Determination of energy minima and saddle points using multireference configuration interaction methods in combination with reduced gradient following: the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene

The implementation of the reduced gradient following (RGF) method into the COLUMBUS quantum-chemical program system is reported using the newly developed analytic MR-CISD/AQCC gradient feature. By this combination a very useful tool has been developed for general searches of stationary points on ground- and excited-state energy surfaces. This procedure is applied to the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene. For H(2)CO we investigated three minima (formaldehyde, s-trans, and s-cis hydroxycarbene) and five saddle points. For the T(1) and T(2) states of acetylene the cis- and trans-minima and the planar and nonplanar saddle points were computed.     

Principal coordinate maps of molecular potential energy surfaces

Obtaining useful representations of molecular conformation spaces and visualizing the associated potential energy surfaces is a complex task, mainly due to the high dimensionality of these spaces. Principal component analysis (PCA), which projects multidimensional data on low-dimensional subspaces, is thus becoming a common technique for studying such spaces. Three issues, relating to the use of principal component techniques for mapping molecular potential energy surfaces, are discussed in this study: the effectiveness of the projection; its accuracy; and the mapping procedure. The effectiveness of PCA is demonstrated through detailed analyses of principal component projections of several peptides. In these cases PCA projected conformation space into a subspace smaller even than that defined by the peptide's backbone dihedral angles. The average accuracy as well as the distribution of errors in the projection (i.e., the errors in reproducing individual distances) are studied as a function of the dimensionality of the projection. The wide variation in accuracy between different systems suggests that it is imperative to indicate the accuracy of the projection whenever PCA projections are used. Furthermore, when projecting potential energy surfaces on the principal two-dimensional (2D) plane, the projection errors result in artificial roughening of the surface. A new mapping procedure, the “minimal energy envelope” procedure, is introduced to overcome this problem. This procedure yields relatively smooth “energy landscapes,” which highlight the basin structure of the real multidimensional energy surface. It is demonstrated that the projected potential energy maps can be used for charting conformational transitions or dynamic trajectories in the system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1255–1267, 1998     

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     

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     

Comment “On the quadratic reaction path evaluated in a reduced potential energy surface model and the problem to locate transition states” [by J. M. Anglada,E. Besalú, J. M. Bofill,and R. Crehuet,J Comput Chem 2001, 22, 4, 387–406]

The difference is explained between steepest ascent and following a reduced gradient (distinguished coordinate method) for the location of saddle points. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 537–540, 2001     

Reply on the comment “On the quadratic reaction path evaluated in a reduced potential energy surface model and the problem to locate transition states” [by J. M. Anglada,E. Besalú, J. M. Bofill,and R. Crehuet,J Comput Chem 2001, 22, 4, 387–406]

Some concepts used in the explanation of the reduced gradient following algorithm are discussed and explained. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 541–544, 2001     

Ab initio MO study of potential energy surface of NH2 with CN reaction

An extensive quantum chemical study of the potential energy surfaces (PES) for the association reaction of NH₂ with CN and the subsequent isomerization and dissociation reactions has been carried out using density functional theory (DFT)/B3LYP/6‐311++G(3df,2p) level of theory on both singlet and triplet states. The reaction mechanism on the triplet surface is more complicated than that on the singlet surface. A total of 19 isomers and 46 transition states have been identified and characterized on the triplet PES. Among them, IM2 (IM2a), IM3 (IM3a, IM3b), and IM10 are the lowest‐lying isomers with thermodynamic stability. Twenty available dissociation channels, depending on the different initial isomers, have been identified. On the singlet surface, only 12 isomers and 16 transition states have been found, and among them IM1(S) and IM2(S) are the lowest‐lying isomers. The higher isomerization and dissociation barriers on the singlet surface indicate that the addition and the subsequent reactions of NH₂+CN are most likely to occur on the triplet PES because of the lower barriers. A prediction can be made for the possible mechanism explaining the production of H+HNCN. Besides HNCN, other major products are NH+HCN and NH+HNC, which are produced by direct dissociation reactions from triplet IM2 and IM3, respectively. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The PyPES library of high quality semi‐global potential energy surfaces

In this article, we present a Python‐based library of high quality semi‐global potential energy surfaces for 50 polyatomic molecules with up to six atoms. We anticipate that these surfaces will find widespread application in the testing of new potential energy surface construction algorithms and nuclear ro‐vibrational structure theories. To this end, we provide the ability to generate the energy derivatives required for Taylor series expansions to sixth order about any point on the potential energy surface in a range of common coordinate systems, including curvilinear internal, Cartesian, and normal mode coordinates. The PyPES package, along with FORTRAN, C, MATLAB and Mathematica wrappers, is available at http://sourceforge.net/projects/pypes-lib . © 2015 Wiley Periodicals, Inc.     

