*Phys Chem Chem Phys ; 2020 Jul 15.*

##### RESUMO

Thermal rate constants for Mu + CH4, Mu + C2H6 and Mu + C3H8 and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C3H8 at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH4 using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

*Nat Commun ; 11(1): 1689, 2020 04 03.*

##### RESUMO

The diffusion of water molecules and clusters across the surfaces of materials is important to a wide range of processes. Interestingly, experiments have shown that on certain substrates, water dimers can diffuse more rapidly than water monomers. Whilst explanations for anomalously fast diffusion have been presented for specific systems, the general underlying physical principles are not yet established. We investigate this through a systematic ab initio study of water monomer and dimer diffusion on a range of surfaces. Calculations reveal different mechanisms for fast water dimer diffusion, which is found to be more widespread than previously anticipated. The key factors affecting diffusion are the balance of water-water versus water-surface bonding and the ease with which hydrogen-bond exchange can occur (either through a classical over-the-barrier process or through quantum-mechanical tunnelling). We anticipate that the insights gained will be useful for understanding future experiments on the diffusion and clustering of hydrogen-bonded adsorbates.

*J Chem Theory Comput ; 16(5): 2883-2895, 2020 May 12.*

##### RESUMO

Quasi-classical mapping Hamiltonian methods have recently emerged as a promising approach for simulating electronically nonadiabatic molecular dynamics. The classical-like dynamics of the overall system within these methods makes them computationally feasible, and they can be derived based on well-defined semiclassical approximations. However, the existence of a variety of different quasi-classical mapping Hamiltonian methods necessitates a systematic comparison of their respective advantages and limitations. Such a benchmark comparison is presented in this paper. The approaches compared include the Ehrenfest method, the symmetrical quasi-classical (SQC) method, and five variations of the linearized semiclassical (LSC) method, three of which employ a modified identity operator. The comparison is based on a number of popular nonadiabatic model systems; the spin-boson model, a Frenkel biexciton model, and Tully's scattering models 1 and 2. The relative accuracy of the different methods is tested by comparing with quantum-mechanically exact results for the dynamics of the electronic populations and coherences. We find that LSC with the modified identity operator typically performs better than the Ehrenfest and standard LSC approaches. In comparison to SQC, these modified methods appear to be slightly more accurate for condensed phase problems, but for scattering models there is little distinction between them.

*Phys Chem Chem Phys ; 22(19): 10687-10698, 2020 May 21.*

##### RESUMO

The aqueous ferrous-ferric system provides a classic example of an electron-transfer process in solution. There has been a long standing argument spanning more than three decades around the importance of nuclear tunnelling in this system, with estimates based on Wolynes theory suggesting a quantum correction factor of 65, while estimates based on a related spin-boson model suggest a smaller factor of 7-36. Recently, we have shown that Wolynes theory can break down for systems with multiple transition states leading to an overestimation of the rate, and we suggest that a liquid system such as the one investigated here may be particularly prone to this. We re-investigate this old yet interesting system with the first application of the recently developed golden-rule quantum transition-state theory (GR-QTST). We find that GR-QTST can be applied to this complex system without apparent difficulties and that it gives a prediction for the quantum rate 6 times smaller than that from Wolynes theory. The fact that these theories give different results suggests that although it is well known that the system can be treated using linear response and therefore resembles a spin-boson model in the classical limit, this approximation is questionable in the quantum case. It also intriguingly suggests the possibility that the previous predictions were overestimating the rate due to a break down of Wolynes theory.

*J Chem Phys ; 152(3): 034106, 2020 Jan 21.*

##### RESUMO

Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunneling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper, we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunneling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunneling is particularly prevalent in the inverted regime, even at room temperature, and thus, this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.

*Phys Chem Chem Phys ; 22(3): 1035-1044, 2020 Jan 21.*

##### RESUMO

We apply the semiclassical instanton method to calculate all feasible tunnelling pathways in the water pentamer. Similarly to the water trimer, there are labile flip dynamics as well as a number of different bifurcation pathways coupled to flips. In contrast to the trimer, the puckering motion of the oxygen ring makes the ring-polymer instanton approach difficult to converge, a problem which is resolved by using a recently developed time-independent formalism of the method. We use the results to predict the complete ground-state tunnelling splitting pattern of 320 states, which should help in the continuing effort to assign the experimental spectrum. A comparison between the rearrangement pathways in the water trimer and pentamer sheds light on the many-body cooperative effects of hydrogen bonding which are important for a full understanding of the liquid state.

