8446
J. Phys. Chem. A 2008, 112, 8446–8454
A Computational Characterization of Boron-Oxygen Multiple Bonding in
HNdCH-CHdCH-NH-BO
Joseph D. Larkin,*,†,⊥ Krishna L. Bhat,# George D. Markham,§ Tony D. James,+
Bernard R. Brooks,⊥ and Charles W. Bock‡,§
Department of Chemistry, Bloomsburg UniVersity of PennsylVania, Bloomsburg, PennsylVania 17815,
Department of Chemistry and Biochemistry, School of Science and Health, Philadelphia UniVersity, School
House Lane and Henry AVenue, Philadelphia, PennsylVania 19144, The Institute for Cancer Research, Fox
Chase Cancer Center, 7701 Burholme AVenue, Philadelphia, PennsylVania 19111, National Heart, Lung, and
Blood Institute, The National Institutes of Health, Building 50, Bethesda, Maryland 20851, Department of
Chemistry, Widener UniVersity, Chester, PennsylVania 19013, and Department of Chemistry, UniVersity of
Bath, Bath BA2 7AY, U.K.
ReceiVed: January 7, 2008; ReVised Manuscript ReceiVed: June 3, 2008
Structures, relative energies, and bonding characteristics for various conformers of 3-imino-N-(oxoboryl)prop1-en-1-amine,HNdCH-CHdCH-NH-BO,andthecorrespondingborocycle(-HNdCH-CHdCH-NH-B-)O
are discussed using results from second-order Møller-Plesset (MP2) perturbation theory with the
Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets. These MP2 results
are compared to those from computationally efficient density functional theory (DFT) calculations using the
LDA, PBE, TPSS, BLYP, B3LYP, BVP86, OLYP, O3LYP, and PBE1PBE functionals in conjunction with
the economical Pople-type 6-311++G(d,p) basis set to evaluate the suitability of these DFT/6-311++G(d,p)
levels for use with larger boron-containing systems. The effects of an aqueous environment were incorporated
into the calculations using COSMO methodology. The calculated boron-oxygen bond lengths, orbital
compositions, and bond orders in all the (acyclic) HNdCH-CHdCH-NH-BO conformers were consistent
with the presence of a boron-oxygen triple bond, similar to that found in H-BtO and H2N-BtO. The
(-HNdCH-CHdCH-NH-B-)O borocycle is predicted to be planar (C2V symmetry), and it is ∼30 kcal/
mol lower in energy than any of the (acyclic) HNdCH-CHdCH-NH-BO conformers; the boron-oxygen
bond in this borocycle has significant double bond character, a bonding scheme for which there has been
only one experimental structure reported in the literature (Vidovic, D.; et al. J. Am. Chem. Soc. 2005, 127,
4566-4569).
Introduction
The chemistry of borates rivals that of the silicates and
phosphates in terms of variation and complexity.1 Indeed, the
importance of boron derivatives in chemistry,2,3 biochemistry,4,5
medicinal chemistry,6–10 and material science11–15 is increasing
rapidly, and advancing the understanding of boron bonding
continues to be an important topic among chemists.16,17 The
boron-oxygen single bond in tricoordinated boronic acids
(1.35-1.38 Å) and esters (1.31-1.35 Å)3 is quite strong, ∼120
kcal/mol;3 not surprisingly, single bond lengths in tetracoordinated species are significantly longer (1.43-1.47 Å), and there
is an associated loss in bond strength (by as much as 12 kcal/
mol).3 Compounds containing boron-oxygen double bonds, that
is, oxoboranes (R-BdO), have been invoked as reactive
intermediates for some time,18 but they have defied most
attempts at isolation and characterization;18–23 the oxophilicity
of boron makes the formation of a B-O-B linkage more facile
than formation of a boron-oxygen multiple bond.16,17 Recently,
* To whom correspondence should be addressed. Telephone: (570) 3894154. E-mail: jlarkin@bloomu.edu.
† Bloomsburg University of Pennsylvania.
⊥ The National Institutes of Health.
# Widener University.
§ Fox Chase Cancer Center.
+ University of Bath.
‡ Philadelphia University.
however, Vidovic et al.24 reported the synthesis of a novel
borocycle, LBO f AlCl3 (where L is a chelating β-diketiminate
{HC(CMe)2(NC6F5)2}-), in which the boron-oxygen bond was
stabilized with a Lewis acid (AlCl3). LBO f AlCl3 had
significant double bond character; for example, single-crystal
X-ray diffraction data collected at 153 K showed that the
boron-oxygen bond length in this borocycle was 1.304(2) Å
compared to 1.354(5)-1.365(4) Å25,26 in singly bonded N2B-O
fragments (diaza- and triazaboroles). Furthermore, calculations
in vacuo performed by the same authors at the B3LYP/6311+G(d) computational level on a (-N(C6F5)dC(CH3)CHdC(CH3)-N(C6F5)-B-)O borocycle (in the absence or in
the presence of a AlCl3 moiety) indicated that the boron-oxygen
functionality in this structure was also predominantly doubledbonded. However, ongoing computational studies of boron
compounds have raised concerns regarding the extent to which
the popular B3LYP functional using split-valence Pople-type
basis sets adequately describes some aspects of boron bonding,27–30
suggesting that more rigorous calculations are required to
confirm the Vidovic et al.24 results.
