Analysis of the Valley-Ridge inflection points through the partitioning technique of the Hessian eigenvalue equation

The Valley-Ridge inflection (VRI) points are related to the branching of a reaction valley or reaction channel. These points are a special class of points of the potential energy surface (PES). They are also special points of the Valley-Ridge borderline of the PES. The nature of the VRI points and their differences with respect to the other points of the Valley-Ridge borderline is analyzed using the Löwdin’s partitioning technique applied to the eigenvalue equation of the Hessian matrix. Eigenvalues and eigenvectors of the Hessian are better imaginable than the former used adjoint matrix.     

Stationary points on the aminomethanol potential energy surface

Summary In this work we study surface fitting equations for a rigid rotor model of aminomethanol. The energies were obtained from the GAUSSIAN88 package using 3-21G bases and fitted on a least square equation, thus generating a Fourier series expansion of the energy as a function of two dihedral angles. The dihedral angles chosen are those that represent rotation around the C-O and N-C axes in the first case, and rotation around C-O and inversion around the amino group in the second case. Results indicate that the hydroxyl hydrogen is subject to almost free rotation around the C-O axis. Further fully relaxed 6-31G* calculations were performed in order to qualify the results obtained for the rigid rotor model.     

Bifurcation of reaction pathways: the set of valley ridge inflection points of a simple three-dimensional potential energy surface

This paper serves for the better understanding of the branching phenomenon of reaction paths of potential energy hypersurfaces in more than two dimensions. We apply the recently proposed reduced gradient following (RGF) method for the analysis of potential energy hypersurfaces having valley-ridge inflection (VRI) points. VRI points indicate the region of possible reaction path bifurcation. The relation between RGF and the so-called global Newton search for stationary points (Branin method) is shown. Using a 3D polynomial test surface, a whole 1D manifold of VRI points is obtained. Its relation to RGF curves, steepest descent and gradient extremals is discussed as well as the relation of the VRI manifold to bifurcation points of these curves. Received: 8 July 1998 / Accepted: 24 August 1998 / Published online: 23 November 1998     

Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

SCF CI potential energy surfaces for the HCN α HCN isomerisation reaction

We report X ¹A' and 2 ¹A' potential energy surfaces for HCN. Thermal isomerisation on the ground-state surface is discussed. An avoided crossing between X ¹A' and 2 ¹A' suggests alternative isomerisation mechanisms via this excited state. The X¹A'-2¹A' interaction may also allow the formation of CN(X ²Σ⁺) in photodissociation of XCN molecules.     

Stationary points on the H2CO potential energy surface: dependence on theoretical level

A total of 36 stationary points have been located on the H₂CO potential energy surface by means of gradient extremal following. These 36 points are believed to represent all the important stationary points on this surface. There is no indication that the structure of the surface becomes less complicated as the size of the basis set is enlarged at the Hartree-Fock level of theory, but many of the second- and third-order saddle points disappear when electron correlation is introduced. Of the ten first-order saddle points (transition structures) located, the majority have reaction paths entering the associated minima in a side-on approach, i.e. these cannot be located by uphill walking from the minimum. Received: 5 February 1998 / Accepted: 21 May 1998 / Published online: 29 July 1998     

The hardness profile as a tool to detect spurious stationary points in the potential energy surface

In the present work, we have computed the energy and hardness profiles for a series of inter and intramolecular conformational changes at several levels of calculation. All processes studied have in common the fact that the choice of a weak methodology or a poor basis set results in the presence of spurious stationary points in the energy profile. At variance with the energy profiles, the hardness profiles calculated as the difference between the vertical ionization potential and electron affinity always show the correct number of stationary points independently of the basis set and methodology used. For this reason, we have concluded that hardness profiles can be used to check the reliability of the energy profiles for those chemical systems that, because of their size, cannot be treated with high level ab initio methods.     

Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points

A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.     

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.     

Intermolecular potential energy surface of Ar-NO

Rotational spectra of an open-shell complex, Ar-NO, in the electronic ground state have been analyzed by employing an analysis using a free-rotor model, where previously observed data by Mills et al. [J. Phys. Chem. 90, 3331 (1986); 90, 4961 (1986)] and additional transitions observed by Fourier-transform microwave spectroscopy in the present study are simultaneously analyzed with a standard deviation of the least-squares fit to be 27.5 kHz. A two-dimensional intermolecular potential energy surface for Ar-NO has been determined from the analysis. The determined potential energy surface is compared with those of Ar-OH and Ar-SH, which are also complexes containing an open-shell species with the 2Pi ground electronic state.     

