Analytical Potential Energy Surface Research Articles

Analytical potential energy surface for O + C2H2 system

Full-dimensional analytical potential energy surfaces (PESs) for the O(1P)+C2H2 and O(3P)+C2H2 reactions are presented. The PESs are constructed by fitting thousands of ab initio data points using permutationally invariant polynomials [5]. Electronic structure data are obtained within the restricted coupled cluster theory with single and double excitations with perturbative triple corrections and correlation consistent basis set of triple-ζ with diffuse functions. Motivated by experiments, formation of DOCC and cyclic DCCO at collision energies of 2.5–4eV is examined using quasi-classical trajectory dynamics on the triplet surface.

Analysis of Potential Energy Surface for Butanone Isomerization

The potential energy surfaces for butanone isomerization have been investigated by density function theory calculation. Six main reaction pathways are confirmed using the intrinsic reaction coordinate method, and the corresponding isomerization products are 1-buten-2-ol, 2-buten-2-ol, butanal or 1-buten-1-ol, methyl 1-propenyl ether, methyl allyl ether, and ethyl vinyl ether, respectively. Among them, there are three pathways through butylene oxide, indicating butylene oxide is an important intermediate product during butanone isomerization. The calculated vertical ionization energies of the reactant and its products are in a good agreement with the experimental values available. From the consideration for the relative energies of transition states and the number of high-energy barriers we infer that the reaction pathway butanone→1-buten-2-ol →2-buten-2-ol is the most competitive. The obtained results are informative for future studies on isomerization of ketone molecules.

Automatic Differentiation of the Energy within Self-consistent Tight-Binding Methods.

We present and implement the calculation of analytical n-order geometric derivatives of the energy obtained within the framework of the density functional based tight binding approach. The use of automatic differentiation techniques allows a unique implementation for the calculation of derivatives up to any order providing that the computational facilities are sufficient. As first applications, the derivatives are used to build an analytical potential energy surface around the optimized geometry of acetylene. We also discuss the relevant anharmonic contributions that have to be considered when building such an analytical potential energy surface for acetylene, ethylene, ethane, benzene, and naphtalene.

Permutation invariant polynomial neural network approach to fitting potential energy surfaces

A simple, general, and rigorous scheme for adapting permutation symmetry in molecular systems is proposed and tested for fitting global potential energy surfaces using neural networks (NNs). The symmetry adaptation is realized by using low-order permutation invariant polynomials (PIPs) as inputs for the NNs. This so-called PIP-NN approach is applied to the H + H2 and Cl + H2 systems and the analytical potential energy surfaces for these two systems were accurately reproduced by PIP-NN. The accuracy of the NN potential energy surfaces was confirmed by quantum scattering calculations.

Global Analytical Potential Energy Surface for the Electronic Ground State of NH3 from High Level ab Initio Calculations

The analytical, full-dimensional, and global representation of the potential energy surface of NH(3) in the lowest adiabatic electronic state developed previously (Marquardt, R.; et al. J. Phys. Chem. B 2005, 109, 8439–8451) is improved by adjustment of parameters to an enlarged set of electronic energies from ab initio calculations using the coupled cluster method with single and double substitutions and a perturbative treatment of connected triple excitations (CCSD(T)) and the method of multireference configuration interaction (MRCI). CCSD(T) data were obtained from an extrapolation of aug-cc-pVXZ results to the basis set limit (CBS), as described in a previous work (Yurchenko, S.N.; et al. J. Chem. Phys 2005, 123, 134308); they cover the region around the NH3 equilibrium structures up to 20,000 hc cm(–1). MRCI energies were computed using the aug-cc-pVQZ basis to describe both low lying singlet dissociation channels. Adjustment was performed simultaneously to energies obtained from the different ab initio methods using a merging strategy that includes 10,000 geometries at the CCSD(T) level and 500 geometries at the MRCI level. Characteristic features of this improved representation are NH3 equilibrium geometry r(eq)(NH(3)) ≈ 101.28 pm, α(eq)(NH(3)) ≈ 107.03°, the inversion barrier at r(inv)(NH(3)) ≈ 99.88 pm and 1774 hc cm(–1) above the NH(3) minimum, and dissociation channel energies 41,051 hc cm(–1) (for NH(3) → ((2)B(2))NH(2) + ((2)S(1/2))H) and 38,450 hc cm(–1) (for NH(3) → ((3)Σ(–))NH +((1)Σ(g)(+))H(2)); the average agreement between calculated and experimental vibrational line positions is 11 cm(–1) for (14)N(1)H(3) in the spectral region up to 5000 cm(–1). A survey of our current knowledge on the vibrational spectroscopy of ammonia and its isotopomers is also given.

