Theoretical Predictions of C3v Symmetric Three-H-Bridged Noble

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Article 3v

Theoretical Predictions of C Symmetric Three-H-Bridged Noble Gas Compounds NgBeHBeR, NgBeHBR and NgBHBR 3

3

+

3

2+

Zhuo Zhe Li, An Yong Li, and Li Fei Ji J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b03976 • Publication Date (Web): 06 Jul 2015 Downloaded from http://pubs.acs.org on July 9, 2015

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The Journal of Physical Chemistry

Theoretical Predictions of C3v Symmetric Three-H-Bridged Noble Gas Compounds NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+ Zhuo Zhe Li, An Yong Li*, Li Fei Ji School of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, P.R.China *Corresponding Author Telephone: 15923061230, E-Mail: [email protected]

Abstract A new series of stable noble gas-Lewis acid compounds NgBeH3BeR, NgBeH3BR+, and NgBH3BR2+ (R = F, H, CH3, Ng = He-Rn) with three 3c-2e H-bridged bonds have been predicted by use of the PBE0 and MP2 methods. The Ng-Be/B bonds are strong and have large binding energies 35~130, 9~38 and 4~13kcal/mol for the doubly-charged cations, singly-charged cations and neutral molecules, respectively. The binding energy and strength of the Ng-Be/B bonds increase largely from He to Rn, but are insensitive to electronegativity of the substituent R. The Ng-B bonds in NgBH3BR2+ should be typical covalent bonds and the Ng-Be bonds in NgBeH3BR+ for heavy Ng atoms Kr, Xe and Rn have some covalent character. The three bridging-H atoms have characteristic infrared vibrational modes with large IR intensity to be detected in spectroscopy experiments. Keywords H-bridged; noble gas; Lewis acid-base adducts; AIM; NBO;

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LMOEDA

1. Introduction In the 1890s, Ramsay and co-workers discovered the noble gas (Ng) elements1. For many years, noble gas atoms had been known to be the most stable atoms in the periodic table of elements and unwilling to form compounds with other atoms. However, in 1962, Neil Bartlett2 successfully synthesized the first stabilized noble gas compound XePtF6, which breaks the inertness myth of noble gases and opens up a new field in chemistry, the Ng chemistry. From then on a large amount of noble gas compounds have been prepared and investigated theoretically and experimentally3-40. The Ng-containing molecules generally have two typical types of structures, the insertion type XNgY3 (X, Y = H, metal, electronegative atom or group), and the donor–acceptor type NgX (X = metal ions, electropositive atoms or groups). The insertion type Ng compounds HNgY (Y = electron-withdrawing group) such as HArF, HKrF/Cl, HXeCl/Br/I4, and HXeY (Y = OH, SH, OBr, I, CN)5~9 were firstly synthesized by Räsänen and co-workers using photodissociation of HY in a Ng matrix and are characteristic of an ionic-covalent structure with an ionic bond Ng+Y− and a covalent bond (H−Ng)+. Many neutral and ionic Ng compounds of the formula XNgY such as ClXeCN, ClXeNC, BrXeCN, XNgCO+, HNgCO+, XNgCN, XNgNC and HNgCN were also discovered and


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studied theoretically and experimentally10. These XNgY compounds can be considered as a result of Ng atom embedded in the molecule of XY11-23, and have considerable binding energies and so are chemically bound compounds rather than vdW complexes. The Ng atoms have saturated electronic configuration and so easily combine with positively charged ions through strong charge-induced dipole interactions to form cationic compounds such as HeH+, HeNe+, Li+Ng, Be2+Ng, Mg2+Ng, AuXe+, AuXe2+, AuXe42+, FeArn+, SrArn+, and NiArn+ 24, 25, which have been experimentally observed. Gerry26-29 and coworkers discovered the Ng compounds NgMX (X = halogen atom) with transition metals M = Cu, Ag, Au and so on using

cavity

pulsed-jet

FTMW

spectrometer.

The

novel

insertion

actinide-containing molecule CUO produced through laser-ablated uranium atom U reacting with CO can be trapped in the matrix of noble gases to form Ng-containing compounds CUO(Ar), CUO(Kr), CUO(Xe), CUO(Ar)4−nXen , CUO(Ar)4−nKrn and CUO(Kr)4−nXen (n=0~4) and so on30-32, these Ng atoms are located in the coordinate sphere of U around the linear CUO molecule to bind with U through Lewis acid-base donor-acceptor interactions. The electron deficient Be/B-containing compounds are good Ng trappers and can be form quite stable compounds with noble atoms through Lewis acid-base interactions. The BeX molecule with a highly electron-withdrawing



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atom or group X such as O, S and NR (R = F, OH) has largely electropositive Be atom and so can bond with Ng through a charge-induced dipole interaction which has some degree of covalent character. In 1987 the thermochemical stability and vibration frequencies of HeBeO were firstly theoretically studied by Frenking33. Later NgBeO (Ng = Ar, Kr, Xe) were detected and characterized by Thompson and Andrews34 using the pulsed-laser ablation matrix isolation spectroscopic technique. However, HeBeO and NeBeO have not yet been experimentally observed. In addition, BeCO3 35, BeS36, BeNR37-39 (R = H, CH3, CN, etc) are also used as Lewis acids to form stable NgX adducts. Xuefeng Wang40 and coworkers proved experimentally the strong chemical bonding between the Be and Ng atoms in NgBeS. It has been proposed that the Lewis acids SX (X = Be, B+, C2+, N3+, O4+) can strongly bind with Ne41. The majority of Ng-containing molecules are usually linear structures with C∞v or D∞h symmetry. In 2008, HXeOXeH42 was shown as a typical example of C2v symmetry and have been explored experimentally. Similarly FXeOXeF43 has been found to have same symmetry and quantum theory study demonstrates its nonlinear optical character. Here we will report a new kind of Ng compounds with C3v symmetry where the Ng atom binds with the neutral molecule BeH3BeR and its isoelectronic cations BeH3BR+ and BH3BR2+ which have three 3c-2e H-bridged bonds between two Be or B atoms.


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Diboron compounds B2Hm (m = 2, 4, 6) have been studied for the complete understanding of chemical bonding of boron. They are divided into three classes as shown in Scheme 1. The first class containing B2H2 (D∞h) and B2H4 (D2d) has no H-bridged bond. B2H4 (C2v) and B2H6 (D2h) are of the second class with a pair of B-H-B 3-center, 2-electron (3c-2e) H-bridged bonds. The last one is B2H4 (C3v) which has three H-bridged bonds. B2H2 (D∞h) adopts a linear geometry with two degenerate π orbitals44, 45. The main difference between it and C2H2 is that each π orbital in B2H2 (D∞h) is filled with one electron, so its ground state is a triplet 3Σ. B2H4 (D2d) has a vacant 2p orbital on each B atom and so can act as a Lewis acid to combine with a Lewis base, and its Lewis base adducts and metal complexes have been experimentally detected

and investigated46~49. The doubly

hydrogen-bridged butterfly-shaped diborane compound B2H4 (C2v) has similar energy with B2H4(D2d)50. The AIM analysis shows that there is a non-nuclear attractor (a (3, −3) critical point in the electron density) along the B-B bond path, which could act as a non-classical electron donor to form hydrogen bond51 and halogen bond52.

Scheme 1 D∞h



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D2d

C2v

D2h C3v Scheme 1. A schemematic representation of diboron compounds.

