The optimal tunneling path for the proton transfer in malonaldehyde

Time-resolved vibronic spectra with nuclear-electronic orbital time-dependent configuration interaction

Time-resolved spectroscopy is an important tool for probing photochemically induced nonequilibrium dynamics and energy transfer. Herein, a method is developed for the ab initio simulation of vibronic spectra and dynamical processes. This framework utilizes the recently developed nuclear-electronic orbital time-dependent configuration interaction (NEO-TDCI) approach, which treats all electrons and specified nuclei quantum mechanically on the same footing. A strategy is presented for calculating time-resolved vibrational and electronic absorption spectra from any initial condition. Although this strategy is general for any TDCI implementation, utilizing the NEO framework allows for the explicit inclusion of quantized nuclei, as illustrated through the calculation of vibrationally hot spectra. Time-resolved spectra produced by either vibrational or electronic Rabi oscillations capture ground-state absorption, stimulated emission, and excited-state absorption between vibronic states. This methodology provides the foundation for fully ab initio simulations of multidimensional spectroscopic experiments.

A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde

We developed an approximate method for quantum reaction dynamics simulations, namely, a structure-based Gaussian (SBG) expansion approach, where SBG bases for the expansion of the wave function Ψ, expressed by a product of single-atom Cartesian Gaussians centered at the positions of respective nuclei, are mainly placed around critical structures on reaction pathways such as on the intrinsic reaction coordinate (IRC) through a transition state. In the present approach, the "pseudo-lattice points" at which SBGs are deployed are selected in a perturbative manner so as to make moderate the expansion length. We first applied the SBG idea to a two-dimensional quadruple-well model and obtained accurate tunneling splitting values between the lowest four states. We then applied it to hydrogen tunneling in malonaldehyde and achieved a tunneling splitting of 27.1 cm^-1 with only 875 SBGs at the MP2/6-31G(d,p) level of theory, in good agreement with 25 cm^-1 by the more elaborate multiconfiguration time-dependent Hartree method. Reasonable results were also obtained for singly and doubly deuterated malonaldehyde. We analyzed the tunneling states by utilizing expansion coefficients of individual SBGs and found that 40-45% of the SBGs in Ψ are nonplanar structures and SBGs away from the IRC contribute a little to hydrogen transfer.

Electronic Born-Oppenheimer approximation in nuclear-electronic orbital dynamics

Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born-Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications.

MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.

Multidimensional H-atom tunneling in the catecholate monoanion

We present the catecholate monoanion as a new model system for the study of multidimensional tunneling. It has a symmetrical O-H double-well structure, and the H atom motion between the two wells is coupled to both low and high frequency modes with different strengths. With a view to studying mode-specific tunneling in the catecholate monoanion, we have developed a full (33) dimensional potential energy surface in transition state (TS) normal modes using a Distributed Gaussian Empirical Valence Bond (DGEVB) based approach. We have computed eigenstates in different subspaces using both unrelaxed and relaxed potentials based on the DGEVB model. With unrelaxed potentials, we present results up to 7D subspaces that include the imaginary frequency mode and six modes coupled to it. With relaxed potentials, we focus on the two most important coupling modes. The structures of the ground and vibrationally excited eigenstates are discussed for both approaches and mode-specific tunneling splitting and their trends are presented.

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.

Instanton theory of ground-state tunneling splittings with general paths

We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. The approach avoids multiple expensive matrix diagonalizations to converge the fluctuation prefactor in the ring-polymer instanton (RPI) method, and instead replaces them by an integration of a Riccati differential equation. When combined with the string method for locating instantons, we avoid the need to converge the calculation with respect to the imaginary time period of the semiclassical orbit, thereby reducing the number of convergence parameters of the optimized object to just one: the number of equally spaced system replicas used to represent the instanton path. The entirety of the numerical effort is thus concentrated in optimizing the shape of the path and evaluating hessians along the path, which is a dramatic improvement over RPI. In addition to the standard instanton approximations, we neglect the coupling of vibrational modes to external rotations. The method is tested on the model potential of malonaldehyde and on the water dimer and trimer, giving close agreement with RPI at a much-reduced cost.