HSCCS自由基势能面的理论研究

在CCSD(T)/6-311G(d,f)//MP2/6-311G(d,f) ZPE水平下,计算得到含有8个异构体和11个过渡态的HSCCS自由基体系势能面,讨论了异构体的结构与稳定性及异构体之间的异构化过程.结果表明异构体m1的能量最低,除m1以外,异构体m2和m3的能量也比较低,在MP2水平上,过渡态TS1的能量比异构体m2仅高3.9kJ/mol,而在CCSD(T)水平上,TS1的能量比m2低14.6 kJ/mol,这说明异构体m2可以迅速转化为能量更低的m1.异构体m3的能量比异构体m1高49.99 kJ/mol,可以推断,在合适的实验条件下可以观测到异构体m1.     

The potential energy surface of the triazadiphosphole formation

The formal GaCl₃-assisted [3+2] cycloaddition of two (Me₃Si)₂N–N(SiMe₃)–PCl₂ molecules resulting in the formation of a triazadiphosphole has been studied by means of B3LYP/6-31G(d,p) computations. These calculations revealed a stepwise reaction mechanism starting from the disguised 1,3-dipole and dipolarophile (Me₃Si)₂N–N(SiMe₃)–PCl₂. Comparison of the potential energy surface for the formation of a triazadiphosphole in the presence and without a Lewis acid indicate, that addition of a Lewis acid such as GaCl₃ decreases the activation barriers to Me₃Si–Cl elimination, in accord with experiment. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Newton trajectories for finding stationary points on molecular potential energy surfaces

We present a new algorithm for computing Newton trajectories based on the Quadratic String Method (QSM) and explain how this can be used to find key stationary points on the molecular potential energy surface (PES). This method starts by using the intersections of Newton trajectories to locate stationary points on the PES. These points could then be used to determine the minimum energy path. The new method, called QSM-NT, is shown to be efficient and reliable for both analytical potential energy surfaces and potential energy surfaces computed from quantum chemistry calculations. The advantages and pitfalls of this method for exploring PES are discussed. In particular, the problem of discontinuous Newton trajectories is elucidated.     

Nitromethane dimer potential energy surface studies

The interaction energy of several conformations of the nitromethane dimer is investigated at the SCF level. The dispersion energy and counterpoise correction are computed for certain relative orientations of the monomers. Fourth-order many body perturbation theory SDQ-MBPT(4) energies are reported for selected points. Double zeta and double zeta plus polarization basis sets were used. All calculations were done with the monomer fixed at the isolated monomer geometry. Interaction energies as large as 6 kcal/mol are found at minima of hydrogen bonding orientations.     

Fluorobenzene-argon ground-state intermolecular potential energy surface

The ground-state intermolecular potential energy surface for the fluorobenzene-argon van der Waals complex is evaluated using the coupled-cluster singles and doubles including connected triple excitations model, with the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. In the surface minima the Ar atom is located above and below the fluorobenzene plane at a distance of 3.562 A from the fluorobenzene center of mass and at an angle of 6.33 degrees with respect to the axis perpendicular to the fluorobenzene plane. The corresponding binding energy is 391.1 cm(-1). Both these results and the eigenvalues obtained from the potential compare well with the experimental data available.     

On the OCS2 Singlet potential energy surface

The reaction between atomic oxygen and carbon disulfide is predicted to lead to at least two primary products, which are the dithiiranone ( 1 ) and the oxathiirane-thione ( 2 ) and/or the carbon disulfide S-oxide ( 4 ). The possible intramolecular equilibria 1 ? 2, 1 ? 3, 2 ? 4 , and 2 ? 5 as well as the fragmentations of the possible intermediates 1 – 5 have been studied theoretically within the semiempirical CNDO /B framework as conceivable ground-state reactions. On the basis of MO correlations and potential energy changes along the reaction paths, supplementary with previously reported experimental data, the single molecular transformations and the eventual product formations are discussed.     

Theoretical study on the potential energy surface of SiC2O

The DFT/B3LYP/6-311G(d) and CCSD(T)/6-311G(2df) (single-point) methods have been used to investigate the potential energy surface of SiC₂O. A total of 11 isomers are located, which are connected by 13 interconversion transition states. The global minimum is the linear SiCCO with ¹Σ⁺ electronic state whose structure can be described as cumulenic double bonding form :SiCCÖ:. The isomer O-cSiCC possessing SiCC three-membered ring with an exocyclic OSi bond also shows considerable stability. Both SiCCO and O-cSiCC are kinetically stable towards isomerization and dissociation. Further calculations are performed at the CCSD(T)/6-311G(2df)//QCISD/6-311G(2d) level to obtain more reliable energies, geometrical parameters, harmonic vibrational frequencies and infrared intensities of the isomers. The energies and geometrical parameters are also calculated with the CASPT2//CASSCF methods.