Generalized electronic diabatic approach to structural similarity and the Hammond postulate

We revisit the notion of structural similarity along a reaction path within the context of a generalized electronic diabatic (GED) molecular model. In this approach, a reaction involving two closed‐shell stable species is described as the evolution of a quantum state that superimposes at least three diabatic electronic species (reactant, product, and an open‐shell transition state) coupled by an external electromagnetic field. Reactant and product amplitudes in this general state are also modulated by changing the geometry of a system of classical positive charges interacting with the electrons. By mapping these amplitudes over nuclear configurational space, we can follow the total quantum state along a reaction coordinate and establish its similarity to each of the diabatic species. As a result, chemical processes, and useful notions such as those of energy barriers and the Hammond postulate, emerge as consequence of Franck–Condon‐like transitions between quantum states. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A Three-State Model for Electronic Transitions Represented in a Generalized Diabatic Approach

We describe the chemical change between two diabatic closed-shell states as an electronic transition mediated by two factors: a bound diabatic transition state and the electromagnetic field. Using a three-state model for bond breaking, we compute the amplitudes of the total quantum state on the diabatic reactant, product, and transition states as a function of the external field. Changes in the total electronic state appear as sharp transitions between diabatic basis functions for particular configurations of the set of external positive charges. Depending on the diabatic states and the external field, the model predicts the possible occurrence of energy barriers for breaking or forming covalent bonds.     

A quantum theory of chemical processes and reaction rates based on diabatic electronic functions coupled in an external field

The method discussed in this work provides a theoretical framework where simple chemical reactions resemble any other standard quantum process, i.e., a transition in quantum state mediated by the electromagnetic field. In our approach, quantum states are represented as a superposition of electronic diabatic basis functions, whose amplitudes can be modulated by the field and by the external control of nuclear configurations. Using a one-dimensional three-state model system, we show how chemical structure and dynamics can be represented in terms of these control parameters, and propose an algorithm to compute the reaction probabilities. Our analysis of effective energy barriers generalizes previous ideas on structural similarity between reactant, and product, and transition states using the geometry of conventional reaction paths. In the present context, exceptions to empirical rules such as the Hammond postulate appear as effects induced by the environment that supplies the external field acting on the quantum system.     

A surface hopping method for chemical reaction dynamics in solution described by diabatic representation: an analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.     

The IRC method in chemical reactions: Reaction ergodography for the addition of LiH to acetylene

The ab initio calculation have been performed on the addition of LiH to acetylene at RHF/3-21G basis set. The geometries and energies of the isolated reactant, molecular complex, transition state and product have been determined on the singlet potential energy surface of the ground state. Our results indicate that there is a meta stable molecular complex near the isolated reactant in the reaction pathway. The process from isolated reactant to molecular complex is a non-bonding-exchanging reaction process, and the process from molecular complex to product is the rate-controlling step of the reaction. We also estimate the activated entropy and the frequency factor of the rate-controlling step by using the RRKM theory. The FMO analysis for the transition state reveals the HOMO of transition state to be formed from both HOMO-LUMO and HOMO-HOMO interactions.     

Steepest descent reaction path integration using a first-order predictor-corrector method

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately integrated paths are also needed when evaluating reaction rates using variational transition state theory or reaction path Hamiltonian models. In this work an Euler-based predictor-corrector integrator is presented and tested using one analytic model surface and five chemical reactions. The use of Hessian updating, as a means for reducing the overall computational cost of the reaction path calculation, is also discussed.     

Oxidation and Reduction Pathways in the Knowles Hydroamination via a Photoredox-Catalyzed Radical Reaction**

Systematic reaction path exploration revealed the entire mechanism of Knowles's light-promoted catalytic intramolecular hydroamination. Bond formation/cleavage competes with single electron transfer (SET) between the catalyst and substrate. These processes are described by adiabatic processes through transition states in an electronic state and non-radiative transitions through the seam of crossings (SX) between different electronic states. This study determined the energetically favorable SET path by introducing a practical computational model representing SET as non-adiabatic transitions via SXs between substrate's potential energy surfaces for different charge states adjusted based on the catalyst's redox potential. Calculations showed that the reduction and proton shuttle process proceeded concertedly. Also, the relative importance of SET paths (giving the product and leading back to the reactant) varies depending on the catalyst's redox potential, affecting the yield.     

Ab initio potential energy surfaces of the ion-molecule reaction: C2H2 + O+

High level ab initio calculations using complete active space self-consistent field and multi reference single and double excitation configuration interaction methods with cc-pVDZ (correlation consistent polarized valence double zeta) and cc-pVTZ (triple zeta) basis sets have been performed to elucidate the reaction mechanism of the ion-molecule reaction, C2H2(1Sigmag+) + O+(4S), for which collision experiment has been performed by Chiu et al. [J. Chem. Phys. 109, 5300 (1998)]. The minor low-energy process leading to the weak spin-forbidden product C2H2+ (2Piu) + O(1D) has been studied previously and will not be discussed here. The major pathways to form charge-transfer (CT) products, C2H2+ (2Piu) + O(3P) (CT1) and C2H2+ (4A2) + O(3P) (CT2), and the covalently bound intermediates are investigated. The approach of the oxygen atom cation to acetylene goes over an energy barrier TS1 of 29 kcal/mol (relative to the reactant) and adiabatically leads the CT2 product or a weakly bound intermediate Int1 between CT2 products. This transition state TS1 is caused by the avoided crossing between the reactant and CT2 electronic states. As the C-O distance becomes shorter beyond the above intermediate, the C1 reaction pathway is energetically more favorable than the Cs pathway and goes over the second transition state TS2 of a relative energy of 39 kcal/mol. Although this TS connects diabatically to the covalent intermediate Int2, there are many states that interact adiabatically with this diabatic state and these lead to the other charge-transfer product CT1 via either of several nonadiabatic transitions. These findings are consistent with the experiment, in which charge transfer and chemical reaction products are detected above 35 and 39 kcal/mol collision energies, respectively.     

Ab initio study of C + H3+ reactions

The reaction C + H3+ --> CH(+) + H2 is frequently used in models of dense interstellar cloud chemistry with the assumption that it is fast, i.e. there are no potential energy barriers inhibiting it. Ab initio molecular orbital study of the triplet CH3+ potential energy surface (triplet because the reactant carbon atom is a ground state triplet) supports this hypothesis. The reaction product is 3 pi CH+; the reaction is to exothermic even though the product is not in its electronic ground state. No path has been found on the potential energy surface for C + H3+ --> CH2(+) + H reaction.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the C?H Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

基态氧(3^O2)氧化硅烯的密度泛函计算研究

采用密度泛函[B3LYP(full)/6-311+G^*]方法研究了基态氧(3^O2)氧化硅烯(Si2H4)的机理。计算了三重态初始中间体(IM(T1)到单重态中间体IM2(S0)反应交叉势能面,报道了各反应中间体、产物和过渡态的构型和能量,用频率分析方法对各过渡态进行了验证,进一步用IRC方法对主要的基元反应进行了考察,确定了历经生成1,2-二氧环氧硅烷中间体的氧化过程的主要反应通道。     

Theoretical Studies on Reaction Mechanism of CH3SO with NO

The potential energy surface （PES） of CH3SO radical with NO reaction has been studied at MP2/6-311G（2df, p） and QCISD/6-311G（2df, p） levels. Geometries of the reactants, transition states （TS） and products were optimized at B3LYP/6-311G （d,p） level. The geometries of the transition states were found for the first time. The calculated results show that the reaction can proceed via singlet-state or triplet-state PES. Because of the high energy barrier of triplet surface, the singlet surface reactions are dominant. The topological analysis of electron density shows that there are two kinds of structaral transition states （the bifurcation-type ring structure transition state and the T-shaped conflict structure transition state） in the titled reaction. The total electronic density of the reactants, TS and products and the spin electronic density on the triplet surface were also discussed in this paper.     

Theoretical studies on ammonia oxide and its unimolecular reactions

The unimolecular reactions of ammonia oxide H₃NO, isomerization and dehydrogenation, are investigated by ab initio MO calculations with the 4-31G basis set. The geometries and energies of the reactant, transition states and products have been determined on the singlet potential energy surface. The reaction ergodography along the intrinsic reaction coordinate (IRC) for the two reactions have been performed. The vibrational frequency correlation diagram of the two reactions are analyzed along the IRC.     

A dimensionless reaction coordinate for quantifying the lateness of transition states

The Hammond‐Leffler postulate asserts that transition states of exothermic reactions are reactant‐like (early), whereas transition states of endothermic reactions are product‐like (late). Related postulates have been proposed to describe the sensitivity of activation barriers for reactions occurring on catalytic surfaces to the catalyst structure. To evaluate the validity of these postulates for different chemical reactions, a general method for classifying transition states as either early or late is needed. One can envision a dimensionless reaction coordinate that changes continuously and monotonically from 0 to 1 along a minimum energy reaction pathway. The value of the dimensionless reaction coordinate for the transition state (W_TS) classifies transition states as (a) early when W_TS < 0.5, (b) late when W_TS > 0.5, and (c) equidistant between reactants and products when W_TS = 0.5. In this article, we derive such a dimensionless reaction coordinate and illustrate its usefulness for several different chemical reactions. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Franck-Condon theory of reactive scattering

A Franck-Condon theory of reactive scattering is introduced which generalizes previous works in a number of respects. We consider the collinear AB + C → A + BC reaction where A, B, and C may be polyatomic species and show how the multi-dimensional continuum-continuum Franck-Condon integral can exactly be reduced to a two-dimensional one involving the nonorthogonal reaction coordinates on the reactant and product diabatic surfaces. These integrals are then written in a rapidly convergent series of products of one-dimensional bound-continuum integrals of a form closely related to those studied in recent theories of photodissociation where accurate analytical and numerical methods are available for treating them. The theory is applied to the case of the D + Hl isotope exchange for a model surface to enable a comparison of exact quantum calculations with those of the Franck-Condon theory for the identical surface in both cases. The calculations are all performed at energies where the reaction is classically forbidden. The relative Dl vibrational distributions (as a function of initial Hl state) are accurately reproduced in a fashion that is fairly insensitive to the choice of the reactant and product diabatic surfaces, but the absolute probabilities are shown to be sensitively dependent on this choice.     

A unified perspective on the hydrogen atom transfer and proton-coupled electron transfer mechanisms in terms of topographic features of the ground and excited potential energy surfaces as exemplified by the reaction between phenol and radicals

The relation between the hydrogen atom transfer (HAT) and proton-coupled electron transfer (PCET) mechanisms is discussed and is illustrated by multiconfigurational electronic structure calculations on the ArOH + R(*) --> ArO(*) + RH reactions. The key topographic features of the Born-Oppenheimer potential energy surfaces that determine the predominant reaction mechanism are the conical intersection seam of the two lowest states and reaction saddle points located on the shoulders of this seam. The saddle point corresponds to a crossing of two interacting valence bond states corresponding to the reactant and product bonding patterns, and the conical intersection corresponds to the noninteracting intersection of the same two diabatic states. The locations of mechanistically relevant conical intersection structures and relevant saddle point structures are presented for the reactions between phenol and the N- and O-centered radicals, (*)NH2 and (*)OOCH3. Points on the conical intersection of the ground doublet D0 and first excited doublet D1 states are found to be in close geometric and energetic proximity to the reaction saddle points. In such systems, either the HAT mechanism or both the HAT mechanism and the proton-coupled electron transfer (PCET) mechanism can take place, depending on the relative energetic accessibility of the reaction saddle points and the D0/D1 conical intersection seams. The discussion shows how the two mechanisms are related and how they blend into each other along intermediate reaction paths. The recognition that the saddle point governing the HAT mechanism is on the shoulder of the conical intersection governing the PCET mechanism is used to provide a unified view of the competition between the two mechanisms (and the blending of the two mechanisms) in terms of the prominent and connected features of the potential energy surface, namely the saddle point and the conical intersection. The character of the dual mechanism may be understood in terms of the dominant valence bond configurations of the intersecting states, which are zero-order approximations to the diabatic states.     

An ab initio-based global potential energy surface for the SH3 system and full-dimensional state-to-state quantum dynamics study for the H2 + HS → H2S + H reaction

An accurate potential energy surface for the ground electronic state of SH₃ system has been constructed with 41,882 high level ab initio energy points and the neural network fitting method. The time-dependent wave packet method has been used to calculate the first state-to-state differential cross sections for the title reaction up to 1.2 eV in full dimensions, based on the reactant–product decoupling scheme. It is found that the majority of H₂S are produced in the ground vibrational state, with a large fraction of available energy for the reaction ending up as product translational motion. The differential cross sections at the threshold energy are dominated by a very narrow peak in the backward direction. With the increase of collision energy, the width of the angular distribution increases considerably, which is a typical feature of a direct reaction via abstract mechanism, similar to the H₂ + OH → H₂O + H reaction. © 2018 Wiley Periodicals, Inc.     

Potential energy surface crossings and the mechanistic spectrum for intramolecular electron transfer in organic radical cations.

The structure of the potential energy surface for the intramolecular electron transfer (IET) of four different model radical cations has been determined by using reaction path mapping and conical intersection optimization at the ab initio CASSCF level of theory. We show that, remarkably, the calculated paths reside in regions of the ground-state energy surface whose structure can be understood in terms of the position and properties of a surface crossing between the ground and the first excited state of the reactant. Thus, in the norbornadiene radical cation and in an analogue compound formed by two cyclopentene units linked by a norbornyl bridge, IET proceeds along direct-overlap and super-exchange concerted paths, respectively, that are located far from a sloped conical intersection point and in a region where the excited-state and ground-state surfaces are well separated. A second potential energy surface structure has been documented for 1,2-diamino ethane radical cation and features two parallel concerted (direct) and stepwise (chemical) paths. In this case a peaked conical intersection is located between the two paths. Finally, a third type of energy surface is documented for the bismethyleneadamantane radical cation and occurs when there is, effectively, a seam of intersection points (not a conical intersection) which separates the reactant and product regions. Since the reaction path cannot avoid the intersection, IET can only occur nonadiabatically. These IET paths indicate that quite different IET mechanisms may operate in radical cations, revealing an unexpectedly enriched and flexible mechanistic spectrum. We show that the origin of each path can be analyzed and understood in terms of the one-dimensional Marcus-Hush model.