the non-cyclic cases, e.g. Ehybrid int Ehybrid (4-H(C2)H(B):H(N)). int The orientation of the water dimer with respect to the azaborine molecule determines the relative stability of the complexes. For instance, the 3-C4:H(N) complex is 22 kJ/mol lower in energy than the similar 3-C2:H(B) trimer as the O2· · · H-N hydrogen bond between the second water molecule and azaborine (Figure 8(e)) is stronger than the O2–H1w · · · H–B bond in 3-C2:H(B) (Figure 8(f)). Indeed, as may be inferred from Table 5, the higher stabilization of 3-C4:H(N) with respect to 3-C2:H(B) corresponds to a stronger attraction of azaborine to w2 (difference of 9 kJ/mol), larger nonadditive terms (8.5 kJ/mol), and to a weaker attraction of two waters in the 3-C2:H(B) complex (by 4.5 kJ/mol). The latter results from larger distances between the two waters and a less favorable O1· · · H−O2 angle in the (1)

hydrogen bonding. In particular, the Eelst (w1· · · w2) term is smaller by about 5 kJ/mol in comparison to the electrostatics of the isolated water dimer at optimal geometry. Among cyclic structures all the n-Cm:H(N) complexes exhibit a larger nonadditive contribution compared to the 3-C2:H(B) trimer. This can be qualitatively explained at the molecularorbital (MO) level: in the 3-C4:H(N) complex the 1,3-azaborine molecule donates an electron to w1 through its π-system (C4(sp2 )) and receives an electron from a lone pair of oxygen of 24


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w2 via the antibonding σ ∗ orbital of its N–H bond. In contrast, in the 3-C2:H(B) complex the azaborine molecule donates two electrons: one from its C2(sp2 ), as in the former case, and another one via the hydrogen atom linked to boron. As a result, both the water molecules in 3-C2:H(B) play a role of electron acceptors which instigates repulsion between them, and results in a larger distance than for the isolated water dimer or a water dimer inside one of the n-Cm:H(N) structures. For all the complexes the nonadditive MP2+SDFT (i.e., the (3)

EMP2 int [3, 3] + Edisp (CKS)[3, 3]), MP3, and CCSD(T) interaction energies are negative. For the n-Cm:H(N) cyclic configurations the contribution of nonadditive interaction energies to the total interaction energies is about 12%. This is comparable to the results for the water trimer. 89 For the 3-C2:H(B) and the non-cyclic complexes the nonadditive interaction energy contribution does not exceed 4%. It should be noted that the MP2+SDFT interaction energies are consequently too attractive with respect to the CCSD(T) results. This could be attributed to the lack of the third-order exchange-dispersion energy contribution in this approach. In contrast, MP3 nonadditive three-body interaction energies stay in close agreement with CCSD(T), only slightly overestimating the destabilizing contribution of the three-body dispersion. (3)

The Edisp (CKS)[3, 3] term for 2-C4:H(N)H(B) and 4-H(C2)H(B):H(N) is close to zero, while for the cyclic configurations (with the exception of 3-C2:H(B)) the third-order dispersion energy contributes, on the average, 6% of the total MP2+SDFT nonadditive interaction energy. The exchange nonadditivity calculated at the HF level is a non-negligible effect which amounts from 11 to 16% of the HF interaction energy for six out of eight complexes. Interestingly, the relative importance of exchange is the most pronounced in 3-C2:H(B), where it constitutes approximately 40% of the HF interaction energy. In contrast, for the linear 4-H(C2)H(B):H(N) complex the exchange nonadditivity is a minor contribution of about 1%. To sum up the above analysis, the polarization nonadditivity is the most important contribution to the three-body interaction energies in the trimer structures under study. Since the postulated partitioning of the nonadditive supermolecular HF and MP2 level 27

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includes the first-order exchange and second- and higher-order induction and exchangeinduction contributions, the main part of the nonadditive energy is composed of the nonadditive damped induction components. The close agreement between the HF and MP2 results reveals that intramonomer correlation effects are negligible in the present case.

Summary and conclusions The optimal structures of complexes of 1,2-, 1,3-, and 1,4-azaborines with one and two water molecules have been found at the MP2 level, and studied with the SAPT and supermolecular methods. They were analyzed also with the IQA, QTAIM, and ELF approaches in order to clarify the interaction character for these species. In comparison with the isoelectronic benzene, the polar character of azaborines leads to additional possibilities of placing water molecules. The most stable structures are obtained when the water molecule binds to the azaborine nitrogen-hydrogen end, although the structures analogous to the benzene-water complex – with water connected to the ring via the carbon atom acting as an electron acceptor – are also present. Another type, specific to azaborines, are structures where water is connected to the ring through two hydrogen bonds. The SAPT analysis of the interaction energy reveals that both dispersion and induction play an important role in the complex stabilization. A more detailed partitioning of the SAPT induction (into terms responsible for a polarization of water by azaborine and vice versa) confirms the findings from the EDD maps: effective polarization toward azaborine for n-Cm corresponds to the almost zero net contribution of azaborine polarizing water, while nonzero net contributions of both induction terms – to deformation of electron densities on both molecules. The population analysis with the ELF method and maps of Laplacian of the density proved to be the most effective in predicting the existence of dimer structures. The complexes of azaborines with two water molecules are usually composed of a twisted water dimer connected to azaborine through both waters. The only two linear-type com-

