Construction Of Potential Energy Surfaces Research Articles

The Construction of Semi-diabatic Potential Energy Surfaces of Excited States for Use in Excited State AIMD Studies by the Equation-of-Motion Coupled-Cluster Method

The semi-diabatic potential energy surfaces (PESs) of the excited states of polyatomic molecules can be constructed for use in ab initio molecular dynamics (AIMD) studies by relying on the continuity of the electronic energy, oscillator strength, and spherical extent of an excited state along with first derivatives of these quantities as computed by using the equation-of-motion coupled-cluster (EOM-CC) method. The semidiabatic PESs of both the π → <TEX>$π^*$</TEX> valence excited state and the 3s-type Rydberg state of ethylene are presented and discussed in this paper, in conjunction with some of the AIMD results we obtained for these states.

A potential energy surface construction scheme for accurate reaction rate calculations: General approach and a test for the H+CH4→H2+CH3 reaction

An approach for the construction of accurate potential energy surfaces for reaction rate calculations is presented. It employs Shepard interpolation with reference points randomly selected from range of geometries relevant for the reaction rate. Quantum dynamics calculations, which use the multiconfigurational time-dependent Hartree approach and flux correlation functions to obtain thermal rate constants, monitor the convergence of the potential energy surface with increasing number of reference points. As a test of the approach, the H+CH4→H2+CH3 reaction is studied and the analytic Jordan–Gilbert potential energy surface is reproduced by the interpolation scheme. About 40 reference points are required in the interpolation to obtain a converged interpolated surface which reproduces the thermal rate constants with errors smaller than 20%.

Extension of the fourfold way for calculation of global diabatic potential energy surfaces of complex, multiarrangement, non-Born–Oppenheimer systems: Application to HNCO(S,S1)

The fourfold way is a general algorithm for generating diabatic electronic wave functions that span the same space as a small set of variationally optimized adiabatic electronic wave functions and for using the resulting diabatic wave functions to generate diabatic potential energy surfaces and their couplings. In this paper we extend the fourfold way so it is applicable to more complex polyatomic systems and in particular to the calculation of global potential energy surfaces for such systems. The extension involves partitioning the active space into three blocks, introducing restricted orbital rotation within two of the blocks, introducing a specific resolution of the subspace containing molecular orbitals that are doubly occupied in all dominant configuration state functions, and introducing specific orientations of the coordinate systems for reference molecular orbitals and resolution molecular orbitals. The major strength of the improved method presented in this paper is that it allows the diabatic molecular orbitals to exhibit a gradual change of chemical character with smooth deformation along the reaction coordinate for a change of chemical arrangement while preserving the orbital character required for a physical ordering of the orbitals. This feature is required for the convenient construction of global potential energy surfaces for non-Born–Oppenheimer rearrangements. The resulting extended algorithm is illustrated by calculating diabatic potential energy surfaces and couplings for the two lowest singlet potential energy surfaces of HNCO.

Investigation of the Ne-NH3 van der Waals complex: Rotational spectrum and ab initio calculations

The Ne-NH3 van der Waals complex was investigated through analysis of microwave spectra and the construction of ab initio potential energy surfaces. Rotational spectra of the ground internal rotor state of Ne-NH3 were recorded between 7 and 24 GHz using a Balle–Flygare-type Fourier transform microwave spectrometer. In total, ten isotopomers were studied, which include Ne20 and Ne22 paired with NH3, NH315, ND3, ND2H, and NDH2. The spectroscopic constants including the N14 quadrupole coupling constants were determined and used to estimate structural and dynamical details of the van der Waals complex. For each deuterium-substituted isotopomer, a tunneling splitting was observed due to the inversion of NH3 within the ground state of the complex. One of these inversion components is missing for the NH3 and NH315 containing isotopomers for spin statistical reasons. Ab initio potential energy surfaces were constructed for three different umbrella angles of NH3 within the complex to provide information about the interaction along the NH3 inversion pathway. The interaction energies were calculated using Møller–Plesset perturbation theory to fourth order. All three surfaces have minima corresponding to structures where the van der Waals bond (the line from the center of mass of NH3 to the Ne atom) lies perpendicular to the C3 axis of NH3, with the neon atom sitting between two hydrogen atoms. At this orientation, the potential well depth is 62.66 cm−1 (285.5 μhartree) at a van der Waals bond length of 3.30 Å (6.24 bohr) for the experimental equilibrium NH3 monomer geometry.

