Exit-channel dynamics in barrierless unimolecular reactions: criteria of vibrational adiabaticity

Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an angle-action reaction path Hamiltonian (RPH). The accuracy of the vibrational adiabatic approximation is found to be completely independent of the shape of the potential energy Vs. Vibrations are adiabatic when two independent dimensionless parameters are small. The first one, denoted as sigma, controls the dynamic coupling. The physical significance of the condition sigma<1 is that the amplitude of the vibrations normal to the reaction path should be much smaller than the radius of curvature of the reaction path. The second parameter, denoted as mu, governs the static coupling. It results from the dependence of the vibrational frequency omega on the reaction coordinate s. The higher omega, the lower its derivative with respect to s and, more unexpectedly, the higher the translational energy epsilon, the lower mu is. A criterion for locating a particular dividing surface in barrierless reactions is proposed. This surface separates two regions of space: one where energy flows freely, and one where energy conversion between translation and vibration is hindered by adiabatic invariance. The nature of the dynamical constraint that prevents the product translational energy distribution from being fully statistical can be identified by a maximum entropy analysis. The constraint is found to bear on the translational momentum ps, i.e., on the square root of the translational energy epsilon1/2. This can be understood by applying Jacobi's form of the least action principle to the vibrationally adiabatic RPH.     

On the use of effective core potentials in the calculation of magnetic properties, such as magnetizabilites and magnetic shieldings

State-of-the art effective core potentials (ECPs) that replace electrons of inner atomic cores involve non-local potentials. If such an effective core potential is added to the Hamiltonian of a system in a magnetic field, the resulting Hamiltonian is not gauge invariant. This means, magnetic properties such as magnetisabilities and magnetic shieldings (or magnetic susceptibilities and nuclear magnetic resonance chemical shifts) calculated with different gauge origins are different even for exact solutions of the Schro?dinger equation. It is possible to restore gauge invariance of the Hamiltonian by adding magnetic field dependent terms arising from the effective core potential. Numerical calculations on atomic and diatomic model systems (potassium mono-cation and potassium dimer) clearly demonstrate that the standard effective core potential Hamiltonian violates gauge invariance, and this affects the calculation of magnetisabilities more strongly than the calculation of magnetic shieldings. The modified magnetic field dependent effective core potential Hamiltonian is gauge invariant, and therefore it is the correct starting point for distributed gauge origin methods. The formalism for gauge including atomic orbitals (GIAO) and individual gauge for localized orbitals methods is worked out. ECP GIAO results for the potassium dimer are presented. The new method performs much better than a previous ECP GIAO implementation that did not account for the non-locality of the potential. For magnetic shieldings, deviations are clearly seen, but they amount to few ppm only. For magnetisabilities, our new ECP GIAO implementation is a major improvement, as demonstrated by the comparison of all-electron and ECP results.     

Semi-empirical calculations of molecular trajectories: Method and applications to some simple molecular systems

The MNDO Hamiltonian as incorporated within MOPAC has been utilized to predict dynamics for some simple reactions. In one option, the intrinsic reaction coordinate has been followed along the path of steepest descent from the transition state backward to reactants and forward to products. In a second option, dynamics of isolated molecular systems have been calculated. In each case, the potential surface (as predicted by the MNDO Hamiltonian) is calculated in situ as the atomic trajectories are calculated from Newton's Laws of Motion. Several specific examples are given and discussed.     

Ab initio adiabatic and diabatic energies and dipole moments of the CaH+ molecular ion

The diabatic and adiabatic potential-energy curves and permanent and transition dipole moments of the highly excited states of the CaH(+) molecular ion have been computed as a function of the internuclear distance R for a large and dense grid varying from 2.5 to 240 au. The adiabatic results are determined by an ab initio approach involving a nonempirical pseudopotential for the Ca core, operatorial core-valence correlation, and full valence configuration interaction. The molecule is thus treated as a two-electron system. The diabatic potential energy curves have been calculated using an effective metric combined to the effective Hamiltonian theory. The diabatic potential-energy curves and their permanent dipole moments for the (1)∑(+) symmetry are examined and corroborate the high imprint of the ionic state in the adiabatic representation. Taking the benefit of the diabatization approach, correction of hydrogen electron affinity was taken into account leading to improved results for the adiabatic potentials but also the permanent and transition electric dipole moments.     

