Narrow Results

The shape evolution of even–even Mo isotopes from the line of stability up to the two-neutron drip-line is investigated within the self-consistent Hartree–Fock–Bogoliubov theory in both the axial and triaxial symmetries. The Skyrme energy density functional SLy4 has been considered in the particle-hole channel, while the zero range delta-interaction has been employed in the particle–particle channel. In order to correctly treat the pairing correlations, a particle-number projection was carried out by the Lipkin–Nogami (LN) method. The two-neutron separation energies and root-mean-square (rms) charge radii are investigated and compared with available experimental data. The evolution of the potential energy surfaces in the (β, γ) deformation plane is presented and discussed. In addition, the obtained ground state deformation parameters are compared to those obtained by other models.

We study the adsorption properties of the N₂ molecule on the Be(0001) surface by calculating the potential energy surfaces and analyzing the electronic densities of states. It is found that the N₂ molecule cannot adsorb molecularly on the clean Be surface, and the dissociation energy barrier of N₂ is estimated to be as large as 4.10 eV. Our studies indicate that the Be surfaces cannot be used as N₂ cleaners, but might be used to drive out N₂ molecules in automotive catalytic converters.

Relativistic mean field theory is used to produce potential energy surfaces (PESs) for Ti isotopes. The relatively flat PESs suggest that ^{48, 52, 60}Ti, being on the way from vibrations to γ-unstable behavior, are the possible examples with the transitional dynamical symmetry E(5). Especially for ⁴⁸Ti, PES shows that it is a better candidate with E(5) symmetry. These conclusions are supported by the experimental data via the observed ratios of excitation energies.

Potential energy surfaces corresponding to the alpha accompanied ternary fragmentation in superheavy mass region have been investigated. The lowest value of potential energy is found for the configuration having alpha particle in between other two fragments. The position of deepest valleys in the potential energy surface indicates the most probable tri-partition of a given nucleus. The isotopic effect on the variation of the deepest valley has also been investigated. For the isotopic chain of Z = 114, the minimum is found at ¹⁴⁰Ce + ⁴He + ¹³⁶Xe, suggesting this to be the most probable tri-partition. Similar possible configurations have been studied for Z = 116, 118 and 120 and the presence of proton/neutron magic number has been found in all the most probable combinations for alpha accompanied ternary fission.

Two 0⁺ excited states of ⁴⁰Ca have been investigated by the potential energy surface (PES) obtained from both adiabatic and diabatic constrained approaches, combined with the relativistic mean field (RMF) theory. A well-defined second minimum appears on the diabatic PES that does not exists on the adiabatic PES. The configurations of these two 0⁺ excited states are determined as 4p–4h and 8p–8h excitation from their counterparts at the spherical configuration. The excited energies were reduced by microscopic correction for the center-of-mass motion, and a gap at 18 appears in their single particle diagrams.

We study nuclear structure properties for various isotopes of Ytterbium (Yb), Hafnium(Hf), Tungsten(W), Osmium(Os), Platinum(Pt) and Mercury(Hg) in $Z$ = 70–80 drip-line region starting from $N=80$ to $N=170$ within the formalism of relativistic mean field (RMF) theory. The pairing correlation is taken care by using BCS approach. We compared our results with finite range droplet model(FRDM) and experimental data and found that the calculated results are in good agreement. Neutron shell closure is obtained at $N=82$ and $126$ in this region. We have also studied probable decay mechanisms of these elements.

The relativistic Hartree–Bogoliubov formalism was employed to explore the role of the nucleon single-particle state in defining the potential energy surface of the ${}^{72}$Kr isotope utilizing density-dependent zero and finite range NN interactions. It is discovered that a significant influence on identifying the ground state minima is the density of states near to the Fermi level.

The reaction path is an important concept in theoretical chemistry. We discuss different definitions, their merits as well as their drawbacks: IRC (steepest descent from saddle), reduced gradient following (RGF), gradient extremals, and some others. Many properties and problems are explained by two-dimensional figures. This paper is both a review and a pointer to future research. The branching points of RGF curves are valley-ridge inflection (VRI) points of the potential energy surface. These points may serve as indicators for bifurcations of the reaction path. The VRI points are calculated with the help of Branin's method. All the important features of the potential energy surface are independent of the coordinate system. Besides the theoretical definitions, we also discuss the numerical use of the methods.

The rovibrational energy levels of HXeOH and its isotopomers have been calculated using a two-layer Lanczos algorithm in Radau-diatom-Jacobi coordinates based on a high level ab initio potential energy surface. The surface is obtained by fitting to 1229 RCCSD(T)/SDB-cc-pVQZ energy points. The equilibrium geometry of HXeOH is determined to have a trans configuration with a nearly collinear HXeO bond angle of 177.32 degrees. The well depth of this minimum is only 0.6123 eV with respect to the OH+Xe+H dissociation limit. The results show that the H–Xe stretching frequency of HXeOH and HXeOD has an anomalous isotopic shift upon ¹⁸O isotope substitution, whereas the D–Xe stretch in DXeOH and DXeOD displays a normal isotopic shift. This trend is consistent with the experimental observations in a Xe solid matrix. The present results predict a lower frequency for the H–Xe stretch than was observed in the solid matrix experiment. Either these results are too low or there is a strong blue shift due to the matrix in the experimental values.

