Advanced Computational Chemistry

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1、Lecturenotesforthecourse554017AdvancedComputationalChemistryPekkaManninen20092Contents1Many-electronwavefunctions71.1MolecularSchr¨odingerequation........................71.1.1Helium-likeatom............................91.2Molecularorbitals:thefirstcontact......................101.2.1Dihy

2、drogenion.............................101.3Spinfunctions..................................121.4AntisymmetryandtheSlaterdeterminant..................131.4.1ApproximatewavefunctionsforHeasSlaterdeterminants.....141.4.2Remarkson“interpretation”......................151.4.3Slatermethod......

3、........................151.4.4Helium-likeatomrevisited.......................161.4.5Slater’srules..............................171.5Furtherreading.................................181.6ExercisesforChapter1.............................182Exactandapproximatewavefunctions192.1Characteristic

4、softheexactwavefunction..................192.2TheCoulombcusp...............................212.2.1HamiltonianforaHe-likeatom....................212.2.2Coulombandnuclearcuspconditions.................212.2.3Electroncorrelation...........................222.3Variationprinciple.............

5、..................232.3.1Linearansatz..............................232.3.2Hellmann–Feynmantheorem......................242.3.3Themolecularelectronicvirialtheorem................252.4One-andN-electronexpansions........................262.5Furtherreading.................................282

6、.6ExercisesforChapter2.............................283Molecularintegralevaluation313.1Atomicbasisfunctions.............................313.1.1TheLaguerrefunctions.........................323.1.2Slater-typeorbitals...........................3333.1.3Gaussian-typeorbitals...................

7、......343.2Gaussianbasissets...............................353.3IntegralsoverGaussianbasissets.......................373.3.1Gaussianoverlapdistributions.....................383.3.2Simpleone-electronintegrals......................383.3.3TheBoysfunction.....................