Exchange-Coulomb potential energy surfaces and related physical properties for Ne-N2

An exchange-Coulomb (XC) potential energy model is developed for the Ne-N2 interaction. The construction of this new potential energy surface is based on recent results for the Heitler-London interaction energy, the long range dispersion energies, and the microwave spectra of the dimer. The adjustable parameters in the final XC1 potential energy surface have been determined by fitting the frequencies of three representative lines of the microwave spectrum for the two isotopomers 20Ne-14N2 and 20Ne-15N2 while simultaneously maintaining agreement with the experimental second virial coefficient data obtained with the initial (unadjusted XC0 potential. With no further adjustment of parameters, the final XC potential reproduces, within 0.005%, the frequencies of the 34 microwave transitions studied experimentally for four isotopomers of Ne-N2. Excellent agreement with experiment is obtained also for the binary diffusion, the interaction viscosity, and the mixture viscosity (for all compositions) coefficients for all temperatures. Agreement with experiment for the relaxation cross-sections associated with viscomagnetic effects, and with the pressure broadening of depolarized Rayleigh light scattering, is very good given the level of computation used for the calculations and the accuracy with which some of these cross-sections currently can be determined from experimental data. Comparisons are made with predictions calculated from the three best literature potential energy surfaces or Ne-N2. The final XC1 potential energy surface is overall the most reliable potential energy for this van der Waals complex to date. The flexibility still inherent in this potential can be exploited, if required, in future studies of the Ne-N2 system.

Efficient potential energy surfaces from partially filled ab initio data over arbitrarily shaped regions

The reproducing kernel Hilbert space (RKHS) method has been previously shown to be accurate and efficient in the construction of potential energy surfaces (PES) by interpolating fully gridded high level ab initio data. This paper extends the RKHS method to handle partially filled data calculated over arbitrarily shaped regions, while keeping nearly intact its accuracy and efficiency. The extension permits points or regions to be added to or removed from the grid as needed before doing expensive ab initio calculations, thus enabling the construction of RKHS PESs from the data distributions that are most likely to occur in practice. The utility of the new technique is demonstrated using data from the lowest global RKHS PES for the reaction O(1D)+H2, showing that ignoring the irrelevant regions of the PES does not adversely impact the accuracy of the surfaces if the relevant region is adequately sampled.

Construction of an accurate potential energy surface by interpolation with Cartesian weighting coordinates

A modified method to construct an accurate potential energy surface by interpolation is presented. The modification is based on the use of Cartesian coordinates in the weighting function. The translational and rotational invariance of the potential is incorporated by a proper definition of the distance between two Cartesian configurations. A numerical algorithm to find the distance is developed. It is shown that the present method is more exact in describing a planar system compared to the previous methods with weightings in internal coordinates. The applicability of the method to reactive systems is also demonstrated by performing classical trajectory simulations on the surface.

Hydrogen bonding at the diatomics-in-molecules level: Water clusters

Further developments of the intermolecular diatomics-in-molecules (DIM) theory towards construction of potential energy surfaces of hydrogen-bonded molecular aggregates are presented. Compared to the previously studied hydrogen fluoride clusters (HF)n [J. Chem. Phys. 111, 4442 (1999)], considerably more complicated and challenging systems, namely, water clusters (H2O)n (n=2–6) have been analyzed in this work. The present DIM, or more precisely, diatomics-in-ionic-systems, scheme is based on the balanced treatment of neutral and ionic contributions to the electronic properties of polyatomic species, and in this case takes into account the mixing of the OH and O−H+ electronic states within the valence bond description of water molecules. The potential curves of diatomic molecules required for the present application, including ionic species O−H, OH+, O2−, have been computed by ab initio quantum chemistry tools. The results of DIM calculations of equilibrium geometry configurations, binding energies, and relative energies for the low-lying isomers of (H2O)n (n=2–6) are compared to the reference data showing a good predictive power of this method.

Construction of an accurate potential energy surface by interpolation for quantum dynamics studies of a three-body system

A method to construct an accurate potential energy surface (PES) by interpolation for a three-body reaction which is suitable for quantum dynamics studies is presented using Cl+H2→HCl+H as an example. Use of the exponential coordinates led to a significant improvement. Dynamics results, both classical and quantal, on the LEPS and LEPS-interpolated PESs were nearly indistinguishable. An accurate analytic PES can be constructed with the ab initio results also, as manifested with the PES contours.

