Vibrational self-consistent fields

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]. 

Wierzbicki, A., and Bowman, J. M. (1988), GVSCF A General Code to Perform Vibrational Self-Consistent Field Calculations, Comp. Phys. Comm. 51,225. 

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. 

Alternatively, one may calculates S(t) itself systematically using controlled approximations. Calculating a correlation function for large systems has a long history in chemical physics [25], including recent applications to VER processes in liquid [26,27]. The vibrational self-consistent field (VSCF) method [28] will also be useful in this respect. 

Tab. 3.1 Selected vibrational energies (cm ) of H5OJ calculated by a variety of methods and experiment for the OH-monomer stretches. 2d+2d are the adiabatic 4d calculations of Ref [56], 4d are the fully coupled 4d calculations of Ref [27], CC-VSCF are the correlation-consistent vibrational self-consistent field calculations of Ref [58] and VCI are the virtual configuration interaction calculations of Ref [27]. The potential used in these calculations is indicated after the back-slash.

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. 

We will focus mainly on Variational Theory in this chapter and use the Vibrational Self-Consistent Field (VSCF) theory as the starting point for this. This theory, however, also lends itself to a very workable form of PT, which we will briefly review as well. A much more detailed account of the PT approach is found in the chapter by Gerber and co-workers. 

Jung, J.O., Gerber, R.B. Vibrational wave functions and spectroscopy of (H20o, n = 2,3,4,5) Vibrational self-consistent field wifh correlation correchons, J. Chem. Phys. 1996,105,10332-48. 

Carter, S., Culik, S., Bowman, J.M. Vibrational self-consistent field method for many-mode systems A new approach and application to the vibration of CO absorbed on Cu(lOO), J. Chem. Phys. 

Direct vibrational self-consistent field method Applications to H2O and H2CO ... 

Hirata et al. used the vibrational self-consistent field (VSCF), vibrational configuration-interaction (VCI), and vibrational second-order Moller-Plesset perturbation (VMP2) methods. The VSCF expressed the vibrational wave functions as products of 52 harmonic oscillator (HO) wave functions. The VCI wave function was a linear combination of the 2000 lowest-energy VSCF model products. The obtained vibrational corrections to V(F, H) and V(F, F) were 18.4Hz and — 42.9 Hz, respectively. The vibrational correction... 

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... 

Christiansen O, Luis J (2005) Beyond vibrational self-consistent-field methods Benchmark calculations for the fundamental vibrations of ethylene. Int J CJuant Chem 104 667... 

A virtual Vibrational Self-Consistent Field (v-VSCF) method has then been developed and implemented for calculating the thermal elfects on molecular properties and has been apphed, among other properties, to the static polarizability. This method is more effieient than expKcit sum-over-states approaches and can be applied to larger systems. In an illustration of this scheme, when going from 0 to 298.15 K, the amplitude of the thermal effects on the diagonal polarizability tensor eomponents has been shown to amount generally to 2-10% but it can also attain 35% like in the case of SOCI2. 

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. 

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