Semiempirical MNDO, AM1, and PM3 direct dynamics trajectory studies of formaldehyde unimolecular dissociation

Post-Transition-State Direct Dynamics Simulations on the Ozonolysis of Catechol

On-the-fly dynamics simulations are performed for the reaction of catechol + O₃. The post transition state (TS) dynamics is studied at temperatures of 400 and 500 K. The PM7 semiempirical method is employed for calculating the potential energy gradient needed for integrating Hamilton's equations of motion. This semiempirical method provides excellent agreement in terms of energy and geometry of the TSs as well as minimum energy states of the system with respect to B3LYP/6-311+G (2df, 2p) calculated results. In the dynamics, first, a peroxyacid is formed, which further dissociates to different fragments. Four major channels forming CO, CO₂, H₂O, and small carboxylic acid (SCA) fragments are seen in this reaction. Rates of each of the channels and the overall unimolecular reaction are calculated at both temperatures. Branching ratios of all these product channels are calculated and compared with experiment. The minimum energy profile of CO₂, CO, and H₂O channels are calculated. A qualitative estimate of activation energies for all the channels are obtained and compared with the explicit TS energies of three product channels, which ultimately correlate with the reaction probabilities.

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Graph theory-based reaction pathway searches and DFT calculations for the mechanism studies of free radical-initiated peptide sequencing mass spectrometry (FRIPS MS): a model gas-phase reaction of GGR tri-peptide

Graph theory-based reaction pathway searches (ACE-Reaction program) and density functional theory calculations were performed to shed light on the mechanisms for the production of [a_n + H]⁺, x_n⁺, y_n⁺, z_n⁺, and [y_n + 2H]⁺ fragments formed in free radical-initiated peptide sequencing (FRIPS) mass spectrometry measurements of a small model system of glycine-glycine-arginine (GGR). In particular, the graph theory-based searches, which are rarely applied to gas-phase reaction studies, allowed us to investigate reaction mechanisms in an exhaustive manner without resorting to chemical intuition. As expected, radical-driven reaction pathways were favorable over charge-driven reaction pathways in terms of kinetics and thermodynamics. Charge- and radical-driven pathways for the formation of [y_n + 2H]⁺ fragments were carefully compared, and it was revealed that the [y_n + 2H]⁺ fragments observed in our FRIPS MS spectra originated from the radical-driven pathway, which is in contrast to the general expectation. The acquired understanding of the FRIPS fragmentation mechanism is expected to aid in the interpretation of FRIPS MS spectra. It should be emphasized that graph theory-based searches are powerful and effective methods for studying reaction mechanisms, including gas-phase reactions in mass spectrometry.

Mode specificity and product energy disposal in unimolecular reactions: insights from the sudden vector projection model

A simple model is proposed to predict mode specificity and product energy disposal in unimolecular dissociation reactions. This so-called Sudden Vector Projection (SVP) model quantifies the coupling of a reactant or product mode with the reaction coordinate at the transition state by projecting the corresponding normal mode vector onto the imaginary frequency mode at the saddle point. Due to the sudden assumption, SVP predictions for mode specificity are expected to be valid only when the reactant molecule has weak intermodal coupling. On the other hand, the sudden limit is generally satisfied for its predictions of product energy disposal in unimolecular reactions with a tight barrier. The SVP model is applied to several prototypical systems and the agreement with available experimental and theoretical results is satisfactory.

Exploring Multiple Potential Energy Surfaces: Photochemistry of Small Carbonyl Compounds

In theoretical studies of chemical reactions involving multiple potential energy surfaces (PESs) such as photochemical reactions, seams of intersection among the PESs often complicate the analysis. In this paper, we review our recipe for exploring multiple PESs by using an automated reaction path search method which has previously been applied to single PESs. Although any such methods for single PESs can be employed in the recipe, the global reaction route mapping (GRRM) method was employed in this study. By combining GRRM with the proposed recipe, all critical regions, that is, transition states, conical intersections, intersection seams, and local minima, associated with multiple PESs, can be explored automatically. As illustrative examples, applications to photochemistry of formaldehyde and acetone are described. In these examples as well as in recent applications to other systems, the present approach led to discovery of many unexpected nonadiabatic pathways, by which some complicated experimental data have been explained very clearly.

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: application to formaldehyde

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.