More interestingly, B2H4 (C3v) contains a B-H 2c-2e bond and three B-H-B 3c-2e hydrogen-bridged bonds53. On the terminal B atom, there is a lone pair electrons. So it can act as a Lewis base to bond with a Lewis acid. If B2H4 (C3v) gets a proton H+, it becomes perfectly symmetrical B2H5+ (D3h) which has been studied theoretically by Duke and Stephens in 197254. If B2H4 (C3v) loses the lone pair of electrons, a valence orbital on the terminal B atom of the resulted doubly-charged cation B2H42+ (C3v) will be stayed to accept lone pair electrons. Analogously, two isoelectronic species  the singly-charged cation BeH3BH+ (C3v) obtained by replacing the terminal B atom by a Be atom and the neutral molecule BeH3BeH(C3v) by replacing the two B atoms by Be atoms have completely similar electronic and geometrical structures with B2H42+ (C3v), all of them can act as Lewis acids and Ng trappers to combine with the Ng atoms, as


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shown in Scheme 2. In principle, replacing the terminal H of the B−H 2c-2e bond by an electronegative electron-withdrawing group such as F will strengthen the ability of accepting electrons of the terminal B/Be atom, conversely, replacing by an electron donating group such as CH3 will weaken the Lewis acid character of the terminal B/Be atom. Scheme 2

Scheme 2. A schemematic representation and molecular graph of NgBH3BR2+.

In this article, we have predicted and characterized theoretically the three B-H-B hydrogen-bridged bonding compounds between the noble gas atoms Ng (Ng = He-Rn) acting as the Lewis bases and the Lewis acids BH3BR2+, BeH3BR+ and BeH3BeR (R = H, F, CH3). The nature and properties of our studies have exhibited geometrical, energetic, and topological parameters, natural population analysis and vibrational frequencies. It has been demonstrated that these techniques of theoretical chemistry are efficient and feasible for investigating the nature and properties of a wide range of chemical bonding.

2. Computational details All the equlibrium structures, harmonic vibrational frequencies, IR intensities,



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and thermodynamical properties have been calculated at the PBE039, /def2-QZVP57-58, MP212, levels.

The

obtained

13, 18, 59-63,

55-56,

/def2-TZVP64 and MP2/def2-TZVPPD58

geometries

are

further

optimized

at

the

MP2/def2-QZVPPD65 level to improve the accuracy of structures. A quasi-relativistic pseudopotential66 is used for the Xe and Rn atoms. Final energies are calculated at the MP4(SDQ)67, 68/def2-QZVPPD//MP2/def2-QZVPPD level. The energies of the Ng-containing compounds have been corrected for the effect of the basis set superposition error (BSSE) using the counterpoise procedure proposed by Boys and Bernardi69. All the calculations are performed with the Gaussian09 program70. The electron density topological properties, the Mayer bond order (MBO) of the Ng-Be/B bonds of the predicted structures and the electron cloud penetration between the Ng and Be/B atoms are computed using Multiwfn software71 to evaluate the nature of the bonding. The natural atomic charges, Wiberg bond indices (WBIs) and the Natural covalent and ionic bond orders of the Ng-Be/B bonds based on the natural resonance theory (NRT) have been calculated using NBO5.0 program72,

73

. Localized molecular orbital energy decomposition

analysis (LMOEDA) proposed by Su and Li74 have also been done to observe the nature of the Ng-B/Be bonds. All the above analyses are performed at the MP2/def2-QZVPPD level. To determine whether a single-reference-based


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electron correlation procedure is appropriate for our systems, we calculated the CCSD T1 diagnostics75 as an assay of the adequacy of the MP2 method.

3. Results and discussion 3.1. Optimized Geometrical Parameters The optimized equlibrium geometries and structural parameters of the three series of the Ng-compounds NgBH3BR2+, NgBeH3BR+ and NgBeH3BeR and the molecules BH3BR2+, BeH3BR+ and BeH3BeR for the substituent R = F, H and CH3, calculated using the MP2/def2-QZVPPD method, are listed in Table 1. The structural

parameters

calculated

by

means

of

PBE0/def2-QZVP

and

MP2/def2-TZVPPD method are listed in supporting Tables S1 and S2, respectively. All the structures obtained by the four methods PBE0/def2-QZVP, MP2/def2-TZVP, MP2/def2-TZVPPD and MP2/def2-QZVPPD have C3v (C3 for R = CH3) symmetry and a linear Ng−Be/B⋅⋅⋅Be/B−R geometry. Frequency analysis

at

the

three

levels

PBE0/def2-QZVP,

MP2/def2-TZVP

and

MP2/def2-TZVPPD show that all these C3v structures are local energy minima on the PES, except for the two doubly-charged cations BH3BF2+ and BH3BCH32+. Their C3v geometries have two large imaginary frequencies, their stable structures have only two 3c-2e B-H-B H-bridged bonds forming a planar BHBH four-numbered ring, similar to diborane B2H6, as shown in supporting Fig. S1.



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Table 1. Calculated geometrical parameters of the C3v NgBeH3BeR, NgBeH3BR+, and NgBH3BR2+ compounds at the MP2/def2-QZVPPD level. The data of the C3v monomers BeH3BeR, BeH3BR+, and BH3BR2+ are listed in the row marked “No”. All bond lengths are in units of Å. Be/B is connected with Ng atom, and Be'/B' is connected with the R group. NgBeH3BR+

NgBeH3BeR

(Ng:R)

NgBH3BR2+

(No:F) (He:F) (Ne:F) (Ar:F) (Kr:F) (Xe:F) (Rn:F)

Ng-Be 1.537 1.857 2.124 2.256 2.410 2.492

Be-Be' 1.760 1.763 1.762 1.766 1.767 1.768 1.769

Be'-R 1.406 1.407 1.408 1.411 1.412 1.412 1.413

Be-H 1.391 1.393 1.395 1.400 1.401 1.402 1.403

H-Be' 1.625 1.615 1.612 1.604 1.603 1.601 1.600

Ng-Be 1.484 1.705 1.994 2.130 2.298 2.380

Be-B 1.616 1.618 1.620 1.626 1.628 1.631 1.632

B-R 1.293 1.294 1.296 1.300 1.301 1.303 1.304

Be-H 1.457 1.460 1.464 1.472 1.474 1.477 1.479

H-B 1.316 1.314 1.311 1.306 1.304 1.302 1.301

Ng-B 1.231 1.503 1.777 1.917 2.095 2.188

B-B' 1.533 1.526 1.523 1.521 1.520 1.520 1.521

B'-R 1.229 1.231 1.235 1.241 1.244 1.247 1.248

B-H 1.275 1.277 1.282 1.288 1.289 1.288 1.288

H-B' 1.525 1.495 1.471 1.442 1.436 1.428 1.426

(No:H) (He:H) (Ne:H) (Ar:H) (Kr:H) (Xe:H) (Rn:H)

1.548 1.861 2.129 2.261 2.416 2.498

1.754 1.758 1.757 1.761 1.762 1.764 1.764

1.332 1.333 1.333 1.335 1.336 1.336 1.337

1.395 1.396 1.399 1.404 1.405 1.406 1.407

1.604 1.595 1.591 1.584 1.582 1.580 1.579

1.494 1.704 1.995 2.133 2.302 2.385

1.615 1.618 1.620 1.627 1.630 1.633 1.635

1.167 1.166 1.167 1.167 1.167 1.167 1.168

1.488 1.491 1.496 1.504 1.506 1.509 1.512

1.284 1.282 1.279 1.275 1.274 1.272 1.271

1.241 1.498 1.772 1.912 2.091 2.183

1.514 1.510 1.506 1.505 1.506 1.507 1.508

1.189 1.179 1.178 1.174 1.173 1.171 1.171

1.294 1.293 1.302 1.310 1.311 1.313 1.313

1.466 1.438 1.416 1.386 1.378 1.369 1.366

(No:CH3)

-

1.763

1.702

1.393

1.620

-

1.625

1.545

1.465

1.304

-

1.554

1.498

1.267

1.526

(He:CH3)

1.549

1.767

1.703

1.394

1.610

1.495

1.627

1.545

1.467

1.302

1.242

1.545

1.486

1.268

1.490

(Ne:CH3)

1.870

1.765

1.704

1.397

1.607

1.713

1.629

1.546

1.472

1.298

1.515

1.539

1.493

1.275

1.464

(Ar:CH3)

2.134

1.769

1.706

1.401

1.599

2.002

1.635

1.549

1.480

1.294

1.783

1.532

1.498

1.284

1.428

(Kr:CH3)