Infrared Cavity Ringdown Spectroscopy of the Water Cluster Bending Vibrations

We report the first measurement of water monomer bending vibrations in gaseous (H2O)n clusters. Infrared cavity ringdown spectroscopy reveals discrete and sequentially blue-shifted bands near 6 μm for n = 2−4 and unresolved broad features for n > 4, supporting both theoretical predictions and solid-state spectroscopy results. These measurements provide a measure of the monomer distortion that accompanies sequential hydrogen bond formation, which will be valuable for the construction of potential energy surfaces for describing water.

Theoretical description of the interaction of CO adsorbed on a n(=1,2,⋯)×Ar/Pt(111) substrate: The transition from chemisorption to physisorption

Potential energy calculations have been performed for the system CO/n×Ar/Pt where the argon atoms play the role of spacer layers. A detailed analysis of the construction of this multidimensional potential energy surface is presented and discussed. The change of the nature of the adsorbate–substrate bond going from chemisorption to physisorption is studied within the frame of a stepwise approach. First we investigate an incommensurate model in which no coupling between the argon and the platinum atoms is considered. Several convergence tests have been done concerning the size and the binding sites of the metal surface, the rare gas network, and the combined system in order to ensure the stabilization of the calculations. A structural analysis of this potential energy surface is made considering the minima of the potential interaction, the bending angle of the CO with respect to the normal to the surface, and the distance between the CO center of mass and the surface. In a second stage of our study the lateral Ar–Ar and the Ar–Pt corrugation interactions are included in order to consider commensurate criteria. A new analysis of the behavior of the main physical observables of the system is given and the dependence of the calculations on the variation of the argon lattice parameter is shown as a function of the number of argon spacer layers. The results show that the equilibrium value of the argon lattice parameter changes when the number of spacer layers increases. It is found that the main contribution to the change in the strength of the force field between the molecule and the metal surface is given by the introduction of the first two argon spacer layers. Additional layers produce a smooth variation within the physisorption regime.

Electron transfer NO 2 + +NO→N02+NO+ in aromatic nitration

A simple model for computing the electron transfer rate constant of a cross-reaction has been proposed in the framework of semiclassical theory and employed to investigate the electron transfer system NO2+ /NO. The encounter complex of electron transfer NO2++NO→N02+NO+ has been optimized at the level of UHF/6-31G. In the construction of diabatic potential energy surfaces the linear coordinate was used and the kinetic quantities, such as the activation energies and the electron transfer matrix elements, have been obtained. For comparison, the related selfexchange reactlon systems NO2+/NO2 and NO+/NO were kinetically investigated. The calculated activation energies for the electron transfer reactions of systems NO2+/NO, NO2+/NO2, and NO+/NO are 81.4, 128.8, and 39.8 kJ.mol-1, respectively. With the solvent effect taken into account, the contribution of solvent reorganization to the activation energy has been estimated according to the geometric parameters of the transition states. The obtained rate constants show that the activity of NO2+ as an oxidizing reagent in the aromatic nitration will be greatly decreased due to a high activation barrier contributed mainly from the change of bond angle ONO.

Toward a Single-Valued DMBE Potential Energy Surface for CHNO(3A). 1. Diatomic Fragments

As a first step toward the construction of a single-valued double many-body expansion potential energy surface for CHNO(3A), we have carried out CASSCF and CASPT2 calculations of six diatomic curves, involving a total of nine electronic states. The ab initio curves have been represented analytically using the extended Hartree−Fock approximate correlation energy model. In all cases, the semiempirical curves have been found to agree well with the available spectroscopic RKR data.

Specific and Nonspecific Solvation Contributions to Intervalence Electron Transfer Transitions and Redox Potentials in Ruthenium Ammine Complexes

A series of binuclear complexes of general formula LmRu−BL−RuL‘mn+ where L and L‘ are monodentate or bidentate ligands bound to one metal center and BL is a bridging ligand are analyzed with the recently reported unified solvation model (USM). The solvent dependence of ΔE1/2 and EIT data are analyzed for cases where L is the same as L‘ and where L and L‘ differ. Data for the change in E1/2 and EIT as the Lewis base, B, is varied in (bpy)2ClRupyz Ru(NH3)4B (where bpy is 2,2‘-bipyridine and pyz is pyrazine) are also correlated. The USM provides the relative contributions of specific and nonspecific solvation to the solvent dependence of the physicochemical property. The factoring of the solvent dependence permits the construction of potential energy surfaces providing unprecedented detail concerning the influence of solvent donor−acceptor and solvation contributions to these measurements. The ability of USM to correlate Franck−Condon energies and the failure of donor numbers (DN) to do so emphasizes the need for a dual parameter treatment of the specific interaction. In contrast to nonsymmetrical binuclear complexes, the solvent dependence of the EIT bands for symmetrical complexes is not correlated by solvent donor and polarity parameters but is fit to the dielectric constants and refractive indices of the Marcus−Hush dielectric continuum model. A rationale for this disparate behavior of symmetrical and unsymmetrical binuclear complexes is given.