Bonding and correlation analysis of various Si2CO isomers on the potential energy surface

At various levels of theory, singlet and triplet potential energy surfaces (PESs) of Si₂CO, which has been studied using matrix isolation infrared spectroscopy, are investigated in detail. A total of 30 isomers and 38 interconversion transition states are obtained at the B3LYP/6‐311G(d) level. At the higher CCSD(T)/6‐311+G(2d)//QCISD/6‐311G(2d)+ZPVE level, the global minimum ¹1 (0.0 kcal/mol) corresponds to a three‐membered ring singlet O‐cCSiSi (¹A′). On the singlet PES, the species ¹2 (0.2 kcal/mol) is a bent SiCSiO structure with a ¹A′ electronic state, followed by a three‐membered ring isomer Si‐cCSiO (¹A′) ¹3 (23.1 kcal/mol) and a linear SiCOSi ¹4 (¹Σ⁺) (38.6 kcal/mol). The isomers ¹1, ¹2, ¹3 , and ¹4 possess not only high thermodynamic stabilities, but also high kinetic stabilities. On the triplet PES, two isomers ³1 (³B₂) (18.8 kcal/mol) and ³7 (³A″) (23.3 kcal/mol) also have high thermodynamic and kinetic stabilities. The bonding natures of the relevant species are analyzed. The similarities and differences between C₃O, C₃S, SiC₂O, and SiC₂S are discussed. The present results are also expected to be useful for understanding the initial growing step of the CO‐doped Si vaporization processes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Potential energy surfaces and vibrational spectra for isotopomers of N_2O

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Saddle points of index 2 on potential energy surfaces and their role in theoretical reactivity investigations

After a general characterization of second order saddle points two boundary cases are derived and illustrated by examples. The utilization of the classification is pointed out. One type, the virtual saddle point of index 2 (V-SP 2), may be understood as geometrical superposition of two saddles of index 1 (transition structures) which belong to relatively independent processes within the chemical system.     

自由基HO2与C2H2反应势能面的理论研究

应用量子化学从头计算和密度泛函理论(DFT)对HO2+C2H2反应体系的反应机理进行了研究.在B3LYP/6-311G**和CCSD(T)/6-311G**水平上计算了HO2+ C2H2反应的二重态反应势能面.计算结果表明,主要反应方式为自由基HO2的H原子和C2H2分子中的C原子结合,经过一系列异构化,最后分解得到主要产物P1 (CH2O+ HCO).此反应是放热反应,化学反应热为-321.99 kJ·mol-1.次要产物为P2 (CO2 +CH3),也是放热反应.     

Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.     

Limiting high pressure rate coefficients for the HO+NO2&→HONO2 reaction on ab initio potential energy surfaces

Phase space limiting high pressure rate coefficients for the title reaction on ab initio potential energy surfaces have been calculated at 50-600 K. Calculated rigidity factors at different levels of theory are presented. The best limiting high pressure rate coefficient obtained at 300 K, 4.0x10^-11cm³ molecule^-1 s^-1, compares very well with the latest IUPAC recommended value. This revised version was published online in June 2006 with corrections to the Cover Date.     

Potential energy surfaces and vibrational spectra for isotopomers of N2O

Potential energy surfaces and vibrational spectra for the four isotopomers (^l5N¹⁴N¹⁶O,^l4N^I5N¹⁶O,¹⁵N₂ ¹⁶O and¹⁵N₂ ¹⁸O) of N₂O have been investigated with the vibrational self-consistent field-configuration interaction method. It is shown that the isotopomers with the same end atom have similar values of the potential parameters, and that substitution with different end atoms can affect the potential obviously. The calculated vibrational levels are in good agreement with the observed values by the optimization of several potential parameters (f ₁ ⁽¹⁾,f ₁₃ ⁽⁰⁾,f ₃ ⁽¹⁾ which are sensitive to isotopic substitutions. Project supported by the National Natural Science Foundation of China (Grant No. 29673029).     

General methodology in two dimensions for classical simulation of reactive and nonreactive events on ab initio potential energy surfaces

A completely general two-dimensional (2D) methodology for the classical simulation of reactive and nonreactive events on ab initio potential energy surfaces is introduced and tested. The methodology requires the minimum amount of information given a priori—geometries and energies at these geometries. From a list of ab initio geometries and energies, simulations may be executed and a distribution of outcomes obtained. The method introduced attempts a local approach at simulating the dynamics of the system, rather than a global analytic fit to the potential energy surface. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1431–1444, 1998     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li_2H

A 285-pomt multi-reference configuration-interaction involving single and double excitations ( MRS DCI) potential energy surface for the electronic ground state of L12H is determined by using 6-311G (2df,2pd)basis set.A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a x2 of 4.64×106 The equn librium geometry occurs at Rc=0.172 nm and,LiHL1=94.10°.The dissociation energy for reaction I2H(2A)→L12(1∑g)+H(2S) is 243.910 kJ/mol,and that for reaction L12H(2A')→HL1(1∑) + L1(2S) is 106.445 kl/mol The inversion barrier height is 50.388 kj/mol.The vibrational energy levels are calculated using the discrete variable representation (DVR) method.     

Note on the theory of bifurcation of chemical reactions

In the present communication two existing definitions of valley ridge inflection, (VRI), point, one attributed to Valtazanos and Ruedenberg and the other one to Basilevsky are discussed. From our study we conclude that both definitions are not equivalent, and we demonstrate in which cases it occurs. However, they are used without any distinction in the bibliography. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Geometric and electronic structures of silicon fluorides (N = 4 – 6) and potential energy surfaces for dissociation reactions → SiF4 + F– and → + F–

The geometric and electronic structures of a series of silicon fluorides (n = 4 ? 6) were computationally studied with the aid of density functional theory (DFT) method with B3LYP and M06‐2X functionals and coupled cluster (CCSD and CCSD(T)) methods with 6‐311++G(d,p) basis set. The nature of the Si‐F bonds in these compounds was analyzed in the framework of the natural bond orbital theory and natural resonance theory. Energy characteristics (heats of reactions and energy barriers) of the dissociation reactions → SiF₄ + F^– and → + F^– were calculated using the DFT and CCSD methods. The potential energy surface of elimination of a fluoride anion from has a specific topology with valley‐ridge inflection points corresponding to bifurcations of the minimal energy reaction path. © 2016 Wiley Periodicals, Inc.