Optical properties of 1,2-diaryl benzimidazole derivatives – A combined experimental and theoretical studies

Some novel 1,2-diaryl benzimidazole derivatives have been designed, synthesized and characterized by mass, 1H, 13C-NMR spectral studies and single crystal XRD. The charge distribution has been calculated from the atomic charges by non-linear optical (NLO) and natural bond orbital (NBO) analyses have been calculated by abinitio method. Synthesized 1,2-diaryl benzimidazole derivatives have the largest μgβ0 value and can be used as potential NLO materials. Analysis of the molecular electrostatic potential (MEP) energy surface exploited the region for non-covalent interactions in the molecule. Calculated bond lengths, bond angles and dihedral angles are found to be slightly higher than that of X-ray diffraction values of its experimental datas.

Role of Vibrational and Translational Energy in the OH + NH3 Reaction: A Quasi-Classical Trajectory Study

Issues such as mode selectivity and Polanyi rules are connected to the effects of vibrational and translational energy in dynamics studies. Using the heavy-light-heavy OH(ν) + NH3(ν) gas-phase reaction, these effects were analyzed by performing quasi-classical trajectory calculations, at low and high collision energies (3.0 and 10.0 kcal mol(-1)), based on an analytical potential energy surface developed by our group. While the independent vibrational excitation of the NH3(ν) modes increases the reactivity by a factor of ∼1.1-2.8 with respect to the vibrational ground-state at both collision energies, OH(ν) stretching acts as a spectator mode. With respect to mode selectivity, we find a different behavior for both reactants. Thus, while the OH(ν) vibrational excitation is maintained in the products, indicating a certain degree of mode selectivity, the vibrational excitation of the NH3(ν) modes is not retained in the products; furthermore, the independent excitation of the N-H asymmetric and symmetric stretch modes leads to similar reaction probabilities, indicating negligible mode selectivity. For this early transition state reaction, translational energy is more effective in driving the reaction than an equivalent amount of energy in vibration, thus extending the validity of Polanyi rules to this polyatomic system. Finally, these results were interpreted on the basis of the existence of little or negligible intramolecular vibrational redistribution in the reactants before collision, while the nonconservation of the zero-point energy has a strong influence.

Dynamics study of the OH + NH3 hydrogen abstraction reaction using QCT calculations based on an analytical potential energy surface

To understand the reactivity and mechanism of the OH + NH3 → H2O + NH2 gas-phase reaction, which evolves through wells in the entrance and exit channels, a detailed dynamics study was carried out using quasi-classical trajectory calculations. The calculations were performed on an analytical potential energy surface (PES) recently developed by our group, PES-2012 [Monge-Palacios et al. J. Chem. Phys. 138, 084305 (2013)]. Most of the available energy appeared as H2O product vibrational energy (54%), reproducing the only experimental evidence, while only the 21% of this energy appeared as NH2 co-product vibrational energy. Both products appeared with cold and broad rotational distributions. The excitation function (constant collision energy in the range 1.0-14.0 kcal mol(-1)) increases smoothly with energy, contrasting with the only theoretical information (reduced-dimensional quantum scattering calculations based on a simplified PES), which presented a peak at low collision energies, related to quantized states. Analysis of the individual reactive trajectories showed that different mechanisms operate depending on the collision energy. Thus, while at high energies (E(coll) ≥ 6 kcal mol(-1)) all trajectories are direct, at low energies about 20%-30% of trajectories are indirect, i.e., with the mediation of a trapping complex, mainly in the product well. Finally, the effect of the zero-point energy constraint on the dynamics properties was analyzed.

A full-dimensional analytical potential energy surface for the F+CH4→HF + CH3 reaction

A full-dimensional analytical potential energy surface (APES) for the F + CH4 →HF + CH3 reaction is developed based on 7127 ab initio energy points at the unrestricted coupled-cluster with single, double, and perturbative triple excitations. The correlation-consistent polarized triple-split valence basis set is used. The APES is represented with a many-body expansion containing 239 parameters determined by the least square fitting method. The two-body terms of the APES are fitted by potential energy curves with multi-reference configuration interaction, which can describe the diatomic molecules (CH, H2, HF, and CF) accurately. It is found that the APES can reproduce the geometry and vibrational frequencies of the saddle point better than those available in the literature. The rate constants based on the present APES support the experimental results of Moore et al. [Int. J. Chem. Kin. 26, 813 (1994)]. The analytical first-order derivation of energy is also provided, making the present APES convenient and efficient for investigating the title reaction with quasiclassical trajectory calculations.