Our particular interest in oxoboranes stems from the results
of our recent computational investigation29 of several (neutral)
reaction mechanisms for the protodeboronation (hydrolysis) of
BoroGlycine, H2N-CH2-B(OH)2
10.1021/jp800125p CCC: $40.75 2008 American Chemical Society
Published on Web 08/15/2008
Boron-Oxygen Multiple Bonding in HNdCH-CHdCH-NH-BO
H2O + H2N-CH2-B(OH)2 f B(OH)3 + H2N-CH3 (1)
and for the 1,2-carbon-to-nitrogen shift of the -B(OH)2 moiety
H2N-CH2-B(OH)2 f H3C-NH-B(OH)2
(2)
Surprisingly, a species of the form H3C-NH2-B(OH)(dO),
in which the boron-oxygen double bond was stabilized by a
water molecule, proved to be an intermediate in the 1,2rearrangement mechanism, leading to this study of boron-oxygen
multiple bonding.
In this article, we report results from a computational
investigation of the structures, relative energies, and boron
bonding in various acyclic conformers of 3-imino-N-(oxoboryl)prop-1-en-1-amine, HNdCH-CHdCH-NH-BO, and the
related borocycle (-HNdCH-CHdCH-NH-B-)O, which
has the same cyclic backbone as the structure synthesized by
Vidovic et al.24 Conformers of HNdCH-CHdCH-NH-BO
are expected to involve a boron-oxygen triple bond;22,31–38 see
Scheme 1A. Such oxoborons (R-BtO) have been known
experimentally for more than 30 years;19,22,31,37–42 they are
intermediates in the oxidation of solid borons, boranes, and other
boron-based materials and release large amounts of energy when
used in the synthesis of boron compounds, making them
favorable candidates to be employed as propellants in airbreathing combusters and as rocket fuels.33,43 Although lifetimes
of these species are only ∼100 ms,35 several small oxoboranes
have been prepared, and their bonding has been characterized
in the gas phase and in the solid state; experimental and
computational boron-oxygen distances in such structures are
relatively short,34,41,42,44 for example, ∼1.2 Å for H-BtO.34,42,45
On the other hand, the experimental and computational results
reported by Vidovic et al.24 suggest that the (-NHdCHCHdCH-NH-B-)O borocycle is more likely to involve a
boron-oxygen double bond; see Scheme 1B. Thus, a rigorous
computational investigation of the model compounds HNdCHCHdCH-NH-BO and (-NHdCH-CHdCH-NH-B-)O
provides an opportunity to characterize various aspects of
boron-oxygen multiple bonding within a consistent molecular
framework.5,46,47
Computational Methods
Equilibrium geometries for the structures described in this
article were obtained using second-order Møller-Plesset (MP2)
perturbation theory48 with the frozen core (FC) option, which
neglects core-electron correlation; the Dunning-Woon correlation-consistent (cc) basis sets, cc-pVDZ, aug-cc-pVDZ, and
cc-pVTZ, were employed for the majority of the computations.49–52
Frequency analyses were performed analytically to confirm that
the optimized structures were local minima on the PES and to
correct reaction enthalpies and free energies to 298 K. The gasSCHEME 1
J. Phys. Chem. A, Vol. 112, No. 36, 2008 8447
phase calculations were carried out using the GAUSSIAN 03
suite of programs.53 Bonding was analyzed with the aid of
natural bond orbitals (NBOs).54–57
Calculations using MP2 methodology with cc basis sets are
not currently practical for investigations of the larger boron
derivatives of primary chemical interest. Density functional
theory (DFT) with Pople-style basis sets58,59 provide an economical alternative, but the reliability of specific functional/
basis set combinations for describing the incredibly diverse
range1 of boron chemistry has yet to be fully established.27–30
Thus, our MP2/cc results were compared to those from several
more computationally efficient DFT/6-311++G(d,p) levels
using the following functionals: LDA(SVWN5);60 BLYP and
B3LYP, which incorporate the dynamical functional of Lee,
Yang, and Parr (LYP),61 coupled with Becke’s pure DFT
exchange functional (B);62 BVP86, which uses Perdew’s 1986
functional63,64 with local correlation replaced by that suggested
by Vosko et al. (VWN);60 OLYP65 and O3LYP,66 which were
constructed from the novel OPTX exchange functional;
PBE1PBE,67,68 which makes use of the one-parameter generalized-gradient approximation (GGA) PBE functional69 with a
25% exchange and 75% correlation weighting; and TPSS, the
nonempirical meta-generalized gradient approximation (MGGA)
functional recently developed by Staroverov, Scuseria, Tao, and
Perdew.70
Results from continuum solvation models were employed to
assess the effects of a bulk aqueous environment on the gasphase results;71 such continuum models only provide a description of long-range interactions and have significant limitations
in describing protic solvents.72,73 Thus, in some cases, explicit
water molecules were used to provide a description of the shortrange/site-specific effects of an aqueous environment. The
conductor-like screening model (COSMO), pioneered by Klamt
and co-workers,74–77 was employed for the continuum calculations in an aqueous medium using the PQS ab initio program
package 3.2 on a PQS Quantum Cube;78 we employed the
default settings in the COSMO module of this software which
were specifically tailored to COSMO theory76,77 and optimized
for the BVP86 functional, that is, the BP86 functional63,64 in
which local correlation was replaced by VWN,60 using the svpand tzvp (Ahlrichs) basis sets.79,80 These COSMO results were
also compared to the corresponding gas-phase results using
natural resonance theory (NRT).54–57
Results and Discussion
Since no experimental data are currently available for any
conformers of HNdCH-CHdCH-NH-BO or for
(-NHdCH-CHdCH-NH-B-)O, we initially considered
H-BO (C∞h) and H2N-BO (Cs) at a variety of computational
levels to establish “baseline” structural and bonding parameters.
