Classically forbidden nonadiabatic transitions in multidimensional chemical dynamics

An accurate method is proposed to deal with such nonadiabatic transitions as those energetically inaccessible, namely, classically forbidden transitions. This is formulated by using the corresponding Zhu-Nakamura formulas and finding the optimal paths in the classically forbidden tunneling regions that maximize the overall transition probabilities. This can be done for both the nonadiabatic tunneling type (so-called normal case in electron transfer) in which two diabatic potentials have opposite signs of slopes and the Landau-Zener type (inverted case) in which two diabatic potentials have the same sign of slopes. The method is numerically demonstrated to be useful for clarifying chemical and biological dynamics.

Wavepacket dynamical study of H-atom tunneling in catecholate monoanion: the role of intermode couplings and energy flow

We present a study of H-atom tunneling in catecholate monoanion through wavepacket dynamical simulations. In our earlier study of this symmetrical double-well system [Phys. Chem. Chem. Phys., 2022, 24, 10887], a limited number of transition state modes were identified as being important for the tunneling process. These include the imaginary frequency mode Q₁, the CO scissor mode Q₁₀, and the OHO bending mode Q₂₉. In this work, starting from non-stationary initial states prepared with excitations in these modes, we have carried out wavepacket dynamics in two and three dimensional spaces. We analyse the dynamical effects of the intermode couplings, in particular the role of energy flow between the studied modes on H-atom tunneling. We find that while Q₁₀ strongly modulates the donor-acceptor distance, it does not exchange energy with Q₁. However, excitation in Q₂₉ or Q₁ does lead to rapid energy exchange between these modes, which modifies the tunneling rate at early times.

Heavy-Atom Quantum Tunnelling in Spin Crossovers of Nitrenes

We simulate two recent matrix-isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak-coupling method (based on a linear approximation of the potentials) in describing these deep-tunnelling reactions. The more rigorous approach of semiclassical golden-rule instanton theory in conjunction with double-hybrid density-functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy-atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Cavity-Modulated Proton Transfer Reactions

Proton transfer is ubiquitous in many fundamental chemical and biological processes, and the ability to modulate and control the proton transfer rate would have a major impact on numerous quantum technological advances. One possibility to modulate the reaction rate of proton transfer processes is given by exploiting the strong light-matter coupling of chemical systems inside optical or nanoplasmonic cavities. In this work, we investigate the proton transfer reactions in the prototype malonaldehyde and Z-3-amino-propenal (aminopropenal) molecules using different quantum electrodynamics methods, in particular, quantum electrodynamics coupled cluster theory and quantum electrodynamical density functional theory. Depending on the cavity mode polarization direction, we show that the optical cavity can increase the reaction energy barrier by 10-20% or decrease the reaction barrier by ∼5%. By using first-principles methods, this work establishes strong light-matter coupling as a viable and practical route to alter and catalyze proton transfer reactions.

A simplistic computational procedure for tunneling splittings caused by proton transfer

In this manuscript, we present an approach for computing tunneling splittings for large amplitude motions. The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule. The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work, we also investigate the performance of different DFT and post-Hartree–Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.

Theoretical Study of Proton Tunneling in the Imidazole-Imidazolium Complex

Proton tunneling in the hydrogen-bonded imidazole–imidazolium complex ion has been studied theoretically. Ab initio CASSCF/6-311++G(d,p) calculations concerning geometry optimization and vibrational frequencies have been carried out for equilibrium and transition state structures of the system. Two-dimensional double-well model potentials were constructed on the basis of ab initio results and used to analyze the proton dynamics in the hydrogen bond and the influence of the excitation of low-frequency hydrogen-bond vibrations on the proton tunneling splittings. The energy of tunneling-split vibrational sublevels of the high-frequency tunneling mode have been calculated for its ground and first excited vibrational state for the series of excitations of the coupled low-frequency intramolecular hydrogen-bond modes. The promoting and suppressing effect of the low-frequency modes on the proton splittings was shown in the ground and first excited vibrational state of the tunneling mode. The vibrational sublevels form the two separate semicontinuous bands between which the absorption transitions may occur. This mechanism explains the experimentally observed splitting and doublet-component broadening of the high-frequency N–H stretching infrared (IR) absorption band.

