Quantum-mechanical model description

In this section, you saw how the ideas of quantum mechanics led to a new, revolutionary atomic model—the quantum mechanical model of the atom. According to this model, electrons have both matter-like and wave-like properties. Their position and momentum cannot both be determined with certainty, so they must be described in terms of probabilities. An orbital represents a mathematical description of the volume of space in which an electron has a high probability of being found. You learned the first three quantum numbers that describe the size, energy, shape, and orientation of an orbital. In the next section, you will use quantum numbers to describe the total number of electrons in an atom and the energy levels in which they are most likely to be found in their ground state. You will also discover how the ideas of quantum mechanics explain the structure and organization of the periodic table. 

So, a new model was proposed and accepted. The modern description of how electrons move around the nucleus in an atom is called the quantum mechanical model. In this model, the electrons do not follow an exact path, or orbit, around the nucleus the way they do in Bohr s model. Instead, for the new model, physicists calculated the chance of finding an electron in a certain position at any given time. The quantum mechanical model looks like a fuzzy... 

The VSEPR approach is largely restricted to Main Group species (as is Lewis theory). It can be applied to compounds of the transition elements where the nd subshell is either empty or filled, but a partly-filled nd subshell exerts an influence on stereochemistry which can often be interpreted satisfactorily by means of crystal field theory. Even in Main Group chemistry, VSEPR is by no means infallible. It remains, however, the simplest means of rationalising molecular shapes. In the absence of experimental data, it makes a reasonably reliable prediction of molecular geometry, an essential preliminary to a detailed description of bonding within a more elaborate, quantum-mechanical model such as valence bond or molecular orbital theory. 

The material model consists of a large assembly of molecules, each well characterized and interacting according to the theory of noncovalent molecular interactions. Within this framework, no dissociation processes, such as those inherently present in water, nor other covalent processes are considered. This material model may be described at different mathematical levels. We start by considering a full quantum mechanical (QM) description in the Born-Oppenheimer approximation and limited to the electronic ground state. The Hamiltonian in the interaction form may be written as ... 

C. Curutchet, R. Cammi, B. Mennucci and S. Corni, Self-consistent quantum mechanical model for the description of excitation energy transfers in molecules at interfaces, J. Chem. Phys., 125 (2006) 54710. 

From its inception, the combined Quantum Mechanics/Molecular Mechanics (QM/MM) method [1-3] has played an important roll in the explicit modeling of solvent [4], Whereas Molecular Mechanics (MM) methods on their own are generally only able to describe the effect of solvent on classical properties, QM/MM methods allow one to examine the effect of the solvent on solute properties that require a quantum mechanical (QM) description. In most cases, the solute, sometimes together with a few solvent molecules, is treated at the QM level of theory. The solvent molecules, except for those included in the QM region, are then treated with an MM force field. The resulting potential can be explored using Monte Carlo (MC) or Molecular Dynamics (MD) simulations. Besides the modeling of solvent, QM/MM methods have been particularly successful in the study of biochemical systems [5] and catalysis [6],... 

The quantum mechanical model provides a description of the hydrogen atom that agrees very well with experimental data. However, the model would not... 

Jerina DM. Lehr RE. Yagi H. et al. 1976. Mutagenicity of B[a]P derivatives and the description of a quantum mechanical model which predicts the ease of carbonium ion formation from diol epoxides. In de Serres FJ. Fouts JR. Bend JR. et al. eds. In vitro metabolic activation in mutagenesis testing. Amsterdam. The Netherlands Elsevier/North Holland. 159-178. 

Notice also that, if we take our system as a quantum mechanical model for an ideal gas, the thermal state of the gas would be completely. specified by the density and temperature of the gtis (which would permit us to compute its pressure). Hence, in going from the microscopic to the macroscopic level of description, an enormous reduction of information from 0(10 ) down to only 2 degrees of freedom has taken place. 

This chapter has shown how the zero-temperature analyses presented earlier in the book may be extended to incorporate finite-temperature effects. By advancing the harmonic approximation we have been able to construct classical and quantum mechanical models of thermal vibrations that are tractable. These models have been used in the present chapter to examine simple models of both the specific heat and thermal expansion. In later chapters we will see how these same concepts emerge in the setting of diffusion in solids and the description of the vibrational entropies that lead to an important class of structural phase transformations. 

Trial wavefunctions are usually constructed by linear combination of Gaussian error functions that are convenient to integrate. The results can be of predictive value and such calculations have become everyday tools for chemists in all branches of chemistry, to guide experiments and not least to rule out untenable hypotheses. This is a remarkable achievement that seemed to be out of reach a few decades ago. Still, simple qualitative models that are amenable to perturbation theory are required to understand and predict trends in a series of related compounds. Our goal here is to describe the minimal quantum mechanical models that can still provide a useful qualitative description of electronically excited states, their electronic stmcture and their reactivity. Such models also provide a language to convey the results of state-of-the-art, but essentially black-box ab initio calculations. 

The quantum mechanical description of the hydrogen atom is more complex than Bohr s picture, but it is a better picture. In the quantum mechanical model, there are several principal shells... 

It is one of the most basic assumptions of chemistry that a complex molecular electronic structure can be thought of as a series of environment-insensitive substructures with a large degree of autonomy. In particular for many molecules we think of the total structure as composed of pairs of electrons (inner shells, lone pairs, bond pairs) and this idea can be translated into a quantum-mechanical model in which each separate pair (or group) has its own wavefunction. If this is so, then most of the analysis which we have used for the total electronic structure can be taken over unchanged in a description of the separate pairs. 

The theory for the van der Waals interactions presented in the previous section applies to macroscopic media only in a qualitative sense. This is because (i) the additivity of the interactions is assumed — i.e., the energies are written as sums of the separate interactions between every pair of molecules (ii) the relationship of the Hamaker constant to the dielectric constant is based on a very oversimplified quantum-mechanical model of a two-level system (iii) finite temperature effects on the interaction are not taken into account since it is a zero-temperature description. Here, we present a simplified derivation of the van der Waals interaction in continuous media, based upon arguments first presented by Ninham et al a more rigorous treatment can be found in Ref. 4. The van der Waals interactions arise from the free energy of the fluctuating electromagnetic field in the system. For bodies whose separations... 

E. Hiickel introduced a simple quantum mechanical model for the description of the electronic structure of planar unsaturated molecules with the bonding connectivity as input. This model has been widely used. Although today s computing power and quantum chemistry software available for all chemists have made the assumptions of the Hiickel model unnecessarily simplistic, the model is still used to make estimates of molecular energies and has established itself as a useful teaching tool. 

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