A.1. H-BO and H2N-BO. A significant amount of
experimental22,31–38,42 and computational data33,45,81–87 has been
reported in the literature for hydroboron monoxide, H-BO, an
intermediate/byproduct of a variety of reactions involving boron
compounds.88 Calculated bond lengths of H-BO at the MP2(FC)/
cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/cc-pVTZ
levels are shown in Figure 1, and vibrational frequencies at the
MP2(FC)/aug-cc-pVDZ level are listed in Table 1S of the
Supporting Information. Structural parameters at a variety of
more-rigorous computational levels are given in Table 2S
(including selected results that incorporate core-electron correlation (FULL),53,89,90 which has virtually no effect on the
calculated geometrical parameters); the analogous structural
parameters at several DFT/6-311++G(d,p) levels are shown
8448 J. Phys. Chem. A, Vol. 112, No. 36, 2008
Figure 1. Optimized structures of HBO, H2NBO, and H2NB(OH)2
(distances are in Å).
in Table 3S. The calculated boron-oxygen bond lengths, 1.218,
1.222, and 1.214 Å at the MP2(FC)/cc-pVDZ, MP2(FC)/augcc-pVDZ, and MP2(FC)/cc-pVTZ levels, respectively, all
overestimate this length compared to that obtained from
microwave spectroscopy, 1.2007 ( 0.0001 Å;34,41,42,44 indeed,
as shown by DeYonker et al.,45 quite sophisticated computational
methodology and large basis sets are required to systematically
approach the microwave result. NBOs54–57 for H-BO at the
MP2/cc-pVDZ, MP2/aug-cc-pVDZ, and MP2/cc-pVTZ levels
consistently showed the presence of one σ- and two π-boronoxygen bonding orbitals. NRT54–57 calculations with the BVP86
functional using the tzvp(svp) basis sets60,63,64,79,80 found the
boron-oxygen bond order to be ∼3.00 in H-BO, consistent
with the presence of a BtO bond; the NRT-derived covalent/
ionic contributions to the total bond order were 1.24/1.76 at
the BVP86/tzvp level; the Löwdin bond order91–93 for the
boron-oxygen bond in H-BO was also calculated and found
to be slightly lower, 2.80(2.86), at the BVP86/tzvp(svp) levels;
see Table 4S. We also list in Table 4S selected covalent bond
orders derived from the atomic overlap matrix (AOM) using
the Bader94 atoms-in-molecules (AIM) approach to the analysis
of electron density.95–97
One measure of the energy content stored in the boron-oxygen
triple bond of R-BtO monomers can be obtained from the
thermochemical parameters for its trimerization to the heteroaromatic ring (R3B3O3) boroxine structure.35,98–100 The
calculated values of ∆H0298 for the conversion of hydroboron
monoxide to H3B3O3 (D3h) are extremely exothermic, -91.1
and -93.2 kcal/mol in vacuo at the MP2(FC)/cc-pVDZ and
MP2(FC)/aug-cc-pVDZ levels, respectively. The calculated
boron-oxygen bond lengths in this boroxine are all the same,
for example, 1.388 Å at the MP2(FC)/cc-pVDZ level and 1.394
Å at the MP2(FC)/aug-cc-pVDZ level, nearly 0.2 Å longer than
the corresponding values in H-BtO. The calculated NRT
BVP86/svp boron-oxygen bond order in H3B3O3 was 1.46
(0.45/1.01), only about 50% of the corresponding value in
H-BtO, suggestive of significant electron delocalization.91,98
The Löwdin bond order was 1.45 at this level, in good
agreement with the NRT value; see Table 4S.
In COSMO aqueous media76,77 at the BVP86/tzvp level, the
boron-oxygen bond length of H-BtO increased from the
corresponding gas-phase value but only by ∼0.005 Å; the
boron-oxygen bond order, 3.00 (1.16/1.84), remained essentially the same. Thus, there appears to be relatively little
difference in the geometrical structure or in the bonding of
H-BtO as a result of any long-range effects of bulk solvation.
The calculated values of ∆H0298 for the conversion of hydroboron monoxide to boroxine in COSMO aqueous media at the
BVP86/tzvp level was -92.0 kcal/mol compared to -99.3 kcal/
mol in vacuo at this level. To assess short-range/site-specific
effects of an aqueous environment, we microsolvated the
Larkin et al.
optimized MP2(FC)/cc-pVDZ gas-phase structure of H-BtO
with a few explicit water molecules initially positioned in the
vicinity of the BtO moiety. Although an exhaustive search of
all possible conformers of these complexes was not practical at
this level, several distinct stable structures were located for 2and 3-water cases. The lowest-energy forms we found in these
hydrated complexes involved an oxygen atom of one of the
water molecules effectively bound to the boron atom in H-BO;
the calculated B-Ow distance was 1.68(1.67) Å, the B-O
distance was 1.26(1.27) Å, and the HBO angle was 140.4°(138.5°)
for the 2(3)-water complexes; see Figure 1S in the Supporting
Information; thus, there is a significant change from the linear
gas-phase geometry of H-BtO upon microsolvation. As would
be expected, the calculated values of ∆H0298 for the formation
of the lowest-energy 2(3)-water H-BO complexes were substantially exothermic, -18.8(-31.6) kcal/mol.