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plexes, i.e. with both waters on opposite sides of azaborines, are less stable by about the value of the missing water-water interaction. The stabilization of cyclic trimers depends on how the water molecules are connected to azaborine. The nonadditive contribution to the interaction energy is sizeable for the cyclic trimers and is dominated by the MP2 nonadditive term. The comparison of the MP2+SDFT results with the benchmark CCSD(T) in a smaller basis shows a systematic overestimation of the nonadditive attraction by the former method, which is probably due to the missing exchange counterpart of the third-order nonadditive dispersion. The SAPT(DFT), MP2, SCS-MP2, and MP2C methods give similar results for the interaction energies. This is in a sharp contrast with recent reports on the inadequacy of MP2 and even SCS-MP2 for a description of intermolecular interaction energies. Apparently, the polar character of azaborines reverts the usual MP2 overstabilization caused by the benzene-like ring.

Acknowledgement This research was supported in part by the computational facilities of PL-Grid Infrastructure. M.H. was supported by the Polish Ministry of Science and Higher Education (Grant No. 2014/15/N/ST4/02179).

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Figure 1: The optimized structures of azaborine isomers: (a) 1,2-azaborine (b) 1,3-azaborine (c) 1,4-azaborine, the orientation of the dipole moment and axes for the coordinate system.

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Figure 2: The optimized structures of 1,2-azaborine:water (up), 1,3-azaborine:water (middle) and 1,4-azaborine:water (down) complexes. Distances are in ˚ A and angles in degrees.

39



Figure 3: The 3D representation of (a) ELF basins and (b) the contour map of the Laplacian of the charge density (∇2 ρ) for 1,3-azaborine. Red lines represent regions where ∇2 ρ < 0, while blue lines show where ∇2 ρ > 0.

Figure 4: Electron density deformation maps of the optimized 1,2-azaborine:water complexes: (a) 2-C2, (b) 2-C3, (c) 2-C4, (d) 2-H(N), (e) 2-H(N)B(H).

Figure 5: The total first-order energy (E(1) = Eelst + Eexch ), the net second-order in(2) (2) (2) duction energy (Eind,tot = Eind + Eexch−ind + δEHF ), the net second-order dispersion energy (2)

(2)

(2)

(Edisp,tot = Edisp + Eexch−disp ), and SAPT(DFT) interaction energies for the optimized dimer structures. 10

5

0

E [kJ/mol]

-5

-10

-15

-20

-25

Firs-order Induction Dispersion SAPT(DFT)

-30

H 4-

H 4-

C 4-

H 3-

H 3-

C 3-

C 3-

H 2-

H 2-

C 2-

C 2-

C 2-

)

(B

H 2)

)

40


(C

)

(B

H 4)

(N

2

)

(C

)

(B

)H

(N

4

3

)

(N

(N

4

3

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 49

Page 41 of 49

sec Figure 6: The IQA primary interaction energy, Eprim int , secondary interaction energy, Eint , prim sec tot total interaction energy, Etot int = Eint + Eint , and classical (ECl ) and non-classical exchangetot correlation (EXC ) contributions to the total IQA energy. 100

50

E [kJ/mol]

0

-50

-100

-150

-200

Primary Secondary Total Classical Non-Classical

)

(B

H

2)

)

(C

)

(B

H

4)

(N

H

H

4-

4-

2

C

4-

)

(C

)

(B

)H

(N

H

3-

4

H

3-

C

3-

3

C

3-

)

(N

(N

H

2-

4

H

2-

3

C

2-

2

C

C

2-

2-

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7: Molecular graphs of the optimized 1,2-azaborine:water complexes: (a) 2-C2, (b) 2-C3, (c) 2-C4, (d) 2-H(N) (e), 2-H(N)B(H).

41



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8: The optimized trimer structures. Distances are in ˚ A and angles in degrees.

