Interpretation of intermolecular geometric isotope effect in hydrogen bonds: nuclear orbital plus molecular orbital study

Isotope Effects on Chemical Shifts in the Study of Hydrogen Bonds in Small Molecules

This review is giving a short introduction to the techniques used to investigate isotope effects on NMR chemical shifts. The review is discussing how isotope effects on chemical shifts can be used to elucidate the importance of either intra- or intermolecular hydrogen bonding in ionic liquids, of ammonium ions in a confined space, how isotope effects can help define dimers, trimers, etc., how isotope effects can lead to structural parameters such as distances and give information about ion pairing. Tautomerism is by advantage investigated by isotope effects on chemical shifts both in symmetric and asymmetric systems. The relationship between hydrogen bond energies and two-bond deuterium isotope effects on chemical shifts is described. Finally, theoretical calculations to obtain isotope effects on chemical shifts are looked into.

Hydrated Metal Ion Salts of the Weakly Coordinating Fluoroanions PF6-, TiF62-, B12F122-, Ga(C2F5)4-, B(3,5-C6H3(CF3)2)4-, and Al(OC(CF3)3)4-. In Search of the Weakest HOH···F Hydrogen Bonds

FTIR spectra of microcrystalline samples of 11 metal ion salt hydrates of a variety of weakly coordinating fluoroanions are reported. The compounds studied were Li(H₂O)₄(Al(OC(CF₃)₃)₄), Li(H₂O)(B(3,5-C₆H₃(CF₃)₂)₄), Li(H₂O)_n(Ga(C₂F₅)₄), Li(H₂O)(PF₆), Li₂(H₂O)₂(TiF₆), Li₂(H₂O)₄(B₁₂F₁₂), Na(H₂O)(PF₆), Na₂(H₂O)₂(B₁₂F₁₂), K₂(H₂O)₂(B₁₂F₁₂), Rb₂(H₂O)₂(B₁₂F₁₂), Cs₂(H₂O)(B₁₂F₁₂), and their partially or completely deuterated isotopologs and isotopomers. The O-D···F hydrogen bonds in Li(HOD)(H₂O)₃(Al(OC(CF₃)₃)₄) (ν(OD) = 2706 cm^-1), Li(HOD)(B(3,5-C₆H₃(CF₃)₂)₄) (ν(OD) = 2705 cm^-1), and Li(HOD)(H₂O)_n(Ga(C₂F₅)₄) (ν(OD) = 2697 cm^-1) rival HOD absorbed in polyvinylidene difluoride (ν(OD) = 2696 cm^-1) and HOD···FCH₃ in a frozen Ar matrix (ν(OD) = 2685 cm^-1) for the weakest hydrogen bonds between a water molecule and an F atom in any compound. As weak as they are, minor differences in O-H···F hydrogen bonds in the same fluoroanion salt can be distinguished spectroscopically. Uncoupled HOD molecules in asymmetric F···HOD···F' hydrogen bonding environments in Rb⁺, Cs⁺, Mg²⁺, and Co²⁺ hydrates of B₁₂F₁₂^2- gave rise to two observable ν(OD) bands even though the two R(O···F) distances differ by only 0.010(4) Å (Mg²⁺), 0.033(2) Å (Co²⁺), 0.074(4) Å (Rb⁺), and 0.106(6) Å (Cs⁺). A plot of ν(OD) for hydrates with a single uncoupled HOD molecule per metal ion (e.g., Li(HOD)(H₂O)₃(Al(OC(CF₃)₃)₄)) vs R(O···F) distance from single-crystal X-ray or neutron diffraction structures was prepared. The ν(OD) values range from 2305 to 2706 cm^-1 and the R(O···F) distances range from 2.58 to 3.17 Å. The plot consists of 53 {ν(OD), R(O···F)} data points, 23 of which are new and have ν(OD) > 2600 cm^-1, in contrast to a 1994 ν(OD) vs R(O···F) plot with 28 data points, none of which had ν(OD) > 2600 cm^-1. There is a clear and significant difference between the new ν(OD) vs R(O···F) plot and a literature ν(OD) vs R(O···O) plot for hydrates containing O-D···O hydrogen bonds. For a given ν(OD) stretching frequency, the exponential regression curves show that R(O···F) is typically 0.1-0.2 Å shorter than R(O···O), in harmony with the lower basicity and smaller size of F atoms vs O atoms.

The any particle molecular orbital/molecular mechanics approach

A computational scheme is proposed to broaden the range of applications of multicomponent methodologies for the study of local properties of big molecular systems existing in the gas phase and in solvated environments. This scheme extends the any particle molecular orbital (APMO) approach in the quantum mechanics/molecular mechanics (QM/MM) framework. As a first assessment of the performance of the proposed approach, we estimate the proton affinities (PAs) of seventy amines in the gas phase and the proton binding energies (PBEs) in the gas phase and in an explicitly solvated environment of the sixty-one protons present in the chignolin protein. These calculations are performed with the QM/MM versions of the APMO second-order proton propagator (APMO-PP2) and the APMO extended Koopmans' theorem (APMO-KT) approaches. Calculated PAs and PBEs show significant reductions in the computational effort with a reduced loss in accuracy. These results suggest that the APMO/MM scheme might be used as a low-cost multi-component alternative for studies of local properties in big molecular systems. Graphical Abstract QMMM regions and CPU times for the APMO/MM approach.

