Diatomics-in-molecule surfaces

An exceedingly accurate Cl calculation on the surface of H3 recently has appeared [239]. Cl calculations on the avoided intersection of potential energy surfaces for H+ + H2 and H + Hi [240] compared surprisingly well to the earlier diatomics-in-molecules surface of Preston and Tully [241]. Cl calculations were reported for He + H2 B E+, and compared to SCF calculations for He + X 2+ H2 and b H2 [242]. Cl calculations have... 

The trajectory surface hopping method is an additional extension of the classical trajectory method. Potential energy surfaces are constructed for each electronic state involved in the collision. In addition, a function has to be obtained that defines the locus of points at which hops between surfaces can occur. Still another function is necessary which gives the probability of such jumps as a function of nuclear positions and velocities.28 Diatomics-in-molecules surfaces approximated the two lowest singlet potential surfaces of H3. The surfaces have been shown30 to be in good agreement with accurate ab initio calculations by Conroy.31... 

Aside from the apparent theoretical simplicity of this reaction, and its importance in combustion processes, this reaction is also the prototypical oxygen atom reaction, and as such it provides a model for many oxidation reactions. Table 1 summarizes the potential surface saddle point parameters of eight surfaces (or fits to surfaces) that have been recently determined. (This table was taken from reference 17.) These surfaces include two LEPS surfaces (WDH and JW ), a diatomics-in-molecules surface (DIM ), a bond-energy-bond-order (BEBO) surface,two ah initio surfaces (HML and POLCI ), a fit to the ah initio surface of reference 90 (SL ), and a fit to that of reference 91 (POLCI-RMOS ). Considering that... 

Fig, 2, Same as Fig. 1 but for the rotated—Morse-oscillator-spline fit to the diatomics-in-molecules surface of Whitlock, Muckerman, and Fisher (reference 4). 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

DIM (diatomics-in-molecules) a semiempirical method used for representing potential energy surfaces... 

A function, which is similar to the London equation and based on the diatomic-in-molecules approach was first used by Kuntz to fit the ab initio surface for collinear reaction... 

Statistical theories, such as those just described, are currently the only practical approach for many ion-neutral reactions because the fine details of the collision process are unknown all the information concerning the dynamics of collision processes is, in principle, contained in the pertinent potential-energy surfaces. Although a number of theoretical groups are engaged in accurate ab initio calculations of potential surfaces (J. J. Kaufman, M. Krauss, R. N. Porter, H. F. Schaefer, I. Shavitt, A. C. Wahl, and others), this is an expensive and tedious task, and various approximate methods are also being applied. Some of these methods are listed in Table VI, for example, the diatomics-in-molecules method (DIM). 

Tully, J. C. Diatomics-in-molecules potential energy surfaces. II. Nanadiabatic and spin-orbit interactions, J. Chem.Phys., 59 (1973) 5 122-5134. 

DIM Diatomics in molecules. A semiempricial method used to construct potential energy surfaces of polyatomic molecules from the energy of the diatomic fragments. 

The semi-empirical diatomics-in-molecules method370 has been used to study the PE surface of linear HeH, 380 and later it was further used in studies of a variety of first-row hydrides, including linear BeH2.381 BeHa has been rather extensively... 

Kuntz et al [60] using the diatomics-in-molecule (DIM) method constructed three slightly dfferent DIM PESs for the two lowest states. All these DIM PESs exhibit no barrier to reaction (insertion or abstraction) on the lowest surface. 

Quantum chemical information is needed in several areas. For example repulsive potentials are missing for many pairs of atoms that have otherwise been well studied. These repulsive potentials enter in the diatomics-in-molecules approach and in dynamical models. Whenever potential surfaces cross (or pseudo-cross) we need the intersurface couplings in order to understand whether electronic motions are adiabatic or diabatic. A priori information on conformations of long-lived complexes would be helpful, because they... 

The calculation includes three diabatic potential energy surfaces obtained using the diatomic in molecules (DIM) method (36). Using this 2D quantum treatment in hyperspher-ical coordinates the nonadiabatic problem can be solved also for problems involving more than three diabatic surfaces. 

In those cases where the dynamics cannot be adequately described by motion on a single adiabatic potential-energy surface, additional dynamical assumptions must be made. The pioneering technique is the trajectory surface hopping (TSH) method (55,56) of Tully and co-workers. In these calculations, the classical trajectories are integrated on an adiabatic potential energy surface (typically generated by diatomics in molecules, DIM... 

The first and second columns of the Tables give the reaction and potential energy surface used. Standard abbreviations are employed for the names of the potential surfaces. Thus. PK = Porter-Karplus potential surface No 2 for H+H2. LSTH = Liu-Siegbahn-Truhlar-Horowitz potential surface for H+Hg. YLL = Yates-Lester-LIu potential surface for H+Hp. LEPS = extended London-Eyring-Polanyi-Sato potential surface and DIM = diatomics-in-molecules potential surface. 

In this Section we discuss and compare the results obtained using the various theories of Section 3, and a variational transition state theory with a tunnelling correction [9]. The reaction we concentrate on is H+BrH - HBr+H. We emphasize the rate constants, but also discuss reaction cross sections. The potential energy surface we used in the H+BrH computations is of a semiempirical diatomics in molecules type, the form of which (called DIM-3C) is due to Last and Baer [ll]. The surface contains a three-centre integral term that has been parameter-ised [33] by comparing ESA-CSA calculations with an experimental [3] room temperature rate constant for the D+BrH -) DBr+H reaction. The minimum potential energy path is collinear, and there is a strong... 

The problem of how to account for different levels of accuracy in calculations at different points on the potential energy surface goes back a long way and there have been many partial solutions. The atom-in-molecules method of Moffitt [9], the diatomics-in-molecules method of Ellison [10], and the counteipoise model of Boys [11] are all successful in some respects. Unfortunately none of them are helpful for the most commonly met problem by those who are ti ng to fit potential functions to data, which is how to join up data produced by different methods on different regions of the surface. I believe there is no answer to this except scientific judgement... 

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