Zorka Smedarchina

An instanton approach to intramolecular hydrogen exchange: Tunneling splittings in malonaldehyde and the hydrogenoxalate anion

Calculations of hydrogen tunneling splittings are reported based on a combination of the instanton approach with quantum‐chemically computed potentials and force fields. The splittings are due to intramolecular hydrogen transfer in symmetric double‐minimum potentials in molecules such as malonaldehyde and the hydrogenoxalate anion. Potential‐energy curves along the tunneling coordinates and harmonic force fields at the stationary points are calculated at the HF/6‐31G** and HF/6‐31+G** level of theory, and combined to yield a complete multidimensional surface. All modes that are displaced between the equilibrium configuration and the transition state are included in the calculation. In the formalism, these modes are linearly coupled to the tunneling mode, the couplings being proportional to the displacements in dimensionless units. These couplings modify the instanton trajectory and subject it to fluctuations. It is argued that within the accuracy of the available potential‐energy surfaces, direct calculat...

Proton tunnelling in polyatomic molecules: A direct-dynamics instanton approach

In this review we discuss a recently introduced method of calculating hydrogen tunnelling rates and tunnelling splittings in medium and large molecules. It is a non-empirical, direct-dynamics method that uses ab initio quantum-chemical output as input data for the calculation of dynamic properties by means of the instanton approach. This approach is based on the recognition that there is a single path that dominates the tunnelling rate. This so-called instanton trajectory is the path that minimizes the classical action. Although it is very difficult to calculate this trajectory for multidimensional systems, it will be shown that the corresponding instanton action, which is the quantity of practical interest, can be obtained with sufficient accuracy to reproduce experimental observations without the explicit evaluation of the instanton trajectory. In this approximation scheme the instanton action is calculated from the one-dimensional action through the introduction of appropriate correction terms for all ...

MODE-SPECIFIC HYDROGEN TUNNELING IN TROPOLONE : AN INSTANTON APPROACH

Calculations are reported of hydrogen and deuterium tunneling splittings in the ground state S0 (X,1A1) and the first excited singlet state S1 (A,1B2) of tropolone‐d0 and ‐d1. The main focus of the calculations is on the splittings observed in vibrationally excited levels of S1, some of which are larger while others are smaller than the zero‐point splitting. To account for these observations, a potential‐energy surface is constructed by standard quantum‐chemical methods and the dynamics on this surface is treated by a method derived from the instanton approach. The potential‐energy surface is a complete multidimensional surface resulting from the combination of a potential‐energy curve along the tunneling coordinate with a harmonic force field calculated at the stationary points. The level of calculation adopted is HF/6‐31G** for S0 and CIS/6‐31G** for S1. A few other, nominally more accurate, methods were tried but proved to be unsatisfactory. To deal with the dynamics, the instanton method, used previ...

Dynamics of molecular inversion: An instanton approach

To describe tunneling of light atoms, a method is developed that takes account of the multidimensional nature of the process but remains tractable without becoming inaccurate. It combines the instanton formalism with ab initio potentials and force fields and makes effective use of a number of practical approximations suggested by the nature of the calculations. The tunneling potential is constructed from ab initio calculations that are fully optimized at stationary points. All other vibrations are represented by their harmonic force fields. Changes in the harmonic force fields between stationary points are expressed as couplings with the tunneling mode. The transfer rate is calculated for the instanton path, i.e., the path of least resistance, modulated by adjacent paths which define the damping required for nonoscillatory transfer. The multidimensional transfer integrals, involving all modes that change between the initial state and the transition state, are reduced to quasi‐one‐dimensional integrals by ...

The structure of phenol-ammonia clusters before and after proton transfer. A theoretical investigation

Abstract Equilibrium structures are reported for clusters of phenol with up to five ammonia molecules at the Hartree-Fock level of theory with checks based on Moller-Plesset and density-functional methods. A systematic build-up of solvent shells is observed. For the clusters with five ammonias a metastable ion-pair structure is obtained. The results are related to the observed proton-transfer dynamics in electronically excited clusters.

A COMPARISON OF TWO METHODS FOR DIRECT TUNNELING DYNAMICS : HYDROGEN EXCHANGE IN THE GLYCOLATE ANION AS A TEST CASE

Two methods for studying tunneling dynamics are compared, namely the instanton model and the approach of Truhlar and co-workers, which are based on the direct output of electronic structure calculations and thus are parameter free. They are employed to evaluate the zero-level tunneling splitting due to intramolecular hydrogen exchange in the glycolate anion. The first method was developed in a series of recent studies and presents a combination of the instanton theory with quantum-chemically computed potentials and force fields. For the compound at hand, which has 21 internal degrees of freedom, a complete potential-energy surface is generated in terms of the normal modes of the transition-state configuration. It is made up of the potential-energy curve along the tunneling coordinate and harmonic force fields at the stationary points. The level of theory used is HF/6–31++G**. All modes that are displaced between the equilibrium configuration and the transition state are linearly coupled to the tunneling m...

Tunneling splittings from ab initio data: indoline, a test case

Abstract A combination of ab initio and semiclassical modeling is used to simulate the observed tunneling splittings of indoline. Through the Instanton approach and the introduction of effective parameters, the semiclassical one-dimensional theory is extended to the multidimensional case without loss of simplicity. To avoid a possible bias in the derivation of the input parameters, the corrections for the effective mass and the effective potential are obtained ab initio at the standard HF/6-31G∗ level. This framework, which is highly sensitive to the input parameters, successfully reproduces all the observed splittings. Reasons for the success of the present formulation are briefly discussed.

Mechanisms of Double Proton Transfer. Theory and Applications

Abstract An analytical two-dimensional (2D) potential-energy surface based on two equal hydrogen bonds coupled by a correlation term, recently introduced [J. Chem. Phys. 127 (2007) 174513] to describe the dynamics of double proton transfer, is reviewed and generalized. It is then applied to the evaluation of proton transfer dynamics in a number of realistic systems, namely several molecules and dimers that exhibit various degrees of correlation between the motions of the two protons. The three parameters required to generate this 2D potential are derived from electronic structure and force field calculations, such that they include implicitly the effect of coupled skeletal modes. It follows that explicit introduction of such coupled modes is not required to obtain the basic relations that define the stationary points of the 2D surface, and thereby the reaction mechanism. Based on these relations, a detailed analysis is reported of a variety of systems exhibiting double proton transfer, including, apart from previously investigated porphine and porphycene, representing weak correlation, and the formic and benzoic acid dimers, representing strong correlation, two newly investigated systems which shed light on the hitherto not represented intermediate correlation category, namely naphthazarin, and the 4-bromopyrazole dimer.

Communication: Selection rules for tunneling splitting of vibrationally excited levels

Five symmetry-based selection rules are formulated that relate the tunneling splitting of a vibrationally excited level to that of the ground level in molecules with a symmetric double-minimum potential. The rules, which explain why excited levels frequently have smaller splittings than zero-point levels, are used to interpret the observed and calculated splittings in malonaldehyde.

An Instanton approach to hindered torsions: methyl glycolate — a case study

Abstract A mixed approach which combines Instanton theory and ab initio calculations is extended to treat torsional motions. Application to the complicated case of methyl glycolate is given. The calculated spiittings are in good agreement with experiment.