Quantum mechanical calculations of electron

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). 

To describe a semi-empirical procedure for quantum mechanical calculations of electron affinities. 

D. W. Schwenke, S. L. Mielke, G. J. Tawa, R. S. Friedman, P. Halvick and D. G. Truhlar, Converged quantum mechanical calculations of electronic-to-vibrational, rotational energy transfer probabilities in a system with a conical intersection, J. Chem. Phys. 203 565 (1993). 

Thermochemical data for gas-phase neutrals and ions are fundamental to the understanding of the thermodynamics of molecular transformations. Furthermore, such data is valuable for comparisons to the results of quantum mechanical calculations of electronic energies since the theoretical models do... 

For the purposes of quantum mechanical calculations of electronic wavefunctions, it is convenient to regard certain fundamental constants (and combinations of such constants) as though they were units. They are customarily called atomic units (abbreviated au), and they may be regarded as forming a coherent system of units for the calculation of electronic properties in theoretical chemistry, although there is no authority from... 

Qualitative models of reactivity and quantum mechanical calculations of reaction paths both indicate an angular approach of the attacking nucleophile to the first-row sp -hybridized electrophilic centers M at intermediate and reactive distances, 29. The geometry of 29 is also characteristic for the case of nucleophilic addition to electron-deficient centers of main-group 12 and 13 elements. By contrast, a linear arrangement 30 of making and breaking bonds is required for sp -hybridized first-row centers (C, N, O)... 

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... 

Due to the complexity of a full quantum mechanical treatment of electron impact ionization, or even a partial wave approximation, for all but relatively simple systems, a large number of semiempirical and semiclassical formulae have been developed. These often make basic assumptions which can limit their range of validity to fairly small classes of atomic or molecular systems. The more successful approaches apply to broad classes of systems and can be very useful for generating cross sections in the absence of good experimental results. The success of such calculations to reproduce experimentally determined cross sections can also give insight into the validity of the approximations and assumptions on which the methods are based. 

The paper [8] includes results of investigating electron mechanisms of the impact of active particles, radicals, hydrated electrons artificially generated by plasma on the behavior of cyanide complexes of zinc in water solutions. The above investigation was conducted using quantum chemistry methods. Quantum-chemical calculation of electron structure of the complexes Zn(CN)42 4EP-20H- with complete optimization of all geometric parameters [9] was performed. 

The use of quantum mechanical calculations of solid properties was initially the province of solid-state physics, and the calculation of electron energy levels in metals and semiconductors is well established. Chemical quantum mechanical... 

While the manipulations involved in the practice of one electron MO theory are simple, it is clear that, unless someone is well familiar with the intricacies involved, mistakes can easily be made. We hope that in Part II we have provided sufficient warning of the pitfalls which await the careless and/or inexperienced worker who tries to apply MO methodology to a chemical problem. Needless to say, the proliferation of canned computer programs capable of performing quantum mechanical calculations of varied degrees of sophistication, makes forays into the theoretical arena irresistible to nonexperts. Whether this will turn out to be a panacea or a source of confusion for the experimentalists remains to be seen. 

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. 

What was the distinction between quantum chemistry and chemical physics After the Journal of Chemical Physics was established, it was easy to say that chemical physics was anything found in the new journal. This included molecular spectroscopy and molecular structures, the quantum mechanical treatment of electronic structure of molecules and crystals and the problem of chemical binding, the kinetics of chemical reactions from the standpoint of basic physical principles, the thermodynamic properties of substances and calculation by statistical mechanical methods, the structure of crystals, and surface phenomena. 

Methods for quantum mechanical calculation of dipole moments and their IE s are well established. The dipole moment for any specified confirmation is defined by the nuclear coordinates of the various atoms n and their charges z , plus the electron density at each point in space expressed as a function of the vector re using the wave function... 

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. ... 

In Ref. 122 we raised the question of whether one can use basis functions (49) in non-BO quantum mechanical calculations of molecular diatomic systems containing positrons and whether those functions are capable of providing a proper representation for the positron-nucleus and positron-electron correlation effects in a diatomic system. e+LiH was chosen as a target system. Along with e+LiH, we also performed the calculations of HPs and Li+ because the total energies of these systems are needed for determining the dissotiation energy. 

At this stage we are at the very beginning of development, implementation, and application of methods for quantum-mechanical calculations of molecular systems without assuming the Born-Oppenheimer approximation. So far we have done several calculations of ground and excited states of small diatomic molecules, extending them beyond two-electron systems and some preliminary calculations on triatomic systems. In the non-BO works, we have used three different correlated Gaussian basis sets. The simplest one without r,y premultipliers (4)j = exp[—r (A t (8> Is) "]) was used in atomic calculations the basis with premultipliers in the form of powers of rj exp[—r (Aj (8> /sjr])... 

B. Pullman and A. Pullman, Results on Quantum Mechanical Calculations of the Electronic Structure of Biochemicals. University of Paris, Paris, 1960. 

---