Ab initio potential energies

An example of a potential energy fiinction based on all these ideas is provided by the 10-parameter fiinction used [88] as a representation of ab initio potential energy curves for Fle-F and Ne-F ... 

Truhlar D G and Horowitz C J 1978 Functional representation of Liu and Siegbahn s accurate ab initio potential energy calculations for H + H2 J. Chem. Phys. 68 2466... 

Figure 47. Ab initio potential energy curves of the HI molecule. The unit of y axis is reaprocal centemeters.

An overview of the time-dependent wavepacket propagation approach for four-atom reactions together with the construction of ab initio potential energy surfaces sufficiently accurate for quantum dynamics calculations has been presented. Today, we are able to perform the full-dimensional (six degrees-of-freedom) quantum dynamics calculations for four-atom reactions. With the most accurate YZCL2 surface for the benchmark four-atom reaction H2 + OH <-> H+H2O and its isotopic analogs, we were able to show the following ... 

Perczel, A., O. Farkas, and I. G. Csizmadia. 1996. Peptide Models XVI. The Identification of Selected HCO-l-SER-NH2 Conformers via a Systematic Grid Search Using Ab Initio Potential Energy Surfaces. J. Comput. Chem. 17, 821-834. 

Absorption and Resonance Emission Spectra of S02(X1A2/C1B2) Calculated from Ab Initio Potential Energy and Transition Dipole Moment Surfaces. 

A dynamical study of molecular collision requires a detailed knowledge of the interaction potential as an input. Ab initio potential energy (PE) values for a chemical reaction for different geometries are usually reported in the form of table of numbers resulting from sophisticated electronic structure calculations. However, for use in dynamical calculations, the PES must be known in some convenient analytical or numerically interpolated form, which is capable of generating potential and its derivatives accurately and efficiently at any arbitrary geometry. 

Fig. 13.5 Ab initio potential energy curves for cc-pVQZ/TZ UCCSD(T) bottom cc-pVQZ/TZ the C" (planar) fragmentation of a 3A" ketene, UCCSD(T) + cc-pV5Z MP2 basis set and...

The empirical valence bond (EVB) approach introduced by Warshel and co-workers is an effective way to incorporate environmental effects on breaking and making of chemical bonds in solution. It is based on parame-terizations of empirical interactions between reactant states, product states, and, where appropriate, a number of intermediate states. The interaction parameters, corresponding to off-diagonal matrix elements of the classical Hamiltonian, are calibrated by ab initio potential energy surfaces in solu-fion and relevant experimental data. This procedure significantly reduces the computational expenses of molecular level calculations in comparison to direct ab initio calculations. The EVB approach thus provides a powerful avenue for studying chemical reactions and proton transfer events in complex media, with a multitude of applications in catalysis, biochemistry, and PEMs. 

In Fig. 5, the agreement of the calculated absolute intensity values with the corresponding experimental values is an indication of the high quality of the ab initio dipole moment surfaces employed in the calculation. The qualitatively correct appearance of the bands indicates that our solution of the rotation-vibration Schrodinger equation and the potential energy surface employed are satisfactory. It should be emphasized that the ab initio potential energy and dipole moment surfaces have not been adjusted to fit experiment. 

B. N. Fu, B. C. Shepler, and J. M. Bowman. Three-state trajectory surface hopping studies of the photodissociation dynamics of formaldehyde on ab initio potential energy surfaces, J. Am. Chem. Soc., 133 7957-7968 (2011). 

Figure 2. Franck-Condon windows lVpc(Gi, r, v5) for the Na3(X) - N83(B) and for the Na3(B) Na3+ (X) + e transitions, X = 621 nm. The FC windows are evaluated as rather small areas of the lobes of vibrational wavefunctions that are transferred from one electronic state to the other. The vertical arrows indicate these regions in statu nascendi subsequently, the nascent lobes of the wavepackets move coherently to other domains of the potential-energy surfaces, yielding, e.g., the situation at t = 653 fs, which is illustrated in the figure. The snapshots of three-dimensional (3d) ab initio densities are superimposed on equicontours of the ab initio potential-energy surfaces of Na3(X), Na3(B), and Na3+ (X), adapted from Ref. 5 and projected in the pseudorotational coordinate space Qx r cos

The 3d ab initio simulations [4] for Na3 are based, in a similar way, on three ab initio potential-energy surfaces for Na3(X), Na3(B), and Na3(X), with 3d ab initio dipole coupling between Na3(X) and Na3(B) evaluated by V. Bonacic-Koutecky et al. [5] plus Condon-type coupling between Na3(B) and Na3(X). Additional potential-energy surfaces interfere at the conical intersections of the pseudo-Jahn-Teller distorted Na3(B) state (see Ref. 6), but we have tested carefully [4] that these interferences are negligible in the frequency domains of the experimental femtosecond/picosecond laser pulse experiments [7] as well as in the continuous-wave experiments [8]. 

It thus appears that a judicious application of correction curves of the form of (III.l) can transform a uniform set of ab initio potential-energy curves into a set of corrected curves that are very representative of the actual system. Such curves must be of similar chemical character such as all valence states or all Rydberg states. Rydberg-valence mixing cannot be easily accounted for in ab initio calculations, and simple empirical corrections do not seem possible for such situations. 

F.J. Aoiz, L. Banares, V.J. Herrero, V.S. Rabanos, K. Stark, H-J. Werner, The F+HD DF(HF)+H(D) reaction revisited Quasiclassical trajectory study on an ab initio potential energy surface and comparison with molecular beam experiments, J. Chem. Phys. 102 (1995) 9248. 

M.Y. Hayes, M.P. Deskevich, D.J. Nesbitt, K. Takahashi, R.T. Skodje, A simple picture for the rotational enhancement of the rate for the F+HC1- HF+C1 reaction A dynamical study using a new ab initio potential energy surface, J. Phys. Chem. A 110 (2006) 436. 

The most reliable values of the calculated tunneling parameters fiH and are presented in Table 2. These values were obtained with the help of the calculated ab initio potential energy profiles, corrected in according with the diffraction data for proton (deuteron) positions [5]. 

This list, which is by no means complete, clearly demonstrates that the generic type of final state distribution is not only observed for atom-diatom systems but also if the recoiling partner is a large polyatomic molecule. In contrast to the many experimental examples, there are only a few systems for which rotational excitation has been analyzed by means of ab initio potential energy surfaces and exact quantum mechanical or classical calculations. In the following we discuss two of them. 

Amatatsu, Y., Morokuma, K., and Yabushita, S. (1991). Ab initio potential energy surfaces and trajectory studies of A-band photodissociation dynamics CH3I —> CH3 + I and CH3 +1, J. Chem. Phys. 94, 4858-4876. 

Schinke, R., Hennig, S., Untch, A., Nonella, M., and Huber, J.R. (1989). Diffuse vibrational structures in photoabsorption spectra A comparison of CH3ONO and CH3SNO using two-dimensional ab initio potential energy surfaces, J. Chem. Phys. 91, 2016-2029. 

TYoe, J. (1988). Unimolecular reaction dynamics on ab initio potential energy surfaces, Ber. Bunsenges. Phys. Chem. 92, 242-252. 

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