Applied Hartree-Fock: Atomic and diatomic energy computations
Authors
Larsen, Anders ; Poulsen, Rolf Sommer
Term
4. term (FYS10)
Education
Publication year
2015
Submitted on
2015-06-02
Pages
68
Abstract
Dette projekt bruger Hartree-Fock-metoden, en udbredt kvantekemisk tilgang hvor hver elektron beskrives som bevægende sig i det gennemsnitlige felt fra de andre elektroner, til at beregne elektronenergier og potentialenergi-kurver (hvordan energien ændrer sig med afstanden mellem atomerne) for to-atomige molekyler. Vi udleder og forklarer teorien og implementerer den via Hartree-Fock-Roothaan-ligningerne (matrixformen brugt i beregninger). For at demonstrere metoden på atomare centralfelt-problemer beregnede vi elektronenergier for neutrale atomer med atomnummer Z = 1-103 samt for anioner og kationer af de første 52 grundstoffer, med god nøjagtighed. Vi forsøgte også at beregne statiske atomare polariserbarheder (hvor let et atoms elektronsky deformeres af et elektrisk felt). Indtil videre præsenterer vi resultater for hydrogen; der kræves mere arbejde for de øvrige atomer. Med en kartesisk Gauss-basis (et sæt matematiske byggesten til at approksimere atomare orbitaler) beregnede vi energi- og potentialenergi-funktioner for molekylerne H2, HeH, He2, LiH og Li2. Disse molekylære resultater var tvetydige og kræver yderligere undersøgelser.
This project uses the Hartree-Fock method, a standard quantum chemistry approach that treats each electron as moving in the average field of the others, to calculate electron energies and potential energy curves (how energy changes with the distance between atoms) for diatomic molecules. We derive and explain the theory and implement it through the Hartree-Fock-Roothaan equations (the matrix form used for computations. To demonstrate the method on atomic central-field problems, we computed electron energies for neutral atoms with atomic numbers Z = 1-103 and for anions and cations of the first 52 elements, achieving good accuracy. We also attempted to calculate static atomic polarizabilities (how easily an atom’s electron cloud is distorted by an electric field). At present we report results for hydrogen; further work is needed for other atoms. Using a Cartesian Gaussian basis (a set of mathematical building blocks for approximating atomic orbitals), we calculated energy and potential energy functions for the diatomic molecules H2, HeH, He2, LiH, and Li2. These molecular results were ambiguous and require further investigation.
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