Collisions colinear

The model which has received the greatest theoretical attention is that of a colinear collision between an atom A and a diatomic molecule BC (Figure 3.1). The molecule is usually assumed to be a harmonic oscillator, and the interaction potential VAB an exponential repulsion. The model was first... 

Figure 3.1 Colinear collision of an atom A with a diatomic molecule BC. Impact is presumed to be between atoms A and B.

Exact calculations of AE have been carried out by Kelley and Wolfsberg [19] for colinear collisions between an atom and a diatomic molecule. The oscillator potential was considered to be both harmonic and Morse-type, and the interaction between the colliding pair was taken both as an exponential repulsion and as a Lennard-Jones 6 12 potential. Two important conclusions were reached First, when the initial energy of the oscillator increases, the total energy transferred from translation to vibration, AE, decreases. Second, the effect of using a Morse-oscillator potential in place of the harmonic oscillator was generally to decrease AE, often by more than a factor of 10. 

The colinear collision problem of atom A colliding with a molecule BC was first attempted quantum mechanically by Zener [14,15] and then by Jackson and Mott [28] for the purpose of investigating thermal accommodation coefficients for atoms impinging on solid surfaces. An exponential repulsion was utilized, along with the harmonic-oscillator approximation. The distorted-wave (DW) method was employed to obtain a 1 — 0 transition probability of the form... 

The case 4+1 — 80, representing, for example, He + HBr, was shown by Kelley to illustrate the difficulty with which vibrational energy is transferred when the Br end is struck (m = 0.0008) as opposed to the values obtained when the H atom is struck (m = 3.8). It was also demonstrated that, considering all values of 0O for this case, the predominant deexcitation mechanism is intramolecular V-R transfer. Since this V-R process depends upon particle masses and collision energy in a manner different from the V-T process, a colinear collision model will not always lead to a proper description of vibrational deexcitation. This conclusion probably applies as well to more complicated systems, such as noble gas collisions with CH4. 

Thus the activation energy for the formation of DF is minimal when F and D2 collide colinearly. At low collision energy most molecules DF are observed backwards, in vibrational states v = 2, 3 and 4, at weak total angular momentum, etc... All the theoretical studies of this reaction, but one use classical trajectories. 

For instance, H -t H2 — Hj -I- H was studied in 3-dimensions within a model where the vibrational states were reduced to a single one for each of the three possible product molecules ° At low collision energy (less than the classical energy threshold) the reaction cross section is non zero because of tunneUing. For the same reaction studied colinearly the following conclusions emerge... 

We will now consider the more general collision problem in which the nuclear potential energy for a given electronic state of the interacting system is a function V(x, X2) of two nuclear coordinates x and X2 Such is the case of the colinear three-atomic reaction... 

A different approach in the treatment of colinear collisions makes use of curvilinear coordinates which have been first introduced in a practically useful way by MARCUS /80/. A curve L in the nuclear configuration plane, conveniently chosen as the "reaction coordinate , is used to define the position of any point A by two variables - the distance x along 1 and the shortest distance y of A from L The curve L coincides with the reaction path in both the reactants and products regions so that the local coordinate system (x,y) goes smoothly from that appropriate for reactants to that appropriate for products. 

We have considered in some detail several exact and approximate methods for calculation of transition probabilities (or cross sections) in colinear collisions. There exists now a great variety of other methods proposed during the last few years. Some of them will be mentioned here only briefly. 

Our detailed many-dimensional consideration of the collision problem is restricted to the simplest case of colinear atom-diatom collisions, since considerable progress in its theoretical study has been made in recent time ... 

Pig,15 Accurate quantum-mechanical reaction probabilities Wnn for the H2 + H reaction as a function of total energy (E) and initial relative translation energy (Ex). Curves 1, 2 and 3 correspond to colinear, complanar and three-dimensional treatment of collisions (according to SCHATZ and KUPPERMANN /lie/). 

Considering, for example, the simple case of the colinear collision A + BC, one introduces the distance R between atom A and the center-off-mass of molecule BC, the internuclear separation r in the molecule BC and the corresponding momenta p and p. The wave... 

The al ini. o potential energy surface of SHAVITT, STEVENS, MINN, and KARPLUS (SSMK), as modified by TRUHLAR and KUPPERMANN / 4/ has been used by these authors for exact quantal calculations of the transition probabilities for the colinear H2 + H and D2 + D reactions. On the basis of these data, CHRISTOV and PARLAPANSKI /132/ directly computed the values of the factor le. in the collision theory expression (23.IV) in the temperature range 300-1000 K. The corresponding values of the factor in the statistical expression (67,... 

We will first consider a strictly colinear reaction described by the scaled SSMK potential energy surface /32b/. The collision diameter can be estimated based on a single experimental value of the rate constant (for instance, for the H2 + H reaction v = 1,15.10 cm mole" sec" at lOOO K). Prom equation (23.IV) with E = 9,8 kcal/mole and 92.= 6,53 (Table I), we find that d = 1,40 The calculations of CHRISTOV and PARLAPANSKI /132/ show, however, that with this value for d the rate constant at room temperature (T = 300 K) is overestimated by two orders of magnitude if the corresponding value for 96= 970 from Table VII is used. It may be concluded that the SSMK... 

It is noteworthy that the half-empirical Sato-Weston potential energy surface /27/, corrected for the bent configurations of the collision complex /71b/, proves to be more adequate to reality than the ab initio SSMK potential surface, which refers to strictly colinear collisions. 

H2 + H reaction according to quantum collision theory based on Porter-Karplus potential surface. Curves 1, 1 and correspond to colinear, complanar and... 

Most of the classical, semiclassical and quantal calculations of transition probabilities (or cross sections) refer to colinear atom-diatom gas phase reactions. However, a consideration of the nonlinear collisions seems to be very important for an adequate description of the chemical elementary processes in physical space. Quite recently, encouraging progress in this direction has been made / /. 

Because of the inelastic collisions with electrons, the metastable atomic beam is tilted with an angle of 20°, with respect to the incident atomic beam. The tilting from the incident beam is used to make the metastable beam colinear with the Laser beams. This colinear geometry... 

The translational to vibrational energy cross section depends critically on the collision time with respect to the period of the molecule vibration ty. Consider a colinear collision of an atom A with a molecule i5(l)- (2), where 1 and 2 number the atoms. When the collision time is short compared to the vibrational period ty during the period of interaction atom B(2) does not experience any effect of the... 

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