Density Functional Studies on Photophysical Properties and Chemical Reactivities of the Triarylboranes: Effect of the Constraint of Planarity
Jun-Ling Jin,[a] Hai-Bin Li,[a] Tian Lu,[b] Yu-Ai Duan,[a] Yun Geng,[a] Yong Wu,[a] Zhong-Min Su*[a]
[a] Institute of Functional Material Chemistry, Faculty of Chemistry Northeast Normal University, Changchun (China). Corresponding E-mail:
[b] Department of Chemistry and Chemical Engineering, School of Chemical and Biological Engineering, University of Science and Technology, Beijing (China).
Supporting Information
CONTENTS
Theoretical methods of reaction activity descriptor and electrostatic potentials Page S2-S3
Figure S1. Contour maps of the Laplacian of the electron density for comppund 2. Page S4
Figure S2. The simplest arylborane compound, C6H5BH2. Page S4
Table S1. Selected bond lengths (Å) at both optimized S0 geometries for compounds Mes3B, 1 and 2, together with the experimental values of 1-2. Page S5
Table S2 Computed absorption (λabs, nm) of compound 1 using different functional with 6-31G(d,p) in THF, together with experimental results. Page S5
Table S3. Computed Wiberg bond index (WBI) values for compounds Mes3B, 1 and 2 at B3PW91/6-31G(d,p) level. Page S6
References Page S6
Theoretical methods of reaction activity descriptor and electrostatic potentials
Reaction activity descriptors: Within the framework of density functional theory (DFT) the chemical potential (μ) [1], hardness (η) [2], and global softness (S) of an N electron system can be defined as follows:
(1)
(2)
(3)
where E is the energy of a molecule under investigation, v(r) is the external potential of the molecule under consideration. On the basis of finite difference approximation, the values of μ, hardness η, and global electrophilicity ω [3] are commonly determined by vertical ionization energy (IE) and electron affinity (EA) from the following formulas:
(4)
(5)
(6)
(7)
The Fukui function f(r) [4] and local softness s(r) [5] are two of the most commonly used reactivity descriptors which allow understanding and predicting the relative reactivities of different sites in a molecule. The Fukui function is defined as the derivative of electron density, ρ(r), with respect to the number of electrons at a constant external potential, v(r). Local softness is defined as the derivative of ρ(r) with respect to μ, at constant v(r).
(8)
(9)
The large values of the f(r) and s(r) for the given site of a molecule under consideration indicate high reactivity. On the basis of finite difference approximation, Fukui function can be calculated unambiguously for two situations:
Nucleophilic attack: (10)
Electrophilic attack: (11)
For studying reactivity at the atomic level, in the finite difference approximation, the condensed Fukui function [6] of an atom k in a molecule can be expressed as:
(12)
(13)
in which qk(N), qk(N+1), and qk(N-1) are the elecrtonic populations on atom k in the N, N+1, and N-1 electron systems, respectively. In the present study, the condensed descriptors were calculated using CHELPG population [7]. The condeced electrophilicity, ωk [5], also provide useful and important prediction and interpretation for the chemical reactivity. The formula is as follows:
(14)
Dual descriptor, Δf(r) [8], is another useful function used to reveal reactive sites. The definition of the dual descriptor Δf (r) has close relationship with Fukui function:
(15)
Unlike Fukui function, the two types of reactive sites can be revealed simultaneously via Δf. The sites with positive Δf is favored for nucleophilic attack, whereas sites with negative Δf is preferred for electrophilic attack.
All the above-mentioned indices, including Fukui functions and related quantities, have been proved by previous works that they essentially provide meaningful and reliable reactivity trends for soft-soft interactions [9]. Therefore, in the present work, all these indices have been computed at B3PW91/6-31G(d,p) level to predict the chemical reactivities of the studied compounds.
Electrostatic potentials: The electrostatic potential V(r) measures the electrostatic interaction between a unit point charge placed at r and the molecule under consideration [10]. Its formula can be expressed as:
(16)
where ZA and RA are the charge and position of nucleus A, respectively. The V(r) were mapped onto the molecular surface with the isosurfaces of the electronic equal to ρ(r)=0.001 a.u.. A positive (negative) value implies that current position is dominated by nuclear (electronic) charges. The electrostatic potential is frequently used to predict the reactive sites and the packing motifs of a molecule.[11]
Figure S1. Contour maps of the Laplacian of the electron density for 2, in the plane defined by atoms B, C1 and C2. The dash lines denote Laplacian is negative, while the solid lines denote Laplacian is positive.