Instanton calculations of tunneling splittings in chiral molecules

We report the ground state tunneling splittings (ΔE_± ) of a number of axially chiral molecules using the ring-polymer instanton (RPI) method (J. Chem. Phys., 2011, 134, 054109). The list includes isotopomers of hydrogen dichalcogenides H₂ X₂ (X = O, S, Se, Te, and Po), hydrogen thioperoxide HSOH and dichlorodisulfane S₂ Cl₂ . Ab initio electronic-structure calculations have been performed on the level of second-order Møller-Plesset perturbation (MP2) theory either with split-valance basis sets or augmented correlation-consistent basis sets on H, O, S, and Cl atoms. Energy-consistent pseudopotential and corresponding triple zeta basis sets of the Stuttgart group are used on Se, Te, and Po atoms. The results are further improved using single point calculations performed at the coupled cluster level with iterative singles and doubles and perturbative triples amplitudes. When available for comparison, our computed values of ΔE_± are found to lie within the same order of magnitude as values reported in the literature, although RPI also provides predictions for H₂ Po₂ and S₂ Cl₂ , which have not previously been directly calculated. Since RPI is a single-shot method which does not require detailed prior knowledge of the optimal tunneling path, it offers an effective way for estimating the tunneling dynamics of more complex chiral molecules, and especially those with small tunneling splittings.

Instanton theory of tunneling in molecules with asymmetric isotopic substitutions

We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.

Trajectory on-the-fly molecular dynamics approach to tunneling splitting in the electronic excited state: A case of tropolone

The semiclassical tunneling method is applied to evaluate the tunneling splitting of tropolone due to the intramolecular proton transfer in the electronic excited state, first time, in a framework of the trajectory on-the-fly molecular dynamics (TOF-MD) approach. To prevent unphysical zero-point vibrational energy transfer among the normal modes of vibration, quantum zero-point vibrational energies are assigned only to the vibrational modes related to intramolecular proton transfer, whereas the remaining modes are treated as bath modes. Practical ways to determine the tunnel-initiating points and tunneling path are introduced. It is shown that the tunneling splitting decreases as the bath-mode energy increases. The experimental tunneling splitting value is well reproduced by the present TOF-MD approach based on the Wentzel-Kramers-Brillouin (WKB) approximation.

Upper and lower bounds for tunneling splittings in a symmetric double-well potential

Ground state tunneling gaps: solid circles are mean of eigenvalues and lower bound gaps.

Concerted Pair Motion Due to Double Hydrogen Bonding: The Formic Acid Dimer Case

Formic acid dimer as the prototypical doubly hydrogen-bonded gas-phase species is discussed from the perspective of the three translational and the three rotational degrees of freedom which are lost when two formic acid molecules form a stable complex. The experimental characterisation of these strongly hindered translations and rotations is reviewed, as are attempts to describe the associated fundamental vibrations, their combinations, and their thermal shifts by different electronic structure calculations and vibrational models. A remarkable match is confirmed for the combination of a CCSD(T)-level harmonic treatment and an MP2-level anharmonic VPT2 correction. Qualitatively correct thermal shifts of the vibrational spectra can be obtained from classical molecular dynamics in CCSD(T)-quality force fields. A detailed analysis suggests that this agreement between experiment and composite theoretical treatment is not strongly affected by fortuitous error cancellation but fully converged variational treatments of the six pair or intermolecular modes and their overtones and combinations in this model system would be welcome.

Tunneling Splittings in Water Clusters from Path Integral Molecular Dynamics

We present calculations of tunneling splittings in selected small water clusters, based on a recently developed path integral molecular dynamics (PIMD) method. The ground-rotational-state tunneling motions associated with the largest splittings in the water dimer, trimer, and hexamer are considered, and we show that the PIMD predictions are in very good agreement with benchmark quantum and experimental results. As the tunneling spectra are highly sensitive to both the details of the quantum dynamics and the potential energy surface, our calculations are a validation of the MB-Pol surface as well as the accuracy of PIMD. The favorable scaling of PIMD with system size paves the way for calculations of tunneling splittings in large, nonrigid molecular systems with motions that cannot be treated accurately by other methods, such as the semiclassical instanton.

Path Integral Energy Landscapes for Water Clusters

The energy landscapes for a discretized path integral representation of the water dimer, trimer and pentamer are characterized in terms of the localized (classical) and delocalized minima and transition states. The transition states are finite-temperature approximations to the exact instanton path, and they are typically used to calculate the tunneling splittings or reaction rates. The features of the path integral landscape are explored, thus elucidating procedures that could usefully be automated when searching for instantons in larger systems. Our work not only clarifies the role of minima and transition states in path integral calculations but also enables us to analyze the quantum-to-classical transition.

