Theory used in MOPAC2016 (note)

    Approximations used in Semempirical Methods
    Construction of the Density Matrix
    Parameters used in Semiempirical Methods
    Basic Roothaan-Hall Equations
    Neglect of diatomic overlap integral
    Neglect of three and four center integrals
    One-center two-electron integrals
    NDDO two-electron two-center integrals
    Final Assembly of Two-Electron Two-Center Integrals
    The one-center one-electron integral H_μμ
    The two-center one-electron integral H_μν
    Core-core repulsion integrals
    The Self-Consistent Field Calculation
    Calculation of ΔH_f

    An SCF Calculation
    Starting density matrix
    Assembly of the starting Fock matrix
    Diagonalization of the Fock matrix
    Exercises involving eigenvectors
    Iterating density matrix
    Iterating Fock matrix
    Calculation of heat of formation

    The Cluster
    The Madelung Problem
    Piezoelectric Effect
    Refractive Index
    Derivatives
    Charge Balanced Unit Cells
    Geometry Specification for Band Structure Calculations
    Electronic Band Structure
    Electronic Density of States
    Brillouin Zone: Generation of Band Structures
    Space-group operations

    Starting electronic configuration
    Microstates
    Permutations
    Energy of microstates
    Zero of energy used in MECI
    Construction of secular determinant
    States arising from various calculations
    Spin angular momentum
    Calculation of spin-states
    Choice of State to be Optimized
    Quantum Numbers
    Polarizability
    Franck-Condon considerations
    Degenerate States
 

Geometry Optimization

    EigenFollowing
    The BFGS function optimizer
    Optimization of one unknown
    Considerations in Geometry Optimization
 

     Derivation of vibrational quantities - This is the best place to start understanding the theoretical background.

   The following pages are quick and superficial descriptions of various quantities
    
    Calculation of Vibrational Frequencies
    Calculation of the Hessian matrix
    Mechanism of the frame in FORCE calculation
    Vibrational Analysis
    Reduced masses
    Effective masses
    Travel
    Force Constants
    Transition dipole

    Description
    Equations used
    Specifying temperature in a DRC simulation
    IRC
    General description of the DRC and IRC
    Option to allow only extrema to be output
    Keywords for use with the IRC and DRC
    Examples of DRC/IRC data
    Output format for IRC and DRC
    Test of DRC
 

    Limitations
    Representation of Point Groups
    Identification of Point-Groups
    Tolerance
    Orientation of the Abelian groups C_2v and D_2h
    Molecular Orbitals
    Normal Coordinates States
    Atomic energy levels and States
 

    Koopmans' Theorem
    Dipole moments
    Bond Orders
    Mulliken populations
    Localized orbitals
    Localized M.O.s
    Localization Theory
    Oscillator Strength
    Convergence in SCF Calculation
    Causes of failure to achieve an SCF
    Use of C.I. in Reaction Path Calculations
    Sparkles
    Capped Bonds
    Algebraic Derivation of Overlap Integrals over Slater Orbitals
    Rotation of atomic orbitals (conventional, i.e., trigonometric)
    Rotation of atomic orbitals (generic)
    Energies of Isolated Atoms
    Reaction paths
    Polarizability and Hyperpolarizability Calculation
    Time-Dependent Hartree-Fock
    COSMO
    Parametric Molecular Electrostatic Potential (PMEP)
    Pressure on a unit cell

    Fundamental Physical Constants
    Various precision levels
    Reasons for low precision
   

    Correction to the Peptide Linkage
     "Size" of a molecule
    Gradients
    Reaction paths
    Grid Calculation
    Thermochemistry
    Use of SADDLE Calculation
    Gibbs free energy