化学反应的高精度从头算势能面

势能面是化学反应动力学研究的基础。近年来随着理论方法的发展与计算技术的进步,不但含三、四个原子反应体系的电子基态势能面的构建精度进一步提高,一些反应体系的多电子态耦合势能面的构建和含六个原子以上反应体系的高维从头算势能面的构建也取得了重要进展。本文结合若干典型体系势能面的构建工作,主要介绍了高精度电子基态势能面,包括Renner-Teller、旋轨耦合等非绝热效应的耦合势能面以及高维势能面方面的研究进展。     

High-dimensional ab initio potential energy surfaces for reaction dynamics calculations

There has been great progress in the development of potential energy surfaces (PESs) for reaction dynamics that are fits to ab initio energies. The fitting techniques described here explicitly represent the invariance of the PES with respect to all permutations of like atoms. A review of a subset of dynamics calculations using such PESs (currently 16 such PESs exist) is then given. Bimolecular reactions of current interest to the community, namely, H + CH(4) and F + CH(4), are focused on. Unimolecular reactions are then reviewed, with a focus on the photodissociation dynamics of H(2)CO and CH(3)CHO, where so-called "roaming" pathways have been discovered. The challenges for electronically non-adiabatic reactions, and associated PESs, are presented with a focus on the OH* + H(2) reaction. Finally, some thoughts on future directions and challenges are given.     

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .     

Numerical Convergence of the Sinc Discrete Variable Representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic Representation

Within the Born-Oppenheimer (BO) approximation, nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface (PES). However, this single PES picture should be reconsidered if a conical intersection (CI) is present, although the energy is well below the CI. The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation, i.e., the diagonal BO correction (DBOC) and the geometric phase (GP), which are divergent at the CI. At the same time, there are cusps in the adiabatic PESs. Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation. A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation (DVR) method. We examine the numerical accuracy of the Sinc DVR method for solving the Schr?dinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation. The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points, without special treatment of the divergence of the DBOC and the GP. The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP, whose accurate form usually is not easy to obtain.     

Complex excited dynamics around a plateau on a retinal-like potential surface: chaos, multi-exponential decays and quantum/classical differences

We investigate the classical and quantum dynamics on the plateau of an excited potential energy surface (PES) whose shape mimics the PES driving the photoisomerization of the protonated Schiff base of retinal (PSBR). We adopt a two-dimensional analytical model of the PES, and perform an extended study by varying the potential parameters, revealing a scenario whose interest goes beyond the relevance for the specific case of PSBR. In fact, we document cases with net differences among classical and quantum dynamical predictions, for barrierless PESs. Classical trajectories released on the PES display the signature of chaos and partial trapping on the plateau, whose origin is purely dynamical, since no barrier exists. At variance, on the same barrierless PESs, quantum dynamics does not predict any trapping, always showing a complete depletion of the excited population according to an approximate mono-exponential law. The plateau on the PES promotes complex and unusual dynamical features, and it is sufficient to introduce a very small barrier along the cis–trans torsional mode to give rise to a multi-exponential decay, also at quantum level. Our results are of general interest because plateaux are often found in the excited states of conjugated chromophores.     

On the role of dynamical barriers in barrierless reactions at low energies: S(1D) + H2

Reaction probabilities as a function of total angular momentum (opacity functions) and the resulting reaction cross sections for the collision of open shell S((1)D) atoms with para-hydrogen have been calculated in the kinetic energy range 0.09-10 meV (1-120 K). The quantum mechanical hyperspherical reactive scattering method and quasi-classical trajectory and statistical quasi-classical trajectory approaches were used. Two different ab initio potential energy surfaces (PESs) have been considered. The widely used reproducing kernel Hilbert space (RKHS) PES by Ho et al. [T.-S. Ho, T. Hollebeek, H. Rabitz, S. D. Chao, R. T. Skodje, A. S. Zyubin, and A. M. Mebel, J. Chem. Phys 116, 4124 (2002)] and the recently published accurate double many-body expansion (DMBE)/complete basis set (CBS) PES by Song and Varandas [Y. Z. Song and A. J. C. Varandas, J. Chem. Phys. 130, 134317 (2009)]. The calculations at low collision energies reveal very different dynamical behaviors on the two PESs. The reactivity on the RKHS PES is found to be considerably larger than that on the DMBE/CBS PES as a result of larger reaction probabilities at low total (here also orbital) angular momentum values and to opacity functions which extend to significantly larger total angular momentum values. The observed differences have their origin in two major distinct topographic features. Although both PESs are essentially barrierless for equilibrium H-H distances, when the H-H bond is compressed the DMBE/CBS PES gives rise to a dynamical barrier which limits the reactivity of the system. This barrier is completely absent in the RHKS PES. In addition, the latter PES exhibits a van der Walls well in the entrance channel which reduces the height of the centrifugal barrier and is able to support resonances. As a result, a significant larger cross section is found on this PES, with marked oscillations attributable to shape resonances and/or to the opening of partial wave contributions. The comparison of the results on both PESs is illustrative of the wealth of the dynamics at low collision energy. It is also illuminating about the difficulties encountered in modeling an all-purpose global potential energy surface.     

