Final Binding Energy Research Articles

Floppy structure of the benzene dimer: Ab initio calculation on the structure and dipole moment

The structure of the benzene dimer has aroused considerable interest due to recent experimental measurements and hence extensive theoretical calculation is topical. Nine structures of the benzene dimer were investigated using the second-order Mo/ller–Plesset theory. The calculations were performed with smaller (MIDI-1+s+p) and larger (6-31+G*) basis sets. The T-shape structure was found to be the most stable but with a very shallow minimum; the wagging motion around the lowest hydrogen in the range of ±10° is practically nonhindered. These results together are consistent with the structure found experimentally. The final binding energy for the T structure (distance of molecular centers equal to 5.0 A) is −2.7±0.4 kcal/mol, which is more than the value derived from experiments. The calculated dipole moment is in excellent agreement with experiment.

SCF, MP2, and CEPA‐1 calculations on the OH ‥ O hydrogen bonded complexes (H2O)2 and (H2O‐H2CO)

AbstractCounterpoise corrected ab initio calculations are reported for (H2O)2 and H2O‐H2CO. Geometry searches were done in the moment‐optimized basis DZP' at the SCF, MP2, and CEPA‐1 levels of theory, followed by more accurate single‐point calculations in basis ESPB, which includes bondfunctions to saturate the dispersion energy. The final equilibrium binding energies obtained are −4.7 ±0.3 kcal/mol for a near‐linear (H2O)2 structure and −4.6 ±0.3 kcal/mol for a strongly bent HOH ‥ OCH2 structure. The energy difference between these systems is much smaller than in all previous ab initio work. Cyclic (C2h) and bifurcated (C2v) transition structures for (H2O)2 are located at 1.0 ±0.1 kcal/mol and 1.9 ±0.3 kcal/mol above the global minimum, respectively. A new partitioning scheme is presented that rigorously partitions the MP2 correlation interaction energy in intra and intermolecular (dispersion) contributions. These terms are large (up to 2 kcal/mol) but of opposite sign for most geometries studied and hence their overall effect upon the final structures is relatively small. The relative merits of the MP2 and CEPA‐1 approaches are discussed are discussed and it is concluded that for economical reasons MP2 is to be preferred, especially for larger systems.

High-accuracy calculation of muonic molecules using random-tempered basis sets.

We use random-tempering formulas and explicitly correlated Slater-type geminals to calculate the S and P bound-state energies of the muonic molecules xy\ensuremath{\mu}, where x,y=p,d,t. The final binding energies are accurate to about 1 \ensuremath{\mu}eV or better except for the weakly bound td\ensuremath{\mu}(11) state. For this state we get a binding energy of 0.660 1721 eV, which is better than any previous calculation.

Model calculations for the C(K V V) and O(K V V) Auger transitions for CO on Ni(100)

Model calculations of the core and valence electron binding energies and the two-hole final state Auger binding energies for the C(KVV) and O(KVV) transitions are performed for the Ni–CO system. The chosen atomic geometry is appropriate for a qualitative description of the CO–C(2×2)–Ni(100) structure. The shifts in these quantities with the adsorption process are determined by making comparisons with previous calculations for molecular CO. The shifts in the one-electron binding energies for the valence levels are typically ∼1 eV while the shifts in the two-hole final state binding energies are substantially larger, being typically ∼3–5 eV. Calculations are also performed for the Auger transition intensities. The changes that must be made for a fixed, oriented molecule on a surface are described and it is pointed out that some transitions exhibit a characteristic azimuthal angular dependence for the emitted Auger electrons.

The “equilibrium distance” between two bodies immersed in a liquid

By virtue of the space occupied by at least one monomolecular layer of a liquid (3) separating continua of two identical (1) or two different materials (1) and (2), it could be argued that the minimum equilibrium distance d 0123 and d 0123 must be greater than the equilibrium distances d 0123 or d 0123 (all of which < 2 Λ) between two identical or ion-identical continua (liquid or solid) in the absence of a third, intervening liquid. As long as actual liquid molecules are intercalated between the two continua, that is indubitably the case. However, within the same thermodynamic model used for deriving the Hamaker coefficients A123 or A??? (using d 0??? or d???), d * 0??? or d * 0??? (the asterisks serving to indicate the “equilibrium distances” as defined by the thermodynamic model) may be used for deriving A??? and A???, and within that framework it is postulated that all the above d 0 and d * 0 values may be taken to be of the same order of magnitude. The agreement among the experimental results obtained by a number of different approaches appear to confirm that all d 0??? and d 0??? are of the same order of magnitude. The agreement between A??? values found via surface tension measurements and the postulated d *??? and A??? values for the same systems derived via the Lifshitz approach, indicates that d *??? is indeed also of the same order of magnitude as d 0??? and d 0???. In real physical systems (e.g., antigen—antibody interactions of the van der Waals type) it can be shown that the interaction begins as one of the “132” type and then tends toward the “41” variety, accompanied by extrusion of liquid (3). However that process is seldom completed; the final equilibrium binding energy has a value intermediate between Δ F 123 and Δ F 13.