Electron and ion transfer reactions on metal electrodes

An extended Anderson model is used as a unifying framework for both ion and electron transfer reactions. The model allows the construction of effective potential energy surfaces as functions of the solvent coordinates and the separation of the reactant from the electrode surface. For electron transfer the reaction coordinate is mainly in the direction of the solvent coordinates; for ion transfer the partial loss of the solvation sheath and the encompanying solvent displacement is the rate determining step, and the reaction coordinate is mainly determined by the separation from the metal surface. Further differences and similarities between the two types of reactions are discussed.

Exchange-Coulomb potential energy surfaces, and related physical properties, for KrN2

Abstract The construction of exchange-Coulomb (XC) potential energy models for closed shell atom-closed shell molecule interactions, based on earlier work for rare gas-rare gas interactions, is discussed with explicit application to the KrN2 interaction. The construction of the new XC potential energy surface for KrN2 is based on recent results for the Heitler-London interaction energy, the long range dispersion energies, and the microwave spectra for this dimer. The adjustable parameters in the final XC potential are determined by fitting experimental second virial coefficients (all within experimental error), as a function of temperature, and three lines of the microwave spectra. With no further adjustment of parameters the resulting potential yields excellent predictions for all the frequencies of all the microwave transitions studied experimentally for seven isotopomers of KrN2, and good agreement with experiment for the binary diffusion, the interaction viscosity, and the mixture viscosity coefficients of KrN2 and for the cross sections associated with depolarized light scattering and nuclear spin relaxation for the KrN2 system. The agreement with experiment for the latter five properties is as good as can be expected from our scaled Mason-Monchick/infinite order sudden calculations for these properties. The final XC2 potential is apparently the most reliable potential to date for the KrN2 interaction and provides a very suitable starting point for further studies of the KrN2 system; the flexibility still inherent in the potential can be used, as required, for this purpose.

A unified model for electrochemical electron and ion transfer reactions

Electron and ion transfer reactions on metal electrodes are considered in an extended Anderson model, in which the interactions of the reactant with the metal and with the solvent depend on the separation from the interface. The model allows the construction of effective potential energy surfaces. Explicit calculations are performed for the transfer of an iodide ion and for the electron transfer reaction of the Fe 2+/Fe 3+ couple.

Theoretical studies of inorganic and organometallic reaction mechanisms. 7. Ab initio potential energy surfaces of carbonyl substitutions on six-coordinate trans-W(CO)4(NO)Cl and Re(CO)5Cl

Carbonyl substitution reactions on trans-W(CO) 4 (NO)Cl and isoelectronic Re(CO) 5 Cl were investigated through the construction of ab initio potential energy surfaces. Hartree-Fock-Roothaan calculations for the substitutions by PMe 3 on W(CO) 4 (NO)Cl predict an associative mechanism with a 7-coordinate intermediate.

The construction and fitting of molecular potential energy surfaces and their use in vibration-rotation calculations

The state-of-the-art in non-empirical calculations of potential energy surfaces for small molecules is discussed, as is the present position with respect to the analytic fitting of such surfaces. The results of some nonempirical vibration-rotation calculations performed on such analytic surfaces are presented and compared with experimental results. An attempt is made to assess the extent to which present methods of electronic structure calculation and present analytic fitting methods are adequate to produce surfaces for the interpretation of high-resolution spectral data.

Hydrogen chemisorbed on nickel surfaces: A wave-mechanical treatment of proton motion

The quantum nature of hydrogen chemisorbed on a metal surface is explored in detail. Starting from the effective-medium construction of the adiabatic potential energy surfaces, we demonstrate that due to zero-point motion chemisorbed hydrogen can be to a large extent delocalized in both ground and excited state configurations. A proper description can then only be given in terms of hydrogen energy bands. The quantitative calculations for Ni surfaces are used to discuss a number of experimental observations, in particular the vibrational excitations of hydrogen as measured by inelastic electron scattering. The further implications of this new description are also commented on.