2.266

1.770

1.707

1.402

1.597

2.139

1.637

1.549

1.482

1.292

1.921

1.531

1.501

1.286

1.419

(Xe:CH3)

2.419

1.771

1.708

1.404

1.595

2.306

1.640

1.550

1.485

1.290

2.098

1.529

1.503

1.287

1.409

(Rn:CH3)

2.500

1.772

1.708

1.404

1.594

2.389

1.642

1.551

1.487

1.289

2.189

1.529

1.505

1.288

1.405


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There are obvious laws on the bond length variation as the Ng atom changes from He to Rn. In each series of NgBH3BR2+, NgBeH3BR+ and NgBeH3BeR for a fixed R, the Ng−Be/B bond length increases from 1.54Å to 2.50Å for the (Be, Be) series, from 1.48Å to 2.39Å for the (Be, B) series, and from 1.23Å to 2.19Å for the (B, B) series as the Ng atom changes from He to Rn. For fixed Ng atom and R, the binding distance r(Ng−Be/B) follows the decreasing order of series (Be, Be) > (Be, B) > (B, B), we will show in the following section that the binding energies greatly increase also in the same order. Fig. 1 shows length variations of the bridge-H bonds Be/B-H and Be′/B′-H, the Be/B-Be/B distance, and the Be′/B′-R bond with respect to Ng for the three series (Be, Be), (Be, B) and (B, B) with R = F, H and CH3 (the Be/B atom is bonded with Ng, the Be′/B′ atom is bonded with R) at MP2/def2-QZVPPD level. We found that the variation amplitudes of these bonds of the (B, B) series are larger than those of the (Be, Be) and (Be, B) series. As the Ng atom varies from No, He to Rn (“No” means the molecule without Ng), the BeH/BH bond always increases, while the Be′H/B′H bond always decreases. Thus when the Ng-containing compounds are formed, the three bridging-H atoms move away from Be/B to Be′/B′. The Be′/B′-R bond increases from No, He to Rn, except that in the compound NgBH3BH2+ this bond decreases, and in NgBH3BCH32+ this bond length for He and Ne is shorter than that of BH3BCH32+ without Ng.



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For NgBeH3BH+, this bond almost does not vary with Ng atoms.

Fig.1 Lengths of the Be/B-Be/B, Be/B-H, Be′/B′-H, and Be′/B′-R bonds with respect to Ng at the MP2/def2-QZVPPD level, bond lengths of the no-Ng molecules are taken as zero.

The distances r(Be, Be), r(Be, B) and r(B, B) for the three series are about 1.5, 1.6 and 1.7Å, respectively. There may be chemical bonds between the two Be/B atoms, this will be clarified in the AIM analysis. The Be/B-Be/B distance increases for the (Be, Be) and (Be, B) series but decreases for the (B, B) series in the order of Ng from No, He to Rn. These phenomena can be understood by the


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bonding characters of these molecules. In a later section the results of electron density topological analysis show that in the (B, B) series the B and B atoms have been bonded to each other and the electron density ρ at the BB bond critical point (BCP) increases from No, He to Rn and so this bond enhances. However, for the (Be, Be) and (Be, B) series there is mostly no bond between the Be and Be atoms and between the Be and B atoms. The terminal substituent R has very small effects on the bond lengths for the (Be, Be) series, small affects for the (Be, B) series, but large influences for the (B, B) series. Thus the Be-containing systems are relatively insensitive to the terminal R group, which may be due to their neutral or small positive charges. 3.2 Binding Energies The BSSE-corrected binding energies between the noble gas atoms and Be/B for the three series NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+ are calculated as the energy differences of the processes Ng + BeH3BeR → NgBeH3BeR, Ng + BeH3BR+ → NgBeH3BR+, and Ng + BH3BR2+ → NgBH3BR2+. Here for NgBH3BR2+ with R = F and CH3, we used the C3v second saddle points BH3BF2+ and BH3BCH32+ to calculate the binding energy. These results are listed in Table 2. The 0K dissociation energy D0 is also calculated using the methods PBE0/def2-QZVP and MP2/def2-TZVPPD, and listed in



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Table 3. The binding energy of PBE0 is 12~22%, 4~9% and 2~8% larger than the MP4(SDQ) energy, respectively for the neutral, singly-charged and doublycharged cationic systems. The MP2/def2-TZVPPD method underestimates the energy for the light noble gases He and Ne but overestimates seriously the binding energy for the heavy Ng atoms Ar~Rn with respect to MP4(SDQ) for neutral systems; for the singly-charged cationic compounds the energies of the Ng atoms He~Kr are also underestimated; but for the doubly-charged cationic systems the results of MP2/def2-TZVPPD are well consistent with those of MP4(SDQ). The MP2/def2-QZVPPD method produces a binding energy close to that of MP4(SDQ) for the cationic systems, but overestimates about 10% the energy of the neutral compounds with heavy Ng atoms from Ar to Rn. Thus by use of the same large basis set def2-QZVPPD MP2 method has almost equal accuracy with MP4(SDQ) for predicting the binding energy.

Table 2. BSSE-corrected Ng−Be/B binding energies (kcal/mol) E1, E2, E3 and E4 calculated by

PBE0/def2-QZVP,

MP2/def2-TZVPPD,

MP4(SDQ)/def2-QZVPPD//MP2/def2-QZVPPD

MP2/def2-QZVPPD

respectively

NgXH3YRq+ (X, Y = Be, B; R = F, H, CH3; q = 0, 1, 2).


