Nuclear Motion in the Intramolecular Dihydrogen ... - ACS Publications

Article Cite This: J. Phys. Chem. A 2019, 123, 6547−6563

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Nuclear Motion in the Intramolecular Dihydrogen-Bound Regime of an Aminoborane Complex Diana L. Reese and Ryan P. Steele* Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112, United States

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S Supporting Information *

ABSTRACT: The 1,3-diaza-2,4-diborobutane (NBNB) molecule serves as the smallest model complex of an intramolecular “dihydrogen bond,” which involves a nominally hydrogen-bonding interaction between amine and borane hydrogen atoms. In the present study, the role of this dihydrogen bond in influencing the inherent molecular dynamics of NBNB is investigated computationally with ab initio molecular dynamics and path integral molecular dynamics techniques, as well as vibrational spectra analysis and static quantum chemistry computations. These simulations indicate that the dihydrogen-bonding interaction impacts both the high- and low-frequency motions of the molecule, with the dominant motions involving low-frequency backbone isomerization and terminal amine rotation. Geometric isotope effects were found to be modest. The analysis also addresses the paradoxical fostering of amine rotation via a relatively strong dihydrogen bond interaction. Electrostatic and geometric factors most directly explain this effect, and although some orbital evidence was found for a small covalent component of this interaction, the dynamics and electronic structure suggest that electrostatic contributions are the controlling factors for molecular motion in NBNB.

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INTRODUCTION Hydrogen bonds (HBs) are ubiquitous phenomena with influence ranging from the structure of proteins and DNA to anomalous thermodynamic properties of water.1 Most generally considered an “association between an electronegative atom and a hydrogen atom attached to a second, relatively electronegative atom”,2 HB interactions also exhibit partial covalent and/or charge-transfer components3,4 that are often reflected in the spectral signatures of hydrated ions, for example.5−30 This classic Xδ−−Hδ+···Yδ− depiction of an HB is potentially challenged by the known presence of other regimes in which HB-like interactions can occur.31 Specifically, when hydrogen is attached to an electropositive atom, such as a metal or boron atom, this now-hydridic moiety can itself act as an acceptor to another hydrogen that is bound to an electronegative atom, in an Xδ−−Hδ+···Hδ−−Mδ+ configuration. This interaction can occur both inter- and intramolecularly and has been termed a “dihydrogen bond” (DHB).31 Despite numerous studies of the nature of this bonding and its impact on structural properties,31−43 relatively little is known about the impact of a DHB on the molecular motion of a molecule, and this dynamical contribution is the focus of the present study. The DHB interaction is present in several known aminoborane complexes,44−55 some of which have been studied specifically for their hydrogen-storage properties. 45 The moderate dehydrogenation temperature for ammonia borane55 (NH3BH3), for example, suggests that the strength of this DHB interaction can have consequences for H2 chemistry.56,57 From this perspective, the DHB may alternatively be considered a © 2019 American Chemical Society

dihydrogen molecule that is strongly distorted between a frustrated Lewis acid−base pair.58−60 Mitchell et al. previously investigated61 the nuclear motion in the alternative, σ-bound regime of metal−H2 complexes via quantum chemistry simulations and observed that the largely intact H2 units were highly fluxional, undergoing propeller-like motion, tumbling, and migration within the ligand sphere. This regime involved only a modest degree of activation of the H−H bond, however, due to the lack of d-orbital interactions in these Mg2+ complexes. Experimental NMR studies have indicated that motion in traditional metal (poly)hydride complexes, on the other hand, includes ligand exchange,62−69 although the interpretation of these multidimensional motions remains challenging.70 The present paper includes an assessment of the molecular motion inherent to one representative DHB complex, including motion along the DHB coordinate and degrees of freedom coupled to this coordinate. The gauche form of 1,3-diaza-2,4-diborobutane, NH3BH2NH2BH3 (hereafter “NBNB”), consists of two isomers that are nominally classified as enantiomers (via backbone isomerization), and this complex will serve as the main complex of study in this work. An intramolecular DHB is known to be present in gauche-NBNB (Figure 1) and acts as the dominant factor in stabilizing the gauche form over the anti counterpart.57,71−73 This interaction is most simply illustrated by the Received: May 31, 2019 Revised: July 2, 2019 Published: July 3, 2019 6547

DOI: 10.1021/acs.jpca.9b05219 J. Phys. Chem. A 2019, 123, 6547−6563

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The Journal of Physical Chemistry A

the present study focused on the isolated molecule case, several of the conclusions drawn from this work are applicable to intermolecular DHB effects. The purpose of the present study was to investigate the contributions of the DHB character in the NBNB molecule to its overall dynamic nuclear motion. To what extent, for example, does the “H2” unit act like bare H2? Or does it behave more like traditional hydride moieties? To what extent does the DHB hinder or foster the low-frequency rotation and isomerization of NBNB? How much do quantum effects, including zero-point motion, anharmonicity, and tunneling, impact the delocalization of the light atoms involved in this unique interaction? The analysis presented in this manuscript determined the fullquantum, thermal nuclear motion distribution, via ab initio path integral molecular dynamics (PIMD), as well as the dynamical motion via classical ab initio molecular dynamics (MD). Vibrational spectra were assessed to connect to experimentally observable signatures of these motions. Geometric isotope effects were also assessed in the fully deuterated NBNB(D) analogue, to assess the structural role of quantum effects. The somewhat unexpected outcome of these analyses was that the −NH+3 ···−H3B− pair behaves much more like an intact Lewis pair than an example of a partially covalent DHB, although the DHB contribution does alter low-frequency motions in the molecule. These effects were also found to be connected to the electronic structure of the DHB interaction.

