Ab Initio, Density-Functional, Semiempirical, and Molecular-Mechanics Methods

1 Ab Initio, Density-Functional, Semiempirical, and Molecular-Mechanics Methods 

The four main approaches to calculating molecular properties are ab initio methods, semiempirical methods, the density-functional method, and the molecular-mechanics method. 

Semiempirical molecular quantum-mechanical methods use a simpler Hamiltonian than the correct molecular Hamiltonian and use parameters whose values are adjusted to fit experimental data or the results of ab initio calculations. An example is the Hiickel MO treatment of conjugated hydrocarbons (Section 17.2), which uses a one-electron Hamiltonian and takes the bond integrals as adjustable parameters rather than quantities to be calculated theoretically. In contrast, an ab initio (or first principles) calculation uses the correct Hamiltonian and does not nse experimental data other than the values of the fundamental physical constants. A Hartree-Fock SCF calculation seeks the antisynunetrized product d of one-electron functions that minimizes / i dr, where H is the true Hamiltonian and is thns an ab initio calcnlation. (Ab initio is Latin for from the beginning and indicates a calculation based on fundamental principles.) The term ab initio should not be interpreted to mean 100% correct. An ab initio SCF MO calculation uses the approximation of taking as an antisynunetrized product of one-electron spin-orbitals and uses a finite (and hence incomplete) basis set. 

The density-functional method (Section 16.5) does not attempt to calculate the molecular wave function bnt calcnlates the molecular electron probability density p and calculates the molecular electronic energy from p. 

The niolecular-mechanics method (Section 17.5) is not a quantum-mechanical method and does not nse a molecular Hamiltonian operator or wave function. Instead, it views the molecule as a collection of atoms held together by bonds and expresses the molecular energy in terms of force constants for bond bending, stretching, and torsion and other parameters. 

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TTiis chapter examines the accuracies of ab initio, density-functional, semiempirical, and molecular-mechanics methods in calculating properties of ground-state closed-shell molecules. Unless otherwise stated, the comparisons are for molecules of first-and second-row atoms (H through Ar). 

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