John Z. H. Zhang

Full-dimensional time-dependent treatment for diatom-diatom reactions: The H2+OH reaction

Extending our previous studies for the H2+OH reaction in five mathematical dimensions (5D) [J. Chem. Phys. 99, 5615 (1993); 100, 2697 (1994)], we present in this paper a full‐dimensional (6D) dynamics study for the title reaction. The 6D treatment uses the time‐dependent wave‐packet approach and employs discrete variable representations for three radial coordinates and coupled angular momentum basis functions for three angular coordinates. The present 6D study employs an energy projection method to extract reaction probabilities for a whole range of energies from a single wave‐packet propagation, while previous studies produced only energy‐averaged reaction probability from a single wave‐packet propagation. The application of the energy‐projection method allows us to efficiently map out the energy dependence of the reaction probability on a fine grid which revealed surprisingly sharp resonancelike features at low collision energies on the Schatz–Elgersma potential surface. Our calculation shows that the potential‐averaged 5D treatment can produce reaction probabilities essentially indistinguishable from the full‐dimensional result. We also report initial state‐selected reaction cross sections and rate constants which are in good agreement with our previous calculations. The effect of OH vibration on H2+OH reaction is examined in the present study and our calculation shows that the OH vibration can enhance the rate constant by about a factor of 1.7 in good agreement with the experimental estimate of about 1.5.

Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein–molecule interaction energy

A scheme to calculate fully quantum mechanical (ab initio) interaction energy involving a macromolecule like protein is presented. In this scheme, the protein is decomposed into individual amino acid-based fragments that are treated with proper molecular caps. The interaction energy between any molecule and the given protein is given by the summation of interactions between the molecule and individually capped protein fragments. This scheme, termed molecular fractionation with conjugate caps (MFCC), makes it possible and practical to carry out full quantum mechanical (ab initio) calculation of intermolecular interaction energies involving proteins or other similar biological molecules. Numerical tests performed on the interaction energies between a water molecule and three small peptides demonstrate that the MFCC method can give excellent ab initio interaction energies compared to the exact treatment in which the whole peptides are included in the calculation. The current scheme scales linearly with the a...

Quantum reactive scattering via the S‐matrix version of the Kohn variational principle: Differential and integral cross sections for D+H2 →HD+H

A comprehensive survey of the quantum scattering methodology that results from applying the S‐matrix version of the Kohn variational principle to the reactive scattering formulation given by Miller [J. Chem. Phys. 50, 407 (1969)] is presented. Results of calculations using this approach are reported for the reaction D+H2 →HD+H. The 3‐d calculations include total angular momentum values from J=0 up to 31 in order to obtain converged integral and differential cross sections over a wide range of energy (0.4–1.35 eV total energy). Results are given for reaction probabilities for individual values of J, integral and differential cross sections for a number of energies, and state‐to‐state rate constants (i.e., a Boltzmann average over translational energy), and comparisons are made to a variety of different experimental results. A particularly interesting qualitative feature which is observed in the calculations is that the energy dependence of the differential cross section in the backward direction (θ=180°) s...

Theory and application of quantum molecular dynamics

This book provides a detailed presentation of modern quantum theories for treating the reaction dynamics of small molecular systems. Its main focus is on the recent development of successful quantum dynamics theories and computational methods for studying the molecular reactive scattering process, with specific applications given in detail for a number of benchmark chemical reaction systems in the gas phase and the gas surface. In contrast to traditional books on collision in physics focusing on abstract theory for nonreactive scattering, this book deals with both the development and the application of the modern reactive or rearrangement scattering theory, and is written in a fashion in which the development of the reactive scattering theory is closely coupled with its computational aspects for practical applications for realistic molecular reactions. The volume includes such topics as methods for calculating rovibrational states of molecules, fundamental quantum theory for scattering (nonreactive and reactive), modern time-independent computational methods for reactive scattering, general time-dependent wave packet methods for reactive scattering, dynamics theory of chemical reactions, dynamics of molecular fragmentation, semiclassical description of quantum mechanics, and also some useful appendices.The book is intended for the reader to not only understand the molecular reaction dynamics from the fundamental scattering theory, but also utilize the provided computational methodologies in their practical applications. It should benefit graduate students and researchers in the field of chemical physics.

Quantum reactive scattering with a deep well: Time‐dependent calculation for H+O2 reaction and bound state characterization for HO2

We show in this paper a time‐dependent (TD) quantum wave packet calculation for the combustion reaction H+O2 using the DMBE IV (double many‐body expansion) potential energy surface which has a deep well and supports long‐lived resonances. The reaction probabilities from the initial states of H+O2(3Σ−g) (v=0–3, j=1) for total angular momentum J=0 are obtained for scattering energies from threshold up to 2.5 eV, which show numerous resonance features. Our results show that, by carrying out the wave packet propagation to several picoseconds, one can resolve essentially all the resonance features for this reaction. The present TD results are in good agreement with other time‐independent calculations. A particular advantage of the time‐dependent approach to this reaction is that resonance structures—strong energy dependence of the reaction probability—can be mapped out in a single wave packet propagation without having to repeat scattering calculations for hundreds of energies. We also report calculations of s...