Developing effective electronic-only coupled-cluster and Møller-Plesset perturbation theories for the muonic molecules

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the nuclear-electronic orbital theory [Phys. Chem. Chem. Phys., 2018, 20, 4466]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Møller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules

An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

Isotope engineering of van der Waals interactions in hexagonal boron nitride

Hexagonal boron nitride is a model lamellar compound where weak, non-local van der Waals interactions ensure the vertical stacking of two-dimensional honeycomb lattices made of strongly bound boron and nitrogen atoms. We study the isotope engineering of lamellar compounds by synthesizing hexagonal boron nitride crystals with nearly pure boron isotopes (¹⁰B and ¹¹B) compared to those with the natural distribution of boron (20 at% ¹⁰B and 80 at% ¹¹B). On the one hand, as with standard semiconductors, both the phonon energy and electronic bandgap varied with the boron isotope mass, the latter due to the quantum effect of zero-point renormalization. On the other hand, temperature-dependent experiments focusing on the shear and breathing motions of adjacent layers revealed the specificity of isotope engineering in a layered material, with a modification of the van der Waals interactions upon isotope purification. The electron density distribution is more diffuse between adjacent layers in ¹⁰BN than in ¹¹BN crystals. Our results open perspectives in understanding and controlling van der Waals bonding in layered materials.

Hidden role of intermolecular proton transfer in the anomalously diffuse vibrational spectrum of a trapped hydronium ion

We report the vibrational spectra of the hydronium and methyl-ammonium ions captured in the C_3v binding pocket of the 18-crown-6 ether ionophore. Although the NH stretching bands of the CH₃NH₃⁺ ion are consistent with harmonic expectations, the OH stretching bands of H₃O⁺ are surprisingly broad, appearing as a diffuse background absorption with little intensity modulation over 800 cm^-1 with an onset ∼400 cm^-1 below the harmonic prediction. This structure persists even when only a single OH group is present in the HD₂O⁺ isotopologue, while the OD stretching region displays a regular progression involving a soft mode at about 85 cm^-1 These results are rationalized in a vibrationally adiabatic (VA) model in which the motion of the H₃O⁺ ion in the crown pocket is strongly coupled with its OH stretches. In this picture, H₃O⁺ resides in the center of the crown in the vibrational zero-point level, while the minima in the VA potentials associated with the excited OH vibrational states are shifted away from the symmetrical configuration displayed by the ground state. Infrared excitation between these strongly H/D isotope-dependent VA potentials then accounts for most of the broadening in the OH stretching manifold. Specifically, low-frequency motions involving concerted motions of the crown scaffold and the H₃O⁺ ion are driven by a Franck-Condon-like mechanism. In essence, vibrational spectroscopy of these systems can be viewed from the perspective of photochemical interconversion between transient, isomeric forms of the complexes corresponding to the initial stage of intermolecular proton transfer.

Unusual H/D isotope effect in isomerization and keto–enol tautomerism reactions of pyruvic acid: nuclear quantum effect restricts some rotational isomerization reactions

H/D isotope effects on isomerization and keto–enol tautomerism reactions of the pyruvic acid molecule have been investigated using the multicomponent B3LYP methods, which can take account of the nuclear quantum effect of protons and deuterons.

Equation of state and thermodynamic Grüneisen parameter of monoclinic 1,1-diamino-2,2-dinitroethylene

In situ synchrotron x-ray diffraction experiments were conducted on 1,1-diamino-2,2-dinitroethylene (FOX-7) at pressures up to 6.8 GPa and temperatures up to 485 K. Within the resolution of the present diffraction data, our results do not reveal evidence for a pressure-induced structural phase transition near 2 GPa, previously observed in several vibrational spectroscopy experiments. Based on unit-cell volume measurements, the least-squares fit using the third-order Birch-Murnaghan equation of state (EOS) yields K 0  =  12.6  ±  1.4 GPa and [Formula: see text]  =  11.3  ±  2.1 for the α-phase of FOX-7, which are in good agreement with recently reported values for the deuterated sample, indicating that the effect of hydrogen-deuterium substitution on the compressibility of FOX-7 is negligibly small. A thermal EOS is also obtained for the α-phase of FOX-7, including pressure dependence of thermal expansivity, (∂α/∂P)T  =  -7.0  ±  2.0  ×  10(-5) K(-1) GPa(-1), and temperature derivative of the bulk modulus, (∂K T/∂T)P  =  -1.1  ×  10(-2) GPa K(-1). From these EOS parameters, we calculate heat capacity at constant volume (C V) and thermodynamic Grüneisen parameter (γ TH) as a function of temperature. At ambient conditions, the calculated γ TH is 1.055, which is in good agreement with the value (1.09) previously obtained from density functional theory (DFT). The obtained C V, however, is 13% larger than that calculated from the first-principles calculations, indicating that the dispersion correction in the DFT calculations may need to be further improved for describing intermolecular interactions of molecular crystals.