Small Polyatomic Molecules

Exercise 1.8. Plot Eg as a function of R for the HF molecule in the presence of an external charge 10 A from the F atom. 

The approach described above for diatomic molecules can be extended to polyatomic molecules. We will outline here VB treatments and consider MO approaches only in a few selected cases in subsequent chapters. 

Diagonalizing the corresponding 2x2 secular equation and some algebraic manipulation gives the four-electron ground-state potential surface 

FIGURE 1.7. The potential energy surface of the CH4 + C1 supersystem for the collinear hydrogen abstraction reaction CH4 + Cl— CH3 + HC1. The counter lines are given in spaces of 10 kcal/mol and the coordinates in angstroms. 

Exercise 1.9. Evaluate the potential surface for the H+H2— H2 + H exchange reaction and determine the energy of the transition state obtained with r12 = r23 = 1.4 A relative to the minimum energy of the system when one hydrogen atom is at infinity. 

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Orr B J and Smith I W M 1987 Collision-induced vibrational energy transfer in small polyatomic molecules J. Rhys. Chem. 91 6106-19... 

Schinke R, Weide K, Heumann B and Engel V 1991 Diffuse structures and periodic orbits in the photodissociation of small polyatomic molecules Faraday Discuss. Chem. Soc. 91 31... 

Abstract. The development of modern spectroscopic techniques and efficient computational methods have allowed a detailed investigation of highly excited vibrational states of small polyatomic molecules. As excitation energy increases, molecular motion becomes chaotic and nonlinear techniques can be applied to their analysis. The corresponding spectra get also complicated, but some interesting low resolution features can be understood simply in terms of classical periodic motions. In this chapter we describe some techniques to systematically construct quantum wave functions localized on specific periodic orbits, and analyze their main characteristics. 

The development of these explicit-rjj methods has yielded a database of benchmark results for small polyatomic molecules. These calculations are listed as MP2-R12 and CCSD(T)-R12 in our tables. We have selected the version called MP2-R12/A as a benchmark reference for our study of the convergence to the MP2 limit. This is the version that Klopper et al. found to agree best with our interference effect. The close agreement with extrapolations of one-electron basis set expansions justifies this choice. 

This chapter assesses the performance of quantum chemical models with regard to the calculation of dipole moments. Several different classes of molecules, including diatomic and small polyatomic molecules, hydrocarbons, molecules with heteroatoms andhypervalent molecules are considered. The chapter concludes with assessment of the ability of quantum chemical models to calculate what are often subtle differences in dipole moments for different conformers. 

Diatomic and small polyatomic molecules O Molecules with heteroatoms A Hypervalent molecules... 

Table 10-1 Mean Absolute Errors in Dipole Moments for Diatomic and Small Polyatomic Molecules...

All density functional models exhibit similar behavior with regard to dipole moments in diatomic and small polyatomic molecules. Figures 10-6 (EDFl) and 10-8 (B3LYP) show clearly that, except for highly polar (ionic) molecules, limiting (6-311+G basis set) dipole moments are usually (but not always) larger than experimental values. 

Dipole moments for hydrocarbons are small (typically less than 1 debye), and provide a good test of different models to reproduce subtle effects. A small selection of data is provided in Table 10-2, for the same models used previously for diatomic and small polyatomic molecules. ... 

Table AlO-l Dipole Moments in Diatomic and Small Polyatomic Molecules. Hartree-Fock Models... 

Applications based on the even-tempered prescription (1) have shown that it can lead to atomic and diatomic Hartree-Fock ground state energies of an accuracy approaching that achieved in numerical Hartree-Fock calculations [4] It is conjectured that a comparable accuracy can be achieved for small polyatomic molecules [12], [13] by constructing basis sets according to the prescription established for diatomic molecules. Similar procedures can... 

R. Schinke. Photodissociation Dynamics Spectroscopy and Fragmentation of Small Polyatomic Molecules. Cambridge University Press, Cambridge (1995). 

Small polyatomic molecules involving single covalent bonds between adjacent atoms, e.g. P4 and S8. 

Theoretical calculation of a is not as straightforward as for, say, the dipole moment to find o one must include the applied electric field in the molecular Hamiltonian and calculate the resulting change in the molecular dipole moment. Theoretical values of the components of a have been calculated for several diatomic and small polyatomic molecules using a Hartree-Fock approach the calculated values are reasonably accurate. See Schaefer, pp. 243-250, for details.)... 

R. W. Field Prof. Rabitz, I like the idea of sending out a scout to map a local region of the potential-energy surface. But I get the impression that the inversion scheme you are proposing would make no use of what is known from frequency-domain spectroscopy or even from nonstandard dynamical models based on multiresonance effective Hamiltonian models. Your inversion scheme may be mathematically rigorous, unbiased, and carefully filtered against a too detailed model of the local potential, but I think it is naive to think that a play-and-leam scheme could assemble a sufficient quantity of information to usefully control the dynamics of even a small polyatomic molecule. 

K. Yamanouchi There are many kinds of small polyatomic molecules that emit detectable fluorescence in the energy region where they predissociate. Acetylene, SO2, and CS2 are examples of such molecules. The two processes, fluorescence emission and dissociation, are in general competing processes. 

PHOTODISSOCIATING SMALL POLYATOMIC MOLECULES IN THE VUV REGION RESONANCES IN THE 1E+-1E+ BAND OF OCS... 

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