for

the

and

compounds

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NgBeH3BR+

NgBeH3BeR

Ng:R E1

E2

E3

E4

E1

E2

He:F

-5.33

-3.59

-4.33

-4.35

-10.32

-8.65

Ne:F

-3.94

-3.27

-3.44

-3.34

-11.98

-9.68

E3

NgBH3BR2+ E4

E1

E2

E3

E4

-9.38

-9.49

-39.68

-36.53

-36.96

-36.82

-11.38

-11.33

-41.81

-38.89

-39.58

-38.75

Ar:F

-9.07

-8.73

-8.78

-8.07

-26.22

-23.96

-25.60

-25.11

-92.17

-89.42

-90.21

-87.94

Kr:F

-10.64

-10.96

-10.30

-9.36

-31.15

-28.98

-30.27

-29.60

-109.81

-107.06

-107.43

-104.78

Xe:F

-12.77

-13.99

-12.31

-11.11

-37.76

-36.11

-36.71

-35.84

-133.72

-132.35

-131.32

-128.47

Rn:F

-13.36

-15.24

-12.92

-11.73

-40.71

-38.63

-39.63

-38.77

-144.69

-142.17

-142.40

-139.59

He:H

-4.88

-3.69

-4.01

-4.01

-9.86

-8.19

-8.99

-9.09

-37.02

-34.76

-35.19

-34.97

Ne:H

-3.77

-3.06

-3.29

-3.17

-11.96

-9.54

-11.32

-11.23

-41.10

-38.79

-39.55

-38.55

Ar:H

-8.74

-8.33

-8.50

-7.77

-25.98

-23.58

-25.28

-24.75

-91.48

-89.35

-90.20

-87.68

Kr:H

-10.26

-10.50

-9.98

-9.01

-30.81

-28.50

-29.84

-29.11

-109.02

-106.84

-107.27

-104.33

Xe:H

-12.31

-12.02

-11.92

-10.69

-37.25

-35.40

-36.08

-35.15

-132.66

-131.77

-130.84

-127.66

Rn:H

-12.91

-14.65

-12.53

-11.30

-40.14

-37.90

-38.93

-37.99

-143.47

-141.40

-142.18

-138.95

He:CH3

-4.77

-3.57

-3.89

-3.91

-9.43

-7.86

-8.60

-8.70

-32.74

-31.09

-31.57

-31.29

Ne:CH3

-3.53

-2.90

-3.10

-2.99

-11.04

-8.88

-10.55

-10.48

-34.23

-33.00

-33.78

-32.78

Ar:CH3

-8.32

-8.08

-8.20

-7.45

-24.12

-22.14

-23.76

-23.22

-79.47

-79.16

-80.05

-77.42

Kr:CH3

-9.79

-10.24

-9.65

-8.66

-28.61

-26.76

-28.06

-27.31

-95.26

-95.16

-95.70

-92.62

Xe:CH3

-11.79

-13.20

-11.56

-10.30

-34.61

-33.37

-33.95

-32.98

-116.72

-118.32

-117.41

-114.04

Rn:CH3

-12.35

-14.43

-12.15

-10.89

-37.28

-35.61

-36.63

-35.64

-126.47

-127.01

-127.42

-124.05

The calculated BSSE correction by PBE0/def2-QZVP method is very small, less than 0.1kcal/mol. The BSSE corrections calculated by MP2/def2-QZVPPD and MP4(SDQ) methods are smaller than 2.5kcal/mol for the (Be, Be) and (Be, B) series and less than 4.3kcal/mol for the (B, B) series. The BSSE correction calculated by MP2/def2-TZVPPD is the largest among all these methods. The doubly-charged cations NgBH3BR2+ have the largest binding energy, about 3~4 times the binding energy of the singly-charged cations NgBeH3BR+, and 8~12 times the binding energy of the neutral compounds NgBeH3BeR, for given Ng atom and R. The binding energy almost linearly increases as the Ng



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atom changes from He to Rn for a given series and R, see Fig.2. However, the Ne atom shows anomaly. For the neutral systems NgBeH3BeR, the binding energy drops from He to Ne, and for the cationic systems NgBeH3BR+ and NgBH3BR2+, the energy has only a small increment from He to Ne. In fact the Ne-anomaly is also reflected in the bond length of Fig.1. The Natural atomic charges in supporting Table S3 and the Natural electron configurations in supporting Table S4 of the Ng atoms in the Ng-containing compounds show that charge transfer from the Ng atom to the three-H-bridged unit increases from Ar to Rn, but decreases from He to Ne. Thus Ne polarizes more difficultly than He. The Ne anomaly was attribute to the fact that Neon possesses occupied valence p orbitals but helium has only one 1s shell76. It was suggested that helium should be moved to group 2 of the periodic table, just above beryllium. The orbital repulsion produced by the valence p electrons of Neon causes the neutral compound unstable, however the electrostatic attraction between the p electrons and the positive charges in the cationic systems relieve this instability.

Table 3. 0K dissociation energy D01 (kcal/mol) calculated by PBE0/def2-QZVP, D02 by MP2/def2-TZVPPD, harmonic vibrational frequency ν of the Ng-Be/B bond calculated by MP2/def2-TZVPPD, and T1 diagnostic by CCSD/def2-QZVPPD//MP2/def2-QZVPPD for the compounds NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+.


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NgBeH3BR+

NgBeH3BeR

Ng:R D01

D02

ν

T1

He:F

3.53

1.88

391.2

Ne:F

2.84

2.27

163.2

NgBH3BR2+

D01

D02

ν

T1

D01

D02

ν

T1

0.0108

8.87

7.13

528.4

0.0117

35.38

32.36

783.6

0.0144

0.0101

11.01

8.71

270.9

0.0108

38.23

35.34

489.0

0.0131

Ar:F

7.84

7.48

193.9

0.0096

25.24

22.93

274.3

0.0102

87.92

85.31

426.6

0.0124

Kr:F

9.48

9.75

173.9

0.0084

30.25

28.04

236.1

0.0089

105.62

103.01

360.0

0.0106

Xe:F

11.71

12.81

168.5

0.0079

36.93

35.21

221.3

0.0083

129.55

128.33

324.4

0.0098

Rn:F

12.35

14.11

162.2

0.0080

39.92

37.76

209.8

0.0083

140.65

138.21

299.0

0.0098

He:H

3.11

1.99

408.2

0.0088

8.37

6.65

553.0

0.0097

32.46

30.09

992.2

0.0109

Ne:H

2.62

2.01

181.9

0.0086

10.90

8.49

306.2

0.0093

37.34

34.97

586.8

0.0108

Ar:H

7.47

7.02

233.8

0.0076

24.87

22.43

330.7

0.0082

87.16

85.04

537.2

0.0095

Kr:H

9.06

9.21

221.0

0.0068

29.76

27.44

298.2

0.0071

104.73

102.55

469.2

0.0081

Xe:H

11.19

10.76

220.1

0.0064

36.25

34.37

285.7

0.0067

128.33

127.45

428.7

0.0077

Rn:H

11.82

13.43

216.3

0.0065

39.19

36.90

276.1

0.0068

139.20

137.15

399.8

0.0080

He:CH3

3.08

1.91

372.4

0.0092

7.98

6.36

507.7

0.0098

27.87

25.94

683.8

0.0130

Ne:CH3

2.50

1.94

156.9

0.0090

10.05

7.90

265.6

0.0095

29.96

28.50

459.0

0.0122

Ar:CH3

7.17

6.85

192.2

0.0083

23.07

21.08

273.1

0.0087

74.22

73.86

414.8

0.0110

Kr:CH3

8.73

9.05

175.0

0.0074

27.63

25.78

237.8

0.0077

89.98

89.84

357.3

0.0094

Xe:CH3

10.80

12.05

171.1

0.0070

33.68

32.42

224.4

0.0073

111.31

112.93

326.5

0.0087a

165.7

a

213.8

a

121.08

121.61

303.2

0.0087a

Rn:CH3 a

11.42

13.31

0.0066

36.40

34.68

0.0070

The T1 diagnostic is obtained by CCSD/def2-TZVPPD//MP2/def2-TZVPPD.

Although the substituent R has small influences on the binding energy of the Ng-Be/B bonds, we can see that the electronegative substituent F and electropositive substituent CH3 have opposite effects. The former enhances the Ng-Be/B bond since it enlarges electron-deficient character of the Lewis acid terminal Be/B center, but the latter weakens the bond since it decreases the acidity of the terminal Be/B center of the Lewis acid. The 0K dissociation energy D0 and the Ng-Be/B stretch frequency also reflect the bond strength. They show all the above laws and characteristics described by the binding energy. The Neon anomaly is also very obvious in the neutral systems and slightly slows down in



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the cationic systems. It is notable that for a given series NgXH3YRq+ (X, Y = Be, B; R = F, H, CH3; q = 0, 1, 2) and Ng atom, the Ng-Be/B stretch frequency of the compounds with the substituent H is larger than that of the compounds with the substituent F and CH3, this is because the mass of H is only 1/19 of F and 1/15 of CH3. For a system with high nondynamical electron correlation its wavefunction possesses multi-reference character, a single-reference-based electron correlation procedure is unreliable. The T1 diagnostic can be used to measure the importance of the nondynamical electron correlation and evaluate the multireference character in the wavefunction. For all the Ng-containing compounds in this work, the CCSD T1 values, listed in Table 3, were much less than the empirical threshold of 0.02. This suggests that the wavefunctions of these systems can be adequately described by single-reference methods.