Multidimensional WKB approximation for particle tunneling

In this paper we present a method for obtaining the WKB approximation for non-separable multidimensional potentials. At its leading order one has to solve the classical Hamilton-Jacobi equation with zero energy for which a very efficient method is proposed. The essence of this method lies in the recognition that in the vicinity to the potential minimum the solution of Schrödinger equation has to approach that of coupled harmonic oscillators. Quantum corrections to the semiclassical result are then obtained very easily and to an arbitrarily high order. The method is applied to the calculation of the tunneling splitting and tunneling lifetime. We show that classical turning points are part of the dynamical problem; they could not be determined simply from looking at the form of the potential, but are obtained from the solution of the pertinent equations of motion.

Quantum effects and quantum chaos in multidimensional tunneling

The ground-state energy splitting due to tunneling in two-dimensional double wells of the form V(x,y)=(x^{2}-R^{2})^{2}/8R^{2}+x^{2}-R^{2}/R^{2}γy+ω^{2}/2y^{2} is calculated. Several results are reported. First, we give a systematic WKB expansion of the splitting in series in powers of R^{-2}, each term of the series being a finite polynomial in γ^{2}. We find an ascending sequence of the values of the parameter γ characterizing the curvature of the classical path, for which the successive corrections to the leading order vanish. This effect arises because curvature of the path and quantum nature of motion cancel each other; it does not appear for one-dimensional double wells. Second, we find that for large curvatures, such as for those describing the proton transfer in a malonaldehyde and hydroxalate anion, this expansion is of no practical use. Thus, the WKB expansion is reordered to a strong coupling form, each term of the series in powers of R^{-2} being an infinite series in powers of γ[over ¯]^{2}, γ[over ¯]=γ/R. Third, we find that the radius of convergence of the series is determined by the singularity at γ[over ¯]_{s}=ω/2. At the singularity the system changes its character from being a double well to become a single well. Close to this singularity the classical action and its first quantum correction are found to be nonanalytic functions of γ[over ¯], most likely of the form [1-(γ[over ¯]/γ[over ¯]_{s})^{2}]^{α}, where α=1/2 and α=-1/2 for the classical action and its first quantum correction, respectively. Since in the semiclassical regime of large R the splitting is exponentially dependent on the value of the classical action and its first quantum correction, close to the singularity we establish strong sensitivity of the splitting on slight variations of the parameter γ[over ¯] entering the Hamiltonian linearly.

Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives

In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.

Development of semiclassical molecular dynamics simulation method

Various quantum mechanical effects such as nonadiabatic transitions, quantum mechanical tunneling and coherence play crucial roles in a variety of chemical and biological systems.

An ab initio potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1–4-mode subspaces

We report a full-dimensional, permutationally invariant potential energy surface (PES) for the cyclic formic acid dimer.

Mode-Specific Tunneling Splittings for a Sequential Double-Hydrogen Transfer Case: An Accurate Quantum Mechanical Scheme

We present the first accurate quantum dynamics calculations of mode-specific tunneling splittings in a sequential double-hydrogen transfer process. This is achieved in the vinylidene-acetylene system, the simplest molecular system of this kind, and by large-scale parallel computations with an efficient theoretical scheme developed by us. In our scheme, basis functions are customized for the hydrogen transfer process; a 4-dimensional basis contraction strategy is combined with the preconditioned inexact spectral transform method; efficient parallel implementation is achieved. Mode-specific permutation tunneling splittings of vinylidene states are reported and tremendous mode-specific promotion effects are revealed; in particular, the CH2 rock mode enhances the ground-state splitting by a factor of 10(3). We find that the ground-state vinylidene has a reversible-isomerization time of 622 ps, much longer than all previous estimates. Our calculations also shed light on the importance of the deep intermediate well and vibrational excitation in the double-hydrogen transfer processes.

Infrared spectra of SF6(-) x HCOOH x Ar(n) (n = 0-2): infrared triggered reaction and Ar-induced reactive inhibition

We present the infrared spectra of SF(6)(-) x HCOOH x Ar(m) (m=0-2) complexes. We find that the binding motif involves a single hydrogen bond between the SF(6)(-) anion and the OH group of the formic acid, with the CH group weakly tethered to a neighboring F atom. Similar to the case of hydrated SF(6)(-), the SF bond involved in the (OH-F) bond is significantly stretched and weakened by the attachment of the HCOOH ligand. The bare complex undergoes reaction upon infrared absorption in the CH/OH stretching region of the formic acid moiety, leading predominantly to the formation of SF(4)(-) + 2HF + CO(2). The reaction can be inhibited by attachment of two Ar atoms. We discuss a likely reaction mechanism in the framework of ab initio calculations, suggesting that reaction proceeds via tunneling through the potential barrier.