ABC Molecules

ABC Molecules.—There have been relatively few investigations of this type of molecule. LiNO and LiON were studied by Peslak, Klett, and David,511 together with FNO and FON. The lithium species had almost identical energies. Clearly, studies using more extensive basis sets are needed to settle the question of the relative stability of the various isomers. FNO is predicted to be more stable than FON, and a description of the bonding via the population analysis was presented. 

NSF has been studied at the minimal-basis-set level, and the results were correlated with the photoelectron spectrum.663 

Several recent papers, dealt with elsewhere, have detailed the investigations on metal carbonyls, usually via SCF calculations. An exception to this is a GVB study of the simple carbonyls TiCO and TiCO+, using a minimum STO basis set plus Ti 4p- 

Solouki, P. Rosmus, and H. Bock, Chem. Phys. Letters, 1974, 26, 20. 

In concluding this section, we note the results of a series of calculations on ONF, using a small basis set, by Pulay and co-workers,559 who evaluated the force constants and showed that reliable results may be obtained even with a (5s2p) basis set. 

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Figure Al.6.26. Stereoscopic view of ground- and excited-state potential energy surfaces for a model collinear ABC system with the masses of HHD. The ground-state surface has a minimum, corresponding to the stable ABC molecule. This minimum is separated by saddle points from two distmct exit chaimels, one leading to AB + C the other to A + BC. The object is to use optical excitation and stimulated emission between the two surfaces to steer the wavepacket selectively out of one of the exit chaimels (reprinted from [54]).

Figure 6.5 Potential energy diagram for stable ABC molecule...

R. D. Levine The coherence that is being discussed by Profs. Troe and Zewail is due to a localized vibrational motion in the AB diatomic product of a photodissociation experiment ABC — AB + C. Such experiments have been done both for the isolated ABC molecule and for the molecule in an environment. As the fragments recede, effective coupling of the AB vibrational motion to the other degrees of freedom can rapidly destroy the localized nature of the vibrational excitation. 

Compounds like 88 (Fig. 25a), in which the Rp-segments are decoupled from the rod-like core by longer aliphatic spacers, can be regarded as polyphilic ABC molecules which are expected to lead to triply segregated smectic phases as shown in Fig. 19c. However, in compound 88, for example, the SmA-phase is composed of only two sets of distinct sublayers, though there are three mutually incompatible... 

The possible dissociation channels for the fragmentation of a triatomic molecule were discussed in Section 1.4. The linear ABC molecule can fragment into three chemical channels, A+B+C, A+BC(n), and AB(n )+C with the diatoms being produced in particular vibrational states denoted by quantum numbers n and n, respectively. Furthermore, each of the fragment atoms and molecules can be created in different electronic states. The total energy Ef = Ei + hu is the same in all cases and therefore the different channels are simultaneously excited by the monochromatic light pulse. The dissociation channels differ merely in the products and in the way the total energy partitions between translation and vibration. 

The six-dimensional Wigner distribution function for the ABC molecule in its lowest state is then a product of six Gaussians,... 

Reactions in a condensed phase are never isolated but under strong influence of the surrounding solvent molecules. The solvent will modify the interaction between the reactants, and it can act as an energy source or sink. Under such conditions the state-to-state dynamics described above cannot be studied, and the focus is then turned to the evaluation of the rate constant k(T) for elementary reactions. The elementary reactions in a solvent include both unimolecular and bimolecular reactions as in the gas phase and, in addition, bimolecular association/recombination reactions. That is, an elementary reaction of the type A + BC —> ABC, which can take place because the products may not fly apart as they do in the gas phase. This happens when the products are not able to escape from the solvent cage and the ABC molecule is stabilized due to energy transfer to the solvent.4 Note that one sometimes distinguishes between association as an outcome of a bimolecular reaction and recombination as the inverse of unimolecular fragmentation. 

The calculations on unsymmetrical ABC molecules are more difficult. Wagner used unsymmetrical group orbitals for the end atoms = siny.prrg + cos y./>7T(, = cosy.J Tr — smy-pTr. . 

The bending vibration of a linear ABC molecule may be treated as a two-dimensional isotropic harmonic oscillator. The v,l) basis set is particularly convenient, where v and l are respectively the vibrational and vibrational angular momentum quantum numbers. The allowed values of l are —v, —v + 2,. .. v. Since there are two quantum numbers, two pairs of creation, annihilation operators are needed to generate all basis states from the v = 0, 1=0) zero-point state. These are, following the notation of Cohen-Tannoudji, et al., (1977), a, ay and at,a9, where... 

In an indirect reaction [2] A + BC —t B-A-C —t AB + C or AC + B. In a first step, the A atom inserts into the BC diatom forming an ABC complex. Two new bonds (AB and AC) are formed while the BC bond is broken. Then the complex dissociates with a breaking of one of these two bonds. This reaction mechanism is called insertion. In contrast with abstraction reactions, all three bonds in the triatomic molecule ABC participate actively in the reaction. Two bonds are formed teni] )orarily while only one exists for the reactants and products. Thus, the potential energy surface involves a very deep well (several eV) which correspond to a stable ABC molecnle or radical. When the lifetime of the ABC molecule is larger than its rotational period, angular distributions of the products are symetric with a backward/forward peak and the population of rovibrational states of the products presents a statistical character. 