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Fig. 2 Binding energies (kcal/mol) of the Ng-Be/B bonds by MP4(SDQ) method

3.3 The Nature of the bonding The large binding energy of the Ng-Be/B bond tells that this bond can not be considered simply as a noncovalent interaction, but should has some covalent character or just be a covalent bond, especially for the compounds NgBH3BR2+



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and the compounds with heavy Ng atoms such as Kr, Xe and Rn. The Ng→Be/B bond is a typical donor-acceptor interaction, if the Ng atom strongly polarizes towards the Be/B atom, the covalent character will be obvious. The polarizability of the Ng atoms increases from He to Rn, and the more electron-withdrawing B atom will also enhance the polarizability. Many quantities can be used to analyze the nature of a chemical bond. Bond order is often applied to express strength of a covalent bond, it is defined as half of the difference of electron numbers on bonding and antibonding molecular orbitals, so bond order measures how many electrons are shared by two atoms. Bond order is zero for a typical ionic bond. There are many kinds of bond orders being defined, here we choose two of them, the Wiberg bond indices (WBI) and Mayer bond orders (MBO) to analyze the Ng-involved bond. As shown in Table 4, although the two values for each compound have difference, they show common laws. Thus, the Ng-B bond in the (B, B) series of compounds is much stronger than the Ng-Be bonds in the neutral and singly-charged cationic compounds, and the Ng-Be/B bond enhances from He to Ng, which verifies the former analysis. It is notable that for the doubly-charged cations NgBH3BR2+ with Ng = Ar, Kr, Xe and Rn, both WBI and MBO of the Ng-B bond are close to one, moreover its binding energy is larger than 80kcal/mol, these mean that this bond in these compounds is already a typical covalent bond. For the compounds NgBH3BR2+ with Ng = He and Ne,


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and NgBeH3BR+ with Ng = Xe and Rn, the WBI of the Ng-Be/B is about 0.5, and their binding energies are in the range of 30~40 kcal/mol, thus these bonds should be partially covalent. These expressions will be further confirmed by other properties in the following. After comparing all these data, we feel, it seems that WBI is more reliable than MBO for expressing the bond order of a chemical bond. Table 4. Wiberg Bond Indices (WBI), Mayer bond orders (MBO) and percentage of covalent component (Cov%) in natural bond order of the Ng-Be/B bond in the compounds NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+ calculated by the MP2/def2-QZVPPD method NgBeH3BR+

NgBeH3BeR

Ng:R

NgBH3BR2+

WBI

MBO

Cov%

WBI

NBO

Cov%

WBI

MBO

Cov%

He:F

0.10

0.20

0%

0.13

0.25

4%

0.57

0.53

35%

Ne:F

0.07

0.16

0%

0.10

0.38

6%

0.47

0.61

24%

Ar:F

0.17

0.29

0%

0.26

0.57

15%

0.94

0.95

58%

Kr:F

0.21

0.38

9%

0.34

0.66

20%

1.04

1.00

71%

Xe:F

0.26

0.50

11%

0.44

0.82

27%

1.11

1.13

87%

Rn:F

0.27

0.48

11%

0.47

0.85

30%

1.11

1.16

92%

He:H

0.10

0.19

0%

0.13

0.24

4%

0.56

0.53

34%

Ne:H

0.06

0.17

0%

0.10

0.37

6%

0.47

0.62

24%

Ar:H

0.16

0.29

3%

0.26

0.55

15%

0.94

0.97

57%

Kr:H

0.20

0.36

0%

0.34

0.65

19%

1.06

1.02

69%

Xe:H

0.26

0.47

4%

0.43

0.82

26%

1.14

1.13

86%

Rn:H

0.27

0.47

3%

0.47

0.86

29%

1.14

1.17

90%

He:CH3

0.10

0.20

0%

0.13

0.24

3%

0.56

0.51

34%

Ne:CH3

0.06

0.13

0%

0.10

0.36

5%

0.45

0.58

23%

Ar:CH3

0.16

0.24

0%

0.26

0.51

15%

0.92

0.92

56%

Kr:CH3

0.20

0.34

4%

0.33

0.59

19%

1.03

0.93

68%

Xe:CH3

0.25

0.47

0%

0.43

0.80

26%

1.11

1.13

84%

Rn:CH3

0.26

0.46

3%

0.46

0.84

28%

1.11

1.16

89%



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

The ionic or covalent character of the Ng-Be/B bond can be expressed by two other sets of chemical bonds’ parameters: Natural bond order and its covalent/ionic components based on natural resonance theory (NRT), and electron density topological properties such as electron density ρc, Laplacian ∇2ρc and electron energy density Hc at the Bond critical point (BCP) of a bond. The local electron energy density Hc can tell whether the accumulation of charge at BCP is stabilizing or destabilizing. It is understood that ∇2ρc > 0 and Hc > 0 mean a noncovalent closed-shell interaction, such as ionic bonds, vdW interactions, and hydrogen bonds and so on, ∇2ρc > 0 and Hc < 0 imply a partially covalent bond, and ∇2ρc < 0 and Hc < 0 mean a typical electron-shared covalent bond. The percentage of covalent component (Cov%) in natural bond order of the Ng-Be/B bond is listed in Table 4, and the quantities on electron density and electron cloud penetration ∆r (defined as the difference between the sum of the non-bonded radii of Ng and Be/B atoms and the bond length) are listed in Table 5. It has been shown that the covalent component of the Ng-B bond in the compounds NgBH3BR2+ with Ng = Ar, Kr, Xe and Rn is larger than 50%, electron density ρc is larger than 0.1a.u., Laplacian ∇2ρc is a negative or small positive value, and especially electron energy density Hc is a quite large negative value (less than or close to −0.1a.u.). These data obviously show that the Ng-B bond in these compounds is indeed a typical covalent bond. For the


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compounds NgBH3BR2+ with Ng = He and Ne, and NgBeH3BR+ with Ng = Xe and Rn, the covalent component of the Ng-Be/B bond is larger than 20%, and electron energy density Hc is a non-ignorable negative value (< −0.01a.u.), which implies that these bonds in these compounds have some partially covalent character. The electron cloud penetration ∆r between the noble gas atom and Be/B atom is very large, 1.3~1.8 Å, which also implies that the Ng-Be/B bond is strong. The substituent R has no obvious affects on these properties. The laws observed in the binding energy are also shown in these properties, and the Neon anomaly is also obvious. Table 5. Electron cloud penetration distance ∆r(Å), electron density ρ, Laplacian ∇2ρ and electron energy density H on the BCPs of the Ng-Be/B bond in the compounds NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+ calculated by the MP2/def2-QZVPPD method. NgBeH3BR+