Since the borocycle described by Vidovic et al.24 and the
model (acyclic) HNdCH-CHdCH-NH-BO and (cyclic)
(-NHdCH-CHdCH-NH-B-)O structures all involve
boron-nitrogen bonds in addition to boron-oxygen bonds, we
also geometry optimized aminoboron monoxide, H2N-BO,5 to
assess the effect of a proximal boron-nitrogen bond on the
boron-oxygen structural and bonding parameters. To the
authors’ knowledge, no experimental synthesis, isolation, or
characterization of H2N-BO, nor any rigorous computational
studies of this small molecule, have been reported. The
calculated boron-oxygen separation in H2N-BO was ∼0.01
Å longer than it was in H-BtO at the MP2(FC)/(cc-pVDZ,
aug-cc-pVDZ, and cc-pVTZ) computational levels; see Figure
1. Selected structural parameters for H2N-BO at a variety of
DFT/6-311++G(d,p) computational levels are listed in Table
3S and show similar increases for the boron-oxygen distance
relative to the corresponding values for H-BtO. The NBOs
of H2N-BO still involve one σ- and two π-bonds at all of the
MP2(FC)/cc levels included in this investigation. The NRT
boron-oxygen bond order in H2N-BO, 2.90 (1.19/1.71) at the
BVP86/tzvp level, was only ∼3% lower than the corresponding
value in H-BtO; the corresponding Löwdin bond order, 2.61,
was ∼7% lower than that in H-BtO. Furthermore, the
weighting of the resonance structure of the form H2NdBdO,
associated with the interaction of the nitrogen lone pair orbital
and an antibonding boron-oxygen orbital, was only ∼9.2% at
this level. Thus, in the gas phase, the boron-oxygen bond in
H2N-BO appears to be best described as a triple bond.
We also calculated thermodynamic parameters for the trimerization of aminoboron monoxide to the boroxine structure
(H2N)3B3O3 (D3h);35 the calculated values of ∆H0298 in the gas
phase were -134.7, -130.2 and -125.3 kcal/mol at the
MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and BVP86/tzvp
computational levels, respectively, significantly more exothermic
than that for the analogous trimerization of hydroboron monoxide. The boron-oxygen bond lengths in the product boroxine
structure were all the same, 1.396 Å at the MP2(FC)/cc-pVDZ
level and 1.400 Å at the MP2(FC)/aug-cc-pVDZ level, slightly
longer than the corresponding values in H3B3O3 but indicative
of significant electron delocalization;98–103 the corresponding
boron-nitrogen bond lengths were 1.409 and 1.413 Å,
respectively.
As might be expected, in the COSMO aqueous media
model,76,77 the calculated boron-oxygen bond length in
H2N-BO increased, but only by ∼0.01 Å at the BVP86/tzvp
level compared to the analogous value in vacuo; the resulting
NRT boron-oxygen bond order, 2.55 (0.98/1.57), however,
suggests that in this aqueous model, the boron-oxygen bonding
Boron-Oxygen Multiple Bonding in HNdCH-CHdCH-NH-BO
J. Phys. Chem. A, Vol. 112, No. 36, 2008 8449
in H2N-BO is best described as intermediate between a double
and triple bond. Indeed, the NRT weighting of the H2NdBdO
bonded resonance structure, 41.7%, was more than four times
greater than the corresponding weighting in vacuo. Micosolvation of the gas-phase structure of H2N-BO with a few water
molecules positioned at various points around the boron-oxygen
functional group, followed by reoptimization of the complex,
often resulted in the corresponding amino boronic acid,
H2N-B(OH)2, hydrogen-bonded to the remaining water molecules. The hydration reaction
H2N-BtO + H2O f H2N-B(OH)2
(3)
is highly exothermic in vacuo; for example, ∆H0298 is -44.2,
-41.7, -46.3, and -43.0 kcal/mol at the MP2(FC)/cc-pVDZ,
MP2(FC)/aug-cc-pVDZ, MP2(FC)/cc-pVTZ, and BVP86/tzvp
levels, respectively. In COSMO aqueous media at the BVP86/
tzvp level, ∆H0298 is -34.7 kcal/mol, ∼8 kcal/mol less negative
than the corresponding value in vacuo. We also located the fourmembered cyclic transition state for this hydrolysis reaction in
vacuo, and the value of ∆H‡ was only +4.8 kcal/mol relative
to the separated reactants at the MP2(FC)/cc-pVDZ level. The
corresponding value of ∆H‡ at the BVP86/tzvp level was
predicted to be slightly lower, +2.2 kcal/mol, whereas in
COSMO aqueous media, ∆H‡ was found to be slightly higher,
+5.5 kcal/mol. The calculated values of ∆H0298 for the
trimerization of H2N-BtO to the corresponding boroxine
structure in this COSMO aqueous medium model was -103.0
kcal/mol compared to -125.3 kcal/mol in vacuo.
The boron-nitrogen bond length in H2N-BO was calculated
to be 1.41, 1.40, and 1.39 Å in vacuo at the MP2/cc-pVDZ,
MP2/aug-cc-pVDZ, and MP2/cc-pVTZ levels, respectively; see
Figure 1. The NRT bond order at the BVP86/tzvp level was
1.10 (0.53/0.59), generally consistent with the presence of a
boron-nitrogen single bond with ∼10% double-bond character.
The calculated B-N distance decreased in COSMO aqueous
medium by ∼0.05 Å at the BVP86/tzvp level, and the NRT
bond order increased to 1.45 (0.61/0.84). These findings suggest
that the boron-nitrogen bond in this model media is most
appropriately described as intermediate between a single and
double bond.
A.2. (Acyclic) HNdCH-CHdCH-NH-BO Conformers.