Insight about the dynamics of a unimolecular reaction can be obtained by examining the reaction s potential energy contour map. Usually this is at best only a qualitative analysis. However, it can be made quantitative for a linear triatomic ABC molecule by using skewed and scaled coordinates (Glasstone et al., 1941 Levine and Bernstein, 1987). The significance of these coordinates becomes readily apparent by considering the internal coordinate classical Hamiltonian for the linear ABC molecule that is. 

In these equations rj and 2 are the AB and BC intemuclear separations, respectively, and M is the total mass. Because of the r,r2 coupling term in Eq. (3.5) and different values for the masses, the intramolecular motion of the linear ABC molecule cannot be studied by simply inspecting the molecule s ( 5, 2) potential energy contour map. However, if the coordinates r, and rj are transformed, so that the kinetic energy is written as... 

There is a pair of terms of the above form for each nucleus with non-zero spin present in the molecule. As before, symmetry can be used to reduce the number of non-zero components of the traceless tensor (ajS)j. For a Cj, molecule (ABj) with a single non-zero spin nucleus, there are 3 non-zero components (aa)j, (bb), (cc)j of which 2 are independent since (aa)j -I- (bb)j -1- (cc), equals zero. For the planar ABC molecule, the additional components ab)j and (ba)j are non-zero. In all analyses performed so far, it has been assumed that these components are equal. It is not clear that this is so and if not, what combinations of parameters are determinable. The (ed>)j component is also non-zero for an AB2 molecule with 2 equivalent nuclei of non-zero spin. If the nuclear spins are /j and /j, the dipolar Hamiltonian is... 

The absorption of the photon in the first step leads to electronic excitation of the ABC molecule. Because it takes only a very short time to absorb a photon, there is no time for the nuclei to move. This implies, that the nuclear frame of the stable ground state molecule is conserved in the excitation step. This step is essentially electronic motion an electron is promoted to a higher lying orbital. Immediately after absorption the excited molecule has therefore the same nuclear configuration as the ground state, but a very different electronic shell. 

Fig.6 shows an example for the fragmentation of an ABC molecule, in which a force located in the ABC-plane leads to the excitation of planar rotational motion in the AB product. Planar forces are expected for example from antibonding orbitals that are symmetric to the nuclear plane. 

Fig. 10 shows the effect of different bond lengths on the vibrational product state distribution. In the stable ABC molecule the AB bond leggth (vq) is assumed to be smaller than in the isolated AB molecule (r ). The wavefunction vi>, describing the vibration of AB in the stable ABC molecule, is shown in the upper part. The wavefunctions v>, describing the free motion of AB, are plotted in the lower part for different v. The overlap for different v represents the probability for the formation of AB in different vibrational states v. Because there is only overlap with states for v larger than 2, high vibrational excitation results in AB. 

This may be considered from a somewhat different point of view. If atom C is eliminated from the ABC molecule without final state interaction, the motion of AB, that was originally hindered by the presence of the C-atom, becomes free and leads to vibrational excitation in AB. This is the physical content described by the matrix element . 

To illustrate how we obtain the normalized eigenvectors for molecular vibrations, we resume our discussion of the linear ABC molecule. When specialized to the more symmetrical case of linear ABA in which the end masses and force constants are equal (uia = ntc and ki = k2= k), the secular determinant roots A in Eq. 6.18 become... 

The force constants of the H-C and C-N bonds in linear HCN are 5.8 X 10 and 17.9 x 10 dyne/cm, respectively. Use the treatment of the linear ABC molecule in Section 6.1 to predict the HCN stretching frequencies in cm Compare these with the actual stretching frequencies, 2062 and 3312cm and comment on the validity of the harmonic approximation to the vibrational potential. 

FIGURE 14.30 Normal modes of vibration for symmetric (ABA) and asymmetric (ABC) linetir tri-atomic molecules. In both cases, the vibrations labeled V2 are doubly degenerate, because there are two equivalent vibrations that are perpendicular to each other. For the symmetric molecule, only V2 and Vj are IR-active. For the ABC molecule, all three vibrations are IR-active. 

Yamauchi et al. (2003, 2005) perfonned 3D observation of a cylindrical morphology of a PS-PI-PDMS p-ABC using the electron tomography technique and pointed out that the cylinders are curved along the cylindrical axes resulting in the small grain size. The curving tendency of the cylinders was attributed to the frustration of the p-ABC molecules... 

The LEP(S) functional form provides an explicit example of a conical intersection. Generally, the two surfaces represented by Eq. (5.3) are quite far apart. The lower surface has a barrier for atom exchange. The upper surface has a well corresponding to a bound but electronically excited ABC molecule. The conical intersection is when the barrier reaches all the way up to the bottom of the well, Figure 5.8. 

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