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43



Table 1: Components of the dipole moment (µ), quadrupole moment (Θ), and static dipole polarizabilities (α) for the azaborines and benzene molecule, calculated at the XCCSD(3)/aTZ level for the dipole and quadrupole moments and the XCCSD/aTZ level for the static polarizabilities. Small off-diagonal terms of Θ and α are not shown in the table. All values are given in a.u. 1,2-azaborine 44

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Page 44 of 49

x

y

1,3-azaborine z

x

y

1,4-azaborine

benzene

z

x

y

z

x

y

z

µ

0.00

−0.49

0.59

0.00

−1.22

0.99

0.00

0.00

1.60

0.00

0.00

0.00

Θ α

xx −5.04 46.48

yy −1.55 87.00

zz 6.59 81.69

xx −5.08 48.24

yy −2.16 93.15

zz 7.24 87.87

xx −4.88 47.37

yy 2.75 80.72

zz 2.13 88.65

xx 2.98 82.83

yy 2.98 82.83

zz −5.95 45.37


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Table 2: Comparison of the summed atomic contribution (n) to the selected basins from the topological ELF analysis and the atomic charges from QTAIM (q), calculated at the MP2/aTZ level for optimized geometries of azaborine isomers. All values are given in a.u. basin 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


C1 C2 C3 C4 H(B) H(N)

1,2-azaborine

1,3-azaborine

1,4-azaborine

n

n

n

3.49 3.96 3.91 4.67 0.37 1.54

q 0.427 −0.021 −0.047 −0.772 −0.692 0.419

3.58 3.92 4.59 4.14 0.38 1.62

q 0.405 −0.027 −0.723 −0.249 −0.690 0.433


q

3.59 5.40

0.366 −0.665

0.39 1.58

−0.694 0.439


Table 3: Components of the SAPT energy and total SAPT, MP2, SCS-MP2, and MP2C interaction energies for the minima of the azaborine complexes with water at the CBS limit. Energies are given in kJ/mol.

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Complexes/Energies 2-C2 2-C3 2-C4 2-H(N) 2-H(N)H(B) 3-C3 3-C4 3-H(N) 3-H(C4)H(B) 4-C2 4-H(N) 4-H(C2)H(B)

(1)

Eelst −15.45 −15.06 −16.45 −31.91 −31.71 −20.27 −18.92 −39.80 −19.90 −20.19 −37.54 −15.99

(1)

Eexch 20.80 20.61 23.01 31.78 33.31 25.73 23.64 37.71 23.00 24.31 34.75 20.09

(2)

Eind −8.50 −8.51 −9.66 −12.71 −12.73 −11.24 −10.16 −16.43 −8.25 −10.91 −14.51 −7.14

(2)

Eexch−ind 5.34 5.20 6.46 7.93 7.99 7.24 6.39 9.88 4.52 7.22 8.40 3.81

(2)

Edisp −16.53 −16.51 −17.34 −13.34 −16.29 −19.13 −18.09 −14.83 −14.27 −17.79 −14.07 −12.93

(2)

Eexch−disp 2.06 2.02 2.30 2.29 2.56 2.49 2.21 2.52 1.78 2.33 2.28 1.56

δEHF −2.26 −2.20 −2.59 −3.69 −3.23 −2.91 −2.81 −4.97 −2.37 −2.69 −4.41 −2.05


ESAPT int −14.54 −14.45 −14.27 −19.65 −20.10 −18.09 −17.74 −25.92 −15.49 −17.72 −25.10 −12.65

EMP2 int −16.22 −16.20 −15.48 −21.66 −22.36 −20.66 −20.17 −28.43 −16.91 −19.55 −27.65 −14.12

ESCS−MP2 int −12.78 −12.64 −12.01 −18.92 −19.04 −16.56 −16.23 −25.69 −14.21 −15.66 −24.64 −11.39

EMP2C int −13.08 −13.03 −12.30 −20.40 −20.84 −16.62 −16.31 −26.83 −15.26 −16.19 −26.11 −12.79

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Table 4: The IQA energetic profiles and delocalization index (δ) for the complexes of azaborine isomers (denoted as (2), (3), and (4) for 1,2-, 1,3-, and 1,4-azaborine, respectively) with a water molecule. For definitions of primary and secondary interactions see the text. Energies are given in kJ/mol and delocalization indices – in a.u.

