Gabriel Hanna

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.

Mechanistic Insights into the Dissociation and Decomposition of Carbonic Acid in Water via the Hydroxide Route: An Ab Initio Metadynamics Study

The dissociation and decomposition of carbonic acid (H2CO3) in water are important reactions in the pH regulation in blood, CO2 transport in biological systems, and the global carbon cycle. H2CO3 is known to have three conformers [cis-cis (CC), cis-trans (CT), and trans-trans (TT)], but their individual reaction dynamics in water has not been probed experimentally. In this paper, we have investigated the energetics and mechanisms of the conformational changes, dissociation (H2CO3 -->/<-- HCO3(-) + H(+)), and decomposition via the hydroxide route (HCO3(-) --> CO2+OH(-)) of all three conformers of H2CO3 in water using Car-Parrinello molecular dynamics (CPMD) in conjunction with metadynamics. It was found that, unlike in the gas phase, the interconversion between the various conformers occurs via two different pathways, one involving a change in one of the two dihedral angles (O=C-O-H) and the other a proton transfer through a hydrogen-bond wire. The free energy barriers/changes for the various conformational changes via the first pathway were calculated and contrasted with the previously calculated values for the gas phase. The CT and TT conformers were found to undergo decomposition in water via a two-step process: first, the dissociation and then the decomposition of HCO3(-) into CO2 and OH(-). The CC conformer does not directly decompose but first undergoes a conformational change to CT or TT prior to decomposition. This is in contrast with the concerted mechanism proposed for the gas phase, which involves a dehydroxylation of one of the OH groups and a simultaneous deprotonation of the other OH group to yield CO2 and H2O. The dissociation in water was seen to involve the repeated formation and breakage of a hydrogen-bond wire with neighboring water molecules, whereas the decomposition is initiated by the diffusion of H(+) away from HCO3(-); this decomposition mechanism differs from that proposed for the water route dehydration (HCO3(-) + H3O(+) --> CO2 + H2O), which involves the participation of a nearbyH3O(+) ion.Our calculated pKa values and decomposition free energy barriers for the CT and TT conformers are consistent with the overall experimental values of 3.45 and 22.28 kcal/mol, respectively, suggesting that the dynamics of the various conformers should be taken into account for a better understanding of aqueous H2CO3 chemistry.

Quantum-classical Liouville dynamics of proton and deuteron transfer rates in a solvated hydrogen-bonded complex.

Proton and deuteron transfer reactions in a hydrogen-bonded complex dissolved in a polar solution are studied using quantum-classical Liouville dynamics. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for species operators and quantum equilibrium sampling are used to calculate the rate constants. Adiabatic and nonadiabatic reaction rates are computed, compared, and analyzed. Large variations of the kinetic isotope effect (KIE) for this reaction have been observed in the literature, which depend on the nature of the approximate calculation used to estimate the proton and deuteron transfer rates. Our estimate of the KIE lies at the low end of the range of previously observed values, suggesting a rather small KIE for this reaction.

Multidimensional spectra via the mixed quantum-classical liouville method: Signatures of nonequilibrium dynamics

Multidimensional optical spectra are often expressed in terms of optical response functions. These optical response functions consist of contributions from a number of Liouville pathways that differ with respect to the chromophores quantum state during the time intervals between light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals are dictated by potential energy surfaces that are explicitly dependent on the chromophores quantum state. One therefore expects the system to hop between potential surfaces in a manner dictated by the Liouville pathways and the spectra to reflect the dynamics during the resulting nonequilibrium process. However, the approach commonly used to model spectra of complex condensed-phase systems is based on the ad hoc assumption that the photoinactive degrees of freedom undergo equilibrium dynamics on the potential surface that corresponds to the chromophores ground state. In this paper, we formulate optical response in terms of mixed quantum-classical Liouville dynamics, which inherently accounts for the underlying nonequilibrium dynamics. It is shown that, when nonadiabatic transitions are neglected, the resulting formulation is equivalent to that obtained via the linearized semiclassical approximation. We demonstrate the feasibility and utility of the approach by using it to calculate the one- and two-dimensional infrared spectra of the hydrogen stretch of a moderately strong hydrogen-bonded complex dissolved in a dipolar liquid. The results are compared with previously reported spectra that were calculated within the framework of the standard equilibrium ground-state dynamical approach [ J. Phys. Chem. B 2008 , 112 , 12991. ], thereby shedding light on the spectral signatures of nonequilibrium dynamics in systems of this type.

A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction

We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.

Explaining the structure of the OH stretching band in the IR spectra of strongly hydrogen-bonded dimers of phosphinic acid and their deuterated analogs in the gas phase: a computational study.

