Quantum Dynamical Investigation of Dihydrogen-Hydride Exchange in a Transition-Metal Polyhydride Complex.

The ongoing shift toward clean, sustainable energy is a primary driving force behind hydrogen fuel research. Safe and effective storage of hydrogen is a major challenge (particularly for mobile applications) and requires a detailed understanding of the atomic level interactions of hydrogen with its host materials. The light mass of hydrogen, however, implies that quantum effects are important, so a quantum dynamical treatment is required to properly account for these effects in computational simulations. As one such example, we describe herein the hydrogen exchange dynamics between a hydride and a dihydrogen ligand in the [FeH(H2)(PH3)4]+ model complex. A global three-dimensional (3D) potential energy surface (PES) was constructed by fitting to and interpolating from a discrete set of grid points computed using density functional theory; exact quantum dynamical calculations were then carried out on the 3D PES using discrete variable representation basis sets. Energy levels and their quantum tunneling splittings were computed up to 3000 cm-1 above the ground state. Within that energy range, all three fundamentals have been identified using wave function plots, as well as the first three overtones of the exchange (reaction coordinate) motion and several of its combination bands. From the tunneling splittings, the Boltzmann-averaged tunneling rates were computed. The Arrhenius plot of the total exchange rate shows a clear transition around 150 K, below which the activation energy is essentially zero and above which it is less than half of the electronic structure barrier. This indicates that exchange rates are governed by quantum tunneling throughout the relevant temperature range with the low-temperature regime dominated by a single quantum (ground) state. This work is the first-ever fully quantum dynamical study to investigate the hydrogen exchange dynamics between hydride and dihydrogen ligands coordinated to a transition-metal complex.

Hitting the Trifecta: How to Simultaneously Push the Limits of Schrödinger Solution with Respect to System Size, Convergence Accuracy, and Number of Computed States.

Methods for solving the Schrödinger equation without approximation are in high demand but are notoriously computationally expensive. In practical terms, there are just three primary factors that currently limit what can be achieved: 1) system size/dimensionality; 2) energy level excitation; and 3) numerical convergence accuracy. Broadly speaking, current methods can deliver on any two of these three goals, but achieving all three at once remains an enormous challenge. In this paper, we shall demonstrate how to "hit the trifecta" in the context of molecular vibrational spectroscopy calculations. In particular, we compute the lowest 1000 vibrational states for the six-atom acetonitrile molecule (CH3CN), to a numerical convergence of accuracy 10-2 cm-1 or better. These calculations encompass all vibrational states throughout most of the dynamically relevant range (i.e., up to ∼4250 cm-1 above the ground state), computed in full quantum dimensionality (12 dimensions), to near spectroscopic accuracy. To our knowledge, no such vibrational spectroscopy calculation has ever previously been performed.

On neglecting Coriolis and related couplings in first-principles rovibrational spectroscopy: Considerations of symmetry, accuracy, and simplicity. II. Case studies for H2O isotopologues, H3+, O3, and NH3.

For centuries, it has been known that vibrational and rotational degrees of freedom are in general not separable. Nevertheless, surprisingly little is known about the best strategies for approximately separating these degrees of freedom in practice-even in the case of semirigid molecules, where the separation is most meaningful. There is also some confusion in the literature about the proper way to quantify the magnitude of the Coriolis (i.e., rotation-vibration) coupling in rovibrational Hamiltonians or its effect on the rovibrational eigenenergies. In this study, a vibrational-coordinate-independent metric is proposed to quantify the magnitude of the Coriolis contribution to the rovibrational Hamiltonian. The impact of Coriolis coupling on the rovibrational eigenenergies is computed numerically exactly, using both full and various truncated Hamiltonians. The role played by the choice of the vibrational coordinate system-and especially by the choice of "embedding" or body-fixed frame-is examined extensively, both numerically and analytically. This investigation targets several molecular prototypes, all of which serve as important benchmarks for the high-resolution spectroscopic community. Most of these are triatomic molecules, including water (H216O), its deuterated isotopologues (D216O and HD16O), H3+, and ozone (16O3), but the tetratomic ammonia molecule (14NH3) is also investigated. These studies provide important insight into the nature of Coriolis coupling under various circumstances. The findings of this study also have significant practical ramifications, vis-à-vis the use of simplifying numerical approximation techniques in nuclear-motion computations.