Novel variational principles of chemical reaction

Minimum principles of chemical reaction coordinates are established. IRC (intrinsic reaction coordinate) draws the path of minimum distance from reactant to product. The distance is measured in the rigged configuration Riemannian space whose metric is determined by the distribution of the adiabatic potential energy. Moreover, minimum property of the intrinsic principle of least action is established for the intrinsic dynamism of chemical reaction. Minimum principle of the path connecting intercell boundary with cell is also discussed.     

Local normal modes and vibrational adiabatic potentials

Local normal-mode analysis for a collinear potential energy surface generates a system of curvilinear coordinates, which are orthogonal in the mass-skewed system. The motion is locally separable in these coordinates. We compare the utility of one of the normal modes as a transversal-vibration coordinate, with the conventional choice of the direction perpendicular to the reaction coordinate in the mass-skewed system. The comparison is done for two commonly used reaction coordinates: BEBO and the steepest-descent path. Results differ for different choices of directions and reaction coordinates. Future work should concentrate on a choice of a reaction coordinate which is itself one of the normal modes.     

Intermolecular coulomb couplings from ab initio electrostatic potentials: application to optical transitions of strongly coupled pigments in photosynthetic antennae and reaction centers

An accurate and numerically efficient method for the calculation of intermolecular Coulomb couplings between charge densities of electronic states and between transition densities of electronic excitations is presented. The coupling of transition densities yields the F?rster type excitation energy transfer coupling, and from the charge density coupling, a shift in molecular excitation energies results. Starting from an ab initio calculation of the charge and transition densities, atomic partial charges are determined such as to fit the resulting electrostatic potentials of the different states and the transition. The different intermolecular couplings are then obtained from the Coulomb couplings between the respective atomic partial charges. The excitation energy transfer couplings obtained in the present TrEsp (transition charge from electrostatic potential) method are compared with couplings obtained from the simple point-dipole and extended dipole approximations and with those from the ab initio transition density cube method of Krüger, Scholes, and Fleming. The present method is of the same accuracy as the latter but computationally more efficient. The method is applied to study strongly coupled pigments in the light-harvesting complexes of green sulfur bacteria (FMO), purple bacteria (LH2), and higher plants (LHC-II) and the "special pairs" of bacterial reaction centers and reaction centers of photosystems I and II. For the pigment dimers in the antennae, it is found that the mutual orientation of the pigments is optimized for maximum excitonic coupling. A driving force for this orientation is the Coulomb coupling between ground-state charge densities. In the case of excitonic couplings in the "special pairs", a breakdown of the point-dipole approximation is found for all three reaction centers, but the extended dipole approximation works surprisingly well, if the extent of the transition dipole is chosen larger than assumed previously. For the "special pairs", a large shift in local transition energies is found due to charge density coupling.     

The action variable in dissipattvely perturbed hamiltonian systems

The action variable of a conservative one-dimensional Hamiltonian system decays exponentially when a linear disapative perturbation is added, irrespective of the Hamiltonian. In multidimensional integrable systems the product of the actions decays exponentially. Various features of these results are discussed, including the connection to adiabatic invariance and semiclassical implications.     

Second-harmonic generation and effect of adsorbates for free-electron metal and semiconductor surfaces

We discuss aspects of a developing microscopic theory of SHG from simple metal and semiconductor surfaces. For semiconductors calculations of the dynamical nonlinear susceptibility on the basis of realistic tight-binding parametrizations of the electronic Hamiltonian provide a practical scheme. In the resulting spectra the effect of the dangling bonds on SHG is clearly seen together with a strong decrease upon saturation with H atoms. In the metal case the adsorbate induced changes of the static nonlinear electron density can be calculated self-consistently by applying density functional theory to the jellium model. The second-order dipole moment determines the effect of adsorbates on the SHG intensity in the adiabatic limit. Quite general a correlation with the nature of the adsorbate expressed by its electronegativity and the characteristic charge transfer, adsorption dipole and polarizabilities in first and second order is found.     

