Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges.

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

The Role of Spin-Orbit Coupling in the Linear Absorption Spectrum and Intersystem Crossing Rate Coefficients of Ruthenium Polypyridyl Dyes.

The successful use of molecular dyes for solar energy conversion requires efficient charge injection, which in turn requires the formation of states with sufficiently long lifetimes (e.g., triplets). The molecular structure elements that confer this property can be found empirically, however computational predictions using ab initio electronic structure methods are invaluable to identify structure-property relations for dye sensitizers. The primary challenge for simulations to elucidate the electronic and nuclear origins of these properties is a spin-orbit interaction which drives transitions between electronic states. In this work, we present a computational analysis of the spin-orbit corrected linear absorption cross sections and intersystem crossing rate coefficients for a derivative set of phosphonated tris(2,2'-bipyridine)ruthenium(2+) dye molecules. After sampling the ground state vibrational distributions, the predicted linear absorption cross sections indicate that the mixture between singlet and triplet states plays a crucial role in defining the line shape of the metal-to-ligand charge transfer bands in these derivatives. Additionally, an analysis of the intersystem crossing rate coefficients suggests that transitions from the singlet into the triplet manifolds are ultrafast with rate coefficients on the order of 1013 s-1 for each dye molecule.

Fantastical excited state optimized structures and where to find them.

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface.

Pitfalls in the n-mode representation of vibrational potentials.

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm.

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Dynamic signatures of electronically nonadiabatic coupling in sodium hydride: a rigorous test for the symmetric quasi-classical model applied to realistic, ab initio electronic states in the adiabatic representation.

Sodium hydride (NaH) in the gas phase presents a seemingly simple electronic structure making it a potentially tractable system for the detailed investigation of nonadiabatic molecular dynamics from both computational and experimental standpoints. The single vibrational degree of freedom, as well as the strong nonadiabatic coupling that arises from the excited electronic states taking on considerable ionic character, provides a realistic chemical system to test the accuracy of quasi-classical methods to model population dynamics where the results are directly comparable against quantum mechanical benchmarks. Using a simulated pump-probe type experiment, this work presents computational predictions of population transfer through the avoided crossings of NaH via symmetric quasi-classical Meyer-Miller (SQC/MM), Ehrenfest, and exact quantum dynamics on realistic, ab initio potential energy surfaces. The main driving force for population transfer arises from the ground vibrational level of the D1Σ+ adiabatic state that is embedded in the manifold of near-dissociation C1Σ+ vibrational states. When coupled through a sharply localized first-order derivative coupling most of the population transfers between t = 15 and t = 30 fs depending on the initially excited vibronic wavepacket. While quantum mechanical effects are expected due to the reduced mass of NaH, predictions of the population dynamics from both the SQC/MM and Ehrenfest models perform remarkably well against the quantum dynamics benchmark. Additionally, an analysis of the vibronic structure in the nonadiabatically coupled regime is presented using a variational eigensolver methodology.

Spectroscopic Signatures of Mode-Dependent Tunnel Splitting in the Iodide-Water Binary Complex.

The gas-phase vibrational spectrum of the isolated iodide-water cluster ion (I-·H2O), first reported in 1996, presents one of the most difficult, long-standing spectroscopic puzzles involving ion microhydration. Although the spectra of the smaller halides are well described in the context of an asymmetrical ground-state structure in which only one OH group is hydrogen-bonded to the ion, the I-·H2O spectrum displays multiplet structures with partially resolved rotational patterns that are additionally influenced by quantum nuclear spin statistics. In this study, this complex behavior is unraveled with a combination of experimental methods, including ion preparation in a temperature-controlled ion trap and spectral simplification through applications of tag-free, two-color IR-IR double-resonance spectroscopy. Analysis of the double-resonance spectra reveals a vibrational ground-state tunneling splitting of about 20 cm-1, which is on the same order as the spacing between the peaks that comprise the multiplet structure. These findings are further supported by the results obtained from a fully coupled, six-dimensional calculation of the vibrational spectrum. The underlying level structure can then be understood as a consequence of experimentally measurable, vibrational mode-dependent tunneling splittings (which, in the case of the ground vibrational state, is comparable to the rotational energy spacing between levels with Ka = 0 and 1), as well as Fermi resonance interactions. The latter include the hydrogen-bonded OH stretches and combination bands that involve the HOH bend overtones and soft-mode excitations of frustrated translation and rotation displacements of the water molecule relative to the ion. These anharmonic couplings yield closely spaced bands that are activated in the IR by borrowing intensity from the OH stretch fundamentals.

Infrared signatures of isomer selectivity and symmetry breaking in the Cs+(H2O)3 complex using many-body potential energy functions.