Ab initio based potential energy surface and kinetics study of the OH + NH3 hydrogen abstraction reaction

A full-dimensional analytical potential energy surface (PES) for the OH + NH3 → H2O + NH2 gas-phase reaction was developed based exclusively on high-level ab initio calculations. This reaction presents a very complicated shape with wells along the reaction path. Using a wide spectrum of properties of the reactive system (equilibrium geometries, vibrational frequencies, and relative energies of the stationary points, topology of the reaction path, and points on the reaction swath) as reference, the resulting analytical PES reproduces reasonably well the input ab initio information obtained at the coupled-cluster single double triple (CCSD(T)) = FULL/aug-cc-pVTZ//CCSD(T) = FC/cc-pVTZ single point level, which represents a severe test of the new surface. As a first application, on this analytical PES we perform an extensive kinetics study using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 200-2000 K. The forward rate constants reproduce the experimental measurements, while the reverse ones are slightly underestimated. However, the detailed analysis of the experimental equilibrium constants (from which the reverse rate constants are obtained) permits us to conclude that the experimental reverse rate constants must be re-evaluated. Another severe test of the new surface is the analysis of the kinetic isotope effects (KIEs), which were not included in the fitting procedure. The KIEs reproduce the values obtained from ab initio calculations in the common temperature range, although unfortunately no experimental information is available for comparison.

Isotope effects on the dynamics properties and reaction mechanism in the Cl(2P) + NH3 reaction: a QCT and QM study

Isotope effects on dynamics properties and reaction mechanism in the title reaction, which evolve through deep wells in the entry and exit channels, were analysed using both quasi-classical trajectory and reduced dimensional quantum mechanical calculations, for collision energies in the range 3.0–10.0 kcal mol−1, on an analytical potential energy surface (PES-2010) recently developed by our group. The analysis of different dynamics properties (reaction probability, product energy partitioning, and product rovibrational distributions) shows the reaction behaviour of the two reactions, Cl + NH3 and Cl + ND3, to be similar: direct mechanism, with a small percentage of indirect mechanisms, that is, trapping complex mediated. We find that the only dynamics property dependent on the isotope effect is the product scattering distribution. In particular, while the perdeuterated reaction favours backward scattering, the perprotio analogue favours forward scattering. This behaviour is related to the smaller maximum impact parameter for the perdeuterated reaction.

Conformational, structural, vibrational and quantum chemical analysis on 4-aminobenzohydrazide and 4-hydroxybenzohydrazide – A comparative study

Experimental and theoretical quantum chemical studies were carried out on 4-hydroxybenzohydrazide (4HBH) and 4-aminobenzohydrazide (4ABH) using FTIR and FT-Raman spectral data. The structural characteristics and vibrational spectroscopic analysis were carried performed by quantum chemical methods with the hybrid exchange-correlation functional B3LYP using 6-31G**, 6-311++G** and aug-cc-pVDZ basis sets. The most stable conformer of the title compounds have been determined from the analysis of potential energy surface. The stable molecular geometries, electronic and thermodynamic parameters, IR intensities, harmonic vibrational frequencies, depolarisation ratio and Raman intensities have been computed. Molecular electrostatic potential and frontier molecular orbitals were constructed to understand the electronic properties. The potential energy distributions (PEDs) were calculated to explain the mixing of fundamental modes. The theoretical geometrical parameters and the fundamental frequencies were compared with the experimental. The interactions of hydroxy and amino group substitutions on the characteristic vibrations of the ring and hydrazide group have been analysed.

Accelerated direct semiclassical molecular dynamics using a compact finite difference Hessian scheme

This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator.

