Quantum mechanical calculations electronic structure

Quantum chemical methods aim to treat the fundamental quantum mechanics of electronic structure, and so can be used to model chemical reactions. Such quantum chemical methods are more flexible and more generally applicable than molecular mechanics methods, and so are often preferable and can be easier to apply. The major problem with electronic structure calculations on enzymes is presented by the very large computational resources required, which significantly limits the size of the system that can be treated. To overcome this problem, small models of enzyme active sites can be studied in isolation (and perhaps with an approximate model of solvation). Alternatively, a quantum chemical treatment of the enzyme active site can be combined with a molecular mechanics description of the protein and solvent environment the QM/MM approach. Both will be described below. 

Figure 1 In a QM/MM calculation, a small region is treated by a quantum mechanical (QM) electronic structure method, and the surroundings treated by simpler, empirical, molecular mechanics. In treating an enzyme-catalysed reaction, the QM region includes the reactive groups, with the bulk of the protein and solvent environment included by molecular mechanics. Here, the approximate transition state for the Claisen rearrangement of chorismate to prephenate (catalysed by the enzyme chorismate mutase) is shown. This was calculated at the RHF(6-31G(d)-CHARMM QM-MM level. The QM region here (the substrate only) is shown by thick tubes, with some important active site residues (treated by MM) also shown. The whole model was based on a 25 A sphere around the active site, and contained 4211 protein atoms, 24 atoms of the substrate and 947 water molecules (including 144 water molecules observed by X-ray crystallography), a total of 7076 atoms. The results showed specific transition state stabilization by the enzyme. Comparison with the same reaction in solution showed that transition state stabilization is important in catalysis by chorismate mutase78.

Ohlaiii a new stable structure as a starting point for a single point, quantum mechanical calculation, which provides a large set ol structural and electronic properties. 

In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

Equation (6.20) and the semiquantitative trends it conveys, can be rationalized not only on the basis of lateral coadsorbate interactions (section 4.5.9.2) and rigorous quantum mechanical calculations on clusters89 (which have shown that 80% of the repulsive O2 - O interaction is indeed an electrostatic (Stark) through-the-vacuum interaction) but also by considering the band structure of a transition metal (Fig. 6.14) and the changes induced by varying O (or EF) on the chemisorption of a molecule such as CO which exhibits both electron acceptor and electron donor characteristics. This example has been adapted from some rigorous recent quantum mechanical calculations of Koper and van Santen.98... 

The value of 3 and its dispersion can be theoretically calculated from equation 6, provided a complete set of electron states of the system is known. Such quantum mechanical calculations have been developed based on molecular Hartree-Fock theory including configuration interactions( 1 3). A detailed theoretical analysis of 3 and contributing 1T -electron states has been presented for several important molecular structures. 

The electronic structure and physical properties of any molecule can in principle be determined by quantum-mechanical calculations. However, only in the last 20 years, with the availability and aid of computers, has it become possible to solve the necessary equations without recourse to rough approximations and dubious simplifications2. Computational chemistry is now an established part of the chemist s armoury. It can be used as an analytical tool in the same sense that an NMR spectrometer or X-ray diffractometer can be used to rationalize the structure of a known molecule. Its true place, however, is a predictive one. Therefore, it is of special interest to predict molecular structures and physical properties and compare these values with experimentally obtained data. Moreover, quantum-mechanical computations are a very powerful tool in order to elucidate and understand intrinsic bond properties of individual species. 

Molecular dynamics simulations, with quantum-mechanically derived energy and forces, can provide valuable insights into the dynamics and structure of systems in which electronic excitations or bond breaking processes are important. In these cases, conventional techniques with classical analytical potentials, are not appropriate. Since the quantum mechanical calculation has to be performed many times, one at each time step, the choice of a computationally fast method is crucial. Moreover, the method should be able to simulate electronic excitations and breaking or forming of bonds, in order to provide a proper treatment of those properties for which classical potentials fail. 

If the five resonance forms of the phenoxy radical (Figure 3.6) can couple to any other phenoxy radical, the theoretical number of dimeric structures possible is 25. The relative frequency of involvement of individual sites in the phenolic coupling reaction depends on their relative electron densities. Quantum mechanical calculations predict that the high electron densities at the phenolic oxygen atom and the carbon atom would give rise to a high proportion of fi-O-4 linkages, which is indeed observed to be the case (Table 3.1). 

V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals," J.Chem.Physics 1 (1933) 362374 Linus Pauling and J. Sherman, "The Nature of the Chemical Bond. VI. Calculation from Thermochemical Data of the Energy of Resonance of Molecules Among Several Electronic Structures," J.Chem.Physics 1 (1933) 606617 and Pauling and Sherman, "The Nature of the Chemical Bond. VH. The Calculation of Resonance Energy in Conjugated Systems," J.Chem.Physics 1 (1933) 679686. 

One of the important electrochemical interfaces is that between water and liquid mercury. The potential energy functions for modeling liquid metals are, in general, more complex than those suitable for modeling sohds or simple molecular liquids, because the electronic structure of the metal plays an important role in the determination of its structure." However, based on the X-ray structure of liquid mercury, which shows a similarity with the solid a-mercury structure, Heinzinger and co-workers presented a water/Hg potential that is similar in form to the water/Pt potential described earlier. This potential was based on quantum mechanical calculations of the adsorption of a water molecule on a cluster of mercury atoms. ... 

The presence of the cation protonated on N-1 cannot account for the fluorescence of aqueous acidic adenine solutions (pH = 2), since the 1-methyl derivative does not fluoresce under the same conditions (Borresen, 1967). It has therefore been suggested that other tautomeric forms of the cation are also present, the fluorescent tautomer probably being protonated on the amino-group with another proton on N-7. Quantum mechanical calculations (Veillard and Pullman, 1963) indicate similar proton affinity for N-1 and N-3, and a lesser one for N-7. There are numerous calculations in the literature on the electronic structure of adenine (see Boyd, 1972, and references quoted therein) and a recent one on N-7-H and N-9-H tautomers protonated on N-1 (Jordan and Sostman, 1972). The N-9-H form is preferred according to hoth MINDO and CNDO/2 calculations. 

An atomic unit of length used in quantum mechanical calculations of electronic wavefunctions. It is symbolized by o and is equivalent to the Bohr radius, the radius of the smallest orbit of the least energetic electron in a Bohr hydrogen atom. The bohr is equal to where a is the fine-structure constant, n is the ratio of the circumference of a circle to its diameter, and is the Rydberg constant. The parameter a includes h, as well as the electron s rest mass and elementary charge, and the permittivity of a vacuum. One bohr equals 5.29177249 x 10 meter (or, about 0.529 angstroms). 

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