NgBeH3BeR

Ng:R

NgBH3BR2+

∆r

ρ

∇2ρ

H

∆r

ρ

∇2ρ

H

∆r

ρ

∇2ρ

H

He:F

1.483

0.025

0.32

0.015

1.279

0.034

0.37

0.016

1.571

0.101

0.96

-0.029

Ne:F

1.405

0.017

0.23

0.012

1.316

0.033

0.38

0.016

1.578

0.085

0.81

-0.023

Ar:F

1.656

0.026

0.21

0.006

1.536

0.044

0.29

0.002

1.743

0.120

0.31

-0.099

Kr:F

1.711

0.026

0.18

0.003

1.585

0.044

0.22

-0.004

1.761

0.122

0.05

-0.116

Xe:F

1.790

0.028

0.16

0.000

1.646

0.046

0.17

-0.010

1.773

0.124

-0.25

-0.123

Rn:F

1.790

0.027

0.14

-0.002

1.638

0.044

0.14

-0.012

1.728

0.118

-0.22

-0.079

He:H

1.473

0.024

0.30

0.015

1.254

0.033

0.35

0.015

1.546

0.098

0.90

-0.029

Ne:H

1.401

0.017

0.22

0.012

1.306

0.033

0.38

0.016

1.570

0.086

0.81

-0.024

Ar:H

1.651

0.025

0.21

0.006

1.525

0.044

0.29

0.002

1.736

0.122

0.29

-0.102

Kr:H

1.705

0.026

0.18

0.003

1.571

0.044

0.22

-0.004

1.754

0.124

0.03

-0.119

Xe:H

1.784

0.028

0.15

0.000

1.632

0.045

0.17

-0.009

1.766

0.126

-0.27

-0.127

Rn:H

1.784

0.027

0.13

-0.001

1.624

0.044

0.13

-0.011

1.723

0.121

-0.24

-0.082



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Page 24 of 48

He:CH3

1.479

0.024

0.30

0.015

1.282

0.033

0.35

0.016

1.580

0.096

0.93

-0.024

Ne:CH3

1.399

0.016

0.22

0.011

1.324

0.032

0.37

0.016

1.583

0.080

0.79

-0.019

Ar:CH3

1.654

0.025

0.21

0.006

1.542

0.043

0.28

0.002

1.752

0.116

0.32

-0.093

Kr:CH3

1.708

0.026

0.18

0.003

1.589

0.043

0.22

-0.003

1.772

0.118

0.07

-0.110

Xe:CH3

1.788

0.027

0.15

0.000

1.650

0.044

0.17

-0.009

1.786

0.121

-0.22

-0.121

Rn:CH3

1.788

0.026

0.13

-0.001

1.642

0.043

0.13

-0.011

1.745

0.117

-0.24

-0.084

a

b

c

d

e

f

g

h

i

j

Fig.3 Contour line diagrams of electron density Laplacian for some typical Ng-compounds, containing (a) XeBeH3BeH, (b)~(d) NgBeH3BH+ for Ng = Kr/Xe/Rn, and (e)~(j) NgBH3BH2+ for Ng from He to Rn. Green solid lines show areas of charge depletion (∇2ρ>0) and blue dotted lines show areas of charge concentration (∇2ρ 0) and concentration (∇2ρ < 0). A concentration of electron density between two atoms implies that there is a covalent bond formed between them. Contour line diagrams of the electron density Laplacian in a symmetry plane of the C3v molecules for all the Ng-containing compounds are shown in supporting Fig. S2 (a)~(i), containing 54 diagrams for all the 54 compounds. Since the Ng-Be/BH3Be/B part of the contour lines is not affected by the substituent R, here we take the contour lines of some typical compounds with R = H are shown in Fig.3. These graphs imply some important bonding characters. For the neutral Ng-containing compounds NgBeH3BeR, there is no electron density concentration between the noble gas and Be atoms and between the two Be atoms; an exception is XeBeH3BeR with a small negative-Laplacian area between Xe and Be, implying the Xe-Be bond has a little covalent character. The singly-charged cations NgBeH3BR+ with Ng = Kr/Xe/Rn have a large negative-Laplacian area between Ng and Be, thus the Ng-Be bond has typical covalent character. For the doubly-charged cationic compounds NgBH3BR2+, there are quite large areas of electron density concentration between Ng = Ar/Kr/Xe/Rn and B atoms and also a small area of charge concentration between He and B atoms, which implies that the Ng-B bond is a typical covalent bond. Here the Neon anomaly also occurs. It is notable that there are large fish-shaped



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

areas of negative Laplacian between the two B atoms, this area is larger and larger from He to Rn, except for the Neon anomaly. This fact implies that in the doubly-charged cations these B−B bonds are typical electron-shared covalent bonds. Here the bonding natures indicating by the Laplacian of electron density agree with the topological parameters on BCPs and other bonding parameters such as binding energies and bond orders. To have a deeper insight into the nature of the Ng−Be/B bonds in these systems, the various terms of the binging energies have been evaluated using the LMOEDA method, and the results are listed in Table 6. Here we sum the exchange and repulsion energies into one term. Different from the general intermolecular weak interactions such as hydrogen bond, halogen bond, pnicogen bond and chalcogen bond, where the absolute largest term is the exchange repulsion energy, here in the Ng-Be/B bonds the largest energy term in absolute value is the polarization energy, which occupancy about 70% of the total attractive energies (including electrostatic, polarization and dispersion terms) for the neutral compounds and about 90% of the total attractive energies (including polarization and dispersion terms) for the cationic systems. In the neutral systems, the second largest term is the dispersion energy accounting for about 20% of the total attraction energy, and the smallest one is the electrostatic term. The substituent R has almost no influence on the energy terms for all these


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systems. It is notable that the total MP2 energy without the BSSE correction by LMOEDA is very close to the non-BSSE-corrected MP2 binding energy calculated using the supermolecule method in subsection 3.2. In the LMOEDA scheme, the electrostatic, exchange, and repulsion terms are isolated from the Heitler–London interaction energy derived from an antisymmetric product of the monomer HF spin orbitals, any effect due to charge transfer should be included in the polarization energy. So polarization energy may be particularly large in the scheme of LMOEDA for systems with strong charge transfer, such as the Ng-containing compounds39. However since charger transfer is a natural result of polarization, including charger transfer in polarization energy should be reasonable. It is remarkable that in the cationic compounds the electrostatic term is repulsive energy, only polarization and dispersion terms are attractive. Here the Neon anomaly occurs again, the electrostatic term for most Ne-containing cationic structures is again attractive. The polarization energy dominant in the binding energy of the Ng-Be/B bond for these Ng-containing compounds suggests that the Ng electron cloud strongly polarizes toward the Be/B atom such that the Ng-Be/B bonds exhibit covalent character. This result of EDA is not surprising but reasonable since the character of very large polarization revealed by EDA has been confirmed by the above other bonding parameters such as bond orders, the covalent/ionic ratio and



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electron density properties of the Ng-Be/B bonds. Here for the NgBH3BR2+ compounds with Ng from Ar to Rn, the polarization energies Epol are very large in absolute value, less than −110kcal/mol, the Ng-B bond should be a typical covalent bond as pointed out by the above analyses; for NgBH3BR2+ with Ng = He and Ne, and NgBeH3BR+ with Ng = Xe/Rn the polarization energies are also large in absolute value, about −50kcal/mol, thus the Ng-B/Be bond has partial covalent character. Table 6. Components (kcal/mol) of the binding energies in the Ng-Be/B bonds calculated using the LMOEDA method at the MP2/def2-QZVPPD level, including the terms of electrostatic interaction (Eele), exchange repulsion (Eex+rep), polarization(Epol) and dispersion (Edis). NgBeH3BR+

NgBeH3BeR

(He:F)

Eele

Eex+rep

Epol

Edis

Etotal

Eele

Eex+rep

Epol

Edis

-0.61

5.49

-7.59

-1.79

-4.50

0.23

5.09

-13.44 -1.38

5.53

-6.27

NgBH3BR2+ Etotal

Eele

Eex+rep

Epol

Edis

Etotal

-9.50

0.87

20.23

-53.02

-5.51

-37.43

-15.82 -2.21 -11.94 -1.15 23.14

-55.62

-7.69

-41.32

(Ne:F)

-1.04

-2.19

-3.97

0.01

6.08

(Ar:F)

-1.55 11.51 -14.65 -4.74

-9.43

1.07

12.52 -35.81 -4.06 -26.28 1.67

40.35 -122.99 -12.36 -93.32

(Kr:F)

-1.54 12.95 -16.73 -5.66 -10.98 1.66

13.84 -41.68 -5.03 -31.20 2.93

41.92 -141.87 -14.66 -111.68

(Xe:F)

-1.35 15.23 -19.93 -6.91 -12.95 2.56

15.72 -49.82 -6.24 -37.76 4.67

43.30 -167.43 -16.83 -136.29

(Rn:F)

-1.19 15.18 -20.24 -7.23 -13.48 2.85

15.54 -52.30 -6.82 -40.73 4.95

40.91 -175.46 -18.07 -147.67

(He:H)

-0.65

5.58

-7.42

-1.68

-4.17

0.21

5.15

-13.22 -1.25

21.47

-52.9

-4.83

-35.66

(Ne:H)

-1.14

5.67

-6.19

-2.13

-3.79

-0.02

6.22

-15.89 -2.16 -11.84 -1.56 24.81

-57.09

-7.38

-41.22

(Ar:H)

-1.68 11.65 -14.43 -4.66

-9.12

1.09

12.65 -35.65 -3.99

1.54

42.63 -125.27 -12.18 -93.27

(Kr:H)

-1.67 13.06 -16.45 -5.57 -10.63 1.68

13.97 -41.39 -4.95 -30.68 2.96

44.22 -144.12 -14.6 -111.54

(Xe:H)

-1.44 15.26 -19.55

-12.53 2.61

15.82 -49.31 -6.16 -37.04 5.01

45.42 -169.46 -16.93 -135.96

(Rn:H)