A quantitative description of the interactions between ions and water is key to characterizing the role played by ions in mediating fundamental processes that take place in aqueous environments. At the molecular level, vibrational spectroscopy provides a unique means to probe the multidimensional potential energy surface of small ion-water clusters. In this study, we combine the MB-nrg potential energy functions recently developed for ion-water interactions with perturbative corrections to vibrational self-consistent field theory and the local-monomer approximation to disentangle many-body effects on the stability and vibrational structure of the Cs+(H2O)3 cluster. Since several low-energy, thermodynamically accessible isomers exist for Cs+(H2O)3, even small changes in the description of the underlying potential energy surface can result in large differences in the relative stability of the various isomers. Our analysis demonstrates that a quantitative account for three-body energies and explicit treatment of cross-monomer vibrational couplings are required to reproduce the experimental spectrum.

Tuning vibrational mode localization with frequency windowing.

Local-mode coordinates have previously been shown to be an effective starting point for anharmonic vibrational spectroscopy calculations. This general approach borrows techniques from localized-orbital machinery in electronic structure theory and generates a new set of spatially localized vibrational modes. These modes exhibit a well-behaved spatial decay of anharmonic mode couplings, which, in turn, allows for a systematic, a priori truncation of couplings and increased computational efficiency. Fully localized modes, however, have been found to lead to unintuitive mixtures of characteristic motions, such as stretches and bends, and accordingly large bilinear couplings. In this work, a very simple, tunable localization frequency window is introduced, in order to realize the transition from normal modes to fully localized modes. Partial localization can be achieved by localizing only pairs of modes within this traveling frequency window, which allows for intuitive interpretation of modes. The optimal window size is suggested to be a few hundreds of wave numbers, based on small- to medium-sized test systems, including water clusters and polypeptides. The new sets of partially localized coordinates retain their spatial coupling decay behavior while providing a reduced number of potential energy evaluations for convergence of anharmonic spectra.

A Free Energy Decomposition Analysis: Insight into Binding Thermodynamics from Absolutely Localized Molecular Orbitals.

Traditional energy decomposition analysis (EDA) methods can provide an interpretive decomposition of non-covalent electronic binding energies. However, by definition, they neglect entropic effects and nuclear contributions to the enthalpy. With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a Gibbs decomposition analysis (GDA) by coupling the absolutely localized molecular orbital treatment of electrons in non-covalent interactions with the simplest possible quantum rigid rotor-harmonic oscillator treatment of nuclear motion at finite temperature. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and water binding to an open metal site in the metal-organic framework Cu(I)-MFU-4l. The results show enthalpic trends that generally track the electronic binding energy and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature.

Caught in the act: real-time observation of the solvent response that promotes excited-state proton transfer in pyranine.

Photo-induced excited-state proton transfer (ESPT) reactions are of central importance in many biological and chemical processes. Identifying mechanistic details of the solvent reorganizations that facilitate proton transfer however, is challenging for current experimental and theoretical approaches. Using optical pump THz probe (OPTP) spectroscopy and molecular dynamics simulations, we were able to elucidate the ultrafast changes in the solvation environment for three derivatives of pyranine: the photoacid HPTS, the methoxy derivative MPTS, and the photobase OPTS. Experimentally, we find damped oscillations in the THz signal at short times and our simulations enable their assignment to vibrational energy transfer beatings between the photoexcited chromophore and nearby solvent molecules. The simulations of HPTS reveal strikingly efficient sub-ps energy transfer into a particular solvent mode, that is active near 4 THz, and which can provide the requisite energy required for solvent reorganization promoting proton transfer. Similar oscillations are present in the THz signal for all three derivatives, however the signal is damped rapidly for HPTS (within 0.4 ps) and more slowly for MPTS (within 1.4 ps) and OPTS (within 2.0 ps). For HPTS, we also characterize an additional phonon-like propagation of the proton into the bulk with a 140 ps period and an 83 ps damping time. Thermalization of the solvent occurs on a time scale exceeding 120 ps.

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics.

The ab initio molecular dynamics (AIMD) method provides a computational route for the real-time simulation of reactive chemistry. An often-overlooked capability of this approach is the opportunity to examine the electronic evolution of a chemical system. For AIMD trajectories based on Hartree-Fock or density functional theory methods, the real-time evolution of single-particle molecular orbitals (MOs) can provide detailed insights into the time-dependent electronic structure of molecules. The evolving electronic Hamiltonians at each MD step pose problems for tracking and visualizing a given MO's character, ordering, and associated phase throughout an MD trajectory, however. This report presents and assesses a simple algorithm for correcting these deficiencies by exploiting similarity projections of the electronic structure between neighboring MD steps. Two aspects bring this analysis beyond a simple step-to-step projection scheme. First, the challenging case of coincidental orbital degeneracies is resolved via a quadrupole-field perturbation that nonetheless rigorously preserves energy conservation. Second, the resulting orbitals are shown to evolve adiabatically, in spite of the "preservation of character" concept that undergirds a projection of neighboring steps' MOs. The method is tested on water clusters, which exhibit considerable dynamic degeneracies, as well as a classic organic nucleophilic substitution reaction, in which the adiabatic evolution of the bonding orbitals clarifies textbook interpretations of the electronic structure during this reactive collision.