三维含时量子散射研究H + CIH体系

用三维含时量子散射理论模拟了H+CIH体系在BW2,mBW2,G3势能面上的动力学行为,其计算结果表明,振动量子态对反应几率影响很大;势能面的地形对转动量子态如何影响反应几率起重要作用;反应几率表现出“黄金规则”,此外,BW2,mBW2势能面上的反应几率几乎相同,而G3势能面上的反应几率较前者低,大概由于G3的势垒高的缘故。     

三维含时量子散射研究H+ClH体系

用三维含时量子散射理论模拟了H+GlH体系在BW2,mBW2,G3势能面上的动力学行为.其计算结果表明,振动量子态对反应几率影响很大;势能面的地形对转动量子态如何影响反应几率起重要作用;反应几率表现出"黄金规则".此外,BW2,mBW2势能面上的反应几率几乎相同,而G3势能面上的反应几率较前者低,大概由于G3的势垒高的缘故.     

N(4S)+ NO(X2Π)→N2(X3Σg-)+O(3P) 反应的立体动力学研究

采用准经典轨线方法研究了在不同碰撞能下，碰撞反应N(4S)+NO(X2Π)→ N2(X3Σg- )+O(3P)在两个最低势能面3A 和 3A'上产物与反应物之间的矢量相关. 结果表明，对于不同的碰撞能，在两个势能面上反应产物的转动取向展示了不同的特征和趋势. 随着碰撞能的增加，发生在3A 势能面上的反应主要受外平面机理支配，而发生在 3A' 势能面上的反应倾向于受内平面机理支配. 这些差异来自于两个势能面的不同构型.     

Influence of the potential energy surface on the reaction cross section: the K + HF → KF + H system

The effect of the potential energy surface on the K + HF → KF + H cross section has been studied using reasonable Sorbie-Murrell (bent saddle point) and LEPS (collinear saddle point) potential energy surfaces (PESs). Trajectory calculations for selected initial conditions (translational energies, rovibrational levels (v, J) of HF, as well as initial parallel or perpendicular alignments between the HF rotational angular momentum and the reactants relative velocity vectors) have been performed on these PESs to compare them with experiments. The Sorbie-Murrell and LEPS-4 PESs lead to steric effect ratio results quite close to the experimental ones, once the error margins are included. The resllts point towards a bent K-F-H saddle point although the PES is very isotropic. This could explain why experimental determinations lead to suggest a collinear saddle point. The K + HF → KF + H reaction exhibits an enormous vibrational enhancement of reactivity with one quantum HF vibrational excitation, even at translational energies well above the HF(v=0) threshold, where tunnelling effect contribution to reactivity can be neglected. This behaviour has not been reproduced in the trajectory calculations and no satisfactory explanation has been obtained for this fact. Nevertheless, the HF(v=1)/HF(v=0) cross section ratio at translational energies not far from the HF(v=0) threshold and the relative cross section for HF(v=0) have been satisfactorily descibed. In what regards rotation, the best theoretical results are those corresponding to the Sorbie-Murrell PES (the cross section increases with J), although important differences with experiment appear for the J = 0–3 interval at the lower translational energy values considered (0.54 and 0.77 eV).     