On neglecting Coriolis and related couplings in first-principles rovibrational spectroscopy: considerations of symmetry, accuracy, and simplicity.

The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy levels is investigated, employing triatomic AB[Formula: see text] molecules as models. In particular, calculations are performed for H[Formula: see text][Formula: see text]O, across a range of vibrational and rotational excitations, both with and without the Coriolis contribution. A variety of different embedding choices are considered, together with a hierarchy of increasingly severe approximations culminating in a generalized version of the so-called "centrifugal sudden" method. Several surprising and remarkable conclusions are found, including that the Eckart embedding is not the best embedding choice.

Exact bound rovibrational spectra of the neon tetramer.

Exact quantum dynamics calculations are performed for the bound rovibrational states of the neon tetramer (Ne4) in its ground electronic state, using pair-wise Lennard-Jones potentials and the ScalIT suite of parallel codes. The vibrational states separate into a low-lying group mostly localized to a single potential well and a higher-energy delocalized group lying above the isomerization threshold-with such a structure serving as a testament to the "intermediate" quantum nature of the Ne4 system. To accurately and efficiently represent both groups of states, the phase-space optimized discrete variable representation (PSO-DVR) approach was used, as implemented in the ScalIT code. The resultant 1D PSO effective potentials also shed significant light on the quantum dynamics of the system. All vibrational states were computed well up into the isomerization band and labeled up to the classical isomerization threshold-defined as the addition of the classical energy of a single bond, ϵ = 24.7 cm-1, to the quantum ground state energy. Rovibrational energy levels for all total angular momentum values in the range J = 1-5 were also computed, treating all Coriolis coupling exactly.

Molecular dimers of methane clathrates: ab initio potential energy surfaces and variational vibrational states.

Motivated by the energetic and environmental relevance of methane clathrates, highly accurate ab initio potential energy surfaces (PESs) have been developed for the three possible dimers of the methane and water molecules: (H2O)2, CH4·H2O, and (CH4)2. While only a single monomer geometry was used for each monomer in the ab initio calculations, the PES parameterization makes it possible to produce distinct surfaces for all isotopologues within the rigid-monomer approximation. The PESs were fitted to computations at the frozen-core coupled-cluster level with single, double, and non-iterative triple excitations, employing basis sets of augmented triple- and quadruple-zeta quality plus bond functions, followed by extrapolations to the complete basis set limit. The long-range parts of the PESs are computed using the asymptotic version of symmetry-adapted perturbation theory based on a density-functional description of the monomers. All PESs are polarizable, i.e., in cluster or condensed-phase applications they approximate many-body effects by the induced dipole polarization model. The PESs were developed in a fully automated procedure applying the autoPES method, which is used for the first time to generate near-spectroscopic quality surfaces. The stationary points (SPs) on the PESs have been determined and compared with literature data. For CH4·H2O, previously unknown SPs have been identified and the first detailed study of the (CH4)2 potential energy landscape has been carried out. The PESs were used in variational quantum nuclear motion computations. For the water dimer, the resulting vibrational transitions are in excellent agreement with available high-resolution spectroscopic data. For (CH4)2, the intermonomer vibrational states are reported for the first time.

Rovibrational quantum dynamics of the vinyl radical and its deuterated isotopologues.

Rotational-vibrational states up to 3200 cm-1, beyond the highest-lying stretching fundamental, are computed variationally for the vinyl radical (VR), H2Cß[double bond, length as m-dash]CαH, and the following deuterated isotopologues of VR: CH2[double bond, length as m-dash]CD, CHD[double bond, length as m-dash]CH, and CD2[double bond, length as m-dash]CD. The height of the CαH tunneling rocking barrier of VR, partially responsible for the complex nuclear dynamics of VR and its isotopologues, is determined to be 1641 ± 25 cm-1 by the focal-point analysis approach. The definitive nuclear-motion computations performed utilize two previously published potential energy hypersurfaces and reveal interesting energy-level and tunneling patterns characterizing the internal motions of the four isotopologues. A full assignment, including symmetry labels, of the vibrational states computed for CH2[double bond, length as m-dash]CH is provided, whenever feasible, based on the analysis of wave functions and the related one- and two-mode reduced density matrices. The computed vibrational states of CH2[double bond, length as m-dash]CD and CD2[double bond, length as m-dash]CD are characterized up to slightly above the top of the barrier. Interestingly, it is the interplay of the ν6 (formally CH2 rock) and ν7 (formally CH rock) modes that determines the tunneling dynamics; thus, the description of tunneling in VR needs, as a minimum, the consideration of two in-plane bending motions at the two ends of the molecule. When feasible, the computed results are compared to their experimental counterparts as well as to previous computational results. Corrections to the placement of the ν4 and ν6 fundamentals of VR are proposed. Tunneling switching, a unique phenomenon characterizing tunneling in slightly asymmetric effective double-well potentials, is observed and discussed for CHD[double bond, length as m-dash]CH. Despite the extensive tunneling dynamics, the rotational energy-level structure of VR exhibits rigid-rotor-type behavior.