SCC-DFTB-PIMD Method To Evaluate a Multidimensional Quantum Free-Energy Surface for a Proton-Transfer Reaction

The self-consistent charge density functional tight binding method was combined with the path-integral molecular dynamics method for the first time to evaluate the two-dimensional free-energy surface including nuclear quantum effects of a proton-transfer reaction in a 2,4-dichlorophenol-trimethylamine complex. A statistically converged two-dimensional quantum free-energy surface was evaluated by the multidimensional blue moon ensemble method. The accuracy was guaranteed by optimizing the repulsive potential between the sp³-hybridized nitrogen and hydrogen atoms in a SCC-DFTB3 parameter set for the system to reproduce high-level quantum chemical calculations. The present study illustrates the usefulness of this new approach to investigate nuclear quantum effects in various realistic proton-transfer reactions.

Intramolecular hydrogen bonding in malonaldehyde and its radical analogues

High level Brueckner doubles with triples correction method-based ab initio calculations have been used to investigate the nature of intramolecular hydrogen bonding and intramolecular hydrogen atom transfer in cis-malonaldehyde (MA) and its radical analogues. The radicals considered here are the ones that correspond to the homolytic cleavage of C-H bonds in cis-MA. The results suggest that cis-MA and its radical analogues, cis-MA_RS, and cis-MA_RA, both exist in planar geometry. The calculated intramolecular O-H⋯O=C bond in cis-MA is shorter than that in the radical analogues. The intramolecular hydrogen bond in cis-MA is stronger than in its radicals by at least 3.0 kcal/mol. The stability of a cis-malonaldehyde radical correlates with the extent of electron spin delocalization; cis-MA_RA, in which the radical spin is more delocalized, is the most stable MA radical, whereas cis-MA_RS, in which the radical spin is strongly localized, is the least stable radical. The natural bond orbital analysis indicates that the intramolecular hydrogen bonding (O⋯H⋯O) in cis-malonaldehyde radicals is stabilized by the interaction between the lone pair orbitals of donor oxygen and the σ^* orbital of acceptor O-H bond (n → σ^*_OH). The calculated barriers indicate that the intramolecular proton transfer in cis-MA involves 2.2 kcal/mol lower barrier than that in cis-MA_RS.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Finding Chemical Reaction Paths with a Multilevel Preconditioning Protocol

Finding transition paths for chemical reactions can be computationally costly owing to the level of quantum-chemical theory needed for accuracy. Here, we show that a multilevel preconditioning scheme that was recently introduced (Tempkin et al. J. Chem. Phys.2014, 140, 184114) can be used to accelerate quantum-chemical string calculations. We demonstrate the method by finding minimum-energy paths for two well-characterized reactions: tautomerization of malonaldehyde and Claissen rearrangement of chorismate to prephanate. For these reactions, we show that preconditioning density functional theory (DFT) with a semiempirical method reduces the computational cost for reaching a converged path that is an optimum under DFT by several fold. The approach also shows promise for free energy calculations when thermal noise can be controlled.

Army ants tunneling for classical simulations

We present an algorithm, called army ants tunneling, for adding tunneling to classical trajectories by means of quantal rare event sampling.

Direct Dynamics Implementation of the Least-Action Tunneling Transmission Coefficient. Application to the CH4/CD3H/CD4 + CF3 Abstraction Reactions

We present two new direct dynamics algorithms for calculating transmission coefficients of polyatomic chemical reactions by the multidimensional least-action tunneling approximation. The new algorithms are called the interpolated least-action tunneling method based on one-dimensional interpolation (ILAT1D) and the double interpolated least-action tunneling (DILAT) method. The DILAT algorithm, which uses a one-dimensional spline under tension to interpolate both of the effective potentials along the nonadiabatic portions of tunneling paths and the imaginary action integrals as functions of tunneling energies, was designed for the calculation of multidimensional LAT transmission coefficients for very large polyatomic systems. The performance of this algorithm has been tested for the CH4/CD3H/CD4 + CF3 hydrogen abstraction reactions with encouraging results, i.e., when the fitting is performed using 13 points, the algorithm is about 30 times faster than the full calculation with deviations that are smaller than 5%. This makes direct dynamics least-action tunneling calculations practical for larger systems, higher levels of electron correlation, and/or larger basis sets.

