Molecular dynamics with quantum transitions for proton transfer: Quantum treatment of hydrogen and donor–acceptor motions

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

Theory of vibrational polariton chemistry in the collective coupling regime

We theoretically demonstrate that the chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

Quantum dynamics in open quantum-classical systems

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Signatures of nanoconfinement on the linear and nonlinear vibrational spectroscopy of a model hydrogen-bonded complex dissolved in a polar solvent

The one-dimensional IR (1D-IR) absorption and IR pump-probe spectra of a hydrogen stretch in a model hydrogen-bonded complex dissolved in a polar solvent confined in spherical hydrophobic cavities of different sizes were simulated using ground-state mixed quantum-classical dynamics. Due to a thorough analysis of key properties of the complex and solvent from equilibrium trajectory data, we were able to gain insight into the microscopic details underlying the spectra. Both the 1D-IR and IR pump-probe spectra manifested the effects of confinement on the relative stabilities of the covalent and ionic forms of the complex through pronounced changes in their peak intensities and numbers. However, in contrast to the 1D-IR spectra, the time-resolved pump-probe spectra were found to be uniquely sensitive to the changes in the molecular dynamics as the cavity size is varied. In particular, it was found that the variations in the time evolutions of the peak intensities in the pump-probe spectra reflect the differences in the solvation dynamics associated with the various forms of the complex in different locations within the cavities. The ability to detect these differences underscores the advantage of using pump-probe spectroscopy for studying nanoconfined systems.

Computational study of the one- and two-dimensional infrared spectra of a proton-transfer mode in a hydrogen-bonded complex dissolved in a polar nanocluster

The signatures of nanosolvation on the one- and two-dimensional (1D and 2D) IR spectra of a proton-transfer mode in a hydrogen-bonded complex dissolved in polar solvent molecule nanoclusters of varying size are elucidated by using mixed quantum-classical molecular dynamics simulations. For this particular system, increasing the number of solvent molecules successively from N=7 to N=9 initiates the transition of the system from a cluster state to a bulk-like state. Both the 1D and 2D IR spectra reflect this transition through pronounced changes in their peak intensities and numbers, but the time-resolved 2D IR spectra also manifest spectral features that uniquely identify the onset of the cluster-to-bulk transition. In particular, it is observed that in the 1D IR spectra, the relative intensities of the peaks change such that the number of peaks decreases from three to two as the size of the cluster increases from N=7 to N=9. In the 2D IR spectra, off-diagonal peaks are observed in the N=7 and N=8 cases at zero waiting time, but not in the N=9 case. It is known that there are no off-diagonal peaks in the 2D IR spectrum of the bulk version of this system at zero waiting time, so the disappearance of these peaks is a unique signature of the onset of bulk-like behavior. Through an examination of the trajectories of various properties of the complex and solvent, it is possible to relate the emergence of these off-diagonal peaks to an interplay between the vibrations of the complex and the solvent polarization dynamics.

First observation of ultrafast intramolecular proton transfer rate between electronic ground states in solution

Despite the importance of ultrafast (time scale exceeding 10(-11) s) intramolecular proton transfer (PT) events between electronic ground states in solution, experimental determination of the rates of such reactions has not yet been accomplished because of the limitations of the utilized methods. The objective of this study was to evaluate the PT rates of intramolecular O···H···O hydrogen-bonded systems in solution through the (1)H spin-lattice relaxation times of the hydroxyl protons, induced by the (1)H-(17)O dipolar interactions (T(1dd)(OH)), taking into account the contribution of the OH reorientational motion to T(1dd)(OH). Solutions of the benzoic acid dimer (BA dimer), 1-benzoyl-6-hydroxy-6-phenylfulvene (Fulvene), and dibenzoylmethane (DBM) were chosen as test systems. For Fulvene in CCl(4), the PT time, τ(PT), was deduced to be 7 × 10(-11) s. In the case of the BA dimer in CCl(4), the τ(PT) value was considerably greater than the OH reorientational correlation time, τ(R(OH)) = 4.3 × 10(-11) s. In contrast, the experimental results for DBM in CCl(4) indicated that the proton is located about midway between the two oxygen atoms, that is, the PT potential energy surface is a single well or a double well with a PT barrier near or below the zero-point energy.