Accurate quantum calculation for the benchmark reaction H2+OH→H2O +H in five‐dimensional space: Reaction probabilities for J=0

A time‐dependent wave packet method has been employed to compute initial state‐specific total reaction probabilities for the benchmark reaction H2+OH→H2O+H on the modified Schatz–Elgersman potential energy surface which is derived from ab initio data. In our quantum treatment, the OH bond length is fixed but the remaining five degrees of freedom are treated exactly in the wave packet calculation. Initial state‐specific total reaction probabilities for the title reaction are presented for total angular momentum J=0 and the effects of reagents rotation and H2 vibration on reaction are examined.

L2 amplitude density method for multichannel inelastic and rearrangement collisions

A new method for quantum mechanical calculations of cross sections for molecular energy transfer and chemical reactions is presented, and it is applied to inelastic and reactive collisions of I, H, and D with H2. The method involves the expansion in a square‐integrable basis set of the amplitude density due to the difference between the true interaction potential and a distortion potential and the solution of a large set of coupled equations for the basis function coefficients. The transition probabilities, which correspond to integrals over the amplitude density, are related straightforwardly to these coefficients.

Quantum scattering via the S‐matrix version of the Kohn variational principle

The S‐matrix version of the Kohn variational principle is used to obtain a very effective method for quantum scattering calculations. The approach is especially useful for the nonlocal (i.e., exchange) interactions that arise in chemically reactive scattering (and also in electron–atom/molecule scattering). The particular version developed in this paper has a more general structure than an earlier one by Miller and Jansen op de Haar [J. Chem. Phys. 86, 6213 (1987)], and applications to an elastic scattering problem, and also to three‐dimensional H+H2 reactive scattering, show that it is also more useful in practice.The S‐matrix version of the Kohn variational principle is used to obtain a very effective method for quantum scattering calculations. The approach is especially useful for the nonlocal (i.e., exchange) interactions that arise in chemically reactive scattering (and also in electron–atom/molecule scattering). The particular version developed in this paper has a more general structure than an earlier one by Miller and Jansen op de Haar [J. Chem. Phys. 86, 6213 (1987)], and applications to an elastic scattering problem, and also to three‐dimensional H+H2 reactive scattering, show that it is also more useful in practice.

Quantum reactive scattering via the S-matrix version of the Kohn variational principle: Integral cross sections For H+H2(ν1=j1=0)→H2(ν2=1, j2= 1, 3) + H in the energy range Etotal = 0.9-1.4 eV

Abstract Fully converged state-to-state integral cross sections are reported for the reaction H + H2 (ν1=j1=0)→ H, (ν2=1, j2=1 and 3) + H over a wide range of energy. The calculations include up to 19 partial waves (i.e. total angular momentum quantum numbers J=0, 1, … 18), which yield converged ν2=1 cross sections for total energies from threshold (≈0.9 eV) up to ≈ 1.4 eV. The calculated cross sections are a relatively smooth function of energy, and thus in substantial disagreement with the recent experimental results of Nieh and Valentini; the energy-averaged magnitudes of the experimental and theoretical cross sections, however, are in good agreement. The present calculations were performed with the LSTH potential energy surface for the H3 system.

Developing Polarized Protein-Specific Charges for Protein Dynamics: MD Free Energy Calculation of pKa Shifts for Asp26/Asp20 in Thioredoxin

Ab initio quantum mechanical calculation of protein in solution is carried out to generate polarized protein-specific charge(s) (PPC) for molecular dynamics (MD) stimulation of protein. The quantum calculation of protein is made possible by developing a fragment-based quantum chemistry approach in combination with the implicit continuum solvent model. The computed electron density of protein is utilized to derive PPCs that represent the polarized electrostatic state of protein near the native structure. These PPCs are atom-centered like those in the standard force fields and are thus computationally attractive for molecular dynamics simulation of protein. Extensive MD simulations have been carried out to investigate the effect of electronic polarization on the structure and dynamics of thioredoxin. Our study shows that the dynamics of thioredoxin is stabilized by electronic polarization through explicit comparison between MD results using PPC and AMBER charges. In particular, MD free-energy calculation using PPCs accurately reproduced the experimental value of pK(a) shift for ionizable residue Asp(26) buried inside thioredoxin, whereas previous calculations using standard force fields overestimated pK(a) shift by twice as much. Accurate prediction of pK(a) shifts by rigorous MD free energy simulation for ionizable residues buried inside protein has been a significant challenge in computational biology for decades. This study presented strong evidence that electronic polarization of protein plays an important role in protein dynamics.