The Intramolecular Hydrogen-Bond in Malonaldehyde as Seen by Infrared Spectroscopy. A Four-Dimensional Model Study

The infrared spectrum of the O–H–O fragment of malonaldehyde is studied using a four-dimensional model. This comprises the OH stretching and the two OH bending vibrations as well an O–O ring deformation mode under the assumption of overall Cs symmetry. The full anharmonic potential energy and dipole moment surfaces are calculated using density functional theory and the respective vibrational eigenvalue problem is solved by an iterative Lanczos method. Fundamental and combination transitions are discussed for the normal species and the symmetrically deuterated isotopomer. Special emphasis is paid to the OH/OD stretching region which reveals the signatures of strong mode mixing what renders a simple assignment in terms of fundamental transitions difficult. In addition results for hot transitions are presented which show a rather different OH/OD band due to the topology of the potential energy surface. The influence of H atom tunneling on the spectrum is briefly addressed employing an alternative three-dimensional model which takes into account the in-plane H atom motion as well as the O–O distance.

Combining the nuclear-electronic orbital approach with vibronic coupling theory: calculation of the tunneling splitting for malonaldehyde

The nuclear-electronic orbital (NEO) method is combined with vibronic coupling theory to calculate hydrogen tunneling splittings in polyatomic molecules. In this NEO-vibronic coupling approach, the transferring proton and all electrons are treated quantum mechanically at the NEO level, and the other nuclei are treated quantum mechanically using vibronic coupling theory. The dynamics of the molecule are described by a vibronic Hamiltonian in a diabatic basis of two localized nuclear-electronic states for the electrons and transferring proton. This ab initio approach is computationally practical and efficient for relatively large molecules, and the accuracy can be improved systematically. The NEO-vibronic coupling approach is used to calculate the hydrogen tunneling splitting for malonaldehyde. The calculated tunneling splitting of 24.5 cm(-1) is in excellent agreement with the experimental value of 21.6 cm(-1). This approach also enables the identification of the dominant modes coupled to the transferring hydrogen motion and provides insight into their roles in the hydrogen tunneling process.

A theory-experiment conundrum for proton transfer

For the past 60 years, the framework for understanding the kinetic behavior of proton transfer has been transition state theory. Found throughout textbooks, this theory, along with the Bell tunneling correction, serves as the standard model for the analysis of proton/hydrogen atom/hydride transfer. In comparison, a different theoretical model has recently emerged, one which proposes that the transition state occurs within the solvent coordinate, not the proton transfer coordinate, and proton transfer proceeds either adiabatically or nonadiabatically toward product formation. This Account discusses the central tenets of the new theoretical model of proton transfer, contrasts these with the standard transition state model, and presents a discrepancy that has arisen between our experimental studies on a nonadiabatic system and the current understanding of proton transfer. Transition state theory posits that in the proton transfer coordinate, the proton must surmount an electronic barrier prior to the formation of the product. This process is thermally activated, and the energy of activation is associated with the degree of bond making and bond breaking in the transition state. In the new model, the reaction path involves the initial fluctuation of the solvent, serving to bring the reactant state and the product state into resonance, at which time the proton is transferred either adiabatically or nonadiabatically to form the product. If this theory is correct, then all of the deductions derived from the standard model regarding the nature of the proton transfer process are called into question. For weakly hydrogen-bonded complexes, two sets of experiments are presented supporting the proposal that proton transfer occurs as a nonadiabatic process. In these studies, the correlation of rate constants to driving force reveals both a normal region and an inverted region for proton transfer. Yet, the experimentally observed kinetic behavior does not align with the recent theoretical formulation for nonadiabatic proton transfer, underscoring the gap in the collective understanding of proton transfer phenomena.

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character.

Real-time observation of intramolecular proton transfer in the electronic ground state of chloromalonaldehyde: Anab initiostudy of time-resolved photoelectron spectra

The authors report on studies of time-resolved photoelectron spectra of intramolecular proton transfer in the ground state of chloromalonaldehyde, employing ab initio photoionization matrix elements and effective potential surfaces of reduced dimensionality, wherein the couplings of proton motion to the other molecular vibrational modes are embedded by averaging over classical trajectories. In the simulations, population is transferred from the vibrational ground state to vibrationally hot wave packets by pumping to an excited electronic state and dumping with a time-delayed pulse. These pump-dump-probe simulations demonstrate that the time-resolved photoelectron spectra track proton transfer in the electronic ground state well and, furthermore, that the geometry dependence of the matrix elements enhances the tracking compared with signals obtained with the Condon approximation. Photoelectron kinetic energy distributions arising from wave packets localized in different basins are also distinguishable and could be understood, as expected, on the basis of the strength of the optical couplings in different regions of the ground state potential surface and the Franck-Condon overlaps of the ground state wave packets with the vibrational eigenstates of the ion potential surface.