Multiconfigurational Ehrenfest approach to quantum coherent dynamics in large molecular systems

This article briefly describes recently developed Multiconfigurational Ehrenfest dynamics method to simulate quantum dynamics in systems with many degrees of freedom. The central idea is to guide the trajectories of basis wave functions by means of the Ehrenfest trajectories. The amplitudes of guided basis functions are coupled through a system of linear equations. The approach has been applied to simulations of nonadiabatic dynamics in Spin-Boson model and in pyrazine molecule. A new application to nonadiabatic dynamics in 24D model of pyrazine, where good spectrum for is obtained with the basis of only 34 basis Ehrenfest configurations is reported. This application provides the ground for future fully quantum direct dynamics. Another new application to the model of sticking to the surface described by the System-Bath Hamiltonian is presented to demonstrate the broadness of the approach, which can be applied to both electronically adiabatic and nonadiabatic dynamics. For all applications the results are in good agreement with those of MCTDH, which is very difficult to achieve with other trajectory-based methods. Therefore MCE can serve as a starting point for future use with "on the fly" direct dynamics. MCE provides an efficient fully quantum method capable of catching coherent dynamics in multidimentional systems, which is a necessary step for developing and understanding coherent control in realistic quantum systems.

At the dawn of the 21st century: Is dynamics the missing link for understanding enzyme catalysis?

Enzymes play a key role in almost all biological processes, accelerating a variety of metabolic reactions as well as controlling energy transduction, the transcription, and translation of genetic information, and signaling. They possess the remarkable capacity to accelerate reactions by many orders of magnitude compared to their uncatalyzed counterparts, making feasible crucial processes that would otherwise not occur on biologically relevant timescales. Thus, there is broad interest in understanding the catalytic power of enzymes on a molecular level. Several proposals have been put forward to try to explain this phenomenon, and one that has rapidly gained momentum in recent years is the idea that enzyme dynamics somehow contributes to catalysis. This review examines the dynamical proposal in a critical way, considering basically all reasonable definitions, including (but not limited to) such proposed effects as "coupling between conformational and chemical motions," "landscape searches" and "entropy funnels." It is shown that none of these proposed effects have been experimentally demonstrated to contribute to catalysis, nor are they supported by consistent theoretical studies. On the other hand, it is clarified that careful simulation studies have excluded most (if not all) dynamical proposals. This review places significant emphasis on clarifying the role of logical definitions of different catalytic proposals, and on the need for a clear formulation in terms of the assumed potential surface and reaction coordinate. Finally, it is pointed out that electrostatic preorganization actually accounts for the observed catalytic effects of enzymes, through the corresponding changes in the activation free energies.

Efficient estimators for quantum instanton evaluation of the kinetic isotope effects: Application to the intramolecular hydrogen transfer in pentadiene

The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in cis-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient "virial" estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum mechanically and uses an empirical valence bond potential based on a molecular mechanics force field.

Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions

Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.

Progress in the theory of mixed quantum-classical dynamics

Quantum-classical Liouville dynamics can be used to study the properties of open quantum systems that are coupled to bath or environmental degrees of freedom whose dynamics can be approximated by classical equations of motion. In contrast to many open quantum system approaches, quantum-classical dynamics provides a detailed description of the bath molecules. Such a description is especially appropriate for the study of quantum rate processes, such as proton and electron transport, where the detailed dynamics of the bath has a strong influence on the quantum rate. The quantum-classical Liouville equation can also serve as a starting point for the derivation of reduced descriptions where all or some of the bath degrees of freedom are projected out. Quantum-classical Liouville dynamics can be simulated in terms of an ensemble of surface-hopping trajectories whose character differs from that in other surface-hopping schemes. The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the formalism.

Solvation and proton transfer in polar molecule nanoclusters

Proton transfer in a phenol-amine complex dissolved in polar molecule nanoclusters is investigated. The proton transfer rates and mechanisms, as well as the solvation of the complex in the cluster, are studied using both adiabatic and nonadiabatic dynamics. The phenol-amine complex exists in ionic and covalent forms and as the size of the cluster increases the ionic form gains stability at the expense of the covalent form. Both the adiabatic and nonadiabatic transfer reaction rates increase with cluster size. Given a fixed cluster size, the stability of the covalent state increases with increasing temperature. The proton transfer rates do not change monotonously with an increase in temperature. A strong correlation between the solvent polarization reaction coordinate and the location of the phenol-amine complex in the cluster is found. The ionic form of the complex strongly prefers the interior of the cluster while the covalent form prefers to lie on the cluster surface.