Rovibrational quantum dynamical computations for deuterated isotopologues of the methane-water dimer.

Rovibrational states of four dimers formed by the light and the heavy isotopologues of the methane and water molecules are computed using a potential energy surface taken from the literature. The general rovibrational energy-level pattern characteristic to all systems studied is analyzed employing two models of a dimer: the rigidly rotating complex and the coupled system of two rigidly rotating monomers. The rigid-rotor model highlights the presence of rovibrational sequences corresponding to formally negative rotational excitation energies, which is explained in terms of the coupled-rotors picture.

Complex rovibrational dynamics of the Ar·NO+ complex.

Rotational-vibrational states of the Ar·NO+ cationic complex are computed, below, above, and well above the complex's first dissociation energy, using variational nuclear motion and close-coupling scattering computations. The HSLH potential energy surface used in this study (J. Chem. Phys., 2011, 135, 044312) is characterized by a first dissociation energy of D0 = 887.0 cm-1 and supports 200 bound vibrational states. The bound-state vibrational energies and the corresponding wave functions allow the interpretation of the scarcely available experimental results about the intermonomer vibrational motion of the complex. A very large number of long-lived quasibound combination states of the three vibrational modes, exhibiting a very similar energy-level structure as that of the bound states, are found embedded in the continuum. Additional short-lived resonance states are also identified and their properties are analyzed.

Rovibrational transitions of the methane-water dimer from intermolecular quantum dynamical computations.

Rovibrational quantum nuclear motion computations, with J = 0, 1, and 2, are reported for the intermolecular degrees of freedom of the methane-water dimer, where J is the quantum number describing the overall rotation of the complex. The computations provide the first explanation of the far-infrared spectrum of this complex published in J. Chem. Phys., 1994, 100, 863. All experimentally reported rovibrational transitions, up to J = 2, can be assigned to transitions between the theoretically computed levels. The deviation of the experimental and computed rovibrational transitions is 0.5 cm(-1) for the ortho and 2 cm(-1) for the para species with a variance of 0.005 cm(-1). In addition to a lower systematic error, the overall agreement of theory and experiment is also better for the ortho species (involving ortho-H2O). Most importantly, for this species all levels of the 24-fold tunneling splitting manifold corresponding to the zero-point vibration (ZPV) are involved in at least one experimentally reported transition. For the para species there are a few energy levels in the computed ZPV manifold that are not involved in the reported experimental transitions. Furthermore, computed energy levels are identified that correspond to the ZPV tunneling splitting manifold of the secondary minimum structure of the dimer, which presumably appear in rovibrational transitions in the same energy regime as the observed transitions, but have not been experimentally reported.

Interpretation of the vibrational energy level structure of the astructural molecular ion H5 (+) and all of its deuterated isotopomers.

Variational nuclear motion computations, employing an exact kinetic energy operator and two different potential energy surfaces, are performed to study the first 60 vibrational states of the molecular ion H5 (+)≡ [H2-H-H2](+) and all of its deuterated isotopologues and isotopomers, altogether 12 species. Detailed investigation of the vibrational wavefunctions mostly results in physically intuitive labels not only for the fundamentals but also for the overtone and combination states computed. The torsional motion associated with the left and right diatomics appears to be well separated from the other vibrational degrees of freedom for all species. The unusual structure of the higher-lying bending states and the heavy mixing of the internal motions is partly due to the astructural character of all these molecular ions. The existence of distinct isotopomers in the H5-nDn (+), n = 1-4 cases, in the energy range studied, is confirmed. Two rules determine the stability order of the isotopomers: first, when possible, H prefers to stay in the middle of the ions rather than at the sides, and, second, the isotopomer with a homonuclear diatomic at the side is always lower in energy. The large number of precise vibrational energies of the present study, as well as the detailed assignment of the states, should serve as benchmarks for future studies by more approximate nuclear-motion treatments, such as diffusion Monte Carlo and multiconfiguration time-dependent Hartree.