47

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Complexes 2-C2 2-C3 2-C4 2-H(N) 2-H(N)H(B) 3-C3 3-C4 3-H(N) 3-H(C4)H(B) 4-C2 4-H(N) 4-H(C2)H(B)

Contact H1w · · · (2) H1w · · · (2) H1w · · · (2) Ow · · · (2) Ow /H1w · · · (2) H1w · · · (3) H1w · · · (3) Ow · · · (3) Ow /H1w · · · (3) H1w · · · (4) Ow · · · (4) Ow /H1w · · · (4)

Primary Eprim Eprim int Cl −50.94 −20.36 −52.76 −22.16 −52.56 −23.50 −154.00 −95.24 −123.82 −48.95 −52.03 −20.26 −43.68 −14.92 −205.53 −139.71 −73.52 −6.22 −46.66 −16.69 −201.06 −138.24 −56.04 5.22

Eprim XC −30.58 −30.45 −28.95 −58.86 −75.16 −31.76 −28.77 −65.82 −67.30 −29.96 −62.83 −61.26

δ prim 0.0662 0.0669 0.0651 0.1311 0.1748 0.0711 0.0669 0.1422 0.1685 0.0677 0.1358 0.1523

Contact Ow /H2w · · · (2) Ow /H2w · · · (2) Ow /H2w · · · (2) H1w /H2w · · · (2) H2w · · · (2) Ow /H2w · · · (3) Ow /H2w · · · (3) H1w /H2w · · · (3) H2w · · · (3) Ow /H2w · · · (4) H1w /H2w · · · (4) H2w · · · (4)

Secondary Esec Esec int Cl −25.60 11.46 −24.15 13.05 −26.44 15.25 68.79 69.84 23.05 23.84 −39.35 6.98 −44.30 1.38 105.75 106.93 −9.31 −8.57 −39.51 3.62 105.18 106.44 −16.42 −15.80


Esec XC −37.06 −37.14 −41.48 −0.92 −0.80 −46.33 −45.68 −1.18 −0.74 −43.13 −1.25 −0.62

δ sec 0.1150 0.1145 0.1269 0.0041 0.038 0.1364 0.1316 0.0053 0.0036 0.1268 0.0058 0.0030

Etot int −76.50 −76.91 −79.00 −85.21 −100.96 −91.38 −87.99 −99.78 −82.84 −86.17 −95.89 −72.46

Total Etot Etot XC Cl −8.90 −67.60 −9.11 −67.59 −8.25 −70.43 −25.41 −59.78 −25.11 −75.85 −13.28 −78.10 −13.54 −74.45 −32.78 −66.99 −14.79 −68.05 −13.08 −73.09 −31.82 −64.07 −10.58 −61.88

δ tot 0.1812 0.1814 0.1920 0.1352 0.1786 0.2075 0.1986 0.1475 0.1721 0.1944 0.1416 0.1553


Table 5: Components of the interaction energy for the minima of complexes of the one azaborine molecule with two waters at the CBS limit. Azaborine is abbreviated as Az in this table. (3)

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Complexes(Az· · · w1· · · w2)/Energies ESAPT (Az· · ·w1) ESAPT (Az· · ·w2) ESAPT (w1· · ·w2) EMP2 int int int int [3, 3] Edisp (CKS)[3, 3] 2-C2:H(N) −14.01 −15.63 −18.91 −6.99 −0.60 2-C4:H(N) −13.11 −15.46 −19.12 −6.95 −0.59 2-C4:H(N)H(B) −14.31 −19.76 −1.08 −1.15 −0.05 3-C3:H(N) −18.65 −20.02 −18.67 −9.02 −0.63 3-C4:H(N) −17.69 −21.02 −18.92 −9.63 −0.62 3-C2:H(B) −17.12 −12.21 −14.52 −1.32 −0.49 4-C2:H(N) −18.19 −19.91 −18.87 −9.58 −0.61 4-H(C2)H(B):H(N) −12.67 −25.07 −0.15 −0.95 0.01

Ehybrid EHF int [3, 3] int −56.14 −7.35 −55.23 −7.33 −36.35 −1.15 −66.99 −9.57 −67.88 −10.01 −45.66 −1.58 −67.16 −9.79 −38.83 −0.88

a

ǫHL exch [3, 3] −1.01 −1.14 −0.13 −1.36 −1.10 −0.52 −1.21 0.01

b

EMP3 int [3, 3] −6.59 −6.55 −1.10 −8.66 −9.25 −1.08 −9.12 −0.93

b

CCSD(T)

Eint

b

[3, 3] −6.60 −6.59 −1.10 −8.73 −9.33 −1.31 −9.18 −0.95

The pair energies are extrapolated as in e.g. Table 3. The nonadditive correlation components are extrapolated using the aTZ→aQZ two-point (3) extrapolation formula from Ref. 61 The total nonadditive MP2+SDFT contribution is a sum of EMP2 int [3, 3] and Edisp (CKS)[3, 3] terms. Energies are givein in kJ/mol. The ESAPT (w1· · ·w2) energy for the optimized dimer minimum is equal to −19.43 kJ/mol. a EHF int int [3, 3] was calculated in aQZ CCSD(T) b HL MP3 basis, while ǫexch [3, 3], Eint [3, 3] and Eint [3, 3] were calculated in the aTZ basis set.


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49


Interaction of BoronâNitrogen Doped Benzene Isomers with Water

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