Primerjava izračunanih in numeričnih rezultatov pri obravnavi molekule vodika : diplomsko delo univerzitetnega študijskega programa I. stopnje

Mlakar, Tibor

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Title:	Primerjava izračunanih in numeričnih rezultatov pri obravnavi molekule vodika : diplomsko delo univerzitetnega študijskega programa I. stopnje
Authors:	ID Mlakar, Tibor (Author) ID Bračko, Marko (Mentor) More about this mentor... ID Bren, Urban (Comentor)
Files:	UN_Mlakar_Tibor_2019.pdf (43,20 MB) MD5: D60F32E0B6D17041EF7DE7B7B38260F3 PID: 20.500.12556/dkum/4ac6865f-951b-4d20-a876-b540012554fc
Language:	Slovenian
Work type:	Bachelor thesis/paper
Typology:	2.11 - Undergraduate Thesis
Organization:	FKKT - Faculty of Chemistry and Chemical Engineering
Abstract:	V mnogih vejah teoretične kemije kot fizike zastavljene sisteme proučujemo z reševanjem Schrödingerjeve enačbe. Rešitvam te enačbe pravimo valovne funkcije, s katerimi lahko določimo vse bistvene parametre nekega sistema. Oblika členov Schrödingerjeve enačbe se spreminja skupaj z izbiro sistema, načeloma kompleksnejši kot je proučevani sistem zahtevnejše je reševanje omenjene enačbe. V diplomskem delu smo iskali rešitve Schrödingerjeve enačbe za najenostavnejši analitično rešljiv sistem - molekulo vodikovega iona (H2+). Analitične rešitve smo poiskali v okviru teorije molekulskih orbital (MO), ki smo jih opisali z linearno kombinacijo atomskih orbital (“linear combination of atomic orbitals” - LCAO). Rešitve istega problema smo iskali tudi numerično, z računskim programom Gaussian, pri čemer smo za računanje uporabili tako semi-empirične kot ab initio metode. Rezultate vseh izračunov smo primerjali z eksperimentalno izmerjenimi vrednostmi. V drugem delu diplomske naloge smo analitično iskali rešitve Schrödingerjeve enačbe za nekoliko večji sistem – molekulo vodika (H2). Zaradi pomankanja znanja novega sistema ni bilo možno obravnavati do konca. Ugotovili smo, da enostaven analitični račun vodi do vrednosti za ravnovesno razdaljo in vezavno energijo, ki se v okviru 30-40% ujemata z eksperimentalnimi podatki. Pri numeričnih metodah se je izkazalo, da posamezne ab initio metode privedejo do podobnih rezultatov, prav tako tudi posamezne semi-empirične metode. Ugotovili smo, da je ujemanje rezultatov za ravnovesno razdaljo pri vseh numeričnih metodah znotraj 10% od eksprimentalnih vrednosti. Pri energijah je ujemanje nekoliko slabše, so pa dobljene vrednosti še vedno v okviru 20% proč od eksperimentalnih rezultatov. Edina izjema sta bili obe semi-empirični metodi, ki sta za izračunano energijo sistema dali popolnoma neprimerne rezultate.
Keywords:	Schrödingerjeva enačba, molekula vodikovega iona, teorija molekulskih orbital, računski program Gaussian, ravnovesna razdalja, energija sistema
Place of publishing:	Maribor
Place of performance:	Maribor
Publisher:	[T. Mlakar]
Year of publishing:	2019
Number of pages:	VIII, 35 str.
PID:	20.500.12556/DKUM-74593
UDC:	678.5(043.2)
COBISS.SI-ID:	22612246
NUK URN:	URN:SI:UM:DK:HRKAAWPT
Publication date in DKUM:	11.09.2019
Views:	1548
Downloads:	227
Metadata:
Categories:	KTFMB - FKKT
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Licences

License:	CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Link:	http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:	The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:	01.09.2019

Secondary language

Language:	English
Title:	Comparison of analitically calculated and numerical results for description of the hydrogen molecule
Abstract:	In many branches of theoretical chemistry and physics, systems are studied by solving the Schrödinger equation. The solutions to this equation are called wave functions, with which we can determine all the essential parameters of a system. The form of the terms of the Schrödinger equation varies with the choice of the system. In the diploma thesis we were looking for solutions of the Schrödinger equation for the simplest analytically solvable system - the hydrogen ion molecule (H2+). Analytical solutions were found with the framework of the molecular orbital (MO) theory, which was described by the linear combination of atomic orbitals (LCAO). We also looked for solutions to the same problem numerically, using the Gaussian computational program, using both semi-empirical and ab initio methods for computation purposes. The results of all calculations were compared with the experimentally measured values. In the second part of the thesis, we analytically sought solutions to the Schrödinger equation for a slightly larger system - the hydrogen molecule (H2). Due to lack of knowledge, the new system could not be fully addressed. We found that a simple analytical calculation leads to values for equilibrium distance and binding energy, which are in the range of 30-40% with the experimental data. For numerical methods, individual ab initio methods were shown to produce similar results, as well as individual semi-empirical methods. We found that the matching of the results for the equilibrium distance for all numerical methods was within 10% of the experimental values. The energies are slightly worse, but the values obtained are still within 20% of the experimental results. The only exceptions were the two semi-empirical methods which gave completely inappropriate results for the calculated energy of the system.
Keywords:	Schrödinger equation, hydrogen ion molecule, molecular orbital theory, Gaussian computational programme, equilibrium distance, energy of the system

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