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METHODS The following analysis of DHB effects and molecular motion involves three broad approaches. The electronic structure of this complex was first assessed in terms of potential energy landscapes and an extensive computational methodology benchmarking procedure to identify relative energies of unique configurations of NBNB and their isomerization barriers. This analysis also allowed for the selection of a density functional that suitably reproduced coupled-cluster benchmark results and enabled dynamics and thermal sampling in subsequent phases. Throughout this electronic structure assessment, molecular orbitals and bonding analyses were used to decipher the contributors to the stability of the different isomeric forms. The thermal structural distribution and dynamics of NBNB were analyzed in the second stage of this analysis, using ab initio MD and PIMD simulations. Finally, in an a posteriori analysis, the role of the intramolecular DHB character in influencing this motion was assessed, and its interaction strength was reassessed in this context. All calculations were performed using a development version of the Q-Chem 5.0 Quantum Chemistry package,76 and figures were generated with VMD,77 Gnuplot,78 and IQmol.79 Electronic Structure. Energies of unique isomers of NBNB were identified along with barriers to isomerization, including terminal amine and borane rotations (in the gauche form) and heavy-atom backbone torsion (gauche−gauche enantiomerization and gauche−anti isomerization). Relative electronic energies for these barriers and minima were calculated using coupled-cluster methods with single and double excitations (CCSD), as well as perturbative triple excitations [CCSD(T)].80,81 Benchmarks in this work were performed with CCSD(T) using the complete basis set extrapolation82 from the Dunning cc-pVTZ and cc-pVQZ basis sets, based on CCSD/cc-pVTZ structures.83 Additional calculations were completed with other basis sets and are included in the Supporting Information (SI) (Table S1).

Figure 1. (Top) optimized gauche-NBNB structure. (Bottom) optimized gauche-CBNC structure. In this figure and for the remainder of this study, atom sphere colors are blue (N), pink (B), and gray (C).

observation that the terminal amine and borane groups are not arranged to minimize steric repulsion alone. This behavior stands in contrast to the structural trend in isoelectronic molecules CH3BH2NH2CH3 (“CBNC”) and n-butane, in which no DHB is present.73 The low stability of the NBNB complex, relative to dissociation into 2NH2BH2 + H2 (16.6 kcal/mol with BHHLYP/cc-pVDZ) or even the cyclic NH2BH2NH2BH2 + H2 product (−0.6 kcal/mol, with a barrier of >34 kcal/mol), also suggests that the H···H unit is somewhat “perilously perched” between the Lewis acid/base subunits, and the properties of this interaction are inherently tied to the electronic structure and stability of the NBNB backbone. Chen et al. were the first to synthesize NBNB and showed via single-crystal X-ray diffraction that the gauche-NBNB isomer is the dominant form, due to a weak DHB interaction.74 These authors also noted that the DHB character in gauche-NBNB prevents significant rotation of the B−N bonds in the terminal borane/amine groups. Nutt calculated the standard enthalpy change for the anti-to-gauche conversion to be −11.2 kcal/mol (favoring gauche) using the B3LYP/6-311+G(2dp)//B3LYP/ 6-31G(d) level of theory,72 while Matus calculated the same quantity as −12.3 kcal/mol using CCSD(T)/(aug-cc-pVTZ → aug-cc-pVQZ)//MP2/cc-pVTZ.71 Sagan determined that the isolated molecule stability of gauche, relative to anti, is due to both the presence of the DHB and the strengthening (shortening) of the N−B bonds in NBNB.73 A follow-up study by Chen argued that, in bulk solid, the anti conformation becomes the more stable isomer due to significant intermolecular DHB effects, whereas the gauche conformation is instead stabilized by intramolecular dihydrogen bonding.75 Although 6548


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The Journal of Physical Chemistry A Table 1. Relative Isomer Energies and Isomerization Barriers, Computed with Coupled-Cluster Methods and the BestPerforming Density Functional in the Tested Set isomer relative energies (kcal/mol)

gauche isomerization barriers (kcal/mol)

method

anti

gauche

borane rotation

amine rotation

racemization

CCSD/CBSDZ‑TZ CCSD/CBSTZ‑QZ CCSD(T)/CBSDZ‑TZ//CCSD(T)/cc-pVDZ CCSD(T)/CBSTZ‑QZ//CCSD(T)/cc-pVDZ CCSD(T)/CBSTZ‑QZ //CCSD/cc-pVTZ BHHLYP/cc-pVDZ

12.36 12.44 12.70 12.77 12.70 12.86

0.00 0.00 0.00 0.00 0.00 0.00

3.31 3.28 3.22 3.26 3.23 3.00

1.29 1.23 1.17 1.17 1.31 1.14

0.25 0.25 0.32 0.31 0.27 0.30

internal bead normal mode.87 The PIMD simulations contained 32 path integral replicas at a temperature of 300 K and were integrated with a time step of 0.5 fs. The MD sampling was performed for a total of 4.4 million steps (2.2 ns) after equilibration. The PIMD simulations were performed for 100 and 18 ps for H- and D-containing structures, respectively. This discrepancy in the classical/quantum trajectory lengths is justified by the need to converge low-frequency motions in the classical sampling. For the PIMD simulations, where the quantum character of the low-frequency motions was confirmed to be minimal, only the properties of the high-frequency motions were the focus, and the sampling was sufficient to converge these properties. Geometric isotope effects were assessed with PIMD simulations of perdeuterated NBNB, hereafter termed NBNB(D). In addition to NVT simulations, several classical MD trajectories of 50 ps each were performed in the NVE ensemble to determine the real-time dynamical fluctuations in the complex, following equilibration in the NVT ensemble for a minimum of 50 ps. Direct sampling of the harmonic ground-state nuclear distribution (at 0 K) was also used for comparison to the PIMD simulations, to assess the role of anharmonicity and thermal isomerization. A total of 6 × 105 configurations was generated for the harmonic sampling of each gauche enantiomer by directly sampling the 0 K ground-state probability density, using the harmonic frequencies from quantum chemistry calculations. These techniques are hereafter denoted as the quantum (H), quantum (D), classical, and harmonic methods. In each case, an in-house analysis routine was employed to generate statistical distributions, averages, and statistical errors for bond lengths, angles, and dihedrals of interest. In the case of PIMD sampling, unique terminal H···H (from N−H···H−B moieties) bond distances were binned as “shortest”, “intermediate”, and “longest” for each bead in a configuration, although binning by the value of the centroid of the beads yielded similar results (Figure S1), suggesting that centroid curvature effects106,107 and ring-polymer overlap were minimal. For nomenclature purposes, terminal hydrogen atoms are hydrogen atoms involved in the terminal amine or borane groups, whereas other hydrogen atoms are denoted as medial. Bond angles were similarly analyzed in two unique ways. First, H···H interaction lengths were classified as above, and angles including one or both of these hydrogen atoms were then analyzed according to their N/B connectivity. For example, “B−H···H shortest” would indicate the B−H···H angle in which the hydrogen atoms have been sorted geometrically and belong to the shortest H···H interaction. This method will be referred to as the “geometric” indexing scheme. Alternatively, because any given hydrogen interconverted between a “shortest”, “intermediate”, or