We present a global potential energy surface (PES) for the ²A state of the O(³P) + C₃H₃ radical reaction. The global PES is constructed mainly using direct ab initio molecular dynamics and further sampling is done using the Diffusion Monte Carlo method. The potential is fully invariant with respect to permutational symmetry of like atoms. Special techniques, based on invariant theory of finite groups, have been used to develop basis functions for fitting that display this symmetry. The resultant potential energy surface shows multiple reaction paths with six different product channels. The products of the reactions are CO + C₂H₃ radicals H + C₃H₂O radicals (with two isomers, propynal and propa-1,2-dien-1-one) and OH + C₃H₂ radicals (with three isomers, vinylidenecarbene, propargylene and cyclopropenylidene). Energies of the PES are in excellent agreement with ab initio energies for each stationary point, the reactants and the products. Most stationary points are fitted at the sub Kcal/mol level. The global potential surface represents all the stationary points and six different product channels correctly. Preliminary dynamics calculations show abstraction and insertion mechanisms for the OH + vinylidenecarbene channel and the H + propynal channel, respectively.

To elucidate the ionization dynamics, in particular the vibrational distribution, of H₂O⁺(Ã) produced by photoionization and the Penning ionization of H₂O and D₂O with He*(2 ³S) atoms, Franck–Condon factors (FCFs) were given for the ionization, and the transition probabilities were presented for the emission. The FCFs were obtained by quantum vibrational calculations using the three-dimensional potential energy surfaces (PESs) of and electronic states. The global PESs were determined by the multi-reference configuration interaction calculations with the Davidson correction and the interpolant moving least squares method combined with the Shepard interpolation. The obtained FCFs exhibit that the state primarily populates the vibrational ground state, as its equilibrium geometry is almost equal to that of , while the bending mode (ν₂) is strongly enhanced for the H₂O⁺(Ã) state; the maximums in the population of H₂O⁺ and D₂O⁺ are approximately v₂ = 11–12 and 15–17, respectively. These results are consistent with the distributions observed by photoelectron spectroscopy. Transition probabilities for the system of H₂O⁺ and D₂O⁺ show that the bending progressions consist primarily of the emission, with combination bands from the (1, v′₂ = 4–8, 0) level being next most important.

The transition states for the H₂NO decomposition and rearrangements mechanisms have been explored by the CBS-Q method or by density functional theory. Six transition states were located on the potential energy surface, which were explored with the Quadratic Complete Basis Set (CBS-Q) and Becke's one-parameter density functional hybrid methods. Interesting deviations between the CBS-Q results and the B1LYP density functional theory lead us to believe that further study into this system is necessary. In the efforts to further assess the stabilities of the transition states, bond order calculations were performed to measure the strength of the bonds in the transition state.

Out of several plausible isomeric structures of the toluene–ICl charge transfer (CT) complex, the most feasible one was determined by a detailed ab initio and DFT study at the HF, B3LYP, and mPW1PW91 levels using 6-31++G(d, p) basis set. Potential energy surface scans were performed with six possible structures (I and Cl facing the o-, m-, and p-carbon atoms of toluene separately); the structures at the local minima of the surfaces were subjected to frequency calculation and the ones having no negative frequency were accepted as the real structure in the ground state. These structures were then subjected to full optimization. It was observed that the I–Cl bond, with its I atom oriented toward the aromatic ring, stands vertically above a C-atom at the ortho or para positions, being inclined at about 9° to the line perpendicular to the aromatic ring. Complexation increases the I–Cl bond length. After correction for basis set superposition error through a counterpoise calculation, we conclude from the binding energy that the preferred structure is the one with ICl above the orthoC atom. The calculated binding energy closely matches the experimental free energy of complexation. The electronic CT transition energy (hν_CT) with this structure in the ground state was calculated in vacuo by the restricted configuration interaction singlets method and in carbontetrachloride medium by the time dependent density functional theory method under the polarizable continuum model. The value of hν_CT obtained from the ground-to-excited state transition electric dipole moments of the complex, is close to (somewhat underestimated) the reported experimental value.

Vibrationally averaged potential energy surfaces for isotopic He–CO₂ complexes (He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O) are presented. Based on the latest ab initio potential of He–¹⁶O¹²C¹⁶O (Ran H, Xie D, J Chem Phys128:124323, 2008.) including the Q₃ normal mode for the v₃ antisymmetric stretching vibration of the CO₂ molecule, the averaged potentials for both He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O are obtained by integrating the potential energy surfaces over the Q₃ normal mode. The averaged potentials have T-shaped global minima and two equivalent linear local minima. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm are employed to calculate the related rovibrational energy levels. The calculated band origin shifts of He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O are 0.1066 and 0.0914 cm^-1, respectively, which agree very well with the observed values of 0.1123 and 0.0929 cm^-1. The calculated rovibrational transitions of He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O are also in very good agreement with the available experimental spectra.

