Calculation Details

This page contains general information about the DFT Database for RNA Catalysis.  Click on any of the following links:

Property Definitions

Following is a list of definitions of electronic and thermodynamic quantities computed for each molecular structure in the database.

Definitions of Thermodynamic Quantities
E Electronic plus nuclear energy
Eelec Electronic energy
ENN Nuclear-nuclear repulsion energy
E0 Zero-point energy
EZPV Zero-point vibrational energy
Evib Thermal vibrational energy correction
Erot Rotational energy
Etrans Translational energy
U
Internal energy
H
Enthalpy
S
Entropy
G
Gibbs free energy (in the gas phase)
Gaq
Gibbs free energy (in solution)
ΔGsol
Solvation free energy
T
Absolute temperature
R
Universal gas constant


Definition of Electronic properties
|D|
Dipole moment
alpha
Isotropic polarizability
qi
Atomic charge (NBO and CHelpG)
phi(r)
Electrostatic potential surface
IP
1st ionization potential (Koopman approximation)
EA
1st electron affinity (Koopman approximation)
nui
Vibrational frequency

Gas-phase calculations

Based on initial tests for reactions involving anions, first-generation database is based on gas-phase optimized structures using Kohn-Sham density-functional theory with hybrid Becke three parameter exchange functional [1,2]and Lee, Yang, Parr correlation functional [3](B3LYP) with the 6-31++G(d,p) basis set. Stability and frequency check is made at the same level to make sure that a stable minimum have been reached. Thermodynamic quantities such as the zero-point vibrational energy, thermal vibrational contributions to enthalpy, entropy and Gibbs free energy is also evaluated by frequency calculations. Electronic energies and other properties, including dipole moments, atomic charges and polarizabilities, are refined via single point calculations at the optimized geometries using the larger 6-311++G(3df,2p) basis set with 'tight' convergence criteria to ensure high precision for properties sensitive to the use of diffuse basis functions. The zero-point energy and other thermal energy corrections obtained from the frequency calculation are used to adjust the single point electronic energy to get the free energy and other thermodynamic quantities. All of the calculations will be implemented with GAUSSIAN03 package [4].

Solvation calculations

Solvation effects are performed by single point calculations based on the gas-phase optimized structures using SM5.42R solvation model [5,6] implemented in MN-GSM [7], polarizable continuum model (PCM) [8,9,10] and a variation of the conductor-like screening model (COSMO) [11] implemented in GAUSSIAN03 [3].  For additional details, see the following references [12].

Calculation of thermodynamic quantities

The Thermodynamic quantities are categorized into gas phase and solvation contributions. The key thermodynamics relations and energy components in the gas phase are as following:

G = H - TS

H = U + RT

U = E0 + Evib + Erot + Etrans

E0= Eelec + ENN + EZPV = E + EZPV

The definitions of each of these quantities is provided below.   Except for E0 and the energy terms that define it, all the other quantities above have explicit temperature dependence.

The free energy in solution is the sum of the free energy in gas phase and the solvation free energy:

Gaq = G + ΔGsol

For additional details, see the following reference [12].


Reference

  1. Becke, A. D. Phys. Rev. A. 1988, 38, 3098­3100.
  2. Becke, A. D. J. Chem. Phys. 1993, 98, 5648­5652.
  3. Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B. 1988, 37, 785­789.
  4. Frisch, M. J. et al. Gaussian 03, Revision B.01; Gaussian, Inc., Pittsburgh PA, 2003.
  5. Li, J.; Zhu, T.; Hawkins, G. D.; Winget, P.; Liotard, D. A.; Cramer, C. J.; Truhlar, D. G. Theor.Chem. Acc. 1999, 103, 9­63.
  6. Xidos, J. D.; Li, J.; Thompson, J. D.; Hawkins, G. D.; Winget, P. D.; Zhu, T.; Rinaldi, D.; Liotard, D. A.; Cramer, C. J.; Truhlar, D. G.; Frisch, M. J. MN-GSM: A Module Incorporating
    the SM5.42 Solvation Models, the CM2 Charge Model, and Lowdin Population Analysis in the

    Gaussian98 Program, 1.8 ed.; University of Minnesota: Minneapolis, MN, 2002.
  7. Xidos, J. D.; Li, J.; Thompson, J. D.; Hawkins, G. D.; Winget, P. D.; Zhu, T.; Rinaldi, D.;
    Liotard, D. A.; Cramer, C. J.; Truhlar, D. G.; Frisch, M. J. MN-GSM,version 1.8, University of
    Minnesota, Minneapolis, MN 55455-0431, 2001.
  8. Tomasi, J.; Persico, M. Chem. Rev. 1994, 94, 2027­2094.
  9. Cossi, M.; Barone, V.; Cammi, R.; Tomasi, J. Chem. Phys. Lett. 1996, 225, 327­335.
  10. Mineva, T.; Russo, N.; Sicilia, E. J. Comput. Chem. 1998, 19, 290­299.
  11. Barone, V.; Cossi, M. J. Phys. Chem. A 1998, 102, 1995­2001.