Anharmonicity VSCF

Figure 12-3. IR-UV double resonance spectrum of GC (structure C) in the mid-IR frequency range (recorded at the FELIX free electron laser facility), compared with three types of ab intio calculations. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces [30]...

Anharmonic CC-VSCF MP2/TZP calculations, harmonic MP2/TZP calculations and compilation of experimental data Miller etal. [111]. 

Initial results obtained for TPA and for photoelectron spectra of small systems, show that anharmonicity must be included in the calculation of EC factors to reproduce experiment [54, 77, 104]. However, it is difficult to treat larger anharmonic systems by means of perturbation theory. Such systems can be handled by applying the variation/perturbation methods of electronic structure theory that have been, and continue to be, extended to the vibrational Schrodinger equation as discussed earlier. The EC integrals tliat appear in the equations for resonant (hyper)polarizabilities may be calculated employing approaches like VSCF, VMP2, VCI and VCC, That will allow us to Include anharmonic contributions to all orders and thereby remove the intrinsic limitations of the perturbation expansion in terms of normal coordinates. 

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. 

State calculations. With the extensions provided, the method can be applied to the full Watson Hamiltonian [51] for the vibrational problem. The efficiency of the method depends greatly on the nature of the anharmonic potential that represents couphng between different vibrational modes. In favorable cases, the latter can be represented as a low-order polynomial in the normal-mode displacements. When this is not the case, the computational effort increases rapidly. The Cl-VSCF is expected to scale as or worse with the number N of vibrational modes. The most favorable situation is obtained when only pairs of normal modes are coupled in the terms of the polynomial representation of the potential. The VSCF-Cl method was implemented in MULTIMODE [47,52], a code for anharmonic vibrational spectra that has been used extensively. MULTIMODE has been successfully applied to relatively large molecules such as benzene [53]. Applications to much larger systems could be difficult in view of the unfavorable scalability trend mentioned above. 

Spectroscopy algorithm, as wiU be outlined in the next Section. VSCF and CC-VSCF can fail for strongly anharmonic soft modes such as torsions. This is related to the fact that for large amplitude torsional motions, normal mode coordinates are not suitable, and when used may give rise to extremely large coupling due to their geometric nature. Other than such exceptions, the method seems in most cases of satisfactory accuracy. 

CC-VSCF was also used for computing anharmonic vibrational spectra from DFT potentials [103,104], The most accurate spectroscopic results are obtained from the hybrid functionals B97 [105] and B3LYP [106], of the non-hybrid DFT functionals, HCTH [107] seems superior to BLYP [108], The spectroscopic accuracy of B97 and B3LYP was about equal to that of MP2. 

Matsunaga et al. [110] introduced VSCF-DPT2, a method that includes the effects of degeneracies in the anharmonic vibrational spectra. The essential extension is to use Degenerate Perturbation Theory (as opposed to Non-degenerate Perturbation Theory) in introducing correlation effects. Also this method was interfaced with electronic strucmre codes, and is incorporated in gamess. There have been several applications of ab initio spectroscopy calculations with this method. 

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). 

---