The structural stability principle and branching points on multidimensional potential energy surfaces

The chemically interesting potential energy surfaces (PES) are considered on which the conditions underlying application of structural stability principle and Morse inequalities are violated. The possibility of treatment of singular branching points on a PES slope in terms of intrinsic reaction curves (IRC) is discussed.     

Some reflections on characterizing potential surfaces for gas-phase ionic reactions

Gas phase ionic chemistry has become an essential element in our general understanding of chemical reactivity. Obtaining experimental data and then extracting information about the potential surfaces for ionic reactions in the gas phase has been critical in making the connections between gas phase and solution ionic chemistry. In this paper we discuss insights that have been important in developing some of the methodologies that are currently used in analyzing gas phase data.     

Gradient extremals and valley floor bifurcations on potential energy surfaces

Gradient extremals are curves in configuration space denned by the condition that the gradient of the potential energy is an eigenvector of the Hessian matrix. Solutions of a corresponding equation go along a valley floor or along a crest of a ridge, if the norm of the gradient is a minimum, and along a cirque or a cliff or a flank of one of the two if the gradient norm is a maximum. Properties of gradient extremals are discussed for simple 2D model surfaces including the problem of valley bifurcations.     

Symmetry and periodicity of potential surfaces: a test for multicenter interactions

Symmetry and periodicity of potential energy surfaces of chemical reactions and conformational changes are determined by the symmetry properties of the nuclear frameworks of all possible nuclear configurations of the given overall stoichiometry. For example, a mirror plane of a nuclear configuration implies a mirror plane of the potential surface (or that of the potential energy hypersurface in higher dimensions), and a local rotational symmetry of substituents implies a translational symmetry, that is, periodicity of the potential surface, if the latter is defined in terms of the usual bond length/bond angle internal coordinates. Such symmetry relations on potential surfaces are rather trivial consequences of molecular symmetry properties; however, when taken collectively for entire domains of nuclear configurations, they lead to nontrivial conclusions. Whereas symmetry properties and energy contents of individual conformations can be studied locally within limited domains of the potential surface, a global analysis of the potential surface may reveal significantly more. In this note, some consequences of the above approach are explored, and a simple test is proposed for the detection and evaluation of the importance of multicenter interactions in conformers related to one another by bond rotations.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Potential energy surfaces for OsH2

Summary We compute the potential energy surfaces of 12 electronic states of OsH₂ (four quintet, four triplet, and four singlet) arising from⁵ D ground state of the Os atom as well as triplet and singlet excited states using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction (MRCI) and relativistic CI (RCI) calculation which include up to 430,000 configurations. We find that the⁵ D ground state of Os atom does not insert into H₂ while the excited³ F state of Os does. The³ B ₁ ground state of OsH₂ (there are two other nearly degenerate states) in the absence of spin-orbit coupling was found to be 22 kcal/mol more stable than Os(⁵ D)+H₂. The spin-orbit mixing of³ B ₁,³ B ₂,³ A ₂, and¹ A ₁ states was so strong that it induces significant change in bond angles (up to 10°) for OsH₂.Dedicated to Prof. Klaus RuedenbergCamille and Henry Dreyfus Teacher-Scholar     

Ab initio quantum chemical study of the formation, decomposition and isomerization of the formaldiminoxy radical (CH2NO): comparison of the Gaussian-2 and CASPT2 techniques in the calculation of potential energy surfaces

The reaction between triplet methylene and nitric oxide, producing the formaldiminoxy (CH₂NO) radical, and the subsequent decomposition and isomerization reactions of CH₂NO have been studied using ab␣initio quantum chemical techniques that include the Gaussian-2 (G2), CASSCF and CASPT2 methods. Stationary points on the potential energy surfaces were located at MP2/6-31G(d) and CASSCF/cc-pVDZ levels of theory, while the electronic energies were determined using G2, G2(MP2), QCISD(T)/cc-pVTZ, RCCSD(T)/cc-pVTZ and CASPT2/cc-pVTZ approaches. G2 is believed to be reliable at equilibrium geometries, but the determination of certain transition state geometries and energies requires a MCSCF-based approach. The calculations suggest that CH₂NO (²A^′) forms in a barrierless reaction and could readily decompose to H+HCNO. A subsequent abstraction reaction then results in H₂+CNO. No molecular elimination channel was found. An alternative pathway is the formation of CH₂ON, which readily isomerizes to CH₂NO. Received: 8 May 1998 / Accepted: 11 August / Published online: 9 October 1998     