The structure of gauche-NBNB has already been shown in Figure 1, with structural parameters obtained from CCSD/cc-pVTZ optimizations indicated in the figure. Tables S2 and S3 include additional structural parameters for optimized gauche and anti isomers at several levels of theory. Most notably, the benchmark H···H distance of the DHB was found to be 1.974 Å, and the gauche−anti isomerization gap was 12.70 kcal/ mol. The computational cost of these coupled-cluster calculations would have prohibited sufficient MD sampling at this level of theory and instead required the use of a density functional that adequately reproduced the high-level results. Therefore, a key step in establishing the methodology for this study was the determination of a reliable density functional (if any) for simulating this model complex. Ninety-seven density functionals were screened, using a cc-pVDZ basis set and the standard pruned quadrature grid according to the Q-Chem default implementation of each functional,84,85 for their ability to reproduce the relative energies of key points on the potential energy landscape. The BHHLYP density functional86 most closely reproduced the energies of critical points on the potential energy surface (Table 1) and was subsequently used in the remainder of the dynamics/sampling calculations. The DHB bond length with this method was computed to be 1.922 Å, and the gauche−anti gap was computed to be 12.86 kcal/mol. The complete analysis of density functionals is included in Table S4, which exhibits a range of gauche−anti gaps of 9.57−18.04 kcal/mol. The electronic structure of this complex, including the nature of the DHB motif, was initially analyzed in terms of molecular orbitals and their corresponding orbital energy eigenvalues. Both Kohn−Sham (BHHLYP) and molecular (HF) orbitals, using the cc-pVDZ basis set, yielded qualitatively similar results. All other methods used for the decomposition of the DHB interaction will be discussed in context in the Results section. Molecular Motion. The degree of nuclear motion in NBNB was assessed via classical and quantum (path integral) molecular dynamics (PIMD87−90) methods. These PIMD simulations capture full quantum effects in a classical-like formalism, in which the delocalization of harmonically coupled replicas of a molecule allows the molecule to sample the quantum, thermal distribution.89,91−100 Simulations with 32 replicas (beads) have been shown to sufficiently capture quantum properties for hydrogen-containing systems at room temperature within the second-order Trotter expansion.101−104 A recently developed linear-prediction algorithm was additionally used to accelerate the SCF convergence within each bead’s trajectory.105 The classical MD and quantum PIMD simulations were performed in the NVT ensemble using a stochastic Langevin thermostat of each centroid degree of freedom (time constant of 100 fs) and, for PIMD, an optimally tuned analogous thermostat for each 6549


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Figure 2. Constrained potential energy curves along terminal B−H (left) and N−H (right) coordinates for NBNB and for reference compounds as indicated. Each plot is shifted on the horizontal axis such that displacements from the equilibrium structure are shown.

“longest” H−H designation through the course of the trajectories, the hydrogen identity can be maintained, based on the original atom ordering, to assess the degree of interconversion. This indexing scheme will be termed “original” in the following analysis. Characterization of the Dihydrogen Bond and Its Strength. The presence of DHBs has commonly been identified using the Quantum Theory of Atoms in Molecule (QTAIM) approach.108 The QTAIM method analyzes the topology of the total electron density, including bond critical points that ostensibly identify the existence of a chemical bond. This analysis was repeated for the present complex, based on the Q-Chem-generated BHHLYP density, as implemented in the Avogadro 1.2 program.109,110 Vibrational spectroscopy can be used as a sensitive probe of perturbations to X−H and H−H bonds and also provides a link between the present computations and experimentally observable properties. Qi et al., for example, used Raman spectroscopy to examine a dimethylamine borane complex under highpressure and standard conditions.111 The red-shifts identified in the C−H stretch and CH3 distortion modes were indicative of a C−H···H−B DHB. Analogously, in the present model complex, harmonic vibrational spectra of both anti- and gauche-NBNB isomers were computed, with a focus on the N−H and B−H stretching regions. Similar vibrational modes in each isomer were qualitatively paired, and subsequent quantitative shifts from anti to gauche isomers were identified. The extent of anharmonicity exhibited by this system will be examined in subsequent sections, both in terms of anharmonicity contributing to isomerization and in terms of anharmonicity along highfrequency modes. Quantification of the strength and nature of this interaction is of particular interest, as these factors play a dominant role in the dynamics of this complex. The difficulty, however, lies in the fact that intramolecular binding strength and its contributing factors are ill-defined. The gauche isomer of NBNB is favored by 12.70 kcal/mol [CCSD(T)/CBSTQ//CCSD/cc-pVTZ]; however, this energy difference potentially stems from factors other than simply the formation of a DHB. A more in-depth discussion of the nature and strength of the DHB will be reserved for the Results section as molecular simulations lend additional insight into this analysis.

