Scientific neologisms

English

Summary

In this thesis, the closed-layer restricted Hartree-Fock (HF) model for simple molecules is developed. To carry out the calculations with this model, the base functions STO-LG from L = 1 to L = 6 are used. The method is studied in the molecules H ₂ and HeH . These are considered simple due to the low number of electrons and charge points they have in their molecular system. Most of the literature related to this method solves simple molecules such as those presented in this thesis. However, they omit important details when giving the solution. For this reason, relevant details in mathematics, physics, chemistry and computers are included. This thesis talks about how the first theories of quantum mechanics motivated the search for what is now known as the "Schrödinger equation". This is capable of measuring the properties of a molecular system. It is important to emphasise that it is difficult to find the analytical solution of the Schrödinger equation for molecular systems with large amounts of electrons. One way to simplify this problem is to work the molecular systems by separating the electrons from the nuclei. This allows the Schrödinger equation to be rewritten only in terms of electrons. In addition, the use of spin should be emphasised due to the Pauli exclusion principle. When introducing antisymmetry in the wave function, it is necessary to involve Slater determinants. Thus we arrive at the Hartree-Fock method. Slater's determinants employ a set of base functions to approximate the behavior of the wave function. In this case, the STO-LG base functions are used, which are built from primitive Gaussian functions. These base functions are intended to behave roughly to Slater-type orbitals. Slater-type orbitals are the best way to describe the behavior of molecular orbitals. The complexity of its construction makes operations in the HF method difficult. Finally, note that the thesis is self-contained; It includes pseudocodes, MATLAB codes and Excel files that facilitate the understanding of the construction and the verification of what is obtained. The code programmed in C ++ is included. This thesis is based on [1] and was carried out in the hope that it may be of help in future theses dealing with similar topics.

Maya

Ts'um

Ti' le meyaj yaan beetik je'ela'an meyaj, u k'aaba'e' Hartree-Fock lelo' ma' cha'aban u piixe' k'aala'an u ti'al múuch mejen ba'alo'ob. U ti'al beetik le p'iiso'obo' ch'a'ab u meyajil u keetilil chuum STO-LG u kaajale' L=1 tak L=6. Le múuch mejen ba'alo'obo u ti'al u meyajtal yéetel múuch mejen ba'alo'ob H₂ yéetel HeH. Lela' ku tuukulta'al múuch mejen ba'alo'b tumen kaabal jach mejen ba'alo'ob leti' yaan tu múuch mejen ba'alo'ob. Tu láakal ba'ax a'alik te'e tsolila' u ti'al u jepalal le múuch mejen ba'alo'ob, bey a'alik ti' le meyaja'; chen ba'ale' lela' ma'atech u ts'aik bix je'e u utskinta'ale'. Le o'olale' táan ts'aik u xookil, toj óol, xak' yéetel ba'ax ku p'ix. Ti' le meyaja' yáaxile' a'alike' yóolaj chan its'atil, leti' tu beetaj kaaxtik u meyajil Schrödinger. Lela' ku p'isik le múuch mejen ba'alo'obo. Jach k'aana'an áaik u ti'al u k'uchul u yi'ila' le Schrödinger jach taalam ti' múuch mejen ba'alo'ob tumen nojoch jach mejen ba'alo'ob. U ti'al u meyajta'al le múuch mejen ba'alo'ob yaan u lu'ujtsa le jach mejen ba'alo'ob ti'e ts'u'ubo'. Lela' ba'ax ken u beete u meyajil Schrödinger chen ti' jach mejen ba'alo'ob, chen ba'ale' yaan a'alik u beeta'ab tu'ux ku piirinsuut tumen u káajal u jok'saj Pauli. Ken okts'ak le yaan yak'al etp'isa'an ti' u keetil iik'il ku kuchul u k'aana'antal ka'a ootsaj múultun Slater. Beyo' kuchul u tsolil Hartree-Fock. U múultun Slater ya'ab bix je'e u keetil chuum u ti'al u kuchul u keetil iikil. U ti'al lela' ku ch'a'abaj u keetil úuchben u múultun Gauss, beyo' ma' taalan u meyajili' le u xookili'. U keetil le chuum ku kaxtik bix u k'uchul ti' yóok'ol kaab Slater. Le yóok'ol kaabo'ob Slater leti' u ma'aloobil u ti'al u ya'alaj bix u meyaj le yóok'ol kaab u múuch mejen ba'alo'ob. Kax beyo' la'yli' taalan u beeta'ab le meyaja' yéetel le tsolil HF. U ts'o'oke' iile'ex le meyaja', junp'éel meyaj ya'ab ba'alo'ob ts'aabi' je'e bix; jejeláas nu'ukul ts'í­ibo'ob, yéetel u nu'ukul ts'í­ib MATLAB beyxan Excel, u ti'al u na'ata'ab le meyaja'. Le meyaja' ch'aa ti' u áanalte'i [1] beetabi' yéetel aalab óolal u ti'al u yáantal u láak ajxooko'ob.

[1] Attila Szabo, Neil S. Ostlund. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications, 1982.