Newton leaves on potential energy surfaces

The reaction path (RP) is an important concept of theoretical chemistry. We generalize the definition of the Newton trajectory (NT), as an RP, to Newton leaves in a higher dimensional subspace of the configuration space. Our standpoint is that of Bofill and Anglada [(2001) Theor. Chem. Acc. 105:436], who used a reduced potential energy surface for finding an RP. An NT follows an RP curve where the gradient is always a pointer to a fixed direction. More generally, a Newton leaf is a subspace of coordinates where the gradient can move in a subspace of directions. We report some known mathematical properties of Newton leaves. We explain the construction of Newton leaves with the example of a 3D test surface in ⁴ [W.Quapp et al. (1998) Theor. Chem. Acc. 100:285], because three coordinate dimensions are the smallest number of dimensions one needs at least to understand a Newton leaf in contrast to the known NTs.Acknowledgement The work was made possible through financial support of the Deutsche Forschungsgemeinschaft. The authors thank D. Heidrich for stimulating discussions.     

Theoretical studies of the potential energy surface and wavepacket dynamics of the Li3 system

The three-dimensional (3D) potential energy surface of the ground state of Li₃ was determined by the multireference configuration interaction method. The vibrational motions and pseudorotation were investigated by a 3D time-dependent wavepacket formalism. The analytical expression of the 3D surface is given and the results of vibrational analyses at several critical points are presented. The low-lying excited states of Li₃ were examined for the C _{2 v} structure and the vertical and adiabatic excitation energies were calculated. The ground and singlet excited states of Li₂ were calculated and their spectroscopic constants compare well with the experimental values. A 3D wavepacket calculation was performed for simulations of the stimulated emission pumping spectrum in which the A state was taken as an intermediate. The recurrences of the autocorrelation functions were characterized by classical trajectory calculations. The autocorrelation functions obtained by wavepacket propagation are reproduced well by the accumulation of the classical trajectories in the short-time region. Received: 2 July 1998 / Accepted: 3 September 1998 / Published online: 8 February 1999     

Gradient incorporation in one-dimensional applications of interpolating moving least-squares methods for fitting potential energy surfaces

We present several approaches to use gradients in higher degree interpolating moving least squares (IMLS) methods for representing a potential energy surface (PES). General procedures are developed to obtain smooth approximations of the PES and its derivatives from quasi-uniform sets of energy and gradient data points. These methods are illustrated and analyzed for the Morse oscillator and a 1-D slice of the ground-state PES for the HCO radical computed using density functional theory. Variations in the IMLS fits with the number and distribution of points and the degree of the polynomial fitting basis set are examined. We determine the effects of gradient inclusion on the accuracy of the IMLS values of the energy, first and second derivatives for two 1-D test cases. Gradient inclusion reduces the number of data points required by up to 40%.     

A topological stochastic approach to the study of multidimensional potential energy surfaces of chemical reactions

In this article we propose a new approach for investigating the properties of multidimensional potential energy surfaces in chemical reactions, based on relations of each multidimensional surface to its one-dimensional image which is the chemical reaction tree. This approach makes it possible to find a common number of independent channels in chemical reactions for complex systems and to construct the probable models.     

The topology of catchment regions of potential energy hypersurfaces

A simple proof is presented for a fundamental topological property of catchment regions of potential energy hypersurfaces: each catchment region C(λ,i), representing a chemical species and its conformational range on the potential energy hypersurface, is simply k-connected for each dimension k=1,2,…3N−6−λ, where λ is the index of the catchment region. The consequences of this property on the structure of the fundamental group of reaction mechanisms (the one-dimensional homotopy group of reaction paths) is discussed. Received: 8 July 1998 / Accepted: 6 October 1998 / Published online: 23 February 1999     

Quantum chemical reaction networks,reaction graphs and the structure of potential energy hypersurfaces

Global properties of the Born-Oppenheimer energy expectation value functional, defined over the nuclear configuration space R, are analyzed. Quantum chemical reaction graphs and reaction networks are defined in terms of intersection graphs of connected sets of nuclear geometries, representing various chemical structures. The set of all possible reaction mechanisms on the given energy hypersurface and the associated activation energy conditions are analyzed using reachability matrices defined over digraphs D ^s() and D ^s(, E).     

