The atom–bond pairwise additive approach, recently introduced by us to describe the potential energy surface for atom–molecule cases, is extended here for the first time to molecule–molecule systems. The idea is to decompose the van der Waals interaction energy into bond–bond pair contributions. This must be considered an improvement with respect to the familiar atom–atom pairwise additive representation since, still using a simple formulation, it indirectly accounts for three body effects. Such an approach also allows to include, in a straightforward way, the effect of the bond length on the intermolecular interaction energy. Cases of study are the weakly bound complexes involving the H2 and N2 molecules, namely N2–H2 and N2–N2, here described as a single bond–bond pair. For both systems ab initio calculations and experimental molecular beam scattering data, as well as second virial coefficients, have been employed to test the accuracy of the chosen representation of the interaction and to improve the obtained potential energy surfaces. The results of this work are important also for the generalization to the cases involving molecular ions and polyatomic molecules.

A bond–bond description of the intermolecular interaction energy: the case of weakly bound N2–H2 and N2–N2 complexes

Five-dimensional ab initio potential energy surfaces (PESs) for CO2–H2 that explicitly incorporate dependence on the Q3 asymmetric-stretch normal-mode coordinate of the CO2 monomer and are parametrically dependent on its Q1 symmetric-stretch coordinate have been calculated. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v3(CO2)=0, and 1 to the Morse/long-range potential function form. These fits to 23 113 points have root-mean-square (rms) deviations of 0.143 and 0.136 cm−1, and require only 167 parameters. The resulting vibrationally averaged PESs provide good representations of the experimental infrared data: for infrared transitions of para- and ortho-H2–CO2, the rms discrepancies are only 0.004 and 0.005 cm−1, respectively. The calculated infrared band origin shifts associated with the ν3 fundamental of CO2 are −0.179 and −0.092 cm−1 for para-H2–CO2 and ortho-H2–CO2, in good agreement with the (extrapolated) experimental values of −...

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Analytic Morse/long-range potential energy surfaces and predicted infrared spectra for CO2–H2

A three-dimensional, analytic potential energy surface for CO2–He that explicitly incorporates its dependence on the Q3 asymmetric-stretch normal-mode coordinate of the CO2 monomer has been obtained by least-squares fitting new ab initio interaction energies to a new three-dimensional Morse/Long-Range (3D-MLR) potential function form. This fit to 2832 points has a root-mean-square (RMS) deviation of 0.032 cm−1 and requires only 55 parameters. The resulting pure ab initio potential provides a good representation of the experimental microwave and infrared data: for 51 pseudo microwave and 49 infrared transitions the RMS discrepancies are 0.0110 and 0.0445 cm−1, respectively. Scaling this surface using only two morphing parameters yields an order of magnitude better agreement with experiments, with RMS discrepancies of only 0.0025 and 0.0038 cm−1, respectively. The calculated infrared band origin shift associated with the ν3 fundamental of CO2 is 0.109 cm−1, in good agreement with the (extrapolated) experimental value of 0.095 cm−1.

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Analytic three-dimensional ‘MLR’ potential energy surface for CO2–He, and its predicted microwave and infrared spectra

Involving the intramolecular vibrational coordinates in the potential energy surfaces and bound states calculations for van der Waals complexes is essential for fully predicting the infrared spectra of the complexes. In this review, we have summarized our recent researches on the potential energy surfaces and predicted infrared spectra of the van der Waals complexes containing a linear molecule and a rare-gas atom or H2 by explicitly involving the dependence of one intramolecular vibrational coordinate related to the transitions in the infrared spectra. By incorporating the potential-optimized discrete variable representation grid points for that coordinate in both potential energy surfaces and bound states calculations for the Kr–H2, He–N2O, H2–N2O, and H2–CO2 complexes, the shift of the band origin, transition frequencies, and line intensities in the observed infrared spectra are reproduced well. Examples of other studies, Ar–HF and H2–OCS, are also reviewed briefly.

Potential energy surfaces and predicted infrared spectra for van der Waals complexes: dependence on one intramolecular vibrational coordinate

A new exchange-Coulomb semiempirical model potential energy surface for the He–N2 interaction has been developed. Together with two recent high-level ab initio potential energy surfaces, it has been tested for the reliability of its predictions of second-virial coefficients and bulk transport phenomena in binary mixtures of He and N2. The agreement with the relevant available measurements is generally within experimental uncertainty for the exchange-Coulomb surface and the ab initio surface of Patel et al. [J. Chem. Phys. 119, 909 (2003)], but with slightly poorer agreement for the earlier ab initio surface of Hu and Thakkar [J. Chem. Phys. 104, 2541 (1996)].

Accuracy of recent potential energy surfaces for the He-N2 interaction. I. Virial and bulk transport coefficients.

An improved three-dimensional potential energy surface for the H2–Kr system is determined from a direct fit of new infrared spectroscopic data for H2–Kr and D2–Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the “secular equation perturbation theory” method used in previous analyses of H2–(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the “iterative secular equation” method was developed which implements direct Hellmann–Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.

A reliable new three-dimensional potential energy surface for H2–Kr

Use of a simple semiclassical estimate of Bessel function phase for arbitrary argument avoids the modulo π errors which the conventional approach tends to introduce into the calculation of absolute quantal phase shifts for high partial waves. This has significant implications for the direct quantum mechanical calculation of second virial coefficients at high temperatures.

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Hua Wei

Papers

A reliable new three-dimensional potential energy surface for H2–Kr

Calculation of absolute scattering phase shifts