quantum mechanical, motion. With two putative oppositely charged moieties in nearly direct contact, and the possibility for the identity of those moieties to change, the central question addressed in this work is the extent to which this interaction directs the inherent dynamics of this molecule. This analysis will be organized into three sections, including high- and lowfrequency motions, as well as a subsequent reanalysis of the DHB character of this complex, in light of the dynamical results. High-Frequency Motion. The dynamics of DHB-containing molecules is, of course, driven by the underlying potential energy surface and the molecule’s electronic structure. Shown in Figure 2 are constrained potential energy curves along the N−H and B−H coordinates for NBNB and the reference compounds borane/borohydride (BH3/BH4−) and ammonia/ammonium (NH3/NH+4 ). In this plot, the constrained distances are all referenced to each molecule’s equilibrium structure, and displacements from this distance are plotted on the horizontal axis. In the left panel of Figure 2, the potential energy along the terminal borane B−H displacement in NBNB is shown to be notably shallower than the borane molecule and more similar to the behavior of the borohydride ion. In the right panel, the NBNB behavior deviates strongly from both reference compounds. In this case, the shallow dissociative region of the curve stems from the fledgling formation of a H−H bond that can stabilize dissociation of the N−H bond. This dihydrogen interaction was further examined through scans of the H···H distance in NBNB (Figure 3). Compared to H2 alone, the NBNB potential energy curve is elongated and rather flat but exhibits a well that would be absent if purely steric interactions were involved. Indeed, the equivalent curve for the dimethyl analogue, gauche-CBNC, exhibits a purely repulsive behavior between the hydrogen atoms in Figure 3, except for a

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RESULTS The DHB-type interaction between the two closest hydrogenic species in NBNB holds the potential for unique, and possibly

Figure 3. Constrained potential energy curves along the H···H distance in NBNB and reference compounds H2 and CBNC. 6550


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Figure 4. Representative canonical (left) and Boys-localized (right) Kohn−Sham orbitals for NBNB, using BHHLYP/cc-pVDZ. Canonical orbitals are displayed at an isovalue of 0.05 au; localized orbitals are displayed at an isovalue of 0.08 au.

Figure 5. Calculated NBNB harmonic spectra in the B−H (left) and N−H (right) stretching regions of the anti (top) and gauche (bottom) isomers. Red and blue lines represent IR-active transitions in reference compounds, as indicated. Correspondence between the qualitative character of vibrational modes in the two isomers is indicated by gray lines. Harmonic stick spectra have been artificially broadened with a 5-cm−1 Lorentzian line shape.

gauche form. This orbital stability, which is greater than the total isomer energy gap, is partially offset by the stability of other orbitals in the anti form, such as the 12.6 kcal/mol-destabilized HOMO-5 orbital, in which the anti configuration allows for the favorable overlap of backbone amine and terminal-borane bonding orbitals. Delocalized, canonical orbitals are nonetheless challenging to map onto specific bonding patterns. Instead, localized orbitals, here defined using the algorithm of Boys112,113 with separate localization of the valence and core spaces, provided a direct examination of the B−H- and N−H-bonding interactions. The four localized orbitals corresponding to the “central” hydrogens are depicted in the right panel of Figure 4. The amine-bonding orbitals (B and D) are generally more compact than their borane counterparts (A and C), but the character of local orbital A is of particular note. In this borane orbital, the relatively large local orbital is partially skewed toward its amine hydrogen partner in the DHB interaction (indicated by an arrow in Figure 4). Interestingly, the analogous amine orbital does not exhibit the same distorted lobe, even at looser isovalues, suggesting that

small barrier near 2.7 Å corresponding to the rotational motion of the methyl group to accommodate the transfering atom. Based on these X−H (Figure 2) and H−H (Figure 3) potential energy analyses, the behavior of NBNB was found to clearly deviate from typical steric considerations and suggests a DHBtype behavior. The relative stability of the gauche isomer and DHB formation has previously been ascribed to B−H σ-bonding molecular orbital donation into the N−H σ* antibonding orbital.55,73 Given its high energy, the anti isomer is likely not of interest for dynamic purposes but does serve as an important DHB-free comparison case to examine the role of the DHB effect. Examination of the valence orbital space in these two isomers showed that the relative stability was dominantly driven by two competing factors (Figure 4). The fourth orbial below the highest-occupied molecular orbital (HOMO-4) is 23.2 kcal/ mol more stable in the gauche form than in its anti counterpart. The main difference in the isomeric behavior of this orbital is the differential overlap between the borane and amine bonding orbitals, which appreciably stabilizes this particular orbital in the 6551


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Figure 6. Bond length distributions for terminal B−H (left) and N−H (right) coordinates in NBNB. The upper panels compare quantum-, classical-, and harmonic-sampling approaches, along with reference cases. The H···H distances are sorted according to shortest/intermediate/longest designations in the lower panels, with additional comparison to NBNB(D) in dotted lines.

borane σ* donation into the amine σ is, indeed, observed in this complex. These orbitals, therefore, yield two conclusions regarding the electronic structure: some evidence was found for the existence of a DHB interaction, and this DHB effect does not affect the borane and amine bondings symmetrically. These potential-surface and electronic properties are reflected in the spectroscopic signatures of molecular motion, including harmonic frequencies. Figure 5 illustrates the changes in harmonic spectra in the B−H stretch region (left) and the N−H stretch region (right) as NBNB undergoes isomerization between anti (top) and gauche (bottom) isomers. The position of IR-active reference transitions for NH3/NH4+ and BH3/BH−4 is also indicated in these figures as solid red/blue lines. The B−H stretching region (2200−2800 cm−1) exhibits five distinct B−H stretching modes in NBNB. Upon isomerization from anti to gauche, four of the five transitions red-shift by 43−90 cm−1. The lowest-frequency B−H stretch (2415 cm−1) in the gauche form dominantly corresponds to the motion of the hydrogen involved in the short DHB interaction. In this relative sense, the borane stretch appeared to be a clear spectroscopic signature of the DHB effect. However, this assignment should be tempered by the observation that this low B−H stretch still sits intermediate to the corresponding stretches in BH3 and BH4− limiting reference cases, which is consistent with the potential energy curves presented in Figure 2. The N−H stretching region (3400−3800 cm−1) also shows five active harmonic peaks, although three of these transitions

overlap in the anti configuration. Isomerization from anti to gauche leads to red shifts in the spectra of 27−57 cm−1, with the lowest-frequency transition (3496 cm−1) again belonging to the DHB pair. In this case, the low amine stretch sits to the red of the lowest-frequency N−H transition in both NH3 and NH4+ reference cases and acquires considerable intensity. This strongly red-shifted stretch transition would likely be the decisive experimental signature of the DHB in this complex. This particularly strong spectral shift is consistent with a donation to the σ* orbital of the amine. The spectroscopic hints toward the behavior of highfrequency motion in NBNB suggested that the quantum, thermal distributions were worth examination. The 300 K MD/ PIMD results for N−H (terminal-amine-only) and B−H (terminal-borane-only) bond distributions are shown in Figure 6. These high-frequency motions naturally exhibit more quantum delocalization, due to zero-point effects, than their classical counterparts would predict. However, the anharmonic shifts are relatively weak, indicating that the harmonic spectra shown in Figure 5 should be near-quantitative. The thermally averaged, DHB-involved amine N−H bond length was computed to be 1.045 Å, whereas the optimized geometry bond length was 1.022 Å. The corresponding DHB borane B−H bond length values were 1.254 Å (PIMD) and 1.228 Å (optimized). Modest geometric isotope effects were observed in these coordinates, with DHB N−D and B−D bond lengths of 1.038 Å and 1.248 Å, respectively. 6552