An analysis of reaction pathways for proton tunnelling in methylamine dehydrogenase

Computational methods have now become a valuable tool to understand the way in which enzymes catalyse chemical reactions and to aid the interpretation of a diverse set of experimental data. This study focuses on the influence of the condensed-phase environment structure on proton transfer mechanisms, with an aim to understand how C-H bond cleavage is mediated in enzymatic reactions. We shall use a combination of molecular simulation, ab initio or semi-empirical quantum chemistry and semi-classical multidimensional tunnelling methods to consider the primary kinetic isotope effects of the enzyme methylamine dehydrogenase (MADH), with reference to an analogous application to triosephosphate isomerase. Analysis of potentially reactive conformations of the system, and correlation with experimental isotope effects, have highlighted that a quantum tunnelling mechanism in MADH may be modulated by specific amino acid residues, such as Asp428, Thr474 and Asp384.

Including quantum effects in the dynamics of complex (i.e., large) molecular systems

The development in the 1950s and 1960s of crossed molecular beam methods for studying chemical reactions at the single-collision molecular level stimulated the need and desire for theoretical methods to describe these and other dynamical processes in molecular systems. Chemical dynamics theory has made great strides in the ensuing decades, so that methods are now available for treating the quantum dynamics of small molecular systems essentially completely. For the large molecular systems that are of so much interest nowadays (e.g., chemical reactions in solution, in clusters, in nanostructures, in biological systems, etc.), however, the only generally available theoretical approach is classical molecular dynamics (MD) simulations. Much effort is currently being devoted to the development of approaches for describing the quantum dynamics of these complex systems. This paper reviews some of these approaches, especially the use of semiclassical approximations for adding quantum effects to classical MD simulations, also showing some new versions that should make these semiclassical approaches even more practical and accurate.

Analysis of kinetic isotope effects for nonadiabatic reactions

Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinate, which is in turn coupled to a bath of harmonic oscillators. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for chemical species operators and quantum equilibrium sampling are used to estimate the reaction rates. Approximate analytical expressions for the quantum equilibrium structure are derived. Reaction rates are shown to be influenced significantly by both the quantum equilibrium structure and nonadiabatic dynamics. Nonadiabatic dynamical effects are found to play the major role in determining the magnitude of the kinetic isotope effect for the model transfer reaction.

Hybrid quantum/classical molecular dynamics for a proton transfer reaction coupled to a dissipative bath

A hybrid quantum/classical molecular dynamics approach is applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. In this approach, the proton is treated quantum mechanically and all bath modes are treated classically. The transition state theory rate constant is obtained from the potential of mean force, which is generated along a collective reaction coordinate with umbrella sampling techniques. The transmission coefficient, which accounts for dynamical recrossings of the dividing surface, is calculated with a reactive flux approach combined with the molecular dynamics with quantum transitions surface hopping method. The hybrid quantum/classical results agree well with numerically exact results in the spatial-diffusion-controlled regime, which is most relevant for proton transfer in proteins. This hybrid quantum/classical approach has already been shown to be computationally practical for studying proton transfer in large biological systems. These results have important implications for future applications to hydrogen transfer reactions in solution and proteins.

Matching-pursuit split-operator Fourier-transform simulations of excited-state intramolecular proton transfer in 2-(2′-hydroxyphenyl)-oxazole

The excited-state intramolecular proton-transfer dynamics associated with the keto-enolic tautomerization reaction in 2-(2(')-hydroxyphenyl)-oxazole is simulated according to a numerically exact quantum-dynamics propagation method and a full-dimensional excited-state potential energy surface, based on an ab initio reaction surface Hamiltonian. The reported simulations involve the propagation of 35-dimensional wave packets according to the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method by Wu and Batista. The underlying propagation scheme recursively applies the time-evolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, photoabsorption cross sections, and time-dependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the Herman-Kluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reaction dynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems.

A coherent state approach to semiclassical nonadiabatic dynamics

A semiclassical (SC) approximation to the quantum mechanical propagator for nonadiabatic systems is derived. Our derivation starts with an exact path integral expression that uses canonical coherent states for the nuclear degrees of freedom and spin coherent states for the electronic degrees of freedom. A stationary path approximation (SPA) is then applied to the path integral to obtain the SC approximation. The SPA results in complex classical trajectories of both nuclear and electronic degrees of freedom and a double ended boundary condition. The root search problem is solved using the previously proposed "real trajectory local search" algorithm. The SC approximation is tested on three simple one dimensional two-state systems proposed by Tully [J. Chem. Phys. 93, 1061 (1990)], and the SC results are compared to Ehrenfest and surface hopping predictions. Excellent agreement with quantum results is reached when the SC trajectory is far away from caustics. We discuss the origin of caustics in this SC formalism and the strengths and weaknesses of this approach.