Electrostatic interactions of charged dipolar proteins in reverse micelles

The electrostatic interactions in a reverse micelle containing a small-ionized protein are studied by Monte Carlo simulation. The electrostatic contribution to the potential of mean force of the protein in the reverse micelle is determined for a neutral protein, a uniformly charged protein, and a uniformly charged protein with a dipole moment. The effect of addition of a simple electrolyte is studied. While symmetrically distributed micellar charge exerts no force on enclosed ionic species, the protein is driven to the micellar wall due to interactions with simple ions. Protein binding to the inner wall of the micelle can be regulated by added salt. The presence of a dipole drives the protein further to the wall. These effects are studied for several proteins characterized by different charges and dipole moments. For a weakly charged protein with a strong dipole moment the contribution of dipolar interaction to the free energy can represent a major driving force for protein solubilization in the microemulsion.     

The dissociative chemisorption of methane on Ni(100): reaction path description of mode-selective chemistry

We derive a model for the dissociative chemisorption of methane on a Ni(100) surface, based on the reaction path Hamiltonian, that includes all 15 molecular degrees of freedom within the harmonic approximation. The total wavefunction is expanded in the adiabatic vibrational states of the molecule, and close-coupled equations are derived for wave packets propagating on vibrationally adiabatic potential energy surfaces, with non-adiabatic couplings linking these states to each other. Vibrational excitation of an incident molecule is shown to significantly enhance the reactivity, if the molecule can undergo transitions to states of lower vibrational energy, with the excess energy converted into motion along the reaction path. Sudden models are used to average over surface impact site and lattice vibrations. Computed dissociative sticking probabilities are in good agreement with experiment, with respect to both magnitude and variation with energy. The ν(1) vibration is shown to have the largest efficacy for promoting reaction, due to its strong non-adiabatic coupling to the ground state, and a significant softening of the vibration at the transition state. Most of the reactivity at 475 K is shown to result from thermally assisted over-the-barrier processes, and not tunneling.     

Role of angular momentum conservation in unimolecular translational energy release: validity of the orbiting transition state theory

The translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary conditions of validity of the orbiting transition state theory (OTST) for the calculation of kinetic energy release distributions (KERDs) have been formulated. One of them examines the central ion-induced dipole potential approximation. As a second criterion, an adiabatic parameter is derived. The lower the released translational energy and the total angular momentum, the larger the reduced mass, the rotational constant of the molecular fragment, and the polarizability of the released atom, the more valid is the OTST. Only the low-energy dissociation of the iodobenzene ion (E approximately 0.45 eV, where E is the internal energy above the reaction threshold) is found to fulfill the criteria of validity of the OTST. The constraints that act on the dissociation dynamics have been studied by the maximum entropy method. Calculations of entropy deficiencies (which measure the deviation from a microcanonical distribution) show that the pair of fragments does not sample the whole of the phase space that is compatible with the mere specification of the internal energy. The major constraint that results from conservation of angular momentum is related to a reduction of the dimensionality of the dynamics of the translational motion to a two-dimensional space. A second and minor constraint that affects the KERD leads to a suppression of small translational releases, i.e., accounts for threshold behavior. At high internal energies, the effects of curvature of the reaction path and of angular momentum conservation are intricately intermeddled and it is not possible to specify the share of each effect.     

Theoretical approach to reactions of polyatomic molecules

A scheme for systematic reduction of the theoretical treatment of elementary reactions involving polyatomic molecules is described; it consists of (1) limitation to the energetically relevant regions of the nuclear configuration space (the reaction path and its near environs) and (2) restriction to the dynamically relevant subspace of the nuclear configuration space (the active modes). Starting from a generalized reaction path Hamiltonian of Nauts and Chapuisat allowing for the use of arbitrary curvilinear coordinates and several large-amplitude modes, the realization of the above-sketched scheme is discussed. A compilation of recent work along these lines, mostly based on the simplified Miller-Handy-Adams reaction path Hamiltonian, is given with particular emphasis on applications of a statistical adiabatic model.     

