Anharmonicity vibrational self-consistent-field

Starting from the normal mode approximation, one can introduce anharmonicity in different ways. Anharmonic perturbation theory [206] and local mode models [204] may be useful in some cases, where anharmonic effects are small or mostly diagonal. Vibrational self-consistent-field and configuration-interaction treatments [207, 208] can also be powerful and offer a hierarchy of approximation levels. Even more rigorous multidimensional treatments include variational calculations [209], diffusion quantum Monte Carlo, and time-dependent Hartree approaches [210]. 

Purely quantum studies of the fully coupled anharmonic (and sometimes nonrigid) rovibrational state densities have also been obtained with a variety of methods. The simplest to implement are spectroscopic perturbation theory based studies [121, 122, 124]. Related semiclassical perturbation treatments have been described by Miller and coworkers [172-174]. Vibrational self-consistent field (SCF) plus configuration interaction (Cl) calculations [175, 176] provide another useful alternative, for which interesting illustrative results have been presented by Christoffel and Bowman for the H + CO2 reaction [123] and by Isaacson for the H2 + OH reaction [121]. The MULTIMODE code provides a general procedure for implementing such SCF-CI calculations [177]. Numerous studies of the state densities for triatomic molecules have also been presented. 

The structure of this review is as follows. In Section 9.2, we briefly discuss methods for computing vibrational states of systems having several coupled vibrational degrees of freedom. This will also cover methods that were not yet adapted for direct use with ab initio potentials, since in our view, such extensions may be possible in the future, at least for some of the algorithms. The focus will be on methods that seem potentially applicable to large polyatomics, rather than those of great accuracy for small systems. Section 9.3 also deals with computational methods for anharmonic vibrational spectroscopy that are applicable to potential surfaces from electronic structure calculations. Our main focus will be on the Vibrational Self-Consistent Field (VSCF) approach in several variants and extensions. The performance of the available method in the present state of the art is discussed in Section 9.4. Future directions are outlined in Section 9.5. 

The computational exploration of the conformatimial landscapes of neutral hydrated monosaccharides is particularly challenging because the relative energies of the many possible conformational structures are very close and, in some cases, the associated vibrational spectra differ only very slightly. Singly hydrated pXyl-O-Ph is a typical example of these difficulties [50]. To improve the theoretical description of such systems, more sophisticated approaches than the standard DFT calculation have been applied. Vibrational anharmonicity has been accommodated ab initio, using Vibrational Self Consistent Field (VSCF) theory, and has reproduced very accurately the observed spectra [47, 50, 53]. The conformational interconversion of hydrated monosaccharides has been simulated using Ab Initio... 

Anharmonic vibrational analysis via the vibrational self-consistent field (VSCF) method (Chaban et al. 1999). 

Chaban, G. M., Jung, J. O., 8c Gerber, R. B. (1999). Ab initio calculation of anharmonic vibrational states of polyatomic systems Electronic structure combined with vibrational self-consistent field. The Journal of Chemical Physics, 111, 1823-1829. 

Glabo, D.A., Allen, W.D., Remington, R.B., Yamaguchi, Y, Schaefer 111, H.F. A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent field higher derivative methods—asymmetric-top molecules, Chem. Phys. 1988,123,187-239. 

The extension of continuum solvation modes to evaluate vibrational frequencies of molecular systems in solution was pioneered by RivaU and co-workers in the 1980s [150] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium. Further extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [151-153] in the framework of the polarizable continuum model (PCM). Wang et al. [154] used an ab initio self consistent reaction field (SCRF) Onsager model to compute vibrational frequencies at different levels of... 

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