*J Chem Phys ; 151(21): 214101, 2019 Dec 07.*

##### RESUMO

We describe a path-integral molecular dynamics implementation of our recently developed golden-rule quantum transition-state theory (GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against the exact results. We demonstrate that for systems exhibiting two or more transition states, rates computed using Wolynes theory [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accurate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit, where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynes theory is not valid in this case, which results in the predictions of unphysical reaction pathways, while the energy constraint employed by GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate results for a strongly anharmonic system by sampling configurations around the instanton pathway without making the semiclassical approximation. These promising results indicate that the GR-QTST method could be an efficient and accurate approach for simulating electron-transfer reactions in complex molecular systems.

*J Chem Phys ; 151(14): 144111, 2019 Oct 14.*

##### RESUMO

We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit. However, for asymmetric barriers, one of the two paths takes an unphysically low energy and dominates the expression, leading to order-of-magnitude errors in the rate predictions. Nevertheless, semiclassical instanton theory remains accurate. We conclude that semiclassical instanton theory can be obtained directly from the semiclassical limit of the quantum instanton only for symmetric systems. We suggest a modification of the quantum instanton approach which avoids sampling the spurious path and thus has a stronger connection to semiclassical instanton theory, giving numerically accurate predictions even for very asymmetric systems in the low temperature limit.

*Faraday Discuss ; 221(0): 150-167, 2019 Dec 16.*

##### RESUMO

The mapping approach addresses the mismatch between the continuous nuclear phase space and discrete electronic states by creating an extended, fully continuous phase space using a set of harmonic oscillators to encode the populations and coherences of the electronic states. Existing quasiclassical dynamics methods based on mapping, such as the linearised semiclassical initial value representation (LSC-IVR) and Poisson bracket mapping equation (PBME) approaches, have been shown to fail in predicting the correct relaxation of electronic-state populations following an initial excitation. Here we generalise our recently published modification to the standard quasiclassical approximation for simulating quantum correlation functions. We show that the electronic-state population operator in any system can be exactly rewritten as a sum of a traceless operator and the identity operator. We show that by treating the latter at a quantum level instead of using the mapping approach, the accuracy of traditional quasiclassical dynamics methods can be drastically improved, without changes to their underlying equations of motion. We demonstrate this approach for the seven-state Frenkel-exciton model of the Fenna-Matthews-Olson light harvesting complex, showing that our modification significantly improves the accuracy of traditional mapping approaches when compared to numerically exact quantum results.

*J Chem Phys ; 151(4): 044119, 2019 Jul 28.*

##### RESUMO

We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-12 coherent state, we use the Stratonovich-Weyl transform to construct a classical phase space of a spin vector constrained to a spherical surface whose radius is consistent with the quantum magnitude of the spin. In contrast with the singly excited harmonic oscillator basis used in Meyer-Miller-Stock-Thoss (MMST) mapping, the theory requires no additional projection operators onto the space of physical states. When treated under a quasiclassical approximation, we show that the resulting dynamics are equivalent to those generated by the MMST Hamiltonian. What differs is the value of the zero-point energy parameter as well as the initial distribution and the measurement operators used in constructing correlation functions. For various spin-boson models, the results of the method are seen to be a significant improvement compared to both standard Ehrenfest dynamics and linearized semiclassical MMST mapping, without adding any computational complexity.

*J Chem Theory Comput ; 15(5): 2816-2825, 2019 May 14.*

##### RESUMO

Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around it. In the standard method, calculating the fluctuation terms involves the diagonalization of a large matrix, which can be unfeasible for large systems with a high number of ring-polymer beads. Here we present a method for computing the instanton fluctuations with a large reduction in computational scaling. This method is applied to three reactions described by fitted, analytic, and on-the-fly ab initio potential-energy surfaces and is shown to be numerically stable for the calculation of thermal reaction rates even at very low temperature.

