Theory used in MOPAC2016 (note)


Semiempirical Theory
An SCF Calculation
Solid state capability
Multi-Electron Configuration Interaction
Geometry Optimization
Normal Coordinate Calculation
Dynamic and Intrinsic Reaction Coordinates
Point Group Theory
Level of Precision with MOPAC
Miscellaneous Electronic




Semiempirical theory

    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 Hμμ
    The two-center one-electron integral Hμν
    Core-core repulsion integrals
    The Self-Consistent Field Calculation
    Calculation of ΔHf

An SCF Calculation

    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



Solid state capability

    The Cluster
    The Madelung Problem
    Piezoelectric Effect
    Refractive Index
    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


Multi-Electron Configuration Interaction

    Starting electronic configuration
    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
    Franck-Condon considerations
    Degenerate States


Geometry Optimization

    The BFGS function optimizer

    Optimization of one unknown
Considerations in Geometry Optimization


Normal Coordinate Calculation

     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
    Force Constants
    Transition dipole


Dynamic and Intrinsic Reaction Coordinates

    Equations used
    Specifying temperature in a DRC simulation
    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

Point Group Theory

    Representation of Point Groups
    Identification of Point-Groups
    Orientation of the Abelian groups C2v and D2h
    Molecular Orbitals
    Normal Coordinates States
    Atomic energy levels and States


Miscellaneous Electronic

    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
    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
    Parametric Molecular Electrostatic Potential (PMEP)
    Pressure on a unit cell


Level of Precision with MOPAC

    Fundamental Physical Constants
    Various precision levels
    Reasons for low precision


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