The potential energy surface for the Kr–N₂O complex is calculated using the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)] with a large basis set including midpoint bond functions. The interaction energies are obtained by the supermolecular approach with the full counterpoise correction for the basis set superposition error. The CCSD(T) potential is found to have two minima corresponding to the T-shaped and linear Kr–ONN structures. The geometry for the T-shaped configuration is very close to the experimental results. The two-dimensional discrete variable representation method is applied to calculate the rovibrational energy levels with N₂O at its ground and ν₃ excited states. The calculated transition frequencies and spectroscopic constants are in good agreement with the observed values.

The reaction path is an important concept of theoretical chemistry. We use a definition with a reduced gradient (see Quapp et al., Theor Chem Acc100:285, 1998), also named Newton trajectory (NT). To follow a reaction path, we design a numerical scheme for a method for finding a transition state between reactant and product on the potential energy surface: the growing string (GS) method. We extend the method (see W. Quapp, J Chem Phys122:174106, 2005) by a second-order scheme for the corrector step, which includes the use of the Hessian matrix. A dramatic performance enhancement for the exactness to follow the NTs, and a dramatic reduction of the number of corrector steps are to report. Hence, we can calculate flows of NTs. The method works in nonredundant internal coordinates. The corresponding metric to work with is curvilinear. The GS calculation is interfaced with the GamessUS package (we have provided this algorithm on ). Examples for applications are the HCN isomerization pathway and NTs for the isomerization C7ax ↔ C5 of alanine dipeptide.

The complex potential energy surface for the self-reaction of CH₂ClO₂ radicals, including 12 intermediates, 33 interconversion transition states, and 21 major dissociation products, was theoretically probed at the CCSD(T)/cc-pVDZ//B3LYP/6-311G(2d,2p) level of theory. The geometries and relative energies for various stationary points were determined. Based on the calculated CCSD(T)/cc-pVDZ potential energy surface, the possible mechanism for the studied system was proposed. It is shown that the most feasible channels are those leading to 2²CH₂ClO + ³O₂, ²CH₂ClO + ²HO₂ + CHClO, ²CH₂ClO + HCl + ²CH(O)O₂, ²CH₂ClO + ³O₂ + ²Cl + CH₂O, and p,s,o-CH₂ClOOOCl + CH₂O with the energy barriers of 5.6, 11.8, 12.4, 12.4, and 13.5 kcal/mol, respectively. Their mechanisms are that CH₂ClO₂ and CH₂ClO₂ form a tetroxide intermediate first, then the intermediate dissociates to yield the productions or through multi-steps reactions to produce the final products.

A previously reported approach [J. Chem. Phys.97:867, (1997)] to back transform the diagonal adiabats into a 2 × 2 diabatic potential matrix has been utilized to generate a global multi-sheeted form for the title system. Global adiabatic dynamics calculations carried out on the new form using the quasi-classical trajectory method yield results that lie essentially within the statistical error of similar calculations performed on the best surface reported thus far for the title reaction. This makes it suitable for future adiabatic and nonadiabatic calculations carried out either using classical or quantum methods.

A systematic study of torsional potential curves in electronic ground state based on second-order Møller–Plesset energy (MP2), density functional theory (DFT), and Austin mode 1 (AM1) methods is presented for para-phenylenevinylene oligomers constructed from two to four aromatic rings. The semiempirical AM1 approach gives the correct location of potential energy minima in comparison with the reference MP2 calculations and literature data. However, the semiempirical AM1 energy barriers at perpendicular orientation are ca. 30% smaller than the MP2 ones. The DFT calculations indicate optimal planar structures and the barriers are three times higher than MP2 values. Excited-state potential energy curves evaluated from vertical excitations at the time-dependent density functional theory (TD-DFT) and ab initio CI levels exhibit much steeper increase of values in the vicinity of perpendicular orientation than in the semiempirical Zerner's intermediate neglect of differential overlap (ZINDO) and ab initio RI-CC2 cases. The effects of vibrational motion of phenylene rings on the torsional broadening of absorption spectra were estimated from semi-classical molecular dynamics simulations and harmonic oscillator sampling. The simulated spectra agree well with the experiment and allow estimating the conformer distribution of the molecules.

We apply a theoretical method to study the O + HCNO reaction, in which the products P_i with i = 1, 2, …, 8 are involved. It is carried out by means of CCSD(T)/6-311G(d,p)//B3LYP/6-311G(d,p) + ZPVE computational method to detect a set of reasonable pathways. It shows that P₅(H + NO + CO) and P₈(HON + CO) are both the major product channel; in addition, there are some degrees of contributions from P₁(HCO + NO) to form P₅(H + NO + CO); P₄(NH + CO₂) is considered a minor product channel, and there are some degrees of contributions from P₂(HNO + CO) to form P₄(NH + CO₂); whereas the other three channels, P₃(NCO + OH), P₆(CNO + OH), and P₇(HCN + O₂) are less favorable or even unfavorable. All these theoretical results are in harmony with the experimental facts.