Quantum mechanical model Atoms

SpartanView models provide information about molecular energy dipole moment atomic charges and vibrational frequencies (these data are accessed from the Properties menu) Energies and charges are available for all quantum mechanical models whereas dipole moments and vibrational frequencies are provided for selected models only... 

How are the electrons distributed in an atom You might recall from your general chemistry course that, according to the quantum mechanical model, the behavior of a specific electron in an atom can be described by a mathematical expression called a wave equation—the same sort of expression used to describe the motion of waves in a fluid. The solution to a wave equation is called a wave function, or orbital, and is denoted by the Greek letter psi, i/y. 

Quantum mechanical model, 138-139 Quantum number A number used to describe energy levels available to electrons in atoms there are four such numbers, 140-142,159q electron spin, 141 orbital, 141... 

We are now ready to build a quantum mechanical model of a hydrogen atom. Our task is to combine our knowledge that an electron has wavelike properties and is described by a wavefunction with the nuclear model of the atom, and explain the ladder of energy levels suggested by spectroscopy. 

Whether the Bohr atomic model or the quantum mechanical model is introduced to students, it is inevitable that they have to learn, among other things, that (i) the atomic nucleus is surrounded by electrons and (ii) most of an atom is empty space. Students understanding of the visual representation of the above two statements was explored by Harrison and Treagust (1996). In the study, 48 Grade 8-10... 

Doyen [158] was one who theoretically examined the reflection of metastable atoms from a solid surface within the framework of a quantum- mechanical model based on the general properties of the solid body symmetry. From the author s viewpoint the probability of metastable atom reflection should be negligibly small, regardless of the chemical nature of the surface involved. However, presence of defects and inhomogeneities of a surface formed by adsorbed layers should lead to an abrupt increase in the reflection coefficient, so that its value can approach the relevant gaseous phase parameter on a very inhomogeneous surface. 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

In the early development of the atomic model scientists initially thought that, they could define the sub-atomic particles by the laws of classical physics—that is, they were tiny bits of matter. However, they later discovered that this particle view of the atom could not explain many of the observations that scientists were making. About this time, a model (the quantum mechanical model) that attributed the properties of both matter and waves to particles began to gain favor. This model described the behavior of electrons in terms of waves (electromagnetic radiation). 

In the development of the quantum mechanical model of the atom, scientists found that an electron in an atom could have only certain distinct quantities of energy associated with it and that in order to change its energy it had to absorb or emit a certain distinct amount of energy. The energy that the atom emits or absorbs is really the difference in the two energy states and we can calculate it by the equation ... 

In this chapter, you learned about the electronic structure of the atom in terms of the older Bohr model and the newer quantum mechanical model. You learned about the wave properties of matter, and how to describe each individual electron in terms of its four quantum numbers. You then learned how to write the electron configuration of an atom and some exceptions to the general rules. 

In this quantum mechanical model of the hydrogen atom, three quantum numbers are used to describe an atomic orbital ... 

Some aspects of the bonding in molecules are explained by a model called molecular orbital theory. In an analogous manner to that used for atomic orbitals, the quantum mechanical model applied to molecules allows only certain energy states of an electron to exist. These quantised energy states are described by using specific wavefunctions called molecular orbitals. 

Figure 5. Normal modes for vibration of tetrahedral [Cr04] (chromate). There are four distinct vibrational frequencies, including one doubly-degenerate vibration (E symmetry) and two triply-degenerate vibrations (F2 symmetry), for a total of nine vibrational modes. Arrows show the characteristic motions of each atom during vibration, and the length of each arrow is proportional to the magnitude of atomic motion. Only F2 modes involve motion of the central chromium atom, and as a result their vibrational frequencies are affected by Cr-isotope substitution. The normal modes shown here were calculated with an ab initio quantum mechanical model, using hybrid Hartree-Fock/Density Functional Theory (B3LYP) and the 6-31G(d) basis set—other ab initio and empirical force-field models give very similar results.

What is the quantum mechanical model of the atom, and how does a understanding of atomic structure enable chemists to explain the properties of substances and their chemical bonding ... 

Distinguish clearly between an electron orbit, as depicted in Bohr s atomic model, and an electron orbital, as depicted in the quantum mechanical model of the atom. 

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. 

In this section, you have seen how a theoretical idea, the quantum mechanical model of the atom, explains the experimentally determined structure of the periodic table, and the properties of its elements. Your understanding of the four quantum numbers enabled you to write electron configurations and draw orbital diagrams for atoms of the elements. You also learned how to read the periodic table to deduce the electron configuration of any element. 

The modern, quantum mechanical model of the atom has broadened your understanding of the elements, the composition of their atoms, and their chemical and physical behaviour in the world around you. 

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