-1.28 15.21 -19.84 -7.14 -13.05 2.91

15.65 -51.71 -6.76 -39.92 5.35

42.83 -177.17 -18.25 -147.25

-6.8

-9.10 -25.9

(He:CH3) -0.69

5.61

-7.29

-1.70

-4.06

0.15

5.14

-12.71 -1.29

-0.18 22.90

-50.36

-4.54

-32.18

(Ne:CH3) -1.15

5.61

-5.94

-2.14

-3.62

-0.12

6.17

-14.97 -2.16 -11.08 -2.57 25.55

-51.85

-6.74

-35.61

(Ar:CH3) -1.76 11.64 -13.99 -4.72

-8.83

0.84

12.58

-33.7

(Kr:CH3) -1.78 13.08 -15.96 -5.65 -10.31 1.39

-8.72

0.61

-4.12 -24.41 -0.41 44.17 -115.57 -11.62 -83.44

13.91 -39.12 -5.11 -28.93 0.84


45.93 -133.01 -13.97 -100.21

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(Xe:CH3) -1.59 15.36 -19.03 -6.91 -12.18 2.27

15.82 -46.65 -6.36 -34.92 2.85

47.25 -156.57 -16.27 -122.73

(Rn:CH3) -1.43 15.31 -19.30 -7.25 -12.67 2.56

15.65 -48.87 -6.95 -37.61 3.31

44.71 -163.56 -17.56 -133.10

The three H-bridged bonds BHBs have some notable characters. The distribution of BCPs and bond paths depends strongly on the Ng atoms and the substituent R. The AIM molecular graphs calculated by the MP2/def2-QZVPPD method have four types for the molecules without Ng atom and six types for the Ng-containing compounds. Fig.s 4 and 5 plot the molecular graphs, and Table 7 list the types of molecular graphs of various molecules. The electron density, Laplacian and electron energy density at the BCPs related to the three H-bridged bonds are listed in supporting Table S5 for the molecules without Ng atom, and in supporting Tables S6~14 for the Ng-containing compounds. We see that for the neutral systems BeH3BeR and NgBeH3BeR, and the singly-charged cationic systems BeH3BR+, NgBeH3BF+, and NgBeH3BCH3+ with Ng from He to Kr, the three H-bridged bonds BHBs form a cage structure. But for the doubly-charged cations BH3BR2+ and NgBH3BR2+, each bridged-H atom only bonds with the electron-deficient B atom; and for the remaining singly-charged cationic Ng compounds, the bridged-H atom also only bonds with the B atom. Moreover, for the doubly-charged cations BH3BR2+ and NgBH3BR2+, and for the singly-charged cationic systems BeH3BH+ and NgBeH3BH+, the B-B or Be-B bond has been formed. It is notable that in the molecules without Ng atom the Be/B−B and Be/B−H bonds have only partial covalent character except for the



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B−H bond in type IV which is a typical covalent bond. In the Ng-containing compounds, all the Be−H, Be−B and H−H bonds in the sub-unit Be/BH3Be/B of these systems are partially covalent with ρ(BCP) less than 0.1a.u., a positive Laplacian ∇2ρ and a small negative electron energy density H, and the B−H and B−B bonds in sub-unit Be/BH3Be/B have typical covalent characters with large ρ(BCP) larger than 0.1a.u., a negative electron energy density H, and a negative or small positive Laplacian ∇2ρ.

I

II

III

IV

Fig.4 Four types of molecular graphs for BeH3BeR, BeH3BR+, and BH3BR2+ systems calculated by MP2/def2-QZVPPD. The purple, orange and green points stand for the nucleus, BCPs and CCPs, respectively.


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Ia

Ib

II

III

IV

IV′

Fig.5 Six types of molecular graphs for NgBeH3BeR, NgBeH3BR+, and NgBH3BR2+ systems calculated by MP2/def2-QZVPPD. The purple, orange and green points stand for the nucleus, BCPs and CCPs, respectively.

Table 7 The types of the molecular graphs of various molecules NgBH3BR2+ (R=F, H, CH3)

NgBeH3BR+

NgBeH3BeR No:F

I

No:H

I

No:CH3

I

No:F

II

No:H

III

No:CH3

II

No:R

IV

He:F

Ia

He:H

Ia

He:CH3

Ia

He:F

Ia

He:H

IV′

He:CH3

III

He:R

IV

Ne:F

Ia

Ne:H

Ia

Ne:CH3

Ia

Ne:F

II

Ne:H

IV′

Ne:CH3

II

Ne:R

IV

Ar:F

Ia

Ar:H

Ib

Ar:CH3

Ia

Ar:F

II

Ar:H

IV′

Ar:CH3

II

Ar:R

IV

Kr:F

Ib

Kr:H

Ib

Kr:CH3

Ia

Kr:F

II

Kr:H

IV′

Kr:CH3

II

Kr:R

IV

Xe:F

Ib

Xe:H

Ib

Xe:CH3

Ia

Xe:F

II

Xe:H

IV′

Xe:CH3

IV′

Xe:R

IV

Rn:F

Ib

Rn:H

Ib

Rn:CH3

Ia

Rn:F

III

Rn:H

IV′

Rn:CH3

IV′

Rn:R

IV



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3.4 Thermodynamic stability and vibrational frequencies The enthalpy change ∆H and Gibbs free energy change ∆G for the process Ng + XH3YRq+ → NgXH3YRq+ (X, Y = Be, B; q = 0, 1, 2) at gas phase and 298.15 K and 1atom were evaluated using the MP2/def2-TZVPPD method and listed in Table 8. For BH3BR2+ (R = F, CH3) here and in Tables 2 and 3 we use different reference states. In Tables 2 and 3 of subsection 3.2, we calculated the binding energy between Ng and Be/B, the reference monomer should have the same configuration within the Ng compound, so there we use the C3v three-H-bridged molecules BH3BR2+ (R = F, CH3) as the reference states although they are unstable. But here we calculate the thermodynamic functions to inspect the stability of the formed Ng-containing compounds, we must use the stable C2v two-H-bridged molecules HBH2BR2+ (R = F, CH3) (see Fig. S1) as reference states to calculate ∆H and ∆G. This treatment causes the results of F and CH3 much different from those of R = H. The values ∆H and ∆G for the substituent H are much negative than those of F and CH3, moreover the processes forming He/NeBH3BR2+ (R = F, CH3) are endothermic and non-spontaneous. For the neutral systems the processes forming He/NeBeH3BeR are also non-spontaneous although exothermal. For all the other Ng-containing compounds the forming processes are exothermal and spontaneous. It is notable that ∆H and ∆G are more and more negative from He to Rn for a given series


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and R, and from CH3 to H to F for the neutral and singly-charged cationic systems and a given Ng atom, following the laws of the binding energies. Here again the Neon anomaly occurs. From these data we found that the forming processes of the doubly-charged cations NgBH3BR2+ are most exothermal and most spontaneous, and the processes of the neutral compounds are least exothermal and least spontaneous. Thus the cationic Ng-containing compounds are more easily observed experimentally. In addition, ∆H is always more negative than ∆G because the entropy change ∆S is negative for the formation process of the Ng-containing compound. Table 8. Reaction enthalpy change (∆H, kcal/mol), Gibbs free energy change (∆G, kcal/mol) at 298.15 K and 1atm for the process Ng + XH3YRq+ → NgXH3YRq+ (X, Y = Be, B; q = 0, 1, 2), Ng + HBH2BR2+ (R = F, CH3) → NgBH3BR2+, calculated at the MP2/def2-TZVPPD level. NgBeH3BeR HeBeH3BeF

