Ab initio potential-energy surface

Thus perturbation theory calculations currently suffer from the same disadvantage of supermolecule calculations for defining the intermolecular potential between organic molecules at short range. They are so expensive when used to obtain results of reasonable accuracy that are converged with respect to basis set, even for small molecules, that it is impossible to calculate the energies at a sufficient number of points to define the potential energy surface. Calcula- 

Values are for the exchange-repulsion electrostatic dispersion Edisp) induction Epoi, and charge transfer E contributions to the total energy Etotai estimated by IMPT calculations using a 6-31G basis set. 

Lessons from Intermolecular Perturbation Theory Calculations on Organic Molecules 

Apart from this detailed orientational dependence in the region of a hydrogen-bonding contact, the electrostatic energy is such a strong orientation-dependent force that minimizing the electrostatic energy (calculated accurately. 

After this digression into the lessons about organic nonbonded interactions that can be learned from limited IMPT calculations in conjunction with experimental results, we should return to considering how to derive accurate intermolecular potentials in a way that can be applied systematically to a range of organic molecules. 

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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. 

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. 

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]. 

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. 

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. 

Table 6.2 Properties of the reactants and the activated complex for the F + H2 reaction. Data from an ab initio potential energy surface [J. Ghem. Phys. 104, 6515 (1996) and Chem. Phys. Lett. 286, 35 (1998)].

Before proceeding to discuss the state-to-state dynamics of these systems, it is important to point out that the ab initio potential energy surface for this system gives calculated spectra that are in excellent agreement with experiment. We take this as evidence that, at least in the region of the well, the potential is quite realistic. Since the dominant electrostatic interaction in this system is that between the quadrupole of the H2 and the dipole of the HF, the intramolecular coupling was included semiempirically in terms of the stretching dependence of these quantities (Clary 1992). 

Kupperman et a/.223-228 compared transition-state, classical, and quantum mechanical thermal rate constants using the SSMK surface.112 In ab initio potential energy surface calculations, the potential energy is known only as a list of values at selected geometries of the system. It becomes necessary, then, if trajectory calculations are to be made, to fit the calculated points to a smooth and continuous map . In their calculations, Kupperman et al. fit the collinear SSMK surface by the rotating Morse function procedure of Wall and Porter.227... 

Before ab initio potential energy surfaces became available, usually the interaction potential between the molecule and the surface had been based on educated guesses or simplified model potentials. Since the complexity of a PES increases significantly with its dimensionality, guessing a, e.g. six-dimensional realistic PES for a diatomic molecule in front of a surface is almost impossible. Low-dimensional simulations can still yield important qualitative insights in certain aspects of the adsorption/ desorption dynamics [4], but they do not allow the quantitative determination of reaction probabilities. Moreover, certain qualitative mechanisms are only operative in a realistic multidimensional treatment. 

An alternative approach is the interpolation of the ab initio PES by some suitable analytical or numerical scheme. For the six-dimensional quantum dynamical studies of hydrogen dissociation on Pd(l 0 0) and Cu(l 0 0) discussed in the next section, ab initio potential energy surfaces have been fitted to an analytical representations [5, 10, 13, 15, 38]. 

Figure 3 Sticking probability of H2/Pd(l 00) as a function of the initial kinetic energy. Circles experiment [44], dashed and solid line theory according to H2 initially in the ground state and with a thermal distribution appropriate for a molecular beam [5]. The inset shows the theoretical results using an improved ab initio potential energy surface.

The reliability of high-dimensional quantum calculations based on ab initio potential energy surfaces is also demonstrated in Fig. 6, where the sticking probability of H2/Cu(l 0 0) obtained by sixdimensional wave packet calculations [32] is compared to experimental results derived from an analysis of adsorption and desorption experiments [27]. The measured experimental sticking probabilities and, via the principle of detailed balance, also desorption distributions had been fitted to the following analytical form of the vibrationally resolved sticking probability as a function of the kinetic energy ... 

Kliiner et al. [19] has analyzed the bimodal velocity distributions observed in NO desorption from NiO(0 01) shown in Fig. 24 by calculating a full ab initio potential energy surface (PES) for an excited state in addition to the PES for the ground state. Calculation of the electronically excited state uses a NiOj cluster embedded in a semi-infinite Madelung potential of point charges 2. The excited state relevant for laser-induced desorption is an NO -like intermediate, where one electron is transferred from the cluster to the NO molecule. 

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