With the above reference data on H-BO and NH2-BO in hand,
an extensive conformational search of the (acyclic) HNdCHCHdCH-NH-BO potential energy surface (PES) at the MP2/
cc-pVDZ level was performed. A variety of conformers with
different cis/trans arrangements about the heavy-atom backbone
were located; these conformers typically differed in energy
among each other by less than ∼5 kcal/mol. Two of these
conformers, 1a and 1b, are shown in Figure 2; 1a (TTT) (Cs)
is the lowest-energy acyclic structure we found, whereas
conformer 1b (CCT) (Cs), which is ∼3 kcal/mol higher in energy
than 1a, see Table 1, has a more “cyclic-like” structure, but the
terminal nitrogen atom was intentionally oriented to eliminate
any possibility of an intramolecular boron-nitrogen dative
bonding interaction. Infrared vibrational frequencies of 1a and
1b at the MP2(FC)/aug-cc-pVDZ level are listed in Table 1S
of the Supporting Information. Calculated xyz-coordinates for
a variety of HNdCH-CHdCH-NH-BO conformers are given
in Table 5S of the Supporting Information.
The calculated boron-oxygen distances for 1a in vacuo,
1.226, 1.231, and 1.223 Å at the MP2(FC)/cc-pVDZ, MP2(FC)/
aug-cc-pVDZ, and MP2(FC)/cc-pVTZ levels, respectively, see
Figure 2, are nearly the same as those in H2N-BtO at the
corresponding computational levels; see Figure 1. An examina-
Figure 2. Optimized structures of the acyclic conformers 1a and 1b
of HNdCH-CHdCH-NH-BO and the borocycle 1c (-NHdCHCHdCH-NH-B-)O (distances are in Å). AIM calculations using the
MP2/cc-pVDZ density find the expected molecular graph for 1c (12
attractors, 12 critical points on attractor interaction lines, and 1 ring
point).
TABLE 1: Relative Energies, E(kcal/mol) (Values
Thermally Corrected to 298 K in Parentheses) for the
Acyclic Conformers 1a (TTT) and 1b (CCT) of
NHdCH-CHdCH-NH-BO and the Cyclic Conformer 1c
(CCC) of (-NHdCH-CHdCH-NH-B-)O at the
MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, and MP2(FC)/
cc-pVTZ Computational Levels
E(kcal/mol)
level
1c (CCC)
MP2(FC)/cc-pVDZ
MP2(FC)/aug-cc-pVDZ
MP2(FC)/cc-pVTZ
0.0(0.0)
0.0(0.0)
0.0(0.0)
1a (TTT)
1b (CCT)
+31.4(+29.8) +34.8(+33.3)
+32.6(+31.1) +35.3(+33.8)
+33.9(+32.3) +36.9(+35.4)
tion of the NBOs in 1a at the MP2(FC)/cc-pVDZ and MP2(FC)/
aug-cc-pVDZ levels confirmed the existence of a boron-oxygen
σ-bonding orbital and predicted a pair of π-bonding orbitals,
similar to what was found in both H-BtO and H2N-BtO.
The NRT (BVP86/tzvp) bond order for 1a, 2.91 (1.21/1.70),
was almost identical to that for H2N-BtO, 2.90 (1.19/1.71),
and the corresponding Löwdin bond order, 2.63, was nearly the
same as that in H2N-BtO, 2.61; see Table 4S. Furthermore,
the weighting of the BtO-bonded resonance structure was
∼62.5% compared to only ∼8.4% for the BdO-bonded structure
at the BVP86/tzvp level. Thus, the boron-oxygen bond in 1a
is best described as a triple bond in vacuo.
Thermodynamic parameters for the conversion of 1a to the
corresponding (NHdCH-CHdCH-NH)3B3O3 boroxine structure42 were also computed; the calculated value of ∆H0298 was
-141.1 kcal/mol at the MP2(FC)/cc-pVDZ computational level
compared to -134.7 kcal/mol for the analogous conversion of
NH2-BO.
In the context of the COSMO BPV86/tzvp aqueous medium
model, the characteristics of the boron-oxygen bonding in all
of the (acyclic) HNdCH-CHdCH-NH-BO derivatives that
we investigated were similar to those that we observed for
H2N-BO; for example, the boron-oxygen distance in 1a
increased slightly, by ∼0.007 Å compared to its value in vacuo,
and the NRT bond order, 2.63 (1.03/1.60), was lower than its
value in vacuo, 2.91 (1.21/1.70), as was the corresponding
Löwdin bond order, 2.55 compared to 2.63. Thus, the
boron-oxygen bonding of NHdCH-CHdCH-NH-BO (1a)
Larkin et al.
8450 J. Phys. Chem. A, Vol. 112, No. 36, 2008
in a COSMO aqueous media model appears to be intermediate
between a double and triple bond.
Short-range/site-specific effects of an aqueous environment
on the structure of NHdCH-CHdCH-NH-BO (1a) were also
investigated using a few explicit water molecules initially
positioned in the vicinity of the boron-oxygen moiety of the
optimized gas-phase MP2(FC)/cc-pVDZ structure. An exhaustive search of all possible conformers of these complexes was
obviously not possible, but a variety of different initial arrangements of the water molecules were considered; of course, this
does not ensure that we obtained the global minimum on the
appropriate PES. As was noted above for H2N-BtO, in some
instances,thesehydratedadductsofNHdCH-CHdCH-NH-BO
(1a) (in vacuo, as well as in COSMO aqueous media) converted
to the corresponding boronic acid during the reoptimization; in
other adducts, the NHdCH-CHdCH-NH-BO structure
remained intact, although in these conformers, the boron-oxygen
bond length was relatively long, ∼1.28 Å. Indeed, the hydration
reaction
HNdCH-CHdCH-NH-BO (1a) + H2O f
HNdCH-CHdCH-NH-B(OH)2
∆H0
was calculated to be highly exothermic; for example,
298
was -49.4 and -46.4 kcal/mol at the MP2(FC)/cc-pVDZ and
MP2(FC)/aug-cc-pVDZ levels, respectively, some 5 kcal/mol
more exothermic than the analogous reaction for H2N-BtO.