Tentative mechanisms of 1,2-dihydropyridine and 4H-pyran formation via the reaction of 3-trimethylsilyl-2-propyn-1-al with 2-aminopyridine and water: experimental and quantum chemistry studies

The reaction of N-(2-pyridyl)-2-(trimethylsilylethynyl)-1,2-dihydropyridine-3,5-dicarbaldehyde self-assembling from three molecules of 3-trimethylsilyl-2-propyn-1-al and one molecule of 2-aminopyridine was monitored by 1H NMR spectroscopy. It was shown that the aldehyde and amine ratio affects the concurrent trimerization of 3-trimethylsilyl-2-propyn-1-al into 4-(trimethylsilylethynyl)-4H-pyran-3,5-dicarbaldehyde involving one molecule of water as a nucleophile. Two plausible mechanisms of 1,2-dihydropyridine and 4H-pyran cascade assembling are proposed and analyzed by quantum chemical methods (MP2 and B3LYP). The transition states were found and the activation barriers were calculated for the key steps of the reactions. The potential energy surface (PES) analysis performed do suggests an alternative radical mechanism leading to 1,2-dihydropyridine and 4H-pyran with significantly lower (by 10 kcal/mol) activation barriers at the limiting stages.

Models for Intrinsic Non-RRKM Dynamics. Decomposition of the SN2 Intermediate Cl––CH3Br

Chemical dynamics simulations, based on both an analytic potential energy surface (PES) and direct dynamics, were used to investigate the intrinsic non-RRKM dynamics of the Cl−–CH3Br ion-dipole complex, an important intermediate in the Cl− + CH3Br SN2 nucleophilic substitution reaction. This intermediate may dissociate to Cl− + CH3Br or isomerize to the ClCH3–Br− ion-dipole complex. The decomposition of microcanonical ensembles of the Cl−–CH3Br intermediate were simulated, and the ensuing populations vs. time of the excited intermediate and Cl− + CH3Br and ClCH3–Br− products were fit with multi-exponential functions. The intrinsic non-RRKM dynamics is more pronounced for the simulations with the analytic PES than by direct dynamics, with the populations for the former and latter primarily represented by tri- and bi-exponential functions, respectively. For the analytic PES and direct dynamics simulations, the intrinsic non-RRKM dynamics is more important for the isomerization pathway to form ClCH3–Br− than for dissociation to Cl− + CH3Br. Since the decomposition probability of Cl−–CH3Br is non-exponential, the Cl−–CH3Br unimolecular rate constant depends on pressure, with both high and low pressure limits. The high pressure limit is the RRKM rate constant and for the simulations with the analytic PES the rate constant decreased by a factor of 3.0, 5.6, and 4.3 in going from the high to low pressure limit for total energies of 40, 60, and 80 kcal/mol. For the direct dynamics simulations these respective factors are 2.4, 1.4, and 1.2. A separable phase space model with intermolecular and intramolecular complexes describes some of the simulation results, but overall models advanced for intrinsic non-RRKM dynamics give incomplete representations of the intermediate and product populations vs. time determined from the simulations.

Bond and mode selectivity in the OH + NH2D reaction: a quasi-classical trajectory calculation

A state-to-state dynamics study was performed to analyze the effects of vibrational excitation on the dynamics of the OH + NH2D gas-phase reaction, which are connected to issues such as bond and mode selectivity. This reaction can evolve along two channels: H-abstraction, H2O(ν) + NHD(ν); and D-abstraction, HOD(ν) + NH2(ν). Based on an analytical potential energy surface previously developed by our group, quasi-classical trajectory calculations and subsequent normal mode analysis were performed. While vibrational excitation of the NH-sym mode of NH2D slightly favours H-abstraction over the D-abstraction, vibrational excitation of the ND mode shows that there is no clear preference for the H- or D-abstraction. These results show that this reaction does not exhibit bond selectivity, suggesting a breakdown of the spectator model. For H-abstraction, vibrational excitation of the non-reactive ND mode is partially retained in the NHD product; and for D-abstraction, excitation of the non-reactive NH mode is also partially retained in the products, indicating that this reaction exhibits mode selectivity only partially. In sum, we rule out bond and mode selectivity for this reaction. All these results were interpreted on the basis of strong coupling between modes along the reaction path, a behaviour which seems to be more the general tendency than the exception in polyatomic reactions.