∆H -3.02

∆G

NgBeH3BR+

4.12

HeBeH3BF

+ +

∆H -8.18

∆G -1.14

NgBH3BR2+ HeBH3BF

2+ 2+

∆H

∆G

17.20

24.39

NeBeH3BeF

-2.57

4.15

NeBeH3BF

-9.90

-2.91

NeBH3BF

13.30

21.82

ArBeH3BeF

-7.89

-0.80

ArBeH3BF+

-24.59

-18.11

ArBH3BF2+

-37.47

-28.94

KrBeH3BeF

-10.14

-3.06

KrBeH3BF+

-30.28

-23.86

KrBH3BF2+

-56.66

-48.09

+

-37.94

-30.92

XeBH3BF

2+

-82.62

-74.06

-41.81

-35.47

RnBH3BF2+

-94.64

-86.14

2+

-31.98

-23.74

2+

-37.53

-29.10

XeBeH3BeF

-13.19

-6.82

XeBeH3BF

RnBeH3BeF

-14.48

-8.15

RnBeH3BF+

4.38

+

HeBeH3BeH NeBeH3BeH

-2.69 -2.38

4.28

HeBeH3BH

+

NeBeH3BH

+

-7.71 -9.71

-0.75 -2.78

HeBH3BH NeBH3BH

2+

ArBeH3BeH

-7.51

-0.50

ArBeH3BH

-24.15

-17.05

ArBH3BH

-88.26

-80.40

KrBeH3BeH

-9.69

-2.70

KrBeH3BH+

-29.70

-22.66

KrBH3BH2+

-107.24

-99.41

-6.35

+

-30.13

2+

-132.73

-124.97

2+

-144.52

-136.83

XeBeH3BeH RnBeH3BeH

-12.64 -13.89

-7.65

XeBeH3BH

+

RnBeH3BH

-37.11 -40.89

-34.59


XeBH3BH RnBH3BH


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

HeBeH3BeCH3

-2.57

4.55

HeBeH3BCH3+ +

-7.38

Page 34 of 48

-0.36

HeBH3BCH32+ 2+

18.83

27.39

NeBeH3BeCH3

-2.22

4.44

NeBeH3BCH3

-9.05

-2.08

NeBH3BCH3

15.57

24.55

ArBeH3BeCH3

-7.24

-0.17

ArBeH3BCH3+

-22.71

-15.58

ArBH3BCH32+

-30.56

-21.18

KrBeH3BeCH3

-9.42

-2.36

KrBeH3BCH3+

-28.01

-20.93

KrBH3BCH32+

-48.07

-39.32

-5.40

XeBeH3BCH3

+

-28.11

XeBH3BCH3

2+

-71.77

-63.04

RnBeH3BCH3

+

RnBH3BCH3

2+

-82.69

-73.38

XeBeH3BeCH3 RnBeH3BeCH3

-12.40 -13.66

-6.69

-35.13 -38.71

-31.73

The three-H-bridged molecules BeH3BeR, BeH3BR+ and BH3BR2+ and their Ng adducts have some important infrared models related to the Ng-X bond and the three bridging-H atoms, of which the modes with relatively strong IR intensity can be used as the fingerprint for future experimental identification of these molecules. They have C3v symmetry except for BH3BF2+ and BH3BCH32+. The reducible representation formed by the atomic small vibrations scans the irreducible representations Γv = 5A1⊕5E for the Ng-containing compound, and Γv = 4A1⊕4E for the non-Ng molecules, they are all infrared, of which one A1 corresponds to the Ng-X bond stretch mode and two A1 and three E modes correspond to the three-bridging-H vibrations. The Ng-X bond stretch frequencies are listed in Table 3, the corresponding infrared intensities are small, only several km/mol. Among the three-bridging-H vibrational modes one A1 mode ν1(A1) and one E mode ν2(E) have main component in the direction of the molecular C3 axis, but another A1 mode ν3(A1) and two E modes ν4(E) and ν5(E) have main component perpendicular to the C3 axis, as shown in Fig. 6. For some


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molecules, the two A1 modes ν1(A1) and/or ν3(A1) can couple with the vibrations of the atoms in the molecular C3 axis and so split into two or four similar A1 modes. The frequencies and infrared intensities of all the three-bridging-H vibrational modes calculated by MP2/def2-TZVPPD are listed in supporting Table S15, they usually have large IR intensities and can be easily observed in the infrared spectroscopy of these three-bridging-H molecules.

ν1(A1)

ν3(A1)

ν2(E)

ν4(E)

ν5(E)

Fig.6 Five infrared vibration modes of three bridging-H atoms.

For the neutral molecules BeH3BeR and their Ng-compounds NgBeH3BeR, the mode with the largest intensity is ν1(A1) in the range 1240~1300cm−1, followed by ν5(E) 1810~1880cm−1, ν2(E) 550~880 cm−1 and ν3(A1) 1850~ 1900cm−1, and the mode of the smallest absorption is ν4(E) 1080~1120cm−1. The



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formation of the Ng-containing compounds causes the frequencies ν1(A1), ν2(E) and ν4(E) blue shift but ν3(A1) and ν5(E) red shift. For the singly-charged cations BeH3BR+ and NgBeH3BR+, ν1(A1) is also the largest absorption mode with frequencies 1640~1660cm−1 for R = F, 1430~1460cm−1 for R = H and 1510~1530 cm−1 for R = CH3, but it is usually red-shifted upon formation of the Ng compounds. For the doubly-charged cations BH3BR2+ and NgBH3BR2+, the mode with the largest infrared intensity is also ν1(A1) in the ranges 1390~1520 cm−1 for R = F, 1080~1280 cm−1 and 1460~1610 cm−1 for R = H, and 1290~1340 cm−1 for R = CH3. The more detailed information about these vibrations are found in the supporting table. We found that there is no obvious law in the vibration frequencies and IR intensities of these modes as the Ng atoms change from He to Rn.

4. Conclusions We have reported the structures, vibrational frequencies, stability, binding energies and bonding natures of the Lewis acid-base adducts NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+ of the noble gas atoms with three series of 3c-2e three-H-bridged molecules and ions BeH3BeR, BeH3BR+ and BH3BR2+ (R = F, H, CH3) using quantum chemical calculations such as geometrical optimization, vibrational analysis, AIM topological analysis, NBO analysis and EDA. At both


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PBE0 and MP2 levels, these Ng-containing compounds exhibit kinetic stability, linear structure and C3v symmetry (except R = CH3). The structures and properties of these systems are insensitive to the substituent group R. The binding energy of the Ng-Be/B bond largely increases from He to Rn and with increasing positive charges of the Lewis acids, but has only small increment as the substituent electronegativity increases from CH3 to H to F. The doubly-charged cationic compounds NgBH3BR2+ have the largest binding energies in the range of 35~130kcal/mol from He to Rn, the Ng-B bonds should be typical covalent bonds. The singly-charged cationic systems NgBeH3BR+ have also large binding energies 9~38kcal/mol from He to Rn, the Ng-Be bonds for Kr, Xe and Rn have large covalent characters. The neutral compounds NgBeH3BeR have the smallest binding energies 4~13kcal/mol, the Ng-Be bonds are closed-shelled interactions. Polarization energy plays a dominant role in binding energy, implying that the Ng-Be/B bonds have typical covalent characters. The three bridging-H atoms in the molecules and ions with and without the noble gas atoms show some common infrared vibrational modes with large IR intensity, which can be detected in spectroscopy experiments as fingerprint of the three bridging-H atoms.



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Associated content Supporting Information Figure S1 plots the geometries of HBH2BF2+ and HBH2BCH32+. Figure S2 shows contour line diagrams of the electron density Laplacian for all the Ng-containing compounds. Table S1 and S2 list geometrical parameters of the C3v compounds NgBeH3BeR, NgBeH3BR+ and NgBH3BR2+, and BeH3BeR, BeH3BR+ and BH3BR2+, calculated by the PBE0/def2-QZVP and MP2/def2-TZVPPD methods, respectively. Table S3 lists natural atom charges of the Ng-containing compounds calculated using the MP2/def2-QZVPPD method. Table S4 lists the natural electron configuration of Ng in the Ng-containing compounds calculated by MP2/def2-QZVPPD. Table S5~S14 list electron density topological properties at the BCPs, RCPs and CCPs of the three-H-bridged systems with and without the Ng atoms obtained by MP2/def2-QZVPPD level. Table S15 lists the vibrational frequencies and IR intensities of the infrared-active three-bridging-H modes of the three-H-bridged systems with and without the Ng atoms calculated by the MP2/def2-TZVPPD method. This material is available free of charge via the Internet at http://pubs.acs.org.

Author Information Corresponding Author: [email protected], [email protected]


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Theoretical Predictions of C3v Symmetric Three-H-Bridged Noble

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