A Comprehensive Review Of Quantum Mechanics And Hartree-Fock Calculations For Selected Atoms

A Comprehensive Review of Quantum Mechanics andHartree-Fock Calculations for Selected AtomsSagnik SenMaulana Abul Kalam Azad University of Technology [email protected] 28, 2025AbstractThis research presents a comparative study of Hartree-Fock (HF)andDen-sity Functional Theory (DFT) methods, evaluating their computational efficiencyand accuracy across multiple atomic systems. The study benchmarks orbital en-ergy predictions, SCF convergence iterations, and total energy assessments acrossadvanced quantum chemistry frameworks. Furthermore, Coupled-Cluster (CCSDand CCSD(T)) methodologies are assessed against HF and DFT to highlight per-formance trade-offs. The integration of machine learning (ML) and AI-drivenoptimization techniques in quantum chemistry models is also explored, showcasingpotential improvements in accuracy and computational speed. The findings contributeto an enhanced understanding of computational resource allocation and methodologicalefficiency in quantum chemical simulations.Keywords: Quantum Chemistry, Hartree-Fock, Density Functional Theory, Coupled-Cluster,Computational Efficiency, Orbital Energy, SCF Convergence, AI in Chemistry, MachineLearning Optimization, Benchmarking Methods1Quantum MechanicsHartree-Fock Calculations Sagnik Sen Contents1 Introduction to Quantum Mechanics 8 1.1 Wave-Particle Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81.2 The Schrodinger Equation . . . . . . . . . . . . . . . . . . . . . .