Quality, quantum-mechanical

Now that truly high-quality quantum mechanical benchmark data are becoming available for small systems, it is interesting to evaluate how existing force fields compare to these benchmarks for non-bonded contacts. It is also interesting to explore the development of fully ab initio force fields, without the use of any empirical data. The former question is examined in this section, and the next section discusses the latter topic. 

Force Fields Fit to High-Quality Quantum Mechanical Data... 

Theorehcal methods such as quantum mechanics or molecular mechanics can produce 3D molecular models of high quality and predict a number of molecular properhes with high precision. Unfortunately, these techniques also require at least some reasonable 3D geometry of the molecule as starhng point. 

Albert Einstein s 1905 work on the photoelectric effect paved the way for one of the greatest advances of twentieth-century science, the theory of quantum mechanics. Light had always been regarded as a wave. Quantum mechanics introduced the concept of light being transmitted in wave packets, or photons, that have particle-like qualities as well as wave-like qualities. 

The AIM theory, which is solidly based on quantum mechanics, differs from orbital-based theories in that it is based directly on the electron density and interprets this density to provide information on bonding. The density may be obtained experimentally or from theoretical electronic structure calculation. Experimental densities of sufficient quality to be analyzed by the AIM theory can be obtained from low-... 

Those who applied quantum mechanics to atoms and molecules had a wealth of chemists data at hand well-defined bond properties including dipole moments, index of refractions, and ultraviolet absorption qualities and polarizability as well as well-defined valence properties of atoms in molecules. If one attempted to set up a wave equation for the water molecule, for example, there were 39 independent variables, reducible to 20 by symmetry considerations. But the experimental facts of chemistry implied or required certain properties that made it possible to solve equations by semiempirical methods. "Chemistry could be said to be solving the mathematicians problems and not the other way around," according to Coulson. 148... 

To illustrate the quality of the MFT method, let us first consider Model 1 describing the S2 — conical intersection in pyrazine. Figure 1 compares quantum-mechanical and MFT results obtained for the adiabatic and diabatic electronic population probabilities P t) and as well as for the mean... 

As an example. Fig. 18 shows the diabatic electronic population probability for Model I. The quantum-mechanical results (thick line) are reproduced well by the QCL calculations, which have assumed a localization time of to = 20 fs. The results obtained for the standard QCL (thin full line) and the energy-conserving QCL (dotted line) are of similar quality, thus indicating that the phase-space distribution p]](x, p) at to = 20 fs is similar for the two schemes. Also shown in Fig. 18 are the results obtained for a standard surface-hopping calculation (dashed line), which largely fail to match the beating of the quantum reference. 

Important classes of chemical reactions in the ground electronic state have equal parity for the in- and out-going channels, e.g., proton transfer and hydride transfer [47, 48], To achieve finite rates, such processes require accessible electronic states with correct parity that play the role of transition structures. These latter acquire here the quality of true molecular species which, due to quantum mechanical couplings with asymptotic channel systems, will be endowed with finite life times. The elementary interconversion step in a chemical reaction is not a nuclear rearrangement associated with a smooth change in electronic structure, it is aFranck-Condon electronic process with timescales in the (sub)femto-second range characteristic of femtochemistry [49],... 

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