Improved Pöschl–Teller potential energy model for diatomic molecules

By employing the dissociation energy and the equilibrium internuclear distance for a diatomic molecule as explicit parameters, we construct an improved Pöschl–Teller potential energy model. We analyze the average absolute deviations of the improved Pöschl–Teller and Morse potentials from the experimental Rydberg–Klein–Rees (RKR) potentials for six diatomic molecules. It is found that the improved Pöschl–Teller potential is more accurate than the Morse potential in fitting experimental RKR potential curves over a large range of internuclear distances for six molecules examined.     

Approximate polynomial expressions for Rydberg-Klein-Rees curves of diatomic covalent molecules

A systematic method for fitting Rydberg -Klein -Rees (RKR) data with polynomial expressions is presented. The procedure is based on a change of variables that takes into account the form of the potential energy curve for large internuclear distances. The coefficients of the polynomial am determined by least squares. Results are presented for CO, HgH, and Ar₂. The form of the potential energy curves obtained is quite reasonable and the dissociation energies calculated are in satisfactory agreement with experimental data.     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Rydberg-London potential for diatomic molecules and unbonded atom pairs

We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form.     

Investigations on adiabatic potential energy curve of Li2()

The SAC-CI method is used to investigate the spectroscopic properties of ⁷Li₂(). The adiabatic potential energy curves are calculated and fitted to the analytic Murrell–Sorbie function. The spectroscopic parameters reproduced by the potential attained at cc-PVTZ are found to be very close to the experiments. With the potential obtained at the SAC-CI/cc-PVTZ level of theory, a total of 62 vibrational states is found when J = 0. For each vibrational state, the vibrational level, classical turning points, inertial rotation and centrifugal distortion constants are calculated. Good agreement is obtained when they are compared with the available RKR data.     

Theoretical description of the electronic structure of the alkali hydride cation NaH+

A theoretical determination of the electronic structure of NaH+ is presented. Potential energy curves and dipole moments have been computed for 48(2)Lambda(+) electronic states (i.e., correlated adiabatically up to Na(6s) + H+) through a model-potential-type method over a wide range of R. Equilibrium distances, transition energies, depths of wells, and/or heights of humps predicted at short and large interatomic separations are reported and compared with available experimental and theoretical values. Variations of the static dipole polarizabilities versus internuclear distance have been determined for the two lowest states.     

The potential barrier of theB 1Γ u state of Na2

With a semiclassical model the measured energy and width of quasibound levels are described for theB ¹Γ _u state of Na₂. A reliable complete potential function of this electronic state is derived including the potential hump which results from the competition between the electron exchange energy and the long range dipole-dipole interaction. The proposed computation of molecular potentials can be used in the general case and shows some advantages over RKR determinations.     

Radiative lifetimes for the B1piu state of the Na2 molecule

A study of the radiative lifetimes calculation of the Na2 B1piu state is presented. RKR electronic potentials are considered. The studied vibrational levels are for v' = 0-33 (B1piu) and v" = 0-65 (chi1sigmag+). The rotation is considered for values of J' = 1-225 (B1piu). The Einstein emission coefficients are calculated for the specified B1piu rovibrational levels (for Q line and R, P lines, for all ground state vibrational levels). With the inverse of Einstein emission coefficients sum, the radiative lifetimes are calculated. These calculated lifetimes are in good agreement with the experimental and previously calculated (with RKR potentials) lifetimes, but now great extension of considered rovibrational levels is considered. The bound-free contribution is irrelevant for Na2 lifetimes of the B1piu state. The perturbation between Na2 B1piu and alpha1sigmau+ states is considered.     

Remark on the ground state potentials and dissociation energies of the alkali hydrides

The ground state Rydberg—Klein—Rees (RKR) potentials and the corresponding molecular constants of the alkali hydrides, recommended in a recent article by Stwalley et al. (J. Phys. Chem. Ref. Data, to be published [1]) are critically evaluated in the framework of the reduced potential curve (RPC) scheme. A comparison with the older RPC analysis of the ground states of the alkali hydrides is briefly discussed. The efficiency of the RPC method for the detection of errors in the RKR potential (spectroscopic constants) and for the estimation of the dissociation energy is emphasized. Although the RKR potentials of NaH and RbH are known only up to 54 and 57% of D_e, respectively, the RPC method permitted here at least a substantial reduction of the uncertainty in the lower limit of D_e(NaH) (by 70 cm⁻¹) and in the lower and upper limits of D_e(RbH) (by 250 and 500 cm⁻¹, respectively) which are now estimated as 15 870, 14 230 and 14 680 cm⁻¹, respectively. The RPC picture even suggests that the values 14 380 and 14 580 cm⁻¹ may possibly be taken as reasonable limits for D_e(RbH). Accurate extensions of the inner wings of the potentials of NaH, RbH and CsH were calculated using the generalized reduced potential curve (GRPC) method. The limit of error of these extensions should be smaller than 0.002 Å if the potentials are correct.     