We also located the transition state for this hydration reaction
in vacuo; the value of ∆H‡ for the formation of the resulting
four-membered ring structure was only +1.8 kcal/mol above
the separated reactants, compared to +4.8 kcal/mol for
H2N-BtO.
The boron-nitrogen bonding in 1a is also similar to that in
H2N-BO; the compositions of the boron-nitrogen NBOs for
NHdCH-CHdCH-NH-BO (1a) and H2N-BO were nearly
the same at the computational levels that we employed, and
the calculated BVP86/tzvp NRT bond order in 1a, 1.09 (0.49/
0.60), was almost identical to that in H2N-BO, 1.10 (0.51/
0.59). The boron-nitrogen bond order for NHdCH-CHdCHNH-BO (1a) in a COSMO BPV86/tzvp aqueous medium was
1.34 (0.55/0.79), attesting to the increased importance of a
NdBdO resonance structure in such an environment.
A.3. (-NHdCH-CHdCH-NH-B-)O Borocycle. The
(-NHdCH-CHdCH-NH-B-)O borocycle, 1c, see Figure
2, was ∼30 kcal/mol lower in energy than any of the acyclic
conformers of HNdCH-CHdCH-NH-BO that we found at
the MP2/cc-pVDZ, MP2/aug-cc-pVDZ, and MP2/cc-pVTZ
levels; see Table 1. Infrared frequencies of 1c, calculated at the
MP2/aug-cc-pVDZ level, are listed in Table 1S of the Supporting Information. The transition state that connects the borocycle
1c and the acyclic conformer 1b of HNdCH-CHdCH-NH-BO
was also located; see Figure 2S of the Supporting Information.
It was 40.5 and 41.0 kcal/mol higher in energy than 1c at the
MP2/cc-pVDZ and MP2/aug-cc-pVDZ levels, respectively. The
calculated boron-oxygen separation in the borocycle 1c, 1.266,
1.277, and 1.265 Å at the MP2(FC)/cc-pVDZ, MP2(FC)/augcc-pVDZ, and MP2(FC)/cc-pVTZ levels, respectively, is ∼0.04
Å longer than it is in the acyclic HNdCH-CHdCH-NH-BO
derivatives at these levels. An examination of the NBOs in 1c
at the MP2(FC)/cc-pVDZ and MP2(FC)/aug-cc-pVDZ levels
confirms the existence of a boron-oxygen σ-bonding orbital
and one π-bonding orbital. The NRT boron-oxygen bond order
for 1c at the BVP86/tzvp level, 2.28 (0.95/1.33), is significantly
lower than the corresponding value for the acyclic conformer,
1a, 2.91 (1.21/1.70) at this level; the Löwdin bond order for 1c
is 2.32, compared to 2.63 for 1a and 2.61 in H2N-BtO. Thus,
in vacuo, it appears reasonable that the boron-oxygen bond in
1c can be regarded as predominately a double bond.
In the COSMO BVP86/tzvp aqueous medium model, the
length of the boron-oxygen bond in 1c increased by ∼0.03 Å
to 1.297 Å compared to its value in vacuo; the corresponding
bond order decreased by ∼0.3 to 1.95 (0.72/1.23); the Löwdin
bond order was only 1.50. We also optimized 1c in the presence
of two and three explicit water molecules, initially positioned
in the vicinity of the BO moiety; although our computer
resources only allowed a limited exploration of these PESs, the
resulting B-OB distances in the reoptimized complexes tended
to be relatively long, for example, ∼1.30 Å at the MP2(FC)/
cc-pVDZ level. Thus, the short-range/site-specific effects of
explicit water molecules on this borocycle appear to be less
dramatic than those that we observed in the acyclic derivatives.
Nevertheless, these findings suggest that the boron-oxygen
bond in 1c has a significant degree of double-bond character in
an aqueous environment.
The calculated value of ∆H0298 for the hydration reaction
(-NHdCH-CHdCH-NH-B-)O (1c) + H2O f
(-NHdCH-CHdCH-NH-B-)(OH)2
was -32.6 kcal/mol at the MP2(FC)/cc-pVDZ level, much less
exothermic than that for the hydrolysis of the acyclic structure
HNdCH-CHdCH-NH-BO (1a) or for H2N-BtO, which
is a reflection of the stability of the borocycle 1c compared to
that of 1a. We located the transition state for this hydrolysis;
the value of ∆H‡ was +7.6 kcal/mol at the MP2(FC)/cc-pVDZ
level, slightly higher than the corresponding values for
H2N-BtO (+4.8 kcal/mol) and HNdCH-CHdCH-NH-BO
(1a) (+1.8 kcal/mol).
The two B-N bonds in this novel borocycle 1c have the same
length, that is, there is no structural distinction between the
“formal” N-B single bond and the N:B dative bond, a reflection
of the extent of electron delocalization in this conformer. The
boron-nitrogen distances in 1c, 1.539, 1.534, 1.529, and 1.538
Å at the MP2(FC)/cc-pVDZ, MP2(FC)/aug-cc-pVDZ, MP2(FC)/
cc-pVTZ and BPV86/tzvp levels, respectively, are ∼0.13 Å
longer than the corresponding boron-nitrogen separation in 1a
and 1b.
