Quantum Tunneling Rates of Gas-Phase Reactions from On-the-Fly Instanton Calculations.

The instanton method obtains approximate tunneling rates from the minimum-action path (known as the instanton) linking reactants to the products at a given temperature. An efficient way to find the instanton is to search for saddle-points on the ring-polymer potential surface, which is obtained by expressing the quantum Boltzmann operator as a discrete path-integral. Here we report a practical implementation of this ring-polymer form of instanton theory into the Molpro electronic-structure package, which allows the rates to be computed on-the-fly, without the need for a fitted analytic potential-energy surface.

Shallow-tunnelling correction factor for use with Wigner-Eyring transition-state theory.

We obtain a shallow-tunnelling correction factor for use with Wigner-Eyring transition-state theory (TST). Our starting point is quantum transition state theory (QTST), which approximates the accurate quantum rate as the instantaneous flux through a delocalised transition-state ensemble of ring-polymers. Expanding the ring-polymer potential to second order gives the well-known Wigner tunnelling-factor which diverges at the cross-over temperature between deep and shallow tunnelling.

Reaction mechanism of the bicopper enzyme peptidylglycine α-hydroxylating monooxygenase.

Peptidylglycine α-hydroxylating monooxygenase is a noninteracting bicopper enzyme that stereospecifically hydroxylates the terminal glycine of small peptides for its later amidation. Neuroendocrine messengers, such as oxytocin, rely on the biological activity of this enzyme. Each catalytic turnover requires one oxygen molecule, two protons from the solvent, and two electrons.

Role of tunneling in the enzyme glutamate mutase.

The role of quantum mechanical atom tunneling during the conversion of glutamate to methylaspartate catalyzed by glutamate mutase is investigated by quantum mechanical/molecular mechanical (QM/MM) simulations based on coupled cluster and density functional calculations. The use of instanton theory allows us to calculate the tunneling contributions of up to 78 atoms in the active site. We calculate kinetic isotope effects (KIEs) and compare them to experimental data.

Kinetic isotope effects calculated with the instanton method.

The ring-opening reaction of the cyclopropylcarbinyl radical proceeds via heavy-atom tunneling at low temperature. We used instanton theory to calculate tunneling rates and kinetic isotope effects with on-the-fly calculation of energies by density functional theory (B3LYP). The accuracy was verified by explicitly correlated coupled-cluster calculations (UCCSD(T)-F12).

The fragmentation-recombination mechanism of the enzyme glutamate mutase studied by QM/MM simulations.

The radical mechanism of the conversion of glutamate to methylaspartate catalyzed by glutamate mutase is studied with quantum mechanical/molecular mechanical (QM/MM) simulations based on density functional theory (DFT/MM). The hydrogen transfer between the substrate and the cofactor is found to be rate limiting with a barrier of 101.1 kJ mol(-1).

Adaptive integration grids in instanton theory improve the numerical accuracy at low temperature.

The instanton method allows to accurately calculate tunneling rates down to very low temperature. However, with lowering the temperature, the computational effort steeply increases as many more discretization points are required. This is caused in practical applications by the majority of the discretization points accumulating at a very small region in configuration space.

Locating Instantons in Many Degrees of Freedom.

We implemented and compared four algorithms to locate instantons, i.e., the most likely tunneling paths at a given temperature.