Vibrational quantum mechanical calculation

There are three steps in carrying out any quantum mechanical calculation in HyperChem. First, prepare a molecule with an appropriate starting geometry. Second, choose a calculation method and its associated (Setup menu) options. Third, choose the type of calculation (single point, geometry optimization, molecular dynamics, Langevin dynamics, Monte Carlo, or vibrational analysis) with the relevant (Compute menu) options. 

In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

Values for the partial charges of atoms can be derived from quantum mechanical calculations, from the molecular dipole moments and from rotation-vibration spectra. However, often they are not well known. If the contribution of the Coulomb energy cannot be calculated precisely, no reliable lattice energy calculations are possible. 

Alper, J. S., H. Dothe, and M. A. Lowe. 1992. Scaled Quantum Mechanical Calculation of the Vibrational Structure of the Solvated Glycine Zwitterion. Chem. Phys. 161, 199-209. 

Alper, J. S., H. Dothe, and M. A. Lowe. 1992. Scaled Quantum Mechanical Calculation of the Vibrational Structure of the Solvated Glycine Zwitterion, Chem. Phys. 161, 199-209. Barron, L. D., A. R. Gargaro, L. Hecht, P. L. Polavarapu. 1991. Experimental and Ab Initio Theoretical Vibrational Roman Optical Activity of Alanine, Spectrochimica Acta 47A, 1001-1016. 

The stable configuration for the H—P pair is predicted by all of the quantum-mechanical calculations to have a hydrogen located at the silicon antibonding site (Si—AB). A model is shown in Fig. 7b, where a phosphorus lone pair lies along the (111) axis and is energetically in the valence band. Here, the theoretical predictions of the H vibrational frequency have been mixed, with the H—Si interaction and frequency overestimated by Hartree-Fock and Hartree-Fock-like methods and lower by local-density calculations. 

Quantitative estimates of E are obtained the same way as for the collision theory, from measurements, or from quantum mechanical calculations, or by comparison with known systems. Quantitative estimates of the A factor require the use of statistical mechanics, the subject that provides the link between thermodynamic properties, such as heat capacities and entropy, and molecular properties (bond lengths, vibrational frequencies, etc.). The transition state theory was originally formulated using statistical mechanics. The following treatment of this advanced subject indicates how such estimates of rate constants are made. For more detailed discussion, see Steinfeld et al. (1989). 

The unusual position of the C =C+ stretching vibration in the IR spectra of 9b [CBnH6Br6] is in agreement with the results from quantum mechanical calculations. A frequency calculation at the B3LYP/6-3 G(d) level of theory... 

The Levich—Dogonadze—Kuznetsov (LDK) treatment [65] considers that the only source of activation is the polarization electrostatic fluctuations (harmonic oscillations) of the solvent around the reacting ion and uses essentially the same model as the Marcus—Hush approach. However, unlike the latter, it provides a quantum mechanical calculation of both the pre-exponential factor and the activation energy but neglects intramolecular (inner sphere) vibrations (1013—1014 s 1). 

Quantum-mechanical calculations for individual initial vibrational states enhancement of cross section by vibrational excitation 448... 

Fig. 3.2. Two-dimensional potential energy surface V(R, 7) (dashed contours) for the photodissociation of C1CN, calculated by Waite and Dunlap (1986) the energies are given in eV. The closed contours represent the total dissociation wavefunction tot R,l E) defined in analogy to (2.70) in Section 2.5 for the vibrational problem. The energy in the excited state is Ef = 2.133 eV. The heavy arrow illustrates a classical trajectory starting at the maximum of the wavefunction and having the same total energy as in the quantum mechanical calculation. The remarkable coincidence of the trajectory with the center of the wavefunction elucidates Ehrenfest s theorem (Cohen-Tannoudji, Diu, and Laloe 1977 ch.III). Reprinted from Schinke (1990).

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