Equivariant Morse theory of theN-body problem: Application to potential surfaces in chemistry

Summary The Morse inequalities linking the critical points of a potential function on the whole configuration space and its restrictions to either planar or linear configurations are derived from the Morse theory in its equivariant form. Brute potential functions arising from standard models of quantum chemistry need eventually morsification which can be achieved without altering the main chemical significances of the potential. Illustrative applications follow in the case of magnesium clusters.     

Covalent-ionic nature of the potential energy surface of the Li-CO2 complex

Unrestricted Hartree-Fock calculations with large basis sets, including d-functions, and the estimation of the correlation energy, show that the potential energy surface for the Li-CO₂ complex is built from the crossing of two states, each of them corresponding to a different electron arrangement. One has a strong ionic character and the other is of van der Waals type. Each portion of the energy surface presents a minimum, which is stable in respect to the dissociation limit.     

A Basis for Orbital Symmetry Rules

The influence of molecular symmetry on reaction rates is examined with an approach in which reactions are viewed as electronic transitions between states of reacants and products (described, in turn by quasiadiabatic potential surface). The moleculer Hamiltonian is used to derive selection rules for these transitions. The complete Hamilatonian has no useful symmetery. Neglect of non-Born-Oppenheimer and spin-orbit terms (and of other angular momentum coupling terms) leads to an apporixmate Hamiltonian and to selection rules which from the basis of the Woodward-Hoffmann rules. This apporch provides an alternative to the adiabatic potantial surfaces, reaction coordinates, and transition state theory used in more familiar discussions of the Woodward-Hoffmann rules. Further, it provides a particulary clear method for discussing violations of these symmetry rules, and for differentiating concerted and nonconcerted reactions.     

Electronic energy inequalities for isoelectronic molecular systems

Within the Born-Oppenheimer approximation an inequality relation is derived between points of electronic energy hypersurfaces of pairs of isoelectronic molecules. The inequality is directly applicable to point pairs fulfilling a symmetry criterion for the nuclear frameworks and it may be extended to coordinate domains on both hypersurfaces. The result is applied to special examples of conformational problems, dissociation reactions and impurity —vacancy centres in solid clusters.     

A vectorizable potential energy functional for reactive scattering

Critical steps in trajectory programs for vector restructuring are analysed. The crucial effect of potential energy routine design on the efficiency of trajectory calculations performed on supercomputers have been investigated using a test program for which time consumptions when different algorithms are implemented are compared. Comparisons have been extended to more realistic computational situations by inserting related routines in a trajectory program and calculating reactive properties of some systems of chemical interest.This paper was presented at the International Conference on The Impact of Supercomputers on Chemistry, held at the University of London, London, UK, 13–16 April 1987     

A procedure of determining potential energy surfaces of triatomic molecules from inversion of spectroscopic data

In this paper,we have suggested an iterative procedure of optimization of the linearparameters in an analytic potential energy function for a triatomic molecule,by combining both variational and second order perturbation methods.The most important feature of this procedure is that the objective function is an analytical expression which can be optimized easily.The application to the water molecule is presented.     

Cations of halogenated methanes: adiabatic ionization energies, potential energy surfaces, and ion fragment appearance energies

The DFT-B3LYP and G3X model chemistry were used to predict the cation structures and energetics of fluorinated, chlorinated, and brominated methanes. Ion–complex structures between methylene cations and HX (X = F, Cl, Br) were found for all H-containing cations, and [CHF–FH]⁺, [CF₂–FH]⁺, [CCl₂–ClH]⁺, and [CCl₂–FH]⁺ structures are more stable than their normal tetravalent structures. Several cations should also be better described as ion–complex structures between methyl cations and halogen atoms, e.g., [CF₃–Br]⁺. Transition states connecting normal and ion–complex structures were also located, and potential energy diagrams were constructed for decomposition of methane cations and to predict the fragmentation pathways. The G3X energies were used to predict the adiabatic ionization energies (IE_as) and ion fragment appearance energies (AEs) from methanes. Many of the experimental AEs correspond to the energies of transition states instead of the thermodynamic dissociation limits. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Diabatic potential energy surfaces of H+ + CO

Ab initio adiabatic and diabatic surfaces of the ground and the first excited electronic states have been computed for the H⁺ + CO system for the collinear (γ = 0°) and the perpendicular (γ = 90°) geometries employing the multi-reference configuration interaction method and Dunning’s cc-pVTZ basis set. Other properties such as mixing angle before coupling potential and before coupling matrix elements have also been obtained in order to provide an understanding of the coupling dynamics of inelastic and charge transfer process.