*J Chem Phys ; 150(10): 104107, 2019 Mar 14.*

##### RESUMO

We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy, and tunneling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and show numerically that it is also accurate for anharmonic systems. There is still a certain amount of freedom available in generalizing the method to multidimensional systems, and the suggestion we make here is exact in the classical limit but not rigorously size consistent in general. It is nonetheless seen to perform well for multidimensional spin-boson models, where it even gives good predictions for rates in the Marcus inverted regime.

*Nat Chem ; 11(4): 367-374, 2019 04.*

##### RESUMO

A microscopic picture of hydrogen-bond structure and dynamics in ion hydration shells remains elusive. Small ion-dihydrate molecular complexes are ideal systems with which to investigate the interplay and competition between ion-water and water-water interactions. Here, state-of-the-art quantum dynamics simulations provide evidence for tunnelling in hydrogen-bond rearrangements in the iodide-dihydrate complex and show that it can be controlled through isotopic substitutions. We find that the iodide ion weakens the neighbouring water-water hydrogen bond, leading to faster water reorientation than in the analogous water trimer. These faster dynamics, which are apparently at odds with the slowdown observed in the first hydration shell of iodide in solution, can be traced back to the presence of a free OH bond in the iodide-dihydrate complex, which effectively triggers the overall structural rearrangements within it. Besides providing indirect support for cooperative hydrogen-bond dynamics in iodide solutions, the analysis presented here suggests that iodide ions may accelerate hydrogen-bond rearrangements at aqueous interfaces, where neighbouring water molecules can be undercoordinated.

*J Chem Phys ; 150(7): 071101, 2019 Feb 21.*

##### RESUMO

Simulating the nonadiabatic dynamics of condensed-phase systems continues to pose a significant challenge for quantum dynamics methods. Approaches based on sampling classical trajectories within the mapping formalism, such as the linearized semiclassical initial value representation (LSC-IVR), can be used to approximate quantum correlation functions in dissipative environments. Such semiclassical methods however commonly fail in quantitatively predicting the electronic-state populations in the long-time limit. Here we present a suggestion to minimize this difficulty by splitting the problem into two parts, one of which involves the identity and treating this operator by quantum-mechanical principles rather than with classical approximations. This strategy is applied to numerical simulations of spin-boson model systems, showing its potential to drastically improve the performance of LSC-IVR and related methods with no change in the equations of motion or the algorithm in general, but rather by simply using different functional forms of the observables.

*J Am Chem Soc ; 141(6): 2526-2534, 2019 Feb 13.*

##### RESUMO

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule, a complex paradigmatic system in which the making and breaking of H-bonds in a highly anharmonic potential energy surface require a quantum mechanical treatment not only of the electrons but also of the nuclei. We combine density functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates but between 100 and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of 2.19 × 1011 s-1 at 150 K and 0.63 × 1011 s-1 at 100 K, in good agreement with experiment. We also reproduce the puzzling N-H stretching band of porphycene with very good accuracy from thermostated ring-polymer molecular dynamics simulations. The position and line shape of this peak, centered at around 2600 cm-1 and spanning 750 cm-1, stem from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to cis-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems.

*Faraday Discuss ; 212(0): 237-258, 2018 12 13.*

##### RESUMO

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.

*J Chem Phys ; 148(20): 200901, 2018 May 28.*

##### RESUMO

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

*Chimia (Aarau) ; 72(5): 309-312, 2018 May 30.*

##### RESUMO

Transition-state theory is one of the most successful theories in chemistry. Not only does it provide a simple formula for computing the rate of a reaction but it defines our understanding of how a chemical reaction occurs - by overcoming an energy barrier. However, the theory is based on classical assumptions and ignores several quantum effects which can be important for certain reactions, particularly those involving hydrogen transfer at low temperatures. We are developing a more general quantum version of transition-state theory which reveals how quantum tunnelling and nonadiabatic effects can strongly affect the rate.

*J Chem Phys ; 148(10): 102311, 2018 Mar 14.*

##### RESUMO

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.