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The Journal of Physical Chemistry A Upon binning of the H···H distances into shortest/ intermediate/longest bonds, two effects were observed. First, the B−H/N−H distributions split slightly into three distributions (lower panels of Figure 6), signifying that the three bonds are unequal in the molecule. In both cases, the shortest H···H interactions corresponded to the longest B−H/N−H distributions. Second, the H···H distributions (Figure 7) exhibited more

Figure 8. Potential energy surface along the ϕBH3 and ϕBackbone coordinates. Raw data has been smoothed via a 10 point interpolation.

unique character of the DHB effect in the gauche form. The borane rotation barrier, for example, exhibits a small barrier in either isomer, but this barrier is larger in the gauche form (3.24 kcal/mol) than in the anti form (1.70 kcal/mol). This surface is symmetric about 0° in the backbone torsion (not shown in Figure 8), which reflects the low-barrier (0.30 kcal/mol) isomerization along this direction. Figure 9 depicts the potential energy surface along ϕNH3 and ϕBH3 in both the gauche (left panel) and anti (right panel)

Figure 7. Quantum, thermal probability distributions of H···H interaction lengths in NBNB, binned according to short/intermediate/long designations. Solid lines: NBNB; dashed lines: NBNB(D).

complex behavior that hints at hindered-rotor effects in the lowfrequency region, the discussion of which will follow in the subsequent subsection. The shortest H−H interaction, however, is surprisingly simple. In particular, this motion exhibits nearly classical, harmonic behavior with a negligible geometric isotope effect, suggesting that (a) this molecule should likely be considered to possess interacting amine/borane groups, rather than a stretched H−H bond, and (b) even this light-atom behavior is dominantly controlled by underlying low-frequency motions that exhibit a nearly classical behavior. Overall, the combination of static quantum chemistry calculations, harmonic spectra, and MD/PIMD distributions paint a picture of NBNB in which high-frequency, hydrogencontaining motions are perturbed relative to comparable motions in reference compounds, but the dynamical behavior does not deviate strongly from harmonic or, in some cases, even classical behavior. Embedded in these results, however, are hints that the low-frequency, and likely classical, motion of the molecule contains additional and larger-amplitude dynamics. Low-Frequency Motion. Based on potential energy surface evaluations and examination of trajectories, the dominant lowfrequency motions of NBNB were expected to involve the dihedral rotation of the terminal borane (ϕBH3) and amine (ϕNH3) groups, relative to the backbone, as well as the backbone N−B−N−B torsion (ϕBackbone) that connects enantiomers. In the following analysis, the dynamical activity of these motions will be assessed, along with their impact on the previously discussed high-frequency motions. Figure 8 depicts the two-dimensional (2D) potential energy surface along ϕBH3 and ϕBackbone. The high- and low-energy portions of this surface represent the anti and gauche isomers, respectively. Although the anti form is once again considered too high in energy to be relevant for thermal distributions at ambient conditions, its presence in this figure serves to highlight the

isomers. These plots are 2π -periodic in both coordinates. In the 3

gauche isomer, two equivalent minima appear at (ϕNH3, ϕBH3) = (46.60, 71.79°) and (73.89, 48.18°), representing the two enantiomeric forms. The minimum-energy isomerization between these minima occurs via a coupled ϕBackbone torsion, and the coupling of these three coordinates is a natural target of investigation throughout this section. In the gauche isomer, the terminal amine rotation and the backbone isomerization, with calculated energetic barriers of 1.14 and 0.30 kcal/mol, respectively, would be relatively unhindered for thermal motion at ambient conditions. Conversely, the terminal borane rotation was found to exhibit a more hindered motion with a barrier height of 3.00 kcal/mol. Despite the lack of putative DHB character, the anti isomer exhibits a slightly more hindered amine rotation than the borane rotor, likely due to the HOMO-5 molecular orbital character previously discussed. The anti terminal amine rotation barrier sits 2.05 kcal/mol above the anti isomer local minimum, whereas the terminal borane rotation barrier is 1.71 kcal/mol. Formation of the DHB in the gauche configuration evidently lowers the energy barrier for amine rotation but raises the barrier for borane rotation, which is consistent with the local-orbital picture in Figure 4. The classical, thermal MD distributions corresponding to these low-frequency motions are shown in Figure 10, along with their terminal-H-averaged distributions. The quantum PIMD analogues are shown in Figure S2 and show little difference. Both panels of Figure 10 depict the three unique terminal amine/borane dihedrals, and these individual distributions provided an assessment of the degree of convergence of the MD sampling. After an aggregate sampling of 2.2 ns, the thermal AIMD distributions approached the convergence of the terminal amine rotation, although the higher borane rotation barrier led to less convergence of the individual hydrogens’ dihedral 6553


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Figure 9. Potential energy surface along the ϕBH3 and ϕNH3 coordinates for gauche (left) and anti (right) isomers. Raw data has been smoothed via a five-point interpolation.

Figure 10. Classical, thermal MD probability distributions for dihedral angles ϕBH3 (left) and ϕNH3 (right). Individual hydrogens’ distributions are shown as thin colored lines; the average of all three terminal hydrogens’ distributions is shown as a thick black line. Harmonic distributions are shown for comparison.