Statistical properties of the energies and electric dipole moments of the bound vibrational states of the system HCO/COH

From the ab initio calculated three-dimensional adiabatic double-minimum potential energy surface of the HCO⁺/COH⁺ system and the corresponding dipole moment surface the energies of all bound vibrational states and their effective dipole moments are determined applying the Suttcliffe–Tennyson Hamiltonian for triatomic molecules. The energy and dipole data are analysed in terms of statistical methods such as the density of states approach and the nearest-neighbor level spacing distribution (NNSD). Special effort is put into investigating the effect of the tunnelling motion across the isomerization barrier on the NNSD representations.     

Obtaining reaction coordinates by likelihood maximization

We present a new approach for calculating reaction coordinates in complex systems. The new method is based on transition path sampling and likelihood maximization. It requires fewer trajectories than a single iteration of existing procedures, and it applies to both low and high friction dynamics. The new method screens a set of candidate collective variables for a good reaction coordinate that depends on a few relevant variables. The Bayesian information criterion determines whether additional variables significantly improve the reaction coordinate. Additionally, we present an advantageous transition path sampling algorithm and an algorithm to generate the most likely transition path in the space of collective variables. The method is demonstrated on two systems: a bistable model potential energy surface and nucleation in the Ising model. For the Ising model of nucleation, we quantify for the first time the role of nuclei surface area in the nucleation reaction coordinate. Surprisingly, increased surface area increases the stability of nuclei in two dimensions but decreases nuclei stability in three dimensions.     

CH与H2分子反应动力学及选态反应的理论研究

次甲基作为化学反应源曾引起广泛的兴趣.Schaefer 及其合作者于1977年对反应CH(~4Σ~-)+H_2→CH_2(~3B_1)+H 进行过量子化学研究,但是计算中限制了一些自由度.近年来,由于能量梯度方法的发展,反应途径哈密顿理论和变分过渡态理论的提出,有可能进一步对该反应进行分子反应动力学性质的研究.本文用从头算UHF/6-31G 方法和能量梯度方法首先优化出上述反应(原子编号为CH_a+H_bH_c→H_bCH_a+H_c)的过渡态;再用     

Toward theoretical analysis of long-range proton transfer kinetics in biomolecular pumps

Motivated by the long-term goal of theoretically analyzing long-range proton transfer (PT) kinetics in biomolecular pumps, researchers made a number of technical developments in the framework of quantum mechanics-molecular mechanics (QM/MM) simulations. A set of collective reaction coordinates is proposed for characterizing the progress of long-range proton transfers; unlike previous suggestions, the new coordinates can describe PT along highly nonlinear three-dimensional pathways. Calculations using a realistic model of carbonic anhydrase demonstrated that adiabatic mapping using these collective coordinates gives reliable energetics and critical geometrical parameters as compared to minimum energy path calculations, which suggests that the new coordinates can be effectively used as reaction coordinate in potential of mean force calculations for long-range PT in complex systems. In addition, the generalized solvent boundary potential was implemented in the QM/MM framework for rectangular geometries, which is useful for studying reactions in membrane systems. The resulting protocol was found to produce water structure in the interior of aquaporin consistent with previous studies including a much larger number of explicit solvent and lipid molecules. The effect of electrostatics for PT through a membrane protein was also illustrated with a simple model channel embedded in different dielectric continuum environments. The encouraging results observed so far suggest that robust theoretical analysis of long-range PT kinetics in biomolecular pumps can soon be realized in a QM/MM framework.     

HCN OH─→CN H_2O反应理论研究

HCN是硝胶推进剂热分解的一种主要产物，了解它与OH的反应机理对理解这些推进剂的作用原理有极大的帮助问．Miller和Bowman认为HCN被OH氧化是碳氢化合物火焰中含氮燃料转化为NOx的重要途径问．实验上，W0oldridge、Hanson和Bowman等人研究了HCN＋OH～CN＋HOH的反应，得到了该反