For a more direct comparison with the experimental results
of Vidovic et al.,24 we also geometry-optimized one conformer
of the (-N(C6F5)dC(CH3)-CHdC(CH3)-N(C6F5)-B-)O borocycle at the MP2/cc-pVDZ level in vacuo; see Figure 3. The
computed boron-oxygen bond length, 1.264 Å, was marginally
shorter than the corresponding distance in NHdCH-CHdCHNH-BO (1c) at this computational level but significantly shorter
than the calculated value at the B3LYP/6-311+G(d) level, 1.292
Å, and even shorter than the experimental X-ray distance in
the crystal structure of (-N(C6F5)dC(CH3)-CHdC(CH3)N(C6F5)-B-)O f AlCl3, 1.304(2) Å.24 The corresponding
boron-oxygen bond length for an acyclic conformer of
N(C6F5)dC(CH3)-CHdC(CH3)-N(C6F5)-BO that is analogous to conformer 1a of HNdCH-CHdCH-NH-BO was
1.226 Å at the MP2/cc-pVDZ level, slightly longer than the
corresponding length in NHdCH-CHdCH-NH-BO (1a) but
∼0.04 Å shorter than this length in (-N(C6F5)dC(CH3)CHdC(CH3)-N(C6F5)-B-)O; this (acyclic) N(C6F5)d
C(CH3)-CHdC(CH3)-N(C6F5)-BO conformer was 34.4 kcal/
mol higher in energy than that for the analogous borocycle. The
NBOs of (-N(C6F5)dC(CH3)-CHdC(CH3)-N(C6F5)-B-)O
indicate the presence of one σ- and only one π-boron-oxygen
Boron-Oxygen Multiple Bonding in HNdCH-CHdCH-NH-BO
J. Phys. Chem. A, Vol. 112, No. 36, 2008 8451
Figure 3. Optimized structures of the borocycle (-N(C6F5)dC(CH3)-CHdC(CH3)-N(C6F5)-B-)O and the acyclic conformer
N(C6F5)dC(CH3)-CHdC(CH3)-N(C6F5)-BO at the MP2/cc-pVDZ computational level.
bonding orbital, suggesting the presence of a double bond,
corroborating the interpretation of Vidovic et al.24
A.4. A
Comparison
of
MP2(FC)/(aug)cc-pVxZ
(x ) D,T) and DFT/6-311++G(d,p) Results for HNdCHCHdCH-NH-BO and (-NHdCH-CHdCH-NH-B-)O.
Calculated boron-oxygen and boron-hydrogen(nitrogen) bond
lengths in H-BtO, H2N-BtO, H2N-B(OH)2, HNdCHCHdCH-NH-BtO (1a-b), and (-NHdCH-CHdCHNH-B-)O (1c) are listed in Table 3S at a variety of DFT/6311++G(d,p) levels; the Pople-style 6-311++G(d,p) basis set
is at the “upper end” of basis sets that are likely to be employed
in studies of larger boron-containing compounds in the near
future. In this investigation, we have performed a limited
comparison between the more rigorous MP2(FC) methodology
using the (aug)cc-pV(D,T)Z, basis sets and the more economical
DFT methodology with the LDA, PBE, TPSS, BLYP, B3LYP,
BVP86, OLYP, O3LYP, and PBE1PBE functionals using the
6-311++G(d,p) basis set.
Comparing the calculated MP2/(cc-pVDZ, aug-cc-pVDZ, ccpVTZ) boron-oxygen bond distances, see Figures 1 and 2, and
the corresponding DFT/6-311++G(d,p) distances given in Table
3S, it is evident that there is reasonable agreement among these
various methods/basis sets to within ∼0.02Å. The calculated
boron-oxygen bond length in H-BtO at both the B3LYP/6311++G(d,p) and the PBE1PBE/6-311++G(d,p) levels was
in particularly good agreement with the microwave data; see
Table 3S. Furthermore, this finding does not appear to be highly
basis-set-dependent; the boron-oxygen bond lengths calculated
using the B3LYP functional with the cc-pVDZ, aug-cc-pVDZ,
and cc-pVTZ basis sets were 1.203, 1.205, and 1.200 Å,
respectively, and the corresponding PBE1PBE distances were
1.202, 1.204, and 1.199 Å.
Values for a variety of DFT/6-311++G(d,p) energy differences among the acyclic conformers 1a and 1b of HNdCHCHdCH-NH-BO and of the borocycle (-NHdCH-CHd
CH-NH-B-)O 1c are listed in Table 6S of the Supporting
Information. A comparison of Tables 1 and 6S shows that there
is good agreement between the relative energies of 1a and 1b
at the various DFT/6-311++G(d,p) and the MP2(FC)/cc levels,
that is, conformer 1b is consistently ∼3-4 kcal/mol higher in
energy than 1a. As might be expected, the variation of energy
values (corrected to 298 K) between the borocycle 1c and the
acyclic conformer 1a is significantly greater, ranging from 27.8
(B3LYP) to 42.5 kcal/mol (LDA). However, ignoring the LDA
value, which includes only local terms in the correlation
functional, the variation is significantly less; the highest value
is 35.3 kcal/mol (PBE1PBE). The corresponding MP2(FC)/
(aug)-cc-pVD(T)Z values range from 29.8 to 32.3 kcal/mol; see
Table 1. Thus, to a large extent, these DFT/6-311++G(d,p)
energy differences are in quite good agreement with the available
MP2(FC)/cc results; unfortunately, no experimental data are
currently available for comparison. In view of our previous
results involving dative bonding interactions,27–30 it appears that
the PBE1PBE/6-311++G(d,p) computational level is a reasonable, economical alternative to the more-costly MP2(FC)/cc
levels for exploring various aspects of boron chemistry.
