By Canuto S., Sabin J.R. (eds.)

ISBN-10: 0123808987

ISBN-13: 9780123808981

Advances in Quantum Chemistry offers surveys of present advancements during this swiftly constructing box. With invited reports written via prime foreign researchers, every one proposing new effects, it presents a unmarried car for following development during this interdisciplinary sector. * Publishes articles, invited reports and court cases of significant foreign meetings and workshops * Written by way of top foreign researchers in quantum and theoretical chemistry * Highlights very important interdisciplinary advancements

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However, another problem remains since no general analytical expression exists for the electronic transition dipole moment: hence this integral must be approximated. This can be done by expanding the transition dipole moment in a Taylor series of the normal 30 V. Barone et al. coordinates (either the set Q’ of the final state or the set Q of the initial state). In our approach the expansion on Q’ has been chosen ! N @ N X N X @ 2 mif 1X if 0 0 0 if ðQ Þ ’ if ðQ0 Þ þ Q0k Q0l þ . . ; ð23Þ 0 Qk þ 2 0 @Q0 @Q @Q k k l k¼1 k¼1 l¼1 0 where Q00 refers to the equilibrium geometry of the final electronic state, while N is the number of normal modes.

Our approach is set up in the Born–Oppenheimer approximation; thus the wave function of each state can be expressed as a product of a nuclear n and an electronic e wave functions: hCi jmjCfi ¼ h n ej mj 0 0 e n i: ð20Þ The electric dipole moment can be separated into an electronic part me and a nuclear part mn. s. in Eq. (21) vanishes. As a consequence, the transition dipole moment integral depends on the nuclear wave functions and on the electronic transition moment mif ¼ h e jme j 0e i. Equation (21) can then be written as hCi j m jCf i ¼ h nj mif j 0 n i: ð22Þ Application of the Eckart conditions [76] allows to minimize the coupling between the rotational and vibrational motions of the nuclei in a molecule, and as much as possible separate the nuclear wave function into rotational and vibrational contributions.

However, all the proposed corrections only affect the width and the shape of the IR bands, while the accuracy of the calculated frequencies still relies on the ability of the classical approach to describe the fundamental vibrations. In this regard, it is worth noting that hybrid density functional theory (DFT) functionals do perform reasonably well for a variety of molecular systems and represent the method of choice for large biological systems. Eventually, more sophisticated post-Hartree–Fock methods can be employed to correct the absolute frequencies of specific vibrational modes, while DFT-based approaches can be still used to obtain accurately solvent shifts.

### Combining Quantum Mechanics and Molecular Mechanics by Canuto S., Sabin J.R. (eds.)

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