G3-RAD theory - G3(B3) for open shell systems

G3-RAD is a variant of G3B3 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 UMPx by restricted open shell ROMPx single point calculations. The G3-RAD energy at 0 degree Kelvin E₀(G3-RAD) is defined as:

E₀(G3-RAD) = E[URCCSD(T)/6-31G(d)//UB3LYP/6-31G(d)]
        + DE(+)
        + DE(2df,p)
        + DE(G3large)
        + DE(HLC)
        + ZPE
        + DE(SO)

The definition of the components being:

DE(+) = E[ROMP4(FC)/6-31+G(d)//UB3LYP/6-31G(d)] - E[ROMP4(FC)/6-31G(d)//UB3LYP/6-31G(d)]

DE(2df,p) = E[ROMP4(FC)/6-31G(2df,p)//UB3LYP/6-31G(d)] - E[ROMP4(FC)/6-31G(d)//UB3LYP/6-31G(d)]

DE(G3large) = E[ROMP2(FULL)/G3large//UB3LYP/6-31G(d)] - E[ROMP2(FC)/6-31G(2df,p)//UB3LYP/6-31G(d)]
                         - E[ROMP2(FC)/6-31+G(d)//UB3LYP/6-31G(d)] + E[ROMP2(FC)/6-31G(d)//UB3LYP/6-31G(d)]

DE(HLC) = -An(beta) - B(n(alpha) - n(beta))
                     A = 6.884 mHartrees; B = 2.747 mHartrees (for molecules)
                     A = 6.561 mHartrees; B = 1.341 mHartrees (for atoms)
                     n(alpha) = No. of alpha valence electrons
                     n(beta) = No. of beta valence electrons

ZPE = 0.9806 * ZPE[UB3LYP/6-31G(d)]

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

• Optimization and frequency calculation at the UB3LYP/6-31G(d) level of theory
• URCCSD(T,FC)/6-31G(d)//UB3LYP/6-31G(d) single point
• ROMP4(FC)/6-31+G(d)//UB3LYP/6-31G(d) single point
• ROMP4(FC)/6-31G(2df,p)//UB3LYP/6-31G(d) single point
• ROMP2(Full)/G3large//UB3LYP/6-31G(d) single point

Comments:

• The basis sets used in G3-RAD are identical to those used in G3B3, but use the (6d,10f) format for polarization functions (instead of (5d,7f)) in the ROMP4/6-31G(2df,p) and ROMP2(FULL)/G3large single point calculations. A local copy of the G3large basis can be found here.
• The higher level correction (HLC) parameters A - D 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 G3-RAD is 3.96 kJ/mol. This compares to values of 5.23 for G3(MP2)B3, 5.17 for G3(MP2)-RAD, 4.26 for G3, 4.14 for G3B3, 4.02 for G3X, and 3.65 for G3X-RAD.

Literature:

• 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.
• L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople,
  "Gaussian-3 (G3) theory for molecules containing first and second-row atoms"
  J. Chem. Phys. 1998, 109, 7764 - 7776.
• L. A. Curtiss, K. Raghavachari,
  "G2 Theory"
  The Encyclopedia of Computational Chemistry, P. v. R. Schleyer (editor-in-chief),
  John Wiley & Sons Ltd, Athens, USA, 1998, 2, 1104 - 1114.
• A. G. Baboul, L. A. Curtiss, P. C. Redfern, K. Raghavachari,
  "Gaussian-3 theory using density functional geometries and zero-point energies"
  J. Chem. Phys. 1999, 110, 7650 - 7657.