The transfer amplitude and angular distributions in heavy-ion reactions

Semiclassical conditions appropriate to a grazing collision have been used to study the dependence of the transfer amplitude on the distance of closest approach, d, for direct reactions. It is found to fall off exponentially with increasing d, the decay constant being a function of the initial and final binding energies of the transferred particle. The dependence on the z projections of the angular momenta of the particle separates out as a multiplicative constant. This simplified form of the transfer amplitude is used to obtain an analytic expression for angular distributions. Comparison is made with experiment for the reaction 26Mg(11B,10B)27Mg at 114 MeV laboratory energy.

The effect of recoil on single-nucleon transfer in heavy-ion reactions

An approximate treatment of the effect of recoil in single-nucleon transfer in heavy-ion reactions is outlined. It is shown that the effect of recoil is to remove the restrictions on the orbital angular-momentum transfer. The effect of recoil is shown to depend upon the energy of the projectile, becoming more significant at higher projectile energies, and for the case where the neutron binding to the residual nucleus is small, it is more important for smaller final binding energies. A simple expression is obtained for the recoil amplitude and cross section for p-wave projectiles.

984. Investigation of emission from the grid of an impulse hydrogen thyratron: V D Baranov et al,Elektrovak Tekh, No 52, 1971, 22–26 ( in Russian)

The non-adiabatic reaction leading to the emission of exoelectrons during the adsorption of oxygen on lithium is exploited to estimate the time that elapses during the dissociation of the molecule. With a three-step model the exoemission probability is calculated. A comparison with experimentally observed probabilities predicts the reaction time to be 75±25 O2p hole lifetimes at the final O2p binding energy. The width of the exoelectron energy distribution reflects this hole lifetime. The absence of visible light emission ( < 10−10 photons/O2) is shown to be compatible with the model.

Energy of a simple triton model

The energy of a simple three-body nuclear problem that has been extensively studied is calculated again. An exact Monte Carlo method is used together with a procedure for reduction of statistical error based upon a variational expression involving a new trial function particularly appropriate for the problem. The resulting acceleration of convergence greatly reduces computing time for a given accuracy. The final binding energy is in excellent agreement with other work.

Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule

Accurate ground-state energies of the hydrogen molecule have been computed using wavefunctions in the form of expansions in elliptic coordinates and including explicitly the interelectronic distance. The computations have been made with 54-term expansions (0.4≤R≤3.7) and with 80-term expansions (0.5≤R≤2.0). For the equilibrium internuclear distance, the best total energies obtained in the two cases are —1.1744701 a.u. and —1.1744746 a.u., respectively, the corresponding binding energies being 38 291.8 and 38 292.7 cm—1. Employing the 54-term wavefunctions, the relativistic corrections and the diagonal corrections for nuclear motion have been computed for several internuclear distances. For equilibrium their contributions to the binding energy have been found to be —0.526 and 4.947 cm—1, respectively. Thus the final theoretical binding energy for H2 amounts to 38 297.1 cm—1 and is a little larger than the experimental value 38 292.9±0.5 cm—1. The discrepancy may be due to the adiabatic approximation.

The Theoretical Constitution of Metallic Lithium

On the basis of previous theoretical developments concerning the nature of cohesion in metals which were applied to sodium, a treatment of metallic lithium is presented. As before, the system of Fock equations are solved by an indirect procedure as a start. These solutions differ appreciably from those for sodium in several important respects and account for a greater percentage of the observed binding energy than in the latter case. The modification of the exchange energy of the electrons arising from these differences is computed. Finally, the work of Wigner on correlation energies of metal electrons is applied directly to obtain a final binding energy of 34 kg.cal. as compared with the observed value of 38.9. The lattice constant is found to agree with the observed one to within about three percent. Some general remarks concerning the applicability of the present development to solids other than metals are made.