Dynamics of the F− + CH3Cl → Cl− + CH3F SN2 reaction on a chemically accurate potential energy surface

Though bimolecular nucleophilic substitution (SN2) reactions play a fundamental role in chemistry, chemically accurate full-dimensional global analytical potential energy surfaces (PESs) have not been developed for these systems. These PESs govern the motion of the atoms in a chemical reaction; thus, the knowledge of the PES is essential to study the dynamics and atomic-level mechanisms. Here, we report a full-dimensional ab initio PES for the F− + CH3Cl → Cl− + CH3F reaction, the PES has an estimated average accuracy of about 0.5 kcal mol−1. Quasiclassical trajectories on this PES reveal that the direct rebound mechanism dominates at high collision energies, whereas the reaction is mainly indirect at low collision energies, where the formation of long-lived hydrogen-bonded and C3v ion–dipole entrance-channel complexes play a major role in the dynamics. A direct stripping mechanism is also found at large impact parameters resulting in significant forward scattering, whereas the direct rebound mechanism scatters towards backward directions. At high collision energies the reaction can be controlled by orienting the reactants into a reactive F− + H3CCl orientation, whereas at low collision energies the initial orientation is not always maintained, because the long-range ion–dipole interactions efficiently steer the reactants into a reactive orientation even if F− initially approaches the non-reactive side of CH3Cl. Mode-specific vibrational distributions show that the reaction produces vibrationally hot CH3F molecules with excited CF stretching, especially at low collision energies.

Toward Detection of Electron-Hole Pair Excitation in H-atom Collisions with Au(111): Adiabatic Molecular Dynamics with a Semi-Empirical Full-Dimensional Potential Energy Surface

We report an analytic potential energy surface (PES) based on several hundred DFT energies for H interacting with a Au(111) surface. Effective medium theory is used to fit the DFT data, which were obtained for the Au atoms held at their equilibrium positions. This procedure also provides an adequate treatment of the PES for displacements of Au atoms that occur during scattering of H atoms. The fitted PES is compared to DFT energies obtained from ab initio molecular dynamics trajectories. We present molecular dynamics simulations of energy and angle resolved scattering probabilities at five incidence angles at an incidence energy, Ei = 5 eV, and at a surface temperature, TS = 10 K. Simple single bounce trajectories are important at all incidence conditions explored here. Double bounce events also make up a significant fraction of the scattering. A qualitative analysis of the double-bounce events reveals that most occur as collisions of an H-atom with two neighboring surface gold atoms. The energy losses observed are consistent with a simple binary collision model, transferring typically less than 150 meV to the solid per bounce.

Quasi-Classical Trajectory Study of the N(2D) + H2(X1ΣG+) → NH(X3Σ–) + H(2S) Reaction Based on an Analytical Potential Energy Surface

Using the multireference configuration interaction method with the Davidson correction and a large orbital basis set (aug-cc-pV5Z), we obtain an energy grid that includes 17,500 points for the construction of a new analytical potential energy surface (APES) for the N((2)D) + H(2)(X(1)Σ(g)(+)) → NH(X(3)Σ(-)) + H((2)S) reaction. The APES, which contains 145 parameters and is represented with a many-body expansion and a new switch function, is fitted from the ab initio energies using an adaptive nonlinear least-squares algorithm. The geometric characteristics of the reported APES in the literature and those of our APES are also compared. On the basis of the APES that we obtained, reaction cross sections are computed by means of quasi-classical trajectory calculations and compared with the experimental and theoretical values available in the literature.

The effects of collision energy and reagent vibrational excitation on the reactivity of the reaction H + LiH: A quasiclassical trajectory study

Quasi-classical trajectory (QCT) calculations are carried out for the reaction H+LiH (ν=0–3, j=0) using a recent analytical potential energy surface (PES) of Prudente et al. [F.V. Prudente, J.M.C. Marques, A.M. Maniero, Time-dependent wave packet calculation of the LiH+H reactive scattering on a new potential energy surface, Chem. Phys. Lett. 474 (2009) 18–22]. The reaction H+LiH proceeds through the highly exothermic LiH depletion and thermoneutral hydrogen-exchange channels. State-selected and energy-resolved reaction probability and integral reaction cross sections are reported and compared with the recent available literature data. The QCT-calculated probabilities are in good agreement with the previous quantum–mechanical (QM) results, meanwhile, the vibrational excitation of the reagent LiH molecule decreases the reactivity of the LiH depletion channel and increases the reactivity of the hydrogen-exchange channel. Moreover, this decrease and increase can be explained by examining the representative reactive trajectories for the different vibrational excitation of the reagent and the topology of the HHLi PES. Our calculated results indicate that the collision energy and the vibrational excitation of the reagent play an important role on the reactivity of this system.