We present a simulation of the OH stretching band in the gas-phase IR spectra of strongly hydrogen-bonded dimers of phosphinic acid and their deuterated analogs [(R(2)POOH(D), with R = CH(2)Cl, CH(3)], which is based on a model for a centrosymmetric hydrogen-bonded dimer that treats the high-frequency OH stretches harmonically and the low-frequency intermonomer (i.e., O···O) stretches anharmonically. This model takes into account the following effects: anharmonic coupling between the OH and O···O stretching modes; Davydov coupling between the two hydrogen bonds in the dimer; promotion of symmetry-forbidden OH stretching transitions; Fermi resonances between the fundamental of the OH stretches and the overtones of the in- and out-of-plane bending modes involving the OH groups; direct relaxation of the OH stretches; and indirect relaxation of the OH stretches via the O···O stretches. Using a set of physically sound parameters as input into this model, we have captured the main features in the experimental OH(D) bands of these dimers. The effects of key parameters on the spectra are also elucidated. By increasing the number and strength of the Fermi resonances and by promoting symmetry-forbidden OH stretching transitions in our simulations, we directly see the emergence of the ABC structure, which is a characteristic feature in the spectra of very strongly hydrogen-bonded dimers. However, in the case of the deuterated dimers, which do not exhibit the ABC structure, the Fermi resonances are found to be much weaker. The results of this model therefore shed light on the origin of the ABC structure in the IR spectra of strongly hydrogen-bonded dimers, which has been a subject of debate for decades.

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.

Vibrational energy relaxation of a hydrogen-bonded complex dissolved in a polar liquid via the mixed quantum-classical Liouville method.

The vibrational energy relaxation (VER) of the hydrogen stretch in a linear hydrogen-bonded complex dissolved in a polar solvent is studied. The study is based on the Azzouz-Borgis model [Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361], which is known to account for many important features of real hydrogen-bonded systems, including ionic-to-covalent tautomerism and a broad distribution of hydrogen stretch frequencies. A description of VER in this strongly coupled system is considered, which consists of the following three consecutive steps: (1) solvation on the adiabatic excited vibrational surface; (2) nonadiabatic transition from the excited to the ground adiabatic vibrational surface; and (3) solvation on the adiabatic ground vibrational surface. The relaxation dynamics during those three steps were simulated via the mixed quantum-classical Liouville method, where the hydrogen is treated quantum-mechanically, while the other particles are treated in a classical-like manner. The solvation on the excited-state surface was found to occur rapidly ( approximately 0.5 ps) and to involve energy exchange with both the intramolecular and intermolecular degrees of freedom. It was also found that, while energy is released to the solvent during the solvation of the covalent tautomer, the solvation of the ionic tautomer involves absorption of energy from the solvent. The decrease in the transition frequency during the solvation process also facilitates the nonadiabatic transitions, which occur rapidly ( approximately 0.8 ps) thereafter. The nonadiabatic transitions were shown to be induced by interactions with a large number of solvent molecules and to be relatively insensitive to their location relative to the complex. Finally, solvation on the ground-state surface was seen to occur on a time scale of approximately 1.0 ps and leads to nonequilibrium ionic and covalent subpopulations. Equilibration on the ground-state surface occurs on a significantly slower time scale ( approximately 7.6 ps). Our results shed new light on the problem of VER in strongly coupled condensed phase systems that lie outside the range of validity of the Landau-Teller formula.

Isotope effects on the vibrational relaxation and multidimensional infrared spectra of the hydrogen stretch in a hydrogen-bonded complex dissolved in a polar liquid.

Isotope effects on rate processes and spectra are often used to elucidate the nature of the interactions underlying molecular structure and dynamics. In this paper, we present a computational study of the effect of substituting hydrogen by deuterium in a solvated hydrogen-bonded complex on the rates of the various processes involved in the vibrational relaxation of the hydrogen/deuterium stretch and on the corresponding 1D and 2D infrared spectra. The vibrational relaxation is simulated via the mixed quantum-classical Liouville method, where the proton/deuteron is treated quantum mechanically while the other particles are treated in a classical-like manner. We find that the vibrational relaxation pathway and the rates of the various steps in it are similar for the deuterium and hydrogen stretches. However, we also find that isotope substitution modifies the 1D and 2D spectra of the stretch in a qualitative manner. The differences between the spectra are explained in terms of the narrowing and broadening of the fundamental and overtone transition frequency ranges, respectively, and the smaller transition dipole moments in the case of the deuterium stretch. Our results demonstrate that isotope substitution may have a rather dramatic effect on the infrared spectra of a vibrational mode strongly coupled to its environment even though the rate and pathway of the underlying vibrational relaxation may not be overly sensitive to it.

Signatures of Nonequilibrium Solvation Dynamics on Multidimensional Spectra

Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophores quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the systems dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophores ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.