A global potential energy surface and time‐dependent quantum wave packet calculation of Au + H2 reaction

A global potential energy surface (PES) corresponding to the ground state of AuH₂ system has been constructed based on 22 853 ab initio energies calculated by the multireference configuration interaction method with a Davidson correction. The neural network method is used to fit the PES, and the root mean square error is only 1.87 meV. The topographical features of the novel global PES are compared with previous PES which is constructed by Zanchet et al. (Zanchet PES). The global minimum energy reaction paths on the two PESs both have a well and a barrier. Relative to the Au + H₂ reactants, the energy of well is 0.316 eV on the new PES, which is 0.421 eV deeper than Zanchet PES. The calculation of Au(²S) + H₂(X¹Σ_g⁺) → AuH(X¹Σ⁺) + H(²S) dynamical reaction is carried out on new PES, by the time‐dependent quantum wave packet method (TDWP) with second order split operator. The reaction probabilities, integral cross‐sections (ICSs) and differential cross‐sections are obtained from the dynamics calculation. The threshold in the reaction is about 1.46 eV, which is 0.07 eV smaller than Zanchet PES due to the different endothermic energies on the two PESs. At low collision energy (<2.3 eV), the total ICS is larger than the result obtained on Zanchet PES, which can be attributed to the difference of the wells and endothermic energies.     

Potential energy surface of HDO up to 25,000 cm-1

A new spectroscopically determined potential energy surface (PES) for HD(16)O is presented. This surface is constructed by adjusting the high accuracy ab initio PES of Polyansky et al. [Science 299, 539 (2003)] by fitting to both published experimental data and our still unpublished data. This refinement used experimentally derived term values up to 25,000 cm(-1) and with J< or =8: a data set of 3478 energy levels once some levels with ambiguous assignment is excluded. To improve the extrapolation properties of the empirical PES, the restraint that the resulting PESs remain close to the ab initio surface was imposed. The new HDO_07 PES reproduces the experimental data, including high J levels not included in the fit, with a root mean square error of 0.035 cm(-1). Predictions for rotation-vibration term values up to J=12 are made.     

Angular distributions for the F+H(2)-->HF+H reaction: the role of the F spin-orbit excited state and comparison with molecular beam experiments

We report quantum mechanical calculations of center-of-mass differential cross sections (DCS) for the F+H(2)-->HF+H reaction performed on the multistate [Alexander-Stark-Werner (ASW)] potential energy surfaces (PES) that describe the open-shell character of this reaction. For comparison, we repeat single-state calculations with the Stark-Werner (SW) and Hartke-Stark-Werner (HSW) PESs. The ASW DCSs differ from those predicted for the SW and HSW PES in the backward direction. These differences arise from nonadiabatic coupling between several electronic states. The DCSs are then used in forward simulations of the laboratory-frame angular distributions (ADs) measured by Lee, Neumark, and co-workers [J. Chem. Phys. 82, 3045 (1985)]. The simulations are scaled to match experiment over the range 12 degrees 相似文献   

Theoretical study of stereodynamics for the O(D) + D2 → OD + D reaction

A quasi-classical trajectory method (QCT) running on the ¹A′ and ¹A″ potential energy surfaces (PESs) given by Dobbyn and Knowles [A.J. Dobbyn, P.J. Knowles, Mol. Phys. 91 (1997) 1107] has been employed to study the dynamical stereochemistry of the chemical reaction O(¹D) + D₂ → OD + D, especially the vector correlations between products and reagents. The results indicate that product rotational angular momentum j′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane on both PESs, with different rotational polarization behaviors of product OD for the two PESs and for different collision energies. Calculations show that the alignment effect of products become weaker with an increase of the collision energy on the ¹A′ PES but is not sensitive to the collision energy on the ¹A″ PES. When the collision energy increases, the product OD mainly tends to the forward scattering on the ¹A′ PES and displays a switch from the backward scattering to the forward one on the ¹A″ PES. These differences are probably attributed to the different characteristics of the two PESs.     

Exploring the accuracy level of new potential energy surfaces for the F + HD reactions: from exact quantum rate constants to the state-to-state reaction dynamics

Exact quantum reactive scattering calculations in the collision energy range 1-250 meV have been carried out for both the isotopic product channels of the title system. The dynamical studies compares an ab initio potential energy surface (PES) recently appeared in the literature (J. Chem. Phys., 2008, 129, 011103) with other phenomenological PESs. Vibrational branching ratios, cross sections and rate constants are presented and compared with molecular beam scattering experiments as well as with chemical kinetics data. In particular, the agreement of the vibrational branching ratios with experimental measurements is improved with respect to previous studies on other PESs, mainly because of the presence of a broad peak in the HF(v' = 3) integral cross section completely absent in the previous simulations. This feature, observed by molecular beam experiments, is the fingerprint of a new reaction mechanism operative in the dynamics described by the new PES. A conjecture for its origin, able to explain many of its characteristic aspects, is analyzed and discussed.     

