A new hybrid Hartree−Fock−density functional (HF-DF) model called the modified Perdew−Wang 1-parameter model for kinetics (MPW1K) is optimized against a database of 20 forward barrier heights, 20 r...

Adiabatic connection for kinetics

This paper briefly reviews the current status of the most popular methods for combined quantum mechanical/molecular mechanical (QM/MM) calculations, including their advantages and disadvantages There is a special emphasis on very general link-atom methods and various ways to treat the charge near the boundary Mechanical and electric embedding are contrasted We consider methods applicable to gas-phase organic chemistry, liquid-phase organic and organometallic chemistry, biochemistry, and solid-state chemistry Then we review some recent tests of QM/MM methods and summarize what we learn about QM/MM from these studies We also discuss some available software Finally, we present a few comments about future directions of research in this exciting area, where we focus on more intimate blends of QM with MM

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QM/MM: what have we learned, where are we, and where do we go from here?

▪ Abstract This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.

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Quantum mechanical methods for enzyme kinetics

Basis-set extrapolation

A review of the theoretical and computational modeling of bimolecular reactions is given. The review is divided into several sections which are as follows: gas-phase thermal reactions; gas-phase state-selected reactions and product state distributions; and condensed-phase bimolecular reactions. The section on gas-phase thermal reactions covers the enthalpies and free energies of reaction, kinetics, saddle points and potential energy surfaces, rate theory for simple barrier reactions and bimolecular reactions over potential wells. The section on gas-phase state-selected reactions focuses on electronically adiabatic reactions and electronically nonadiabatic reactions. Finally, the section on condensed-phase bimolecular reactions covers reactions in liquids, reactions on surfaces and in solids and tunneling at low temperature.

Modeling the Kinetics of Bimolecular Reactions

Potential energy surfaces for atom transfer reactions involving hydrogens and halogens

The diatomics‐in‐molecules (DIM) theory is extended to include larger valence bond (VB) basis sets and the optimization of mixing between the diatomic VB structures. This mixing is essential to the calculation of DIM potential‐energy hypersurfaces (PEH) using basis sets large enough to generate more than one diatomic state of a given symmetry. In keeping with the philosophy of DIM, the diatomic state mixing is treated as being independent of the number of atoms in the molecule. The method is used to calculate ground and excited state potential energies for CH2, CH3, and CH4. These extended DIM results demonstrate a number of improvements over earlier DIM methods and are in good agreement with ab initio and experimental results.

Optimization of diatomic state mixing in diatomics‐in‐molecules theory: The CHn potential‐energy surfaces

A previously proposed adjustable potential‐energy expression [D. L. Bunker and N. C. Blais, J. Chem. Phys. 41, 2377 (1964)] has been modified and extended. Besides its former properties, it now has variable cross section and provision for potential barriers and bound intermediates.

Revised General A + BC Potential for Trajectory Studies

The bond‐energy‐bond‐order (BEBO) method of Johnston and Parr predicts ClHCl, BrHBr, and IHI are all bound and symmetric. When corrected for anharmonicity of the asymmetric stretch normal mode, it predicts the following vibrational frequencies in cm−1 (experimental results are in parentheses; s is the symmetric stretch and a is the asymmetric stretch): ClHCl, s: 371 (259); ClDCl, s: 370 (265), a: 318 (463); BrHBr, s: 222 (165), a: 533 (727); BrDBr, s: 222 (170), 442 (496); IHI, s: 165 (121), a: 862 (686); IDI, s: 165 (124), a: 677 (470). The predictions of the London‐Eyring‐Polanyi‐Sato (LEPS) method for vibration frequencies are presented but are in much worse agreement with experiment. The BEBO method predicts the following depths of the potential energy minima (in kcal/mole) and equilibrium bond distances (in 10−8 cm), respectively: ClHCl, 1.56, 1.45; BrHBr, 3.02, 1.60; IHI, 6.77, 1.79.

Computed bond energies and vibrational frequencies for ClHCl, BrHBr, and IHI, including isotope effects and anharmonicity

Several variants of diatomics‐in‐molecules (DIM) theory are used to calculate the potential‐energy hypersurfaces (PEH) for H3 and H4. The minimum basis set calculations yield qualitatively incorrect PEHs for these systems. Extension of the basis set to include the excited 2S* state or ionic states of hydrogen can result in a good ’’optimized’’ DIM PEH for H3, but the H4 energies remain poor. Extension of the theory to include triatomic contributions explicitly does not correct the H4 energies in the minimum basis set application.

Christopher A. Parr

Papers

Potential energy surfaces for atom transfer reactions involving hydrogens and halogens

Optimization of diatomic state mixing in diatomics‐in‐molecules theory: The CHn potential‐energy surfaces

Revised General A + BC Potential for Trajectory Studies

Computed bond energies and vibrational frequencies for ClHCl, BrHBr, and IHI, including isotope effects and anharmonicity

Optimized diatomics‐in‐molecules potential energies for H3 and H4