Rovibrational energy levels of the F(-)(H2O) and F(-)(D2O) complexes.

The variational nuclear-motion codes ElVibRot and GENIUSH have been used to compute rotational-vibrational states of the F(-)(H2O) anion and its deuterated isotopologue, F(-)(D2O), employing a full-dimensional, semiglobal potential energy surface (PES) called SLBCL, developed as part of this study for the ground electronic state of the complex. The PES is determined from all-electron, explicitly correlated coupled-cluster singles, doubles, and connected triples [CCSD(T)-F12a] computations with an atom-centered, fixed-exponent Gaussian basis set of cc-pCVTZ-F12 quality. The SLBCL PES accurately reproduces the two equivalent minima of the complex, the corresponding transition barrier of C2v point-group symmetry, as well as the proton transfer and the dissociation asymptotes towards the products HF + OH(-) and F(-) + H2O, respectively. The code ElVibRot has been updated so that it can use curvilinear internal coordinates corresponding to a reaction path. The variationally computed vibrational energy levels are compared to relevant experimental and previously determined first-principles results. The vibrational states reveal the presence of pronounced anharmonic effects and considerable intermode couplings resulting in strong resonances, involving in particular the HOH bend and the ionic OH stretch motions. Tunneling results in particularly significant splittings for F(-)(H2O); as expected, the splittings are orders of magnitude smaller for the F(-)(D2O) molecule. The rovibrational energy levels reveal that, despite the large-amplitude vibrational motions, the rotations of F(-)(H2O) basically follow rigid-rotor characteristics.

Domino Tunneling.

Matrix-isolation experiments near 3 K and state-of-the-art quantum chemical computations demonstrate that oxalic acid [1, (COOH)2] exhibits a sequential quantum mechanical tunneling phenomenon not previously observed. Intensities of numerous infrared (IR) bands were used to monitor the temporal evolution of the lowest-energy O-H rotamers (1cTc, 1cTt, 1tTt) of oxalic acid for up to 19 days following near-infrared irradiation of the matrix. The relative energies of these rotamers are 0.0 (1cTc), 2.6 (1cTt), and 4.0 (1tTt) kcal mol(-1). A 1tTt → 1cTt → 1cTc isomerization cascade was observed with half-lives (t1/2) in different matrix sites ranging from 30 to 360 h, even though the sequential barriers of 9.7 and 10.4 kcal mol(-1) are much too high to be surmounted thermally under cryogenic conditions. A general mathematical model was developed for the complex kinetics of a reaction cascade with species in distinct matrix sites. With this model, a precise, global nonlinear least-squares fit was achieved simultaneously on the temporal profiles of nine IR bands of the 1cTc, 1cTt, and 1tTt rotamers. Classes of both fast (t(1/2) = 30-50 h) and slow (t(1/2) > 250 h) matrix sites were revealed, with the decay rate of the former in close agreement with first-principles computations for the conformational tunneling rates of the corresponding isolated molecules. Rigorous kinetic and theoretical analyses thus show that a "domino" tunneling mechanism is at work in these oxalic acid transformations.

Communication: rigidity of the molecular ion H(+)(5).

The fourth-age quantum chemical code GENIUSH is used for the variational determination of rotational-vibrational energy levels corresponding to reduced- and full-dimensional models of H(+)(5), a molecular ion exhibiting several strongly coupled large-amplitude motions. The computations are supplemented with one- and two-dimensional analytic results which help to understand the peculiar rovibrational energy-level structure computed correctly for the first time. An unusual aspect of the results is that the canonical Eckart-embedding of molecule-fixed axes, a cornerstone of the computational spectroscopy of semirigid molecules, is found to be inadequate. Furthermore, it is shown that while the 1D "active torsion" model provides proper results when compared to the full, 9D treatment, models excluding the torsion have limited physical significance. The structure of the rovibrational energy levels of H(+)(5) proves that this is a prototypical astructural molecule: the rotational and vibrational level spacings are of the same order of magnitude and the level structure drastically deviates from that computed via perturbed rigid-rotor and harmonic-oscillator models.