Donnerstag, 8. Januar 2015

Happy New Years!

Apparently, the past few months it was pretty quiet here. The reason was that I was completely occupied writing up a paper on the central project of my Ph.D. project followed by my thesis. Furthermore, there were the formalities of handing it in and organizing the defence, which I definitely underestimated.
After all, I got everything aligned and there will probably more activity in the next time. To begin with, I present to you my take on Theoretical Chemistry, which constitutes the foreword of my thesis.

In the next posts, as soon as I figure out a comfortable way of translating Tex code into HTML, I will publish my take on the Hartree-Fock self-consistent field method, Configuration-Interaction for ground and excited states, Perturbation Theory applied to HF as well as to CI, yielding the Intermediate-State Representation for the description of correlated excited-states.

So long.

On Theoretical Chemistry

 Chemistry is defined as the science of the interaction and interconversion of complex atomic systems called molecules, including metals and salts. Since molecules are the subunits of any common matter, chemistry is ubiquitous and has a long history as scientific discipline. In the early 20th century, it was discovered that atoms themselves are not indivisible as their Greek-descending name (a-tomos, in-divisible) suggests, but are composed of protons, neutrons and electrons. Nowadays, only the latter are still seen as indivisible, or in other words fundamental with respect to the standard model of particle physics. Protons and neutrons, in contrast consist of even smaller subunits: so-called up and down quarks.

These quarks, which  are again fundamental particles, carry fractions of the elementary charge of either plus two thirds (up quarks) or minus one third (down quarks). Protons consist of two up quarks and one down quark and thus carry one positive elementary charge, while for neutrons the charges of one up quark and two down quarks cancel out. The very number of quarks that constitute each proton and neutron does, in combination with their fractional charge, lead to an important coincidence: any atomic nucleus consisting of an arbitrary number of protons and neutrons will carry an exact multiple of the elementary charge and can in turn be neutralized by adding the respective number of electrons. Formally, this process yields the neutral atoms that constitute the periodic table of the elements.

Due to the huge binding energy of quarks, which is the result of the so-called strong interaction between them, they can only be observed in groups. Similarly, with the exception of hydrogen, neutrons and protons are fused together in the atomic core, where they are held in place by the very same short-ranged forces of the strong interaction. Despite the 10^5 times smaller size compared to the atom including the electrons, the nucleus contains virtually the complete mass of an atom. The biggest part of this mass is due to the huge binding energy according to Einstein's equation m = Ec^(-2), whereas the resting mass contributes less than 1%.

Ultimately, atoms may be rationalized as the frozen interaction energy of their elementary building blocks carrying a positive charge, which incidentally is a multiple of the elementary charge. Moreover, this charge exclusively determines which chemical element a nucleus belongs to, and gives rise to the Coulomb potential that attracts the much lighter, negatively charged electrons. It is the delicate interplay of many electrons in the field of complex nuclear arrangements which guides the nuclear motion and in turn the whole of chemistry with its vast number of stable molecules and reactions. Following this line of thought, chemistry could formally be categorized as the sub-field of particle physics concerned with the quantum mechanics of the electromagnetic interaction in complex systems composed of electrons and nuclei.
However, such a categorization would neither reflect the vast number of thinkable and/or stable molecules emerging from the interplay of electrons in the field of the nuclei, nor the great relevance this discipline had long before the connections to the underlying physical equations were discovered. The sheer infinite possibilities to combine atoms to molecules, investigate their properties in creative ways and find empirical solutions to chemical problems (e.g. acid-base models, Lewis-structures gave rise to an independent scientific discipline. Nevertheless, the utilization of the laws of quantum-mechanics to establish a first-principles approach for chemical problems is and has been very promising ever since these connections were first discovered at the beginning of the 20th century, as evident from the following quote:

"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation."
Paul A. M. Dirac, 1929

In the past decades ever faster computers in combination with powerful algorithms and wisely chosen approximations made it possible to solve these insoluble equations on a regular basis. Eventually, the empirical top-down models developed by chemists over hundreds of years could for the first time be challenged by a first-principles bottom-up approach providing a new quality of insights into the elementary steps of chemical reactions such electron transfer as well as into the electronic structure of matter. This first-principles approach is what characterizes the field of theoretical chemistry, which emerged from a fruitful collaboration of chemists, physicists, mathematicians and computer scientists over the past hundred years.

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