Investigating proton tunneling dynamics in the time-dependent Schrödinger equation

Understanding the temporal evolution of the wave function in the proton tunneling reactions allows us to make theoretical predictions on the possible femtosecond spectroscopy patterns. However, the analytical solution of the time-dependent Schrödinger equation of complex molecules is challenging and requires a high computational cost. In this study, we solve the time-dependent Schrödinger equation using the Fourier grid Hamiltonian method, highlighting its simplicity of calculation, even for multidimensional tunneling reactions. The obtained model is applied to studying malonaldehyde's two-dimensional intramolecular proton tunneling, comparing the results with those obtained using other computational methods.

Triel Bond Formed by Malondialdehyde and Its Influence on the Intramolecular H-Bond and Proton Transfer

Malondialdehyde (MDA) engages in a triel bond (TrB) with TrX₃ (Tr = B and Al; X = H, F, Cl, and Br) in three modes, in which the hydroxyl O, carbonyl O, and central carbon atoms of MDA act as the electron donors, respectively. A H···X secondary interaction coexists with the TrB in the former two types of complexes. The carbonyl O forms a stronger TrB than the hydroxyl O, and both of them are better electron donors than the central carbon atom. The TrB formed by the hydroxyl O enhances the intramolecular H-bond in MDA and thus promotes proton transfer in MDA-BX₃ (X = Cl and Br) and MDA-AlX₃ (X = halogen), while a weakening H-bond and the inhibition of proton transfer are caused by the TrB formed by the carbonyl O. The TrB formed by the central carbon atom imposes little influence on the H-bond. The BH₂ substitution on the central C-H bond can also realise the proton transfer in the triel-bonded complexes between the hydroxyl O and TrH₃ (Tr = B and Al).

Asymmetric substitution changes the UV-induced nonradiative decay pathway and the spectra behaviors of β-diketones

Asymmetric substitution has not been termed as an essential factor in studying photo-induced ultrafast dynamics of molecular system. Asymmetric 4-hydroxybut-3-en-2-one (HEO), together with symmetric malonaldehyde (MA) and acetylacetone (AA), have been provided as target sample to study the nonradiative decay (ND) processes of β-diketones. An effective ND pathway of the three molecules is presented that their excited second (S₂) states transfer to first (S₁) state by nonadiabatic surface hopping, and then transfer to triplet (T₁) state by crossing minimum energy crossing point (MECP), after which decay to ground (S₀) state through MECP. More importantly, the asymmetric substitution of HEO induces the proton transfer in the S₁ state and generates a proton-transferred conformer with lowest energy, which does not occur for MA and AA. This change exploits a new ND pathway that the S₁ state decays to the proton transferred T₁ state and then undergoes reverse proton transfer to S₀ state through the MECPs between the three states. The two pathways of HEO give detailed energy and geometric information on surface hopping of S₂/S₁ and MECPs of S₁/T₁/S₀, and interpret the reason of the ND pathway while not spectra emission. This result is significantly different from the previous reported ND pathway of photoisomerization or conical intersection between different states. This work shows that asymmetric substitution changes the molecular structure and then changes their spectra behaviors.

Monitoring transient events in infrared spectra using local mode analysis

Time-resolved Fourier transformed infrared (FTIR) spectroscopy of chemical reactions is highly sensitive to minimal spatiotemporal changes. Structural features are decoded and represented in a comprehensible manner by combining FTIR spectroscopy with biomolecular simulations. Local mode analysis (LMA) is a tool to connect molecular motion based on a quantum mechanics simulation with infrared (IR) spectral features and vice versa. Here, we present the python-based software tool of LMA and demonstrate the novel feature of LMA to extract transient structural details and identify the related IR spectra at the case example of malonaldehyde (MA). Deuterated MA exists in two almost equally populated tautomeric states separated by a low barrier for proton transfer so IR spectra represent a mixture of both states. By state-dependent LMA, we obtain pure spectra for each tautomeric state occurring within the quantum mechanics trajectory. By time-resolved LMA, we obtain a clear view of the transition between states in the spectrum. Through local mode decomposition and the band-pass filter, marker bands for each state are identified. Thus, LMA is beneficial to analyze the experimental spectra based on a mixture of states by determining the individual contributions to the spectrum and motion of each state.

Kinetic isotope effects and how to describe them

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.

The dissociation and recombination rates of CH4 through the Ni(111) surface: The effect of lattice motion

Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH₄ through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH₄ and CD₄, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.

Thermal Rate Constants for the O(3P) + CH4 → OH + CH3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape

The rate constants and kinetic isotope effects for the O(³P) + CH₄ reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.