ϕBH3 coordinates was again constructed, in analogy to Figure 9 but with the terminal amine/borane ends replaced by methyl groups as CBNC. For the sake of directly assessing these size effects, only single-point energy calculations were performed at the same Cartesian coordinates of the NBNB-constrained scan. This alchemical comparison case will henceforth be denoted CBNC//NBNB. As shown in Figure 11 (compared to Figure 9), CBNC//NBNB exhibits a qualitatively different potential

distributions. Due to the rotational equivalence of these three sites and the considerable convergence within each well, however, the aggregate distribution was still sufficient to assess the degree of molecular motion. With the exception of the harmonic-sampling case, in which only rectilinear, local excursions were sampled, the distribution between the peaks in the amine rotation was not found to reach baseline (Figure 10), indicating that a significant population exists in the transition-state region between the indistinguishable structures that are created by amine rotation. This result partially contradicts a statement previously made by Chen, indicating that the intramolecular DHB presence should prevent free rotation of the terminal amine/borane groups.74 The terminal borane rotation, on the other hand, was found to be more hindered than the amine rotation, as the distributions clearly reach baseline between peaks. This latter rotational motion was found to be active on the timescale of the simulations, but it existed as transient, discrete events, rather than continuously active rotation. The contrast of the relatively unhindered amine rotation and the hindered borane rotation paints a cloudy picture for the role of the DHB. After all, a strong interaction between the hydrogenic moieties in the DHB, effectively adding a “clamp” between these central hydrogens, should nearly equally impact the rotation of both terminal units. Initial inspection first led to the hypothesis that the elongated B−H bond (1.22 Å), compared to the N−H bond (1.02 Å), was primarily responsible for an underlying steric difference. To assess this conjecture, a two-dimensional potential energy surface along the ϕNH3 and

Figure 11. Potential energy surface along the two ϕCH3 coordinates in CBNC//NBNB. The horizontal axis corresponds to the original amine dihedral angle; the vertical axis corresponds to the original borane dihedral angle. Raw data has been smoothed via a five-point interpolation. The zero of energy in this plot has been set to the geometry of the NBNB equilibrium structure. 6554


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isomerize via ϕBackbone, as well as the rotation of the terminal amine. Along the horizontal axis, probability density connects equivalent minima. Conversely, the terminal borane shows no probability density between equivalent isomers via the borane rotation, although this rotation was still active on the timescale of the simulations. Quantum contributions were expectedly found to be negligible for this low-frequency motion (Figure S3), and classical MD simulations were able to capture the majority of the distribution. In Figures 13 and 14, interactions between terminal boronand nitrogen-bound hydrogens are sorted based on bond distance (insets). Identification of exclusive H−H pairs, starting with the shortest bond distance, yielded three unique H−H combinations that have been designated “shortest”, “intermediate”, and “longest” H−H distances in the figures. These motions were binned with respect to the ϕBH 3 and ϕNH 3 dihedrals. In all three cases, the breadth in the dihedral direction of the distribution is greater for the terminal amine rotation than for the terminal borane rotation. However, the degree of motion in the hydrogen direction is also strongly coupled to this delocalization (or lack thereof) in the low-frequency modes. Examination of the combined and renormalized probability densities of the three H−H lengths and terminal amine and borane rotations clearly indicates more active rotation pathways for the terminal amine group compared to those for the borane group. While nominally over-barrier, thermal, classical motion is not particularly unexpected for barriers of this height, this result (combined with known barriers for anti-NBNB) implies that the rotation of the terminal amine group is fostered at least, in part, by the formation of the DHB, whereas the borane rotation is not

landscape. Even with corresponding geometries, the qualitative shift in the low-energy pathway for rotation indicates that bond length alone cannot be the dominant factor. In NBNB, the rotation of the terminal amine is appreciably more favorable than the rotation of the terminal borane, whereas in CBNC// NBNB, the terminal methyl (née amine) group exhibited a significantly higher rotation barrier than the terminal methyl (borane) group. Alternative explanations must involve the difference in electronic structures of NBNB and CBNC, and a resolution based on these factors is reserved for the subsequent subsection. The distributions associated with the ϕBH3 and ϕNH3 dihedral angles (Figure 12) clearly illustrate the ability of NBNB to

Figure 12. Classical, thermal (300 K) probability distributions along the ϕNH3 and ϕBH3 dihedral angles.

Figure 13. Classical, thermal MD probability distributions for the borane rotational dihedral angle ϕBH3 and the H···H interactions. The total distribution is shown in the large, left panel, whereas the individually binned (and normalized) short/intermediate/long interactions are plotted as insets in the right panel. 6555


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Figure 14. Classical, thermal MD probability distributions for the amine rotational dihedral angle ϕNH3 and the H···H interactions. The total distribution is shown in the large, left panel, whereas the individually binned (and normalized) short/intermediate/long interactions are plotted as insets in the right panel.

Figure 15. Dynamical fluctuations of structural parameters during a representative NVE MD trajectory from equilibrated NVT initial conditions. Colors represent data assigned to each of the three hydrogen-containing quantities, assigned at the beginning of the trajectory.

impacted in the same manner. In both cases, the total distribution is comprised of overlapping short/intermediate contributions, which reflects the rotational and backbone isomerization motions. The lack of overlap between medium

and long H···H interactions indicates a larger discrepancy in bond length and emphasizes that a terminal rotation is necessary to interconvert between bonding regimes. Quantum simulations do show slightly more probability density delocalized along the 6556


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Figure 16. Quantum, thermal PIMD probability distributions (left) for the backbone dihedral angle ϕBackbone of NBNB, along with the amine rotation dihedral angle ϕNH3 (top) and the borane rotation dihedral angle ϕBH3 (bottom). These quantum results are compared to the two-well harmonicsampling case (middle), and differences in these normalized distributions are shown in the right panels.

