Page 57 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

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Scheme 1.3. Characteristics of ab Initio MO Methods
CHAPTER 1
Chemical Bonding STO-3G. STO-3G is a minimum basis set consisting of 1s orbitals for hydrogen and 2s and 2p orbitals for
and Molecular Structure second-row elements, described by Gaussian functions.
Split-Valence Gaussian Orbitals. (3-21G, 4-31G, 6-31G) Split-valence orbitals are described by two or
more Gaussian functions. Also in this category are Dunning-Huzinaga orbitals.
Polarized Orbitals. These basis sets add further orbitals, such as p for hydrogen and d for carbon that
allow for change of shape and separation of centers of charge. Numbers in front of the d, f
designations indicate inclusion of multiple orbitals of each type. For example, 6-311(2df,2pd) orbitals
have two d functions and one f function on second-row elements and two p functions and one d
function on hydrogen.
∗
Diffuse Basis Sets. (6-31+G , 6-31++G ) Diffuse basis sets include expanded orbitals that are used for
∗
∗
molecules with relatively loosely bound electrons, such as anions and excited states. 6-31+G have
diffuse p orbitals on second-row elements. 6-31++G orbitals have diffuse orbitals on both
∗
second-row elements and hydrogen.
Correlation Calculations
MP2, MP4. MP (Moeller-Plesset) calculations treat correlation by a perturbation method based on adding
excited state character. MP2 includes a contribution from the interaction of doubly excited states with
the ground state. MP4 includes, single, double, and quadruple excited states in the calculation.
CISD. CISD (configuration interaction, single double) are LCAO expressions that treat configuration
interactions by including one or two excited states. The designations CISDT and CISDTQ expand this
to three and four excitations, respectively.
CAS-SCF. CAS-SCF (complete active space self-consistent field) calculations select the chemically most
significant electrons and orbitals and apply configuration interactions to this set.
Composite Calculations
G1, G2, G2(MP2), and G3 are composite computations using the 6-311G ∗∗ basis set and MP2/6-31G ∗
geometry optimization. The protocols are designed for efficient calculation of energies and electronic
properties. The G2 method calculates electron correlation at the MP4 level, while G2(MP2) correlation
calculations are at the MP2 level. A scaling factor derived from a series of calibration molecules is
applied to energies.
CBS. CBS protocols include CBS-4, CBS-Q, and CBS-APNO. The objectives are the same as for G1 and
G2. The final energy calculation (for CBS-Q) is at the MP4(SQD)/6-31G(d, p) level, with a correction
for higher-order correlation. A scaling factor is applied for energy calculations.
References to Scheme 1.3
STO-3G: W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Phys. Chem., 51, 2657 (1969).
3-21G, 4-21G, and 6-31G: R. Ditchfield, W. J. Hehre, and J. A. Pople, J. Chem. Phys., 54, 724 (1971);
W. J. Hehre and W. A. Lathan, J. Chem. Phys., 56, 5255 (1972); W. J. Hehre, R. Ditchfield, and
J. A. Pople, J. Chem. Phys., 56, 2257 (1972); M. M. Francl, W. J. Pietro, W. J. Hehre, J. S. Binkley,
M. S. Gordon, D. J. DeFrees, and J. A. Pople, J. Chem. Phys., 77, 3654 (1982).
Dunning-Huzinaga Orbitals: T. H. Dunning, Jr., and P. J. Hay, in Modern Theoretical Chemistry, Vol. 3,
H. F. Schaefer, ed., Plenum Publishing, New York, 1977, pp 1–27.
MP: J. S. Binkley and J. A. Pople, Int. J. Quantum Chem., 9, 229 (1975).
G1, G2, G3: J. A. Pople, M. Head-Gordon, D. J. Fox, K. Raghavachari, and L. A. Curtiss, J. Chem.
Phys., 90, 5622 (1989); L. A. Curtiss, C. Jones, G. W. Trucks, K. Raghavachari, and J. A. Pople, J.
Chem. Phys., 93, 2537 (1990); L. A. Curtiss, K. Raghavachari, G. W. Tucks, and J. A. Pople,
J. Chem. Phys., 94, 7221 (1991); L. A. Curtiss, K. Raghavachari, and J. A. Pople, J. Chem. Phys., 98,
1293 (1993); M. Head-Gordon, J. Chem. Phys., 100, 13213 (1996); L. A. Curtiss and K. Raghavachari,
Theor. Chem. Acc., 108, 61 (2002).
CBS-Q: J. W. Ochterski, G. A. Petersson, and J. A. Montgomery, J. Chem. Phys., 104, 2598 (1996);
G. A. Petersson, Computational Thermochemistry, ACS Symposium Series, Vol, 677, pp 237–266
(1998).