Self-consistent polarization neglect of diatomic differential overlap: application to water clusters

Semiempirical self-consistent field (SCF) methods based on the neglect of diatomic differential overlap (NDDO) formalism have the ability to treat the formation and breaking of chemical bonds but have been found to poorly describe hydrogen bonding and weak electrostatic complexes. In contrast, most empirical potentials are not able to describe bond breaking and formation but have the ability to add missing elements of hydrogen bonding by using classical electrostatic interactions. We present a new method which combines aspects of both NDDO-based SCF techniques and classical descriptions of polarization to describe the diffuse nature of the electronic wavefunction in a self-consistent manner. We develop the "self-consistent polarization neglect of diatomic differential overlap" (SCP-NDDO) theory with the additional description of molecular dispersion developed as a second-order perturbation theory expression. The current study seeks to model water-water interactions as a test case. To this end, we have parametrized the method to accurate ab initio complete basis set limit estimates of small water cluster binding energies of Xantheas and co-workers [J. Chem. Phys. 116, 1493 (2002); 120, 823 (2004)]. Overall agreement with the ab initio binding energies (n=2-6, and 8) is achieved with a rms error of 0.19 kcal/mol. We achieve noticeable improvements in the structure, vibrational frequencies, and energetic predictions of water clusters (n< or =21) relative to standard NDDO-based methods.

Phase Space Analysis of Formaldehyde Dissociation Branching and Comparison with Quasiclassical Trajectory Calculations†

We investigate the dependence of the branching ratio of formaldehyde dissociation to molecular and radical products on the total energy and angular momentum and the HCO rotational state distributions by using a combination of transition state/Rice-Ramsperger-Kassel-Marcus theory and phase space theory. Comparisons are made with recent quasiclassical trajectory (QCT) calculations [Farnum, J. D.; Zhang, X.; Bowman, J. M. J. Chem. Phys. 2007, 126, 134305]. The combined phase-space analysis is in semiquantitative agreement with the QCT results for the rotational distributions of HCO but is only in qualitative agreement for the branching ratio. Nevertheless, that level of agreement serves to provide insight into the QCT results, which showed suppression of the radical channel with increasing total angular momentum for a fixed total energy.

Formaldehyde photodissociation: Dependence on total angular momentum and rotational alignment of the CO product

Quasiclassical trajectory calculations are reported to investigate the effects of rotational excitation of formaldehyde on the branching ratios of the fragmentation products, H2+CO and H+HCO. The results of tens of thousands of trajectories show that increased rotational excitation causes suppression of the radical channel and enhancement of the molecular channel. Decomposing the molecular channel into "direct" and "roaming" channels shows that increased rotation switches from suppressing to enhancing the roaming products across our chosen energy range. However, decomposition into these pathways is difficult because the difference between them does not appear to have a distinct boundary. A vector correlation investigation of the CO rotation shows different characteristics in the roaming versus direct channels and this difference is a potentially useful signature of the roaming mechanism, as first speculated by Kable and Houston in their experimental study of photodissociation of acetaldehyde [P. L. Houston and S. H. Kable, Proc. Nat. Acad. Sci. 103, 16079 (2006)].

Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

In previous research [J. Chem. Phys. 111, 3800 (1999)] a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentum conservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorithm, with its new components, has been implemented into the VENUS/NWChem software package and compared with the velocity-Verlet algorithm for the H(2)CO-->H(2)+CO, O(3)+C(3)H(6), and F(-)+CH(3)OOH chemical reactions.

Quantum dynamics study on multichannel dissociation and isomerization reactions of formaldehyde

We study quantum dynamics of the multichannel reactions of H(2)CO including the molecular and radical dissociation channels as well as the isomerization ones, H(2)CO-->trans-HCOH and trans-HCOH-->cis-HCOH. For this purpose, the previously developed potential energy function [T. Yonehara and S. Kato, J. Chem. Phys. 117, 11131 (2002)] is refined to give accurate transition state energies and to describe the radical dissociation channel. The cumulative reaction probabilities for the molecular dissociation and two isomerization channels are calculated by using the full Watson Hamiltonian. We also carry out wave packet dynamics calculations starting from the transition state region for the molecular dissociation. A contracted basis set for the angular coordinates is constructed to reduce the size of dynamics calculations. The intramolecular vibrational relaxation dynamics is found to be fast and almost complete within 300 fs. Using the energy filtered wave functions, the time propagation of HCOH population is obtained in the energy range from 81 to 94 kcal/mol. The branching ratio of the radical product is estimated by calculating the time dependent reactive fluxes to the molecular and radical dissociation products.

New insights on reaction dynamics from formaldehyde photodissociation

We review the photodissociation dynamics of formaldehyde with an emphasis on recent calculations that make use of a global ab initio-based potential energy surface for the S(0) state. These calculations together with recent experiments reveal striking departures from conventional transition state theory for the formation of the molecular products H(2) + CO. The evidence for this departure is reviewed in detail by examining properties of the new potential surface and results of quasiclassical trajectory dynamics calculations using this surface. We also review very recent work on the dynamics governing the formation of radical products, H + HCO. These products can be formed on the T(1) surface as well as the S(0) one, and we present some results contrasting the dynamics on these two surfaces. This work makes use of a new semi-global ab initio-based T(1) potential energy surface.

Molecular Dynamics of Complex Gas-Phase Reactive Systems by Time-Dependent Groups

A novel way of assembling the total potential for performing molecular dynamical studies of complex gas-phase reactive chemical systems is introduced. The method breaks the calculation of the total potential and gradients of the potential into time-dependent groups that are governed by spatial cutoffs. These groups evolve during the course of the simulation and their number may increase or diminish as the dynamics of the system determine. In an effort to extend the simulation time of these complex reactive processes and to use high levels of theory when necessary, multiple levels of theory may be used over the groups for the calculation of both the intragroup and intergroup interactions. Representative simulations are performed to illustrate the method and a computationally facile method of obtaining the groups of a simulation are also discussed.

Quasiclassical trajectory study of formaldehyde unimolecular dissociation: H2CO→H2+CO, H+HCO

We report quasiclassical trajectory calculations of the dynamics of the two reaction channels of formaldehyde dissociation on a global ab initio potential energy surface: the molecular channel H(2)CO-->H(2) + CO and the radical H(2)CO-->H + HCO. For the molecular channel, it is confirmed that above the threshold of the radical channel a second, intramolecular hydrogen abstraction pathway is opened to produce CO with low rotation and vibrationally hot H(2). The low-j(CO) and high-nu(H(2) ) products from the second pathway increase with the total energy. The competition between the molecular and radical pathways is also studied. It shows that the branching ratio of the molecular products decreases with increasing energy, while the branching ratio of the radical products increases. The results agree well with very recent velocity-map imaging experiments of Suits and co-workers and solves a mystery first posed by Moore and co-workers. For the radical channel, we present the translational energy distributions and HCO rotation distributions at various energies. There is mixed agreement with the experiments of Wittig and co-workers, and this provides an indirect confirmation of their speculation that the triplet surface plays a role in the formation of the radical products.

On-the-flyab initiotrajectory calculations of the dynamics of Cl atom reactions with methane, ethane and methanol

The dynamics of Cl atom reactions with methane, ethane, and methanol have been studied by calculation of quasi-classical trajectories, with computation of potential energies and gradients only at the geometries through which the trajectories pass. Trajectories were started from the transition state, with 2 kcal mol(-1) of energy given to the mode with an imaginary frequency (representing the reaction coordinate at the transition state) and inclusion of zero-point energy in some or all of the remaining vibrational modes. The trajectories were propagated as far as separated products, with the majority of potential energy calculations performed at the HF/6-31G level of theory. The rotational quantum state population distributions of the HCl products from the reactions of Cl atoms with methane, ethane and methanol peaked at J'=1, 2, and 6, respectively. The calculations thereby exhibit somewhat greater rotational excitation than is found experimentally, but correctly describe the trend of increasing HCl product rotation for the three respective reactions. In agreement with previous observations, only 4% of the energy available to the products of the reaction of Cl atoms with methane was channeled into CH3 radical internal energy, and 1% into HCl rotation, with 92% ending up as translational energy. For the reaction of Cl atoms with ethane and with methanol, the corresponding values for radical internal energy, HCl rotation and product translation are 21, 3, and 78%, and 46, 13, and 42%, respectively. For the latter two reactions, the radical internal energy is mostly accounted for by rotational motion. The clear increase in rotational excitation of the HCl products from the Cl atom reaction with methanol is explained in terms of a dipole-dipole interaction between the departing polar fragments. A smaller set of more computationally expensive trajectory calculations using potentials and gradients from the MP2/6-311G(d,p) level of theory were performed for reactions of Cl atoms with methanol, and give results in better agreement with experimentally measured HCl rotational excitation, consistent with the model of dipole-induced product rotation because the MP2/6-311G(d,p) calculations give smaller dipole moments for both products than the HF/6-31G calculations. The calculated angles between the rotational angular momentum vectors and recoil velocities of the radical peak sharply at 90 degrees for the reactions of Cl atoms with ethane and methanol, but exhibit a much broader distribution for reaction with methane.