H−H bond than the amine or borane dihedral, and this result is consistent with the quantum nature of the H−H stretching mode. The NVT distributions at 300 K in Figures 13 and 14, particularly the curved “paths” in the latter, suggest that the rotational and backbone motions are active and interconvert equivalent isomers. To confirm that these motions are, indeed, responsible for these curved distributions, selected NVE trajectories from equilibrated NVT initial conditions were examined. These results are shown in Figure 15. Over the course of one short, representative trajectory (50 ps), terminal amine rotation was active, terminal borane rotation was inactive (or very hindered), gauche−gauche isomerization was active, and the heavy-atom backbone showed significant motion throughout. Due to the terminal amine rotation, terminal hydrogen atoms trade off their participation in the DHB interaction. Furthermore, the backbone and amine rotations were partially coupled. The fleeting regions of quiet backbone motion near 20 and 30 ps, for example, were correlated with similarly stable regions without amine rotation isomerization. Overall, the implied dynamics from the thermal distributions was confirmed in these constant-energy trajectories. Anharmonicity in this complex was assessed via the difference between quantum PIMD and harmonic direct-sampling protocols. Although a standard geometry optimization would identify a single enantiomer, harmonic sampling of both enantiomers was performed for the sake of a fair method comparison, with equal weight given to the two isomers’ distributions. Shown in Figure 16 are the 2D distributions corresponding to backbone motion and amine/borane motions, along with a distribution of the quantum−harmonic difference. Particularly for this low-frequency backbone isomerization, anharmonic and/or thermal effects were found to be significant. Even with the two-well harmonic adjustment, the harmonic

distributions are appreciably more peaked and narrower than their PIMD counterparts. The harmonic approach underestimated the tunneling and/or thermal backbone motion. This discrepancy was mainly confined to the backbone motion in the ϕBackbone/ϕBH3 case (vertical axis of lower panels of Figure 16), although the “skew” of this borane distribution was also altered due to anharmonic effects. The amine rotation was much more strongly impacted (upper panels of Figure 16), with the degree of amine rotation significantly enhanced in the PIMD simulations. Overall, the thermal, quantum sampling indicates a significantly different degree of motion, compared to a 0 K harmonic interpretation. Dihydrogen Bond Characterization and Strength. The dihydrogen bond has been multiply defined as (a) an interaction between a conventional hydrogen bond donor and a weak-base component, where the weak base is typically a metal or hydrogen atom bound to a boron atom,36 (b) an electrostatic interaction between a protonic hydrogen and a hydridic hydrogen,42 (c) a hydridic hydrogen interacting with a sigma-bonding pair of electrons,31 or even (d) an “electrostatic interaction between oppositely charged hydrogen atoms with a small covalent contribution”.35 Although most of these definitions are compatible, no single, quantitative measure of the existence of a DHB is presently known. In light of the dynamical effects observed in the previous sections, the role of DHB-type interactions in NBNB is revisited here. QTAIM analysis predicts a bond critical point in NBNB along a somewhat curved path connecting the closest two terminal nitrogen and boron hydrogens (Figure 17), consistent with previous analyses.57,71−73 On one hand, such results should be tempered by the inherent limitations of QTAIM, such as the prediction of bond critical points between rare-gas dimers. On the other hand, this analysis does not predict critical points between the other hydrogen atoms in the NBNB molecule or 6557


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play a role in fostering the terminal amine rotation in NBNB, as well. The natural bond orbital (NBO) charges114 (Figure 18) indicate that the terminal boron and its hydrogen atoms are all negatively charged, whereas the overall positively charged amine group possesses positively charged hydrogens and a negatively charged nitrogen. As the amine group rotates, electrostatic effects would dictate that the terminal amine hydrogens could favorably interact with the terminal boron hydrogens and the terminal boron atom itself. This effective handoff of the interaction between amine hydrogens and all atoms of the terminal borane group allows for a favorable electrostatic interaction in any configuration along the amine rotational motion. The same effect is not available during the rotation of the borane group, where the nominally hydridic hydrogens would alternately interact with positive hydrogens and negative nitrogen on the amine. The passing of the terminal amine hydrogen atoms between terminal borane and borane hydrogens is also analyzed in Figure 19, where N(backbone)−B−H and B(backbone)−N−H

Figure 17. QTAIM analysis of NBNB. The yellow sphere represents a bond critical point between the closest terminal nitrogen- and boronbound hydrogen atoms. The dotted line depicts the QTAIM bond path.

between any of the hydrogen atoms in the CBNC analogue, at the very least suggesting that the electron density topology is unique in this closest pair of hydrogen atoms in NBNB. The probability distributions presented in the previous two subsections lend additional insight into the character of the DHB. The relatively unhindered terminal amine rotation, for example, suggested that the H−H interaction may stem from more subtle electronic effects. In particular, a covalent contribution to the DHB would seemingly impact both motions approximately equally. Based on this notion, electrostatic and/ or polarization effects were investigated as alternative factors. Previous studies have identified DHB distances of 1.7−2.2 Å, significantly shorter than the H−H van der Waals distance of 2.4 Å, and interaction strengths (1−7 kcal/mol31,36,37) that are on the order of typical hydrogen bonds. Additionally, the B−H···(H−N) angles are strongly bent, with typical bending angles of 90−135°.36,37 These bends were hypothesized to come from several factors. In the case of the related ammonia borane dimer (NH3BH3)2, for example, this angle was attributed to the formation of multiple DHBs.36 The bent geometry has also been rationalized by partial charges on the atoms. The nominally protonic N−H hydrogen can interact with negative charges on both the B and H atoms, rather than just the hydridic hydrogen, effectively “maximizing the electrostatic interaction”.43 This electrostatic interaction of the amine hydrogen with both terminal boron and boron-bound hydrogen atoms appears to

Figure 19. Classical, thermal angular probability distributions of the amine and borane orientation angles. Solid lines correspond to distributions in which a specific H atom was being followed throughout the trajectories (“original”), whereas dotted lines correspond to distributions in which the hydrogen involved in the short H···H interaction has been selected (“geometric”).

Figure 18. NBO charges (au) for the gauche isomer of NBNB (left) and CBNC//NBNB (right). 6558


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The Journal of Physical Chemistry A angular distributions are compared. This figure compares hydrogen atoms when sorted according to the “geometric” indexing and according to their “original” identity, as defined in the Methods section. The distributions exhibit a shift in the B−N−H angle, depending on the indexing scheme for the hydrogen atom, whereas the N−B−H angular distributions exhibit little dependence on the indexing technique. This result indicates that the borane component rotates with little change in DHB angle. The orientation angle of the amine, on the other hand, changes appreciably in the DHB configuration. This effect is ascribed to a combination of geometric factorsthe equilibrium borane rotation axis is more “tilted”, relative to the backbone, and makes/breaks the DHB during rotation and the aforementioned electrostatic interactions that can preferentially impact the amine during this rotation. With these factors in mind, estimates of the intramolecular DHB strength can be revisited. The DHB bond strength in NBNB has previously been estimated using the extendedtransition-state-natural orbitals for the chemical valence method, in which a preferential electronic stabilization of 6.1 kcal/mol was estimated for the gauche isomer. Differences in the polarity of terminal groups have yielded an electrostatic stabilization estimate of 6.9 kcal/mol.73 The dimer of ammonia borane, (NH3BH3)2, provides an alternative route to DHB energy estimates in an intermolecular arrangement. This dimer has been shown to exhibit two DHBs when aligned in an antiparallel fashion.40,41 Halving the interaction strength yielded a DHB estimate of ΔH(0 K) = 6.75 kcal/mol with CCSD(T)/CBS.57 Using the present BHHLYP/cc-pVDZ methodology in this dimer context, the DHB strength is estimated here to be approximately 7.17 kcal/mol. An alchemical thermodynamic cycle (details in SI) involving interconversion between gauche and anti isomers of NBNB, CBNC, and CBNC//NBNB was also used to estimate the DHB strength as 4.48 kcal/mol. Although the intramolecular DHB and contributing factors are not uniquely defined, the crude agreement among these DHB strength estimates suggests a relatively narrow range for this interaction and places this interaction in the realm of traditional hydrogen bond strengths. As an additional comparison case, electron density difference plots were generated for the ammonia borane dimer and NBNB, where the total density difference is defined as Δρ = ρtotAB − (ρfragA + ρfragB). For the dimer case, each ammonia borane molecule was treated as a fragment, and in the NBNB case, the molecule was fragmented as the closed-shell NH3BH+2 and NH2BH3− ions. These plots (Figure 20) show a widespread electron density rearrangement upon complexation, but they provide no evidence of a covalent interaction between the terminal amine and borane groups. No electron density difference, for example, appears in the middle of the interatomic region between these atoms in either case. Instead, polarization and charge transfer are illustrated in these plots. The densitybased energy decomposition analysis (EDA) of Khaliullin115 (Table 2) showed that electrostatic contributions carry a plurality of the interaction strength in the ammonia borane dimer reference system, with charge transfer and polarization components trailing only slightly behind. This result confirmed that the previous electrostatic argument could contribute significantly enough to the interaction strength to dictate the hindered rotational motion. The nontrivial contribution of polarization (20%) and charge transfer (32%), however, also

Figure 20. Density difference plots for the NB dimer (top) and NBNB (bottom), using an isovalue of 0.001 au. Blue lobes denote negative density differences, and red lobes denote positive differences, with the sign convention defined in the text.

Table 2. Energy Decomposition Analysis for the NB Dimer Comparison Complex energy component

interaction energy (kcal/mol)

electrostatics polarization charge transfer remnant higher-order terms total

−6.40 −3.02 −4.72 +0.69 −13.45

serve as a cautionary result for any future simulations of this complex, using fixed-charge classical potential models. Therefore, the motion in the NBNB molecule can be summarized as follows. The B−H and N−H stretches behave quantum-mechanically but do not deviate significantly from a harmonic reference picture. These high-frequency motions are inherently coupled to larger-amplitude, low-frequency motions, including borane/amine rotation and backbone isomerization. The embedded rotors exhibit an unexpectedly differing hindered-rotor behavior, which has been ascribed to a combination of geometric effects and an asymmetric electrostatic interaction upon rotation. The lowest-frequency backbone motion undergoes rapid interconversion at ambient temperatures and modulates these higher-frequency motions throughout. 6559


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CONCLUSIONS The NBNB molecule serves as the smallest model complex for intramolecular DHB interactions. Its molecular and electronic structure both indicate the presence of an attractive interaction of the −B−H···H−N− type, which is absent in methyl analogues. Ab initio PIMD and MD simulations indicated active motion along the N−B−N−B backbone, isomerizing between enantiomeric gauche structures but not accessing the high-energy anti isomers on the timescale of the simulations. Extensive rotation of the terminal amine group was observed, but, paradoxically, the borane group to which the amine undergoes a DHB interaction was not found to rotate nearly as easily. Electrostatic and geometric factors most directly explain this effect. Although some orbital evidence was found for a small covalent component of this interaction, the dynamics and subsequent electronic analysis suggested that electrostatic contributions are the controlling factor for molecular motion. Of course, these partial-charge effects are driven by the underlying electronic structure of the molecule; so, the two factors cannot necessarily be decoupled. The dominant nuclear motion in NBNB, namely, the lowfrequency motions that convert between isomers and activate embedded rotors, can be effectively modeled by classical dynamic techniques. Geometric isotope effects were found to be nonzero but small, which is consistent with the highfrequency motions behaving approximately harmonically. Nonetheless, a 0 K harmonic sampling of the low-frequency motions was found to be inadequate for capturing the full motion of the molecule, even when sampling of equivalent isomers was included. As such, direct dynamics/sampling approaches are suggested to fully access the inherent molecular motion in DHB-containing complexes.

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for High-Performance Computing at the University of Utah are gratefully acknowledged.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b05219.

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REFERENCES

Benchmark energetic (Table S1) and structural (Tables S2 and S3) parameters, including an assessment of DFT accuracy (Table S4); centroid distribution analysis (Figure S1); low-frequency PIMD comparison (Figures S2 and S3) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ryan P. Steele: 0000-0002-3292-9805 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Petroleum Research Fund of the American Chemical Society, under grant number 55473ND6. The path integral methodology development occurred under the auspices of the National Science Foundation, under CAREER grant CHE-1452596. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation grant number ACI-1548562. The support and resources of the Center 6560


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