Reproducing kernel potential energy surfaces in biomolecular simulations: Nitric oxide binding to myoglobin

Multidimensional potential energy surfaces based on reproducing kernel-interpolation are employed to explore the energetics and dynamics of free and bound nitric oxide in myoglobin (Mb). Combining a force field description for the majority of degrees of freedom and the higher-accuracy representation for the NO ligand and the Fe out-of-plane motion allows for a simulation approach akin to a mixed quantum mechanics/molecular mechanics treatment. However, the kernel-representation can be evaluated at conventional force-field speed. With the explicit inclusion of the Fe-out-of-plane (Fe-oop) coordinate, the dynamics and structural equilibrium after photodissociation of the ligand are correctly described compared to experiment. Experimentally, the Fe-oop coordinate plays an important role for the ligand dynamics. This is also found here where the isomerization dynamics between the Fe-ON and Fe-NO state is significantly affected whether or not this co-ordinate is explicitly included. Although the Fe-ON conformation is metastable when considering only the bound (2)A state, it may disappear once the (4)A state is included. This explains the absence of the Fe-ON state in previous experimental investigations of MbNO.

Reaction Rate Constants of CH4(ads) ⇌ CH3(ads) + H(ads) on Ni(111): The Effect of Lattice Motion

Methane dissociation on metal surfaces is of great commercial importance. The dissociation and recombination rate constants of CH4 on Ni(111) are calculated using the quantum instanton approach with the path integral Monte Carlo method. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically to reveal the effects of lattice motion and quantum tunneling. For the dissociation of CH4, the rates have the smallest value on the rigid lattice, while they possess the largest value on the quantum lattice. For instance, at 300 K, the rates on the classical and quantum lattices are 5 and 12 times larger than that on the rigid lattice, respectively. The curve of the Arrhenius plot for the dissociation rates on the rigid lattice demonstrates that the quantum tunneling effect of the ruptured H atom is remarkable, while the nearly invariable dissociation rates at low temperatures on the quantum lattice confirm that the thermally assisted tunneling should be dominant at low temperatures. For the recombination of CH4, the quantum lattice still has rates that are much larger than that of the rigid lattice. For instance, the ratio of the recombination rates on the quantum and rigid lattices is 12 at 300 K. The quantum tunneling effect seems to play a minor role in the recombination rates on the rigid lattice; however, the thermally assisted tunneling is still very significant for the recombination process.

Symmetry breaking in the axial symmetrical configurations of enolic propanedial, propanedithial, and propanediselenal: pseudo Jahn–Teller effect versus the resonance-assisted hydrogen bond theory

The origin of the symmetry breaking in the axial symmetrical configurations of enolic propanedial (1), propanedithial (2), and propanediselenal (3) have been investigated by means of time-dependence density functional theory and natural bond orbital interpretations. The results obtained at the quantum chemistry composite (G2MP2, CBS-QB3), ab initio molecular orbital (MP2/6-311++G**), and hybrid density functional theory (B3LYP/6-311++G**) levels of theory showed that the hydrogen-centered synchronous axial symmetrical (C2v) configurations of compounds 1–3 possessing the maximum π-electron delocalization within the M1=C2–C3=C4–M5–H6 keto-enol groups are less stable than their corresponding plane symmetrical (Cs) forms. Importantly, the symmetry breaking in the C2v configurations of the enol forms of compounds 1–3 to their corresponding plane symmetrical Cs configurations is due to the pseudo Jahn–Teller effect (PJTE) by mixing the ground A1 and excited B2 electronic states resulting in a PJT (A1 + B2) ⊗ b2 problem. We may expect that by the decrease of the energy gaps between reference states in the C2v forms that are involved in the PJTE decrease from compound 1 to compound 3, the PJT stabilization energy (PJTSE) may increase but the results obtained showed that the corresponding PJTSEs decrease. This fact can be justified by the increase of the electron delocalizations from the nonbonding orbitals of the C=M moieties to the antibonding orbitals of the H–M bonds, which leads to an increase of the π-electron delocalization within the M1=C2–C3=C4–M5–H6 keto-enol groups. In confrontation between the impacts of the resonance-assisted hydrogen bond and PJTE in the structural and configurational properties of compounds 1–3, PJTE has an overwhelming contribution and causes the symmetry breaking of the C2v configurations to their corresponding Cs forms. The correlations between the structural parameters, synchronicity indices, natural charges, PJTSEs, electron delocalizations, and the hardness of compounds 1–3 have been investigated.

Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral

Enzymatic reactions are integral components in many biological functions and malfunctions. The iconic structure of each reaction path for elucidating the reaction mechanism in details is the molecular structure of the rate-limiting transition state (RLTS). But RLTS is very hard to get caught or to get visualized by experimentalists. In spite of the lack of explicit molecular structure of the RLTS in experiment, we still can trace out the RLTS unique "fingerprints" by measuring the isotope effects on the reaction rate. This set of "fingerprints" is considered as a most direct probe of RLTS. By contrast, for computer simulations, oftentimes molecular structures of a number of TS can be precisely visualized on computer screen, however, theoreticians are not sure which TS is the actual rate-limiting one. As a result, this is an excellent stage setting for a perfect "marriage" between experiment and theory for determining the structure of RLTS, along with the reaction mechanism, i.e., experimentalists are responsible for "fingerprinting", whereas theoreticians are responsible for providing candidates that match the "fingerprints". In this Review, the origin of isotope effects on a chemical reaction is discussed from the perspectives of classical and quantum worlds, respectively (e.g., the origins of the inverse kinetic isotope effects and all the equilibrium isotope effects are purely from quantum). The conventional Bigeleisen equation for isotope effect calculations, as well as its refined version in the framework of Feynman's path integral and Kleinert's variational perturbation (KP) theory for systematically incorporating anharmonicity and (non-parabolic) quantum tunneling, are also presented. In addition, the outstanding interplay between theory and experiment for successfully deducing the RLTS structures and the reaction mechanisms is demonstrated by applications on biochemical reactions, namely models of bacterial squalene-to-hopene polycyclization and RNA 2'-O-transphosphorylation. For all these applications, we used our recently-developed path-integral method based on the KP theory, called automated integration-free path-integral (AIF-PI) method, to perform ab initio path-integral calculations of isotope effects. As opposed to the conventional path-integral molecular dynamics (PIMD) and Monte Carlo (PIMC) simulations, values calculated from our AIF-PI path-integral method can be as precise as (not as accurate as) the numerical precision of the computing machine. Lastly, comments are made on the general challenges in theoretical modeling of candidates matching the experimental "fingerprints" of RLTS. This article is part of a Special Issue entitled: Enzyme Transition States from Theory and Experiment.

The direct and precursor mediated dissociation rates of H2 on a Ni(111) surface

The dissociation and recombination rates of physisorbed H2, and the direct and steady state dissociation (i.e., the precursor mediated dissociation) rates of gas phase H2 on Ni(111), as well as the corresponding kinetic isotope effects, are calculated using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. All these rates except the recombination one first decrease and then increase with the increasing temperature, and their minimum values appear at about 250, 300 and 250 K, respectively. These non-monotonic behaviors reveal that the quantum effect of H2 should be very remarkable at low temperatures. The steady state rates are smaller than the direct rates at low temperatures, however, they become larger than the direct ones at high temperatures, these two kinds of rates become equal at about 400 and 300 K on the rigid and quantum lattices, respectively. The quantum motion of the lattice can enhance the direct and steady state rates, and it increases the steady state rate much more than the direct one, for instance, the direct and steady state rates on the quantum lattice are 1.30 and 2.08 times larger than that on the rigid one at 300 K. The calculated kinetic isotope effects are much larger than 1, which reveals that H2 always has a larger rate than that of D2, and the direct process predicts much larger kinetic isotope effects than the steady state process at low temperatures. In addition, the kinetic isotope effects are not affected by the lattice motion.

Multisurface Adiabatic Reactive Molecular Dynamics

Adiabatic reactive molecular dynamics (ARMD) simulation method is a surface-crossing algorithm for modeling chemical reactions in classical molecular dynamics simulations using empirical force fields. As the ARMD Hamiltonian is time dependent during crossing, it allows only approximate energy conservation. In the current work, the range of applicability of conventional ARMD is explored, and a new multisurface ARMD (MS-ARMD) method is presented, implemented in CHARMM and applied to the vibrationally induced photodissociation of sulfuric acid (H2SO4) in the gas phase. For this, an accurate global potential energy surface (PES) involving 12 H2SO4 and 4 H2O + SO3 force fields fitted to MP2/6-311G++(2d,2p) reference energies is employed. The MS-ARMD simulations conserve total energy and feature both intramolecular H-transfer reactions and water elimination. An analytical treatment of the dynamics in the crossing region finds that conventional ARMD can approximately conserve total energy for limiting cases. In one of them, the reduced mass of the system is large, which often occurs for simulations of solvated biomolecular systems. On the other hand, MS-ARMD is a general approach for modeling chemical reactions including gas-phase, homogeneous, heterogeneous, and enzymatic catalytic reactions while conserving total energy in atomistic simulations.