G3X(MP2)-RAD theory - G3X(MP2)B3 for open shell systems

G3X(MP2)-RAD is a variant of G3X(MP2) theory optimized for open shell systems. The most important changes concern the use of URCCSD(T) instead of UQCISD(T) single point calculations and the replacement of all UMP2 by restricted open shell ROMP2 single point calculations. G3X(MP2)-RAD differs from G3(MP2)-RAD in using a larger basis set in geometry optimizations and in adding a basis set correction term at Hartree-Fock level. The G3X(MP2)-RAD energy at 0 degree Kelvin E₀(G3(MP2)-RAD) is defined as:

E₀(G3X(MP2)-RAD) = E[URCCSD(T)/6-31G(d)//UB3LYP/6-31G(2df,p)]
        + DE(G3MP2large)
        + DE(G3Xlarge)
        + DE(HLC)
        + ZPE
        + DE(SO)

The definition of the components being:

DE(G3MP2large) = E[ROMP2(FC)/G3MP2large//UB3LYP/6-31G(2df,p)] - E[ROMP2(FC)/6-31G(d)//UB3LYP/6-31G(2df,p)]

DE(G3Xlarge) = E[ROHF/G3Xlarge//UB3LYP/6-31G(2df,p)] - E[ROHF/G3MP2large//UB3LYP/6-31G(2df,p)]

DE(HLC) = -An(beta) - B(n(alpha) - n(beta))
                     A = 9.556 mHartrees; B = 3.992 mHartrees (for molecules)
                     A = 9.684 mHartrees; B = 1.970 mHartrees (for atoms and atomic ions)
                     n(alpha) = No. of alpha valence electrons
                     n(beta) = No. of beta valence electrons

ZPE = 0.9854 * ZPE[B3LYP/6-31G(2df,p)]

The necessary energies can be calculated most efficiently in the following sequence:

• Optimization and frequency calculation at the UB3LYP/6-31G(2df,p) level of theory
• URCCSD(T)/6-31G(d)//UB3LYP/6-31G(2df,p) single point (available in MOLPRO)
• ROMP2(FC)/G3MP2large//UB3LYP/6-31G(2df,p) single point
• ROHF/G3Xlarge//UB3LYP/6-31G(2df,p) single point

Comments:

• The basis sets used in G3X(MP2)-RAD are identical to those used in G3X(MP2), and use the (5d,7f) format for polarization functions in the ROMP2(FC)/G3MP2large single point calculation.
• The higher level correction (HLC) parameters A and B have been reoptimized to give the best possible performance for the G2/97 test set.
• Spin orbit correction terms E(SO) (mainly of experimental origin) are added only for atoms
• The mean absolute deviation for the full G2/97 test set for G3X(MP2)-RAD is 4.92 kJ/mol. This compares to values of 5.23 for G3(MP2)B3, 5.17 kJ/mol for G3(MP2)-RAD, 4.26 for G3, 4.14 for G3B3, 4.02 for G3X, 3.96 for G3-RAD, and 3.65 for G3X-RAD (Radom et al., 2003).

Literature:

• L. A. Curtiss, P. C. Redfern, K. Raghavachari, J. A. Pople,
  "Gaussian-3X „(G3X)… theory: Use of improved geometries, zero-point energies, and Hartree–Fock basis sets"
  J. Chem. Phys. 2001, 114, 108 - 117.
• D. J. Henry, C. J. Parkinson, L. Radom,
  "An Assessment of the Performance of High-Level Theoretical Procedures in the Computation of the Heats of Formation of Small Open-Shell Molecules"
  J. Phys. Chem. A 2002, 106, 7927 - 7936.
• D. J. Henry, M. B. Sullivan, L. Radom,
  "G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry"
  J. Chem. Phys. 2003, 118, 4849 - 4860.