The quantum atom

Orbital quantum no. (n) quantum no. (/) quantum no. (wi) (spin up or down) 

Note that the 3d orbital energy is below that of the 4p, which explains the electronic structure of the transition ( i-block) metals. After Fig. Al.l, Pollard and Heron (1996). 

Very soon afterwards, however, two scientists independently produced the definitive statement on the classification of the elements - Julius Lothar Meyer (1830-95) in Germany and Dmitri Ivanovich Mendeleev (1834-1907) (also spelled Mendeleeff or Mendelejeff) in Russia. It is the latter who is now credited with the construction of the first periodic table. At the age of 35, Mendeleev was Professor of Chemistry at the University of St Petersberg, when he published his first paper (1869) on the periodic system. He was apparently unaware of the work of Newlands or Lothar Meyer, but came to the same conclusions, and was also prepared to go further, and predict that certain elements must remain to be discovered because of discrepancies in his table. Amongst other things, he concluded the following  

In the modern periodic table, horizontal rows are known as periods, and are labeled with Arabic numerals. These correspond to the principal quantum numbers described in the previous section. Because the outer shells of the elements H and He are 5 rather than p orbitals, these elements are usually considered differently from those in the rest of the table, and thus the 1st period consists of the elements Li, Be, B, C, N, O, F, and Ne, and the 2nd Na to Ar. Periods 1 and 2 are known as short periods, because they contain only eight elements. From the discussion above, it can be seen that these periods correspond to the filling of the p orbitals (the 2p levels for the first period, and the 3p for the second), and they are consequently referred to as p-block elements. The 3rd and 4th periods are extended by an additional series of elements inserted after the second member of the period (Ca and Sr respectively), consisting of an extra ten elements (Sc to Zn in period 3 and Y 

Properties across the periods can also vary systematically. For all periods, elements towards the left-hand side tend to form positively charged ions, 

The hydrogen atom was Schrttdinger s immediate goal when he developed his equation, and the solution obtained in 1926 persuaded him and indeed most interested physicists that his theory was successful. The mathematical details are not easy, and Schrodinger himself needed advice from colleagues before he could obtain the solution What is important is to understand the qualitative features. 

Our development so far allows us to write Schrodinger s equation for an electron in a hydrogen atom as 

The energy depends only on n, and is given by the same equation as in the Bohr theory 

The first term is called the radial wavefunction, and describes the in-out motion of the electron. It is written with the subscripts to show that the mathematical form of the function depends on the values of n and l we shall look at some examples below. The second term in eqn 4.18 is exactly the same spherical harmonic that arises in the particle-on-a-sphere problem. It 

The hydrogen-atom solutions are called atomic orbitals, by analogy with the orbits of the Bohr theory. Orbitals with / = 1 are called s orbitals, and those with l = 2, 3, and 4, arc called p, d, and / orbitals, respectively. (This notation comes from the names used to describe different series of spectroscopic lines.) The value of n is also specified, so that, for example, 2p is used to denote orbitals with n = 2 and l = 1 in this case, there are three possible m values, and 2p refers to the whole set of these. Table 4.1 lists the orbitals with n up to three, showing their names and the number of possible m values in each case. 

There can be no doubt but that in quantum mechanics one has the complete solution to the problems of chemistry. 

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Having found a place (the sp -sp bon d t to establish the boundary between classical atom s and quantum atoms, the next cpiesiion is how to cap the quantum atoms. Let s first of all look at an illustrative example of the problem. ... 

Finally, the parametrization of the van der Waals part of the QM-MM interaction must be considered. This applies to all QM-MM implementations irrespective of the quantum method being employed. From Eq. (9) it can be seen that each quantum atom needs to have two Lennard-Jones parameters associated with it in order to have a van der Walls interaction with classical atoms. Generally, there are two approaches to this problem. The first is to derive a set of parameters, e, and G, for each common atom type and then to use this standard set for any study that requires a QM-MM study. This is the most common aproach, and the derived Lennard-Jones parameters for the quantum atoms are simply the parameters found in the MM force field for the analogous atom types. For example, a study that employed a QM-MM method implemented in the program CHARMM [48] would use the appropriate Lennard-Jones parameters of the CHARMM force field [52] for the atoms in the quantum region. 

The second approach is to derive Lennard-Jones parameters for the quantum atoms that are specific to the problem in hand. This is a less common approach but has been shown to improve the quantitative accuracy of the QM-MM approach in specific cases [53,54]. The disadvantage of this approach, however, is that it is necessary to derive Lennard-Jones parameters for the quanmm region for every different study. Since the derivation of Lennard-Jones parameters is not a trivial exercise, this method of finding van der Walls parameters for the QM-MM interaction has not been widely used. 

It was not until the advent of the quantum atom that chemists were able to understand their most abiding mystery why elements have the properties they do. Why is helium so inert and sodium so reactive Why do hydrogen atoms come in pairs in hydrogen gas, while carbon atoms join to four others in diamond ... 

These propensities are, as I indicated at the outset, largely codified in the Periodic Table. We shall shortly see that the quantum atom provides an explanation for the Periodic Table. But where did this table come from in the first place ... 

Following the wave-mechanical reformulation of the quantum atomic model it became evident that the observed angular momentum of an s-state was not the result of orbital rotation of charge. As a result, the Bohr model was finally rejected within twenty years of publication and replaced by a whole succession of more refined atomic models. Closer examination will show however, that even the most refined contemporary model is still beset by conceptual problems. It could therefore be argued that some other hidden assumption, rather than Bohr s quantization rule, is responsible for the failure of the entire family of quantum-mechanical atomic models. Not only should the Bohr model be re-examined for some fatal flaw, but also for the valid assumptions that led on to the successful features of the quantum approach. 

The force fields used in the QM/MM methods are typically adopted from fully classical force fields. While this is in general suitable for the solvent-solvent interactions it is not clear how to model, e.g., the van der Waals interaction between the solute and the solvent. The van der Waals interactions are typically treated as Lennard-Jones (LJ) potentials with parameters for the quantum atoms taken from the classical force field or optimized for the particular QM/MM method for some molecular complexes. However, it is not certain that optimizing the (dispersion and short-range repulsion) parameters on small complexes will improve the results in a QM/MM simulation of liquids [37],... 

It is the operational essence of the atomic hypothesis that one can assign properties to atoms and groupings of atoms in molecules and on this basis identify them in a given system or use their properties to predict the behaviour of the system in which they are found. The primary purpose of this section is to demonstrate that the quantum atoms transform this atomic hypothesis into an atomic theory of matter by identifying the atoms of chemistry and defining their properties. This section is not a review of applications, but is rather intended to introduce and illustrate the uses of various atomic properties. 

FIGURE 4,3 The two energy curves (thick lines) for the quantum atom in (a) the apparent or reactive ground state and (b) the shifted or critical ground state (Putz, 2012a). 

However, the periodicity condition (4.518) for paths is to be maintained and properly implemented in approximating the effective-classical partition function (4.525) being, nevertheless, closely and powerfully related with the quantum beloved concept of stationary orbits defined/described by periodic quantum waves/paths. This way, the effective-classical path integral approach appears as the true quantum justification of the quantum atom and of the quantum stabilization of matter in general, providing reliable results without involving observables or operators relaying on special quantum postulates other than the variational principles - with universal (classical or quantum) value. 

Haroche S, Raimond J-M (2006) Exploring the quantum Atoms, cavities, and photons. Oxford University Press, Oxford... 

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