A surface hopping method for chemical reaction dynamics in solution described by diabatic representation: An analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.

Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions

A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.

Quantum-instanton evaluation of the kinetic isotope effects

A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H2 --> H2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than approximately 10%.

Quantum-classical Liouville dynamics of nonadiabatic proton transfer

A proton transfer reaction in a linear hydrogen-bonded complex dissolved in a polar solvent is studied using mixed quantum-classical Liouville dynamics. In this system, the proton is treated quantum mechanically and the remainder of the degrees of freedom is treated classically. The rates and mechanisms of the reaction are investigated using both adiabatic and nonadiabatic molecular dynamics. We use a nonadiabatic dynamics algorithm which allows the system to evolve on single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Reactive-flux correlation function expressions are used to compute the rate coefficients and the role of the dynamics on the coherently coupled surfaces is elucidated.

Exploring excited-state hydrogen atom transfer along an ammonia wire cluster: Competitive reaction paths and vibrational mode selectivity

The excited-state hydrogen-atom transfer (ESHAT) reaction of the 7-hydroxyquinoline(NH(3))(3) cluster involves a crossing from the initially excited (1)pipi(*) to a (1)pisigma(*) state. The nonadiabatic coupling between these states induces homolytic dissociation of the O-H bond and H-atom transfer to the closest NH(3) molecule, forming a biradical structure denoted HT1, followed by two more Grotthus-type translocation steps along the ammonia wire. We investigate this reaction at the configuration interaction singles level, using a basis set with diffuse orbitals. Intrinsic reaction coordinate calculations of the enol-->HT1 step predict that the H-atom transfer is preceded and followed by extensive twisting and bending of the ammonia wire, as well as large O-H...NH(3) hydrogen bond contraction and expansion. The calculations also predict an excited-state proton transfer path involving synchronous proton motions; however, it lies 20-25 kcal/mol above the ESHAT path. Higher singlet and triplet potential curves are calculated along the ESHAT reaction coordinate: Two singlet-triplet curve crossings occur within the HT1 product well and intersystem crossing to these T(n) states branches the reaction back to the enol reactant side, decreasing the ESHAT yield. In fact, a product yield of approximately 40% 7-ketoquinoline.(NH(3))(3) is experimentally observed. The vibrational mode selectivity of the enol-->HT1 reaction step [C. Manca, C. Tanner, S. Coussan, A. Bach, and S. Leutwyler, J. Chem. Phys. 121, 2578 (2004)] is shown to be due to the large sensitivity of the diffuse pisigma(*) state to vibrational displacements along the intermolecular coordinates.

Quantum dynamics of complex molecular systems

This Perspective presents a broad overview of the present status of theoretical capabilities for describing quantum dynamics in molecular systems with many degrees of freedom, e.g., chemical reactions in solution, clusters, solids, or biomolecular environments.

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.

Path integral evaluation of the quantum instanton rate constant for proton transfer in a polar solvent

The quantum instanton approximation for thermal rate constants, a type of quantum transition state theory (QTST), is applied to a model proton transfer reaction in liquid methyl chloride developed by Azzouz and Borgis. Monte Carlo path integral methods are used to carry out the calculations, and two other closely related QTST's, namely, the centroid-density and Hansen-Andersen QTST, are also evaluated for comparison using the present path integral approach. A technique is then introduced that calculates the kinetic isotope effect directly via thermodynamic integration of the rate with respect to hydrogen mass, which has the practical advantage of avoiding costly evaluation of the activation free energy. The present application to the Azzouz-Borgis problem shows that the above three types of QTST provide very similar results for the rate, within 30% of each other, which is nontrivial considering the totally different derivations of these QTSTs; the latter rates are also in reasonable agreement with some other previous results (e.g., obtained via molecular dynamics with quantum transitions), within a factor of approximately 2(7) for the H(D) transfer, thus significantly diminishing the possible range of the exact rates. In addition, it is revealed that a small but nonnegligible inconsistency exists in the parametrization of the Azzouz-Borgis model employed in previous studies, which resulted in the large apparent discrepancy in the calculated rates.