It is of interest to assess geometrical and energetic results
associated with climbing the DFT ladder (“Jacob’s ladder”);
LDA f PBE f TPSS,104 using the modest 6-311++G(d,p)
basis set. The calculated LDA/6-311++G(d,p) boron-oxygen
bond length in H-BtO, 1.202 Å, is in excellent agreement
with the experimental microwave value of 1.201 Å, as well as
with the corresponding B3LYP and PBE1PBE values. The initial
LDA f PBE step on the ladder at this computational level
results in a boron-oxygen bond length that is ∼0.01 Å longer
and nearly the same as the MP2(FC)/6-311++G(d,p) length,
1.212 Å. The second step on the DFT ladder is PBE f TPSS.
At this step, the boron-oxygen bond length changes minimally;
see Table 3S. The energy difference between the borocycle 1c
and the acyclic derivative 1b improves dramatically in going
from LDA to PBE compared to the various MP2(FC)/cc
differences and most of the DFT/6-311++G(d,p) differences;
see Tables 1 and 6S. The energy change in going from PBE to
TPSS is minimal.
Concluding Remarks
The importance of boron chemistry is increasing rapidly in a
variety of fields, and unveiling the intricacies of boron bonding
remains an active area of research.3,17,19,24,26,29,81,82 In this article,
we report results from a computational investigation of the
boron-oxygen bonding in H-BO and H2N-BO, as well as in
the acyclic conformers of HNdCH-CHdCH-NH-BO (1a,
1b) and in the corresponding borocycle (-NHdCH-CHdCHNH-B-)O (1c); MP2 methodology with the correlationconsistent cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets and
DFT methodology with the 6-311++G(d,p) basis set were
employed for the calculations.
Experimentally and/or computationally derived distances
between the boron and oxygen atoms, a key parameter in any
discussion of bond order,105 the calculated composition of the
molecular orbitals at a variety of MP2/cc and DFT/6-
Larkin et al.
8452 J. Phys. Chem. A, Vol. 112, No. 36, 2008
311++G(d,p) levels, and the computed NRT bond orders at
the BVP86/(svp)tzvp-Ahlrichs levels are consistent with the
presence of a boron-oxygen triple bond in H-BO, H2N-BO,
andvarious(acyclic)conformersofHNdCH-CHdCH-NH-BO
in vacuo. Using the COSMO BVP86/(svp)tzvp models to
simulate the long-range effects of an aqueous medium, the
boron-oxygen bond in H-BO was still best described as a triple
bond, whereas for H2N-BO and HNdCH-CHdCH-NH-BO
(1a, 1b), this bond appears to be more appropriately described
as intermediate between a double and triple bond. Incorporating
several explicit water molecules in the vicinity of the
boron-oxygen bond during the optimization of complexes of
H2N-BtO and HNdCH-CHdCH-NH-BO (1a), to account
for short-range/site-specific effects on the boron-oxygen bonding, often resulted in the corresponding boronic acid, suggesting
that in an aqueous environment, the presence of H2N-BtO or
HNdCH-CHdCH-NH-BO (1a, 1b) would be short-lived.
The boron-nitrogen bond in H2N-BtO and HNdCHCHdCH-NH-BtO (1a, 1b) was predominantly a single bond
in vacuo but was predicted to have substantial double-bond
character by the COSMO BVP86/tzvp aqueous media model.
At all of the MP2(FC)/(aug)-cc-pVxZ and DFT/6-311+G(d,p) computational levels that we employed in this investigation, the (-NHdCH-CHdCH-NH-B-)O borocycle,
1c (C2V symmetry), was ∼30 kcal/mol lower in energy than
any of the HNdCH-CHdCH-NH-BtO acyclic conformers that we found; see Tables 1 and 5S. All indications are
that the boron-oxygen bond in this borocycle is predominantly a double bond, in accord with the available experimental results on (-N(C6F5)dC(CH3)-CHdC(CH3)N(C 6F 5)-B-)O. 24 The calculated lengths of the two
boron-nitrogen bonds in 1c and (-N(C6F5)dC(CH3)CHdC(CH3)-N(C6F5)-B-)O were identical, a measure of
the extent of electron delocalization in this conformer.
The hydration reactions
HNdCH-CHdCH-NH-BO (1a, 1c) +
H2O f HNdCH-CHdCH-NH-B(OH)2
were calculated to be highly exothermic; the calculated values
of ∆H0298 for 1a and 1c were -49.4 and -32.6 kcal/mol,
respectively, at the MP2(FC)/cc-pVDZ level, an indication of
the amount of energy stored in the boron-oxygen bond in these
compounds. Furthermore, the calculated value of ∆H0298 for
the trimerization reaction of HNdCH-CHdCH-NH-BO (1a)
to form the ((NHdCH-CHdCH-NH)3B3O3) boroxine structure was -141.1 kcal/mol at the MP2(FC)/cc-pVDZ computational level. These findings help to quantify the high-energy
content of BO multiple bonds.
Acknowledgment. This research was supported, in part, by
the Intramural Research Program of the NIH, NHLBI. K.L.B.
would like to thank the National Textile Center (C03-PH01);
G.D.M. would like to thank NIH (GM31186, CA06927) and
NCI for financial support of this work, which was also supported
by an appropriation from the Commonwealth of Pennsylvania.
The High Performance Computing Facility at the Fox Chase
Cancer Center was used for some of the calculations described
in this manuscript.
Supporting Information Available: Additional theoretical
results. This material is available free of charge via the Internet
at http://pubs.acs.org.
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