The role of exchange-correlation functionals in the potential energy surface and dynamics of N(2) dissociation on W surfaces

We study the dissociative adsorption of N(2) on W(100) and W(110) by means of density functional theory and classical dynamics. Working with a full six-dimensional adiabatic potential energy surface (PES), we find that the theoretical results of the dynamical problem strongly depend on the choice of approximate exchange-correlation functional for the determination of the PES. We consider the Perdew-Wang-91 [Perdew et al., Phys. Rev. B 46, 6671 (1992)] and Perdew-Burke-Ernzerhof (RPBE) [Hammer et al., Phys. Rev. B 59, 7413 (1999)] functionals and carry out a systematic comparison between the dynamics determined by the respective PESs. Even though it has been shown in earlier works that the RPBE may provide better values for the chemisorption energies, our study brings evidence that it gives rise to a PES with excessive repulsion far from the surface.     

Hydrogen adsorbed in a metal organic framework-5: coupled translation-rotation eigenstates from quantum five-dimensional calculations

We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (T-R) eigenstates of a H(2) molecule adsorbed in metal organic framework-5 (MOF-5), a prototypical nanoporous material, which was treated as rigid. The anisotropic interactions between H(2) and MOF-5 were represented by the analytical 5D intermolecular potential energy surface (PES) used previously in the simulations of the thermodynamics of hydrogen sorption in this system [Belof et al., J. Phys. Chem. C 113, 9316 (2009)]. The global and local minima on this 5D PES correspond to all of the known binding sites of H(2) in MOF-5, three of which, α-, β-, and γ-sites are located on the inorganic cluster node of the framework, while two of them, the δ- and ε-sites, are on the phenylene link. In addition, 2D rotational PESs were calculated ab initio for each of these binding sites, keeping the center of mass of H(2) fixed at the respective equilibrium geometries; purely rotational energy levels of H(2) on these 2D PESs were computed by means of quantum 2D calculations. On the 5D PES, the three adjacent γ-sites lie just 1.1 meV above the minimum-energy α-site, and are separated from it by a very low barrier. These features allow extensive wave function delocalization of even the lowest translationally excited T-R eigenstates over the α- and γ-sites, presenting significant challenges for both the quantum bound-state calculations and the analysis of the results. Detailed comparison is made with the available experimental data.     

A theoretical study of the mechanism and kinetics of F+N3 reactions.

Both the singlet(1A') and triplet(3A') potential energy surfaces (PESs) of F+N(3) reactions are investigated using the complete-active-space self-consistent field (CASSCF) and the multireference configuration interaction (MRCI) methods with a proper active space. The minimum energy crossing point (MECP) at the intersection seam between the 1A' and 3A' PESs is located and used to clarify the reaction mechanisms. Two triplet transition states are found, with one in the cis form and the other one in the trans form. Further kinetic calculations are performed with the canonical unified statistical (CUS) theory on the singlet PES and the improved canonical variational transition-state (ICVT) method on the triplet PES. The rate constants are also reported. At 298 K, the calculated rate constant is in reasonably good agreement with experimental values, and spin-orbit coupling effects lower it by 28 %. The spectroscopic constants derived from the fitted potential-energy curves for the singlet and triplet states of NF are in very good agreement with experimental values. Our calculations indicate that the adiabatic reaction on the singlet PES leading to NF(a(1)Delta)+N(2) is the major channel, whereas the nonadiabatic reaction through the MECP, which leads to NF(X(3)Sigma(-))+N(2), is a minor channel.     

Barrier Height Effect on Cl+H2(D2) Reaction

Three-dimensional time-dependent quantum wave packet calculation was performed to study the reaction dynamics of Cl+H2(D2) on two potential energy surfaces (CW PESs). The first CW PES is with spin-orbit correction; the second is without spin-orbit correction. The integral cross-section and reaction probability as a function of collision energy are calculated in the collision energy range of 0.1 eV to 1.4 eV. For reaction of Cl with D2, the reaction section with spin-orbit correction has a shift toward the high energy because the barrier height increases. As for the reaction of Cl with H2 at low collision energy, it is more reactive on the PES with spin-orbit correction than on the low barrier height PES without spin-orbit correction, due to the tunnel effect for the reaction of the Cl with H2. When the collision energy is higher than 0.7 eV, the reactivity on the low barrier height PES is larger than that on the high barrier height PES. It is believed that the barrier height plays a very important role in the reactivity of Cl with (H2, D2). For the Cl+H2 reaction the barrier width is also very important because of the tunneling effect.