A method is described for constructing analytical potentials for the ground states of stable triatomic species from spectroscopic data. The method leads to potentials which reproduce both the equilibrium and asymptotic properties of the molecule. Application of the method to H₂O leads to a potential surface which agrees with known experimental and theoretical data. For example, the predicted reaction coordinate for the C _2v insertion of O(¹D) into H₂ is in good agreement with published calculations.

An analytic potential for stable states of diatomic molecules is proposed V=–D_e(1 +a₁r+a₂r²+a₃r³)e^–a₁r. The constants a₁, a₂ and a₃ are obtained from the harmonic, cubic and quartic force constants. The potential is shown to be superior to the Hulburt–Hirschfelder potential when tested on a least-squares basis against the spectroscopic RKR potential.

[1] Developing a better understanding of single-/multiphase flow through reservoir rocks largely relies on characterizing and modeling the pore system. For simple homogeneous rock materials, a complete description of the real pore structure can be obtained from the pore network extracted from a rock image at a single resolution, and then an accurate prediction of fluid flow properties can be achieved by using network model. However, for complex rocks (e.g., carbonates, heterogeneous sandstones, deformed rocks), a comprehensive description of the real pore structure may involve several decades of length scales (e.g., from submicron to centimeters), which cannot be captured by a single-resolution image due to the restriction of image size and resolution. Hence, the reconstruction of a single 3-D multiple-scale model of a porous medium is an important step in quantitatively characterizing such heterogeneous rocks and predicting their multiphase flow properties. In this paper, we present a novel methodology for the numerical construction of the multiscale pore structure of a complex rock from a number of CT images/models of a carbonate sample at several length scales. The success of this reconstruction relies heavily on image segmentation, pore network extraction and stochastic network generation, which are provided by our existing software system, referred to as Pore Analysis Tools (PAT). Specifically, the statistical description of pore networks of 3-D rock images at multiple resolutions makes it possible for us to: (a) construct an arbitrary sized network which is equivalent in a specified domain, and (b) integrate multiple networks of different sizes into a single network incorporating all scales. Using multiscale networks of carbonate rocks generated in this manner, two-phase network modeling results are presented to show how the resulting flow properties are dependent on inclusion of information from multiple scales. These outcomes reinforce the importance of capturing both geometry and topology in the hierarchical pore structure for such complex pore systems. The example presented reveals that isolated large-scale (e.g., macro-) pores are mainly connected by small-scale (e.g., micro-) pores, which in turn determines the combined effective petrophysical properties (capillary pressure, absolute and relative permeability). It is also demonstrated that multi- (three) scale networks reveal the effects of the interacting multiscale pore systems (e.g., micropores, macropores, and vugs) on bulk flow properties in terms of two-phase flow properties.