Ab initio study of substituent effects in the interactions of dimethyl ether with aromatic rings

Ab initio calculations have been used to investigate the interaction energies of dimers of dimethyl ether with benzene, hexafluorobenzene, and several monosubstituted benzenes. The potential energy curves were explored at the MP2/aug-cc-pVDZ level for two basic configurations of the dimers, one in which the oxygen atom of the dimethyl ether was pointed towards the aromatic ring and the other in which the oxygen atom was pointed away from the aromatic ring. Once the optimum intermolecular distances between the dimethyl and the aromatic ring had been determined for each of the dimers in both configurations at the MP2/aug-cc-pVDZ level, single point energy calculations were performed at the MP2/aug-cc-pVTZ level. A CCSD(T) correction term to the energy was determined and this was combined with the MP2/aug-cc-pVTZ energies to estimate the CCSD(T)/aug-cc-pVTZ interaction energies of the dimers. The estimated CCSD(T)/aug-cc-pVTZ interaction energies are predicted to be attractive for all of the dimers in both configurations and dispersion interactions are found to be a large component of the stabilization of the dimers. For the dimers with the dimethyl ether oxygen pointing towards the aromatic ring, the strengths of interaction energies are found to increase as the aromatic ring becomes more electron deficient, while for the dimers with the dimethyl ether oxygen pointing away from the aromatic ring, they increase as the aromatic ring becomes more electron rich. In both cases, the trends can be explained in terms of the electrostatic potentials of the dimethyl ether and the aromatic rings.     

Energetics and structure of the hydrated gaseous halide anions

Energetics and geometries for the hydrated gaseous halide anions have been computed from a simple model in which the molecular dipole of water was composed of two parts, one due to a lone pair on oxygen (60%) and the rest to formal charges on the nuclei. The calculations were made for both the symmetric and nonsymmetric structures. A variety of structures were used to compute potential energies and distances with up to six water molecules. The total energy consisted of a sum of electrostatic, polarization, dispersion, and repulsion terms. Various sets of repulsive potential parameters, ranging from those determined from molecular beam experiments to those determined using experimental ion–water distances or energies, have been employed to compute repulsive interaction energies. It was found that the range parameters play a significant role in deciding the magnitudes of the distances and energies, as the latter are most sensitive to them. It was also shown that with a simple correlation scheme the consistency of the experimental energies and distances can be tested separately without using repulsive potential parameters from other sources. It also suggests that a range of parameters can be used to compute repulsion energies. Despite the fact that the model is greatly simplified, the agreement of both the predicted ion-oxygen distances and energies with both experiment and other calculations is excellent. A detailed analysis of our calculation suggests that the negative ion clusters with one to three water molecules contain symmetric orientation of water molecules, while those with more than three may contain asymmetric orientations of water molecules or a mixture of both. From the log–log plots of hydration energies versus (R + radius of water molecule), we have proposed empirical expressions of the type ΔE_n?1,n = 10·0^x (R + 1.38)^?y with both Pauling's and Ladd's radii for univalent ions with which stepwise hydration energies of the latter can be predicted if we know thier radii. The values predicted for the alkali cations are in excellent agreement with the experimental and theoretical values, indicating the consistency of the simple model.     

Quantifying the anisotropy of intermolecular potential energy surfaces: a critical assessment of available N2-N2 potentials

Based on definition of angular central moments, a quantitative measure is proposed for comparative assessment of the anisotropy of different intermolecular potential energy surfaces at different intermolecular distances. Angular spreadness, skewness and peakedness are three features of anisotropy that are used here to describe the distribution of values of interaction energy around its isotropic component. In agreement with qualitative interpretations, the proposed measure exhibits a sharp change in the R-dependent pattern of anisotropy at an intermediate distance where the repulsive forces on the average overcome the attractive ones. The R-dependence of anisotropy of available N(2)-N(2) potentials is examined in comparison with bare ab initio data and considerable discrepancies are found at distances shorter than the onset of repulsion. It is shown that the full experimentally derived potentials with simplified functional forms do not reproduce the correct anisotropy of interaction energy.     