Figure S2. The simplest arylborane compound, C6H5BH2. The calculation level is B3PW91/6-31G(d,p). For the twisted model (right), the dihedral angle between the BH2 subunit and benzene plane was fixed at 90 degree for the optimization.
Table S1. Selected bond lengths (Å) at both optimized S0 geometries for Mes3B, 1 and 2, together with the experimental values of 1-2. Calculations were performed at the B3PW91/6-31G(d,p) level in vacuum.
Mes3B / 1 / 2S0 / Expt. a / S0 / Expt. / S0 / Expt.
B-C1 / 1.583 / 1.579 / 1.523 / 1.520 / 1.525 / 1.522
C1-C2 / 1.419 / 1.414 / 1.412 / 1.414 / 1.415 / 1.417
C1-C3 / 1.419 / 1.418 / 1.412 / 1.410 / 1.415 / 1.416
C2-C4 / 1.397 / 1.392 / 1.398 / 1.395 / 1.397 / 1.393
C3-C5 / 1.397 / 1.391 / 1.398 / 1.390 / 1.398 / 1.398
C4-C6 / 1.395 / 1.389 / 1.391 / 1.381 / 1.391 / 1.387
C5-C6 / 1.394 / 1.383 / 1.391 / 1.386 / 1.391 / 1.381
C2-C8 / 1.512 / 1.513 / 1.538 / 1.537 / 1.540 / 1.535
C3-C7 / 1.512 / 1.515 / 1.538 / 1.539 / 1.540 / 1.535
a The experimental results were from J. Am. Chem. Soc. 1986, 108, 4235.
Table S2. Computed absorption (λabs, nm) of compound 1 using different functional with 6-31G(d,p) in THF, together with experimental results.
Funct. / B3LYP / B3PW91 / PBE0 / BMK / CAM-B3LYP / B971 / M06 / Exp.λabs / 310.8 / 310.9 / 301.5 / 281.0 / 271.6 / 309.8 / 302.0 / 320
Table S3. Computed Wiberg bond index (WBI) values for the three compounds at B3PW91/6-31G(d,p) level.
Bonds / Mes3B / 1 / 2B-C1 / 0.888 / 0.949 / 0.951
C1-C2 / 1.351 / 1.337 / 1.333
C1-C3 / 1.352 / 1.337 / 1.333
C2-C4 / 1.421 / 1.414 / 1.416
C3-C5 / 1.420 / 1.414 / 1.416
C4-C6 / 1.393 / 1.427 / 1.426
C5-C6 / 1.394 / 1.428 / 1.426
C3-C7 / 1.027 / 0.982 / 0.982
C2-C8 / 1.028 / 0.982 / 0.982
References:
[1] Yang W, Parr RG (1985) Proc Natl Acad Sci U S A 82:6723-6726.
[2] Parr RG, Pearson RG (1983) J Am Chem Soc 105:7512-7516.
[3] a) Parr RG, Donnelly RA, Levy M, Palke WE (1977) J Chem Phys 68:3801-3807; b) Parr RG, Szentpály Lv, Liu S (1999) J Am Chem Soc 121:1922-1924.
[4] a) Parr RG, Yang W (1984) J Am Chem Soc 106:4049-4050; b) Ayers PW, Parr RG (2000) J Am Chem Soc 122:2010-2018.
[5] Chattaraj PK, Sarkar U, Roy DR (2006) Chem Soc Rev 106:2065-2091.
[6] Yang W, Mortier WJ (1986) J Am Chem Soc 108:5708-5711.
[7] Breneman CM, Wiberg KB (1990) J Comput Chem 11:361-373.
[8] Morell C, Grand A, Toro-Labbé A (2004) J Phys Chem A 109:205-212.
[9] a) Mondal P, Hazarika KK, Deka RC (2003) PhysChemComm 6:24-27; b) Domingo LR, Aurell MJ, Pérez P, Contreras R (2002) J Phys Chem A 106:6871-6875.
[10] Naray-Szabo G, Ferenczy GG (1995) Chem Soc Rev 95:829-847.
[11] a) Duarte DR, Vallejos M, Peruchena N (2010) J Mol Model 16:737-748; b) Geng Y, Li H-B, Wu S-X, Su Z-M (2012) J Mater Chem 22:20840-20851.
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