An ab initio intermolecular potential energy surface for the F(2) dimer

Two analytical representations for the potential energy surface of the F(2) dimer were constructed on the basis of ab initio calculations up to the fourth-order of M?ller-Plesset (MP) perturbation theory. The best estimate of the complete basis set limit of interaction energy was derived for analysis of basis set incompleteness errors. At the MP4/aug-cc-pVTZ level of theory, the most stable structure of the dimer was obtained at R = 6.82 au, theta(a) = 12.9 degrees , theta(b) = 76.0 degrees , and phi = 180 degrees , with a well depth of 716 microE(h). Two other minima were found for canted and X-shaped configurations with potential energies around -596 and -629 microE(h), respectively. Hexadecapole moments of monomers play an important role in the anisotropy of interaction energy that is highly R-dependent at intermediate intermolecular distances. The quality of potentials was tested by computing values of the second virial coefficient. The fitted MP4 potential has a more reasonable agreement with experimental values.     

Application of in-situ attenuated total reflection-Fourier transform infrared spectroscopy for the understanding of complex reaction mechanism and kinetics: formic acid oxidation on a Pt film electrode at elevated temperatures

The potential of in-situ Fourier transform infrared (FTIR) spectroscopy measurements in an attenuated total reflection configuration (ATR-FTIRS) for the evaluation of reaction pathways, elementary reaction steps, and their kinetics is demonstrated for formic acid electrooxidation on a Pt film electrode. Quantitative kinetic information on two elementary steps, formic acid dehydration and CO(ad) oxidation, and on the contributions of the related pathways in the dual path reaction mechanism are derived from IR spectroscopic signals in simultaneous electrochemical and ATR-FTIRS measurements over a wide temperature range (25-80 degrees C). Linearly and multiply bonded CO(ad) and bridge-bonded formate are the only formic acid related stable reaction intermediates detected. With increasing temperature, the steady-state IR signal of CO(ad) increases, while that of formate decreases. Reaction rates for CO(ad) formation via formic acid dehydration and for CO(ad) oxidation as well as the activation energies of these processes were determined at different temperatures, potentials, and surface conditions (with and without preadsorbed CO from formic acid dehydration) from the temporal evolution of the IR intensities of CO(ad) during adsorption/reaction transients, using an IR intensity-CO(ad) coverage calibration. At potentials up to 0.75 V and temperatures from 25 to 80 degrees C, the "indirect" CO pathway contributes less than 5% (at potentials < or =0.6 V significantly below 1%) to the total Faradaic reaction current, making the "direct" pathway by far the dominant one under the present reaction conditions. Much higher activation energies for CO(ad) formation and CO(ad) oxidation compared with the effective activation energy of the total reaction, derived from the Faradaic currents, support this conclusion.     

Rapid evaluation of the binding energies in hydrogen-bonded amide-thymine and amide-uracil dimers in gas phase

The binding energies and the equilibrium hydrogen bond distances as well as the potential energy curves of 48 hydrogen‐bonded amide–thymine and amide–uracil dimers are evaluated from the analytic potential energy function established in our lab recently. The calculation results show that the potential energy curves obtained from the analytic potential energy function are in good agreement with those obtained from MP2/6‐311+G** calculations by including the BSSE correction. For all the 48 dimers, the analytic potential energy function yields the binding energies of the MP2/6‐311+G** with BSSE correction within the error limits of 0.50 kcal/mol for 46 dimers, only two differences are larger than 0.50 kcal/mol and the largest one is only 0.60 kcal/mol. The analytic potential energy function produces the equilibrium hydrogen bond distances of the MP2/6‐311+G** with BSSE correction within the error limits of 0.050 Å for all the 48 dimers. The analytic potential energy function is further applied to four more complicated hydrogen‐bonded amide–base systems involving amino acid side chain and β‐sheet. The values of the binding energies and equilibrium hydrogen bond distances obtained from the analytic potential energy function are also in good agreement with those obtained from MP2 calculations with the BSSE correction. These results demonstrate that the analytic potential energy function can be used to evaluate the binding energies in hydrogen‐bonded amide–base dimers quickly and accurately. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Determination of the solid-fluid coexistence of the n - 6 Lennard-Jones system from free energy calculations

The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T? = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.     

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.     

Pseudopotential investigation of some alkali metal molecules

The effect of electron correlation on the results of pseudopotential calculations was examined using a simple analytical semiempirical pseudopotential and a correlated floating-type one-center wave function. Investigations were performed for the XH alkali metal hydride molecules (X ? Na, K, Rb, Cs). The inclusion of the electron correlation in the ground state proved important for the calculation of the dissociation and ionization energies, but it is less significant for the determination of the equilibrium nuclear distances. The ground state potential energy curves are also determined.     

Towards a complete basis set limit of Hartree–Fock method: correlation-consistent versus polarized-consistent basis sets

In this paper the convergence pattern of correlation-consistent (cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree–Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules.